LMFDB - Embedded newform 4007.2.a.b.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4007,2,Mod(1,4007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4007, 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("4007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4007 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4007.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:	$31.9960560899$
Analytic rank:	$0$
Dimension:	$195$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	4007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.41162 q^{2} -0.257694 q^{3} +3.81590 q^{4} +2.26401 q^{5} +0.621460 q^{6} -3.03056 q^{7} -4.37927 q^{8} -2.93359 q^{9} +O(q^{10})$	\(q-2.41162 q^{2} -0.257694 q^{3} +3.81590 q^{4} +2.26401 q^{5} +0.621460 q^{6} -3.03056 q^{7} -4.37927 q^{8} -2.93359 q^{9} -5.45992 q^{10} +1.56587 q^{11} -0.983336 q^{12} +1.51676 q^{13} +7.30855 q^{14} -0.583421 q^{15} +2.92931 q^{16} -0.0510465 q^{17} +7.07471 q^{18} +7.11956 q^{19} +8.63923 q^{20} +0.780957 q^{21} -3.77628 q^{22} +5.80048 q^{23} +1.12851 q^{24} +0.125723 q^{25} -3.65785 q^{26} +1.52905 q^{27} -11.5643 q^{28} +5.43566 q^{29} +1.40699 q^{30} +2.82012 q^{31} +1.69415 q^{32} -0.403516 q^{33} +0.123105 q^{34} -6.86120 q^{35} -11.1943 q^{36} -2.23623 q^{37} -17.1697 q^{38} -0.390860 q^{39} -9.91468 q^{40} -6.79396 q^{41} -1.88337 q^{42} +1.46076 q^{43} +5.97521 q^{44} -6.64167 q^{45} -13.9885 q^{46} +1.86923 q^{47} -0.754866 q^{48} +2.18427 q^{49} -0.303197 q^{50} +0.0131544 q^{51} +5.78781 q^{52} +4.30128 q^{53} -3.68749 q^{54} +3.54514 q^{55} +13.2716 q^{56} -1.83467 q^{57} -13.1087 q^{58} -9.90106 q^{59} -2.22628 q^{60} -13.4843 q^{61} -6.80106 q^{62} +8.89042 q^{63} -9.94427 q^{64} +3.43396 q^{65} +0.973126 q^{66} -6.30130 q^{67} -0.194789 q^{68} -1.49475 q^{69} +16.5466 q^{70} -10.7586 q^{71} +12.8470 q^{72} +10.6336 q^{73} +5.39294 q^{74} -0.0323982 q^{75} +27.1676 q^{76} -4.74546 q^{77} +0.942606 q^{78} -6.89708 q^{79} +6.63198 q^{80} +8.40675 q^{81} +16.3844 q^{82} +9.19104 q^{83} +2.98006 q^{84} -0.115570 q^{85} -3.52280 q^{86} -1.40074 q^{87} -6.85736 q^{88} +18.0123 q^{89} +16.0172 q^{90} -4.59663 q^{91} +22.1341 q^{92} -0.726729 q^{93} -4.50788 q^{94} +16.1187 q^{95} -0.436572 q^{96} +15.2610 q^{97} -5.26764 q^{98} -4.59363 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 195 q + 14 q^{2} + 22 q^{3} + 220 q^{4} + 14 q^{5} + 13 q^{6} + 48 q^{7} + 39 q^{8} + 245 q^{9}+O(q^{10}) $ 195 * q + 14 * q^2 + 22 * q^3 + 220 * q^4 + 14 * q^5 + 13 * q^6 + 48 * q^7 + 39 * q^8 + 245 * q^9	\( 195 q + 14 q^{2} + 22 q^{3} + 220 q^{4} + 14 q^{5} + 13 q^{6} + 48 q^{7} + 39 q^{8} + 245 q^{9} + 40 q^{10} + 13 q^{11} + 57 q^{12} + 97 q^{13} + 9 q^{14} + 23 q^{15} + 270 q^{16} + 66 q^{17} + 60 q^{18} + 33 q^{19} + 24 q^{20} + 27 q^{21} + 127 q^{22} + 42 q^{23} + 33 q^{24} + 357 q^{25} + 8 q^{26} + 79 q^{27} + 131 q^{28} + 57 q^{29} + 51 q^{30} + 41 q^{31} + 67 q^{32} + 74 q^{33} + 26 q^{34} + 14 q^{35} + 279 q^{36} + 133 q^{37} + 7 q^{38} + 28 q^{39} + 97 q^{40} + 64 q^{41} - q^{42} + 123 q^{43} + 21 q^{44} + 40 q^{45} + 84 q^{46} + 14 q^{47} + 122 q^{48} + 335 q^{49} + 35 q^{50} + 37 q^{51} + 220 q^{52} + 83 q^{53} + 21 q^{54} + 47 q^{55} + q^{56} + 235 q^{57} + 138 q^{58} + 18 q^{59} - 4 q^{60} + 81 q^{61} + 39 q^{62} + 102 q^{63} + 343 q^{64} + 165 q^{65} - 54 q^{66} + 147 q^{67} + 74 q^{68} - 2 q^{69} + 13 q^{70} + 31 q^{71} + 112 q^{72} + 300 q^{73} + 5 q^{74} + 84 q^{75} + 64 q^{76} + 67 q^{77} + 61 q^{78} + 144 q^{79} - 8 q^{80} + 359 q^{81} + 85 q^{82} + 26 q^{83} + 12 q^{84} + 201 q^{85} - 2 q^{86} + 80 q^{87} + 347 q^{88} + 29 q^{89} + 62 q^{90} + 70 q^{91} + 79 q^{92} + 76 q^{93} + 72 q^{94} + 71 q^{95} + 31 q^{96} + 264 q^{97} + 30 q^{98} + 19 q^{99}+O(q^{100}) \) 195 * q + 14 * q^2 + 22 * q^3 + 220 * q^4 + 14 * q^5 + 13 * q^6 + 48 * q^7 + 39 * q^8 + 245 * q^9 + 40 * q^10 + 13 * q^11 + 57 * q^12 + 97 * q^13 + 9 * q^14 + 23 * q^15 + 270 * q^16 + 66 * q^17 + 60 * q^18 + 33 * q^19 + 24 * q^20 + 27 * q^21 + 127 * q^22 + 42 * q^23 + 33 * q^24 + 357 * q^25 + 8 * q^26 + 79 * q^27 + 131 * q^28 + 57 * q^29 + 51 * q^30 + 41 * q^31 + 67 * q^32 + 74 * q^33 + 26 * q^34 + 14 * q^35 + 279 * q^36 + 133 * q^37 + 7 * q^38 + 28 * q^39 + 97 * q^40 + 64 * q^41 - q^42 + 123 * q^43 + 21 * q^44 + 40 * q^45 + 84 * q^46 + 14 * q^47 + 122 * q^48 + 335 * q^49 + 35 * q^50 + 37 * q^51 + 220 * q^52 + 83 * q^53 + 21 * q^54 + 47 * q^55 + q^56 + 235 * q^57 + 138 * q^58 + 18 * q^59 - 4 * q^60 + 81 * q^61 + 39 * q^62 + 102 * q^63 + 343 * q^64 + 165 * q^65 - 54 * q^66 + 147 * q^67 + 74 * q^68 - 2 * q^69 + 13 * q^70 + 31 * q^71 + 112 * q^72 + 300 * q^73 + 5 * q^74 + 84 * q^75 + 64 * q^76 + 67 * q^77 + 61 * q^78 + 144 * q^79 - 8 * q^80 + 359 * q^81 + 85 * q^82 + 26 * q^83 + 12 * q^84 + 201 * q^85 - 2 * q^86 + 80 * q^87 + 347 * q^88 + 29 * q^89 + 62 * q^90 + 70 * q^91 + 79 * q^92 + 76 * q^93 + 72 * q^94 + 71 * q^95 + 31 * q^96 + 264 * q^97 + 30 * q^98 + 19 * 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 $

$2$	−2.41162	−1.70527	−0.852636	−	0.522506i	$-0.824997\pi$
$2$	−2.41162	−1.70527	−0.852636	+	0.522506i	$0.824997\pi$
$3$	−0.257694	−0.148780	−0.0743899	−	0.997229i	$-0.523701\pi$
$3$	−0.257694	−0.148780	−0.0743899	+	0.997229i	$0.523701\pi$
$4$	3.81590	1.90795
$5$	2.26401	1.01249	0.506247	−	0.862388i	$-0.331032\pi$
$5$	2.26401	1.01249	0.506247	+	0.862388i	$0.331032\pi$
$6$	0.621460	0.253710
$7$	−3.03056	−1.14544	−0.572721	−	0.819750i	$-0.694112\pi$
$7$	−3.03056	−1.14544	−0.572721	+	0.819750i	$0.694112\pi$
$8$	−4.37927	−1.54830
$9$	−2.93359	−0.977865
$10$	−5.45992	−1.72658
$11$	1.56587	0.472128	0.236064	−	0.971738i	$-0.424143\pi$
$11$	1.56587	0.472128	0.236064	+	0.971738i	$0.424143\pi$
$12$	−0.983336	−0.283865
$13$	1.51676	0.420674	0.210337	−	0.977629i	$-0.432544\pi$
$13$	1.51676	0.420674	0.210337	+	0.977629i	$0.432544\pi$
$14$	7.30855	1.95329
$15$	−0.583421	−0.150639
$16$	2.92931	0.732328
$17$	−0.0510465	−0.0123806	−0.00619030	−	0.999981i	$-0.501970\pi$
$17$	−0.0510465	−0.0123806	−0.00619030	+	0.999981i	$0.501970\pi$
$18$	7.07471	1.66752
$19$	7.11956	1.63334	0.816670	−	0.577105i	$-0.195818\pi$
$19$	7.11956	1.63334	0.816670	+	0.577105i	$0.195818\pi$
$20$	8.63923	1.93179
$21$	0.780957	0.170419
$22$	−3.77628	−0.805106
$23$	5.80048	1.20948	0.604742	−	0.796422i	$-0.293276\pi$
$23$	5.80048	1.20948	0.604742	+	0.796422i	$0.293276\pi$
$24$	1.12851	0.230356
$25$	0.125723	0.0251447
$26$	−3.65785	−0.717363
$27$	1.52905	0.294266
$28$	−11.5643	−2.18545
$29$	5.43566	1.00938	0.504688	−	0.863302i	$-0.331607\pi$
$29$	5.43566	1.00938	0.504688	+	0.863302i	$0.331607\pi$
$30$	1.40699	0.256880
$31$	2.82012	0.506509	0.253254	−	0.967400i	$-0.418499\pi$
$31$	2.82012	0.506509	0.253254	+	0.967400i	$0.418499\pi$
$32$	1.69415	0.299486
$33$	−0.403516	−0.0702431
$34$	0.123105	0.0211123
$35$	−6.86120	−1.15975
$36$	−11.1943	−1.86572
$37$	−2.23623	−0.367634	−0.183817	−	0.982960i	$-0.558845\pi$
$37$	−2.23623	−0.367634	−0.183817	+	0.982960i	$0.558845\pi$
$38$	−17.1697	−2.78529
$39$	−0.390860	−0.0625878
$40$	−9.91468	−1.56765
$41$	−6.79396	−1.06104	−0.530519	−	0.847673i	$-0.678003\pi$
$41$	−6.79396	−1.06104	−0.530519	+	0.847673i	$0.678003\pi$
$42$	−1.88337	−0.290610
$43$	1.46076	0.222764	0.111382	−	0.993778i	$-0.464472\pi$
$43$	1.46076	0.222764	0.111382	+	0.993778i	$0.464472\pi$
$44$	5.97521	0.900797
$45$	−6.64167	−0.990082
$46$	−13.9885	−2.06250
$47$	1.86923	0.272656	0.136328	−	0.990664i	$-0.456470\pi$
$47$	1.86923	0.272656	0.136328	+	0.990664i	$0.456470\pi$
$48$	−0.754866	−0.108956
$49$	2.18427	0.312039
$50$	−0.303197	−0.0428785
$51$	0.0131544	0.00184198
$52$	5.78781	0.802625
$53$	4.30128	0.590827	0.295413	−	0.955370i	$-0.404543\pi$
$53$	4.30128	0.590827	0.295413	+	0.955370i	$0.404543\pi$
$54$	−3.68749	−0.501804
$55$	3.54514	0.478027
$56$	13.2716	1.77349
$57$	−1.83467	−0.243008
$58$	−13.1087	−1.72126
$59$	−9.90106	−1.28901	−0.644504	−	0.764601i	$-0.722936\pi$
$59$	−9.90106	−1.28901	−0.644504	+	0.764601i	$0.722936\pi$
$60$	−2.22628	−0.287411
$61$	−13.4843	−1.72649	−0.863243	−	0.504789i	$-0.831570\pi$
$61$	−13.4843	−1.72649	−0.863243	+	0.504789i	$0.831570\pi$
$62$	−6.80106	−0.863735
$63$	8.89042	1.12009
$64$	−9.94427	−1.24303
$65$	3.43396	0.425930
$66$	0.973126	0.119784
$67$	−6.30130	−0.769826	−0.384913	−	0.922953i	$-0.625769\pi$
$67$	−6.30130	−0.769826	−0.384913	+	0.922953i	$0.625769\pi$
$68$	−0.194789	−0.0236216
$69$	−1.49475	−0.179947
$70$	16.5466	1.97770
$71$	−10.7586	−1.27681	−0.638407	−	0.769699i	$-0.720406\pi$
$71$	−10.7586	−1.27681	−0.638407	+	0.769699i	$0.720406\pi$
$72$	12.8470	1.51403
$73$	10.6336	1.24457	0.622283	−	0.782792i	$-0.286205\pi$
$73$	10.6336	1.24457	0.622283	+	0.782792i	$0.286205\pi$
$74$	5.39294	0.626917
$75$	−0.0323982	−0.00374102
$76$	27.1676	3.11633
$77$	−4.74546	−0.540795
$78$	0.942606	0.106729
$79$	−6.89708	−0.775982	−0.387991	−	0.921663i	$-0.626831\pi$
$79$	−6.89708	−0.775982	−0.387991	+	0.921663i	$0.626831\pi$
$80$	6.63198	0.741478
$81$	8.40675	0.934084
$82$	16.3844	1.80936
$83$	9.19104	1.00885	0.504424	−	0.863456i	$-0.331705\pi$
$83$	9.19104	1.00885	0.504424	+	0.863456i	$0.331705\pi$
$84$	2.98006	0.325151
$85$	−0.115570	−0.0125353
$86$	−3.52280	−0.379873
$87$	−1.40074	−0.150175
$88$	−6.85736	−0.730998
$89$	18.0123	1.90930	0.954648	−	0.297738i	$-0.0962322\pi$
$89$	18.0123	1.90930	0.954648	+	0.297738i	$0.0962322\pi$
$90$	16.0172	1.68836
$91$	−4.59663	−0.481858
$92$	22.1341	2.30764
$93$	−0.726729	−0.0753583
$94$	−4.50788	−0.464952
$95$	16.1187	1.65375
$96$	−0.436572	−0.0445575
$97$	15.2610	1.54952	0.774758	−	0.632258i	$-0.217872\pi$
$97$	15.2610	1.54952	0.774758	+	0.632258i	$0.217872\pi$
$98$	−5.26764	−0.532112
$99$	−4.59363	−0.461677
$100$	0.479749	0.0479749
$101$	−2.04612	−0.203597	−0.101798	−	0.994805i	$-0.532460\pi$
$101$	−2.04612	−0.203597	−0.101798	+	0.994805i	$0.532460\pi$
$102$	−0.0317234	−0.00314108
$103$	6.62768	0.653045	0.326523	−	0.945189i	$-0.394123\pi$
$103$	6.62768	0.653045	0.326523	+	0.945189i	$0.394123\pi$
$104$	−6.64230	−0.651331
$105$	1.76809	0.172548
$106$	−10.3731	−1.00752
$107$	−9.08863	−0.878631	−0.439315	−	0.898333i	$-0.644779\pi$
$107$	−9.08863	−0.878631	−0.439315	+	0.898333i	$0.644779\pi$
$108$	5.83472	0.561446
$109$	−10.8780	−1.04192	−0.520962	−	0.853580i	$-0.674427\pi$
$109$	−10.8780	−1.04192	−0.520962	+	0.853580i	$0.674427\pi$
$110$	−8.54953	−0.815165
$111$	0.576264	0.0546966
$112$	−8.87745	−0.838840
$113$	−2.58032	−0.242736	−0.121368	−	0.992608i	$-0.538728\pi$
$113$	−2.58032	−0.242736	−0.121368	+	0.992608i	$0.538728\pi$
$114$	4.42452	0.414395
$115$	13.1323	1.22459
$116$	20.7420	1.92584
$117$	−4.44956	−0.411362
$118$	23.8776	2.19811
$119$	0.154699	0.0141813
$120$	2.55496	0.233235
$121$	−8.54805	−0.777095
$122$	32.5189	2.94413
$123$	1.75076	0.157861
$124$	10.7613	0.966394
$125$	−11.0354	−0.987035
$126$	−21.4403	−1.91005
$127$	18.0933	1.60552	0.802760	−	0.596303i	$-0.203364\pi$
$127$	18.0933	1.60552	0.802760	+	0.596303i	$0.203364\pi$
$128$	20.5935	1.82022
$129$	−0.376430	−0.0331428
$130$	−8.28139	−0.726326
$131$	−18.0410	−1.57625	−0.788124	−	0.615516i	$-0.788948\pi$
$131$	−18.0410	−1.57625	−0.788124	+	0.615516i	$0.788948\pi$
$132$	−1.53978	−0.134020
$133$	−21.5762	−1.87090
$134$	15.1963	1.31276
$135$	3.46178	0.297943
$136$	0.223546	0.0191689
$137$	12.8486	1.09773	0.548865	−	0.835911i	$-0.315060\pi$
$137$	12.8486	1.09773	0.548865	+	0.835911i	$0.315060\pi$
$138$	3.60476	0.306858
$139$	8.53315	0.723772	0.361886	−	0.932222i	$-0.382133\pi$
$139$	8.53315	0.723772	0.361886	+	0.932222i	$0.382133\pi$
$140$	−26.1817	−2.21276
$141$	−0.481691	−0.0405657
$142$	25.9457	2.17731
$143$	2.37505	0.198612
$144$	−8.59341	−0.716118
$145$	12.3064	1.02199
$146$	−25.6441	−2.12232
$147$	−0.562875	−0.0464251
$148$	−8.53325	−0.701429
$149$	22.2606	1.82366	0.911829	−	0.410571i	$-0.134671\pi$
$149$	22.2606	1.82366	0.911829	+	0.410571i	$0.134671\pi$
$150$	0.0781321	0.00637946
$151$	19.4155	1.58001	0.790007	−	0.613098i	$-0.210077\pi$
$151$	19.4155	1.58001	0.790007	+	0.613098i	$0.210077\pi$
$152$	−31.1785	−2.52891
$153$	0.149750	0.0121066
$154$	11.4442	0.922203
$155$	6.38477	0.512837
$156$	−1.49149	−0.119414
$157$	−0.0257574	−0.00205566	−0.00102783	−	0.999999i	$-0.500327\pi$
$157$	−0.0257574	−0.00205566	−0.00102783	+	0.999999i	$0.500327\pi$
$158$	16.6331	1.32326
$159$	−1.10842	−0.0879031
$160$	3.83557	0.303228
$161$	−17.5787	−1.38539
$162$	−20.2739	−1.59287
$163$	11.5379	0.903718	0.451859	−	0.892089i	$-0.350761\pi$
$163$	11.5379	0.903718	0.451859	+	0.892089i	$0.350761\pi$
$164$	−25.9251	−2.02441
$165$	−0.913562	−0.0711207
$166$	−22.1653	−1.72036
$167$	−20.3277	−1.57300	−0.786501	−	0.617589i	$-0.788110\pi$
$167$	−20.3277	−1.57300	−0.786501	+	0.617589i	$0.788110\pi$
$168$	−3.42002	−0.263860
$169$	−10.6994	−0.823033
$170$	0.278710	0.0213761
$171$	−20.8859	−1.59719
$172$	5.57413	0.425023
$173$	13.4864	1.02535	0.512677	−	0.858582i	$-0.328654\pi$
$173$	13.4864	1.02535	0.512677	+	0.858582i	$0.328654\pi$
$174$	3.37804	0.256089
$175$	−0.381012	−0.0288018
$176$	4.58692	0.345752
$177$	2.55144	0.191778
$178$	−43.4387	−3.25587
$179$	−1.92585	−0.143945	−0.0719724	−	0.997407i	$-0.522929\pi$
$179$	−1.92585	−0.143945	−0.0719724	+	0.997407i	$0.522929\pi$
$180$	−25.3440	−1.88903
$181$	16.5487	1.23005	0.615027	−	0.788506i	$-0.289145\pi$
$181$	16.5487	1.23005	0.615027	+	0.788506i	$0.289145\pi$
$182$	11.0853	0.821699
$183$	3.47482	0.256866
$184$	−25.4018	−1.87265
$185$	−5.06284	−0.372228
$186$	1.75259	0.128506
$187$	−0.0799323	−0.00584523
$188$	7.13282	0.520214
$189$	−4.63388	−0.337065
$190$	−38.8722	−2.82009
$191$	−15.2861	−1.10607	−0.553033	−	0.833159i	$-0.686530\pi$
$191$	−15.2861	−1.10607	−0.553033	+	0.833159i	$0.686530\pi$
$192$	2.56258	0.184938
$193$	−8.73990	−0.629112	−0.314556	−	0.949239i	$-0.601856\pi$
$193$	−8.73990	−0.629112	−0.314556	+	0.949239i	$0.601856\pi$
$194$	−36.8036	−2.64235
$195$	−0.884910	−0.0633698
$196$	8.33498	0.595356
$197$	−14.8770	−1.05994	−0.529970	−	0.848016i	$-0.677797\pi$
$197$	−14.8770	−1.05994	−0.529970	+	0.848016i	$0.677797\pi$
$198$	11.0781	0.787285
$199$	8.43369	0.597848	0.298924	−	0.954277i	$-0.403372\pi$
$199$	8.43369	0.597848	0.298924	+	0.954277i	$0.403372\pi$
$200$	−0.550577	−0.0389316
$201$	1.62381	0.114535
$202$	4.93446	0.347187
$203$	−16.4731	−1.15618
$204$	0.0501959	0.00351442
$205$	−15.3816	−1.07430
$206$	−15.9834	−1.11362
$207$	−17.0162	−1.18271
$208$	4.44307	0.308071
$209$	11.1483	0.771145
$210$	−4.26396	−0.294241
$211$	−2.53181	−0.174297	−0.0871486	−	0.996195i	$-0.527775\pi$
$211$	−2.53181	−0.174297	−0.0871486	+	0.996195i	$0.527775\pi$
$212$	16.4133	1.12727
$213$	2.77243	0.189964
$214$	21.9183	1.49830
$215$	3.30717	0.225547
$216$	−6.69613	−0.455614
$217$	−8.54654	−0.580177
$218$	26.2336	1.77676
$219$	−2.74021	−0.185166
$220$	13.5279	0.912052
$221$	−0.0774254	−0.00520820
$222$	−1.38973	−0.0932725
$223$	2.54527	0.170444	0.0852220	−	0.996362i	$-0.472840\pi$
$223$	2.54527	0.170444	0.0852220	+	0.996362i	$0.472840\pi$
$224$	−5.13422	−0.343044
$225$	−0.368822	−0.0245881
$226$	6.22275	0.413931
$227$	2.50916	0.166539	0.0832693	−	0.996527i	$-0.473464\pi$
$227$	2.50916	0.166539	0.0832693	+	0.996527i	$0.473464\pi$
$228$	−7.00092	−0.463647
$229$	3.38307	0.223560	0.111780	−	0.993733i	$-0.464345\pi$
$229$	3.38307	0.223560	0.111780	+	0.993733i	$0.464345\pi$
$230$	−31.6701	−2.08827
$231$	1.22288	0.0804594
$232$	−23.8042	−1.56282
$233$	19.7903	1.29651	0.648254	−	0.761424i	$-0.275500\pi$
$233$	19.7903	1.29651	0.648254	+	0.761424i	$0.275500\pi$
$234$	10.7306	0.701484
$235$	4.23196	0.276063
$236$	−37.7815	−2.45937
$237$	1.77734	0.115450
$238$	−0.373076	−0.0241829
$239$	7.09195	0.458740	0.229370	−	0.973339i	$-0.426333\pi$
$239$	7.09195	0.458740	0.229370	+	0.973339i	$0.426333\pi$
$240$	−1.70902	−0.110317
$241$	10.9696	0.706617	0.353309	−	0.935507i	$-0.385057\pi$
$241$	10.9696	0.706617	0.353309	+	0.935507i	$0.385057\pi$
$242$	20.6146	1.32516
$243$	−6.75353	−0.433239
$244$	−51.4547	−3.29405
$245$	4.94521	0.315938
$246$	−4.22218	−0.269196
$247$	10.7987	0.687104
$248$	−12.3501	−0.784230
$249$	−2.36848	−0.150096
$250$	26.6132	1.68316
$251$	20.7662	1.31075	0.655376	−	0.755303i	$-0.272510\pi$
$251$	20.7662	1.31075	0.655376	+	0.755303i	$0.272510\pi$
$252$	33.9250	2.13707
$253$	9.08280	0.571031
$254$	−43.6341	−2.73785
$255$	0.0297816	0.00186500
$256$	−29.7751	−1.86094
$257$	5.40317	0.337041	0.168520	−	0.985698i	$-0.446101\pi$
$257$	5.40317	0.337041	0.168520	+	0.985698i	$0.446101\pi$
$258$	0.907805	0.0565175
$259$	6.77703	0.421104
$260$	13.1036	0.812654
$261$	−15.9460	−0.987034
$262$	43.5080	2.68793
$263$	−5.05125	−0.311473	−0.155737	−	0.987799i	$-0.549775\pi$
$263$	−5.05125	−0.311473	−0.155737	+	0.987799i	$0.549775\pi$
$264$	1.76710	0.108758
$265$	9.73813	0.598209
$266$	52.0337	3.19039
$267$	−4.64165	−0.284065
$268$	−24.0452	−1.46879
$269$	15.4053	0.939275	0.469637	−	0.882859i	$-0.344385\pi$
$269$	15.4053	0.939275	0.469637	+	0.882859i	$0.344385\pi$
$270$	−8.34850	−0.508074
$271$	9.84975	0.598330	0.299165	−	0.954201i	$-0.403292\pi$
$271$	9.84975	0.598330	0.299165	+	0.954201i	$0.403292\pi$
$272$	−0.149531	−0.00906666
$273$	1.18452	0.0716907
$274$	−30.9859	−1.87193
$275$	0.196867	0.0118715
$276$	−5.70382	−0.343329
$277$	17.6352	1.05960	0.529798	−	0.848124i	$-0.322268\pi$
$277$	17.6352	1.05960	0.529798	+	0.848124i	$0.322268\pi$
$278$	−20.5787	−1.23423
$279$	−8.27309	−0.495297
$280$	30.0470	1.79565
$281$	−12.4506	−0.742740	−0.371370	−	0.928485i	$-0.621112\pi$
$281$	−12.4506	−0.742740	−0.371370	+	0.928485i	$0.621112\pi$
$282$	1.16165	0.0691755
$283$	1.91123	0.113611	0.0568053	−	0.998385i	$-0.481909\pi$
$283$	1.91123	0.113611	0.0568053	+	0.998385i	$0.481909\pi$
$284$	−41.0539	−2.43610
$285$	−4.15370	−0.246044
$286$	−5.72772	−0.338687
$287$	20.5895	1.21536
$288$	−4.96995	−0.292857
$289$	−16.9974	−0.999847
$290$	−29.6783	−1.74277
$291$	−3.93266	−0.230537
$292$	40.5767	2.37457
$293$	7.26331	0.424327	0.212164	−	0.977234i	$-0.431949\pi$
$293$	7.26331	0.424327	0.212164	+	0.977234i	$0.431949\pi$
$294$	1.35744	0.0791675
$295$	−22.4161	−1.30511
$296$	9.79306	0.569210
$297$	2.39430	0.138931
$298$	−53.6840	−3.10983
$299$	8.79794	0.508798
$300$	−0.123628	−0.00713769
$301$	−4.42692	−0.255163
$302$	−46.8228	−2.69435
$303$	0.527273	0.0302910
$304$	20.8554	1.19614
$305$	−30.5285	−1.74806
$306$	−0.361139	−0.0206450
$307$	18.8926	1.07826	0.539128	−	0.842224i	$-0.318754\pi$
$307$	18.8926	1.07826	0.539128	+	0.842224i	$0.318754\pi$
$308$	−18.1082	−1.03181
$309$	−1.70792	−0.0971599
$310$	−15.3976	−0.874527
$311$	−16.4353	−0.931959	−0.465980	−	0.884795i	$-0.654298\pi$
$311$	−16.4353	−0.931959	−0.465980	+	0.884795i	$0.654298\pi$
$312$	1.71168	0.0969049
$313$	33.4597	1.89126	0.945628	−	0.325251i	$-0.105449\pi$
$313$	33.4597	1.89126	0.945628	+	0.325251i	$0.105449\pi$
$314$	0.0621170	0.00350546
$315$	20.1280	1.13408
$316$	−26.3186	−1.48054
$317$	5.03638	0.282872	0.141436	−	0.989947i	$-0.454828\pi$
$317$	5.03638	0.282872	0.141436	+	0.989947i	$0.454828\pi$
$318$	2.67308	0.149899
$319$	8.51154	0.476555
$320$	−22.5139	−1.25856
$321$	2.34209	0.130722
$322$	42.3931	2.36247
$323$	−0.363429	−0.0202217
$324$	32.0794	1.78219
$325$	0.190693	0.0105777
$326$	−27.8250	−1.54108
$327$	2.80320	0.155017
$328$	29.7526	1.64281
$329$	−5.66482	−0.312312
$330$	2.20316	0.121280
$331$	11.9636	0.657577	0.328788	−	0.944404i	$-0.393360\pi$
$331$	11.9636	0.657577	0.328788	+	0.944404i	$0.393360\pi$
$332$	35.0721	1.92483
$333$	6.56020	0.359497
$334$	49.0226	2.68240
$335$	−14.2662	−0.779445
$336$	2.28767	0.124802
$337$	−1.48647	−0.0809731	−0.0404866	−	0.999180i	$-0.512891\pi$
$337$	−1.48647	−0.0809731	−0.0404866	+	0.999180i	$0.512891\pi$
$338$	25.8030	1.40350
$339$	0.664934	0.0361142
$340$	−0.441003	−0.0239167
$341$	4.41595	0.239137
$342$	50.3688	2.72364
$343$	14.5943	0.788020
$344$	−6.39706	−0.344907
$345$	−3.38412	−0.182195
$346$	−32.5241	−1.74851
$347$	26.4756	1.42128	0.710641	−	0.703555i	$-0.248405\pi$
$347$	26.4756	1.42128	0.710641	+	0.703555i	$0.248405\pi$
$348$	−5.34508	−0.286526
$349$	11.8100	0.632174	0.316087	−	0.948730i	$-0.397631\pi$
$349$	11.8100	0.632174	0.316087	+	0.948730i	$0.397631\pi$
$350$	0.918856	0.0491149
$351$	2.31921	0.123790
$352$	2.65282	0.141396
$353$	−20.1991	−1.07509	−0.537545	−	0.843235i	$-0.680648\pi$
$353$	−20.1991	−1.07509	−0.537545	+	0.843235i	$0.680648\pi$
$354$	−6.15311	−0.327034
$355$	−24.3576	−1.29277
$356$	68.7330	3.64284
$357$	−0.0398651	−0.00210989
$358$	4.64441	0.245465
$359$	5.18391	0.273596	0.136798	−	0.990599i	$-0.456319\pi$
$359$	5.18391	0.273596	0.136798	+	0.990599i	$0.456319\pi$
$360$	29.0857	1.53295
$361$	31.6882	1.66780
$362$	−39.9091	−2.09758
$363$	2.20278	0.115616
$364$	−17.5403	−0.919362
$365$	24.0745	1.26012
$366$	−8.37994	−0.438026
$367$	−2.57715	−0.134526	−0.0672632	−	0.997735i	$-0.521427\pi$
$367$	−2.57715	−0.134526	−0.0672632	+	0.997735i	$0.521427\pi$
$368$	16.9914	0.885738
$369$	19.9307	1.03755
$370$	12.2096	0.634749
$371$	−13.0353	−0.676758
$372$	−2.77313	−0.143780
$373$	−12.0673	−0.624821	−0.312410	−	0.949947i	$-0.601136\pi$
$373$	−12.0673	−0.624821	−0.312410	+	0.949947i	$0.601136\pi$
$374$	0.192766	0.00996770
$375$	2.84376	0.146851
$376$	−8.18588	−0.422154
$377$	8.24460	0.424618
$378$	11.1751	0.574788
$379$	19.1096	0.981596	0.490798	−	0.871273i	$-0.336705\pi$
$379$	19.1096	0.981596	0.490798	+	0.871273i	$0.336705\pi$
$380$	61.5075	3.15527
$381$	−4.66253	−0.238869
$382$	36.8644	1.88614
$383$	−26.2953	−1.34363	−0.671814	−	0.740720i	$-0.734484\pi$
$383$	−26.2953	−1.34363	−0.671814	+	0.740720i	$0.734484\pi$
$384$	−5.30682	−0.270812
$385$	−10.7438	−0.547552
$386$	21.0773	1.07281
$387$	−4.28528	−0.217833
$388$	58.2343	2.95640
$389$	23.2853	1.18061	0.590307	−	0.807179i	$-0.299007\pi$
$389$	23.2853	1.18061	0.590307	+	0.807179i	$0.299007\pi$
$390$	2.13407	0.108063
$391$	−0.296094	−0.0149741
$392$	−9.56552	−0.483132
$393$	4.64906	0.234514
$394$	35.8776	1.80749
$395$	−15.6150	−0.785678
$396$	−17.5288	−0.880858
$397$	32.3490	1.62355	0.811775	−	0.583971i	$-0.198502\pi$
$397$	32.3490	1.62355	0.811775	+	0.583971i	$0.198502\pi$
$398$	−20.3388	−1.01949
$399$	5.56007	0.278352
$400$	0.368283	0.0184142
$401$	−9.42154	−0.470489	−0.235245	−	0.971936i	$-0.575589\pi$
$401$	−9.42154	−0.470489	−0.235245	+	0.971936i	$0.575589\pi$
$402$	−3.91601	−0.195313
$403$	4.27745	0.213075
$404$	−7.80780	−0.388452
$405$	19.0329	0.945754
$406$	39.7268	1.97161
$407$	−3.50165	−0.173570
$408$	−0.0576066	−0.00285195
$409$	12.6422	0.625115	0.312557	−	0.949899i	$-0.398814\pi$
$409$	12.6422	0.625115	0.312557	+	0.949899i	$0.398814\pi$
$410$	37.0945	1.83197
$411$	−3.31101	−0.163320
$412$	25.2906	1.24598
$413$	30.0057	1.47649
$414$	41.0367	2.01684
$415$	20.8086	1.02145
$416$	2.56962	0.125986
$417$	−2.19894	−0.107683
$418$	−26.8855	−1.31501
$419$	−39.1147	−1.91088	−0.955440	−	0.295186i	$-0.904618\pi$
$419$	−39.1147	−1.91088	−0.955440	+	0.295186i	$0.904618\pi$
$420$	6.74686	0.329213
$421$	17.0054	0.828794	0.414397	−	0.910096i	$-0.363993\pi$
$421$	17.0054	0.828794	0.414397	+	0.910096i	$0.363993\pi$
$422$	6.10576	0.297224
$423$	−5.48358	−0.266621
$424$	−18.8365	−0.914780
$425$	−0.00641775	−0.000311307 0
$426$	−6.68605	−0.323940
$427$	40.8649	1.97759
$428$	−34.6813	−1.67638
$429$	−0.612037	−0.0295494
$430$	−7.97564	−0.384619
$431$	−6.99226	−0.336805	−0.168403	−	0.985718i	$-0.553861\pi$
$431$	−6.99226	−0.336805	−0.168403	+	0.985718i	$0.553861\pi$
$432$	4.47907	0.215499
$433$	36.4926	1.75372	0.876860	−	0.480745i	$-0.159634\pi$
$433$	36.4926	1.75372	0.876860	+	0.480745i	$0.159634\pi$
$434$	20.6110	0.989359
$435$	−3.17128	−0.152051
$436$	−41.5095	−1.98794
$437$	41.2969	1.97550
$438$	6.60834	0.315759
$439$	−9.42035	−0.449609	−0.224804	−	0.974404i	$-0.572174\pi$
$439$	−9.42035	−0.449609	−0.224804	+	0.974404i	$0.572174\pi$
$440$	−15.5251	−0.740131
$441$	−6.40777	−0.305132
$442$	0.186721	0.00888139
$443$	15.8697	0.753994	0.376997	−	0.926214i	$-0.376957\pi$
$443$	15.8697	0.753994	0.376997	+	0.926214i	$0.376957\pi$
$444$	2.19897	0.104358
$445$	40.7799	1.93315
$446$	−6.13823	−0.290653
$447$	−5.73642	−0.271323
$448$	30.1367	1.42382
$449$	−25.0630	−1.18280	−0.591399	−	0.806379i	$-0.701424\pi$
$449$	−25.0630	−1.18280	−0.591399	+	0.806379i	$0.701424\pi$
$450$	0.889457	0.0419294
$451$	−10.6385	−0.500946
$452$	−9.84626	−0.463129
$453$	−5.00327	−0.235074
$454$	−6.05113	−0.283994
$455$	−10.4068	−0.487878
$456$	8.03451	0.376250
$457$	−0.555206	−0.0259715	−0.0129857	−	0.999916i	$-0.504134\pi$
$457$	−0.555206	−0.0259715	−0.0129857	+	0.999916i	$0.504134\pi$
$458$	−8.15868	−0.381230
$459$	−0.0780528	−0.00364319
$460$	50.1116	2.33647
$461$	17.8298	0.830416	0.415208	−	0.909727i	$-0.363709\pi$
$461$	17.8298	0.830416	0.415208	+	0.909727i	$0.363709\pi$
$462$	−2.94911	−0.137205
$463$	−5.13388	−0.238592	−0.119296	−	0.992859i	$-0.538064\pi$
$463$	−5.13388	−0.238592	−0.119296	+	0.992859i	$0.538064\pi$
$464$	15.9227	0.739195
$465$	−1.64532	−0.0762998
$466$	−47.7267	−2.21090
$467$	−28.7984	−1.33263	−0.666316	−	0.745670i	$-0.732130\pi$
$467$	−28.7984	−1.33263	−0.666316	+	0.745670i	$0.732130\pi$
$468$	−16.9791	−0.784859
$469$	19.0965	0.881792
$470$	−10.2059	−0.470762
$471$	0.00663752	0.000305841 0
$472$	43.3594	1.99578
$473$	2.28736	0.105173
$474$	−4.28626	−0.196874
$475$	0.895097	0.0410698
$476$	0.590318	0.0270572
$477$	−12.6182	−0.577749
$478$	−17.1031	−0.782277
$479$	29.2150	1.33487	0.667433	−	0.744670i	$-0.267393\pi$
$479$	29.2150	1.33487	0.667433	+	0.744670i	$0.267393\pi$
$480$	−0.988403	−0.0451142
$481$	−3.39183	−0.154654
$482$	−26.4546	−1.20497
$483$	4.52992	0.206119
$484$	−32.6185	−1.48266
$485$	34.5509	1.56888
$486$	16.2869	0.738790
$487$	−13.7281	−0.622080	−0.311040	−	0.950397i	$-0.600677\pi$
$487$	−13.7281	−0.622080	−0.311040	+	0.950397i	$0.600677\pi$
$488$	59.0512	2.67312
$489$	−2.97325	−0.134455
$490$	−11.9260	−0.538760
$491$	17.8077	0.803651	0.401826	−	0.915716i	$-0.368376\pi$
$491$	17.8077	0.803651	0.401826	+	0.915716i	$0.368376\pi$
$492$	6.68075	0.301191
$493$	−0.277472	−0.0124967
$494$	−26.0423	−1.17170
$495$	−10.4000	−0.467445
$496$	8.26102	0.370931
$497$	32.6046	1.46252
$498$	5.71186	0.255955
$499$	34.3420	1.53736	0.768680	−	0.639634i	$-0.220914\pi$
$499$	34.3420	1.53736	0.768680	+	0.639634i	$0.220914\pi$
$500$	−42.1100	−1.88322
$501$	5.23832	0.234031
$502$	−50.0802	−2.23519
$503$	−14.0276	−0.625459	−0.312729	−	0.949842i	$-0.601243\pi$
$503$	−14.0276	−0.625459	−0.312729	+	0.949842i	$0.601243\pi$
$504$	−38.9335	−1.73424
$505$	−4.63243	−0.206140
$506$	−21.9042	−0.973762
$507$	2.75718	0.122451
$508$	69.0422	3.06325
$509$	−13.3924	−0.593609	−0.296805	−	0.954938i	$-0.595921\pi$
$509$	−13.3924	−0.593609	−0.296805	+	0.954938i	$0.595921\pi$
$510$	−0.0718219	−0.00318033
$511$	−32.2257	−1.42558
$512$	30.6192	1.35319
$513$	10.8862	0.480637
$514$	−13.0304	−0.574746
$515$	15.0051	0.661204
$516$	−1.43642	−0.0632348
$517$	2.92698	0.128728
$518$	−16.3436	−0.718097
$519$	−3.47537	−0.152552
$520$	−15.0382	−0.659469
$521$	11.4524	0.501739	0.250870	−	0.968021i	$-0.419283\pi$
$521$	11.4524	0.501739	0.250870	+	0.968021i	$0.419283\pi$
$522$	38.4557	1.68316
$523$	−35.0363	−1.53203	−0.766015	−	0.642823i	$-0.777763\pi$
$523$	−35.0363	−1.53203	−0.766015	+	0.642823i	$0.777763\pi$
$524$	−68.8427	−3.00741
$525$	0.0981846	0.00428513
$526$	12.1817	0.531147
$527$	−0.143957	−0.00627089
$528$	−1.18202	−0.0514410
$529$	10.6455	0.462849
$530$	−23.4847	−1.02011
$531$	29.0457	1.26048
$532$	−82.3329	−3.56958
$533$	−10.3048	−0.446351
$534$	11.1939	0.484407
$535$	−20.5767	−0.889608
$536$	27.5951	1.19193
$537$	0.496280	0.0214161
$538$	−37.1516	−1.60172
$539$	3.42029	0.147322
$540$	13.2098	0.568461
$541$	30.4033	1.30714	0.653569	−	0.756867i	$-0.273271\pi$
$541$	30.4033	1.30714	0.653569	+	0.756867i	$0.273271\pi$
$542$	−23.7538	−1.02032
$543$	−4.26450	−0.183007
$544$	−0.0864805	−0.00370782
$545$	−24.6279	−1.05494
$546$	−2.85662	−0.122252
$547$	2.37048	0.101354	0.0506771	−	0.998715i	$-0.483862\pi$
$547$	2.37048	0.101354	0.0506771	+	0.998715i	$0.483862\pi$
$548$	49.0290	2.09442
$549$	39.5574	1.68827
$550$	−0.474767	−0.0202442
$551$	38.6995	1.64866
$552$	6.54590	0.278612
$553$	20.9020	0.888843
$554$	−42.5293	−1.80690
$555$	1.30467	0.0553800
$556$	32.5617	1.38092
$557$	−3.79447	−0.160777	−0.0803884	−	0.996764i	$-0.525616\pi$
$557$	−3.79447	−0.160777	−0.0803884	+	0.996764i	$0.525616\pi$
$558$	19.9515	0.844616
$559$	2.21563	0.0937110
$560$	−20.0986	−0.849320
$561$	0.0205981	0.000869652 0
$562$	30.0261	1.26657
$563$	−29.2989	−1.23480	−0.617401	−	0.786648i	$-0.711814\pi$
$563$	−29.2989	−1.23480	−0.617401	+	0.786648i	$0.711814\pi$
$564$	−1.83809	−0.0773974
$565$	−5.84186	−0.245769
$566$	−4.60915	−0.193737
$567$	−25.4771	−1.06994
$568$	47.1149	1.97690
$569$	30.0392	1.25931	0.629655	−	0.776875i	$-0.283196\pi$
$569$	30.0392	1.25931	0.629655	+	0.776875i	$0.283196\pi$
$570$	10.0171	0.419572
$571$	8.17247	0.342007	0.171004	−	0.985270i	$-0.445299\pi$
$571$	8.17247	0.342007	0.171004	+	0.985270i	$0.445299\pi$
$572$	9.06297	0.378942
$573$	3.93915	0.164560
$574$	−49.6540	−2.07252
$575$	0.729256	0.0304121
$576$	29.1724	1.21552
$577$	−33.9919	−1.41510	−0.707551	−	0.706663i	$-0.750200\pi$
$577$	−33.9919	−1.41510	−0.707551	+	0.706663i	$0.750200\pi$
$578$	40.9912	1.70501
$579$	2.25222	0.0935991
$580$	46.9599	1.94990
$581$	−27.8540	−1.15558
$582$	9.48407	0.393128
$583$	6.73525	0.278946
$584$	−46.5672	−1.92697
$585$	−10.0738	−0.416502
$586$	−17.5163	−0.723593
$587$	−17.8712	−0.737624	−0.368812	−	0.929504i	$-0.620235\pi$
$587$	−17.8712	−0.737624	−0.368812	+	0.929504i	$0.620235\pi$
$588$	−2.14788	−0.0885769
$589$	20.0780	0.827301
$590$	54.0590	2.22557
$591$	3.83371	0.157698
$592$	−6.55062	−0.269229
$593$	0.650019	0.0266931	0.0133465	−	0.999911i	$-0.495752\pi$
$593$	0.650019	0.0266931	0.0133465	+	0.999911i	$0.495752\pi$
$594$	−5.77413	−0.236916
$595$	0.350240	0.0143585
$596$	84.9442	3.47945
$597$	−2.17331	−0.0889477
$598$	−21.2173	−0.867639
$599$	−13.7225	−0.560685	−0.280343	−	0.959900i	$-0.590448\pi$
$599$	−13.7225	−0.560685	−0.280343	+	0.959900i	$0.590448\pi$
$600$	0.141880	0.00579224
$601$	42.6296	1.73890	0.869449	−	0.494023i	$-0.164474\pi$
$601$	42.6296	1.73890	0.869449	+	0.494023i	$0.164474\pi$
$602$	10.6760	0.435123
$603$	18.4855	0.752786
$604$	74.0878	3.01459
$605$	−19.3528	−0.786805
$606$	−1.27158	−0.0516545
$607$	34.7593	1.41084	0.705419	−	0.708791i	$-0.250759\pi$
$607$	34.7593	1.41084	0.705419	+	0.708791i	$0.250759\pi$
$608$	12.0616	0.489163
$609$	4.24501	0.172017
$610$	73.6231	2.98091
$611$	2.83518	0.114699
$612$	0.571431	0.0230987
$613$	8.98197	0.362778	0.181389	−	0.983411i	$-0.441941\pi$
$613$	8.98197	0.362778	0.181389	+	0.983411i	$0.441941\pi$
$614$	−45.5617	−1.83872
$615$	3.96374	0.159833
$616$	20.7816	0.837316
$617$	−48.5954	−1.95638	−0.978188	−	0.207722i	$-0.933395\pi$
$617$	−48.5954	−1.95638	−0.978188	+	0.207722i	$0.933395\pi$
$618$	4.11884	0.165684
$619$	−4.96997	−0.199760	−0.0998800	−	0.994999i	$-0.531846\pi$
$619$	−4.96997	−0.199760	−0.0998800	+	0.994999i	$0.531846\pi$
$620$	24.3637	0.978469
$621$	8.86923	0.355910
$622$	39.6356	1.58924
$623$	−54.5872	−2.18699
$624$	−1.14495	−0.0458348
$625$	−25.6128	−1.02451
$626$	−80.6921	−3.22510
$627$	−2.87286	−0.114731
$628$	−0.0982877	−0.00392210
$629$	0.114152	0.00455154
$630$	−48.5410	−1.93392
$631$	24.5670	0.977997	0.488999	−	0.872285i	$-0.337362\pi$
$631$	24.5670	0.977997	0.488999	+	0.872285i	$0.337362\pi$
$632$	30.2041	1.20146
$633$	0.652433	0.0259319
$634$	−12.1458	−0.482373
$635$	40.9633	1.62558
$636$	−4.22961	−0.167715
$637$	3.31302	0.131267
$638$	−20.5266	−0.812655
$639$	31.5614	1.24855
$640$	46.6238	1.84297
$641$	−23.4605	−0.926635	−0.463317	−	0.886192i	$-0.653341\pi$
$641$	−23.4605	−0.926635	−0.463317	+	0.886192i	$0.653341\pi$
$642$	−5.64822	−0.222917
$643$	−29.8604	−1.17758	−0.588789	−	0.808287i	$-0.700395\pi$
$643$	−29.8604	−1.17758	−0.588789	+	0.808287i	$0.700395\pi$
$644$	−67.0785	−2.64326
$645$	−0.852239	−0.0335569
$646$	0.876452	0.0344836
$647$	−25.8515	−1.01633	−0.508163	−	0.861261i	$-0.669675\pi$
$647$	−25.8515	−1.01633	−0.508163	+	0.861261i	$0.669675\pi$
$648$	−36.8154	−1.44625
$649$	−15.5038	−0.608577
$650$	−0.459878	−0.0180379
$651$	2.20239	0.0863186
$652$	44.0275	1.72425
$653$	38.4458	1.50450	0.752249	−	0.658878i	$-0.228969\pi$
$653$	38.4458	1.50450	0.752249	+	0.658878i	$0.228969\pi$
$654$	−6.76025	−0.264347
$655$	−40.8449	−1.59594
$656$	−19.9016	−0.777028
$657$	−31.1946	−1.21702
$658$	13.6614	0.532576
$659$	−18.5771	−0.723663	−0.361831	−	0.932244i	$-0.617848\pi$
$659$	−18.5771	−0.723663	−0.361831	+	0.932244i	$0.617848\pi$
$660$	−3.48606	−0.135695
$661$	−43.0465	−1.67431	−0.837157	−	0.546963i	$-0.815784\pi$
$661$	−43.0465	−1.67431	−0.837157	+	0.546963i	$0.815784\pi$
$662$	−28.8515	−1.12135
$663$	0.0199521	0.000774874 0
$664$	−40.2500	−1.56200
$665$	−48.8488	−1.89427
$666$	−15.8207	−0.613039
$667$	31.5294	1.22082
$668$	−77.5684	−3.00121
$669$	−0.655902	−0.0253586
$670$	34.4046	1.32917
$671$	−21.1146	−0.815122
$672$	1.32306	0.0510381
$673$	−18.7166	−0.721474	−0.360737	−	0.932668i	$-0.617475\pi$
$673$	−18.7166	−0.721474	−0.360737	+	0.932668i	$0.617475\pi$
$674$	3.58480	0.138081
$675$	0.192238	0.00739924
$676$	−40.8280	−1.57031
$677$	5.81844	0.223621	0.111810	−	0.993730i	$-0.464335\pi$
$677$	5.81844	0.223621	0.111810	+	0.993730i	$0.464335\pi$
$678$	−1.60357	−0.0615846
$679$	−46.2492	−1.77488
$680$	0.506110	0.0194084
$681$	−0.646595	−0.0247776
$682$	−10.6496	−0.407793
$683$	20.8603	0.798196	0.399098	−	0.916908i	$-0.369323\pi$
$683$	20.8603	0.798196	0.399098	+	0.916908i	$0.369323\pi$
$684$	−79.6986	−3.04735
$685$	29.0893	1.11145
$686$	−35.1960	−1.34379
$687$	−0.871798	−0.0332612
$688$	4.27903	0.163136
$689$	6.52402	0.248545
$690$	8.16121	0.310692
$691$	−22.9557	−0.873275	−0.436637	−	0.899638i	$-0.643831\pi$
$691$	−22.9557	−0.873275	−0.436637	+	0.899638i	$0.643831\pi$
$692$	51.4629	1.95632
$693$	13.9213	0.528825
$694$	−63.8489	−2.42367
$695$	19.3191	0.732815
$696$	6.13420	0.232516
$697$	0.346808	0.0131363
$698$	−28.4812	−1.07803
$699$	−5.09985	−0.192894
$700$	−1.45391	−0.0549525
$701$	36.0238	1.36060	0.680299	−	0.732934i	$-0.261850\pi$
$701$	36.0238	1.36060	0.680299	+	0.732934i	$0.261850\pi$
$702$	−5.59304	−0.211096
$703$	−15.9210	−0.600472
$704$	−15.5714	−0.586871
$705$	−1.09055	−0.0410725
$706$	48.7126	1.83332
$707$	6.20088	0.233208
$708$	9.73607	0.365904
$709$	−38.7056	−1.45362	−0.726810	−	0.686838i	$-0.758998\pi$
$709$	−38.7056	−1.45362	−0.726810	+	0.686838i	$0.758998\pi$
$710$	58.7412	2.20452
$711$	20.2332	0.758805
$712$	−78.8805	−2.95617
$713$	16.3581	0.612614
$714$	0.0961395	0.00359793
$715$	5.37713	0.201093
$716$	−7.34885	−0.274640
$717$	−1.82755	−0.0682513
$718$	−12.5016	−0.466556
$719$	−25.0001	−0.932348	−0.466174	−	0.884693i	$-0.654368\pi$
$719$	−25.0001	−0.932348	−0.466174	+	0.884693i	$0.654368\pi$
$720$	−19.4555	−0.725065
$721$	−20.0856	−0.748026
$722$	−76.4199	−2.84405
$723$	−2.82681	−0.105130
$724$	63.1482	2.34688
$725$	0.683390	0.0253805
$726$	−5.31227	−0.197157
$727$	12.4757	0.462699	0.231349	−	0.972871i	$-0.425686\pi$
$727$	12.4757	0.462699	0.231349	+	0.972871i	$0.425686\pi$
$728$	20.1299	0.746063
$729$	−23.4799	−0.869627
$730$	−58.0584	−2.14884
$731$	−0.0745668	−0.00275795
$732$	13.2596	0.490088
$733$	44.0716	1.62782	0.813911	−	0.580990i	$-0.197334\pi$
$733$	44.0716	1.62782	0.813911	+	0.580990i	$0.197334\pi$
$734$	6.21511	0.229404
$735$	−1.27435	−0.0470052
$736$	9.82688	0.362223
$737$	−9.86702	−0.363456
$738$	−48.0653	−1.76931
$739$	−7.70822	−0.283551	−0.141776	−	0.989899i	$-0.545281\pi$
$739$	−7.70822	−0.283551	−0.141776	+	0.989899i	$0.545281\pi$
$740$	−19.3193	−0.710193
$741$	−2.78276	−0.102227
$742$	31.4361	1.15406
$743$	29.3921	1.07829	0.539145	−	0.842213i	$-0.318747\pi$
$743$	29.3921	1.07829	0.539145	+	0.842213i	$0.318747\pi$
$744$	3.18254	0.116678
$745$	50.3981	1.84644
$746$	29.1017	1.06549
$747$	−26.9628	−0.986516
$748$	−0.305014	−0.0111524
$749$	27.5436	1.00642
$750$	−6.85805	−0.250421
$751$	−24.5805	−0.896954	−0.448477	−	0.893794i	$-0.648033\pi$
$751$	−24.5805	−0.896954	−0.448477	+	0.893794i	$0.648033\pi$
$752$	5.47557	0.199674
$753$	−5.35133	−0.195013
$754$	−19.8828	−0.724090
$755$	43.9569	1.59975
$756$	−17.6824	−0.643104
$757$	41.3266	1.50204	0.751021	−	0.660278i	$-0.229562\pi$
$757$	41.3266	1.50204	0.751021	+	0.660278i	$0.229562\pi$
$758$	−46.0851	−1.67389
$759$	−2.34058	−0.0849578
$760$	−70.5882	−2.56050
$761$	−44.8176	−1.62464	−0.812318	−	0.583215i	$-0.801794\pi$
$761$	−44.8176	−1.62464	−0.812318	+	0.583215i	$0.801794\pi$
$762$	11.2443	0.407336
$763$	32.9664	1.19347
$764$	−58.3305	−2.11032
$765$	0.339034	0.0122578
$766$	63.4142	2.29125
$767$	−15.0175	−0.542252
$768$	7.67286	0.276871
$769$	39.0067	1.40662	0.703309	−	0.710884i	$-0.251705\pi$
$769$	39.0067	1.40662	0.703309	+	0.710884i	$0.251705\pi$
$770$	25.9098	0.933725
$771$	−1.39237	−0.0501448
$772$	−33.3506	−1.20031
$773$	−29.3272	−1.05483	−0.527413	−	0.849609i	$-0.676838\pi$
$773$	−29.3272	−1.05483	−0.527413	+	0.849609i	$0.676838\pi$
$774$	10.3345	0.371465
$775$	0.354556	0.0127360
$776$	−66.8318	−2.39912
$777$	−1.74640	−0.0626518
$778$	−56.1553	−2.01327
$779$	−48.3701	−1.73304
$780$	−3.37673	−0.120906
$781$	−16.8466	−0.602819
$782$	0.714066	0.0255350
$783$	8.31141	0.297025
$784$	6.39842	0.228515
$785$	−0.0583149	−0.00208135
$786$	−11.2118	−0.399910
$787$	−14.0619	−0.501252	−0.250626	−	0.968084i	$-0.580636\pi$
$787$	−14.0619	−0.501252	−0.250626	+	0.968084i	$0.580636\pi$
$788$	−56.7691	−2.02232
$789$	1.30168	0.0463409
$790$	37.6575	1.33979
$791$	7.81981	0.278040
$792$	20.1167	0.714817
$793$	−20.4524	−0.726287
$794$	−78.0134	−2.76859
$795$	−2.50946	−0.0890014
$796$	32.1821	1.14067
$797$	13.1030	0.464131	0.232065	−	0.972700i	$-0.425452\pi$
$797$	13.1030	0.464131	0.232065	+	0.972700i	$0.425452\pi$
$798$	−13.4088	−0.474665
$799$	−0.0954180	−0.00337565
$800$	0.212994	0.00753049
$801$	−52.8406	−1.86703
$802$	22.7212	0.802312
$803$	16.6508	0.587594
$804$	6.19630	0.218526
$805$	−39.7982	−1.40270
$806$	−10.3156	−0.363351
$807$	−3.96984	−0.139745
$808$	8.96050	0.315229
$809$	16.8938	0.593954	0.296977	−	0.954885i	$-0.404021\pi$
$809$	16.8938	0.593954	0.296977	+	0.954885i	$0.404021\pi$
$810$	−45.9002	−1.61277
$811$	49.3589	1.73323	0.866613	−	0.498981i	$-0.166292\pi$
$811$	49.3589	1.73323	0.866613	+	0.498981i	$0.166292\pi$
$812$	−62.8597	−2.20594
$813$	−2.53822	−0.0890194
$814$	8.44465	0.295985
$815$	26.1219	0.915009
$816$	0.0385333	0.00134894
$817$	10.4000	0.363849
$818$	−30.4881	−1.06599
$819$	13.4846	0.471192
$820$	−58.6946	−2.04970
$821$	34.6550	1.20947	0.604734	−	0.796428i	$-0.293280\pi$
$821$	34.6550	1.20947	0.604734	+	0.796428i	$0.293280\pi$
$822$	7.98489	0.278505
$823$	0.0386524	0.00134734	0.000673669	−	1.00000i	$-0.499786\pi$
$823$	0.0386524	0.00134734	0.000673669		1.00000i	$0.499786\pi$
$824$	−29.0244	−1.01111
$825$	−0.0507314	−0.00176624
$826$	−72.3623	−2.51781
$827$	2.76658	0.0962032	0.0481016	−	0.998842i	$-0.484683\pi$
$827$	2.76658	0.0962032	0.0481016	+	0.998842i	$0.484683\pi$
$828$	−64.9323	−2.25655
$829$	−1.24109	−0.0431048	−0.0215524	−	0.999768i	$-0.506861\pi$
$829$	−1.24109	−0.0431048	−0.0215524	+	0.999768i	$0.506861\pi$
$830$	−50.1823	−1.74185
$831$	−4.54448	−0.157646
$832$	−15.0831	−0.522912
$833$	−0.111500	−0.00386323
$834$	5.30301	0.183628
$835$	−46.0220	−1.59266
$836$	42.5409	1.47131
$837$	4.31211	0.149048
$838$	94.3298	3.25857
$839$	21.8086	0.752917	0.376459	−	0.926433i	$-0.377142\pi$
$839$	21.8086	0.752917	0.376459	+	0.926433i	$0.377142\pi$
$840$	−7.74294	−0.267157
$841$	0.546391	0.0188411
$842$	−41.0106	−1.41332
$843$	3.20844	0.110505
$844$	−9.66115	−0.332550
$845$	−24.2236	−0.833317
$846$	13.2243	0.454661
$847$	25.9053	0.890118
$848$	12.5998	0.432679
$849$	−0.492512	−0.0169030
$850$	0.0154772	0.000530862 0
$851$	−12.9712	−0.444648
$852$	10.5793	0.362442
$853$	39.3802	1.34835	0.674176	−	0.738570i	$-0.264499\pi$
$853$	39.3802	1.34835	0.674176	+	0.738570i	$0.264499\pi$
$854$	−98.5505	−3.37233
$855$	−47.2858	−1.61714
$856$	39.8015	1.36039
$857$	13.0065	0.444293	0.222146	−	0.975013i	$-0.428694\pi$
$857$	13.0065	0.444293	0.222146	+	0.975013i	$0.428694\pi$
$858$	1.47600	0.0503898
$859$	−48.0041	−1.63788	−0.818940	−	0.573879i	$-0.805438\pi$
$859$	−48.0041	−1.63788	−0.818940	+	0.573879i	$0.805438\pi$
$860$	12.6199	0.430333
$861$	−5.30579	−0.180821
$862$	16.8627	0.574345
$863$	13.3283	0.453700	0.226850	−	0.973930i	$-0.427157\pi$
$863$	13.3283	0.453700	0.226850	+	0.973930i	$0.427157\pi$
$864$	2.59044	0.0881287
$865$	30.5333	1.03816
$866$	−88.0061	−2.99057
$867$	4.38013	0.148757
$868$	−32.6128	−1.10695
$869$	−10.7999	−0.366363
$870$	7.64791	0.259289
$871$	−9.55757	−0.323846
$872$	47.6377	1.61322
$873$	−44.7695	−1.51522
$874$	−99.5923	−3.36876
$875$	33.4434	1.13059
$876$	−10.4564	−0.353288
$877$	−11.4142	−0.385429	−0.192714	−	0.981255i	$-0.561729\pi$
$877$	−11.4142	−0.385429	−0.192714	+	0.981255i	$0.561729\pi$
$878$	22.7183	0.766705
$879$	−1.87171	−0.0631313
$880$	10.3848	0.350072
$881$	29.2567	0.985683	0.492841	−	0.870119i	$-0.335958\pi$
$881$	29.2567	0.985683	0.492841	+	0.870119i	$0.335958\pi$
$882$	15.4531	0.520333
$883$	−2.58051	−0.0868410	−0.0434205	−	0.999057i	$-0.513826\pi$
$883$	−2.58051	−0.0868410	−0.0434205	+	0.999057i	$0.513826\pi$
$884$	−0.295448	−0.00993699
$885$	5.77649	0.194174
$886$	−38.2718	−1.28576
$887$	42.3821	1.42305	0.711526	−	0.702660i	$-0.248004\pi$
$887$	42.3821	1.42305	0.711526	+	0.702660i	$0.248004\pi$
$888$	−2.52361	−0.0846869
$889$	−54.8327	−1.83903
$890$	−98.3455	−3.29655
$891$	13.1639	0.441007
$892$	9.71251	0.325199
$893$	13.3081	0.445340
$894$	13.8341	0.462680
$895$	−4.36013	−0.145743
$896$	−62.4097	−2.08496
$897$	−2.26718	−0.0756988
$898$	60.4425	2.01699
$899$	15.3292	0.511258
$900$	−1.40739	−0.0469129
$901$	−0.219566	−0.00731479
$902$	25.6559	0.854249
$903$	1.14079	0.0379632
$904$	11.2999	0.375830
$905$	37.4663	1.24542
$906$	12.0660	0.400865
$907$	−23.7289	−0.787906	−0.393953	−	0.919131i	$-0.628893\pi$
$907$	−23.7289	−0.787906	−0.393953	+	0.919131i	$0.628893\pi$
$908$	9.57470	0.317748
$909$	6.00248	0.199090
$910$	25.0972	0.831965
$911$	−48.2949	−1.60008	−0.800040	−	0.599946i	$-0.795189\pi$
$911$	−48.2949	−1.60008	−0.800040	+	0.599946i	$0.795189\pi$
$912$	−5.37432	−0.177962
$913$	14.3920	0.476305
$914$	1.33895	0.0442884
$915$	7.86701	0.260075
$916$	12.9095	0.426541
$917$	54.6743	1.80550
$918$	0.188234	0.00621264
$919$	13.8575	0.457118	0.228559	−	0.973530i	$-0.426599\pi$
$919$	13.8575	0.457118	0.228559	+	0.973530i	$0.426599\pi$
$920$	−57.5099	−1.89605
$921$	−4.86850	−0.160423
$922$	−42.9986	−1.41608
$923$	−16.3183	−0.537122
$924$	4.66638	0.153513
$925$	−0.281147	−0.00924406
$926$	12.3810	0.406864
$927$	−19.4429	−0.638590
$928$	9.20882	0.302294
$929$	25.9562	0.851596	0.425798	−	0.904818i	$-0.359994\pi$
$929$	25.9562	0.851596	0.425798	+	0.904818i	$0.359994\pi$
$930$	3.96788	0.130112
$931$	15.5511	0.509666
$932$	75.5180	2.47367
$933$	4.23527	0.138657
$934$	69.4508	2.27250
$935$	−0.180967	−0.00591826
$936$	19.4858	0.636914
$937$	41.3099	1.34953	0.674767	−	0.738031i	$-0.264244\pi$
$937$	41.3099	1.34953	0.674767	+	0.738031i	$0.264244\pi$
$938$	−46.0534	−1.50370
$939$	−8.62238	−0.281381
$940$	16.1487	0.526714
$941$	17.8518	0.581953	0.290977	−	0.956730i	$-0.406020\pi$
$941$	17.8518	0.581953	0.290977	+	0.956730i	$0.406020\pi$
$942$	−0.0160072	−0.000521542 0
$943$	−39.4082	−1.28331
$944$	−29.0033	−0.943977
$945$	−10.4911	−0.341277
$946$	−5.51625	−0.179349
$947$	10.4194	0.338584	0.169292	−	0.985566i	$-0.445852\pi$
$947$	10.4194	0.338584	0.169292	+	0.985566i	$0.445852\pi$
$948$	6.78215	0.220274
$949$	16.1286	0.523556
$950$	−2.15863	−0.0700352
$951$	−1.29785	−0.0420856
$952$	−0.677470	−0.0219569
$953$	27.2441	0.882523	0.441261	−	0.897379i	$-0.354531\pi$
$953$	27.2441	0.882523	0.441261	+	0.897379i	$0.354531\pi$
$954$	30.4303	0.985218
$955$	−34.6079	−1.11989
$956$	27.0622	0.875254
$957$	−2.19337	−0.0709017
$958$	−70.4554	−2.27631
$959$	−38.9384	−1.25739
$960$	5.80169	0.187249
$961$	−23.0469	−0.743449
$962$	8.17980	0.263727
$963$	26.6623	0.859182
$964$	41.8591	1.34819
$965$	−19.7872	−0.636972
$966$	−10.9244	−0.351488
$967$	−13.0159	−0.418564	−0.209282	−	0.977855i	$-0.567113\pi$
$967$	−13.0159	−0.418564	−0.209282	+	0.977855i	$0.567113\pi$
$968$	37.4342	1.20318
$969$	0.0936536	0.00300859
$970$	−83.3236	−2.67536
$971$	42.5712	1.36617	0.683087	−	0.730337i	$-0.260637\pi$
$971$	42.5712	1.36617	0.683087	+	0.730337i	$0.260637\pi$
$972$	−25.7708	−0.826599
$973$	−25.8602	−0.829040
$974$	33.1070	1.06082
$975$	−0.0491403	−0.00157375
$976$	−39.4997	−1.26435
$977$	−24.2065	−0.774436	−0.387218	−	0.921988i	$-0.626564\pi$
$977$	−24.2065	−0.774436	−0.387218	+	0.921988i	$0.626564\pi$
$978$	7.17034	0.229282
$979$	28.2049	0.901431
$980$	18.8704	0.602794
$981$	31.9117	1.01886
$982$	−42.9454	−1.37044
$983$	34.2752	1.09321	0.546604	−	0.837391i	$-0.315920\pi$
$983$	34.2752	1.09321	0.546604	+	0.837391i	$0.315920\pi$
$984$	−7.66706	−0.244417
$985$	−33.6816	−1.07318
$986$	0.669156	0.0213103
$987$	1.45979	0.0464657
$988$	41.2067	1.31096
$989$	8.47311	0.269429
$990$	25.0808	0.797121
$991$	32.0505	1.01812	0.509059	−	0.860731i	$-0.329993\pi$
$991$	32.0505	1.01812	0.509059	+	0.860731i	$0.329993\pi$
$992$	4.77771	0.151692
$993$	−3.08294	−0.0978341
$994$	−78.6299	−2.49399
$995$	19.0939	0.605318
$996$	−9.03788	−0.286376
$997$	47.6944	1.51050	0.755249	−	0.655438i	$-0.227516\pi$
$997$	47.6944	1.51050	0.755249	+	0.655438i	$0.227516\pi$
$998$	−82.8198	−2.62162
$999$	−3.41932	−0.108182

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4007.2.a.b.1.19	✓	195

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4007.2.a.b.1.19	✓	195	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:	\( N \)	\(=\)	\( 4007 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.41162 q^{2} -0.257694 q^{3} +3.81590 q^{4} +2.26401 q^{5} +0.621460 q^{6} -3.03056 q^{7} -4.37927 q^{8} -2.93359 q^{9} +O(q^{10})\)	\(q-2.41162 q^{2} -0.257694 q^{3} +3.81590 q^{4} +2.26401 q^{5} +0.621460 q^{6} -3.03056 q^{7} -4.37927 q^{8} -2.93359 q^{9} -5.45992 q^{10} +1.56587 q^{11} -0.983336 q^{12} +1.51676 q^{13} +7.30855 q^{14} -0.583421 q^{15} +2.92931 q^{16} -0.0510465 q^{17} +7.07471 q^{18} +7.11956 q^{19} +8.63923 q^{20} +0.780957 q^{21} -3.77628 q^{22} +5.80048 q^{23} +1.12851 q^{24} +0.125723 q^{25} -3.65785 q^{26} +1.52905 q^{27} -11.5643 q^{28} +5.43566 q^{29} +1.40699 q^{30} +2.82012 q^{31} +1.69415 q^{32} -0.403516 q^{33} +0.123105 q^{34} -6.86120 q^{35} -11.1943 q^{36} -2.23623 q^{37} -17.1697 q^{38} -0.390860 q^{39} -9.91468 q^{40} -6.79396 q^{41} -1.88337 q^{42} +1.46076 q^{43} +5.97521 q^{44} -6.64167 q^{45} -13.9885 q^{46} +1.86923 q^{47} -0.754866 q^{48} +2.18427 q^{49} -0.303197 q^{50} +0.0131544 q^{51} +5.78781 q^{52} +4.30128 q^{53} -3.68749 q^{54} +3.54514 q^{55} +13.2716 q^{56} -1.83467 q^{57} -13.1087 q^{58} -9.90106 q^{59} -2.22628 q^{60} -13.4843 q^{61} -6.80106 q^{62} +8.89042 q^{63} -9.94427 q^{64} +3.43396 q^{65} +0.973126 q^{66} -6.30130 q^{67} -0.194789 q^{68} -1.49475 q^{69} +16.5466 q^{70} -10.7586 q^{71} +12.8470 q^{72} +10.6336 q^{73} +5.39294 q^{74} -0.0323982 q^{75} +27.1676 q^{76} -4.74546 q^{77} +0.942606 q^{78} -6.89708 q^{79} +6.63198 q^{80} +8.40675 q^{81} +16.3844 q^{82} +9.19104 q^{83} +2.98006 q^{84} -0.115570 q^{85} -3.52280 q^{86} -1.40074 q^{87} -6.85736 q^{88} +18.0123 q^{89} +16.0172 q^{90} -4.59663 q^{91} +22.1341 q^{92} -0.726729 q^{93} -4.50788 q^{94} +16.1187 q^{95} -0.436572 q^{96} +15.2610 q^{97} -5.26764 q^{98} -4.59363 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 195 q + 14 q^{2} + 22 q^{3} + 220 q^{4} + 14 q^{5} + 13 q^{6} + 48 q^{7} + 39 q^{8} + 245 q^{9}+O(q^{10}) \) 195 * q + 14 * q^2 + 22 * q^3 + 220 * q^4 + 14 * q^5 + 13 * q^6 + 48 * q^7 + 39 * q^8 + 245 * q^9	\( 195 q + 14 q^{2} + 22 q^{3} + 220 q^{4} + 14 q^{5} + 13 q^{6} + 48 q^{7} + 39 q^{8} + 245 q^{9} + 40 q^{10} + 13 q^{11} + 57 q^{12} + 97 q^{13} + 9 q^{14} + 23 q^{15} + 270 q^{16} + 66 q^{17} + 60 q^{18} + 33 q^{19} + 24 q^{20} + 27 q^{21} + 127 q^{22} + 42 q^{23} + 33 q^{24} + 357 q^{25} + 8 q^{26} + 79 q^{27} + 131 q^{28} + 57 q^{29} + 51 q^{30} + 41 q^{31} + 67 q^{32} + 74 q^{33} + 26 q^{34} + 14 q^{35} + 279 q^{36} + 133 q^{37} + 7 q^{38} + 28 q^{39} + 97 q^{40} + 64 q^{41} - q^{42} + 123 q^{43} + 21 q^{44} + 40 q^{45} + 84 q^{46} + 14 q^{47} + 122 q^{48} + 335 q^{49} + 35 q^{50} + 37 q^{51} + 220 q^{52} + 83 q^{53} + 21 q^{54} + 47 q^{55} + q^{56} + 235 q^{57} + 138 q^{58} + 18 q^{59} - 4 q^{60} + 81 q^{61} + 39 q^{62} + 102 q^{63} + 343 q^{64} + 165 q^{65} - 54 q^{66} + 147 q^{67} + 74 q^{68} - 2 q^{69} + 13 q^{70} + 31 q^{71} + 112 q^{72} + 300 q^{73} + 5 q^{74} + 84 q^{75} + 64 q^{76} + 67 q^{77} + 61 q^{78} + 144 q^{79} - 8 q^{80} + 359 q^{81} + 85 q^{82} + 26 q^{83} + 12 q^{84} + 201 q^{85} - 2 q^{86} + 80 q^{87} + 347 q^{88} + 29 q^{89} + 62 q^{90} + 70 q^{91} + 79 q^{92} + 76 q^{93} + 72 q^{94} + 71 q^{95} + 31 q^{96} + 264 q^{97} + 30 q^{98} + 19 q^{99}+O(q^{100}) \) 195 * q + 14 * q^2 + 22 * q^3 + 220 * q^4 + 14 * q^5 + 13 * q^6 + 48 * q^7 + 39 * q^8 + 245 * q^9 + 40 * q^10 + 13 * q^11 + 57 * q^12 + 97 * q^13 + 9 * q^14 + 23 * q^15 + 270 * q^16 + 66 * q^17 + 60 * q^18 + 33 * q^19 + 24 * q^20 + 27 * q^21 + 127 * q^22 + 42 * q^23 + 33 * q^24 + 357 * q^25 + 8 * q^26 + 79 * q^27 + 131 * q^28 + 57 * q^29 + 51 * q^30 + 41 * q^31 + 67 * q^32 + 74 * q^33 + 26 * q^34 + 14 * q^35 + 279 * q^36 + 133 * q^37 + 7 * q^38 + 28 * q^39 + 97 * q^40 + 64 * q^41 - q^42 + 123 * q^43 + 21 * q^44 + 40 * q^45 + 84 * q^46 + 14 * q^47 + 122 * q^48 + 335 * q^49 + 35 * q^50 + 37 * q^51 + 220 * q^52 + 83 * q^53 + 21 * q^54 + 47 * q^55 + q^56 + 235 * q^57 + 138 * q^58 + 18 * q^59 - 4 * q^60 + 81 * q^61 + 39 * q^62 + 102 * q^63 + 343 * q^64 + 165 * q^65 - 54 * q^66 + 147 * q^67 + 74 * q^68 - 2 * q^69 + 13 * q^70 + 31 * q^71 + 112 * q^72 + 300 * q^73 + 5 * q^74 + 84 * q^75 + 64 * q^76 + 67 * q^77 + 61 * q^78 + 144 * q^79 - 8 * q^80 + 359 * q^81 + 85 * q^82 + 26 * q^83 + 12 * q^84 + 201 * q^85 - 2 * q^86 + 80 * q^87 + 347 * q^88 + 29 * q^89 + 62 * q^90 + 70 * q^91 + 79 * q^92 + 76 * q^93 + 72 * q^94 + 71 * q^95 + 31 * q^96 + 264 * q^97 + 30 * q^98 + 19 * q^99

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