LMFDB - Embedded newform 4029.2.a.k.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.61491 q^{2} +1.00000 q^{3} +4.83775 q^{4} -2.62328 q^{5} -2.61491 q^{6} -4.80522 q^{7} -7.42046 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.61491 q^{2} +1.00000 q^{3} +4.83775 q^{4} -2.62328 q^{5} -2.61491 q^{6} -4.80522 q^{7} -7.42046 q^{8} +1.00000 q^{9} +6.85964 q^{10} +5.03885 q^{11} +4.83775 q^{12} -0.424255 q^{13} +12.5652 q^{14} -2.62328 q^{15} +9.72832 q^{16} +1.00000 q^{17} -2.61491 q^{18} -1.69266 q^{19} -12.6908 q^{20} -4.80522 q^{21} -13.1761 q^{22} +2.20587 q^{23} -7.42046 q^{24} +1.88160 q^{25} +1.10939 q^{26} +1.00000 q^{27} -23.2464 q^{28} +0.0142232 q^{29} +6.85964 q^{30} +4.78194 q^{31} -10.5978 q^{32} +5.03885 q^{33} -2.61491 q^{34} +12.6054 q^{35} +4.83775 q^{36} -11.1161 q^{37} +4.42615 q^{38} -0.424255 q^{39} +19.4659 q^{40} +10.7076 q^{41} +12.5652 q^{42} -2.19176 q^{43} +24.3767 q^{44} -2.62328 q^{45} -5.76814 q^{46} -11.5926 q^{47} +9.72832 q^{48} +16.0901 q^{49} -4.92021 q^{50} +1.00000 q^{51} -2.05244 q^{52} -1.42050 q^{53} -2.61491 q^{54} -13.2183 q^{55} +35.6569 q^{56} -1.69266 q^{57} -0.0371923 q^{58} -3.70537 q^{59} -12.6908 q^{60} -12.6621 q^{61} -12.5043 q^{62} -4.80522 q^{63} +8.25553 q^{64} +1.11294 q^{65} -13.1761 q^{66} -4.61390 q^{67} +4.83775 q^{68} +2.20587 q^{69} -32.9621 q^{70} -7.41269 q^{71} -7.42046 q^{72} -4.98159 q^{73} +29.0675 q^{74} +1.88160 q^{75} -8.18866 q^{76} -24.2128 q^{77} +1.10939 q^{78} +1.00000 q^{79} -25.5201 q^{80} +1.00000 q^{81} -27.9994 q^{82} +4.67216 q^{83} -23.2464 q^{84} -2.62328 q^{85} +5.73126 q^{86} +0.0142232 q^{87} -37.3906 q^{88} -1.95995 q^{89} +6.85964 q^{90} +2.03864 q^{91} +10.6714 q^{92} +4.78194 q^{93} +30.3135 q^{94} +4.44032 q^{95} -10.5978 q^{96} -13.9016 q^{97} -42.0742 q^{98} +5.03885 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9}+O(q^{10}) $ 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9	\( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9} + 5 q^{10} + 26 q^{11} + 34 q^{12} + 7 q^{13} + 19 q^{14} + 11 q^{15} + 40 q^{16} + 31 q^{17} + 4 q^{18} + 32 q^{19} + 23 q^{20} + 4 q^{21} + 2 q^{22} + 29 q^{23} + 12 q^{24} + 32 q^{25} + 13 q^{26} + 31 q^{27} - 13 q^{28} + 25 q^{29} + 5 q^{30} + 22 q^{31} + 28 q^{32} + 26 q^{33} + 4 q^{34} + 20 q^{35} + 34 q^{36} - 4 q^{37} + 19 q^{38} + 7 q^{39} - 3 q^{40} + 33 q^{41} + 19 q^{42} + 6 q^{43} + 30 q^{44} + 11 q^{45} - 11 q^{46} + 23 q^{47} + 40 q^{48} + 31 q^{49} + 6 q^{50} + 31 q^{51} - 7 q^{52} + 12 q^{53} + 4 q^{54} + 40 q^{56} + 32 q^{57} + 9 q^{58} + 27 q^{59} + 23 q^{60} - 4 q^{61} + 25 q^{62} + 4 q^{63} + 10 q^{64} + 54 q^{65} + 2 q^{66} + 34 q^{68} + 29 q^{69} - 59 q^{70} + 35 q^{71} + 12 q^{72} + 5 q^{73} + 48 q^{74} + 32 q^{75} + 32 q^{76} + 42 q^{77} + 13 q^{78} + 31 q^{79} + 24 q^{80} + 31 q^{81} + 5 q^{82} + 67 q^{83} - 13 q^{84} + 11 q^{85} - 20 q^{86} + 25 q^{87} - 7 q^{88} + 22 q^{89} + 5 q^{90} + 16 q^{91} + 57 q^{92} + 22 q^{93} + 45 q^{94} + 73 q^{95} + 28 q^{96} - 13 q^{97} - 19 q^{98} + 26 q^{99}+O(q^{100}) \) 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9 + 5 * q^10 + 26 * q^11 + 34 * q^12 + 7 * q^13 + 19 * q^14 + 11 * q^15 + 40 * q^16 + 31 * q^17 + 4 * q^18 + 32 * q^19 + 23 * q^20 + 4 * q^21 + 2 * q^22 + 29 * q^23 + 12 * q^24 + 32 * q^25 + 13 * q^26 + 31 * q^27 - 13 * q^28 + 25 * q^29 + 5 * q^30 + 22 * q^31 + 28 * q^32 + 26 * q^33 + 4 * q^34 + 20 * q^35 + 34 * q^36 - 4 * q^37 + 19 * q^38 + 7 * q^39 - 3 * q^40 + 33 * q^41 + 19 * q^42 + 6 * q^43 + 30 * q^44 + 11 * q^45 - 11 * q^46 + 23 * q^47 + 40 * q^48 + 31 * q^49 + 6 * q^50 + 31 * q^51 - 7 * q^52 + 12 * q^53 + 4 * q^54 + 40 * q^56 + 32 * q^57 + 9 * q^58 + 27 * q^59 + 23 * q^60 - 4 * q^61 + 25 * q^62 + 4 * q^63 + 10 * q^64 + 54 * q^65 + 2 * q^66 + 34 * q^68 + 29 * q^69 - 59 * q^70 + 35 * q^71 + 12 * q^72 + 5 * q^73 + 48 * q^74 + 32 * q^75 + 32 * q^76 + 42 * q^77 + 13 * q^78 + 31 * q^79 + 24 * q^80 + 31 * q^81 + 5 * q^82 + 67 * q^83 - 13 * q^84 + 11 * q^85 - 20 * q^86 + 25 * q^87 - 7 * q^88 + 22 * q^89 + 5 * q^90 + 16 * q^91 + 57 * q^92 + 22 * q^93 + 45 * q^94 + 73 * q^95 + 28 * q^96 - 13 * q^97 - 19 * q^98 + 26 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.61491	−1.84902	−0.924510	−	0.381158i	$-0.875525\pi$
$2$	−2.61491	−1.84902	−0.924510	+	0.381158i	$0.875525\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.83775	2.41887
$5$	−2.62328	−1.17317	−0.586583	−	0.809889i	$-0.699527\pi$
$5$	−2.62328	−1.17317	−0.586583	+	0.809889i	$0.699527\pi$
$6$	−2.61491	−1.06753
$7$	−4.80522	−1.81620	−0.908101	−	0.418751i	$-0.862468\pi$
$7$	−4.80522	−1.81620	−0.908101	+	0.418751i	$0.862468\pi$
$8$	−7.42046	−2.62353
$9$	1.00000	0.333333
$10$	6.85964	2.16921
$11$	5.03885	1.51927	0.759636	−	0.650349i	$-0.225377\pi$
$11$	5.03885	1.51927	0.759636	+	0.650349i	$0.225377\pi$
$12$	4.83775	1.39654
$13$	−0.424255	−0.117667	−0.0588336	−	0.998268i	$-0.518738\pi$
$13$	−0.424255	−0.117667	−0.0588336	+	0.998268i	$0.518738\pi$
$14$	12.5652	3.35819
$15$	−2.62328	−0.677328
$16$	9.72832	2.43208
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.61491	−0.616340
$19$	−1.69266	−0.388322	−0.194161	−	0.980970i	$-0.562198\pi$
$19$	−1.69266	−0.388322	−0.194161	+	0.980970i	$0.562198\pi$
$20$	−12.6908	−2.83774
$21$	−4.80522	−1.04858
$22$	−13.1761	−2.80916
$23$	2.20587	0.459955	0.229978	−	0.973196i	$-0.426135\pi$
$23$	2.20587	0.459955	0.229978	+	0.973196i	$0.426135\pi$
$24$	−7.42046	−1.51469
$25$	1.88160	0.376319
$26$	1.10939	0.217569
$27$	1.00000	0.192450
$28$	−23.2464	−4.39316
$29$	0.0142232	0.00264118	0.00132059	−	0.999999i	$-0.499580\pi$
$29$	0.0142232	0.00264118	0.00132059	+	0.999999i	$0.499580\pi$
$30$	6.85964	1.25239
$31$	4.78194	0.858861	0.429431	−	0.903100i	$-0.358714\pi$
$31$	4.78194	0.858861	0.429431	+	0.903100i	$0.358714\pi$
$32$	−10.5978	−1.87344
$33$	5.03885	0.877152
$34$	−2.61491	−0.448453
$35$	12.6054	2.13071
$36$	4.83775	0.806292
$37$	−11.1161	−1.82747	−0.913736	−	0.406309i	$-0.866816\pi$
$37$	−11.1161	−1.82747	−0.913736	+	0.406309i	$0.866816\pi$
$38$	4.42615	0.718016
$39$	−0.424255	−0.0679352
$40$	19.4659	3.07783
$41$	10.7076	1.67225	0.836124	−	0.548540i	$-0.184816\pi$
$41$	10.7076	1.67225	0.836124	+	0.548540i	$0.184816\pi$
$42$	12.5652	1.93885
$43$	−2.19176	−0.334241	−0.167120	−	0.985936i	$-0.553447\pi$
$43$	−2.19176	−0.334241	−0.167120	+	0.985936i	$0.553447\pi$
$44$	24.3767	3.67493
$45$	−2.62328	−0.391055
$46$	−5.76814	−0.850466
$47$	−11.5926	−1.69095	−0.845475	−	0.534014i	$-0.820683\pi$
$47$	−11.5926	−1.69095	−0.845475	+	0.534014i	$0.820683\pi$
$48$	9.72832	1.40416
$49$	16.0901	2.29859
$50$	−4.92021	−0.695822
$51$	1.00000	0.140028
$52$	−2.05244	−0.284622
$53$	−1.42050	−0.195120	−0.0975600	−	0.995230i	$-0.531104\pi$
$53$	−1.42050	−0.195120	−0.0975600	+	0.995230i	$0.531104\pi$
$54$	−2.61491	−0.355844
$55$	−13.2183	−1.78236
$56$	35.6569	4.76485
$57$	−1.69266	−0.224198
$58$	−0.0371923	−0.00488359
$59$	−3.70537	−0.482398	−0.241199	−	0.970476i	$-0.577541\pi$
$59$	−3.70537	−0.482398	−0.241199	+	0.970476i	$0.577541\pi$
$60$	−12.6908	−1.63837
$61$	−12.6621	−1.62122	−0.810609	−	0.585588i	$-0.800864\pi$
$61$	−12.6621	−1.62122	−0.810609	+	0.585588i	$0.800864\pi$
$62$	−12.5043	−1.58805
$63$	−4.80522	−0.605401
$64$	8.25553	1.03194
$65$	1.11294	0.138043
$66$	−13.1761	−1.62187
$67$	−4.61390	−0.563678	−0.281839	−	0.959462i	$-0.590944\pi$
$67$	−4.61390	−0.563678	−0.281839	+	0.959462i	$0.590944\pi$
$68$	4.83775	0.586663
$69$	2.20587	0.265555
$70$	−32.9621	−3.93972
$71$	−7.41269	−0.879724	−0.439862	−	0.898065i	$-0.644973\pi$
$71$	−7.41269	−0.879724	−0.439862	+	0.898065i	$0.644973\pi$
$72$	−7.42046	−0.874509
$73$	−4.98159	−0.583051	−0.291526	−	0.956563i	$-0.594163\pi$
$73$	−4.98159	−0.583051	−0.291526	+	0.956563i	$0.594163\pi$
$74$	29.0675	3.37903
$75$	1.88160	0.217268
$76$	−8.18866	−0.939303
$77$	−24.2128	−2.75930
$78$	1.10939	0.125614
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	−25.5201	−2.85323
$81$	1.00000	0.111111
$82$	−27.9994	−3.09202
$83$	4.67216	0.512837	0.256418	−	0.966566i	$-0.417458\pi$
$83$	4.67216	0.512837	0.256418	+	0.966566i	$0.417458\pi$
$84$	−23.2464	−2.53639
$85$	−2.62328	−0.284535
$86$	5.73126	0.618018
$87$	0.0142232	0.00152488
$88$	−37.3906	−3.98585
$89$	−1.95995	−0.207755	−0.103877	−	0.994590i	$-0.533125\pi$
$89$	−1.95995	−0.207755	−0.103877	+	0.994590i	$0.533125\pi$
$90$	6.85964	0.723069
$91$	2.03864	0.213708
$92$	10.6714	1.11257
$93$	4.78194	0.495864
$94$	30.3135	3.12660
$95$	4.44032	0.455567
$96$	−10.5978	−1.08163
$97$	−13.9016	−1.41150	−0.705748	−	0.708463i	$-0.749389\pi$
$97$	−13.9016	−1.41150	−0.705748	+	0.708463i	$0.749389\pi$
$98$	−42.0742	−4.25014
$99$	5.03885	0.506424
$100$	9.10270	0.910270
$101$	17.9380	1.78490	0.892448	−	0.451151i	$-0.148986\pi$
$101$	17.9380	1.78490	0.892448	+	0.451151i	$0.148986\pi$
$102$	−2.61491	−0.258915
$103$	6.26519	0.617328	0.308664	−	0.951171i	$-0.400118\pi$
$103$	6.26519	0.617328	0.308664	+	0.951171i	$0.400118\pi$
$104$	3.14817	0.308703
$105$	12.6054	1.23016
$106$	3.71447	0.360781
$107$	15.0928	1.45908	0.729538	−	0.683941i	$-0.239735\pi$
$107$	15.0928	1.45908	0.729538	+	0.683941i	$0.239735\pi$
$108$	4.83775	0.465513
$109$	−1.33822	−0.128179	−0.0640893	−	0.997944i	$-0.520414\pi$
$109$	−1.33822	−0.128179	−0.0640893	+	0.997944i	$0.520414\pi$
$110$	34.5647	3.29561
$111$	−11.1161	−1.05509
$112$	−46.7467	−4.41715
$113$	−11.1926	−1.05291	−0.526456	−	0.850202i	$-0.676480\pi$
$113$	−11.1926	−1.05291	−0.526456	+	0.850202i	$0.676480\pi$
$114$	4.42615	0.414547
$115$	−5.78661	−0.539604
$116$	0.0688081	0.00638868
$117$	−0.424255	−0.0392224
$118$	9.68921	0.891964
$119$	−4.80522	−0.440494
$120$	19.4659	1.77699
$121$	14.3900	1.30818
$122$	33.1103	2.99766
$123$	10.7076	0.965473
$124$	23.1338	2.07748
$125$	8.18044	0.731681
$126$	12.5652	1.11940
$127$	7.49201	0.664809	0.332404	−	0.943137i	$-0.392140\pi$
$127$	7.49201	0.664809	0.332404	+	0.943137i	$0.392140\pi$
$128$	−0.391945	−0.0346433
$129$	−2.19176	−0.192974
$130$	−2.91024	−0.255245
$131$	−9.03147	−0.789083	−0.394542	−	0.918878i	$-0.629097\pi$
$131$	−9.03147	−0.789083	−0.394542	+	0.918878i	$0.629097\pi$
$132$	24.3767	2.12172
$133$	8.13359	0.705272
$134$	12.0649	1.04225
$135$	−2.62328	−0.225776
$136$	−7.42046	−0.636299
$137$	17.5708	1.50117	0.750587	−	0.660771i	$-0.229771\pi$
$137$	17.5708	1.50117	0.750587	+	0.660771i	$0.229771\pi$
$138$	−5.76814	−0.491017
$139$	−7.16731	−0.607923	−0.303962	−	0.952684i	$-0.598309\pi$
$139$	−7.16731	−0.607923	−0.303962	+	0.952684i	$0.598309\pi$
$140$	60.9819	5.15391
$141$	−11.5926	−0.976271
$142$	19.3835	1.62663
$143$	−2.13776	−0.178768
$144$	9.72832	0.810693
$145$	−0.0373114	−0.00309854
$146$	13.0264	1.07807
$147$	16.0901	1.32709
$148$	−53.7768	−4.42042
$149$	−3.43129	−0.281102	−0.140551	−	0.990073i	$-0.544887\pi$
$149$	−3.43129	−0.281102	−0.140551	+	0.990073i	$0.544887\pi$
$150$	−4.92021	−0.401733
$151$	12.2495	0.996848	0.498424	−	0.866933i	$-0.333912\pi$
$151$	12.2495	0.996848	0.498424	+	0.866933i	$0.333912\pi$
$152$	12.5603	1.01877
$153$	1.00000	0.0808452
$154$	63.3142	5.10201
$155$	−12.5444	−1.00759
$156$	−2.05244	−0.164327
$157$	3.22816	0.257635	0.128818	−	0.991668i	$-0.458882\pi$
$157$	3.22816	0.257635	0.128818	+	0.991668i	$0.458882\pi$
$158$	−2.61491	−0.208031
$159$	−1.42050	−0.112653
$160$	27.8009	2.19785
$161$	−10.5997	−0.835372
$162$	−2.61491	−0.205447
$163$	12.3203	0.964997	0.482498	−	0.875897i	$-0.339729\pi$
$163$	12.3203	0.964997	0.482498	+	0.875897i	$0.339729\pi$
$164$	51.8007	4.04496
$165$	−13.2183	−1.02904
$166$	−12.2173	−0.948245
$167$	−12.1321	−0.938811	−0.469405	−	0.882983i	$-0.655532\pi$
$167$	−12.1321	−0.938811	−0.469405	+	0.882983i	$0.655532\pi$
$168$	35.6569	2.75099
$169$	−12.8200	−0.986154
$170$	6.85964	0.526110
$171$	−1.69266	−0.129441
$172$	−10.6032	−0.808486
$173$	21.7686	1.65504	0.827519	−	0.561438i	$-0.189752\pi$
$173$	21.7686	1.65504	0.827519	+	0.561438i	$0.189752\pi$
$174$	−0.0371923	−0.00281954
$175$	−9.04149	−0.683472
$176$	49.0196	3.69499
$177$	−3.70537	−0.278513
$178$	5.12510	0.384143
$179$	−14.3372	−1.07161	−0.535806	−	0.844341i	$-0.679992\pi$
$179$	−14.3372	−1.07161	−0.535806	+	0.844341i	$0.679992\pi$
$180$	−12.6908	−0.945914
$181$	18.8588	1.40177	0.700883	−	0.713276i	$-0.252789\pi$
$181$	18.8588	1.40177	0.700883	+	0.713276i	$0.252789\pi$
$182$	−5.33086	−0.395149
$183$	−12.6621	−0.936011
$184$	−16.3685	−1.20671
$185$	29.1606	2.14393
$186$	−12.5043	−0.916862
$187$	5.03885	0.368477
$188$	−56.0820	−4.09020
$189$	−4.80522	−0.349528
$190$	−11.6110	−0.842352
$191$	0.813947	0.0588951	0.0294476	−	0.999566i	$-0.490625\pi$
$191$	0.813947	0.0588951	0.0294476	+	0.999566i	$0.490625\pi$
$192$	8.25553	0.595791
$193$	15.2769	1.09966	0.549828	−	0.835278i	$-0.314693\pi$
$193$	15.2769	1.09966	0.549828	+	0.835278i	$0.314693\pi$
$194$	36.3515	2.60988
$195$	1.11294	0.0796993
$196$	77.8400	5.56000
$197$	18.6764	1.33064	0.665320	−	0.746558i	$-0.268295\pi$
$197$	18.6764	1.33064	0.665320	+	0.746558i	$0.268295\pi$
$198$	−13.1761	−0.936387
$199$	−0.597834	−0.0423793	−0.0211897	−	0.999775i	$-0.506745\pi$
$199$	−0.597834	−0.0423793	−0.0211897	+	0.999775i	$0.506745\pi$
$200$	−13.9623	−0.987284
$201$	−4.61390	−0.325439
$202$	−46.9062	−3.30031
$203$	−0.0683454	−0.00479691
$204$	4.83775	0.338710
$205$	−28.0891	−1.96183
$206$	−16.3829	−1.14145
$207$	2.20587	0.153318
$208$	−4.12729	−0.286176
$209$	−8.52906	−0.589967
$210$	−32.9621	−2.27460
$211$	20.2479	1.39392	0.696962	−	0.717108i	$-0.254535\pi$
$211$	20.2479	1.39392	0.696962	+	0.717108i	$0.254535\pi$
$212$	−6.87200	−0.471971
$213$	−7.41269	−0.507909
$214$	−39.4663	−2.69786
$215$	5.74961	0.392120
$216$	−7.42046	−0.504898
$217$	−22.9782	−1.55986
$218$	3.49933	0.237005
$219$	−4.98159	−0.336625
$220$	−63.9469	−4.31130
$221$	−0.424255	−0.0285385
$222$	29.0675	1.95088
$223$	−9.04780	−0.605886	−0.302943	−	0.953009i	$-0.597969\pi$
$223$	−9.04780	−0.605886	−0.302943	+	0.953009i	$0.597969\pi$
$224$	50.9245	3.40254
$225$	1.88160	0.125440
$226$	29.2677	1.94686
$227$	15.1259	1.00394	0.501971	−	0.864885i	$-0.332608\pi$
$227$	15.1259	1.00394	0.501971	+	0.864885i	$0.332608\pi$
$228$	−8.18866	−0.542307
$229$	11.4726	0.758128	0.379064	−	0.925370i	$-0.376246\pi$
$229$	11.4726	0.758128	0.379064	+	0.925370i	$0.376246\pi$
$230$	15.1315	0.997739
$231$	−24.2128	−1.59308
$232$	−0.105542	−0.00692920
$233$	6.68129	0.437706	0.218853	−	0.975758i	$-0.429769\pi$
$233$	6.68129	0.437706	0.218853	+	0.975758i	$0.429769\pi$
$234$	1.10939	0.0725230
$235$	30.4106	1.98377
$236$	−17.9257	−1.16686
$237$	1.00000	0.0649570
$238$	12.5652	0.814481
$239$	−23.0293	−1.48964	−0.744819	−	0.667266i	$-0.767464\pi$
$239$	−23.0293	−1.48964	−0.744819	+	0.667266i	$0.767464\pi$
$240$	−25.5201	−1.64732
$241$	8.26243	0.532230	0.266115	−	0.963941i	$-0.414260\pi$
$241$	8.26243	0.532230	0.266115	+	0.963941i	$0.414260\pi$
$242$	−37.6286	−2.41886
$243$	1.00000	0.0641500
$244$	−61.2562	−3.92152
$245$	−42.2089	−2.69663
$246$	−27.9994	−1.78518
$247$	0.718119	0.0456928
$248$	−35.4841	−2.25325
$249$	4.67216	0.296086
$250$	−21.3911	−1.35289
$251$	11.8050	0.745128	0.372564	−	0.928007i	$-0.378479\pi$
$251$	11.8050	0.745128	0.372564	+	0.928007i	$0.378479\pi$
$252$	−23.2464	−1.46439
$253$	11.1150	0.698797
$254$	−19.5909	−1.22924
$255$	−2.62328	−0.164276
$256$	−15.4862	−0.967885
$257$	23.7690	1.48267	0.741335	−	0.671135i	$-0.234193\pi$
$257$	23.7690	1.48267	0.741335	+	0.671135i	$0.234193\pi$
$258$	5.73126	0.356813
$259$	53.4152	3.31906
$260$	5.38413	0.333909
$261$	0.0142232	0.000880392 0
$262$	23.6165	1.45903
$263$	27.3452	1.68618	0.843089	−	0.537774i	$-0.180735\pi$
$263$	27.3452	1.68618	0.843089	+	0.537774i	$0.180735\pi$
$264$	−37.3906	−2.30123
$265$	3.72636	0.228908
$266$	−21.2686	−1.30406
$267$	−1.95995	−0.119947
$268$	−22.3209	−1.36347
$269$	−21.3647	−1.30263	−0.651314	−	0.758808i	$-0.725782\pi$
$269$	−21.3647	−1.30263	−0.651314	+	0.758808i	$0.725782\pi$
$270$	6.85964	0.417464
$271$	−10.5082	−0.638330	−0.319165	−	0.947699i	$-0.603402\pi$
$271$	−10.5082	−0.638330	−0.319165	+	0.947699i	$0.603402\pi$
$272$	9.72832	0.589866
$273$	2.03864	0.123384
$274$	−45.9460	−2.77570
$275$	9.48109	0.571731
$276$	10.6714	0.642345
$277$	−1.59108	−0.0955988	−0.0477994	−	0.998857i	$-0.515221\pi$
$277$	−1.59108	−0.0955988	−0.0477994	+	0.998857i	$0.515221\pi$
$278$	18.7419	1.12406
$279$	4.78194	0.286287
$280$	−93.5381	−5.58997
$281$	−26.3797	−1.57368	−0.786842	−	0.617155i	$-0.788285\pi$
$281$	−26.3797	−1.57368	−0.786842	+	0.617155i	$0.788285\pi$
$282$	30.3135	1.80514
$283$	17.1406	1.01890	0.509451	−	0.860500i	$-0.329848\pi$
$283$	17.1406	1.01890	0.509451	+	0.860500i	$0.329848\pi$
$284$	−35.8607	−2.12794
$285$	4.44032	0.263022
$286$	5.59005	0.330546
$287$	−51.4524	−3.03714
$288$	−10.5978	−0.624479
$289$	1.00000	0.0588235
$290$	0.0975658	0.00572926
$291$	−13.9016	−0.814927
$292$	−24.0997	−1.41033
$293$	15.7659	0.921052	0.460526	−	0.887646i	$-0.347661\pi$
$293$	15.7659	0.921052	0.460526	+	0.887646i	$0.347661\pi$
$294$	−42.0742	−2.45382
$295$	9.72023	0.565934
$296$	82.4863	4.79442
$297$	5.03885	0.292384
$298$	8.97251	0.519764
$299$	−0.935851	−0.0541217
$300$	9.10270	0.525544
$301$	10.5319	0.607049
$302$	−32.0313	−1.84319
$303$	17.9380	1.03051
$304$	−16.4667	−0.944431
$305$	33.2163	1.90196
$306$	−2.61491	−0.149484
$307$	−2.76806	−0.157981	−0.0789906	−	0.996875i	$-0.525170\pi$
$307$	−2.76806	−0.157981	−0.0789906	+	0.996875i	$0.525170\pi$
$308$	−117.135	−6.67441
$309$	6.26519	0.356414
$310$	32.8023	1.86305
$311$	19.7793	1.12158	0.560790	−	0.827958i	$-0.310498\pi$
$311$	19.7793	1.12158	0.560790	+	0.827958i	$0.310498\pi$
$312$	3.14817	0.178230
$313$	20.6041	1.16462	0.582308	−	0.812969i	$-0.302150\pi$
$313$	20.6041	1.16462	0.582308	+	0.812969i	$0.302150\pi$
$314$	−8.44134	−0.476373
$315$	12.6054	0.710236
$316$	4.83775	0.272145
$317$	−7.73561	−0.434475	−0.217237	−	0.976119i	$-0.569705\pi$
$317$	−7.73561	−0.434475	−0.217237	+	0.976119i	$0.569705\pi$
$318$	3.71447	0.208297
$319$	0.0716685	0.00401266
$320$	−21.6566	−1.21064
$321$	15.0928	0.842397
$322$	27.7172	1.54462
$323$	−1.69266	−0.0941820
$324$	4.83775	0.268764
$325$	−0.798278	−0.0442805
$326$	−32.2163	−1.78430
$327$	−1.33822	−0.0740039
$328$	−79.4554	−4.38719
$329$	55.7049	3.07111
$330$	34.5647	1.90272
$331$	−13.1774	−0.724296	−0.362148	−	0.932121i	$-0.617956\pi$
$331$	−13.1774	−0.724296	−0.362148	+	0.932121i	$0.617956\pi$
$332$	22.6028	1.24049
$333$	−11.1161	−0.609157
$334$	31.7244	1.73588
$335$	12.1036	0.661288
$336$	−46.7467	−2.55024
$337$	−15.7916	−0.860225	−0.430112	−	0.902775i	$-0.641526\pi$
$337$	−15.7916	−0.860225	−0.430112	+	0.902775i	$0.641526\pi$
$338$	33.5232	1.82342
$339$	−11.1926	−0.607899
$340$	−12.6908	−0.688254
$341$	24.0955	1.30484
$342$	4.42615	0.239339
$343$	−43.6800	−2.35850
$344$	16.2639	0.876890
$345$	−5.78661	−0.311541
$346$	−56.9230	−3.06020
$347$	−34.0392	−1.82732	−0.913661	−	0.406478i	$-0.866757\pi$
$347$	−34.0392	−1.82732	−0.913661	+	0.406478i	$0.866757\pi$
$348$	0.0688081	0.00368850
$349$	−13.3243	−0.713234	−0.356617	−	0.934251i	$-0.616070\pi$
$349$	−13.3243	−0.713234	−0.356617	+	0.934251i	$0.616070\pi$
$350$	23.6427	1.26375
$351$	−0.424255	−0.0226451
$352$	−53.4005	−2.84626
$353$	5.72620	0.304775	0.152387	−	0.988321i	$-0.451304\pi$
$353$	5.72620	0.304775	0.152387	+	0.988321i	$0.451304\pi$
$354$	9.68921	0.514976
$355$	19.4456	1.03206
$356$	−9.48177	−0.502533
$357$	−4.80522	−0.254319
$358$	37.4904	1.98143
$359$	−0.808049	−0.0426472	−0.0213236	−	0.999773i	$-0.506788\pi$
$359$	−0.808049	−0.0426472	−0.0213236	+	0.999773i	$0.506788\pi$
$360$	19.4659	1.02594
$361$	−16.1349	−0.849206
$362$	−49.3141	−2.59189
$363$	14.3900	0.755281
$364$	9.86243	0.516932
$365$	13.0681	0.684016
$366$	33.1103	1.73070
$367$	5.29883	0.276597	0.138298	−	0.990391i	$-0.455837\pi$
$367$	5.29883	0.276597	0.138298	+	0.990391i	$0.455837\pi$
$368$	21.4594	1.11865
$369$	10.7076	0.557416
$370$	−76.2523	−3.96417
$371$	6.82579	0.354377
$372$	23.1338	1.19943
$373$	−2.49991	−0.129440	−0.0647202	−	0.997903i	$-0.520616\pi$
$373$	−2.49991	−0.129440	−0.0647202	+	0.997903i	$0.520616\pi$
$374$	−13.1761	−0.681322
$375$	8.18044	0.422436
$376$	86.0222	4.43626
$377$	−0.00603426	−0.000310780 0
$378$	12.5652	0.646285
$379$	19.6511	1.00941	0.504705	−	0.863292i	$-0.331601\pi$
$379$	19.6511	1.00941	0.504705	+	0.863292i	$0.331601\pi$
$380$	21.4811	1.10196
$381$	7.49201	0.383827
$382$	−2.12840	−0.108898
$383$	23.5058	1.20109	0.600545	−	0.799591i	$-0.294950\pi$
$383$	23.5058	1.20109	0.600545	+	0.799591i	$0.294950\pi$
$384$	−0.391945	−0.0200013
$385$	63.5169	3.23712
$386$	−39.9478	−2.03329
$387$	−2.19176	−0.111414
$388$	−67.2525	−3.41423
$389$	−18.5680	−0.941437	−0.470718	−	0.882284i	$-0.656005\pi$
$389$	−18.5680	−0.941437	−0.470718	+	0.882284i	$0.656005\pi$
$390$	−2.91024	−0.147366
$391$	2.20587	0.111556
$392$	−119.396	−6.03041
$393$	−9.03147	−0.455577
$394$	−48.8371	−2.46038
$395$	−2.62328	−0.131992
$396$	24.3767	1.22498
$397$	−11.2993	−0.567096	−0.283548	−	0.958958i	$-0.591512\pi$
$397$	−11.2993	−0.567096	−0.283548	+	0.958958i	$0.591512\pi$
$398$	1.56328	0.0783602
$399$	8.13359	0.407189
$400$	18.3048	0.915239
$401$	12.9628	0.647331	0.323666	−	0.946172i	$-0.395085\pi$
$401$	12.9628	0.647331	0.323666	+	0.946172i	$0.395085\pi$
$402$	12.0649	0.601744
$403$	−2.02876	−0.101060
$404$	86.7794	4.31744
$405$	−2.62328	−0.130352
$406$	0.178717	0.00886958
$407$	−56.0123	−2.77642
$408$	−7.42046	−0.367367
$409$	32.4363	1.60387	0.801936	−	0.597410i	$-0.203803\pi$
$409$	32.4363	1.60387	0.801936	+	0.597410i	$0.203803\pi$
$410$	73.4504	3.62745
$411$	17.5708	0.866704
$412$	30.3094	1.49324
$413$	17.8051	0.876133
$414$	−5.76814	−0.283489
$415$	−12.2564	−0.601643
$416$	4.49615	0.220442
$417$	−7.16731	−0.350985
$418$	22.3027	1.09086
$419$	9.92000	0.484624	0.242312	−	0.970198i	$-0.422094\pi$
$419$	9.92000	0.484624	0.242312	+	0.970198i	$0.422094\pi$
$420$	60.9819	2.97561
$421$	7.37803	0.359583	0.179792	−	0.983705i	$-0.442458\pi$
$421$	7.37803	0.359583	0.179792	+	0.983705i	$0.442458\pi$
$422$	−52.9465	−2.57739
$423$	−11.5926	−0.563650
$424$	10.5407	0.511903
$425$	1.88160	0.0912709
$426$	19.3835	0.939134
$427$	60.8442	2.94446
$428$	73.0151	3.52932
$429$	−2.13776	−0.103212
$430$	−15.0347	−0.725038
$431$	31.6327	1.52369	0.761847	−	0.647757i	$-0.224293\pi$
$431$	31.6327	1.52369	0.761847	+	0.647757i	$0.224293\pi$
$432$	9.72832	0.468054
$433$	21.2106	1.01932	0.509658	−	0.860377i	$-0.329772\pi$
$433$	21.2106	1.01932	0.509658	+	0.860377i	$0.329772\pi$
$434$	60.0860	2.88422
$435$	−0.0373114	−0.00178894
$436$	−6.47399	−0.310048
$437$	−3.73378	−0.178611
$438$	13.0264	0.622426
$439$	−12.1855	−0.581581	−0.290791	−	0.956787i	$-0.593918\pi$
$439$	−12.1855	−0.581581	−0.290791	+	0.956787i	$0.593918\pi$
$440$	98.0859	4.67606
$441$	16.0901	0.766196
$442$	1.10939	0.0527683
$443$	27.0387	1.28465	0.642323	−	0.766434i	$-0.277971\pi$
$443$	27.0387	1.28465	0.642323	+	0.766434i	$0.277971\pi$
$444$	−53.7768	−2.55213
$445$	5.14151	0.243731
$446$	23.6592	1.12029
$447$	−3.43129	−0.162294
$448$	−39.6696	−1.87421
$449$	−36.3117	−1.71365	−0.856827	−	0.515604i	$-0.827568\pi$
$449$	−36.3117	−1.71365	−0.856827	+	0.515604i	$0.827568\pi$
$450$	−4.92021	−0.231941
$451$	53.9541	2.54060
$452$	−54.1470	−2.54686
$453$	12.2495	0.575530
$454$	−39.5529	−1.85631
$455$	−5.34792	−0.250714
$456$	12.5603	0.588190
$457$	29.0585	1.35930	0.679650	−	0.733537i	$-0.262132\pi$
$457$	29.0585	1.35930	0.679650	+	0.733537i	$0.262132\pi$
$458$	−29.9997	−1.40179
$459$	1.00000	0.0466760
$460$	−27.9942	−1.30523
$461$	29.6091	1.37903	0.689517	−	0.724270i	$-0.257823\pi$
$461$	29.6091	1.37903	0.689517	+	0.724270i	$0.257823\pi$
$462$	63.3142	2.94564
$463$	−6.29861	−0.292721	−0.146361	−	0.989231i	$-0.546756\pi$
$463$	−6.29861	−0.292721	−0.146361	+	0.989231i	$0.546756\pi$
$464$	0.138368	0.00642355
$465$	−12.5444	−0.581731
$466$	−17.4710	−0.809326
$467$	−17.7787	−0.822702	−0.411351	−	0.911477i	$-0.634943\pi$
$467$	−17.7787	−0.822702	−0.411351	+	0.911477i	$0.634943\pi$
$468$	−2.05244	−0.0948741
$469$	22.1708	1.02375
$470$	−79.5209	−3.66802
$471$	3.22816	0.148746
$472$	27.4956	1.26559
$473$	−11.0440	−0.507802
$474$	−2.61491	−0.120107
$475$	−3.18490	−0.146133
$476$	−23.2464	−1.06550
$477$	−1.42050	−0.0650400
$478$	60.2194	2.75437
$479$	−5.08581	−0.232377	−0.116188	−	0.993227i	$-0.537068\pi$
$479$	−5.08581	−0.232377	−0.116188	+	0.993227i	$0.537068\pi$
$480$	27.8009	1.26893
$481$	4.71605	0.215034
$482$	−21.6055	−0.984104
$483$	−10.5997	−0.482302
$484$	69.6153	3.16433
$485$	36.4678	1.65592
$486$	−2.61491	−0.118615
$487$	−16.2181	−0.734912	−0.367456	−	0.930041i	$-0.619771\pi$
$487$	−16.2181	−0.734912	−0.367456	+	0.930041i	$0.619771\pi$
$488$	93.9587	4.25331
$489$	12.3203	0.557141
$490$	110.372	4.98612
$491$	18.6235	0.840468	0.420234	−	0.907416i	$-0.361948\pi$
$491$	18.6235	0.840468	0.420234	+	0.907416i	$0.361948\pi$
$492$	51.8007	2.33536
$493$	0.0142232	0.000640579 0
$494$	−1.87782	−0.0844870
$495$	−13.2183	−0.594119
$496$	46.5202	2.08882
$497$	35.6196	1.59776
$498$	−12.2173	−0.547470
$499$	42.0101	1.88063	0.940315	−	0.340306i	$-0.110531\pi$
$499$	42.0101	1.88063	0.940315	+	0.340306i	$0.110531\pi$
$500$	39.5749	1.76984
$501$	−12.1321	−0.542023
$502$	−30.8691	−1.37776
$503$	−2.25841	−0.100698	−0.0503488	−	0.998732i	$-0.516033\pi$
$503$	−2.25841	−0.100698	−0.0503488	+	0.998732i	$0.516033\pi$
$504$	35.6569	1.58828
$505$	−47.0563	−2.09398
$506$	−29.0648	−1.29209
$507$	−12.8200	−0.569357
$508$	36.2445	1.60809
$509$	−38.1268	−1.68994	−0.844970	−	0.534814i	$-0.820382\pi$
$509$	−38.1268	−1.68994	−0.844970	+	0.534814i	$0.820382\pi$
$510$	6.85964	0.303750
$511$	23.9376	1.05894
$512$	41.2788	1.82428
$513$	−1.69266	−0.0747327
$514$	−62.1538	−2.74149
$515$	−16.4354	−0.724228
$516$	−10.6032	−0.466780
$517$	−58.4133	−2.56901
$518$	−139.676	−6.13700
$519$	21.7686	0.955536
$520$	−8.25853	−0.362160
$521$	−21.4571	−0.940053	−0.470026	−	0.882652i	$-0.655756\pi$
$521$	−21.4571	−0.940053	−0.470026	+	0.882652i	$0.655756\pi$
$522$	−0.0371923	−0.00162786
$523$	−4.99511	−0.218421	−0.109210	−	0.994019i	$-0.534832\pi$
$523$	−4.99511	−0.218421	−0.109210	+	0.994019i	$0.534832\pi$
$524$	−43.6920	−1.90869
$525$	−9.04149	−0.394603
$526$	−71.5052	−3.11778
$527$	4.78194	0.208304
$528$	49.0196	2.13330
$529$	−18.1341	−0.788441
$530$	−9.74409	−0.423256
$531$	−3.70537	−0.160799
$532$	39.3483	1.70596
$533$	−4.54276	−0.196769
$534$	5.12510	0.221785
$535$	−39.5926	−1.71174
$536$	34.2372	1.47882
$537$	−14.3372	−0.618695
$538$	55.8668	2.40859
$539$	81.0757	3.49218
$540$	−12.6908	−0.546124
$541$	12.2190	0.525336	0.262668	−	0.964886i	$-0.415398\pi$
$541$	12.2190	0.525336	0.262668	+	0.964886i	$0.415398\pi$
$542$	27.4781	1.18028
$543$	18.8588	0.809310
$544$	−10.5978	−0.454375
$545$	3.51053	0.150375
$546$	−5.33086	−0.228140
$547$	38.3094	1.63799	0.818995	−	0.573800i	$-0.194531\pi$
$547$	38.3094	1.63799	0.818995	+	0.573800i	$0.194531\pi$
$548$	85.0031	3.63115
$549$	−12.6621	−0.540406
$550$	−24.7922	−1.05714
$551$	−0.0240750	−0.00102563
$552$	−16.3685	−0.696692
$553$	−4.80522	−0.204339
$554$	4.16053	0.176764
$555$	29.1606	1.23780
$556$	−34.6736	−1.47049
$557$	14.7175	0.623601	0.311801	−	0.950148i	$-0.399068\pi$
$557$	14.7175	0.623601	0.311801	+	0.950148i	$0.399068\pi$
$558$	−12.5043	−0.529350
$559$	0.929867	0.0393292
$560$	122.630	5.18205
$561$	5.03885	0.212740
$562$	68.9806	2.90977
$563$	−28.2021	−1.18858	−0.594289	−	0.804252i	$-0.702566\pi$
$563$	−28.2021	−1.18858	−0.594289	+	0.804252i	$0.702566\pi$
$564$	−56.0820	−2.36148
$565$	29.3614	1.23524
$566$	−44.8211	−1.88397
$567$	−4.80522	−0.201800
$568$	55.0055	2.30798
$569$	3.98075	0.166882	0.0834408	−	0.996513i	$-0.473409\pi$
$569$	3.98075	0.166882	0.0834408	+	0.996513i	$0.473409\pi$
$570$	−11.6110	−0.486332
$571$	4.41742	0.184863	0.0924317	−	0.995719i	$-0.470536\pi$
$571$	4.41742	0.184863	0.0924317	+	0.995719i	$0.470536\pi$
$572$	−10.3419	−0.432418
$573$	0.813947	0.0340031
$574$	134.543	5.61573
$575$	4.15056	0.173090
$576$	8.25553	0.343980
$577$	12.5308	0.521665	0.260832	−	0.965384i	$-0.416003\pi$
$577$	12.5308	0.521665	0.260832	+	0.965384i	$0.416003\pi$
$578$	−2.61491	−0.108766
$579$	15.2769	0.634887
$580$	−0.180503	−0.00749498
$581$	−22.4508	−0.931415
$582$	36.3515	1.50682
$583$	−7.15767	−0.296440
$584$	36.9657	1.52965
$585$	1.11294	0.0460144
$586$	−41.2263	−1.70304
$587$	−1.65542	−0.0683267	−0.0341633	−	0.999416i	$-0.510877\pi$
$587$	−1.65542	−0.0683267	−0.0341633	+	0.999416i	$0.510877\pi$
$588$	77.8400	3.21007
$589$	−8.09418	−0.333515
$590$	−25.4175	−1.04642
$591$	18.6764	0.768245
$592$	−108.141	−4.44456
$593$	−27.4662	−1.12790	−0.563951	−	0.825808i	$-0.690719\pi$
$593$	−27.4662	−1.12790	−0.563951	+	0.825808i	$0.690719\pi$
$594$	−13.1761	−0.540624
$595$	12.6054	0.516772
$596$	−16.5997	−0.679951
$597$	−0.597834	−0.0244677
$598$	2.44717	0.100072
$599$	−17.4117	−0.711423	−0.355712	−	0.934596i	$-0.615761\pi$
$599$	−17.4117	−0.711423	−0.355712	+	0.934596i	$0.615761\pi$
$600$	−13.9623	−0.570009
$601$	6.64335	0.270988	0.135494	−	0.990778i	$-0.456738\pi$
$601$	6.64335	0.270988	0.135494	+	0.990778i	$0.456738\pi$
$602$	−27.5400	−1.12245
$603$	−4.61390	−0.187893
$604$	59.2599	2.41125
$605$	−37.7491	−1.53472
$606$	−46.9062	−1.90543
$607$	13.4506	0.545941	0.272971	−	0.962022i	$-0.411994\pi$
$607$	13.4506	0.545941	0.272971	+	0.962022i	$0.411994\pi$
$608$	17.9384	0.727497
$609$	−0.0683454	−0.00276950
$610$	−86.8576	−3.51676
$611$	4.91821	0.198970
$612$	4.83775	0.195554
$613$	−7.45281	−0.301016	−0.150508	−	0.988609i	$-0.548091\pi$
$613$	−7.45281	−0.301016	−0.150508	+	0.988609i	$0.548091\pi$
$614$	7.23821	0.292110
$615$	−28.0891	−1.13266
$616$	179.670	7.23911
$617$	−14.1094	−0.568023	−0.284011	−	0.958821i	$-0.591665\pi$
$617$	−14.1094	−0.568023	−0.284011	+	0.958821i	$0.591665\pi$
$618$	−16.3829	−0.659017
$619$	−12.7217	−0.511329	−0.255664	−	0.966766i	$-0.582294\pi$
$619$	−12.7217	−0.511329	−0.255664	+	0.966766i	$0.582294\pi$
$620$	−60.6864	−2.43723
$621$	2.20587	0.0885184
$622$	−51.7210	−2.07382
$623$	9.41801	0.377324
$624$	−4.12729	−0.165224
$625$	−30.8676	−1.23470
$626$	−53.8780	−2.15340
$627$	−8.52906	−0.340618
$628$	15.6170	0.623187
$629$	−11.1161	−0.443227
$630$	−32.9621	−1.31324
$631$	−0.578439	−0.0230273	−0.0115137	−	0.999934i	$-0.503665\pi$
$631$	−0.578439	−0.0230273	−0.0115137	+	0.999934i	$0.503665\pi$
$632$	−7.42046	−0.295170
$633$	20.2479	0.804782
$634$	20.2279	0.803353
$635$	−19.6536	−0.779931
$636$	−6.87200	−0.272493
$637$	−6.82632	−0.270469
$638$	−0.187407	−0.00741949
$639$	−7.41269	−0.293241
$640$	1.02818	0.0406424
$641$	30.4589	1.20305	0.601527	−	0.798853i	$-0.294559\pi$
$641$	30.4589	1.20305	0.601527	+	0.798853i	$0.294559\pi$
$642$	−39.4663	−1.55761
$643$	16.2566	0.641099	0.320549	−	0.947232i	$-0.396133\pi$
$643$	16.2566	0.641099	0.320549	+	0.947232i	$0.396133\pi$
$644$	−51.2786	−2.02066
$645$	5.74961	0.226391
$646$	4.42615	0.174144
$647$	−8.27283	−0.325238	−0.162619	−	0.986689i	$-0.551994\pi$
$647$	−8.27283	−0.325238	−0.162619	+	0.986689i	$0.551994\pi$
$648$	−7.42046	−0.291503
$649$	−18.6708	−0.732894
$650$	2.08742	0.0818755
$651$	−22.9782	−0.900588
$652$	59.6023	2.33421
$653$	−21.0857	−0.825146	−0.412573	−	0.910925i	$-0.635370\pi$
$653$	−21.0857	−0.825146	−0.412573	+	0.910925i	$0.635370\pi$
$654$	3.49933	0.136835
$655$	23.6921	0.925726
$656$	104.167	4.06704
$657$	−4.98159	−0.194350
$658$	−145.663	−5.67854
$659$	45.7095	1.78059	0.890295	−	0.455384i	$-0.150498\pi$
$659$	45.7095	1.78059	0.890295	+	0.455384i	$0.150498\pi$
$660$	−63.9469	−2.48913
$661$	−16.7803	−0.652676	−0.326338	−	0.945253i	$-0.605815\pi$
$661$	−16.7803	−0.652676	−0.326338	+	0.945253i	$0.605815\pi$
$662$	34.4577	1.33924
$663$	−0.424255	−0.0164767
$664$	−34.6696	−1.34544
$665$	−21.3367	−0.827401
$666$	29.0675	1.12634
$667$	0.0313744	0.00121482
$668$	−58.6921	−2.27087
$669$	−9.04780	−0.349808
$670$	−31.6497	−1.22273
$671$	−63.8025	−2.46307
$672$	50.9245	1.96446
$673$	19.5956	0.755356	0.377678	−	0.925937i	$-0.376723\pi$
$673$	19.5956	0.755356	0.377678	+	0.925937i	$0.376723\pi$
$674$	41.2937	1.59057
$675$	1.88160	0.0724227
$676$	−62.0200	−2.38538
$677$	19.6776	0.756272	0.378136	−	0.925750i	$-0.376565\pi$
$677$	19.6776	0.756272	0.378136	+	0.925750i	$0.376565\pi$
$678$	29.2677	1.12402
$679$	66.8003	2.56356
$680$	19.4659	0.746484
$681$	15.1259	0.579626
$682$	−63.0075	−2.41268
$683$	−39.9552	−1.52884	−0.764421	−	0.644718i	$-0.776975\pi$
$683$	−39.9552	−1.52884	−0.764421	+	0.644718i	$0.776975\pi$
$684$	−8.18866	−0.313101
$685$	−46.0931	−1.76113
$686$	114.219	4.36091
$687$	11.4726	0.437706
$688$	−21.3222	−0.812900
$689$	0.602653	0.0229592
$690$	15.1315	0.576045
$691$	39.6863	1.50974	0.754869	−	0.655876i	$-0.227700\pi$
$691$	39.6863	1.50974	0.754869	+	0.655876i	$0.227700\pi$
$692$	105.311	4.00333
$693$	−24.2128	−0.919768
$694$	89.0095	3.37875
$695$	18.8019	0.713195
$696$	−0.105542	−0.00400058
$697$	10.7076	0.405580
$698$	34.8419	1.31878
$699$	6.68129	0.252709
$700$	−43.7404	−1.65323
$701$	2.43342	0.0919089	0.0459544	−	0.998944i	$-0.485367\pi$
$701$	2.43342	0.0919089	0.0459544	+	0.998944i	$0.485367\pi$
$702$	1.10939	0.0418712
$703$	18.8157	0.709648
$704$	41.5984	1.56780
$705$	30.4106	1.14533
$706$	−14.9735	−0.563535
$707$	−86.1959	−3.24173
$708$	−17.9257	−0.673688
$709$	−4.13449	−0.155274	−0.0776370	−	0.996982i	$-0.524738\pi$
$709$	−4.13449	−0.155274	−0.0776370	+	0.996982i	$0.524738\pi$
$710$	−50.8484	−1.90830
$711$	1.00000	0.0375029
$712$	14.5438	0.545050
$713$	10.5483	0.395038
$714$	12.5652	0.470241
$715$	5.60794	0.209725
$716$	−69.3597	−2.59209
$717$	−23.0293	−0.860043
$718$	2.11297	0.0788555
$719$	45.6694	1.70318	0.851591	−	0.524207i	$-0.175638\pi$
$719$	45.6694	1.70318	0.851591	+	0.524207i	$0.175638\pi$
$720$	−25.5201	−0.951078
$721$	−30.1056	−1.12119
$722$	42.1913	1.57020
$723$	8.26243	0.307283
$724$	91.2343	3.39070
$725$	0.0267623	0.000993926 0
$726$	−37.6286	−1.39653
$727$	29.0454	1.07724	0.538618	−	0.842550i	$-0.318947\pi$
$727$	29.0454	1.07724	0.538618	+	0.842550i	$0.318947\pi$
$728$	−15.1276	−0.560667
$729$	1.00000	0.0370370
$730$	−34.1719	−1.26476
$731$	−2.19176	−0.0810653
$732$	−61.2562	−2.26409
$733$	41.0333	1.51560	0.757800	−	0.652487i	$-0.226274\pi$
$733$	41.0333	1.51560	0.757800	+	0.652487i	$0.226274\pi$
$734$	−13.8560	−0.511433
$735$	−42.2089	−1.55690
$736$	−23.3772	−0.861697
$737$	−23.2488	−0.856379
$738$	−27.9994	−1.03067
$739$	−14.5607	−0.535626	−0.267813	−	0.963471i	$-0.586301\pi$
$739$	−14.5607	−0.535626	−0.267813	+	0.963471i	$0.586301\pi$
$740$	141.072	5.18589
$741$	0.718119	0.0263808
$742$	−17.8488	−0.655251
$743$	12.0311	0.441379	0.220690	−	0.975344i	$-0.429169\pi$
$743$	12.0311	0.441379	0.220690	+	0.975344i	$0.429169\pi$
$744$	−35.4841	−1.30091
$745$	9.00124	0.329780
$746$	6.53704	0.239338
$747$	4.67216	0.170946
$748$	24.3767	0.891300
$749$	−72.5242	−2.64997
$750$	−21.3911	−0.781093
$751$	15.0478	0.549102	0.274551	−	0.961573i	$-0.411471\pi$
$751$	15.0478	0.549102	0.274551	+	0.961573i	$0.411471\pi$
$752$	−112.776	−4.11253
$753$	11.8050	0.430200
$754$	0.0157790	0.000574639 0
$755$	−32.1338	−1.16947
$756$	−23.2464	−0.845465
$757$	42.6301	1.54942	0.774709	−	0.632318i	$-0.217896\pi$
$757$	42.6301	1.54942	0.774709	+	0.632318i	$0.217896\pi$
$758$	−51.3858	−1.86642
$759$	11.1150	0.403450
$760$	−32.9492	−1.19519
$761$	47.5086	1.72219	0.861093	−	0.508447i	$-0.169780\pi$
$761$	47.5086	1.72219	0.861093	+	0.508447i	$0.169780\pi$
$762$	−19.5909	−0.709705
$763$	6.43046	0.232798
$764$	3.93767	0.142460
$765$	−2.62328	−0.0948449
$766$	−61.4656	−2.22084
$767$	1.57202	0.0567625
$768$	−15.4862	−0.558808
$769$	−2.73285	−0.0985492	−0.0492746	−	0.998785i	$-0.515691\pi$
$769$	−2.73285	−0.0985492	−0.0492746	+	0.998785i	$0.515691\pi$
$770$	−166.091	−5.98550
$771$	23.7690	0.856020
$772$	73.9059	2.65993
$773$	−43.1338	−1.55142	−0.775708	−	0.631092i	$-0.782607\pi$
$773$	−43.1338	−1.55142	−0.775708	+	0.631092i	$0.782607\pi$
$774$	5.73126	0.206006
$775$	8.99768	0.323206
$776$	103.156	3.70310
$777$	53.4152	1.91626
$778$	48.5537	1.74073
$779$	−18.1243	−0.649372
$780$	5.38413	0.192783
$781$	−37.3514	−1.33654
$782$	−5.76814	−0.206268
$783$	0.0142232	0.000508295 0
$784$	156.530	5.59035
$785$	−8.46837	−0.302249
$786$	23.6165	0.842372
$787$	4.42299	0.157662	0.0788312	−	0.996888i	$-0.474881\pi$
$787$	4.42299	0.157662	0.0788312	+	0.996888i	$0.474881\pi$
$788$	90.3518	3.21865
$789$	27.3452	0.973515
$790$	6.85964	0.244055
$791$	53.7829	1.91230
$792$	−37.3906	−1.32862
$793$	5.37197	0.190764
$794$	29.5467	1.04857
$795$	3.72636	0.132160
$796$	−2.89217	−0.102510
$797$	−41.7670	−1.47946	−0.739731	−	0.672903i	$-0.765047\pi$
$797$	−41.7670	−1.47946	−0.739731	+	0.672903i	$0.765047\pi$
$798$	−21.2686	−0.752901
$799$	−11.5926	−0.410116
$800$	−19.9407	−0.705010
$801$	−1.95995	−0.0692516
$802$	−33.8965	−1.19693
$803$	−25.1015	−0.885813
$804$	−22.3209	−0.787197
$805$	27.8059	0.980030
$806$	5.30503	0.186862
$807$	−21.3647	−0.752073
$808$	−133.108	−4.68272
$809$	44.1029	1.55058	0.775288	−	0.631607i	$-0.217605\pi$
$809$	44.1029	1.55058	0.775288	+	0.631607i	$0.217605\pi$
$810$	6.85964	0.241023
$811$	−31.3037	−1.09922	−0.549611	−	0.835421i	$-0.685224\pi$
$811$	−31.3037	−1.09922	−0.549611	+	0.835421i	$0.685224\pi$
$812$	−0.330638	−0.0116031
$813$	−10.5082	−0.368540
$814$	146.467	5.13366
$815$	−32.3195	−1.13210
$816$	9.72832	0.340559
$817$	3.70991	0.129793
$818$	−84.8180	−2.96559
$819$	2.03864	0.0712358
$820$	−135.888	−4.74541
$821$	29.8272	1.04097	0.520487	−	0.853869i	$-0.325750\pi$
$821$	29.8272	1.04097	0.520487	+	0.853869i	$0.325750\pi$
$822$	−45.9460	−1.60255
$823$	−20.8186	−0.725690	−0.362845	−	0.931849i	$-0.618195\pi$
$823$	−20.8186	−0.725690	−0.362845	+	0.931849i	$0.618195\pi$
$824$	−46.4906	−1.61958
$825$	9.48109	0.330089
$826$	−46.5588	−1.61999
$827$	29.7121	1.03319	0.516595	−	0.856230i	$-0.327199\pi$
$827$	29.7121	1.03319	0.516595	+	0.856230i	$0.327199\pi$
$828$	10.6714	0.370858
$829$	38.3261	1.33112	0.665560	−	0.746345i	$-0.268193\pi$
$829$	38.3261	1.33112	0.665560	+	0.746345i	$0.268193\pi$
$830$	32.0494	1.11245
$831$	−1.59108	−0.0551940
$832$	−3.50245	−0.121426
$833$	16.0901	0.557490
$834$	18.7419	0.648977
$835$	31.8259	1.10138
$836$	−41.2614	−1.42706
$837$	4.78194	0.165288
$838$	−25.9399	−0.896079
$839$	56.9351	1.96562	0.982809	−	0.184625i	$-0.0591069\pi$
$839$	56.9351	1.96562	0.982809	+	0.184625i	$0.0591069\pi$
$840$	−93.5381	−3.22737
$841$	−28.9998	−0.999993
$842$	−19.2929	−0.664876
$843$	−26.3797	−0.908567
$844$	97.9543	3.37173
$845$	33.6305	1.15692
$846$	30.3135	1.04220
$847$	−69.1472	−2.37593
$848$	−13.8190	−0.474548
$849$	17.1406	0.588263
$850$	−4.92021	−0.168762
$851$	−24.5206	−0.840555
$852$	−35.8607	−1.22857
$853$	−23.8274	−0.815833	−0.407917	−	0.913019i	$-0.633745\pi$
$853$	−23.8274	−0.815833	−0.407917	+	0.913019i	$0.633745\pi$
$854$	−159.102	−5.44436
$855$	4.44032	0.151856
$856$	−111.995	−3.82792
$857$	47.9327	1.63735	0.818674	−	0.574258i	$-0.194710\pi$
$857$	47.9327	1.63735	0.818674	+	0.574258i	$0.194710\pi$
$858$	5.59005	0.190841
$859$	−14.4560	−0.493233	−0.246616	−	0.969113i	$-0.579319\pi$
$859$	−14.4560	−0.493233	−0.246616	+	0.969113i	$0.579319\pi$
$860$	27.8152	0.948489
$861$	−51.4524	−1.75349
$862$	−82.7167	−2.81734
$863$	20.3483	0.692664	0.346332	−	0.938112i	$-0.387427\pi$
$863$	20.3483	0.692664	0.346332	+	0.938112i	$0.387427\pi$
$864$	−10.5978	−0.360543
$865$	−57.1052	−1.94163
$866$	−55.4638	−1.88474
$867$	1.00000	0.0339618
$868$	−111.163	−3.77312
$869$	5.03885	0.170931
$870$	0.0975658	0.00330779
$871$	1.95747	0.0663264
$872$	9.93023	0.336280
$873$	−13.9016	−0.470498
$874$	9.76350	0.330255
$875$	−39.3088	−1.32888
$876$	−24.0997	−0.814253
$877$	−46.9534	−1.58550	−0.792751	−	0.609545i	$-0.791352\pi$
$877$	−46.9534	−1.58550	−0.792751	+	0.609545i	$0.791352\pi$
$878$	31.8639	1.07535
$879$	15.7659	0.531769
$880$	−128.592	−4.33484
$881$	9.76965	0.329148	0.164574	−	0.986365i	$-0.447375\pi$
$881$	9.76965	0.329148	0.164574	+	0.986365i	$0.447375\pi$
$882$	−42.0742	−1.41671
$883$	−16.0773	−0.541043	−0.270522	−	0.962714i	$-0.587196\pi$
$883$	−16.0773	−0.541043	−0.270522	+	0.962714i	$0.587196\pi$
$884$	−2.05244	−0.0690311
$885$	9.72023	0.326742
$886$	−70.7037	−2.37534
$887$	27.6320	0.927791	0.463895	−	0.885890i	$-0.346451\pi$
$887$	27.6320	0.927791	0.463895	+	0.885890i	$0.346451\pi$
$888$	82.4863	2.76806
$889$	−36.0008	−1.20743
$890$	−13.4446	−0.450663
$891$	5.03885	0.168808
$892$	−43.7710	−1.46556
$893$	19.6223	0.656634
$894$	8.97251	0.300086
$895$	37.6105	1.25718
$896$	1.88338	0.0629193
$897$	−0.935851	−0.0312472
$898$	94.9517	3.16858
$899$	0.0680143	0.00226840
$900$	9.10270	0.303423
$901$	−1.42050	−0.0473236
$902$	−141.085	−4.69762
$903$	10.5319	0.350480
$904$	83.0543	2.76234
$905$	−49.4720	−1.64451
$906$	−32.0313	−1.06417
$907$	−23.6067	−0.783847	−0.391923	−	0.919998i	$-0.628190\pi$
$907$	−23.6067	−0.783847	−0.391923	+	0.919998i	$0.628190\pi$
$908$	73.1753	2.42841
$909$	17.9380	0.594965
$910$	13.9843	0.463576
$911$	11.7648	0.389786	0.194893	−	0.980824i	$-0.437564\pi$
$911$	11.7648	0.389786	0.194893	+	0.980824i	$0.437564\pi$
$912$	−16.4667	−0.545268
$913$	23.5423	0.779138
$914$	−75.9853	−2.51337
$915$	33.2163	1.09810
$916$	55.5014	1.83382
$917$	43.3982	1.43313
$918$	−2.61491	−0.0863049
$919$	21.2321	0.700381	0.350190	−	0.936679i	$-0.386117\pi$
$919$	21.2321	0.700381	0.350190	+	0.936679i	$0.386117\pi$
$920$	42.9393	1.41567
$921$	−2.76806	−0.0912105
$922$	−77.4251	−2.54986
$923$	3.14487	0.103515
$924$	−117.135	−3.85347
$925$	−20.9160	−0.687713
$926$	16.4703	0.541247
$927$	6.26519	0.205776
$928$	−0.150734	−0.00494808
$929$	3.36978	0.110559	0.0552794	−	0.998471i	$-0.482395\pi$
$929$	3.36978	0.110559	0.0552794	+	0.998471i	$0.482395\pi$
$930$	32.8023	1.07563
$931$	−27.2351	−0.892594
$932$	32.3224	1.05875
$933$	19.7793	0.647544
$934$	46.4898	1.52119
$935$	−13.2183	−0.432285
$936$	3.14817	0.102901
$937$	−42.1364	−1.37654	−0.688268	−	0.725457i	$-0.741629\pi$
$937$	−42.1364	−1.37654	−0.688268	+	0.725457i	$0.741629\pi$
$938$	−57.9746	−1.89294
$939$	20.6041	0.672391
$940$	147.119	4.79848
$941$	27.4126	0.893625	0.446813	−	0.894628i	$-0.352559\pi$
$941$	27.4126	0.893625	0.446813	+	0.894628i	$0.352559\pi$
$942$	−8.44134	−0.275034
$943$	23.6196	0.769159
$944$	−36.0470	−1.17323
$945$	12.6054	0.410055
$946$	28.8790	0.938937
$947$	−9.86369	−0.320527	−0.160263	−	0.987074i	$-0.551234\pi$
$947$	−9.86369	−0.320527	−0.160263	+	0.987074i	$0.551234\pi$
$948$	4.83775	0.157123
$949$	2.11347	0.0686060
$950$	8.32823	0.270203
$951$	−7.73561	−0.250844
$952$	35.6569	1.15565
$953$	51.1565	1.65712	0.828561	−	0.559899i	$-0.189160\pi$
$953$	51.1565	1.65712	0.828561	+	0.559899i	$0.189160\pi$
$954$	3.71447	0.120260
$955$	−2.13521	−0.0690938
$956$	−111.410	−3.60325
$957$	0.0716685	0.00231671
$958$	13.2989	0.429669
$959$	−84.4315	−2.72644
$960$	−21.6566	−0.698962
$961$	−8.13309	−0.262358
$962$	−12.3321	−0.397601
$963$	15.0928	0.486358
$964$	39.9716	1.28740
$965$	−40.0756	−1.29008
$966$	27.7172	0.891786
$967$	−35.9081	−1.15473	−0.577364	−	0.816487i	$-0.695918\pi$
$967$	−35.9081	−1.15473	−0.577364	+	0.816487i	$0.695918\pi$
$968$	−106.781	−3.43206
$969$	−1.69266	−0.0543760
$970$	−95.3600	−3.06183
$971$	1.48731	0.0477302	0.0238651	−	0.999715i	$-0.492403\pi$
$971$	1.48731	0.0477302	0.0238651	+	0.999715i	$0.492403\pi$
$972$	4.83775	0.155171
$973$	34.4405	1.10411
$974$	42.4088	1.35887
$975$	−0.798278	−0.0255654
$976$	−123.181	−3.94293
$977$	56.9095	1.82070	0.910348	−	0.413844i	$-0.135814\pi$
$977$	56.9095	1.82070	0.910348	+	0.413844i	$0.135814\pi$
$978$	−32.2163	−1.03017
$979$	−9.87592	−0.315636
$980$	−204.196	−6.52280
$981$	−1.33822	−0.0427262
$982$	−48.6988	−1.55404
$983$	27.8735	0.889026	0.444513	−	0.895772i	$-0.353377\pi$
$983$	27.8735	0.889026	0.444513	+	0.895772i	$0.353377\pi$
$984$	−79.4554	−2.53294
$985$	−48.9935	−1.56106
$986$	−0.0371923	−0.00118444
$987$	55.7049	1.77311
$988$	3.47408	0.110525
$989$	−4.83474	−0.153736
$990$	34.5647	1.09854
$991$	−50.3605	−1.59975	−0.799877	−	0.600164i	$-0.795102\pi$
$991$	−50.3605	−1.59975	−0.799877	+	0.600164i	$0.795102\pi$
$992$	−50.6778	−1.60902
$993$	−13.1774	−0.418172
$994$	−93.1420	−2.95428
$995$	1.56829	0.0497180
$996$	22.6028	0.716196
$997$	−7.60988	−0.241007	−0.120504	−	0.992713i	$-0.538451\pi$
$997$	−7.60988	−0.241007	−0.120504	+	0.992713i	$0.538451\pi$
$998$	−109.853	−3.47732
$999$	−11.1161	−0.351697

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.k.1.1	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.k.1.1	✓	31	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q-2.61491 q^{2} +1.00000 q^{3} +4.83775 q^{4} -2.62328 q^{5} -2.61491 q^{6} -4.80522 q^{7} -7.42046 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.61491 q^{2} +1.00000 q^{3} +4.83775 q^{4} -2.62328 q^{5} -2.61491 q^{6} -4.80522 q^{7} -7.42046 q^{8} +1.00000 q^{9} +6.85964 q^{10} +5.03885 q^{11} +4.83775 q^{12} -0.424255 q^{13} +12.5652 q^{14} -2.62328 q^{15} +9.72832 q^{16} +1.00000 q^{17} -2.61491 q^{18} -1.69266 q^{19} -12.6908 q^{20} -4.80522 q^{21} -13.1761 q^{22} +2.20587 q^{23} -7.42046 q^{24} +1.88160 q^{25} +1.10939 q^{26} +1.00000 q^{27} -23.2464 q^{28} +0.0142232 q^{29} +6.85964 q^{30} +4.78194 q^{31} -10.5978 q^{32} +5.03885 q^{33} -2.61491 q^{34} +12.6054 q^{35} +4.83775 q^{36} -11.1161 q^{37} +4.42615 q^{38} -0.424255 q^{39} +19.4659 q^{40} +10.7076 q^{41} +12.5652 q^{42} -2.19176 q^{43} +24.3767 q^{44} -2.62328 q^{45} -5.76814 q^{46} -11.5926 q^{47} +9.72832 q^{48} +16.0901 q^{49} -4.92021 q^{50} +1.00000 q^{51} -2.05244 q^{52} -1.42050 q^{53} -2.61491 q^{54} -13.2183 q^{55} +35.6569 q^{56} -1.69266 q^{57} -0.0371923 q^{58} -3.70537 q^{59} -12.6908 q^{60} -12.6621 q^{61} -12.5043 q^{62} -4.80522 q^{63} +8.25553 q^{64} +1.11294 q^{65} -13.1761 q^{66} -4.61390 q^{67} +4.83775 q^{68} +2.20587 q^{69} -32.9621 q^{70} -7.41269 q^{71} -7.42046 q^{72} -4.98159 q^{73} +29.0675 q^{74} +1.88160 q^{75} -8.18866 q^{76} -24.2128 q^{77} +1.10939 q^{78} +1.00000 q^{79} -25.5201 q^{80} +1.00000 q^{81} -27.9994 q^{82} +4.67216 q^{83} -23.2464 q^{84} -2.62328 q^{85} +5.73126 q^{86} +0.0142232 q^{87} -37.3906 q^{88} -1.95995 q^{89} +6.85964 q^{90} +2.03864 q^{91} +10.6714 q^{92} +4.78194 q^{93} +30.3135 q^{94} +4.44032 q^{95} -10.5978 q^{96} -13.9016 q^{97} -42.0742 q^{98} +5.03885 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9}+O(q^{10}) \) 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9	\( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9} + 5 q^{10} + 26 q^{11} + 34 q^{12} + 7 q^{13} + 19 q^{14} + 11 q^{15} + 40 q^{16} + 31 q^{17} + 4 q^{18} + 32 q^{19} + 23 q^{20} + 4 q^{21} + 2 q^{22} + 29 q^{23} + 12 q^{24} + 32 q^{25} + 13 q^{26} + 31 q^{27} - 13 q^{28} + 25 q^{29} + 5 q^{30} + 22 q^{31} + 28 q^{32} + 26 q^{33} + 4 q^{34} + 20 q^{35} + 34 q^{36} - 4 q^{37} + 19 q^{38} + 7 q^{39} - 3 q^{40} + 33 q^{41} + 19 q^{42} + 6 q^{43} + 30 q^{44} + 11 q^{45} - 11 q^{46} + 23 q^{47} + 40 q^{48} + 31 q^{49} + 6 q^{50} + 31 q^{51} - 7 q^{52} + 12 q^{53} + 4 q^{54} + 40 q^{56} + 32 q^{57} + 9 q^{58} + 27 q^{59} + 23 q^{60} - 4 q^{61} + 25 q^{62} + 4 q^{63} + 10 q^{64} + 54 q^{65} + 2 q^{66} + 34 q^{68} + 29 q^{69} - 59 q^{70} + 35 q^{71} + 12 q^{72} + 5 q^{73} + 48 q^{74} + 32 q^{75} + 32 q^{76} + 42 q^{77} + 13 q^{78} + 31 q^{79} + 24 q^{80} + 31 q^{81} + 5 q^{82} + 67 q^{83} - 13 q^{84} + 11 q^{85} - 20 q^{86} + 25 q^{87} - 7 q^{88} + 22 q^{89} + 5 q^{90} + 16 q^{91} + 57 q^{92} + 22 q^{93} + 45 q^{94} + 73 q^{95} + 28 q^{96} - 13 q^{97} - 19 q^{98} + 26 q^{99}+O(q^{100}) \) 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9 + 5 * q^10 + 26 * q^11 + 34 * q^12 + 7 * q^13 + 19 * q^14 + 11 * q^15 + 40 * q^16 + 31 * q^17 + 4 * q^18 + 32 * q^19 + 23 * q^20 + 4 * q^21 + 2 * q^22 + 29 * q^23 + 12 * q^24 + 32 * q^25 + 13 * q^26 + 31 * q^27 - 13 * q^28 + 25 * q^29 + 5 * q^30 + 22 * q^31 + 28 * q^32 + 26 * q^33 + 4 * q^34 + 20 * q^35 + 34 * q^36 - 4 * q^37 + 19 * q^38 + 7 * q^39 - 3 * q^40 + 33 * q^41 + 19 * q^42 + 6 * q^43 + 30 * q^44 + 11 * q^45 - 11 * q^46 + 23 * q^47 + 40 * q^48 + 31 * q^49 + 6 * q^50 + 31 * q^51 - 7 * q^52 + 12 * q^53 + 4 * q^54 + 40 * q^56 + 32 * q^57 + 9 * q^58 + 27 * q^59 + 23 * q^60 - 4 * q^61 + 25 * q^62 + 4 * q^63 + 10 * q^64 + 54 * q^65 + 2 * q^66 + 34 * q^68 + 29 * q^69 - 59 * q^70 + 35 * q^71 + 12 * q^72 + 5 * q^73 + 48 * q^74 + 32 * q^75 + 32 * q^76 + 42 * q^77 + 13 * q^78 + 31 * q^79 + 24 * q^80 + 31 * q^81 + 5 * q^82 + 67 * q^83 - 13 * q^84 + 11 * q^85 - 20 * q^86 + 25 * q^87 - 7 * q^88 + 22 * q^89 + 5 * q^90 + 16 * q^91 + 57 * q^92 + 22 * q^93 + 45 * q^94 + 73 * q^95 + 28 * q^96 - 13 * q^97 - 19 * q^98 + 26 * q^99

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