LMFDB - Embedded newform 4001.2.a.b.1.11

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			1.11
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)

$f(q)$	$=$	$q-2.64594 q^{2} -1.99415 q^{3} +5.00101 q^{4} -3.20075 q^{5} +5.27640 q^{6} +3.40947 q^{7} -7.94051 q^{8} +0.976617 q^{9} +O(q^{10})$	\(q-2.64594 q^{2} -1.99415 q^{3} +5.00101 q^{4} -3.20075 q^{5} +5.27640 q^{6} +3.40947 q^{7} -7.94051 q^{8} +0.976617 q^{9} +8.46900 q^{10} +4.31844 q^{11} -9.97275 q^{12} -1.86918 q^{13} -9.02125 q^{14} +6.38276 q^{15} +11.0081 q^{16} -2.01826 q^{17} -2.58407 q^{18} +5.36675 q^{19} -16.0070 q^{20} -6.79897 q^{21} -11.4263 q^{22} +0.806760 q^{23} +15.8345 q^{24} +5.24480 q^{25} +4.94574 q^{26} +4.03492 q^{27} +17.0508 q^{28} -1.06073 q^{29} -16.8884 q^{30} +2.13299 q^{31} -13.2458 q^{32} -8.61160 q^{33} +5.34020 q^{34} -10.9128 q^{35} +4.88407 q^{36} +0.385677 q^{37} -14.2001 q^{38} +3.72741 q^{39} +25.4156 q^{40} +11.8883 q^{41} +17.9897 q^{42} +3.23663 q^{43} +21.5966 q^{44} -3.12591 q^{45} -2.13464 q^{46} +3.16840 q^{47} -21.9518 q^{48} +4.62446 q^{49} -13.8774 q^{50} +4.02471 q^{51} -9.34779 q^{52} +5.24253 q^{53} -10.6762 q^{54} -13.8222 q^{55} -27.0729 q^{56} -10.7021 q^{57} +2.80663 q^{58} +3.68316 q^{59} +31.9203 q^{60} +5.89671 q^{61} -5.64376 q^{62} +3.32974 q^{63} +13.0314 q^{64} +5.98278 q^{65} +22.7858 q^{66} -3.76625 q^{67} -10.0933 q^{68} -1.60880 q^{69} +28.8748 q^{70} -6.14898 q^{71} -7.75483 q^{72} +12.9440 q^{73} -1.02048 q^{74} -10.4589 q^{75} +26.8392 q^{76} +14.7236 q^{77} -9.86253 q^{78} +9.83252 q^{79} -35.2342 q^{80} -10.9761 q^{81} -31.4559 q^{82} -16.4947 q^{83} -34.0017 q^{84} +6.45995 q^{85} -8.56393 q^{86} +2.11525 q^{87} -34.2906 q^{88} +3.74435 q^{89} +8.27097 q^{90} -6.37290 q^{91} +4.03462 q^{92} -4.25349 q^{93} -8.38341 q^{94} -17.1776 q^{95} +26.4141 q^{96} +9.59660 q^{97} -12.2360 q^{98} +4.21746 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.64594	−1.87096	−0.935482	−	0.353374i	$-0.885034\pi$
$2$	−2.64594	−1.87096	−0.935482	+	0.353374i	$0.885034\pi$
$3$	−1.99415	−1.15132	−0.575660	−	0.817689i	$-0.695255\pi$
$3$	−1.99415	−1.15132	−0.575660	+	0.817689i	$0.695255\pi$
$4$	5.00101	2.50051
$5$	−3.20075	−1.43142	−0.715710	−	0.698398i	$-0.753897\pi$
$5$	−3.20075	−1.43142	−0.715710	+	0.698398i	$0.753897\pi$
$6$	5.27640	2.15408
$7$	3.40947	1.28866	0.644328	−	0.764749i	$-0.277137\pi$
$7$	3.40947	1.28866	0.644328	+	0.764749i	$0.277137\pi$
$8$	−7.94051	−2.80739
$9$	0.976617	0.325539
$10$	8.46900	2.67813
$11$	4.31844	1.30206	0.651029	−	0.759053i	$-0.274338\pi$
$11$	4.31844	1.30206	0.651029	+	0.759053i	$0.274338\pi$
$12$	−9.97275	−2.87888
$13$	−1.86918	−0.518417	−0.259208	−	0.965821i	$-0.583462\pi$
$13$	−1.86918	−0.518417	−0.259208	+	0.965821i	$0.583462\pi$
$14$	−9.02125	−2.41103
$15$	6.38276	1.64802
$16$	11.0081	2.75203
$17$	−2.01826	−0.489500	−0.244750	−	0.969586i	$-0.578706\pi$
$17$	−2.01826	−0.489500	−0.244750	+	0.969586i	$0.578706\pi$
$18$	−2.58407	−0.609072
$19$	5.36675	1.23122	0.615608	−	0.788052i	$-0.288910\pi$
$19$	5.36675	1.23122	0.615608	+	0.788052i	$0.288910\pi$
$20$	−16.0070	−3.57927
$21$	−6.79897	−1.48366
$22$	−11.4263	−2.43610
$23$	0.806760	0.168221	0.0841106	−	0.996456i	$-0.473195\pi$
$23$	0.806760	0.168221	0.0841106	+	0.996456i	$0.473195\pi$
$24$	15.8345	3.23221
$25$	5.24480	1.04896
$26$	4.94574	0.969939
$27$	4.03492	0.776521
$28$	17.0508	3.22229
$29$	−1.06073	−0.196973	−0.0984863	−	0.995138i	$-0.531400\pi$
$29$	−1.06073	−0.196973	−0.0984863	+	0.995138i	$0.531400\pi$
$30$	−16.8884	−3.08339
$31$	2.13299	0.383096	0.191548	−	0.981483i	$-0.438649\pi$
$31$	2.13299	0.383096	0.191548	+	0.981483i	$0.438649\pi$
$32$	−13.2458	−2.34155
$33$	−8.61160	−1.49909
$34$	5.34020	0.915837
$35$	−10.9128	−1.84461
$36$	4.88407	0.814012
$37$	0.385677	0.0634049	0.0317024	−	0.999497i	$-0.489907\pi$
$37$	0.385677	0.0634049	0.0317024	+	0.999497i	$0.489907\pi$
$38$	−14.2001	−2.30356
$39$	3.72741	0.596864
$40$	25.4156	4.01856
$41$	11.8883	1.85665	0.928323	−	0.371775i	$-0.121251\pi$
$41$	11.8883	1.85665	0.928323	+	0.371775i	$0.121251\pi$
$42$	17.9897	2.77587
$43$	3.23663	0.493581	0.246790	−	0.969069i	$-0.420624\pi$
$43$	3.23663	0.493581	0.246790	+	0.969069i	$0.420624\pi$
$44$	21.5966	3.25581
$45$	−3.12591	−0.465983
$46$	−2.13464	−0.314736
$47$	3.16840	0.462159	0.231079	−	0.972935i	$-0.425774\pi$
$47$	3.16840	0.462159	0.231079	+	0.972935i	$0.425774\pi$
$48$	−21.9518	−3.16846
$49$	4.62446	0.660636
$50$	−13.8774	−1.96257
$51$	4.02471	0.563571
$52$	−9.34779	−1.29630
$53$	5.24253	0.720117	0.360059	−	0.932930i	$-0.382757\pi$
$53$	5.24253	0.720117	0.360059	+	0.932930i	$0.382757\pi$
$54$	−10.6762	−1.45284
$55$	−13.8222	−1.86379
$56$	−27.0729	−3.61777
$57$	−10.7021	−1.41753
$58$	2.80663	0.368529
$59$	3.68316	0.479507	0.239753	−	0.970834i	$-0.422933\pi$
$59$	3.68316	0.479507	0.239753	+	0.970834i	$0.422933\pi$
$60$	31.9203	4.12089
$61$	5.89671	0.754996	0.377498	−	0.926010i	$-0.376784\pi$
$61$	5.89671	0.754996	0.377498	+	0.926010i	$0.376784\pi$
$62$	−5.64376	−0.716758
$63$	3.32974	0.419508
$64$	13.0314	1.62893
$65$	5.98278	0.742072
$66$	22.7858	2.80474
$67$	−3.76625	−0.460121	−0.230060	−	0.973176i	$-0.573892\pi$
$67$	−3.76625	−0.460121	−0.230060	+	0.973176i	$0.573892\pi$
$68$	−10.0933	−1.22400
$69$	−1.60880	−0.193676
$70$	28.8748	3.45120
$71$	−6.14898	−0.729750	−0.364875	−	0.931057i	$-0.618888\pi$
$71$	−6.14898	−0.729750	−0.364875	+	0.931057i	$0.618888\pi$
$72$	−7.75483	−0.913916
$73$	12.9440	1.51498	0.757489	−	0.652848i	$-0.226426\pi$
$73$	12.9440	1.51498	0.757489	+	0.652848i	$0.226426\pi$
$74$	−1.02048	−0.118628
$75$	−10.4589	−1.20769
$76$	26.8392	3.07867
$77$	14.7236	1.67791
$78$	−9.86253	−1.11671
$79$	9.83252	1.10625	0.553123	−	0.833100i	$-0.313436\pi$
$79$	9.83252	1.10625	0.553123	+	0.833100i	$0.313436\pi$
$80$	−35.2342	−3.93930
$81$	−10.9761	−1.21956
$82$	−31.4559	−3.47372
$83$	−16.4947	−1.81053	−0.905266	−	0.424844i	$-0.860329\pi$
$83$	−16.4947	−1.81053	−0.905266	+	0.424844i	$0.860329\pi$
$84$	−34.0017	−3.70989
$85$	6.45995	0.700680
$86$	−8.56393	−0.923472
$87$	2.11525	0.226779
$88$	−34.2906	−3.65539
$89$	3.74435	0.396900	0.198450	−	0.980111i	$-0.436409\pi$
$89$	3.74435	0.396900	0.198450	+	0.980111i	$0.436409\pi$
$90$	8.27097	0.871837
$91$	−6.37290	−0.668062
$92$	4.03462	0.420638
$93$	−4.25349	−0.441066
$94$	−8.38341	−0.864683
$95$	−17.1776	−1.76239
$96$	26.4141	2.69587
$97$	9.59660	0.974387	0.487194	−	0.873294i	$-0.338021\pi$
$97$	9.59660	0.974387	0.487194	+	0.873294i	$0.338021\pi$
$98$	−12.2360	−1.23603
$99$	4.21746	0.423871
$100$	26.2293	2.62293
$101$	−10.0822	−1.00322	−0.501609	−	0.865094i	$-0.667259\pi$
$101$	−10.0822	−1.00322	−0.501609	+	0.865094i	$0.667259\pi$
$102$	−10.6491	−1.05442
$103$	−6.12184	−0.603203	−0.301601	−	0.953434i	$-0.597521\pi$
$103$	−6.12184	−0.603203	−0.301601	+	0.953434i	$0.597521\pi$
$104$	14.8422	1.45540
$105$	21.7618	2.12374
$106$	−13.8714	−1.34731
$107$	−9.82712	−0.950024	−0.475012	−	0.879979i	$-0.657556\pi$
$107$	−9.82712	−0.950024	−0.475012	+	0.879979i	$0.657556\pi$
$108$	20.1787	1.94170
$109$	15.7209	1.50579	0.752896	−	0.658139i	$-0.228656\pi$
$109$	15.7209	1.50579	0.752896	+	0.658139i	$0.228656\pi$
$110$	36.5729	3.48709
$111$	−0.769096	−0.0729993
$112$	37.5318	3.54642
$113$	−0.110757	−0.0104191	−0.00520955	−	0.999986i	$-0.501658\pi$
$113$	−0.110757	−0.0104191	−0.00520955	+	0.999986i	$0.501658\pi$
$114$	28.3171	2.65214
$115$	−2.58224	−0.240795
$116$	−5.30472	−0.492531
$117$	−1.82547	−0.168765
$118$	−9.74544	−0.897140
$119$	−6.88119	−0.630798
$120$	−50.6824	−4.62665
$121$	7.64891	0.695356
$122$	−15.6024	−1.41257
$123$	−23.7071	−2.13759
$124$	10.6671	0.957933
$125$	−0.783554	−0.0700832
$126$	−8.81030	−0.784884
$127$	−2.27451	−0.201830	−0.100915	−	0.994895i	$-0.532177\pi$
$127$	−2.27451	−0.201830	−0.100915	+	0.994895i	$0.532177\pi$
$128$	−7.98878	−0.706115
$129$	−6.45430	−0.568270
$130$	−15.8301	−1.38839
$131$	10.4771	0.915390	0.457695	−	0.889109i	$-0.348675\pi$
$131$	10.4771	0.915390	0.457695	+	0.889109i	$0.348675\pi$
$132$	−43.0667	−3.74848
$133$	18.2977	1.58662
$134$	9.96528	0.860869
$135$	−12.9148	−1.11153
$136$	16.0260	1.37422
$137$	−14.3593	−1.22680	−0.613400	−	0.789772i	$-0.710199\pi$
$137$	−14.3593	−1.22680	−0.613400	+	0.789772i	$0.710199\pi$
$138$	4.25679	0.362362
$139$	−15.1615	−1.28598	−0.642990	−	0.765875i	$-0.722306\pi$
$139$	−15.1615	−1.28598	−0.642990	+	0.765875i	$0.722306\pi$
$140$	−54.5753	−4.61245
$141$	−6.31826	−0.532093
$142$	16.2699	1.36534
$143$	−8.07193	−0.675009
$144$	10.7507	0.895892
$145$	3.39513	0.281950
$146$	−34.2490	−2.83447
$147$	−9.22184	−0.760604
$148$	1.92877	0.158544
$149$	−3.22192	−0.263950	−0.131975	−	0.991253i	$-0.542132\pi$
$149$	−3.22192	−0.263950	−0.131975	+	0.991253i	$0.542132\pi$
$150$	27.6737	2.25954
$151$	−4.90091	−0.398830	−0.199415	−	0.979915i	$-0.563904\pi$
$151$	−4.90091	−0.398830	−0.199415	+	0.979915i	$0.563904\pi$
$152$	−42.6147	−3.45651
$153$	−1.97107	−0.159351
$154$	−38.9577	−3.13930
$155$	−6.82716	−0.548371
$156$	18.6409	1.49246
$157$	−7.94891	−0.634392	−0.317196	−	0.948360i	$-0.602741\pi$
$157$	−7.94891	−0.634392	−0.317196	+	0.948360i	$0.602741\pi$
$158$	−26.0163	−2.06975
$159$	−10.4544	−0.829086
$160$	42.3965	3.35174
$161$	2.75062	0.216779
$162$	29.0421	2.28176
$163$	6.74197	0.528072	0.264036	−	0.964513i	$-0.414946\pi$
$163$	6.74197	0.528072	0.264036	+	0.964513i	$0.414946\pi$
$164$	59.4537	4.64256
$165$	27.5636	2.14582
$166$	43.6441	3.38744
$167$	−16.9841	−1.31427	−0.657135	−	0.753773i	$-0.728232\pi$
$167$	−16.9841	−1.31427	−0.657135	+	0.753773i	$0.728232\pi$
$168$	53.9873	4.16521
$169$	−9.50617	−0.731244
$170$	−17.0927	−1.31095
$171$	5.24126	0.400809
$172$	16.1864	1.23420
$173$	−2.69534	−0.204923	−0.102461	−	0.994737i	$-0.532672\pi$
$173$	−2.69534	−0.204923	−0.102461	+	0.994737i	$0.532672\pi$
$174$	−5.59683	−0.424295
$175$	17.8820	1.35175
$176$	47.5378	3.58330
$177$	−7.34476	−0.552066
$178$	−9.90734	−0.742586
$179$	−2.43214	−0.181787	−0.0908933	−	0.995861i	$-0.528972\pi$
$179$	−2.43214	−0.181787	−0.0908933	+	0.995861i	$0.528972\pi$
$180$	−15.6327	−1.16519
$181$	20.0356	1.48923	0.744617	−	0.667492i	$-0.232632\pi$
$181$	20.0356	1.48923	0.744617	+	0.667492i	$0.232632\pi$
$182$	16.8623	1.24992
$183$	−11.7589	−0.869243
$184$	−6.40609	−0.472263
$185$	−1.23446	−0.0907589
$186$	11.2545	0.825219
$187$	−8.71573	−0.637358
$188$	15.8452	1.15563
$189$	13.7569	1.00067
$190$	45.4510	3.29736
$191$	17.3048	1.25213	0.626065	−	0.779771i	$-0.284665\pi$
$191$	17.3048	1.25213	0.626065	+	0.779771i	$0.284665\pi$
$192$	−25.9865	−1.87542
$193$	0.996820	0.0717526	0.0358763	−	0.999356i	$-0.488578\pi$
$193$	0.996820	0.0717526	0.0358763	+	0.999356i	$0.488578\pi$
$194$	−25.3921	−1.82304
$195$	−11.9305	−0.854363
$196$	23.1270	1.65193
$197$	−22.3401	−1.59167	−0.795833	−	0.605516i	$-0.792967\pi$
$197$	−22.3401	−1.59167	−0.795833	+	0.605516i	$0.792967\pi$
$198$	−11.1592	−0.793047
$199$	−18.0552	−1.27990	−0.639950	−	0.768416i	$-0.721045\pi$
$199$	−18.0552	−1.27990	−0.639950	+	0.768416i	$0.721045\pi$
$200$	−41.6464	−2.94485
$201$	7.51045	0.529746
$202$	26.6770	1.87699
$203$	−3.61652	−0.253830
$204$	20.1276	1.40921
$205$	−38.0516	−2.65764
$206$	16.1980	1.12857
$207$	0.787896	0.0547625
$208$	−20.5761	−1.42670
$209$	23.1760	1.60312
$210$	−57.5805	−3.97343
$211$	−12.6680	−0.872104	−0.436052	−	0.899921i	$-0.643624\pi$
$211$	−12.6680	−0.872104	−0.436052	+	0.899921i	$0.643624\pi$
$212$	26.2180	1.80066
$213$	12.2620	0.840176
$214$	26.0020	1.77746
$215$	−10.3596	−0.706521
$216$	−32.0393	−2.18000
$217$	7.27235	0.493679
$218$	−41.5967	−2.81728
$219$	−25.8122	−1.74422
$220$	−69.1252	−4.66042
$221$	3.77249	0.253765
$222$	2.03498	0.136579
$223$	7.58790	0.508123	0.254062	−	0.967188i	$-0.418233\pi$
$223$	7.58790	0.508123	0.254062	+	0.967188i	$0.418233\pi$
$224$	−45.1611	−3.01745
$225$	5.12216	0.341477
$226$	0.293056	0.0194938
$227$	3.11318	0.206629	0.103314	−	0.994649i	$-0.467055\pi$
$227$	3.11318	0.206629	0.103314	+	0.994649i	$0.467055\pi$
$228$	−53.5212	−3.54453
$229$	−3.68371	−0.243426	−0.121713	−	0.992565i	$-0.538839\pi$
$229$	−3.68371	−0.243426	−0.121713	+	0.992565i	$0.538839\pi$
$230$	6.83246	0.450519
$231$	−29.3609	−1.93181
$232$	8.42274	0.552980
$233$	23.9967	1.57208	0.786039	−	0.618177i	$-0.212128\pi$
$233$	23.9967	1.57208	0.786039	+	0.618177i	$0.212128\pi$
$234$	4.83009	0.315753
$235$	−10.1413	−0.661543
$236$	18.4195	1.19901
$237$	−19.6075	−1.27364
$238$	18.2072	1.18020
$239$	21.6496	1.40040	0.700198	−	0.713949i	$-0.253095\pi$
$239$	21.6496	1.40040	0.700198	+	0.713949i	$0.253095\pi$
$240$	70.2621	4.53540
$241$	−22.2259	−1.43170	−0.715848	−	0.698257i	$-0.753959\pi$
$241$	−22.2259	−1.43170	−0.715848	+	0.698257i	$0.753959\pi$
$242$	−20.2386	−1.30099
$243$	9.78312	0.627587
$244$	29.4895	1.88787
$245$	−14.8017	−0.945648
$246$	62.7276	3.99936
$247$	−10.0314	−0.638284
$248$	−16.9370	−1.07550
$249$	32.8929	2.08450
$250$	2.07324	0.131123
$251$	−9.69826	−0.612149	−0.306074	−	0.952008i	$-0.599016\pi$
$251$	−9.69826	−0.612149	−0.306074	+	0.952008i	$0.599016\pi$
$252$	16.6521	1.04898
$253$	3.48395	0.219034
$254$	6.01823	0.377617
$255$	−12.8821	−0.806707
$256$	−4.92497	−0.307811
$257$	2.23493	0.139411	0.0697055	−	0.997568i	$-0.477794\pi$
$257$	2.23493	0.139411	0.0697055	+	0.997568i	$0.477794\pi$
$258$	17.0777	1.06321
$259$	1.31495	0.0817071
$260$	29.9199	1.85556
$261$	−1.03593	−0.0641222
$262$	−27.7218	−1.71266
$263$	12.5568	0.774287	0.387143	−	0.922019i	$-0.373462\pi$
$263$	12.5568	0.774287	0.387143	+	0.922019i	$0.373462\pi$
$264$	68.3805	4.20853
$265$	−16.7800	−1.03079
$266$	−48.4148	−2.96850
$267$	−7.46678	−0.456960
$268$	−18.8351	−1.15053
$269$	−7.24683	−0.441847	−0.220923	−	0.975291i	$-0.570907\pi$
$269$	−7.24683	−0.441847	−0.220923	+	0.975291i	$0.570907\pi$
$270$	34.1718	2.07963
$271$	16.7259	1.01603	0.508014	−	0.861349i	$-0.330380\pi$
$271$	16.7259	1.01603	0.508014	+	0.861349i	$0.330380\pi$
$272$	−22.2172	−1.34712
$273$	12.7085	0.769153
$274$	37.9940	2.29530
$275$	22.6494	1.36581
$276$	−8.04562	−0.484289
$277$	−24.8169	−1.49110	−0.745551	−	0.666449i	$-0.767814\pi$
$277$	−24.8169	−1.49110	−0.745551	+	0.666449i	$0.767814\pi$
$278$	40.1164	2.40602
$279$	2.08311	0.124713
$280$	86.6536	5.17854
$281$	1.92599	0.114895	0.0574474	−	0.998349i	$-0.481704\pi$
$281$	1.92599	0.114895	0.0574474	+	0.998349i	$0.481704\pi$
$282$	16.7177	0.995527
$283$	15.5384	0.923663	0.461832	−	0.886968i	$-0.347192\pi$
$283$	15.5384	0.923663	0.461832	+	0.886968i	$0.347192\pi$
$284$	−30.7511	−1.82474
$285$	34.2547	2.02907
$286$	21.3579	1.26292
$287$	40.5329	2.39258
$288$	−12.9361	−0.762265
$289$	−12.9266	−0.760390
$290$	−8.98332	−0.527519
$291$	−19.1370	−1.12183
$292$	64.7330	3.78821
$293$	25.5720	1.49393	0.746967	−	0.664861i	$-0.231509\pi$
$293$	25.5720	1.49393	0.746967	+	0.664861i	$0.231509\pi$
$294$	24.4005	1.42306
$295$	−11.7889	−0.686375
$296$	−3.06247	−0.178002
$297$	17.4246	1.01108
$298$	8.52502	0.493841
$299$	−1.50798	−0.0872087
$300$	−52.3051	−3.01984
$301$	11.0352	0.636056
$302$	12.9675	0.746197
$303$	20.1054	1.15503
$304$	59.0778	3.38834
$305$	−18.8739	−1.08072
$306$	5.21533	0.298141
$307$	23.5501	1.34407	0.672037	−	0.740518i	$-0.265420\pi$
$307$	23.5501	1.34407	0.672037	+	0.740518i	$0.265420\pi$
$308$	73.6328	4.19562
$309$	12.2078	0.694480
$310$	18.0643	1.02598
$311$	9.64461	0.546896	0.273448	−	0.961887i	$-0.411836\pi$
$311$	9.64461	0.546896	0.273448	+	0.961887i	$0.411836\pi$
$312$	−29.5976	−1.67563
$313$	−34.4906	−1.94952	−0.974761	−	0.223252i	$-0.928333\pi$
$313$	−34.4906	−1.94952	−0.974761	+	0.223252i	$0.928333\pi$
$314$	21.0323	1.18692
$315$	−10.6577	−0.600492
$316$	49.1726	2.76617
$317$	−23.7307	−1.33285	−0.666424	−	0.745573i	$-0.732176\pi$
$317$	−23.7307	−1.33285	−0.666424	+	0.745573i	$0.732176\pi$
$318$	27.6617	1.55119
$319$	−4.58070	−0.256470
$320$	−41.7103	−2.33168
$321$	19.5967	1.09378
$322$	−7.27799	−0.405586
$323$	−10.8315	−0.602681
$324$	−54.8915	−3.04953
$325$	−9.80348	−0.543799
$326$	−17.8389	−0.988003
$327$	−31.3498	−1.73365
$328$	−94.3994	−5.21234
$329$	10.8026	0.595564
$330$	−72.9316	−4.01475
$331$	9.02441	0.496026	0.248013	−	0.968757i	$-0.420222\pi$
$331$	9.02441	0.496026	0.248013	+	0.968757i	$0.420222\pi$
$332$	−82.4904	−4.52725
$333$	0.376658	0.0206407
$334$	44.9390	2.45895
$335$	12.0548	0.658625
$336$	−74.8438	−4.08306
$337$	19.5411	1.06447	0.532237	−	0.846595i	$-0.321352\pi$
$337$	19.5411	1.06447	0.532237	+	0.846595i	$0.321352\pi$
$338$	25.1528	1.36813
$339$	0.220865	0.0119957
$340$	32.3063	1.75205
$341$	9.21117	0.498813
$342$	−13.8681	−0.749899
$343$	−8.09934	−0.437323
$344$	−25.7005	−1.38568
$345$	5.14936	0.277232
$346$	7.13171	0.383403
$347$	−30.7229	−1.64929	−0.824645	−	0.565650i	$-0.808625\pi$
$347$	−30.7229	−1.64929	−0.824645	+	0.565650i	$0.808625\pi$
$348$	10.5784	0.567061
$349$	7.43968	0.398237	0.199118	−	0.979975i	$-0.436192\pi$
$349$	7.43968	0.398237	0.199118	+	0.979975i	$0.436192\pi$
$350$	−47.3147	−2.52908
$351$	−7.54199	−0.402562
$352$	−57.2012	−3.04883
$353$	4.99329	0.265766	0.132883	−	0.991132i	$-0.457577\pi$
$353$	4.99329	0.265766	0.132883	+	0.991132i	$0.457577\pi$
$354$	19.4338	1.03290
$355$	19.6814	1.04458
$356$	18.7255	0.992452
$357$	13.7221	0.726250
$358$	6.43530	0.340116
$359$	29.5168	1.55784	0.778918	−	0.627126i	$-0.215769\pi$
$359$	29.5168	1.55784	0.778918	+	0.627126i	$0.215769\pi$
$360$	24.8213	1.30820
$361$	9.80200	0.515895
$362$	−53.0130	−2.78630
$363$	−15.2530	−0.800577
$364$	−31.8710	−1.67049
$365$	−41.4304	−2.16857
$366$	31.1134	1.62632
$367$	−11.5670	−0.603794	−0.301897	−	0.953341i	$-0.597620\pi$
$367$	−11.5670	−0.603794	−0.301897	+	0.953341i	$0.597620\pi$
$368$	8.88090	0.462949
$369$	11.6103	0.604410
$370$	3.26630	0.169807
$371$	17.8742	0.927984
$372$	−21.2717	−1.10289
$373$	5.13829	0.266051	0.133025	−	0.991113i	$-0.457531\pi$
$373$	5.13829	0.266051	0.133025	+	0.991113i	$0.457531\pi$
$374$	23.0613	1.19247
$375$	1.56252	0.0806882
$376$	−25.1587	−1.29746
$377$	1.98269	0.102114
$378$	−36.4000	−1.87222
$379$	3.43012	0.176193	0.0880966	−	0.996112i	$-0.471922\pi$
$379$	3.43012	0.176193	0.0880966	+	0.996112i	$0.471922\pi$
$380$	−85.9055	−4.40686
$381$	4.53571	0.232371
$382$	−45.7874	−2.34269
$383$	29.4775	1.50623	0.753114	−	0.657890i	$-0.228551\pi$
$383$	29.4775	1.50623	0.753114	+	0.657890i	$0.228551\pi$
$384$	15.9308	0.812965
$385$	−47.1265	−2.40179
$386$	−2.63753	−0.134247
$387$	3.16094	0.160680
$388$	47.9927	2.43646
$389$	1.35668	0.0687865	0.0343933	−	0.999408i	$-0.489050\pi$
$389$	1.35668	0.0687865	0.0343933	+	0.999408i	$0.489050\pi$
$390$	31.5675	1.59848
$391$	−1.62825	−0.0823443
$392$	−36.7205	−1.85467
$393$	−20.8929	−1.05391
$394$	59.1106	2.97795
$395$	−31.4715	−1.58350
$396$	21.0916	1.05989
$397$	21.3686	1.07246	0.536230	−	0.844072i	$-0.319848\pi$
$397$	21.3686	1.07246	0.536230	+	0.844072i	$0.319848\pi$
$398$	47.7731	2.39465
$399$	−36.4884	−1.82670
$400$	57.7353	2.88677
$401$	18.8594	0.941792	0.470896	−	0.882189i	$-0.343931\pi$
$401$	18.8594	0.941792	0.470896	+	0.882189i	$0.343931\pi$
$402$	−19.8722	−0.991136
$403$	−3.98693	−0.198603
$404$	−50.4213	−2.50856
$405$	35.1317	1.74571
$406$	9.56911	0.474907
$407$	1.66552	0.0825568
$408$	−31.9582	−1.58217
$409$	−4.69732	−0.232267	−0.116134	−	0.993234i	$-0.537050\pi$
$409$	−4.69732	−0.232267	−0.116134	+	0.993234i	$0.537050\pi$
$410$	100.682	4.97235
$411$	28.6346	1.41244
$412$	−30.6154	−1.50831
$413$	12.5576	0.617920
$414$	−2.08473	−0.102459
$415$	52.7955	2.59163
$416$	24.7588	1.21390
$417$	30.2342	1.48057
$418$	−61.3223	−2.99937
$419$	−11.4956	−0.561599	−0.280799	−	0.959766i	$-0.590600\pi$
$419$	−11.4956	−0.561599	−0.280799	+	0.959766i	$0.590600\pi$
$420$	108.831	5.31041
$421$	−7.20369	−0.351086	−0.175543	−	0.984472i	$-0.556168\pi$
$421$	−7.20369	−0.351086	−0.175543	+	0.984472i	$0.556168\pi$
$422$	33.5189	1.63168
$423$	3.09431	0.150451
$424$	−41.6284	−2.02165
$425$	−10.5854	−0.513466
$426$	−32.4445	−1.57194
$427$	20.1046	0.972931
$428$	−49.1456	−2.37554
$429$	16.0966	0.777152
$430$	27.4110	1.32188
$431$	21.6986	1.04518	0.522591	−	0.852583i	$-0.324965\pi$
$431$	21.6986	1.04518	0.522591	+	0.852583i	$0.324965\pi$
$432$	44.4168	2.13701
$433$	9.21027	0.442617	0.221309	−	0.975204i	$-0.428967\pi$
$433$	9.21027	0.442617	0.221309	+	0.975204i	$0.428967\pi$
$434$	−19.2422	−0.923656
$435$	−6.77039	−0.324615
$436$	78.6206	3.76524
$437$	4.32968	0.207117
$438$	68.2975	3.26338
$439$	12.4852	0.595886	0.297943	−	0.954584i	$-0.403700\pi$
$439$	12.4852	0.595886	0.297943	+	0.954584i	$0.403700\pi$
$440$	109.756	5.23240
$441$	4.51632	0.215063
$442$	−9.98179	−0.474785
$443$	7.55623	0.359007	0.179504	−	0.983757i	$-0.442551\pi$
$443$	7.55623	0.359007	0.179504	+	0.983757i	$0.442551\pi$
$444$	−3.84626	−0.182535
$445$	−11.9847	−0.568131
$446$	−20.0771	−0.950680
$447$	6.42498	0.303891
$448$	44.4302	2.09913
$449$	24.0242	1.13377	0.566885	−	0.823797i	$-0.308148\pi$
$449$	24.0242	1.13377	0.566885	+	0.823797i	$0.308148\pi$
$450$	−13.5529	−0.638892
$451$	51.3390	2.41746
$452$	−0.553895	−0.0260530
$453$	9.77313	0.459182
$454$	−8.23729	−0.386595
$455$	20.3981	0.956276
$456$	84.9800	3.97955
$457$	−10.3946	−0.486238	−0.243119	−	0.969997i	$-0.578171\pi$
$457$	−10.3946	−0.486238	−0.243119	+	0.969997i	$0.578171\pi$
$458$	9.74688	0.455442
$459$	−8.14352	−0.380107
$460$	−12.9138	−0.602109
$461$	16.7445	0.779871	0.389936	−	0.920842i	$-0.372497\pi$
$461$	16.7445	0.779871	0.389936	+	0.920842i	$0.372497\pi$
$462$	77.6874	3.61434
$463$	14.2816	0.663722	0.331861	−	0.943328i	$-0.392323\pi$
$463$	14.2816	0.663722	0.331861	+	0.943328i	$0.392323\pi$
$464$	−11.6766	−0.542074
$465$	13.6143	0.631350
$466$	−63.4940	−2.94130
$467$	−21.0998	−0.976383	−0.488191	−	0.872737i	$-0.662343\pi$
$467$	−21.0998	−0.976383	−0.488191	+	0.872737i	$0.662343\pi$
$468$	−9.12921	−0.421998
$469$	−12.8409	−0.592938
$470$	26.8332	1.23772
$471$	15.8513	0.730388
$472$	−29.2462	−1.34616
$473$	13.9772	0.642671
$474$	51.8803	2.38294
$475$	28.1475	1.29150
$476$	−34.4129	−1.57731
$477$	5.11995	0.234426
$478$	−57.2836	−2.62009
$479$	26.0672	1.19104	0.595521	−	0.803340i	$-0.296946\pi$
$479$	26.0672	1.19104	0.595521	+	0.803340i	$0.296946\pi$
$480$	−84.5448	−3.85892
$481$	−0.720899	−0.0328702
$482$	58.8084	2.67865
$483$	−5.48514	−0.249583
$484$	38.2523	1.73874
$485$	−30.7163	−1.39476
$486$	−25.8856	−1.17419
$487$	8.54562	0.387239	0.193620	−	0.981077i	$-0.437977\pi$
$487$	8.54562	0.387239	0.193620	+	0.981077i	$0.437977\pi$
$488$	−46.8229	−2.11957
$489$	−13.4445	−0.607980
$490$	39.1645	1.76927
$491$	−17.2202	−0.777137	−0.388569	−	0.921420i	$-0.627030\pi$
$491$	−17.2202	−0.777137	−0.388569	+	0.921420i	$0.627030\pi$
$492$	−118.559	−5.34507
$493$	2.14083	0.0964181
$494$	26.5426	1.19421
$495$	−13.4990	−0.606736
$496$	23.4801	1.05429
$497$	−20.9647	−0.940397
$498$	−87.0328	−3.90003
$499$	6.65088	0.297734	0.148867	−	0.988857i	$-0.452437\pi$
$499$	6.65088	0.297734	0.148867	+	0.988857i	$0.452437\pi$
$500$	−3.91856	−0.175244
$501$	33.8688	1.51315
$502$	25.6610	1.14531
$503$	33.0825	1.47507	0.737537	−	0.675307i	$-0.235989\pi$
$503$	33.0825	1.47507	0.737537	+	0.675307i	$0.235989\pi$
$504$	−26.4398	−1.17772
$505$	32.2707	1.43603
$506$	−9.21832	−0.409804
$507$	18.9567	0.841896
$508$	−11.3749	−0.504678
$509$	42.7383	1.89434	0.947170	−	0.320731i	$-0.103929\pi$
$509$	42.7383	1.89434	0.947170	+	0.320731i	$0.103929\pi$
$510$	34.0852	1.50932
$511$	44.1320	1.95229
$512$	29.0088	1.28202
$513$	21.6544	0.956066
$514$	−5.91350	−0.260833
$515$	19.5945	0.863436
$516$	−32.2781	−1.42096
$517$	13.6826	0.601758
$518$	−3.47929	−0.152871
$519$	5.37490	0.235932
$520$	−47.5063	−2.08329
$521$	44.4193	1.94604	0.973022	−	0.230713i	$-0.0741057\pi$
$521$	44.4193	1.94604	0.973022	+	0.230713i	$0.0741057\pi$
$522$	2.74100	0.119970
$523$	42.8647	1.87434	0.937171	−	0.348869i	$-0.113434\pi$
$523$	42.8647	1.87434	0.937171	+	0.348869i	$0.113434\pi$
$524$	52.3962	2.28894
$525$	−35.6593	−1.55630
$526$	−33.2246	−1.44866
$527$	−4.30492	−0.187525
$528$	−94.7974	−4.12553
$529$	−22.3491	−0.971702
$530$	44.3990	1.92857
$531$	3.59704	0.156098
$532$	91.5073	3.96734
$533$	−22.2214	−0.962517
$534$	19.7567	0.854955
$535$	31.4542	1.35988
$536$	29.9059	1.29174
$537$	4.85004	0.209295
$538$	19.1747	0.826679
$539$	19.9704	0.860187
$540$	−64.5870	−2.77938
$541$	−42.7484	−1.83790	−0.918949	−	0.394376i	$-0.870961\pi$
$541$	−42.7484	−1.83790	−0.918949	+	0.394376i	$0.870961\pi$
$542$	−44.2558	−1.90095
$543$	−39.9539	−1.71458
$544$	26.7335	1.14619
$545$	−50.3188	−2.15542
$546$	−33.6259	−1.43906
$547$	−27.3023	−1.16736	−0.583681	−	0.811983i	$-0.698388\pi$
$547$	−27.3023	−1.16736	−0.583681	+	0.811983i	$0.698388\pi$
$548$	−71.8112	−3.06762
$549$	5.75883	0.245781
$550$	−59.9289	−2.55538
$551$	−5.69267	−0.242516
$552$	12.7747	0.543726
$553$	33.5237	1.42557
$554$	65.6641	2.78980
$555$	2.46168	0.104493
$556$	−75.8227	−3.21560
$557$	17.1377	0.726147	0.363073	−	0.931761i	$-0.381727\pi$
$557$	17.1377	0.726147	0.363073	+	0.931761i	$0.381727\pi$
$558$	−5.51179	−0.233333
$559$	−6.04983	−0.255881
$560$	−120.130	−5.07641
$561$	17.3804	0.733803
$562$	−5.09606	−0.214964
$563$	12.6239	0.532035	0.266017	−	0.963968i	$-0.414292\pi$
$563$	12.6239	0.532035	0.266017	+	0.963968i	$0.414292\pi$
$564$	−31.5977	−1.33050
$565$	0.354504	0.0149141
$566$	−41.1138	−1.72814
$567$	−37.4225	−1.57160
$568$	48.8261	2.04870
$569$	35.0313	1.46859	0.734293	−	0.678832i	$-0.237514\pi$
$569$	35.0313	1.46859	0.734293	+	0.678832i	$0.237514\pi$
$570$	−90.6359	−3.79632
$571$	−38.3818	−1.60623	−0.803114	−	0.595825i	$-0.796825\pi$
$571$	−38.3818	−1.60623	−0.803114	+	0.595825i	$0.796825\pi$
$572$	−40.3679	−1.68786
$573$	−34.5082	−1.44160
$574$	−107.248	−4.47643
$575$	4.23130	0.176457
$576$	12.7267	0.530279
$577$	28.1142	1.17041	0.585204	−	0.810886i	$-0.301014\pi$
$577$	28.1142	1.17041	0.585204	+	0.810886i	$0.301014\pi$
$578$	34.2031	1.42266
$579$	−1.98780	−0.0826103
$580$	16.9791	0.705019
$581$	−56.2382	−2.33316
$582$	50.6355	2.09891
$583$	22.6396	0.937635
$584$	−102.782	−4.25314
$585$	5.84288	0.241573
$586$	−67.6621	−2.79510
$587$	0.821607	0.0339113	0.0169557	−	0.999856i	$-0.494603\pi$
$587$	0.821607	0.0339113	0.0169557	+	0.999856i	$0.494603\pi$
$588$	−46.1185	−1.90190
$589$	11.4472	0.471674
$590$	31.1927	1.28418
$591$	44.5494	1.83252
$592$	4.24557	0.174492
$593$	−20.0644	−0.823945	−0.411973	−	0.911196i	$-0.635160\pi$
$593$	−20.0644	−0.823945	−0.411973	+	0.911196i	$0.635160\pi$
$594$	−46.1044	−1.89169
$595$	22.0250	0.902936
$596$	−16.1129	−0.660009
$597$	36.0047	1.47358
$598$	3.99003	0.163164
$599$	−22.1249	−0.903998	−0.451999	−	0.892018i	$-0.649289\pi$
$599$	−22.1249	−0.903998	−0.451999	+	0.892018i	$0.649289\pi$
$600$	83.0490	3.39046
$601$	−8.60938	−0.351184	−0.175592	−	0.984463i	$-0.556184\pi$
$601$	−8.60938	−0.351184	−0.175592	+	0.984463i	$0.556184\pi$
$602$	−29.1984	−1.19004
$603$	−3.67818	−0.149787
$604$	−24.5095	−0.997278
$605$	−24.4823	−0.995346
$606$	−53.1978	−2.16101
$607$	−41.3332	−1.67766	−0.838832	−	0.544390i	$-0.816761\pi$
$607$	−41.3332	−1.67766	−0.838832	+	0.544390i	$0.816761\pi$
$608$	−71.0869	−2.88295
$609$	7.21187	0.292240
$610$	49.9393	2.02198
$611$	−5.92231	−0.239591
$612$	−9.85733	−0.398459
$613$	39.0196	1.57599	0.787994	−	0.615683i	$-0.211120\pi$
$613$	39.0196	1.57599	0.787994	+	0.615683i	$0.211120\pi$
$614$	−62.3121	−2.51471
$615$	75.8804	3.05979
$616$	−116.913	−4.71054
$617$	21.8297	0.878829	0.439414	−	0.898284i	$-0.355186\pi$
$617$	21.8297	0.878829	0.439414	+	0.898284i	$0.355186\pi$
$618$	−32.3012	−1.29935
$619$	−38.3648	−1.54201	−0.771005	−	0.636829i	$-0.780246\pi$
$619$	−38.3648	−1.54201	−0.771005	+	0.636829i	$0.780246\pi$
$620$	−34.1427	−1.37120
$621$	3.25521	0.130627
$622$	−25.5191	−1.02322
$623$	12.7662	0.511468
$624$	41.0318	1.64259
$625$	−23.7161	−0.948642
$626$	91.2600	3.64748
$627$	−46.2163	−1.84570
$628$	−39.7526	−1.58630
$629$	−0.778396	−0.0310367
$630$	28.1996	1.12350
$631$	32.7312	1.30301	0.651504	−	0.758645i	$-0.274138\pi$
$631$	32.7312	1.30301	0.651504	+	0.758645i	$0.274138\pi$
$632$	−78.0752	−3.10567
$633$	25.2619	1.00407
$634$	62.7901	2.49371
$635$	7.28014	0.288904
$636$	−52.2825	−2.07313
$637$	−8.64393	−0.342485
$638$	12.1203	0.479846
$639$	−6.00520	−0.237562
$640$	25.5701	1.01075
$641$	−37.5281	−1.48227	−0.741135	−	0.671356i	$-0.765712\pi$
$641$	−37.5281	−1.48227	−0.741135	+	0.671356i	$0.765712\pi$
$642$	−51.8518	−2.04643
$643$	−17.9463	−0.707734	−0.353867	−	0.935296i	$-0.615134\pi$
$643$	−17.9463	−0.707734	−0.353867	+	0.935296i	$0.615134\pi$
$644$	13.7559	0.542058
$645$	20.6586	0.813432
$646$	28.6595	1.12759
$647$	43.9094	1.72626	0.863128	−	0.504984i	$-0.168502\pi$
$647$	43.9094	1.72626	0.863128	+	0.504984i	$0.168502\pi$
$648$	87.1556	3.42379
$649$	15.9055	0.624346
$650$	25.9394	1.01743
$651$	−14.5021	−0.568383
$652$	33.7167	1.32045
$653$	4.59271	0.179726	0.0898632	−	0.995954i	$-0.471357\pi$
$653$	4.59271	0.179726	0.0898632	+	0.995954i	$0.471357\pi$
$654$	82.9499	3.24360
$655$	−33.5346	−1.31031
$656$	130.868	5.10954
$657$	12.6413	0.493184
$658$	−28.5830	−1.11428
$659$	17.7980	0.693312	0.346656	−	0.937992i	$-0.387317\pi$
$659$	17.7980	0.693312	0.346656	+	0.937992i	$0.387317\pi$
$660$	137.846	5.36564
$661$	−7.85173	−0.305397	−0.152698	−	0.988273i	$-0.548796\pi$
$661$	−7.85173	−0.305397	−0.152698	+	0.988273i	$0.548796\pi$
$662$	−23.8781	−0.928047
$663$	−7.52289	−0.292165
$664$	130.977	5.08288
$665$	−58.5665	−2.27111
$666$	−0.996616	−0.0386181
$667$	−0.855755	−0.0331350
$668$	−84.9378	−3.28634
$669$	−15.1314	−0.585013
$670$	−31.8964	−1.23226
$671$	25.4646	0.983049
$672$	90.0578	3.47406
$673$	8.30514	0.320139	0.160070	−	0.987106i	$-0.448828\pi$
$673$	8.30514	0.320139	0.160070	+	0.987106i	$0.448828\pi$
$674$	−51.7048	−1.99159
$675$	21.1624	0.814540
$676$	−47.5405	−1.82848
$677$	−22.8151	−0.876856	−0.438428	−	0.898766i	$-0.644465\pi$
$677$	−22.8151	−0.876856	−0.438428	+	0.898766i	$0.644465\pi$
$678$	−0.584395	−0.0224436
$679$	32.7193	1.25565
$680$	−51.2953	−1.96708
$681$	−6.20813	−0.237896
$682$	−24.3722	−0.933261
$683$	−26.0992	−0.998659	−0.499330	−	0.866412i	$-0.666420\pi$
$683$	−26.0992	−0.998659	−0.499330	+	0.866412i	$0.666420\pi$
$684$	26.2116	1.00223
$685$	45.9606	1.75607
$686$	21.4304	0.818216
$687$	7.34585	0.280262
$688$	35.6291	1.35835
$689$	−9.79923	−0.373321
$690$	−13.6249	−0.518691
$691$	−40.3821	−1.53621	−0.768104	−	0.640325i	$-0.778800\pi$
$691$	−40.3821	−1.53621	−0.768104	+	0.640325i	$0.778800\pi$
$692$	−13.4794	−0.512411
$693$	14.3793	0.546224
$694$	81.2910	3.08576
$695$	48.5281	1.84078
$696$	−16.7962	−0.636657
$697$	−23.9938	−0.908828
$698$	−19.6850	−0.745087
$699$	−47.8530	−1.80997
$700$	89.4280	3.38006
$701$	4.65945	0.175985	0.0879925	−	0.996121i	$-0.471955\pi$
$701$	4.65945	0.175985	0.0879925	+	0.996121i	$0.471955\pi$
$702$	19.9557	0.753178
$703$	2.06983	0.0780651
$704$	56.2754	2.12096
$705$	20.2232	0.761648
$706$	−13.2120	−0.497239
$707$	−34.3750	−1.29280
$708$	−36.7313	−1.38045
$709$	39.2115	1.47262	0.736308	−	0.676646i	$-0.236567\pi$
$709$	39.2115	1.47262	0.736308	+	0.676646i	$0.236567\pi$
$710$	−52.0758	−1.95437
$711$	9.60261	0.360126
$712$	−29.7320	−1.11426
$713$	1.72081	0.0644448
$714$	−36.3079	−1.35879
$715$	25.8362	0.966221
$716$	−12.1632	−0.454558
$717$	−43.1724	−1.61230
$718$	−78.0997	−2.91465
$719$	−18.7233	−0.698259	−0.349130	−	0.937074i	$-0.613523\pi$
$719$	−18.7233	−0.698259	−0.349130	+	0.937074i	$0.613523\pi$
$720$	−34.4103	−1.28240
$721$	−20.8722	−0.777321
$722$	−25.9355	−0.965221
$723$	44.3216	1.64834
$724$	100.198	3.72384
$725$	−5.56332	−0.206617
$726$	40.3587	1.49785
$727$	−20.0218	−0.742566	−0.371283	−	0.928520i	$-0.621082\pi$
$727$	−20.0218	−0.742566	−0.371283	+	0.928520i	$0.621082\pi$
$728$	50.6041	1.87551
$729$	13.4192	0.497009
$730$	109.623	4.05731
$731$	−6.53236	−0.241608
$732$	−58.8064	−2.17355
$733$	−7.86616	−0.290543	−0.145272	−	0.989392i	$-0.546406\pi$
$733$	−7.86616	−0.290543	−0.145272	+	0.989392i	$0.546406\pi$
$734$	30.6057	1.12968
$735$	29.5168	1.08874
$736$	−10.6862	−0.393898
$737$	−16.2643	−0.599104
$738$	−30.7203	−1.13083
$739$	−38.3531	−1.41084	−0.705421	−	0.708789i	$-0.749242\pi$
$739$	−38.3531	−1.41084	−0.705421	+	0.708789i	$0.749242\pi$
$740$	−6.17353	−0.226943
$741$	20.0041	0.734869
$742$	−47.2942	−1.73622
$743$	32.4177	1.18929	0.594645	−	0.803989i	$-0.297293\pi$
$743$	32.4177	1.18929	0.594645	+	0.803989i	$0.297293\pi$
$744$	33.7748	1.23825
$745$	10.3126	0.377823
$746$	−13.5956	−0.497771
$747$	−16.1090	−0.589399
$748$	−43.5875	−1.59372
$749$	−33.5052	−1.22425
$750$	−4.13434	−0.150965
$751$	−7.40699	−0.270285	−0.135142	−	0.990826i	$-0.543149\pi$
$751$	−7.40699	−0.270285	−0.135142	+	0.990826i	$0.543149\pi$
$752$	34.8781	1.27187
$753$	19.3397	0.704779
$754$	−5.24609	−0.191052
$755$	15.6866	0.570894
$756$	68.7986	2.50218
$757$	31.6570	1.15059	0.575297	−	0.817945i	$-0.304886\pi$
$757$	31.6570	1.15059	0.575297	+	0.817945i	$0.304886\pi$
$758$	−9.07589	−0.329651
$759$	−6.94749	−0.252178
$760$	136.399	4.94772
$761$	15.6918	0.568826	0.284413	−	0.958702i	$-0.408201\pi$
$761$	15.6918	0.568826	0.284413	+	0.958702i	$0.408201\pi$
$762$	−12.0012	−0.434758
$763$	53.6000	1.94045
$764$	86.5414	3.13096
$765$	6.30889	0.228098
$766$	−77.9957	−2.81810
$767$	−6.88449	−0.248585
$768$	9.82111	0.354389
$769$	35.0984	1.26568	0.632840	−	0.774282i	$-0.281889\pi$
$769$	35.0984	1.26568	0.632840	+	0.774282i	$0.281889\pi$
$770$	124.694	4.49366
$771$	−4.45677	−0.160507
$772$	4.98511	0.179418
$773$	−25.7645	−0.926683	−0.463342	−	0.886180i	$-0.653350\pi$
$773$	−25.7645	−0.926683	−0.463342	+	0.886180i	$0.653350\pi$
$774$	−8.36367	−0.300626
$775$	11.1871	0.401852
$776$	−76.2019	−2.73549
$777$	−2.62220	−0.0940711
$778$	−3.58970	−0.128697
$779$	63.8017	2.28593
$780$	−59.6647	−2.13634
$781$	−26.5540	−0.950177
$782$	4.30826	0.154063
$783$	−4.27996	−0.152953
$784$	50.9065	1.81809
$785$	25.4425	0.908080
$786$	55.2814	1.97182
$787$	−26.4428	−0.942585	−0.471293	−	0.881977i	$-0.656212\pi$
$787$	−26.4428	−0.942585	−0.471293	+	0.881977i	$0.656212\pi$
$788$	−111.723	−3.97997
$789$	−25.0401	−0.891452
$790$	83.2717	2.96267
$791$	−0.377621	−0.0134266
$792$	−33.4888	−1.18997
$793$	−11.0220	−0.391403
$794$	−56.5402	−2.00654
$795$	33.4618	1.18677
$796$	−90.2944	−3.20040
$797$	−41.7701	−1.47957	−0.739787	−	0.672841i	$-0.765074\pi$
$797$	−41.7701	−1.47957	−0.739787	+	0.672841i	$0.765074\pi$
$798$	96.5462	3.41770
$799$	−6.39466	−0.226227
$800$	−69.4716	−2.45619
$801$	3.65679	0.129206
$802$	−49.9008	−1.76206
$803$	55.8978	1.97259
$804$	37.5599	1.32463
$805$	−8.80405	−0.310302
$806$	10.5492	0.371580
$807$	14.4512	0.508707
$808$	80.0580	2.81643
$809$	−44.3212	−1.55825	−0.779126	−	0.626868i	$-0.784337\pi$
$809$	−44.3212	−1.55825	−0.779126	+	0.626868i	$0.784337\pi$
$810$	−92.9564	−3.26615
$811$	−4.76808	−0.167430	−0.0837150	−	0.996490i	$-0.526679\pi$
$811$	−4.76808	−0.167430	−0.0837150	+	0.996490i	$0.526679\pi$
$812$	−18.0863	−0.634704
$813$	−33.3539	−1.16977
$814$	−4.40687	−0.154461
$815$	−21.5794	−0.755892
$816$	44.3044	1.55096
$817$	17.3702	0.607705
$818$	12.4288	0.434564
$819$	−6.22388	−0.217480
$820$	−190.297	−6.64544
$821$	4.19011	0.146236	0.0731180	−	0.997323i	$-0.476705\pi$
$821$	4.19011	0.146236	0.0731180	+	0.997323i	$0.476705\pi$
$822$	−75.7655	−2.64263
$823$	29.6461	1.03340	0.516699	−	0.856167i	$-0.327161\pi$
$823$	29.6461	1.03340	0.516699	+	0.856167i	$0.327161\pi$
$824$	48.6105	1.69343
$825$	−45.1661	−1.57248
$826$	−33.2267	−1.15611
$827$	−26.3826	−0.917412	−0.458706	−	0.888588i	$-0.651687\pi$
$827$	−26.3826	−0.917412	−0.458706	+	0.888588i	$0.651687\pi$
$828$	3.94028	0.136934
$829$	27.1071	0.941467	0.470733	−	0.882275i	$-0.343989\pi$
$829$	27.1071	0.941467	0.470733	+	0.882275i	$0.343989\pi$
$830$	−139.694	−4.84885
$831$	49.4885	1.71674
$832$	−24.3580	−0.844463
$833$	−9.33336	−0.323382
$834$	−79.9979	−2.77010
$835$	54.3619	1.88127
$836$	115.903	4.00860
$837$	8.60643	0.297482
$838$	30.4168	1.05073
$839$	−45.4996	−1.57082	−0.785410	−	0.618976i	$-0.787548\pi$
$839$	−45.4996	−1.57082	−0.785410	+	0.618976i	$0.787548\pi$
$840$	−172.800	−5.96216
$841$	−27.8749	−0.961202
$842$	19.0605	0.656870
$843$	−3.84070	−0.132281
$844$	−63.3531	−2.18070
$845$	30.4269	1.04672
$846$	−8.18738	−0.281488
$847$	26.0787	0.896075
$848$	57.7104	1.98178
$849$	−30.9859	−1.06343
$850$	28.0083	0.960677
$851$	0.311149	0.0106660
$852$	61.3223	2.10087
$853$	−33.3558	−1.14208	−0.571041	−	0.820921i	$-0.693460\pi$
$853$	−33.3558	−1.14208	−0.571041	+	0.820921i	$0.693460\pi$
$854$	−53.1957	−1.82032
$855$	−16.7760	−0.573726
$856$	78.0324	2.66709
$857$	6.28659	0.214746	0.107373	−	0.994219i	$-0.465756\pi$
$857$	6.28659	0.214746	0.107373	+	0.994219i	$0.465756\pi$
$858$	−42.5907	−1.45402
$859$	9.78132	0.333734	0.166867	−	0.985979i	$-0.446635\pi$
$859$	9.78132	0.333734	0.166867	+	0.985979i	$0.446635\pi$
$860$	−51.8087	−1.76666
$861$	−80.8284	−2.75463
$862$	−57.4131	−1.95550
$863$	−19.5565	−0.665709	−0.332855	−	0.942978i	$-0.608012\pi$
$863$	−19.5565	−0.665709	−0.332855	+	0.942978i	$0.608012\pi$
$864$	−53.4458	−1.81826
$865$	8.62711	0.293331
$866$	−24.3698	−0.828121
$867$	25.7776	0.875452
$868$	36.3691	1.23445
$869$	42.4612	1.44040
$870$	17.9141	0.607343
$871$	7.03979	0.238534
$872$	−124.832	−4.22735
$873$	9.37220	0.317201
$874$	−11.4561	−0.387508
$875$	−2.67150	−0.0903132
$876$	−129.087	−4.36145
$877$	−1.18896	−0.0401482	−0.0200741	−	0.999798i	$-0.506390\pi$
$877$	−1.18896	−0.0401482	−0.0200741	+	0.999798i	$0.506390\pi$
$878$	−33.0351	−1.11488
$879$	−50.9943	−1.72000
$880$	−152.157	−5.12920
$881$	31.9666	1.07698	0.538492	−	0.842631i	$-0.318994\pi$
$881$	31.9666	1.07698	0.538492	+	0.842631i	$0.318994\pi$
$882$	−11.9499	−0.402375
$883$	−31.3395	−1.05466	−0.527330	−	0.849661i	$-0.676807\pi$
$883$	−31.3395	−1.05466	−0.527330	+	0.849661i	$0.676807\pi$
$884$	18.8663	0.634541
$885$	23.5088	0.790238
$886$	−19.9934	−0.671690
$887$	15.2247	0.511194	0.255597	−	0.966783i	$-0.417728\pi$
$887$	15.2247	0.511194	0.255597	+	0.966783i	$0.417728\pi$
$888$	6.10701	0.204938
$889$	−7.75487	−0.260090
$890$	31.7109	1.06295
$891$	−47.3995	−1.58794
$892$	37.9472	1.27057
$893$	17.0040	0.569018
$894$	−17.0001	−0.568569
$895$	7.78467	0.260213
$896$	−27.2375	−0.909940
$897$	3.00713	0.100405
$898$	−63.5665	−2.12124
$899$	−2.26252	−0.0754594
$900$	25.6160	0.853867
$901$	−10.5808	−0.352497
$902$	−135.840	−4.52298
$903$	−22.0057	−0.732305
$904$	0.879464	0.0292505
$905$	−64.1289	−2.13172
$906$	−25.8591	−0.859112
$907$	8.41726	0.279491	0.139745	−	0.990187i	$-0.455372\pi$
$907$	8.41726	0.279491	0.139745	+	0.990187i	$0.455372\pi$
$908$	15.5690	0.516677
$909$	−9.84647	−0.326587
$910$	−53.9721	−1.78916
$911$	−8.66797	−0.287183	−0.143591	−	0.989637i	$-0.545865\pi$
$911$	−8.66797	−0.287183	−0.143591	+	0.989637i	$0.545865\pi$
$912$	−117.810	−3.90107
$913$	−71.2315	−2.35742
$914$	27.5035	0.909733
$915$	37.6373	1.24425
$916$	−18.4223	−0.608689
$917$	35.7214	1.17962
$918$	21.5473	0.711167
$919$	49.7293	1.64042	0.820209	−	0.572064i	$-0.193857\pi$
$919$	49.7293	1.64042	0.820209	+	0.572064i	$0.193857\pi$
$920$	20.5043	0.676006
$921$	−46.9623	−1.54746
$922$	−44.3051	−1.45911
$923$	11.4935	0.378315
$924$	−146.834	−4.83050
$925$	2.02280	0.0665092
$926$	−37.7883	−1.24180
$927$	−5.97869	−0.196366
$928$	14.0502	0.461221
$929$	−30.8518	−1.01221	−0.506107	−	0.862471i	$-0.668916\pi$
$929$	−30.8518	−1.01221	−0.506107	+	0.862471i	$0.668916\pi$
$930$	−36.0228	−1.18123
$931$	24.8183	0.813387
$932$	120.008	3.93099
$933$	−19.2328	−0.629652
$934$	55.8289	1.82678
$935$	27.8969	0.912326
$936$	14.4952	0.473789
$937$	37.5152	1.22557	0.612784	−	0.790251i	$-0.290050\pi$
$937$	37.5152	1.22557	0.612784	+	0.790251i	$0.290050\pi$
$938$	33.9763	1.10936
$939$	68.7792	2.24452
$940$	−50.7166	−1.65419
$941$	48.1286	1.56895	0.784474	−	0.620162i	$-0.212933\pi$
$941$	48.1286	1.56895	0.784474	+	0.620162i	$0.212933\pi$
$942$	−41.9416	−1.36653
$943$	9.59104	0.312327
$944$	40.5446	1.31962
$945$	−44.0325	−1.43238
$946$	−36.9828	−1.20241
$947$	8.11752	0.263784	0.131892	−	0.991264i	$-0.457895\pi$
$947$	8.11752	0.263784	0.131892	+	0.991264i	$0.457895\pi$
$948$	−98.0573	−3.18475
$949$	−24.1946	−0.785390
$950$	−74.4768	−2.41635
$951$	47.3225	1.53454
$952$	54.6401	1.77090
$953$	−2.87512	−0.0931344	−0.0465672	−	0.998915i	$-0.514828\pi$
$953$	−2.87512	−0.0931344	−0.0465672	+	0.998915i	$0.514828\pi$
$954$	−13.5471	−0.438603
$955$	−55.3883	−1.79232
$956$	108.270	3.50170
$957$	9.13458	0.295279
$958$	−68.9723	−2.22840
$959$	−48.9576	−1.58092
$960$	83.1764	2.68451
$961$	−26.4504	−0.853238
$962$	1.90746	0.0614989
$963$	−9.59733	−0.309270
$964$	−111.152	−3.57996
$965$	−3.19057	−0.102708
$966$	14.5134	0.466960
$967$	31.1425	1.00148	0.500738	−	0.865599i	$-0.333062\pi$
$967$	31.1425	1.00148	0.500738	+	0.865599i	$0.333062\pi$
$968$	−60.7363	−1.95214
$969$	21.5996	0.693879
$970$	81.2737	2.60954
$971$	16.8233	0.539886	0.269943	−	0.962876i	$-0.412995\pi$
$971$	16.8233	0.539886	0.269943	+	0.962876i	$0.412995\pi$
$972$	48.9255	1.56929
$973$	−51.6925	−1.65719
$974$	−22.6112	−0.724511
$975$	19.5496	0.626087
$976$	64.9116	2.07777
$977$	−44.0565	−1.40949	−0.704745	−	0.709460i	$-0.748939\pi$
$977$	−44.0565	−1.40949	−0.704745	+	0.709460i	$0.748939\pi$
$978$	35.5733	1.13751
$979$	16.1697	0.516787
$980$	−74.0236	−2.36460
$981$	15.3533	0.490194
$982$	45.5637	1.45400
$983$	32.4601	1.03532	0.517659	−	0.855587i	$-0.326804\pi$
$983$	32.4601	1.03532	0.517659	+	0.855587i	$0.326804\pi$
$984$	188.246	6.00107
$985$	71.5051	2.27834
$986$	−5.66451	−0.180395
$987$	−21.5419	−0.685685
$988$	−50.1672	−1.59603
$989$	2.61118	0.0830308
$990$	35.7177	1.13518
$991$	−54.5632	−1.73326	−0.866629	−	0.498953i	$-0.833718\pi$
$991$	−54.5632	−1.73326	−0.866629	+	0.498953i	$0.833718\pi$
$992$	−28.2531	−0.897037
$993$	−17.9960	−0.571085
$994$	55.4715	1.75945
$995$	57.7902	1.83207
$996$	164.498	5.21232
$997$	−1.81459	−0.0574686	−0.0287343	−	0.999587i	$-0.509148\pi$
$997$	−1.81459	−0.0574686	−0.0287343	+	0.999587i	$0.509148\pi$
$998$	−17.5979	−0.557050
$999$	1.55618	0.0492352

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4001.2.a.b.1.11	✓	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4001.2.a.b.1.11	✓	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)

\(f(q)\)	\(=\)	\(q-2.64594 q^{2} -1.99415 q^{3} +5.00101 q^{4} -3.20075 q^{5} +5.27640 q^{6} +3.40947 q^{7} -7.94051 q^{8} +0.976617 q^{9} +O(q^{10})\)	\(q-2.64594 q^{2} -1.99415 q^{3} +5.00101 q^{4} -3.20075 q^{5} +5.27640 q^{6} +3.40947 q^{7} -7.94051 q^{8} +0.976617 q^{9} +8.46900 q^{10} +4.31844 q^{11} -9.97275 q^{12} -1.86918 q^{13} -9.02125 q^{14} +6.38276 q^{15} +11.0081 q^{16} -2.01826 q^{17} -2.58407 q^{18} +5.36675 q^{19} -16.0070 q^{20} -6.79897 q^{21} -11.4263 q^{22} +0.806760 q^{23} +15.8345 q^{24} +5.24480 q^{25} +4.94574 q^{26} +4.03492 q^{27} +17.0508 q^{28} -1.06073 q^{29} -16.8884 q^{30} +2.13299 q^{31} -13.2458 q^{32} -8.61160 q^{33} +5.34020 q^{34} -10.9128 q^{35} +4.88407 q^{36} +0.385677 q^{37} -14.2001 q^{38} +3.72741 q^{39} +25.4156 q^{40} +11.8883 q^{41} +17.9897 q^{42} +3.23663 q^{43} +21.5966 q^{44} -3.12591 q^{45} -2.13464 q^{46} +3.16840 q^{47} -21.9518 q^{48} +4.62446 q^{49} -13.8774 q^{50} +4.02471 q^{51} -9.34779 q^{52} +5.24253 q^{53} -10.6762 q^{54} -13.8222 q^{55} -27.0729 q^{56} -10.7021 q^{57} +2.80663 q^{58} +3.68316 q^{59} +31.9203 q^{60} +5.89671 q^{61} -5.64376 q^{62} +3.32974 q^{63} +13.0314 q^{64} +5.98278 q^{65} +22.7858 q^{66} -3.76625 q^{67} -10.0933 q^{68} -1.60880 q^{69} +28.8748 q^{70} -6.14898 q^{71} -7.75483 q^{72} +12.9440 q^{73} -1.02048 q^{74} -10.4589 q^{75} +26.8392 q^{76} +14.7236 q^{77} -9.86253 q^{78} +9.83252 q^{79} -35.2342 q^{80} -10.9761 q^{81} -31.4559 q^{82} -16.4947 q^{83} -34.0017 q^{84} +6.45995 q^{85} -8.56393 q^{86} +2.11525 q^{87} -34.2906 q^{88} +3.74435 q^{89} +8.27097 q^{90} -6.37290 q^{91} +4.03462 q^{92} -4.25349 q^{93} -8.38341 q^{94} -17.1776 q^{95} +26.4141 q^{96} +9.59660 q^{97} -12.2360 q^{98} +4.21746 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9}+O(q^{10}) \) 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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