LMFDB - Embedded newform 4026.2.a.t.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4026,2,Mod(1,4026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4026, 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("4026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4026 = 2 \cdot 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4026.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:	$32.1477718538$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.2777.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} + x + 2 $ x^4 - x^3 - 4*x^2 + x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.679643$ of defining polynomial
Character	$\chi$	$=$	4026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.141558 q^{5} +1.00000 q^{6} -4.12152 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.141558 q^{5} +1.00000 q^{6} -4.12152 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.141558 q^{10} -1.00000 q^{11} +1.00000 q^{12} +3.20580 q^{13} -4.12152 q^{14} -0.141558 q^{15} +1.00000 q^{16} -6.07617 q^{17} +1.00000 q^{18} -2.09621 q^{19} -0.141558 q^{20} -4.12152 q^{21} -1.00000 q^{22} +1.03893 q^{23} +1.00000 q^{24} -4.97996 q^{25} +3.20580 q^{26} +1.00000 q^{27} -4.12152 q^{28} +3.48081 q^{29} -0.141558 q^{30} +8.30728 q^{31} +1.00000 q^{32} -1.00000 q^{33} -6.07617 q^{34} +0.583434 q^{35} +1.00000 q^{36} -10.7320 q^{37} -2.09621 q^{38} +3.20580 q^{39} -0.141558 q^{40} -12.1858 q^{41} -4.12152 q^{42} -11.4942 q^{43} -1.00000 q^{44} -0.141558 q^{45} +1.03893 q^{46} -3.63429 q^{47} +1.00000 q^{48} +9.98692 q^{49} -4.97996 q^{50} -6.07617 q^{51} +3.20580 q^{52} +13.6276 q^{53} +1.00000 q^{54} +0.141558 q^{55} -4.12152 q^{56} -2.09621 q^{57} +3.48081 q^{58} -6.13872 q^{59} -0.141558 q^{60} -1.00000 q^{61} +8.30728 q^{62} -4.12152 q^{63} +1.00000 q^{64} -0.453806 q^{65} -1.00000 q^{66} +4.89737 q^{67} -6.07617 q^{68} +1.03893 q^{69} +0.583434 q^{70} -10.6494 q^{71} +1.00000 q^{72} -13.1421 q^{73} -10.7320 q^{74} -4.97996 q^{75} -2.09621 q^{76} +4.12152 q^{77} +3.20580 q^{78} +3.28028 q^{79} -0.141558 q^{80} +1.00000 q^{81} -12.1858 q^{82} +8.23111 q^{83} -4.12152 q^{84} +0.860131 q^{85} -11.4942 q^{86} +3.48081 q^{87} -1.00000 q^{88} +6.57701 q^{89} -0.141558 q^{90} -13.2128 q^{91} +1.03893 q^{92} +8.30728 q^{93} -3.63429 q^{94} +0.296735 q^{95} +1.00000 q^{96} +1.38842 q^{97} +9.98692 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} - 6 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^5 + 4 * q^6 - 6 * q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} - 6 q^{7} + 4 q^{8} + 4 q^{9} - 4 q^{10} - 4 q^{11} + 4 q^{12} - 5 q^{13} - 6 q^{14} - 4 q^{15} + 4 q^{16} - 10 q^{17} + 4 q^{18} - 8 q^{19} - 4 q^{20} - 6 q^{21} - 4 q^{22} - 7 q^{23} + 4 q^{24} - 6 q^{25} - 5 q^{26} + 4 q^{27} - 6 q^{28} - 4 q^{29} - 4 q^{30} - 9 q^{31} + 4 q^{32} - 4 q^{33} - 10 q^{34} - q^{35} + 4 q^{36} - 11 q^{37} - 8 q^{38} - 5 q^{39} - 4 q^{40} - 17 q^{41} - 6 q^{42} - 11 q^{43} - 4 q^{44} - 4 q^{45} - 7 q^{46} - 7 q^{47} + 4 q^{48} - 6 q^{49} - 6 q^{50} - 10 q^{51} - 5 q^{52} + 16 q^{53} + 4 q^{54} + 4 q^{55} - 6 q^{56} - 8 q^{57} - 4 q^{58} + 3 q^{59} - 4 q^{60} - 4 q^{61} - 9 q^{62} - 6 q^{63} + 4 q^{64} - 2 q^{65} - 4 q^{66} + 5 q^{67} - 10 q^{68} - 7 q^{69} - q^{70} - 10 q^{71} + 4 q^{72} - 9 q^{73} - 11 q^{74} - 6 q^{75} - 8 q^{76} + 6 q^{77} - 5 q^{78} - 11 q^{79} - 4 q^{80} + 4 q^{81} - 17 q^{82} + 5 q^{83} - 6 q^{84} - 8 q^{85} - 11 q^{86} - 4 q^{87} - 4 q^{88} + 8 q^{89} - 4 q^{90} - 3 q^{91} - 7 q^{92} - 9 q^{93} - 7 q^{94} + 7 q^{95} + 4 q^{96} - 12 q^{97} - 6 q^{98} - 4 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^5 + 4 * q^6 - 6 * q^7 + 4 * q^8 + 4 * q^9 - 4 * q^10 - 4 * q^11 + 4 * q^12 - 5 * q^13 - 6 * q^14 - 4 * q^15 + 4 * q^16 - 10 * q^17 + 4 * q^18 - 8 * q^19 - 4 * q^20 - 6 * q^21 - 4 * q^22 - 7 * q^23 + 4 * q^24 - 6 * q^25 - 5 * q^26 + 4 * q^27 - 6 * q^28 - 4 * q^29 - 4 * q^30 - 9 * q^31 + 4 * q^32 - 4 * q^33 - 10 * q^34 - q^35 + 4 * q^36 - 11 * q^37 - 8 * q^38 - 5 * q^39 - 4 * q^40 - 17 * q^41 - 6 * q^42 - 11 * q^43 - 4 * q^44 - 4 * q^45 - 7 * q^46 - 7 * q^47 + 4 * q^48 - 6 * q^49 - 6 * q^50 - 10 * q^51 - 5 * q^52 + 16 * q^53 + 4 * q^54 + 4 * q^55 - 6 * q^56 - 8 * q^57 - 4 * q^58 + 3 * q^59 - 4 * q^60 - 4 * q^61 - 9 * q^62 - 6 * q^63 + 4 * q^64 - 2 * q^65 - 4 * q^66 + 5 * q^67 - 10 * q^68 - 7 * q^69 - q^70 - 10 * q^71 + 4 * q^72 - 9 * q^73 - 11 * q^74 - 6 * q^75 - 8 * q^76 + 6 * q^77 - 5 * q^78 - 11 * q^79 - 4 * q^80 + 4 * q^81 - 17 * q^82 + 5 * q^83 - 6 * q^84 - 8 * q^85 - 11 * q^86 - 4 * q^87 - 4 * q^88 + 8 * q^89 - 4 * q^90 - 3 * q^91 - 7 * q^92 - 9 * q^93 - 7 * q^94 + 7 * q^95 + 4 * q^96 - 12 * q^97 - 6 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−0.141558	−0.0633067	−0.0316533	−	0.999499i	$-0.510077\pi$
$5$	−0.141558	−0.0633067	−0.0316533	+	0.999499i	$0.510077\pi$
$6$	1.00000	0.408248
$7$	−4.12152	−1.55779	−0.778894	−	0.627156i	$-0.784219\pi$
$7$	−4.12152	−1.55779	−0.778894	+	0.627156i	$0.784219\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−0.141558	−0.0447646
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.00000	0.288675
$13$	3.20580	0.889128	0.444564	−	0.895747i	$-0.353359\pi$
$13$	3.20580	0.889128	0.444564	+	0.895747i	$0.353359\pi$
$14$	−4.12152	−1.10152
$15$	−0.141558	−0.0365501
$16$	1.00000	0.250000
$17$	−6.07617	−1.47369	−0.736844	−	0.676063i	$-0.763685\pi$
$17$	−6.07617	−1.47369	−0.736844	+	0.676063i	$0.763685\pi$
$18$	1.00000	0.235702
$19$	−2.09621	−0.480903	−0.240452	−	0.970661i	$-0.577296\pi$
$19$	−2.09621	−0.480903	−0.240452	+	0.970661i	$0.577296\pi$
$20$	−0.141558	−0.0316533
$21$	−4.12152	−0.899389
$22$	−1.00000	−0.213201
$23$	1.03893	0.216632	0.108316	−	0.994117i	$-0.465454\pi$
$23$	1.03893	0.216632	0.108316	+	0.994117i	$0.465454\pi$
$24$	1.00000	0.204124
$25$	−4.97996	−0.995992
$26$	3.20580	0.628709
$27$	1.00000	0.192450
$28$	−4.12152	−0.778894
$29$	3.48081	0.646369	0.323185	−	0.946336i	$-0.395246\pi$
$29$	3.48081	0.646369	0.323185	+	0.946336i	$0.395246\pi$
$30$	−0.141558	−0.0258448
$31$	8.30728	1.49203	0.746016	−	0.665928i	$-0.231964\pi$
$31$	8.30728	1.49203	0.746016	+	0.665928i	$0.231964\pi$
$32$	1.00000	0.176777
$33$	−1.00000	−0.174078
$34$	−6.07617	−1.04205
$35$	0.583434	0.0986184
$36$	1.00000	0.166667
$37$	−10.7320	−1.76432	−0.882161	−	0.470948i	$-0.843912\pi$
$37$	−10.7320	−1.76432	−0.882161	+	0.470948i	$0.843912\pi$
$38$	−2.09621	−0.340050
$39$	3.20580	0.513339
$40$	−0.141558	−0.0223823
$41$	−12.1858	−1.90310	−0.951548	−	0.307500i	$-0.900507\pi$
$41$	−12.1858	−1.90310	−0.951548	+	0.307500i	$0.900507\pi$
$42$	−4.12152	−0.635964
$43$	−11.4942	−1.75285	−0.876423	−	0.481541i	$-0.840077\pi$
$43$	−11.4942	−1.75285	−0.876423	+	0.481541i	$0.840077\pi$
$44$	−1.00000	−0.150756
$45$	−0.141558	−0.0211022
$46$	1.03893	0.153182
$47$	−3.63429	−0.530116	−0.265058	−	0.964232i	$-0.585391\pi$
$47$	−3.63429	−0.530116	−0.265058	+	0.964232i	$0.585391\pi$
$48$	1.00000	0.144338
$49$	9.98692	1.42670
$50$	−4.97996	−0.704273
$51$	−6.07617	−0.850834
$52$	3.20580	0.444564
$53$	13.6276	1.87190	0.935950	−	0.352133i	$-0.114544\pi$
$53$	13.6276	1.87190	0.935950	+	0.352133i	$0.114544\pi$
$54$	1.00000	0.136083
$55$	0.141558	0.0190877
$56$	−4.12152	−0.550761
$57$	−2.09621	−0.277650
$58$	3.48081	0.457052
$59$	−6.13872	−0.799193	−0.399597	−	0.916691i	$-0.630850\pi$
$59$	−6.13872	−0.799193	−0.399597	+	0.916691i	$0.630850\pi$
$60$	−0.141558	−0.0182751
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	8.30728	1.05503
$63$	−4.12152	−0.519263
$64$	1.00000	0.125000
$65$	−0.453806	−0.0562878
$66$	−1.00000	−0.123091
$67$	4.89737	0.598309	0.299155	−	0.954205i	$-0.403295\pi$
$67$	4.89737	0.598309	0.299155	+	0.954205i	$0.403295\pi$
$68$	−6.07617	−0.736844
$69$	1.03893	0.125072
$70$	0.583434	0.0697337
$71$	−10.6494	−1.26385	−0.631923	−	0.775031i	$-0.717734\pi$
$71$	−10.6494	−1.26385	−0.631923	+	0.775031i	$0.717734\pi$
$72$	1.00000	0.117851
$73$	−13.1421	−1.53817	−0.769083	−	0.639149i	$-0.779287\pi$
$73$	−13.1421	−1.53817	−0.769083	+	0.639149i	$0.779287\pi$
$74$	−10.7320	−1.24756
$75$	−4.97996	−0.575036
$76$	−2.09621	−0.240452
$77$	4.12152	0.469691
$78$	3.20580	0.362985
$79$	3.28028	0.369060	0.184530	−	0.982827i	$-0.440924\pi$
$79$	3.28028	0.369060	0.184530	+	0.982827i	$0.440924\pi$
$80$	−0.141558	−0.0158267
$81$	1.00000	0.111111
$82$	−12.1858	−1.34569
$83$	8.23111	0.903482	0.451741	−	0.892149i	$-0.350803\pi$
$83$	8.23111	0.903482	0.451741	+	0.892149i	$0.350803\pi$
$84$	−4.12152	−0.449695
$85$	0.860131	0.0932943
$86$	−11.4942	−1.23945
$87$	3.48081	0.373182
$88$	−1.00000	−0.106600
$89$	6.57701	0.697162	0.348581	−	0.937279i	$-0.386664\pi$
$89$	6.57701	0.697162	0.348581	+	0.937279i	$0.386664\pi$
$90$	−0.141558	−0.0149215
$91$	−13.2128	−1.38507
$92$	1.03893	0.108316
$93$	8.30728	0.861425
$94$	−3.63429	−0.374849
$95$	0.296735	0.0304444
$96$	1.00000	0.102062
$97$	1.38842	0.140973	0.0704863	−	0.997513i	$-0.477545\pi$
$97$	1.38842	0.140973	0.0704863	+	0.997513i	$0.477545\pi$
$98$	9.98692	1.00883
$99$	−1.00000	−0.100504
$100$	−4.97996	−0.497996
$101$	−9.68491	−0.963685	−0.481843	−	0.876258i	$-0.660032\pi$
$101$	−9.68491	−0.963685	−0.481843	+	0.876258i	$0.660032\pi$
$102$	−6.07617	−0.601631
$103$	−15.4369	−1.52104	−0.760522	−	0.649312i	$-0.775057\pi$
$103$	−15.4369	−1.52104	−0.760522	+	0.649312i	$0.775057\pi$
$104$	3.20580	0.314354
$105$	0.583434	0.0569374
$106$	13.6276	1.32363
$107$	−10.0740	−0.973894	−0.486947	−	0.873432i	$-0.661890\pi$
$107$	−10.0740	−0.973894	−0.486947	+	0.873432i	$0.661890\pi$
$108$	1.00000	0.0962250
$109$	−9.65747	−0.925018	−0.462509	−	0.886615i	$-0.653051\pi$
$109$	−9.65747	−0.925018	−0.462509	+	0.886615i	$0.653051\pi$
$110$	0.141558	0.0134970
$111$	−10.7320	−1.01863
$112$	−4.12152	−0.389447
$113$	−8.91244	−0.838412	−0.419206	−	0.907891i	$-0.637691\pi$
$113$	−8.91244	−0.838412	−0.419206	+	0.907891i	$0.637691\pi$
$114$	−2.09621	−0.196328
$115$	−0.147069	−0.0137142
$116$	3.48081	0.323185
$117$	3.20580	0.296376
$118$	−6.13872	−0.565115
$119$	25.0431	2.29569
$120$	−0.141558	−0.0129224
$121$	1.00000	0.0909091
$122$	−1.00000	−0.0905357
$123$	−12.1858	−1.09875
$124$	8.30728	0.746016
$125$	1.41274	0.126360
$126$	−4.12152	−0.367174
$127$	6.81096	0.604375	0.302187	−	0.953249i	$-0.402283\pi$
$127$	6.81096	0.604375	0.302187	+	0.953249i	$0.402283\pi$
$128$	1.00000	0.0883883
$129$	−11.4942	−1.01201
$130$	−0.453806	−0.0398015
$131$	3.40349	0.297364	0.148682	−	0.988885i	$-0.452497\pi$
$131$	3.40349	0.297364	0.148682	+	0.988885i	$0.452497\pi$
$132$	−1.00000	−0.0870388
$133$	8.63957	0.749145
$134$	4.89737	0.423068
$135$	−0.141558	−0.0121834
$136$	−6.07617	−0.521027
$137$	20.4560	1.74768	0.873839	−	0.486216i	$-0.161623\pi$
$137$	20.4560	1.74768	0.873839	+	0.486216i	$0.161623\pi$
$138$	1.03893	0.0884396
$139$	11.9561	1.01410	0.507052	−	0.861916i	$-0.330735\pi$
$139$	11.9561	1.01410	0.507052	+	0.861916i	$0.330735\pi$
$140$	0.583434	0.0493092
$141$	−3.63429	−0.306063
$142$	−10.6494	−0.893675
$143$	−3.20580	−0.268082
$144$	1.00000	0.0833333
$145$	−0.492736	−0.0409195
$146$	−13.1421	−1.08765
$147$	9.98692	0.823707
$148$	−10.7320	−0.882161
$149$	−21.2887	−1.74404	−0.872019	−	0.489473i	$-0.837189\pi$
$149$	−21.2887	−1.74404	−0.872019	+	0.489473i	$0.837189\pi$
$150$	−4.97996	−0.406612
$151$	12.1523	0.988943	0.494472	−	0.869194i	$-0.335362\pi$
$151$	12.1523	0.988943	0.494472	+	0.869194i	$0.335362\pi$
$152$	−2.09621	−0.170025
$153$	−6.07617	−0.491229
$154$	4.12152	0.332121
$155$	−1.17596	−0.0944556
$156$	3.20580	0.256669
$157$	20.6454	1.64768	0.823840	−	0.566822i	$-0.191827\pi$
$157$	20.6454	1.64768	0.823840	+	0.566822i	$0.191827\pi$
$158$	3.28028	0.260965
$159$	13.6276	1.08074
$160$	−0.141558	−0.0111911
$161$	−4.28197	−0.337466
$162$	1.00000	0.0785674
$163$	14.3279	1.12224	0.561122	−	0.827733i	$-0.310370\pi$
$163$	14.3279	1.12224	0.561122	+	0.827733i	$0.310370\pi$
$164$	−12.1858	−0.951548
$165$	0.141558	0.0110203
$166$	8.23111	0.638858
$167$	0.976378	0.0755544	0.0377772	−	0.999286i	$-0.487972\pi$
$167$	0.976378	0.0755544	0.0377772	+	0.999286i	$0.487972\pi$
$168$	−4.12152	−0.317982
$169$	−2.72286	−0.209451
$170$	0.860131	0.0659690
$171$	−2.09621	−0.160301
$172$	−11.4942	−0.876423
$173$	−16.6715	−1.26751	−0.633757	−	0.773532i	$-0.718488\pi$
$173$	−16.6715	−1.26751	−0.633757	+	0.773532i	$0.718488\pi$
$174$	3.48081	0.263879
$175$	20.5250	1.55154
$176$	−1.00000	−0.0753778
$177$	−6.13872	−0.461415
$178$	6.57701	0.492968
$179$	−13.8561	−1.03566	−0.517829	−	0.855484i	$-0.673259\pi$
$179$	−13.8561	−1.03566	−0.517829	+	0.855484i	$0.673259\pi$
$180$	−0.141558	−0.0105511
$181$	−14.6802	−1.09117	−0.545585	−	0.838056i	$-0.683692\pi$
$181$	−14.6802	−1.09117	−0.545585	+	0.838056i	$0.683692\pi$
$182$	−13.2128	−0.979395
$183$	−1.00000	−0.0739221
$184$	1.03893	0.0765909
$185$	1.51919	0.111693
$186$	8.30728	0.609119
$187$	6.07617	0.444334
$188$	−3.63429	−0.265058
$189$	−4.12152	−0.299796
$190$	0.296735	0.0215274
$191$	−10.2075	−0.738588	−0.369294	−	0.929313i	$-0.620400\pi$
$191$	−10.2075	−0.738588	−0.369294	+	0.929313i	$0.620400\pi$
$192$	1.00000	0.0721688
$193$	−1.08641	−0.0782016	−0.0391008	−	0.999235i	$-0.512449\pi$
$193$	−1.08641	−0.0782016	−0.0391008	+	0.999235i	$0.512449\pi$
$194$	1.38842	0.0996827
$195$	−0.453806	−0.0324978
$196$	9.98692	0.713352
$197$	18.4930	1.31757	0.658787	−	0.752329i	$-0.271070\pi$
$197$	18.4930	1.31757	0.658787	+	0.752329i	$0.271070\pi$
$198$	−1.00000	−0.0710669
$199$	−12.9026	−0.914644	−0.457322	−	0.889301i	$-0.651191\pi$
$199$	−12.9026	−0.914644	−0.457322	+	0.889301i	$0.651191\pi$
$200$	−4.97996	−0.352136
$201$	4.89737	0.345434
$202$	−9.68491	−0.681428
$203$	−14.3462	−1.00691
$204$	−6.07617	−0.425417
$205$	1.72499	0.120479
$206$	−15.4369	−1.07554
$207$	1.03893	0.0722106
$208$	3.20580	0.222282
$209$	2.09621	0.144998
$210$	0.583434	0.0402608
$211$	−8.62787	−0.593967	−0.296984	−	0.954883i	$-0.595981\pi$
$211$	−8.62787	−0.593967	−0.296984	+	0.954883i	$0.595981\pi$
$212$	13.6276	0.935950
$213$	−10.6494	−0.729682
$214$	−10.0740	−0.688647
$215$	1.62709	0.110967
$216$	1.00000	0.0680414
$217$	−34.2386	−2.32427
$218$	−9.65747	−0.654086
$219$	−13.1421	−0.888061
$220$	0.141558	0.00954384
$221$	−19.4790	−1.31030
$222$	−10.7320	−0.720282
$223$	23.1120	1.54770	0.773848	−	0.633372i	$-0.218330\pi$
$223$	23.1120	1.54770	0.773848	+	0.633372i	$0.218330\pi$
$224$	−4.12152	−0.275381
$225$	−4.97996	−0.331997
$226$	−8.91244	−0.592847
$227$	24.9251	1.65434	0.827169	−	0.561953i	$-0.189950\pi$
$227$	24.9251	1.65434	0.827169	+	0.561953i	$0.189950\pi$
$228$	−2.09621	−0.138825
$229$	−24.0161	−1.58703	−0.793513	−	0.608554i	$-0.791750\pi$
$229$	−24.0161	−1.58703	−0.793513	+	0.608554i	$0.791750\pi$
$230$	−0.147069	−0.00969743
$231$	4.12152	0.271176
$232$	3.48081	0.228526
$233$	−13.6401	−0.893593	−0.446797	−	0.894636i	$-0.647435\pi$
$233$	−13.6401	−0.893593	−0.446797	+	0.894636i	$0.647435\pi$
$234$	3.20580	0.209570
$235$	0.514464	0.0335599
$236$	−6.13872	−0.399597
$237$	3.28028	0.213077
$238$	25.0431	1.62330
$239$	17.5843	1.13743	0.568716	−	0.822534i	$-0.307440\pi$
$239$	17.5843	1.13743	0.568716	+	0.822534i	$0.307440\pi$
$240$	−0.141558	−0.00913753
$241$	−16.3309	−1.05197	−0.525983	−	0.850495i	$-0.676302\pi$
$241$	−16.3309	−1.05197	−0.525983	+	0.850495i	$0.676302\pi$
$242$	1.00000	0.0642824
$243$	1.00000	0.0641500
$244$	−1.00000	−0.0640184
$245$	−1.41373	−0.0903198
$246$	−12.1858	−0.776936
$247$	−6.72002	−0.427585
$248$	8.30728	0.527513
$249$	8.23111	0.521625
$250$	1.41274	0.0893498
$251$	−2.29008	−0.144548	−0.0722742	−	0.997385i	$-0.523026\pi$
$251$	−2.29008	−0.144548	−0.0722742	+	0.997385i	$0.523026\pi$
$252$	−4.12152	−0.259631
$253$	−1.03893	−0.0653169
$254$	6.81096	0.427358
$255$	0.860131	0.0538635
$256$	1.00000	0.0625000
$257$	23.5486	1.46892	0.734462	−	0.678650i	$-0.237435\pi$
$257$	23.5486	1.46892	0.734462	+	0.678650i	$0.237435\pi$
$258$	−11.4942	−0.715597
$259$	44.2320	2.74844
$260$	−0.453806	−0.0281439
$261$	3.48081	0.215456
$262$	3.40349	0.210268
$263$	−7.65701	−0.472151	−0.236076	−	0.971735i	$-0.575861\pi$
$263$	−7.65701	−0.472151	−0.236076	+	0.971735i	$0.575861\pi$
$264$	−1.00000	−0.0615457
$265$	−1.92910	−0.118504
$266$	8.63957	0.529726
$267$	6.57701	0.402507
$268$	4.89737	0.299155
$269$	−16.5778	−1.01076	−0.505382	−	0.862896i	$-0.668648\pi$
$269$	−16.5778	−1.01076	−0.505382	+	0.862896i	$0.668648\pi$
$270$	−0.141558	−0.00861495
$271$	5.49825	0.333995	0.166997	−	0.985957i	$-0.446593\pi$
$271$	5.49825	0.333995	0.166997	+	0.985957i	$0.446593\pi$
$272$	−6.07617	−0.368422
$273$	−13.2128	−0.799673
$274$	20.4560	1.23579
$275$	4.97996	0.300303
$276$	1.03893	0.0625362
$277$	26.1541	1.57145	0.785724	−	0.618578i	$-0.212291\pi$
$277$	26.1541	1.57145	0.785724	+	0.618578i	$0.212291\pi$
$278$	11.9561	0.717079
$279$	8.30728	0.497344
$280$	0.583434	0.0348669
$281$	26.3603	1.57252	0.786262	−	0.617894i	$-0.212014\pi$
$281$	26.3603	1.57252	0.786262	+	0.617894i	$0.212014\pi$
$282$	−3.63429	−0.216419
$283$	4.34283	0.258154	0.129077	−	0.991635i	$-0.458798\pi$
$283$	4.34283	0.258154	0.129077	+	0.991635i	$0.458798\pi$
$284$	−10.6494	−0.631923
$285$	0.296735	0.0175771
$286$	−3.20580	−0.189563
$287$	50.2238	2.96462
$288$	1.00000	0.0589256
$289$	19.9198	1.17176
$290$	−0.492736	−0.0289345
$291$	1.38842	0.0813905
$292$	−13.1421	−0.769083
$293$	−6.14254	−0.358851	−0.179426	−	0.983772i	$-0.557424\pi$
$293$	−6.14254	−0.358851	−0.179426	+	0.983772i	$0.557424\pi$
$294$	9.98692	0.582449
$295$	0.868985	0.0505943
$296$	−10.7320	−0.623782
$297$	−1.00000	−0.0580259
$298$	−21.2887	−1.23322
$299$	3.33060	0.192613
$300$	−4.97996	−0.287518
$301$	47.3735	2.73056
$302$	12.1523	0.699289
$303$	−9.68491	−0.556384
$304$	−2.09621	−0.120226
$305$	0.141558	0.00810559
$306$	−6.07617	−0.347352
$307$	15.1598	0.865214	0.432607	−	0.901583i	$-0.357594\pi$
$307$	15.1598	0.865214	0.432607	+	0.901583i	$0.357594\pi$
$308$	4.12152	0.234845
$309$	−15.4369	−0.878175
$310$	−1.17596	−0.0667902
$311$	21.6585	1.22814	0.614069	−	0.789252i	$-0.289532\pi$
$311$	21.6585	1.22814	0.614069	+	0.789252i	$0.289532\pi$
$312$	3.20580	0.181493
$313$	−26.4405	−1.49450	−0.747252	−	0.664540i	$-0.768627\pi$
$313$	−26.4405	−1.49450	−0.747252	+	0.664540i	$0.768627\pi$
$314$	20.6454	1.16509
$315$	0.583434	0.0328728
$316$	3.28028	0.184530
$317$	20.9714	1.17787	0.588936	−	0.808180i	$-0.299547\pi$
$317$	20.9714	1.17787	0.588936	+	0.808180i	$0.299547\pi$
$318$	13.6276	0.764200
$319$	−3.48081	−0.194888
$320$	−0.141558	−0.00791334
$321$	−10.0740	−0.562278
$322$	−4.28197	−0.238625
$323$	12.7369	0.708701
$324$	1.00000	0.0555556
$325$	−15.9648	−0.885565
$326$	14.3279	0.793547
$327$	−9.65747	−0.534059
$328$	−12.1858	−0.672846
$329$	14.9788	0.825809
$330$	0.141558	0.00779251
$331$	−4.70763	−0.258755	−0.129377	−	0.991595i	$-0.541298\pi$
$331$	−4.70763	−0.258755	−0.129377	+	0.991595i	$0.541298\pi$
$332$	8.23111	0.451741
$333$	−10.7320	−0.588107
$334$	0.976378	0.0534251
$335$	−0.693262	−0.0378770
$336$	−4.12152	−0.224847
$337$	−11.1378	−0.606715	−0.303358	−	0.952877i	$-0.598108\pi$
$337$	−11.1378	−0.606715	−0.303358	+	0.952877i	$0.598108\pi$
$338$	−2.72286	−0.148104
$339$	−8.91244	−0.484057
$340$	0.860131	0.0466471
$341$	−8.30728	−0.449864
$342$	−2.09621	−0.113350
$343$	−12.3107	−0.664713
$344$	−11.4942	−0.619725
$345$	−0.147069	−0.00791792
$346$	−16.6715	−0.896267
$347$	16.2066	0.870015	0.435007	−	0.900427i	$-0.356746\pi$
$347$	16.2066	0.870015	0.435007	+	0.900427i	$0.356746\pi$
$348$	3.48081	0.186591
$349$	−2.76024	−0.147752	−0.0738762	−	0.997267i	$-0.523537\pi$
$349$	−2.76024	−0.147752	−0.0738762	+	0.997267i	$0.523537\pi$
$350$	20.5250	1.09711
$351$	3.20580	0.171113
$352$	−1.00000	−0.0533002
$353$	23.8571	1.26978	0.634891	−	0.772601i	$-0.281045\pi$
$353$	23.8571	1.26978	0.634891	+	0.772601i	$0.281045\pi$
$354$	−6.13872	−0.326269
$355$	1.50750	0.0800100
$356$	6.57701	0.348581
$357$	25.0431	1.32542
$358$	−13.8561	−0.732320
$359$	1.29076	0.0681237	0.0340619	−	0.999420i	$-0.489156\pi$
$359$	1.29076	0.0681237	0.0340619	+	0.999420i	$0.489156\pi$
$360$	−0.141558	−0.00746076
$361$	−14.6059	−0.768732
$362$	−14.6802	−0.771573
$363$	1.00000	0.0524864
$364$	−13.2128	−0.692537
$365$	1.86037	0.0973762
$366$	−1.00000	−0.0522708
$367$	20.2235	1.05566	0.527830	−	0.849350i	$-0.323006\pi$
$367$	20.2235	1.05566	0.527830	+	0.849350i	$0.323006\pi$
$368$	1.03893	0.0541579
$369$	−12.1858	−0.634365
$370$	1.51919	0.0789791
$371$	−56.1666	−2.91602
$372$	8.30728	0.430712
$373$	−15.9413	−0.825411	−0.412705	−	0.910865i	$-0.635416\pi$
$373$	−15.9413	−0.825411	−0.412705	+	0.910865i	$0.635416\pi$
$374$	6.07617	0.314191
$375$	1.41274	0.0729538
$376$	−3.63429	−0.187424
$377$	11.1588	0.574705
$378$	−4.12152	−0.211988
$379$	11.4199	0.586603	0.293302	−	0.956020i	$-0.405246\pi$
$379$	11.4199	0.586603	0.293302	+	0.956020i	$0.405246\pi$
$380$	0.296735	0.0152222
$381$	6.81096	0.348936
$382$	−10.2075	−0.522260
$383$	12.9754	0.663014	0.331507	−	0.943453i	$-0.392443\pi$
$383$	12.9754	0.663014	0.331507	+	0.943453i	$0.392443\pi$
$384$	1.00000	0.0510310
$385$	−0.583434	−0.0297346
$386$	−1.08641	−0.0552969
$387$	−11.4942	−0.584282
$388$	1.38842	0.0704863
$389$	13.0325	0.660774	0.330387	−	0.943845i	$-0.392821\pi$
$389$	13.0325	0.660774	0.330387	+	0.943845i	$0.392821\pi$
$390$	−0.453806	−0.0229794
$391$	−6.31271	−0.319248
$392$	9.98692	0.504416
$393$	3.40349	0.171683
$394$	18.4930	0.931666
$395$	−0.464350	−0.0233640
$396$	−1.00000	−0.0502519
$397$	−18.3338	−0.920148	−0.460074	−	0.887881i	$-0.652177\pi$
$397$	−18.3338	−0.920148	−0.460074	+	0.887881i	$0.652177\pi$
$398$	−12.9026	−0.646751
$399$	8.63957	0.432519
$400$	−4.97996	−0.248998
$401$	13.6881	0.683549	0.341774	−	0.939782i	$-0.388972\pi$
$401$	13.6881	0.683549	0.341774	+	0.939782i	$0.388972\pi$
$402$	4.89737	0.244259
$403$	26.6315	1.32661
$404$	−9.68491	−0.481843
$405$	−0.141558	−0.00703408
$406$	−14.3462	−0.711990
$407$	10.7320	0.531963
$408$	−6.07617	−0.300815
$409$	−17.0807	−0.844588	−0.422294	−	0.906459i	$-0.638775\pi$
$409$	−17.0807	−0.844588	−0.422294	+	0.906459i	$0.638775\pi$
$410$	1.72499	0.0851913
$411$	20.4560	1.00902
$412$	−15.4369	−0.760522
$413$	25.3009	1.24497
$414$	1.03893	0.0510606
$415$	−1.16518	−0.0571964
$416$	3.20580	0.157177
$417$	11.9561	0.585493
$418$	2.09621	0.102529
$419$	9.01000	0.440167	0.220084	−	0.975481i	$-0.429367\pi$
$419$	9.01000	0.440167	0.220084	+	0.975481i	$0.429367\pi$
$420$	0.583434	0.0284687
$421$	−25.0472	−1.22072	−0.610362	−	0.792122i	$-0.708976\pi$
$421$	−25.0472	−1.22072	−0.610362	+	0.792122i	$0.708976\pi$
$422$	−8.62787	−0.419998
$423$	−3.63429	−0.176705
$424$	13.6276	0.661816
$425$	30.2591	1.46778
$426$	−10.6494	−0.515963
$427$	4.12152	0.199454
$428$	−10.0740	−0.486947
$429$	−3.20580	−0.154777
$430$	1.62709	0.0784655
$431$	−26.7573	−1.28886	−0.644428	−	0.764665i	$-0.722904\pi$
$431$	−26.7573	−1.28886	−0.644428	+	0.764665i	$0.722904\pi$
$432$	1.00000	0.0481125
$433$	9.15683	0.440049	0.220025	−	0.975494i	$-0.429386\pi$
$433$	9.15683	0.440049	0.220025	+	0.975494i	$0.429386\pi$
$434$	−34.2386	−1.64351
$435$	−0.492736	−0.0236249
$436$	−9.65747	−0.462509
$437$	−2.17781	−0.104179
$438$	−13.1421	−0.627954
$439$	−14.0922	−0.672585	−0.336293	−	0.941758i	$-0.609173\pi$
$439$	−14.0922	−0.672585	−0.336293	+	0.941758i	$0.609173\pi$
$440$	0.141558	0.00674852
$441$	9.98692	0.475568
$442$	−19.4790	−0.926520
$443$	12.1070	0.575221	0.287610	−	0.957748i	$-0.407139\pi$
$443$	12.1070	0.575221	0.287610	+	0.957748i	$0.407139\pi$
$444$	−10.7320	−0.509316
$445$	−0.931029	−0.0441350
$446$	23.1120	1.09439
$447$	−21.2887	−1.00692
$448$	−4.12152	−0.194723
$449$	8.72185	0.411610	0.205805	−	0.978593i	$-0.434019\pi$
$449$	8.72185	0.411610	0.205805	+	0.978593i	$0.434019\pi$
$450$	−4.97996	−0.234758
$451$	12.1858	0.573805
$452$	−8.91244	−0.419206
$453$	12.1523	0.570967
$454$	24.9251	1.16979
$455$	1.87037	0.0876844
$456$	−2.09621	−0.0981640
$457$	9.43637	0.441415	0.220707	−	0.975340i	$-0.429163\pi$
$457$	9.43637	0.441415	0.220707	+	0.975340i	$0.429163\pi$
$458$	−24.0161	−1.12220
$459$	−6.07617	−0.283611
$460$	−0.147069	−0.00685712
$461$	−4.54215	−0.211549	−0.105774	−	0.994390i	$-0.533732\pi$
$461$	−4.54215	−0.211549	−0.105774	+	0.994390i	$0.533732\pi$
$462$	4.12152	0.191750
$463$	−29.0462	−1.34989	−0.674946	−	0.737868i	$-0.735833\pi$
$463$	−29.0462	−1.34989	−0.674946	+	0.737868i	$0.735833\pi$
$464$	3.48081	0.161592
$465$	−1.17596	−0.0545339
$466$	−13.6401	−0.631866
$467$	16.5206	0.764484	0.382242	−	0.924062i	$-0.375152\pi$
$467$	16.5206	0.764484	0.382242	+	0.924062i	$0.375152\pi$
$468$	3.20580	0.148188
$469$	−20.1846	−0.932039
$470$	0.514464	0.0237304
$471$	20.6454	0.951289
$472$	−6.13872	−0.282558
$473$	11.4942	0.528503
$474$	3.28028	0.150668
$475$	10.4390	0.478976
$476$	25.0431	1.14785
$477$	13.6276	0.623967
$478$	17.5843	0.804286
$479$	−7.57701	−0.346203	−0.173101	−	0.984904i	$-0.555379\pi$
$479$	−7.57701	−0.346203	−0.173101	+	0.984904i	$0.555379\pi$
$480$	−0.141558	−0.00646121
$481$	−34.4045	−1.56871
$482$	−16.3309	−0.743852
$483$	−4.28197	−0.194836
$484$	1.00000	0.0454545
$485$	−0.196542	−0.00892451
$486$	1.00000	0.0453609
$487$	−10.6477	−0.482492	−0.241246	−	0.970464i	$-0.577556\pi$
$487$	−10.6477	−0.482492	−0.241246	+	0.970464i	$0.577556\pi$
$488$	−1.00000	−0.0452679
$489$	14.3279	0.647928
$490$	−1.41373	−0.0638658
$491$	15.7856	0.712396	0.356198	−	0.934410i	$-0.384073\pi$
$491$	15.7856	0.712396	0.356198	+	0.934410i	$0.384073\pi$
$492$	−12.1858	−0.549376
$493$	−21.1500	−0.952547
$494$	−6.72002	−0.302348
$495$	0.141558	0.00636256
$496$	8.30728	0.373008
$497$	43.8916	1.96881
$498$	8.23111	0.368845
$499$	5.02889	0.225124	0.112562	−	0.993645i	$-0.464094\pi$
$499$	5.02889	0.225124	0.112562	+	0.993645i	$0.464094\pi$
$500$	1.41274	0.0631798
$501$	0.976378	0.0436214
$502$	−2.29008	−0.102211
$503$	23.0398	1.02729	0.513646	−	0.858002i	$-0.328294\pi$
$503$	23.0398	1.02729	0.513646	+	0.858002i	$0.328294\pi$
$504$	−4.12152	−0.183587
$505$	1.37098	0.0610077
$506$	−1.03893	−0.0461861
$507$	−2.72286	−0.120926
$508$	6.81096	0.302187
$509$	3.23922	0.143576	0.0717879	−	0.997420i	$-0.477130\pi$
$509$	3.23922	0.143576	0.0717879	+	0.997420i	$0.477130\pi$
$510$	0.860131	0.0380872
$511$	54.1654	2.39614
$512$	1.00000	0.0441942
$513$	−2.09621	−0.0925499
$514$	23.5486	1.03869
$515$	2.18522	0.0962922
$516$	−11.4942	−0.506003
$517$	3.63429	0.159836
$518$	44.2320	1.94344
$519$	−16.6715	−0.731799
$520$	−0.453806	−0.0199007
$521$	8.38842	0.367503	0.183752	−	0.982973i	$-0.441176\pi$
$521$	8.38842	0.367503	0.183752	+	0.982973i	$0.441176\pi$
$522$	3.48081	0.152351
$523$	−6.44188	−0.281684	−0.140842	−	0.990032i	$-0.544981\pi$
$523$	−6.44188	−0.281684	−0.140842	+	0.990032i	$0.544981\pi$
$524$	3.40349	0.148682
$525$	20.5250	0.895785
$526$	−7.65701	−0.333861
$527$	−50.4764	−2.19879
$528$	−1.00000	−0.0435194
$529$	−21.9206	−0.953071
$530$	−1.92910	−0.0837948
$531$	−6.13872	−0.266398
$532$	8.63957	0.374573
$533$	−39.0651	−1.69210
$534$	6.57701	0.284615
$535$	1.42606	0.0616540
$536$	4.89737	0.211534
$537$	−13.8561	−0.597937
$538$	−16.5778	−0.714718
$539$	−9.98692	−0.430167
$540$	−0.141558	−0.00609169
$541$	21.9407	0.943303	0.471651	−	0.881785i	$-0.343658\pi$
$541$	21.9407	0.943303	0.471651	+	0.881785i	$0.343658\pi$
$542$	5.49825	0.236170
$543$	−14.6802	−0.629987
$544$	−6.07617	−0.260514
$545$	1.36709	0.0585598
$546$	−13.2128	−0.565454
$547$	−23.9617	−1.02453	−0.512264	−	0.858828i	$-0.671193\pi$
$547$	−23.9617	−1.02453	−0.512264	+	0.858828i	$0.671193\pi$
$548$	20.4560	0.873839
$549$	−1.00000	−0.0426790
$550$	4.97996	0.212346
$551$	−7.29650	−0.310841
$552$	1.03893	0.0442198
$553$	−13.5197	−0.574918
$554$	26.1541	1.11118
$555$	1.51919	0.0644862
$556$	11.9561	0.507052
$557$	−11.2583	−0.477031	−0.238516	−	0.971139i	$-0.576661\pi$
$557$	−11.2583	−0.477031	−0.238516	+	0.971139i	$0.576661\pi$
$558$	8.30728	0.351675
$559$	−36.8480	−1.55851
$560$	0.583434	0.0246546
$561$	6.07617	0.256536
$562$	26.3603	1.11194
$563$	−19.7170	−0.830972	−0.415486	−	0.909600i	$-0.636388\pi$
$563$	−19.7170	−0.830972	−0.415486	+	0.909600i	$0.636388\pi$
$564$	−3.63429	−0.153031
$565$	1.26163	0.0530771
$566$	4.34283	0.182543
$567$	−4.12152	−0.173088
$568$	−10.6494	−0.446837
$569$	25.9039	1.08595	0.542975	−	0.839749i	$-0.317298\pi$
$569$	25.9039	1.08595	0.542975	+	0.839749i	$0.317298\pi$
$570$	0.296735	0.0124289
$571$	−41.3680	−1.73120	−0.865598	−	0.500739i	$-0.833062\pi$
$571$	−41.3680	−1.73120	−0.865598	+	0.500739i	$0.833062\pi$
$572$	−3.20580	−0.134041
$573$	−10.2075	−0.426424
$574$	50.2238	2.09630
$575$	−5.17383	−0.215764
$576$	1.00000	0.0416667
$577$	11.1863	0.465692	0.232846	−	0.972514i	$-0.425196\pi$
$577$	11.1863	0.465692	0.232846	+	0.972514i	$0.425196\pi$
$578$	19.9198	0.828556
$579$	−1.08641	−0.0451497
$580$	−0.492736	−0.0204598
$581$	−33.9247	−1.40743
$582$	1.38842	0.0575518
$583$	−13.6276	−0.564399
$584$	−13.1421	−0.543824
$585$	−0.453806	−0.0187626
$586$	−6.14254	−0.253746
$587$	−33.2794	−1.37359	−0.686795	−	0.726852i	$-0.740983\pi$
$587$	−33.2794	−1.37359	−0.686795	+	0.726852i	$0.740983\pi$
$588$	9.98692	0.411854
$589$	−17.4138	−0.717523
$590$	0.868985	0.0357756
$591$	18.4930	0.760702
$592$	−10.7320	−0.441081
$593$	26.3719	1.08296	0.541481	−	0.840713i	$-0.317864\pi$
$593$	26.3719	1.08296	0.541481	+	0.840713i	$0.317864\pi$
$594$	−1.00000	−0.0410305
$595$	−3.54505	−0.145333
$596$	−21.2887	−0.872019
$597$	−12.9026	−0.528070
$598$	3.33060	0.136198
$599$	−4.26734	−0.174359	−0.0871795	−	0.996193i	$-0.527785\pi$
$599$	−4.26734	−0.174359	−0.0871795	+	0.996193i	$0.527785\pi$
$600$	−4.97996	−0.203306
$601$	−40.8516	−1.66637	−0.833187	−	0.552992i	$-0.813486\pi$
$601$	−40.8516	−1.66637	−0.833187	+	0.552992i	$0.813486\pi$
$602$	47.3735	1.93080
$603$	4.89737	0.199436
$604$	12.1523	0.494472
$605$	−0.141558	−0.00575515
$606$	−9.68491	−0.393423
$607$	21.3095	0.864926	0.432463	−	0.901652i	$-0.357645\pi$
$607$	21.3095	0.864926	0.432463	+	0.901652i	$0.357645\pi$
$608$	−2.09621	−0.0850125
$609$	−14.3462	−0.581338
$610$	0.141558	0.00573152
$611$	−11.6508	−0.471341
$612$	−6.07617	−0.245615
$613$	−0.770245	−0.0311099	−0.0155549	−	0.999879i	$-0.504951\pi$
$613$	−0.770245	−0.0311099	−0.0155549	+	0.999879i	$0.504951\pi$
$614$	15.1598	0.611798
$615$	1.72499	0.0695584
$616$	4.12152	0.166061
$617$	10.7834	0.434124	0.217062	−	0.976158i	$-0.430353\pi$
$617$	10.7834	0.434124	0.217062	+	0.976158i	$0.430353\pi$
$618$	−15.4369	−0.620963
$619$	−15.1693	−0.609706	−0.304853	−	0.952399i	$-0.598607\pi$
$619$	−15.1693	−0.609706	−0.304853	+	0.952399i	$0.598607\pi$
$620$	−1.17596	−0.0472278
$621$	1.03893	0.0416908
$622$	21.6585	0.868425
$623$	−27.1073	−1.08603
$624$	3.20580	0.128335
$625$	24.6998	0.987993
$626$	−26.4405	−1.05677
$627$	2.09621	0.0837145
$628$	20.6454	0.823840
$629$	65.2092	2.60006
$630$	0.583434	0.0232446
$631$	31.8380	1.26745	0.633726	−	0.773558i	$-0.281525\pi$
$631$	31.8380	1.26745	0.633726	+	0.773558i	$0.281525\pi$
$632$	3.28028	0.130483
$633$	−8.62787	−0.342927
$634$	20.9714	0.832881
$635$	−0.964146	−0.0382610
$636$	13.6276	0.540371
$637$	32.0161	1.26852
$638$	−3.48081	−0.137806
$639$	−10.6494	−0.421282
$640$	−0.141558	−0.00559557
$641$	−8.57120	−0.338542	−0.169271	−	0.985570i	$-0.554141\pi$
$641$	−8.57120	−0.338542	−0.169271	+	0.985570i	$0.554141\pi$
$642$	−10.0740	−0.397591
$643$	−36.2644	−1.43013	−0.715063	−	0.699060i	$-0.753602\pi$
$643$	−36.2644	−1.43013	−0.715063	+	0.699060i	$0.753602\pi$
$644$	−4.28197	−0.168733
$645$	1.62709	0.0640668
$646$	12.7369	0.501128
$647$	−22.8435	−0.898072	−0.449036	−	0.893514i	$-0.648232\pi$
$647$	−22.8435	−0.898072	−0.449036	+	0.893514i	$0.648232\pi$
$648$	1.00000	0.0392837
$649$	6.13872	0.240966
$650$	−15.9648	−0.626189
$651$	−34.2386	−1.34192
$652$	14.3279	0.561122
$653$	7.67582	0.300378	0.150189	−	0.988657i	$-0.452012\pi$
$653$	7.67582	0.300378	0.150189	+	0.988657i	$0.452012\pi$
$654$	−9.65747	−0.377637
$655$	−0.481791	−0.0188251
$656$	−12.1858	−0.475774
$657$	−13.1421	−0.512722
$658$	14.9788	0.583935
$659$	−12.0351	−0.468821	−0.234411	−	0.972138i	$-0.575316\pi$
$659$	−12.0351	−0.468821	−0.234411	+	0.972138i	$0.575316\pi$
$660$	0.141558	0.00551014
$661$	8.10296	0.315169	0.157584	−	0.987506i	$-0.449629\pi$
$661$	8.10296	0.315169	0.157584	+	0.987506i	$0.449629\pi$
$662$	−4.70763	−0.182967
$663$	−19.4790	−0.756501
$664$	8.23111	0.319429
$665$	−1.22300	−0.0474259
$666$	−10.7320	−0.415855
$667$	3.61631	0.140024
$668$	0.976378	0.0377772
$669$	23.1120	0.893562
$670$	−0.693262	−0.0267831
$671$	1.00000	0.0386046
$672$	−4.12152	−0.158991
$673$	−41.1326	−1.58555	−0.792773	−	0.609517i	$-0.791363\pi$
$673$	−41.1326	−1.58555	−0.792773	+	0.609517i	$0.791363\pi$
$674$	−11.1378	−0.429013
$675$	−4.97996	−0.191679
$676$	−2.72286	−0.104725
$677$	−22.5115	−0.865187	−0.432593	−	0.901589i	$-0.642401\pi$
$677$	−22.5115	−0.865187	−0.432593	+	0.901589i	$0.642401\pi$
$678$	−8.91244	−0.342280
$679$	−5.72239	−0.219605
$680$	0.860131	0.0329845
$681$	24.9251	0.955133
$682$	−8.30728	−0.318102
$683$	3.99443	0.152842	0.0764212	−	0.997076i	$-0.475651\pi$
$683$	3.99443	0.152842	0.0764212	+	0.997076i	$0.475651\pi$
$684$	−2.09621	−0.0801506
$685$	−2.89572	−0.110640
$686$	−12.3107	−0.470023
$687$	−24.0161	−0.916270
$688$	−11.4942	−0.438212
$689$	43.6874	1.66436
$690$	−0.147069	−0.00559881
$691$	14.0003	0.532597	0.266298	−	0.963891i	$-0.414199\pi$
$691$	14.0003	0.532597	0.266298	+	0.963891i	$0.414199\pi$
$692$	−16.6715	−0.633757
$693$	4.12152	0.156564
$694$	16.2066	0.615193
$695$	−1.69248	−0.0641995
$696$	3.48081	0.131940
$697$	74.0427	2.80457
$698$	−2.76024	−0.104477
$699$	−13.6401	−0.515916
$700$	20.5250	0.775772
$701$	−50.5365	−1.90874	−0.954369	−	0.298629i	$-0.903471\pi$
$701$	−50.5365	−1.90874	−0.954369	+	0.298629i	$0.903471\pi$
$702$	3.20580	0.120995
$703$	22.4964	0.848468
$704$	−1.00000	−0.0376889
$705$	0.514464	0.0193758
$706$	23.8571	0.897872
$707$	39.9166	1.50122
$708$	−6.13872	−0.230707
$709$	0.101016	0.00379374	0.00189687	−	0.999998i	$-0.499396\pi$
$709$	0.101016	0.00379374	0.00189687	+	0.999998i	$0.499396\pi$
$710$	1.50750	0.0565756
$711$	3.28028	0.123020
$712$	6.57701	0.246484
$713$	8.63068	0.323221
$714$	25.0431	0.937213
$715$	0.453806	0.0169714
$716$	−13.8561	−0.517829
$717$	17.5843	0.656697
$718$	1.29076	0.0481707
$719$	24.0233	0.895919	0.447959	−	0.894054i	$-0.352151\pi$
$719$	24.0233	0.895919	0.447959	+	0.894054i	$0.352151\pi$
$720$	−0.141558	−0.00527556
$721$	63.6235	2.36946
$722$	−14.6059	−0.543576
$723$	−16.3309	−0.607353
$724$	−14.6802	−0.545585
$725$	−17.3343	−0.643779
$726$	1.00000	0.0371135
$727$	−29.1543	−1.08127	−0.540637	−	0.841256i	$-0.681817\pi$
$727$	−29.1543	−1.08127	−0.540637	+	0.841256i	$0.681817\pi$
$728$	−13.2128	−0.489697
$729$	1.00000	0.0370370
$730$	1.86037	0.0688554
$731$	69.8406	2.58315
$732$	−1.00000	−0.0369611
$733$	4.37797	0.161704	0.0808520	−	0.996726i	$-0.474236\pi$
$733$	4.37797	0.161704	0.0808520	+	0.996726i	$0.474236\pi$
$734$	20.2235	0.746465
$735$	−1.41373	−0.0521462
$736$	1.03893	0.0382955
$737$	−4.89737	−0.180397
$738$	−12.1858	−0.448564
$739$	21.5661	0.793321	0.396660	−	0.917965i	$-0.370169\pi$
$739$	21.5661	0.793321	0.396660	+	0.917965i	$0.370169\pi$
$740$	1.51919	0.0558467
$741$	−6.72002	−0.246866
$742$	−56.1666	−2.06194
$743$	31.5248	1.15653	0.578267	−	0.815847i	$-0.303729\pi$
$743$	31.5248	1.15653	0.578267	+	0.815847i	$0.303729\pi$
$744$	8.30728	0.304560
$745$	3.01359	0.110409
$746$	−15.9413	−0.583654
$747$	8.23111	0.301161
$748$	6.07617	0.222167
$749$	41.5203	1.51712
$750$	1.41274	0.0515861
$751$	−9.90616	−0.361481	−0.180741	−	0.983531i	$-0.557849\pi$
$751$	−9.90616	−0.361481	−0.180741	+	0.983531i	$0.557849\pi$
$752$	−3.63429	−0.132529
$753$	−2.29008	−0.0834550
$754$	11.1588	0.406378
$755$	−1.72026	−0.0626067
$756$	−4.12152	−0.149898
$757$	−35.5382	−1.29166	−0.645829	−	0.763482i	$-0.723488\pi$
$757$	−35.5382	−1.29166	−0.645829	+	0.763482i	$0.723488\pi$
$758$	11.4199	0.414791
$759$	−1.03893	−0.0377108
$760$	0.296735	0.0107637
$761$	1.84848	0.0670074	0.0335037	−	0.999439i	$-0.489333\pi$
$761$	1.84848	0.0670074	0.0335037	+	0.999439i	$0.489333\pi$
$762$	6.81096	0.246735
$763$	39.8035	1.44098
$764$	−10.2075	−0.369294
$765$	0.860131	0.0310981
$766$	12.9754	0.468822
$767$	−19.6795	−0.710586
$768$	1.00000	0.0360844
$769$	20.7852	0.749535	0.374768	−	0.927119i	$-0.377722\pi$
$769$	20.7852	0.749535	0.374768	+	0.927119i	$0.377722\pi$
$770$	−0.583434	−0.0210255
$771$	23.5486	0.848083
$772$	−1.08641	−0.0391008
$773$	−46.5851	−1.67555	−0.837774	−	0.546017i	$-0.816143\pi$
$773$	−46.5851	−1.67555	−0.837774	+	0.546017i	$0.816143\pi$
$774$	−11.4942	−0.413150
$775$	−41.3699	−1.48605
$776$	1.38842	0.0498413
$777$	44.2320	1.58681
$778$	13.0325	0.467238
$779$	25.5439	0.915205
$780$	−0.453806	−0.0162489
$781$	10.6494	0.381064
$782$	−6.31271	−0.225742
$783$	3.48081	0.124394
$784$	9.98692	0.356676
$785$	−2.92252	−0.104309
$786$	3.40349	0.121398
$787$	−7.12882	−0.254115	−0.127057	−	0.991895i	$-0.540553\pi$
$787$	−7.12882	−0.254115	−0.127057	+	0.991895i	$0.540553\pi$
$788$	18.4930	0.658787
$789$	−7.65701	−0.272597
$790$	−0.464350	−0.0165208
$791$	36.7328	1.30607
$792$	−1.00000	−0.0355335
$793$	−3.20580	−0.113841
$794$	−18.3338	−0.650643
$795$	−1.92910	−0.0684182
$796$	−12.9026	−0.457322
$797$	−31.2999	−1.10870	−0.554349	−	0.832284i	$-0.687033\pi$
$797$	−31.2999	−1.10870	−0.554349	+	0.832284i	$0.687033\pi$
$798$	8.63957	0.305837
$799$	22.0826	0.781226
$800$	−4.97996	−0.176068
$801$	6.57701	0.232387
$802$	13.6881	0.483342
$803$	13.1421	0.463775
$804$	4.89737	0.172717
$805$	0.606147	0.0213639
$806$	26.6315	0.938053
$807$	−16.5778	−0.583565
$808$	−9.68491	−0.340714
$809$	9.41755	0.331103	0.165552	−	0.986201i	$-0.447060\pi$
$809$	9.41755	0.331103	0.165552	+	0.986201i	$0.447060\pi$
$810$	−0.141558	−0.00497384
$811$	−18.6933	−0.656411	−0.328206	−	0.944606i	$-0.606444\pi$
$811$	−18.6933	−0.656411	−0.328206	+	0.944606i	$0.606444\pi$
$812$	−14.3462	−0.503453
$813$	5.49825	0.192832
$814$	10.7320	0.376155
$815$	−2.02822	−0.0710456
$816$	−6.07617	−0.212709
$817$	24.0942	0.842950
$818$	−17.0807	−0.597214
$819$	−13.2128	−0.461691
$820$	1.72499	0.0602393
$821$	−18.0311	−0.629291	−0.314645	−	0.949209i	$-0.601886\pi$
$821$	−18.0311	−0.629291	−0.314645	+	0.949209i	$0.601886\pi$
$822$	20.4560	0.713486
$823$	−3.70343	−0.129093	−0.0645467	−	0.997915i	$-0.520560\pi$
$823$	−3.70343	−0.129093	−0.0645467	+	0.997915i	$0.520560\pi$
$824$	−15.4369	−0.537770
$825$	4.97996	0.173380
$826$	25.3009	0.880329
$827$	−31.5107	−1.09573	−0.547867	−	0.836565i	$-0.684560\pi$
$827$	−31.5107	−1.09573	−0.547867	+	0.836565i	$0.684560\pi$
$828$	1.03893	0.0361053
$829$	−52.5805	−1.82619	−0.913097	−	0.407742i	$-0.866316\pi$
$829$	−52.5805	−1.82619	−0.913097	+	0.407742i	$0.866316\pi$
$830$	−1.16518	−0.0404440
$831$	26.1541	0.907275
$832$	3.20580	0.111141
$833$	−60.6822	−2.10251
$834$	11.9561	0.414006
$835$	−0.138214	−0.00478310
$836$	2.09621	0.0724989
$837$	8.30728	0.287142
$838$	9.01000	0.311245
$839$	51.0110	1.76110	0.880548	−	0.473957i	$-0.157175\pi$
$839$	51.0110	1.76110	0.880548	+	0.473957i	$0.157175\pi$
$840$	0.583434	0.0201304
$841$	−16.8840	−0.582207
$842$	−25.0472	−0.863183
$843$	26.3603	0.907897
$844$	−8.62787	−0.296984
$845$	0.385443	0.0132596
$846$	−3.63429	−0.124950
$847$	−4.12152	−0.141617
$848$	13.6276	0.467975
$849$	4.34283	0.149046
$850$	30.2591	1.03788
$851$	−11.1497	−0.382208
$852$	−10.6494	−0.364841
$853$	−36.6286	−1.25414	−0.627070	−	0.778963i	$-0.715746\pi$
$853$	−36.6286	−1.25414	−0.627070	+	0.778963i	$0.715746\pi$
$854$	4.12152	0.141035
$855$	0.296735	0.0101481
$856$	−10.0740	−0.344324
$857$	15.7322	0.537400	0.268700	−	0.963224i	$-0.413406\pi$
$857$	15.7322	0.537400	0.268700	+	0.963224i	$0.413406\pi$
$858$	−3.20580	−0.109444
$859$	21.1581	0.721904	0.360952	−	0.932584i	$-0.382452\pi$
$859$	21.1581	0.721904	0.360952	+	0.932584i	$0.382452\pi$
$860$	1.62709	0.0554835
$861$	50.2238	1.71162
$862$	−26.7573	−0.911359
$863$	29.1693	0.992935	0.496467	−	0.868055i	$-0.334630\pi$
$863$	29.1693	0.992935	0.496467	+	0.868055i	$0.334630\pi$
$864$	1.00000	0.0340207
$865$	2.35999	0.0802421
$866$	9.15683	0.311162
$867$	19.9198	0.676513
$868$	−34.2386	−1.16213
$869$	−3.28028	−0.111276
$870$	−0.492736	−0.0167053
$871$	15.7000	0.531974
$872$	−9.65747	−0.327043
$873$	1.38842	0.0469909
$874$	−2.17781	−0.0736656
$875$	−5.82265	−0.196842
$876$	−13.1421	−0.444030
$877$	9.60683	0.324400	0.162200	−	0.986758i	$-0.448141\pi$
$877$	9.60683	0.324400	0.162200	+	0.986758i	$0.448141\pi$
$878$	−14.0922	−0.475590
$879$	−6.14254	−0.207183
$880$	0.141558	0.00477192
$881$	26.1553	0.881193	0.440596	−	0.897705i	$-0.354767\pi$
$881$	26.1553	0.881193	0.440596	+	0.897705i	$0.354767\pi$
$882$	9.98692	0.336277
$883$	31.8621	1.07225	0.536123	−	0.844140i	$-0.319888\pi$
$883$	31.8621	1.07225	0.536123	+	0.844140i	$0.319888\pi$
$884$	−19.4790	−0.655149
$885$	0.868985	0.0292106
$886$	12.1070	0.406742
$887$	−46.3211	−1.55531	−0.777654	−	0.628692i	$-0.783591\pi$
$887$	−46.3211	−1.55531	−0.777654	+	0.628692i	$0.783591\pi$
$888$	−10.7320	−0.360141
$889$	−28.0715	−0.941488
$890$	−0.931029	−0.0312082
$891$	−1.00000	−0.0335013
$892$	23.1120	0.773848
$893$	7.61824	0.254935
$894$	−21.2887	−0.712000
$895$	1.96145	0.0655640
$896$	−4.12152	−0.137690
$897$	3.33060	0.111205
$898$	8.72185	0.291052
$899$	28.9160	0.964403
$900$	−4.97996	−0.165999
$901$	−82.8038	−2.75860
$902$	12.1858	0.405741
$903$	47.3735	1.57649
$904$	−8.91244	−0.296423
$905$	2.07810	0.0690783
$906$	12.1523	0.403734
$907$	39.1875	1.30120	0.650600	−	0.759421i	$-0.274517\pi$
$907$	39.1875	1.30120	0.650600	+	0.759421i	$0.274517\pi$
$908$	24.9251	0.827169
$909$	−9.68491	−0.321228
$910$	1.87037	0.0620022
$911$	14.2144	0.470942	0.235471	−	0.971881i	$-0.424337\pi$
$911$	14.2144	0.470942	0.235471	+	0.971881i	$0.424337\pi$
$912$	−2.09621	−0.0694124
$913$	−8.23111	−0.272410
$914$	9.43637	0.312127
$915$	0.141558	0.00467976
$916$	−24.0161	−0.793513
$917$	−14.0275	−0.463230
$918$	−6.07617	−0.200544
$919$	27.2300	0.898236	0.449118	−	0.893473i	$-0.351738\pi$
$919$	27.2300	0.898236	0.449118	+	0.893473i	$0.351738\pi$
$920$	−0.147069	−0.00484872
$921$	15.1598	0.499531
$922$	−4.54215	−0.149588
$923$	−34.1397	−1.12372
$924$	4.12152	0.135588
$925$	53.4447	1.75725
$926$	−29.0462	−0.954517
$927$	−15.4369	−0.507015
$928$	3.48081	0.114263
$929$	24.3386	0.798523	0.399261	−	0.916837i	$-0.369267\pi$
$929$	24.3386	0.798523	0.399261	+	0.916837i	$0.369267\pi$
$930$	−1.17596	−0.0385613
$931$	−20.9347	−0.686106
$932$	−13.6401	−0.446797
$933$	21.6585	0.709066
$934$	16.5206	0.540572
$935$	−0.860131	−0.0281293
$936$	3.20580	0.104785
$937$	−27.4643	−0.897221	−0.448611	−	0.893727i	$-0.648081\pi$
$937$	−27.4643	−0.897221	−0.448611	+	0.893727i	$0.648081\pi$
$938$	−20.1846	−0.659051
$939$	−26.4405	−0.862853
$940$	0.514464	0.0167800
$941$	−25.5288	−0.832216	−0.416108	−	0.909315i	$-0.636606\pi$
$941$	−25.5288	−0.832216	−0.416108	+	0.909315i	$0.636606\pi$
$942$	20.6454	0.672663
$943$	−12.6601	−0.412271
$944$	−6.13872	−0.199798
$945$	0.583434	0.0189791
$946$	11.4942	0.373708
$947$	51.8280	1.68418	0.842092	−	0.539334i	$-0.181324\pi$
$947$	51.8280	1.68418	0.842092	+	0.539334i	$0.181324\pi$
$948$	3.28028	0.106539
$949$	−42.1309	−1.36763
$950$	10.4390	0.338687
$951$	20.9714	0.680045
$952$	25.0431	0.811650
$953$	22.2287	0.720059	0.360029	−	0.932941i	$-0.382767\pi$
$953$	22.2287	0.720059	0.360029	+	0.932941i	$0.382767\pi$
$954$	13.6276	0.441211
$955$	1.44495	0.0467575
$956$	17.5843	0.568716
$957$	−3.48081	−0.112518
$958$	−7.57701	−0.244802
$959$	−84.3099	−2.72251
$960$	−0.141558	−0.00456877
$961$	38.0109	1.22616
$962$	−34.4045	−1.10924
$963$	−10.0740	−0.324631
$964$	−16.3309	−0.525983
$965$	0.153790	0.00495069
$966$	−4.28197	−0.137770
$967$	55.5194	1.78538	0.892692	−	0.450667i	$-0.148814\pi$
$967$	55.5194	1.78538	0.892692	+	0.450667i	$0.148814\pi$
$968$	1.00000	0.0321412
$969$	12.7369	0.409169
$970$	−0.196542	−0.00631058
$971$	−13.6863	−0.439216	−0.219608	−	0.975588i	$-0.570478\pi$
$971$	−13.6863	−0.439216	−0.219608	+	0.975588i	$0.570478\pi$
$972$	1.00000	0.0320750
$973$	−49.2773	−1.57976
$974$	−10.6477	−0.341173
$975$	−15.9648	−0.511281
$976$	−1.00000	−0.0320092
$977$	26.0277	0.832700	0.416350	−	0.909204i	$-0.363309\pi$
$977$	26.0277	0.832700	0.416350	+	0.909204i	$0.363309\pi$
$978$	14.3279	0.458154
$979$	−6.57701	−0.210202
$980$	−1.41373	−0.0451599
$981$	−9.65747	−0.308339
$982$	15.7856	0.503740
$983$	16.6940	0.532457	0.266229	−	0.963910i	$-0.414222\pi$
$983$	16.6940	0.532457	0.266229	+	0.963910i	$0.414222\pi$
$984$	−12.1858	−0.388468
$985$	−2.61784	−0.0834113
$986$	−21.1500	−0.673552
$987$	14.9788	0.476781
$988$	−6.72002	−0.213792
$989$	−11.9416	−0.379722
$990$	0.141558	0.00449901
$991$	−14.0313	−0.445718	−0.222859	−	0.974851i	$-0.571539\pi$
$991$	−14.0313	−0.445718	−0.222859	+	0.974851i	$0.571539\pi$
$992$	8.30728	0.263756
$993$	−4.70763	−0.149392
$994$	43.8916	1.39216
$995$	1.82647	0.0579031
$996$	8.23111	0.260813
$997$	51.6721	1.63647	0.818237	−	0.574882i	$-0.194952\pi$
$997$	51.6721	1.63647	0.818237	+	0.574882i	$0.194952\pi$
$998$	5.02889	0.159187
$999$	−10.7320	−0.339544

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.t.1.3	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.t.1.3	✓	4	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:	\( N \)	\(=\)	\( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.141558 q^{5} +1.00000 q^{6} -4.12152 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.141558 q^{5} +1.00000 q^{6} -4.12152 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.141558 q^{10} -1.00000 q^{11} +1.00000 q^{12} +3.20580 q^{13} -4.12152 q^{14} -0.141558 q^{15} +1.00000 q^{16} -6.07617 q^{17} +1.00000 q^{18} -2.09621 q^{19} -0.141558 q^{20} -4.12152 q^{21} -1.00000 q^{22} +1.03893 q^{23} +1.00000 q^{24} -4.97996 q^{25} +3.20580 q^{26} +1.00000 q^{27} -4.12152 q^{28} +3.48081 q^{29} -0.141558 q^{30} +8.30728 q^{31} +1.00000 q^{32} -1.00000 q^{33} -6.07617 q^{34} +0.583434 q^{35} +1.00000 q^{36} -10.7320 q^{37} -2.09621 q^{38} +3.20580 q^{39} -0.141558 q^{40} -12.1858 q^{41} -4.12152 q^{42} -11.4942 q^{43} -1.00000 q^{44} -0.141558 q^{45} +1.03893 q^{46} -3.63429 q^{47} +1.00000 q^{48} +9.98692 q^{49} -4.97996 q^{50} -6.07617 q^{51} +3.20580 q^{52} +13.6276 q^{53} +1.00000 q^{54} +0.141558 q^{55} -4.12152 q^{56} -2.09621 q^{57} +3.48081 q^{58} -6.13872 q^{59} -0.141558 q^{60} -1.00000 q^{61} +8.30728 q^{62} -4.12152 q^{63} +1.00000 q^{64} -0.453806 q^{65} -1.00000 q^{66} +4.89737 q^{67} -6.07617 q^{68} +1.03893 q^{69} +0.583434 q^{70} -10.6494 q^{71} +1.00000 q^{72} -13.1421 q^{73} -10.7320 q^{74} -4.97996 q^{75} -2.09621 q^{76} +4.12152 q^{77} +3.20580 q^{78} +3.28028 q^{79} -0.141558 q^{80} +1.00000 q^{81} -12.1858 q^{82} +8.23111 q^{83} -4.12152 q^{84} +0.860131 q^{85} -11.4942 q^{86} +3.48081 q^{87} -1.00000 q^{88} +6.57701 q^{89} -0.141558 q^{90} -13.2128 q^{91} +1.03893 q^{92} +8.30728 q^{93} -3.63429 q^{94} +0.296735 q^{95} +1.00000 q^{96} +1.38842 q^{97} +9.98692 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} - 6 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^5 + 4 * q^6 - 6 * q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} - 6 q^{7} + 4 q^{8} + 4 q^{9} - 4 q^{10} - 4 q^{11} + 4 q^{12} - 5 q^{13} - 6 q^{14} - 4 q^{15} + 4 q^{16} - 10 q^{17} + 4 q^{18} - 8 q^{19} - 4 q^{20} - 6 q^{21} - 4 q^{22} - 7 q^{23} + 4 q^{24} - 6 q^{25} - 5 q^{26} + 4 q^{27} - 6 q^{28} - 4 q^{29} - 4 q^{30} - 9 q^{31} + 4 q^{32} - 4 q^{33} - 10 q^{34} - q^{35} + 4 q^{36} - 11 q^{37} - 8 q^{38} - 5 q^{39} - 4 q^{40} - 17 q^{41} - 6 q^{42} - 11 q^{43} - 4 q^{44} - 4 q^{45} - 7 q^{46} - 7 q^{47} + 4 q^{48} - 6 q^{49} - 6 q^{50} - 10 q^{51} - 5 q^{52} + 16 q^{53} + 4 q^{54} + 4 q^{55} - 6 q^{56} - 8 q^{57} - 4 q^{58} + 3 q^{59} - 4 q^{60} - 4 q^{61} - 9 q^{62} - 6 q^{63} + 4 q^{64} - 2 q^{65} - 4 q^{66} + 5 q^{67} - 10 q^{68} - 7 q^{69} - q^{70} - 10 q^{71} + 4 q^{72} - 9 q^{73} - 11 q^{74} - 6 q^{75} - 8 q^{76} + 6 q^{77} - 5 q^{78} - 11 q^{79} - 4 q^{80} + 4 q^{81} - 17 q^{82} + 5 q^{83} - 6 q^{84} - 8 q^{85} - 11 q^{86} - 4 q^{87} - 4 q^{88} + 8 q^{89} - 4 q^{90} - 3 q^{91} - 7 q^{92} - 9 q^{93} - 7 q^{94} + 7 q^{95} + 4 q^{96} - 12 q^{97} - 6 q^{98} - 4 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^5 + 4 * q^6 - 6 * q^7 + 4 * q^8 + 4 * q^9 - 4 * q^10 - 4 * q^11 + 4 * q^12 - 5 * q^13 - 6 * q^14 - 4 * q^15 + 4 * q^16 - 10 * q^17 + 4 * q^18 - 8 * q^19 - 4 * q^20 - 6 * q^21 - 4 * q^22 - 7 * q^23 + 4 * q^24 - 6 * q^25 - 5 * q^26 + 4 * q^27 - 6 * q^28 - 4 * q^29 - 4 * q^30 - 9 * q^31 + 4 * q^32 - 4 * q^33 - 10 * q^34 - q^35 + 4 * q^36 - 11 * q^37 - 8 * q^38 - 5 * q^39 - 4 * q^40 - 17 * q^41 - 6 * q^42 - 11 * q^43 - 4 * q^44 - 4 * q^45 - 7 * q^46 - 7 * q^47 + 4 * q^48 - 6 * q^49 - 6 * q^50 - 10 * q^51 - 5 * q^52 + 16 * q^53 + 4 * q^54 + 4 * q^55 - 6 * q^56 - 8 * q^57 - 4 * q^58 + 3 * q^59 - 4 * q^60 - 4 * q^61 - 9 * q^62 - 6 * q^63 + 4 * q^64 - 2 * q^65 - 4 * q^66 + 5 * q^67 - 10 * q^68 - 7 * q^69 - q^70 - 10 * q^71 + 4 * q^72 - 9 * q^73 - 11 * q^74 - 6 * q^75 - 8 * q^76 + 6 * q^77 - 5 * q^78 - 11 * q^79 - 4 * q^80 + 4 * q^81 - 17 * q^82 + 5 * q^83 - 6 * q^84 - 8 * q^85 - 11 * q^86 - 4 * q^87 - 4 * q^88 + 8 * q^89 - 4 * q^90 - 3 * q^91 - 7 * q^92 - 9 * q^93 - 7 * q^94 + 7 * q^95 + 4 * q^96 - 12 * q^97 - 6 * q^98 - 4 * q^99

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