LMFDB - Embedded newform 301.2.a.c.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [301,2,Mod(1,301)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(301, 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("301.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 301 = 7 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	301.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:	$2.40349710084$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.301909.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 6x^{3} + 5x^{2} + 6x - 1 $ x^5 - x^4 - 6x^3 + 5x^2 + 6*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.70268$ of defining polynomial
Character	$\chi$	$=$	301.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.70268 q^{2} +2.87445 q^{3} +0.899115 q^{4} -1.38803 q^{5} +4.89427 q^{6} -1.00000 q^{7} -1.87445 q^{8} +5.26248 q^{9} +O(q^{10})$	\(q+1.70268 q^{2} +2.87445 q^{3} +0.899115 q^{4} -1.38803 q^{5} +4.89427 q^{6} -1.00000 q^{7} -1.87445 q^{8} +5.26248 q^{9} -2.36337 q^{10} +0.783746 q^{11} +2.58446 q^{12} +1.07622 q^{13} -1.70268 q^{14} -3.98982 q^{15} -4.98982 q^{16} -0.390873 q^{17} +8.96032 q^{18} +0.150209 q^{19} -1.24800 q^{20} -2.87445 q^{21} +1.33447 q^{22} +2.70517 q^{23} -5.38803 q^{24} -3.07338 q^{25} +1.83246 q^{26} +6.50340 q^{27} -0.899115 q^{28} -8.09786 q^{29} -6.79339 q^{30} -7.66784 q^{31} -4.74716 q^{32} +2.25284 q^{33} -0.665532 q^{34} +1.38803 q^{35} +4.73158 q^{36} +0.672684 q^{37} +0.255757 q^{38} +3.09355 q^{39} +2.60179 q^{40} +7.61628 q^{41} -4.89427 q^{42} +1.00000 q^{43} +0.704678 q^{44} -7.30447 q^{45} +4.60603 q^{46} +3.66069 q^{47} -14.3430 q^{48} +1.00000 q^{49} -5.23298 q^{50} -1.12355 q^{51} +0.967648 q^{52} +4.47389 q^{53} +11.0732 q^{54} -1.08786 q^{55} +1.87445 q^{56} +0.431768 q^{57} -13.7881 q^{58} +11.5159 q^{59} -3.58731 q^{60} +12.2228 q^{61} -13.0559 q^{62} -5.26248 q^{63} +1.89676 q^{64} -1.49383 q^{65} +3.83587 q^{66} -8.24315 q^{67} -0.351440 q^{68} +7.77588 q^{69} +2.36337 q^{70} -2.52247 q^{71} -9.86428 q^{72} +9.98213 q^{73} +1.14536 q^{74} -8.83428 q^{75} +0.135055 q^{76} -0.783746 q^{77} +5.26733 q^{78} +4.00715 q^{79} +6.92601 q^{80} +2.90627 q^{81} +12.9681 q^{82} +12.5723 q^{83} -2.58446 q^{84} +0.542543 q^{85} +1.70268 q^{86} -23.2769 q^{87} -1.46910 q^{88} +7.40069 q^{89} -12.4372 q^{90} -1.07622 q^{91} +2.43226 q^{92} -22.0408 q^{93} +6.23298 q^{94} -0.208494 q^{95} -13.6455 q^{96} +7.83513 q^{97} +1.70268 q^{98} +4.12445 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + q^{2} + 5 q^{3} + 3 q^{4} + 4 q^{5} - 5 q^{7} + 6 q^{9}+O(q^{10}) $ 5 * q + q^2 + 5 * q^3 + 3 * q^4 + 4 * q^5 - 5 * q^7 + 6 * q^9	\( 5 q + q^{2} + 5 q^{3} + 3 q^{4} + 4 q^{5} - 5 q^{7} + 6 q^{9} + 7 q^{10} + 13 q^{11} + 8 q^{12} - q^{13} - q^{14} - 5 q^{16} + q^{17} - 6 q^{18} + 18 q^{19} + 2 q^{20} - 5 q^{21} - 5 q^{22} - 5 q^{23} - 16 q^{24} - q^{25} - 4 q^{26} + 11 q^{27} - 3 q^{28} + 2 q^{29} - 8 q^{30} - 3 q^{31} - 9 q^{32} + 26 q^{33} - 15 q^{34} - 4 q^{35} + 9 q^{36} - 9 q^{37} + 7 q^{38} + 5 q^{39} + 4 q^{40} + 17 q^{41} + 5 q^{43} + 11 q^{44} - 20 q^{45} - q^{46} + 7 q^{47} - 13 q^{48} + 5 q^{49} + 25 q^{50} - 34 q^{52} - 30 q^{53} + 5 q^{54} + 21 q^{55} - 9 q^{57} - 46 q^{58} + 9 q^{59} - 21 q^{60} - 10 q^{61} - 19 q^{62} - 6 q^{63} - 26 q^{64} - 4 q^{65} - 29 q^{66} - 10 q^{67} + 33 q^{68} - 19 q^{69} - 7 q^{70} + 17 q^{71} - 20 q^{72} - q^{73} - 10 q^{75} + 20 q^{76} - 13 q^{77} + 29 q^{78} - 4 q^{79} + 11 q^{80} - 11 q^{81} + 28 q^{82} + 23 q^{83} - 8 q^{84} - 23 q^{85} + q^{86} - 3 q^{87} - 13 q^{88} + 35 q^{89} - 31 q^{90} + q^{91} - 25 q^{92} - 21 q^{93} - 20 q^{94} + 22 q^{95} + 22 q^{96} - 2 q^{97} + q^{98} + 18 q^{99}+O(q^{100}) \) 5 * q + q^2 + 5 * q^3 + 3 * q^4 + 4 * q^5 - 5 * q^7 + 6 * q^9 + 7 * q^10 + 13 * q^11 + 8 * q^12 - q^13 - q^14 - 5 * q^16 + q^17 - 6 * q^18 + 18 * q^19 + 2 * q^20 - 5 * q^21 - 5 * q^22 - 5 * q^23 - 16 * q^24 - q^25 - 4 * q^26 + 11 * q^27 - 3 * q^28 + 2 * q^29 - 8 * q^30 - 3 * q^31 - 9 * q^32 + 26 * q^33 - 15 * q^34 - 4 * q^35 + 9 * q^36 - 9 * q^37 + 7 * q^38 + 5 * q^39 + 4 * q^40 + 17 * q^41 + 5 * q^43 + 11 * q^44 - 20 * q^45 - q^46 + 7 * q^47 - 13 * q^48 + 5 * q^49 + 25 * q^50 - 34 * q^52 - 30 * q^53 + 5 * q^54 + 21 * q^55 - 9 * q^57 - 46 * q^58 + 9 * q^59 - 21 * q^60 - 10 * q^61 - 19 * q^62 - 6 * q^63 - 26 * q^64 - 4 * q^65 - 29 * q^66 - 10 * q^67 + 33 * q^68 - 19 * q^69 - 7 * q^70 + 17 * q^71 - 20 * q^72 - q^73 - 10 * q^75 + 20 * q^76 - 13 * q^77 + 29 * q^78 - 4 * q^79 + 11 * q^80 - 11 * q^81 + 28 * q^82 + 23 * q^83 - 8 * q^84 - 23 * q^85 + q^86 - 3 * q^87 - 13 * q^88 + 35 * q^89 - 31 * q^90 + q^91 - 25 * q^92 - 21 * q^93 - 20 * q^94 + 22 * q^95 + 22 * q^96 - 2 * q^97 + q^98 + 18 * 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 $

$2$	1.70268	1.20398	0.601988	−	0.798505i	$-0.294376\pi$
$2$	1.70268	1.20398	0.601988	+	0.798505i	$0.294376\pi$
$3$	2.87445	1.65957	0.829783	−	0.558086i	$-0.188464\pi$
$3$	2.87445	1.65957	0.829783	+	0.558086i	$0.188464\pi$
$4$	0.899115	0.449558
$5$	−1.38803	−0.620745	−0.310373	−	0.950615i	$-0.600454\pi$
$5$	−1.38803	−0.620745	−0.310373	+	0.950615i	$0.600454\pi$
$6$	4.89427	1.99808
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.87445	−0.662719
$9$	5.26248	1.75416
$10$	−2.36337	−0.747362
$11$	0.783746	0.236308	0.118154	−	0.992995i	$-0.462302\pi$
$11$	0.783746	0.236308	0.118154	+	0.992995i	$0.462302\pi$
$12$	2.58446	0.746071
$13$	1.07622	0.298491	0.149245	−	0.988800i	$-0.452316\pi$
$13$	1.07622	0.298491	0.149245	+	0.988800i	$0.452316\pi$
$14$	−1.70268	−0.455060
$15$	−3.98982	−1.03017
$16$	−4.98982	−1.24746
$17$	−0.390873	−0.0948007	−0.0474004	−	0.998876i	$-0.515094\pi$
$17$	−0.390873	−0.0948007	−0.0474004	+	0.998876i	$0.515094\pi$
$18$	8.96032	2.11197
$19$	0.150209	0.0344602	0.0172301	−	0.999852i	$-0.494515\pi$
$19$	0.150209	0.0344602	0.0172301	+	0.999852i	$0.494515\pi$
$20$	−1.24800	−0.279061
$21$	−2.87445	−0.627257
$22$	1.33447	0.284510
$23$	2.70517	0.564066	0.282033	−	0.959405i	$-0.408991\pi$
$23$	2.70517	0.564066	0.282033	+	0.959405i	$0.408991\pi$
$24$	−5.38803	−1.09983
$25$	−3.07338	−0.614676
$26$	1.83246	0.359375
$27$	6.50340	1.25158
$28$	−0.899115	−0.169917
$29$	−8.09786	−1.50373	−0.751867	−	0.659314i	$-0.770847\pi$
$29$	−8.09786	−1.50373	−0.751867	+	0.659314i	$0.770847\pi$
$30$	−6.79339	−1.24030
$31$	−7.66784	−1.37718	−0.688592	−	0.725149i	$-0.741771\pi$
$31$	−7.66784	−1.37718	−0.688592	+	0.725149i	$0.741771\pi$
$32$	−4.74716	−0.839187
$33$	2.25284	0.392169
$34$	−0.665532	−0.114138
$35$	1.38803	0.234620
$36$	4.73158	0.788596
$37$	0.672684	0.110589	0.0552943	−	0.998470i	$-0.482390\pi$
$37$	0.672684	0.110589	0.0552943	+	0.998470i	$0.482390\pi$
$38$	0.255757	0.0414893
$39$	3.09355	0.495365
$40$	2.60179	0.411380
$41$	7.61628	1.18946	0.594731	−	0.803924i	$-0.297258\pi$
$41$	7.61628	1.18946	0.594731	+	0.803924i	$0.297258\pi$
$42$	−4.89427	−0.755202
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	0.704678	0.106234
$45$	−7.30447	−1.08889
$46$	4.60603	0.679122
$47$	3.66069	0.533966	0.266983	−	0.963701i	$-0.413973\pi$
$47$	3.66069	0.533966	0.266983	+	0.963701i	$0.413973\pi$
$48$	−14.3430	−2.07024
$49$	1.00000	0.142857
$50$	−5.23298	−0.740054
$51$	−1.12355	−0.157328
$52$	0.967648	0.134189
$53$	4.47389	0.614536	0.307268	−	0.951623i	$-0.400585\pi$
$53$	4.47389	0.614536	0.307268	+	0.951623i	$0.400585\pi$
$54$	11.0732	1.50687
$55$	−1.08786	−0.146687
$56$	1.87445	0.250484
$57$	0.431768	0.0571891
$58$	−13.7881	−1.81046
$59$	11.5159	1.49924	0.749620	−	0.661868i	$-0.230236\pi$
$59$	11.5159	1.49924	0.749620	+	0.661868i	$0.230236\pi$
$60$	−3.58731	−0.463120
$61$	12.2228	1.56497	0.782484	−	0.622670i	$-0.213952\pi$
$61$	12.2228	1.56497	0.782484	+	0.622670i	$0.213952\pi$
$62$	−13.0559	−1.65810
$63$	−5.26248	−0.663010
$64$	1.89676	0.237095
$65$	−1.49383	−0.185287
$66$	3.83587	0.472162
$67$	−8.24315	−1.00706	−0.503531	−	0.863977i	$-0.667966\pi$
$67$	−8.24315	−1.00706	−0.503531	+	0.863977i	$0.667966\pi$
$68$	−0.351440	−0.0426184
$69$	7.77588	0.936105
$70$	2.36337	0.282476
$71$	−2.52247	−0.299363	−0.149681	−	0.988734i	$-0.547825\pi$
$71$	−2.52247	−0.299363	−0.149681	+	0.988734i	$0.547825\pi$
$72$	−9.86428	−1.16252
$73$	9.98213	1.16832	0.584160	−	0.811638i	$-0.301424\pi$
$73$	9.98213	1.16832	0.584160	+	0.811638i	$0.301424\pi$
$74$	1.14536	0.133146
$75$	−8.83428	−1.02009
$76$	0.135055	0.0154919
$77$	−0.783746	−0.0893162
$78$	5.26733	0.596407
$79$	4.00715	0.450840	0.225420	−	0.974262i	$-0.427625\pi$
$79$	4.00715	0.450840	0.225420	+	0.974262i	$0.427625\pi$
$80$	6.92601	0.774352
$81$	2.90627	0.322919
$82$	12.9681	1.43208
$83$	12.5723	1.37999	0.689994	−	0.723815i	$-0.257613\pi$
$83$	12.5723	1.37999	0.689994	+	0.723815i	$0.257613\pi$
$84$	−2.58446	−0.281988
$85$	0.542543	0.0588471
$86$	1.70268	0.183605
$87$	−23.2769	−2.49555
$88$	−1.46910	−0.156606
$89$	7.40069	0.784472	0.392236	−	0.919865i	$-0.371702\pi$
$89$	7.40069	0.784472	0.392236	+	0.919865i	$0.371702\pi$
$90$	−12.4372	−1.31099
$91$	−1.07622	−0.112819
$92$	2.43226	0.253580
$93$	−22.0408	−2.28553
$94$	6.23298	0.642882
$95$	−0.208494	−0.0213910
$96$	−13.6455	−1.39269
$97$	7.83513	0.795537	0.397768	−	0.917486i	$-0.369785\pi$
$97$	7.83513	0.795537	0.397768	+	0.917486i	$0.369785\pi$
$98$	1.70268	0.171997
$99$	4.12445	0.414523
$100$	−2.76332	−0.276332
$101$	−14.3728	−1.43014	−0.715071	−	0.699052i	$-0.753606\pi$
$101$	−14.3728	−1.43014	−0.715071	+	0.699052i	$0.753606\pi$
$102$	−1.91304	−0.189419
$103$	−17.1508	−1.68992	−0.844960	−	0.534830i	$-0.820376\pi$
$103$	−17.1508	−1.68992	−0.844960	+	0.534830i	$0.820376\pi$
$104$	−2.01733	−0.197815
$105$	3.98982	0.389367
$106$	7.61760	0.739887
$107$	−14.4830	−1.40013	−0.700064	−	0.714080i	$-0.746845\pi$
$107$	−14.4830	−1.40013	−0.700064	+	0.714080i	$0.746845\pi$
$108$	5.84730	0.562657
$109$	−15.1121	−1.44748	−0.723738	−	0.690075i	$-0.757578\pi$
$109$	−15.1121	−1.44748	−0.723738	+	0.690075i	$0.757578\pi$
$110$	−1.85228	−0.176608
$111$	1.93360	0.183529
$112$	4.98982	0.471494
$113$	11.6386	1.09487	0.547433	−	0.836850i	$-0.315605\pi$
$113$	11.6386	1.09487	0.547433	+	0.836850i	$0.315605\pi$
$114$	0.735162	0.0688542
$115$	−3.75485	−0.350141
$116$	−7.28091	−0.676015
$117$	5.66360	0.523600
$118$	19.6078	1.80505
$119$	0.390873	0.0358313
$120$	7.47874	0.682712
$121$	−10.3857	−0.944158
$122$	20.8115	1.88418
$123$	21.8926	1.97399
$124$	−6.89427	−0.619124
$125$	11.2061	1.00230
$126$	−8.96032	−0.798248
$127$	−3.93783	−0.349426	−0.174713	−	0.984619i	$-0.555900\pi$
$127$	−3.93783	−0.349426	−0.174713	+	0.984619i	$0.555900\pi$
$128$	12.7239	1.12464
$129$	2.87445	0.253081
$130$	−2.54351	−0.223080
$131$	−15.9610	−1.39452	−0.697261	−	0.716817i	$-0.745598\pi$
$131$	−15.9610	−1.39452	−0.697261	+	0.716817i	$0.745598\pi$
$132$	2.02556	0.176303
$133$	−0.150209	−0.0130247
$134$	−14.0354	−1.21248
$135$	−9.02690	−0.776912
$136$	0.732674	0.0628263
$137$	−17.9053	−1.52975	−0.764877	−	0.644177i	$-0.777200\pi$
$137$	−17.9053	−1.52975	−0.764877	+	0.644177i	$0.777200\pi$
$138$	13.2398	1.12705
$139$	18.2312	1.54635	0.773176	−	0.634191i	$-0.218667\pi$
$139$	18.2312	1.54635	0.773176	+	0.634191i	$0.218667\pi$
$140$	1.24800	0.105475
$141$	10.5225	0.886152
$142$	−4.29496	−0.360425
$143$	0.843486	0.0705358
$144$	−26.2588	−2.18824
$145$	11.2401	0.933436
$146$	16.9964	1.40663
$147$	2.87445	0.237081
$148$	0.604820	0.0497159
$149$	19.8646	1.62737	0.813685	−	0.581306i	$-0.197458\pi$
$149$	19.8646	1.62737	0.813685	+	0.581306i	$0.197458\pi$
$150$	−15.0419	−1.22817
$151$	3.95516	0.321867	0.160933	−	0.986965i	$-0.448550\pi$
$151$	3.95516	0.321867	0.160933	+	0.986965i	$0.448550\pi$
$152$	−0.281559	−0.0228375
$153$	−2.05696	−0.166296
$154$	−1.33447	−0.107534
$155$	10.6432	0.854881
$156$	2.78146	0.222695
$157$	−3.34288	−0.266791	−0.133395	−	0.991063i	$-0.542588\pi$
$157$	−3.34288	−0.266791	−0.133395	+	0.991063i	$0.542588\pi$
$158$	6.82289	0.542800
$159$	12.8600	1.01986
$160$	6.58919	0.520921
$161$	−2.70517	−0.213197
$162$	4.94844	0.388786
$163$	5.63143	0.441088	0.220544	−	0.975377i	$-0.429217\pi$
$163$	5.63143	0.441088	0.220544	+	0.975377i	$0.429217\pi$
$164$	6.84791	0.534732
$165$	−3.12701	−0.243437
$166$	21.4066	1.66147
$167$	11.3987	0.882056	0.441028	−	0.897493i	$-0.354614\pi$
$167$	11.3987	0.882056	0.441028	+	0.897493i	$0.354614\pi$
$168$	5.38803	0.415695
$169$	−11.8417	−0.910903
$170$	0.923777	0.0708505
$171$	0.790470	0.0604488
$172$	0.899115	0.0685569
$173$	−6.41809	−0.487959	−0.243979	−	0.969780i	$-0.578453\pi$
$173$	−6.41809	−0.487959	−0.243979	+	0.969780i	$0.578453\pi$
$174$	−39.6331	−3.00458
$175$	3.07338	0.232326
$176$	−3.91075	−0.294784
$177$	33.1019	2.48809
$178$	12.6010	0.944485
$179$	−5.87651	−0.439231	−0.219615	−	0.975587i	$-0.570480\pi$
$179$	−5.87651	−0.439231	−0.219615	+	0.975587i	$0.570480\pi$
$180$	−6.56756	−0.489517
$181$	−16.7093	−1.24199	−0.620996	−	0.783814i	$-0.713272\pi$
$181$	−16.7093	−1.24199	−0.620996	+	0.783814i	$0.713272\pi$
$182$	−1.83246	−0.135831
$183$	35.1339	2.59717
$184$	−5.07071	−0.373818
$185$	−0.933704	−0.0686473
$186$	−37.5285	−2.75172
$187$	−0.306346	−0.0224022
$188$	3.29138	0.240049
$189$	−6.50340	−0.473053
$190$	−0.354998	−0.0257543
$191$	17.0428	1.23317	0.616586	−	0.787288i	$-0.288515\pi$
$191$	17.0428	1.23317	0.616586	+	0.787288i	$0.288515\pi$
$192$	5.45214	0.393475
$193$	−8.84022	−0.636333	−0.318167	−	0.948035i	$-0.603067\pi$
$193$	−8.84022	−0.636333	−0.318167	+	0.948035i	$0.603067\pi$
$194$	13.3407	0.957807
$195$	−4.29394	−0.307495
$196$	0.899115	0.0642225
$197$	−11.4830	−0.818128	−0.409064	−	0.912506i	$-0.634145\pi$
$197$	−11.4830	−0.818128	−0.409064	+	0.912506i	$0.634145\pi$
$198$	7.02261	0.499075
$199$	−22.5224	−1.59657	−0.798286	−	0.602278i	$-0.794260\pi$
$199$	−22.5224	−1.59657	−0.798286	+	0.602278i	$0.794260\pi$
$200$	5.76090	0.407357
$201$	−23.6946	−1.67129
$202$	−24.4722	−1.72186
$203$	8.09786	0.568358
$204$	−1.01020	−0.0707280
$205$	−10.5716	−0.738353
$206$	−29.2023	−2.03462
$207$	14.2359	0.989463
$208$	−5.37016	−0.372354
$209$	0.117725	0.00814324
$210$	6.79339	0.468788
$211$	16.6109	1.14354	0.571772	−	0.820413i	$-0.306256\pi$
$211$	16.6109	1.14354	0.571772	+	0.820413i	$0.306256\pi$
$212$	4.02254	0.276269
$213$	−7.25074	−0.496812
$214$	−24.6600	−1.68572
$215$	−1.38803	−0.0946627
$216$	−12.1903	−0.829446
$217$	7.66784	0.520527
$218$	−25.7310	−1.74273
$219$	28.6932	1.93890
$220$	−0.978113	−0.0659444
$221$	−0.420667	−0.0282971
$222$	3.29230	0.220964
$223$	−9.31689	−0.623905	−0.311952	−	0.950098i	$-0.600983\pi$
$223$	−9.31689	−0.623905	−0.311952	+	0.950098i	$0.600983\pi$
$224$	4.74716	0.317183
$225$	−16.1736	−1.07824
$226$	19.8168	1.31819
$227$	22.5567	1.49714	0.748571	−	0.663055i	$-0.230741\pi$
$227$	22.5567	1.49714	0.748571	+	0.663055i	$0.230741\pi$
$228$	0.388209	0.0257098
$229$	1.77613	0.117370	0.0586849	−	0.998277i	$-0.481309\pi$
$229$	1.77613	0.117370	0.0586849	+	0.998277i	$0.481309\pi$
$230$	−6.39330	−0.421562
$231$	−2.25284	−0.148226
$232$	15.1791	0.996554
$233$	5.10985	0.334758	0.167379	−	0.985893i	$-0.446470\pi$
$233$	5.10985	0.334758	0.167379	+	0.985893i	$0.446470\pi$
$234$	9.64330	0.630402
$235$	−5.08114	−0.331457
$236$	10.3541	0.673995
$237$	11.5184	0.748199
$238$	0.665532	0.0431400
$239$	18.3762	1.18866	0.594329	−	0.804222i	$-0.297418\pi$
$239$	18.3762	1.18866	0.594329	+	0.804222i	$0.297418\pi$
$240$	19.9085	1.28509
$241$	−21.0564	−1.35636	−0.678180	−	0.734896i	$-0.737231\pi$
$241$	−21.0564	−1.35636	−0.678180	+	0.734896i	$0.737231\pi$
$242$	−17.6836	−1.13674
$243$	−11.1563	−0.715675
$244$	10.9897	0.703544
$245$	−1.38803	−0.0886779
$246$	37.2761	2.37664
$247$	0.161658	0.0102861
$248$	14.3730	0.912687
$249$	36.1385	2.29018
$250$	19.0803	1.20675
$251$	0.489094	0.0308713	0.0154357	−	0.999881i	$-0.495086\pi$
$251$	0.489094	0.0308713	0.0154357	+	0.999881i	$0.495086\pi$
$252$	−4.73158	−0.298061
$253$	2.12016	0.133294
$254$	−6.70487	−0.420701
$255$	1.55952	0.0976607
$256$	17.8712	1.11695
$257$	−0.121980	−0.00760891	−0.00380445	−	0.999993i	$-0.501211\pi$
$257$	−0.121980	−0.00760891	−0.00380445	+	0.999993i	$0.501211\pi$
$258$	4.89427	0.304704
$259$	−0.672684	−0.0417985
$260$	−1.34312	−0.0832970
$261$	−42.6148	−2.63779
$262$	−27.1765	−1.67897
$263$	6.16655	0.380246	0.190123	−	0.981760i	$-0.439111\pi$
$263$	6.16655	0.380246	0.190123	+	0.981760i	$0.439111\pi$
$264$	−4.22285	−0.259898
$265$	−6.20989	−0.381470
$266$	−0.255757	−0.0156815
$267$	21.2729	1.30188
$268$	−7.41154	−0.452732
$269$	−4.95747	−0.302262	−0.151131	−	0.988514i	$-0.548292\pi$
$269$	−4.95747	−0.302262	−0.151131	+	0.988514i	$0.548292\pi$
$270$	−15.3699	−0.935383
$271$	−23.5283	−1.42924	−0.714620	−	0.699513i	$-0.753400\pi$
$271$	−23.5283	−1.42924	−0.714620	+	0.699513i	$0.753400\pi$
$272$	1.95039	0.118260
$273$	−3.09355	−0.187230
$274$	−30.4870	−1.84179
$275$	−2.40875	−0.145253
$276$	6.99141	0.420833
$277$	−22.9274	−1.37757	−0.688787	−	0.724964i	$-0.741856\pi$
$277$	−22.9274	−1.37757	−0.688787	+	0.724964i	$0.741856\pi$
$278$	31.0419	1.86177
$279$	−40.3519	−2.41580
$280$	−2.60179	−0.155487
$281$	−8.05005	−0.480225	−0.240113	−	0.970745i	$-0.577184\pi$
$281$	−8.05005	−0.480225	−0.240113	+	0.970745i	$0.577184\pi$
$282$	17.9164	1.06691
$283$	−13.2879	−0.789882	−0.394941	−	0.918707i	$-0.629235\pi$
$283$	−13.2879	−0.789882	−0.394941	+	0.918707i	$0.629235\pi$
$284$	−2.26800	−0.134581
$285$	−0.599306	−0.0354998
$286$	1.43619	0.0849234
$287$	−7.61628	−0.449575
$288$	−24.9818	−1.47207
$289$	−16.8472	−0.991013
$290$	19.1382	1.12383
$291$	22.5217	1.32025
$292$	8.97509	0.525227
$293$	7.38820	0.431624	0.215812	−	0.976435i	$-0.430760\pi$
$293$	7.38820	0.431624	0.215812	+	0.976435i	$0.430760\pi$
$294$	4.89427	0.285440
$295$	−15.9844	−0.930646
$296$	−1.26091	−0.0732891
$297$	5.09701	0.295759
$298$	33.8230	1.95931
$299$	2.91136	0.168368
$300$	−7.94304	−0.458591
$301$	−1.00000	−0.0576390
$302$	6.73437	0.387520
$303$	−41.3138	−2.37342
$304$	−0.749515	−0.0429876
$305$	−16.9656	−0.971447
$306$	−3.50235	−0.200216
$307$	3.66984	0.209449	0.104724	−	0.994501i	$-0.466604\pi$
$307$	3.66984	0.209449	0.104724	+	0.994501i	$0.466604\pi$
$308$	−0.704678	−0.0401528
$309$	−49.2992	−2.80453
$310$	18.1219	1.02926
$311$	−5.48043	−0.310767	−0.155383	−	0.987854i	$-0.549661\pi$
$311$	−5.48043	−0.310767	−0.155383	+	0.987854i	$0.549661\pi$
$312$	−5.79872	−0.328288
$313$	20.5633	1.16231	0.581154	−	0.813794i	$-0.302601\pi$
$313$	20.5633	1.16231	0.581154	+	0.813794i	$0.302601\pi$
$314$	−5.69185	−0.321210
$315$	7.30447	0.411560
$316$	3.60289	0.202678
$317$	−24.9463	−1.40112	−0.700562	−	0.713591i	$-0.747067\pi$
$317$	−24.9463	−1.40112	−0.700562	+	0.713591i	$0.747067\pi$
$318$	21.8964	1.22789
$319$	−6.34667	−0.355345
$320$	−2.63275	−0.147175
$321$	−41.6308	−2.32361
$322$	−4.60603	−0.256684
$323$	−0.0587126	−0.00326686
$324$	2.61307	0.145170
$325$	−3.30764	−0.183475
$326$	9.58852	0.531059
$327$	−43.4390	−2.40218
$328$	−14.2764	−0.788280
$329$	−3.66069	−0.201820
$330$	−5.32429	−0.293093
$331$	−19.0382	−1.04644	−0.523218	−	0.852199i	$-0.675269\pi$
$331$	−19.0382	−1.04644	−0.523218	+	0.852199i	$0.675269\pi$
$332$	11.3039	0.620384
$333$	3.53999	0.193990
$334$	19.4083	1.06197
$335$	11.4417	0.625128
$336$	14.3430	0.782475
$337$	2.53019	0.137828	0.0689141	−	0.997623i	$-0.478047\pi$
$337$	2.53019	0.137828	0.0689141	+	0.997623i	$0.478047\pi$
$338$	−20.1627	−1.09671
$339$	33.4546	1.81700
$340$	0.487809	0.0264552
$341$	−6.00964	−0.325440
$342$	1.34592	0.0727789
$343$	−1.00000	−0.0539949
$344$	−1.87445	−0.101064
$345$	−10.7931	−0.581083
$346$	−10.9280	−0.587490
$347$	24.4867	1.31452	0.657258	−	0.753665i	$-0.271716\pi$
$347$	24.4867	1.31452	0.657258	+	0.753665i	$0.271716\pi$
$348$	−20.9286	−1.12189
$349$	5.12234	0.274193	0.137096	−	0.990558i	$-0.456223\pi$
$349$	5.12234	0.274193	0.137096	+	0.990558i	$0.456223\pi$
$350$	5.23298	0.279714
$351$	6.99910	0.373585
$352$	−3.72057	−0.198307
$353$	8.90319	0.473869	0.236934	−	0.971526i	$-0.423857\pi$
$353$	8.90319	0.473869	0.236934	+	0.971526i	$0.423857\pi$
$354$	56.3618	2.99560
$355$	3.50127	0.185828
$356$	6.65408	0.352665
$357$	1.12355	0.0594644
$358$	−10.0058	−0.528823
$359$	36.6025	1.93181	0.965904	−	0.258901i	$-0.0833605\pi$
$359$	36.6025	1.93181	0.965904	+	0.258901i	$0.0833605\pi$
$360$	13.6919	0.721626
$361$	−18.9774	−0.998812
$362$	−28.4506	−1.49533
$363$	−29.8533	−1.56689
$364$	−0.967648	−0.0507186
$365$	−13.8555	−0.725229
$366$	59.8217	3.12693
$367$	14.7946	0.772272	0.386136	−	0.922442i	$-0.373810\pi$
$367$	14.7946	0.772272	0.386136	+	0.922442i	$0.373810\pi$
$368$	−13.4983	−0.703648
$369$	40.0805	2.08651
$370$	−1.58980	−0.0826497
$371$	−4.47389	−0.232273
$372$	−19.8173	−1.02748
$373$	10.6459	0.551225	0.275612	−	0.961269i	$-0.411119\pi$
$373$	10.6459	0.551225	0.275612	+	0.961269i	$0.411119\pi$
$374$	−0.521608	−0.0269717
$375$	32.2113	1.66339
$376$	−6.86179	−0.353870
$377$	−8.71510	−0.448851
$378$	−11.0732	−0.569544
$379$	17.6746	0.907881	0.453941	−	0.891032i	$-0.350018\pi$
$379$	17.6746	0.907881	0.453941	+	0.891032i	$0.350018\pi$
$380$	−0.187460	−0.00961650
$381$	−11.3191	−0.579896
$382$	29.0184	1.48471
$383$	13.2519	0.677143	0.338571	−	0.940941i	$-0.390056\pi$
$383$	13.2519	0.677143	0.338571	+	0.940941i	$0.390056\pi$
$384$	36.5742	1.86642
$385$	1.08786	0.0554426
$386$	−15.0521	−0.766130
$387$	5.26248	0.267507
$388$	7.04468	0.357639
$389$	7.27818	0.369018	0.184509	−	0.982831i	$-0.440930\pi$
$389$	7.27818	0.369018	0.184509	+	0.982831i	$0.440930\pi$
$390$	−7.31120	−0.370217
$391$	−1.05738	−0.0534739
$392$	−1.87445	−0.0946742
$393$	−45.8793	−2.31430
$394$	−19.5518	−0.985006
$395$	−5.56204	−0.279857
$396$	3.70836	0.186352
$397$	−15.5003	−0.777938	−0.388969	−	0.921251i	$-0.627169\pi$
$397$	−15.5003	−0.777938	−0.388969	+	0.921251i	$0.627169\pi$
$398$	−38.3485	−1.92223
$399$	−0.431768	−0.0216154
$400$	15.3356	0.766780
$401$	36.6553	1.83048	0.915238	−	0.402914i	$-0.132002\pi$
$401$	36.6553	1.83048	0.915238	+	0.402914i	$0.132002\pi$
$402$	−40.3442	−2.01219
$403$	−8.25230	−0.411077
$404$	−12.9228	−0.642931
$405$	−4.03398	−0.200450
$406$	13.7881	0.684290
$407$	0.527213	0.0261330
$408$	2.10604	0.104264
$409$	−25.1160	−1.24191	−0.620953	−	0.783848i	$-0.713254\pi$
$409$	−25.1160	−1.24191	−0.620953	+	0.783848i	$0.713254\pi$
$410$	−18.0001	−0.888959
$411$	−51.4680	−2.53873
$412$	−15.4206	−0.759716
$413$	−11.5159	−0.566660
$414$	24.2391	1.19129
$415$	−17.4507	−0.856621
$416$	−5.10900	−0.250489
$417$	52.4048	2.56627
$418$	0.200449	0.00980427
$419$	12.2917	0.600491	0.300245	−	0.953862i	$-0.402931\pi$
$419$	12.2917	0.600491	0.300245	+	0.953862i	$0.402931\pi$
$420$	3.58731	0.175043
$421$	−0.669707	−0.0326395	−0.0163198	−	0.999867i	$-0.505195\pi$
$421$	−0.669707	−0.0326395	−0.0163198	+	0.999867i	$0.505195\pi$
$422$	28.2831	1.37680
$423$	19.2643	0.936662
$424$	−8.38610	−0.407265
$425$	1.20130	0.0582717
$426$	−12.3457	−0.598150
$427$	−12.2228	−0.591503
$428$	−13.0219	−0.629438
$429$	2.42456	0.117059
$430$	−2.36337	−0.113972
$431$	21.0499	1.01394	0.506970	−	0.861964i	$-0.330766\pi$
$431$	21.0499	1.01394	0.506970	+	0.861964i	$0.330766\pi$
$432$	−32.4508	−1.56129
$433$	20.2640	0.973826	0.486913	−	0.873451i	$-0.338123\pi$
$433$	20.2640	0.973826	0.486913	+	0.873451i	$0.338123\pi$
$434$	13.0559	0.626702
$435$	32.3090	1.54910
$436$	−13.5875	−0.650724
$437$	0.406340	0.0194379
$438$	48.8553	2.33439
$439$	34.1114	1.62805	0.814024	−	0.580832i	$-0.197273\pi$
$439$	34.1114	1.62805	0.814024	+	0.580832i	$0.197273\pi$
$440$	2.03915	0.0972125
$441$	5.26248	0.250594
$442$	−0.716261	−0.0340690
$443$	−33.3805	−1.58596	−0.792978	−	0.609251i	$-0.791470\pi$
$443$	−33.3805	−1.58596	−0.792978	+	0.609251i	$0.791470\pi$
$444$	1.73853	0.0825068
$445$	−10.2724	−0.486957
$446$	−15.8637	−0.751166
$447$	57.0998	2.70073
$448$	−1.89676	−0.0896134
$449$	−20.6206	−0.973148	−0.486574	−	0.873639i	$-0.661754\pi$
$449$	−20.6206	−0.973148	−0.486574	+	0.873639i	$0.661754\pi$
$450$	−27.5384	−1.29817
$451$	5.96923	0.281080
$452$	10.4644	0.492205
$453$	11.3689	0.534159
$454$	38.4068	1.80252
$455$	1.49383	0.0700317
$456$	−0.809329	−0.0379003
$457$	−13.8762	−0.649102	−0.324551	−	0.945868i	$-0.605213\pi$
$457$	−13.8762	−0.649102	−0.324551	+	0.945868i	$0.605213\pi$
$458$	3.02417	0.141310
$459$	−2.54201	−0.118651
$460$	−3.37604	−0.157409
$461$	−6.14973	−0.286422	−0.143211	−	0.989692i	$-0.545743\pi$
$461$	−6.14973	−0.286422	−0.143211	+	0.989692i	$0.545743\pi$
$462$	−3.83587	−0.178461
$463$	17.3514	0.806387	0.403193	−	0.915115i	$-0.367900\pi$
$463$	17.3514	0.806387	0.403193	+	0.915115i	$0.367900\pi$
$464$	40.4069	1.87584
$465$	30.5933	1.41873
$466$	8.70044	0.403040
$467$	1.46344	0.0677200	0.0338600	−	0.999427i	$-0.489220\pi$
$467$	1.46344	0.0677200	0.0338600	+	0.999427i	$0.489220\pi$
$468$	5.09223	0.235388
$469$	8.24315	0.380633
$470$	−8.65155	−0.399066
$471$	−9.60895	−0.442757
$472$	−21.5860	−0.993575
$473$	0.783746	0.0360367
$474$	19.6121	0.900813
$475$	−0.461648	−0.0211819
$476$	0.351440	0.0161082
$477$	23.5438	1.07800
$478$	31.2888	1.43112
$479$	13.2199	0.604034	0.302017	−	0.953303i	$-0.402340\pi$
$479$	13.2199	0.604034	0.302017	+	0.953303i	$0.402340\pi$
$480$	18.9403	0.864503
$481$	0.723958	0.0330096
$482$	−35.8522	−1.63302
$483$	−7.77588	−0.353815
$484$	−9.33798	−0.424454
$485$	−10.8754	−0.493825
$486$	−18.9955	−0.861655
$487$	1.58310	0.0717371	0.0358685	−	0.999357i	$-0.488580\pi$
$487$	1.58310	0.0717371	0.0358685	+	0.999357i	$0.488580\pi$
$488$	−22.9111	−1.03714
$489$	16.1873	0.732014
$490$	−2.36337	−0.106766
$491$	−15.0591	−0.679607	−0.339804	−	0.940496i	$-0.610361\pi$
$491$	−15.0591	−0.679607	−0.339804	+	0.940496i	$0.610361\pi$
$492$	19.6840	0.887423
$493$	3.16524	0.142555
$494$	0.275252	0.0123842
$495$	−5.72485	−0.257313
$496$	38.2612	1.71798
$497$	2.52247	0.113148
$498$	61.5322	2.75732
$499$	31.3820	1.40485	0.702426	−	0.711756i	$-0.252100\pi$
$499$	31.3820	1.40485	0.702426	+	0.711756i	$0.252100\pi$
$500$	10.0756	0.450592
$501$	32.7650	1.46383
$502$	0.832770	0.0371683
$503$	−31.6260	−1.41013	−0.705066	−	0.709142i	$-0.749083\pi$
$503$	−31.6260	−1.41013	−0.705066	+	0.709142i	$0.749083\pi$
$504$	9.86428	0.439390
$505$	19.9498	0.887754
$506$	3.60996	0.160482
$507$	−34.0385	−1.51170
$508$	−3.54057	−0.157087
$509$	−16.8526	−0.746980	−0.373490	−	0.927634i	$-0.621839\pi$
$509$	−16.8526	−0.746980	−0.373490	+	0.927634i	$0.621839\pi$
$510$	2.65535	0.117581
$511$	−9.98213	−0.441584
$512$	4.98110	0.220136
$513$	0.976867	0.0431297
$514$	−0.207693	−0.00916094
$515$	23.8058	1.04901
$516$	2.58446	0.113775
$517$	2.86905	0.126181
$518$	−1.14536	−0.0503244
$519$	−18.4485	−0.809800
$520$	2.80011	0.122793
$521$	6.26842	0.274625	0.137312	−	0.990528i	$-0.456154\pi$
$521$	6.26842	0.274625	0.137312	+	0.990528i	$0.456154\pi$
$522$	−72.5594	−3.17584
$523$	16.6248	0.726950	0.363475	−	0.931604i	$-0.381590\pi$
$523$	16.6248	0.726950	0.363475	+	0.931604i	$0.381590\pi$
$524$	−14.3508	−0.626918
$525$	8.83428	0.385560
$526$	10.4996	0.457806
$527$	2.99715	0.130558
$528$	−11.2413	−0.489214
$529$	−15.6821	−0.681829
$530$	−10.5734	−0.459281
$531$	60.6021	2.62991
$532$	−0.135055	−0.00585537
$533$	8.19681	0.355043
$534$	36.2210	1.56744
$535$	20.1029	0.869123
$536$	15.4514	0.667399
$537$	−16.8918	−0.728933
$538$	−8.44098	−0.363916
$539$	0.783746	0.0337583
$540$	−8.11622	−0.349267
$541$	32.3561	1.39110	0.695549	−	0.718479i	$-0.255161\pi$
$541$	32.3561	1.39110	0.695549	+	0.718479i	$0.255161\pi$
$542$	−40.0611	−1.72077
$543$	−48.0301	−2.06117
$544$	1.85554	0.0795555
$545$	20.9760	0.898514
$546$	−5.26733	−0.225421
$547$	−40.0084	−1.71063	−0.855317	−	0.518105i	$-0.826638\pi$
$547$	−40.0084	−1.71063	−0.855317	+	0.518105i	$0.826638\pi$
$548$	−16.0989	−0.687712
$549$	64.3222	2.74521
$550$	−4.10132	−0.174881
$551$	−1.21637	−0.0518191
$552$	−14.5755	−0.620375
$553$	−4.00715	−0.170401
$554$	−39.0380	−1.65857
$555$	−2.68389	−0.113925
$556$	16.3920	0.695175
$557$	1.01018	0.0428027	0.0214014	−	0.999771i	$-0.493187\pi$
$557$	1.01018	0.0428027	0.0214014	+	0.999771i	$0.493187\pi$
$558$	−68.7063	−2.90857
$559$	1.07622	0.0455194
$560$	−6.92601	−0.292678
$561$	−0.880576	−0.0371779
$562$	−13.7066	−0.578180
$563$	19.4950	0.821617	0.410809	−	0.911722i	$-0.365246\pi$
$563$	19.4950	0.821617	0.410809	+	0.911722i	$0.365246\pi$
$564$	9.46092	0.398376
$565$	−16.1547	−0.679633
$566$	−22.6250	−0.950998
$567$	−2.90627	−0.122052
$568$	4.72826	0.198393
$569$	38.5052	1.61422	0.807110	−	0.590401i	$-0.201030\pi$
$569$	38.5052	1.61422	0.807110	+	0.590401i	$0.201030\pi$
$570$	−1.02043	−0.0427409
$571$	9.01373	0.377213	0.188606	−	0.982053i	$-0.439603\pi$
$571$	9.01373	0.377213	0.188606	+	0.982053i	$0.439603\pi$
$572$	0.758391	0.0317099
$573$	48.9887	2.04653
$574$	−12.9681	−0.541277
$575$	−8.31400	−0.346718
$576$	9.98166	0.415902
$577$	−29.0213	−1.20817	−0.604086	−	0.796919i	$-0.706462\pi$
$577$	−29.0213	−1.20817	−0.604086	+	0.796919i	$0.706462\pi$
$578$	−28.6854	−1.19316
$579$	−25.4108	−1.05604
$580$	10.1061	0.419633
$581$	−12.5723	−0.521586
$582$	38.3472	1.58954
$583$	3.50639	0.145220
$584$	−18.7110	−0.774268
$585$	−7.86124	−0.325022
$586$	12.5797	0.519664
$587$	−8.23272	−0.339801	−0.169900	−	0.985461i	$-0.554345\pi$
$587$	−8.23272	−0.339801	−0.169900	+	0.985461i	$0.554345\pi$
$588$	2.58446	0.106582
$589$	−1.15178	−0.0474581
$590$	−27.2162	−1.12048
$591$	−33.0073	−1.35774
$592$	−3.35657	−0.137954
$593$	−24.5147	−1.00670	−0.503349	−	0.864083i	$-0.667899\pi$
$593$	−24.5147	−1.00670	−0.503349	+	0.864083i	$0.667899\pi$
$594$	8.67858	0.356086
$595$	−0.542543	−0.0222421
$596$	17.8605	0.731597
$597$	−64.7397	−2.64962
$598$	4.95712	0.202712
$599$	−23.2871	−0.951487	−0.475743	−	0.879584i	$-0.657821\pi$
$599$	−23.2871	−0.951487	−0.475743	+	0.879584i	$0.657821\pi$
$600$	16.5594	0.676037
$601$	−1.49880	−0.0611375	−0.0305687	−	0.999533i	$-0.509732\pi$
$601$	−1.49880	−0.0611375	−0.0305687	+	0.999533i	$0.509732\pi$
$602$	−1.70268	−0.0693960
$603$	−43.3794	−1.76655
$604$	3.55615	0.144698
$605$	14.4157	0.586082
$606$	−70.3442	−2.85754
$607$	28.7819	1.16822	0.584111	−	0.811674i	$-0.301443\pi$
$607$	28.7819	1.16822	0.584111	+	0.811674i	$0.301443\pi$
$608$	−0.713064	−0.0289186
$609$	23.2769	0.943228
$610$	−28.8869	−1.16960
$611$	3.93972	0.159384
$612$	−1.84945	−0.0747595
$613$	26.7980	1.08236	0.541182	−	0.840906i	$-0.317977\pi$
$613$	26.7980	1.08236	0.541182	+	0.840906i	$0.317977\pi$
$614$	6.24856	0.252171
$615$	−30.3876	−1.22535
$616$	1.46910	0.0591915
$617$	−41.6977	−1.67869	−0.839344	−	0.543601i	$-0.817060\pi$
$617$	−41.6977	−1.67869	−0.839344	+	0.543601i	$0.817060\pi$
$618$	−83.9407	−3.37659
$619$	1.17011	0.0470309	0.0235154	−	0.999723i	$-0.492514\pi$
$619$	1.17011	0.0470309	0.0235154	+	0.999723i	$0.492514\pi$
$620$	9.56944	0.384318
$621$	17.5928	0.705974
$622$	−9.33142	−0.374156
$623$	−7.40069	−0.296503
$624$	−15.4363	−0.617946
$625$	−0.187462	−0.00749847
$626$	35.0127	1.39939
$627$	0.338396	0.0135143
$628$	−3.00563	−0.119938
$629$	−0.262934	−0.0104839
$630$	12.4372	0.495509
$631$	−27.1062	−1.07908	−0.539540	−	0.841960i	$-0.681402\pi$
$631$	−27.1062	−1.07908	−0.539540	+	0.841960i	$0.681402\pi$
$632$	−7.51122	−0.298780
$633$	47.7473	1.89779
$634$	−42.4756	−1.68692
$635$	5.46582	0.216905
$636$	11.5626	0.458487
$637$	1.07622	0.0426415
$638$	−10.8063	−0.427827
$639$	−13.2745	−0.525130
$640$	−17.6611	−0.698117
$641$	4.95325	0.195642	0.0978209	−	0.995204i	$-0.468813\pi$
$641$	4.95325	0.195642	0.0978209	+	0.995204i	$0.468813\pi$
$642$	−70.8839	−2.79757
$643$	7.72863	0.304787	0.152394	−	0.988320i	$-0.451302\pi$
$643$	7.72863	0.304787	0.152394	+	0.988320i	$0.451302\pi$
$644$	−2.43226	−0.0958443
$645$	−3.98982	−0.157099
$646$	−0.0999687	−0.00393322
$647$	16.7681	0.659221	0.329610	−	0.944117i	$-0.393083\pi$
$647$	16.7681	0.659221	0.329610	+	0.944117i	$0.393083\pi$
$648$	−5.44766	−0.214004
$649$	9.02553	0.354283
$650$	−5.63185	−0.220899
$651$	22.0408	0.863849
$652$	5.06331	0.198294
$653$	−41.6569	−1.63016	−0.815080	−	0.579349i	$-0.803307\pi$
$653$	−41.6569	−1.63016	−0.815080	+	0.579349i	$0.803307\pi$
$654$	−73.9627	−2.89217
$655$	22.1544	0.865643
$656$	−38.0039	−1.48380
$657$	52.5308	2.04942
$658$	−6.23298	−0.242987
$659$	32.8607	1.28007	0.640035	−	0.768346i	$-0.278920\pi$
$659$	32.8607	1.28007	0.640035	+	0.768346i	$0.278920\pi$
$660$	−2.81154	−0.109439
$661$	11.5322	0.448549	0.224275	−	0.974526i	$-0.427999\pi$
$661$	11.5322	0.448549	0.224275	+	0.974526i	$0.427999\pi$
$662$	−32.4160	−1.25988
$663$	−1.20919	−0.0469609
$664$	−23.5662	−0.914545
$665$	0.208494	0.00808505
$666$	6.02746	0.233559
$667$	−21.9061	−0.848206
$668$	10.2487	0.396535
$669$	−26.7810	−1.03541
$670$	19.4816	0.752639
$671$	9.57957	0.369815
$672$	13.6455	0.526386
$673$	22.3257	0.860594	0.430297	−	0.902687i	$-0.358409\pi$
$673$	22.3257	0.860594	0.430297	+	0.902687i	$0.358409\pi$
$674$	4.30810	0.165942
$675$	−19.9874	−0.769315
$676$	−10.6471	−0.409504
$677$	−26.0445	−1.00097	−0.500485	−	0.865745i	$-0.666845\pi$
$677$	−26.0445	−1.00097	−0.500485	+	0.865745i	$0.666845\pi$
$678$	56.9624	2.18763
$679$	−7.83513	−0.300685
$680$	−1.01697	−0.0389991
$681$	64.8382	2.48461
$682$	−10.2325	−0.391822
$683$	−17.6667	−0.675999	−0.337999	−	0.941146i	$-0.609750\pi$
$683$	−17.6667	−0.675999	−0.337999	+	0.941146i	$0.609750\pi$
$684$	0.710724	0.0271752
$685$	24.8531	0.949587
$686$	−1.70268	−0.0650086
$687$	5.10539	0.194783
$688$	−4.98982	−0.190235
$689$	4.81490	0.183433
$690$	−18.3772	−0.699610
$691$	3.91799	0.149047	0.0745236	−	0.997219i	$-0.476256\pi$
$691$	3.91799	0.149047	0.0745236	+	0.997219i	$0.476256\pi$
$692$	−5.77061	−0.219366
$693$	−4.12445	−0.156675
$694$	41.6930	1.58265
$695$	−25.3055	−0.959891
$696$	43.6315	1.65385
$697$	−2.97700	−0.112762
$698$	8.72171	0.330121
$699$	14.6880	0.555553
$700$	2.76332	0.104444
$701$	−43.6766	−1.64964	−0.824822	−	0.565393i	$-0.808725\pi$
$701$	−43.6766	−1.64964	−0.824822	+	0.565393i	$0.808725\pi$
$702$	11.9172	0.449787
$703$	0.101043	0.00381091
$704$	1.48658	0.0560275
$705$	−14.6055	−0.550075
$706$	15.1593	0.570527
$707$	14.3728	0.540543
$708$	29.7624	1.11854
$709$	28.9501	1.08725	0.543623	−	0.839330i	$-0.317052\pi$
$709$	28.9501	1.08725	0.543623	+	0.839330i	$0.317052\pi$
$710$	5.96153	0.223732
$711$	21.0876	0.790845
$712$	−13.8723	−0.519885
$713$	−20.7428	−0.776823
$714$	1.91304	0.0715937
$715$	−1.17078	−0.0437848
$716$	−5.28366	−0.197460
$717$	52.8216	1.97266
$718$	62.3223	2.32585
$719$	15.6158	0.582371	0.291186	−	0.956667i	$-0.405950\pi$
$719$	15.6158	0.582371	0.291186	+	0.956667i	$0.405950\pi$
$720$	36.4480	1.35834
$721$	17.1508	0.638730
$722$	−32.3125	−1.20255
$723$	−60.5255	−2.25097
$724$	−15.0236	−0.558347
$725$	24.8878	0.924309
$726$	−50.8306	−1.88650
$727$	7.82353	0.290159	0.145079	−	0.989420i	$-0.453656\pi$
$727$	7.82353	0.290159	0.145079	+	0.989420i	$0.453656\pi$
$728$	2.01733	0.0747672
$729$	−40.7870	−1.51063
$730$	−23.5914	−0.873158
$731$	−0.390873	−0.0144570
$732$	31.5894	1.16758
$733$	43.4841	1.60612	0.803061	−	0.595897i	$-0.203203\pi$
$733$	43.4841	1.60612	0.803061	+	0.595897i	$0.203203\pi$
$734$	25.1904	0.929796
$735$	−3.98982	−0.147167
$736$	−12.8419	−0.473357
$737$	−6.46054	−0.237977
$738$	68.2443	2.51211
$739$	14.8464	0.546135	0.273068	−	0.961995i	$-0.411962\pi$
$739$	14.8464	0.546135	0.273068	+	0.961995i	$0.411962\pi$
$740$	−0.839507	−0.0308609
$741$	0.464678	0.0170704
$742$	−7.61760	−0.279651
$743$	0.410691	0.0150668	0.00753339	−	0.999972i	$-0.497602\pi$
$743$	0.410691	0.0150668	0.00753339	+	0.999972i	$0.497602\pi$
$744$	41.3145	1.51466
$745$	−27.5726	−1.01018
$746$	18.1266	0.663661
$747$	66.1614	2.42072
$748$	−0.275440	−0.0100711
$749$	14.4830	0.529199
$750$	54.8456	2.00268
$751$	5.47145	0.199656	0.0998280	−	0.995005i	$-0.468171\pi$
$751$	5.47145	0.199656	0.0998280	+	0.995005i	$0.468171\pi$
$752$	−18.2662	−0.666099
$753$	1.40588	0.0512330
$754$	−14.8390	−0.540405
$755$	−5.48988	−0.199797
$756$	−5.84730	−0.212664
$757$	−5.80246	−0.210894	−0.105447	−	0.994425i	$-0.533627\pi$
$757$	−5.80246	−0.210894	−0.105447	+	0.994425i	$0.533627\pi$
$758$	30.0941	1.09307
$759$	6.09431	0.221210
$760$	0.390812	0.0141762
$761$	9.33447	0.338374	0.169187	−	0.985584i	$-0.445886\pi$
$761$	9.33447	0.338374	0.169187	+	0.985584i	$0.445886\pi$
$762$	−19.2728	−0.698181
$763$	15.1121	0.547094
$764$	15.3234	0.554382
$765$	2.85512	0.103227
$766$	22.5638	0.815264
$767$	12.3937	0.447509
$768$	51.3699	1.85365
$769$	−41.6860	−1.50323	−0.751617	−	0.659600i	$-0.770726\pi$
$769$	−41.6860	−1.50323	−0.751617	+	0.659600i	$0.770726\pi$
$770$	1.85228	0.0667515
$771$	−0.350626	−0.0126275
$772$	−7.94838	−0.286068
$773$	26.6855	0.959811	0.479905	−	0.877320i	$-0.340671\pi$
$773$	26.6855	0.959811	0.479905	+	0.877320i	$0.340671\pi$
$774$	8.96032	0.322072
$775$	23.5662	0.846522
$776$	−14.6866	−0.527217
$777$	−1.93360	−0.0693674
$778$	12.3924	0.444289
$779$	1.14403	0.0409892
$780$	−3.86074	−0.138237
$781$	−1.97698	−0.0707419
$782$	−1.80037	−0.0643813
$783$	−52.6636	−1.88204
$784$	−4.98982	−0.178208
$785$	4.64001	0.165609
$786$	−78.1176	−2.78636
$787$	19.2370	0.685725	0.342862	−	0.939386i	$-0.388604\pi$
$787$	19.2370	0.685725	0.342862	+	0.939386i	$0.388604\pi$
$788$	−10.3245	−0.367796
$789$	17.7255	0.631043
$790$	−9.47037	−0.336941
$791$	−11.6386	−0.413820
$792$	−7.73109	−0.274712
$793$	13.1545	0.467128
$794$	−26.3920	−0.936618
$795$	−17.8500	−0.633075
$796$	−20.2503	−0.717751
$797$	26.9257	0.953756	0.476878	−	0.878970i	$-0.341768\pi$
$797$	26.9257	0.953756	0.476878	+	0.878970i	$0.341768\pi$
$798$	−0.735162	−0.0260245
$799$	−1.43087	−0.0506204
$800$	14.5898	0.515828
$801$	38.9460	1.37609
$802$	62.4121	2.20385
$803$	7.82346	0.276084
$804$	−21.3041	−0.751339
$805$	3.75485	0.132341
$806$	−14.0510	−0.494926
$807$	−14.2500	−0.501624
$808$	26.9411	0.947783
$809$	−43.1886	−1.51843	−0.759216	−	0.650839i	$-0.774417\pi$
$809$	−43.1886	−1.51843	−0.759216	+	0.650839i	$0.774417\pi$
$810$	−6.86857	−0.241337
$811$	14.6261	0.513592	0.256796	−	0.966466i	$-0.417333\pi$
$811$	14.6261	0.513592	0.256796	+	0.966466i	$0.417333\pi$
$812$	7.28091	0.255510
$813$	−67.6309	−2.37192
$814$	0.897675	0.0314635
$815$	−7.81659	−0.273803
$816$	5.60630	0.196260
$817$	0.150209	0.00525514
$818$	−42.7645	−1.49522
$819$	−5.66360	−0.197902
$820$	−9.50509	−0.331932
$821$	26.5934	0.928117	0.464059	−	0.885805i	$-0.346393\pi$
$821$	26.5934	0.928117	0.464059	+	0.885805i	$0.346393\pi$
$822$	−87.6334	−3.05657
$823$	−40.0768	−1.39699	−0.698495	−	0.715615i	$-0.746147\pi$
$823$	−40.0768	−1.39699	−0.698495	+	0.715615i	$0.746147\pi$
$824$	32.1484	1.11994
$825$	−6.92383	−0.241057
$826$	−19.6078	−0.682244
$827$	−12.7626	−0.443799	−0.221899	−	0.975070i	$-0.571226\pi$
$827$	−12.7626	−0.443799	−0.221899	+	0.975070i	$0.571226\pi$
$828$	12.7997	0.444821
$829$	55.4091	1.92444	0.962220	−	0.272275i	$-0.0877759\pi$
$829$	55.4091	1.92444	0.962220	+	0.272275i	$0.0877759\pi$
$830$	−29.7129	−1.03135
$831$	−65.9037	−2.28618
$832$	2.04134	0.0707706
$833$	−0.390873	−0.0135430
$834$	89.2286	3.08973
$835$	−15.8217	−0.547532
$836$	0.105849	0.00366086
$837$	−49.8670	−1.72366
$838$	20.9289	0.722976
$839$	−13.0028	−0.448907	−0.224453	−	0.974485i	$-0.572060\pi$
$839$	−13.0028	−0.448907	−0.224453	+	0.974485i	$0.572060\pi$
$840$	−7.47874	−0.258041
$841$	36.5753	1.26122
$842$	−1.14030	−0.0392972
$843$	−23.1395	−0.796966
$844$	14.9351	0.514089
$845$	16.4367	0.565439
$846$	32.8009	1.12772
$847$	10.3857	0.356858
$848$	−22.3239	−0.766607
$849$	−38.1953	−1.31086
$850$	2.04543	0.0701577
$851$	1.81972	0.0623792
$852$	−6.51925	−0.223346
$853$	−1.13136	−0.0387370	−0.0193685	−	0.999812i	$-0.506166\pi$
$853$	−1.13136	−0.0387370	−0.0193685	+	0.999812i	$0.506166\pi$
$854$	−20.8115	−0.712155
$855$	−1.09720	−0.0375233
$856$	27.1478	0.927892
$857$	−49.4257	−1.68835	−0.844174	−	0.536069i	$-0.819909\pi$
$857$	−49.4257	−1.68835	−0.844174	+	0.536069i	$0.819909\pi$
$858$	4.12825	0.140936
$859$	−40.4654	−1.38066	−0.690330	−	0.723495i	$-0.742535\pi$
$859$	−40.4654	−1.38066	−0.690330	+	0.723495i	$0.742535\pi$
$860$	−1.24800	−0.0425564
$861$	−21.8926	−0.746099
$862$	35.8413	1.22076
$863$	−33.8222	−1.15132	−0.575660	−	0.817689i	$-0.695255\pi$
$863$	−33.8222	−1.15132	−0.575660	+	0.817689i	$0.695255\pi$
$864$	−30.8727	−1.05031
$865$	8.90850	0.302898
$866$	34.5031	1.17246
$867$	−48.4265	−1.64465
$868$	6.89427	0.234007
$869$	3.14059	0.106537
$870$	55.0119	1.86508
$871$	−8.87147	−0.300598
$872$	28.3269	0.959270
$873$	41.2322	1.39550
$874$	0.691866	0.0234027
$875$	−11.2061	−0.378835
$876$	25.7985	0.871649
$877$	44.8766	1.51537	0.757687	−	0.652618i	$-0.226329\pi$
$877$	44.8766	1.51537	0.757687	+	0.652618i	$0.226329\pi$
$878$	58.0807	1.96013
$879$	21.2370	0.716308
$880$	5.42824	0.182986
$881$	−43.1831	−1.45487	−0.727437	−	0.686174i	$-0.759289\pi$
$881$	−43.1831	−1.45487	−0.727437	+	0.686174i	$0.759289\pi$
$882$	8.96032	0.301710
$883$	43.7514	1.47235	0.736176	−	0.676790i	$-0.236630\pi$
$883$	43.7514	1.47235	0.736176	+	0.676790i	$0.236630\pi$
$884$	−0.378228	−0.0127212
$885$	−45.9463	−1.54447
$886$	−56.8363	−1.90945
$887$	38.7950	1.30261	0.651305	−	0.758816i	$-0.274222\pi$
$887$	38.7950	1.30261	0.651305	+	0.758816i	$0.274222\pi$
$888$	−3.62444	−0.121628
$889$	3.93783	0.132071
$890$	−17.4906	−0.586285
$891$	2.27778	0.0763084
$892$	−8.37696	−0.280481
$893$	0.549867	0.0184006
$894$	97.2226	3.25161
$895$	8.15676	0.272650
$896$	−12.7239	−0.425075
$897$	8.36858	0.279419
$898$	−35.1103	−1.17165
$899$	62.0931	2.07092
$900$	−14.5419	−0.484731
$901$	−1.74873	−0.0582585
$902$	10.1637	0.338414
$903$	−2.87445	−0.0956558
$904$	−21.8160	−0.725589
$905$	23.1930	0.770960
$906$	19.3576	0.643115
$907$	−42.9385	−1.42575	−0.712875	−	0.701291i	$-0.752607\pi$
$907$	−42.9385	−1.42575	−0.712875	+	0.701291i	$0.752607\pi$
$908$	20.2811	0.673051
$909$	−75.6364	−2.50870
$910$	2.54351	0.0843165
$911$	41.2615	1.36705	0.683527	−	0.729925i	$-0.260445\pi$
$911$	41.2615	1.36705	0.683527	+	0.729925i	$0.260445\pi$
$912$	−2.15444	−0.0713408
$913$	9.85348	0.326103
$914$	−23.6268	−0.781503
$915$	−48.7668	−1.61218
$916$	1.59694	0.0527645
$917$	15.9610	0.527080
$918$	−4.32822	−0.142853
$919$	−43.6349	−1.43938	−0.719691	−	0.694295i	$-0.755716\pi$
$919$	−43.6349	−1.43938	−0.719691	+	0.694295i	$0.755716\pi$
$920$	7.03829	0.232045
$921$	10.5488	0.347594
$922$	−10.4710	−0.344845
$923$	−2.71475	−0.0893569
$924$	−2.02556	−0.0666362
$925$	−2.06741	−0.0679761
$926$	29.5438	0.970870
$927$	−90.2558	−2.96439
$928$	38.4418	1.26191
$929$	−1.76186	−0.0578047	−0.0289024	−	0.999582i	$-0.509201\pi$
$929$	−1.76186	−0.0578047	−0.0289024	+	0.999582i	$0.509201\pi$
$930$	52.0906	1.70812
$931$	0.150209	0.00492289
$932$	4.59435	0.150493
$933$	−15.7533	−0.515738
$934$	2.49177	0.0815332
$935$	0.425216	0.0139061
$936$	−10.6162	−0.347000
$937$	−2.78859	−0.0910991	−0.0455496	−	0.998962i	$-0.514504\pi$
$937$	−2.78859	−0.0910991	−0.0455496	+	0.998962i	$0.514504\pi$
$938$	14.0354	0.458273
$939$	59.1083	1.92893
$940$	−4.56853	−0.149009
$941$	38.3796	1.25114	0.625569	−	0.780169i	$-0.284867\pi$
$941$	38.3796	1.25114	0.625569	+	0.780169i	$0.284867\pi$
$942$	−16.3610	−0.533069
$943$	20.6033	0.670936
$944$	−57.4622	−1.87024
$945$	9.02690	0.293645
$946$	1.33447	0.0433873
$947$	25.8287	0.839321	0.419661	−	0.907681i	$-0.362149\pi$
$947$	25.8287	0.839321	0.419661	+	0.907681i	$0.362149\pi$
$948$	10.3563	0.336358
$949$	10.7430	0.348733
$950$	−0.786038	−0.0255025
$951$	−71.7070	−2.32526
$952$	−0.732674	−0.0237461
$953$	16.6325	0.538779	0.269390	−	0.963031i	$-0.413178\pi$
$953$	16.6325	0.538779	0.269390	+	0.963031i	$0.413178\pi$
$954$	40.0875	1.29788
$955$	−23.6559	−0.765485
$956$	16.5223	0.534370
$957$	−18.2432	−0.589719
$958$	22.5093	0.727242
$959$	17.9053	0.578192
$960$	−7.56773	−0.244247
$961$	27.7958	0.896637
$962$	1.23267	0.0397428
$963$	−76.2167	−2.45605
$964$	−18.9321	−0.609762
$965$	12.2705	0.395001
$966$	−13.2398	−0.425984
$967$	36.3359	1.16848	0.584241	−	0.811580i	$-0.301392\pi$
$967$	36.3359	1.16848	0.584241	+	0.811580i	$0.301392\pi$
$968$	19.4676	0.625712
$969$	−0.168767	−0.00542156
$970$	−18.5173	−0.594554
$971$	35.1424	1.12777	0.563887	−	0.825852i	$-0.309305\pi$
$971$	35.1424	1.12777	0.563887	+	0.825852i	$0.309305\pi$
$972$	−10.0308	−0.321737
$973$	−18.2312	−0.584466
$974$	2.69551	0.0863697
$975$	−9.50765	−0.304489
$976$	−60.9896	−1.95223
$977$	−25.3118	−0.809797	−0.404899	−	0.914362i	$-0.632693\pi$
$977$	−25.3118	−0.809797	−0.404899	+	0.914362i	$0.632693\pi$
$978$	27.5618	0.881328
$979$	5.80027	0.185377
$980$	−1.24800	−0.0398658
$981$	−79.5271	−2.53911
$982$	−25.6408	−0.818231
$983$	−40.3255	−1.28618	−0.643092	−	0.765789i	$-0.722349\pi$
$983$	−40.3255	−1.28618	−0.643092	+	0.765789i	$0.722349\pi$
$984$	−41.0367	−1.30820
$985$	15.9387	0.507849
$986$	5.38938	0.171633
$987$	−10.5225	−0.334934
$988$	0.145349	0.00462417
$989$	2.70517	0.0860193
$990$	−9.74759	−0.309799
$991$	49.6200	1.57623	0.788116	−	0.615527i	$-0.211057\pi$
$991$	49.6200	1.57623	0.788116	+	0.615527i	$0.211057\pi$
$992$	36.4004	1.15572
$993$	−54.7245	−1.73663
$994$	4.29496	0.136228
$995$	31.2618	0.991065
$996$	32.4926	1.02957
$997$	−56.3076	−1.78328	−0.891639	−	0.452747i	$-0.850444\pi$
$997$	−56.3076	−1.78328	−0.891639	+	0.452747i	$0.850444\pi$
$998$	53.4335	1.69141
$999$	4.37473	0.138410

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	301.2.a.c.1.4	✓	5
3.2	odd	2		2709.2.a.j.1.2		5
4.3	odd	2		4816.2.a.r.1.1		5
5.4	even	2		7525.2.a.f.1.2		5
7.6	odd	2		2107.2.a.g.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
301.2.a.c.1.4	✓	5	1.1	even	1	trivial
2107.2.a.g.1.4		5	7.6	odd	2
2709.2.a.j.1.2		5	3.2	odd	2
4816.2.a.r.1.1		5	4.3	odd	2
7525.2.a.f.1.2		5	5.4	even	2

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:	\( N \)	\(=\)	\( 301 = 7 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	301.a (trivial)

\(f(q)\)	\(=\)	\(q+1.70268 q^{2} +2.87445 q^{3} +0.899115 q^{4} -1.38803 q^{5} +4.89427 q^{6} -1.00000 q^{7} -1.87445 q^{8} +5.26248 q^{9} +O(q^{10})\)	\(q+1.70268 q^{2} +2.87445 q^{3} +0.899115 q^{4} -1.38803 q^{5} +4.89427 q^{6} -1.00000 q^{7} -1.87445 q^{8} +5.26248 q^{9} -2.36337 q^{10} +0.783746 q^{11} +2.58446 q^{12} +1.07622 q^{13} -1.70268 q^{14} -3.98982 q^{15} -4.98982 q^{16} -0.390873 q^{17} +8.96032 q^{18} +0.150209 q^{19} -1.24800 q^{20} -2.87445 q^{21} +1.33447 q^{22} +2.70517 q^{23} -5.38803 q^{24} -3.07338 q^{25} +1.83246 q^{26} +6.50340 q^{27} -0.899115 q^{28} -8.09786 q^{29} -6.79339 q^{30} -7.66784 q^{31} -4.74716 q^{32} +2.25284 q^{33} -0.665532 q^{34} +1.38803 q^{35} +4.73158 q^{36} +0.672684 q^{37} +0.255757 q^{38} +3.09355 q^{39} +2.60179 q^{40} +7.61628 q^{41} -4.89427 q^{42} +1.00000 q^{43} +0.704678 q^{44} -7.30447 q^{45} +4.60603 q^{46} +3.66069 q^{47} -14.3430 q^{48} +1.00000 q^{49} -5.23298 q^{50} -1.12355 q^{51} +0.967648 q^{52} +4.47389 q^{53} +11.0732 q^{54} -1.08786 q^{55} +1.87445 q^{56} +0.431768 q^{57} -13.7881 q^{58} +11.5159 q^{59} -3.58731 q^{60} +12.2228 q^{61} -13.0559 q^{62} -5.26248 q^{63} +1.89676 q^{64} -1.49383 q^{65} +3.83587 q^{66} -8.24315 q^{67} -0.351440 q^{68} +7.77588 q^{69} +2.36337 q^{70} -2.52247 q^{71} -9.86428 q^{72} +9.98213 q^{73} +1.14536 q^{74} -8.83428 q^{75} +0.135055 q^{76} -0.783746 q^{77} +5.26733 q^{78} +4.00715 q^{79} +6.92601 q^{80} +2.90627 q^{81} +12.9681 q^{82} +12.5723 q^{83} -2.58446 q^{84} +0.542543 q^{85} +1.70268 q^{86} -23.2769 q^{87} -1.46910 q^{88} +7.40069 q^{89} -12.4372 q^{90} -1.07622 q^{91} +2.43226 q^{92} -22.0408 q^{93} +6.23298 q^{94} -0.208494 q^{95} -13.6455 q^{96} +7.83513 q^{97} +1.70268 q^{98} +4.12445 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + q^{2} + 5 q^{3} + 3 q^{4} + 4 q^{5} - 5 q^{7} + 6 q^{9}+O(q^{10}) \) 5 * q + q^2 + 5 * q^3 + 3 * q^4 + 4 * q^5 - 5 * q^7 + 6 * q^9	\( 5 q + q^{2} + 5 q^{3} + 3 q^{4} + 4 q^{5} - 5 q^{7} + 6 q^{9} + 7 q^{10} + 13 q^{11} + 8 q^{12} - q^{13} - q^{14} - 5 q^{16} + q^{17} - 6 q^{18} + 18 q^{19} + 2 q^{20} - 5 q^{21} - 5 q^{22} - 5 q^{23} - 16 q^{24} - q^{25} - 4 q^{26} + 11 q^{27} - 3 q^{28} + 2 q^{29} - 8 q^{30} - 3 q^{31} - 9 q^{32} + 26 q^{33} - 15 q^{34} - 4 q^{35} + 9 q^{36} - 9 q^{37} + 7 q^{38} + 5 q^{39} + 4 q^{40} + 17 q^{41} + 5 q^{43} + 11 q^{44} - 20 q^{45} - q^{46} + 7 q^{47} - 13 q^{48} + 5 q^{49} + 25 q^{50} - 34 q^{52} - 30 q^{53} + 5 q^{54} + 21 q^{55} - 9 q^{57} - 46 q^{58} + 9 q^{59} - 21 q^{60} - 10 q^{61} - 19 q^{62} - 6 q^{63} - 26 q^{64} - 4 q^{65} - 29 q^{66} - 10 q^{67} + 33 q^{68} - 19 q^{69} - 7 q^{70} + 17 q^{71} - 20 q^{72} - q^{73} - 10 q^{75} + 20 q^{76} - 13 q^{77} + 29 q^{78} - 4 q^{79} + 11 q^{80} - 11 q^{81} + 28 q^{82} + 23 q^{83} - 8 q^{84} - 23 q^{85} + q^{86} - 3 q^{87} - 13 q^{88} + 35 q^{89} - 31 q^{90} + q^{91} - 25 q^{92} - 21 q^{93} - 20 q^{94} + 22 q^{95} + 22 q^{96} - 2 q^{97} + q^{98} + 18 q^{99}+O(q^{100}) \) 5 * q + q^2 + 5 * q^3 + 3 * q^4 + 4 * q^5 - 5 * q^7 + 6 * q^9 + 7 * q^10 + 13 * q^11 + 8 * q^12 - q^13 - q^14 - 5 * q^16 + q^17 - 6 * q^18 + 18 * q^19 + 2 * q^20 - 5 * q^21 - 5 * q^22 - 5 * q^23 - 16 * q^24 - q^25 - 4 * q^26 + 11 * q^27 - 3 * q^28 + 2 * q^29 - 8 * q^30 - 3 * q^31 - 9 * q^32 + 26 * q^33 - 15 * q^34 - 4 * q^35 + 9 * q^36 - 9 * q^37 + 7 * q^38 + 5 * q^39 + 4 * q^40 + 17 * q^41 + 5 * q^43 + 11 * q^44 - 20 * q^45 - q^46 + 7 * q^47 - 13 * q^48 + 5 * q^49 + 25 * q^50 - 34 * q^52 - 30 * q^53 + 5 * q^54 + 21 * q^55 - 9 * q^57 - 46 * q^58 + 9 * q^59 - 21 * q^60 - 10 * q^61 - 19 * q^62 - 6 * q^63 - 26 * q^64 - 4 * q^65 - 29 * q^66 - 10 * q^67 + 33 * q^68 - 19 * q^69 - 7 * q^70 + 17 * q^71 - 20 * q^72 - q^73 - 10 * q^75 + 20 * q^76 - 13 * q^77 + 29 * q^78 - 4 * q^79 + 11 * q^80 - 11 * q^81 + 28 * q^82 + 23 * q^83 - 8 * q^84 - 23 * q^85 + q^86 - 3 * q^87 - 13 * q^88 + 35 * q^89 - 31 * q^90 + q^91 - 25 * q^92 - 21 * q^93 - 20 * q^94 + 22 * q^95 + 22 * q^96 - 2 * q^97 + q^98 + 18 * q^99

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