LMFDB - Embedded newform 1441.2.a.f.1.30

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1441,2,Mod(1,1441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1441, 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("1441.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1441 = 11 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1441.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:	$11.5064429313$
Analytic rank:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.30
Character	$\chi$	$=$	1441.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.75484 q^{2} -3.02228 q^{3} +5.58915 q^{4} -3.63313 q^{5} -8.32590 q^{6} +2.50300 q^{7} +9.88754 q^{8} +6.13418 q^{9} +O(q^{10})$	\(q+2.75484 q^{2} -3.02228 q^{3} +5.58915 q^{4} -3.63313 q^{5} -8.32590 q^{6} +2.50300 q^{7} +9.88754 q^{8} +6.13418 q^{9} -10.0087 q^{10} -1.00000 q^{11} -16.8920 q^{12} -2.06751 q^{13} +6.89537 q^{14} +10.9803 q^{15} +16.0603 q^{16} +3.53483 q^{17} +16.8987 q^{18} -0.848543 q^{19} -20.3061 q^{20} -7.56477 q^{21} -2.75484 q^{22} -0.787208 q^{23} -29.8829 q^{24} +8.19960 q^{25} -5.69566 q^{26} -9.47238 q^{27} +13.9896 q^{28} +9.43676 q^{29} +30.2491 q^{30} +7.50250 q^{31} +24.4685 q^{32} +3.02228 q^{33} +9.73791 q^{34} -9.09372 q^{35} +34.2849 q^{36} -9.22406 q^{37} -2.33760 q^{38} +6.24859 q^{39} -35.9227 q^{40} +8.85356 q^{41} -20.8397 q^{42} +11.6284 q^{43} -5.58915 q^{44} -22.2863 q^{45} -2.16863 q^{46} +4.17080 q^{47} -48.5387 q^{48} -0.734988 q^{49} +22.5886 q^{50} -10.6833 q^{51} -11.5556 q^{52} +2.97671 q^{53} -26.0949 q^{54} +3.63313 q^{55} +24.7485 q^{56} +2.56453 q^{57} +25.9968 q^{58} +10.0281 q^{59} +61.3707 q^{60} -1.10107 q^{61} +20.6682 q^{62} +15.3539 q^{63} +35.2862 q^{64} +7.51152 q^{65} +8.32590 q^{66} -12.1720 q^{67} +19.7567 q^{68} +2.37916 q^{69} -25.0517 q^{70} -4.97440 q^{71} +60.6520 q^{72} -5.08926 q^{73} -25.4108 q^{74} -24.7815 q^{75} -4.74263 q^{76} -2.50300 q^{77} +17.2139 q^{78} -6.33586 q^{79} -58.3491 q^{80} +10.2257 q^{81} +24.3901 q^{82} +0.754819 q^{83} -42.2806 q^{84} -12.8425 q^{85} +32.0345 q^{86} -28.5205 q^{87} -9.88754 q^{88} -1.97690 q^{89} -61.3951 q^{90} -5.17498 q^{91} -4.39982 q^{92} -22.6747 q^{93} +11.4899 q^{94} +3.08286 q^{95} -73.9506 q^{96} +3.88331 q^{97} -2.02477 q^{98} -6.13418 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9}+O(q^{10}) $ 31 * q + 6 * q^2 + 4 * q^3 + 38 * q^4 + 8 * q^5 + 7 * q^6 + 4 * q^7 + 24 * q^8 + 45 * q^9	\( 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9} - 8 q^{10} - 31 q^{11} + 10 q^{12} - 8 q^{13} + 29 q^{14} + 36 q^{15} + 52 q^{16} - q^{17} + 33 q^{18} - 2 q^{19} + 22 q^{20} - 13 q^{21} - 6 q^{22} + 45 q^{23} + 16 q^{24} + 41 q^{25} + 24 q^{26} + 22 q^{27} + 17 q^{28} + 5 q^{29} + 29 q^{30} + 28 q^{31} + 69 q^{32} - 4 q^{33} + 14 q^{34} + 36 q^{35} + 63 q^{36} - 3 q^{37} + 4 q^{38} + 40 q^{39} - 48 q^{40} + 21 q^{41} - 9 q^{42} - 20 q^{43} - 38 q^{44} + 28 q^{45} - 24 q^{46} + 57 q^{47} - 46 q^{48} + 37 q^{49} + 64 q^{50} + 17 q^{51} - 11 q^{52} + 32 q^{53} - 26 q^{54} - 8 q^{55} + 84 q^{56} + 10 q^{57} - 17 q^{58} + 70 q^{59} - 33 q^{60} - 51 q^{61} - 34 q^{62} + 32 q^{63} + 80 q^{64} - q^{65} - 7 q^{66} + 24 q^{67} - 13 q^{68} + 19 q^{69} - 9 q^{70} + 128 q^{71} + 118 q^{72} - 27 q^{73} - 23 q^{74} + 41 q^{75} - 34 q^{76} - 4 q^{77} + 9 q^{78} + 2 q^{79} - 45 q^{80} + 43 q^{81} - 18 q^{82} + 46 q^{83} - 103 q^{84} - 50 q^{85} + 78 q^{86} - 9 q^{87} - 24 q^{88} + 52 q^{89} - 46 q^{90} + 38 q^{91} + 54 q^{92} + 4 q^{93} + 3 q^{94} + 70 q^{95} - 21 q^{96} + 3 q^{97} - 120 q^{98} - 45 q^{99}+O(q^{100}) \) 31 * q + 6 * q^2 + 4 * q^3 + 38 * q^4 + 8 * q^5 + 7 * q^6 + 4 * q^7 + 24 * q^8 + 45 * q^9 - 8 * q^10 - 31 * q^11 + 10 * q^12 - 8 * q^13 + 29 * q^14 + 36 * q^15 + 52 * q^16 - q^17 + 33 * q^18 - 2 * q^19 + 22 * q^20 - 13 * q^21 - 6 * q^22 + 45 * q^23 + 16 * q^24 + 41 * q^25 + 24 * q^26 + 22 * q^27 + 17 * q^28 + 5 * q^29 + 29 * q^30 + 28 * q^31 + 69 * q^32 - 4 * q^33 + 14 * q^34 + 36 * q^35 + 63 * q^36 - 3 * q^37 + 4 * q^38 + 40 * q^39 - 48 * q^40 + 21 * q^41 - 9 * q^42 - 20 * q^43 - 38 * q^44 + 28 * q^45 - 24 * q^46 + 57 * q^47 - 46 * q^48 + 37 * q^49 + 64 * q^50 + 17 * q^51 - 11 * q^52 + 32 * q^53 - 26 * q^54 - 8 * q^55 + 84 * q^56 + 10 * q^57 - 17 * q^58 + 70 * q^59 - 33 * q^60 - 51 * q^61 - 34 * q^62 + 32 * q^63 + 80 * q^64 - q^65 - 7 * q^66 + 24 * q^67 - 13 * q^68 + 19 * q^69 - 9 * q^70 + 128 * q^71 + 118 * q^72 - 27 * q^73 - 23 * q^74 + 41 * q^75 - 34 * q^76 - 4 * q^77 + 9 * q^78 + 2 * q^79 - 45 * q^80 + 43 * q^81 - 18 * q^82 + 46 * q^83 - 103 * q^84 - 50 * q^85 + 78 * q^86 - 9 * q^87 - 24 * q^88 + 52 * q^89 - 46 * q^90 + 38 * q^91 + 54 * q^92 + 4 * q^93 + 3 * q^94 + 70 * q^95 - 21 * q^96 + 3 * q^97 - 120 * 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 $

$2$	2.75484	1.94797	0.973983	−	0.226619i	$-0.0727673\pi$
$2$	2.75484	1.94797	0.973983	+	0.226619i	$0.0727673\pi$
$3$	−3.02228	−1.74491	−0.872457	−	0.488690i	$-0.837475\pi$
$3$	−3.02228	−1.74491	−0.872457	+	0.488690i	$0.837475\pi$
$4$	5.58915	2.79457
$5$	−3.63313	−1.62478	−0.812392	−	0.583112i	$-0.801835\pi$
$5$	−3.63313	−1.62478	−0.812392	+	0.583112i	$0.801835\pi$
$6$	−8.32590	−3.39904
$7$	2.50300	0.946045	0.473023	−	0.881050i	$-0.343163\pi$
$7$	2.50300	0.946045	0.473023	+	0.881050i	$0.343163\pi$
$8$	9.88754	3.49577
$9$	6.13418	2.04473
$10$	−10.0087	−3.16502
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−16.8920	−4.87629
$13$	−2.06751	−0.573424	−0.286712	−	0.958017i	$-0.592562\pi$
$13$	−2.06751	−0.573424	−0.286712	+	0.958017i	$0.592562\pi$
$14$	6.89537	1.84286
$15$	10.9803	2.83511
$16$	16.0603	4.01507
$17$	3.53483	0.857323	0.428662	−	0.903465i	$-0.358985\pi$
$17$	3.53483	0.857323	0.428662	+	0.903465i	$0.358985\pi$
$18$	16.8987	3.98306
$19$	−0.848543	−0.194669	−0.0973345	−	0.995252i	$-0.531032\pi$
$19$	−0.848543	−0.194669	−0.0973345	+	0.995252i	$0.531032\pi$
$20$	−20.3061	−4.54058
$21$	−7.56477	−1.65077
$22$	−2.75484	−0.587334
$23$	−0.787208	−0.164144	−0.0820721	−	0.996626i	$-0.526154\pi$
$23$	−0.787208	−0.164144	−0.0820721	+	0.996626i	$0.526154\pi$
$24$	−29.8829	−6.09982
$25$	8.19960	1.63992
$26$	−5.69566	−1.11701
$27$	−9.47238	−1.82296
$28$	13.9896	2.64379
$29$	9.43676	1.75236	0.876181	−	0.481982i	$-0.160083\pi$
$29$	9.43676	1.75236	0.876181	+	0.481982i	$0.160083\pi$
$30$	30.2491	5.52270
$31$	7.50250	1.34749	0.673744	−	0.738965i	$-0.264685\pi$
$31$	7.50250	1.34749	0.673744	+	0.738965i	$0.264685\pi$
$32$	24.4685	4.32546
$33$	3.02228	0.526112
$34$	9.73791	1.67004
$35$	−9.09372	−1.53712
$36$	34.2849	5.71414
$37$	−9.22406	−1.51643	−0.758213	−	0.652007i	$-0.773927\pi$
$37$	−9.22406	−1.51643	−0.758213	+	0.652007i	$0.773927\pi$
$38$	−2.33760	−0.379209
$39$	6.24859	1.00058
$40$	−35.9227	−5.67987
$41$	8.85356	1.38269	0.691347	−	0.722523i	$-0.257018\pi$
$41$	8.85356	1.38269	0.691347	+	0.722523i	$0.257018\pi$
$42$	−20.8397	−3.21564
$43$	11.6284	1.77332	0.886660	−	0.462422i	$-0.153019\pi$
$43$	11.6284	1.77332	0.886660	+	0.462422i	$0.153019\pi$
$44$	−5.58915	−0.842596
$45$	−22.2863	−3.32224
$46$	−2.16863	−0.319747
$47$	4.17080	0.608373	0.304187	−	0.952612i	$-0.401615\pi$
$47$	4.17080	0.608373	0.304187	+	0.952612i	$0.401615\pi$
$48$	−48.5387	−7.00596
$49$	−0.734988	−0.104998
$50$	22.5886	3.19451
$51$	−10.6833	−1.49596
$52$	−11.5556	−1.60248
$53$	2.97671	0.408882	0.204441	−	0.978879i	$-0.434462\pi$
$53$	2.97671	0.408882	0.204441	+	0.978879i	$0.434462\pi$
$54$	−26.0949	−3.55107
$55$	3.63313	0.489891
$56$	24.7485	3.30716
$57$	2.56453	0.339681
$58$	25.9968	3.41354
$59$	10.0281	1.30555	0.652773	−	0.757554i	$-0.273606\pi$
$59$	10.0281	1.30555	0.652773	+	0.757554i	$0.273606\pi$
$60$	61.3707	7.92292
$61$	−1.10107	−0.140978	−0.0704890	−	0.997513i	$-0.522456\pi$
$61$	−1.10107	−0.140978	−0.0704890	+	0.997513i	$0.522456\pi$
$62$	20.6682	2.62486
$63$	15.3539	1.93441
$64$	35.2862	4.41077
$65$	7.51152	0.931689
$66$	8.32590	1.02485
$67$	−12.1720	−1.48704	−0.743522	−	0.668712i	$-0.766846\pi$
$67$	−12.1720	−1.48704	−0.743522	+	0.668712i	$0.766846\pi$
$68$	19.7567	2.39585
$69$	2.37916	0.286418
$70$	−25.0517	−2.99426
$71$	−4.97440	−0.590352	−0.295176	−	0.955443i	$-0.595378\pi$
$71$	−4.97440	−0.590352	−0.295176	+	0.955443i	$0.595378\pi$
$72$	60.6520	7.14790
$73$	−5.08926	−0.595653	−0.297826	−	0.954620i	$-0.596262\pi$
$73$	−5.08926	−0.595653	−0.297826	+	0.954620i	$0.596262\pi$
$74$	−25.4108	−2.95395
$75$	−24.7815	−2.86152
$76$	−4.74263	−0.544017
$77$	−2.50300	−0.285243
$78$	17.2139	1.94909
$79$	−6.33586	−0.712840	−0.356420	−	0.934326i	$-0.616003\pi$
$79$	−6.33586	−0.712840	−0.356420	+	0.934326i	$0.616003\pi$
$80$	−58.3491	−6.52362
$81$	10.2257	1.13618
$82$	24.3901	2.69344
$83$	0.754819	0.0828522	0.0414261	−	0.999142i	$-0.486810\pi$
$83$	0.754819	0.0828522	0.0414261	+	0.999142i	$0.486810\pi$
$84$	−42.2806	−4.61320
$85$	−12.8425	−1.39296
$86$	32.0345	3.45437
$87$	−28.5205	−3.05772
$88$	−9.88754	−1.05401
$89$	−1.97690	−0.209551	−0.104776	−	0.994496i	$-0.533412\pi$
$89$	−1.97690	−0.209551	−0.104776	+	0.994496i	$0.533412\pi$
$90$	−61.3951	−6.47161
$91$	−5.17498	−0.542485
$92$	−4.39982	−0.458713
$93$	−22.6747	−2.35125
$94$	11.4899	1.18509
$95$	3.08286	0.316295
$96$	−73.9506	−7.54755
$97$	3.88331	0.394291	0.197145	−	0.980374i	$-0.436833\pi$
$97$	3.88331	0.394291	0.197145	+	0.980374i	$0.436833\pi$
$98$	−2.02477	−0.204533
$99$	−6.13418	−0.616509
$100$	45.8288	4.58288
$101$	9.95510	0.990569	0.495285	−	0.868731i	$-0.335064\pi$
$101$	9.95510	0.990569	0.495285	+	0.868731i	$0.335064\pi$
$102$	−29.4307	−2.91407
$103$	−1.14022	−0.112349	−0.0561744	−	0.998421i	$-0.517890\pi$
$103$	−1.14022	−0.112349	−0.0561744	+	0.998421i	$0.517890\pi$
$104$	−20.4426	−2.00456
$105$	27.4838	2.68214
$106$	8.20036	0.796489
$107$	−19.2210	−1.85816	−0.929082	−	0.369873i	$-0.879401\pi$
$107$	−19.2210	−1.85816	−0.929082	+	0.369873i	$0.879401\pi$
$108$	−52.9426	−5.09440
$109$	−19.7160	−1.88845	−0.944224	−	0.329303i	$-0.893186\pi$
$109$	−19.7160	−1.88845	−0.944224	+	0.329303i	$0.893186\pi$
$110$	10.0087	0.954291
$111$	27.8777	2.64604
$112$	40.1989	3.79844
$113$	−6.63732	−0.624386	−0.312193	−	0.950019i	$-0.601064\pi$
$113$	−6.63732	−0.624386	−0.312193	+	0.950019i	$0.601064\pi$
$114$	7.06488	0.661687
$115$	2.86003	0.266699
$116$	52.7435	4.89711
$117$	−12.6825	−1.17250
$118$	27.6258	2.54316
$119$	8.84769	0.811067
$120$	108.568	9.91089
$121$	1.00000	0.0909091
$122$	−3.03328	−0.274620
$123$	−26.7579	−2.41268
$124$	41.9326	3.76566
$125$	−11.6246	−1.03973
$126$	42.2975	3.76816
$127$	6.14543	0.545319	0.272659	−	0.962111i	$-0.412097\pi$
$127$	6.14543	0.545319	0.272659	+	0.962111i	$0.412097\pi$
$128$	48.2709	4.26658
$129$	−35.1444	−3.09429
$130$	20.6930	1.81490
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	16.8920	1.47026
$133$	−2.12390	−0.184166
$134$	−33.5319	−2.89671
$135$	34.4144	2.96192
$136$	34.9508	2.99701
$137$	−9.60662	−0.820749	−0.410374	−	0.911917i	$-0.634602\pi$
$137$	−9.60662	−0.820749	−0.410374	+	0.911917i	$0.634602\pi$
$138$	6.55422	0.557932
$139$	−17.4478	−1.47991	−0.739953	−	0.672658i	$-0.765152\pi$
$139$	−17.4478	−1.47991	−0.739953	+	0.672658i	$0.765152\pi$
$140$	−50.8261	−4.29559
$141$	−12.6053	−1.06156
$142$	−13.7037	−1.14999
$143$	2.06751	0.172894
$144$	98.5168	8.20973
$145$	−34.2849	−2.84721
$146$	−14.0201	−1.16031
$147$	2.22134	0.183213
$148$	−51.5547	−4.23777
$149$	9.32661	0.764066	0.382033	−	0.924149i	$-0.375224\pi$
$149$	9.32661	0.764066	0.382033	+	0.924149i	$0.375224\pi$
$150$	−68.2691	−5.57415
$151$	10.6661	0.867998	0.433999	−	0.900913i	$-0.357102\pi$
$151$	10.6661	0.867998	0.433999	+	0.900913i	$0.357102\pi$
$152$	−8.39000	−0.680518
$153$	21.6833	1.75299
$154$	−6.89537	−0.555645
$155$	−27.2575	−2.18938
$156$	34.9243	2.79618
$157$	16.4538	1.31316	0.656579	−	0.754257i	$-0.272003\pi$
$157$	16.4538	1.31316	0.656579	+	0.754257i	$0.272003\pi$
$158$	−17.4543	−1.38859
$159$	−8.99645	−0.713465
$160$	−88.8971	−7.02793
$161$	−1.97038	−0.155288
$162$	28.1701	2.21325
$163$	18.2504	1.42948	0.714742	−	0.699389i	$-0.246544\pi$
$163$	18.2504	1.42948	0.714742	+	0.699389i	$0.246544\pi$
$164$	49.4839	3.86404
$165$	−10.9803	−0.854817
$166$	2.07941	0.161393
$167$	2.94901	0.228201	0.114101	−	0.993469i	$-0.463601\pi$
$167$	2.94901	0.228201	0.114101	+	0.993469i	$0.463601\pi$
$168$	−74.7970	−5.77071
$169$	−8.72541	−0.671185
$170$	−35.3790	−2.71345
$171$	−5.20512	−0.398045
$172$	64.9931	4.95568
$173$	6.14293	0.467039	0.233519	−	0.972352i	$-0.424976\pi$
$173$	6.14293	0.467039	0.233519	+	0.972352i	$0.424976\pi$
$174$	−78.5696	−5.95634
$175$	20.5236	1.55144
$176$	−16.0603	−1.21059
$177$	−30.3077	−2.27807
$178$	−5.44605	−0.408199
$179$	10.3679	0.774931	0.387465	−	0.921884i	$-0.373351\pi$
$179$	10.3679	0.774931	0.387465	+	0.921884i	$0.373351\pi$
$180$	−124.561	−9.28425
$181$	−3.36660	−0.250238	−0.125119	−	0.992142i	$-0.539931\pi$
$181$	−3.36660	−0.250238	−0.125119	+	0.992142i	$0.539931\pi$
$182$	−14.2562	−1.05674
$183$	3.32775	0.245994
$184$	−7.78355	−0.573811
$185$	33.5122	2.46386
$186$	−62.4651	−4.58016
$187$	−3.53483	−0.258493
$188$	23.3112	1.70014
$189$	−23.7094	−1.72460
$190$	8.49279	0.616132
$191$	−11.6486	−0.842865	−0.421432	−	0.906860i	$-0.638473\pi$
$191$	−11.6486	−0.842865	−0.421432	+	0.906860i	$0.638473\pi$
$192$	−106.645	−7.69642
$193$	1.55115	0.111655	0.0558273	−	0.998440i	$-0.482220\pi$
$193$	1.55115	0.111655	0.0558273	+	0.998440i	$0.482220\pi$
$194$	10.6979	0.768065
$195$	−22.7019	−1.62572
$196$	−4.10796	−0.293425
$197$	−12.9283	−0.921104	−0.460552	−	0.887633i	$-0.652349\pi$
$197$	−12.9283	−0.921104	−0.460552	+	0.887633i	$0.652349\pi$
$198$	−16.8987	−1.20094
$199$	−17.8186	−1.26313	−0.631564	−	0.775324i	$-0.717587\pi$
$199$	−17.8186	−1.26313	−0.631564	+	0.775324i	$0.717587\pi$
$200$	81.0739	5.73279
$201$	36.7871	2.59476
$202$	27.4247	1.92960
$203$	23.6202	1.65781
$204$	−59.7103	−4.18056
$205$	−32.1661	−2.24658
$206$	−3.14112	−0.218852
$207$	−4.82888	−0.335630
$208$	−33.2048	−2.30234
$209$	0.848543	0.0586949
$210$	75.7134	5.22472
$211$	12.9338	0.890399	0.445199	−	0.895431i	$-0.353133\pi$
$211$	12.9338	0.890399	0.445199	+	0.895431i	$0.353133\pi$
$212$	16.6373	1.14265
$213$	15.0340	1.03011
$214$	−52.9508	−3.61964
$215$	−42.2476	−2.88126
$216$	−93.6585	−6.37266
$217$	18.7788	1.27479
$218$	−54.3144	−3.67863
$219$	15.3812	1.03936
$220$	20.3061	1.36904
$221$	−7.30830	−0.491610
$222$	76.7987	5.15439
$223$	−26.4737	−1.77281	−0.886404	−	0.462912i	$-0.846805\pi$
$223$	−26.4737	−1.77281	−0.886404	+	0.462912i	$0.846805\pi$
$224$	61.2446	4.09208
$225$	50.2979	3.35319
$226$	−18.2848	−1.21628
$227$	3.61164	0.239713	0.119857	−	0.992791i	$-0.461757\pi$
$227$	3.61164	0.239713	0.119857	+	0.992791i	$0.461757\pi$
$228$	14.3336	0.949264
$229$	−11.0254	−0.728578	−0.364289	−	0.931286i	$-0.618688\pi$
$229$	−11.0254	−0.728578	−0.364289	+	0.931286i	$0.618688\pi$
$230$	7.87891	0.519520
$231$	7.56477	0.497725
$232$	93.3063	6.12586
$233$	−1.79669	−0.117705	−0.0588525	−	0.998267i	$-0.518744\pi$
$233$	−1.79669	−0.117705	−0.0588525	+	0.998267i	$0.518744\pi$
$234$	−34.9382	−2.28398
$235$	−15.1530	−0.988475
$236$	56.0485	3.64844
$237$	19.1488	1.24385
$238$	24.3740	1.57993
$239$	25.9539	1.67882	0.839408	−	0.543501i	$-0.182902\pi$
$239$	25.9539	1.67882	0.839408	+	0.543501i	$0.182902\pi$
$240$	176.347	11.3832
$241$	−6.54820	−0.421806	−0.210903	−	0.977507i	$-0.567640\pi$
$241$	−6.54820	−0.421806	−0.210903	+	0.977507i	$0.567640\pi$
$242$	2.75484	0.177088
$243$	−2.48765	−0.159583
$244$	−6.15406	−0.393973
$245$	2.67030	0.170599
$246$	−73.7139	−4.69983
$247$	1.75437	0.111628
$248$	74.1812	4.71051
$249$	−2.28128	−0.144570
$250$	−32.0238	−2.02536
$251$	−3.97720	−0.251039	−0.125519	−	0.992091i	$-0.540060\pi$
$251$	−3.97720	−0.251039	−0.125519	+	0.992091i	$0.540060\pi$
$252$	85.8150	5.40584
$253$	0.787208	0.0494913
$254$	16.9297	1.06226
$255$	38.8136	2.43060
$256$	62.4062	3.90039
$257$	−19.5843	−1.22163	−0.610817	−	0.791772i	$-0.709159\pi$
$257$	−19.5843	−1.22163	−0.610817	+	0.791772i	$0.709159\pi$
$258$	−96.8173	−6.02758
$259$	−23.0878	−1.43461
$260$	41.9830	2.60368
$261$	57.8868	3.58310
$262$	2.75484	0.170195
$263$	4.34483	0.267914	0.133957	−	0.990987i	$-0.457232\pi$
$263$	4.34483	0.267914	0.133957	+	0.990987i	$0.457232\pi$
$264$	29.8829	1.83917
$265$	−10.8148	−0.664345
$266$	−5.85101	−0.358749
$267$	5.97476	0.365649
$268$	−68.0310	−4.15566
$269$	8.94814	0.545578	0.272789	−	0.962074i	$-0.412054\pi$
$269$	8.94814	0.545578	0.272789	+	0.962074i	$0.412054\pi$
$270$	94.8061	5.76971
$271$	12.4114	0.753939	0.376970	−	0.926226i	$-0.376966\pi$
$271$	12.4114	0.753939	0.376970	+	0.926226i	$0.376966\pi$
$272$	56.7705	3.44221
$273$	15.6402	0.946590
$274$	−26.4647	−1.59879
$275$	−8.19960	−0.494455
$276$	13.2975	0.800415
$277$	−10.7859	−0.648061	−0.324031	−	0.946047i	$-0.605038\pi$
$277$	−10.7859	−0.648061	−0.324031	+	0.946047i	$0.605038\pi$
$278$	−48.0660	−2.88281
$279$	46.0217	2.75525
$280$	−89.9144	−5.37342
$281$	11.4359	0.682209	0.341105	−	0.940025i	$-0.389199\pi$
$281$	11.4359	0.682209	0.341105	+	0.940025i	$0.389199\pi$
$282$	−34.7257	−2.06788
$283$	13.3334	0.792586	0.396293	−	0.918124i	$-0.370296\pi$
$283$	13.3334	0.792586	0.396293	+	0.918124i	$0.370296\pi$
$284$	−27.8026	−1.64978
$285$	−9.31728	−0.551908
$286$	5.69566	0.336791
$287$	22.1605	1.30809
$288$	150.094	8.84438
$289$	−4.50495	−0.264997
$290$	−94.4495	−5.54627
$291$	−11.7365	−0.688004
$292$	−28.4446	−1.66460
$293$	11.2448	0.656925	0.328463	−	0.944517i	$-0.393469\pi$
$293$	11.2448	0.656925	0.328463	+	0.944517i	$0.393469\pi$
$294$	6.11944	0.356893
$295$	−36.4333	−2.12123
$296$	−91.2033	−5.30108
$297$	9.47238	0.549643
$298$	25.6933	1.48837
$299$	1.62756	0.0941242
$300$	−138.508	−7.99673
$301$	29.1060	1.67764
$302$	29.3835	1.69083
$303$	−30.0871	−1.72846
$304$	−13.6278	−0.781610
$305$	4.00034	0.229059
$306$	59.7341	3.41477
$307$	19.6063	1.11899	0.559497	−	0.828833i	$-0.310994\pi$
$307$	19.6063	1.11899	0.559497	+	0.828833i	$0.310994\pi$
$308$	−13.9896	−0.797134
$309$	3.44606	0.196039
$310$	−75.0901	−4.26483
$311$	20.7582	1.17709	0.588545	−	0.808465i	$-0.299701\pi$
$311$	20.7582	1.17709	0.588545	+	0.808465i	$0.299701\pi$
$312$	61.7832	3.49778
$313$	−22.5776	−1.27616	−0.638082	−	0.769969i	$-0.720272\pi$
$313$	−22.5776	−1.27616	−0.638082	+	0.769969i	$0.720272\pi$
$314$	45.3277	2.55799
$315$	−55.7825	−3.14299
$316$	−35.4121	−1.99209
$317$	27.0019	1.51658	0.758289	−	0.651918i	$-0.226035\pi$
$317$	27.0019	1.51658	0.758289	+	0.651918i	$0.226035\pi$
$318$	−24.7838	−1.38981
$319$	−9.43676	−0.528357
$320$	−128.199	−7.16655
$321$	58.0913	3.24234
$322$	−5.42809	−0.302496
$323$	−2.99946	−0.166894
$324$	57.1527	3.17515
$325$	−16.9528	−0.940369
$326$	50.2770	2.78459
$327$	59.5872	3.29518
$328$	87.5399	4.83358
$329$	10.4395	0.575549
$330$	−30.2491	−1.66516
$331$	6.46780	0.355503	0.177751	−	0.984075i	$-0.443118\pi$
$331$	6.46780	0.355503	0.177751	+	0.984075i	$0.443118\pi$
$332$	4.21880	0.231537
$333$	−56.5821	−3.10068
$334$	8.12405	0.444528
$335$	44.2223	2.41612
$336$	−121.492	−6.62796
$337$	−10.2166	−0.556536	−0.278268	−	0.960503i	$-0.589760\pi$
$337$	−10.2166	−0.556536	−0.278268	+	0.960503i	$0.589760\pi$
$338$	−24.0371	−1.30745
$339$	20.0598	1.08950
$340$	−71.7786	−3.89274
$341$	−7.50250	−0.406283
$342$	−14.3393	−0.775379
$343$	−19.3607	−1.04538
$344$	114.977	6.19912
$345$	−8.64380	−0.465367
$346$	16.9228	0.909776
$347$	−11.2610	−0.604523	−0.302262	−	0.953225i	$-0.597742\pi$
$347$	−11.2610	−0.604523	−0.302262	+	0.953225i	$0.597742\pi$
$348$	−159.406	−8.54503
$349$	−29.5061	−1.57943	−0.789714	−	0.613476i	$-0.789771\pi$
$349$	−29.5061	−1.57943	−0.789714	+	0.613476i	$0.789771\pi$
$350$	56.5393	3.02215
$351$	19.5842	1.04533
$352$	−24.4685	−1.30417
$353$	−20.9734	−1.11630	−0.558150	−	0.829740i	$-0.688489\pi$
$353$	−20.9734	−1.11630	−0.558150	+	0.829740i	$0.688489\pi$
$354$	−83.4929	−4.43760
$355$	18.0726	0.959194
$356$	−11.0492	−0.585607
$357$	−26.7402	−1.41524
$358$	28.5618	1.50954
$359$	11.5883	0.611606	0.305803	−	0.952095i	$-0.401075\pi$
$359$	11.5883	0.611606	0.305803	+	0.952095i	$0.401075\pi$
$360$	−220.356	−11.6138
$361$	−18.2800	−0.962104
$362$	−9.27446	−0.487455
$363$	−3.02228	−0.158629
$364$	−28.9237	−1.51601
$365$	18.4899	0.967806
$366$	9.16743	0.479189
$367$	24.9212	1.30088	0.650439	−	0.759559i	$-0.274585\pi$
$367$	24.9212	1.30088	0.650439	+	0.759559i	$0.274585\pi$
$368$	−12.6428	−0.659051
$369$	54.3093	2.82723
$370$	92.3207	4.79953
$371$	7.45070	0.386821
$372$	−126.732	−6.57075
$373$	−10.3744	−0.537169	−0.268584	−	0.963256i	$-0.586556\pi$
$373$	−10.3744	−0.537169	−0.268584	+	0.963256i	$0.586556\pi$
$374$	−9.73791	−0.503535
$375$	35.1327	1.81424
$376$	41.2389	2.12673
$377$	−19.5106	−1.00485
$378$	−65.3156	−3.35947
$379$	23.1271	1.18796	0.593981	−	0.804479i	$-0.297555\pi$
$379$	23.1271	1.18796	0.593981	+	0.804479i	$0.297555\pi$
$380$	17.2306	0.883910
$381$	−18.5732	−0.951535
$382$	−32.0901	−1.64187
$383$	−10.0647	−0.514281	−0.257141	−	0.966374i	$-0.582780\pi$
$383$	−10.0647	−0.514281	−0.257141	+	0.966374i	$0.582780\pi$
$384$	−145.888	−7.44482
$385$	9.09372	0.463459
$386$	4.27318	0.217499
$387$	71.3310	3.62596
$388$	21.7044	1.10188
$389$	−10.5450	−0.534654	−0.267327	−	0.963606i	$-0.586140\pi$
$389$	−10.5450	−0.534654	−0.267327	+	0.963606i	$0.586140\pi$
$390$	−62.5402	−3.16685
$391$	−2.78265	−0.140725
$392$	−7.26722	−0.367050
$393$	−3.02228	−0.152454
$394$	−35.6154	−1.79428
$395$	23.0190	1.15821
$396$	−34.2849	−1.72288
$397$	−29.6374	−1.48746	−0.743730	−	0.668480i	$-0.766945\pi$
$397$	−29.6374	−1.48746	−0.743730	+	0.668480i	$0.766945\pi$
$398$	−49.0874	−2.46053
$399$	6.41903	0.321353
$400$	131.688	6.58440
$401$	1.36064	0.0679470	0.0339735	−	0.999423i	$-0.489184\pi$
$401$	1.36064	0.0679470	0.0339735	+	0.999423i	$0.489184\pi$
$402$	101.343	5.05452
$403$	−15.5115	−0.772682
$404$	55.6405	2.76822
$405$	−37.1511	−1.84605
$406$	65.0699	3.22937
$407$	9.22406	0.457220
$408$	−105.631	−5.22952
$409$	10.4583	0.517129	0.258565	−	0.965994i	$-0.416750\pi$
$409$	10.4583	0.517129	0.258565	+	0.965994i	$0.416750\pi$
$410$	−88.6125	−4.37626
$411$	29.0339	1.43214
$412$	−6.37284	−0.313967
$413$	25.1003	1.23511
$414$	−13.3028	−0.653796
$415$	−2.74235	−0.134617
$416$	−50.5888	−2.48032
$417$	52.7323	2.58231
$418$	2.33760	0.114336
$419$	−24.0616	−1.17548	−0.587742	−	0.809048i	$-0.699983\pi$
$419$	−24.0616	−1.17548	−0.587742	+	0.809048i	$0.699983\pi$
$420$	153.611	7.49544
$421$	7.89044	0.384557	0.192278	−	0.981340i	$-0.438412\pi$
$421$	7.89044	0.384557	0.192278	+	0.981340i	$0.438412\pi$
$422$	35.6305	1.73447
$423$	25.5844	1.24396
$424$	29.4323	1.42936
$425$	28.9842	1.40594
$426$	41.4163	2.00663
$427$	−2.75599	−0.133372
$428$	−107.429	−5.19278
$429$	−6.24859	−0.301685
$430$	−116.385	−5.61260
$431$	23.7528	1.14413	0.572067	−	0.820207i	$-0.306142\pi$
$431$	23.7528	1.14413	0.572067	+	0.820207i	$0.306142\pi$
$432$	−152.129	−7.31932
$433$	−10.9301	−0.525269	−0.262634	−	0.964895i	$-0.584591\pi$
$433$	−10.9301	−0.525269	−0.262634	+	0.964895i	$0.584591\pi$
$434$	51.7325	2.48324
$435$	103.619	4.96814
$436$	−110.196	−5.27741
$437$	0.667979	0.0319538
$438$	42.3727	2.02464
$439$	39.1696	1.86946	0.934731	−	0.355357i	$-0.115641\pi$
$439$	39.1696	1.86946	0.934731	+	0.355357i	$0.115641\pi$
$440$	35.9227	1.71255
$441$	−4.50855	−0.214693
$442$	−20.1332	−0.957639
$443$	22.7552	1.08113	0.540566	−	0.841302i	$-0.318210\pi$
$443$	22.7552	1.08113	0.540566	+	0.841302i	$0.318210\pi$
$444$	155.813	7.39454
$445$	7.18234	0.340475
$446$	−72.9308	−3.45337
$447$	−28.1876	−1.33323
$448$	88.3213	4.17279
$449$	16.5467	0.780888	0.390444	−	0.920627i	$-0.372322\pi$
$449$	16.5467	0.780888	0.390444	+	0.920627i	$0.372322\pi$
$450$	138.563	6.53190
$451$	−8.85356	−0.416898
$452$	−37.0970	−1.74489
$453$	−32.2361	−1.51458
$454$	9.94950	0.466953
$455$	18.8013	0.881420
$456$	25.3569	1.18745
$457$	−25.0853	−1.17344	−0.586719	−	0.809790i	$-0.699581\pi$
$457$	−25.0853	−1.17344	−0.586719	+	0.809790i	$0.699581\pi$
$458$	−30.3732	−1.41925
$459$	−33.4833	−1.56287
$460$	15.9851	0.745309
$461$	−34.0651	−1.58657	−0.793286	−	0.608849i	$-0.791631\pi$
$461$	−34.0651	−1.58657	−0.793286	+	0.608849i	$0.791631\pi$
$462$	20.8397	0.969553
$463$	−6.11637	−0.284252	−0.142126	−	0.989849i	$-0.545394\pi$
$463$	−6.11637	−0.284252	−0.142126	+	0.989849i	$0.545394\pi$
$464$	151.557	7.03586
$465$	82.3799	3.82028
$466$	−4.94959	−0.229286
$467$	−4.69871	−0.217430	−0.108715	−	0.994073i	$-0.534674\pi$
$467$	−4.69871	−0.217430	−0.108715	+	0.994073i	$0.534674\pi$
$468$	−70.8843	−3.27663
$469$	−30.4665	−1.40681
$470$	−41.7442	−1.92552
$471$	−49.7281	−2.29135
$472$	99.1530	4.56389
$473$	−11.6284	−0.534676
$474$	52.7518	2.42297
$475$	−6.95771	−0.319242
$476$	49.4511	2.26659
$477$	18.2597	0.836053
$478$	71.4988	3.27028
$479$	24.1553	1.10368	0.551842	−	0.833949i	$-0.313925\pi$
$479$	24.1553	1.10368	0.551842	+	0.833949i	$0.313925\pi$
$480$	268.672	12.2631
$481$	19.0708	0.869555
$482$	−18.0392	−0.821665
$483$	5.95505	0.270964
$484$	5.58915	0.254052
$485$	−14.1086	−0.640637
$486$	−6.85309	−0.310862
$487$	−27.5998	−1.25067	−0.625333	−	0.780358i	$-0.715037\pi$
$487$	−27.5998	−1.25067	−0.625333	+	0.780358i	$0.715037\pi$
$488$	−10.8869	−0.492827
$489$	−55.1579	−2.49433
$490$	7.35626	0.332322
$491$	−27.6126	−1.24614	−0.623069	−	0.782167i	$-0.714114\pi$
$491$	−27.6126	−1.24614	−0.623069	+	0.782167i	$0.714114\pi$
$492$	−149.554	−6.74242
$493$	33.3574	1.50234
$494$	4.83301	0.217447
$495$	22.2863	1.00169
$496$	120.492	5.41026
$497$	−12.4509	−0.558500
$498$	−6.28455	−0.281618
$499$	−26.9464	−1.20629	−0.603144	−	0.797632i	$-0.706086\pi$
$499$	−26.9464	−1.20629	−0.603144	+	0.797632i	$0.706086\pi$
$500$	−64.9714	−2.90561
$501$	−8.91273	−0.398191
$502$	−10.9566	−0.489015
$503$	−5.70051	−0.254173	−0.127087	−	0.991892i	$-0.540563\pi$
$503$	−5.70051	−0.254173	−0.127087	+	0.991892i	$0.540563\pi$
$504$	151.812	6.76224
$505$	−36.1681	−1.60946
$506$	2.16863	0.0964075
$507$	26.3706	1.17116
$508$	34.3477	1.52393
$509$	−36.0592	−1.59830	−0.799149	−	0.601133i	$-0.794716\pi$
$509$	−36.0592	−1.59830	−0.799149	+	0.601133i	$0.794716\pi$
$510$	106.925	4.73474
$511$	−12.7384	−0.563514
$512$	75.3775	3.33124
$513$	8.03772	0.354874
$514$	−53.9516	−2.37970
$515$	4.14255	0.182543
$516$	−196.427	−8.64723
$517$	−4.17080	−0.183431
$518$	−63.6033	−2.79457
$519$	−18.5657	−0.814943
$520$	74.2704	3.25697
$521$	1.55298	0.0680374	0.0340187	−	0.999421i	$-0.489169\pi$
$521$	1.55298	0.0680374	0.0340187	+	0.999421i	$0.489169\pi$
$522$	159.469	6.97977
$523$	−5.65371	−0.247219	−0.123610	−	0.992331i	$-0.539447\pi$
$523$	−5.65371	−0.247219	−0.123610	+	0.992331i	$0.539447\pi$
$524$	5.58915	0.244163
$525$	−62.0281	−2.70713
$526$	11.9693	0.521887
$527$	26.5201	1.15523
$528$	48.5387	2.11238
$529$	−22.3803	−0.973057
$530$	−29.7929	−1.29412
$531$	61.5141	2.66948
$532$	−11.8708	−0.514665
$533$	−18.3048	−0.792869
$534$	16.4595	0.712272
$535$	69.8323	3.01911
$536$	−120.351	−5.19837
$537$	−31.3346	−1.35219
$538$	24.6507	1.06277
$539$	0.734988	0.0316582
$540$	192.347	8.27730
$541$	2.01640	0.0866918	0.0433459	−	0.999060i	$-0.486198\pi$
$541$	2.01640	0.0866918	0.0433459	+	0.999060i	$0.486198\pi$
$542$	34.1914	1.46865
$543$	10.1748	0.436643
$544$	86.4920	3.70831
$545$	71.6306	3.06832
$546$	43.0864	1.84393
$547$	18.3776	0.785770	0.392885	−	0.919588i	$-0.371477\pi$
$547$	18.3776	0.785770	0.392885	+	0.919588i	$0.371477\pi$
$548$	−53.6928	−2.29364
$549$	−6.75418	−0.288261
$550$	−22.5886	−0.963181
$551$	−8.00749	−0.341131
$552$	23.5241	1.00125
$553$	−15.8587	−0.674379
$554$	−29.7134	−1.26240
$555$	−101.283	−4.29923
$556$	−97.5186	−4.13571
$557$	27.8889	1.18169	0.590845	−	0.806785i	$-0.298794\pi$
$557$	27.8889	1.18169	0.590845	+	0.806785i	$0.298794\pi$
$558$	126.782	5.36713
$559$	−24.0419	−1.01686
$560$	−146.048	−6.17164
$561$	10.6833	0.451048
$562$	31.5041	1.32892
$563$	11.7864	0.496738	0.248369	−	0.968666i	$-0.420105\pi$
$563$	11.7864	0.496738	0.248369	+	0.968666i	$0.420105\pi$
$564$	−70.4530	−2.96661
$565$	24.1142	1.01449
$566$	36.7313	1.54393
$567$	25.5948	1.07488
$568$	−49.1845	−2.06374
$569$	−7.21760	−0.302578	−0.151289	−	0.988490i	$-0.548342\pi$
$569$	−7.21760	−0.302578	−0.151289	+	0.988490i	$0.548342\pi$
$570$	−25.6676	−1.07510
$571$	42.2346	1.76746	0.883731	−	0.467995i	$-0.155023\pi$
$571$	42.2346	1.76746	0.883731	+	0.467995i	$0.155023\pi$
$572$	11.5556	0.483165
$573$	35.2054	1.47073
$574$	61.0486	2.54812
$575$	−6.45479	−0.269183
$576$	216.452	9.01883
$577$	−19.8408	−0.825982	−0.412991	−	0.910735i	$-0.635516\pi$
$577$	−19.8408	−0.825982	−0.412991	+	0.910735i	$0.635516\pi$
$578$	−12.4104	−0.516205
$579$	−4.68802	−0.194828
$580$	−191.624	−7.95674
$581$	1.88931	0.0783819
$582$	−32.3321	−1.34021
$583$	−2.97671	−0.123283
$584$	−50.3202	−2.08227
$585$	46.0770	1.90505
$586$	30.9775	1.27967
$587$	−26.1520	−1.07941	−0.539704	−	0.841855i	$-0.681464\pi$
$587$	−26.1520	−1.07941	−0.539704	+	0.841855i	$0.681464\pi$
$588$	12.4154	0.512002
$589$	−6.36619	−0.262314
$590$	−100.368	−4.13208
$591$	39.0730	1.60725
$592$	−148.141	−6.08856
$593$	−5.04003	−0.206969	−0.103485	−	0.994631i	$-0.532999\pi$
$593$	−5.04003	−0.206969	−0.103485	+	0.994631i	$0.532999\pi$
$594$	26.0949	1.07069
$595$	−32.1448	−1.31781
$596$	52.1278	2.13524
$597$	53.8528	2.20405
$598$	4.48367	0.183351
$599$	−12.1898	−0.498061	−0.249030	−	0.968496i	$-0.580112\pi$
$599$	−12.1898	−0.498061	−0.249030	+	0.968496i	$0.580112\pi$
$600$	−245.028	−10.0032
$601$	−16.1866	−0.660263	−0.330132	−	0.943935i	$-0.607093\pi$
$601$	−16.1866	−0.660263	−0.330132	+	0.943935i	$0.607093\pi$
$602$	80.1824	3.26799
$603$	−74.6651	−3.04060
$604$	59.6146	2.42569
$605$	−3.63313	−0.147708
$606$	−82.8852	−3.36698
$607$	9.63318	0.390999	0.195499	−	0.980704i	$-0.437367\pi$
$607$	9.63318	0.390999	0.195499	+	0.980704i	$0.437367\pi$
$608$	−20.7625	−0.842032
$609$	−71.3869	−2.89274
$610$	11.0203	0.446198
$611$	−8.62316	−0.348856
$612$	121.191	4.89887
$613$	34.4063	1.38966	0.694829	−	0.719175i	$-0.255480\pi$
$613$	34.4063	1.38966	0.694829	+	0.719175i	$0.255480\pi$
$614$	54.0124	2.17976
$615$	97.2150	3.92009
$616$	−24.7485	−0.997146
$617$	−17.5407	−0.706161	−0.353081	−	0.935593i	$-0.614866\pi$
$617$	−17.5407	−0.706161	−0.353081	+	0.935593i	$0.614866\pi$
$618$	9.49334	0.381878
$619$	16.7135	0.671771	0.335886	−	0.941903i	$-0.390964\pi$
$619$	16.7135	0.671771	0.335886	+	0.941903i	$0.390964\pi$
$620$	−152.346	−6.11838
$621$	7.45673	0.299228
$622$	57.1855	2.29293
$623$	−4.94819	−0.198245
$624$	100.354	4.01738
$625$	1.23546	0.0494183
$626$	−62.1978	−2.48592
$627$	−2.56453	−0.102418
$628$	91.9629	3.66972
$629$	−32.6055	−1.30007
$630$	−153.672	−6.12244
$631$	6.70750	0.267021	0.133511	−	0.991047i	$-0.457375\pi$
$631$	6.70750	0.267021	0.133511	+	0.991047i	$0.457375\pi$
$632$	−62.6461	−2.49193
$633$	−39.0896	−1.55367
$634$	74.3860	2.95424
$635$	−22.3271	−0.886025
$636$	−50.2825	−1.99383
$637$	1.51959	0.0602085
$638$	−25.9968	−1.02922
$639$	−30.5139	−1.20711
$640$	−175.374	−6.93227
$641$	−10.2222	−0.403753	−0.201877	−	0.979411i	$-0.564704\pi$
$641$	−10.2222	−0.403753	−0.201877	+	0.979411i	$0.564704\pi$
$642$	160.032	6.31597
$643$	−27.5885	−1.08798	−0.543991	−	0.839091i	$-0.683088\pi$
$643$	−27.5885	−1.08798	−0.543991	+	0.839091i	$0.683088\pi$
$644$	−11.0128	−0.433963
$645$	127.684	5.02755
$646$	−8.26303	−0.325104
$647$	−46.3262	−1.82127	−0.910635	−	0.413212i	$-0.864407\pi$
$647$	−46.3262	−1.82127	−0.910635	+	0.413212i	$0.864407\pi$
$648$	101.107	3.97184
$649$	−10.0281	−0.393637
$650$	−46.7021	−1.83181
$651$	−56.7547	−2.22439
$652$	102.004	3.99480
$653$	35.8546	1.40310	0.701549	−	0.712621i	$-0.252492\pi$
$653$	35.8546	1.40310	0.701549	+	0.712621i	$0.252492\pi$
$654$	164.153	6.41890
$655$	−3.63313	−0.141958
$656$	142.191	5.55161
$657$	−31.2184	−1.21795
$658$	28.7592	1.12115
$659$	23.0927	0.899563	0.449781	−	0.893139i	$-0.351502\pi$
$659$	23.0927	0.899563	0.449781	+	0.893139i	$0.351502\pi$
$660$	−61.3707	−2.38885
$661$	−22.4338	−0.872574	−0.436287	−	0.899808i	$-0.643707\pi$
$661$	−22.4338	−0.872574	−0.436287	+	0.899808i	$0.643707\pi$
$662$	17.8178	0.692507
$663$	22.0877	0.857817
$664$	7.46330	0.289632
$665$	7.71641	0.299229
$666$	−155.875	−6.04002
$667$	−7.42869	−0.287640
$668$	16.4824	0.637725
$669$	80.0109	3.09340
$670$	121.825	4.70653
$671$	1.10107	0.0425064
$672$	−185.098	−7.14033
$673$	−14.0108	−0.540075	−0.270038	−	0.962850i	$-0.587036\pi$
$673$	−14.0108	−0.540075	−0.270038	+	0.962850i	$0.587036\pi$
$674$	−28.1452	−1.08411
$675$	−77.6698	−2.98951
$676$	−48.7676	−1.87568
$677$	−18.1017	−0.695706	−0.347853	−	0.937549i	$-0.613089\pi$
$677$	−18.1017	−0.695706	−0.347853	+	0.937549i	$0.613089\pi$
$678$	55.2617	2.12231
$679$	9.71994	0.373017
$680$	−126.981	−4.86949
$681$	−10.9154	−0.418279
$682$	−20.6682	−0.791426
$683$	0.627047	0.0239933	0.0119966	−	0.999928i	$-0.496181\pi$
$683$	0.627047	0.0239933	0.0119966	+	0.999928i	$0.496181\pi$
$684$	−29.0922	−1.11237
$685$	34.9020	1.33354
$686$	−53.3356	−2.03636
$687$	33.3218	1.27131
$688$	186.756	7.12001
$689$	−6.15437	−0.234463
$690$	−23.8123	−0.906519
$691$	−7.17834	−0.273077	−0.136538	−	0.990635i	$-0.543598\pi$
$691$	−7.17834	−0.273077	−0.136538	+	0.990635i	$0.543598\pi$
$692$	34.3338	1.30517
$693$	−15.3539	−0.583245
$694$	−31.0223	−1.17759
$695$	63.3902	2.40453
$696$	−281.998	−10.6891
$697$	31.2959	1.18542
$698$	−81.2847	−3.07667
$699$	5.43010	0.205385
$700$	114.710	4.33561
$701$	−19.7430	−0.745682	−0.372841	−	0.927895i	$-0.621616\pi$
$701$	−19.7430	−0.745682	−0.372841	+	0.927895i	$0.621616\pi$
$702$	53.9515	2.03627
$703$	7.82701	0.295201
$704$	−35.2862	−1.32990
$705$	45.7967	1.72480
$706$	−57.7784	−2.17452
$707$	24.9176	0.937123
$708$	−169.394	−6.36622
$709$	−0.488091	−0.0183306	−0.00916532	−	0.999958i	$-0.502917\pi$
$709$	−0.488091	−0.0183306	−0.00916532	+	0.999958i	$0.502917\pi$
$710$	49.7872	1.86848
$711$	−38.8653	−1.45756
$712$	−19.5467	−0.732543
$713$	−5.90603	−0.221182
$714$	−73.6650	−2.75684
$715$	−7.51152	−0.280915
$716$	57.9475	2.16560
$717$	−78.4399	−2.92939
$718$	31.9239	1.19139
$719$	−27.2986	−1.01807	−0.509033	−	0.860747i	$-0.669997\pi$
$719$	−27.2986	−1.01807	−0.509033	+	0.860747i	$0.669997\pi$
$720$	−357.924	−13.3390
$721$	−2.85396	−0.106287
$722$	−50.3584	−1.87415
$723$	19.7905	0.736016
$724$	−18.8164	−0.699308
$725$	77.3777	2.87373
$726$	−8.32590	−0.309003
$727$	8.61914	0.319666	0.159833	−	0.987144i	$-0.448904\pi$
$727$	8.61914	0.319666	0.159833	+	0.987144i	$0.448904\pi$
$728$	−51.1678	−1.89640
$729$	−23.1586	−0.857725
$730$	50.9368	1.88525
$731$	41.1046	1.52031
$732$	18.5993	0.687450
$733$	−0.00782392	−0.000288983 0	−0.000144492	−	1.00000i	$-0.500046\pi$
$733$	−0.00782392	−0.000288983 0	−0.000144492		1.00000i	$0.500046\pi$
$734$	68.6540	2.53407
$735$	−8.07041	−0.297681
$736$	−19.2618	−0.709999
$737$	12.1720	0.448361
$738$	149.614	5.50735
$739$	15.3739	0.565537	0.282768	−	0.959188i	$-0.408747\pi$
$739$	15.3739	0.565537	0.282768	+	0.959188i	$0.408747\pi$
$740$	187.305	6.88545
$741$	−5.30220	−0.194781
$742$	20.5255	0.753515
$743$	17.5353	0.643306	0.321653	−	0.946858i	$-0.395761\pi$
$743$	17.5353	0.643306	0.321653	+	0.946858i	$0.395761\pi$
$744$	−224.197	−8.21944
$745$	−33.8848	−1.24144
$746$	−28.5800	−1.04639
$747$	4.63020	0.169410
$748$	−19.7567	−0.722377
$749$	−48.1102	−1.75791
$750$	96.7849	3.53409
$751$	−2.56627	−0.0936447	−0.0468223	−	0.998903i	$-0.514909\pi$
$751$	−2.56627	−0.0936447	−0.0468223	+	0.998903i	$0.514909\pi$
$752$	66.9842	2.44266
$753$	12.0202	0.438041
$754$	−53.7486	−1.95741
$755$	−38.7514	−1.41031
$756$	−132.515	−4.81953
$757$	17.5583	0.638166	0.319083	−	0.947727i	$-0.396625\pi$
$757$	17.5583	0.638166	0.319083	+	0.947727i	$0.396625\pi$
$758$	63.7116	2.31411
$759$	−2.37916	−0.0863582
$760$	30.4819	1.10569
$761$	52.7571	1.91244	0.956222	−	0.292641i	$-0.0945340\pi$
$761$	52.7571	1.91244	0.956222	+	0.292641i	$0.0945340\pi$
$762$	−51.1663	−1.85356
$763$	−49.3491	−1.78656
$764$	−65.1059	−2.35545
$765$	−78.7782	−2.84823
$766$	−27.7266	−1.00180
$767$	−20.7332	−0.748631
$768$	−188.609	−6.80585
$769$	−13.3608	−0.481804	−0.240902	−	0.970549i	$-0.577443\pi$
$769$	−13.3608	−0.481804	−0.240902	+	0.970549i	$0.577443\pi$
$770$	25.0517	0.902802
$771$	59.1892	2.13165
$772$	8.66963	0.312027
$773$	22.0102	0.791652	0.395826	−	0.918325i	$-0.370458\pi$
$773$	22.0102	0.791652	0.395826	+	0.918325i	$0.370458\pi$
$774$	196.505	7.06324
$775$	61.5175	2.20977
$776$	38.3964	1.37835
$777$	69.7779	2.50327
$778$	−29.0498	−1.04149
$779$	−7.51262	−0.269168
$780$	−126.884	−4.54319
$781$	4.97440	0.177998
$782$	−7.66576	−0.274127
$783$	−89.3886	−3.19449
$784$	−11.8041	−0.421576
$785$	−59.7788	−2.13360
$786$	−8.32590	−0.296975
$787$	7.91912	0.282286	0.141143	−	0.989989i	$-0.454922\pi$
$787$	7.91912	0.282286	0.141143	+	0.989989i	$0.454922\pi$
$788$	−72.2583	−2.57409
$789$	−13.1313	−0.467487
$790$	63.4136	2.25616
$791$	−16.6132	−0.590698
$792$	−60.6520	−2.15517
$793$	2.27648	0.0808401
$794$	−81.6465	−2.89752
$795$	32.6852	1.15923
$796$	−99.5908	−3.52990
$797$	−41.8248	−1.48151	−0.740755	−	0.671775i	$-0.765532\pi$
$797$	−41.8248	−1.48151	−0.740755	+	0.671775i	$0.765532\pi$
$798$	17.6834	0.625986
$799$	14.7431	0.521573
$800$	200.632	7.09340
$801$	−12.1267	−0.428475
$802$	3.74834	0.132358
$803$	5.08926	0.179596
$804$	205.609	7.25126
$805$	7.15865	0.252309
$806$	−42.7317	−1.50516
$807$	−27.0438	−0.951986
$808$	98.4314	3.46280
$809$	−32.3188	−1.13627	−0.568134	−	0.822936i	$-0.692334\pi$
$809$	−32.3188	−1.13627	−0.568134	+	0.822936i	$0.692334\pi$
$810$	−102.345	−3.59605
$811$	13.6826	0.480460	0.240230	−	0.970716i	$-0.422777\pi$
$811$	13.6826	0.480460	0.240230	+	0.970716i	$0.422777\pi$
$812$	132.017	4.63289
$813$	−37.5107	−1.31556
$814$	25.4108	0.890649
$815$	−66.3061	−2.32260
$816$	−171.576	−6.00637
$817$	−9.86722	−0.345210
$818$	28.8109	1.00735
$819$	−31.7443	−1.10923
$820$	−179.781	−6.27823
$821$	−12.4281	−0.433744	−0.216872	−	0.976200i	$-0.569585\pi$
$821$	−12.4281	−0.433744	−0.216872	+	0.976200i	$0.569585\pi$
$822$	79.9838	2.78975
$823$	−41.9023	−1.46062	−0.730312	−	0.683114i	$-0.760625\pi$
$823$	−41.9023	−1.46062	−0.730312	+	0.683114i	$0.760625\pi$
$824$	−11.2739	−0.392746
$825$	24.7815	0.862781
$826$	69.1473	2.40594
$827$	−23.6426	−0.822133	−0.411067	−	0.911605i	$-0.634844\pi$
$827$	−23.6426	−0.822133	−0.411067	+	0.911605i	$0.634844\pi$
$828$	−26.9893	−0.937944
$829$	−1.21810	−0.0423065	−0.0211532	−	0.999776i	$-0.506734\pi$
$829$	−1.21810	−0.0423065	−0.0211532	+	0.999776i	$0.506734\pi$
$830$	−7.55475	−0.262229
$831$	32.5980	1.13081
$832$	−72.9545	−2.52924
$833$	−2.59806	−0.0900174
$834$	145.269	5.03025
$835$	−10.7141	−0.370777
$836$	4.74263	0.164027
$837$	−71.0665	−2.45642
$838$	−66.2858	−2.28980
$839$	14.7211	0.508228	0.254114	−	0.967174i	$-0.418216\pi$
$839$	14.7211	0.508228	0.254114	+	0.967174i	$0.418216\pi$
$840$	271.747	9.37615
$841$	60.0524	2.07077
$842$	21.7369	0.749104
$843$	−34.5625	−1.19040
$844$	72.2889	2.48829
$845$	31.7005	1.09053
$846$	70.4811	2.42319
$847$	2.50300	0.0860041
$848$	47.8068	1.64169
$849$	−40.2972	−1.38300
$850$	79.8469	2.73873
$851$	7.26126	0.248913
$852$	84.0274	2.87873
$853$	39.6327	1.35700	0.678500	−	0.734601i	$-0.262630\pi$
$853$	39.6327	1.35700	0.678500	+	0.734601i	$0.262630\pi$
$854$	−7.59230	−0.259803
$855$	18.9108	0.646737
$856$	−190.048	−6.49572
$857$	−16.7982	−0.573816	−0.286908	−	0.957958i	$-0.592627\pi$
$857$	−16.7982	−0.573816	−0.286908	+	0.957958i	$0.592627\pi$
$858$	−17.2139	−0.587672
$859$	−43.5716	−1.48665	−0.743323	−	0.668933i	$-0.766751\pi$
$859$	−43.5716	−1.48665	−0.743323	+	0.668933i	$0.766751\pi$
$860$	−236.128	−8.05190
$861$	−66.9751	−2.28251
$862$	65.4353	2.22873
$863$	23.6641	0.805537	0.402768	−	0.915302i	$-0.368048\pi$
$863$	23.6641	0.805537	0.402768	+	0.915302i	$0.368048\pi$
$864$	−231.775	−7.88514
$865$	−22.3180	−0.758836
$866$	−30.1108	−1.02321
$867$	13.6152	0.462397
$868$	104.957	3.56248
$869$	6.33586	0.214929
$870$	285.453	9.67777
$871$	25.1657	0.852706
$872$	−194.942	−6.60158
$873$	23.8210	0.806217
$874$	1.84018	0.0622449
$875$	−29.0963	−0.983633
$876$	85.9676	2.90458
$877$	31.5766	1.06627	0.533134	−	0.846031i	$-0.321014\pi$
$877$	31.5766	1.06627	0.533134	+	0.846031i	$0.321014\pi$
$878$	107.906	3.64165
$879$	−33.9848	−1.14628
$880$	58.3491	1.96695
$881$	−5.06462	−0.170631	−0.0853157	−	0.996354i	$-0.527190\pi$
$881$	−5.06462	−0.170631	−0.0853157	+	0.996354i	$0.527190\pi$
$882$	−12.4203	−0.418214
$883$	13.6758	0.460229	0.230114	−	0.973164i	$-0.426090\pi$
$883$	13.6758	0.460229	0.230114	+	0.973164i	$0.426090\pi$
$884$	−40.8472	−1.37384
$885$	110.112	3.70136
$886$	62.6870	2.10601
$887$	22.3129	0.749194	0.374597	−	0.927188i	$-0.377781\pi$
$887$	22.3129	0.749194	0.374597	+	0.927188i	$0.377781\pi$
$888$	275.642	9.24994
$889$	15.3820	0.515896
$890$	19.7862	0.663235
$891$	−10.2257	−0.342572
$892$	−147.965	−4.95425
$893$	−3.53910	−0.118431
$894$	−77.6525	−2.59709
$895$	−37.6678	−1.25909
$896$	120.822	4.03638
$897$	−4.91894	−0.164239
$898$	45.5836	1.52114
$899$	70.7993	2.36129
$900$	281.122	9.37074
$901$	10.5222	0.350544
$902$	−24.3901	−0.812103
$903$	−87.9665	−2.92734
$904$	−65.6267	−2.18271
$905$	12.2313	0.406582
$906$	−88.8053	−2.95036
$907$	−18.5496	−0.615929	−0.307965	−	0.951398i	$-0.599648\pi$
$907$	−18.5496	−0.615929	−0.307965	+	0.951398i	$0.599648\pi$
$908$	20.1860	0.669896
$909$	61.0664	2.02544
$910$	51.7947	1.71698
$911$	46.9614	1.55590	0.777951	−	0.628325i	$-0.216259\pi$
$911$	46.9614	1.55590	0.777951	+	0.628325i	$0.216259\pi$
$912$	41.1872	1.36384
$913$	−0.754819	−0.0249809
$914$	−69.1059	−2.28582
$915$	−12.0901	−0.399688
$916$	−61.6225	−2.03607
$917$	2.50300	0.0826564
$918$	−92.2412	−3.04441
$919$	10.8833	0.359006	0.179503	−	0.983757i	$-0.442551\pi$
$919$	10.8833	0.359006	0.179503	+	0.983757i	$0.442551\pi$
$920$	28.2786	0.932318
$921$	−59.2559	−1.95255
$922$	−93.8440	−3.09059
$923$	10.2846	0.338522
$924$	42.2806	1.39093
$925$	−75.6336	−2.48682
$926$	−16.8496	−0.553713
$927$	−6.99430	−0.229723
$928$	230.903	7.57977
$929$	−7.48623	−0.245615	−0.122808	−	0.992430i	$-0.539190\pi$
$929$	−7.48623	−0.245615	−0.122808	+	0.992430i	$0.539190\pi$
$930$	226.943	7.44177
$931$	0.623668	0.0204399
$932$	−10.0420	−0.328936
$933$	−62.7371	−2.05392
$934$	−12.9442	−0.423547
$935$	12.8425	0.419995
$936$	−125.398	−4.09878
$937$	−15.0767	−0.492533	−0.246266	−	0.969202i	$-0.579204\pi$
$937$	−15.0767	−0.492533	−0.246266	+	0.969202i	$0.579204\pi$
$938$	−83.9303	−2.74042
$939$	68.2360	2.22680
$940$	−84.6926	−2.76237
$941$	−1.77063	−0.0577208	−0.0288604	−	0.999583i	$-0.509188\pi$
$941$	−1.77063	−0.0577208	−0.0288604	+	0.999583i	$0.509188\pi$
$942$	−136.993	−4.46347
$943$	−6.96959	−0.226961
$944$	161.054	5.24186
$945$	86.1392	2.80211
$946$	−32.0345	−1.04153
$947$	−45.0954	−1.46540	−0.732701	−	0.680550i	$-0.761741\pi$
$947$	−45.0954	−1.46540	−0.732701	+	0.680550i	$0.761741\pi$
$948$	107.025	3.47602
$949$	10.5221	0.341561
$950$	−19.1674	−0.621872
$951$	−81.6074	−2.64630
$952$	87.4819	2.83530
$953$	−0.699266	−0.0226515	−0.0113257	−	0.999936i	$-0.503605\pi$
$953$	−0.699266	−0.0226515	−0.0113257	+	0.999936i	$0.503605\pi$
$954$	50.3025	1.62860
$955$	42.3209	1.36947
$956$	145.060	4.69158
$957$	28.5205	0.921938
$958$	66.5440	2.14994
$959$	−24.0454	−0.776465
$960$	387.454	12.5050
$961$	25.2875	0.815725
$962$	52.5371	1.69386
$963$	−117.905	−3.79944
$964$	−36.5988	−1.17877
$965$	−5.63554	−0.181414
$966$	16.4052	0.527829
$967$	−46.5717	−1.49765	−0.748823	−	0.662770i	$-0.769381\pi$
$967$	−46.5717	−1.49765	−0.748823	+	0.662770i	$0.769381\pi$
$968$	9.88754	0.317797
$969$	9.06520	0.291216
$970$	−38.8669	−1.24794
$971$	−50.6799	−1.62640	−0.813198	−	0.581987i	$-0.802275\pi$
$971$	−50.6799	−1.62640	−0.813198	+	0.581987i	$0.802275\pi$
$972$	−13.9039	−0.445967
$973$	−43.6719	−1.40006
$974$	−76.0331	−2.43626
$975$	51.2360	1.64086
$976$	−17.6836	−0.566037
$977$	−3.78091	−0.120962	−0.0604810	−	0.998169i	$-0.519263\pi$
$977$	−3.78091	−0.120962	−0.0604810	+	0.998169i	$0.519263\pi$
$978$	−151.951	−4.85887
$979$	1.97690	0.0631821
$980$	14.9247	0.476753
$981$	−120.941	−3.86136
$982$	−76.0682	−2.42743
$983$	−21.4578	−0.684397	−0.342198	−	0.939628i	$-0.611171\pi$
$983$	−21.4578	−0.684397	−0.342198	+	0.939628i	$0.611171\pi$
$984$	−264.570	−8.43419
$985$	46.9702	1.49659
$986$	91.8943	2.92651
$987$	−31.5511	−1.00428
$988$	9.80543	0.311952
$989$	−9.15400	−0.291080
$990$	61.3951	1.95126
$991$	51.6491	1.64069	0.820343	−	0.571871i	$-0.193782\pi$
$991$	51.6491	1.64069	0.820343	+	0.571871i	$0.193782\pi$
$992$	183.575	5.82850
$993$	−19.5475	−0.620322
$994$	−34.3003	−1.08794
$995$	64.7372	2.05231
$996$	−12.7504	−0.404012
$997$	−24.3685	−0.771757	−0.385879	−	0.922550i	$-0.626102\pi$
$997$	−24.3685	−0.771757	−0.385879	+	0.922550i	$0.626102\pi$
$998$	−74.2331	−2.34981
$999$	87.3739	2.76439

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.2.a.f.1.30	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.2.a.f.1.30	✓	31	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:	\( N \)	\(=\)	\( 1441 = 11 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1441.a (trivial)

\(f(q)\)	\(=\)	\(q+2.75484 q^{2} -3.02228 q^{3} +5.58915 q^{4} -3.63313 q^{5} -8.32590 q^{6} +2.50300 q^{7} +9.88754 q^{8} +6.13418 q^{9} +O(q^{10})\)	\(q+2.75484 q^{2} -3.02228 q^{3} +5.58915 q^{4} -3.63313 q^{5} -8.32590 q^{6} +2.50300 q^{7} +9.88754 q^{8} +6.13418 q^{9} -10.0087 q^{10} -1.00000 q^{11} -16.8920 q^{12} -2.06751 q^{13} +6.89537 q^{14} +10.9803 q^{15} +16.0603 q^{16} +3.53483 q^{17} +16.8987 q^{18} -0.848543 q^{19} -20.3061 q^{20} -7.56477 q^{21} -2.75484 q^{22} -0.787208 q^{23} -29.8829 q^{24} +8.19960 q^{25} -5.69566 q^{26} -9.47238 q^{27} +13.9896 q^{28} +9.43676 q^{29} +30.2491 q^{30} +7.50250 q^{31} +24.4685 q^{32} +3.02228 q^{33} +9.73791 q^{34} -9.09372 q^{35} +34.2849 q^{36} -9.22406 q^{37} -2.33760 q^{38} +6.24859 q^{39} -35.9227 q^{40} +8.85356 q^{41} -20.8397 q^{42} +11.6284 q^{43} -5.58915 q^{44} -22.2863 q^{45} -2.16863 q^{46} +4.17080 q^{47} -48.5387 q^{48} -0.734988 q^{49} +22.5886 q^{50} -10.6833 q^{51} -11.5556 q^{52} +2.97671 q^{53} -26.0949 q^{54} +3.63313 q^{55} +24.7485 q^{56} +2.56453 q^{57} +25.9968 q^{58} +10.0281 q^{59} +61.3707 q^{60} -1.10107 q^{61} +20.6682 q^{62} +15.3539 q^{63} +35.2862 q^{64} +7.51152 q^{65} +8.32590 q^{66} -12.1720 q^{67} +19.7567 q^{68} +2.37916 q^{69} -25.0517 q^{70} -4.97440 q^{71} +60.6520 q^{72} -5.08926 q^{73} -25.4108 q^{74} -24.7815 q^{75} -4.74263 q^{76} -2.50300 q^{77} +17.2139 q^{78} -6.33586 q^{79} -58.3491 q^{80} +10.2257 q^{81} +24.3901 q^{82} +0.754819 q^{83} -42.2806 q^{84} -12.8425 q^{85} +32.0345 q^{86} -28.5205 q^{87} -9.88754 q^{88} -1.97690 q^{89} -61.3951 q^{90} -5.17498 q^{91} -4.39982 q^{92} -22.6747 q^{93} +11.4899 q^{94} +3.08286 q^{95} -73.9506 q^{96} +3.88331 q^{97} -2.02477 q^{98} -6.13418 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9}+O(q^{10}) \) 31 * q + 6 * q^2 + 4 * q^3 + 38 * q^4 + 8 * q^5 + 7 * q^6 + 4 * q^7 + 24 * q^8 + 45 * q^9	\( 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9} - 8 q^{10} - 31 q^{11} + 10 q^{12} - 8 q^{13} + 29 q^{14} + 36 q^{15} + 52 q^{16} - q^{17} + 33 q^{18} - 2 q^{19} + 22 q^{20} - 13 q^{21} - 6 q^{22} + 45 q^{23} + 16 q^{24} + 41 q^{25} + 24 q^{26} + 22 q^{27} + 17 q^{28} + 5 q^{29} + 29 q^{30} + 28 q^{31} + 69 q^{32} - 4 q^{33} + 14 q^{34} + 36 q^{35} + 63 q^{36} - 3 q^{37} + 4 q^{38} + 40 q^{39} - 48 q^{40} + 21 q^{41} - 9 q^{42} - 20 q^{43} - 38 q^{44} + 28 q^{45} - 24 q^{46} + 57 q^{47} - 46 q^{48} + 37 q^{49} + 64 q^{50} + 17 q^{51} - 11 q^{52} + 32 q^{53} - 26 q^{54} - 8 q^{55} + 84 q^{56} + 10 q^{57} - 17 q^{58} + 70 q^{59} - 33 q^{60} - 51 q^{61} - 34 q^{62} + 32 q^{63} + 80 q^{64} - q^{65} - 7 q^{66} + 24 q^{67} - 13 q^{68} + 19 q^{69} - 9 q^{70} + 128 q^{71} + 118 q^{72} - 27 q^{73} - 23 q^{74} + 41 q^{75} - 34 q^{76} - 4 q^{77} + 9 q^{78} + 2 q^{79} - 45 q^{80} + 43 q^{81} - 18 q^{82} + 46 q^{83} - 103 q^{84} - 50 q^{85} + 78 q^{86} - 9 q^{87} - 24 q^{88} + 52 q^{89} - 46 q^{90} + 38 q^{91} + 54 q^{92} + 4 q^{93} + 3 q^{94} + 70 q^{95} - 21 q^{96} + 3 q^{97} - 120 q^{98} - 45 q^{99}+O(q^{100}) \) 31 * q + 6 * q^2 + 4 * q^3 + 38 * q^4 + 8 * q^5 + 7 * q^6 + 4 * q^7 + 24 * q^8 + 45 * q^9 - 8 * q^10 - 31 * q^11 + 10 * q^12 - 8 * q^13 + 29 * q^14 + 36 * q^15 + 52 * q^16 - q^17 + 33 * q^18 - 2 * q^19 + 22 * q^20 - 13 * q^21 - 6 * q^22 + 45 * q^23 + 16 * q^24 + 41 * q^25 + 24 * q^26 + 22 * q^27 + 17 * q^28 + 5 * q^29 + 29 * q^30 + 28 * q^31 + 69 * q^32 - 4 * q^33 + 14 * q^34 + 36 * q^35 + 63 * q^36 - 3 * q^37 + 4 * q^38 + 40 * q^39 - 48 * q^40 + 21 * q^41 - 9 * q^42 - 20 * q^43 - 38 * q^44 + 28 * q^45 - 24 * q^46 + 57 * q^47 - 46 * q^48 + 37 * q^49 + 64 * q^50 + 17 * q^51 - 11 * q^52 + 32 * q^53 - 26 * q^54 - 8 * q^55 + 84 * q^56 + 10 * q^57 - 17 * q^58 + 70 * q^59 - 33 * q^60 - 51 * q^61 - 34 * q^62 + 32 * q^63 + 80 * q^64 - q^65 - 7 * q^66 + 24 * q^67 - 13 * q^68 + 19 * q^69 - 9 * q^70 + 128 * q^71 + 118 * q^72 - 27 * q^73 - 23 * q^74 + 41 * q^75 - 34 * q^76 - 4 * q^77 + 9 * q^78 + 2 * q^79 - 45 * q^80 + 43 * q^81 - 18 * q^82 + 46 * q^83 - 103 * q^84 - 50 * q^85 + 78 * q^86 - 9 * q^87 - 24 * q^88 + 52 * q^89 - 46 * q^90 + 38 * q^91 + 54 * q^92 + 4 * q^93 + 3 * q^94 + 70 * q^95 - 21 * q^96 + 3 * q^97 - 120 * q^98 - 45 * q^99

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