LMFDB - Embedded newform 4003.2.a.c.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4003,2,Mod(1,4003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4003, 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("4003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4003.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:	$31.9641159291$
Analytic rank:	$0$
Dimension:	$179$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	4003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.46969 q^{2} +0.639879 q^{3} +4.09938 q^{4} -1.75762 q^{5} -1.58030 q^{6} -0.0776251 q^{7} -5.18482 q^{8} -2.59056 q^{9} +O(q^{10})$	\(q-2.46969 q^{2} +0.639879 q^{3} +4.09938 q^{4} -1.75762 q^{5} -1.58030 q^{6} -0.0776251 q^{7} -5.18482 q^{8} -2.59056 q^{9} +4.34079 q^{10} -0.622748 q^{11} +2.62311 q^{12} -2.61937 q^{13} +0.191710 q^{14} -1.12467 q^{15} +4.60616 q^{16} -0.276397 q^{17} +6.39787 q^{18} -6.23326 q^{19} -7.20516 q^{20} -0.0496707 q^{21} +1.53800 q^{22} -1.37220 q^{23} -3.31766 q^{24} -1.91076 q^{25} +6.46904 q^{26} -3.57728 q^{27} -0.318215 q^{28} -1.18130 q^{29} +2.77758 q^{30} +0.419170 q^{31} -1.00615 q^{32} -0.398483 q^{33} +0.682615 q^{34} +0.136436 q^{35} -10.6197 q^{36} -9.00901 q^{37} +15.3942 q^{38} -1.67608 q^{39} +9.11296 q^{40} +6.47523 q^{41} +0.122671 q^{42} +3.50454 q^{43} -2.55288 q^{44} +4.55322 q^{45} +3.38891 q^{46} -0.474996 q^{47} +2.94738 q^{48} -6.99397 q^{49} +4.71900 q^{50} -0.176860 q^{51} -10.7378 q^{52} -3.44910 q^{53} +8.83477 q^{54} +1.09456 q^{55} +0.402473 q^{56} -3.98853 q^{57} +2.91744 q^{58} +3.79175 q^{59} -4.61043 q^{60} -1.11631 q^{61} -1.03522 q^{62} +0.201092 q^{63} -6.72744 q^{64} +4.60387 q^{65} +0.984131 q^{66} -13.0788 q^{67} -1.13306 q^{68} -0.878041 q^{69} -0.336954 q^{70} -0.468661 q^{71} +13.4316 q^{72} +8.13902 q^{73} +22.2495 q^{74} -1.22266 q^{75} -25.5525 q^{76} +0.0483409 q^{77} +4.13940 q^{78} +6.79858 q^{79} -8.09589 q^{80} +5.48264 q^{81} -15.9918 q^{82} +15.1662 q^{83} -0.203619 q^{84} +0.485801 q^{85} -8.65515 q^{86} -0.755887 q^{87} +3.22884 q^{88} -8.61138 q^{89} -11.2450 q^{90} +0.203329 q^{91} -5.62516 q^{92} +0.268218 q^{93} +1.17309 q^{94} +10.9557 q^{95} -0.643812 q^{96} +11.3026 q^{97} +17.2730 q^{98} +1.61326 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 179 q + 22 q^{2} + 16 q^{3} + 196 q^{4} + 61 q^{5} + 7 q^{6} + 21 q^{7} + 60 q^{8} + 221 q^{9}+O(q^{10}) $ 179 * q + 22 * q^2 + 16 * q^3 + 196 * q^4 + 61 * q^5 + 7 * q^6 + 21 * q^7 + 60 * q^8 + 221 * q^9	\( 179 q + 22 q^{2} + 16 q^{3} + 196 q^{4} + 61 q^{5} + 7 q^{6} + 21 q^{7} + 60 q^{8} + 221 q^{9} + 9 q^{10} + 46 q^{11} + 33 q^{12} + 47 q^{13} + 22 q^{14} + 36 q^{15} + 222 q^{16} + 103 q^{17} + 43 q^{18} + 12 q^{19} + 102 q^{20} + 50 q^{21} + 39 q^{22} + 121 q^{23} - 3 q^{24} + 246 q^{25} + 52 q^{26} + 49 q^{27} + 41 q^{28} + 138 q^{29} + 28 q^{30} + 5 q^{31} + 137 q^{32} + 63 q^{33} + 2 q^{34} + 72 q^{35} + 279 q^{36} + 118 q^{37} + 123 q^{38} + q^{39} + 9 q^{40} + 50 q^{41} + 48 q^{42} + 48 q^{43} + 108 q^{44} + 158 q^{45} + 13 q^{46} + 85 q^{47} + 50 q^{48} + 230 q^{49} + 78 q^{50} + 15 q^{51} + 41 q^{52} + 399 q^{53} - 5 q^{54} + 24 q^{55} + 53 q^{56} + 45 q^{57} + 27 q^{58} + 48 q^{59} + 66 q^{60} + 46 q^{61} + 81 q^{62} + 78 q^{63} + 252 q^{64} + 153 q^{65} + 6 q^{66} + 70 q^{67} + 240 q^{68} + 120 q^{69} - 31 q^{70} + 86 q^{71} + 89 q^{72} + 45 q^{73} + 68 q^{74} + 17 q^{75} - 13 q^{76} + 362 q^{77} + 69 q^{78} + 31 q^{79} + 169 q^{80} + 303 q^{81} + 25 q^{82} + 106 q^{83} + 13 q^{84} + 115 q^{85} + 95 q^{86} + 32 q^{87} + 83 q^{88} + 105 q^{89} - 38 q^{90} + 3 q^{91} + 310 q^{92} + 298 q^{93} - 17 q^{94} + 102 q^{95} - 82 q^{96} + 34 q^{97} + 81 q^{98} + 58 q^{99}+O(q^{100}) \) 179 * q + 22 * q^2 + 16 * q^3 + 196 * q^4 + 61 * q^5 + 7 * q^6 + 21 * q^7 + 60 * q^8 + 221 * q^9 + 9 * q^10 + 46 * q^11 + 33 * q^12 + 47 * q^13 + 22 * q^14 + 36 * q^15 + 222 * q^16 + 103 * q^17 + 43 * q^18 + 12 * q^19 + 102 * q^20 + 50 * q^21 + 39 * q^22 + 121 * q^23 - 3 * q^24 + 246 * q^25 + 52 * q^26 + 49 * q^27 + 41 * q^28 + 138 * q^29 + 28 * q^30 + 5 * q^31 + 137 * q^32 + 63 * q^33 + 2 * q^34 + 72 * q^35 + 279 * q^36 + 118 * q^37 + 123 * q^38 + q^39 + 9 * q^40 + 50 * q^41 + 48 * q^42 + 48 * q^43 + 108 * q^44 + 158 * q^45 + 13 * q^46 + 85 * q^47 + 50 * q^48 + 230 * q^49 + 78 * q^50 + 15 * q^51 + 41 * q^52 + 399 * q^53 - 5 * q^54 + 24 * q^55 + 53 * q^56 + 45 * q^57 + 27 * q^58 + 48 * q^59 + 66 * q^60 + 46 * q^61 + 81 * q^62 + 78 * q^63 + 252 * q^64 + 153 * q^65 + 6 * q^66 + 70 * q^67 + 240 * q^68 + 120 * q^69 - 31 * q^70 + 86 * q^71 + 89 * q^72 + 45 * q^73 + 68 * q^74 + 17 * q^75 - 13 * q^76 + 362 * q^77 + 69 * q^78 + 31 * q^79 + 169 * q^80 + 303 * q^81 + 25 * q^82 + 106 * q^83 + 13 * q^84 + 115 * q^85 + 95 * q^86 + 32 * q^87 + 83 * q^88 + 105 * q^89 - 38 * q^90 + 3 * q^91 + 310 * q^92 + 298 * q^93 - 17 * q^94 + 102 * q^95 - 82 * q^96 + 34 * q^97 + 81 * q^98 + 58 * 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 $

$2$	−2.46969	−1.74634	−0.873168	−	0.487419i	$-0.837938\pi$
$2$	−2.46969	−1.74634	−0.873168	+	0.487419i	$0.837938\pi$
$3$	0.639879	0.369434	0.184717	−	0.982792i	$-0.440863\pi$
$3$	0.639879	0.369434	0.184717	+	0.982792i	$0.440863\pi$
$4$	4.09938	2.04969
$5$	−1.75762	−0.786033	−0.393016	−	0.919532i	$-0.628568\pi$
$5$	−1.75762	−0.786033	−0.393016	+	0.919532i	$0.628568\pi$
$6$	−1.58030	−0.645156
$7$	−0.0776251	−0.0293395	−0.0146698	−	0.999892i	$-0.504670\pi$
$7$	−0.0776251	−0.0293395	−0.0146698	+	0.999892i	$0.504670\pi$
$8$	−5.18482	−1.83311
$9$	−2.59056	−0.863518
$10$	4.34079	1.37268
$11$	−0.622748	−0.187766	−0.0938828	−	0.995583i	$-0.529928\pi$
$11$	−0.622748	−0.187766	−0.0938828	+	0.995583i	$0.529928\pi$
$12$	2.62311	0.757226
$13$	−2.61937	−0.726483	−0.363241	−	0.931695i	$-0.618330\pi$
$13$	−2.61937	−0.726483	−0.363241	+	0.931695i	$0.618330\pi$
$14$	0.191710	0.0512367
$15$	−1.12467	−0.290387
$16$	4.60616	1.15154
$17$	−0.276397	−0.0670361	−0.0335180	−	0.999438i	$-0.510671\pi$
$17$	−0.276397	−0.0670361	−0.0335180	+	0.999438i	$0.510671\pi$
$18$	6.39787	1.50799
$19$	−6.23326	−1.43001	−0.715003	−	0.699121i	$-0.753575\pi$
$19$	−6.23326	−1.43001	−0.715003	+	0.699121i	$0.753575\pi$
$20$	−7.20516	−1.61112
$21$	−0.0496707	−0.0108390
$22$	1.53800	0.327902
$23$	−1.37220	−0.286123	−0.143062	−	0.989714i	$-0.545695\pi$
$23$	−1.37220	−0.286123	−0.143062	+	0.989714i	$0.545695\pi$
$24$	−3.31766	−0.677214
$25$	−1.91076	−0.382153
$26$	6.46904	1.26868
$27$	−3.57728	−0.688447
$28$	−0.318215	−0.0601370
$29$	−1.18130	−0.219361	−0.109681	−	0.993967i	$-0.534983\pi$
$29$	−1.18130	−0.219361	−0.109681	+	0.993967i	$0.534983\pi$
$30$	2.77758	0.507114
$31$	0.419170	0.0752852	0.0376426	−	0.999291i	$-0.488015\pi$
$31$	0.419170	0.0752852	0.0376426	+	0.999291i	$0.488015\pi$
$32$	−1.00615	−0.177863
$33$	−0.398483	−0.0693670
$34$	0.682615	0.117068
$35$	0.136436	0.0230618
$36$	−10.6197	−1.76995
$37$	−9.00901	−1.48107	−0.740536	−	0.672017i	$-0.765428\pi$
$37$	−9.00901	−1.48107	−0.740536	+	0.672017i	$0.765428\pi$
$38$	15.3942	2.49727
$39$	−1.67608	−0.268388
$40$	9.11296	1.44089
$41$	6.47523	1.01126	0.505630	−	0.862750i	$-0.331260\pi$
$41$	6.47523	1.01126	0.505630	+	0.862750i	$0.331260\pi$
$42$	0.122671	0.0189286
$43$	3.50454	0.534438	0.267219	−	0.963636i	$-0.413895\pi$
$43$	3.50454	0.534438	0.267219	+	0.963636i	$0.413895\pi$
$44$	−2.55288	−0.384861
$45$	4.55322	0.678754
$46$	3.38891	0.499667
$47$	−0.474996	−0.0692853	−0.0346427	−	0.999400i	$-0.511029\pi$
$47$	−0.474996	−0.0692853	−0.0346427	+	0.999400i	$0.511029\pi$
$48$	2.94738	0.425418
$49$	−6.99397	−0.999139
$50$	4.71900	0.667367
$51$	−0.176860	−0.0247654
$52$	−10.7378	−1.48906
$53$	−3.44910	−0.473770	−0.236885	−	0.971538i	$-0.576127\pi$
$53$	−3.44910	−0.473770	−0.236885	+	0.971538i	$0.576127\pi$
$54$	8.83477	1.20226
$55$	1.09456	0.147590
$56$	0.402473	0.0537827
$57$	−3.98853	−0.528293
$58$	2.91744	0.383079
$59$	3.79175	0.493643	0.246822	−	0.969061i	$-0.420614\pi$
$59$	3.79175	0.493643	0.246822	+	0.969061i	$0.420614\pi$
$60$	−4.61043	−0.595204
$61$	−1.11631	−0.142929	−0.0714644	−	0.997443i	$-0.522767\pi$
$61$	−1.11631	−0.142929	−0.0714644	+	0.997443i	$0.522767\pi$
$62$	−1.03522	−0.131473
$63$	0.201092	0.0253352
$64$	−6.72744	−0.840930
$65$	4.60387	0.571039
$66$	0.984131	0.121138
$67$	−13.0788	−1.59783	−0.798917	−	0.601442i	$-0.794593\pi$
$67$	−13.0788	−1.59783	−0.798917	+	0.601442i	$0.794593\pi$
$68$	−1.13306	−0.137403
$69$	−0.878041	−0.105704
$70$	−0.336954	−0.0402737
$71$	−0.468661	−0.0556198	−0.0278099	−	0.999613i	$-0.508853\pi$
$71$	−0.468661	−0.0556198	−0.0278099	+	0.999613i	$0.508853\pi$
$72$	13.4316	1.58293
$73$	8.13902	0.952601	0.476300	−	0.879283i	$-0.341978\pi$
$73$	8.13902	0.952601	0.476300	+	0.879283i	$0.341978\pi$
$74$	22.2495	2.58645
$75$	−1.22266	−0.141180
$76$	−25.5525	−2.93107
$77$	0.0483409	0.00550896
$78$	4.13940	0.468695
$79$	6.79858	0.764900	0.382450	−	0.923976i	$-0.375080\pi$
$79$	6.79858	0.764900	0.382450	+	0.923976i	$0.375080\pi$
$80$	−8.09589	−0.905148
$81$	5.48264	0.609182
$82$	−15.9918	−1.76600
$83$	15.1662	1.66471	0.832355	−	0.554243i	$-0.186992\pi$
$83$	15.1662	1.66471	0.832355	+	0.554243i	$0.186992\pi$
$84$	−0.203619	−0.0222166
$85$	0.485801	0.0526925
$86$	−8.65515	−0.933308
$87$	−0.755887	−0.0810396
$88$	3.22884	0.344195
$89$	−8.61138	−0.912804	−0.456402	−	0.889774i	$-0.650862\pi$
$89$	−8.61138	−0.912804	−0.456402	+	0.889774i	$0.650862\pi$
$90$	−11.2450	−1.18533
$91$	0.203329	0.0213147
$92$	−5.62516	−0.586464
$93$	0.268218	0.0278129
$94$	1.17309	0.120995
$95$	10.9557	1.12403
$96$	−0.643812	−0.0657088
$97$	11.3026	1.14760	0.573802	−	0.818994i	$-0.305468\pi$
$97$	11.3026	1.14760	0.573802	+	0.818994i	$0.305468\pi$
$98$	17.2730	1.74483
$99$	1.61326	0.162139
$100$	−7.83295	−0.783295
$101$	5.36680	0.534017	0.267008	−	0.963694i	$-0.413965\pi$
$101$	5.36680	0.534017	0.267008	+	0.963694i	$0.413965\pi$
$102$	0.436791	0.0432487
$103$	−1.01634	−0.100143	−0.0500715	−	0.998746i	$-0.515945\pi$
$103$	−1.01634	−0.100143	−0.0500715	+	0.998746i	$0.515945\pi$
$104$	13.5810	1.33172
$105$	0.0873023	0.00851983
$106$	8.51821	0.827362
$107$	−10.2687	−0.992713	−0.496356	−	0.868119i	$-0.665329\pi$
$107$	−10.2687	−0.992713	−0.496356	+	0.868119i	$0.665329\pi$
$108$	−14.6646	−1.41110
$109$	−17.3745	−1.66418	−0.832088	−	0.554644i	$-0.812855\pi$
$109$	−17.3745	−1.66418	−0.832088	+	0.554644i	$0.812855\pi$
$110$	−2.70322	−0.257742
$111$	−5.76467	−0.547158
$112$	−0.357554	−0.0337856
$113$	−10.1745	−0.957134	−0.478567	−	0.878051i	$-0.658844\pi$
$113$	−10.1745	−0.957134	−0.478567	+	0.878051i	$0.658844\pi$
$114$	9.85044	0.922578
$115$	2.41181	0.224902
$116$	−4.84259	−0.449623
$117$	6.78563	0.627331
$118$	−9.36445	−0.862067
$119$	0.0214553	0.00196681
$120$	5.83119	0.532312
$121$	−10.6122	−0.964744
$122$	2.75694	0.249602
$123$	4.14336	0.373594
$124$	1.71834	0.154311
$125$	12.1465	1.08642
$126$	−0.496636	−0.0442438
$127$	11.3092	1.00353	0.501764	−	0.865005i	$-0.332685\pi$
$127$	11.3092	1.00353	0.501764	+	0.865005i	$0.332685\pi$
$128$	18.6270	1.64641
$129$	2.24248	0.197440
$130$	−11.3701	−0.997226
$131$	8.92797	0.780041	0.390020	−	0.920806i	$-0.372468\pi$
$131$	8.92797	0.780041	0.390020	+	0.920806i	$0.372468\pi$
$132$	−1.63353	−0.142181
$133$	0.483857	0.0419557
$134$	32.3007	2.79035
$135$	6.28750	0.541142
$136$	1.43307	0.122885
$137$	13.5105	1.15428	0.577141	−	0.816644i	$-0.304168\pi$
$137$	13.5105	1.15428	0.577141	+	0.816644i	$0.304168\pi$
$138$	2.16849	0.184594
$139$	3.35825	0.284843	0.142421	−	0.989806i	$-0.454511\pi$
$139$	3.35825	0.284843	0.142421	+	0.989806i	$0.454511\pi$
$140$	0.559302	0.0472696
$141$	−0.303940	−0.0255964
$142$	1.15745	0.0971308
$143$	1.63121	0.136409
$144$	−11.9325	−0.994376
$145$	2.07627	0.172425
$146$	−20.1009	−1.66356
$147$	−4.47530	−0.369116
$148$	−36.9313	−3.03574
$149$	19.6756	1.61189	0.805943	−	0.591993i	$-0.201659\pi$
$149$	19.6756	1.61189	0.805943	+	0.591993i	$0.201659\pi$
$150$	3.01959	0.246548
$151$	4.69726	0.382258	0.191129	−	0.981565i	$-0.438785\pi$
$151$	4.69726	0.382258	0.191129	+	0.981565i	$0.438785\pi$
$152$	32.3183	2.62136
$153$	0.716021	0.0578869
$154$	−0.119387	−0.00962049
$155$	−0.736743	−0.0591767
$156$	−6.87089	−0.550111
$157$	6.31085	0.503661	0.251831	−	0.967771i	$-0.418967\pi$
$157$	6.31085	0.503661	0.251831	+	0.967771i	$0.418967\pi$
$158$	−16.7904	−1.33577
$159$	−2.20701	−0.175027
$160$	1.76843	0.139806
$161$	0.106517	0.00839472
$162$	−13.5404	−1.06384
$163$	6.75346	0.528972	0.264486	−	0.964390i	$-0.414798\pi$
$163$	6.75346	0.528972	0.264486	+	0.964390i	$0.414798\pi$
$164$	26.5444	2.07277
$165$	0.700383	0.0545247
$166$	−37.4559	−2.90714
$167$	−6.35223	−0.491550	−0.245775	−	0.969327i	$-0.579042\pi$
$167$	−6.35223	−0.491550	−0.245775	+	0.969327i	$0.579042\pi$
$168$	0.257534	0.0198691
$169$	−6.13889	−0.472223
$170$	−1.19978	−0.0920189
$171$	16.1476	1.23484
$172$	14.3665	1.09543
$173$	8.61162	0.654730	0.327365	−	0.944898i	$-0.393839\pi$
$173$	8.61162	0.654730	0.327365	+	0.944898i	$0.393839\pi$
$174$	1.86681	0.141522
$175$	0.148323	0.0112122
$176$	−2.86848	−0.216220
$177$	2.42626	0.182369
$178$	21.2675	1.59406
$179$	15.9192	1.18985	0.594927	−	0.803780i	$-0.297181\pi$
$179$	15.9192	1.18985	0.594927	+	0.803780i	$0.297181\pi$
$180$	18.6654	1.39123
$181$	17.1541	1.27506	0.637528	−	0.770427i	$-0.279957\pi$
$181$	17.1541	1.27506	0.637528	+	0.770427i	$0.279957\pi$
$182$	−0.502160	−0.0372226
$183$	−0.714303	−0.0528028
$184$	7.11461	0.524496
$185$	15.8344	1.16417
$186$	−0.662417	−0.0485707
$187$	0.172126	0.0125871
$188$	−1.94719	−0.142013
$189$	0.277687	0.0201987
$190$	−27.0572	−1.96294
$191$	−23.4411	−1.69614	−0.848071	−	0.529883i	$-0.822236\pi$
$191$	−23.4411	−1.69614	−0.848071	+	0.529883i	$0.822236\pi$
$192$	−4.30475	−0.310668
$193$	−8.90737	−0.641166	−0.320583	−	0.947220i	$-0.603879\pi$
$193$	−8.90737	−0.641166	−0.320583	+	0.947220i	$0.603879\pi$
$194$	−27.9139	−2.00410
$195$	2.94592	0.210961
$196$	−28.6710	−2.04793
$197$	−16.5719	−1.18070	−0.590348	−	0.807149i	$-0.701010\pi$
$197$	−16.5719	−1.18070	−0.590348	+	0.807149i	$0.701010\pi$
$198$	−3.98426	−0.283149
$199$	−22.9296	−1.62544	−0.812720	−	0.582655i	$-0.802014\pi$
$199$	−22.9296	−1.62544	−0.812720	+	0.582655i	$0.802014\pi$
$200$	9.90697	0.700529
$201$	−8.36886	−0.590294
$202$	−13.2544	−0.932573
$203$	0.0916983	0.00643596
$204$	−0.725018	−0.0507614
$205$	−11.3810	−0.794884
$206$	2.51005	0.174883
$207$	3.55476	0.247073
$208$	−12.0652	−0.836574
$209$	3.88175	0.268506
$210$	−0.215610	−0.0148785
$211$	−25.5205	−1.75690	−0.878451	−	0.477833i	$-0.841422\pi$
$211$	−25.5205	−1.75690	−0.878451	+	0.477833i	$0.841422\pi$
$212$	−14.1392	−0.971082
$213$	−0.299886	−0.0205478
$214$	25.3605	1.73361
$215$	−6.15967	−0.420086
$216$	18.5476	1.26200
$217$	−0.0325382	−0.00220883
$218$	42.9097	2.90621
$219$	5.20799	0.351923
$220$	4.48700	0.302514
$221$	0.723986	0.0487005
$222$	14.2370	0.955522
$223$	−14.1307	−0.946261	−0.473130	−	0.880992i	$-0.656876\pi$
$223$	−14.1307	−0.946261	−0.473130	+	0.880992i	$0.656876\pi$
$224$	0.0781023	0.00521843
$225$	4.94994	0.329996
$226$	25.1278	1.67148
$227$	−20.0704	−1.33212	−0.666060	−	0.745898i	$-0.732020\pi$
$227$	−20.0704	−1.33212	−0.666060	+	0.745898i	$0.732020\pi$
$228$	−16.3505	−1.08284
$229$	8.76531	0.579228	0.289614	−	0.957143i	$-0.406473\pi$
$229$	8.76531	0.579228	0.289614	+	0.957143i	$0.406473\pi$
$230$	−5.95642	−0.392755
$231$	0.0309323	0.00203520
$232$	6.12482	0.402114
$233$	−13.5172	−0.885544	−0.442772	−	0.896634i	$-0.646005\pi$
$233$	−13.5172	−0.885544	−0.442772	+	0.896634i	$0.646005\pi$
$234$	−16.7584	−1.09553
$235$	0.834864	0.0544605
$236$	15.5438	1.01182
$237$	4.35027	0.282580
$238$	−0.0529881	−0.00343471
$239$	4.80739	0.310964	0.155482	−	0.987839i	$-0.450307\pi$
$239$	4.80739	0.310964	0.155482	+	0.987839i	$0.450307\pi$
$240$	−5.18039	−0.334392
$241$	−23.9040	−1.53979	−0.769895	−	0.638170i	$-0.779692\pi$
$241$	−23.9040	−1.53979	−0.769895	+	0.638170i	$0.779692\pi$
$242$	26.2088	1.68477
$243$	14.2401	0.913500
$244$	−4.57618	−0.292960
$245$	12.2928	0.785356
$246$	−10.2328	−0.652421
$247$	16.3272	1.03888
$248$	−2.17332	−0.138006
$249$	9.70455	0.615001
$250$	−29.9981	−1.89725
$251$	22.8838	1.44441	0.722205	−	0.691679i	$-0.243129\pi$
$251$	22.8838	1.44441	0.722205	+	0.691679i	$0.243129\pi$
$252$	0.824353	0.0519294
$253$	0.854534	0.0537241
$254$	−27.9302	−1.75250
$255$	0.310854	0.0194664
$256$	−32.5481	−2.03426
$257$	−22.6514	−1.41295	−0.706477	−	0.707736i	$-0.749717\pi$
$257$	−22.6514	−1.41295	−0.706477	+	0.707736i	$0.749717\pi$
$258$	−5.53824	−0.344796
$259$	0.699325	0.0434539
$260$	18.8730	1.17045
$261$	3.06022	0.189423
$262$	−22.0494	−1.36221
$263$	27.3715	1.68780	0.843900	−	0.536501i	$-0.180254\pi$
$263$	27.3715	1.68780	0.843900	+	0.536501i	$0.180254\pi$
$264$	2.06607	0.127158
$265$	6.06221	0.372399
$266$	−1.19498	−0.0732688
$267$	−5.51024	−0.337221
$268$	−53.6151	−3.27506
$269$	19.5875	1.19427	0.597136	−	0.802140i	$-0.296305\pi$
$269$	19.5875	1.19427	0.597136	+	0.802140i	$0.296305\pi$
$270$	−15.5282	−0.945016
$271$	−10.0696	−0.611687	−0.305844	−	0.952082i	$-0.598939\pi$
$271$	−10.0696	−0.611687	−0.305844	+	0.952082i	$0.598939\pi$
$272$	−1.27313	−0.0771947
$273$	0.130106	0.00787437
$274$	−33.3669	−2.01577
$275$	1.18992	0.0717552
$276$	−3.59942	−0.216660
$277$	30.5292	1.83432	0.917160	−	0.398520i	$-0.130476\pi$
$277$	30.5292	1.83432	0.917160	+	0.398520i	$0.130476\pi$
$278$	−8.29384	−0.497432
$279$	−1.08588	−0.0650102
$280$	−0.707395	−0.0422749
$281$	−16.3866	−0.977541	−0.488770	−	0.872412i	$-0.662554\pi$
$281$	−16.3866	−0.977541	−0.488770	+	0.872412i	$0.662554\pi$
$282$	0.750638	0.0446998
$283$	31.9209	1.89750	0.948750	−	0.316029i	$-0.102350\pi$
$283$	31.9209	1.89750	0.948750	+	0.316029i	$0.102350\pi$
$284$	−1.92122	−0.114003
$285$	7.01032	0.415256
$286$	−4.02858	−0.238215
$287$	−0.502640	−0.0296699
$288$	2.60648	0.153588
$289$	−16.9236	−0.995506
$290$	−5.12776	−0.301112
$291$	7.23228	0.423964
$292$	33.3649	1.95254
$293$	−2.56430	−0.149808	−0.0749041	−	0.997191i	$-0.523865\pi$
$293$	−2.56430	−0.149808	−0.0749041	+	0.997191i	$0.523865\pi$
$294$	11.0526	0.644601
$295$	−6.66446	−0.388020
$296$	46.7101	2.71497
$297$	2.22774	0.129267
$298$	−48.5926	−2.81490
$299$	3.59430	0.207864
$300$	−5.01214	−0.289376
$301$	−0.272041	−0.0156802
$302$	−11.6008	−0.667550
$303$	3.43410	0.197284
$304$	−28.7114	−1.64671
$305$	1.96205	0.112347
$306$	−1.76835	−0.101090
$307$	5.29605	0.302261	0.151131	−	0.988514i	$-0.451709\pi$
$307$	5.29605	0.302261	0.151131	+	0.988514i	$0.451709\pi$
$308$	0.198168	0.0112917
$309$	−0.650334	−0.0369962
$310$	1.81953	0.103342
$311$	28.2574	1.60233	0.801165	−	0.598444i	$-0.204214\pi$
$311$	28.2574	1.60233	0.801165	+	0.598444i	$0.204214\pi$
$312$	8.69018	0.491984
$313$	17.9679	1.01561	0.507804	−	0.861473i	$-0.330457\pi$
$313$	17.9679	1.01561	0.507804	+	0.861473i	$0.330457\pi$
$314$	−15.5859	−0.879561
$315$	−0.353444	−0.0199143
$316$	27.8700	1.56781
$317$	−4.80103	−0.269652	−0.134826	−	0.990869i	$-0.543048\pi$
$317$	−4.80103	−0.269652	−0.134826	+	0.990869i	$0.543048\pi$
$318$	5.45062	0.305656
$319$	0.735651	0.0411885
$320$	11.8243	0.660999
$321$	−6.57072	−0.366742
$322$	−0.263064	−0.0146600
$323$	1.72285	0.0958620
$324$	22.4754	1.24864
$325$	5.00500	0.277627
$326$	−16.6790	−0.923762
$327$	−11.1176	−0.614803
$328$	−33.5729	−1.85375
$329$	0.0368716	0.00203280
$330$	−1.72973	−0.0952185
$331$	20.4770	1.12552	0.562758	−	0.826622i	$-0.309740\pi$
$331$	20.4770	1.12552	0.562758	+	0.826622i	$0.309740\pi$
$332$	62.1721	3.41214
$333$	23.3383	1.27893
$334$	15.6880	0.858412
$335$	22.9876	1.25595
$336$	−0.228791	−0.0124816
$337$	0.331751	0.0180716	0.00903582	−	0.999959i	$-0.497124\pi$
$337$	0.331751	0.0180716	0.00903582	+	0.999959i	$0.497124\pi$
$338$	15.1612	0.824660
$339$	−6.51043	−0.353598
$340$	1.99148	0.108003
$341$	−0.261038	−0.0141360
$342$	−39.8796	−2.15644
$343$	1.08628	0.0586538
$344$	−18.1704	−0.979685
$345$	1.54326	0.0830865
$346$	−21.2681	−1.14338
$347$	10.1908	0.547069	0.273535	−	0.961862i	$-0.411807\pi$
$347$	10.1908	0.547069	0.273535	+	0.961862i	$0.411807\pi$
$348$	−3.09867	−0.166106
$349$	−27.5442	−1.47441	−0.737205	−	0.675670i	$-0.763855\pi$
$349$	−27.5442	−1.47441	−0.737205	+	0.675670i	$0.763855\pi$
$350$	−0.366313	−0.0195802
$351$	9.37022	0.500145
$352$	0.626576	0.0333966
$353$	−37.0364	−1.97125	−0.985623	−	0.168959i	$-0.945959\pi$
$353$	−37.0364	−1.97125	−0.985623	+	0.168959i	$0.945959\pi$
$354$	−5.99211	−0.318477
$355$	0.823728	0.0437190
$356$	−35.3013	−1.87097
$357$	0.0137288	0.000726606 0
$358$	−39.3154	−2.07788
$359$	−23.0040	−1.21410	−0.607052	−	0.794662i	$-0.707648\pi$
$359$	−23.0040	−1.21410	−0.607052	+	0.794662i	$0.707648\pi$
$360$	−23.6076	−1.24423
$361$	19.8535	1.04492
$362$	−42.3654	−2.22668
$363$	−6.79051	−0.356409
$364$	0.833523	0.0436885
$365$	−14.3053	−0.748775
$366$	1.76411	0.0922114
$367$	17.5877	0.918070	0.459035	−	0.888418i	$-0.348195\pi$
$367$	17.5877	0.918070	0.459035	+	0.888418i	$0.348195\pi$
$368$	−6.32056	−0.329482
$369$	−16.7744	−0.873242
$370$	−39.1062	−2.03303
$371$	0.267737	0.0139002
$372$	1.09953	0.0570079
$373$	0.537812	0.0278468	0.0139234	−	0.999903i	$-0.495568\pi$
$373$	0.537812	0.0278468	0.0139234	+	0.999903i	$0.495568\pi$
$374$	−0.425097	−0.0219813
$375$	7.77229	0.401360
$376$	2.46277	0.127008
$377$	3.09426	0.159362
$378$	−0.685800	−0.0352738
$379$	−23.8711	−1.22618	−0.613089	−	0.790014i	$-0.710073\pi$
$379$	−23.8711	−1.22618	−0.613089	+	0.790014i	$0.710073\pi$
$380$	44.9116	2.30392
$381$	7.23650	0.370737
$382$	57.8924	2.96203
$383$	0.749125	0.0382785	0.0191392	−	0.999817i	$-0.493907\pi$
$383$	0.749125	0.0382785	0.0191392	+	0.999817i	$0.493907\pi$
$384$	11.9190	0.608240
$385$	−0.0849650	−0.00433022
$386$	21.9985	1.11969
$387$	−9.07872	−0.461497
$388$	46.3336	2.35223
$389$	−30.6065	−1.55181	−0.775906	−	0.630849i	$-0.782707\pi$
$389$	−30.6065	−1.55181	−0.775906	+	0.630849i	$0.782707\pi$
$390$	−7.27550	−0.368409
$391$	0.379271	0.0191806
$392$	36.2625	1.83153
$393$	5.71282	0.288174
$394$	40.9274	2.06189
$395$	−11.9493	−0.601236
$396$	6.61338	0.332335
$397$	30.0655	1.50895	0.754473	−	0.656331i	$-0.227893\pi$
$397$	30.0655	1.50895	0.754473	+	0.656331i	$0.227893\pi$
$398$	56.6292	2.83856
$399$	0.309610	0.0154999
$400$	−8.80128	−0.440064
$401$	16.2471	0.811342	0.405671	−	0.914019i	$-0.367038\pi$
$401$	16.2471	0.811342	0.405671	+	0.914019i	$0.367038\pi$
$402$	20.6685	1.03085
$403$	−1.09796	−0.0546934
$404$	22.0006	1.09457
$405$	−9.63641	−0.478837
$406$	−0.226467	−0.0112394
$407$	5.61034	0.278094
$408$	0.916990	0.0453978
$409$	12.9372	0.639702	0.319851	−	0.947468i	$-0.396367\pi$
$409$	12.9372	0.639702	0.319851	+	0.947468i	$0.396367\pi$
$410$	28.1076	1.38813
$411$	8.64510	0.426432
$412$	−4.16636	−0.205262
$413$	−0.294335	−0.0144833
$414$	−8.77915	−0.431472
$415$	−26.6565	−1.30852
$416$	2.63547	0.129215
$417$	2.14887	0.105231
$418$	−9.58673	−0.468902
$419$	38.5722	1.88438	0.942189	−	0.335082i	$-0.108764\pi$
$419$	38.5722	1.88438	0.942189	+	0.335082i	$0.108764\pi$
$420$	0.357885	0.0174630
$421$	22.7141	1.10702	0.553508	−	0.832844i	$-0.313289\pi$
$421$	22.7141	1.10702	0.553508	+	0.832844i	$0.313289\pi$
$422$	63.0277	3.06814
$423$	1.23050	0.0598291
$424$	17.8830	0.868474
$425$	0.528129	0.0256180
$426$	0.740626	0.0358834
$427$	0.0866537	0.00419347
$428$	−42.0953	−2.03475
$429$	1.04378	0.0503940
$430$	15.2125	0.733611
$431$	12.4009	0.597329	0.298664	−	0.954358i	$-0.403459\pi$
$431$	12.4009	0.597329	0.298664	+	0.954358i	$0.403459\pi$
$432$	−16.4775	−0.792774
$433$	29.2259	1.40451	0.702255	−	0.711926i	$-0.252177\pi$
$433$	29.2259	1.40451	0.702255	+	0.711926i	$0.252177\pi$
$434$	0.0803592	0.00385737
$435$	1.32856	0.0636997
$436$	−71.2247	−3.41104
$437$	8.55326	0.409158
$438$	−12.8621	−0.614576
$439$	−5.71773	−0.272892	−0.136446	−	0.990647i	$-0.543568\pi$
$439$	−5.71773	−0.272892	−0.136446	+	0.990647i	$0.543568\pi$
$440$	−5.67508	−0.270549
$441$	18.1183	0.862775
$442$	−1.78802	−0.0850475
$443$	21.7892	1.03523	0.517617	−	0.855612i	$-0.326819\pi$
$443$	21.7892	1.03523	0.517617	+	0.855612i	$0.326819\pi$
$444$	−23.6316	−1.12151
$445$	15.1356	0.717494
$446$	34.8985	1.65249
$447$	12.5900	0.595486
$448$	0.522219	0.0246725
$449$	12.7188	0.600238	0.300119	−	0.953902i	$-0.402974\pi$
$449$	12.7188	0.600238	0.300119	+	0.953902i	$0.402974\pi$
$450$	−12.2248	−0.576284
$451$	−4.03244	−0.189880
$452$	−41.7091	−1.96183
$453$	3.00568	0.141219
$454$	49.5677	2.32633
$455$	−0.357376	−0.0167540
$456$	20.6798	0.968421
$457$	−15.7316	−0.735894	−0.367947	−	0.929847i	$-0.619939\pi$
$457$	−15.7316	−0.735894	−0.367947	+	0.929847i	$0.619939\pi$
$458$	−21.6476	−1.01153
$459$	0.988748	0.0461508
$460$	9.88691	0.460980
$461$	−5.35434	−0.249376	−0.124688	−	0.992196i	$-0.539793\pi$
$461$	−5.35434	−0.249376	−0.124688	+	0.992196i	$0.539793\pi$
$462$	−0.0763933	−0.00355414
$463$	−0.396006	−0.0184040	−0.00920199	−	0.999958i	$-0.502929\pi$
$463$	−0.396006	−0.0184040	−0.00920199	+	0.999958i	$0.502929\pi$
$464$	−5.44124	−0.252603
$465$	−0.471426	−0.0218619
$466$	33.3834	1.54646
$467$	39.0548	1.80724	0.903620	−	0.428336i	$-0.140900\pi$
$467$	39.0548	1.80724	0.903620	+	0.428336i	$0.140900\pi$
$468$	27.8169	1.28583
$469$	1.01525	0.0468797
$470$	−2.06186	−0.0951064
$471$	4.03818	0.186070
$472$	−19.6595	−0.904904
$473$	−2.18245	−0.100349
$474$	−10.7438	−0.493480
$475$	11.9103	0.546481
$476$	0.0879536	0.00403134
$477$	8.93508	0.409109
$478$	−11.8728	−0.543048
$479$	−8.11202	−0.370648	−0.185324	−	0.982677i	$-0.559333\pi$
$479$	−8.11202	−0.370648	−0.185324	+	0.982677i	$0.559333\pi$
$480$	1.13158	0.0516492
$481$	23.5979	1.07597
$482$	59.0355	2.68899
$483$	0.0681580	0.00310130
$484$	−43.5034	−1.97743
$485$	−19.8657	−0.902054
$486$	−35.1686	−1.59528
$487$	28.2477	1.28003	0.640013	−	0.768364i	$-0.278929\pi$
$487$	28.2477	1.28003	0.640013	+	0.768364i	$0.278929\pi$
$488$	5.78787	0.262005
$489$	4.32139	0.195420
$490$	−30.3593	−1.37150
$491$	−5.36976	−0.242334	−0.121167	−	0.992632i	$-0.538664\pi$
$491$	−5.36976	−0.242334	−0.121167	+	0.992632i	$0.538664\pi$
$492$	16.9852	0.765752
$493$	0.326507	0.0147051
$494$	−40.3232	−1.81423
$495$	−2.83551	−0.127447
$496$	1.93077	0.0866939
$497$	0.0363798	0.00163186
$498$	−23.9672	−1.07400
$499$	−0.247100	−0.0110617	−0.00553086	−	0.999985i	$-0.501761\pi$
$499$	−0.247100	−0.0110617	−0.00553086	+	0.999985i	$0.501761\pi$
$500$	49.7932	2.22682
$501$	−4.06465	−0.181595
$502$	−56.5159	−2.52243
$503$	−19.1889	−0.855589	−0.427794	−	0.903876i	$-0.640709\pi$
$503$	−19.1889	−0.855589	−0.427794	+	0.903876i	$0.640709\pi$
$504$	−1.04263	−0.0464423
$505$	−9.43281	−0.419755
$506$	−2.11044	−0.0938203
$507$	−3.92815	−0.174455
$508$	46.3606	2.05692
$509$	28.5030	1.26337	0.631687	−	0.775224i	$-0.282363\pi$
$509$	28.5030	1.26337	0.631687	+	0.775224i	$0.282363\pi$
$510$	−0.767713	−0.0339949
$511$	−0.631793	−0.0279489
$512$	43.1298	1.90608
$513$	22.2981	0.984484
$514$	55.9419	2.46749
$515$	1.78634	0.0787156
$516$	9.19279	0.404690
$517$	0.295803	0.0130094
$518$	−1.72712	−0.0758852
$519$	5.51039	0.241879
$520$	−23.8702	−1.04678
$521$	40.7952	1.78727	0.893634	−	0.448796i	$-0.148147\pi$
$521$	40.7952	1.78727	0.893634	+	0.448796i	$0.148147\pi$
$522$	−7.55779	−0.330796
$523$	22.2202	0.971620	0.485810	−	0.874064i	$-0.338525\pi$
$523$	22.2202	0.971620	0.485810	+	0.874064i	$0.338525\pi$
$524$	36.5992	1.59884
$525$	0.0949089	0.00414216
$526$	−67.5992	−2.94747
$527$	−0.115857	−0.00504683
$528$	−1.83548	−0.0798789
$529$	−21.1171	−0.918134
$530$	−14.9718	−0.650334
$531$	−9.82273	−0.426270
$532$	1.98351	0.0859963
$533$	−16.9610	−0.734663
$534$	13.6086	0.588901
$535$	18.0485	0.780305
$536$	67.8114	2.92901
$537$	10.1863	0.439573
$538$	−48.3751	−2.08560
$539$	4.35548	0.187604
$540$	25.7749	1.10917
$541$	−39.4200	−1.69480	−0.847399	−	0.530957i	$-0.821832\pi$
$541$	−39.4200	−1.69480	−0.847399	+	0.530957i	$0.821832\pi$
$542$	24.8689	1.06821
$543$	10.9766	0.471049
$544$	0.278096	0.0119233
$545$	30.5378	1.30810
$546$	−0.321322	−0.0137513
$547$	−28.0759	−1.20044	−0.600218	−	0.799836i	$-0.704920\pi$
$547$	−28.0759	−1.20044	−0.600218	+	0.799836i	$0.704920\pi$
$548$	55.3848	2.36592
$549$	2.89186	0.123422
$550$	−2.93875	−0.125309
$551$	7.36333	0.313688
$552$	4.55249	0.193767
$553$	−0.527741	−0.0224418
$554$	−75.3976	−3.20334
$555$	10.1321	0.430084
$556$	13.7667	0.583840
$557$	7.46987	0.316508	0.158254	−	0.987398i	$-0.449413\pi$
$557$	7.46987	0.316508	0.158254	+	0.987398i	$0.449413\pi$
$558$	2.68180	0.113530
$559$	−9.17970	−0.388260
$560$	0.628444	0.0265566
$561$	0.110139	0.00465009
$562$	40.4698	1.70712
$563$	8.17106	0.344369	0.172184	−	0.985065i	$-0.444917\pi$
$563$	8.17106	0.344369	0.172184	+	0.985065i	$0.444917\pi$
$564$	−1.24597	−0.0524646
$565$	17.8829	0.752339
$566$	−78.8348	−3.31367
$567$	−0.425591	−0.0178731
$568$	2.42992	0.101957
$569$	−24.5159	−1.02776	−0.513879	−	0.857862i	$-0.671792\pi$
$569$	−24.5159	−1.02776	−0.513879	+	0.857862i	$0.671792\pi$
$570$	−17.3133	−0.725176
$571$	0.765742	0.0320453	0.0160227	−	0.999872i	$-0.494900\pi$
$571$	0.765742	0.0320453	0.0160227	+	0.999872i	$0.494900\pi$
$572$	6.68694	0.279595
$573$	−14.9995	−0.626613
$574$	1.24137	0.0518136
$575$	2.62195	0.109343
$576$	17.4278	0.726159
$577$	30.7583	1.28049	0.640243	−	0.768172i	$-0.278834\pi$
$577$	30.7583	1.28049	0.640243	+	0.768172i	$0.278834\pi$
$578$	41.7961	1.73849
$579$	−5.69964	−0.236869
$580$	8.51144	0.353418
$581$	−1.17728	−0.0488418
$582$	−17.8615	−0.740383
$583$	2.14792	0.0889578
$584$	−42.1994	−1.74622
$585$	−11.9266	−0.493103
$586$	6.33304	0.261615
$587$	−18.1973	−0.751083	−0.375541	−	0.926806i	$-0.622543\pi$
$587$	−18.1973	−0.751083	−0.375541	+	0.926806i	$0.622543\pi$
$588$	−18.3459	−0.756574
$589$	−2.61280	−0.107658
$590$	16.4592	0.677613
$591$	−10.6040	−0.436190
$592$	−41.4969	−1.70551
$593$	−27.7814	−1.14084	−0.570422	−	0.821352i	$-0.693220\pi$
$593$	−27.7814	−1.14084	−0.570422	+	0.821352i	$0.693220\pi$
$594$	−5.50184	−0.225743
$595$	−0.0377104	−0.00154597
$596$	80.6577	3.30387
$597$	−14.6722	−0.600493
$598$	−8.87681	−0.363000
$599$	8.64097	0.353060	0.176530	−	0.984295i	$-0.443513\pi$
$599$	8.64097	0.353060	0.176530	+	0.984295i	$0.443513\pi$
$600$	6.33926	0.258799
$601$	5.81863	0.237347	0.118673	−	0.992933i	$-0.462136\pi$
$601$	5.81863	0.237347	0.118673	+	0.992933i	$0.462136\pi$
$602$	0.671857	0.0273828
$603$	33.8814	1.37976
$604$	19.2559	0.783510
$605$	18.6522	0.758320
$606$	−8.48118	−0.344524
$607$	37.7277	1.53132	0.765660	−	0.643246i	$-0.222413\pi$
$607$	37.7277	1.53132	0.765660	+	0.643246i	$0.222413\pi$
$608$	6.27157	0.254346
$609$	0.0586758	0.00237766
$610$	−4.84566	−0.196195
$611$	1.24419	0.0503346
$612$	2.93524	0.118650
$613$	32.7466	1.32262	0.661311	−	0.750112i	$-0.270001\pi$
$613$	32.7466	1.32262	0.661311	+	0.750112i	$0.270001\pi$
$614$	−13.0796	−0.527850
$615$	−7.28246	−0.293657
$616$	−0.250639	−0.0100985
$617$	4.70353	0.189357	0.0946784	−	0.995508i	$-0.469818\pi$
$617$	4.70353	0.189357	0.0946784	+	0.995508i	$0.469818\pi$
$618$	1.60613	0.0646079
$619$	−14.1488	−0.568687	−0.284344	−	0.958722i	$-0.591776\pi$
$619$	−14.1488	−0.568687	−0.284344	+	0.958722i	$0.591776\pi$
$620$	−3.02019	−0.121294
$621$	4.90873	0.196981
$622$	−69.7871	−2.79821
$623$	0.668459	0.0267813
$624$	−7.72029	−0.309059
$625$	−11.7952	−0.471806
$626$	−44.3753	−1.77359
$627$	2.48385	0.0991953
$628$	25.8706	1.03235
$629$	2.49006	0.0992852
$630$	0.872898	0.0347771
$631$	27.8998	1.11068	0.555338	−	0.831625i	$-0.312589\pi$
$631$	27.8998	1.11068	0.555338	+	0.831625i	$0.312589\pi$
$632$	−35.2494	−1.40215
$633$	−16.3300	−0.649059
$634$	11.8571	0.470904
$635$	−19.8773	−0.788805
$636$	−9.04735	−0.358751
$637$	18.3198	0.725857
$638$	−1.81683	−0.0719290
$639$	1.21409	0.0480287
$640$	−32.7392	−1.29413
$641$	31.6041	1.24829	0.624144	−	0.781309i	$-0.285448\pi$
$641$	31.6041	1.24829	0.624144	+	0.781309i	$0.285448\pi$
$642$	16.2277	0.640455
$643$	−3.52386	−0.138967	−0.0694837	−	0.997583i	$-0.522135\pi$
$643$	−3.52386	−0.138967	−0.0694837	+	0.997583i	$0.522135\pi$
$644$	0.436654	0.0172066
$645$	−3.94144	−0.155194
$646$	−4.25491	−0.167407
$647$	−4.82955	−0.189869	−0.0949346	−	0.995484i	$-0.530264\pi$
$647$	−4.82955	−0.189869	−0.0949346	+	0.995484i	$0.530264\pi$
$648$	−28.4265	−1.11670
$649$	−2.36130	−0.0926893
$650$	−12.3608	−0.484831
$651$	−0.0208205	−0.000816019 0
$652$	27.6850	1.08423
$653$	29.6467	1.16016	0.580082	−	0.814558i	$-0.303020\pi$
$653$	29.6467	1.16016	0.580082	+	0.814558i	$0.303020\pi$
$654$	27.4570	1.07365
$655$	−15.6920	−0.613137
$656$	29.8259	1.16451
$657$	−21.0846	−0.822588
$658$	−0.0910616	−0.00354995
$659$	39.9981	1.55810	0.779052	−	0.626959i	$-0.215701\pi$
$659$	39.9981	1.55810	0.779052	+	0.626959i	$0.215701\pi$
$660$	2.87114	0.111759
$661$	−15.1275	−0.588392	−0.294196	−	0.955745i	$-0.595052\pi$
$661$	−15.1275	−0.588392	−0.294196	+	0.955745i	$0.595052\pi$
$662$	−50.5718	−1.96553
$663$	0.463263	0.0179916
$664$	−78.6342	−3.05160
$665$	−0.850438	−0.0329786
$666$	−57.6385	−2.23345
$667$	1.62097	0.0627644
$668$	−26.0402	−1.00753
$669$	−9.04193	−0.349581
$670$	−56.7724	−2.19331
$671$	0.695180	0.0268371
$672$	0.0499760	0.00192787
$673$	−4.50642	−0.173710	−0.0868550	−	0.996221i	$-0.527682\pi$
$673$	−4.50642	−0.173710	−0.0868550	+	0.996221i	$0.527682\pi$
$674$	−0.819323	−0.0315591
$675$	6.83533	0.263092
$676$	−25.1657	−0.967910
$677$	0.251554	0.00966799	0.00483400	−	0.999988i	$-0.498461\pi$
$677$	0.251554	0.00966799	0.00483400	+	0.999988i	$0.498461\pi$
$678$	16.0788	0.617501
$679$	−0.877364	−0.0336701
$680$	−2.51879	−0.0965913
$681$	−12.8426	−0.492130
$682$	0.644683	0.0246862
$683$	−19.7567	−0.755969	−0.377984	−	0.925812i	$-0.623383\pi$
$683$	−19.7567	−0.755969	−0.377984	+	0.925812i	$0.623383\pi$
$684$	66.1951	2.53103
$685$	−23.7464	−0.907304
$686$	−2.68279	−0.102429
$687$	5.60874	0.213987
$688$	16.1425	0.615427
$689$	9.03447	0.344186
$690$	−3.81139	−0.145097
$691$	38.9366	1.48122	0.740609	−	0.671936i	$-0.234537\pi$
$691$	38.9366	1.48122	0.740609	+	0.671936i	$0.234537\pi$
$692$	35.3023	1.34199
$693$	−0.125230	−0.00475709
$694$	−25.1681	−0.955367
$695$	−5.90253	−0.223896
$696$	3.91914	0.148555
$697$	−1.78973	−0.0677909
$698$	68.0258	2.57481
$699$	−8.64939	−0.327150
$700$	0.608033	0.0229815
$701$	−7.69697	−0.290710	−0.145355	−	0.989380i	$-0.546432\pi$
$701$	−7.69697	−0.290710	−0.145355	+	0.989380i	$0.546432\pi$
$702$	−23.1416	−0.873422
$703$	56.1554	2.11794
$704$	4.18950	0.157898
$705$	0.534212	0.0201196
$706$	91.4684	3.44246
$707$	−0.416599	−0.0156678
$708$	9.94615	0.373799
$709$	−48.2786	−1.81314	−0.906571	−	0.422053i	$-0.861310\pi$
$709$	−48.2786	−1.81314	−0.906571	+	0.422053i	$0.861310\pi$
$710$	−2.03436	−0.0763480
$711$	−17.6121	−0.660505
$712$	44.6485	1.67327
$713$	−0.575185	−0.0215409
$714$	−0.0339059	−0.00126890
$715$	−2.86705	−0.107222
$716$	65.2587	2.43883
$717$	3.07615	0.114881
$718$	56.8128	2.12024
$719$	−27.2538	−1.01639	−0.508197	−	0.861241i	$-0.669688\pi$
$719$	−27.2538	−1.01639	−0.508197	+	0.861241i	$0.669688\pi$
$720$	20.9728	0.781612
$721$	0.0788935	0.00293815
$722$	−49.0320	−1.82478
$723$	−15.2956	−0.568851
$724$	70.3212	2.61347
$725$	2.25718	0.0838296
$726$	16.7705	0.622411
$727$	19.3640	0.718169	0.359085	−	0.933305i	$-0.383089\pi$
$727$	19.3640	0.718169	0.359085	+	0.933305i	$0.383089\pi$
$728$	−1.05422	−0.0390722
$729$	−7.33602	−0.271704
$730$	35.3298	1.30761
$731$	−0.968645	−0.0358266
$732$	−2.92820	−0.108229
$733$	−32.4867	−1.19992	−0.599962	−	0.800029i	$-0.704817\pi$
$733$	−32.4867	−1.19992	−0.599962	+	0.800029i	$0.704817\pi$
$734$	−43.4362	−1.60326
$735$	7.86588	0.290137
$736$	1.38063	0.0508908
$737$	8.14482	0.300018
$738$	41.4277	1.52497
$739$	41.9311	1.54246	0.771230	−	0.636557i	$-0.219642\pi$
$739$	41.9311	1.54246	0.771230	+	0.636557i	$0.219642\pi$
$740$	64.9113	2.38619
$741$	10.4474	0.383796
$742$	−0.661227	−0.0242744
$743$	19.5219	0.716189	0.358095	−	0.933685i	$-0.383427\pi$
$743$	19.5219	0.716189	0.358095	+	0.933685i	$0.383427\pi$
$744$	−1.39066	−0.0509842
$745$	−34.5822	−1.26700
$746$	−1.32823	−0.0486300
$747$	−39.2890	−1.43751
$748$	0.705608	0.0257996
$749$	0.797109	0.0291257
$750$	−19.1952	−0.700909
$751$	−29.2466	−1.06722	−0.533612	−	0.845729i	$-0.679166\pi$
$751$	−29.2466	−1.06722	−0.533612	+	0.845729i	$0.679166\pi$
$752$	−2.18791	−0.0797848
$753$	14.6428	0.533614
$754$	−7.64186	−0.278300
$755$	−8.25601	−0.300467
$756$	1.13834	0.0414011
$757$	−5.96924	−0.216956	−0.108478	−	0.994099i	$-0.534598\pi$
$757$	−5.96924	−0.216956	−0.108478	+	0.994099i	$0.534598\pi$
$758$	58.9544	2.14132
$759$	0.546798	0.0198475
$760$	−56.8034	−2.06048
$761$	−51.0740	−1.85143	−0.925716	−	0.378218i	$-0.876537\pi$
$761$	−51.0740	−1.85143	−0.925716	+	0.378218i	$0.876537\pi$
$762$	−17.8719	−0.647432
$763$	1.34870	0.0488261
$764$	−96.0942	−3.47656
$765$	−1.25849	−0.0455010
$766$	−1.85011	−0.0668471
$767$	−9.93199	−0.358623
$768$	−20.8268	−0.751524
$769$	−6.24105	−0.225058	−0.112529	−	0.993648i	$-0.535895\pi$
$769$	−6.24105	−0.225058	−0.112529	+	0.993648i	$0.535895\pi$
$770$	0.209838	0.00756202
$771$	−14.4941	−0.521993
$772$	−36.5147	−1.31419
$773$	−12.3269	−0.443369	−0.221684	−	0.975118i	$-0.571155\pi$
$773$	−12.3269	−0.443369	−0.221684	+	0.975118i	$0.571155\pi$
$774$	22.4216	0.805929
$775$	−0.800936	−0.0287705
$776$	−58.6019	−2.10369
$777$	0.447483	0.0160534
$778$	75.5887	2.70999
$779$	−40.3617	−1.44611
$780$	12.0764	0.432405
$781$	0.291858	0.0104435
$782$	−0.936683	−0.0334957
$783$	4.22583	0.151019
$784$	−32.2154	−1.15055
$785$	−11.0921	−0.395894
$786$	−14.1089	−0.503248
$787$	−8.75601	−0.312118	−0.156059	−	0.987748i	$-0.549879\pi$
$787$	−8.75601	−0.312118	−0.156059	+	0.987748i	$0.549879\pi$
$788$	−67.9344	−2.42006
$789$	17.5144	0.623531
$790$	29.5112	1.04996
$791$	0.789795	0.0280819
$792$	−8.36449	−0.297219
$793$	2.92403	0.103835
$794$	−74.2526	−2.63513
$795$	3.87908	0.137577
$796$	−93.9973	−3.33165
$797$	26.6158	0.942781	0.471390	−	0.881925i	$-0.343752\pi$
$797$	26.6158	0.942781	0.471390	+	0.881925i	$0.343752\pi$
$798$	−0.764641	−0.0270680
$799$	0.131287	0.00464461
$800$	1.92251	0.0679710
$801$	22.3083	0.788223
$802$	−40.1254	−1.41688
$803$	−5.06856	−0.178866
$804$	−34.3072	−1.20992
$805$	−0.187217	−0.00659852
$806$	2.71163	0.0955131
$807$	12.5336	0.441205
$808$	−27.8259	−0.978913
$809$	21.1454	0.743433	0.371717	−	0.928346i	$-0.378769\pi$
$809$	21.1454	0.743433	0.371717	+	0.928346i	$0.378769\pi$
$810$	23.7990	0.836211
$811$	−56.2823	−1.97634	−0.988169	−	0.153372i	$-0.950987\pi$
$811$	−56.2823	−1.97634	−0.988169	+	0.153372i	$0.950987\pi$
$812$	0.375906	0.0131917
$813$	−6.44335	−0.225978
$814$	−13.8558	−0.485646
$815$	−11.8700	−0.415789
$816$	−0.814647	−0.0285183
$817$	−21.8447	−0.764250
$818$	−31.9508	−1.11713
$819$	−0.526735	−0.0184056
$820$	−46.6551	−1.62927
$821$	7.43052	0.259327	0.129663	−	0.991558i	$-0.458610\pi$
$821$	7.43052	0.259327	0.129663	+	0.991558i	$0.458610\pi$
$822$	−21.3507	−0.744693
$823$	51.3661	1.79051	0.895255	−	0.445553i	$-0.146993\pi$
$823$	51.3661	1.79051	0.895255	+	0.445553i	$0.146993\pi$
$824$	5.26954	0.183573
$825$	0.761407	0.0265088
$826$	0.726916	0.0252927
$827$	1.33372	0.0463779	0.0231890	−	0.999731i	$-0.492618\pi$
$827$	1.33372	0.0463779	0.0231890	+	0.999731i	$0.492618\pi$
$828$	14.5723	0.506422
$829$	43.1032	1.49704	0.748519	−	0.663114i	$-0.230765\pi$
$829$	43.1032	1.49704	0.748519	+	0.663114i	$0.230765\pi$
$830$	65.8334	2.28511
$831$	19.5350	0.677660
$832$	17.6217	0.610922
$833$	1.93311	0.0669784
$834$	−5.30705	−0.183768
$835$	11.1648	0.386374
$836$	15.9128	0.550354
$837$	−1.49949	−0.0518299
$838$	−95.2616	−3.29076
$839$	−16.4811	−0.568990	−0.284495	−	0.958677i	$-0.591826\pi$
$839$	−16.4811	−0.568990	−0.284495	+	0.958677i	$0.591826\pi$
$840$	−0.452647	−0.0156178
$841$	−27.6045	−0.951881
$842$	−56.0968	−1.93322
$843$	−10.4854	−0.361137
$844$	−104.618	−3.60110
$845$	10.7899	0.371182
$846$	−3.03897	−0.104482
$847$	0.823772	0.0283051
$848$	−15.8871	−0.545565
$849$	20.4255	0.701001
$850$	−1.30432	−0.0447377
$851$	12.3621	0.423769
$852$	−1.22935	−0.0421167
$853$	−32.0353	−1.09687	−0.548434	−	0.836194i	$-0.684776\pi$
$853$	−32.0353	−1.09687	−0.548434	+	0.836194i	$0.684776\pi$
$854$	−0.214008	−0.00732320
$855$	−28.3814	−0.970622
$856$	53.2414	1.81975
$857$	53.7988	1.83773	0.918867	−	0.394568i	$-0.129106\pi$
$857$	53.7988	1.83773	0.918867	+	0.394568i	$0.129106\pi$
$858$	−2.57780	−0.0880048
$859$	−36.2488	−1.23679	−0.618396	−	0.785866i	$-0.712217\pi$
$859$	−36.2488	−1.23679	−0.618396	+	0.785866i	$0.712217\pi$
$860$	−25.2508	−0.861045
$861$	−0.321629	−0.0109611
$862$	−30.6263	−1.04314
$863$	23.8972	0.813472	0.406736	−	0.913546i	$-0.366667\pi$
$863$	23.8972	0.813472	0.406736	+	0.913546i	$0.366667\pi$
$864$	3.59927	0.122450
$865$	−15.1360	−0.514639
$866$	−72.1791	−2.45275
$867$	−10.8291	−0.367774
$868$	−0.133386	−0.00452743
$869$	−4.23380	−0.143622
$870$	−3.28114	−0.111241
$871$	34.2583	1.16080
$872$	90.0837	3.05062
$873$	−29.2800	−0.990977
$874$	−21.1239	−0.714528
$875$	−0.942874	−0.0318750
$876$	21.3495	0.721333
$877$	−12.9459	−0.437153	−0.218576	−	0.975820i	$-0.570141\pi$
$877$	−12.9459	−0.437153	−0.218576	+	0.975820i	$0.570141\pi$
$878$	14.1210	0.476562
$879$	−1.64084	−0.0553443
$880$	5.04170	0.169956
$881$	−16.4095	−0.552851	−0.276426	−	0.961035i	$-0.589150\pi$
$881$	−16.4095	−0.552851	−0.276426	+	0.961035i	$0.589150\pi$
$882$	−44.7466	−1.50670
$883$	34.4101	1.15799	0.578995	−	0.815331i	$-0.303445\pi$
$883$	34.4101	1.15799	0.578995	+	0.815331i	$0.303445\pi$
$884$	2.96789	0.0998210
$885$	−4.26444	−0.143348
$886$	−53.8125	−1.80787
$887$	−14.4982	−0.486801	−0.243401	−	0.969926i	$-0.578263\pi$
$887$	−14.4982	−0.486801	−0.243401	+	0.969926i	$0.578263\pi$
$888$	29.8888	1.00300
$889$	−0.877876	−0.0294430
$890$	−37.3802	−1.25299
$891$	−3.41431	−0.114384
$892$	−57.9271	−1.93954
$893$	2.96077	0.0990785
$894$	−31.0934	−1.03992
$895$	−27.9799	−0.935264
$896$	−1.44592	−0.0483049
$897$	2.29991	0.0767919
$898$	−31.4115	−1.04822
$899$	−0.495165	−0.0165147
$900$	20.2917	0.676389
$901$	0.953320	0.0317597
$902$	9.95888	0.331594
$903$	−0.174073	−0.00579279
$904$	52.7529	1.75453
$905$	−30.1505	−1.00224
$906$	−7.42310	−0.246616
$907$	−1.14545	−0.0380340	−0.0190170	−	0.999819i	$-0.506054\pi$
$907$	−1.14545	−0.0380340	−0.0190170	+	0.999819i	$0.506054\pi$
$908$	−82.2762	−2.73043
$909$	−13.9030	−0.461133
$910$	0.882608	0.0292582
$911$	−42.1429	−1.39626	−0.698128	−	0.715973i	$-0.745983\pi$
$911$	−42.1429	−1.39626	−0.698128	+	0.715973i	$0.745983\pi$
$912$	−18.3718	−0.608351
$913$	−9.44474	−0.312575
$914$	38.8523	1.28512
$915$	1.25547	0.0415047
$916$	35.9324	1.18724
$917$	−0.693035	−0.0228860
$918$	−2.44190	−0.0805948
$919$	−6.72125	−0.221714	−0.110857	−	0.993836i	$-0.535359\pi$
$919$	−6.72125	−0.221714	−0.110857	+	0.993836i	$0.535359\pi$
$920$	−12.5048	−0.412271
$921$	3.38883	0.111666
$922$	13.2236	0.435495
$923$	1.22760	0.0404068
$924$	0.126803	0.00417152
$925$	17.2141	0.565996
$926$	0.978014	0.0321395
$927$	2.63289	0.0864753
$928$	1.18856	0.0390163
$929$	−55.5226	−1.82164	−0.910818	−	0.412808i	$-0.864548\pi$
$929$	−55.5226	−1.82164	−0.910818	+	0.412808i	$0.864548\pi$
$930$	1.16428	0.0381782
$931$	43.5952	1.42878
$932$	−55.4123	−1.81509
$933$	18.0813	0.591955
$934$	−96.4533	−3.15605
$935$	−0.302532	−0.00989385
$936$	−35.1823	−1.14997
$937$	1.39422	0.0455471	0.0227735	−	0.999741i	$-0.492750\pi$
$937$	1.39422	0.0455471	0.0227735	+	0.999741i	$0.492750\pi$
$938$	−2.50734	−0.0818677
$939$	11.4973	0.375200
$940$	3.42242	0.111627
$941$	−10.6883	−0.348428	−0.174214	−	0.984708i	$-0.555739\pi$
$941$	−10.6883	−0.348428	−0.174214	+	0.984708i	$0.555739\pi$
$942$	−9.97307	−0.324940
$943$	−8.88530	−0.289345
$944$	17.4654	0.568450
$945$	−0.488068	−0.0158769
$946$	5.38998	0.175243
$947$	−15.8304	−0.514418	−0.257209	−	0.966356i	$-0.582803\pi$
$947$	−15.8304	−0.514418	−0.257209	+	0.966356i	$0.582803\pi$
$948$	17.8334	0.579202
$949$	−21.3191	−0.692048
$950$	−29.4147	−0.954340
$951$	−3.07207	−0.0996188
$952$	−0.111242	−0.00360538
$953$	−30.8070	−0.997937	−0.498968	−	0.866620i	$-0.666288\pi$
$953$	−30.8070	−0.997937	−0.498968	+	0.866620i	$0.666288\pi$
$954$	−22.0669	−0.714442
$955$	41.2007	1.33322
$956$	19.7073	0.637380
$957$	0.470727	0.0152164
$958$	20.0342	0.647276
$959$	−1.04876	−0.0338661
$960$	7.56612	0.244195
$961$	−30.8243	−0.994332
$962$	−58.2796	−1.87901
$963$	26.6016	0.857226
$964$	−97.9915	−3.15609
$965$	15.6558	0.503978
$966$	−0.168329	−0.00541591
$967$	−3.16907	−0.101911	−0.0509553	−	0.998701i	$-0.516227\pi$
$967$	−3.16907	−0.101911	−0.0509553	+	0.998701i	$0.516227\pi$
$968$	55.0223	1.76848
$969$	1.10242	0.0354147
$970$	49.0621	1.57529
$971$	−30.1645	−0.968024	−0.484012	−	0.875061i	$-0.660821\pi$
$971$	−30.1645	−0.968024	−0.484012	+	0.875061i	$0.660821\pi$
$972$	58.3754	1.87239
$973$	−0.260684	−0.00835716
$974$	−69.7631	−2.23535
$975$	3.20259	0.102565
$976$	−5.14190	−0.164588
$977$	−6.80390	−0.217676	−0.108838	−	0.994060i	$-0.534713\pi$
$977$	−6.80390	−0.217676	−0.108838	+	0.994060i	$0.534713\pi$
$978$	−10.6725	−0.341269
$979$	5.36272	0.171393
$980$	50.3927	1.60974
$981$	45.0096	1.43705
$982$	13.2617	0.423197
$983$	−11.5281	−0.367690	−0.183845	−	0.982955i	$-0.558854\pi$
$983$	−11.5281	−0.367690	−0.183845	+	0.982955i	$0.558854\pi$
$984$	−21.4826	−0.684840
$985$	29.1271	0.928066
$986$	−0.806371	−0.0256801
$987$	0.0235934	0.000750985 0
$988$	66.9314	2.12937
$989$	−4.80893	−0.152915
$990$	7.00283	0.222565
$991$	−42.4652	−1.34895	−0.674476	−	0.738297i	$-0.735630\pi$
$991$	−42.4652	−1.34895	−0.674476	+	0.738297i	$0.735630\pi$
$992$	−0.421747	−0.0133905
$993$	13.1028	0.415804
$994$	−0.0898470	−0.00284977
$995$	40.3017	1.27765
$996$	39.7826	1.26056
$997$	−45.0388	−1.42639	−0.713197	−	0.700964i	$-0.752753\pi$
$997$	−45.0388	−1.42639	−0.713197	+	0.700964i	$0.752753\pi$
$998$	0.610261	0.0193175
$999$	32.2277	1.01964

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4003.2.a.c.1.12	✓	179

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4003.2.a.c.1.12	✓	179	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:	\( N \)	\(=\)	\( 4003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4003.a (trivial)

\(f(q)\)	\(=\)	\(q-2.46969 q^{2} +0.639879 q^{3} +4.09938 q^{4} -1.75762 q^{5} -1.58030 q^{6} -0.0776251 q^{7} -5.18482 q^{8} -2.59056 q^{9} +O(q^{10})\)	\(q-2.46969 q^{2} +0.639879 q^{3} +4.09938 q^{4} -1.75762 q^{5} -1.58030 q^{6} -0.0776251 q^{7} -5.18482 q^{8} -2.59056 q^{9} +4.34079 q^{10} -0.622748 q^{11} +2.62311 q^{12} -2.61937 q^{13} +0.191710 q^{14} -1.12467 q^{15} +4.60616 q^{16} -0.276397 q^{17} +6.39787 q^{18} -6.23326 q^{19} -7.20516 q^{20} -0.0496707 q^{21} +1.53800 q^{22} -1.37220 q^{23} -3.31766 q^{24} -1.91076 q^{25} +6.46904 q^{26} -3.57728 q^{27} -0.318215 q^{28} -1.18130 q^{29} +2.77758 q^{30} +0.419170 q^{31} -1.00615 q^{32} -0.398483 q^{33} +0.682615 q^{34} +0.136436 q^{35} -10.6197 q^{36} -9.00901 q^{37} +15.3942 q^{38} -1.67608 q^{39} +9.11296 q^{40} +6.47523 q^{41} +0.122671 q^{42} +3.50454 q^{43} -2.55288 q^{44} +4.55322 q^{45} +3.38891 q^{46} -0.474996 q^{47} +2.94738 q^{48} -6.99397 q^{49} +4.71900 q^{50} -0.176860 q^{51} -10.7378 q^{52} -3.44910 q^{53} +8.83477 q^{54} +1.09456 q^{55} +0.402473 q^{56} -3.98853 q^{57} +2.91744 q^{58} +3.79175 q^{59} -4.61043 q^{60} -1.11631 q^{61} -1.03522 q^{62} +0.201092 q^{63} -6.72744 q^{64} +4.60387 q^{65} +0.984131 q^{66} -13.0788 q^{67} -1.13306 q^{68} -0.878041 q^{69} -0.336954 q^{70} -0.468661 q^{71} +13.4316 q^{72} +8.13902 q^{73} +22.2495 q^{74} -1.22266 q^{75} -25.5525 q^{76} +0.0483409 q^{77} +4.13940 q^{78} +6.79858 q^{79} -8.09589 q^{80} +5.48264 q^{81} -15.9918 q^{82} +15.1662 q^{83} -0.203619 q^{84} +0.485801 q^{85} -8.65515 q^{86} -0.755887 q^{87} +3.22884 q^{88} -8.61138 q^{89} -11.2450 q^{90} +0.203329 q^{91} -5.62516 q^{92} +0.268218 q^{93} +1.17309 q^{94} +10.9557 q^{95} -0.643812 q^{96} +11.3026 q^{97} +17.2730 q^{98} +1.61326 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 179 q + 22 q^{2} + 16 q^{3} + 196 q^{4} + 61 q^{5} + 7 q^{6} + 21 q^{7} + 60 q^{8} + 221 q^{9}+O(q^{10}) \) 179 * q + 22 * q^2 + 16 * q^3 + 196 * q^4 + 61 * q^5 + 7 * q^6 + 21 * q^7 + 60 * q^8 + 221 * q^9	\( 179 q + 22 q^{2} + 16 q^{3} + 196 q^{4} + 61 q^{5} + 7 q^{6} + 21 q^{7} + 60 q^{8} + 221 q^{9} + 9 q^{10} + 46 q^{11} + 33 q^{12} + 47 q^{13} + 22 q^{14} + 36 q^{15} + 222 q^{16} + 103 q^{17} + 43 q^{18} + 12 q^{19} + 102 q^{20} + 50 q^{21} + 39 q^{22} + 121 q^{23} - 3 q^{24} + 246 q^{25} + 52 q^{26} + 49 q^{27} + 41 q^{28} + 138 q^{29} + 28 q^{30} + 5 q^{31} + 137 q^{32} + 63 q^{33} + 2 q^{34} + 72 q^{35} + 279 q^{36} + 118 q^{37} + 123 q^{38} + q^{39} + 9 q^{40} + 50 q^{41} + 48 q^{42} + 48 q^{43} + 108 q^{44} + 158 q^{45} + 13 q^{46} + 85 q^{47} + 50 q^{48} + 230 q^{49} + 78 q^{50} + 15 q^{51} + 41 q^{52} + 399 q^{53} - 5 q^{54} + 24 q^{55} + 53 q^{56} + 45 q^{57} + 27 q^{58} + 48 q^{59} + 66 q^{60} + 46 q^{61} + 81 q^{62} + 78 q^{63} + 252 q^{64} + 153 q^{65} + 6 q^{66} + 70 q^{67} + 240 q^{68} + 120 q^{69} - 31 q^{70} + 86 q^{71} + 89 q^{72} + 45 q^{73} + 68 q^{74} + 17 q^{75} - 13 q^{76} + 362 q^{77} + 69 q^{78} + 31 q^{79} + 169 q^{80} + 303 q^{81} + 25 q^{82} + 106 q^{83} + 13 q^{84} + 115 q^{85} + 95 q^{86} + 32 q^{87} + 83 q^{88} + 105 q^{89} - 38 q^{90} + 3 q^{91} + 310 q^{92} + 298 q^{93} - 17 q^{94} + 102 q^{95} - 82 q^{96} + 34 q^{97} + 81 q^{98} + 58 q^{99}+O(q^{100}) \) 179 * q + 22 * q^2 + 16 * q^3 + 196 * q^4 + 61 * q^5 + 7 * q^6 + 21 * q^7 + 60 * q^8 + 221 * q^9 + 9 * q^10 + 46 * q^11 + 33 * q^12 + 47 * q^13 + 22 * q^14 + 36 * q^15 + 222 * q^16 + 103 * q^17 + 43 * q^18 + 12 * q^19 + 102 * q^20 + 50 * q^21 + 39 * q^22 + 121 * q^23 - 3 * q^24 + 246 * q^25 + 52 * q^26 + 49 * q^27 + 41 * q^28 + 138 * q^29 + 28 * q^30 + 5 * q^31 + 137 * q^32 + 63 * q^33 + 2 * q^34 + 72 * q^35 + 279 * q^36 + 118 * q^37 + 123 * q^38 + q^39 + 9 * q^40 + 50 * q^41 + 48 * q^42 + 48 * q^43 + 108 * q^44 + 158 * q^45 + 13 * q^46 + 85 * q^47 + 50 * q^48 + 230 * q^49 + 78 * q^50 + 15 * q^51 + 41 * q^52 + 399 * q^53 - 5 * q^54 + 24 * q^55 + 53 * q^56 + 45 * q^57 + 27 * q^58 + 48 * q^59 + 66 * q^60 + 46 * q^61 + 81 * q^62 + 78 * q^63 + 252 * q^64 + 153 * q^65 + 6 * q^66 + 70 * q^67 + 240 * q^68 + 120 * q^69 - 31 * q^70 + 86 * q^71 + 89 * q^72 + 45 * q^73 + 68 * q^74 + 17 * q^75 - 13 * q^76 + 362 * q^77 + 69 * q^78 + 31 * q^79 + 169 * q^80 + 303 * q^81 + 25 * q^82 + 106 * q^83 + 13 * q^84 + 115 * q^85 + 95 * q^86 + 32 * q^87 + 83 * q^88 + 105 * q^89 - 38 * q^90 + 3 * q^91 + 310 * q^92 + 298 * q^93 - 17 * q^94 + 102 * q^95 - 82 * q^96 + 34 * q^97 + 81 * q^98 + 58 * q^99

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