LMFDB - Embedded newform 6001.2.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6001,2,Mod(1,6001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6001, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6001 = 17 \cdot 353 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6001.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:	$47.9182262530$
Analytic rank:	$1$
Dimension:	$113$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	6001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.72078 q^{2} -0.920111 q^{3} +5.40267 q^{4} -2.98260 q^{5} +2.50342 q^{6} -1.43517 q^{7} -9.25792 q^{8} -2.15340 q^{9} +O(q^{10})$	\(q-2.72078 q^{2} -0.920111 q^{3} +5.40267 q^{4} -2.98260 q^{5} +2.50342 q^{6} -1.43517 q^{7} -9.25792 q^{8} -2.15340 q^{9} +8.11501 q^{10} -3.97803 q^{11} -4.97105 q^{12} +2.53691 q^{13} +3.90479 q^{14} +2.74432 q^{15} +14.3835 q^{16} -1.00000 q^{17} +5.85892 q^{18} -3.32766 q^{19} -16.1140 q^{20} +1.32052 q^{21} +10.8234 q^{22} +2.94126 q^{23} +8.51831 q^{24} +3.89591 q^{25} -6.90238 q^{26} +4.74170 q^{27} -7.75375 q^{28} -6.78486 q^{29} -7.46671 q^{30} +6.35643 q^{31} -20.6185 q^{32} +3.66023 q^{33} +2.72078 q^{34} +4.28054 q^{35} -11.6341 q^{36} -8.62003 q^{37} +9.05383 q^{38} -2.33424 q^{39} +27.6127 q^{40} +0.427022 q^{41} -3.59284 q^{42} -6.92221 q^{43} -21.4920 q^{44} +6.42272 q^{45} -8.00253 q^{46} -3.65806 q^{47} -13.2344 q^{48} -4.94029 q^{49} -10.5999 q^{50} +0.920111 q^{51} +13.7061 q^{52} +1.28730 q^{53} -12.9011 q^{54} +11.8649 q^{55} +13.2867 q^{56} +3.06181 q^{57} +18.4601 q^{58} +11.8272 q^{59} +14.8267 q^{60} +15.5815 q^{61} -17.2945 q^{62} +3.09049 q^{63} +27.3315 q^{64} -7.56659 q^{65} -9.95871 q^{66} +11.8963 q^{67} -5.40267 q^{68} -2.70629 q^{69} -11.6464 q^{70} -5.94783 q^{71} +19.9360 q^{72} +3.54035 q^{73} +23.4532 q^{74} -3.58467 q^{75} -17.9782 q^{76} +5.70916 q^{77} +6.35096 q^{78} -2.62588 q^{79} -42.9001 q^{80} +2.09730 q^{81} -1.16184 q^{82} -5.81991 q^{83} +7.13431 q^{84} +2.98260 q^{85} +18.8338 q^{86} +6.24283 q^{87} +36.8283 q^{88} +6.71779 q^{89} -17.4748 q^{90} -3.64090 q^{91} +15.8906 q^{92} -5.84862 q^{93} +9.95279 q^{94} +9.92507 q^{95} +18.9713 q^{96} -4.75650 q^{97} +13.4414 q^{98} +8.56628 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9}+O(q^{10}) $ 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9	\( 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9} - 5 q^{10} - 40 q^{11} - 19 q^{12} - 18 q^{13} - 48 q^{14} - 63 q^{15} + 79 q^{16} - 113 q^{17} - 32 q^{18} - 46 q^{19} - 56 q^{20} - 46 q^{21} + 14 q^{22} - 35 q^{23} - 42 q^{24} + 88 q^{25} - 89 q^{26} - 41 q^{27} + 20 q^{28} - 51 q^{29} - 18 q^{30} - 57 q^{31} - 93 q^{32} - 40 q^{33} + 11 q^{34} - 69 q^{35} + 18 q^{36} + 16 q^{37} - 74 q^{38} - 51 q^{39} + 2 q^{40} - 87 q^{41} - 23 q^{42} - 32 q^{43} - 110 q^{44} - 17 q^{45} - 17 q^{46} - 161 q^{47} - 36 q^{48} + 56 q^{49} - 69 q^{50} + 11 q^{51} - 49 q^{52} - 48 q^{53} - 38 q^{54} - 79 q^{55} - 171 q^{56} + 20 q^{57} + 13 q^{58} - 174 q^{59} - 146 q^{60} - 34 q^{61} - 34 q^{62} - 14 q^{63} + 62 q^{64} - 22 q^{65} - 60 q^{66} - 50 q^{67} - 103 q^{68} - 59 q^{69} - 58 q^{70} - 189 q^{71} - 123 q^{72} - 4 q^{73} - 24 q^{74} - 106 q^{75} - 92 q^{76} - 78 q^{77} - 42 q^{78} + 8 q^{79} - 150 q^{80} + 13 q^{81} + 6 q^{82} - 109 q^{83} - 114 q^{84} + 19 q^{85} - 116 q^{86} - 106 q^{87} + 54 q^{88} - 170 q^{89} - q^{90} - 43 q^{91} - 94 q^{92} - 69 q^{93} - 35 q^{94} - 78 q^{95} - 44 q^{96} - 3 q^{97} - 68 q^{98} - 119 q^{99}+O(q^{100}) \) 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9 - 5 * q^10 - 40 * q^11 - 19 * q^12 - 18 * q^13 - 48 * q^14 - 63 * q^15 + 79 * q^16 - 113 * q^17 - 32 * q^18 - 46 * q^19 - 56 * q^20 - 46 * q^21 + 14 * q^22 - 35 * q^23 - 42 * q^24 + 88 * q^25 - 89 * q^26 - 41 * q^27 + 20 * q^28 - 51 * q^29 - 18 * q^30 - 57 * q^31 - 93 * q^32 - 40 * q^33 + 11 * q^34 - 69 * q^35 + 18 * q^36 + 16 * q^37 - 74 * q^38 - 51 * q^39 + 2 * q^40 - 87 * q^41 - 23 * q^42 - 32 * q^43 - 110 * q^44 - 17 * q^45 - 17 * q^46 - 161 * q^47 - 36 * q^48 + 56 * q^49 - 69 * q^50 + 11 * q^51 - 49 * q^52 - 48 * q^53 - 38 * q^54 - 79 * q^55 - 171 * q^56 + 20 * q^57 + 13 * q^58 - 174 * q^59 - 146 * q^60 - 34 * q^61 - 34 * q^62 - 14 * q^63 + 62 * q^64 - 22 * q^65 - 60 * q^66 - 50 * q^67 - 103 * q^68 - 59 * q^69 - 58 * q^70 - 189 * q^71 - 123 * q^72 - 4 * q^73 - 24 * q^74 - 106 * q^75 - 92 * q^76 - 78 * q^77 - 42 * q^78 + 8 * q^79 - 150 * q^80 + 13 * q^81 + 6 * q^82 - 109 * q^83 - 114 * q^84 + 19 * q^85 - 116 * q^86 - 106 * q^87 + 54 * q^88 - 170 * q^89 - q^90 - 43 * q^91 - 94 * q^92 - 69 * q^93 - 35 * q^94 - 78 * q^95 - 44 * q^96 - 3 * q^97 - 68 * q^98 - 119 * 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 $

$2$	−2.72078	−1.92388	−0.961942	−	0.273252i	$-0.911901\pi$
$2$	−2.72078	−1.92388	−0.961942	+	0.273252i	$0.911901\pi$
$3$	−0.920111	−0.531226	−0.265613	−	0.964080i	$-0.585574\pi$
$3$	−0.920111	−0.531226	−0.265613	+	0.964080i	$0.585574\pi$
$4$	5.40267	2.70133
$5$	−2.98260	−1.33386	−0.666930	−	0.745121i	$-0.732392\pi$
$5$	−2.98260	−1.33386	−0.666930	+	0.745121i	$0.732392\pi$
$6$	2.50342	1.02202
$7$	−1.43517	−0.542444	−0.271222	−	0.962517i	$-0.587428\pi$
$7$	−1.43517	−0.542444	−0.271222	+	0.962517i	$0.587428\pi$
$8$	−9.25792	−3.27317
$9$	−2.15340	−0.717798
$10$	8.11501	2.56619
$11$	−3.97803	−1.19942	−0.599711	−	0.800217i	$-0.704718\pi$
$11$	−3.97803	−1.19942	−0.599711	+	0.800217i	$0.704718\pi$
$12$	−4.97105	−1.43502
$13$	2.53691	0.703612	0.351806	−	0.936073i	$-0.385568\pi$
$13$	2.53691	0.703612	0.351806	+	0.936073i	$0.385568\pi$
$14$	3.90479	1.04360
$15$	2.74432	0.708582
$16$	14.3835	3.59587
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	5.85892	1.38096
$19$	−3.32766	−0.763416	−0.381708	−	0.924283i	$-0.624664\pi$
$19$	−3.32766	−0.763416	−0.381708	+	0.924283i	$0.624664\pi$
$20$	−16.1140	−3.60320
$21$	1.32052	0.288160
$22$	10.8234	2.30755
$23$	2.94126	0.613295	0.306647	−	0.951823i	$-0.400793\pi$
$23$	2.94126	0.613295	0.306647	+	0.951823i	$0.400793\pi$
$24$	8.51831	1.73879
$25$	3.89591	0.779182
$26$	−6.90238	−1.35367
$27$	4.74170	0.912540
$28$	−7.75375	−1.46532
$29$	−6.78486	−1.25992	−0.629959	−	0.776629i	$-0.716928\pi$
$29$	−6.78486	−1.25992	−0.629959	+	0.776629i	$0.716928\pi$
$30$	−7.46671	−1.36323
$31$	6.35643	1.14165	0.570824	−	0.821072i	$-0.306624\pi$
$31$	6.35643	1.14165	0.570824	+	0.821072i	$0.306624\pi$
$32$	−20.6185	−3.64486
$33$	3.66023	0.637165
$34$	2.72078	0.466611
$35$	4.28054	0.723544
$36$	−11.6341	−1.93901
$37$	−8.62003	−1.41712	−0.708562	−	0.705649i	$-0.750656\pi$
$37$	−8.62003	−1.41712	−0.708562	+	0.705649i	$0.750656\pi$
$38$	9.05383	1.46873
$39$	−2.33424	−0.373777
$40$	27.6127	4.36595
$41$	0.427022	0.0666897	0.0333449	−	0.999444i	$-0.489384\pi$
$41$	0.427022	0.0666897	0.0333449	+	0.999444i	$0.489384\pi$
$42$	−3.59284	−0.554387
$43$	−6.92221	−1.05563	−0.527814	−	0.849360i	$-0.676988\pi$
$43$	−6.92221	−1.05563	−0.527814	+	0.849360i	$0.676988\pi$
$44$	−21.4920	−3.24004
$45$	6.42272	0.957442
$46$	−8.00253	−1.17991
$47$	−3.65806	−0.533583	−0.266792	−	0.963754i	$-0.585964\pi$
$47$	−3.65806	−0.533583	−0.266792	+	0.963754i	$0.585964\pi$
$48$	−13.2344	−1.91022
$49$	−4.94029	−0.705755
$50$	−10.5999	−1.49906
$51$	0.920111	0.128841
$52$	13.7061	1.90069
$53$	1.28730	0.176824	0.0884120	−	0.996084i	$-0.471821\pi$
$53$	1.28730	0.176824	0.0884120	+	0.996084i	$0.471821\pi$
$54$	−12.9011	−1.75562
$55$	11.8649	1.59986
$56$	13.2867	1.77551
$57$	3.06181	0.405547
$58$	18.4601	2.42394
$59$	11.8272	1.53978	0.769888	−	0.638179i	$-0.220312\pi$
$59$	11.8272	1.53978	0.769888	+	0.638179i	$0.220312\pi$
$60$	14.8267	1.91411
$61$	15.5815	1.99500	0.997502	−	0.0706435i	$-0.0225053\pi$
$61$	15.5815	1.99500	0.997502	+	0.0706435i	$0.0225053\pi$
$62$	−17.2945	−2.19640
$63$	3.09049	0.389365
$64$	27.3315	3.41643
$65$	−7.56659	−0.938519
$66$	−9.95871	−1.22583
$67$	11.8963	1.45336	0.726681	−	0.686975i	$-0.241062\pi$
$67$	11.8963	1.45336	0.726681	+	0.686975i	$0.241062\pi$
$68$	−5.40267	−0.655169
$69$	−2.70629	−0.325798
$70$	−11.6464	−1.39201
$71$	−5.94783	−0.705878	−0.352939	−	0.935646i	$-0.614818\pi$
$71$	−5.94783	−0.705878	−0.352939	+	0.935646i	$0.614818\pi$
$72$	19.9360	2.34948
$73$	3.54035	0.414367	0.207183	−	0.978302i	$-0.433570\pi$
$73$	3.54035	0.414367	0.207183	+	0.978302i	$0.433570\pi$
$74$	23.4532	2.72638
$75$	−3.58467	−0.413922
$76$	−17.9782	−2.06224
$77$	5.70916	0.650619
$78$	6.35096	0.719104
$79$	−2.62588	−0.295434	−0.147717	−	0.989030i	$-0.547193\pi$
$79$	−2.62588	−0.295434	−0.147717	+	0.989030i	$0.547193\pi$
$80$	−42.9001	−4.79638
$81$	2.09730	0.233033
$82$	−1.16184	−0.128303
$83$	−5.81991	−0.638818	−0.319409	−	0.947617i	$-0.603484\pi$
$83$	−5.81991	−0.638818	−0.319409	+	0.947617i	$0.603484\pi$
$84$	7.13431	0.778417
$85$	2.98260	0.323509
$86$	18.8338	2.03091
$87$	6.24283	0.669302
$88$	36.8283	3.92591
$89$	6.71779	0.712084	0.356042	−	0.934470i	$-0.384126\pi$
$89$	6.71779	0.712084	0.356042	+	0.934470i	$0.384126\pi$
$90$	−17.4748	−1.84201
$91$	−3.64090	−0.381670
$92$	15.8906	1.65671
$93$	−5.84862	−0.606474
$94$	9.95279	1.02655
$95$	9.92507	1.01829
$96$	18.9713	1.93625
$97$	−4.75650	−0.482950	−0.241475	−	0.970407i	$-0.577631\pi$
$97$	−4.75650	−0.482950	−0.241475	+	0.970407i	$0.577631\pi$
$98$	13.4414	1.35779
$99$	8.56628	0.860943
$100$	21.0483	2.10483
$101$	−8.58400	−0.854140	−0.427070	−	0.904219i	$-0.640454\pi$
$101$	−8.58400	−0.854140	−0.427070	+	0.904219i	$0.640454\pi$
$102$	−2.50342	−0.247876
$103$	9.73400	0.959120	0.479560	−	0.877509i	$-0.340796\pi$
$103$	9.73400	0.959120	0.479560	+	0.877509i	$0.340796\pi$
$104$	−23.4865	−2.30304
$105$	−3.93857	−0.384366
$106$	−3.50246	−0.340189
$107$	14.8173	1.43244	0.716222	−	0.697872i	$-0.245870\pi$
$107$	14.8173	1.43244	0.716222	+	0.697872i	$0.245870\pi$
$108$	25.6178	2.46507
$109$	−2.16462	−0.207333	−0.103667	−	0.994612i	$-0.533057\pi$
$109$	−2.16462	−0.207333	−0.103667	+	0.994612i	$0.533057\pi$
$110$	−32.2818	−3.07795
$111$	7.93139	0.752814
$112$	−20.6427	−1.95055
$113$	1.21706	0.114492	0.0572458	−	0.998360i	$-0.481768\pi$
$113$	1.21706	0.114492	0.0572458	+	0.998360i	$0.481768\pi$
$114$	−8.33053	−0.780226
$115$	−8.77260	−0.818049
$116$	−36.6563	−3.40346
$117$	−5.46297	−0.505051
$118$	−32.1794	−2.96235
$119$	1.43517	0.131562
$120$	−25.4067	−2.31931
$121$	4.82475	0.438614
$122$	−42.3938	−3.83816
$123$	−0.392908	−0.0354273
$124$	34.3417	3.08397
$125$	3.29306	0.294541
$126$	−8.40856	−0.749094
$127$	17.5500	1.55731	0.778657	−	0.627450i	$-0.215901\pi$
$127$	17.5500	1.55731	0.778657	+	0.627450i	$0.215901\pi$
$128$	−33.1261	−2.92796
$129$	6.36921	0.560777
$130$	20.5870	1.80560
$131$	−3.46213	−0.302488	−0.151244	−	0.988496i	$-0.548328\pi$
$131$	−3.46213	−0.302488	−0.151244	+	0.988496i	$0.548328\pi$
$132$	19.7750	1.72119
$133$	4.77575	0.414110
$134$	−32.3672	−2.79610
$135$	−14.1426	−1.21720
$136$	9.25792	0.793860
$137$	−6.30377	−0.538567	−0.269284	−	0.963061i	$-0.586787\pi$
$137$	−6.30377	−0.538567	−0.269284	+	0.963061i	$0.586787\pi$
$138$	7.36322	0.626799
$139$	22.5738	1.91468	0.957342	−	0.288957i	$-0.0933085\pi$
$139$	22.5738	1.91468	0.957342	+	0.288957i	$0.0933085\pi$
$140$	23.1263	1.95453
$141$	3.36582	0.283453
$142$	16.1828	1.35803
$143$	−10.0919	−0.843928
$144$	−30.9733	−2.58111
$145$	20.2365	1.68055
$146$	−9.63254	−0.797194
$147$	4.54561	0.374916
$148$	−46.5711	−3.82812
$149$	−8.10218	−0.663756	−0.331878	−	0.943322i	$-0.607682\pi$
$149$	−8.10218	−0.663756	−0.331878	+	0.943322i	$0.607682\pi$
$150$	9.75311	0.796338
$151$	−5.73930	−0.467057	−0.233529	−	0.972350i	$-0.575027\pi$
$151$	−5.73930	−0.467057	−0.233529	+	0.972350i	$0.575027\pi$
$152$	30.8072	2.49879
$153$	2.15340	0.174092
$154$	−15.5334	−1.25172
$155$	−18.9587	−1.52280
$156$	−12.6111	−1.00970
$157$	5.57322	0.444791	0.222396	−	0.974956i	$-0.428612\pi$
$157$	5.57322	0.444791	0.222396	+	0.974956i	$0.428612\pi$
$158$	7.14445	0.568382
$159$	−1.18446	−0.0939336
$160$	61.4967	4.86174
$161$	−4.22121	−0.332678
$162$	−5.70629	−0.448329
$163$	−2.42277	−0.189766	−0.0948829	−	0.995488i	$-0.530248\pi$
$163$	−2.42277	−0.189766	−0.0948829	+	0.995488i	$0.530248\pi$
$164$	2.30706	0.180151
$165$	−10.9170	−0.849889
$166$	15.8347	1.22901
$167$	17.5085	1.35485	0.677423	−	0.735594i	$-0.263097\pi$
$167$	17.5085	1.35485	0.677423	+	0.735594i	$0.263097\pi$
$168$	−12.2252	−0.943197
$169$	−6.56410	−0.504931
$170$	−8.11501	−0.622393
$171$	7.16576	0.547979
$172$	−37.3984	−2.85160
$173$	20.4721	1.55646	0.778231	−	0.627978i	$-0.216117\pi$
$173$	20.4721	1.55646	0.778231	+	0.627978i	$0.216117\pi$
$174$	−16.9854	−1.28766
$175$	−5.59129	−0.422662
$176$	−57.2179	−4.31296
$177$	−10.8824	−0.817970
$178$	−18.2777	−1.36997
$179$	−1.41508	−0.105768	−0.0528842	−	0.998601i	$-0.516841\pi$
$179$	−1.41508	−0.105768	−0.0528842	+	0.998601i	$0.516841\pi$
$180$	34.6998	2.58637
$181$	−8.21996	−0.610985	−0.305493	−	0.952194i	$-0.598821\pi$
$181$	−8.21996	−0.610985	−0.305493	+	0.952194i	$0.598821\pi$
$182$	9.90609	0.734288
$183$	−14.3367	−1.05980
$184$	−27.2299	−2.00742
$185$	25.7101	1.89024
$186$	15.9128	1.16679
$187$	3.97803	0.290903
$188$	−19.7633	−1.44139
$189$	−6.80514	−0.495001
$190$	−27.0040	−1.95907
$191$	−19.3542	−1.40042	−0.700212	−	0.713935i	$-0.746911\pi$
$191$	−19.3542	−1.40042	−0.700212	+	0.713935i	$0.746911\pi$
$192$	−25.1480	−1.81490
$193$	7.78363	0.560278	0.280139	−	0.959959i	$-0.409619\pi$
$193$	7.78363	0.560278	0.280139	+	0.959959i	$0.409619\pi$
$194$	12.9414	0.929140
$195$	6.96210	0.498566
$196$	−26.6907	−1.90648
$197$	6.44654	0.459297	0.229648	−	0.973274i	$-0.426242\pi$
$197$	6.44654	0.459297	0.229648	+	0.973274i	$0.426242\pi$
$198$	−23.3070	−1.65636
$199$	−5.03100	−0.356638	−0.178319	−	0.983973i	$-0.557066\pi$
$199$	−5.03100	−0.356638	−0.178319	+	0.983973i	$0.557066\pi$
$200$	−36.0680	−2.55039
$201$	−10.9459	−0.772064
$202$	23.3552	1.64327
$203$	9.73744	0.683434
$204$	4.97105	0.348043
$205$	−1.27364	−0.0889547
$206$	−26.4841	−1.84524
$207$	−6.33369	−0.440222
$208$	36.4895	2.53009
$209$	13.2375	0.915659
$210$	10.7160	0.739475
$211$	−12.9947	−0.894592	−0.447296	−	0.894386i	$-0.647613\pi$
$211$	−12.9947	−0.894592	−0.447296	+	0.894386i	$0.647613\pi$
$212$	6.95484	0.477661
$213$	5.47267	0.374981
$214$	−40.3147	−2.75586
$215$	20.6462	1.40806
$216$	−43.8982	−2.98690
$217$	−9.12256	−0.619280
$218$	5.88947	0.398885
$219$	−3.25752	−0.220123
$220$	64.1020	4.32176
$221$	−2.53691	−0.170651
$222$	−21.5796	−1.44833
$223$	−4.96919	−0.332761	−0.166381	−	0.986062i	$-0.553208\pi$
$223$	−4.96919	−0.332761	−0.166381	+	0.986062i	$0.553208\pi$
$224$	29.5910	1.97713
$225$	−8.38943	−0.559295
$226$	−3.31136	−0.220269
$227$	11.0559	0.733803	0.366901	−	0.930260i	$-0.380419\pi$
$227$	11.0559	0.733803	0.366901	+	0.930260i	$0.380419\pi$
$228$	16.5420	1.09552
$229$	−0.447707	−0.0295853	−0.0147926	−	0.999891i	$-0.504709\pi$
$229$	−0.447707	−0.0295853	−0.0147926	+	0.999891i	$0.504709\pi$
$230$	23.8684	1.57383
$231$	−5.25306	−0.345626
$232$	62.8137	4.12392
$233$	2.00270	0.131201	0.0656006	−	0.997846i	$-0.479104\pi$
$233$	2.00270	0.131201	0.0656006	+	0.997846i	$0.479104\pi$
$234$	14.8636	0.971661
$235$	10.9105	0.711725
$236$	63.8986	4.15945
$237$	2.41610	0.156943
$238$	−3.90479	−0.253110
$239$	−11.9494	−0.772945	−0.386473	−	0.922301i	$-0.626307\pi$
$239$	−11.9494	−0.772945	−0.386473	+	0.922301i	$0.626307\pi$
$240$	39.4729	2.54796
$241$	7.51833	0.484298	0.242149	−	0.970239i	$-0.422148\pi$
$241$	7.51833	0.484298	0.242149	+	0.970239i	$0.422148\pi$
$242$	−13.1271	−0.843843
$243$	−16.1548	−1.03633
$244$	84.1815	5.38917
$245$	14.7349	0.941378
$246$	1.06902	0.0681581
$247$	−8.44196	−0.537149
$248$	−58.8473	−3.73681
$249$	5.35497	0.339357
$250$	−8.95972	−0.566662
$251$	−9.20160	−0.580800	−0.290400	−	0.956905i	$-0.593788\pi$
$251$	−9.20160	−0.580800	−0.290400	+	0.956905i	$0.593788\pi$
$252$	16.6969	1.05180
$253$	−11.7004	−0.735600
$254$	−47.7499	−2.99609
$255$	−2.74432	−0.171856
$256$	35.4660	2.21662
$257$	9.40843	0.586881	0.293441	−	0.955977i	$-0.405200\pi$
$257$	9.40843	0.586881	0.293441	+	0.955977i	$0.405200\pi$
$258$	−17.3292	−1.07887
$259$	12.3712	0.768710
$260$	−40.8797	−2.53525
$261$	14.6105	0.904367
$262$	9.41972	0.581952
$263$	−17.4357	−1.07513	−0.537565	−	0.843222i	$-0.680656\pi$
$263$	−17.4357	−1.07513	−0.537565	+	0.843222i	$0.680656\pi$
$264$	−33.8861	−2.08555
$265$	−3.83950	−0.235859
$266$	−12.9938	−0.796701
$267$	−6.18111	−0.378278
$268$	64.2716	3.92601
$269$	16.6560	1.01554	0.507768	−	0.861494i	$-0.330471\pi$
$269$	16.6560	1.01554	0.507768	+	0.861494i	$0.330471\pi$
$270$	38.4789	2.34175
$271$	14.2028	0.862756	0.431378	−	0.902171i	$-0.358028\pi$
$271$	14.2028	0.862756	0.431378	+	0.902171i	$0.358028\pi$
$272$	−14.3835	−0.872126
$273$	3.35003	0.202753
$274$	17.1512	1.03614
$275$	−15.4981	−0.934568
$276$	−14.6212	−0.880090
$277$	16.4958	0.991138	0.495569	−	0.868569i	$-0.334960\pi$
$277$	16.4958	0.991138	0.495569	+	0.868569i	$0.334960\pi$
$278$	−61.4184	−3.68363
$279$	−13.6879	−0.819474
$280$	−39.6289	−2.36828
$281$	−26.8787	−1.60345	−0.801725	−	0.597693i	$-0.796084\pi$
$281$	−26.8787	−1.60345	−0.801725	+	0.597693i	$0.796084\pi$
$282$	−9.15768	−0.545332
$283$	17.9739	1.06844	0.534220	−	0.845346i	$-0.320606\pi$
$283$	17.9739	1.06844	0.534220	+	0.845346i	$0.320606\pi$
$284$	−32.1342	−1.90681
$285$	−9.13217	−0.540943
$286$	27.4579	1.62362
$287$	−0.612850	−0.0361754
$288$	44.3997	2.61628
$289$	1.00000	0.0588235
$290$	−55.0593	−3.23319
$291$	4.37651	0.256556
$292$	19.1273	1.11934
$293$	8.02704	0.468945	0.234472	−	0.972123i	$-0.424664\pi$
$293$	8.02704	0.468945	0.234472	+	0.972123i	$0.424664\pi$
$294$	−12.3676	−0.721295
$295$	−35.2759	−2.05385
$296$	79.8035	4.63849
$297$	−18.8626	−1.09452
$298$	22.0443	1.27699
$299$	7.46170	0.431521
$300$	−19.3668	−1.11814
$301$	9.93456	0.572618
$302$	15.6154	0.898565
$303$	7.89824	0.453742
$304$	−47.8632	−2.74514
$305$	−46.4733	−2.66105
$306$	−5.85892	−0.334932
$307$	−13.0890	−0.747031	−0.373516	−	0.927624i	$-0.621848\pi$
$307$	−13.0890	−0.747031	−0.373516	+	0.927624i	$0.621848\pi$
$308$	30.8447	1.75754
$309$	−8.95637	−0.509510
$310$	51.5825	2.92969
$311$	−6.09816	−0.345795	−0.172897	−	0.984940i	$-0.555313\pi$
$311$	−6.09816	−0.345795	−0.172897	+	0.984940i	$0.555313\pi$
$312$	21.6102	1.22344
$313$	−12.1844	−0.688703	−0.344352	−	0.938841i	$-0.611901\pi$
$313$	−12.1844	−0.688703	−0.344352	+	0.938841i	$0.611901\pi$
$314$	−15.1635	−0.855728
$315$	−9.21770	−0.519358
$316$	−14.1867	−0.798066
$317$	16.0666	0.902392	0.451196	−	0.892425i	$-0.350998\pi$
$317$	16.0666	0.902392	0.451196	+	0.892425i	$0.350998\pi$
$318$	3.22265	0.180717
$319$	26.9904	1.51117
$320$	−81.5188	−4.55704
$321$	−13.6336	−0.760953
$322$	11.4850	0.640034
$323$	3.32766	0.185156
$324$	11.3310	0.629500
$325$	9.88356	0.548241
$326$	6.59183	0.365088
$327$	1.99169	0.110141
$328$	−3.95334	−0.218287
$329$	5.24994	0.289439
$330$	29.7028	1.63509
$331$	−16.6309	−0.914115	−0.457057	−	0.889437i	$-0.651097\pi$
$331$	−16.6309	−0.914115	−0.457057	+	0.889437i	$0.651097\pi$
$332$	−31.4430	−1.72566
$333$	18.5623	1.01721
$334$	−47.6367	−2.60657
$335$	−35.4819	−1.93858
$336$	18.9936	1.03619
$337$	15.4363	0.840870	0.420435	−	0.907323i	$-0.361877\pi$
$337$	15.4363	0.840870	0.420435	+	0.907323i	$0.361877\pi$
$338$	17.8595	0.971428
$339$	−1.11983	−0.0608209
$340$	16.1140	0.873904
$341$	−25.2861	−1.36932
$342$	−19.4965	−1.05425
$343$	17.1363	0.925276
$344$	64.0853	3.45525
$345$	8.07177	0.434569
$346$	−55.7000	−2.99445
$347$	7.68858	0.412745	0.206372	−	0.978474i	$-0.433834\pi$
$347$	7.68858	0.412745	0.206372	+	0.978474i	$0.433834\pi$
$348$	33.7279	1.80801
$349$	18.8201	1.00742	0.503708	−	0.863874i	$-0.331969\pi$
$349$	18.8201	1.00742	0.503708	+	0.863874i	$0.331969\pi$
$350$	15.2127	0.813153
$351$	12.0293	0.642074
$352$	82.0209	4.37173
$353$	−1.00000	−0.0532246
$353$	−1.00000	−0.0532246
$354$	29.6086	1.57368
$355$	17.7400	0.941542
$356$	36.2940	1.92358
$357$	−1.32052	−0.0698892
$358$	3.85014	0.203486
$359$	9.85518	0.520137	0.260068	−	0.965590i	$-0.416255\pi$
$359$	9.85518	0.520137	0.260068	+	0.965590i	$0.416255\pi$
$360$	−59.4610	−3.13387
$361$	−7.92671	−0.417195
$362$	22.3647	1.17546
$363$	−4.43931	−0.233003
$364$	−19.6705	−1.03102
$365$	−10.5595	−0.552707
$366$	39.0070	2.03893
$367$	−17.8815	−0.933405	−0.466702	−	0.884414i	$-0.654558\pi$
$367$	−17.8815	−0.933405	−0.466702	+	0.884414i	$0.654558\pi$
$368$	42.3055	2.20533
$369$	−0.919548	−0.0478698
$370$	−69.9516	−3.63661
$371$	−1.84749	−0.0959171
$372$	−31.5982	−1.63829
$373$	36.3286	1.88102	0.940511	−	0.339763i	$-0.110347\pi$
$373$	36.3286	1.88102	0.940511	+	0.339763i	$0.110347\pi$
$374$	−10.8234	−0.559663
$375$	−3.02998	−0.156468
$376$	33.8660	1.74651
$377$	−17.2126	−0.886493
$378$	18.5153	0.952326
$379$	−3.45662	−0.177554	−0.0887772	−	0.996052i	$-0.528296\pi$
$379$	−3.45662	−0.177554	−0.0887772	+	0.996052i	$0.528296\pi$
$380$	53.6218	2.75074
$381$	−16.1480	−0.827286
$382$	52.6587	2.69425
$383$	30.3595	1.55130	0.775650	−	0.631164i	$-0.217422\pi$
$383$	30.3595	1.55130	0.775650	+	0.631164i	$0.217422\pi$
$384$	30.4797	1.55541
$385$	−17.0281	−0.867834
$386$	−21.1776	−1.07791
$387$	14.9063	0.757728
$388$	−25.6978	−1.30461
$389$	30.3081	1.53668	0.768341	−	0.640041i	$-0.221083\pi$
$389$	30.3081	1.53668	0.768341	+	0.640041i	$0.221083\pi$
$390$	−18.9424	−0.959184
$391$	−2.94126	−0.148746
$392$	45.7368	2.31006
$393$	3.18555	0.160690
$394$	−17.5396	−0.883634
$395$	7.83195	0.394068
$396$	46.2807	2.32569
$397$	3.23233	0.162226	0.0811130	−	0.996705i	$-0.474153\pi$
$397$	3.23233	0.162226	0.0811130	+	0.996705i	$0.474153\pi$
$398$	13.6883	0.686130
$399$	−4.39422	−0.219986
$400$	56.0367	2.80183
$401$	25.9481	1.29579	0.647893	−	0.761732i	$-0.275650\pi$
$401$	25.9481	1.29579	0.647893	+	0.761732i	$0.275650\pi$
$402$	29.7814	1.48536
$403$	16.1257	0.803277
$404$	−46.3765	−2.30732
$405$	−6.25540	−0.310833
$406$	−26.4935	−1.31485
$407$	34.2908	1.69973
$408$	−8.51831	−0.421719
$409$	15.0223	0.742803	0.371401	−	0.928472i	$-0.378877\pi$
$409$	15.0223	0.742803	0.371401	+	0.928472i	$0.378877\pi$
$410$	3.46529	0.171139
$411$	5.80017	0.286101
$412$	52.5896	2.59090
$413$	−16.9741	−0.835242
$414$	17.2326	0.846937
$415$	17.3585	0.852094
$416$	−52.3072	−2.56457
$417$	−20.7704	−1.01713
$418$	−36.0164	−1.76162
$419$	29.9455	1.46293	0.731467	−	0.681877i	$-0.238836\pi$
$419$	29.9455	1.46293	0.731467	+	0.681877i	$0.238836\pi$
$420$	−21.2788	−1.03830
$421$	−25.0184	−1.21932	−0.609662	−	0.792661i	$-0.708695\pi$
$421$	−25.0184	−1.21932	−0.609662	+	0.792661i	$0.708695\pi$
$422$	35.3558	1.72109
$423$	7.87725	0.383005
$424$	−11.9177	−0.578775
$425$	−3.89591	−0.188979
$426$	−14.8900	−0.721421
$427$	−22.3621	−1.08218
$428$	80.0531	3.86951
$429$	9.28568	0.448317
$430$	−56.1739	−2.70894
$431$	−28.4742	−1.37155	−0.685777	−	0.727812i	$-0.740537\pi$
$431$	−28.4742	−1.37155	−0.685777	+	0.727812i	$0.740537\pi$
$432$	68.2020	3.28137
$433$	−30.2161	−1.45209	−0.726046	−	0.687646i	$-0.758644\pi$
$433$	−30.2161	−1.45209	−0.726046	+	0.687646i	$0.758644\pi$
$434$	24.8205	1.19142
$435$	−18.6199	−0.892754
$436$	−11.6947	−0.560076
$437$	−9.78750	−0.468199
$438$	8.86300	0.423491
$439$	−11.2037	−0.534726	−0.267363	−	0.963596i	$-0.586152\pi$
$439$	−11.2037	−0.534726	−0.267363	+	0.963596i	$0.586152\pi$
$440$	−109.844	−5.23661
$441$	10.6384	0.506590
$442$	6.90238	0.328313
$443$	−11.3437	−0.538956	−0.269478	−	0.963007i	$-0.586851\pi$
$443$	−11.3437	−0.538956	−0.269478	+	0.963007i	$0.586851\pi$
$444$	42.8506	2.03360
$445$	−20.0365	−0.949821
$446$	13.5201	0.640194
$447$	7.45491	0.352605
$448$	−39.2253	−1.85322
$449$	−29.5398	−1.39407	−0.697035	−	0.717038i	$-0.745498\pi$
$449$	−29.5398	−1.39407	−0.697035	+	0.717038i	$0.745498\pi$
$450$	22.8258	1.07602
$451$	−1.69871	−0.0799891
$452$	6.57538	0.309280
$453$	5.28079	0.248113
$454$	−30.0806	−1.41175
$455$	10.8593	0.509094
$456$	−28.3460	−1.32742
$457$	−15.7758	−0.737960	−0.368980	−	0.929437i	$-0.620293\pi$
$457$	−15.7758	−0.737960	−0.368980	+	0.929437i	$0.620293\pi$
$458$	1.21811	0.0569187
$459$	−4.74170	−0.221323
$460$	−47.3954	−2.20982
$461$	−1.74017	−0.0810477	−0.0405238	−	0.999179i	$-0.512903\pi$
$461$	−1.74017	−0.0810477	−0.0405238	+	0.999179i	$0.512903\pi$
$462$	14.2924	0.664945
$463$	−19.2747	−0.895772	−0.447886	−	0.894091i	$-0.647823\pi$
$463$	−19.2747	−0.895772	−0.447886	+	0.894091i	$0.647823\pi$
$464$	−97.5898	−4.53049
$465$	17.4441	0.808951
$466$	−5.44891	−0.252416
$467$	6.13715	0.283993	0.141997	−	0.989867i	$-0.454648\pi$
$467$	6.13715	0.283993	0.141997	+	0.989867i	$0.454648\pi$
$468$	−29.5146	−1.36431
$469$	−17.0732	−0.788367
$470$	−29.6852	−1.36928
$471$	−5.12798	−0.236285
$472$	−109.496	−5.03995
$473$	27.5368	1.26614
$474$	−6.57369	−0.301939
$475$	−12.9642	−0.594840
$476$	7.75375	0.355392
$477$	−2.77206	−0.126924
$478$	32.5119	1.48706
$479$	−36.5883	−1.67176	−0.835880	−	0.548912i	$-0.815042\pi$
$479$	−36.5883	−1.67176	−0.835880	+	0.548912i	$0.815042\pi$
$480$	−56.5838	−2.58268
$481$	−21.8682	−0.997105
$482$	−20.4557	−0.931734
$483$	3.88398	0.176727
$484$	26.0665	1.18484
$485$	14.1868	0.644187
$486$	43.9538	1.99379
$487$	−32.9072	−1.49117	−0.745585	−	0.666411i	$-0.767830\pi$
$487$	−32.9072	−1.49117	−0.745585	+	0.666411i	$0.767830\pi$
$488$	−144.252	−6.52998
$489$	2.22922	0.100809
$490$	−40.0905	−1.81110
$491$	−22.8413	−1.03081	−0.515407	−	0.856945i	$-0.672359\pi$
$491$	−22.8413	−1.03081	−0.515407	+	0.856945i	$0.672359\pi$
$492$	−2.12275	−0.0957010
$493$	6.78486	0.305575
$494$	22.9687	1.03341
$495$	−25.5498	−1.14838
$496$	91.4275	4.10522
$497$	8.53616	0.382899
$498$	−14.5697	−0.652884
$499$	−4.34806	−0.194646	−0.0973230	−	0.995253i	$-0.531028\pi$
$499$	−4.34806	−0.194646	−0.0973230	+	0.995253i	$0.531028\pi$
$500$	17.7913	0.795652
$501$	−16.1097	−0.719730
$502$	25.0356	1.11739
$503$	34.3591	1.53200	0.765998	−	0.642843i	$-0.222245\pi$
$503$	34.3591	1.53200	0.765998	+	0.642843i	$0.222245\pi$
$504$	−28.6115	−1.27446
$505$	25.6027	1.13930
$506$	31.8343	1.41521
$507$	6.03970	0.268232
$508$	94.8170	4.20682
$509$	−16.9210	−0.750008	−0.375004	−	0.927023i	$-0.622359\pi$
$509$	−16.9210	−0.750008	−0.375004	+	0.927023i	$0.622359\pi$
$510$	7.46671	0.330632
$511$	−5.08101	−0.224771
$512$	−30.2431	−1.33657
$513$	−15.7787	−0.696648
$514$	−25.5983	−1.12909
$515$	−29.0326	−1.27933
$516$	34.4107	1.51485
$517$	14.5519	0.639991
$518$	−33.6594	−1.47891
$519$	−18.8366	−0.826834
$520$	70.0508	3.07193
$521$	33.6870	1.47585	0.737926	−	0.674881i	$-0.235805\pi$
$521$	33.6870	1.47585	0.737926	+	0.674881i	$0.235805\pi$
$522$	−39.7520	−1.73990
$523$	17.8461	0.780356	0.390178	−	0.920739i	$-0.372413\pi$
$523$	17.8461	0.780356	0.390178	+	0.920739i	$0.372413\pi$
$524$	−18.7048	−0.817121
$525$	5.14461	0.224529
$526$	47.4387	2.06843
$527$	−6.35643	−0.276890
$528$	52.6468	2.29116
$529$	−14.3490	−0.623869
$530$	10.4464	0.453765
$531$	−25.4687	−1.10525
$532$	25.8018	1.11865
$533$	1.08332	0.0469237
$534$	16.8175	0.727763
$535$	−44.1942	−1.91068
$536$	−110.135	−4.75710
$537$	1.30204	0.0561870
$538$	−45.3174	−1.95377
$539$	19.6526	0.846498
$540$	−76.4077	−3.28806
$541$	−17.8813	−0.768776	−0.384388	−	0.923172i	$-0.625587\pi$
$541$	−17.8813	−0.768776	−0.384388	+	0.923172i	$0.625587\pi$
$542$	−38.6426	−1.65984
$543$	7.56328	0.324571
$544$	20.6185	0.884009
$545$	6.45620	0.276553
$546$	−9.11471	−0.390073
$547$	11.6915	0.499894	0.249947	−	0.968260i	$-0.419587\pi$
$547$	11.6915	0.499894	0.249947	+	0.968260i	$0.419587\pi$
$548$	−34.0572	−1.45485
$549$	−33.5531	−1.43201
$550$	42.1669	1.79800
$551$	22.5777	0.961842
$552$	25.0546	1.06639
$553$	3.76858	0.160256
$554$	−44.8816	−1.90683
$555$	−23.6562	−1.00415
$556$	121.959	5.17220
$557$	8.00025	0.338982	0.169491	−	0.985532i	$-0.445788\pi$
$557$	8.00025	0.338982	0.169491	+	0.985532i	$0.445788\pi$
$558$	37.2418	1.57657
$559$	−17.5610	−0.742752
$560$	61.5690	2.60177
$561$	−3.66023	−0.154535
$562$	73.1312	3.08485
$563$	−5.25079	−0.221295	−0.110647	−	0.993860i	$-0.535292\pi$
$563$	−5.25079	−0.221295	−0.110647	+	0.993860i	$0.535292\pi$
$564$	18.1844	0.765702
$565$	−3.63001	−0.152716
$566$	−48.9032	−2.05555
$567$	−3.00998	−0.126407
$568$	55.0646	2.31046
$569$	−27.1494	−1.13816	−0.569082	−	0.822281i	$-0.692701\pi$
$569$	−27.1494	−1.13816	−0.569082	+	0.822281i	$0.692701\pi$
$570$	24.8467	1.04071
$571$	−0.101381	−0.00424266	−0.00212133	−	0.999998i	$-0.500675\pi$
$571$	−0.101381	−0.00424266	−0.00212133	+	0.999998i	$0.500675\pi$
$572$	−54.5232	−2.27973
$573$	17.8081	0.743942
$574$	1.66743	0.0695973
$575$	11.4589	0.477868
$576$	−58.8554	−2.45231
$577$	−42.0403	−1.75016	−0.875079	−	0.483979i	$-0.839191\pi$
$577$	−42.0403	−1.75016	−0.875079	+	0.483979i	$0.839191\pi$
$578$	−2.72078	−0.113170
$579$	−7.16180	−0.297634
$580$	109.331	4.53973
$581$	8.35257	0.346523
$582$	−11.9075	−0.493584
$583$	−5.12092	−0.212087
$584$	−32.7763	−1.35629
$585$	16.2938	0.673668
$586$	−21.8398	−0.902196
$587$	−15.4074	−0.635931	−0.317966	−	0.948102i	$-0.603000\pi$
$587$	−15.4074	−0.635931	−0.317966	+	0.948102i	$0.603000\pi$
$588$	24.5584	1.01277
$589$	−21.1520	−0.871553
$590$	95.9782	3.95136
$591$	−5.93153	−0.243991
$592$	−123.986	−5.09579
$593$	−4.30987	−0.176985	−0.0884926	−	0.996077i	$-0.528205\pi$
$593$	−4.30987	−0.176985	−0.0884926	+	0.996077i	$0.528205\pi$
$594$	51.3211	2.10573
$595$	−4.28054	−0.175485
$596$	−43.7734	−1.79303
$597$	4.62908	0.189455
$598$	−20.3017	−0.830198
$599$	36.0458	1.47279	0.736395	−	0.676552i	$-0.236527\pi$
$599$	36.0458	1.47279	0.736395	+	0.676552i	$0.236527\pi$
$600$	33.1866	1.35484
$601$	26.5951	1.08484	0.542418	−	0.840109i	$-0.317509\pi$
$601$	26.5951	1.08484	0.542418	+	0.840109i	$0.317509\pi$
$602$	−27.0298	−1.10165
$603$	−25.6174	−1.04322
$604$	−31.0075	−1.26168
$605$	−14.3903	−0.585049
$606$	−21.4894	−0.872947
$607$	−18.1209	−0.735503	−0.367752	−	0.929924i	$-0.619872\pi$
$607$	−18.1209	−0.735503	−0.367752	+	0.929924i	$0.619872\pi$
$608$	68.6111	2.78255
$609$	−8.95953	−0.363058
$610$	126.444	5.11956
$611$	−9.28017	−0.375435
$612$	11.6341	0.470280
$613$	−37.0239	−1.49538	−0.747691	−	0.664046i	$-0.768838\pi$
$613$	−37.0239	−1.49538	−0.747691	+	0.664046i	$0.768838\pi$
$614$	35.6125	1.43720
$615$	1.17189	0.0472551
$616$	−52.8549	−2.12959
$617$	−35.2026	−1.41720	−0.708602	−	0.705608i	$-0.750674\pi$
$617$	−35.2026	−1.41720	−0.708602	+	0.705608i	$0.750674\pi$
$618$	24.3683	0.980238
$619$	0.187380	0.00753144	0.00376572	−	0.999993i	$-0.498801\pi$
$619$	0.187380	0.00753144	0.00376572	+	0.999993i	$0.498801\pi$
$620$	−102.427	−4.11359
$621$	13.9466	0.559656
$622$	16.5918	0.665270
$623$	−9.64117	−0.386265
$624$	−33.5744	−1.34405
$625$	−29.3014	−1.17206
$626$	33.1511	1.32499
$627$	−12.1800	−0.486422
$628$	30.1103	1.20153
$629$	8.62003	0.343703
$630$	25.0794	0.999186
$631$	−14.2103	−0.565702	−0.282851	−	0.959164i	$-0.591280\pi$
$631$	−14.2103	−0.565702	−0.282851	+	0.959164i	$0.591280\pi$
$632$	24.3102	0.967006
$633$	11.9566	0.475231
$634$	−43.7138	−1.73610
$635$	−52.3448	−2.07724
$636$	−6.39923	−0.253746
$637$	−12.5331	−0.496578
$638$	−73.4351	−2.90732
$639$	12.8080	0.506678
$640$	98.8018	3.90549
$641$	26.2575	1.03711	0.518554	−	0.855045i	$-0.326471\pi$
$641$	26.2575	1.03711	0.518554	+	0.855045i	$0.326471\pi$
$642$	37.0940	1.46399
$643$	−9.50238	−0.374737	−0.187369	−	0.982290i	$-0.559996\pi$
$643$	−9.50238	−0.374737	−0.187369	+	0.982290i	$0.559996\pi$
$644$	−22.8058	−0.898674
$645$	−18.9968	−0.747998
$646$	−9.05383	−0.356218
$647$	−13.8117	−0.542994	−0.271497	−	0.962439i	$-0.587519\pi$
$647$	−13.8117	−0.542994	−0.271497	+	0.962439i	$0.587519\pi$
$648$	−19.4166	−0.762756
$649$	−47.0492	−1.84684
$650$	−26.8910	−1.05475
$651$	8.39377	0.328978
$652$	−13.0894	−0.512621
$653$	7.45576	0.291766	0.145883	−	0.989302i	$-0.453398\pi$
$653$	7.45576	0.291766	0.145883	+	0.989302i	$0.453398\pi$
$654$	−5.41897	−0.211898
$655$	10.3262	0.403477
$656$	6.14206	0.239807
$657$	−7.62378	−0.297432
$658$	−14.2840	−0.556847
$659$	−43.9120	−1.71057	−0.855283	−	0.518160i	$-0.826617\pi$
$659$	−43.9120	−1.71057	−0.855283	+	0.518160i	$0.826617\pi$
$660$	−58.9810	−2.29583
$661$	−22.8966	−0.890575	−0.445288	−	0.895388i	$-0.646899\pi$
$661$	−22.8966	−0.890575	−0.445288	+	0.895388i	$0.646899\pi$
$662$	45.2490	1.75865
$663$	2.33424	0.0906543
$664$	53.8803	2.09096
$665$	−14.2442	−0.552365
$666$	−50.5041	−1.95699
$667$	−19.9560	−0.772701
$668$	94.5923	3.65989
$669$	4.57220	0.176772
$670$	96.5385	3.72961
$671$	−61.9836	−2.39285
$672$	−27.2270	−1.05031
$673$	5.89012	0.227047	0.113524	−	0.993535i	$-0.463786\pi$
$673$	5.89012	0.227047	0.113524	+	0.993535i	$0.463786\pi$
$674$	−41.9989	−1.61774
$675$	18.4732	0.711035
$676$	−35.4636	−1.36399
$677$	−7.08537	−0.272313	−0.136156	−	0.990687i	$-0.543475\pi$
$677$	−7.08537	−0.272313	−0.136156	+	0.990687i	$0.543475\pi$
$678$	3.04682	0.117013
$679$	6.82639	0.261973
$680$	−27.6127	−1.05890
$681$	−10.1726	−0.389815
$682$	68.7980	2.63441
$683$	−35.9719	−1.37643	−0.688213	−	0.725509i	$-0.741605\pi$
$683$	−35.9719	−1.37643	−0.688213	+	0.725509i	$0.741605\pi$
$684$	38.7142	1.48027
$685$	18.8016	0.718373
$686$	−46.6243	−1.78012
$687$	0.411940	0.0157165
$688$	−99.5654	−3.79590
$689$	3.26576	0.124415
$690$	−21.9615	−0.836062
$691$	−51.5353	−1.96049	−0.980247	−	0.197776i	$-0.936628\pi$
$691$	−51.5353	−1.96049	−0.980247	+	0.197776i	$0.936628\pi$
$692$	110.604	4.20452
$693$	−12.2941	−0.467013
$694$	−20.9190	−0.794073
$695$	−67.3286	−2.55392
$696$	−57.7956	−2.19074
$697$	−0.427022	−0.0161746
$698$	−51.2054	−1.93815
$699$	−1.84271	−0.0696975
$700$	−30.2079	−1.14175
$701$	24.3672	0.920338	0.460169	−	0.887831i	$-0.347789\pi$
$701$	24.3672	0.920338	0.460169	+	0.887831i	$0.347789\pi$
$702$	−32.7290	−1.23528
$703$	28.6845	1.08186
$704$	−108.725	−4.09775
$705$	−10.0389	−0.378087
$706$	2.72078	0.102398
$707$	12.3195	0.463323
$708$	−58.7939	−2.20961
$709$	22.1215	0.830792	0.415396	−	0.909641i	$-0.363643\pi$
$709$	22.1215	0.830792	0.415396	+	0.909641i	$0.363643\pi$
$710$	−48.2668	−1.81142
$711$	5.65455	0.212062
$712$	−62.1927	−2.33077
$713$	18.6959	0.700167
$714$	3.59284	0.134459
$715$	30.1001	1.12568
$716$	−7.64523	−0.285716
$717$	10.9948	0.410609
$718$	−26.8138	−1.00068
$719$	51.4700	1.91951	0.959754	−	0.280843i	$-0.0906140\pi$
$719$	51.4700	1.91951	0.959754	+	0.280843i	$0.0906140\pi$
$720$	92.3810	3.44283
$721$	−13.9700	−0.520268
$722$	21.5669	0.802636
$723$	−6.91770	−0.257272
$724$	−44.4097	−1.65047
$725$	−26.4332	−0.981705
$726$	12.0784	0.448272
$727$	30.9059	1.14624	0.573118	−	0.819473i	$-0.305734\pi$
$727$	30.9059	1.14624	0.573118	+	0.819473i	$0.305734\pi$
$728$	33.7071	1.24927
$729$	8.57236	0.317495
$730$	28.7300	1.06335
$731$	6.92221	0.256027
$732$	−77.4563	−2.86287
$733$	3.39652	0.125453	0.0627267	−	0.998031i	$-0.480020\pi$
$733$	3.39652	0.125453	0.0627267	+	0.998031i	$0.480020\pi$
$734$	48.6516	1.79576
$735$	−13.5577	−0.500085
$736$	−60.6442	−2.23538
$737$	−47.3238	−1.74319
$738$	2.50189	0.0920959
$739$	5.44312	0.200228	0.100114	−	0.994976i	$-0.468079\pi$
$739$	5.44312	0.200228	0.100114	+	0.994976i	$0.468079\pi$
$740$	138.903	5.10618
$741$	7.76754	0.285348
$742$	5.02663	0.184533
$743$	−24.2900	−0.891112	−0.445556	−	0.895254i	$-0.646994\pi$
$743$	−24.2900	−0.891112	−0.445556	+	0.895254i	$0.646994\pi$
$744$	54.1461	1.98509
$745$	24.1656	0.885358
$746$	−98.8422	−3.61887
$747$	12.5326	0.458543
$748$	21.4920	0.785825
$749$	−21.2654	−0.777021
$750$	8.24393	0.301026
$751$	11.8494	0.432392	0.216196	−	0.976350i	$-0.430635\pi$
$751$	11.8494	0.432392	0.216196	+	0.976350i	$0.430635\pi$
$752$	−52.6156	−1.91869
$753$	8.46649	0.308536
$754$	46.8317	1.70551
$755$	17.1180	0.622989
$756$	−36.7659	−1.33716
$757$	−44.0934	−1.60260	−0.801301	−	0.598262i	$-0.795858\pi$
$757$	−44.0934	−1.60260	−0.801301	+	0.598262i	$0.795858\pi$
$758$	9.40470	0.341594
$759$	10.7657	0.390770
$760$	−91.8855	−3.33304
$761$	−19.0264	−0.689708	−0.344854	−	0.938656i	$-0.612072\pi$
$761$	−19.0264	−0.689708	−0.344854	+	0.938656i	$0.612072\pi$
$762$	43.9352	1.59160
$763$	3.10660	0.112467
$764$	−104.564	−3.78301
$765$	−6.42272	−0.232214
$766$	−82.6017	−2.98452
$767$	30.0046	1.08340
$768$	−32.6326	−1.17753
$769$	5.09489	0.183727	0.0918633	−	0.995772i	$-0.470718\pi$
$769$	5.09489	0.183727	0.0918633	+	0.995772i	$0.470718\pi$
$770$	46.3299	1.66961
$771$	−8.65680	−0.311767
$772$	42.0523	1.51350
$773$	28.5788	1.02791	0.513954	−	0.857818i	$-0.328180\pi$
$773$	28.5788	1.02791	0.513954	+	0.857818i	$0.328180\pi$
$774$	−40.5567	−1.45778
$775$	24.7641	0.889552
$776$	44.0353	1.58078
$777$	−11.3829	−0.408359
$778$	−82.4618	−2.95640
$779$	−1.42098	−0.0509120
$780$	37.6139	1.34679
$781$	23.6607	0.846646
$782$	8.00253	0.286170
$783$	−32.1718	−1.14973
$784$	−71.0584	−2.53780
$785$	−16.6227	−0.593289
$786$	−8.66719	−0.309148
$787$	−35.2258	−1.25566	−0.627832	−	0.778349i	$-0.716058\pi$
$787$	−35.2258	−1.25566	−0.627832	+	0.778349i	$0.716058\pi$
$788$	34.8285	1.24071
$789$	16.0428	0.571138
$790$	−21.3090	−0.758141
$791$	−1.74669	−0.0621052
$792$	−79.3059	−2.81801
$793$	39.5288	1.40371
$794$	−8.79448	−0.312104
$795$	3.53277	0.125294
$796$	−27.1808	−0.963398
$797$	47.0868	1.66790	0.833951	−	0.551839i	$-0.186074\pi$
$797$	47.0868	1.66790	0.833951	+	0.551839i	$0.186074\pi$
$798$	11.9557	0.423228
$799$	3.65806	0.129413
$800$	−80.3277	−2.84001
$801$	−14.4661	−0.511133
$802$	−70.5991	−2.49294
$803$	−14.0836	−0.497001
$804$	−59.1370	−2.08560
$805$	12.5902	0.443746
$806$	−43.8745	−1.54541
$807$	−15.3254	−0.539479
$808$	79.4700	2.79574
$809$	0.619078	0.0217656	0.0108828	−	0.999941i	$-0.496536\pi$
$809$	0.619078	0.0217656	0.0108828	+	0.999941i	$0.496536\pi$
$810$	17.0196	0.598008
$811$	−33.3678	−1.17170	−0.585851	−	0.810419i	$-0.699240\pi$
$811$	−33.3678	−1.17170	−0.585851	+	0.810419i	$0.699240\pi$
$812$	52.6081	1.84618
$813$	−13.0681	−0.458319
$814$	−93.2978	−3.27009
$815$	7.22615	0.253121
$816$	13.2344	0.463296
$817$	23.0347	0.805883
$818$	−40.8723	−1.42907
$819$	7.84029	0.273962
$820$	−6.88104	−0.240296
$821$	−54.6488	−1.90726	−0.953629	−	0.300986i	$-0.902684\pi$
$821$	−54.6488	−1.90726	−0.953629	+	0.300986i	$0.902684\pi$
$822$	−15.7810	−0.550426
$823$	37.9294	1.32214	0.661068	−	0.750326i	$-0.270103\pi$
$823$	37.9294	1.32214	0.661068	+	0.750326i	$0.270103\pi$
$824$	−90.1166	−3.13936
$825$	14.2599	0.496467
$826$	46.1829	1.60691
$827$	54.4662	1.89398	0.946988	−	0.321270i	$-0.104110\pi$
$827$	54.4662	1.89398	0.946988	+	0.321270i	$0.104110\pi$
$828$	−34.2188	−1.18919
$829$	22.4058	0.778185	0.389093	−	0.921199i	$-0.372789\pi$
$829$	22.4058	0.778185	0.389093	+	0.921199i	$0.372789\pi$
$830$	−47.2287	−1.63933
$831$	−15.1780	−0.526519
$832$	69.3374	2.40384
$833$	4.94029	0.171171
$834$	56.5118	1.95684
$835$	−52.2207	−1.80717
$836$	71.5179	2.47350
$837$	30.1403	1.04180
$838$	−81.4752	−2.81452
$839$	−19.6905	−0.679793	−0.339896	−	0.940463i	$-0.610392\pi$
$839$	−19.6905	−0.679793	−0.339896	+	0.940463i	$0.610392\pi$
$840$	36.4630	1.25809
$841$	17.0344	0.587392
$842$	68.0698	2.34584
$843$	24.7314	0.851795
$844$	−70.2060	−2.41659
$845$	19.5781	0.673506
$846$	−21.4323	−0.736858
$847$	−6.92434	−0.237923
$848$	18.5158	0.635836
$849$	−16.5380	−0.567583
$850$	10.5999	0.363574
$851$	−25.3537	−0.869115
$852$	29.5670	1.01295
$853$	20.3598	0.697105	0.348553	−	0.937289i	$-0.386673\pi$
$853$	20.3598	0.697105	0.348553	+	0.937289i	$0.386673\pi$
$854$	60.8424	2.08198
$855$	−21.3726	−0.730927
$856$	−137.178	−4.68863
$857$	−12.6644	−0.432608	−0.216304	−	0.976326i	$-0.569400\pi$
$857$	−12.6644	−0.432608	−0.216304	+	0.976326i	$0.569400\pi$
$858$	−25.2643	−0.862510
$859$	17.5993	0.600480	0.300240	−	0.953864i	$-0.402933\pi$
$859$	17.5993	0.600480	0.300240	+	0.953864i	$0.402933\pi$
$860$	111.545	3.80364
$861$	0.563890	0.0192173
$862$	77.4721	2.63871
$863$	38.4115	1.30754	0.653770	−	0.756693i	$-0.273186\pi$
$863$	38.4115	1.30754	0.653770	+	0.756693i	$0.273186\pi$
$864$	−97.7665	−3.32608
$865$	−61.0600	−2.07610
$866$	82.2114	2.79366
$867$	−0.920111	−0.0312486
$868$	−49.2862	−1.67288
$869$	10.4458	0.354351
$870$	50.6606	1.71756
$871$	30.1798	1.02260
$872$	20.0399	0.678636
$873$	10.2426	0.346661
$874$	26.6297	0.900762
$875$	−4.72611	−0.159772
$876$	−17.5993	−0.594625
$877$	42.8359	1.44647	0.723233	−	0.690604i	$-0.242655\pi$
$877$	42.8359	1.44647	0.723233	+	0.690604i	$0.242655\pi$
$878$	30.4830	1.02875
$879$	−7.38577	−0.249116
$880$	170.658	5.75289
$881$	−10.6409	−0.358500	−0.179250	−	0.983804i	$-0.557367\pi$
$881$	−10.6409	−0.358500	−0.179250	+	0.983804i	$0.557367\pi$
$882$	−28.9448	−0.974621
$883$	−42.6879	−1.43656	−0.718281	−	0.695753i	$-0.755071\pi$
$883$	−42.6879	−1.43656	−0.718281	+	0.695753i	$0.755071\pi$
$884$	−13.7061	−0.460985
$885$	32.4578	1.09106
$886$	30.8638	1.03689
$887$	2.66425	0.0894566	0.0447283	−	0.998999i	$-0.485758\pi$
$887$	2.66425	0.0894566	0.0447283	+	0.998999i	$0.485758\pi$
$888$	−73.4281	−2.46409
$889$	−25.1873	−0.844755
$890$	54.5149	1.82735
$891$	−8.34312	−0.279505
$892$	−26.8468	−0.898899
$893$	12.1728	0.407346
$894$	−20.2832	−0.678371
$895$	4.22063	0.141080
$896$	47.5416	1.58825
$897$	−6.86560	−0.229236
$898$	80.3714	2.68203
$899$	−43.1275	−1.43838
$900$	−45.3253	−1.51084
$901$	−1.28730	−0.0428861
$902$	4.62182	0.153890
$903$	−9.14090	−0.304190
$904$	−11.2675	−0.374750
$905$	24.5169	0.814968
$906$	−14.3679	−0.477341
$907$	54.4578	1.80824	0.904121	−	0.427276i	$-0.140527\pi$
$907$	54.4578	1.80824	0.904121	+	0.427276i	$0.140527\pi$
$908$	59.7311	1.98225
$909$	18.4848	0.613101
$910$	−29.5459	−0.979438
$911$	−54.1837	−1.79519	−0.897593	−	0.440825i	$-0.854686\pi$
$911$	−54.1837	−1.79519	−0.897593	+	0.440825i	$0.854686\pi$
$912$	44.0395	1.45829
$913$	23.1518	0.766213
$914$	42.9225	1.41975
$915$	42.7606	1.41362
$916$	−2.41881	−0.0799197
$917$	4.96875	0.164083
$918$	12.9011	0.425801
$919$	11.5520	0.381065	0.190532	−	0.981681i	$-0.438979\pi$
$919$	11.5520	0.381065	0.190532	+	0.981681i	$0.438979\pi$
$920$	81.2160	2.67761
$921$	12.0434	0.396843
$922$	4.73462	0.155926
$923$	−15.0891	−0.496664
$924$	−28.3805	−0.933651
$925$	−33.5828	−1.10420
$926$	52.4423	1.72336
$927$	−20.9612	−0.688455
$928$	139.893	4.59223
$929$	−3.70553	−0.121575	−0.0607873	−	0.998151i	$-0.519361\pi$
$929$	−3.70553	−0.121575	−0.0607873	+	0.998151i	$0.519361\pi$
$930$	−47.4617	−1.55633
$931$	16.4396	0.538785
$932$	10.8199	0.354418
$933$	5.61099	0.183695
$934$	−16.6979	−0.546371
$935$	−11.8649	−0.388023
$936$	50.5757	1.65312
$937$	−24.3083	−0.794119	−0.397060	−	0.917793i	$-0.629969\pi$
$937$	−24.3083	−0.794119	−0.397060	+	0.917793i	$0.629969\pi$
$938$	46.4525	1.51673
$939$	11.2110	0.365857
$940$	58.9460	1.92261
$941$	27.3936	0.893005	0.446502	−	0.894782i	$-0.352669\pi$
$941$	27.3936	0.893005	0.446502	+	0.894782i	$0.352669\pi$
$942$	13.9521	0.454585
$943$	1.25598	0.0409005
$944$	170.117	5.53683
$945$	20.2970	0.660262
$946$	−74.9217	−2.43591
$947$	14.8493	0.482537	0.241268	−	0.970458i	$-0.422437\pi$
$947$	14.8493	0.482537	0.241268	+	0.970458i	$0.422437\pi$
$948$	13.0534	0.423954
$949$	8.98155	0.291553
$950$	35.2729	1.14440
$951$	−14.7831	−0.479375
$952$	−13.2867	−0.430624
$953$	31.0146	1.00466	0.502331	−	0.864675i	$-0.332476\pi$
$953$	31.0146	1.00466	0.502331	+	0.864675i	$0.332476\pi$
$954$	7.54218	0.244187
$955$	57.7260	1.86797
$956$	−64.5589	−2.08798
$957$	−24.8342	−0.802775
$958$	99.5488	3.21627
$959$	9.04698	0.292142
$960$	75.0064	2.42082
$961$	9.40421	0.303362
$962$	59.4987	1.91832
$963$	−31.9076	−1.02821
$964$	40.6190	1.30825
$965$	−23.2155	−0.747332
$966$	−10.5675	−0.340003
$967$	−20.1318	−0.647396	−0.323698	−	0.946160i	$-0.604926\pi$
$967$	−20.1318	−0.647396	−0.323698	+	0.946160i	$0.604926\pi$
$968$	−44.6672	−1.43566
$969$	−3.06181	−0.0983596
$970$	−38.5991	−1.23934
$971$	−6.04493	−0.193991	−0.0969956	−	0.995285i	$-0.530923\pi$
$971$	−6.04493	−0.193991	−0.0969956	+	0.995285i	$0.530923\pi$
$972$	−87.2792	−2.79948
$973$	−32.3972	−1.03861
$974$	89.5335	2.86884
$975$	−9.09398	−0.291240
$976$	224.116	7.17376
$977$	24.7090	0.790512	0.395256	−	0.918571i	$-0.370656\pi$
$977$	24.7090	0.790512	0.395256	+	0.918571i	$0.370656\pi$
$978$	−6.06522	−0.193944
$979$	−26.7236	−0.854090
$980$	79.6077	2.54298
$981$	4.66129	0.148823
$982$	62.1463	1.98317
$983$	−40.5781	−1.29424	−0.647121	−	0.762387i	$-0.724027\pi$
$983$	−40.5781	−1.29424	−0.647121	+	0.762387i	$0.724027\pi$
$984$	3.63751	0.115960
$985$	−19.2275	−0.612638
$986$	−18.4601	−0.587891
$987$	−4.83053	−0.153757
$988$	−45.6091	−1.45102
$989$	−20.3600	−0.647411
$990$	69.5155	2.20935
$991$	11.5130	0.365721	0.182861	−	0.983139i	$-0.441464\pi$
$991$	11.5130	0.365721	0.182861	+	0.983139i	$0.441464\pi$
$992$	−131.060	−4.16115
$993$	15.3022	0.485602
$994$	−23.2250	−0.736654
$995$	15.0055	0.475705
$996$	28.9311	0.916717
$997$	−41.4699	−1.31337	−0.656683	−	0.754167i	$-0.728041\pi$
$997$	−41.4699	−1.31337	−0.656683	+	0.754167i	$0.728041\pi$
$998$	11.8301	0.374476
$999$	−40.8736	−1.29318

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6001.2.a.a.1.3	✓	113

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6001.2.a.a.1.3	✓	113	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:	\( N \)	\(=\)	\( 6001 = 17 \cdot 353 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.72078 q^{2} -0.920111 q^{3} +5.40267 q^{4} -2.98260 q^{5} +2.50342 q^{6} -1.43517 q^{7} -9.25792 q^{8} -2.15340 q^{9} +O(q^{10})\)	\(q-2.72078 q^{2} -0.920111 q^{3} +5.40267 q^{4} -2.98260 q^{5} +2.50342 q^{6} -1.43517 q^{7} -9.25792 q^{8} -2.15340 q^{9} +8.11501 q^{10} -3.97803 q^{11} -4.97105 q^{12} +2.53691 q^{13} +3.90479 q^{14} +2.74432 q^{15} +14.3835 q^{16} -1.00000 q^{17} +5.85892 q^{18} -3.32766 q^{19} -16.1140 q^{20} +1.32052 q^{21} +10.8234 q^{22} +2.94126 q^{23} +8.51831 q^{24} +3.89591 q^{25} -6.90238 q^{26} +4.74170 q^{27} -7.75375 q^{28} -6.78486 q^{29} -7.46671 q^{30} +6.35643 q^{31} -20.6185 q^{32} +3.66023 q^{33} +2.72078 q^{34} +4.28054 q^{35} -11.6341 q^{36} -8.62003 q^{37} +9.05383 q^{38} -2.33424 q^{39} +27.6127 q^{40} +0.427022 q^{41} -3.59284 q^{42} -6.92221 q^{43} -21.4920 q^{44} +6.42272 q^{45} -8.00253 q^{46} -3.65806 q^{47} -13.2344 q^{48} -4.94029 q^{49} -10.5999 q^{50} +0.920111 q^{51} +13.7061 q^{52} +1.28730 q^{53} -12.9011 q^{54} +11.8649 q^{55} +13.2867 q^{56} +3.06181 q^{57} +18.4601 q^{58} +11.8272 q^{59} +14.8267 q^{60} +15.5815 q^{61} -17.2945 q^{62} +3.09049 q^{63} +27.3315 q^{64} -7.56659 q^{65} -9.95871 q^{66} +11.8963 q^{67} -5.40267 q^{68} -2.70629 q^{69} -11.6464 q^{70} -5.94783 q^{71} +19.9360 q^{72} +3.54035 q^{73} +23.4532 q^{74} -3.58467 q^{75} -17.9782 q^{76} +5.70916 q^{77} +6.35096 q^{78} -2.62588 q^{79} -42.9001 q^{80} +2.09730 q^{81} -1.16184 q^{82} -5.81991 q^{83} +7.13431 q^{84} +2.98260 q^{85} +18.8338 q^{86} +6.24283 q^{87} +36.8283 q^{88} +6.71779 q^{89} -17.4748 q^{90} -3.64090 q^{91} +15.8906 q^{92} -5.84862 q^{93} +9.95279 q^{94} +9.92507 q^{95} +18.9713 q^{96} -4.75650 q^{97} +13.4414 q^{98} +8.56628 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9}+O(q^{10}) \) 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9	\( 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9} - 5 q^{10} - 40 q^{11} - 19 q^{12} - 18 q^{13} - 48 q^{14} - 63 q^{15} + 79 q^{16} - 113 q^{17} - 32 q^{18} - 46 q^{19} - 56 q^{20} - 46 q^{21} + 14 q^{22} - 35 q^{23} - 42 q^{24} + 88 q^{25} - 89 q^{26} - 41 q^{27} + 20 q^{28} - 51 q^{29} - 18 q^{30} - 57 q^{31} - 93 q^{32} - 40 q^{33} + 11 q^{34} - 69 q^{35} + 18 q^{36} + 16 q^{37} - 74 q^{38} - 51 q^{39} + 2 q^{40} - 87 q^{41} - 23 q^{42} - 32 q^{43} - 110 q^{44} - 17 q^{45} - 17 q^{46} - 161 q^{47} - 36 q^{48} + 56 q^{49} - 69 q^{50} + 11 q^{51} - 49 q^{52} - 48 q^{53} - 38 q^{54} - 79 q^{55} - 171 q^{56} + 20 q^{57} + 13 q^{58} - 174 q^{59} - 146 q^{60} - 34 q^{61} - 34 q^{62} - 14 q^{63} + 62 q^{64} - 22 q^{65} - 60 q^{66} - 50 q^{67} - 103 q^{68} - 59 q^{69} - 58 q^{70} - 189 q^{71} - 123 q^{72} - 4 q^{73} - 24 q^{74} - 106 q^{75} - 92 q^{76} - 78 q^{77} - 42 q^{78} + 8 q^{79} - 150 q^{80} + 13 q^{81} + 6 q^{82} - 109 q^{83} - 114 q^{84} + 19 q^{85} - 116 q^{86} - 106 q^{87} + 54 q^{88} - 170 q^{89} - q^{90} - 43 q^{91} - 94 q^{92} - 69 q^{93} - 35 q^{94} - 78 q^{95} - 44 q^{96} - 3 q^{97} - 68 q^{98} - 119 q^{99}+O(q^{100}) \) 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9 - 5 * q^10 - 40 * q^11 - 19 * q^12 - 18 * q^13 - 48 * q^14 - 63 * q^15 + 79 * q^16 - 113 * q^17 - 32 * q^18 - 46 * q^19 - 56 * q^20 - 46 * q^21 + 14 * q^22 - 35 * q^23 - 42 * q^24 + 88 * q^25 - 89 * q^26 - 41 * q^27 + 20 * q^28 - 51 * q^29 - 18 * q^30 - 57 * q^31 - 93 * q^32 - 40 * q^33 + 11 * q^34 - 69 * q^35 + 18 * q^36 + 16 * q^37 - 74 * q^38 - 51 * q^39 + 2 * q^40 - 87 * q^41 - 23 * q^42 - 32 * q^43 - 110 * q^44 - 17 * q^45 - 17 * q^46 - 161 * q^47 - 36 * q^48 + 56 * q^49 - 69 * q^50 + 11 * q^51 - 49 * q^52 - 48 * q^53 - 38 * q^54 - 79 * q^55 - 171 * q^56 + 20 * q^57 + 13 * q^58 - 174 * q^59 - 146 * q^60 - 34 * q^61 - 34 * q^62 - 14 * q^63 + 62 * q^64 - 22 * q^65 - 60 * q^66 - 50 * q^67 - 103 * q^68 - 59 * q^69 - 58 * q^70 - 189 * q^71 - 123 * q^72 - 4 * q^73 - 24 * q^74 - 106 * q^75 - 92 * q^76 - 78 * q^77 - 42 * q^78 + 8 * q^79 - 150 * q^80 + 13 * q^81 + 6 * q^82 - 109 * q^83 - 114 * q^84 + 19 * q^85 - 116 * q^86 - 106 * q^87 + 54 * q^88 - 170 * q^89 - q^90 - 43 * q^91 - 94 * q^92 - 69 * q^93 - 35 * q^94 - 78 * q^95 - 44 * q^96 - 3 * q^97 - 68 * q^98 - 119 * q^99

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