LMFDB - Embedded newform 2669.2.a.b.1.35

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2669,2,Mod(1,2669)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2669, 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("2669.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2669 = 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2669.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:	$21.3120722995$
Analytic rank:	$1$
Dimension:	$45$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.35
Character	$\chi$	$=$	2669.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.60442 q^{2} +0.427927 q^{3} +0.574167 q^{4} +1.60288 q^{5} +0.686575 q^{6} +0.796104 q^{7} -2.28764 q^{8} -2.81688 q^{9} +O(q^{10})$	\(q+1.60442 q^{2} +0.427927 q^{3} +0.574167 q^{4} +1.60288 q^{5} +0.686575 q^{6} +0.796104 q^{7} -2.28764 q^{8} -2.81688 q^{9} +2.57170 q^{10} -5.12411 q^{11} +0.245702 q^{12} +0.169069 q^{13} +1.27729 q^{14} +0.685916 q^{15} -4.81867 q^{16} +1.00000 q^{17} -4.51946 q^{18} -8.09609 q^{19} +0.920321 q^{20} +0.340674 q^{21} -8.22123 q^{22} +7.76776 q^{23} -0.978941 q^{24} -2.43077 q^{25} +0.271257 q^{26} -2.48920 q^{27} +0.457097 q^{28} +2.62533 q^{29} +1.10050 q^{30} -3.99616 q^{31} -3.15590 q^{32} -2.19274 q^{33} +1.60442 q^{34} +1.27606 q^{35} -1.61736 q^{36} +5.69046 q^{37} -12.9895 q^{38} +0.0723491 q^{39} -3.66681 q^{40} -9.29771 q^{41} +0.546585 q^{42} -0.754712 q^{43} -2.94209 q^{44} -4.51512 q^{45} +12.4628 q^{46} -2.98869 q^{47} -2.06204 q^{48} -6.36622 q^{49} -3.89999 q^{50} +0.427927 q^{51} +0.0970737 q^{52} -9.99622 q^{53} -3.99372 q^{54} -8.21333 q^{55} -1.82120 q^{56} -3.46454 q^{57} +4.21213 q^{58} -11.0637 q^{59} +0.393830 q^{60} -4.19806 q^{61} -6.41153 q^{62} -2.24253 q^{63} +4.57395 q^{64} +0.270997 q^{65} -3.51809 q^{66} +6.52244 q^{67} +0.574167 q^{68} +3.32403 q^{69} +2.04734 q^{70} +10.2782 q^{71} +6.44399 q^{72} +12.5495 q^{73} +9.12990 q^{74} -1.04019 q^{75} -4.64851 q^{76} -4.07932 q^{77} +0.116078 q^{78} +1.86612 q^{79} -7.72375 q^{80} +7.38544 q^{81} -14.9174 q^{82} +2.25901 q^{83} +0.195604 q^{84} +1.60288 q^{85} -1.21088 q^{86} +1.12345 q^{87} +11.7221 q^{88} +2.67857 q^{89} -7.24415 q^{90} +0.134596 q^{91} +4.45999 q^{92} -1.71007 q^{93} -4.79511 q^{94} -12.9771 q^{95} -1.35049 q^{96} +2.24436 q^{97} -10.2141 q^{98} +14.4340 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 45 q - 2 q^{2} - 20 q^{3} + 34 q^{4} - 10 q^{5} - 14 q^{6} - 20 q^{7} - 9 q^{8} + 39 q^{9}+O(q^{10}) $ 45 * q - 2 * q^2 - 20 * q^3 + 34 * q^4 - 10 * q^5 - 14 * q^6 - 20 * q^7 - 9 * q^8 + 39 * q^9	\( 45 q - 2 q^{2} - 20 q^{3} + 34 q^{4} - 10 q^{5} - 14 q^{6} - 20 q^{7} - 9 q^{8} + 39 q^{9} - 21 q^{10} - 26 q^{11} - 23 q^{12} - 6 q^{13} - 7 q^{14} - 10 q^{15} + 20 q^{16} + 45 q^{17} - 3 q^{18} - 56 q^{19} - 26 q^{20} + 2 q^{21} - 23 q^{22} - 38 q^{23} - 35 q^{24} + 27 q^{25} - 10 q^{26} - 71 q^{27} - 29 q^{28} - 29 q^{29} + 9 q^{30} - 57 q^{31} + 4 q^{33} - 2 q^{34} - 16 q^{35} + 44 q^{36} - 14 q^{37} - 6 q^{38} - 25 q^{39} - 48 q^{40} - 23 q^{41} - q^{42} - 43 q^{43} - 29 q^{44} - 63 q^{45} - 42 q^{46} + 11 q^{47} - 6 q^{48} - 9 q^{49} + 14 q^{50} - 20 q^{51} - 27 q^{52} + 7 q^{53} + 10 q^{54} - 41 q^{55} - 14 q^{56} - 5 q^{57} - 58 q^{58} - 59 q^{59} + q^{60} - 40 q^{61} - 34 q^{62} - 56 q^{63} - 67 q^{64} - 3 q^{65} - 53 q^{66} - 44 q^{67} + 34 q^{68} - 17 q^{69} + 14 q^{70} - 18 q^{71} - 25 q^{72} - 2 q^{73} - 5 q^{74} - 85 q^{75} - 123 q^{76} - 4 q^{77} + 33 q^{78} - 119 q^{79} - 17 q^{80} + 21 q^{81} - 6 q^{82} - 32 q^{83} + 54 q^{84} - 10 q^{85} - 14 q^{86} - 3 q^{87} - 33 q^{88} - 25 q^{89} - 23 q^{90} - 177 q^{91} - 62 q^{92} + 36 q^{93} - 64 q^{94} - 47 q^{95} - 153 q^{96} - 82 q^{97} + 13 q^{98} - 45 q^{99}+O(q^{100}) \) 45 * q - 2 * q^2 - 20 * q^3 + 34 * q^4 - 10 * q^5 - 14 * q^6 - 20 * q^7 - 9 * q^8 + 39 * q^9 - 21 * q^10 - 26 * q^11 - 23 * q^12 - 6 * q^13 - 7 * q^14 - 10 * q^15 + 20 * q^16 + 45 * q^17 - 3 * q^18 - 56 * q^19 - 26 * q^20 + 2 * q^21 - 23 * q^22 - 38 * q^23 - 35 * q^24 + 27 * q^25 - 10 * q^26 - 71 * q^27 - 29 * q^28 - 29 * q^29 + 9 * q^30 - 57 * q^31 + 4 * q^33 - 2 * q^34 - 16 * q^35 + 44 * q^36 - 14 * q^37 - 6 * q^38 - 25 * q^39 - 48 * q^40 - 23 * q^41 - q^42 - 43 * q^43 - 29 * q^44 - 63 * q^45 - 42 * q^46 + 11 * q^47 - 6 * q^48 - 9 * q^49 + 14 * q^50 - 20 * q^51 - 27 * q^52 + 7 * q^53 + 10 * q^54 - 41 * q^55 - 14 * q^56 - 5 * q^57 - 58 * q^58 - 59 * q^59 + q^60 - 40 * q^61 - 34 * q^62 - 56 * q^63 - 67 * q^64 - 3 * q^65 - 53 * q^66 - 44 * q^67 + 34 * q^68 - 17 * q^69 + 14 * q^70 - 18 * q^71 - 25 * q^72 - 2 * q^73 - 5 * q^74 - 85 * q^75 - 123 * q^76 - 4 * q^77 + 33 * q^78 - 119 * q^79 - 17 * q^80 + 21 * q^81 - 6 * q^82 - 32 * q^83 + 54 * q^84 - 10 * q^85 - 14 * q^86 - 3 * q^87 - 33 * q^88 - 25 * q^89 - 23 * q^90 - 177 * q^91 - 62 * q^92 + 36 * q^93 - 64 * q^94 - 47 * q^95 - 153 * q^96 - 82 * q^97 + 13 * q^98 - 45 * 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 $

$2$	1.60442	1.13450	0.567249	−	0.823547i	$-0.308008\pi$
$2$	1.60442	1.13450	0.567249	+	0.823547i	$0.308008\pi$
$3$	0.427927	0.247064	0.123532	−	0.992341i	$-0.460578\pi$
$3$	0.427927	0.247064	0.123532	+	0.992341i	$0.460578\pi$
$4$	0.574167	0.287084
$5$	1.60288	0.716830	0.358415	−	0.933562i	$-0.383317\pi$
$5$	1.60288	0.716830	0.358415	+	0.933562i	$0.383317\pi$
$6$	0.686575	0.280293
$7$	0.796104	0.300899	0.150449	−	0.988618i	$-0.451928\pi$
$7$	0.796104	0.300899	0.150449	+	0.988618i	$0.451928\pi$
$8$	−2.28764	−0.808802
$9$	−2.81688	−0.938960
$10$	2.57170	0.813241
$11$	−5.12411	−1.54498	−0.772488	−	0.635029i	$-0.780988\pi$
$11$	−5.12411	−1.54498	−0.772488	+	0.635029i	$0.780988\pi$
$12$	0.245702	0.0709279
$13$	0.169069	0.0468912	0.0234456	−	0.999725i	$-0.492536\pi$
$13$	0.169069	0.0468912	0.0234456	+	0.999725i	$0.492536\pi$
$14$	1.27729	0.341369
$15$	0.685916	0.177103
$16$	−4.81867	−1.20467
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−4.51946	−1.06525
$19$	−8.09609	−1.85737	−0.928686	−	0.370868i	$-0.879060\pi$
$19$	−8.09609	−1.85737	−0.928686	+	0.370868i	$0.879060\pi$
$20$	0.920321	0.205790
$21$	0.340674	0.0743412
$22$	−8.22123	−1.75277
$23$	7.76776	1.61969	0.809845	−	0.586644i	$-0.199551\pi$
$23$	7.76776	1.61969	0.809845	+	0.586644i	$0.199551\pi$
$24$	−0.978941	−0.199826
$25$	−2.43077	−0.486155
$26$	0.271257	0.0531980
$27$	−2.48920	−0.479047
$28$	0.457097	0.0863831
$29$	2.62533	0.487511	0.243756	−	0.969837i	$-0.421621\pi$
$29$	2.62533	0.487511	0.243756	+	0.969837i	$0.421621\pi$
$30$	1.10050	0.200922
$31$	−3.99616	−0.717732	−0.358866	−	0.933389i	$-0.616836\pi$
$31$	−3.99616	−0.717732	−0.358866	+	0.933389i	$0.616836\pi$
$32$	−3.15590	−0.557889
$33$	−2.19274	−0.381708
$34$	1.60442	0.275156
$35$	1.27606	0.215693
$36$	−1.61736	−0.269560
$37$	5.69046	0.935507	0.467753	−	0.883859i	$-0.345064\pi$
$37$	5.69046	0.935507	0.467753	+	0.883859i	$0.345064\pi$
$38$	−12.9895	−2.10718
$39$	0.0723491	0.0115851
$40$	−3.66681	−0.579773
$41$	−9.29771	−1.45206	−0.726029	−	0.687664i	$-0.758636\pi$
$41$	−9.29771	−1.45206	−0.726029	+	0.687664i	$0.758636\pi$
$42$	0.546585	0.0843399
$43$	−0.754712	−0.115092	−0.0575462	−	0.998343i	$-0.518328\pi$
$43$	−0.754712	−0.115092	−0.0575462	+	0.998343i	$0.518328\pi$
$44$	−2.94209	−0.443537
$45$	−4.51512	−0.673074
$46$	12.4628	1.83753
$47$	−2.98869	−0.435945	−0.217972	−	0.975955i	$-0.569944\pi$
$47$	−2.98869	−0.435945	−0.217972	+	0.975955i	$0.569944\pi$
$48$	−2.06204	−0.297629
$49$	−6.36622	−0.909460
$50$	−3.89999	−0.551541
$51$	0.427927	0.0599218
$52$	0.0970737	0.0134617
$53$	−9.99622	−1.37309	−0.686543	−	0.727089i	$-0.740873\pi$
$53$	−9.99622	−1.37309	−0.686543	+	0.727089i	$0.740873\pi$
$54$	−3.99372	−0.543477
$55$	−8.21333	−1.10749
$56$	−1.82120	−0.243368
$57$	−3.46454	−0.458889
$58$	4.21213	0.553080
$59$	−11.0637	−1.44037	−0.720186	−	0.693781i	$-0.755944\pi$
$59$	−11.0637	−1.44037	−0.720186	+	0.693781i	$0.755944\pi$
$60$	0.393830	0.0508433
$61$	−4.19806	−0.537506	−0.268753	−	0.963209i	$-0.586612\pi$
$61$	−4.19806	−0.537506	−0.268753	+	0.963209i	$0.586612\pi$
$62$	−6.41153	−0.814265
$63$	−2.24253	−0.282532
$64$	4.57395	0.571743
$65$	0.270997	0.0336130
$66$	−3.51809	−0.433046
$67$	6.52244	0.796843	0.398422	−	0.917202i	$-0.369558\pi$
$67$	6.52244	0.796843	0.398422	+	0.917202i	$0.369558\pi$
$68$	0.574167	0.0696280
$69$	3.32403	0.400167
$70$	2.04734	0.244704
$71$	10.2782	1.21980	0.609900	−	0.792478i	$-0.291209\pi$
$71$	10.2782	1.21980	0.609900	+	0.792478i	$0.291209\pi$
$72$	6.44399	0.759432
$73$	12.5495	1.46880	0.734402	−	0.678715i	$-0.237463\pi$
$73$	12.5495	1.46880	0.734402	+	0.678715i	$0.237463\pi$
$74$	9.12990	1.06133
$75$	−1.04019	−0.120111
$76$	−4.64851	−0.533221
$77$	−4.07932	−0.464882
$78$	0.116078	0.0131433
$79$	1.86612	0.209955	0.104977	−	0.994475i	$-0.466523\pi$
$79$	1.86612	0.209955	0.104977	+	0.994475i	$0.466523\pi$
$80$	−7.72375	−0.863541
$81$	7.38544	0.820604
$82$	−14.9174	−1.64736
$83$	2.25901	0.247958	0.123979	−	0.992285i	$-0.460434\pi$
$83$	2.25901	0.247958	0.123979	+	0.992285i	$0.460434\pi$
$84$	0.195604	0.0213421
$85$	1.60288	0.173857
$86$	−1.21088	−0.130572
$87$	1.12345	0.120446
$88$	11.7221	1.24958
$89$	2.67857	0.283928	0.141964	−	0.989872i	$-0.454658\pi$
$89$	2.67857	0.283928	0.141964	+	0.989872i	$0.454658\pi$
$90$	−7.24415	−0.763601
$91$	0.134596	0.0141095
$92$	4.45999	0.464986
$93$	−1.71007	−0.177325
$94$	−4.79511	−0.494578
$95$	−12.9771	−1.33142
$96$	−1.35049	−0.137834
$97$	2.24436	0.227880	0.113940	−	0.993488i	$-0.463653\pi$
$97$	2.24436	0.227880	0.113940	+	0.993488i	$0.463653\pi$
$98$	−10.2141	−1.03178
$99$	14.4340	1.45067
$100$	−1.39567	−0.139567
$101$	−0.0522611	−0.00520017	−0.00260009	−	0.999997i	$-0.500828\pi$
$101$	−0.0522611	−0.00520017	−0.00260009	+	0.999997i	$0.500828\pi$
$102$	0.686575	0.0679811
$103$	−12.0717	−1.18946	−0.594731	−	0.803925i	$-0.702741\pi$
$103$	−12.0717	−1.18946	−0.594731	+	0.803925i	$0.702741\pi$
$104$	−0.386768	−0.0379257
$105$	0.546060	0.0532900
$106$	−16.0382	−1.55776
$107$	8.01376	0.774720	0.387360	−	0.921929i	$-0.373387\pi$
$107$	8.01376	0.774720	0.387360	+	0.921929i	$0.373387\pi$
$108$	−1.42922	−0.137526
$109$	20.1902	1.93387	0.966936	−	0.255018i	$-0.0820813\pi$
$109$	20.1902	1.93387	0.966936	+	0.255018i	$0.0820813\pi$
$110$	−13.1776	−1.25644
$111$	2.43510	0.231130
$112$	−3.83616	−0.362483
$113$	3.28129	0.308677	0.154339	−	0.988018i	$-0.450675\pi$
$113$	3.28129	0.308677	0.154339	+	0.988018i	$0.450675\pi$
$114$	−5.55858	−0.520608
$115$	12.4508	1.16104
$116$	1.50738	0.139956
$117$	−0.476246	−0.0440290
$118$	−17.7509	−1.63410
$119$	0.796104	0.0729787
$120$	−1.56913	−0.143241
$121$	15.2565	1.38695
$122$	−6.73545	−0.609799
$123$	−3.97874	−0.358751
$124$	−2.29446	−0.206049
$125$	−11.9106	−1.06532
$126$	−3.59796	−0.320532
$127$	−5.73888	−0.509243	−0.254622	−	0.967041i	$-0.581951\pi$
$127$	−5.73888	−0.509243	−0.254622	+	0.967041i	$0.581951\pi$
$128$	13.6503	1.20653
$129$	−0.322962	−0.0284352
$130$	0.434793	0.0381339
$131$	−10.7337	−0.937808	−0.468904	−	0.883249i	$-0.655351\pi$
$131$	−10.7337	−0.937808	−0.468904	+	0.883249i	$0.655351\pi$
$132$	−1.25900	−0.109582
$133$	−6.44533	−0.558881
$134$	10.4647	0.904016
$135$	−3.98989	−0.343395
$136$	−2.28764	−0.196163
$137$	−6.95066	−0.593835	−0.296918	−	0.954903i	$-0.595959\pi$
$137$	−6.95066	−0.593835	−0.296918	+	0.954903i	$0.595959\pi$
$138$	5.33315	0.453988
$139$	6.31333	0.535490	0.267745	−	0.963490i	$-0.413722\pi$
$139$	6.31333	0.535490	0.267745	+	0.963490i	$0.413722\pi$
$140$	0.732671	0.0619220
$141$	−1.27894	−0.107706
$142$	16.4906	1.38386
$143$	−0.866327	−0.0724459
$144$	13.5736	1.13113
$145$	4.20809	0.349463
$146$	20.1346	1.66635
$147$	−2.72428	−0.224695
$148$	3.26728	0.268568
$149$	−5.36895	−0.439841	−0.219921	−	0.975518i	$-0.570580\pi$
$149$	−5.36895	−0.439841	−0.219921	+	0.975518i	$0.570580\pi$
$150$	−1.66891	−0.136266
$151$	−8.20447	−0.667671	−0.333835	−	0.942631i	$-0.608343\pi$
$151$	−8.20447	−0.667671	−0.333835	+	0.942631i	$0.608343\pi$
$152$	18.5209	1.50224
$153$	−2.81688	−0.227731
$154$	−6.54495	−0.527407
$155$	−6.40537	−0.514492
$156$	0.0415404	0.00332590
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	2.99404	0.238193
$159$	−4.27765	−0.339240
$160$	−5.05853	−0.399912
$161$	6.18394	0.487363
$162$	11.8494	0.930973
$163$	−22.9789	−1.79984	−0.899922	−	0.436050i	$-0.856377\pi$
$163$	−22.9789	−1.79984	−0.899922	+	0.436050i	$0.856377\pi$
$164$	−5.33844	−0.416862
$165$	−3.51471	−0.273620
$166$	3.62440	0.281308
$167$	−15.1001	−1.16848	−0.584241	−	0.811580i	$-0.698608\pi$
$167$	−15.1001	−1.16848	−0.584241	+	0.811580i	$0.698608\pi$
$168$	−0.779339	−0.0601273
$169$	−12.9714	−0.997801
$170$	2.57170	0.197240
$171$	22.8057	1.74400
$172$	−0.433331	−0.0330412
$173$	−3.24976	−0.247074	−0.123537	−	0.992340i	$-0.539424\pi$
$173$	−3.24976	−0.247074	−0.123537	+	0.992340i	$0.539424\pi$
$174$	1.80248	0.136646
$175$	−1.93515	−0.146283
$176$	24.6914	1.86118
$177$	−4.73446	−0.355864
$178$	4.29755	0.322115
$179$	−12.2997	−0.919320	−0.459660	−	0.888095i	$-0.652029\pi$
$179$	−12.2997	−0.919320	−0.459660	+	0.888095i	$0.652029\pi$
$180$	−2.59243	−0.193229
$181$	20.2694	1.50661	0.753307	−	0.657669i	$-0.228458\pi$
$181$	20.2694	1.50661	0.753307	+	0.657669i	$0.228458\pi$
$182$	0.215949	0.0160072
$183$	−1.79646	−0.132798
$184$	−17.7698	−1.31001
$185$	9.12113	0.670599
$186$	−2.74366	−0.201175
$187$	−5.12411	−0.374712
$188$	−1.71601	−0.125153
$189$	−1.98166	−0.144145
$190$	−20.8207	−1.51049
$191$	1.85556	0.134263	0.0671317	−	0.997744i	$-0.478615\pi$
$191$	1.85556	0.134263	0.0671317	+	0.997744i	$0.478615\pi$
$192$	1.95731	0.141257
$193$	8.29945	0.597407	0.298704	−	0.954346i	$-0.403446\pi$
$193$	8.29945	0.597407	0.298704	+	0.954346i	$0.403446\pi$
$194$	3.60089	0.258529
$195$	0.115967	0.00830456
$196$	−3.65527	−0.261091
$197$	−14.0303	−0.999616	−0.499808	−	0.866136i	$-0.666596\pi$
$197$	−14.0303	−0.999616	−0.499808	+	0.866136i	$0.666596\pi$
$198$	23.1582	1.64578
$199$	10.7084	0.759098	0.379549	−	0.925172i	$-0.376079\pi$
$199$	10.7084	0.759098	0.379549	+	0.925172i	$0.376079\pi$
$200$	5.56073	0.393203
$201$	2.79113	0.196871
$202$	−0.0838488	−0.00589958
$203$	2.09003	0.146692
$204$	0.245702	0.0172025
$205$	−14.9031	−1.04088
$206$	−19.3681	−1.34944
$207$	−21.8808	−1.52082
$208$	−0.814686	−0.0564883
$209$	41.4853	2.86960
$210$	0.876110	0.0604574
$211$	−22.6571	−1.55978	−0.779888	−	0.625919i	$-0.784724\pi$
$211$	−22.6571	−1.55978	−0.779888	+	0.625919i	$0.784724\pi$
$212$	−5.73950	−0.394191
$213$	4.39833	0.301369
$214$	12.8574	0.878917
$215$	−1.20971	−0.0825017
$216$	5.69438	0.387454
$217$	−3.18136	−0.215965
$218$	32.3936	2.19397
$219$	5.37025	0.362888
$220$	−4.71583	−0.317941
$221$	0.169069	0.0113728
$222$	3.90693	0.262216
$223$	8.43709	0.564989	0.282495	−	0.959269i	$-0.408838\pi$
$223$	8.43709	0.564989	0.282495	+	0.959269i	$0.408838\pi$
$224$	−2.51242	−0.167868
$225$	6.84720	0.456480
$226$	5.26456	0.350194
$227$	27.4294	1.82055	0.910277	−	0.413999i	$-0.135868\pi$
$227$	27.4294	1.82055	0.910277	+	0.413999i	$0.135868\pi$
$228$	−1.98922	−0.131739
$229$	16.4346	1.08603	0.543014	−	0.839723i	$-0.317283\pi$
$229$	16.4346	1.08603	0.543014	+	0.839723i	$0.317283\pi$
$230$	19.9763	1.31720
$231$	−1.74565	−0.114855
$232$	−6.00580	−0.394300
$233$	−4.76838	−0.312387	−0.156194	−	0.987726i	$-0.549922\pi$
$233$	−4.76838	−0.312387	−0.156194	+	0.987726i	$0.549922\pi$
$234$	−0.764099	−0.0499507
$235$	−4.79051	−0.312498
$236$	−6.35242	−0.413507
$237$	0.798563	0.0518722
$238$	1.27729	0.0827941
$239$	−2.45956	−0.159096	−0.0795480	−	0.996831i	$-0.525348\pi$
$239$	−2.45956	−0.159096	−0.0795480	+	0.996831i	$0.525348\pi$
$240$	−3.30520	−0.213350
$241$	0.458406	0.0295285	0.0147643	−	0.999891i	$-0.495300\pi$
$241$	0.458406	0.0295285	0.0147643	+	0.999891i	$0.495300\pi$
$242$	24.4778	1.57350
$243$	10.6280	0.681788
$244$	−2.41039	−0.154309
$245$	−10.2043	−0.651928
$246$	−6.38357	−0.407002
$247$	−1.36880	−0.0870944
$248$	9.14176	0.580503
$249$	0.966690	0.0612615
$250$	−19.1097	−1.20860
$251$	−2.76720	−0.174664	−0.0873321	−	0.996179i	$-0.527834\pi$
$251$	−2.76720	−0.174664	−0.0873321	+	0.996179i	$0.527834\pi$
$252$	−1.28759	−0.0811103
$253$	−39.8028	−2.50238
$254$	−9.20758	−0.577735
$255$	0.685916	0.0429537
$256$	12.7530	0.797061
$257$	−6.75946	−0.421644	−0.210822	−	0.977525i	$-0.567614\pi$
$257$	−6.75946	−0.421644	−0.210822	+	0.977525i	$0.567614\pi$
$258$	−0.518166	−0.0322596
$259$	4.53020	0.281493
$260$	0.155598	0.00964975
$261$	−7.39523	−0.457753
$262$	−17.2214	−1.06394
$263$	−2.72424	−0.167984	−0.0839918	−	0.996466i	$-0.526767\pi$
$263$	−2.72424	−0.167984	−0.0839918	+	0.996466i	$0.526767\pi$
$264$	5.01620	0.308726
$265$	−16.0228	−0.984270
$266$	−10.3410	−0.634049
$267$	1.14623	0.0701482
$268$	3.74497	0.228761
$269$	1.83164	0.111677	0.0558384	−	0.998440i	$-0.482217\pi$
$269$	1.83164	0.111677	0.0558384	+	0.998440i	$0.482217\pi$
$270$	−6.40146	−0.389581
$271$	−26.7903	−1.62740	−0.813698	−	0.581288i	$-0.802549\pi$
$271$	−26.7903	−1.62740	−0.813698	+	0.581288i	$0.802549\pi$
$272$	−4.81867	−0.292175
$273$	0.0575974	0.00348595
$274$	−11.1518	−0.673704
$275$	12.4556	0.751098
$276$	1.90855	0.114881
$277$	0.731982	0.0439805	0.0219903	−	0.999758i	$-0.493000\pi$
$277$	0.731982	0.0439805	0.0219903	+	0.999758i	$0.493000\pi$
$278$	10.1292	0.607512
$279$	11.2567	0.673921
$280$	−2.91916	−0.174453
$281$	11.6643	0.695834	0.347917	−	0.937525i	$-0.386889\pi$
$281$	11.6643	0.695834	0.347917	+	0.937525i	$0.386889\pi$
$282$	−2.05196	−0.122192
$283$	−14.8613	−0.883413	−0.441706	−	0.897160i	$-0.645627\pi$
$283$	−14.8613	−0.883413	−0.441706	+	0.897160i	$0.645627\pi$
$284$	5.90142	0.350185
$285$	−5.55324	−0.328945
$286$	−1.38995	−0.0821896
$287$	−7.40194	−0.436923
$288$	8.88978	0.523835
$289$	1.00000	0.0588235
$290$	6.75154	0.396464
$291$	0.960420	0.0563008
$292$	7.20549	0.421669
$293$	−20.6803	−1.20816	−0.604078	−	0.796925i	$-0.706459\pi$
$293$	−20.6803	−1.20816	−0.604078	+	0.796925i	$0.706459\pi$
$294$	−4.37089	−0.254915
$295$	−17.7338	−1.03250
$296$	−13.0177	−0.756639
$297$	12.7549	0.740116
$298$	−8.61405	−0.498999
$299$	1.31328	0.0759492
$300$	−0.597245	−0.0344820
$301$	−0.600829	−0.0346312
$302$	−13.1634	−0.757470
$303$	−0.0223639	−0.00128477
$304$	39.0124	2.23751
$305$	−6.72899	−0.385301
$306$	−4.51946	−0.258360
$307$	−2.49267	−0.142264	−0.0711322	−	0.997467i	$-0.522661\pi$
$307$	−2.49267	−0.142264	−0.0711322	+	0.997467i	$0.522661\pi$
$308$	−2.34221	−0.133460
$309$	−5.16581	−0.293873
$310$	−10.2769	−0.583689
$311$	29.6524	1.68143	0.840716	−	0.541476i	$-0.182134\pi$
$311$	29.6524	1.68143	0.840716	+	0.541476i	$0.182134\pi$
$312$	−0.165508	−0.00937006
$313$	−8.14214	−0.460221	−0.230111	−	0.973164i	$-0.573909\pi$
$313$	−8.14214	−0.460221	−0.230111	+	0.973164i	$0.573909\pi$
$314$	1.60442	0.0905427
$315$	−3.59450	−0.202527
$316$	1.07146	0.0602746
$317$	29.3376	1.64776	0.823881	−	0.566762i	$-0.191804\pi$
$317$	29.3376	1.64776	0.823881	+	0.566762i	$0.191804\pi$
$318$	−6.86316	−0.384867
$319$	−13.4525	−0.753194
$320$	7.33149	0.409843
$321$	3.42930	0.191405
$322$	9.92165	0.552912
$323$	−8.09609	−0.450479
$324$	4.24048	0.235582
$325$	−0.410968	−0.0227964
$326$	−36.8678	−2.04192
$327$	8.63994	0.477790
$328$	21.2698	1.17443
$329$	−2.37930	−0.131175
$330$	−5.63907	−0.310421
$331$	−19.4081	−1.06677	−0.533384	−	0.845873i	$-0.679080\pi$
$331$	−19.4081	−1.06677	−0.533384	+	0.845873i	$0.679080\pi$
$332$	1.29705	0.0711847
$333$	−16.0293	−0.878403
$334$	−24.2270	−1.32564
$335$	10.4547	0.571201
$336$	−1.64160	−0.0895564
$337$	15.0851	0.821740	0.410870	−	0.911694i	$-0.365225\pi$
$337$	15.0851	0.821740	0.410870	+	0.911694i	$0.365225\pi$
$338$	−20.8116	−1.13200
$339$	1.40415	0.0762630
$340$	0.920321	0.0499114
$341$	20.4768	1.10888
$342$	36.5900	1.97856
$343$	−10.6409	−0.574554
$344$	1.72651	0.0930870
$345$	5.32803	0.286851
$346$	−5.21398	−0.280305
$347$	13.8916	0.745738	0.372869	−	0.927884i	$-0.378374\pi$
$347$	13.8916	0.745738	0.372869	+	0.927884i	$0.378374\pi$
$348$	0.645047	0.0345782
$349$	5.12055	0.274097	0.137049	−	0.990564i	$-0.456238\pi$
$349$	5.12055	0.274097	0.137049	+	0.990564i	$0.456238\pi$
$350$	−3.10479	−0.165958
$351$	−0.420846	−0.0224631
$352$	16.1712	0.861926
$353$	19.3830	1.03165	0.515826	−	0.856693i	$-0.327485\pi$
$353$	19.3830	1.03165	0.515826	+	0.856693i	$0.327485\pi$
$354$	−7.59607	−0.403726
$355$	16.4748	0.874390
$356$	1.53795	0.0815110
$357$	0.340674	0.0180304
$358$	−19.7338	−1.04297
$359$	13.7165	0.723927	0.361963	−	0.932192i	$-0.382107\pi$
$359$	13.7165	0.723927	0.361963	+	0.932192i	$0.382107\pi$
$360$	10.3290	0.544384
$361$	46.5467	2.44983
$362$	32.5207	1.70925
$363$	6.52866	0.342666
$364$	0.0772807	0.00405061
$365$	20.1153	1.05288
$366$	−2.88228	−0.150659
$367$	−15.4611	−0.807063	−0.403531	−	0.914966i	$-0.632217\pi$
$367$	−15.4611	−0.807063	−0.403531	+	0.914966i	$0.632217\pi$
$368$	−37.4302	−1.95119
$369$	26.1905	1.36342
$370$	14.6341	0.760793
$371$	−7.95803	−0.413160
$372$	−0.981863	−0.0509072
$373$	−18.0129	−0.932670	−0.466335	−	0.884608i	$-0.654426\pi$
$373$	−18.0129	−0.932670	−0.466335	+	0.884608i	$0.654426\pi$
$374$	−8.22123	−0.425110
$375$	−5.09688	−0.263202
$376$	6.83703	0.352593
$377$	0.443861	0.0228600
$378$	−3.17942	−0.163532
$379$	36.3546	1.86741	0.933706	−	0.358042i	$-0.116556\pi$
$379$	36.3546	1.86741	0.933706	+	0.358042i	$0.116556\pi$
$380$	−7.45101	−0.382229
$381$	−2.45582	−0.125815
$382$	2.97709	0.152321
$383$	−23.6529	−1.20861	−0.604304	−	0.796754i	$-0.706549\pi$
$383$	−23.6529	−1.20861	−0.604304	+	0.796754i	$0.706549\pi$
$384$	5.84134	0.298090
$385$	−6.53867	−0.333241
$386$	13.3158	0.677757
$387$	2.12593	0.108067
$388$	1.28863	0.0654205
$389$	−23.1389	−1.17319	−0.586594	−	0.809881i	$-0.699531\pi$
$389$	−23.1389	−1.17319	−0.586594	+	0.809881i	$0.699531\pi$
$390$	0.186060	0.00942150
$391$	7.76776	0.392832
$392$	14.5636	0.735573
$393$	−4.59324	−0.231698
$394$	−22.5105	−1.13406
$395$	2.99117	0.150502
$396$	8.28752	0.416464
$397$	−31.8514	−1.59858	−0.799289	−	0.600947i	$-0.794790\pi$
$397$	−31.8514	−1.59858	−0.799289	+	0.600947i	$0.794790\pi$
$398$	17.1808	0.861195
$399$	−2.75813	−0.138079
$400$	11.7131	0.585654
$401$	13.1877	0.658565	0.329282	−	0.944232i	$-0.393193\pi$
$401$	13.1877	0.658565	0.329282	+	0.944232i	$0.393193\pi$
$402$	4.47815	0.223350
$403$	−0.675626	−0.0336553
$404$	−0.0300066	−0.00149288
$405$	11.8380	0.588234
$406$	3.35329	0.166421
$407$	−29.1586	−1.44534
$408$	−0.978941	−0.0484648
$409$	37.9713	1.87756	0.938780	−	0.344518i	$-0.111958\pi$
$409$	37.9713	1.87756	0.938780	+	0.344518i	$0.111958\pi$
$410$	−23.9109	−1.18087
$411$	−2.97438	−0.146715
$412$	−6.93118	−0.341475
$413$	−8.80786	−0.433407
$414$	−35.1061	−1.72537
$415$	3.62092	0.177744
$416$	−0.533563	−0.0261601
$417$	2.70164	0.132300
$418$	66.5598	3.25555
$419$	1.66817	0.0814957	0.0407478	−	0.999169i	$-0.487026\pi$
$419$	1.66817	0.0814957	0.0407478	+	0.999169i	$0.487026\pi$
$420$	0.313530	0.0152987
$421$	0.631440	0.0307745	0.0153872	−	0.999882i	$-0.495102\pi$
$421$	0.631440	0.0307745	0.0153872	+	0.999882i	$0.495102\pi$
$422$	−36.3515	−1.76956
$423$	8.41877	0.409334
$424$	22.8677	1.11055
$425$	−2.43077	−0.117910
$426$	7.05677	0.341902
$427$	−3.34209	−0.161735
$428$	4.60124	0.222409
$429$	−0.370724	−0.0178987
$430$	−1.94089	−0.0935980
$431$	17.4819	0.842071	0.421036	−	0.907044i	$-0.361667\pi$
$431$	17.4819	0.842071	0.421036	+	0.907044i	$0.361667\pi$
$432$	11.9946	0.577091
$433$	−11.7023	−0.562375	−0.281187	−	0.959653i	$-0.590728\pi$
$433$	−11.7023	−0.562375	−0.281187	+	0.959653i	$0.590728\pi$
$434$	−5.10424	−0.245011
$435$	1.80075	0.0863395
$436$	11.5926	0.555183
$437$	−62.8885	−3.00836
$438$	8.61614	0.411695
$439$	−24.4106	−1.16505	−0.582527	−	0.812812i	$-0.697936\pi$
$439$	−24.4106	−1.16505	−0.582527	+	0.812812i	$0.697936\pi$
$440$	18.7891	0.895736
$441$	17.9329	0.853946
$442$	0.271257	0.0129024
$443$	40.2221	1.91101	0.955505	−	0.294976i	$-0.0953115\pi$
$443$	40.2221	1.91101	0.955505	+	0.294976i	$0.0953115\pi$
$444$	1.39816	0.0663535
$445$	4.29343	0.203528
$446$	13.5366	0.640978
$447$	−2.29752	−0.108669
$448$	3.64134	0.172037
$449$	−23.1973	−1.09475	−0.547375	−	0.836888i	$-0.684373\pi$
$449$	−23.1973	−1.09475	−0.547375	+	0.836888i	$0.684373\pi$
$450$	10.9858	0.517875
$451$	47.6425	2.24340
$452$	1.88401	0.0886162
$453$	−3.51092	−0.164957
$454$	44.0084	2.06541
$455$	0.215742	0.0101141
$456$	7.92560	0.371150
$457$	−8.27534	−0.387104	−0.193552	−	0.981090i	$-0.562001\pi$
$457$	−8.27534	−0.387104	−0.193552	+	0.981090i	$0.562001\pi$
$458$	26.3680	1.23210
$459$	−2.48920	−0.116186
$460$	7.14883	0.333316
$461$	−7.94830	−0.370189	−0.185095	−	0.982721i	$-0.559259\pi$
$461$	−7.94830	−0.370189	−0.185095	+	0.982721i	$0.559259\pi$
$462$	−2.80076	−0.130303
$463$	−10.0074	−0.465081	−0.232540	−	0.972587i	$-0.574704\pi$
$463$	−10.0074	−0.465081	−0.232540	+	0.972587i	$0.574704\pi$
$464$	−12.6506	−0.587288
$465$	−2.74103	−0.127112
$466$	−7.65050	−0.354402
$467$	27.0301	1.25080	0.625401	−	0.780303i	$-0.284935\pi$
$467$	27.0301	1.25080	0.625401	+	0.780303i	$0.284935\pi$
$468$	−0.273445	−0.0126400
$469$	5.19254	0.239769
$470$	−7.68599	−0.354528
$471$	0.427927	0.0197178
$472$	25.3098	1.16498
$473$	3.86723	0.177815
$474$	1.28123	0.0588489
$475$	19.6798	0.902970
$476$	0.457097	0.0209510
$477$	28.1581	1.28927
$478$	−3.94618	−0.180494
$479$	18.4661	0.843739	0.421870	−	0.906656i	$-0.361374\pi$
$479$	18.4661	0.843739	0.421870	+	0.906656i	$0.361374\pi$
$480$	−2.16468	−0.0988036
$481$	0.962079	0.0438670
$482$	0.735476	0.0335000
$483$	2.64628	0.120410
$484$	8.75978	0.398172
$485$	3.59743	0.163351
$486$	17.0518	0.773487
$487$	26.7804	1.21354	0.606768	−	0.794879i	$-0.292466\pi$
$487$	26.7804	1.21354	0.606768	+	0.794879i	$0.292466\pi$
$488$	9.60363	0.434736
$489$	−9.83328	−0.444676
$490$	−16.3720	−0.739610
$491$	−37.0368	−1.67145	−0.835724	−	0.549149i	$-0.814952\pi$
$491$	−37.0368	−1.67145	−0.835724	+	0.549149i	$0.814952\pi$
$492$	−2.28446	−0.102991
$493$	2.62533	0.118239
$494$	−2.19613	−0.0988084
$495$	23.1360	1.03988
$496$	19.2562	0.864628
$497$	8.18253	0.367037
$498$	1.55098	0.0695010
$499$	−14.7214	−0.659019	−0.329510	−	0.944152i	$-0.606883\pi$
$499$	−14.7214	−0.659019	−0.329510	+	0.944152i	$0.606883\pi$
$500$	−6.83870	−0.305836
$501$	−6.46175	−0.288690
$502$	−4.43975	−0.198156
$503$	−15.4330	−0.688122	−0.344061	−	0.938947i	$-0.611803\pi$
$503$	−15.4330	−0.688122	−0.344061	+	0.938947i	$0.611803\pi$
$504$	5.13009	0.228512
$505$	−0.0837683	−0.00372764
$506$	−63.8605	−2.83895
$507$	−5.55082	−0.246520
$508$	−3.29507	−0.146195
$509$	−30.2821	−1.34223	−0.671114	−	0.741354i	$-0.734184\pi$
$509$	−30.2821	−1.34223	−0.671114	+	0.741354i	$0.734184\pi$
$510$	1.10050	0.0487309
$511$	9.99067	0.441961
$512$	−6.83950	−0.302266
$513$	20.1528	0.889767
$514$	−10.8450	−0.478353
$515$	−19.3495	−0.852642
$516$	−0.185434	−0.00816327
$517$	15.3144	0.673525
$518$	7.26835	0.319353
$519$	−1.39066	−0.0610431
$520$	−0.619943	−0.0271863
$521$	−30.7979	−1.34928	−0.674640	−	0.738147i	$-0.735701\pi$
$521$	−30.7979	−1.34928	−0.674640	+	0.738147i	$0.735701\pi$
$522$	−11.8651	−0.519320
$523$	−1.57834	−0.0690159	−0.0345080	−	0.999404i	$-0.510986\pi$
$523$	−1.57834	−0.0690159	−0.0345080	+	0.999404i	$0.510986\pi$
$524$	−6.16294	−0.269229
$525$	−0.828102	−0.0361413
$526$	−4.37082	−0.190577
$527$	−3.99616	−0.174076
$528$	10.5661	0.459831
$529$	37.3381	1.62339
$530$	−25.7072	−1.11665
$531$	31.1651	1.35245
$532$	−3.70070	−0.160446
$533$	−1.57195	−0.0680888
$534$	1.83904	0.0795830
$535$	12.8451	0.555342
$536$	−14.9210	−0.644488
$537$	−5.26336	−0.227131
$538$	2.93872	0.126697
$539$	32.6212	1.40509
$540$	−2.29086	−0.0985830
$541$	−31.9747	−1.37470	−0.687350	−	0.726326i	$-0.741226\pi$
$541$	−31.9747	−1.37470	−0.687350	+	0.726326i	$0.741226\pi$
$542$	−42.9829	−1.84628
$543$	8.67383	0.372229
$544$	−3.15590	−0.135308
$545$	32.3625	1.38626
$546$	0.0924104	0.00395480
$547$	−15.8021	−0.675650	−0.337825	−	0.941209i	$-0.609691\pi$
$547$	−15.8021	−0.675650	−0.337825	+	0.941209i	$0.609691\pi$
$548$	−3.99084	−0.170480
$549$	11.8254	0.504697
$550$	19.9839	0.852118
$551$	−21.2549	−0.905489
$552$	−7.60418	−0.323655
$553$	1.48563	0.0631752
$554$	1.17441	0.0498958
$555$	3.90318	0.165681
$556$	3.62491	0.153730
$557$	−2.33906	−0.0991089	−0.0495545	−	0.998771i	$-0.515780\pi$
$557$	−2.33906	−0.0991089	−0.0495545	+	0.998771i	$0.515780\pi$
$558$	18.0605	0.764561
$559$	−0.127598	−0.00539683
$560$	−6.14890	−0.259839
$561$	−2.19274	−0.0925777
$562$	18.7145	0.789422
$563$	−46.1975	−1.94699	−0.973495	−	0.228707i	$-0.926550\pi$
$563$	−46.1975	−1.94699	−0.973495	+	0.228707i	$0.926550\pi$
$564$	−0.734325	−0.0309207
$565$	5.25951	0.221269
$566$	−23.8438	−1.00223
$567$	5.87958	0.246919
$568$	−23.5128	−0.986577
$569$	27.9950	1.17361	0.586807	−	0.809727i	$-0.300385\pi$
$569$	27.9950	1.17361	0.586807	+	0.809727i	$0.300385\pi$
$570$	−8.90973	−0.373188
$571$	21.1553	0.885321	0.442661	−	0.896689i	$-0.354035\pi$
$571$	21.1553	0.885321	0.442661	+	0.896689i	$0.354035\pi$
$572$	−0.497416	−0.0207980
$573$	0.794042	0.0331716
$574$	−11.8758	−0.495687
$575$	−18.8817	−0.787420
$576$	−12.8842	−0.536844
$577$	−16.5335	−0.688299	−0.344149	−	0.938915i	$-0.611833\pi$
$577$	−16.5335	−0.688299	−0.344149	+	0.938915i	$0.611833\pi$
$578$	1.60442	0.0667351
$579$	3.55156	0.147598
$580$	2.41614	0.100325
$581$	1.79840	0.0746104
$582$	1.54092	0.0638731
$583$	51.2217	2.12139
$584$	−28.7086	−1.18797
$585$	−0.763366	−0.0315613
$586$	−33.1799	−1.37065
$587$	−24.5856	−1.01476	−0.507378	−	0.861723i	$-0.669385\pi$
$587$	−24.5856	−1.01476	−0.507378	+	0.861723i	$0.669385\pi$
$588$	−1.56419	−0.0645061
$589$	32.3533	1.33309
$590$	−28.4525	−1.17137
$591$	−6.00393	−0.246969
$592$	−27.4204	−1.12697
$593$	26.8639	1.10317	0.551585	−	0.834119i	$-0.314023\pi$
$593$	26.8639	1.10317	0.551585	+	0.834119i	$0.314023\pi$
$594$	20.4643	0.839659
$595$	1.27606	0.0523133
$596$	−3.08267	−0.126271
$597$	4.58241	0.187546
$598$	2.10706	0.0861642
$599$	46.3709	1.89467	0.947333	−	0.320251i	$-0.103767\pi$
$599$	46.3709	1.89467	0.947333	+	0.320251i	$0.103767\pi$
$600$	2.37958	0.0971462
$601$	−11.2868	−0.460398	−0.230199	−	0.973144i	$-0.573938\pi$
$601$	−11.2868	−0.460398	−0.230199	+	0.973144i	$0.573938\pi$
$602$	−0.963983	−0.0392890
$603$	−18.3729	−0.748204
$604$	−4.71074	−0.191677
$605$	24.4543	0.994210
$606$	−0.0358812	−0.00145757
$607$	−17.7824	−0.721764	−0.360882	−	0.932612i	$-0.617524\pi$
$607$	−17.7824	−0.721764	−0.360882	+	0.932612i	$0.617524\pi$
$608$	25.5504	1.03621
$609$	0.894382	0.0362422
$610$	−10.7961	−0.437122
$611$	−0.505293	−0.0204420
$612$	−1.61736	−0.0653779
$613$	−23.3517	−0.943167	−0.471584	−	0.881821i	$-0.656317\pi$
$613$	−23.3517	−0.943167	−0.471584	+	0.881821i	$0.656317\pi$
$614$	−3.99930	−0.161398
$615$	−6.37744	−0.257163
$616$	9.33201	0.375997
$617$	−1.05979	−0.0426657	−0.0213329	−	0.999772i	$-0.506791\pi$
$617$	−1.05979	−0.0426657	−0.0213329	+	0.999772i	$0.506791\pi$
$618$	−8.28814	−0.333398
$619$	−5.58428	−0.224451	−0.112226	−	0.993683i	$-0.535798\pi$
$619$	−5.58428	−0.224451	−0.112226	+	0.993683i	$0.535798\pi$
$620$	−3.67775	−0.147702
$621$	−19.3355	−0.775907
$622$	47.5749	1.90758
$623$	2.13242	0.0854336
$624$	−0.348626	−0.0139562
$625$	−6.93747	−0.277499
$626$	−13.0634	−0.522120
$627$	17.7527	0.708973
$628$	0.574167	0.0229118
$629$	5.69046	0.226894
$630$	−5.76710	−0.229767
$631$	−40.8799	−1.62740	−0.813702	−	0.581283i	$-0.802551\pi$
$631$	−40.8799	−1.62740	−0.813702	+	0.581283i	$0.802551\pi$
$632$	−4.26900	−0.169812
$633$	−9.69556	−0.385364
$634$	47.0698	1.86938
$635$	−9.19873	−0.365041
$636$	−2.45609	−0.0973902
$637$	−1.07633	−0.0426457
$638$	−21.5834	−0.854496
$639$	−28.9525	−1.14534
$640$	21.8798	0.864877
$641$	−16.4901	−0.651319	−0.325659	−	0.945487i	$-0.605586\pi$
$641$	−16.4901	−0.651319	−0.325659	+	0.945487i	$0.605586\pi$
$642$	5.50205	0.217149
$643$	−5.95791	−0.234957	−0.117478	−	0.993075i	$-0.537481\pi$
$643$	−5.95791	−0.234957	−0.117478	+	0.993075i	$0.537481\pi$
$644$	3.55062	0.139914
$645$	−0.517669	−0.0203832
$646$	−12.9895	−0.511067
$647$	−15.2777	−0.600628	−0.300314	−	0.953840i	$-0.597091\pi$
$647$	−15.2777	−0.600628	−0.300314	+	0.953840i	$0.597091\pi$
$648$	−16.8952	−0.663706
$649$	56.6917	2.22534
$650$	−0.659365	−0.0258624
$651$	−1.36139	−0.0533571
$652$	−13.1937	−0.516706
$653$	27.0071	1.05687	0.528435	−	0.848974i	$-0.322779\pi$
$653$	27.0071	1.05687	0.528435	+	0.848974i	$0.322779\pi$
$654$	13.8621	0.542051
$655$	−17.2048	−0.672249
$656$	44.8025	1.74925
$657$	−35.3503	−1.37915
$658$	−3.81741	−0.148818
$659$	23.8050	0.927313	0.463656	−	0.886015i	$-0.346537\pi$
$659$	23.8050	0.927313	0.463656	+	0.886015i	$0.346537\pi$
$660$	−2.01803	−0.0785517
$661$	2.87298	0.111746	0.0558730	−	0.998438i	$-0.482206\pi$
$661$	2.87298	0.111746	0.0558730	+	0.998438i	$0.482206\pi$
$662$	−31.1388	−1.21024
$663$	0.0723491	0.00280980
$664$	−5.16779	−0.200549
$665$	−10.3311	−0.400623
$666$	−25.7178	−0.996545
$667$	20.3929	0.789617
$668$	−8.67000	−0.335452
$669$	3.61046	0.139588
$670$	16.7737	0.648026
$671$	21.5113	0.830435
$672$	−1.07513	−0.0414741
$673$	37.0874	1.42961	0.714806	−	0.699322i	$-0.246515\pi$
$673$	37.0874	1.42961	0.714806	+	0.699322i	$0.246515\pi$
$674$	24.2029	0.932261
$675$	6.05068	0.232891
$676$	−7.44776	−0.286452
$677$	−23.0386	−0.885447	−0.442723	−	0.896658i	$-0.645988\pi$
$677$	−23.0386	−0.885447	−0.442723	+	0.896658i	$0.645988\pi$
$678$	2.25285	0.0865201
$679$	1.78674	0.0685688
$680$	−3.66681	−0.140616
$681$	11.7378	0.449793
$682$	32.8534	1.25802
$683$	−32.4648	−1.24223	−0.621115	−	0.783720i	$-0.713320\pi$
$683$	−32.4648	−1.24223	−0.621115	+	0.783720i	$0.713320\pi$
$684$	13.0943	0.500673
$685$	−11.1411	−0.425679
$686$	−17.0725	−0.651830
$687$	7.03281	0.268318
$688$	3.63670	0.138648
$689$	−1.69005	−0.0643857
$690$	8.54840	0.325432
$691$	−37.3368	−1.42036	−0.710180	−	0.704021i	$-0.751386\pi$
$691$	−37.3368	−1.42036	−0.710180	+	0.704021i	$0.751386\pi$
$692$	−1.86590	−0.0709310
$693$	11.4910	0.436505
$694$	22.2879	0.846038
$695$	10.1195	0.383855
$696$	−2.57004	−0.0974172
$697$	−9.29771	−0.352176
$698$	8.21553	0.310962
$699$	−2.04052	−0.0771796
$700$	−1.11110	−0.0419956
$701$	−15.6420	−0.590791	−0.295395	−	0.955375i	$-0.595451\pi$
$701$	−15.6420	−0.590791	−0.295395	+	0.955375i	$0.595451\pi$
$702$	−0.675214	−0.0254843
$703$	−46.0705	−1.73758
$704$	−23.4374	−0.883330
$705$	−2.04999	−0.0772070
$706$	31.0985	1.17041
$707$	−0.0416053	−0.00156473
$708$	−2.71837	−0.102163
$709$	4.51150	0.169433	0.0847165	−	0.996405i	$-0.473002\pi$
$709$	4.51150	0.169433	0.0847165	+	0.996405i	$0.473002\pi$
$710$	26.4325	0.991993
$711$	−5.25663	−0.197139
$712$	−6.12759	−0.229641
$713$	−31.0412	−1.16250
$714$	0.546585	0.0204554
$715$	−1.38862	−0.0519314
$716$	−7.06206	−0.263922
$717$	−1.05251	−0.0393068
$718$	22.0070	0.821293
$719$	−35.7259	−1.33235	−0.666175	−	0.745795i	$-0.732070\pi$
$719$	−35.7259	−1.33235	−0.666175	+	0.745795i	$0.732070\pi$
$720$	21.7569	0.810830
$721$	−9.61034	−0.357908
$722$	74.6806	2.77932
$723$	0.196164	0.00729542
$724$	11.6380	0.432524
$725$	−6.38158	−0.237006
$726$	10.4747	0.388754
$727$	21.6223	0.801926	0.400963	−	0.916094i	$-0.368676\pi$
$727$	21.6223	0.801926	0.400963	+	0.916094i	$0.368676\pi$
$728$	−0.307907	−0.0114118
$729$	−17.6083	−0.652159
$730$	32.2734	1.19449
$731$	−0.754712	−0.0279140
$732$	−1.03147	−0.0381242
$733$	6.71271	0.247940	0.123970	−	0.992286i	$-0.460437\pi$
$733$	6.71271	0.247940	0.123970	+	0.992286i	$0.460437\pi$
$734$	−24.8061	−0.915611
$735$	−4.36669	−0.161068
$736$	−24.5142	−0.903607
$737$	−33.4217	−1.23110
$738$	42.0206	1.54680
$739$	18.3485	0.674960	0.337480	−	0.941333i	$-0.390425\pi$
$739$	18.3485	0.674960	0.337480	+	0.941333i	$0.390425\pi$
$740$	5.23705	0.192518
$741$	−0.585745	−0.0215179
$742$	−12.7680	−0.468729
$743$	33.6322	1.23384	0.616922	−	0.787024i	$-0.288379\pi$
$743$	33.6322	1.23384	0.616922	+	0.787024i	$0.288379\pi$
$744$	3.91201	0.143421
$745$	−8.60578	−0.315292
$746$	−28.9002	−1.05811
$747$	−6.36335	−0.232823
$748$	−2.94209	−0.107574
$749$	6.37979	0.233112
$750$	−8.17755	−0.298602
$751$	−3.81984	−0.139388	−0.0696940	−	0.997568i	$-0.522202\pi$
$751$	−3.81984	−0.139388	−0.0696940	+	0.997568i	$0.522202\pi$
$752$	14.4015	0.525168
$753$	−1.18416	−0.0431532
$754$	0.712140	0.0259346
$755$	−13.1508	−0.478606
$756$	−1.13780	−0.0413815
$757$	45.8834	1.66766	0.833831	−	0.552020i	$-0.186143\pi$
$757$	45.8834	1.66766	0.833831	+	0.552020i	$0.186143\pi$
$758$	58.3281	2.11857
$759$	−17.0327	−0.618248
$760$	29.6868	1.07685
$761$	45.3334	1.64333	0.821666	−	0.569969i	$-0.193045\pi$
$761$	45.3334	1.64333	0.821666	+	0.569969i	$0.193045\pi$
$762$	−3.94017	−0.142737
$763$	16.0735	0.581900
$764$	1.06540	0.0385448
$765$	−4.51512	−0.163244
$766$	−37.9492	−1.37116
$767$	−1.87053	−0.0675408
$768$	5.45735	0.196925
$769$	−20.7699	−0.748982	−0.374491	−	0.927231i	$-0.622183\pi$
$769$	−20.7699	−0.748982	−0.374491	+	0.927231i	$0.622183\pi$
$770$	−10.4908	−0.378061
$771$	−2.89256	−0.104173
$772$	4.76527	0.171506
$773$	−4.20640	−0.151294	−0.0756469	−	0.997135i	$-0.524102\pi$
$773$	−4.20640	−0.151294	−0.0756469	+	0.997135i	$0.524102\pi$
$774$	3.41089	0.122602
$775$	9.71377	0.348929
$776$	−5.13427	−0.184310
$777$	1.93859	0.0695467
$778$	−37.1245	−1.33098
$779$	75.2751	2.69701
$780$	0.0665844	0.00238410
$781$	−52.6667	−1.88456
$782$	12.4628	0.445667
$783$	−6.53496	−0.233541
$784$	30.6767	1.09560
$785$	1.60288	0.0572093
$786$	−7.36949	−0.262861
$787$	−29.3351	−1.04568	−0.522842	−	0.852429i	$-0.675128\pi$
$787$	−29.3351	−1.04568	−0.522842	+	0.852429i	$0.675128\pi$
$788$	−8.05572	−0.286973
$789$	−1.16577	−0.0415026
$790$	4.79909	0.170744
$791$	2.61224	0.0928807
$792$	−33.0197	−1.17330
$793$	−0.709760	−0.0252043
$794$	−51.1031	−1.81358
$795$	−6.85657	−0.243177
$796$	6.14841	0.217925
$797$	−7.76881	−0.275185	−0.137593	−	0.990489i	$-0.543936\pi$
$797$	−7.76881	−0.275185	−0.137593	+	0.990489i	$0.543936\pi$
$798$	−4.42520	−0.156650
$799$	−2.98869	−0.105732
$800$	7.67127	0.271220
$801$	−7.54520	−0.266597
$802$	21.1587	0.747140
$803$	−64.3048	−2.26927
$804$	1.60257	0.0565184
$805$	9.91212	0.349356
$806$	−1.08399	−0.0381819
$807$	0.783807	0.0275913
$808$	0.119554	0.00420591
$809$	−0.836594	−0.0294131	−0.0147065	−	0.999892i	$-0.504681\pi$
$809$	−0.836594	−0.0294131	−0.0147065	+	0.999892i	$0.504681\pi$
$810$	18.9931	0.667350
$811$	−42.3411	−1.48680	−0.743399	−	0.668849i	$-0.766787\pi$
$811$	−42.3411	−1.48680	−0.743399	+	0.668849i	$0.766787\pi$
$812$	1.20003	0.0421127
$813$	−11.4643	−0.402070
$814$	−46.7826	−1.63973
$815$	−36.8324	−1.29018
$816$	−2.06204	−0.0721857
$817$	6.11022	0.213769
$818$	60.9219	2.13009
$819$	−0.379141	−0.0132483
$820$	−8.55688	−0.298819
$821$	−16.3456	−0.570466	−0.285233	−	0.958458i	$-0.592071\pi$
$821$	−16.3456	−0.570466	−0.285233	+	0.958458i	$0.592071\pi$
$822$	−4.77215	−0.166448
$823$	−44.0447	−1.53530	−0.767651	−	0.640868i	$-0.778574\pi$
$823$	−44.0447	−1.53530	−0.767651	+	0.640868i	$0.778574\pi$
$824$	27.6157	0.962038
$825$	5.33007	0.185569
$826$	−14.1315	−0.491699
$827$	−32.8327	−1.14171	−0.570853	−	0.821053i	$-0.693387\pi$
$827$	−32.8327	−1.14171	−0.570853	+	0.821053i	$0.693387\pi$
$828$	−12.5633	−0.436603
$829$	−11.3885	−0.395539	−0.197769	−	0.980249i	$-0.563370\pi$
$829$	−11.3885	−0.395539	−0.197769	+	0.980249i	$0.563370\pi$
$830$	5.80948	0.201650
$831$	0.313235	0.0108660
$832$	0.773311	0.0268097
$833$	−6.36622	−0.220576
$834$	4.33458	0.150094
$835$	−24.2037	−0.837604
$836$	23.8195	0.823814
$837$	9.94724	0.343827
$838$	2.67645	0.0924566
$839$	−30.9687	−1.06916	−0.534580	−	0.845118i	$-0.679530\pi$
$839$	−30.9687	−1.06916	−0.534580	+	0.845118i	$0.679530\pi$
$840$	−1.24919	−0.0431010
$841$	−22.1077	−0.762333
$842$	1.01310	0.0349136
$843$	4.99147	0.171915
$844$	−13.0089	−0.447786
$845$	−20.7916	−0.715254
$846$	13.5072	0.464389
$847$	12.1458	0.417333
$848$	48.1685	1.65411
$849$	−6.35955	−0.218259
$850$	−3.89999	−0.133768
$851$	44.2021	1.51523
$852$	2.52538	0.0865179
$853$	−16.0708	−0.550254	−0.275127	−	0.961408i	$-0.588720\pi$
$853$	−16.0708	−0.550254	−0.275127	+	0.961408i	$0.588720\pi$
$854$	−5.36212	−0.183488
$855$	36.5548	1.25015
$856$	−18.3326	−0.626594
$857$	26.5727	0.907706	0.453853	−	0.891077i	$-0.350049\pi$
$857$	26.5727	0.907706	0.453853	+	0.891077i	$0.350049\pi$
$858$	−0.594798	−0.0203061
$859$	52.9246	1.80576	0.902882	−	0.429889i	$-0.141447\pi$
$859$	52.9246	1.80576	0.902882	+	0.429889i	$0.141447\pi$
$860$	−0.694577	−0.0236849
$861$	−3.16749	−0.107948
$862$	28.0483	0.955327
$863$	21.6015	0.735324	0.367662	−	0.929959i	$-0.380158\pi$
$863$	21.6015	0.735324	0.367662	+	0.929959i	$0.380158\pi$
$864$	7.85566	0.267255
$865$	−5.20897	−0.177110
$866$	−18.7753	−0.638012
$867$	0.427927	0.0145332
$868$	−1.82663	−0.0619999
$869$	−9.56220	−0.324376
$870$	2.88917	0.0979519
$871$	1.10274	0.0373650
$872$	−46.1879	−1.56412
$873$	−6.32208	−0.213970
$874$	−100.900	−3.41298
$875$	−9.48211	−0.320554
$876$	3.08342	0.104179
$877$	34.5351	1.16617	0.583084	−	0.812412i	$-0.301846\pi$
$877$	34.5351	1.16617	0.583084	+	0.812412i	$0.301846\pi$
$878$	−39.1648	−1.32175
$879$	−8.84966	−0.298492
$880$	39.5773	1.33415
$881$	4.12210	0.138877	0.0694385	−	0.997586i	$-0.477879\pi$
$881$	4.12210	0.138877	0.0694385	+	0.997586i	$0.477879\pi$
$882$	28.7719	0.968799
$883$	−27.5207	−0.926145	−0.463072	−	0.886320i	$-0.653253\pi$
$883$	−27.5207	−0.926145	−0.463072	+	0.886320i	$0.653253\pi$
$884$	0.0970737	0.00326494
$885$	−7.58877	−0.255094
$886$	64.5332	2.16803
$887$	22.9026	0.768994	0.384497	−	0.923126i	$-0.374375\pi$
$887$	22.9026	0.768994	0.384497	+	0.923126i	$0.374375\pi$
$888$	−5.57063	−0.186938
$889$	−4.56874	−0.153231
$890$	6.88846	0.230902
$891$	−37.8438	−1.26782
$892$	4.84430	0.162199
$893$	24.1967	0.809711
$894$	−3.68619	−0.123285
$895$	−19.7149	−0.658996
$896$	10.8671	0.363044
$897$	0.561990	0.0187643
$898$	−37.2183	−1.24199
$899$	−10.4912	−0.349902
$900$	3.93143	0.131048
$901$	−9.99622	−0.333022
$902$	76.4386	2.54513
$903$	−0.257111	−0.00855612
$904$	−7.50639	−0.249659
$905$	32.4894	1.07999
$906$	−5.63299	−0.187143
$907$	7.44036	0.247053	0.123526	−	0.992341i	$-0.460580\pi$
$907$	7.44036	0.247053	0.123526	+	0.992341i	$0.460580\pi$
$908$	15.7491	0.522651
$909$	0.147213	0.00488275
$910$	0.346141	0.0114744
$911$	4.19888	0.139115	0.0695576	−	0.997578i	$-0.477841\pi$
$911$	4.19888	0.139115	0.0695576	+	0.997578i	$0.477841\pi$
$912$	16.6944	0.552808
$913$	−11.5754	−0.383090
$914$	−13.2771	−0.439168
$915$	−2.87951	−0.0951938
$916$	9.43620	0.311781
$917$	−8.54514	−0.282185
$918$	−3.99372	−0.131813
$919$	−28.6033	−0.943536	−0.471768	−	0.881723i	$-0.656384\pi$
$919$	−28.6033	−0.943536	−0.471768	+	0.881723i	$0.656384\pi$
$920$	−28.4829	−0.939053
$921$	−1.06668	−0.0351484
$922$	−12.7524	−0.419979
$923$	1.73773	0.0571980
$924$	−1.00230	−0.0329731
$925$	−13.8322	−0.454801
$926$	−16.0560	−0.527633
$927$	34.0046	1.11686
$928$	−8.28526	−0.271977
$929$	59.1168	1.93956	0.969780	−	0.243980i	$-0.0784532\pi$
$929$	59.1168	1.93956	0.969780	+	0.243980i	$0.0784532\pi$
$930$	−4.39777	−0.144208
$931$	51.5415	1.68920
$932$	−2.73785	−0.0896812
$933$	12.6890	0.415421
$934$	43.3676	1.41903
$935$	−8.21333	−0.268605
$936$	1.08948	0.0356107
$937$	3.81663	0.124684	0.0623420	−	0.998055i	$-0.480143\pi$
$937$	3.81663	0.124684	0.0623420	+	0.998055i	$0.480143\pi$
$938$	8.33102	0.272018
$939$	−3.48424	−0.113704
$940$	−2.75055	−0.0897131
$941$	−24.3408	−0.793487	−0.396744	−	0.917930i	$-0.629860\pi$
$941$	−24.3408	−0.793487	−0.396744	+	0.917930i	$0.629860\pi$
$942$	0.686575	0.0223698
$943$	−72.2223	−2.35188
$944$	53.3123	1.73517
$945$	−3.17637	−0.103327
$946$	6.20466	0.201731
$947$	−40.8380	−1.32706	−0.663529	−	0.748151i	$-0.730942\pi$
$947$	−40.8380	−1.32706	−0.663529	+	0.748151i	$0.730942\pi$
$948$	0.458509	0.0148917
$949$	2.12172	0.0688740
$950$	31.5746	1.02442
$951$	12.5543	0.407102
$952$	−1.82120	−0.0590253
$953$	4.38954	0.142191	0.0710956	−	0.997470i	$-0.477350\pi$
$953$	4.38954	0.142191	0.0710956	+	0.997470i	$0.477350\pi$
$954$	45.1775	1.46268
$955$	2.97423	0.0962440
$956$	−1.41220	−0.0456738
$957$	−5.75667	−0.186087
$958$	29.6275	0.957220
$959$	−5.53345	−0.178684
$960$	3.13734	0.101257
$961$	−15.0307	−0.484861
$962$	1.54358	0.0497670
$963$	−22.5738	−0.727430
$964$	0.263201	0.00847715
$965$	13.3030	0.428240
$966$	4.24574	0.136604
$967$	6.80764	0.218919	0.109459	−	0.993991i	$-0.465088\pi$
$967$	6.80764	0.218919	0.109459	+	0.993991i	$0.465088\pi$
$968$	−34.9013	−1.12177
$969$	−3.46454	−0.111297
$970$	5.77180	0.185321
$971$	−41.2859	−1.32493	−0.662465	−	0.749093i	$-0.730489\pi$
$971$	−41.2859	−1.32493	−0.662465	+	0.749093i	$0.730489\pi$
$972$	6.10226	0.195730
$973$	5.02607	0.161128
$974$	42.9671	1.37675
$975$	−0.175864	−0.00563216
$976$	20.2290	0.647516
$977$	6.06788	0.194129	0.0970643	−	0.995278i	$-0.469055\pi$
$977$	6.06788	0.194129	0.0970643	+	0.995278i	$0.469055\pi$
$978$	−15.7767	−0.504484
$979$	−13.7253	−0.438662
$980$	−5.85897	−0.187158
$981$	−56.8734	−1.81583
$982$	−59.4227	−1.89625
$983$	38.8505	1.23914	0.619570	−	0.784941i	$-0.287307\pi$
$983$	38.8505	1.23914	0.619570	+	0.784941i	$0.287307\pi$
$984$	9.10191	0.290158
$985$	−22.4889	−0.716555
$986$	4.21213	0.134142
$987$	−1.01817	−0.0324087
$988$	−0.785918	−0.0250034
$989$	−5.86242	−0.186414
$990$	37.1198	1.17975
$991$	−30.5745	−0.971231	−0.485615	−	0.874173i	$-0.661404\pi$
$991$	−30.5745	−0.971231	−0.485615	+	0.874173i	$0.661404\pi$
$992$	12.6115	0.400415
$993$	−8.30526	−0.263559
$994$	13.1282	0.416402
$995$	17.1643	0.544144
$996$	0.555041	0.0175872
$997$	7.94616	0.251657	0.125829	−	0.992052i	$-0.459841\pi$
$997$	7.94616	0.251657	0.125829	+	0.992052i	$0.459841\pi$
$998$	−23.6193	−0.747656
$999$	−14.1647	−0.448151

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2669.2.a.b.1.35	✓	45

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2669.2.a.b.1.35	✓	45	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:	\( N \)	\(=\)	\( 2669 = 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2669.a (trivial)

\(f(q)\)	\(=\)	\(q+1.60442 q^{2} +0.427927 q^{3} +0.574167 q^{4} +1.60288 q^{5} +0.686575 q^{6} +0.796104 q^{7} -2.28764 q^{8} -2.81688 q^{9} +O(q^{10})\)	\(q+1.60442 q^{2} +0.427927 q^{3} +0.574167 q^{4} +1.60288 q^{5} +0.686575 q^{6} +0.796104 q^{7} -2.28764 q^{8} -2.81688 q^{9} +2.57170 q^{10} -5.12411 q^{11} +0.245702 q^{12} +0.169069 q^{13} +1.27729 q^{14} +0.685916 q^{15} -4.81867 q^{16} +1.00000 q^{17} -4.51946 q^{18} -8.09609 q^{19} +0.920321 q^{20} +0.340674 q^{21} -8.22123 q^{22} +7.76776 q^{23} -0.978941 q^{24} -2.43077 q^{25} +0.271257 q^{26} -2.48920 q^{27} +0.457097 q^{28} +2.62533 q^{29} +1.10050 q^{30} -3.99616 q^{31} -3.15590 q^{32} -2.19274 q^{33} +1.60442 q^{34} +1.27606 q^{35} -1.61736 q^{36} +5.69046 q^{37} -12.9895 q^{38} +0.0723491 q^{39} -3.66681 q^{40} -9.29771 q^{41} +0.546585 q^{42} -0.754712 q^{43} -2.94209 q^{44} -4.51512 q^{45} +12.4628 q^{46} -2.98869 q^{47} -2.06204 q^{48} -6.36622 q^{49} -3.89999 q^{50} +0.427927 q^{51} +0.0970737 q^{52} -9.99622 q^{53} -3.99372 q^{54} -8.21333 q^{55} -1.82120 q^{56} -3.46454 q^{57} +4.21213 q^{58} -11.0637 q^{59} +0.393830 q^{60} -4.19806 q^{61} -6.41153 q^{62} -2.24253 q^{63} +4.57395 q^{64} +0.270997 q^{65} -3.51809 q^{66} +6.52244 q^{67} +0.574167 q^{68} +3.32403 q^{69} +2.04734 q^{70} +10.2782 q^{71} +6.44399 q^{72} +12.5495 q^{73} +9.12990 q^{74} -1.04019 q^{75} -4.64851 q^{76} -4.07932 q^{77} +0.116078 q^{78} +1.86612 q^{79} -7.72375 q^{80} +7.38544 q^{81} -14.9174 q^{82} +2.25901 q^{83} +0.195604 q^{84} +1.60288 q^{85} -1.21088 q^{86} +1.12345 q^{87} +11.7221 q^{88} +2.67857 q^{89} -7.24415 q^{90} +0.134596 q^{91} +4.45999 q^{92} -1.71007 q^{93} -4.79511 q^{94} -12.9771 q^{95} -1.35049 q^{96} +2.24436 q^{97} -10.2141 q^{98} +14.4340 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 45 q - 2 q^{2} - 20 q^{3} + 34 q^{4} - 10 q^{5} - 14 q^{6} - 20 q^{7} - 9 q^{8} + 39 q^{9}+O(q^{10}) \) 45 * q - 2 * q^2 - 20 * q^3 + 34 * q^4 - 10 * q^5 - 14 * q^6 - 20 * q^7 - 9 * q^8 + 39 * q^9	\( 45 q - 2 q^{2} - 20 q^{3} + 34 q^{4} - 10 q^{5} - 14 q^{6} - 20 q^{7} - 9 q^{8} + 39 q^{9} - 21 q^{10} - 26 q^{11} - 23 q^{12} - 6 q^{13} - 7 q^{14} - 10 q^{15} + 20 q^{16} + 45 q^{17} - 3 q^{18} - 56 q^{19} - 26 q^{20} + 2 q^{21} - 23 q^{22} - 38 q^{23} - 35 q^{24} + 27 q^{25} - 10 q^{26} - 71 q^{27} - 29 q^{28} - 29 q^{29} + 9 q^{30} - 57 q^{31} + 4 q^{33} - 2 q^{34} - 16 q^{35} + 44 q^{36} - 14 q^{37} - 6 q^{38} - 25 q^{39} - 48 q^{40} - 23 q^{41} - q^{42} - 43 q^{43} - 29 q^{44} - 63 q^{45} - 42 q^{46} + 11 q^{47} - 6 q^{48} - 9 q^{49} + 14 q^{50} - 20 q^{51} - 27 q^{52} + 7 q^{53} + 10 q^{54} - 41 q^{55} - 14 q^{56} - 5 q^{57} - 58 q^{58} - 59 q^{59} + q^{60} - 40 q^{61} - 34 q^{62} - 56 q^{63} - 67 q^{64} - 3 q^{65} - 53 q^{66} - 44 q^{67} + 34 q^{68} - 17 q^{69} + 14 q^{70} - 18 q^{71} - 25 q^{72} - 2 q^{73} - 5 q^{74} - 85 q^{75} - 123 q^{76} - 4 q^{77} + 33 q^{78} - 119 q^{79} - 17 q^{80} + 21 q^{81} - 6 q^{82} - 32 q^{83} + 54 q^{84} - 10 q^{85} - 14 q^{86} - 3 q^{87} - 33 q^{88} - 25 q^{89} - 23 q^{90} - 177 q^{91} - 62 q^{92} + 36 q^{93} - 64 q^{94} - 47 q^{95} - 153 q^{96} - 82 q^{97} + 13 q^{98} - 45 q^{99}+O(q^{100}) \) 45 * q - 2 * q^2 - 20 * q^3 + 34 * q^4 - 10 * q^5 - 14 * q^6 - 20 * q^7 - 9 * q^8 + 39 * q^9 - 21 * q^10 - 26 * q^11 - 23 * q^12 - 6 * q^13 - 7 * q^14 - 10 * q^15 + 20 * q^16 + 45 * q^17 - 3 * q^18 - 56 * q^19 - 26 * q^20 + 2 * q^21 - 23 * q^22 - 38 * q^23 - 35 * q^24 + 27 * q^25 - 10 * q^26 - 71 * q^27 - 29 * q^28 - 29 * q^29 + 9 * q^30 - 57 * q^31 + 4 * q^33 - 2 * q^34 - 16 * q^35 + 44 * q^36 - 14 * q^37 - 6 * q^38 - 25 * q^39 - 48 * q^40 - 23 * q^41 - q^42 - 43 * q^43 - 29 * q^44 - 63 * q^45 - 42 * q^46 + 11 * q^47 - 6 * q^48 - 9 * q^49 + 14 * q^50 - 20 * q^51 - 27 * q^52 + 7 * q^53 + 10 * q^54 - 41 * q^55 - 14 * q^56 - 5 * q^57 - 58 * q^58 - 59 * q^59 + q^60 - 40 * q^61 - 34 * q^62 - 56 * q^63 - 67 * q^64 - 3 * q^65 - 53 * q^66 - 44 * q^67 + 34 * q^68 - 17 * q^69 + 14 * q^70 - 18 * q^71 - 25 * q^72 - 2 * q^73 - 5 * q^74 - 85 * q^75 - 123 * q^76 - 4 * q^77 + 33 * q^78 - 119 * q^79 - 17 * q^80 + 21 * q^81 - 6 * q^82 - 32 * q^83 + 54 * q^84 - 10 * q^85 - 14 * q^86 - 3 * q^87 - 33 * q^88 - 25 * q^89 - 23 * q^90 - 177 * q^91 - 62 * q^92 + 36 * q^93 - 64 * q^94 - 47 * q^95 - 153 * q^96 - 82 * q^97 + 13 * q^98 - 45 * q^99

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