LMFDB - Embedded newform 4001.2.a.b.1.15

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			1.15
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)

$f(q)$	$=$	$q-2.55462 q^{2} +2.40673 q^{3} +4.52611 q^{4} +3.51168 q^{5} -6.14829 q^{6} +3.52515 q^{7} -6.45325 q^{8} +2.79234 q^{9} +O(q^{10})$	\(q-2.55462 q^{2} +2.40673 q^{3} +4.52611 q^{4} +3.51168 q^{5} -6.14829 q^{6} +3.52515 q^{7} -6.45325 q^{8} +2.79234 q^{9} -8.97103 q^{10} -5.09895 q^{11} +10.8931 q^{12} -0.353446 q^{13} -9.00544 q^{14} +8.45166 q^{15} +7.43343 q^{16} +1.22514 q^{17} -7.13338 q^{18} +0.445154 q^{19} +15.8942 q^{20} +8.48408 q^{21} +13.0259 q^{22} +9.35822 q^{23} -15.5312 q^{24} +7.33191 q^{25} +0.902921 q^{26} -0.499785 q^{27} +15.9552 q^{28} -6.41904 q^{29} -21.5908 q^{30} +4.59805 q^{31} -6.08311 q^{32} -12.2718 q^{33} -3.12979 q^{34} +12.3792 q^{35} +12.6384 q^{36} -0.0828449 q^{37} -1.13720 q^{38} -0.850647 q^{39} -22.6618 q^{40} +4.27416 q^{41} -21.6736 q^{42} -9.28723 q^{43} -23.0784 q^{44} +9.80581 q^{45} -23.9067 q^{46} +2.53171 q^{47} +17.8902 q^{48} +5.42670 q^{49} -18.7303 q^{50} +2.94859 q^{51} -1.59973 q^{52} -1.29833 q^{53} +1.27676 q^{54} -17.9059 q^{55} -22.7487 q^{56} +1.07136 q^{57} +16.3982 q^{58} -7.77128 q^{59} +38.2531 q^{60} +7.07624 q^{61} -11.7463 q^{62} +9.84342 q^{63} +0.673206 q^{64} -1.24119 q^{65} +31.3498 q^{66} +15.5801 q^{67} +5.54514 q^{68} +22.5227 q^{69} -31.6243 q^{70} +6.33364 q^{71} -18.0197 q^{72} +12.7305 q^{73} +0.211638 q^{74} +17.6459 q^{75} +2.01482 q^{76} -17.9746 q^{77} +2.17308 q^{78} -0.799467 q^{79} +26.1038 q^{80} -9.57986 q^{81} -10.9189 q^{82} +2.66341 q^{83} +38.3999 q^{84} +4.30232 q^{85} +23.7254 q^{86} -15.4489 q^{87} +32.9048 q^{88} -12.6340 q^{89} -25.0502 q^{90} -1.24595 q^{91} +42.3563 q^{92} +11.0663 q^{93} -6.46758 q^{94} +1.56324 q^{95} -14.6404 q^{96} +7.86963 q^{97} -13.8632 q^{98} -14.2380 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.55462	−1.80639	−0.903196	−	0.429228i	$-0.858786\pi$
$2$	−2.55462	−1.80639	−0.903196	+	0.429228i	$0.858786\pi$
$3$	2.40673	1.38952	0.694762	−	0.719239i	$-0.255510\pi$
$3$	2.40673	1.38952	0.694762	+	0.719239i	$0.255510\pi$
$4$	4.52611	2.26305
$5$	3.51168	1.57047	0.785236	−	0.619196i	$-0.212542\pi$
$5$	3.51168	1.57047	0.785236	+	0.619196i	$0.212542\pi$
$6$	−6.14829	−2.51003
$7$	3.52515	1.33238	0.666191	−	0.745781i	$-0.267923\pi$
$7$	3.52515	1.33238	0.666191	+	0.745781i	$0.267923\pi$
$8$	−6.45325	−2.28157
$9$	2.79234	0.930779
$10$	−8.97103	−2.83689
$11$	−5.09895	−1.53739	−0.768696	−	0.639615i	$-0.779094\pi$
$11$	−5.09895	−1.53739	−0.768696	+	0.639615i	$0.779094\pi$
$12$	10.8931	3.14457
$13$	−0.353446	−0.0980281	−0.0490141	−	0.998798i	$-0.515608\pi$
$13$	−0.353446	−0.0980281	−0.0490141	+	0.998798i	$0.515608\pi$
$14$	−9.00544	−2.40681
$15$	8.45166	2.18221
$16$	7.43343	1.85836
$17$	1.22514	0.297141	0.148571	−	0.988902i	$-0.452533\pi$
$17$	1.22514	0.297141	0.148571	+	0.988902i	$0.452533\pi$
$18$	−7.13338	−1.68135
$19$	0.445154	0.102125	0.0510627	−	0.998695i	$-0.483739\pi$
$19$	0.445154	0.102125	0.0510627	+	0.998695i	$0.483739\pi$
$20$	15.8942	3.55406
$21$	8.48408	1.85138
$22$	13.0259	2.77713
$23$	9.35822	1.95132	0.975662	−	0.219280i	$-0.0703710\pi$
$23$	9.35822	1.95132	0.975662	+	0.219280i	$0.0703710\pi$
$24$	−15.5312	−3.17030
$25$	7.33191	1.46638
$26$	0.902921	0.177077
$27$	−0.499785	−0.0961838
$28$	15.9552	3.01525
$29$	−6.41904	−1.19199	−0.595993	−	0.802990i	$-0.703241\pi$
$29$	−6.41904	−1.19199	−0.595993	+	0.802990i	$0.703241\pi$
$30$	−21.5908	−3.94193
$31$	4.59805	0.825834	0.412917	−	0.910769i	$-0.364510\pi$
$31$	4.59805	0.825834	0.412917	+	0.910769i	$0.364510\pi$
$32$	−6.08311	−1.07535
$33$	−12.2718	−2.13624
$34$	−3.12979	−0.536754
$35$	12.3792	2.09247
$36$	12.6384	2.10640
$37$	−0.0828449	−0.0136196	−0.00680981	−	0.999977i	$-0.502168\pi$
$37$	−0.0828449	−0.0136196	−0.00680981	+	0.999977i	$0.502168\pi$
$38$	−1.13720	−0.184478
$39$	−0.850647	−0.136213
$40$	−22.6618	−3.58314
$41$	4.27416	0.667512	0.333756	−	0.942660i	$-0.391684\pi$
$41$	4.27416	0.667512	0.333756	+	0.942660i	$0.391684\pi$
$42$	−21.6736	−3.34432
$43$	−9.28723	−1.41629	−0.708144	−	0.706068i	$-0.750467\pi$
$43$	−9.28723	−1.41629	−0.708144	+	0.706068i	$0.750467\pi$
$44$	−23.0784	−3.47920
$45$	9.80581	1.46176
$46$	−23.9067	−3.52486
$47$	2.53171	0.369288	0.184644	−	0.982805i	$-0.440887\pi$
$47$	2.53171	0.369288	0.184644	+	0.982805i	$0.440887\pi$
$48$	17.8902	2.58223
$49$	5.42670	0.775243
$50$	−18.7303	−2.64886
$51$	2.94859	0.412885
$52$	−1.59973	−0.221843
$53$	−1.29833	−0.178339	−0.0891694	−	0.996016i	$-0.528421\pi$
$53$	−1.29833	−0.178339	−0.0891694	+	0.996016i	$0.528421\pi$
$54$	1.27676	0.173746
$55$	−17.9059	−2.41443
$56$	−22.7487	−3.03992
$57$	1.07136	0.141906
$58$	16.3982	2.15319
$59$	−7.77128	−1.01173	−0.505867	−	0.862611i	$-0.668828\pi$
$59$	−7.77128	−1.01173	−0.505867	+	0.862611i	$0.668828\pi$
$60$	38.2531	4.93846
$61$	7.07624	0.906020	0.453010	−	0.891505i	$-0.350350\pi$
$61$	7.07624	0.906020	0.453010	+	0.891505i	$0.350350\pi$
$62$	−11.7463	−1.49178
$63$	9.84342	1.24015
$64$	0.673206	0.0841507
$65$	−1.24119	−0.153950
$66$	31.3498	3.85889
$67$	15.5801	1.90341	0.951704	−	0.307017i	$-0.0993310\pi$
$67$	15.5801	1.90341	0.951704	+	0.307017i	$0.0993310\pi$
$68$	5.54514	0.672447
$69$	22.5227	2.71141
$70$	−31.6243	−3.77982
$71$	6.33364	0.751665	0.375832	−	0.926688i	$-0.377357\pi$
$71$	6.33364	0.751665	0.375832	+	0.926688i	$0.377357\pi$
$72$	−18.0197	−2.12364
$73$	12.7305	1.49000	0.744999	−	0.667066i	$-0.232450\pi$
$73$	12.7305	1.49000	0.744999	+	0.667066i	$0.232450\pi$
$74$	0.211638	0.0246024
$75$	17.6459	2.03758
$76$	2.01482	0.231115
$77$	−17.9746	−2.04839
$78$	2.17308	0.246053
$79$	−0.799467	−0.0899471	−0.0449736	−	0.998988i	$-0.514320\pi$
$79$	−0.799467	−0.0899471	−0.0449736	+	0.998988i	$0.514320\pi$
$80$	26.1038	2.91850
$81$	−9.57986	−1.06443
$82$	−10.9189	−1.20579
$83$	2.66341	0.292347	0.146174	−	0.989259i	$-0.453304\pi$
$83$	2.66341	0.292347	0.146174	+	0.989259i	$0.453304\pi$
$84$	38.3999	4.18977
$85$	4.30232	0.466652
$86$	23.7254	2.55837
$87$	−15.4489	−1.65629
$88$	32.9048	3.50767
$89$	−12.6340	−1.33920	−0.669599	−	0.742723i	$-0.733534\pi$
$89$	−12.6340	−1.33920	−0.669599	+	0.742723i	$0.733534\pi$
$90$	−25.0502	−2.64052
$91$	−1.24595	−0.130611
$92$	42.3563	4.41595
$93$	11.0663	1.14752
$94$	−6.46758	−0.667080
$95$	1.56324	0.160385
$96$	−14.6404	−1.49423
$97$	7.86963	0.799040	0.399520	−	0.916725i	$-0.369177\pi$
$97$	7.86963	0.799040	0.399520	+	0.916725i	$0.369177\pi$
$98$	−13.8632	−1.40039
$99$	−14.2380	−1.43097
$100$	33.1850	3.31850
$101$	−11.6404	−1.15827	−0.579133	−	0.815233i	$-0.696609\pi$
$101$	−11.6404	−1.15827	−0.579133	+	0.815233i	$0.696609\pi$
$102$	−7.53254	−0.745833
$103$	15.0025	1.47824	0.739119	−	0.673575i	$-0.235242\pi$
$103$	15.0025	1.47824	0.739119	+	0.673575i	$0.235242\pi$
$104$	2.28087	0.223658
$105$	29.7934	2.90754
$106$	3.31674	0.322150
$107$	−9.94886	−0.961792	−0.480896	−	0.876778i	$-0.659689\pi$
$107$	−9.94886	−0.961792	−0.480896	+	0.876778i	$0.659689\pi$
$108$	−2.26208	−0.217669
$109$	11.2873	1.08113	0.540563	−	0.841304i	$-0.318211\pi$
$109$	11.2873	1.08113	0.540563	+	0.841304i	$0.318211\pi$
$110$	45.7428	4.36141
$111$	−0.199385	−0.0189248
$112$	26.2040	2.47604
$113$	14.6614	1.37923	0.689615	−	0.724176i	$-0.257780\pi$
$113$	14.6614	1.37923	0.689615	+	0.724176i	$0.257780\pi$
$114$	−2.73693	−0.256337
$115$	32.8631	3.06450
$116$	−29.0533	−2.69753
$117$	−0.986939	−0.0912426
$118$	19.8527	1.82759
$119$	4.31882	0.395906
$120$	−54.5407	−4.97886
$121$	14.9993	1.36357
$122$	−18.0771	−1.63663
$123$	10.2867	0.927524
$124$	20.8113	1.86891
$125$	8.18894	0.732441
$126$	−25.1462	−2.24021
$127$	0.785559	0.0697070	0.0348535	−	0.999392i	$-0.488904\pi$
$127$	0.785559	0.0697070	0.0348535	+	0.999392i	$0.488904\pi$
$128$	10.4464	0.923343
$129$	−22.3518	−1.96797
$130$	3.17077	0.278095
$131$	−8.11721	−0.709204	−0.354602	−	0.935017i	$-0.615384\pi$
$131$	−8.11721	−0.709204	−0.354602	+	0.935017i	$0.615384\pi$
$132$	−55.5434	−4.83443
$133$	1.56924	0.136070
$134$	−39.8012	−3.43830
$135$	−1.75509	−0.151054
$136$	−7.90617	−0.677949
$137$	5.38620	0.460174	0.230087	−	0.973170i	$-0.426099\pi$
$137$	5.38620	0.460174	0.230087	+	0.973170i	$0.426099\pi$
$138$	−57.5370	−4.89788
$139$	−5.75940	−0.488506	−0.244253	−	0.969712i	$-0.578543\pi$
$139$	−5.75940	−0.488506	−0.244253	+	0.969712i	$0.578543\pi$
$140$	56.0297	4.73537
$141$	6.09314	0.513135
$142$	−16.1801	−1.35780
$143$	1.80220	0.150708
$144$	20.7566	1.72972
$145$	−22.5416	−1.87198
$146$	−32.5218	−2.69152
$147$	13.0606	1.07722
$148$	−0.374965	−0.0308219
$149$	−16.8085	−1.37701	−0.688503	−	0.725234i	$-0.741732\pi$
$149$	−16.8085	−1.37701	−0.688503	+	0.725234i	$0.741732\pi$
$150$	−45.0787	−3.68066
$151$	−2.73254	−0.222371	−0.111186	−	0.993800i	$-0.535465\pi$
$151$	−2.73254	−0.222371	−0.111186	+	0.993800i	$0.535465\pi$
$152$	−2.87269	−0.233006
$153$	3.42102	0.276573
$154$	45.9183	3.70020
$155$	16.1469	1.29695
$156$	−3.85012	−0.308256
$157$	6.77702	0.540865	0.270433	−	0.962739i	$-0.412833\pi$
$157$	6.77702	0.540865	0.270433	+	0.962739i	$0.412833\pi$
$158$	2.04234	0.162480
$159$	−3.12472	−0.247806
$160$	−21.3620	−1.68881
$161$	32.9892	2.59991
$162$	24.4730	1.92278
$163$	−15.2624	−1.19544	−0.597720	−	0.801705i	$-0.703927\pi$
$163$	−15.2624	−1.19544	−0.597720	+	0.801705i	$0.703927\pi$
$164$	19.3453	1.51061
$165$	−43.0946	−3.35491
$166$	−6.80402	−0.528094
$167$	13.2940	1.02872	0.514360	−	0.857574i	$-0.328029\pi$
$167$	13.2940	1.02872	0.514360	+	0.857574i	$0.328029\pi$
$168$	−54.7499	−4.22405
$169$	−12.8751	−0.990390
$170$	−10.9908	−0.842957
$171$	1.24302	0.0950562
$172$	−42.0350	−3.20514
$173$	5.89000	0.447808	0.223904	−	0.974611i	$-0.428120\pi$
$173$	5.89000	0.447808	0.223904	+	0.974611i	$0.428120\pi$
$174$	39.4661	2.99192
$175$	25.8461	1.95378
$176$	−37.9027	−2.85702
$177$	−18.7034	−1.40583
$178$	32.2750	2.41912
$179$	13.4178	1.00290	0.501448	−	0.865188i	$-0.332801\pi$
$179$	13.4178	1.00290	0.501448	+	0.865188i	$0.332801\pi$
$180$	44.3821	3.30805
$181$	12.2281	0.908908	0.454454	−	0.890770i	$-0.349834\pi$
$181$	12.2281	0.908908	0.454454	+	0.890770i	$0.349834\pi$
$182$	3.18293	0.235935
$183$	17.0306	1.25894
$184$	−60.3910	−4.45208
$185$	−0.290925	−0.0213892
$186$	−28.2701	−2.07287
$187$	−6.24695	−0.456822
$188$	11.4588	0.835719
$189$	−1.76182	−0.128154
$190$	−3.99349	−0.289718
$191$	−25.3620	−1.83513	−0.917565	−	0.397585i	$-0.869848\pi$
$191$	−25.3620	−1.83513	−0.917565	+	0.397585i	$0.869848\pi$
$192$	1.62022	0.116930
$193$	−15.3996	−1.10849	−0.554244	−	0.832354i	$-0.686993\pi$
$193$	−15.3996	−1.10849	−0.554244	+	0.832354i	$0.686993\pi$
$194$	−20.1039	−1.44338
$195$	−2.98720	−0.213918
$196$	24.5618	1.75442
$197$	21.6149	1.54000	0.769998	−	0.638046i	$-0.220257\pi$
$197$	21.6149	1.54000	0.769998	+	0.638046i	$0.220257\pi$
$198$	36.3727	2.58490
$199$	0.935357	0.0663057	0.0331529	−	0.999450i	$-0.489445\pi$
$199$	0.935357	0.0663057	0.0331529	+	0.999450i	$0.489445\pi$
$200$	−47.3147	−3.34565
$201$	37.4970	2.64483
$202$	29.7369	2.09228
$203$	−22.6281	−1.58818
$204$	13.3456	0.934381
$205$	15.0095	1.04831
$206$	−38.3257	−2.67028
$207$	26.1313	1.81625
$208$	−2.62731	−0.182171
$209$	−2.26982	−0.157007
$210$	−76.1110	−5.25216
$211$	19.6612	1.35353	0.676765	−	0.736199i	$-0.263381\pi$
$211$	19.6612	1.35353	0.676765	+	0.736199i	$0.263381\pi$
$212$	−5.87636	−0.403590
$213$	15.2433	1.04446
$214$	25.4156	1.73737
$215$	−32.6138	−2.22424
$216$	3.22524	0.219450
$217$	16.2088	1.10033
$218$	−28.8348	−1.95294
$219$	30.6390	2.07039
$220$	−81.0440	−5.46398
$221$	−0.433022	−0.0291282
$222$	0.509354	0.0341856
$223$	−10.0202	−0.671004	−0.335502	−	0.942040i	$-0.608906\pi$
$223$	−10.0202	−0.671004	−0.335502	+	0.942040i	$0.608906\pi$
$224$	−21.4439	−1.43278
$225$	20.4732	1.36488
$226$	−37.4544	−2.49143
$227$	−6.75105	−0.448083	−0.224041	−	0.974580i	$-0.571925\pi$
$227$	−6.75105	−0.448083	−0.224041	+	0.974580i	$0.571925\pi$
$228$	4.84911	0.321140
$229$	14.7685	0.975932	0.487966	−	0.872863i	$-0.337739\pi$
$229$	14.7685	0.975932	0.487966	+	0.872863i	$0.337739\pi$
$230$	−83.9529	−5.53569
$231$	−43.2599	−2.84629
$232$	41.4237	2.71960
$233$	9.02909	0.591515	0.295758	−	0.955263i	$-0.404428\pi$
$233$	9.02909	0.591515	0.295758	+	0.955263i	$0.404428\pi$
$234$	2.52126	0.164820
$235$	8.89057	0.579957
$236$	−35.1737	−2.28961
$237$	−1.92410	−0.124984
$238$	−11.0330	−0.715161
$239$	−7.53759	−0.487566	−0.243783	−	0.969830i	$-0.578388\pi$
$239$	−7.53759	−0.487566	−0.243783	+	0.969830i	$0.578388\pi$
$240$	62.8248	4.05533
$241$	−0.590570	−0.0380419	−0.0190210	−	0.999819i	$-0.506055\pi$
$241$	−0.590570	−0.0380419	−0.0190210	+	0.999819i	$0.506055\pi$
$242$	−38.3176	−2.46315
$243$	−21.5568	−1.38287
$244$	32.0278	2.05037
$245$	19.0569	1.21750
$246$	−26.2788	−1.67547
$247$	−0.157338	−0.0100112
$248$	−29.6724	−1.88420
$249$	6.41011	0.406224
$250$	−20.9197	−1.32308
$251$	5.33818	0.336943	0.168471	−	0.985707i	$-0.446117\pi$
$251$	5.33818	0.336943	0.168471	+	0.985707i	$0.446117\pi$
$252$	44.5524	2.80654
$253$	−47.7171	−2.99995
$254$	−2.00681	−0.125918
$255$	10.3545	0.648425
$256$	−28.0331	−1.75207
$257$	14.8048	0.923496	0.461748	−	0.887011i	$-0.347222\pi$
$257$	14.8048	0.923496	0.461748	+	0.887011i	$0.347222\pi$
$258$	57.1005	3.55492
$259$	−0.292041	−0.0181465
$260$	−5.61775	−0.348398
$261$	−17.9241	−1.10948
$262$	20.7364	1.28110
$263$	−9.17985	−0.566054	−0.283027	−	0.959112i	$-0.591339\pi$
$263$	−9.17985	−0.566054	−0.283027	+	0.959112i	$0.591339\pi$
$264$	79.1929	4.87399
$265$	−4.55931	−0.280076
$266$	−4.00881	−0.245796
$267$	−30.4065	−1.86085
$268$	70.5170	4.30751
$269$	−21.5102	−1.31150	−0.655751	−	0.754977i	$-0.727648\pi$
$269$	−21.5102	−1.31150	−0.655751	+	0.754977i	$0.727648\pi$
$270$	4.48359	0.272863
$271$	−30.7485	−1.86784	−0.933920	−	0.357481i	$-0.883636\pi$
$271$	−30.7485	−1.86784	−0.933920	+	0.357481i	$0.883636\pi$
$272$	9.10703	0.552195
$273$	−2.99866	−0.181487
$274$	−13.7597	−0.831255
$275$	−37.3851	−2.25440
$276$	101.940	6.13607
$277$	−0.316138	−0.0189949	−0.00949745	−	0.999955i	$-0.503023\pi$
$277$	−0.316138	−0.0189949	−0.00949745	+	0.999955i	$0.503023\pi$
$278$	14.7131	0.882434
$279$	12.8393	0.768669
$280$	−79.8862	−4.77412
$281$	−24.1824	−1.44260	−0.721302	−	0.692621i	$-0.756456\pi$
$281$	−24.1824	−1.44260	−0.721302	+	0.692621i	$0.756456\pi$
$282$	−15.5657	−0.926924
$283$	14.5123	0.862666	0.431333	−	0.902193i	$-0.358043\pi$
$283$	14.5123	0.862666	0.431333	+	0.902193i	$0.358043\pi$
$284$	28.6667	1.70106
$285$	3.76229	0.222859
$286$	−4.60395	−0.272237
$287$	15.0671	0.889381
$288$	−16.9861	−1.00092
$289$	−15.4990	−0.911707
$290$	57.5854	3.38153
$291$	18.9401	1.11029
$292$	57.6198	3.37194
$293$	−12.8933	−0.753232	−0.376616	−	0.926369i	$-0.622912\pi$
$293$	−12.8933	−0.753232	−0.376616	+	0.926369i	$0.622912\pi$
$294$	−33.3649	−1.94588
$295$	−27.2903	−1.58890
$296$	0.534619	0.0310741
$297$	2.54838	0.147872
$298$	42.9394	2.48741
$299$	−3.30762	−0.191285
$300$	79.8673	4.61114
$301$	−32.7389	−1.88704
$302$	6.98062	0.401690
$303$	−28.0153	−1.60944
$304$	3.30902	0.189785
$305$	24.8495	1.42288
$306$	−8.73942	−0.499599
$307$	−26.2910	−1.50050	−0.750252	−	0.661151i	$-0.770068\pi$
$307$	−26.2910	−1.50050	−0.750252	+	0.661151i	$0.770068\pi$
$308$	−81.3549	−4.63562
$309$	36.1069	2.05405
$310$	−41.2492	−2.34280
$311$	−35.0596	−1.98805	−0.994024	−	0.109159i	$-0.965184\pi$
$311$	−35.0596	−1.98805	−0.994024	+	0.109159i	$0.965184\pi$
$312$	5.48944	0.310778
$313$	2.41352	0.136420	0.0682102	−	0.997671i	$-0.478271\pi$
$313$	2.41352	0.136420	0.0682102	+	0.997671i	$0.478271\pi$
$314$	−17.3127	−0.977015
$315$	34.5670	1.94763
$316$	−3.61847	−0.203555
$317$	−17.0471	−0.957460	−0.478730	−	0.877962i	$-0.658903\pi$
$317$	−17.0471	−0.957460	−0.478730	+	0.877962i	$0.658903\pi$
$318$	7.98248	0.447635
$319$	32.7304	1.83255
$320$	2.36409	0.132156
$321$	−23.9442	−1.33643
$322$	−84.2749	−4.69646
$323$	0.545378	0.0303457
$324$	−43.3595	−2.40886
$325$	−2.59143	−0.143747
$326$	38.9896	2.15943
$327$	27.1654	1.50225
$328$	−27.5822	−1.52297
$329$	8.92468	0.492033
$330$	110.091	6.06029
$331$	−2.47954	−0.136288	−0.0681440	−	0.997675i	$-0.521708\pi$
$331$	−2.47954	−0.136288	−0.0681440	+	0.997675i	$0.521708\pi$
$332$	12.0549	0.661598
$333$	−0.231331	−0.0126769
$334$	−33.9612	−1.85827
$335$	54.7122	2.98925
$336$	63.0658	3.44052
$337$	22.4278	1.22172	0.610861	−	0.791738i	$-0.290823\pi$
$337$	22.4278	1.22172	0.610861	+	0.791738i	$0.290823\pi$
$338$	32.8910	1.78903
$339$	35.2860	1.91647
$340$	19.4728	1.05606
$341$	−23.4452	−1.26963
$342$	−3.17545	−0.171709
$343$	−5.54612	−0.299462
$344$	59.9328	3.23136
$345$	79.0925	4.25820
$346$	−15.0467	−0.808918
$347$	5.51687	0.296161	0.148081	−	0.988975i	$-0.452691\pi$
$347$	5.51687	0.296161	0.148081	+	0.988975i	$0.452691\pi$
$348$	−69.9233	−3.74828
$349$	−31.8235	−1.70347	−0.851737	−	0.523969i	$-0.824451\pi$
$349$	−31.8235	−1.70347	−0.851737	+	0.523969i	$0.824451\pi$
$350$	−66.0271	−3.52930
$351$	0.176647	0.00942872
$352$	31.0175	1.65324
$353$	8.64697	0.460232	0.230116	−	0.973163i	$-0.426089\pi$
$353$	8.64697	0.460232	0.230116	+	0.973163i	$0.426089\pi$
$354$	47.7801	2.53948
$355$	22.2417	1.18047
$356$	−57.1827	−3.03068
$357$	10.3942	0.550121
$358$	−34.2776	−1.81163
$359$	−1.07069	−0.0565090	−0.0282545	−	0.999601i	$-0.508995\pi$
$359$	−1.07069	−0.0565090	−0.0282545	+	0.999601i	$0.508995\pi$
$360$	−63.2794	−3.33511
$361$	−18.8018	−0.989570
$362$	−31.2382	−1.64185
$363$	36.0992	1.89472
$364$	−5.63930	−0.295580
$365$	44.7056	2.34000
$366$	−43.5068	−2.27414
$367$	14.4814	0.755923	0.377961	−	0.925821i	$-0.376625\pi$
$367$	14.4814	0.755923	0.377961	+	0.925821i	$0.376625\pi$
$368$	69.5637	3.62626
$369$	11.9349	0.621306
$370$	0.743204	0.0386374
$371$	−4.57680	−0.237616
$372$	50.0870	2.59689
$373$	−4.76462	−0.246703	−0.123351	−	0.992363i	$-0.539364\pi$
$373$	−4.76462	−0.246703	−0.123351	+	0.992363i	$0.539364\pi$
$374$	15.9586	0.825201
$375$	19.7086	1.01775
$376$	−16.3378	−0.842557
$377$	2.26878	0.116848
$378$	4.50079	0.231496
$379$	28.7046	1.47446	0.737229	−	0.675643i	$-0.236134\pi$
$379$	28.7046	1.47446	0.737229	+	0.675643i	$0.236134\pi$
$380$	7.07539	0.362960
$381$	1.89063	0.0968597
$382$	64.7904	3.31497
$383$	10.3699	0.529876	0.264938	−	0.964265i	$-0.414648\pi$
$383$	10.3699	0.529876	0.264938	+	0.964265i	$0.414648\pi$
$384$	25.1417	1.28301
$385$	−63.1210	−3.21694
$386$	39.3402	2.00236
$387$	−25.9331	−1.31825
$388$	35.6188	1.80827
$389$	26.5424	1.34575	0.672876	−	0.739755i	$-0.265059\pi$
$389$	26.5424	1.34575	0.672876	+	0.739755i	$0.265059\pi$
$390$	7.63118	0.386420
$391$	11.4652	0.579819
$392$	−35.0199	−1.76877
$393$	−19.5359	−0.985457
$394$	−55.2179	−2.78184
$395$	−2.80748	−0.141259
$396$	−64.4427	−3.23837
$397$	−18.8686	−0.946989	−0.473494	−	0.880797i	$-0.657008\pi$
$397$	−18.8686	−0.946989	−0.473494	+	0.880797i	$0.657008\pi$
$398$	−2.38949	−0.119774
$399$	3.77672	0.189073
$400$	54.5013	2.72506
$401$	−18.8086	−0.939258	−0.469629	−	0.882864i	$-0.655612\pi$
$401$	−18.8086	−0.939258	−0.469629	+	0.882864i	$0.655612\pi$
$402$	−95.7907	−4.77761
$403$	−1.62516	−0.0809550
$404$	−52.6858	−2.62122
$405$	−33.6414	−1.67166
$406$	57.8063	2.86888
$407$	0.422422	0.0209387
$408$	−19.0280	−0.942026
$409$	−16.2427	−0.803148	−0.401574	−	0.915826i	$-0.631537\pi$
$409$	−16.2427	−0.803148	−0.401574	+	0.915826i	$0.631537\pi$
$410$	−38.3436	−1.89366
$411$	12.9631	0.639424
$412$	67.9028	3.34533
$413$	−27.3950	−1.34802
$414$	−66.7557	−3.28086
$415$	9.35306	0.459124
$416$	2.15005	0.105415
$417$	−13.8613	−0.678791
$418$	5.79854	0.283616
$419$	−5.03656	−0.246052	−0.123026	−	0.992403i	$-0.539260\pi$
$419$	−5.03656	−0.246052	−0.123026	+	0.992403i	$0.539260\pi$
$420$	134.848	6.57992
$421$	−25.8441	−1.25956	−0.629782	−	0.776772i	$-0.716856\pi$
$421$	−25.8441	−1.25956	−0.629782	+	0.776772i	$0.716856\pi$
$422$	−50.2269	−2.44501
$423$	7.06940	0.343726
$424$	8.37843	0.406893
$425$	8.98266	0.435723
$426$	−38.9410	−1.88670
$427$	24.9448	1.20717
$428$	−45.0296	−2.17659
$429$	4.33741	0.209412
$430$	83.3160	4.01785
$431$	31.3134	1.50831	0.754157	−	0.656695i	$-0.228046\pi$
$431$	31.3134	1.50831	0.754157	+	0.656695i	$0.228046\pi$
$432$	−3.71512	−0.178744
$433$	−9.53010	−0.457988	−0.228994	−	0.973428i	$-0.573544\pi$
$433$	−9.53010	−0.457988	−0.228994	+	0.973428i	$0.573544\pi$
$434$	−41.4075	−1.98762
$435$	−54.2516	−2.60116
$436$	51.0874	2.44664
$437$	4.16585	0.199280
$438$	−78.2710	−3.73993
$439$	28.4026	1.35558	0.677791	−	0.735254i	$-0.262937\pi$
$439$	28.4026	1.35558	0.677791	+	0.735254i	$0.262937\pi$
$440$	115.551	5.50869
$441$	15.1532	0.721580
$442$	1.10621	0.0526170
$443$	−26.2582	−1.24756	−0.623782	−	0.781598i	$-0.714405\pi$
$443$	−26.2582	−1.24756	−0.623782	+	0.781598i	$0.714405\pi$
$444$	−0.902438	−0.0428278
$445$	−44.3665	−2.10317
$446$	25.5979	1.21210
$447$	−40.4535	−1.91338
$448$	2.37315	0.112121
$449$	−19.5626	−0.923215	−0.461608	−	0.887084i	$-0.652727\pi$
$449$	−19.5626	−0.923215	−0.461608	+	0.887084i	$0.652727\pi$
$450$	−52.3013	−2.46551
$451$	−21.7937	−1.02623
$452$	66.3591	3.12127
$453$	−6.57649	−0.308990
$454$	17.2464	0.809413
$455$	−4.37538	−0.205121
$456$	−6.91379	−0.323768
$457$	5.10525	0.238813	0.119407	−	0.992845i	$-0.461901\pi$
$457$	5.10525	0.238813	0.119407	+	0.992845i	$0.461901\pi$
$458$	−37.7280	−1.76292
$459$	−0.612310	−0.0285802
$460$	148.742	6.93513
$461$	−38.1937	−1.77886	−0.889430	−	0.457072i	$-0.848898\pi$
$461$	−38.1937	−1.77886	−0.889430	+	0.457072i	$0.848898\pi$
$462$	110.513	5.14152
$463$	−3.88947	−0.180759	−0.0903796	−	0.995907i	$-0.528808\pi$
$463$	−3.88947	−0.180759	−0.0903796	+	0.995907i	$0.528808\pi$
$464$	−47.7155	−2.21514
$465$	38.8612	1.80214
$466$	−23.0659	−1.06851
$467$	10.8376	0.501504	0.250752	−	0.968051i	$-0.419322\pi$
$467$	10.8376	0.501504	0.250752	+	0.968051i	$0.419322\pi$
$468$	−4.46699	−0.206487
$469$	54.9221	2.53607
$470$	−22.7121	−1.04763
$471$	16.3104	0.751546
$472$	50.1501	2.30834
$473$	47.3551	2.17739
$474$	4.91535	0.225770
$475$	3.26383	0.149755
$476$	19.5475	0.895956
$477$	−3.62537	−0.165994
$478$	19.2557	0.880735
$479$	6.20721	0.283615	0.141807	−	0.989894i	$-0.454709\pi$
$479$	6.20721	0.283615	0.141807	+	0.989894i	$0.454709\pi$
$480$	−51.4124	−2.34664
$481$	0.0292812	0.00133511
$482$	1.50868	0.0687187
$483$	79.3959	3.61264
$484$	67.8884	3.08584
$485$	27.6356	1.25487
$486$	55.0694	2.49800
$487$	−15.1882	−0.688244	−0.344122	−	0.938925i	$-0.611823\pi$
$487$	−15.1882	−0.688244	−0.344122	+	0.938925i	$0.611823\pi$
$488$	−45.6648	−2.06715
$489$	−36.7324	−1.66109
$490$	−48.6831	−2.19928
$491$	−5.62931	−0.254047	−0.127024	−	0.991900i	$-0.540542\pi$
$491$	−5.62931	−0.254047	−0.127024	+	0.991900i	$0.540542\pi$
$492$	46.5589	2.09904
$493$	−7.86425	−0.354188
$494$	0.401939	0.0180841
$495$	−49.9993	−2.24730
$496$	34.1793	1.53469
$497$	22.3270	1.00150
$498$	−16.3754	−0.733800
$499$	38.9865	1.74527	0.872637	−	0.488369i	$-0.162408\pi$
$499$	38.9865	1.74527	0.872637	+	0.488369i	$0.162408\pi$
$500$	37.0640	1.65755
$501$	31.9950	1.42943
$502$	−13.6370	−0.608651
$503$	−30.5385	−1.36165	−0.680823	−	0.732448i	$-0.738378\pi$
$503$	−30.5385	−1.36165	−0.680823	+	0.732448i	$0.738378\pi$
$504$	−63.5221	−2.82950
$505$	−40.8775	−1.81902
$506$	121.899	5.41908
$507$	−30.9868	−1.37617
$508$	3.55552	0.157751
$509$	−17.2270	−0.763572	−0.381786	−	0.924251i	$-0.624691\pi$
$509$	−17.2270	−0.763572	−0.381786	+	0.924251i	$0.624691\pi$
$510$	−26.4519	−1.17131
$511$	44.8771	1.98525
$512$	50.7212	2.24158
$513$	−0.222482	−0.00982280
$514$	−37.8206	−1.66820
$515$	52.6840	2.32153
$516$	−101.167	−4.45362
$517$	−12.9091	−0.567741
$518$	0.746055	0.0327798
$519$	14.1756	0.622241
$520$	8.00970	0.351249
$521$	34.3181	1.50350	0.751751	−	0.659447i	$-0.229209\pi$
$521$	34.3181	1.50350	0.751751	+	0.659447i	$0.229209\pi$
$522$	45.7894	2.00415
$523$	27.8798	1.21910	0.609549	−	0.792748i	$-0.291351\pi$
$523$	27.8798	1.21910	0.609549	+	0.792748i	$0.291351\pi$
$524$	−36.7394	−1.60497
$525$	62.2046	2.71483
$526$	23.4511	1.02252
$527$	5.63328	0.245389
$528$	−91.2214	−3.96990
$529$	64.5763	2.80766
$530$	11.6473	0.505928
$531$	−21.7001	−0.941702
$532$	7.10253	0.307934
$533$	−1.51068	−0.0654349
$534$	77.6772	3.36142
$535$	−34.9372	−1.51047
$536$	−100.542	−4.34276
$537$	32.2931	1.39355
$538$	54.9505	2.36909
$539$	−27.6705	−1.19185
$540$	−7.94372	−0.341843
$541$	−42.1269	−1.81118	−0.905588	−	0.424158i	$-0.860570\pi$
$541$	−42.1269	−1.81118	−0.905588	+	0.424158i	$0.860570\pi$
$542$	78.5510	3.37405
$543$	29.4297	1.26295
$544$	−7.45269	−0.319531
$545$	39.6373	1.69788
$546$	7.66045	0.327837
$547$	−40.3783	−1.72645	−0.863226	−	0.504817i	$-0.831560\pi$
$547$	−40.3783	−1.72645	−0.863226	+	0.504817i	$0.831560\pi$
$548$	24.3785	1.04140
$549$	19.7593	0.843305
$550$	95.5048	4.07234
$551$	−2.85746	−0.121732
$552$	−145.345	−6.18628
$553$	−2.81824	−0.119844
$554$	0.807614	0.0343122
$555$	−0.700177	−0.0297209
$556$	−26.0677	−1.10552
$557$	−14.4863	−0.613802	−0.306901	−	0.951741i	$-0.599292\pi$
$557$	−14.4863	−0.613802	−0.306901	+	0.951741i	$0.599292\pi$
$558$	−32.7996	−1.38852
$559$	3.28253	0.138836
$560$	92.0200	3.88856
$561$	−15.0347	−0.634766
$562$	61.7770	2.60591
$563$	−16.6356	−0.701108	−0.350554	−	0.936543i	$-0.614007\pi$
$563$	−16.6356	−0.701108	−0.350554	+	0.936543i	$0.614007\pi$
$564$	27.5782	1.16125
$565$	51.4862	2.16604
$566$	−37.0735	−1.55831
$567$	−33.7705	−1.41823
$568$	−40.8726	−1.71498
$569$	−30.2930	−1.26995	−0.634974	−	0.772534i	$-0.718989\pi$
$569$	−30.2930	−1.26995	−0.634974	+	0.772534i	$0.718989\pi$
$570$	−9.61125	−0.402571
$571$	31.3960	1.31388	0.656940	−	0.753943i	$-0.271850\pi$
$571$	31.3960	1.31388	0.656940	+	0.753943i	$0.271850\pi$
$572$	8.15695	0.341059
$573$	−61.0395	−2.54996
$574$	−38.4907	−1.60657
$575$	68.6137	2.86139
$576$	1.87982	0.0783258
$577$	36.1967	1.50689	0.753445	−	0.657511i	$-0.228391\pi$
$577$	36.1967	1.50689	0.753445	+	0.657511i	$0.228391\pi$
$578$	39.5942	1.64690
$579$	−37.0627	−1.54027
$580$	−102.026	−4.23639
$581$	9.38893	0.389519
$582$	−48.3847	−2.00561
$583$	6.62010	0.274177
$584$	−82.1534	−3.39953
$585$	−3.46582	−0.143294
$586$	32.9374	1.36063
$587$	−10.1363	−0.418370	−0.209185	−	0.977876i	$-0.567081\pi$
$587$	−10.1363	−0.418370	−0.209185	+	0.977876i	$0.567081\pi$
$588$	59.1136	2.43781
$589$	2.04684	0.0843386
$590$	69.7164	2.87018
$591$	52.0211	2.13986
$592$	−0.615822	−0.0253101
$593$	−29.0057	−1.19112	−0.595560	−	0.803311i	$-0.703070\pi$
$593$	−29.0057	−1.19112	−0.595560	+	0.803311i	$0.703070\pi$
$594$	−6.51016	−0.267115
$595$	15.1663	0.621759
$596$	−76.0770	−3.11624
$597$	2.25115	0.0921335
$598$	8.44973	0.345535
$599$	−6.04943	−0.247173	−0.123587	−	0.992334i	$-0.539440\pi$
$599$	−6.04943	−0.247173	−0.123587	+	0.992334i	$0.539440\pi$
$600$	−113.874	−4.64887
$601$	−13.7169	−0.559526	−0.279763	−	0.960069i	$-0.590256\pi$
$601$	−13.7169	−0.559526	−0.279763	+	0.960069i	$0.590256\pi$
$602$	83.6356	3.40873
$603$	43.5048	1.77165
$604$	−12.3678	−0.503238
$605$	52.6728	2.14145
$606$	71.5687	2.90728
$607$	−14.0943	−0.572069	−0.286035	−	0.958219i	$-0.592337\pi$
$607$	−14.0943	−0.572069	−0.286035	+	0.958219i	$0.592337\pi$
$608$	−2.70792	−0.109821
$609$	−54.4597	−2.20682
$610$	−63.4812	−2.57028
$611$	−0.894823	−0.0362007
$612$	15.4839	0.625899
$613$	−24.6314	−0.994854	−0.497427	−	0.867506i	$-0.665722\pi$
$613$	−24.6314	−0.994854	−0.497427	+	0.867506i	$0.665722\pi$
$614$	67.1636	2.71050
$615$	36.1238	1.45665
$616$	115.995	4.67355
$617$	10.3455	0.416492	0.208246	−	0.978076i	$-0.433224\pi$
$617$	10.3455	0.416492	0.208246	+	0.978076i	$0.433224\pi$
$618$	−92.2395	−3.71042
$619$	10.9672	0.440809	0.220404	−	0.975409i	$-0.429262\pi$
$619$	10.9672	0.440809	0.220404	+	0.975409i	$0.429262\pi$
$620$	73.0826	2.93507
$621$	−4.67710	−0.187686
$622$	89.5642	3.59120
$623$	−44.5367	−1.78432
$624$	−6.32322	−0.253132
$625$	−7.90260	−0.316104
$626$	−6.16564	−0.246429
$627$	−5.46284	−0.218165
$628$	30.6735	1.22401
$629$	−0.101497	−0.00404695
$630$	−88.3056	−3.51818
$631$	0.888044	0.0353525	0.0176762	−	0.999844i	$-0.494373\pi$
$631$	0.888044	0.0353525	0.0176762	+	0.999844i	$0.494373\pi$
$632$	5.15917	0.205221
$633$	47.3191	1.88076
$634$	43.5489	1.72955
$635$	2.75863	0.109473
$636$	−14.1428	−0.560799
$637$	−1.91804	−0.0759956
$638$	−83.6138	−3.31030
$639$	17.6857	0.699634
$640$	36.6846	1.45008
$641$	0.884608	0.0349399	0.0174700	−	0.999847i	$-0.494439\pi$
$641$	0.884608	0.0349399	0.0174700	+	0.999847i	$0.494439\pi$
$642$	61.1684	2.41413
$643$	22.1672	0.874188	0.437094	−	0.899416i	$-0.356008\pi$
$643$	22.1672	0.874188	0.437094	+	0.899416i	$0.356008\pi$
$644$	149.312	5.88373
$645$	−78.4925	−3.09064
$646$	−1.39324	−0.0548162
$647$	9.43374	0.370879	0.185439	−	0.982656i	$-0.440629\pi$
$647$	9.43374	0.370879	0.185439	+	0.982656i	$0.440629\pi$
$648$	61.8213	2.42857
$649$	39.6254	1.55543
$650$	6.62014	0.259663
$651$	39.0102	1.52893
$652$	−69.0791	−2.70535
$653$	17.8173	0.697245	0.348622	−	0.937263i	$-0.386650\pi$
$653$	17.8173	0.697245	0.348622	+	0.937263i	$0.386650\pi$
$654$	−69.3974	−2.71365
$655$	−28.5051	−1.11379
$656$	31.7717	1.24048
$657$	35.5480	1.38686
$658$	−22.7992	−0.888805
$659$	31.2464	1.21719	0.608593	−	0.793483i	$-0.291734\pi$
$659$	31.2464	1.21719	0.608593	+	0.793483i	$0.291734\pi$
$660$	−195.051	−7.59234
$661$	16.8636	0.655919	0.327960	−	0.944692i	$-0.393639\pi$
$661$	16.8636	0.655919	0.327960	+	0.944692i	$0.393639\pi$
$662$	6.33430	0.246190
$663$	−1.04217	−0.0404744
$664$	−17.1877	−0.667011
$665$	5.51066	0.213694
$666$	0.590964	0.0228994
$667$	−60.0708	−2.32595
$668$	60.1701	2.32805
$669$	−24.1160	−0.932377
$670$	−139.769	−5.39976
$671$	−36.0814	−1.39291
$672$	−51.6096	−1.99088
$673$	13.7763	0.531036	0.265518	−	0.964106i	$-0.414457\pi$
$673$	13.7763	0.531036	0.265518	+	0.964106i	$0.414457\pi$
$674$	−57.2947	−2.20691
$675$	−3.66438	−0.141042
$676$	−58.2740	−2.24131
$677$	25.7184	0.988438	0.494219	−	0.869338i	$-0.335454\pi$
$677$	25.7184	0.988438	0.494219	+	0.869338i	$0.335454\pi$
$678$	−90.1426	−3.46190
$679$	27.7416	1.06463
$680$	−27.7640	−1.06470
$681$	−16.2479	−0.622622
$682$	59.8938	2.29345
$683$	−49.8079	−1.90584	−0.952922	−	0.303214i	$-0.901940\pi$
$683$	−49.8079	−1.90584	−0.952922	+	0.303214i	$0.901940\pi$
$684$	5.62605	0.215117
$685$	18.9146	0.722691
$686$	14.1682	0.540946
$687$	35.5438	1.35608
$688$	−69.0359	−2.63197
$689$	0.458888	0.0174822
$690$	−202.052	−7.69198
$691$	9.33284	0.355038	0.177519	−	0.984117i	$-0.443193\pi$
$691$	9.33284	0.355038	0.177519	+	0.984117i	$0.443193\pi$
$692$	26.6588	1.01341
$693$	−50.1911	−1.90660
$694$	−14.0935	−0.534983
$695$	−20.2252	−0.767185
$696$	99.6956	3.77895
$697$	5.23647	0.198345
$698$	81.2972	3.07714
$699$	21.7306	0.821925
$700$	116.982	4.42151
$701$	−35.9991	−1.35967	−0.679834	−	0.733366i	$-0.737948\pi$
$701$	−35.9991	−1.35967	−0.679834	+	0.733366i	$0.737948\pi$
$702$	−0.451267	−0.0170320
$703$	−0.0368788	−0.00139091
$704$	−3.43264	−0.129373
$705$	21.3972	0.805865
$706$	−22.0898	−0.831359
$707$	−41.0343	−1.54325
$708$	−84.6534	−3.18147
$709$	−28.6493	−1.07595	−0.537973	−	0.842962i	$-0.680810\pi$
$709$	−28.6493	−1.07595	−0.537973	+	0.842962i	$0.680810\pi$
$710$	−56.8193	−2.13239
$711$	−2.23238	−0.0837209
$712$	81.5302	3.05547
$713$	43.0296	1.61147
$714$	−26.5534	−0.993734
$715$	6.32876	0.236682
$716$	60.7306	2.26961
$717$	−18.1409	−0.677485
$718$	2.73522	0.102077
$719$	−16.0244	−0.597608	−0.298804	−	0.954315i	$-0.596588\pi$
$719$	−16.0244	−0.597608	−0.298804	+	0.954315i	$0.596588\pi$
$720$	72.8907	2.71648
$721$	52.8860	1.96958
$722$	48.0316	1.78755
$723$	−1.42134	−0.0528602
$724$	55.3457	2.05691
$725$	−47.0639	−1.74791
$726$	−92.2199	−3.42260
$727$	−25.9717	−0.963237	−0.481618	−	0.876381i	$-0.659951\pi$
$727$	−25.9717	−0.963237	−0.481618	+	0.876381i	$0.659951\pi$
$728$	8.04043	0.297998
$729$	−23.1417	−0.857099
$730$	−114.206	−4.22696
$731$	−11.3782	−0.420838
$732$	77.0823	2.84904
$733$	−2.78609	−0.102906	−0.0514532	−	0.998675i	$-0.516385\pi$
$733$	−2.78609	−0.102906	−0.0514532	+	0.998675i	$0.516385\pi$
$734$	−36.9945	−1.36549
$735$	45.8647	1.69174
$736$	−56.9271	−2.09836
$737$	−79.4420	−2.92628
$738$	−30.4892	−1.12232
$739$	−30.7886	−1.13258	−0.566288	−	0.824208i	$-0.691621\pi$
$739$	−30.7886	−1.13258	−0.566288	+	0.824208i	$0.691621\pi$
$740$	−1.31676	−0.0484050
$741$	−0.378669	−0.0139108
$742$	11.6920	0.429227
$743$	−14.2263	−0.521911	−0.260955	−	0.965351i	$-0.584038\pi$
$743$	−14.2263	−0.521911	−0.260955	+	0.965351i	$0.584038\pi$
$744$	−71.4133	−2.61814
$745$	−59.0261	−2.16255
$746$	12.1718	0.445642
$747$	7.43715	0.272111
$748$	−28.2744	−1.03381
$749$	−35.0712	−1.28148
$750$	−50.3480	−1.83845
$751$	25.4622	0.929129	0.464564	−	0.885539i	$-0.346211\pi$
$751$	25.4622	0.929129	0.464564	+	0.885539i	$0.346211\pi$
$752$	18.8193	0.686270
$753$	12.8475	0.468190
$754$	−5.79588	−0.211074
$755$	−9.59582	−0.349228
$756$	−7.97419	−0.290018
$757$	−3.16487	−0.115029	−0.0575145	−	0.998345i	$-0.518318\pi$
$757$	−3.16487	−0.115029	−0.0575145	+	0.998345i	$0.518318\pi$
$758$	−73.3296	−2.66345
$759$	−114.842	−4.16850
$760$	−10.0880	−0.365930
$761$	32.0100	1.16036	0.580181	−	0.814488i	$-0.302982\pi$
$761$	32.0100	1.16036	0.580181	+	0.814488i	$0.302982\pi$
$762$	−4.82984	−0.174967
$763$	39.7894	1.44047
$764$	−114.791	−4.15300
$765$	12.0135	0.434350
$766$	−26.4912	−0.957164
$767$	2.74673	0.0991785
$768$	−67.4681	−2.43455
$769$	6.79258	0.244947	0.122473	−	0.992472i	$-0.460917\pi$
$769$	6.79258	0.244947	0.122473	+	0.992472i	$0.460917\pi$
$770$	161.250	5.81106
$771$	35.6310	1.28322
$772$	−69.7003	−2.50857
$773$	−33.1736	−1.19317	−0.596587	−	0.802549i	$-0.703477\pi$
$773$	−33.1736	−1.19317	−0.596587	+	0.802549i	$0.703477\pi$
$774$	66.2493	2.38128
$775$	33.7125	1.21099
$776$	−50.7847	−1.82307
$777$	−0.702863	−0.0252151
$778$	−67.8059	−2.43096
$779$	1.90266	0.0681699
$780$	−13.5204	−0.484108
$781$	−32.2949	−1.15560
$782$	−29.2892	−1.04738
$783$	3.20814	0.114650
$784$	40.3390	1.44068
$785$	23.7988	0.849414
$786$	49.9069	1.78012
$787$	−39.5558	−1.41001	−0.705006	−	0.709202i	$-0.749056\pi$
$787$	−39.5558	−1.41001	−0.705006	+	0.709202i	$0.749056\pi$
$788$	97.8313	3.48510
$789$	−22.0934	−0.786546
$790$	7.17205	0.255170
$791$	51.6837	1.83766
$792$	91.8814	3.26486
$793$	−2.50107	−0.0888155
$794$	48.2022	1.71063
$795$	−10.9730	−0.389173
$796$	4.23353	0.150053
$797$	−10.3530	−0.366722	−0.183361	−	0.983046i	$-0.558698\pi$
$797$	−10.3530	−0.366722	−0.183361	+	0.983046i	$0.558698\pi$
$798$	−9.64811	−0.341540
$799$	3.10172	0.109731
$800$	−44.6008	−1.57688
$801$	−35.2783	−1.24650
$802$	48.0490	1.69667
$803$	−64.9124	−2.29071
$804$	169.715	5.98540
$805$	115.847	4.08309
$806$	4.15167	0.146236
$807$	−51.7692	−1.82236
$808$	75.1186	2.64266
$809$	1.86785	0.0656700	0.0328350	−	0.999461i	$-0.489546\pi$
$809$	1.86785	0.0656700	0.0328350	+	0.999461i	$0.489546\pi$
$810$	85.9412	3.01967
$811$	51.6194	1.81260	0.906302	−	0.422632i	$-0.138894\pi$
$811$	51.6194	1.81260	0.906302	+	0.422632i	$0.138894\pi$
$812$	−102.417	−3.59414
$813$	−74.0034	−2.59541
$814$	−1.07913	−0.0378235
$815$	−53.5966	−1.87741
$816$	21.9181	0.767288
$817$	−4.13425	−0.144639
$818$	41.4939	1.45080
$819$	−3.47911	−0.121570
$820$	67.9346	2.37238
$821$	15.8072	0.551674	0.275837	−	0.961204i	$-0.411045\pi$
$821$	15.8072	0.551674	0.275837	+	0.961204i	$0.411045\pi$
$822$	−33.1159	−1.15505
$823$	−0.0293980	−0.00102475	−0.000512376	−	1.00000i	$-0.500163\pi$
$823$	−0.0293980	−0.00102475	−0.000512376		1.00000i	$0.500163\pi$
$824$	−96.8148	−3.37270
$825$	−89.9757	−3.13255
$826$	69.9838	2.43505
$827$	44.2492	1.53870	0.769349	−	0.638829i	$-0.220581\pi$
$827$	44.2492	1.53870	0.769349	+	0.638829i	$0.220581\pi$
$828$	118.273	4.11027
$829$	43.2558	1.50234	0.751168	−	0.660111i	$-0.229491\pi$
$829$	43.2558	1.50234	0.751168	+	0.660111i	$0.229491\pi$
$830$	−23.8936	−0.829357
$831$	−0.760858	−0.0263939
$832$	−0.237942	−0.00824914
$833$	6.64850	0.230357
$834$	35.4104	1.22616
$835$	46.6843	1.61558
$836$	−10.2734	−0.355314
$837$	−2.29804	−0.0794318
$838$	12.8665	0.444466
$839$	−7.67883	−0.265103	−0.132551	−	0.991176i	$-0.542317\pi$
$839$	−7.67883	−0.265103	−0.132551	+	0.991176i	$0.542317\pi$
$840$	−192.264	−6.63375
$841$	12.2041	0.420831
$842$	66.0219	2.27527
$843$	−58.2005	−2.00453
$844$	88.9885	3.06311
$845$	−45.2132	−1.55538
$846$	−18.0597	−0.620904
$847$	52.8748	1.81680
$848$	−9.65102	−0.331417
$849$	34.9271	1.19870
$850$	−22.9473	−0.787086
$851$	−0.775281	−0.0265763
$852$	68.9930	2.36366
$853$	−30.2289	−1.03502	−0.517508	−	0.855678i	$-0.673140\pi$
$853$	−30.2289	−1.03502	−0.517508	+	0.855678i	$0.673140\pi$
$854$	−63.7247	−2.18061
$855$	4.36509	0.149283
$856$	64.2025	2.19440
$857$	−3.54349	−0.121043	−0.0605216	−	0.998167i	$-0.519276\pi$
$857$	−3.54349	−0.121043	−0.0605216	+	0.998167i	$0.519276\pi$
$858$	−11.0804	−0.378280
$859$	20.8200	0.710370	0.355185	−	0.934796i	$-0.384418\pi$
$859$	20.8200	0.710370	0.355185	+	0.934796i	$0.384418\pi$
$860$	−147.613	−5.03358
$861$	36.2623	1.23582
$862$	−79.9940	−2.72461
$863$	−44.3342	−1.50915	−0.754576	−	0.656212i	$-0.772158\pi$
$863$	−44.3342	−1.50915	−0.754576	+	0.656212i	$0.772158\pi$
$864$	3.04025	0.103431
$865$	20.6838	0.703271
$866$	24.3458	0.827305
$867$	−37.3019	−1.26684
$868$	73.3629	2.49010
$869$	4.07644	0.138284
$870$	138.592	4.69872
$871$	−5.50670	−0.186588
$872$	−72.8397	−2.46666
$873$	21.9747	0.743730
$874$	−10.6422	−0.359977
$875$	28.8673	0.975892
$876$	138.675	4.68540
$877$	−4.57800	−0.154588	−0.0772940	−	0.997008i	$-0.524628\pi$
$877$	−4.57800	−0.154588	−0.0772940	+	0.997008i	$0.524628\pi$
$878$	−72.5580	−2.44871
$879$	−31.0306	−1.04664
$880$	−133.102	−4.48687
$881$	−19.7130	−0.664147	−0.332073	−	0.943254i	$-0.607748\pi$
$881$	−19.7130	−0.664147	−0.332073	+	0.943254i	$0.607748\pi$
$882$	−38.7107	−1.30346
$883$	−55.6168	−1.87165	−0.935827	−	0.352460i	$-0.885345\pi$
$883$	−55.6168	−1.87165	−0.935827	+	0.352460i	$0.885345\pi$
$884$	−1.95990	−0.0659187
$885$	−65.6803	−2.20782
$886$	67.0798	2.25359
$887$	48.2233	1.61918	0.809590	−	0.586995i	$-0.199689\pi$
$887$	48.2233	1.61918	0.809590	+	0.586995i	$0.199689\pi$
$888$	1.28668	0.0431783
$889$	2.76921	0.0928765
$890$	113.340	3.79916
$891$	48.8472	1.63644
$892$	−45.3526	−1.51852
$893$	1.12700	0.0377137
$894$	103.343	3.45632
$895$	47.1192	1.57502
$896$	36.8253	1.23025
$897$	−7.96054	−0.265795
$898$	49.9750	1.66769
$899$	−29.5151	−0.984383
$900$	92.6638	3.08879
$901$	−1.59064	−0.0529918
$902$	55.6748	1.85377
$903$	−78.7936	−2.62209
$904$	−94.6138	−3.14681
$905$	42.9413	1.42742
$906$	16.8005	0.558158
$907$	33.4445	1.11051	0.555253	−	0.831682i	$-0.312622\pi$
$907$	33.4445	1.11051	0.555253	+	0.831682i	$0.312622\pi$
$908$	−30.5560	−1.01404
$909$	−32.5040	−1.07809
$910$	11.1775	0.370529
$911$	48.7372	1.61474	0.807368	−	0.590048i	$-0.200891\pi$
$911$	48.7372	1.61474	0.807368	+	0.590048i	$0.200891\pi$
$912$	7.96391	0.263712
$913$	−13.5806	−0.449452
$914$	−13.0420	−0.431391
$915$	59.8060	1.97713
$916$	66.8439	2.20859
$917$	−28.6144	−0.944931
$918$	1.56422	0.0516270
$919$	−0.445218	−0.0146864	−0.00734319	−	0.999973i	$-0.502337\pi$
$919$	−0.445218	−0.0146864	−0.00734319	+	0.999973i	$0.502337\pi$
$920$	−212.074	−6.99187
$921$	−63.2752	−2.08499
$922$	97.5707	3.21332
$923$	−2.23860	−0.0736843
$924$	−195.799	−6.44131
$925$	−0.607412	−0.0199716
$926$	9.93614	0.326522
$927$	41.8920	1.37591
$928$	39.0477	1.28180
$929$	−22.0155	−0.722307	−0.361153	−	0.932506i	$-0.617617\pi$
$929$	−22.0155	−0.722307	−0.361153	+	0.932506i	$0.617617\pi$
$930$	−99.2757	−3.25538
$931$	2.41572	0.0791720
$932$	40.8666	1.33863
$933$	−84.3790	−2.76244
$934$	−27.6860	−0.905913
$935$	−21.9373	−0.717427
$936$	6.36897	0.208176
$937$	14.3889	0.470064	0.235032	−	0.971988i	$-0.424480\pi$
$937$	14.3889	0.470064	0.235032	+	0.971988i	$0.424480\pi$
$938$	−140.305	−4.58113
$939$	5.80869	0.189559
$940$	40.2397	1.31247
$941$	21.1587	0.689754	0.344877	−	0.938648i	$-0.387921\pi$
$941$	21.1587	0.689754	0.344877	+	0.938648i	$0.387921\pi$
$942$	−41.6671	−1.35759
$943$	39.9985	1.30253
$944$	−57.7673	−1.88016
$945$	−6.18695	−0.201262
$946$	−120.975	−3.93322
$947$	−44.4077	−1.44306	−0.721529	−	0.692384i	$-0.756560\pi$
$947$	−44.4077	−1.44306	−0.721529	+	0.692384i	$0.756560\pi$
$948$	−8.70868	−0.282845
$949$	−4.49955	−0.146062
$950$	−8.33787	−0.270516
$951$	−41.0277	−1.33041
$952$	−27.8705	−0.903287
$953$	−9.16837	−0.296993	−0.148496	−	0.988913i	$-0.547443\pi$
$953$	−9.16837	−0.296993	−0.148496	+	0.988913i	$0.547443\pi$
$954$	9.26145	0.299851
$955$	−89.0633	−2.88202
$956$	−34.1159	−1.10339
$957$	78.7731	2.54637
$958$	−15.8571	−0.512319
$959$	18.9872	0.613128
$960$	5.68971	0.183635
$961$	−9.85794	−0.317998
$962$	−0.0748024	−0.00241173
$963$	−27.7806	−0.895217
$964$	−2.67298	−0.0860909
$965$	−54.0785	−1.74085
$966$	−202.827	−6.52584
$967$	0.604773	0.0194482	0.00972410	−	0.999953i	$-0.496905\pi$
$967$	0.604773	0.0194482	0.00972410	+	0.999953i	$0.496905\pi$
$968$	−96.7943	−3.11109
$969$	1.31258	0.0421661
$970$	−70.5987	−2.26679
$971$	−32.9034	−1.05592	−0.527960	−	0.849269i	$-0.677043\pi$
$971$	−32.9034	−1.05592	−0.527960	+	0.849269i	$0.677043\pi$
$972$	−97.5682	−3.12950
$973$	−20.3028	−0.650877
$974$	38.8002	1.24324
$975$	−6.23687	−0.199740
$976$	52.6008	1.68371
$977$	−26.9227	−0.861333	−0.430666	−	0.902511i	$-0.641721\pi$
$977$	−26.9227	−0.861333	−0.430666	+	0.902511i	$0.641721\pi$
$978$	93.8374	3.00059
$979$	64.4200	2.05887
$980$	86.2534	2.75526
$981$	31.5179	1.00629
$982$	14.3808	0.458909
$983$	−7.23485	−0.230756	−0.115378	−	0.993322i	$-0.536808\pi$
$983$	−7.23485	−0.230756	−0.115378	+	0.993322i	$0.536808\pi$
$984$	−66.3829	−2.11621
$985$	75.9046	2.41852
$986$	20.0902	0.639803
$987$	21.4793	0.683693
$988$	−0.712127	−0.0226558
$989$	−86.9119	−2.76364
$990$	127.729	4.05951
$991$	19.4088	0.616539	0.308270	−	0.951299i	$-0.400250\pi$
$991$	19.4088	0.616539	0.308270	+	0.951299i	$0.400250\pi$
$992$	−27.9704	−0.888062
$993$	−5.96759	−0.189376
$994$	−57.0372	−1.80911
$995$	3.28468	0.104131
$996$	29.0128	0.919307
$997$	−44.0654	−1.39557	−0.697783	−	0.716310i	$-0.745830\pi$
$997$	−44.0654	−1.39557	−0.697783	+	0.716310i	$0.745830\pi$
$998$	−99.5958	−3.15265
$999$	0.0414047	0.00130999

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4001.2.a.b.1.15	✓	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4001.2.a.b.1.15	✓	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)

\(f(q)\)	\(=\)	\(q-2.55462 q^{2} +2.40673 q^{3} +4.52611 q^{4} +3.51168 q^{5} -6.14829 q^{6} +3.52515 q^{7} -6.45325 q^{8} +2.79234 q^{9} +O(q^{10})\)	\(q-2.55462 q^{2} +2.40673 q^{3} +4.52611 q^{4} +3.51168 q^{5} -6.14829 q^{6} +3.52515 q^{7} -6.45325 q^{8} +2.79234 q^{9} -8.97103 q^{10} -5.09895 q^{11} +10.8931 q^{12} -0.353446 q^{13} -9.00544 q^{14} +8.45166 q^{15} +7.43343 q^{16} +1.22514 q^{17} -7.13338 q^{18} +0.445154 q^{19} +15.8942 q^{20} +8.48408 q^{21} +13.0259 q^{22} +9.35822 q^{23} -15.5312 q^{24} +7.33191 q^{25} +0.902921 q^{26} -0.499785 q^{27} +15.9552 q^{28} -6.41904 q^{29} -21.5908 q^{30} +4.59805 q^{31} -6.08311 q^{32} -12.2718 q^{33} -3.12979 q^{34} +12.3792 q^{35} +12.6384 q^{36} -0.0828449 q^{37} -1.13720 q^{38} -0.850647 q^{39} -22.6618 q^{40} +4.27416 q^{41} -21.6736 q^{42} -9.28723 q^{43} -23.0784 q^{44} +9.80581 q^{45} -23.9067 q^{46} +2.53171 q^{47} +17.8902 q^{48} +5.42670 q^{49} -18.7303 q^{50} +2.94859 q^{51} -1.59973 q^{52} -1.29833 q^{53} +1.27676 q^{54} -17.9059 q^{55} -22.7487 q^{56} +1.07136 q^{57} +16.3982 q^{58} -7.77128 q^{59} +38.2531 q^{60} +7.07624 q^{61} -11.7463 q^{62} +9.84342 q^{63} +0.673206 q^{64} -1.24119 q^{65} +31.3498 q^{66} +15.5801 q^{67} +5.54514 q^{68} +22.5227 q^{69} -31.6243 q^{70} +6.33364 q^{71} -18.0197 q^{72} +12.7305 q^{73} +0.211638 q^{74} +17.6459 q^{75} +2.01482 q^{76} -17.9746 q^{77} +2.17308 q^{78} -0.799467 q^{79} +26.1038 q^{80} -9.57986 q^{81} -10.9189 q^{82} +2.66341 q^{83} +38.3999 q^{84} +4.30232 q^{85} +23.7254 q^{86} -15.4489 q^{87} +32.9048 q^{88} -12.6340 q^{89} -25.0502 q^{90} -1.24595 q^{91} +42.3563 q^{92} +11.0663 q^{93} -6.46758 q^{94} +1.56324 q^{95} -14.6404 q^{96} +7.86963 q^{97} -13.8632 q^{98} -14.2380 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9}+O(q^{10}) \) 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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