LMFDB - Embedded newform 6041.2.a.c.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6041,2,Mod(1,6041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6041, 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("6041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6041 = 7 \cdot 863 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6041.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:	$48.2376278611$
Analytic rank:	$1$
Dimension:	$83$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	6041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.90567 q^{2} -1.35998 q^{3} +1.63156 q^{4} +3.50685 q^{5} +2.59167 q^{6} +1.00000 q^{7} +0.702124 q^{8} -1.15045 q^{9} +O(q^{10})$	\(q-1.90567 q^{2} -1.35998 q^{3} +1.63156 q^{4} +3.50685 q^{5} +2.59167 q^{6} +1.00000 q^{7} +0.702124 q^{8} -1.15045 q^{9} -6.68289 q^{10} +0.961333 q^{11} -2.21889 q^{12} -1.89595 q^{13} -1.90567 q^{14} -4.76925 q^{15} -4.60113 q^{16} +2.80860 q^{17} +2.19238 q^{18} -0.842259 q^{19} +5.72164 q^{20} -1.35998 q^{21} -1.83198 q^{22} -6.67395 q^{23} -0.954876 q^{24} +7.29801 q^{25} +3.61304 q^{26} +5.64454 q^{27} +1.63156 q^{28} -3.25764 q^{29} +9.08860 q^{30} +1.30725 q^{31} +7.36397 q^{32} -1.30739 q^{33} -5.35225 q^{34} +3.50685 q^{35} -1.87703 q^{36} -3.05284 q^{37} +1.60506 q^{38} +2.57845 q^{39} +2.46225 q^{40} +7.51755 q^{41} +2.59167 q^{42} -2.77818 q^{43} +1.56847 q^{44} -4.03447 q^{45} +12.7183 q^{46} +0.152811 q^{47} +6.25745 q^{48} +1.00000 q^{49} -13.9076 q^{50} -3.81964 q^{51} -3.09335 q^{52} +0.365369 q^{53} -10.7566 q^{54} +3.37125 q^{55} +0.702124 q^{56} +1.14546 q^{57} +6.20796 q^{58} -8.78411 q^{59} -7.78132 q^{60} +2.19902 q^{61} -2.49118 q^{62} -1.15045 q^{63} -4.83099 q^{64} -6.64880 q^{65} +2.49145 q^{66} -0.242808 q^{67} +4.58240 q^{68} +9.07644 q^{69} -6.68289 q^{70} -2.90972 q^{71} -0.807761 q^{72} -0.668531 q^{73} +5.81770 q^{74} -9.92516 q^{75} -1.37419 q^{76} +0.961333 q^{77} -4.91366 q^{78} +4.97288 q^{79} -16.1355 q^{80} -4.22510 q^{81} -14.3259 q^{82} -16.4700 q^{83} -2.21889 q^{84} +9.84935 q^{85} +5.29427 q^{86} +4.43032 q^{87} +0.674975 q^{88} -14.6548 q^{89} +7.68834 q^{90} -1.89595 q^{91} -10.8889 q^{92} -1.77783 q^{93} -0.291206 q^{94} -2.95368 q^{95} -10.0149 q^{96} -9.91226 q^{97} -1.90567 q^{98} -1.10597 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 83 q - 8 q^{2} - 12 q^{3} + 48 q^{4} - 11 q^{5} - 8 q^{6} + 83 q^{7} - 18 q^{8} + 39 q^{9}+O(q^{10}) $ 83 * q - 8 * q^2 - 12 * q^3 + 48 * q^4 - 11 * q^5 - 8 * q^6 + 83 * q^7 - 18 * q^8 + 39 * q^9	\( 83 q - 8 q^{2} - 12 q^{3} + 48 q^{4} - 11 q^{5} - 8 q^{6} + 83 q^{7} - 18 q^{8} + 39 q^{9} - 20 q^{10} - 26 q^{11} - 14 q^{12} - 22 q^{13} - 8 q^{14} - 37 q^{15} - 10 q^{16} - 9 q^{17} - 27 q^{18} - 42 q^{19} - 22 q^{20} - 12 q^{21} - 44 q^{22} - 46 q^{23} - 24 q^{24} - 20 q^{25} - 9 q^{26} - 39 q^{27} + 48 q^{28} - 36 q^{29} - 11 q^{30} - 107 q^{31} - 19 q^{32} - 25 q^{33} - 24 q^{34} - 11 q^{35} - 32 q^{36} - 75 q^{37} - 16 q^{38} - 78 q^{39} - 34 q^{40} - 17 q^{41} - 8 q^{42} - 87 q^{43} - 32 q^{44} - 17 q^{45} - 56 q^{46} - 39 q^{47} - 16 q^{48} + 83 q^{49} - 26 q^{50} - 71 q^{51} - 53 q^{52} - 28 q^{53} - 25 q^{54} - 94 q^{55} - 18 q^{56} - 79 q^{57} - 69 q^{58} - 26 q^{59} - 43 q^{60} - 56 q^{61} - 6 q^{62} + 39 q^{63} - 108 q^{64} - 26 q^{65} + 10 q^{66} - 123 q^{67} - 11 q^{68} + 2 q^{69} - 20 q^{70} - 96 q^{71} - 11 q^{72} - 53 q^{73} - 26 q^{74} - 27 q^{75} - 65 q^{76} - 26 q^{77} - 43 q^{78} - 160 q^{79} + 12 q^{80} - 53 q^{81} - 20 q^{82} - 2 q^{83} - 14 q^{84} - 110 q^{85} + 24 q^{86} - 52 q^{87} - 79 q^{88} - 5 q^{89} - 4 q^{90} - 22 q^{91} - 51 q^{92} - 30 q^{93} - 9 q^{94} - 76 q^{95} - 3 q^{96} - 44 q^{97} - 8 q^{98} - 82 q^{99}+O(q^{100}) \) 83 * q - 8 * q^2 - 12 * q^3 + 48 * q^4 - 11 * q^5 - 8 * q^6 + 83 * q^7 - 18 * q^8 + 39 * q^9 - 20 * q^10 - 26 * q^11 - 14 * q^12 - 22 * q^13 - 8 * q^14 - 37 * q^15 - 10 * q^16 - 9 * q^17 - 27 * q^18 - 42 * q^19 - 22 * q^20 - 12 * q^21 - 44 * q^22 - 46 * q^23 - 24 * q^24 - 20 * q^25 - 9 * q^26 - 39 * q^27 + 48 * q^28 - 36 * q^29 - 11 * q^30 - 107 * q^31 - 19 * q^32 - 25 * q^33 - 24 * q^34 - 11 * q^35 - 32 * q^36 - 75 * q^37 - 16 * q^38 - 78 * q^39 - 34 * q^40 - 17 * q^41 - 8 * q^42 - 87 * q^43 - 32 * q^44 - 17 * q^45 - 56 * q^46 - 39 * q^47 - 16 * q^48 + 83 * q^49 - 26 * q^50 - 71 * q^51 - 53 * q^52 - 28 * q^53 - 25 * q^54 - 94 * q^55 - 18 * q^56 - 79 * q^57 - 69 * q^58 - 26 * q^59 - 43 * q^60 - 56 * q^61 - 6 * q^62 + 39 * q^63 - 108 * q^64 - 26 * q^65 + 10 * q^66 - 123 * q^67 - 11 * q^68 + 2 * q^69 - 20 * q^70 - 96 * q^71 - 11 * q^72 - 53 * q^73 - 26 * q^74 - 27 * q^75 - 65 * q^76 - 26 * q^77 - 43 * q^78 - 160 * q^79 + 12 * q^80 - 53 * q^81 - 20 * q^82 - 2 * q^83 - 14 * q^84 - 110 * q^85 + 24 * q^86 - 52 * q^87 - 79 * q^88 - 5 * q^89 - 4 * q^90 - 22 * q^91 - 51 * q^92 - 30 * q^93 - 9 * q^94 - 76 * q^95 - 3 * q^96 - 44 * q^97 - 8 * q^98 - 82 * 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 $

$2$	−1.90567	−1.34751	−0.673754	−	0.738955i	$-0.735319\pi$
$2$	−1.90567	−1.34751	−0.673754	+	0.738955i	$0.735319\pi$
$3$	−1.35998	−0.785185	−0.392593	−	0.919712i	$-0.628422\pi$
$3$	−1.35998	−0.785185	−0.392593	+	0.919712i	$0.628422\pi$
$4$	1.63156	0.815780
$5$	3.50685	1.56831	0.784156	−	0.620564i	$-0.213096\pi$
$5$	3.50685	1.56831	0.784156	+	0.620564i	$0.213096\pi$
$6$	2.59167	1.05804
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	0.702124	0.248238
$9$	−1.15045	−0.383484
$10$	−6.68289	−2.11331
$11$	0.961333	0.289853	0.144926	−	0.989442i	$-0.453705\pi$
$11$	0.961333	0.289853	0.144926	+	0.989442i	$0.453705\pi$
$12$	−2.21889	−0.640538
$13$	−1.89595	−0.525841	−0.262920	−	0.964818i	$-0.584686\pi$
$13$	−1.89595	−0.525841	−0.262920	+	0.964818i	$0.584686\pi$
$14$	−1.90567	−0.509310
$15$	−4.76925	−1.23142
$16$	−4.60113	−1.15028
$17$	2.80860	0.681186	0.340593	−	0.940211i	$-0.389372\pi$
$17$	2.80860	0.681186	0.340593	+	0.940211i	$0.389372\pi$
$18$	2.19238	0.516748
$19$	−0.842259	−0.193227	−0.0966137	−	0.995322i	$-0.530801\pi$
$19$	−0.842259	−0.193227	−0.0966137	+	0.995322i	$0.530801\pi$
$20$	5.72164	1.27940
$21$	−1.35998	−0.296772
$22$	−1.83198	−0.390579
$23$	−6.67395	−1.39161	−0.695807	−	0.718229i	$-0.744953\pi$
$23$	−6.67395	−1.39161	−0.695807	+	0.718229i	$0.744953\pi$
$24$	−0.954876	−0.194913
$25$	7.29801	1.45960
$26$	3.61304	0.708575
$27$	5.64454	1.08629
$28$	1.63156	0.308336
$29$	−3.25764	−0.604928	−0.302464	−	0.953161i	$-0.597809\pi$
$29$	−3.25764	−0.604928	−0.302464	+	0.953161i	$0.597809\pi$
$30$	9.08860	1.65934
$31$	1.30725	0.234789	0.117394	−	0.993085i	$-0.462546\pi$
$31$	1.30725	0.234789	0.117394	+	0.993085i	$0.462546\pi$
$32$	7.36397	1.30178
$33$	−1.30739	−0.227588
$34$	−5.35225	−0.917904
$35$	3.50685	0.592766
$36$	−1.87703	−0.312839
$37$	−3.05284	−0.501884	−0.250942	−	0.968002i	$-0.580740\pi$
$37$	−3.05284	−0.501884	−0.250942	+	0.968002i	$0.580740\pi$
$38$	1.60506	0.260376
$39$	2.57845	0.412882
$40$	2.46225	0.389315
$41$	7.51755	1.17404	0.587022	−	0.809571i	$-0.300300\pi$
$41$	7.51755	1.17404	0.587022	+	0.809571i	$0.300300\pi$
$42$	2.59167	0.399903
$43$	−2.77818	−0.423668	−0.211834	−	0.977306i	$-0.567944\pi$
$43$	−2.77818	−0.423668	−0.211834	+	0.977306i	$0.567944\pi$
$44$	1.56847	0.236456
$45$	−4.03447	−0.601423
$46$	12.7183	1.87521
$47$	0.152811	0.0222897	0.0111449	−	0.999938i	$-0.496452\pi$
$47$	0.152811	0.0222897	0.0111449	+	0.999938i	$0.496452\pi$
$48$	6.25745	0.903185
$49$	1.00000	0.142857
$50$	−13.9076	−1.96683
$51$	−3.81964	−0.534857
$52$	−3.09335	−0.428970
$53$	0.365369	0.0501873	0.0250937	−	0.999685i	$-0.492012\pi$
$53$	0.365369	0.0501873	0.0250937	+	0.999685i	$0.492012\pi$
$54$	−10.7566	−1.46379
$55$	3.37125	0.454579
$56$	0.702124	0.0938253
$57$	1.14546	0.151719
$58$	6.20796	0.815145
$59$	−8.78411	−1.14359	−0.571797	−	0.820395i	$-0.693753\pi$
$59$	−8.78411	−1.14359	−0.571797	+	0.820395i	$0.693753\pi$
$60$	−7.78132	−1.00456
$61$	2.19902	0.281556	0.140778	−	0.990041i	$-0.455040\pi$
$61$	2.19902	0.281556	0.140778	+	0.990041i	$0.455040\pi$
$62$	−2.49118	−0.316380
$63$	−1.15045	−0.144943
$64$	−4.83099	−0.603874
$65$	−6.64880	−0.824682
$66$	2.49145	0.306677
$67$	−0.242808	−0.0296638	−0.0148319	−	0.999890i	$-0.504721\pi$
$67$	−0.242808	−0.0296638	−0.0148319	+	0.999890i	$0.504721\pi$
$68$	4.58240	0.555698
$69$	9.07644	1.09268
$70$	−6.68289	−0.798758
$71$	−2.90972	−0.345320	−0.172660	−	0.984981i	$-0.555236\pi$
$71$	−2.90972	−0.345320	−0.172660	+	0.984981i	$0.555236\pi$
$72$	−0.807761	−0.0951955
$73$	−0.668531	−0.0782456	−0.0391228	−	0.999234i	$-0.512456\pi$
$73$	−0.668531	−0.0782456	−0.0391228	+	0.999234i	$0.512456\pi$
$74$	5.81770	0.676293
$75$	−9.92516	−1.14606
$76$	−1.37419	−0.157631
$77$	0.961333	0.109554
$78$	−4.91366	−0.556363
$79$	4.97288	0.559492	0.279746	−	0.960074i	$-0.409750\pi$
$79$	4.97288	0.559492	0.279746	+	0.960074i	$0.409750\pi$
$80$	−16.1355	−1.80400
$81$	−4.22510	−0.469456
$82$	−14.3259	−1.58203
$83$	−16.4700	−1.80782	−0.903910	−	0.427723i	$-0.859316\pi$
$83$	−16.4700	−1.80782	−0.903910	+	0.427723i	$0.859316\pi$
$84$	−2.21889	−0.242101
$85$	9.84935	1.06831
$86$	5.29427	0.570896
$87$	4.43032	0.474980
$88$	0.674975	0.0719526
$89$	−14.6548	−1.55340	−0.776702	−	0.629868i	$-0.783109\pi$
$89$	−14.6548	−1.55340	−0.776702	+	0.629868i	$0.783109\pi$
$90$	7.68834	0.810423
$91$	−1.89595	−0.198749
$92$	−10.8889	−1.13525
$93$	−1.77783	−0.184353
$94$	−0.291206	−0.0300356
$95$	−2.95368	−0.303041
$96$	−10.0149	−1.02214
$97$	−9.91226	−1.00644	−0.503219	−	0.864159i	$-0.667851\pi$
$97$	−9.91226	−1.00644	−0.503219	+	0.864159i	$0.667851\pi$
$98$	−1.90567	−0.192501
$99$	−1.10597	−0.111154
$100$	11.9071	1.19071
$101$	−13.1552	−1.30899	−0.654494	−	0.756067i	$-0.727118\pi$
$101$	−13.1552	−1.30899	−0.654494	+	0.756067i	$0.727118\pi$
$102$	7.27896	0.720725
$103$	10.8826	1.07230	0.536149	−	0.844124i	$-0.319879\pi$
$103$	10.8826	1.07230	0.536149	+	0.844124i	$0.319879\pi$
$104$	−1.33119	−0.130534
$105$	−4.76925	−0.465431
$106$	−0.696271	−0.0676279
$107$	6.31572	0.610563	0.305282	−	0.952262i	$-0.401249\pi$
$107$	6.31572	0.610563	0.305282	+	0.952262i	$0.401249\pi$
$108$	9.20939	0.886174
$109$	12.5079	1.19804	0.599022	−	0.800733i	$-0.295556\pi$
$109$	12.5079	1.19804	0.599022	+	0.800733i	$0.295556\pi$
$110$	−6.42448	−0.612550
$111$	4.15181	0.394072
$112$	−4.60113	−0.434766
$113$	−11.3297	−1.06581	−0.532903	−	0.846177i	$-0.678899\pi$
$113$	−11.3297	−1.06581	−0.532903	+	0.846177i	$0.678899\pi$
$114$	−2.18285	−0.204443
$115$	−23.4046	−2.18249
$116$	−5.31503	−0.493488
$117$	2.18120	0.201652
$118$	16.7396	1.54100
$119$	2.80860	0.257464
$120$	−3.34861	−0.305685
$121$	−10.0758	−0.915985
$122$	−4.19060	−0.379399
$123$	−10.2237	−0.921842
$124$	2.13286	0.191536
$125$	8.05879	0.720800
$126$	2.19238	0.195312
$127$	−7.17406	−0.636595	−0.318298	−	0.947991i	$-0.603111\pi$
$127$	−7.17406	−0.636595	−0.318298	+	0.947991i	$0.603111\pi$
$128$	−5.52168	−0.488052
$129$	3.77826	0.332658
$130$	12.6704	1.11127
$131$	−6.47617	−0.565825	−0.282913	−	0.959146i	$-0.591301\pi$
$131$	−6.47617	−0.565825	−0.282913	+	0.959146i	$0.591301\pi$
$132$	−2.13309	−0.185662
$133$	−0.842259	−0.0730331
$134$	0.462712	0.0399722
$135$	19.7946	1.70364
$136$	1.97199	0.169097
$137$	17.6954	1.51182	0.755911	−	0.654674i	$-0.227194\pi$
$137$	17.6954	1.51182	0.755911	+	0.654674i	$0.227194\pi$
$138$	−17.2967	−1.47239
$139$	−22.4465	−1.90388	−0.951942	−	0.306277i	$-0.900917\pi$
$139$	−22.4465	−1.90388	−0.951942	+	0.306277i	$0.900917\pi$
$140$	5.72164	0.483567
$141$	−0.207819	−0.0175016
$142$	5.54495	0.465322
$143$	−1.82263	−0.152416
$144$	5.29338	0.441115
$145$	−11.4240	−0.948715
$146$	1.27400	0.105437
$147$	−1.35998	−0.112169
$148$	−4.98089	−0.409427
$149$	13.8800	1.13710	0.568549	−	0.822650i	$-0.307505\pi$
$149$	13.8800	1.13710	0.568549	+	0.822650i	$0.307505\pi$
$150$	18.9140	1.54432
$151$	3.45360	0.281050	0.140525	−	0.990077i	$-0.455121\pi$
$151$	3.45360	0.281050	0.140525	+	0.990077i	$0.455121\pi$
$152$	−0.591370	−0.0479665
$153$	−3.23116	−0.261224
$154$	−1.83198	−0.147625
$155$	4.58433	0.368222
$156$	4.20689	0.336821
$157$	16.6095	1.32558	0.662791	−	0.748805i	$-0.269372\pi$
$157$	16.6095	1.32558	0.662791	+	0.748805i	$0.269372\pi$
$158$	−9.47664	−0.753921
$159$	−0.496895	−0.0394063
$160$	25.8244	2.04159
$161$	−6.67395	−0.525981
$162$	8.05163	0.632596
$163$	−8.35964	−0.654778	−0.327389	−	0.944890i	$-0.606169\pi$
$163$	−8.35964	−0.654778	−0.327389	+	0.944890i	$0.606169\pi$
$164$	12.2653	0.957761
$165$	−4.58484	−0.356929
$166$	31.3864	2.43605
$167$	−22.6022	−1.74901	−0.874505	−	0.485017i	$-0.838813\pi$
$167$	−22.6022	−1.74901	−0.874505	+	0.485017i	$0.838813\pi$
$168$	−0.954876	−0.0736702
$169$	−9.40539	−0.723492
$170$	−18.7696	−1.43956
$171$	0.968978	0.0740996
$172$	−4.53276	−0.345620
$173$	0.0739769	0.00562436	0.00281218	−	0.999996i	$-0.499105\pi$
$173$	0.0739769	0.00562436	0.00281218	+	0.999996i	$0.499105\pi$
$174$	−8.44271	−0.640040
$175$	7.29801	0.551678
$176$	−4.42322	−0.333413
$177$	11.9462	0.897933
$178$	27.9271	2.09323
$179$	2.48643	0.185845	0.0929224	−	0.995673i	$-0.470379\pi$
$179$	2.48643	0.185845	0.0929224	+	0.995673i	$0.470379\pi$
$180$	−6.58247	−0.490629
$181$	6.41288	0.476665	0.238333	−	0.971184i	$-0.423399\pi$
$181$	6.41288	0.476665	0.238333	+	0.971184i	$0.423399\pi$
$182$	3.61304	0.267816
$183$	−2.99063	−0.221073
$184$	−4.68594	−0.345452
$185$	−10.7059	−0.787111
$186$	3.38796	0.248417
$187$	2.70000	0.197444
$188$	0.249320	0.0181835
$189$	5.64454	0.410580
$190$	5.62872	0.408350
$191$	18.0173	1.30368	0.651842	−	0.758355i	$-0.273997\pi$
$191$	18.0173	1.30368	0.651842	+	0.758355i	$0.273997\pi$
$192$	6.57006	0.474153
$193$	−23.4485	−1.68786	−0.843928	−	0.536456i	$-0.819763\pi$
$193$	−23.4485	−1.68786	−0.843928	+	0.536456i	$0.819763\pi$
$194$	18.8895	1.35618
$195$	9.04224	0.647528
$196$	1.63156	0.116540
$197$	23.7650	1.69319	0.846593	−	0.532240i	$-0.178650\pi$
$197$	23.7650	1.69319	0.846593	+	0.532240i	$0.178650\pi$
$198$	2.10760	0.149781
$199$	−4.61687	−0.327281	−0.163640	−	0.986520i	$-0.552324\pi$
$199$	−4.61687	−0.327281	−0.163640	+	0.986520i	$0.552324\pi$
$200$	5.12411	0.362329
$201$	0.330215	0.0232916
$202$	25.0694	1.76387
$203$	−3.25764	−0.228641
$204$	−6.23198	−0.436326
$205$	26.3629	1.84127
$206$	−20.7386	−1.44493
$207$	7.67806	0.533662
$208$	8.72350	0.604866
$209$	−0.809691	−0.0560075
$210$	9.08860	0.627173
$211$	−20.2773	−1.39595	−0.697974	−	0.716123i	$-0.745915\pi$
$211$	−20.2773	−1.39595	−0.697974	+	0.716123i	$0.745915\pi$
$212$	0.596122	0.0409418
$213$	3.95716	0.271140
$214$	−12.0356	−0.822740
$215$	−9.74265	−0.664443
$216$	3.96317	0.269659
$217$	1.30725	0.0887419
$218$	−23.8359	−1.61437
$219$	0.909189	0.0614373
$220$	5.50040	0.370837
$221$	−5.32496	−0.358195
$222$	−7.91195	−0.531016
$223$	25.0297	1.67611	0.838057	−	0.545582i	$-0.183691\pi$
$223$	25.0297	1.67611	0.838057	+	0.545582i	$0.183691\pi$
$224$	7.36397	0.492026
$225$	−8.39602	−0.559735
$226$	21.5905	1.43618
$227$	25.8121	1.71321	0.856604	−	0.515974i	$-0.172570\pi$
$227$	25.8121	1.71321	0.856604	+	0.515974i	$0.172570\pi$
$228$	1.86888	0.123770
$229$	21.7041	1.43425	0.717125	−	0.696945i	$-0.245458\pi$
$229$	21.7041	1.43425	0.717125	+	0.696945i	$0.245458\pi$
$230$	44.6012	2.94092
$231$	−1.30739	−0.0860202
$232$	−2.28726	−0.150166
$233$	−16.1090	−1.05534	−0.527668	−	0.849450i	$-0.676934\pi$
$233$	−16.1090	−1.05534	−0.527668	+	0.849450i	$0.676934\pi$
$234$	−4.15663	−0.271727
$235$	0.535884	0.0349572
$236$	−14.3318	−0.932920
$237$	−6.76302	−0.439305
$238$	−5.35225	−0.346935
$239$	−10.4179	−0.673880	−0.336940	−	0.941526i	$-0.609392\pi$
$239$	−10.4179	−0.673880	−0.336940	+	0.941526i	$0.609392\pi$
$240$	21.9440	1.41648
$241$	−26.4570	−1.70425	−0.852123	−	0.523342i	$-0.824685\pi$
$241$	−26.4570	−1.70425	−0.852123	+	0.523342i	$0.824685\pi$
$242$	19.2012	1.23430
$243$	−11.1875	−0.717682
$244$	3.58783	0.229687
$245$	3.50685	0.224045
$246$	19.4830	1.24219
$247$	1.59688	0.101607
$248$	0.917852	0.0582837
$249$	22.3989	1.41947
$250$	−15.3574	−0.971285
$251$	−11.0271	−0.696025	−0.348012	−	0.937490i	$-0.613143\pi$
$251$	−11.0271	−0.696025	−0.348012	+	0.937490i	$0.613143\pi$
$252$	−1.87703	−0.118242
$253$	−6.41588	−0.403363
$254$	13.6714	0.857818
$255$	−13.3949	−0.838823
$256$	20.1845	1.26153
$257$	3.13178	0.195355	0.0976776	−	0.995218i	$-0.468859\pi$
$257$	3.13178	0.195355	0.0976776	+	0.995218i	$0.468859\pi$
$258$	−7.20011	−0.448259
$259$	−3.05284	−0.189694
$260$	−10.8479	−0.672759
$261$	3.74775	0.231980
$262$	12.3414	0.762455
$263$	−7.08968	−0.437168	−0.218584	−	0.975818i	$-0.570144\pi$
$263$	−7.08968	−0.437168	−0.218584	+	0.975818i	$0.570144\pi$
$264$	−0.917953	−0.0564961
$265$	1.28130	0.0787094
$266$	1.60506	0.0984127
$267$	19.9302	1.21971
$268$	−0.396156	−0.0241991
$269$	−8.48964	−0.517622	−0.258811	−	0.965928i	$-0.583331\pi$
$269$	−8.48964	−0.517622	−0.258811	+	0.965928i	$0.583331\pi$
$270$	−37.7218	−2.29567
$271$	26.2619	1.59530	0.797649	−	0.603123i	$-0.206077\pi$
$271$	26.2619	1.59530	0.797649	+	0.603123i	$0.206077\pi$
$272$	−12.9227	−0.783557
$273$	2.57845	0.156055
$274$	−33.7216	−2.03719
$275$	7.01582	0.423070
$276$	14.8088	0.891382
$277$	7.48718	0.449861	0.224931	−	0.974375i	$-0.427784\pi$
$277$	7.48718	0.449861	0.224931	+	0.974375i	$0.427784\pi$
$278$	42.7755	2.56550
$279$	−1.50393	−0.0900379
$280$	2.46225	0.147147
$281$	27.7176	1.65349	0.826745	−	0.562576i	$-0.190190\pi$
$281$	27.7176	1.65349	0.826745	+	0.562576i	$0.190190\pi$
$282$	0.396034	0.0235835
$283$	7.71632	0.458687	0.229344	−	0.973346i	$-0.426342\pi$
$283$	7.71632	0.458687	0.229344	+	0.973346i	$0.426342\pi$
$284$	−4.74738	−0.281705
$285$	4.01694	0.237943
$286$	3.47333	0.205382
$287$	7.51755	0.443747
$288$	−8.47190	−0.499211
$289$	−9.11176	−0.535986
$290$	21.7704	1.27840
$291$	13.4805	0.790240
$292$	−1.09075	−0.0638312
$293$	−24.0336	−1.40406	−0.702030	−	0.712147i	$-0.747723\pi$
$293$	−24.0336	−1.40406	−0.702030	+	0.712147i	$0.747723\pi$
$294$	2.59167	0.151149
$295$	−30.8046	−1.79351
$296$	−2.14348	−0.124587
$297$	5.42628	0.314864
$298$	−26.4507	−1.53225
$299$	12.6534	0.731768
$300$	−16.1935	−0.934931
$301$	−2.77818	−0.160131
$302$	−6.58141	−0.378718
$303$	17.8908	1.02780
$304$	3.87534	0.222266
$305$	7.71164	0.441567
$306$	6.15751	0.352002
$307$	−11.0015	−0.627886	−0.313943	−	0.949442i	$-0.601650\pi$
$307$	−11.0015	−0.627886	−0.313943	+	0.949442i	$0.601650\pi$
$308$	1.56847	0.0893719
$309$	−14.8002	−0.841952
$310$	−8.73620	−0.496183
$311$	−12.6774	−0.718867	−0.359433	−	0.933171i	$-0.617030\pi$
$311$	−12.6774	−0.718867	−0.359433	+	0.933171i	$0.617030\pi$
$312$	1.81039	0.102493
$313$	4.05234	0.229052	0.114526	−	0.993420i	$-0.463465\pi$
$313$	4.05234	0.229052	0.114526	+	0.993420i	$0.463465\pi$
$314$	−31.6521	−1.78623
$315$	−4.03447	−0.227316
$316$	8.11354	0.456422
$317$	8.28259	0.465197	0.232598	−	0.972573i	$-0.425277\pi$
$317$	8.28259	0.465197	0.232598	+	0.972573i	$0.425277\pi$
$318$	0.946916	0.0531004
$319$	−3.13167	−0.175340
$320$	−16.9416	−0.947063
$321$	−8.58925	−0.479405
$322$	12.7183	0.708764
$323$	−2.36557	−0.131624
$324$	−6.89350	−0.382972
$325$	−13.8366	−0.767519
$326$	15.9307	0.882319
$327$	−17.0106	−0.940686
$328$	5.27825	0.291443
$329$	0.152811	0.00842472
$330$	8.73716	0.480965
$331$	13.7659	0.756645	0.378322	−	0.925674i	$-0.376501\pi$
$331$	13.7659	0.756645	0.378322	+	0.925674i	$0.376501\pi$
$332$	−26.8718	−1.47478
$333$	3.51215	0.192465
$334$	43.0722	2.35681
$335$	−0.851493	−0.0465221
$336$	6.25745	0.341372
$337$	−1.09062	−0.0594101	−0.0297050	−	0.999559i	$-0.509457\pi$
$337$	−1.09062	−0.0594101	−0.0297050	+	0.999559i	$0.509457\pi$
$338$	17.9235	0.974911
$339$	15.4081	0.836855
$340$	16.0698	0.871507
$341$	1.25670	0.0680542
$342$	−1.84655	−0.0998499
$343$	1.00000	0.0539949
$344$	−1.95062	−0.105171
$345$	31.8297	1.71366
$346$	−0.140975	−0.00757888
$347$	−22.8006	−1.22400	−0.611999	−	0.790859i	$-0.709634\pi$
$347$	−22.8006	−1.22400	−0.611999	+	0.790859i	$0.709634\pi$
$348$	7.22833	0.387479
$349$	31.1482	1.66732	0.833661	−	0.552276i	$-0.186241\pi$
$349$	31.1482	1.66732	0.833661	+	0.552276i	$0.186241\pi$
$350$	−13.9076	−0.743391
$351$	−10.7017	−0.571216
$352$	7.07922	0.377324
$353$	28.0113	1.49089	0.745446	−	0.666566i	$-0.232236\pi$
$353$	28.0113	1.49089	0.745446	+	0.666566i	$0.232236\pi$
$354$	−22.7655	−1.20997
$355$	−10.2040	−0.541570
$356$	−23.9101	−1.26724
$357$	−3.81964	−0.202157
$358$	−4.73831	−0.250427
$359$	12.0528	0.636120	0.318060	−	0.948071i	$-0.396969\pi$
$359$	12.0528	0.636120	0.318060	+	0.948071i	$0.396969\pi$
$360$	−2.83270	−0.149296
$361$	−18.2906	−0.962663
$362$	−12.2208	−0.642311
$363$	13.7029	0.719218
$364$	−3.09335	−0.162136
$365$	−2.34444	−0.122713
$366$	5.69913	0.297898
$367$	−32.1238	−1.67685	−0.838424	−	0.545019i	$-0.816522\pi$
$367$	−32.1238	−1.67685	−0.838424	+	0.545019i	$0.816522\pi$
$368$	30.7077	1.60075
$369$	−8.64858	−0.450227
$370$	20.4018	1.06064
$371$	0.365369	0.0189690
$372$	−2.90064	−0.150391
$373$	7.25455	0.375626	0.187813	−	0.982205i	$-0.439860\pi$
$373$	7.25455	0.375626	0.187813	+	0.982205i	$0.439860\pi$
$374$	−5.14530	−0.266057
$375$	−10.9598	−0.565962
$376$	0.107292	0.00553316
$377$	6.17630	0.318096
$378$	−10.7566	−0.553259
$379$	−32.4347	−1.66606	−0.833030	−	0.553228i	$-0.813396\pi$
$379$	−32.4347	−1.66606	−0.833030	+	0.553228i	$0.813396\pi$
$380$	−4.81910	−0.247215
$381$	9.75659	0.499845
$382$	−34.3349	−1.75673
$383$	−17.3602	−0.887063	−0.443532	−	0.896259i	$-0.646275\pi$
$383$	−17.3602	−0.887063	−0.443532	+	0.896259i	$0.646275\pi$
$384$	7.50938	0.383212
$385$	3.37125	0.171815
$386$	44.6849	2.27440
$387$	3.19616	0.162470
$388$	−16.1724	−0.821031
$389$	9.74397	0.494039	0.247020	−	0.969010i	$-0.420549\pi$
$389$	9.74397	0.494039	0.247020	+	0.969010i	$0.420549\pi$
$390$	−17.2315	−0.872550
$391$	−18.7445	−0.947948
$392$	0.702124	0.0354626
$393$	8.80746	0.444278
$394$	−45.2881	−2.28158
$395$	17.4391	0.877458
$396$	−1.80445	−0.0906771
$397$	−28.7269	−1.44176	−0.720881	−	0.693059i	$-0.756262\pi$
$397$	−28.7269	−1.44176	−0.720881	+	0.693059i	$0.756262\pi$
$398$	8.79820	0.441014
$399$	1.14546	0.0573445
$400$	−33.5791	−1.67896
$401$	36.3380	1.81463	0.907316	−	0.420449i	$-0.138127\pi$
$401$	36.3380	1.81463	0.907316	+	0.420449i	$0.138127\pi$
$402$	−0.629279	−0.0313856
$403$	−2.47847	−0.123462
$404$	−21.4634	−1.06785
$405$	−14.8168	−0.736253
$406$	6.20796	0.308096
$407$	−2.93480	−0.145473
$408$	−2.68187	−0.132772
$409$	−14.2036	−0.702321	−0.351160	−	0.936315i	$-0.614213\pi$
$409$	−14.2036	−0.702321	−0.351160	+	0.936315i	$0.614213\pi$
$410$	−50.2389	−2.48112
$411$	−24.0654	−1.18706
$412$	17.7557	0.874758
$413$	−8.78411	−0.432238
$414$	−14.6318	−0.719114
$415$	−57.7579	−2.83523
$416$	−13.9617	−0.684528
$417$	30.5268	1.49490
$418$	1.54300	0.0754706
$419$	−11.9299	−0.582814	−0.291407	−	0.956599i	$-0.594123\pi$
$419$	−11.9299	−0.582814	−0.291407	+	0.956599i	$0.594123\pi$
$420$	−7.78132	−0.379689
$421$	−2.21899	−0.108147	−0.0540736	−	0.998537i	$-0.517221\pi$
$421$	−2.21899	−0.108147	−0.0540736	+	0.998537i	$0.517221\pi$
$422$	38.6418	1.88105
$423$	−0.175801	−0.00854775
$424$	0.256535	0.0124584
$425$	20.4972	0.994261
$426$	−7.54103	−0.365364
$427$	2.19902	0.106418
$428$	10.3045	0.498085
$429$	2.47875	0.119675
$430$	18.5662	0.895343
$431$	5.70394	0.274749	0.137374	−	0.990519i	$-0.456134\pi$
$431$	5.70394	0.274749	0.137374	+	0.990519i	$0.456134\pi$
$432$	−25.9713	−1.24954
$433$	18.9290	0.909672	0.454836	−	0.890575i	$-0.349698\pi$
$433$	18.9290	0.909672	0.454836	+	0.890575i	$0.349698\pi$
$434$	−2.49118	−0.119580
$435$	15.5365	0.744917
$436$	20.4075	0.977340
$437$	5.62119	0.268898
$438$	−1.73261	−0.0827873
$439$	−12.8593	−0.613743	−0.306871	−	0.951751i	$-0.599282\pi$
$439$	−12.8593	−0.613743	−0.306871	+	0.951751i	$0.599282\pi$
$440$	2.36704	0.112844
$441$	−1.15045	−0.0547835
$442$	10.1476	0.482671
$443$	−24.9659	−1.18617	−0.593084	−	0.805141i	$-0.702090\pi$
$443$	−24.9659	−1.18617	−0.593084	+	0.805141i	$0.702090\pi$
$444$	6.77392	0.321476
$445$	−51.3922	−2.43622
$446$	−47.6983	−2.25858
$447$	−18.8766	−0.892832
$448$	−4.83099	−0.228243
$449$	−37.6068	−1.77477	−0.887387	−	0.461026i	$-0.847481\pi$
$449$	−37.6068	−1.77477	−0.887387	+	0.461026i	$0.847481\pi$
$450$	16.0000	0.754247
$451$	7.22687	0.340300
$452$	−18.4850	−0.869462
$453$	−4.69683	−0.220676
$454$	−49.1892	−2.30856
$455$	−6.64880	−0.311701
$456$	0.804252	0.0376626
$457$	3.60631	0.168696	0.0843479	−	0.996436i	$-0.473119\pi$
$457$	3.60631	0.168696	0.0843479	+	0.996436i	$0.473119\pi$
$458$	−41.3608	−1.93266
$459$	15.8533	0.739966
$460$	−38.1859	−1.78043
$461$	−17.9370	−0.835412	−0.417706	−	0.908582i	$-0.637166\pi$
$461$	−17.9370	−0.835412	−0.417706	+	0.908582i	$0.637166\pi$
$462$	2.49145	0.115913
$463$	7.29677	0.339110	0.169555	−	0.985521i	$-0.445767\pi$
$463$	7.29677	0.339110	0.169555	+	0.985521i	$0.445767\pi$
$464$	14.9888	0.695838
$465$	−6.23460	−0.289123
$466$	30.6984	1.42208
$467$	38.4428	1.77892	0.889460	−	0.457014i	$-0.151081\pi$
$467$	38.4428	1.77892	0.889460	+	0.457014i	$0.151081\pi$
$468$	3.55875	0.164503
$469$	−0.242808	−0.0112119
$470$	−1.02122	−0.0471052
$471$	−22.5886	−1.04083
$472$	−6.16754	−0.283884
$473$	−2.67075	−0.122801
$474$	12.8880	0.591967
$475$	−6.14681	−0.282035
$476$	4.58240	0.210034
$477$	−0.420340	−0.0192460
$478$	19.8531	0.908059
$479$	−30.7222	−1.40373	−0.701866	−	0.712309i	$-0.747649\pi$
$479$	−30.7222	−1.40373	−0.701866	+	0.712309i	$0.747649\pi$
$480$	−35.1206	−1.60303
$481$	5.78803	0.263911
$482$	50.4182	2.29649
$483$	9.07644	0.412992
$484$	−16.4393	−0.747242
$485$	−34.7608	−1.57841
$486$	21.3197	0.967082
$487$	−5.94959	−0.269601	−0.134801	−	0.990873i	$-0.543039\pi$
$487$	−5.94959	−0.269601	−0.134801	+	0.990873i	$0.543039\pi$
$488$	1.54399	0.0698929
$489$	11.3689	0.514122
$490$	−6.68289	−0.301902
$491$	−15.8636	−0.715914	−0.357957	−	0.933738i	$-0.616527\pi$
$491$	−15.8636	−0.715914	−0.357957	+	0.933738i	$0.616527\pi$
$492$	−16.6806	−0.752020
$493$	−9.14940	−0.412068
$494$	−3.04311	−0.136916
$495$	−3.87847	−0.174324
$496$	−6.01483	−0.270074
$497$	−2.90972	−0.130519
$498$	−42.6848	−1.91275
$499$	22.3516	1.00060	0.500298	−	0.865854i	$-0.333224\pi$
$499$	22.3516	1.00060	0.500298	+	0.865854i	$0.333224\pi$
$500$	13.1484	0.588014
$501$	30.7385	1.37330
$502$	21.0140	0.937899
$503$	−17.7505	−0.791457	−0.395729	−	0.918368i	$-0.629508\pi$
$503$	−17.7505	−0.791457	−0.395729	+	0.918368i	$0.629508\pi$
$504$	−0.807761	−0.0359805
$505$	−46.1333	−2.05290
$506$	12.2265	0.543535
$507$	12.7911	0.568075
$508$	−11.7049	−0.519322
$509$	−1.97975	−0.0877507	−0.0438754	−	0.999037i	$-0.513970\pi$
$509$	−1.97975	−0.0877507	−0.0438754	+	0.999037i	$0.513970\pi$
$510$	25.5262	1.13032
$511$	−0.668531	−0.0295741
$512$	−27.4215	−1.21187
$513$	−4.75416	−0.209901
$514$	−5.96813	−0.263243
$515$	38.1638	1.68170
$516$	6.16446	0.271375
$517$	0.146902	0.00646073
$518$	5.81770	0.255615
$519$	−0.100607	−0.00441617
$520$	−4.66829	−0.204718
$521$	8.86670	0.388457	0.194229	−	0.980956i	$-0.437780\pi$
$521$	8.86670	0.388457	0.194229	+	0.980956i	$0.437780\pi$
$522$	−7.14197	−0.312595
$523$	−0.360339	−0.0157565	−0.00787825	−	0.999969i	$-0.502508\pi$
$523$	−0.360339	−0.0157565	−0.00787825	+	0.999969i	$0.502508\pi$
$524$	−10.5663	−0.461589
$525$	−9.92516	−0.433169
$526$	13.5106	0.589088
$527$	3.67154	0.159935
$528$	6.01549	0.261791
$529$	21.5416	0.936591
$530$	−2.44172	−0.106062
$531$	10.1057	0.438550
$532$	−1.37419	−0.0595789
$533$	−14.2529	−0.617360
$534$	−37.9803	−1.64357
$535$	22.1483	0.957554
$536$	−0.170482	−0.00736369
$537$	−3.38150	−0.145923
$538$	16.1784	0.697501
$539$	0.961333	0.0414075
$540$	32.2960	1.38980
$541$	−33.1030	−1.42321	−0.711605	−	0.702580i	$-0.752031\pi$
$541$	−33.1030	−1.42321	−0.711605	+	0.702580i	$0.752031\pi$
$542$	−50.0464	−2.14968
$543$	−8.72139	−0.374271
$544$	20.6825	0.886753
$545$	43.8635	1.87891
$546$	−4.91366	−0.210285
$547$	−22.8738	−0.978012	−0.489006	−	0.872280i	$-0.662640\pi$
$547$	−22.8738	−0.978012	−0.489006	+	0.872280i	$0.662640\pi$
$548$	28.8711	1.23331
$549$	−2.52987	−0.107972
$550$	−13.3698	−0.570090
$551$	2.74377	0.116889
$552$	6.37279	0.271244
$553$	4.97288	0.211468
$554$	−14.2681	−0.606192
$555$	14.5598	0.618028
$556$	−36.6227	−1.55315
$557$	8.81487	0.373498	0.186749	−	0.982408i	$-0.440205\pi$
$557$	8.81487	0.373498	0.186749	+	0.982408i	$0.440205\pi$
$558$	2.86598	0.121327
$559$	5.26727	0.222782
$560$	−16.1355	−0.681849
$561$	−3.67195	−0.155030
$562$	−52.8204	−2.22809
$563$	27.7604	1.16996	0.584981	−	0.811047i	$-0.301102\pi$
$563$	27.7604	1.16996	0.584981	+	0.811047i	$0.301102\pi$
$564$	−0.339070	−0.0142774
$565$	−39.7315	−1.67152
$566$	−14.7047	−0.618085
$567$	−4.22510	−0.177438
$568$	−2.04298	−0.0857217
$569$	−19.5445	−0.819349	−0.409674	−	0.912232i	$-0.634358\pi$
$569$	−19.5445	−0.819349	−0.409674	+	0.912232i	$0.634358\pi$
$570$	−7.65495	−0.320630
$571$	−22.8648	−0.956862	−0.478431	−	0.878125i	$-0.658794\pi$
$571$	−22.8648	−0.956862	−0.478431	+	0.878125i	$0.658794\pi$
$572$	−2.97374	−0.124338
$573$	−24.5031	−1.02363
$574$	−14.3259	−0.597953
$575$	−48.7066	−2.03120
$576$	5.55783	0.231576
$577$	−26.0786	−1.08567	−0.542833	−	0.839840i	$-0.682648\pi$
$577$	−26.0786	−1.08567	−0.542833	+	0.839840i	$0.682648\pi$
$578$	17.3640	0.722245
$579$	31.8894	1.32528
$580$	−18.6390	−0.773943
$581$	−16.4700	−0.683292
$582$	−25.6893	−1.06486
$583$	0.351241	0.0145469
$584$	−0.469392	−0.0194236
$585$	7.64913	0.316253
$586$	45.8001	1.89198
$587$	−2.85020	−0.117640	−0.0588201	−	0.998269i	$-0.518734\pi$
$587$	−2.85020	−0.117640	−0.0588201	+	0.998269i	$0.518734\pi$
$588$	−2.21889	−0.0915055
$589$	−1.10104	−0.0453677
$590$	58.7032	2.41677
$591$	−32.3200	−1.32947
$592$	14.0465	0.577309
$593$	−32.5432	−1.33639	−0.668195	−	0.743987i	$-0.732933\pi$
$593$	−32.5432	−1.33639	−0.668195	+	0.743987i	$0.732933\pi$
$594$	−10.3407	−0.424283
$595$	9.84935	0.403784
$596$	22.6461	0.927621
$597$	6.27885	0.256976
$598$	−24.1132	−0.986063
$599$	21.5736	0.881474	0.440737	−	0.897636i	$-0.354717\pi$
$599$	21.5736	0.881474	0.440737	+	0.897636i	$0.354717\pi$
$600$	−6.96869	−0.284496
$601$	−13.8517	−0.565022	−0.282511	−	0.959264i	$-0.591167\pi$
$601$	−13.8517	−0.565022	−0.282511	+	0.959264i	$0.591167\pi$
$602$	5.29427	0.215778
$603$	0.279340	0.0113756
$604$	5.63476	0.229275
$605$	−35.3345	−1.43655
$606$	−34.0938	−1.38497
$607$	−31.3875	−1.27398	−0.636990	−	0.770872i	$-0.719821\pi$
$607$	−31.3875	−1.27398	−0.636990	+	0.770872i	$0.719821\pi$
$608$	−6.20237	−0.251539
$609$	4.43032	0.179526
$610$	−14.6958	−0.595016
$611$	−0.289721	−0.0117208
$612$	−5.27183	−0.213101
$613$	16.5766	0.669522	0.334761	−	0.942303i	$-0.391344\pi$
$613$	16.5766	0.669522	0.334761	+	0.942303i	$0.391344\pi$
$614$	20.9651	0.846082
$615$	−35.8531	−1.44574
$616$	0.674975	0.0271955
$617$	7.79231	0.313706	0.156853	−	0.987622i	$-0.449865\pi$
$617$	7.79231	0.313706	0.156853	+	0.987622i	$0.449865\pi$
$618$	28.2042	1.13454
$619$	−7.08048	−0.284588	−0.142294	−	0.989824i	$-0.545448\pi$
$619$	−7.08048	−0.284588	−0.142294	+	0.989824i	$0.545448\pi$
$620$	7.47961	0.300388
$621$	−37.6713	−1.51170
$622$	24.1588	0.968679
$623$	−14.6548	−0.587131
$624$	−11.8638	−0.474932
$625$	−8.22907	−0.329163
$626$	−7.72241	−0.308649
$627$	1.10116	0.0439762
$628$	27.0994	1.08138
$629$	−8.57422	−0.341877
$630$	7.68834	0.306311
$631$	−14.7755	−0.588203	−0.294102	−	0.955774i	$-0.595020\pi$
$631$	−14.7755	−0.588203	−0.294102	+	0.955774i	$0.595020\pi$
$632$	3.49158	0.138887
$633$	27.5768	1.09608
$634$	−15.7838	−0.626856
$635$	−25.1584	−0.998380
$636$	−0.810714	−0.0321469
$637$	−1.89595	−0.0751201
$638$	5.96792	0.236272
$639$	3.34749	0.132425
$640$	−19.3637	−0.765418
$641$	6.15809	0.243230	0.121615	−	0.992577i	$-0.461193\pi$
$641$	6.15809	0.243230	0.121615	+	0.992577i	$0.461193\pi$
$642$	16.3682	0.646003
$643$	−13.1985	−0.520497	−0.260249	−	0.965542i	$-0.583805\pi$
$643$	−13.1985	−0.520497	−0.260249	+	0.965542i	$0.583805\pi$
$644$	−10.8889	−0.429084
$645$	13.2498	0.521711
$646$	4.50798	0.177364
$647$	4.59949	0.180825	0.0904123	−	0.995904i	$-0.471182\pi$
$647$	4.59949	0.180825	0.0904123	+	0.995904i	$0.471182\pi$
$648$	−2.96655	−0.116537
$649$	−8.44445	−0.331474
$650$	26.3680	1.03424
$651$	−1.77783	−0.0696788
$652$	−13.6393	−0.534154
$653$	−0.842895	−0.0329850	−0.0164925	−	0.999864i	$-0.505250\pi$
$653$	−0.842895	−0.0329850	−0.0164925	+	0.999864i	$0.505250\pi$
$654$	32.4164	1.26758
$655$	−22.7110	−0.887391
$656$	−34.5892	−1.35048
$657$	0.769113	0.0300059
$658$	−0.291206	−0.0113524
$659$	−26.1909	−1.02025	−0.510127	−	0.860099i	$-0.670402\pi$
$659$	−26.1909	−1.02025	−0.510127	+	0.860099i	$0.670402\pi$
$660$	−7.48043	−0.291176
$661$	32.5012	1.26415	0.632074	−	0.774908i	$-0.282204\pi$
$661$	32.5012	1.26415	0.632074	+	0.774908i	$0.282204\pi$
$662$	−26.2333	−1.01959
$663$	7.24184	0.281250
$664$	−11.5640	−0.448770
$665$	−2.95368	−0.114539
$666$	−6.69298	−0.259348
$667$	21.7413	0.841826
$668$	−36.8768	−1.42681
$669$	−34.0399	−1.31606
$670$	1.62266	0.0626889
$671$	2.11399	0.0816097
$672$	−10.0149	−0.386331
$673$	30.5763	1.17863	0.589314	−	0.807904i	$-0.299398\pi$
$673$	30.5763	1.17863	0.589314	+	0.807904i	$0.299398\pi$
$674$	2.07836	0.0800556
$675$	41.1939	1.58555
$676$	−15.3455	−0.590210
$677$	49.1459	1.88883	0.944415	−	0.328756i	$-0.106629\pi$
$677$	49.1459	1.88883	0.944415	+	0.328756i	$0.106629\pi$
$678$	−29.3627	−1.12767
$679$	−9.91226	−0.380398
$680$	6.91547	0.265196
$681$	−35.1039	−1.34519
$682$	−2.39485	−0.0917037
$683$	−9.43751	−0.361116	−0.180558	−	0.983564i	$-0.557790\pi$
$683$	−9.43751	−0.361116	−0.180558	+	0.983564i	$0.557790\pi$
$684$	1.58095	0.0604490
$685$	62.0552	2.37101
$686$	−1.90567	−0.0727586
$687$	−29.5172	−1.12615
$688$	12.7828	0.487338
$689$	−0.692720	−0.0263905
$690$	−60.6568	−2.30917
$691$	−46.2996	−1.76132	−0.880660	−	0.473748i	$-0.842901\pi$
$691$	−46.2996	−1.76132	−0.880660	+	0.473748i	$0.842901\pi$
$692$	0.120698	0.00458824
$693$	−1.10597	−0.0420122
$694$	43.4502	1.64935
$695$	−78.7165	−2.98589
$696$	3.11064	0.117908
$697$	21.1138	0.799742
$698$	−59.3580	−2.24673
$699$	21.9080	0.828635
$700$	11.9071	0.450048
$701$	−23.0854	−0.871924	−0.435962	−	0.899965i	$-0.643592\pi$
$701$	−23.0854	−0.871924	−0.435962	+	0.899965i	$0.643592\pi$
$702$	20.3939	0.769719
$703$	2.57128	0.0969778
$704$	−4.64419	−0.175035
$705$	−0.728792	−0.0274479
$706$	−53.3802	−2.00899
$707$	−13.1552	−0.494751
$708$	19.4910	0.732515
$709$	12.7960	0.480565	0.240282	−	0.970703i	$-0.422760\pi$
$709$	12.7960	0.480565	0.240282	+	0.970703i	$0.422760\pi$
$710$	19.4453	0.729770
$711$	−5.72106	−0.214556
$712$	−10.2895	−0.385615
$713$	−8.72452	−0.326736
$714$	7.27896	0.272408
$715$	−6.39171	−0.239036
$716$	4.05676	0.151608
$717$	14.1682	0.529121
$718$	−22.9685	−0.857177
$719$	−46.3619	−1.72901	−0.864504	−	0.502626i	$-0.832367\pi$
$719$	−46.3619	−1.72901	−0.864504	+	0.502626i	$0.832367\pi$
$720$	18.5631	0.691807
$721$	10.8826	0.405290
$722$	34.8558	1.29720
$723$	35.9810	1.33815
$724$	10.4630	0.388854
$725$	−23.7743	−0.882954
$726$	−26.1132	−0.969153
$727$	7.68959	0.285191	0.142596	−	0.989781i	$-0.454455\pi$
$727$	7.68959	0.285191	0.142596	+	0.989781i	$0.454455\pi$
$728$	−1.33119	−0.0493372
$729$	27.8902	1.03297
$730$	4.46771	0.165358
$731$	−7.80279	−0.288597
$732$	−4.87938	−0.180347
$733$	−7.31478	−0.270178	−0.135089	−	0.990833i	$-0.543132\pi$
$733$	−7.31478	−0.270178	−0.135089	+	0.990833i	$0.543132\pi$
$734$	61.2172	2.25957
$735$	−4.76925	−0.175916
$736$	−49.1467	−1.81157
$737$	−0.233420	−0.00859812
$738$	16.4813	0.606685
$739$	−1.96664	−0.0723441	−0.0361720	−	0.999346i	$-0.511516\pi$
$739$	−1.96664	−0.0723441	−0.0361720	+	0.999346i	$0.511516\pi$
$740$	−17.4673	−0.642109
$741$	−2.17172	−0.0797802
$742$	−0.696271	−0.0255609
$743$	31.5766	1.15843	0.579217	−	0.815173i	$-0.303358\pi$
$743$	31.5766	1.15843	0.579217	+	0.815173i	$0.303358\pi$
$744$	−1.24826	−0.0457635
$745$	48.6752	1.78332
$746$	−13.8247	−0.506160
$747$	18.9480	0.693270
$748$	4.40521	0.161070
$749$	6.31572	0.230771
$750$	20.8857	0.762638
$751$	16.3767	0.597593	0.298797	−	0.954317i	$-0.403415\pi$
$751$	16.3767	0.597593	0.298797	+	0.954317i	$0.403415\pi$
$752$	−0.703102	−0.0256395
$753$	14.9966	0.546508
$754$	−11.7700	−0.428637
$755$	12.1113	0.440774
$756$	9.20939	0.334942
$757$	−14.5086	−0.527323	−0.263661	−	0.964615i	$-0.584930\pi$
$757$	−14.5086	−0.527323	−0.263661	+	0.964615i	$0.584930\pi$
$758$	61.8097	2.24503
$759$	8.72548	0.316715
$760$	−2.07385	−0.0752264
$761$	11.4258	0.414185	0.207093	−	0.978321i	$-0.433600\pi$
$761$	11.4258	0.414185	0.207093	+	0.978321i	$0.433600\pi$
$762$	−18.5928	−0.673546
$763$	12.5079	0.452818
$764$	29.3962	1.06352
$765$	−11.3312	−0.409681
$766$	33.0827	1.19533
$767$	16.6542	0.601348
$768$	−27.4505	−0.990534
$769$	−30.1510	−1.08727	−0.543637	−	0.839321i	$-0.682953\pi$
$769$	−30.1510	−1.08727	−0.543637	+	0.839321i	$0.682953\pi$
$770$	−6.42448	−0.231522
$771$	−4.25917	−0.153390
$772$	−38.2575	−1.37692
$773$	26.0479	0.936879	0.468439	−	0.883496i	$-0.344816\pi$
$773$	26.0479	0.936879	0.468439	+	0.883496i	$0.344816\pi$
$774$	−6.09081	−0.218930
$775$	9.54033	0.342699
$776$	−6.95964	−0.249837
$777$	4.15181	0.148945
$778$	−18.5688	−0.665722
$779$	−6.33172	−0.226857
$780$	14.7530	0.528241
$781$	−2.79721	−0.100092
$782$	35.7207	1.27737
$783$	−18.3878	−0.657128
$784$	−4.60113	−0.164326
$785$	58.2470	2.07893
$786$	−16.7841	−0.598668
$787$	20.0453	0.714537	0.357268	−	0.934002i	$-0.383708\pi$
$787$	20.0453	0.714537	0.357268	+	0.934002i	$0.383708\pi$
$788$	38.7740	1.38127
$789$	9.64183	0.343258
$790$	−33.2332	−1.18238
$791$	−11.3297	−0.402837
$792$	−0.776527	−0.0275927
$793$	−4.16922	−0.148053
$794$	54.7438	1.94279
$795$	−1.74254	−0.0618014
$796$	−7.53269	−0.266989
$797$	31.3863	1.11176	0.555880	−	0.831262i	$-0.312381\pi$
$797$	31.3863	1.11176	0.555880	+	0.831262i	$0.312381\pi$
$798$	−2.18285	−0.0772722
$799$	0.429184	0.0151834
$800$	53.7423	1.90008
$801$	16.8596	0.595706
$802$	−69.2480	−2.44523
$803$	−0.642680	−0.0226797
$804$	0.538765	0.0190008
$805$	−23.4046	−0.824902
$806$	4.72314	0.166366
$807$	11.5457	0.406430
$808$	−9.23657	−0.324941
$809$	13.4488	0.472836	0.236418	−	0.971651i	$-0.424026\pi$
$809$	13.4488	0.472836	0.236418	+	0.971651i	$0.424026\pi$
$810$	28.2359	0.992107
$811$	−29.6868	−1.04245	−0.521223	−	0.853421i	$-0.674524\pi$
$811$	−29.6868	−1.04245	−0.521223	+	0.853421i	$0.674524\pi$
$812$	−5.31503	−0.186521
$813$	−35.7157	−1.25260
$814$	5.59274	0.196025
$815$	−29.3160	−1.02690
$816$	17.5747	0.615237
$817$	2.33994	0.0818642
$818$	27.0672	0.946383
$819$	2.18120	0.0762171
$820$	43.0127	1.50207
$821$	34.0480	1.18828	0.594142	−	0.804360i	$-0.297492\pi$
$821$	34.0480	1.18828	0.594142	+	0.804360i	$0.297492\pi$
$822$	45.8607	1.59957
$823$	30.5275	1.06412	0.532060	−	0.846707i	$-0.321418\pi$
$823$	30.5275	1.06412	0.532060	+	0.846707i	$0.321418\pi$
$824$	7.64096	0.266185
$825$	−9.54138	−0.332188
$826$	16.7396	0.582444
$827$	−32.8792	−1.14332	−0.571661	−	0.820490i	$-0.693701\pi$
$827$	−32.8792	−1.14332	−0.571661	+	0.820490i	$0.693701\pi$
$828$	12.5272	0.435351
$829$	12.8088	0.444866	0.222433	−	0.974948i	$-0.428600\pi$
$829$	12.8088	0.444866	0.222433	+	0.974948i	$0.428600\pi$
$830$	110.067	3.82049
$831$	−10.1824	−0.353224
$832$	9.15930	0.317542
$833$	2.80860	0.0973123
$834$	−58.1738	−2.01439
$835$	−79.2625	−2.74299
$836$	−1.32106	−0.0456898
$837$	7.37882	0.255049
$838$	22.7344	0.785347
$839$	−6.88699	−0.237765	−0.118883	−	0.992908i	$-0.537931\pi$
$839$	−6.88699	−0.237765	−0.118883	+	0.992908i	$0.537931\pi$
$840$	−3.34861	−0.115538
$841$	−18.3878	−0.634063
$842$	4.22866	0.145729
$843$	−37.6953	−1.29830
$844$	−33.0836	−1.13879
$845$	−32.9833	−1.13466
$846$	0.335018	0.0115182
$847$	−10.0758	−0.346210
$848$	−1.68111	−0.0577296
$849$	−10.4940	−0.360155
$850$	−39.0608	−1.33978
$851$	20.3745	0.698429
$852$	6.45634	0.221191
$853$	−46.0448	−1.57654	−0.788271	−	0.615328i	$-0.789024\pi$
$853$	−46.0448	−1.57654	−0.788271	+	0.615328i	$0.789024\pi$
$854$	−4.19060	−0.143399
$855$	3.39806	0.116211
$856$	4.43442	0.151565
$857$	31.1372	1.06363	0.531814	−	0.846861i	$-0.321511\pi$
$857$	31.1372	1.06363	0.531814	+	0.846861i	$0.321511\pi$
$858$	−4.72366	−0.161263
$859$	−43.0198	−1.46782	−0.733908	−	0.679249i	$-0.762306\pi$
$859$	−43.0198	−1.46782	−0.733908	+	0.679249i	$0.762306\pi$
$860$	−15.8957	−0.542039
$861$	−10.2237	−0.348423
$862$	−10.8698	−0.370227
$863$	1.00000	0.0340404
$863$	1.00000	0.0340404
$864$	41.5662	1.41411
$865$	0.259426	0.00882076
$866$	−36.0724	−1.22579
$867$	12.3918	0.420848
$868$	2.13286	0.0723938
$869$	4.78059	0.162170
$870$	−29.6073	−1.00378
$871$	0.460352	0.0155984
$872$	8.78213	0.297400
$873$	11.4036	0.385953
$874$	−10.7121	−0.362342
$875$	8.05879	0.272437
$876$	1.48340	0.0501193
$877$	1.33567	0.0451023	0.0225511	−	0.999746i	$-0.492821\pi$
$877$	1.33567	0.0451023	0.0225511	+	0.999746i	$0.492821\pi$
$878$	24.5056	0.827024
$879$	32.6853	1.10245
$880$	−15.5116	−0.522895
$881$	7.43173	0.250381	0.125191	−	0.992133i	$-0.460046\pi$
$881$	7.43173	0.250381	0.125191	+	0.992133i	$0.460046\pi$
$882$	2.19238	0.0738212
$883$	16.5559	0.557150	0.278575	−	0.960414i	$-0.410138\pi$
$883$	16.5559	0.557150	0.278575	+	0.960414i	$0.410138\pi$
$884$	−8.68798	−0.292209
$885$	41.8936	1.40824
$886$	47.5767	1.59837
$887$	47.0686	1.58041	0.790205	−	0.612843i	$-0.209974\pi$
$887$	47.0686	1.58041	0.790205	+	0.612843i	$0.209974\pi$
$888$	2.91509	0.0978239
$889$	−7.17406	−0.240610
$890$	97.9362	3.28283
$891$	−4.06173	−0.136073
$892$	40.8375	1.36734
$893$	−0.128706	−0.00430698
$894$	35.9724	1.20310
$895$	8.71956	0.291463
$896$	−5.52168	−0.184466
$897$	−17.2084	−0.574573
$898$	71.6659	2.39152
$899$	−4.25854	−0.142030
$900$	−13.6986	−0.456620
$901$	1.02618	0.0341869
$902$	−13.7720	−0.458557
$903$	3.77826	0.125733
$904$	−7.95483	−0.264574
$905$	22.4890	0.747560
$906$	8.95059	0.297363
$907$	4.54163	0.150802	0.0754012	−	0.997153i	$-0.475976\pi$
$907$	4.54163	0.150802	0.0754012	+	0.997153i	$0.475976\pi$
$908$	42.1140	1.39760
$909$	15.1344	0.501976
$910$	12.6704	0.420019
$911$	18.2142	0.603464	0.301732	−	0.953393i	$-0.402435\pi$
$911$	18.2142	0.603464	0.301732	+	0.953393i	$0.402435\pi$
$912$	−5.27039	−0.174520
$913$	−15.8332	−0.524002
$914$	−6.87241	−0.227319
$915$	−10.4877	−0.346712
$916$	35.4116	1.17003
$917$	−6.47617	−0.213862
$918$	−30.2110	−0.997111
$919$	−4.61368	−0.152191	−0.0760956	−	0.997101i	$-0.524245\pi$
$919$	−4.61368	−0.152191	−0.0760956	+	0.997101i	$0.524245\pi$
$920$	−16.4329	−0.541777
$921$	14.9618	0.493007
$922$	34.1820	1.12572
$923$	5.51667	0.181583
$924$	−2.13309	−0.0701735
$925$	−22.2797	−0.732552
$926$	−13.9052	−0.456954
$927$	−12.5199	−0.411209
$928$	−23.9891	−0.787482
$929$	−19.8903	−0.652579	−0.326290	−	0.945270i	$-0.605798\pi$
$929$	−19.8903	−0.652579	−0.326290	+	0.945270i	$0.605798\pi$
$930$	11.8811	0.389595
$931$	−0.842259	−0.0276039
$932$	−26.2828	−0.860922
$933$	17.2410	0.564444
$934$	−73.2590	−2.39711
$935$	9.46850	0.309653
$936$	1.53147	0.0500577
$937$	16.4590	0.537693	0.268846	−	0.963183i	$-0.413358\pi$
$937$	16.4590	0.537693	0.268846	+	0.963183i	$0.413358\pi$
$938$	0.462712	0.0151081
$939$	−5.51111	−0.179848
$940$	0.874327	0.0285174
$941$	−46.4297	−1.51357	−0.756783	−	0.653666i	$-0.773230\pi$
$941$	−46.4297	−1.51357	−0.756783	+	0.653666i	$0.773230\pi$
$942$	43.0463	1.40252
$943$	−50.1717	−1.63382
$944$	40.4168	1.31546
$945$	19.7946	0.643917
$946$	5.08956	0.165476
$947$	−55.9985	−1.81971	−0.909853	−	0.414931i	$-0.863806\pi$
$947$	−55.9985	−1.81971	−0.909853	+	0.414931i	$0.863806\pi$
$948$	−11.0343	−0.358376
$949$	1.26750	0.0411447
$950$	11.7138	0.380045
$951$	−11.2642	−0.365265
$952$	1.97199	0.0639125
$953$	37.5068	1.21496	0.607482	−	0.794334i	$-0.292180\pi$
$953$	37.5068	1.21496	0.607482	+	0.794334i	$0.292180\pi$
$954$	0.801027	0.0259342
$955$	63.1839	2.04458
$956$	−16.9975	−0.549738
$957$	4.25901	0.137674
$958$	58.5461	1.89154
$959$	17.6954	0.571415
$960$	23.0402	0.743620
$961$	−29.2911	−0.944874
$962$	−11.0300	−0.355623
$963$	−7.26593	−0.234141
$964$	−43.1662	−1.39029
$965$	−82.2303	−2.64709
$966$	−17.2967	−0.556511
$967$	40.8483	1.31359	0.656797	−	0.754068i	$-0.271911\pi$
$967$	40.8483	1.31359	0.656797	+	0.754068i	$0.271911\pi$
$968$	−7.07449	−0.227383
$969$	3.21713	0.103349
$970$	66.2425	2.12692
$971$	−3.56346	−0.114357	−0.0571784	−	0.998364i	$-0.518210\pi$
$971$	−3.56346	−0.114357	−0.0571784	+	0.998364i	$0.518210\pi$
$972$	−18.2532	−0.585470
$973$	−22.4465	−0.719601
$974$	11.3379	0.363290
$975$	18.8176	0.602644
$976$	−10.1180	−0.323869
$977$	−24.3392	−0.778679	−0.389339	−	0.921094i	$-0.627297\pi$
$977$	−24.3392	−0.778679	−0.389339	+	0.921094i	$0.627297\pi$
$978$	−21.6654	−0.692783
$979$	−14.0881	−0.450258
$980$	5.72164	0.182771
$981$	−14.3898	−0.459431
$982$	30.2307	0.964701
$983$	25.5570	0.815143	0.407572	−	0.913173i	$-0.366376\pi$
$983$	25.5570	0.815143	0.407572	+	0.913173i	$0.366376\pi$
$984$	−7.17832	−0.228837
$985$	83.3404	2.65545
$986$	17.4357	0.555266
$987$	−0.207819	−0.00661496
$988$	2.60540	0.0828888
$989$	18.5414	0.589582
$990$	7.39106	0.234903
$991$	−13.5827	−0.431468	−0.215734	−	0.976452i	$-0.569214\pi$
$991$	−13.5827	−0.431468	−0.215734	+	0.976452i	$0.569214\pi$
$992$	9.62655	0.305643
$993$	−18.7214	−0.594106
$994$	5.54495	0.175875
$995$	−16.1907	−0.513279
$996$	36.5452	1.15798
$997$	−34.6471	−1.09728	−0.548642	−	0.836057i	$-0.684855\pi$
$997$	−34.6471	−1.09728	−0.548642	+	0.836057i	$0.684855\pi$
$998$	−42.5947	−1.34831
$999$	−17.2319	−0.545193

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6041.2.a.c.1.16	✓	83

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6041.2.a.c.1.16	✓	83	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:	\( N \)	\(=\)	\( 6041 = 7 \cdot 863 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6041.a (trivial)

\(f(q)\)	\(=\)	\(q-1.90567 q^{2} -1.35998 q^{3} +1.63156 q^{4} +3.50685 q^{5} +2.59167 q^{6} +1.00000 q^{7} +0.702124 q^{8} -1.15045 q^{9} +O(q^{10})\)	\(q-1.90567 q^{2} -1.35998 q^{3} +1.63156 q^{4} +3.50685 q^{5} +2.59167 q^{6} +1.00000 q^{7} +0.702124 q^{8} -1.15045 q^{9} -6.68289 q^{10} +0.961333 q^{11} -2.21889 q^{12} -1.89595 q^{13} -1.90567 q^{14} -4.76925 q^{15} -4.60113 q^{16} +2.80860 q^{17} +2.19238 q^{18} -0.842259 q^{19} +5.72164 q^{20} -1.35998 q^{21} -1.83198 q^{22} -6.67395 q^{23} -0.954876 q^{24} +7.29801 q^{25} +3.61304 q^{26} +5.64454 q^{27} +1.63156 q^{28} -3.25764 q^{29} +9.08860 q^{30} +1.30725 q^{31} +7.36397 q^{32} -1.30739 q^{33} -5.35225 q^{34} +3.50685 q^{35} -1.87703 q^{36} -3.05284 q^{37} +1.60506 q^{38} +2.57845 q^{39} +2.46225 q^{40} +7.51755 q^{41} +2.59167 q^{42} -2.77818 q^{43} +1.56847 q^{44} -4.03447 q^{45} +12.7183 q^{46} +0.152811 q^{47} +6.25745 q^{48} +1.00000 q^{49} -13.9076 q^{50} -3.81964 q^{51} -3.09335 q^{52} +0.365369 q^{53} -10.7566 q^{54} +3.37125 q^{55} +0.702124 q^{56} +1.14546 q^{57} +6.20796 q^{58} -8.78411 q^{59} -7.78132 q^{60} +2.19902 q^{61} -2.49118 q^{62} -1.15045 q^{63} -4.83099 q^{64} -6.64880 q^{65} +2.49145 q^{66} -0.242808 q^{67} +4.58240 q^{68} +9.07644 q^{69} -6.68289 q^{70} -2.90972 q^{71} -0.807761 q^{72} -0.668531 q^{73} +5.81770 q^{74} -9.92516 q^{75} -1.37419 q^{76} +0.961333 q^{77} -4.91366 q^{78} +4.97288 q^{79} -16.1355 q^{80} -4.22510 q^{81} -14.3259 q^{82} -16.4700 q^{83} -2.21889 q^{84} +9.84935 q^{85} +5.29427 q^{86} +4.43032 q^{87} +0.674975 q^{88} -14.6548 q^{89} +7.68834 q^{90} -1.89595 q^{91} -10.8889 q^{92} -1.77783 q^{93} -0.291206 q^{94} -2.95368 q^{95} -10.0149 q^{96} -9.91226 q^{97} -1.90567 q^{98} -1.10597 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 83 q - 8 q^{2} - 12 q^{3} + 48 q^{4} - 11 q^{5} - 8 q^{6} + 83 q^{7} - 18 q^{8} + 39 q^{9}+O(q^{10}) \) 83 * q - 8 * q^2 - 12 * q^3 + 48 * q^4 - 11 * q^5 - 8 * q^6 + 83 * q^7 - 18 * q^8 + 39 * q^9	\( 83 q - 8 q^{2} - 12 q^{3} + 48 q^{4} - 11 q^{5} - 8 q^{6} + 83 q^{7} - 18 q^{8} + 39 q^{9} - 20 q^{10} - 26 q^{11} - 14 q^{12} - 22 q^{13} - 8 q^{14} - 37 q^{15} - 10 q^{16} - 9 q^{17} - 27 q^{18} - 42 q^{19} - 22 q^{20} - 12 q^{21} - 44 q^{22} - 46 q^{23} - 24 q^{24} - 20 q^{25} - 9 q^{26} - 39 q^{27} + 48 q^{28} - 36 q^{29} - 11 q^{30} - 107 q^{31} - 19 q^{32} - 25 q^{33} - 24 q^{34} - 11 q^{35} - 32 q^{36} - 75 q^{37} - 16 q^{38} - 78 q^{39} - 34 q^{40} - 17 q^{41} - 8 q^{42} - 87 q^{43} - 32 q^{44} - 17 q^{45} - 56 q^{46} - 39 q^{47} - 16 q^{48} + 83 q^{49} - 26 q^{50} - 71 q^{51} - 53 q^{52} - 28 q^{53} - 25 q^{54} - 94 q^{55} - 18 q^{56} - 79 q^{57} - 69 q^{58} - 26 q^{59} - 43 q^{60} - 56 q^{61} - 6 q^{62} + 39 q^{63} - 108 q^{64} - 26 q^{65} + 10 q^{66} - 123 q^{67} - 11 q^{68} + 2 q^{69} - 20 q^{70} - 96 q^{71} - 11 q^{72} - 53 q^{73} - 26 q^{74} - 27 q^{75} - 65 q^{76} - 26 q^{77} - 43 q^{78} - 160 q^{79} + 12 q^{80} - 53 q^{81} - 20 q^{82} - 2 q^{83} - 14 q^{84} - 110 q^{85} + 24 q^{86} - 52 q^{87} - 79 q^{88} - 5 q^{89} - 4 q^{90} - 22 q^{91} - 51 q^{92} - 30 q^{93} - 9 q^{94} - 76 q^{95} - 3 q^{96} - 44 q^{97} - 8 q^{98} - 82 q^{99}+O(q^{100}) \) 83 * q - 8 * q^2 - 12 * q^3 + 48 * q^4 - 11 * q^5 - 8 * q^6 + 83 * q^7 - 18 * q^8 + 39 * q^9 - 20 * q^10 - 26 * q^11 - 14 * q^12 - 22 * q^13 - 8 * q^14 - 37 * q^15 - 10 * q^16 - 9 * q^17 - 27 * q^18 - 42 * q^19 - 22 * q^20 - 12 * q^21 - 44 * q^22 - 46 * q^23 - 24 * q^24 - 20 * q^25 - 9 * q^26 - 39 * q^27 + 48 * q^28 - 36 * q^29 - 11 * q^30 - 107 * q^31 - 19 * q^32 - 25 * q^33 - 24 * q^34 - 11 * q^35 - 32 * q^36 - 75 * q^37 - 16 * q^38 - 78 * q^39 - 34 * q^40 - 17 * q^41 - 8 * q^42 - 87 * q^43 - 32 * q^44 - 17 * q^45 - 56 * q^46 - 39 * q^47 - 16 * q^48 + 83 * q^49 - 26 * q^50 - 71 * q^51 - 53 * q^52 - 28 * q^53 - 25 * q^54 - 94 * q^55 - 18 * q^56 - 79 * q^57 - 69 * q^58 - 26 * q^59 - 43 * q^60 - 56 * q^61 - 6 * q^62 + 39 * q^63 - 108 * q^64 - 26 * q^65 + 10 * q^66 - 123 * q^67 - 11 * q^68 + 2 * q^69 - 20 * q^70 - 96 * q^71 - 11 * q^72 - 53 * q^73 - 26 * q^74 - 27 * q^75 - 65 * q^76 - 26 * q^77 - 43 * q^78 - 160 * q^79 + 12 * q^80 - 53 * q^81 - 20 * q^82 - 2 * q^83 - 14 * q^84 - 110 * q^85 + 24 * q^86 - 52 * q^87 - 79 * q^88 - 5 * q^89 - 4 * q^90 - 22 * q^91 - 51 * q^92 - 30 * q^93 - 9 * q^94 - 76 * q^95 - 3 * q^96 - 44 * q^97 - 8 * q^98 - 82 * q^99

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