LMFDB - Embedded newform 4029.2.a.g.1.20

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:	$1$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
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)

$f(q)$	$=$	$q+2.23779 q^{2} -1.00000 q^{3} +3.00772 q^{4} -1.81110 q^{5} -2.23779 q^{6} +1.95143 q^{7} +2.25507 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.23779 q^{2} -1.00000 q^{3} +3.00772 q^{4} -1.81110 q^{5} -2.23779 q^{6} +1.95143 q^{7} +2.25507 q^{8} +1.00000 q^{9} -4.05288 q^{10} -3.76214 q^{11} -3.00772 q^{12} -2.59580 q^{13} +4.36690 q^{14} +1.81110 q^{15} -0.969055 q^{16} -1.00000 q^{17} +2.23779 q^{18} +4.69225 q^{19} -5.44729 q^{20} -1.95143 q^{21} -8.41890 q^{22} +8.25169 q^{23} -2.25507 q^{24} -1.71991 q^{25} -5.80886 q^{26} -1.00000 q^{27} +5.86936 q^{28} +2.34239 q^{29} +4.05288 q^{30} +2.99280 q^{31} -6.67869 q^{32} +3.76214 q^{33} -2.23779 q^{34} -3.53424 q^{35} +3.00772 q^{36} -11.3888 q^{37} +10.5003 q^{38} +2.59580 q^{39} -4.08417 q^{40} -6.99883 q^{41} -4.36690 q^{42} -10.2836 q^{43} -11.3155 q^{44} -1.81110 q^{45} +18.4656 q^{46} -5.57496 q^{47} +0.969055 q^{48} -3.19192 q^{49} -3.84879 q^{50} +1.00000 q^{51} -7.80744 q^{52} -0.114191 q^{53} -2.23779 q^{54} +6.81363 q^{55} +4.40061 q^{56} -4.69225 q^{57} +5.24178 q^{58} -7.88650 q^{59} +5.44729 q^{60} -9.67642 q^{61} +6.69726 q^{62} +1.95143 q^{63} -13.0074 q^{64} +4.70126 q^{65} +8.41890 q^{66} -5.84569 q^{67} -3.00772 q^{68} -8.25169 q^{69} -7.90890 q^{70} +5.46855 q^{71} +2.25507 q^{72} +8.54565 q^{73} -25.4857 q^{74} +1.71991 q^{75} +14.1130 q^{76} -7.34156 q^{77} +5.80886 q^{78} -1.00000 q^{79} +1.75506 q^{80} +1.00000 q^{81} -15.6619 q^{82} +7.99217 q^{83} -5.86936 q^{84} +1.81110 q^{85} -23.0125 q^{86} -2.34239 q^{87} -8.48391 q^{88} -0.507717 q^{89} -4.05288 q^{90} -5.06552 q^{91} +24.8188 q^{92} -2.99280 q^{93} -12.4756 q^{94} -8.49815 q^{95} +6.67869 q^{96} -17.5617 q^{97} -7.14287 q^{98} -3.76214 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{2} - 22 q^{3} + 16 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 6 q^{8} + 22 q^{9}+O(q^{10}) $ 22 * q + 2 * q^2 - 22 * q^3 + 16 * q^4 + 5 * q^5 - 2 * q^6 - 4 * q^7 + 6 * q^8 + 22 * q^9	\( 22 q + 2 q^{2} - 22 q^{3} + 16 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 6 q^{8} + 22 q^{9} - 5 q^{10} - 2 q^{11} - 16 q^{12} - 11 q^{13} - 7 q^{14} - 5 q^{15} - 22 q^{17} + 2 q^{18} - 36 q^{19} + 4 q^{21} - 9 q^{22} + 21 q^{23} - 6 q^{24} + 9 q^{25} - 16 q^{26} - 22 q^{27} - 17 q^{28} - q^{29} + 5 q^{30} - 12 q^{31} - 11 q^{32} + 2 q^{33} - 2 q^{34} - 14 q^{35} + 16 q^{36} - 6 q^{37} + q^{38} + 11 q^{39} - 24 q^{40} - 17 q^{41} + 7 q^{42} - 36 q^{43} + 16 q^{44} + 5 q^{45} - 23 q^{46} - 17 q^{47} - 6 q^{49} - 33 q^{50} + 22 q^{51} - 57 q^{52} - 2 q^{53} - 2 q^{54} - 24 q^{55} - 64 q^{56} + 36 q^{57} - 7 q^{58} - 59 q^{59} - 30 q^{61} - 4 q^{62} - 4 q^{63} - 22 q^{64} + 36 q^{65} + 9 q^{66} - 16 q^{67} - 16 q^{68} - 21 q^{69} - 39 q^{70} - 11 q^{71} + 6 q^{72} - 19 q^{73} - 28 q^{74} - 9 q^{75} - 77 q^{76} + 2 q^{77} + 16 q^{78} - 22 q^{79} - 2 q^{80} + 22 q^{81} + 33 q^{82} - 23 q^{83} + 17 q^{84} - 5 q^{85} + 6 q^{86} + q^{87} - 23 q^{88} + 12 q^{89} - 5 q^{90} - 24 q^{91} + 66 q^{92} + 12 q^{93} - 61 q^{94} - 11 q^{95} + 11 q^{96} - 9 q^{97} + 17 q^{98} - 2 q^{99}+O(q^{100}) \) 22 * q + 2 * q^2 - 22 * q^3 + 16 * q^4 + 5 * q^5 - 2 * q^6 - 4 * q^7 + 6 * q^8 + 22 * q^9 - 5 * q^10 - 2 * q^11 - 16 * q^12 - 11 * q^13 - 7 * q^14 - 5 * q^15 - 22 * q^17 + 2 * q^18 - 36 * q^19 + 4 * q^21 - 9 * q^22 + 21 * q^23 - 6 * q^24 + 9 * q^25 - 16 * q^26 - 22 * q^27 - 17 * q^28 - q^29 + 5 * q^30 - 12 * q^31 - 11 * q^32 + 2 * q^33 - 2 * q^34 - 14 * q^35 + 16 * q^36 - 6 * q^37 + q^38 + 11 * q^39 - 24 * q^40 - 17 * q^41 + 7 * q^42 - 36 * q^43 + 16 * q^44 + 5 * q^45 - 23 * q^46 - 17 * q^47 - 6 * q^49 - 33 * q^50 + 22 * q^51 - 57 * q^52 - 2 * q^53 - 2 * q^54 - 24 * q^55 - 64 * q^56 + 36 * q^57 - 7 * q^58 - 59 * q^59 - 30 * q^61 - 4 * q^62 - 4 * q^63 - 22 * q^64 + 36 * q^65 + 9 * q^66 - 16 * q^67 - 16 * q^68 - 21 * q^69 - 39 * q^70 - 11 * q^71 + 6 * q^72 - 19 * q^73 - 28 * q^74 - 9 * q^75 - 77 * q^76 + 2 * q^77 + 16 * q^78 - 22 * q^79 - 2 * q^80 + 22 * q^81 + 33 * q^82 - 23 * q^83 + 17 * q^84 - 5 * q^85 + 6 * q^86 + q^87 - 23 * q^88 + 12 * q^89 - 5 * q^90 - 24 * q^91 + 66 * q^92 + 12 * q^93 - 61 * q^94 - 11 * q^95 + 11 * q^96 - 9 * q^97 + 17 * q^98 - 2 * 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 $

$2$	2.23779	1.58236	0.791180	−	0.611584i	$-0.209467\pi$
$2$	2.23779	1.58236	0.791180	+	0.611584i	$0.209467\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.00772	1.50386
$5$	−1.81110	−0.809950	−0.404975	−	0.914328i	$-0.632720\pi$
$5$	−1.81110	−0.809950	−0.404975	+	0.914328i	$0.632720\pi$
$6$	−2.23779	−0.913576
$7$	1.95143	0.737571	0.368786	−	0.929515i	$-0.379774\pi$
$7$	1.95143	0.737571	0.368786	+	0.929515i	$0.379774\pi$
$8$	2.25507	0.797288
$9$	1.00000	0.333333
$10$	−4.05288	−1.28163
$11$	−3.76214	−1.13433	−0.567165	−	0.823604i	$-0.691960\pi$
$11$	−3.76214	−1.13433	−0.567165	+	0.823604i	$0.691960\pi$
$12$	−3.00772	−0.868254
$13$	−2.59580	−0.719945	−0.359973	−	0.932963i	$-0.617214\pi$
$13$	−2.59580	−0.719945	−0.359973	+	0.932963i	$0.617214\pi$
$14$	4.36690	1.16710
$15$	1.81110	0.467625
$16$	−0.969055	−0.242264
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	2.23779	0.527453
$19$	4.69225	1.07648	0.538238	−	0.842793i	$-0.319090\pi$
$19$	4.69225	1.07648	0.538238	+	0.842793i	$0.319090\pi$
$20$	−5.44729	−1.21805
$21$	−1.95143	−0.425837
$22$	−8.41890	−1.79492
$23$	8.25169	1.72060	0.860298	−	0.509791i	$-0.170277\pi$
$23$	8.25169	1.72060	0.860298	+	0.509791i	$0.170277\pi$
$24$	−2.25507	−0.460315
$25$	−1.71991	−0.343981
$26$	−5.80886	−1.13921
$27$	−1.00000	−0.192450
$28$	5.86936	1.10920
$29$	2.34239	0.434970	0.217485	−	0.976064i	$-0.430215\pi$
$29$	2.34239	0.434970	0.217485	+	0.976064i	$0.430215\pi$
$30$	4.05288	0.739950
$31$	2.99280	0.537522	0.268761	−	0.963207i	$-0.413386\pi$
$31$	2.99280	0.537522	0.268761	+	0.963207i	$0.413386\pi$
$32$	−6.67869	−1.18064
$33$	3.76214	0.654905
$34$	−2.23779	−0.383778
$35$	−3.53424	−0.597396
$36$	3.00772	0.501287
$37$	−11.3888	−1.87230	−0.936151	−	0.351597i	$-0.885639\pi$
$37$	−11.3888	−1.87230	−0.936151	+	0.351597i	$0.885639\pi$
$38$	10.5003	1.70337
$39$	2.59580	0.415660
$40$	−4.08417	−0.645764
$41$	−6.99883	−1.09303	−0.546517	−	0.837448i	$-0.684047\pi$
$41$	−6.99883	−1.09303	−0.546517	+	0.837448i	$0.684047\pi$
$42$	−4.36690	−0.673827
$43$	−10.2836	−1.56823	−0.784113	−	0.620618i	$-0.786882\pi$
$43$	−10.2836	−1.56823	−0.784113	+	0.620618i	$0.786882\pi$
$44$	−11.3155	−1.70587
$45$	−1.81110	−0.269983
$46$	18.4656	2.72260
$47$	−5.57496	−0.813191	−0.406596	−	0.913608i	$-0.633284\pi$
$47$	−5.57496	−0.813191	−0.406596	+	0.913608i	$0.633284\pi$
$48$	0.969055	0.139871
$49$	−3.19192	−0.455989
$50$	−3.84879	−0.544302
$51$	1.00000	0.140028
$52$	−7.80744	−1.08270
$53$	−0.114191	−0.0156853	−0.00784267	−	0.999969i	$-0.502496\pi$
$53$	−0.114191	−0.0156853	−0.00784267	+	0.999969i	$0.502496\pi$
$54$	−2.23779	−0.304525
$55$	6.81363	0.918750
$56$	4.40061	0.588057
$57$	−4.69225	−0.621504
$58$	5.24178	0.688279
$59$	−7.88650	−1.02674	−0.513368	−	0.858169i	$-0.671602\pi$
$59$	−7.88650	−1.02674	−0.513368	+	0.858169i	$0.671602\pi$
$60$	5.44729	0.703243
$61$	−9.67642	−1.23894	−0.619469	−	0.785021i	$-0.712652\pi$
$61$	−9.67642	−1.23894	−0.619469	+	0.785021i	$0.712652\pi$
$62$	6.69726	0.850553
$63$	1.95143	0.245857
$64$	−13.0074	−1.62593
$65$	4.70126	0.583119
$66$	8.41890	1.03630
$67$	−5.84569	−0.714165	−0.357082	−	0.934073i	$-0.616228\pi$
$67$	−5.84569	−0.714165	−0.357082	+	0.934073i	$0.616228\pi$
$68$	−3.00772	−0.364740
$69$	−8.25169	−0.993387
$70$	−7.90890	−0.945294
$71$	5.46855	0.648997	0.324499	−	0.945886i	$-0.394804\pi$
$71$	5.46855	0.648997	0.324499	+	0.945886i	$0.394804\pi$
$72$	2.25507	0.265763
$73$	8.54565	1.00019	0.500096	−	0.865970i	$-0.333298\pi$
$73$	8.54565	1.00019	0.500096	+	0.865970i	$0.333298\pi$
$74$	−25.4857	−2.96266
$75$	1.71991	0.198598
$76$	14.1130	1.61887
$77$	−7.34156	−0.836648
$78$	5.80886	0.657724
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	1.75506	0.196222
$81$	1.00000	0.111111
$82$	−15.6619	−1.72957
$83$	7.99217	0.877255	0.438628	−	0.898669i	$-0.355465\pi$
$83$	7.99217	0.877255	0.438628	+	0.898669i	$0.355465\pi$
$84$	−5.86936	−0.640399
$85$	1.81110	0.196442
$86$	−23.0125	−2.48150
$87$	−2.34239	−0.251130
$88$	−8.48391	−0.904388
$89$	−0.507717	−0.0538179	−0.0269090	−	0.999638i	$-0.508566\pi$
$89$	−0.507717	−0.0538179	−0.0269090	+	0.999638i	$0.508566\pi$
$90$	−4.05288	−0.427211
$91$	−5.06552	−0.531011
$92$	24.8188	2.58754
$93$	−2.99280	−0.310338
$94$	−12.4756	−1.28676
$95$	−8.49815	−0.871892
$96$	6.67869	0.681641
$97$	−17.5617	−1.78312	−0.891560	−	0.452903i	$-0.850388\pi$
$97$	−17.5617	−1.78312	−0.891560	+	0.452903i	$0.850388\pi$
$98$	−7.14287	−0.721538
$99$	−3.76214	−0.378110
$100$	−5.17300	−0.517300
$101$	−15.1908	−1.51155	−0.755773	−	0.654834i	$-0.772738\pi$
$101$	−15.1908	−1.51155	−0.755773	+	0.654834i	$0.772738\pi$
$102$	2.23779	0.221575
$103$	−1.70206	−0.167709	−0.0838546	−	0.996478i	$-0.526723\pi$
$103$	−1.70206	−0.167709	−0.0838546	+	0.996478i	$0.526723\pi$
$104$	−5.85371	−0.574004
$105$	3.53424	0.344907
$106$	−0.255536	−0.0248199
$107$	10.0728	0.973776	0.486888	−	0.873464i	$-0.338132\pi$
$107$	10.0728	0.973776	0.486888	+	0.873464i	$0.338132\pi$
$108$	−3.00772	−0.289418
$109$	8.05222	0.771263	0.385632	−	0.922653i	$-0.373984\pi$
$109$	8.05222	0.771263	0.385632	+	0.922653i	$0.373984\pi$
$110$	15.2475	1.45379
$111$	11.3888	1.08097
$112$	−1.89104	−0.178687
$113$	7.21783	0.678996	0.339498	−	0.940607i	$-0.389743\pi$
$113$	7.21783	0.678996	0.339498	+	0.940607i	$0.389743\pi$
$114$	−10.5003	−0.983442
$115$	−14.9447	−1.39360
$116$	7.04525	0.654135
$117$	−2.59580	−0.239982
$118$	−17.6484	−1.62466
$119$	−1.95143	−0.178887
$120$	4.08417	0.372832
$121$	3.15373	0.286703
$122$	−21.6538	−1.96045
$123$	6.99883	0.631063
$124$	9.00150	0.808358
$125$	12.1704	1.08856
$126$	4.36690	0.389034
$127$	−0.563128	−0.0499695	−0.0249848	−	0.999688i	$-0.507954\pi$
$127$	−0.563128	−0.0499695	−0.0249848	+	0.999688i	$0.507954\pi$
$128$	−15.7505	−1.39216
$129$	10.2836	0.905416
$130$	10.5204	0.922705
$131$	2.02455	0.176885	0.0884427	−	0.996081i	$-0.471811\pi$
$131$	2.02455	0.176885	0.0884427	+	0.996081i	$0.471811\pi$
$132$	11.3155	0.984886
$133$	9.15660	0.793978
$134$	−13.0815	−1.13007
$135$	1.81110	0.155875
$136$	−2.25507	−0.193371
$137$	−1.14889	−0.0981560	−0.0490780	−	0.998795i	$-0.515628\pi$
$137$	−1.14889	−0.0981560	−0.0490780	+	0.998795i	$0.515628\pi$
$138$	−18.4656	−1.57189
$139$	0.0588397	0.00499072	0.00249536	−	0.999997i	$-0.499206\pi$
$139$	0.0588397	0.00499072	0.00249536	+	0.999997i	$0.499206\pi$
$140$	−10.6300	−0.898400
$141$	5.57496	0.469496
$142$	12.2375	1.02695
$143$	9.76577	0.816655
$144$	−0.969055	−0.0807546
$145$	−4.24230	−0.352304
$146$	19.1234	1.58266
$147$	3.19192	0.263265
$148$	−34.2543	−2.81568
$149$	−2.77566	−0.227391	−0.113695	−	0.993516i	$-0.536269\pi$
$149$	−2.77566	−0.227391	−0.113695	+	0.993516i	$0.536269\pi$
$150$	3.84879	0.314253
$151$	4.94163	0.402145	0.201072	−	0.979576i	$-0.435557\pi$
$151$	4.94163	0.402145	0.201072	+	0.979576i	$0.435557\pi$
$152$	10.5814	0.858262
$153$	−1.00000	−0.0808452
$154$	−16.4289	−1.32388
$155$	−5.42026	−0.435366
$156$	7.80744	0.625095
$157$	−16.9089	−1.34948	−0.674739	−	0.738056i	$-0.735744\pi$
$157$	−16.9089	−1.34948	−0.674739	+	0.738056i	$0.735744\pi$
$158$	−2.23779	−0.178029
$159$	0.114191	0.00905594
$160$	12.0958	0.956257
$161$	16.1026	1.26906
$162$	2.23779	0.175818
$163$	−1.68611	−0.132066	−0.0660330	−	0.997817i	$-0.521034\pi$
$163$	−1.68611	−0.132066	−0.0660330	+	0.997817i	$0.521034\pi$
$164$	−21.0505	−1.64377
$165$	−6.81363	−0.530441
$166$	17.8848	1.38813
$167$	19.4262	1.50324	0.751622	−	0.659594i	$-0.229272\pi$
$167$	19.4262	1.50324	0.751622	+	0.659594i	$0.229272\pi$
$168$	−4.40061	−0.339515
$169$	−6.26183	−0.481679
$170$	4.05288	0.310841
$171$	4.69225	0.358825
$172$	−30.9301	−2.35839
$173$	−16.5711	−1.25988	−0.629938	−	0.776645i	$-0.716920\pi$
$173$	−16.5711	−1.25988	−0.629938	+	0.776645i	$0.716920\pi$
$174$	−5.24178	−0.397378
$175$	−3.35627	−0.253710
$176$	3.64573	0.274807
$177$	7.88650	0.592786
$178$	−1.13617	−0.0851593
$179$	12.3294	0.921541	0.460771	−	0.887519i	$-0.347573\pi$
$179$	12.3294	0.921541	0.460771	+	0.887519i	$0.347573\pi$
$180$	−5.44729	−0.406017
$181$	−13.6785	−1.01671	−0.508356	−	0.861147i	$-0.669747\pi$
$181$	−13.6785	−1.01671	−0.508356	+	0.861147i	$0.669747\pi$
$182$	−11.3356	−0.840250
$183$	9.67642	0.715301
$184$	18.6082	1.37181
$185$	20.6262	1.51647
$186$	−6.69726	−0.491067
$187$	3.76214	0.275115
$188$	−16.7679	−1.22293
$189$	−1.95143	−0.141946
$190$	−19.0171	−1.37965
$191$	20.6767	1.49611	0.748055	−	0.663636i	$-0.230988\pi$
$191$	20.6767	1.49611	0.748055	+	0.663636i	$0.230988\pi$
$192$	13.0074	0.938730
$193$	21.3988	1.54032	0.770159	−	0.637852i	$-0.220177\pi$
$193$	21.3988	1.54032	0.770159	+	0.637852i	$0.220177\pi$
$194$	−39.2994	−2.82154
$195$	−4.70126	−0.336664
$196$	−9.60041	−0.685744
$197$	−10.7364	−0.764936	−0.382468	−	0.923969i	$-0.624926\pi$
$197$	−10.7364	−0.764936	−0.382468	+	0.923969i	$0.624926\pi$
$198$	−8.41890	−0.598305
$199$	−1.53583	−0.108872	−0.0544362	−	0.998517i	$-0.517336\pi$
$199$	−1.53583	−0.108872	−0.0544362	+	0.998517i	$0.517336\pi$
$200$	−3.87851	−0.274252
$201$	5.84569	0.412323
$202$	−33.9940	−2.39181
$203$	4.57100	0.320822
$204$	3.00772	0.210583
$205$	12.6756	0.885303
$206$	−3.80886	−0.265376
$207$	8.25169	0.573532
$208$	2.51547	0.174417
$209$	−17.6529	−1.22108
$210$	7.90890	0.545766
$211$	−3.51013	−0.241647	−0.120824	−	0.992674i	$-0.538554\pi$
$211$	−3.51013	−0.241647	−0.120824	+	0.992674i	$0.538554\pi$
$212$	−0.343455	−0.0235886
$213$	−5.46855	−0.374699
$214$	22.5409	1.54086
$215$	18.6246	1.27019
$216$	−2.25507	−0.153438
$217$	5.84023	0.396461
$218$	18.0192	1.22042
$219$	−8.54565	−0.577461
$220$	20.4935	1.38167
$221$	2.59580	0.174612
$222$	25.4857	1.71049
$223$	−20.5413	−1.37555	−0.687774	−	0.725925i	$-0.741412\pi$
$223$	−20.5413	−1.37555	−0.687774	+	0.725925i	$0.741412\pi$
$224$	−13.0330	−0.870804
$225$	−1.71991	−0.114660
$226$	16.1520	1.07442
$227$	16.7047	1.10873	0.554365	−	0.832274i	$-0.312961\pi$
$227$	16.7047	1.10873	0.554365	+	0.832274i	$0.312961\pi$
$228$	−14.1130	−0.934655
$229$	5.27118	0.348329	0.174165	−	0.984717i	$-0.444278\pi$
$229$	5.27118	0.348329	0.174165	+	0.984717i	$0.444278\pi$
$230$	−33.4431	−2.20517
$231$	7.34156	0.483039
$232$	5.28225	0.346797
$233$	6.08348	0.398542	0.199271	−	0.979944i	$-0.436143\pi$
$233$	6.08348	0.398542	0.199271	+	0.979944i	$0.436143\pi$
$234$	−5.80886	−0.379737
$235$	10.0968	0.658644
$236$	−23.7204	−1.54407
$237$	1.00000	0.0649570
$238$	−4.36690	−0.283064
$239$	3.51883	0.227615	0.113807	−	0.993503i	$-0.463695\pi$
$239$	3.51883	0.227615	0.113807	+	0.993503i	$0.463695\pi$
$240$	−1.75506	−0.113289
$241$	7.23237	0.465878	0.232939	−	0.972491i	$-0.425166\pi$
$241$	7.23237	0.465878	0.232939	+	0.972491i	$0.425166\pi$
$242$	7.05740	0.453667
$243$	−1.00000	−0.0641500
$244$	−29.1040	−1.86319
$245$	5.78090	0.369328
$246$	15.6619	0.998569
$247$	−12.1801	−0.775004
$248$	6.74897	0.428560
$249$	−7.99217	−0.506483
$250$	27.2349	1.72249
$251$	−13.5031	−0.852306	−0.426153	−	0.904651i	$-0.640132\pi$
$251$	−13.5031	−0.852306	−0.426153	+	0.904651i	$0.640132\pi$
$252$	5.86936	0.369735
$253$	−31.0441	−1.95172
$254$	−1.26016	−0.0790697
$255$	−1.81110	−0.113416
$256$	−9.23163	−0.576977
$257$	9.71592	0.606062	0.303031	−	0.952981i	$-0.402001\pi$
$257$	9.71592	0.606062	0.303031	+	0.952981i	$0.402001\pi$
$258$	23.0125	1.43269
$259$	−22.2244	−1.38096
$260$	14.1401	0.876930
$261$	2.34239	0.144990
$262$	4.53052	0.279896
$263$	−1.41230	−0.0870862	−0.0435431	−	0.999052i	$-0.513865\pi$
$263$	−1.41230	−0.0870862	−0.0435431	+	0.999052i	$0.513865\pi$
$264$	8.48391	0.522148
$265$	0.206812	0.0127043
$266$	20.4906	1.25636
$267$	0.507717	0.0310718
$268$	−17.5822	−1.07400
$269$	1.19613	0.0729291	0.0364646	−	0.999335i	$-0.488390\pi$
$269$	1.19613	0.0729291	0.0364646	+	0.999335i	$0.488390\pi$
$270$	4.05288	0.246650
$271$	−17.0012	−1.03275	−0.516375	−	0.856362i	$-0.672719\pi$
$271$	−17.0012	−1.03275	−0.516375	+	0.856362i	$0.672719\pi$
$272$	0.969055	0.0587576
$273$	5.06552	0.306579
$274$	−2.57097	−0.155318
$275$	6.47053	0.390188
$276$	−24.8188	−1.49392
$277$	9.60726	0.577244	0.288622	−	0.957443i	$-0.406803\pi$
$277$	9.60726	0.577244	0.288622	+	0.957443i	$0.406803\pi$
$278$	0.131671	0.00789711
$279$	2.99280	0.179174
$280$	−7.96997	−0.476297
$281$	7.03133	0.419454	0.209727	−	0.977760i	$-0.432743\pi$
$281$	7.03133	0.419454	0.209727	+	0.977760i	$0.432743\pi$
$282$	12.4756	0.742912
$283$	1.92263	0.114289	0.0571443	−	0.998366i	$-0.481800\pi$
$283$	1.92263	0.114289	0.0571443	+	0.998366i	$0.481800\pi$
$284$	16.4479	0.976001
$285$	8.49815	0.503387
$286$	21.8538	1.29224
$287$	−13.6577	−0.806190
$288$	−6.67869	−0.393546
$289$	1.00000	0.0588235
$290$	−9.49340	−0.557472
$291$	17.5617	1.02948
$292$	25.7029	1.50415
$293$	32.7412	1.91276	0.956380	−	0.292127i	$-0.0943630\pi$
$293$	32.7412	1.91276	0.956380	+	0.292127i	$0.0943630\pi$
$294$	7.14287	0.416580
$295$	14.2833	0.831604
$296$	−25.6825	−1.49277
$297$	3.76214	0.218302
$298$	−6.21135	−0.359814
$299$	−21.4197	−1.23874
$300$	5.17300	0.298663
$301$	−20.0676	−1.15668
$302$	11.0584	0.636337
$303$	15.1908	0.872691
$304$	−4.54705	−0.260791
$305$	17.5250	1.00348
$306$	−2.23779	−0.127926
$307$	8.25901	0.471366	0.235683	−	0.971830i	$-0.424267\pi$
$307$	8.25901	0.471366	0.235683	+	0.971830i	$0.424267\pi$
$308$	−22.0814	−1.25820
$309$	1.70206	0.0968269
$310$	−12.1294	−0.688905
$311$	3.47577	0.197093	0.0985463	−	0.995132i	$-0.468581\pi$
$311$	3.47577	0.197093	0.0985463	+	0.995132i	$0.468581\pi$
$312$	5.85371	0.331401
$313$	−14.0764	−0.795647	−0.397823	−	0.917462i	$-0.630234\pi$
$313$	−14.0764	−0.795647	−0.397823	+	0.917462i	$0.630234\pi$
$314$	−37.8387	−2.13536
$315$	−3.53424	−0.199132
$316$	−3.00772	−0.169198
$317$	−7.90270	−0.443860	−0.221930	−	0.975063i	$-0.571236\pi$
$317$	−7.90270	−0.443860	−0.221930	+	0.975063i	$0.571236\pi$
$318$	0.255536	0.0143298
$319$	−8.81240	−0.493400
$320$	23.5578	1.31692
$321$	−10.0728	−0.562210
$322$	36.0343	2.00811
$323$	−4.69225	−0.261084
$324$	3.00772	0.167096
$325$	4.46453	0.247647
$326$	−3.77316	−0.208976
$327$	−8.05222	−0.445289
$328$	−15.7829	−0.871463
$329$	−10.8791	−0.599786
$330$	−15.2475	−0.839347
$331$	−11.8845	−0.653231	−0.326616	−	0.945157i	$-0.605908\pi$
$331$	−11.8845	−0.653231	−0.326616	+	0.945157i	$0.605908\pi$
$332$	24.0382	1.31927
$333$	−11.3888	−0.624101
$334$	43.4718	2.37867
$335$	10.5872	0.578438
$336$	1.89104	0.103165
$337$	8.76999	0.477732	0.238866	−	0.971053i	$-0.423224\pi$
$337$	8.76999	0.477732	0.238866	+	0.971053i	$0.423224\pi$
$338$	−14.0127	−0.762189
$339$	−7.21783	−0.392019
$340$	5.44729	0.295421
$341$	−11.2593	−0.609727
$342$	10.5003	0.567791
$343$	−19.8888	−1.07390
$344$	−23.1902	−1.25033
$345$	14.9447	0.804594
$346$	−37.0827	−1.99358
$347$	11.5045	0.617592	0.308796	−	0.951128i	$-0.400074\pi$
$347$	11.5045	0.617592	0.308796	+	0.951128i	$0.400074\pi$
$348$	−7.04525	−0.377665
$349$	12.4215	0.664905	0.332453	−	0.943120i	$-0.392124\pi$
$349$	12.4215	0.664905	0.332453	+	0.943120i	$0.392124\pi$
$350$	−7.51065	−0.401461
$351$	2.59580	0.138553
$352$	25.1262	1.33923
$353$	−2.72075	−0.144811	−0.0724053	−	0.997375i	$-0.523068\pi$
$353$	−2.72075	−0.144811	−0.0724053	+	0.997375i	$0.523068\pi$
$354$	17.6484	0.938000
$355$	−9.90410	−0.525655
$356$	−1.52707	−0.0809346
$357$	1.95143	0.103281
$358$	27.5906	1.45821
$359$	−21.7697	−1.14896	−0.574482	−	0.818517i	$-0.694796\pi$
$359$	−21.7697	−1.14896	−0.574482	+	0.818517i	$0.694796\pi$
$360$	−4.08417	−0.215255
$361$	3.01722	0.158801
$362$	−30.6096	−1.60880
$363$	−3.15373	−0.165528
$364$	−15.2357	−0.798566
$365$	−15.4770	−0.810106
$366$	21.6538	1.13186
$367$	−26.8512	−1.40162	−0.700812	−	0.713346i	$-0.747179\pi$
$367$	−26.8512	−1.40162	−0.700812	+	0.713346i	$0.747179\pi$
$368$	−7.99635	−0.416838
$369$	−6.99883	−0.364345
$370$	46.1573	2.39960
$371$	−0.222836	−0.0115691
$372$	−9.00150	−0.466706
$373$	−10.1751	−0.526849	−0.263424	−	0.964680i	$-0.584852\pi$
$373$	−10.1751	−0.526849	−0.263424	+	0.964680i	$0.584852\pi$
$374$	8.41890	0.435331
$375$	−12.1704	−0.628479
$376$	−12.5719	−0.648348
$377$	−6.08037	−0.313155
$378$	−4.36690	−0.224609
$379$	0.958161	0.0492174	0.0246087	−	0.999697i	$-0.492166\pi$
$379$	0.958161	0.0492174	0.0246087	+	0.999697i	$0.492166\pi$
$380$	−25.5601	−1.31120
$381$	0.563128	0.0288499
$382$	46.2701	2.36738
$383$	−9.08530	−0.464237	−0.232119	−	0.972688i	$-0.574566\pi$
$383$	−9.08530	−0.464237	−0.232119	+	0.972688i	$0.574566\pi$
$384$	15.7505	0.803767
$385$	13.2963	0.677643
$386$	47.8860	2.43734
$387$	−10.2836	−0.522742
$388$	−52.8207	−2.68156
$389$	4.47536	0.226910	0.113455	−	0.993543i	$-0.463808\pi$
$389$	4.47536	0.226910	0.113455	+	0.993543i	$0.463808\pi$
$390$	−10.5204	−0.532724
$391$	−8.25169	−0.417306
$392$	−7.19802	−0.363555
$393$	−2.02455	−0.102125
$394$	−24.0258	−1.21040
$395$	1.81110	0.0911265
$396$	−11.3155	−0.568624
$397$	9.64683	0.484160	0.242080	−	0.970256i	$-0.422170\pi$
$397$	9.64683	0.484160	0.242080	+	0.970256i	$0.422170\pi$
$398$	−3.43688	−0.172275
$399$	−9.15660	−0.458403
$400$	1.66668	0.0833342
$401$	−31.0672	−1.55142	−0.775712	−	0.631087i	$-0.782609\pi$
$401$	−31.0672	−1.55142	−0.775712	+	0.631087i	$0.782609\pi$
$402$	13.0815	0.652444
$403$	−7.76870	−0.386986
$404$	−45.6898	−2.27315
$405$	−1.81110	−0.0899944
$406$	10.2290	0.507655
$407$	42.8462	2.12381
$408$	2.25507	0.111643
$409$	12.2724	0.606829	0.303414	−	0.952859i	$-0.401873\pi$
$409$	12.2724	0.606829	0.303414	+	0.952859i	$0.401873\pi$
$410$	28.3654	1.40087
$411$	1.14889	0.0566704
$412$	−5.11933	−0.252211
$413$	−15.3900	−0.757290
$414$	18.4656	0.907534
$415$	−14.4747	−0.710533
$416$	17.3365	0.849994
$417$	−0.0588397	−0.00288139
$418$	−39.5036	−1.93219
$419$	13.8528	0.676751	0.338376	−	0.941011i	$-0.390123\pi$
$419$	13.8528	0.676751	0.338376	+	0.941011i	$0.390123\pi$
$420$	10.6300	0.518691
$421$	−6.03003	−0.293886	−0.146943	−	0.989145i	$-0.546943\pi$
$421$	−6.03003	−0.293886	−0.146943	+	0.989145i	$0.546943\pi$
$422$	−7.85495	−0.382373
$423$	−5.57496	−0.271064
$424$	−0.257509	−0.0125057
$425$	1.71991	0.0834277
$426$	−12.2375	−0.592908
$427$	−18.8828	−0.913805
$428$	30.2962	1.46442
$429$	−9.76577	−0.471496
$430$	41.6779	2.00989
$431$	−21.0328	−1.01311	−0.506557	−	0.862207i	$-0.669082\pi$
$431$	−21.0328	−1.01311	−0.506557	+	0.862207i	$0.669082\pi$
$432$	0.969055	0.0466237
$433$	−0.333772	−0.0160400	−0.00802002	−	0.999968i	$-0.502553\pi$
$433$	−0.333772	−0.0160400	−0.00802002	+	0.999968i	$0.502553\pi$
$434$	13.0692	0.627343
$435$	4.24230	0.203403
$436$	24.2188	1.15987
$437$	38.7190	1.85218
$438$	−19.1234	−0.913751
$439$	29.1345	1.39052	0.695258	−	0.718760i	$-0.255290\pi$
$439$	29.1345	1.39052	0.695258	+	0.718760i	$0.255290\pi$
$440$	15.3652	0.732509
$441$	−3.19192	−0.151996
$442$	5.80886	0.276299
$443$	10.8007	0.513159	0.256580	−	0.966523i	$-0.417404\pi$
$443$	10.8007	0.513159	0.256580	+	0.966523i	$0.417404\pi$
$444$	34.2543	1.62563
$445$	0.919528	0.0435898
$446$	−45.9672	−2.17661
$447$	2.77566	0.131284
$448$	−25.3831	−1.19924
$449$	17.9946	0.849217	0.424609	−	0.905377i	$-0.360412\pi$
$449$	17.9946	0.849217	0.424609	+	0.905377i	$0.360412\pi$
$450$	−3.84879	−0.181434
$451$	26.3306	1.23986
$452$	21.7092	1.02112
$453$	−4.94163	−0.232178
$454$	37.3817	1.75441
$455$	9.17418	0.430092
$456$	−10.5814	−0.495518
$457$	19.4318	0.908981	0.454490	−	0.890752i	$-0.349821\pi$
$457$	19.4318	0.908981	0.454490	+	0.890752i	$0.349821\pi$
$458$	11.7958	0.551182
$459$	1.00000	0.0466760
$460$	−44.9494	−2.09578
$461$	−30.3980	−1.41578	−0.707889	−	0.706324i	$-0.750352\pi$
$461$	−30.3980	−1.41578	−0.707889	+	0.706324i	$0.750352\pi$
$462$	16.4289	0.764342
$463$	26.7211	1.24183	0.620917	−	0.783876i	$-0.286760\pi$
$463$	26.7211	1.24183	0.620917	+	0.783876i	$0.286760\pi$
$464$	−2.26990	−0.105378
$465$	5.42026	0.251359
$466$	13.6136	0.630636
$467$	−3.80523	−0.176085	−0.0880424	−	0.996117i	$-0.528061\pi$
$467$	−3.80523	−0.176085	−0.0880424	+	0.996117i	$0.528061\pi$
$468$	−7.80744	−0.360899
$469$	−11.4075	−0.526747
$470$	22.5946	1.04221
$471$	16.9089	0.779122
$472$	−17.7846	−0.818604
$473$	38.6882	1.77889
$474$	2.23779	0.102785
$475$	−8.07023	−0.370287
$476$	−5.86936	−0.269021
$477$	−0.114191	−0.00522845
$478$	7.87443	0.360168
$479$	−1.23300	−0.0563370	−0.0281685	−	0.999603i	$-0.508968\pi$
$479$	−1.23300	−0.0563370	−0.0281685	+	0.999603i	$0.508968\pi$
$480$	−12.0958	−0.552095
$481$	29.5630	1.34796
$482$	16.1846	0.737186
$483$	−16.1026	−0.732693
$484$	9.48555	0.431161
$485$	31.8060	1.44424
$486$	−2.23779	−0.101508
$487$	39.2384	1.77806	0.889031	−	0.457847i	$-0.151379\pi$
$487$	39.2384	1.77806	0.889031	+	0.457847i	$0.151379\pi$
$488$	−21.8210	−0.987791
$489$	1.68611	0.0762483
$490$	12.9365	0.584410
$491$	31.5183	1.42240	0.711201	−	0.702988i	$-0.248151\pi$
$491$	31.5183	1.42240	0.711201	+	0.702988i	$0.248151\pi$
$492$	21.0505	0.949031
$493$	−2.34239	−0.105496
$494$	−27.2566	−1.22633
$495$	6.81363	0.306250
$496$	−2.90018	−0.130222
$497$	10.6715	0.478682
$498$	−17.8848	−0.801439
$499$	−14.1479	−0.633347	−0.316673	−	0.948535i	$-0.602566\pi$
$499$	−14.1479	−0.633347	−0.316673	+	0.948535i	$0.602566\pi$
$500$	36.6053	1.63704
$501$	−19.4262	−0.867899
$502$	−30.2171	−1.34865
$503$	10.0123	0.446425	0.223212	−	0.974770i	$-0.428346\pi$
$503$	10.0123	0.446425	0.223212	+	0.974770i	$0.428346\pi$
$504$	4.40061	0.196019
$505$	27.5122	1.22428
$506$	−69.4702	−3.08833
$507$	6.26183	0.278098
$508$	−1.69373	−0.0751472
$509$	−8.40023	−0.372333	−0.186167	−	0.982518i	$-0.559606\pi$
$509$	−8.40023	−0.372333	−0.186167	+	0.982518i	$0.559606\pi$
$510$	−4.05288	−0.179464
$511$	16.6762	0.737713
$512$	10.8426	0.479180
$513$	−4.69225	−0.207168
$514$	21.7422	0.959008
$515$	3.08261	0.135836
$516$	30.9301	1.36162
$517$	20.9738	0.922427
$518$	−49.7336	−2.18517
$519$	16.5711	0.727390
$520$	10.6017	0.464914
$521$	9.69486	0.424740	0.212370	−	0.977189i	$-0.431882\pi$
$521$	9.69486	0.424740	0.212370	+	0.977189i	$0.431882\pi$
$522$	5.24178	0.229426
$523$	−16.6578	−0.728396	−0.364198	−	0.931322i	$-0.618657\pi$
$523$	−16.6578	−0.728396	−0.364198	+	0.931322i	$0.618657\pi$
$524$	6.08927	0.266011
$525$	3.35627	0.146480
$526$	−3.16044	−0.137802
$527$	−2.99280	−0.130368
$528$	−3.64573	−0.158660
$529$	45.0904	1.96045
$530$	0.462802	0.0201028
$531$	−7.88650	−0.342245
$532$	27.5405	1.19403
$533$	18.1676	0.786924
$534$	1.13617	0.0491667
$535$	−18.2429	−0.788710
$536$	−13.1825	−0.569395
$537$	−12.3294	−0.532052
$538$	2.67668	0.115400
$539$	12.0085	0.517242
$540$	5.44729	0.234414
$541$	−9.91670	−0.426352	−0.213176	−	0.977014i	$-0.568381\pi$
$541$	−9.91670	−0.426352	−0.213176	+	0.977014i	$0.568381\pi$
$542$	−38.0452	−1.63418
$543$	13.6785	0.586999
$544$	6.67869	0.286347
$545$	−14.5834	−0.624685
$546$	11.3356	0.485118
$547$	43.7273	1.86965	0.934823	−	0.355113i	$-0.115558\pi$
$547$	43.7273	1.86965	0.934823	+	0.355113i	$0.115558\pi$
$548$	−3.45553	−0.147613
$549$	−9.67642	−0.412979
$550$	14.4797	0.617417
$551$	10.9911	0.468235
$552$	−18.6082	−0.792016
$553$	−1.95143	−0.0829832
$554$	21.4991	0.913407
$555$	−20.6262	−0.875535
$556$	0.176974	0.00750535
$557$	18.6756	0.791310	0.395655	−	0.918399i	$-0.370518\pi$
$557$	18.6756	0.791310	0.395655	+	0.918399i	$0.370518\pi$
$558$	6.69726	0.283518
$559$	26.6940	1.12904
$560$	3.42487	0.144727
$561$	−3.76214	−0.158838
$562$	15.7347	0.663727
$563$	−33.2960	−1.40326	−0.701630	−	0.712542i	$-0.747544\pi$
$563$	−33.2960	−1.40326	−0.701630	+	0.712542i	$0.747544\pi$
$564$	16.7679	0.706057
$565$	−13.0722	−0.549953
$566$	4.30246	0.180846
$567$	1.95143	0.0819523
$568$	12.3320	0.517438
$569$	20.9741	0.879282	0.439641	−	0.898174i	$-0.355106\pi$
$569$	20.9741	0.879282	0.439641	+	0.898174i	$0.355106\pi$
$570$	19.0171	0.796539
$571$	19.2148	0.804116	0.402058	−	0.915614i	$-0.368295\pi$
$571$	19.2148	0.804116	0.402058	+	0.915614i	$0.368295\pi$
$572$	29.3727	1.22814
$573$	−20.6767	−0.863780
$574$	−30.5632	−1.27568
$575$	−14.1921	−0.591853
$576$	−13.0074	−0.541976
$577$	−38.0650	−1.58467	−0.792334	−	0.610088i	$-0.791134\pi$
$577$	−38.0650	−1.58467	−0.792334	+	0.610088i	$0.791134\pi$
$578$	2.23779	0.0930800
$579$	−21.3988	−0.889303
$580$	−12.7597	−0.529816
$581$	15.5962	0.647038
$582$	39.2994	1.62901
$583$	0.429603	0.0177924
$584$	19.2710	0.797442
$585$	4.70126	0.194373
$586$	73.2680	3.02667
$587$	−27.1955	−1.12248	−0.561240	−	0.827653i	$-0.689675\pi$
$587$	−27.1955	−1.12248	−0.561240	+	0.827653i	$0.689675\pi$
$588$	9.60041	0.395914
$589$	14.0430	0.578630
$590$	31.9630	1.31590
$591$	10.7364	0.441636
$592$	11.0364	0.453591
$593$	−23.9193	−0.982246	−0.491123	−	0.871090i	$-0.663413\pi$
$593$	−23.9193	−0.982246	−0.491123	+	0.871090i	$0.663413\pi$
$594$	8.41890	0.345432
$595$	3.53424	0.144890
$596$	−8.34841	−0.341964
$597$	1.53583	0.0628575
$598$	−47.9329	−1.96012
$599$	−27.2480	−1.11332	−0.556661	−	0.830740i	$-0.687918\pi$
$599$	−27.2480	−1.11332	−0.556661	+	0.830740i	$0.687918\pi$
$600$	3.87851	0.158340
$601$	19.9215	0.812614	0.406307	−	0.913737i	$-0.366816\pi$
$601$	19.9215	0.812614	0.406307	+	0.913737i	$0.366816\pi$
$602$	−44.9072	−1.83028
$603$	−5.84569	−0.238055
$604$	14.8631	0.604769
$605$	−5.71174	−0.232215
$606$	33.9940	1.38091
$607$	−2.36221	−0.0958791	−0.0479396	−	0.998850i	$-0.515265\pi$
$607$	−2.36221	−0.0958791	−0.0479396	+	0.998850i	$0.515265\pi$
$608$	−31.3381	−1.27093
$609$	−4.57100	−0.185226
$610$	39.2173	1.58786
$611$	14.4715	0.585453
$612$	−3.00772	−0.121580
$613$	43.6360	1.76244	0.881220	−	0.472707i	$-0.156723\pi$
$613$	43.6360	1.76244	0.881220	+	0.472707i	$0.156723\pi$
$614$	18.4820	0.745871
$615$	−12.6756	−0.511130
$616$	−16.5557	−0.667050
$617$	−3.93826	−0.158549	−0.0792743	−	0.996853i	$-0.525260\pi$
$617$	−3.93826	−0.158549	−0.0792743	+	0.996853i	$0.525260\pi$
$618$	3.80886	0.153215
$619$	−18.0327	−0.724796	−0.362398	−	0.932023i	$-0.618042\pi$
$619$	−18.0327	−0.724796	−0.362398	+	0.932023i	$0.618042\pi$
$620$	−16.3026	−0.654730
$621$	−8.25169	−0.331129
$622$	7.77805	0.311871
$623$	−0.990774	−0.0396945
$624$	−2.51547	−0.100700
$625$	−13.4424	−0.537696
$626$	−31.5001	−1.25900
$627$	17.6529	0.704990
$628$	−50.8573	−2.02943
$629$	11.3888	0.454100
$630$	−7.90890	−0.315098
$631$	−29.2305	−1.16365	−0.581823	−	0.813315i	$-0.697660\pi$
$631$	−29.2305	−1.16365	−0.581823	+	0.813315i	$0.697660\pi$
$632$	−2.25507	−0.0897020
$633$	3.51013	0.139515
$634$	−17.6846	−0.702345
$635$	1.01988	0.0404728
$636$	0.343455	0.0136189
$637$	8.28559	0.328287
$638$	−19.7203	−0.780735
$639$	5.46855	0.216332
$640$	28.5259	1.12758
$641$	42.7169	1.68722	0.843608	−	0.536960i	$-0.180427\pi$
$641$	42.7169	1.68722	0.843608	+	0.536960i	$0.180427\pi$
$642$	−22.5409	−0.889618
$643$	31.6514	1.24821	0.624104	−	0.781341i	$-0.285464\pi$
$643$	31.6514	1.24821	0.624104	+	0.781341i	$0.285464\pi$
$644$	48.4321	1.90849
$645$	−18.6246	−0.733342
$646$	−10.5003	−0.413128
$647$	−30.2531	−1.18937	−0.594687	−	0.803957i	$-0.702724\pi$
$647$	−30.2531	−1.18937	−0.594687	+	0.803957i	$0.702724\pi$
$648$	2.25507	0.0885876
$649$	29.6702	1.16466
$650$	9.99069	0.391867
$651$	−5.84023	−0.228897
$652$	−5.07134	−0.198609
$653$	−33.9225	−1.32749	−0.663746	−	0.747958i	$-0.731034\pi$
$653$	−33.9225	−1.32749	−0.663746	+	0.747958i	$0.731034\pi$
$654$	−18.0192	−0.704607
$655$	−3.66666	−0.143268
$656$	6.78225	0.264803
$657$	8.54565	0.333397
$658$	−24.3453	−0.949077
$659$	34.0418	1.32608	0.663040	−	0.748584i	$-0.269266\pi$
$659$	34.0418	1.32608	0.663040	+	0.748584i	$0.269266\pi$
$660$	−20.4935	−0.797709
$661$	9.94741	0.386910	0.193455	−	0.981109i	$-0.438031\pi$
$661$	9.94741	0.386910	0.193455	+	0.981109i	$0.438031\pi$
$662$	−26.5951	−1.03365
$663$	−2.59580	−0.100812
$664$	18.0229	0.699425
$665$	−16.5835	−0.643082
$666$	−25.4857	−0.987552
$667$	19.3287	0.748409
$668$	58.4286	2.26067
$669$	20.5413	0.794173
$670$	23.6919	0.915296
$671$	36.4041	1.40536
$672$	13.0330	0.502759
$673$	−33.9010	−1.30679	−0.653393	−	0.757019i	$-0.726655\pi$
$673$	−33.9010	−1.30679	−0.653393	+	0.757019i	$0.726655\pi$
$674$	19.6254	0.755944
$675$	1.71991	0.0661992
$676$	−18.8338	−0.724378
$677$	−19.1554	−0.736202	−0.368101	−	0.929786i	$-0.619992\pi$
$677$	−19.1554	−0.736202	−0.368101	+	0.929786i	$0.619992\pi$
$678$	−16.1520	−0.620314
$679$	−34.2704	−1.31518
$680$	4.08417	0.156621
$681$	−16.7047	−0.640125
$682$	−25.1961	−0.964807
$683$	−28.7044	−1.09834	−0.549171	−	0.835710i	$-0.685056\pi$
$683$	−28.7044	−1.09834	−0.549171	+	0.835710i	$0.685056\pi$
$684$	14.1130	0.539623
$685$	2.08075	0.0795015
$686$	−44.5071	−1.69929
$687$	−5.27118	−0.201108
$688$	9.96533	0.379925
$689$	0.296417	0.0112926
$690$	33.4431	1.27316
$691$	−15.3479	−0.583861	−0.291931	−	0.956439i	$-0.594298\pi$
$691$	−15.3479	−0.583861	−0.291931	+	0.956439i	$0.594298\pi$
$692$	−49.8412	−1.89468
$693$	−7.34156	−0.278883
$694$	25.7446	0.977253
$695$	−0.106565	−0.00404223
$696$	−5.28225	−0.200223
$697$	6.99883	0.265100
$698$	27.7967	1.05212
$699$	−6.08348	−0.230098
$700$	−10.0947	−0.381545
$701$	−3.70554	−0.139956	−0.0699782	−	0.997549i	$-0.522293\pi$
$701$	−3.70554	−0.139956	−0.0699782	+	0.997549i	$0.522293\pi$
$702$	5.80886	0.219241
$703$	−53.4390	−2.01549
$704$	48.9358	1.84434
$705$	−10.0968	−0.380268
$706$	−6.08847	−0.229143
$707$	−29.6439	−1.11487
$708$	23.7204	0.891467
$709$	−18.9114	−0.710234	−0.355117	−	0.934822i	$-0.615559\pi$
$709$	−18.9114	−0.710234	−0.355117	+	0.934822i	$0.615559\pi$
$710$	−22.1633	−0.831775
$711$	−1.00000	−0.0375029
$712$	−1.14494	−0.0429084
$713$	24.6956	0.924859
$714$	4.36690	0.163427
$715$	−17.6868	−0.661450
$716$	37.0833	1.38587
$717$	−3.51883	−0.131413
$718$	−48.7162	−1.81807
$719$	−45.2707	−1.68831	−0.844156	−	0.536098i	$-0.819898\pi$
$719$	−45.2707	−1.68831	−0.844156	+	0.536098i	$0.819898\pi$
$720$	1.75506	0.0654072
$721$	−3.32145	−0.123697
$722$	6.75193	0.251281
$723$	−7.23237	−0.268975
$724$	−41.1410	−1.52899
$725$	−4.02868	−0.149622
$726$	−7.05740	−0.261925
$727$	−16.4775	−0.611117	−0.305558	−	0.952173i	$-0.598843\pi$
$727$	−16.4775	−0.611117	−0.305558	+	0.952173i	$0.598843\pi$
$728$	−11.4231	−0.423369
$729$	1.00000	0.0370370
$730$	−34.6344	−1.28188
$731$	10.2836	0.380351
$732$	29.1040	1.07571
$733$	24.8492	0.917826	0.458913	−	0.888481i	$-0.348239\pi$
$733$	24.8492	0.917826	0.458913	+	0.888481i	$0.348239\pi$
$734$	−60.0875	−2.21787
$735$	−5.78090	−0.213232
$736$	−55.1105	−2.03140
$737$	21.9923	0.810098
$738$	−15.6619	−0.576524
$739$	−23.4306	−0.861907	−0.430953	−	0.902374i	$-0.641823\pi$
$739$	−23.4306	−0.861907	−0.430953	+	0.902374i	$0.641823\pi$
$740$	62.0380	2.28056
$741$	12.1801	0.447449
$742$	−0.498661	−0.0183064
$743$	50.4334	1.85022	0.925110	−	0.379698i	$-0.123972\pi$
$743$	50.4334	1.85022	0.925110	+	0.379698i	$0.123972\pi$
$744$	−6.74897	−0.247429
$745$	5.02701	0.184175
$746$	−22.7699	−0.833664
$747$	7.99217	0.292418
$748$	11.3155	0.413735
$749$	19.6564	0.718229
$750$	−27.2349	−0.994479
$751$	11.6575	0.425389	0.212694	−	0.977119i	$-0.431776\pi$
$751$	11.6575	0.425389	0.212694	+	0.977119i	$0.431776\pi$
$752$	5.40244	0.197007
$753$	13.5031	0.492079
$754$	−13.6066	−0.495523
$755$	−8.94981	−0.325717
$756$	−5.86936	−0.213466
$757$	15.3495	0.557889	0.278944	−	0.960307i	$-0.410015\pi$
$757$	15.3495	0.557889	0.278944	+	0.960307i	$0.410015\pi$
$758$	2.14417	0.0778797
$759$	31.0441	1.12683
$760$	−19.1639	−0.695149
$761$	42.8607	1.55370	0.776849	−	0.629686i	$-0.216817\pi$
$761$	42.8607	1.55370	0.776849	+	0.629686i	$0.216817\pi$
$762$	1.26016	0.0456509
$763$	15.7133	0.568861
$764$	62.1896	2.24994
$765$	1.81110	0.0654806
$766$	−20.3310	−0.734590
$767$	20.4718	0.739193
$768$	9.23163	0.333118
$769$	3.78756	0.136583	0.0682915	−	0.997665i	$-0.478245\pi$
$769$	3.78756	0.136583	0.0682915	+	0.997665i	$0.478245\pi$
$770$	29.7544	1.07228
$771$	−9.71592	−0.349910
$772$	64.3615	2.31642
$773$	−30.8308	−1.10891	−0.554453	−	0.832215i	$-0.687073\pi$
$773$	−30.8308	−1.10891	−0.554453	+	0.832215i	$0.687073\pi$
$774$	−23.0125	−0.827166
$775$	−5.14733	−0.184897
$776$	−39.6029	−1.42166
$777$	22.2244	0.797295
$778$	10.0149	0.359053
$779$	−32.8403	−1.17662
$780$	−14.1401	−0.506296
$781$	−20.5735	−0.736177
$782$	−18.4656	−0.660328
$783$	−2.34239	−0.0837101
$784$	3.09315	0.110470
$785$	30.6238	1.09301
$786$	−4.53052	−0.161598
$787$	−11.1238	−0.396521	−0.198260	−	0.980149i	$-0.563529\pi$
$787$	−11.1238	−0.396521	−0.198260	+	0.980149i	$0.563529\pi$
$788$	−32.2921	−1.15036
$789$	1.41230	0.0502792
$790$	4.05288	0.144195
$791$	14.0851	0.500808
$792$	−8.48391	−0.301463
$793$	25.1180	0.891967
$794$	21.5876	0.766115
$795$	−0.206812	−0.00733486
$796$	−4.61936	−0.163729
$797$	−33.5511	−1.18844	−0.594221	−	0.804302i	$-0.702539\pi$
$797$	−33.5511	−1.18844	−0.594221	+	0.804302i	$0.702539\pi$
$798$	−20.4906	−0.725359
$799$	5.57496	0.197228
$800$	11.4867	0.406117
$801$	−0.507717	−0.0179393
$802$	−69.5221	−2.45491
$803$	−32.1500	−1.13455
$804$	17.5822	0.620077
$805$	−29.1635	−1.02788
$806$	−17.3847	−0.612351
$807$	−1.19613	−0.0421056
$808$	−34.2564	−1.20514
$809$	−20.7901	−0.730942	−0.365471	−	0.930823i	$-0.619092\pi$
$809$	−20.7901	−0.730942	−0.365471	+	0.930823i	$0.619092\pi$
$810$	−4.05288	−0.142404
$811$	−17.9988	−0.632025	−0.316012	−	0.948755i	$-0.602344\pi$
$811$	−17.9988	−0.632025	−0.316012	+	0.948755i	$0.602344\pi$
$812$	13.7483	0.482471
$813$	17.0012	0.596259
$814$	95.8810	3.36063
$815$	3.05371	0.106967
$816$	−0.969055	−0.0339237
$817$	−48.2530	−1.68816
$818$	27.4630	0.960221
$819$	−5.06552	−0.177004
$820$	38.1247	1.33137
$821$	15.9642	0.557153	0.278576	−	0.960414i	$-0.410137\pi$
$821$	15.9642	0.557153	0.278576	+	0.960414i	$0.410137\pi$
$822$	2.57097	0.0896730
$823$	51.8631	1.80783	0.903917	−	0.427709i	$-0.140679\pi$
$823$	51.8631	1.80783	0.903917	+	0.427709i	$0.140679\pi$
$824$	−3.83827	−0.133713
$825$	−6.47053	−0.225275
$826$	−34.4395	−1.19831
$827$	−32.6733	−1.13616	−0.568081	−	0.822973i	$-0.692314\pi$
$827$	−32.6733	−1.13616	−0.568081	+	0.822973i	$0.692314\pi$
$828$	24.8188	0.862512
$829$	21.1259	0.733733	0.366866	−	0.930274i	$-0.380431\pi$
$829$	21.1259	0.733733	0.366866	+	0.930274i	$0.380431\pi$
$830$	−32.3913	−1.12432
$831$	−9.60726	−0.333272
$832$	33.7647	1.17058
$833$	3.19192	0.110594
$834$	−0.131671	−0.00455940
$835$	−35.1829	−1.21755
$836$	−53.0951	−1.83633
$837$	−2.99280	−0.103446
$838$	30.9996	1.07086
$839$	−34.9790	−1.20761	−0.603804	−	0.797133i	$-0.706349\pi$
$839$	−34.9790	−1.20761	−0.603804	+	0.797133i	$0.706349\pi$
$840$	7.96997	0.274990
$841$	−23.5132	−0.810801
$842$	−13.4940	−0.465033
$843$	−7.03133	−0.242172
$844$	−10.5575	−0.363404
$845$	11.3408	0.390136
$846$	−12.4756	−0.428920
$847$	6.15429	0.211464
$848$	0.110657	0.00379999
$849$	−1.92263	−0.0659846
$850$	3.84879	0.132013
$851$	−93.9766	−3.22148
$852$	−16.4479	−0.563495
$853$	−26.6178	−0.911377	−0.455689	−	0.890139i	$-0.650607\pi$
$853$	−26.6178	−0.911377	−0.455689	+	0.890139i	$0.650607\pi$
$854$	−42.2559	−1.44597
$855$	−8.49815	−0.290631
$856$	22.7149	0.776381
$857$	32.4342	1.10793	0.553965	−	0.832540i	$-0.313114\pi$
$857$	32.4342	1.10793	0.553965	+	0.832540i	$0.313114\pi$
$858$	−21.8538	−0.746076
$859$	−30.8311	−1.05194	−0.525972	−	0.850502i	$-0.676298\pi$
$859$	−30.8311	−1.05194	−0.525972	+	0.850502i	$0.676298\pi$
$860$	56.0175	1.91018
$861$	13.6577	0.465454
$862$	−47.0670	−1.60311
$863$	49.5641	1.68718	0.843591	−	0.536986i	$-0.180437\pi$
$863$	49.5641	1.68718	0.843591	+	0.536986i	$0.180437\pi$
$864$	6.67869	0.227214
$865$	30.0119	1.02044
$866$	−0.746912	−0.0253811
$867$	−1.00000	−0.0339618
$868$	17.5658	0.596222
$869$	3.76214	0.127622
$870$	9.49340	0.321857
$871$	15.1742	0.514160
$872$	18.1583	0.614919
$873$	−17.5617	−0.594373
$874$	86.6452	2.93082
$875$	23.7498	0.802888
$876$	−25.7029	−0.868421
$877$	−20.9459	−0.707292	−0.353646	−	0.935379i	$-0.615058\pi$
$877$	−20.9459	−0.707292	−0.353646	+	0.935379i	$0.615058\pi$
$878$	65.1971	2.20030
$879$	−32.7412	−1.10433
$880$	−6.60279	−0.222580
$881$	37.3911	1.25974	0.629869	−	0.776702i	$-0.283109\pi$
$881$	37.3911	1.25974	0.629869	+	0.776702i	$0.283109\pi$
$882$	−7.14287	−0.240513
$883$	10.5333	0.354474	0.177237	−	0.984168i	$-0.443284\pi$
$883$	10.5333	0.354474	0.177237	+	0.984168i	$0.443284\pi$
$884$	7.80744	0.262593
$885$	−14.2833	−0.480127
$886$	24.1698	0.812002
$887$	1.58558	0.0532387	0.0266194	−	0.999646i	$-0.491526\pi$
$887$	1.58558	0.0532387	0.0266194	+	0.999646i	$0.491526\pi$
$888$	25.6825	0.861848
$889$	−1.09890	−0.0368561
$890$	2.05771	0.0689747
$891$	−3.76214	−0.126037
$892$	−61.7826	−2.06863
$893$	−26.1591	−0.875381
$894$	6.21135	0.207739
$895$	−22.3298	−0.746402
$896$	−30.7361	−1.02682
$897$	21.4197	0.715184
$898$	40.2682	1.34377
$899$	7.01029	0.233806
$900$	−5.17300	−0.172433
$901$	0.114191	0.00380426
$902$	58.9225	1.96190
$903$	20.0676	0.667809
$904$	16.2767	0.541356
$905$	24.7731	0.823486
$906$	−11.0584	−0.367389
$907$	50.1822	1.66627	0.833136	−	0.553068i	$-0.186543\pi$
$907$	50.1822	1.66627	0.833136	+	0.553068i	$0.186543\pi$
$908$	50.2431	1.66737
$909$	−15.1908	−0.503848
$910$	20.5299	0.680560
$911$	−20.5319	−0.680253	−0.340126	−	0.940380i	$-0.610470\pi$
$911$	−20.5319	−0.680253	−0.340126	+	0.940380i	$0.610470\pi$
$912$	4.54705	0.150568
$913$	−30.0677	−0.995096
$914$	43.4843	1.43833
$915$	−17.5250	−0.579358
$916$	15.8542	0.523839
$917$	3.95076	0.130466
$918$	2.23779	0.0738582
$919$	29.4959	0.972980	0.486490	−	0.873686i	$-0.338277\pi$
$919$	29.4959	0.972980	0.486490	+	0.873686i	$0.338277\pi$
$920$	−33.7013	−1.11110
$921$	−8.25901	−0.272144
$922$	−68.0246	−2.24027
$923$	−14.1952	−0.467242
$924$	22.0814	0.726424
$925$	19.5876	0.644037
$926$	59.7963	1.96503
$927$	−1.70206	−0.0559031
$928$	−15.6441	−0.513542
$929$	16.1683	0.530466	0.265233	−	0.964184i	$-0.414551\pi$
$929$	16.1683	0.530466	0.265233	+	0.964184i	$0.414551\pi$
$930$	12.1294	0.397740
$931$	−14.9773	−0.490861
$932$	18.2974	0.599351
$933$	−3.47577	−0.113791
$934$	−8.51531	−0.278629
$935$	−6.81363	−0.222830
$936$	−5.85371	−0.191335
$937$	−7.04849	−0.230264	−0.115132	−	0.993350i	$-0.536729\pi$
$937$	−7.04849	−0.230264	−0.115132	+	0.993350i	$0.536729\pi$
$938$	−25.5275	−0.833504
$939$	14.0764	0.459367
$940$	30.3684	0.990509
$941$	−39.7685	−1.29642	−0.648209	−	0.761463i	$-0.724482\pi$
$941$	−39.7685	−1.29642	−0.648209	+	0.761463i	$0.724482\pi$
$942$	37.8387	1.23285
$943$	−57.7522	−1.88067
$944$	7.64246	0.248741
$945$	3.53424	0.114969
$946$	86.5762	2.81484
$947$	−9.56244	−0.310738	−0.155369	−	0.987857i	$-0.549657\pi$
$947$	−9.56244	−0.310738	−0.155369	+	0.987857i	$0.549657\pi$
$948$	3.00772	0.0976862
$949$	−22.1828	−0.720083
$950$	−18.0595	−0.585928
$951$	7.90270	0.256262
$952$	−4.40061	−0.142625
$953$	−29.9479	−0.970106	−0.485053	−	0.874485i	$-0.661200\pi$
$953$	−29.9479	−0.970106	−0.485053	+	0.874485i	$0.661200\pi$
$954$	−0.255536	−0.00827329
$955$	−37.4476	−1.21178
$956$	10.5837	0.342300
$957$	8.81240	0.284864
$958$	−2.75919	−0.0891454
$959$	−2.24197	−0.0723970
$960$	−23.5578	−0.760324
$961$	−22.0432	−0.711070
$962$	66.1558	2.13295
$963$	10.0728	0.324592
$964$	21.7530	0.700615
$965$	−38.7554	−1.24758
$966$	−36.0343	−1.15938
$967$	−42.8699	−1.37860	−0.689301	−	0.724475i	$-0.742082\pi$
$967$	−42.8699	−1.37860	−0.689301	+	0.724475i	$0.742082\pi$
$968$	7.11190	0.228585
$969$	4.69225	0.150737
$970$	71.1753	2.28530
$971$	−28.2290	−0.905911	−0.452955	−	0.891533i	$-0.649630\pi$
$971$	−28.2290	−0.905911	−0.452955	+	0.891533i	$0.649630\pi$
$972$	−3.00772	−0.0964727
$973$	0.114822	0.00368101
$974$	87.8075	2.81353
$975$	−4.46453	−0.142979
$976$	9.37698	0.300150
$977$	−37.3882	−1.19615	−0.598077	−	0.801438i	$-0.704068\pi$
$977$	−37.3882	−1.19615	−0.598077	+	0.801438i	$0.704068\pi$
$978$	3.77316	0.120652
$979$	1.91011	0.0610472
$980$	17.3873	0.555418
$981$	8.05222	0.257088
$982$	70.5315	2.25075
$983$	−18.5618	−0.592030	−0.296015	−	0.955183i	$-0.595658\pi$
$983$	−18.5618	−0.592030	−0.296015	+	0.955183i	$0.595658\pi$
$984$	15.7829	0.503139
$985$	19.4447	0.619560
$986$	−5.24178	−0.166932
$987$	10.8791	0.346287
$988$	−36.6345	−1.16550
$989$	−84.8567	−2.69829
$990$	15.2475	0.484598
$991$	−30.1711	−0.958416	−0.479208	−	0.877701i	$-0.659076\pi$
$991$	−30.1711	−0.958416	−0.479208	+	0.877701i	$0.659076\pi$
$992$	−19.9880	−0.634618
$993$	11.8845	0.377143
$994$	23.8806	0.757446
$995$	2.78155	0.0881811
$996$	−24.0382	−0.761681
$997$	31.0348	0.982883	0.491442	−	0.870911i	$-0.336470\pi$
$997$	31.0348	0.982883	0.491442	+	0.870911i	$0.336470\pi$
$998$	−31.6601	−1.00218
$999$	11.3888	0.360325

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.g.1.20	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.g.1.20	✓	22	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)

\(f(q)\)	\(=\)	\(q+2.23779 q^{2} -1.00000 q^{3} +3.00772 q^{4} -1.81110 q^{5} -2.23779 q^{6} +1.95143 q^{7} +2.25507 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.23779 q^{2} -1.00000 q^{3} +3.00772 q^{4} -1.81110 q^{5} -2.23779 q^{6} +1.95143 q^{7} +2.25507 q^{8} +1.00000 q^{9} -4.05288 q^{10} -3.76214 q^{11} -3.00772 q^{12} -2.59580 q^{13} +4.36690 q^{14} +1.81110 q^{15} -0.969055 q^{16} -1.00000 q^{17} +2.23779 q^{18} +4.69225 q^{19} -5.44729 q^{20} -1.95143 q^{21} -8.41890 q^{22} +8.25169 q^{23} -2.25507 q^{24} -1.71991 q^{25} -5.80886 q^{26} -1.00000 q^{27} +5.86936 q^{28} +2.34239 q^{29} +4.05288 q^{30} +2.99280 q^{31} -6.67869 q^{32} +3.76214 q^{33} -2.23779 q^{34} -3.53424 q^{35} +3.00772 q^{36} -11.3888 q^{37} +10.5003 q^{38} +2.59580 q^{39} -4.08417 q^{40} -6.99883 q^{41} -4.36690 q^{42} -10.2836 q^{43} -11.3155 q^{44} -1.81110 q^{45} +18.4656 q^{46} -5.57496 q^{47} +0.969055 q^{48} -3.19192 q^{49} -3.84879 q^{50} +1.00000 q^{51} -7.80744 q^{52} -0.114191 q^{53} -2.23779 q^{54} +6.81363 q^{55} +4.40061 q^{56} -4.69225 q^{57} +5.24178 q^{58} -7.88650 q^{59} +5.44729 q^{60} -9.67642 q^{61} +6.69726 q^{62} +1.95143 q^{63} -13.0074 q^{64} +4.70126 q^{65} +8.41890 q^{66} -5.84569 q^{67} -3.00772 q^{68} -8.25169 q^{69} -7.90890 q^{70} +5.46855 q^{71} +2.25507 q^{72} +8.54565 q^{73} -25.4857 q^{74} +1.71991 q^{75} +14.1130 q^{76} -7.34156 q^{77} +5.80886 q^{78} -1.00000 q^{79} +1.75506 q^{80} +1.00000 q^{81} -15.6619 q^{82} +7.99217 q^{83} -5.86936 q^{84} +1.81110 q^{85} -23.0125 q^{86} -2.34239 q^{87} -8.48391 q^{88} -0.507717 q^{89} -4.05288 q^{90} -5.06552 q^{91} +24.8188 q^{92} -2.99280 q^{93} -12.4756 q^{94} -8.49815 q^{95} +6.67869 q^{96} -17.5617 q^{97} -7.14287 q^{98} -3.76214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{2} - 22 q^{3} + 16 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 6 q^{8} + 22 q^{9}+O(q^{10}) \) 22 * q + 2 * q^2 - 22 * q^3 + 16 * q^4 + 5 * q^5 - 2 * q^6 - 4 * q^7 + 6 * q^8 + 22 * q^9	\( 22 q + 2 q^{2} - 22 q^{3} + 16 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 6 q^{8} + 22 q^{9} - 5 q^{10} - 2 q^{11} - 16 q^{12} - 11 q^{13} - 7 q^{14} - 5 q^{15} - 22 q^{17} + 2 q^{18} - 36 q^{19} + 4 q^{21} - 9 q^{22} + 21 q^{23} - 6 q^{24} + 9 q^{25} - 16 q^{26} - 22 q^{27} - 17 q^{28} - q^{29} + 5 q^{30} - 12 q^{31} - 11 q^{32} + 2 q^{33} - 2 q^{34} - 14 q^{35} + 16 q^{36} - 6 q^{37} + q^{38} + 11 q^{39} - 24 q^{40} - 17 q^{41} + 7 q^{42} - 36 q^{43} + 16 q^{44} + 5 q^{45} - 23 q^{46} - 17 q^{47} - 6 q^{49} - 33 q^{50} + 22 q^{51} - 57 q^{52} - 2 q^{53} - 2 q^{54} - 24 q^{55} - 64 q^{56} + 36 q^{57} - 7 q^{58} - 59 q^{59} - 30 q^{61} - 4 q^{62} - 4 q^{63} - 22 q^{64} + 36 q^{65} + 9 q^{66} - 16 q^{67} - 16 q^{68} - 21 q^{69} - 39 q^{70} - 11 q^{71} + 6 q^{72} - 19 q^{73} - 28 q^{74} - 9 q^{75} - 77 q^{76} + 2 q^{77} + 16 q^{78} - 22 q^{79} - 2 q^{80} + 22 q^{81} + 33 q^{82} - 23 q^{83} + 17 q^{84} - 5 q^{85} + 6 q^{86} + q^{87} - 23 q^{88} + 12 q^{89} - 5 q^{90} - 24 q^{91} + 66 q^{92} + 12 q^{93} - 61 q^{94} - 11 q^{95} + 11 q^{96} - 9 q^{97} + 17 q^{98} - 2 q^{99}+O(q^{100}) \) 22 * q + 2 * q^2 - 22 * q^3 + 16 * q^4 + 5 * q^5 - 2 * q^6 - 4 * q^7 + 6 * q^8 + 22 * q^9 - 5 * q^10 - 2 * q^11 - 16 * q^12 - 11 * q^13 - 7 * q^14 - 5 * q^15 - 22 * q^17 + 2 * q^18 - 36 * q^19 + 4 * q^21 - 9 * q^22 + 21 * q^23 - 6 * q^24 + 9 * q^25 - 16 * q^26 - 22 * q^27 - 17 * q^28 - q^29 + 5 * q^30 - 12 * q^31 - 11 * q^32 + 2 * q^33 - 2 * q^34 - 14 * q^35 + 16 * q^36 - 6 * q^37 + q^38 + 11 * q^39 - 24 * q^40 - 17 * q^41 + 7 * q^42 - 36 * q^43 + 16 * q^44 + 5 * q^45 - 23 * q^46 - 17 * q^47 - 6 * q^49 - 33 * q^50 + 22 * q^51 - 57 * q^52 - 2 * q^53 - 2 * q^54 - 24 * q^55 - 64 * q^56 + 36 * q^57 - 7 * q^58 - 59 * q^59 - 30 * q^61 - 4 * q^62 - 4 * q^63 - 22 * q^64 + 36 * q^65 + 9 * q^66 - 16 * q^67 - 16 * q^68 - 21 * q^69 - 39 * q^70 - 11 * q^71 + 6 * q^72 - 19 * q^73 - 28 * q^74 - 9 * q^75 - 77 * q^76 + 2 * q^77 + 16 * q^78 - 22 * q^79 - 2 * q^80 + 22 * q^81 + 33 * q^82 - 23 * q^83 + 17 * q^84 - 5 * q^85 + 6 * q^86 + q^87 - 23 * q^88 + 12 * q^89 - 5 * q^90 - 24 * q^91 + 66 * q^92 + 12 * q^93 - 61 * q^94 - 11 * q^95 + 11 * q^96 - 9 * q^97 + 17 * q^98 - 2 * q^99

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