LMFDB - Embedded newform 4001.2.a.b.1.14

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			1.14
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)

$f(q)$	$=$	$q-2.61059 q^{2} -0.259768 q^{3} +4.81518 q^{4} -4.09316 q^{5} +0.678147 q^{6} +2.08780 q^{7} -7.34928 q^{8} -2.93252 q^{9} +O(q^{10})$	\(q-2.61059 q^{2} -0.259768 q^{3} +4.81518 q^{4} -4.09316 q^{5} +0.678147 q^{6} +2.08780 q^{7} -7.34928 q^{8} -2.93252 q^{9} +10.6856 q^{10} -4.54556 q^{11} -1.25083 q^{12} -2.98042 q^{13} -5.45038 q^{14} +1.06327 q^{15} +9.55560 q^{16} +4.39920 q^{17} +7.65561 q^{18} -0.751344 q^{19} -19.7093 q^{20} -0.542342 q^{21} +11.8666 q^{22} -0.781648 q^{23} +1.90911 q^{24} +11.7540 q^{25} +7.78065 q^{26} +1.54108 q^{27} +10.0531 q^{28} -4.78053 q^{29} -2.77577 q^{30} -3.90479 q^{31} -10.2472 q^{32} +1.18079 q^{33} -11.4845 q^{34} -8.54569 q^{35} -14.1206 q^{36} -6.77693 q^{37} +1.96145 q^{38} +0.774216 q^{39} +30.0818 q^{40} -11.6528 q^{41} +1.41583 q^{42} +0.552335 q^{43} -21.8877 q^{44} +12.0033 q^{45} +2.04056 q^{46} -1.35892 q^{47} -2.48224 q^{48} -2.64111 q^{49} -30.6848 q^{50} -1.14277 q^{51} -14.3512 q^{52} -8.71995 q^{53} -4.02312 q^{54} +18.6057 q^{55} -15.3438 q^{56} +0.195175 q^{57} +12.4800 q^{58} -11.9100 q^{59} +5.11984 q^{60} -0.470997 q^{61} +10.1938 q^{62} -6.12251 q^{63} +7.64001 q^{64} +12.1993 q^{65} -3.08256 q^{66} -8.34431 q^{67} +21.1830 q^{68} +0.203047 q^{69} +22.3093 q^{70} +10.0343 q^{71} +21.5519 q^{72} +7.49575 q^{73} +17.6918 q^{74} -3.05331 q^{75} -3.61786 q^{76} -9.49020 q^{77} -2.02116 q^{78} -10.3980 q^{79} -39.1126 q^{80} +8.39724 q^{81} +30.4208 q^{82} -13.4273 q^{83} -2.61147 q^{84} -18.0067 q^{85} -1.44192 q^{86} +1.24183 q^{87} +33.4066 q^{88} +11.9262 q^{89} -31.3357 q^{90} -6.22250 q^{91} -3.76378 q^{92} +1.01434 q^{93} +3.54757 q^{94} +3.07538 q^{95} +2.66189 q^{96} -18.5687 q^{97} +6.89485 q^{98} +13.3299 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.61059	−1.84597	−0.922983	−	0.384841i	$-0.874256\pi$
$2$	−2.61059	−1.84597	−0.922983	+	0.384841i	$0.874256\pi$
$3$	−0.259768	−0.149977	−0.0749885	−	0.997184i	$-0.523892\pi$
$3$	−0.259768	−0.149977	−0.0749885	+	0.997184i	$0.523892\pi$
$4$	4.81518	2.40759
$5$	−4.09316	−1.83052	−0.915259	−	0.402865i	$-0.868014\pi$
$5$	−4.09316	−1.83052	−0.915259	+	0.402865i	$0.868014\pi$
$6$	0.678147	0.276852
$7$	2.08780	0.789113	0.394556	−	0.918872i	$-0.370898\pi$
$7$	2.08780	0.789113	0.394556	+	0.918872i	$0.370898\pi$
$8$	−7.34928	−2.59836
$9$	−2.93252	−0.977507
$10$	10.6856	3.37907
$11$	−4.54556	−1.37054	−0.685269	−	0.728290i	$-0.740315\pi$
$11$	−4.54556	−1.37054	−0.685269	+	0.728290i	$0.740315\pi$
$12$	−1.25083	−0.361083
$13$	−2.98042	−0.826619	−0.413309	−	0.910591i	$-0.635627\pi$
$13$	−2.98042	−0.826619	−0.413309	+	0.910591i	$0.635627\pi$
$14$	−5.45038	−1.45668
$15$	1.06327	0.274536
$16$	9.55560	2.38890
$17$	4.39920	1.06696	0.533482	−	0.845812i	$-0.320883\pi$
$17$	4.39920	1.06696	0.533482	+	0.845812i	$0.320883\pi$
$18$	7.65561	1.80444
$19$	−0.751344	−0.172370	−0.0861851	−	0.996279i	$-0.527468\pi$
$19$	−0.751344	−0.172370	−0.0861851	+	0.996279i	$0.527468\pi$
$20$	−19.7093	−4.40714
$21$	−0.542342	−0.118349
$22$	11.8666	2.52997
$23$	−0.781648	−0.162985	−0.0814925	−	0.996674i	$-0.525969\pi$
$23$	−0.781648	−0.162985	−0.0814925	+	0.996674i	$0.525969\pi$
$24$	1.90911	0.389695
$25$	11.7540	2.35080
$26$	7.78065	1.52591
$27$	1.54108	0.296580
$28$	10.0531	1.89986
$29$	−4.78053	−0.887723	−0.443861	−	0.896095i	$-0.646392\pi$
$29$	−4.78053	−0.887723	−0.443861	+	0.896095i	$0.646392\pi$
$30$	−2.77577	−0.506783
$31$	−3.90479	−0.701322	−0.350661	−	0.936502i	$-0.614043\pi$
$31$	−3.90479	−0.701322	−0.350661	+	0.936502i	$0.614043\pi$
$32$	−10.2472	−1.81146
$33$	1.18079	0.205549
$34$	−11.4845	−1.96958
$35$	−8.54569	−1.44449
$36$	−14.1206	−2.35344
$37$	−6.77693	−1.11412	−0.557060	−	0.830472i	$-0.688071\pi$
$37$	−6.77693	−1.11412	−0.557060	+	0.830472i	$0.688071\pi$
$38$	1.96145	0.318190
$39$	0.774216	0.123974
$40$	30.0818	4.75635
$41$	−11.6528	−1.81987	−0.909934	−	0.414753i	$-0.863868\pi$
$41$	−11.6528	−1.81987	−0.909934	+	0.414753i	$0.863868\pi$
$42$	1.41583	0.218468
$43$	0.552335	0.0842303	0.0421152	−	0.999113i	$-0.486590\pi$
$43$	0.552335	0.0842303	0.0421152	+	0.999113i	$0.486590\pi$
$44$	−21.8877	−3.29969
$45$	12.0033	1.78934
$46$	2.04056	0.300865
$47$	−1.35892	−0.198218	−0.0991091	−	0.995077i	$-0.531599\pi$
$47$	−1.35892	−0.198218	−0.0991091	+	0.995077i	$0.531599\pi$
$48$	−2.48224	−0.358280
$49$	−2.64111	−0.377301
$50$	−30.6848	−4.33949
$51$	−1.14277	−0.160020
$52$	−14.3512	−1.99016
$53$	−8.71995	−1.19778	−0.598888	−	0.800833i	$-0.704391\pi$
$53$	−8.71995	−1.19778	−0.598888	+	0.800833i	$0.704391\pi$
$54$	−4.02312	−0.547477
$55$	18.6057	2.50879
$56$	−15.3438	−2.05040
$57$	0.195175	0.0258516
$58$	12.4800	1.63871
$59$	−11.9100	−1.55055	−0.775275	−	0.631624i	$-0.782389\pi$
$59$	−11.9100	−1.55055	−0.775275	+	0.631624i	$0.782389\pi$
$60$	5.11984	0.660969
$61$	−0.470997	−0.0603050	−0.0301525	−	0.999545i	$-0.509599\pi$
$61$	−0.470997	−0.0603050	−0.0301525	+	0.999545i	$0.509599\pi$
$62$	10.1938	1.29462
$63$	−6.12251	−0.771363
$64$	7.64001	0.955001
$65$	12.1993	1.51314
$66$	−3.08256	−0.379436
$67$	−8.34431	−1.01942	−0.509710	−	0.860346i	$-0.670247\pi$
$67$	−8.34431	−1.01942	−0.509710	+	0.860346i	$0.670247\pi$
$68$	21.1830	2.56881
$69$	0.203047	0.0244440
$70$	22.3093	2.66647
$71$	10.0343	1.19085	0.595423	−	0.803412i	$-0.296984\pi$
$71$	10.0343	1.19085	0.595423	+	0.803412i	$0.296984\pi$
$72$	21.5519	2.53992
$73$	7.49575	0.877311	0.438656	−	0.898655i	$-0.355455\pi$
$73$	7.49575	0.877311	0.438656	+	0.898655i	$0.355455\pi$
$74$	17.6918	2.05663
$75$	−3.05331	−0.352565
$76$	−3.61786	−0.414997
$77$	−9.49020	−1.08151
$78$	−2.02116	−0.228851
$79$	−10.3980	−1.16987	−0.584936	−	0.811080i	$-0.698880\pi$
$79$	−10.3980	−1.16987	−0.584936	+	0.811080i	$0.698880\pi$
$80$	−39.1126	−4.37293
$81$	8.39724	0.933027
$82$	30.4208	3.35941
$83$	−13.4273	−1.47384	−0.736920	−	0.675980i	$-0.763721\pi$
$83$	−13.4273	−1.47384	−0.736920	+	0.675980i	$0.763721\pi$
$84$	−2.61147	−0.284935
$85$	−18.0067	−1.95310
$86$	−1.44192	−0.155486
$87$	1.24183	0.133138
$88$	33.4066	3.56115
$89$	11.9262	1.26418	0.632088	−	0.774897i	$-0.282198\pi$
$89$	11.9262	1.26418	0.632088	+	0.774897i	$0.282198\pi$
$90$	−31.3357	−3.30307
$91$	−6.22250	−0.652295
$92$	−3.76378	−0.392401
$93$	1.01434	0.105182
$94$	3.54757	0.365904
$95$	3.07538	0.315527
$96$	2.66189	0.271678
$97$	−18.5687	−1.88537	−0.942683	−	0.333689i	$-0.891706\pi$
$97$	−18.5687	−1.88537	−0.942683	+	0.333689i	$0.891706\pi$
$98$	6.89485	0.696485
$99$	13.3299	1.33971
$100$	56.5976	5.65976
$101$	−11.1905	−1.11350	−0.556749	−	0.830681i	$-0.687951\pi$
$101$	−11.1905	−1.11350	−0.556749	+	0.830681i	$0.687951\pi$
$102$	2.98331	0.295391
$103$	10.2361	1.00859	0.504296	−	0.863531i	$-0.331752\pi$
$103$	10.2361	1.00859	0.504296	+	0.863531i	$0.331752\pi$
$104$	21.9039	2.14786
$105$	2.21989	0.216639
$106$	22.7642	2.21105
$107$	3.78086	0.365509	0.182755	−	0.983159i	$-0.441499\pi$
$107$	3.78086	0.365509	0.182755	+	0.983159i	$0.441499\pi$
$108$	7.42056	0.714044
$109$	−9.49382	−0.909343	−0.454671	−	0.890659i	$-0.650243\pi$
$109$	−9.49382	−0.909343	−0.454671	+	0.890659i	$0.650243\pi$
$110$	−48.5719	−4.63115
$111$	1.76043	0.167092
$112$	19.9501	1.88511
$113$	−5.83525	−0.548934	−0.274467	−	0.961597i	$-0.588501\pi$
$113$	−5.83525	−0.548934	−0.274467	+	0.961597i	$0.588501\pi$
$114$	−0.509522	−0.0477211
$115$	3.19942	0.298347
$116$	−23.0191	−2.13727
$117$	8.74013	0.808026
$118$	31.0921	2.86226
$119$	9.18464	0.841955
$120$	−7.81428	−0.713343
$121$	9.66210	0.878373
$122$	1.22958	0.111321
$123$	3.02703	0.272938
$124$	−18.8023	−1.68850
$125$	−27.6452	−2.47266
$126$	15.9834	1.42391
$127$	−8.99415	−0.798102	−0.399051	−	0.916929i	$-0.630660\pi$
$127$	−8.99415	−0.798102	−0.399051	+	0.916929i	$0.630660\pi$
$128$	0.549442	0.0485643
$129$	−0.143479	−0.0126326
$130$	−31.8475	−2.79321
$131$	7.48803	0.654233	0.327116	−	0.944984i	$-0.393923\pi$
$131$	7.48803	0.654233	0.327116	+	0.944984i	$0.393923\pi$
$132$	5.68571	0.494878
$133$	−1.56865	−0.136020
$134$	21.7836	1.88181
$135$	−6.30788	−0.542896
$136$	−32.3310	−2.77236
$137$	1.45083	0.123953	0.0619764	−	0.998078i	$-0.480260\pi$
$137$	1.45083	0.123953	0.0619764	+	0.998078i	$0.480260\pi$
$138$	−0.530072	−0.0451228
$139$	−12.7844	−1.08436	−0.542179	−	0.840263i	$-0.682401\pi$
$139$	−12.7844	−1.08436	−0.542179	+	0.840263i	$0.682401\pi$
$140$	−41.1490	−3.47773
$141$	0.353002	0.0297282
$142$	−26.1953	−2.19826
$143$	13.5477	1.13291
$144$	−28.0220	−2.33517
$145$	19.5675	1.62499
$146$	−19.5683	−1.61949
$147$	0.686074	0.0565865
$148$	−32.6321	−2.68235
$149$	−0.904473	−0.0740973	−0.0370487	−	0.999313i	$-0.511796\pi$
$149$	−0.904473	−0.0740973	−0.0370487	+	0.999313i	$0.511796\pi$
$150$	7.97093	0.650824
$151$	16.4418	1.33801	0.669007	−	0.743256i	$-0.266720\pi$
$151$	16.4418	1.33801	0.669007	+	0.743256i	$0.266720\pi$
$152$	5.52184	0.447880
$153$	−12.9008	−1.04296
$154$	24.7750	1.99643
$155$	15.9830	1.28378
$156$	3.72799	0.298478
$157$	−23.7994	−1.89940	−0.949701	−	0.313159i	$-0.898613\pi$
$157$	−23.7994	−1.89940	−0.949701	+	0.313159i	$0.898613\pi$
$158$	27.1450	2.15954
$159$	2.26516	0.179639
$160$	41.9434	3.31592
$161$	−1.63192	−0.128614
$162$	−21.9218	−1.72234
$163$	−19.3108	−1.51254	−0.756271	−	0.654259i	$-0.772981\pi$
$163$	−19.3108	−1.51254	−0.756271	+	0.654259i	$0.772981\pi$
$164$	−56.1105	−4.38150
$165$	−4.83316	−0.376261
$166$	35.0532	2.72066
$167$	4.19358	0.324509	0.162254	−	0.986749i	$-0.448123\pi$
$167$	4.19358	0.324509	0.162254	+	0.986749i	$0.448123\pi$
$168$	3.98582	0.307513
$169$	−4.11712	−0.316701
$170$	47.0080	3.60535
$171$	2.20333	0.168493
$172$	2.65959	0.202792
$173$	11.4519	0.870673	0.435336	−	0.900268i	$-0.356629\pi$
$173$	11.4519	0.870673	0.435336	+	0.900268i	$0.356629\pi$
$174$	−3.24190	−0.245768
$175$	24.5399	1.85504
$176$	−43.4355	−3.27408
$177$	3.09383	0.232547
$178$	−31.1344	−2.33362
$179$	4.80326	0.359013	0.179506	−	0.983757i	$-0.442550\pi$
$179$	4.80326	0.359013	0.179506	+	0.983757i	$0.442550\pi$
$180$	57.7980	4.30801
$181$	20.4628	1.52098	0.760492	−	0.649347i	$-0.224958\pi$
$181$	20.4628	1.52098	0.760492	+	0.649347i	$0.224958\pi$
$182$	16.2444	1.20412
$183$	0.122350	0.00904435
$184$	5.74455	0.423494
$185$	27.7391	2.03942
$186$	−2.64802	−0.194163
$187$	−19.9968	−1.46231
$188$	−6.54342	−0.477228
$189$	3.21745	0.234035
$190$	−8.02855	−0.582452
$191$	−6.12788	−0.443398	−0.221699	−	0.975115i	$-0.571160\pi$
$191$	−6.12788	−0.443398	−0.221699	+	0.975115i	$0.571160\pi$
$192$	−1.98463	−0.143228
$193$	−1.47115	−0.105896	−0.0529480	−	0.998597i	$-0.516862\pi$
$193$	−1.47115	−0.105896	−0.0529480	+	0.998597i	$0.516862\pi$
$194$	48.4753	3.48032
$195$	−3.16899	−0.226936
$196$	−12.7174	−0.908386
$197$	−0.514119	−0.0366295	−0.0183147	−	0.999832i	$-0.505830\pi$
$197$	−0.514119	−0.0366295	−0.0183147	+	0.999832i	$0.505830\pi$
$198$	−34.7990	−2.47306
$199$	20.6196	1.46169	0.730844	−	0.682545i	$-0.239127\pi$
$199$	20.6196	1.46169	0.730844	+	0.682545i	$0.239127\pi$
$200$	−86.3834	−6.10823
$201$	2.16758	0.152889
$202$	29.2138	2.05548
$203$	−9.98078	−0.700513
$204$	−5.50265	−0.385262
$205$	47.6970	3.33130
$206$	−26.7223	−1.86183
$207$	2.29220	0.159319
$208$	−28.4797	−1.97471
$209$	3.41528	0.236240
$210$	−5.79523	−0.399909
$211$	−0.169116	−0.0116424	−0.00582122	−	0.999983i	$-0.501853\pi$
$211$	−0.169116	−0.0116424	−0.00582122	+	0.999983i	$0.501853\pi$
$212$	−41.9881	−2.88376
$213$	−2.60657	−0.178600
$214$	−9.87027	−0.674718
$215$	−2.26080	−0.154185
$216$	−11.3258	−0.770624
$217$	−8.15242	−0.553422
$218$	24.7845	1.67862
$219$	−1.94715	−0.131576
$220$	89.5899	6.04015
$221$	−13.1115	−0.881972
$222$	−4.59575	−0.308447
$223$	−3.78724	−0.253613	−0.126806	−	0.991928i	$-0.540473\pi$
$223$	−3.78724	−0.253613	−0.126806	+	0.991928i	$0.540473\pi$
$224$	−21.3940	−1.42945
$225$	−34.4688	−2.29792
$226$	15.2334	1.01331
$227$	−14.0626	−0.933368	−0.466684	−	0.884424i	$-0.654552\pi$
$227$	−14.0626	−0.933368	−0.466684	+	0.884424i	$0.654552\pi$
$228$	0.939803	0.0622400
$229$	−6.47850	−0.428111	−0.214056	−	0.976821i	$-0.568667\pi$
$229$	−6.47850	−0.428111	−0.214056	+	0.976821i	$0.568667\pi$
$230$	−8.35236	−0.550738
$231$	2.46525	0.162201
$232$	35.1335	2.30663
$233$	8.11537	0.531655	0.265828	−	0.964021i	$-0.414355\pi$
$233$	8.11537	0.531655	0.265828	+	0.964021i	$0.414355\pi$
$234$	−22.8169	−1.49159
$235$	5.56227	0.362842
$236$	−57.3488	−3.73309
$237$	2.70108	0.175454
$238$	−23.9773	−1.55422
$239$	−24.2326	−1.56748	−0.783739	−	0.621091i	$-0.786690\pi$
$239$	−24.2326	−1.56748	−0.783739	+	0.621091i	$0.786690\pi$
$240$	10.1602	0.655838
$241$	12.3097	0.792937	0.396469	−	0.918048i	$-0.370236\pi$
$241$	12.3097	0.792937	0.396469	+	0.918048i	$0.370236\pi$
$242$	−25.2238	−1.62145
$243$	−6.80456	−0.436513
$244$	−2.26793	−0.145190
$245$	10.8105	0.690657
$246$	−7.90234	−0.503835
$247$	2.23932	0.142484
$248$	28.6974	1.82229
$249$	3.48798	0.221042
$250$	72.1703	4.56445
$251$	−15.5663	−0.982537	−0.491269	−	0.871008i	$-0.663467\pi$
$251$	−15.5663	−0.982537	−0.491269	+	0.871008i	$0.663467\pi$
$252$	−29.4810	−1.85713
$253$	3.55303	0.223377
$254$	23.4800	1.47327
$255$	4.67755	0.292919
$256$	−16.7144	−1.04465
$257$	12.3264	0.768901	0.384450	−	0.923146i	$-0.374391\pi$
$257$	12.3264	0.768901	0.384450	+	0.923146i	$0.374391\pi$
$258$	0.374564	0.0233194
$259$	−14.1488	−0.879167
$260$	58.7420	3.64302
$261$	14.0190	0.867755
$262$	−19.5482	−1.20769
$263$	−5.57478	−0.343756	−0.171878	−	0.985118i	$-0.554983\pi$
$263$	−5.57478	−0.343756	−0.171878	+	0.985118i	$0.554983\pi$
$264$	−8.67795	−0.534091
$265$	35.6922	2.19255
$266$	4.09511	0.251087
$267$	−3.09804	−0.189597
$268$	−40.1794	−2.45434
$269$	24.8679	1.51622	0.758111	−	0.652126i	$-0.226123\pi$
$269$	24.8679	1.51622	0.758111	+	0.652126i	$0.226123\pi$
$270$	16.4673	1.00217
$271$	−14.2423	−0.865161	−0.432580	−	0.901595i	$-0.642397\pi$
$271$	−14.2423	−0.865161	−0.432580	+	0.901595i	$0.642397\pi$
$272$	42.0370	2.54887
$273$	1.61640	0.0978293
$274$	−3.78752	−0.228813
$275$	−53.4285	−3.22186
$276$	0.977708	0.0588511
$277$	32.3841	1.94577	0.972887	−	0.231282i	$-0.0742921\pi$
$277$	32.3841	1.94577	0.972887	+	0.231282i	$0.0742921\pi$
$278$	33.3748	2.00169
$279$	11.4509	0.685547
$280$	62.8047	3.75330
$281$	−5.35320	−0.319345	−0.159673	−	0.987170i	$-0.551044\pi$
$281$	−5.35320	−0.319345	−0.159673	+	0.987170i	$0.551044\pi$
$282$	−0.921545	−0.0548772
$283$	−4.26767	−0.253687	−0.126843	−	0.991923i	$-0.540485\pi$
$283$	−4.26767	−0.253687	−0.126843	+	0.991923i	$0.540485\pi$
$284$	48.3167	2.86707
$285$	−0.798883	−0.0473218
$286$	−35.3674	−2.09132
$287$	−24.3288	−1.43608
$288$	30.0501	1.77072
$289$	2.35299	0.138411
$290$	−51.0827	−2.99968
$291$	4.82355	0.282761
$292$	36.0934	2.11221
$293$	7.60370	0.444213	0.222107	−	0.975022i	$-0.428707\pi$
$293$	7.60370	0.444213	0.222107	+	0.975022i	$0.428707\pi$
$294$	−1.79106	−0.104457
$295$	48.7496	2.83831
$296$	49.8056	2.89489
$297$	−7.00506	−0.406475
$298$	2.36121	0.136781
$299$	2.32964	0.134726
$300$	−14.7022	−0.848833
$301$	1.15316	0.0664672
$302$	−42.9228	−2.46993
$303$	2.90693	0.166999
$304$	−7.17955	−0.411775
$305$	1.92787	0.110389
$306$	33.6786	1.92528
$307$	6.82587	0.389573	0.194786	−	0.980846i	$-0.437599\pi$
$307$	6.82587	0.389573	0.194786	+	0.980846i	$0.437599\pi$
$308$	−45.6970	−2.60383
$309$	−2.65901	−0.151266
$310$	−41.7250	−2.36982
$311$	−22.8574	−1.29612	−0.648061	−	0.761588i	$-0.724420\pi$
$311$	−22.8574	−1.29612	−0.648061	+	0.761588i	$0.724420\pi$
$312$	−5.68993	−0.322129
$313$	−1.85118	−0.104635	−0.0523175	−	0.998631i	$-0.516661\pi$
$313$	−1.85118	−0.104635	−0.0523175	+	0.998631i	$0.516661\pi$
$314$	62.1306	3.50623
$315$	25.0604	1.41199
$316$	−50.0685	−2.81657
$317$	−20.6041	−1.15724	−0.578621	−	0.815597i	$-0.696409\pi$
$317$	−20.6041	−1.15724	−0.578621	+	0.815597i	$0.696409\pi$
$318$	−5.91340	−0.331607
$319$	21.7302	1.21666
$320$	−31.2718	−1.74815
$321$	−0.982145	−0.0548180
$322$	4.26028	0.237416
$323$	−3.30532	−0.183913
$324$	40.4342	2.24635
$325$	−35.0318	−1.94321
$326$	50.4127	2.79210
$327$	2.46619	0.136380
$328$	85.6400	4.72868
$329$	−2.83714	−0.156417
$330$	12.6174	0.694565
$331$	−6.35867	−0.349504	−0.174752	−	0.984612i	$-0.555912\pi$
$331$	−6.35867	−0.349504	−0.174752	+	0.984612i	$0.555912\pi$
$332$	−64.6550	−3.54840
$333$	19.8735	1.08906
$334$	−10.9477	−0.599032
$335$	34.1546	1.86607
$336$	−5.18240	−0.282723
$337$	7.40140	0.403180	0.201590	−	0.979470i	$-0.435389\pi$
$337$	7.40140	0.403180	0.201590	+	0.979470i	$0.435389\pi$
$338$	10.7481	0.584620
$339$	1.51581	0.0823274
$340$	−86.7053	−4.70226
$341$	17.7495	0.961188
$342$	−5.75200	−0.311033
$343$	−20.1287	−1.08685
$344$	−4.05927	−0.218861
$345$	−0.831105	−0.0447452
$346$	−29.8962	−1.60723
$347$	2.97440	0.159674	0.0798371	−	0.996808i	$-0.474560\pi$
$347$	2.97440	0.159674	0.0798371	+	0.996808i	$0.474560\pi$
$348$	5.97963	0.320542
$349$	−0.315419	−0.0168840	−0.00844199	−	0.999964i	$-0.502687\pi$
$349$	−0.315419	−0.0168840	−0.00844199	+	0.999964i	$0.502687\pi$
$350$	−64.0637	−3.42435
$351$	−4.59305	−0.245159
$352$	46.5792	2.48268
$353$	−23.4323	−1.24717	−0.623587	−	0.781754i	$-0.714325\pi$
$353$	−23.4323	−1.24717	−0.623587	+	0.781754i	$0.714325\pi$
$354$	−8.07673	−0.429273
$355$	−41.0718	−2.17987
$356$	57.4268	3.04362
$357$	−2.38587	−0.126274
$358$	−12.5394	−0.662725
$359$	20.2783	1.07025	0.535124	−	0.844774i	$-0.320265\pi$
$359$	20.2783	1.07025	0.535124	+	0.844774i	$0.320265\pi$
$360$	−88.2155	−4.64937
$361$	−18.4355	−0.970289
$362$	−53.4199	−2.80769
$363$	−2.50990	−0.131736
$364$	−29.9625	−1.57046
$365$	−30.6813	−1.60593
$366$	−0.319405	−0.0166956
$367$	−36.3136	−1.89555	−0.947776	−	0.318936i	$-0.896675\pi$
$367$	−36.3136	−1.89555	−0.947776	+	0.318936i	$0.896675\pi$
$368$	−7.46912	−0.389355
$369$	34.1722	1.77893
$370$	−72.4154	−3.76470
$371$	−18.2055	−0.945181
$372$	4.88423	0.253235
$373$	3.70281	0.191724	0.0958620	−	0.995395i	$-0.469439\pi$
$373$	3.70281	0.191724	0.0958620	+	0.995395i	$0.469439\pi$
$374$	52.2035	2.69938
$375$	7.18133	0.370842
$376$	9.98705	0.515043
$377$	14.2480	0.733808
$378$	−8.39945	−0.432021
$379$	27.7795	1.42694	0.713468	−	0.700687i	$-0.247123\pi$
$379$	27.7795	1.42694	0.713468	+	0.700687i	$0.247123\pi$
$380$	14.8085	0.759659
$381$	2.33639	0.119697
$382$	15.9974	0.818497
$383$	31.5241	1.61081	0.805404	−	0.592726i	$-0.201948\pi$
$383$	31.5241	1.61081	0.805404	+	0.592726i	$0.201948\pi$
$384$	−0.142727	−0.00728352
$385$	38.8449	1.97972
$386$	3.84058	0.195480
$387$	−1.61973	−0.0823357
$388$	−89.4117	−4.53919
$389$	23.2436	1.17850	0.589250	−	0.807951i	$-0.299423\pi$
$389$	23.2436	1.17850	0.589250	+	0.807951i	$0.299423\pi$
$390$	8.27294	0.418917
$391$	−3.43863	−0.173899
$392$	19.4102	0.980365
$393$	−1.94515	−0.0981198
$394$	1.34215	0.0676168
$395$	42.5609	2.14147
$396$	64.1861	3.22547
$397$	−33.6923	−1.69097	−0.845484	−	0.534001i	$-0.820688\pi$
$397$	−33.6923	−1.69097	−0.845484	+	0.534001i	$0.820688\pi$
$398$	−53.8294	−2.69823
$399$	0.407486	0.0203998
$400$	112.316	5.61582
$401$	−19.3137	−0.964480	−0.482240	−	0.876039i	$-0.660177\pi$
$401$	−19.3137	−0.964480	−0.482240	+	0.876039i	$0.660177\pi$
$402$	−5.65867	−0.282229
$403$	11.6379	0.579726
$404$	−53.8843	−2.68085
$405$	−34.3713	−1.70792
$406$	26.0557	1.29312
$407$	30.8049	1.52694
$408$	8.39854	0.415790
$409$	34.4975	1.70579	0.852896	−	0.522080i	$-0.174844\pi$
$409$	34.4975	1.70579	0.852896	+	0.522080i	$0.174844\pi$
$410$	−124.517	−6.14947
$411$	−0.376879	−0.0185901
$412$	49.2886	2.42828
$413$	−24.8656	−1.22356
$414$	−5.98400	−0.294097
$415$	54.9602	2.69789
$416$	30.5409	1.49739
$417$	3.32097	0.162629
$418$	−8.91590	−0.436091
$419$	15.4010	0.752389	0.376194	−	0.926541i	$-0.377232\pi$
$419$	15.4010	0.752389	0.376194	+	0.926541i	$0.377232\pi$
$420$	10.6892	0.521579
$421$	40.2951	1.96386	0.981931	−	0.189241i	$-0.0606027\pi$
$421$	40.2951	1.96386	0.981931	+	0.189241i	$0.0606027\pi$
$422$	0.441493	0.0214916
$423$	3.98505	0.193760
$424$	64.0853	3.11226
$425$	51.7082	2.50822
$426$	6.80470	0.329689
$427$	−0.983345	−0.0475874
$428$	18.2055	0.879997
$429$	−3.51924	−0.169911
$430$	5.90202	0.284621
$431$	21.3448	1.02814	0.514072	−	0.857747i	$-0.328136\pi$
$431$	21.3448	1.02814	0.514072	+	0.857747i	$0.328136\pi$
$432$	14.7259	0.708501
$433$	19.7426	0.948770	0.474385	−	0.880317i	$-0.342670\pi$
$433$	19.7426	0.948770	0.474385	+	0.880317i	$0.342670\pi$
$434$	21.2826	1.02160
$435$	−5.08301	−0.243711
$436$	−45.7144	−2.18932
$437$	0.587287	0.0280938
$438$	5.08322	0.242886
$439$	20.9962	1.00209	0.501047	−	0.865420i	$-0.332948\pi$
$439$	20.9962	1.00209	0.501047	+	0.865420i	$0.332948\pi$
$440$	−136.739	−6.51876
$441$	7.74510	0.368814
$442$	34.2286	1.62809
$443$	37.6209	1.78742	0.893711	−	0.448642i	$-0.148092\pi$
$443$	37.6209	1.78742	0.893711	+	0.448642i	$0.148092\pi$
$444$	8.47677	0.402290
$445$	−48.8159	−2.31410
$446$	9.88694	0.468160
$447$	0.234953	0.0111129
$448$	15.9508	0.753604
$449$	17.4333	0.822727	0.411363	−	0.911471i	$-0.365053\pi$
$449$	17.4333	0.822727	0.411363	+	0.911471i	$0.365053\pi$
$450$	89.9840	4.24188
$451$	52.9687	2.49420
$452$	−28.0978	−1.32161
$453$	−4.27104	−0.200671
$454$	36.7117	1.72297
$455$	25.4697	1.19404
$456$	−1.43440	−0.0671717
$457$	5.70445	0.266843	0.133421	−	0.991059i	$-0.457404\pi$
$457$	5.70445	0.266843	0.133421	+	0.991059i	$0.457404\pi$
$458$	16.9127	0.790278
$459$	6.77951	0.316440
$460$	15.4058	0.718297
$461$	41.5258	1.93405	0.967025	−	0.254682i	$-0.0819709\pi$
$461$	41.5258	1.93405	0.967025	+	0.254682i	$0.0819709\pi$
$462$	−6.43575	−0.299418
$463$	−11.1028	−0.515989	−0.257994	−	0.966146i	$-0.583062\pi$
$463$	−11.1028	−0.515989	−0.257994	+	0.966146i	$0.583062\pi$
$464$	−45.6809	−2.12068
$465$	−4.15186	−0.192538
$466$	−21.1859	−0.981418
$467$	−36.6735	−1.69705	−0.848524	−	0.529157i	$-0.822508\pi$
$467$	−36.6735	−1.69705	−0.848524	+	0.529157i	$0.822508\pi$
$468$	42.0853	1.94539
$469$	−17.4212	−0.804437
$470$	−14.5208	−0.669794
$471$	6.18232	0.284866
$472$	87.5299	4.02889
$473$	−2.51067	−0.115441
$474$	−7.05140	−0.323882
$475$	−8.83130	−0.405208
$476$	44.2257	2.02708
$477$	25.5714	1.17083
$478$	63.2614	2.89351
$479$	−22.7530	−1.03961	−0.519807	−	0.854284i	$-0.673996\pi$
$479$	−22.7530	−1.03961	−0.519807	+	0.854284i	$0.673996\pi$
$480$	−10.8955	−0.497311
$481$	20.1981	0.920953
$482$	−32.1356	−1.46374
$483$	0.423921	0.0192891
$484$	46.5248	2.11476
$485$	76.0047	3.45120
$486$	17.7639	0.805788
$487$	−25.5086	−1.15590	−0.577952	−	0.816071i	$-0.696148\pi$
$487$	−25.5086	−1.15590	−0.577952	+	0.816071i	$0.696148\pi$
$488$	3.46149	0.156694
$489$	5.01633	0.226846
$490$	−28.2217	−1.27493
$491$	−12.1885	−0.550059	−0.275030	−	0.961436i	$-0.588688\pi$
$491$	−12.1885	−0.550059	−0.275030	+	0.961436i	$0.588688\pi$
$492$	14.5757	0.657123
$493$	−21.0305	−0.947168
$494$	−5.84594	−0.263021
$495$	−54.5616	−2.45236
$496$	−37.3127	−1.67539
$497$	20.9495	0.939712
$498$	−9.10570	−0.408036
$499$	35.7400	1.59994	0.799970	−	0.600039i	$-0.204848\pi$
$499$	35.7400	1.59994	0.799970	+	0.600039i	$0.204848\pi$
$500$	−133.117	−5.95315
$501$	−1.08936	−0.0486688
$502$	40.6373	1.81373
$503$	−5.33213	−0.237748	−0.118874	−	0.992909i	$-0.537928\pi$
$503$	−5.33213	−0.237748	−0.118874	+	0.992909i	$0.537928\pi$
$504$	44.9960	2.00428
$505$	45.8046	2.03828
$506$	−9.27550	−0.412346
$507$	1.06949	0.0474979
$508$	−43.3085	−1.92150
$509$	8.18131	0.362630	0.181315	−	0.983425i	$-0.441965\pi$
$509$	8.18131	0.362630	0.181315	+	0.983425i	$0.441965\pi$
$510$	−12.2112	−0.540719
$511$	15.6496	0.692297
$512$	42.5355	1.87982
$513$	−1.15788	−0.0511216
$514$	−32.1792	−1.41936
$515$	−41.8980	−1.84625
$516$	−0.690876	−0.0304141
$517$	6.17703	0.271666
$518$	36.9368	1.62291
$519$	−2.97484	−0.130581
$520$	−89.6563	−3.93169
$521$	−10.1797	−0.445979	−0.222990	−	0.974821i	$-0.571582\pi$
$521$	−10.1797	−0.445979	−0.222990	+	0.974821i	$0.571582\pi$
$522$	−36.5979	−1.60185
$523$	4.14289	0.181156	0.0905780	−	0.995889i	$-0.471129\pi$
$523$	4.14289	0.181156	0.0905780	+	0.995889i	$0.471129\pi$
$524$	36.0562	1.57512
$525$	−6.37468	−0.278214
$526$	14.5535	0.634562
$527$	−17.1780	−0.748285
$528$	11.2831	0.491036
$529$	−22.3890	−0.973436
$530$	−93.1776	−4.04738
$531$	34.9263	1.51567
$532$	−7.55335	−0.327479
$533$	34.7303	1.50434
$534$	8.08772	0.349990
$535$	−15.4757	−0.669072
$536$	61.3247	2.64882
$537$	−1.24773	−0.0538436
$538$	−64.9198	−2.79889
$539$	12.0053	0.517105
$540$	−30.3736	−1.30707
$541$	43.9279	1.88861	0.944303	−	0.329077i	$-0.106738\pi$
$541$	43.9279	1.88861	0.944303	+	0.329077i	$0.106738\pi$
$542$	37.1809	1.59706
$543$	−5.31556	−0.228113
$544$	−45.0795	−1.93277
$545$	38.8597	1.66457
$546$	−4.21977	−0.180589
$547$	1.21345	0.0518835	0.0259418	−	0.999663i	$-0.491742\pi$
$547$	1.21345	0.0518835	0.0259418	+	0.999663i	$0.491742\pi$
$548$	6.98601	0.298427
$549$	1.38121	0.0589485
$550$	139.480	5.94744
$551$	3.59183	0.153017
$552$	−1.49225	−0.0635143
$553$	−21.7090	−0.923160
$554$	−84.5417	−3.59183
$555$	−7.20572	−0.305866
$556$	−61.5592	−2.61069
$557$	4.58400	0.194230	0.0971152	−	0.995273i	$-0.469038\pi$
$557$	4.58400	0.194230	0.0971152	+	0.995273i	$0.469038\pi$
$558$	−29.8936	−1.26550
$559$	−1.64619	−0.0696264
$560$	−81.6592	−3.45073
$561$	5.19453	0.219313
$562$	13.9750	0.589500
$563$	10.8044	0.455351	0.227675	−	0.973737i	$-0.426888\pi$
$563$	10.8044	0.455351	0.227675	+	0.973737i	$0.426888\pi$
$564$	1.69977	0.0715732
$565$	23.8846	1.00483
$566$	11.1411	0.468297
$567$	17.5317	0.736263
$568$	−73.7445	−3.09425
$569$	−10.1723	−0.426444	−0.213222	−	0.977004i	$-0.568396\pi$
$569$	−10.1723	−0.426444	−0.213222	+	0.977004i	$0.568396\pi$
$570$	2.08556	0.0873543
$571$	14.4371	0.604172	0.302086	−	0.953281i	$-0.402317\pi$
$571$	14.4371	0.604172	0.302086	+	0.953281i	$0.402317\pi$
$572$	65.2344	2.72759
$573$	1.59182	0.0664994
$574$	63.5124	2.65096
$575$	−9.18749	−0.383145
$576$	−22.4045	−0.933520
$577$	−6.36585	−0.265014	−0.132507	−	0.991182i	$-0.542303\pi$
$577$	−6.36585	−0.265014	−0.132507	+	0.991182i	$0.542303\pi$
$578$	−6.14269	−0.255502
$579$	0.382158	0.0158820
$580$	94.2211	3.91232
$581$	−28.0335	−1.16303
$582$	−12.5923	−0.521968
$583$	39.6370	1.64160
$584$	−55.0884	−2.27957
$585$	−35.7748	−1.47911
$586$	−19.8502	−0.820002
$587$	27.5890	1.13872	0.569361	−	0.822088i	$-0.307191\pi$
$587$	27.5890	1.13872	0.569361	+	0.822088i	$0.307191\pi$
$588$	3.30357	0.136237
$589$	2.93385	0.120887
$590$	−127.265	−5.23942
$591$	0.133552	0.00549358
$592$	−64.7576	−2.66152
$593$	7.29011	0.299369	0.149684	−	0.988734i	$-0.452174\pi$
$593$	7.29011	0.299369	0.149684	+	0.988734i	$0.452174\pi$
$594$	18.2873	0.750338
$595$	−37.5942	−1.54121
$596$	−4.35520	−0.178396
$597$	−5.35632	−0.219219
$598$	−6.08173	−0.248700
$599$	4.71237	0.192542	0.0962712	−	0.995355i	$-0.469308\pi$
$599$	4.71237	0.192542	0.0962712	+	0.995355i	$0.469308\pi$
$600$	22.4396	0.916093
$601$	−39.4421	−1.60888	−0.804439	−	0.594035i	$-0.797534\pi$
$601$	−39.4421	−1.60888	−0.804439	+	0.594035i	$0.797534\pi$
$602$	−3.01044	−0.122696
$603$	24.4699	0.996490
$604$	79.1701	3.22139
$605$	−39.5486	−1.60788
$606$	−7.58881	−0.308274
$607$	−3.10118	−0.125873	−0.0629364	−	0.998018i	$-0.520047\pi$
$607$	−3.10118	−0.125873	−0.0629364	+	0.998018i	$0.520047\pi$
$608$	7.69917	0.312243
$609$	2.59268	0.105061
$610$	−5.03287	−0.203775
$611$	4.05014	0.163851
$612$	−62.1195	−2.51103
$613$	−4.68215	−0.189110	−0.0945552	−	0.995520i	$-0.530143\pi$
$613$	−4.68215	−0.189110	−0.0945552	+	0.995520i	$0.530143\pi$
$614$	−17.8195	−0.719138
$615$	−12.3901	−0.499618
$616$	69.7461	2.81015
$617$	−11.6286	−0.468150	−0.234075	−	0.972219i	$-0.575206\pi$
$617$	−11.6286	−0.468150	−0.234075	+	0.972219i	$0.575206\pi$
$618$	6.94158	0.279231
$619$	−24.8642	−0.999377	−0.499689	−	0.866205i	$-0.666552\pi$
$619$	−24.8642	−0.999377	−0.499689	+	0.866205i	$0.666552\pi$
$620$	76.9609	3.09082
$621$	−1.20458	−0.0483381
$622$	59.6712	2.39260
$623$	24.8995	0.997577
$624$	7.39810	0.296161
$625$	54.3863	2.17545
$626$	4.83268	0.193153
$627$	−0.887179	−0.0354305
$628$	−114.599	−4.57298
$629$	−29.8131	−1.18873
$630$	−65.4225	−2.60649
$631$	−43.7745	−1.74264	−0.871318	−	0.490719i	$-0.836734\pi$
$631$	−43.7745	−1.74264	−0.871318	+	0.490719i	$0.836734\pi$
$632$	76.4181	3.03975
$633$	0.0439310	0.00174610
$634$	53.7889	2.13623
$635$	36.8145	1.46094
$636$	10.9072	0.432497
$637$	7.87160	0.311884
$638$	−56.7286	−2.24591
$639$	−29.4257	−1.16406
$640$	−2.24896	−0.0888978
$641$	−32.1088	−1.26822	−0.634111	−	0.773242i	$-0.718634\pi$
$641$	−32.1088	−1.26822	−0.634111	+	0.773242i	$0.718634\pi$
$642$	2.56398	0.101192
$643$	−36.6281	−1.44447	−0.722235	−	0.691648i	$-0.756885\pi$
$643$	−36.6281	−1.44447	−0.722235	+	0.691648i	$0.756885\pi$
$644$	−7.85800	−0.309649
$645$	0.587282	0.0231242
$646$	8.62883	0.339497
$647$	−26.4551	−1.04006	−0.520028	−	0.854149i	$-0.674079\pi$
$647$	−26.4551	−1.04006	−0.520028	+	0.854149i	$0.674079\pi$
$648$	−61.7137	−2.42434
$649$	54.1376	2.12509
$650$	91.4536	3.58711
$651$	2.11773	0.0830005
$652$	−92.9852	−3.64158
$653$	40.1265	1.57027	0.785136	−	0.619324i	$-0.212593\pi$
$653$	40.1265	1.57027	0.785136	+	0.619324i	$0.212593\pi$
$654$	−6.43820	−0.251754
$655$	−30.6497	−1.19758
$656$	−111.350	−4.34748
$657$	−21.9814	−0.857578
$658$	7.40661	0.288740
$659$	−28.2317	−1.09975	−0.549876	−	0.835246i	$-0.685325\pi$
$659$	−28.2317	−1.09975	−0.549876	+	0.835246i	$0.685325\pi$
$660$	−23.2726	−0.905883
$661$	0.299228	0.0116386	0.00581931	−	0.999983i	$-0.498148\pi$
$661$	0.299228	0.0116386	0.00581931	+	0.999983i	$0.498148\pi$
$662$	16.5999	0.645173
$663$	3.40593	0.132275
$664$	98.6812	3.82957
$665$	6.42076	0.248986
$666$	−51.8815	−2.01037
$667$	3.73670	0.144685
$668$	20.1928	0.781284
$669$	0.983803	0.0380360
$670$	−89.1637	−3.44470
$671$	2.14094	0.0826502
$672$	5.55748	0.214384
$673$	−1.75600	−0.0676889	−0.0338445	−	0.999427i	$-0.510775\pi$
$673$	−1.75600	−0.0676889	−0.0338445	+	0.999427i	$0.510775\pi$
$674$	−19.3220	−0.744256
$675$	18.1138	0.697201
$676$	−19.8247	−0.762487
$677$	7.46432	0.286877	0.143439	−	0.989659i	$-0.454184\pi$
$677$	7.46432	0.286877	0.143439	+	0.989659i	$0.454184\pi$
$678$	−3.95715	−0.151974
$679$	−38.7677	−1.48777
$680$	132.336	5.07485
$681$	3.65301	0.139984
$682$	−46.3366	−1.77432
$683$	20.7657	0.794577	0.397288	−	0.917694i	$-0.369951\pi$
$683$	20.7657	0.794577	0.397288	+	0.917694i	$0.369951\pi$
$684$	10.6094	0.405662
$685$	−5.93848	−0.226898
$686$	52.5477	2.00628
$687$	1.68290	0.0642068
$688$	5.27789	0.201218
$689$	25.9891	0.990105
$690$	2.16967	0.0825980
$691$	27.7378	1.05520	0.527598	−	0.849494i	$-0.323093\pi$
$691$	27.7378	1.05520	0.527598	+	0.849494i	$0.323093\pi$
$692$	55.1430	2.09622
$693$	27.8302	1.05718
$694$	−7.76494	−0.294753
$695$	52.3286	1.98494
$696$	−9.12654	−0.345941
$697$	−51.2632	−1.94173
$698$	0.823429	0.0311672
$699$	−2.10811	−0.0797360
$700$	118.164	4.46619
$701$	12.9063	0.487466	0.243733	−	0.969842i	$-0.421628\pi$
$701$	12.9063	0.487466	0.243733	+	0.969842i	$0.421628\pi$
$702$	11.9906	0.452555
$703$	5.09181	0.192041
$704$	−34.7281	−1.30887
$705$	−1.44490	−0.0544180
$706$	61.1721	2.30224
$707$	−23.3635	−0.878675
$708$	14.8974	0.559877
$709$	−16.2486	−0.610228	−0.305114	−	0.952316i	$-0.598695\pi$
$709$	−16.2486	−0.610228	−0.305114	+	0.952316i	$0.598695\pi$
$710$	107.222	4.02396
$711$	30.4925	1.14356
$712$	−87.6490	−3.28479
$713$	3.05218	0.114305
$714$	6.22853	0.233097
$715$	−55.4528	−2.07382
$716$	23.1286	0.864356
$717$	6.29485	0.235085
$718$	−52.9383	−1.97564
$719$	33.5096	1.24970	0.624849	−	0.780745i	$-0.285160\pi$
$719$	33.5096	1.24970	0.624849	+	0.780745i	$0.285160\pi$
$720$	114.699	4.27456
$721$	21.3709	0.795893
$722$	48.1275	1.79112
$723$	−3.19766	−0.118922
$724$	98.5318	3.66191
$725$	−56.1904	−2.08686
$726$	6.55232	0.243180
$727$	−25.6974	−0.953065	−0.476532	−	0.879157i	$-0.658107\pi$
$727$	−25.6974	−0.953065	−0.476532	+	0.879157i	$0.658107\pi$
$728$	45.7309	1.69490
$729$	−23.4241	−0.867560
$730$	80.0964	2.96450
$731$	2.42983	0.0898707
$732$	0.589136	0.0217751
$733$	−2.69767	−0.0996407	−0.0498203	−	0.998758i	$-0.515865\pi$
$733$	−2.69767	−0.0996407	−0.0498203	+	0.998758i	$0.515865\pi$
$734$	94.7998	3.49913
$735$	−2.80821	−0.103583
$736$	8.00970	0.295241
$737$	37.9296	1.39715
$738$	−89.2096	−3.28385
$739$	6.64878	0.244579	0.122290	−	0.992494i	$-0.460976\pi$
$739$	6.64878	0.244579	0.122290	+	0.992494i	$0.460976\pi$
$740$	133.569	4.91008
$741$	−0.581703	−0.0213694
$742$	47.5270	1.74477
$743$	−26.3333	−0.966074	−0.483037	−	0.875600i	$-0.660466\pi$
$743$	−26.3333	−0.966074	−0.483037	+	0.875600i	$0.660466\pi$
$744$	−7.45467	−0.273301
$745$	3.70216	0.135637
$746$	−9.66651	−0.353916
$747$	39.3759	1.44069
$748$	−96.2884	−3.52065
$749$	7.89366	0.288428
$750$	−18.7475	−0.684562
$751$	−32.0977	−1.17126	−0.585630	−	0.810578i	$-0.699153\pi$
$751$	−32.0977	−1.17126	−0.585630	+	0.810578i	$0.699153\pi$
$752$	−12.9853	−0.473524
$753$	4.04362	0.147358
$754$	−37.1956	−1.35459
$755$	−67.2989	−2.44926
$756$	15.4926	0.563461
$757$	35.0330	1.27330	0.636648	−	0.771155i	$-0.280320\pi$
$757$	35.0330	1.27330	0.636648	+	0.771155i	$0.280320\pi$
$758$	−72.5209	−2.63408
$759$	−0.922962	−0.0335014
$760$	−22.6018	−0.819853
$761$	−29.3804	−1.06504	−0.532520	−	0.846417i	$-0.678755\pi$
$761$	−29.3804	−1.06504	−0.532520	+	0.846417i	$0.678755\pi$
$762$	−6.09935	−0.220956
$763$	−19.8212	−0.717574
$764$	−29.5068	−1.06752
$765$	52.8049	1.90917
$766$	−82.2966	−2.97350
$767$	35.4968	1.28171
$768$	4.34186	0.156673
$769$	9.96773	0.359446	0.179723	−	0.983717i	$-0.442480\pi$
$769$	9.96773	0.359446	0.179723	+	0.983717i	$0.442480\pi$
$770$	−101.408	−3.65450
$771$	−3.20200	−0.115317
$772$	−7.08387	−0.254954
$773$	−17.4115	−0.626249	−0.313124	−	0.949712i	$-0.601376\pi$
$773$	−17.4115	−0.626249	−0.313124	+	0.949712i	$0.601376\pi$
$774$	4.22846	0.151989
$775$	−45.8969	−1.64867
$776$	136.467	4.89887
$777$	3.67541	0.131855
$778$	−60.6796	−2.17547
$779$	8.75530	0.313691
$780$	−15.2593	−0.546369
$781$	−45.6113	−1.63210
$782$	8.97685	0.321012
$783$	−7.36717	−0.263281
$784$	−25.2374	−0.901334
$785$	97.4150	3.47689
$786$	5.07799	0.181126
$787$	36.6531	1.30654	0.653271	−	0.757124i	$-0.273396\pi$
$787$	36.6531	1.30654	0.653271	+	0.757124i	$0.273396\pi$
$788$	−2.47558	−0.0881888
$789$	1.44815	0.0515554
$790$	−111.109	−3.95308
$791$	−12.1828	−0.433171
$792$	−97.9655	−3.48105
$793$	1.40377	0.0498492
$794$	87.9568	3.12147
$795$	−9.27167	−0.328832
$796$	99.2873	3.51915
$797$	−2.56965	−0.0910217	−0.0455108	−	0.998964i	$-0.514492\pi$
$797$	−2.56965	−0.0910217	−0.0455108	+	0.998964i	$0.514492\pi$
$798$	−1.06378	−0.0376573
$799$	−5.97815	−0.211492
$800$	−120.445	−4.25839
$801$	−34.9738	−1.23574
$802$	50.4201	1.78040
$803$	−34.0724	−1.20239
$804$	10.4373	0.368095
$805$	6.67973	0.235429
$806$	−30.3818	−1.07015
$807$	−6.45987	−0.227398
$808$	82.2422	2.89327
$809$	−27.1561	−0.954758	−0.477379	−	0.878698i	$-0.658413\pi$
$809$	−27.1561	−0.954758	−0.477379	+	0.878698i	$0.658413\pi$
$810$	89.7293	3.15277
$811$	17.6456	0.619621	0.309810	−	0.950798i	$-0.399734\pi$
$811$	17.6456	0.619621	0.309810	+	0.950798i	$0.399734\pi$
$812$	−48.0593	−1.68655
$813$	3.69970	0.129754
$814$	−80.4190	−2.81869
$815$	79.0424	2.76874
$816$	−10.9199	−0.382271
$817$	−0.414994	−0.0145188
$818$	−90.0589	−3.14884
$819$	18.2476	0.637623
$820$	229.670	8.02041
$821$	16.6200	0.580042	0.290021	−	0.957020i	$-0.406338\pi$
$821$	16.6200	0.580042	0.290021	+	0.957020i	$0.406338\pi$
$822$	0.983876	0.0343166
$823$	19.9273	0.694622	0.347311	−	0.937750i	$-0.387095\pi$
$823$	19.9273	0.694622	0.347311	+	0.937750i	$0.387095\pi$
$824$	−75.2280	−2.62069
$825$	13.8790	0.483204
$826$	64.9140	2.25865
$827$	−26.3134	−0.915006	−0.457503	−	0.889208i	$-0.651256\pi$
$827$	−26.3134	−0.915006	−0.457503	+	0.889208i	$0.651256\pi$
$828$	11.0374	0.383575
$829$	37.8647	1.31510	0.657548	−	0.753413i	$-0.271594\pi$
$829$	37.8647	1.31510	0.657548	+	0.753413i	$0.271594\pi$
$830$	−143.479	−4.98022
$831$	−8.41235	−0.291821
$832$	−22.7704	−0.789422
$833$	−11.6188	−0.402566
$834$	−8.66970	−0.300207
$835$	−17.1650	−0.594019
$836$	16.4452	0.568769
$837$	−6.01759	−0.207998
$838$	−40.2057	−1.38888
$839$	−40.8660	−1.41085	−0.705425	−	0.708785i	$-0.749244\pi$
$839$	−40.8660	−1.41085	−0.705425	+	0.708785i	$0.749244\pi$
$840$	−16.3146	−0.562908
$841$	−6.14649	−0.211948
$842$	−105.194	−3.62522
$843$	1.39059	0.0478944
$844$	−0.814326	−0.0280302
$845$	16.8520	0.579728
$846$	−10.4033	−0.357674
$847$	20.1725	0.693135
$848$	−83.3243	−2.86137
$849$	1.10860	0.0380471
$850$	−134.989	−4.63008
$851$	5.29718	0.181585
$852$	−12.5511	−0.429994
$853$	−9.64903	−0.330376	−0.165188	−	0.986262i	$-0.552823\pi$
$853$	−9.64903	−0.330376	−0.165188	+	0.986262i	$0.552823\pi$
$854$	2.56711	0.0878447
$855$	−9.01860	−0.308430
$856$	−27.7866	−0.949726
$857$	21.3960	0.730873	0.365437	−	0.930836i	$-0.380920\pi$
$857$	21.3960	0.730873	0.365437	+	0.930836i	$0.380920\pi$
$858$	9.18730	0.313649
$859$	−30.2944	−1.03363	−0.516815	−	0.856097i	$-0.672882\pi$
$859$	−30.2944	−1.03363	−0.516815	+	0.856097i	$0.672882\pi$
$860$	−10.8862	−0.371215
$861$	6.31982	0.215379
$862$	−55.7226	−1.89792
$863$	30.0519	1.02298	0.511489	−	0.859290i	$-0.329094\pi$
$863$	30.0519	1.02298	0.511489	+	0.859290i	$0.329094\pi$
$864$	−15.7917	−0.537245
$865$	−46.8745	−1.59378
$866$	−51.5399	−1.75140
$867$	−0.611230	−0.0207585
$868$	−39.2553	−1.33241
$869$	47.2649	1.60335
$870$	13.2696	0.449883
$871$	24.8695	0.842672
$872$	69.7727	2.36280
$873$	54.4531	1.84296
$874$	−1.53317	−0.0518601
$875$	−57.7175	−1.95121
$876$	−9.37589	−0.316782
$877$	−26.0876	−0.880916	−0.440458	−	0.897773i	$-0.645184\pi$
$877$	−26.0876	−0.880916	−0.440458	+	0.897773i	$0.645184\pi$
$878$	−54.8125	−1.84983
$879$	−1.97520	−0.0666217
$880$	177.789	5.99326
$881$	34.4083	1.15925	0.579623	−	0.814885i	$-0.303200\pi$
$881$	34.4083	1.15925	0.579623	+	0.814885i	$0.303200\pi$
$882$	−20.2193	−0.680819
$883$	−40.6746	−1.36881	−0.684405	−	0.729102i	$-0.739938\pi$
$883$	−40.6746	−1.36881	−0.684405	+	0.729102i	$0.739938\pi$
$884$	−63.1340	−2.12343
$885$	−12.6636	−0.425681
$886$	−98.2127	−3.29952
$887$	−40.9423	−1.37471	−0.687354	−	0.726322i	$-0.741228\pi$
$887$	−40.9423	−1.37471	−0.687354	+	0.726322i	$0.741228\pi$
$888$	−12.9379	−0.434167
$889$	−18.7780	−0.629792
$890$	127.438	4.27174
$891$	−38.1701	−1.27875
$892$	−18.2363	−0.610595
$893$	1.02101	0.0341669
$894$	−0.613366	−0.0205140
$895$	−19.6605	−0.657180
$896$	1.14712	0.0383227
$897$	−0.605165	−0.0202059
$898$	−45.5111	−1.51873
$899$	18.6670	0.622579
$900$	−165.974	−5.53245
$901$	−38.3608	−1.27798
$902$	−138.279	−4.60420
$903$	−0.299554	−0.00996855
$904$	42.8849	1.42633
$905$	−83.7574	−2.78419
$906$	11.1499	0.370432
$907$	−52.5203	−1.74391	−0.871953	−	0.489589i	$-0.837147\pi$
$907$	−52.5203	−1.74391	−0.871953	+	0.489589i	$0.837147\pi$
$908$	−67.7140	−2.24717
$909$	32.8164	1.08845
$910$	−66.4910	−2.20416
$911$	18.6592	0.618206	0.309103	−	0.951029i	$-0.399971\pi$
$911$	18.6592	0.618206	0.309103	+	0.951029i	$0.399971\pi$
$912$	1.86501	0.0617568
$913$	61.0347	2.01995
$914$	−14.8920	−0.492583
$915$	−0.500798	−0.0165559
$916$	−31.1951	−1.03072
$917$	15.6335	0.516263
$918$	−17.6985	−0.584138
$919$	−18.8814	−0.622840	−0.311420	−	0.950272i	$-0.600805\pi$
$919$	−18.8814	−0.622840	−0.311420	+	0.950272i	$0.600805\pi$
$920$	−23.5134	−0.775214
$921$	−1.77314	−0.0584269
$922$	−108.407	−3.57019
$923$	−29.9063	−0.984376
$924$	11.8706	0.390514
$925$	−79.6560	−2.61907
$926$	28.9848	0.952498
$927$	−30.0176	−0.985906
$928$	48.9870	1.60808
$929$	−6.17839	−0.202706	−0.101353	−	0.994851i	$-0.532317\pi$
$929$	−6.17839	−0.202706	−0.101353	+	0.994851i	$0.532317\pi$
$930$	10.8388	0.355418
$931$	1.98438	0.0650355
$932$	39.0769	1.28001
$933$	5.93761	0.194388
$934$	95.7395	3.13269
$935$	81.8503	2.67679
$936$	−64.2337	−2.09954
$937$	7.14764	0.233503	0.116752	−	0.993161i	$-0.462752\pi$
$937$	7.14764	0.233503	0.116752	+	0.993161i	$0.462752\pi$
$938$	45.4797	1.48496
$939$	0.480877	0.0156928
$940$	26.7833	0.873575
$941$	−31.8887	−1.03954	−0.519770	−	0.854306i	$-0.673982\pi$
$941$	−31.8887	−1.03954	−0.519770	+	0.854306i	$0.673982\pi$
$942$	−16.1395	−0.525854
$943$	9.10843	0.296611
$944$	−113.807	−3.70411
$945$	−13.1696	−0.428406
$946$	6.55433	0.213100
$947$	21.9422	0.713027	0.356513	−	0.934290i	$-0.383965\pi$
$947$	21.9422	0.713027	0.356513	+	0.934290i	$0.383965\pi$
$948$	13.0062	0.422421
$949$	−22.3405	−0.725202
$950$	23.0549	0.747999
$951$	5.35228	0.173560
$952$	−67.5005	−2.18770
$953$	−46.7805	−1.51537	−0.757684	−	0.652621i	$-0.773669\pi$
$953$	−46.7805	−1.51537	−0.757684	+	0.652621i	$0.773669\pi$
$954$	−66.7565	−2.16132
$955$	25.0824	0.811648
$956$	−116.684	−3.77384
$957$	−5.64480	−0.182471
$958$	59.3989	1.91909
$959$	3.02904	0.0978127
$960$	8.12341	0.262182
$961$	−15.7526	−0.508148
$962$	−52.7289	−1.70005
$963$	−11.0874	−0.357288
$964$	59.2734	1.90907
$965$	6.02167	0.193845
$966$	−1.10668	−0.0356069
$967$	27.2626	0.876706	0.438353	−	0.898803i	$-0.355562\pi$
$967$	27.2626	0.876706	0.438353	+	0.898803i	$0.355562\pi$
$968$	−71.0095	−2.28233
$969$	0.858614	0.0275827
$970$	−198.417	−6.37079
$971$	30.5592	0.980692	0.490346	−	0.871528i	$-0.336870\pi$
$971$	30.5592	0.980692	0.490346	+	0.871528i	$0.336870\pi$
$972$	−32.7652	−1.05094
$973$	−26.6912	−0.855681
$974$	66.5924	2.13376
$975$	9.10013	0.291437
$976$	−4.50066	−0.144063
$977$	31.6056	1.01115	0.505576	−	0.862782i	$-0.331280\pi$
$977$	31.6056	1.01115	0.505576	+	0.862782i	$0.331280\pi$
$978$	−13.0956	−0.418751
$979$	−54.2113	−1.73260
$980$	52.0544	1.66282
$981$	27.8408	0.888889
$982$	31.8192	1.01539
$983$	2.31068	0.0736993	0.0368496	−	0.999321i	$-0.488268\pi$
$983$	2.31068	0.0736993	0.0368496	+	0.999321i	$0.488268\pi$
$984$	−22.2465	−0.709193
$985$	2.10437	0.0670509
$986$	54.9021	1.74844
$987$	0.736997	0.0234589
$988$	10.7827	0.343044
$989$	−0.431732	−0.0137283
$990$	142.438	4.52698
$991$	53.3558	1.69490	0.847451	−	0.530873i	$-0.178136\pi$
$991$	53.3558	1.69490	0.847451	+	0.530873i	$0.178136\pi$
$992$	40.0132	1.27042
$993$	1.65178	0.0524176
$994$	−54.6905	−1.73468
$995$	−84.3996	−2.67565
$996$	16.7953	0.532178
$997$	−6.96753	−0.220664	−0.110332	−	0.993895i	$-0.535191\pi$
$997$	−6.96753	−0.220664	−0.110332	+	0.993895i	$0.535191\pi$
$998$	−93.3024	−2.95344
$999$	−10.4438	−0.330426

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4001.2.a.b.1.14	✓	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4001.2.a.b.1.14	✓	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)

\(f(q)\)	\(=\)	\(q-2.61059 q^{2} -0.259768 q^{3} +4.81518 q^{4} -4.09316 q^{5} +0.678147 q^{6} +2.08780 q^{7} -7.34928 q^{8} -2.93252 q^{9} +O(q^{10})\)	\(q-2.61059 q^{2} -0.259768 q^{3} +4.81518 q^{4} -4.09316 q^{5} +0.678147 q^{6} +2.08780 q^{7} -7.34928 q^{8} -2.93252 q^{9} +10.6856 q^{10} -4.54556 q^{11} -1.25083 q^{12} -2.98042 q^{13} -5.45038 q^{14} +1.06327 q^{15} +9.55560 q^{16} +4.39920 q^{17} +7.65561 q^{18} -0.751344 q^{19} -19.7093 q^{20} -0.542342 q^{21} +11.8666 q^{22} -0.781648 q^{23} +1.90911 q^{24} +11.7540 q^{25} +7.78065 q^{26} +1.54108 q^{27} +10.0531 q^{28} -4.78053 q^{29} -2.77577 q^{30} -3.90479 q^{31} -10.2472 q^{32} +1.18079 q^{33} -11.4845 q^{34} -8.54569 q^{35} -14.1206 q^{36} -6.77693 q^{37} +1.96145 q^{38} +0.774216 q^{39} +30.0818 q^{40} -11.6528 q^{41} +1.41583 q^{42} +0.552335 q^{43} -21.8877 q^{44} +12.0033 q^{45} +2.04056 q^{46} -1.35892 q^{47} -2.48224 q^{48} -2.64111 q^{49} -30.6848 q^{50} -1.14277 q^{51} -14.3512 q^{52} -8.71995 q^{53} -4.02312 q^{54} +18.6057 q^{55} -15.3438 q^{56} +0.195175 q^{57} +12.4800 q^{58} -11.9100 q^{59} +5.11984 q^{60} -0.470997 q^{61} +10.1938 q^{62} -6.12251 q^{63} +7.64001 q^{64} +12.1993 q^{65} -3.08256 q^{66} -8.34431 q^{67} +21.1830 q^{68} +0.203047 q^{69} +22.3093 q^{70} +10.0343 q^{71} +21.5519 q^{72} +7.49575 q^{73} +17.6918 q^{74} -3.05331 q^{75} -3.61786 q^{76} -9.49020 q^{77} -2.02116 q^{78} -10.3980 q^{79} -39.1126 q^{80} +8.39724 q^{81} +30.4208 q^{82} -13.4273 q^{83} -2.61147 q^{84} -18.0067 q^{85} -1.44192 q^{86} +1.24183 q^{87} +33.4066 q^{88} +11.9262 q^{89} -31.3357 q^{90} -6.22250 q^{91} -3.76378 q^{92} +1.01434 q^{93} +3.54757 q^{94} +3.07538 q^{95} +2.66189 q^{96} -18.5687 q^{97} +6.89485 q^{98} +13.3299 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9}+O(q^{10}) \) 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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