LMFDB - Embedded newform 4026.2.a.bc.1.8

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:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - x^{8} - 30x^{7} + 7x^{6} + 284x^{5} + 100x^{4} - 777x^{3} - 250x^{2} + 574x - 68 $ x^9 - x^8 - 30x^7 + 7x^6 + 284x^5 + 100x^4 - 777x^3 - 250x^2 + 574*x - 68
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-2.63661$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.63661 q^{5} +1.00000 q^{6} -1.65542 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.63661 q^{5} +1.00000 q^{6} -1.65542 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.63661 q^{10} +1.00000 q^{11} +1.00000 q^{12} +6.43612 q^{13} -1.65542 q^{14} +3.63661 q^{15} +1.00000 q^{16} -1.11715 q^{17} +1.00000 q^{18} -5.55489 q^{19} +3.63661 q^{20} -1.65542 q^{21} +1.00000 q^{22} -3.64436 q^{23} +1.00000 q^{24} +8.22493 q^{25} +6.43612 q^{26} +1.00000 q^{27} -1.65542 q^{28} -1.74243 q^{29} +3.63661 q^{30} +1.99225 q^{31} +1.00000 q^{32} +1.00000 q^{33} -1.11715 q^{34} -6.02012 q^{35} +1.00000 q^{36} +10.6804 q^{37} -5.55489 q^{38} +6.43612 q^{39} +3.63661 q^{40} -3.65909 q^{41} -1.65542 q^{42} +6.64405 q^{43} +1.00000 q^{44} +3.63661 q^{45} -3.64436 q^{46} +11.2187 q^{47} +1.00000 q^{48} -4.25958 q^{49} +8.22493 q^{50} -1.11715 q^{51} +6.43612 q^{52} -7.64051 q^{53} +1.00000 q^{54} +3.63661 q^{55} -1.65542 q^{56} -5.55489 q^{57} -1.74243 q^{58} -0.0748538 q^{59} +3.63661 q^{60} -1.00000 q^{61} +1.99225 q^{62} -1.65542 q^{63} +1.00000 q^{64} +23.4056 q^{65} +1.00000 q^{66} -13.9718 q^{67} -1.11715 q^{68} -3.64436 q^{69} -6.02012 q^{70} -5.87217 q^{71} +1.00000 q^{72} -7.77814 q^{73} +10.6804 q^{74} +8.22493 q^{75} -5.55489 q^{76} -1.65542 q^{77} +6.43612 q^{78} +1.55257 q^{79} +3.63661 q^{80} +1.00000 q^{81} -3.65909 q^{82} +15.0909 q^{83} -1.65542 q^{84} -4.06265 q^{85} +6.64405 q^{86} -1.74243 q^{87} +1.00000 q^{88} -3.71513 q^{89} +3.63661 q^{90} -10.6545 q^{91} -3.64436 q^{92} +1.99225 q^{93} +11.2187 q^{94} -20.2010 q^{95} +1.00000 q^{96} +11.9593 q^{97} -4.25958 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 9 q^{2} + 9 q^{3} + 9 q^{4} + 8 q^{5} + 9 q^{6} + 9 q^{7} + 9 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q + 9 * q^2 + 9 * q^3 + 9 * q^4 + 8 * q^5 + 9 * q^6 + 9 * q^7 + 9 * q^8 + 9 * q^9	\( 9 q + 9 q^{2} + 9 q^{3} + 9 q^{4} + 8 q^{5} + 9 q^{6} + 9 q^{7} + 9 q^{8} + 9 q^{9} + 8 q^{10} + 9 q^{11} + 9 q^{12} + 8 q^{13} + 9 q^{14} + 8 q^{15} + 9 q^{16} + q^{17} + 9 q^{18} + 5 q^{19} + 8 q^{20} + 9 q^{21} + 9 q^{22} - q^{23} + 9 q^{24} + 23 q^{25} + 8 q^{26} + 9 q^{27} + 9 q^{28} - 14 q^{29} + 8 q^{30} + 25 q^{31} + 9 q^{32} + 9 q^{33} + q^{34} + 5 q^{35} + 9 q^{36} + 16 q^{37} + 5 q^{38} + 8 q^{39} + 8 q^{40} + 5 q^{41} + 9 q^{42} + 5 q^{43} + 9 q^{44} + 8 q^{45} - q^{46} + 8 q^{47} + 9 q^{48} + 30 q^{49} + 23 q^{50} + q^{51} + 8 q^{52} + q^{53} + 9 q^{54} + 8 q^{55} + 9 q^{56} + 5 q^{57} - 14 q^{58} + 4 q^{59} + 8 q^{60} - 9 q^{61} + 25 q^{62} + 9 q^{63} + 9 q^{64} - 14 q^{65} + 9 q^{66} - 4 q^{67} + q^{68} - q^{69} + 5 q^{70} + 20 q^{71} + 9 q^{72} + 15 q^{73} + 16 q^{74} + 23 q^{75} + 5 q^{76} + 9 q^{77} + 8 q^{78} - 2 q^{79} + 8 q^{80} + 9 q^{81} + 5 q^{82} + 21 q^{83} + 9 q^{84} - 16 q^{85} + 5 q^{86} - 14 q^{87} + 9 q^{88} + 10 q^{89} + 8 q^{90} - 19 q^{91} - q^{92} + 25 q^{93} + 8 q^{94} - 7 q^{95} + 9 q^{96} + 3 q^{97} + 30 q^{98} + 9 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 9 * q^3 + 9 * q^4 + 8 * q^5 + 9 * q^6 + 9 * q^7 + 9 * q^8 + 9 * q^9 + 8 * q^10 + 9 * q^11 + 9 * q^12 + 8 * q^13 + 9 * q^14 + 8 * q^15 + 9 * q^16 + q^17 + 9 * q^18 + 5 * q^19 + 8 * q^20 + 9 * q^21 + 9 * q^22 - q^23 + 9 * q^24 + 23 * q^25 + 8 * q^26 + 9 * q^27 + 9 * q^28 - 14 * q^29 + 8 * q^30 + 25 * q^31 + 9 * q^32 + 9 * q^33 + q^34 + 5 * q^35 + 9 * q^36 + 16 * q^37 + 5 * q^38 + 8 * q^39 + 8 * q^40 + 5 * q^41 + 9 * q^42 + 5 * q^43 + 9 * q^44 + 8 * q^45 - q^46 + 8 * q^47 + 9 * q^48 + 30 * q^49 + 23 * q^50 + q^51 + 8 * q^52 + q^53 + 9 * q^54 + 8 * q^55 + 9 * q^56 + 5 * q^57 - 14 * q^58 + 4 * q^59 + 8 * q^60 - 9 * q^61 + 25 * q^62 + 9 * q^63 + 9 * q^64 - 14 * q^65 + 9 * q^66 - 4 * q^67 + q^68 - q^69 + 5 * q^70 + 20 * q^71 + 9 * q^72 + 15 * q^73 + 16 * q^74 + 23 * q^75 + 5 * q^76 + 9 * q^77 + 8 * q^78 - 2 * q^79 + 8 * q^80 + 9 * q^81 + 5 * q^82 + 21 * q^83 + 9 * q^84 - 16 * q^85 + 5 * q^86 - 14 * q^87 + 9 * q^88 + 10 * q^89 + 8 * q^90 - 19 * q^91 - q^92 + 25 * q^93 + 8 * q^94 - 7 * q^95 + 9 * q^96 + 3 * q^97 + 30 * q^98 + 9 * 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
$5$	3.63661	1.62634	0.813171	−	0.582026i	$-0.197740\pi$
$5$	3.63661	1.62634	0.813171	+	0.582026i	$0.197740\pi$
$6$	1.00000	0.408248
$7$	−1.65542	−0.625690	−0.312845	−	0.949804i	$-0.601282\pi$
$7$	−1.65542	−0.625690	−0.312845	+	0.949804i	$0.601282\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	3.63661	1.15000
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.00000	0.288675
$13$	6.43612	1.78506	0.892529	−	0.450991i	$-0.148929\pi$
$13$	6.43612	1.78506	0.892529	+	0.450991i	$0.148929\pi$
$14$	−1.65542	−0.442430
$15$	3.63661	0.938968
$16$	1.00000	0.250000
$17$	−1.11715	−0.270950	−0.135475	−	0.990781i	$-0.543256\pi$
$17$	−1.11715	−0.270950	−0.135475	+	0.990781i	$0.543256\pi$
$18$	1.00000	0.235702
$19$	−5.55489	−1.27438	−0.637190	−	0.770707i	$-0.719903\pi$
$19$	−5.55489	−1.27438	−0.637190	+	0.770707i	$0.719903\pi$
$20$	3.63661	0.813171
$21$	−1.65542	−0.361243
$22$	1.00000	0.213201
$23$	−3.64436	−0.759901	−0.379951	−	0.925007i	$-0.624059\pi$
$23$	−3.64436	−0.759901	−0.379951	+	0.925007i	$0.624059\pi$
$24$	1.00000	0.204124
$25$	8.22493	1.64499
$26$	6.43612	1.26223
$27$	1.00000	0.192450
$28$	−1.65542	−0.312845
$29$	−1.74243	−0.323561	−0.161780	−	0.986827i	$-0.551724\pi$
$29$	−1.74243	−0.323561	−0.161780	+	0.986827i	$0.551724\pi$
$30$	3.63661	0.663951
$31$	1.99225	0.357819	0.178909	−	0.983866i	$-0.442743\pi$
$31$	1.99225	0.357819	0.178909	+	0.983866i	$0.442743\pi$
$32$	1.00000	0.176777
$33$	1.00000	0.174078
$34$	−1.11715	−0.191590
$35$	−6.02012	−1.01759
$36$	1.00000	0.166667
$37$	10.6804	1.75585	0.877924	−	0.478801i	$-0.158928\pi$
$37$	10.6804	1.75585	0.877924	+	0.478801i	$0.158928\pi$
$38$	−5.55489	−0.901122
$39$	6.43612	1.03060
$40$	3.63661	0.574998
$41$	−3.65909	−0.571454	−0.285727	−	0.958311i	$-0.592235\pi$
$41$	−3.65909	−0.571454	−0.285727	+	0.958311i	$0.592235\pi$
$42$	−1.65542	−0.255437
$43$	6.64405	1.01321	0.506604	−	0.862179i	$-0.330901\pi$
$43$	6.64405	1.01321	0.506604	+	0.862179i	$0.330901\pi$
$44$	1.00000	0.150756
$45$	3.63661	0.542114
$46$	−3.64436	−0.537331
$47$	11.2187	1.63641	0.818205	−	0.574926i	$-0.194969\pi$
$47$	11.2187	1.63641	0.818205	+	0.574926i	$0.194969\pi$
$48$	1.00000	0.144338
$49$	−4.25958	−0.608511
$50$	8.22493	1.16318
$51$	−1.11715	−0.156433
$52$	6.43612	0.892529
$53$	−7.64051	−1.04951	−0.524753	−	0.851255i	$-0.675842\pi$
$53$	−7.64051	−1.04951	−0.524753	+	0.851255i	$0.675842\pi$
$54$	1.00000	0.136083
$55$	3.63661	0.490360
$56$	−1.65542	−0.221215
$57$	−5.55489	−0.735763
$58$	−1.74243	−0.228792
$59$	−0.0748538	−0.00974514	−0.00487257	−	0.999988i	$-0.501551\pi$
$59$	−0.0748538	−0.00974514	−0.00487257	+	0.999988i	$0.501551\pi$
$60$	3.63661	0.469484
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	1.99225	0.253016
$63$	−1.65542	−0.208563
$64$	1.00000	0.125000
$65$	23.4056	2.90311
$66$	1.00000	0.123091
$67$	−13.9718	−1.70693	−0.853465	−	0.521150i	$-0.825503\pi$
$67$	−13.9718	−1.70693	−0.853465	+	0.521150i	$0.825503\pi$
$68$	−1.11715	−0.135475
$69$	−3.64436	−0.438729
$70$	−6.02012	−0.719542
$71$	−5.87217	−0.696899	−0.348449	−	0.937328i	$-0.613292\pi$
$71$	−5.87217	−0.696899	−0.348449	+	0.937328i	$0.613292\pi$
$72$	1.00000	0.117851
$73$	−7.77814	−0.910362	−0.455181	−	0.890399i	$-0.650425\pi$
$73$	−7.77814	−0.910362	−0.455181	+	0.890399i	$0.650425\pi$
$74$	10.6804	1.24157
$75$	8.22493	0.949733
$76$	−5.55489	−0.637190
$77$	−1.65542	−0.188653
$78$	6.43612	0.728747
$79$	1.55257	0.174677	0.0873387	−	0.996179i	$-0.472164\pi$
$79$	1.55257	0.174677	0.0873387	+	0.996179i	$0.472164\pi$
$80$	3.63661	0.406585
$81$	1.00000	0.111111
$82$	−3.65909	−0.404079
$83$	15.0909	1.65644	0.828222	−	0.560399i	$-0.189352\pi$
$83$	15.0909	1.65644	0.828222	+	0.560399i	$0.189352\pi$
$84$	−1.65542	−0.180621
$85$	−4.06265	−0.440657
$86$	6.64405	0.716446
$87$	−1.74243	−0.186808
$88$	1.00000	0.106600
$89$	−3.71513	−0.393803	−0.196902	−	0.980423i	$-0.563088\pi$
$89$	−3.71513	−0.393803	−0.196902	+	0.980423i	$0.563088\pi$
$90$	3.63661	0.383332
$91$	−10.6545	−1.11689
$92$	−3.64436	−0.379951
$93$	1.99225	0.206587
$94$	11.2187	1.15712
$95$	−20.2010	−2.07258
$96$	1.00000	0.102062
$97$	11.9593	1.21428	0.607141	−	0.794594i	$-0.292316\pi$
$97$	11.9593	1.21428	0.607141	+	0.794594i	$0.292316\pi$
$98$	−4.25958	−0.430283
$99$	1.00000	0.100504
$100$	8.22493	0.822493
$101$	1.24249	0.123632	0.0618161	−	0.998088i	$-0.480311\pi$
$101$	1.24249	0.123632	0.0618161	+	0.998088i	$0.480311\pi$
$102$	−1.11715	−0.110615
$103$	−19.1188	−1.88384	−0.941918	−	0.335844i	$-0.890978\pi$
$103$	−19.1188	−1.88384	−0.941918	+	0.335844i	$0.890978\pi$
$104$	6.43612	0.631113
$105$	−6.02012	−0.587504
$106$	−7.64051	−0.742112
$107$	−6.86786	−0.663941	−0.331971	−	0.943290i	$-0.607713\pi$
$107$	−6.86786	−0.663941	−0.331971	+	0.943290i	$0.607713\pi$
$108$	1.00000	0.0962250
$109$	2.33976	0.224108	0.112054	−	0.993702i	$-0.464257\pi$
$109$	2.33976	0.224108	0.112054	+	0.993702i	$0.464257\pi$
$110$	3.63661	0.346737
$111$	10.6804	1.01374
$112$	−1.65542	−0.156423
$113$	13.9624	1.31347	0.656736	−	0.754120i	$-0.271937\pi$
$113$	13.9624	1.31347	0.656736	+	0.754120i	$0.271937\pi$
$114$	−5.55489	−0.520263
$115$	−13.2531	−1.23586
$116$	−1.74243	−0.161780
$117$	6.43612	0.595019
$118$	−0.0748538	−0.00689085
$119$	1.84936	0.169531
$120$	3.63661	0.331975
$121$	1.00000	0.0909091
$122$	−1.00000	−0.0905357
$123$	−3.65909	−0.329929
$124$	1.99225	0.178909
$125$	11.7278	1.04897
$126$	−1.65542	−0.147477
$127$	−9.26320	−0.821976	−0.410988	−	0.911641i	$-0.634816\pi$
$127$	−9.26320	−0.821976	−0.410988	+	0.911641i	$0.634816\pi$
$128$	1.00000	0.0883883
$129$	6.64405	0.584976
$130$	23.4056	2.05281
$131$	−11.9435	−1.04351	−0.521756	−	0.853095i	$-0.674723\pi$
$131$	−11.9435	−1.04351	−0.521756	+	0.853095i	$0.674723\pi$
$132$	1.00000	0.0870388
$133$	9.19568	0.797367
$134$	−13.9718	−1.20698
$135$	3.63661	0.312989
$136$	−1.11715	−0.0957952
$137$	19.9918	1.70802	0.854008	−	0.520260i	$-0.174165\pi$
$137$	19.9918	1.70802	0.854008	+	0.520260i	$0.174165\pi$
$138$	−3.64436	−0.310228
$139$	−2.90764	−0.246623	−0.123311	−	0.992368i	$-0.539351\pi$
$139$	−2.90764	−0.246623	−0.123311	+	0.992368i	$0.539351\pi$
$140$	−6.02012	−0.508793
$141$	11.2187	0.944782
$142$	−5.87217	−0.492782
$143$	6.43612	0.538215
$144$	1.00000	0.0833333
$145$	−6.33653	−0.526220
$146$	−7.77814	−0.643723
$147$	−4.25958	−0.351324
$148$	10.6804	0.877924
$149$	−15.0404	−1.23215	−0.616077	−	0.787686i	$-0.711279\pi$
$149$	−15.0404	−1.23215	−0.616077	+	0.787686i	$0.711279\pi$
$150$	8.22493	0.671562
$151$	−14.3901	−1.17105	−0.585526	−	0.810654i	$-0.699112\pi$
$151$	−14.3901	−1.17105	−0.585526	+	0.810654i	$0.699112\pi$
$152$	−5.55489	−0.450561
$153$	−1.11715	−0.0903166
$154$	−1.65542	−0.133398
$155$	7.24504	0.581935
$156$	6.43612	0.515302
$157$	−1.62798	−0.129927	−0.0649635	−	0.997888i	$-0.520693\pi$
$157$	−1.62798	−0.129927	−0.0649635	+	0.997888i	$0.520693\pi$
$158$	1.55257	0.123516
$159$	−7.64051	−0.605932
$160$	3.63661	0.287499
$161$	6.03295	0.475463
$162$	1.00000	0.0785674
$163$	20.7016	1.62147	0.810737	−	0.585410i	$-0.199066\pi$
$163$	20.7016	1.62147	0.810737	+	0.585410i	$0.199066\pi$
$164$	−3.65909	−0.285727
$165$	3.63661	0.283110
$166$	15.0909	1.17128
$167$	1.30094	0.100670	0.0503349	−	0.998732i	$-0.483971\pi$
$167$	1.30094	0.100670	0.0503349	+	0.998732i	$0.483971\pi$
$168$	−1.65542	−0.127719
$169$	28.4236	2.18643
$170$	−4.06265	−0.311591
$171$	−5.55489	−0.424793
$172$	6.64405	0.506604
$173$	−24.3719	−1.85296	−0.926482	−	0.376340i	$-0.877182\pi$
$173$	−24.3719	−1.85296	−0.926482	+	0.376340i	$0.877182\pi$
$174$	−1.74243	−0.132093
$175$	−13.6157	−1.02925
$176$	1.00000	0.0753778
$177$	−0.0748538	−0.00562636
$178$	−3.71513	−0.278461
$179$	9.74345	0.728260	0.364130	−	0.931348i	$-0.381366\pi$
$179$	9.74345	0.728260	0.364130	+	0.931348i	$0.381366\pi$
$180$	3.63661	0.271057
$181$	11.1669	0.830030	0.415015	−	0.909815i	$-0.363776\pi$
$181$	11.1669	0.830030	0.415015	+	0.909815i	$0.363776\pi$
$182$	−10.6545	−0.789763
$183$	−1.00000	−0.0739221
$184$	−3.64436	−0.268666
$185$	38.8404	2.85561
$186$	1.99225	0.146079
$187$	−1.11715	−0.0816944
$188$	11.2187	0.818205
$189$	−1.65542	−0.120414
$190$	−20.2010	−1.46553
$191$	−24.2346	−1.75356	−0.876779	−	0.480894i	$-0.840312\pi$
$191$	−24.2346	−1.75356	−0.876779	+	0.480894i	$0.840312\pi$
$192$	1.00000	0.0721688
$193$	3.02708	0.217894	0.108947	−	0.994048i	$-0.465252\pi$
$193$	3.02708	0.217894	0.108947	+	0.994048i	$0.465252\pi$
$194$	11.9593	0.858628
$195$	23.4056	1.67611
$196$	−4.25958	−0.304256
$197$	−13.1681	−0.938191	−0.469096	−	0.883147i	$-0.655420\pi$
$197$	−13.1681	−0.938191	−0.469096	+	0.883147i	$0.655420\pi$
$198$	1.00000	0.0710669
$199$	−22.3693	−1.58572	−0.792860	−	0.609404i	$-0.791409\pi$
$199$	−22.3693	−1.58572	−0.792860	+	0.609404i	$0.791409\pi$
$200$	8.22493	0.581590
$201$	−13.9718	−0.985497
$202$	1.24249	0.0874211
$203$	2.88445	0.202449
$204$	−1.11715	−0.0782165
$205$	−13.3067	−0.929379
$206$	−19.1188	−1.33207
$207$	−3.64436	−0.253300
$208$	6.43612	0.446264
$209$	−5.55489	−0.384240
$210$	−6.02012	−0.415428
$211$	−3.82917	−0.263611	−0.131806	−	0.991276i	$-0.542077\pi$
$211$	−3.82917	−0.263611	−0.131806	+	0.991276i	$0.542077\pi$
$212$	−7.64051	−0.524753
$213$	−5.87217	−0.402355
$214$	−6.86786	−0.469477
$215$	24.1618	1.64782
$216$	1.00000	0.0680414
$217$	−3.29801	−0.223884
$218$	2.33976	0.158468
$219$	−7.77814	−0.525598
$220$	3.63661	0.245180
$221$	−7.19014	−0.483661
$222$	10.6804	0.716822
$223$	11.0856	0.742346	0.371173	−	0.928564i	$-0.378956\pi$
$223$	11.0856	0.742346	0.371173	+	0.928564i	$0.378956\pi$
$224$	−1.65542	−0.110607
$225$	8.22493	0.548328
$226$	13.9624	0.928765
$227$	15.8836	1.05423	0.527116	−	0.849794i	$-0.323273\pi$
$227$	15.8836	1.05423	0.527116	+	0.849794i	$0.323273\pi$
$228$	−5.55489	−0.367882
$229$	15.1029	0.998028	0.499014	−	0.866594i	$-0.333696\pi$
$229$	15.1029	0.998028	0.499014	+	0.866594i	$0.333696\pi$
$230$	−13.2531	−0.873884
$231$	−1.65542	−0.108919
$232$	−1.74243	−0.114396
$233$	8.29255	0.543263	0.271631	−	0.962401i	$-0.412437\pi$
$233$	8.29255	0.543263	0.271631	+	0.962401i	$0.412437\pi$
$234$	6.43612	0.420742
$235$	40.7979	2.66136
$236$	−0.0748538	−0.00487257
$237$	1.55257	0.100850
$238$	1.84936	0.119876
$239$	19.3939	1.25449	0.627245	−	0.778822i	$-0.284182\pi$
$239$	19.3939	1.25449	0.627245	+	0.778822i	$0.284182\pi$
$240$	3.63661	0.234742
$241$	−1.41796	−0.0913387	−0.0456694	−	0.998957i	$-0.514542\pi$
$241$	−1.41796	−0.0913387	−0.0456694	+	0.998957i	$0.514542\pi$
$242$	1.00000	0.0642824
$243$	1.00000	0.0641500
$244$	−1.00000	−0.0640184
$245$	−15.4904	−0.989647
$246$	−3.65909	−0.233295
$247$	−35.7519	−2.27484
$248$	1.99225	0.126508
$249$	15.0909	0.956349
$250$	11.7278	0.741731
$251$	7.12400	0.449663	0.224831	−	0.974398i	$-0.427817\pi$
$251$	7.12400	0.449663	0.224831	+	0.974398i	$0.427817\pi$
$252$	−1.65542	−0.104282
$253$	−3.64436	−0.229119
$254$	−9.26320	−0.581225
$255$	−4.06265	−0.254413
$256$	1.00000	0.0625000
$257$	−11.5558	−0.720829	−0.360415	−	0.932792i	$-0.617365\pi$
$257$	−11.5558	−0.720829	−0.360415	+	0.932792i	$0.617365\pi$
$258$	6.64405	0.413640
$259$	−17.6806	−1.09862
$260$	23.4056	1.45156
$261$	−1.74243	−0.107854
$262$	−11.9435	−0.737875
$263$	−0.693770	−0.0427797	−0.0213898	−	0.999771i	$-0.506809\pi$
$263$	−0.693770	−0.0427797	−0.0213898	+	0.999771i	$0.506809\pi$
$264$	1.00000	0.0615457
$265$	−27.7856	−1.70685
$266$	9.19568	0.563824
$267$	−3.71513	−0.227362
$268$	−13.9718	−0.853465
$269$	8.18407	0.498992	0.249496	−	0.968376i	$-0.419735\pi$
$269$	8.18407	0.498992	0.249496	+	0.968376i	$0.419735\pi$
$270$	3.63661	0.221317
$271$	4.99753	0.303578	0.151789	−	0.988413i	$-0.451497\pi$
$271$	4.99753	0.303578	0.151789	+	0.988413i	$0.451497\pi$
$272$	−1.11715	−0.0677374
$273$	−10.6545	−0.644839
$274$	19.9918	1.20775
$275$	8.22493	0.495982
$276$	−3.64436	−0.219365
$277$	−2.65986	−0.159815	−0.0799077	−	0.996802i	$-0.525463\pi$
$277$	−2.65986	−0.159815	−0.0799077	+	0.996802i	$0.525463\pi$
$278$	−2.90764	−0.174389
$279$	1.99225	0.119273
$280$	−6.02012	−0.359771
$281$	−22.2999	−1.33030	−0.665152	−	0.746708i	$-0.731633\pi$
$281$	−22.2999	−1.33030	−0.665152	+	0.746708i	$0.731633\pi$
$282$	11.2187	0.668062
$283$	−22.3131	−1.32638	−0.663189	−	0.748452i	$-0.730797\pi$
$283$	−22.3131	−1.32638	−0.663189	+	0.748452i	$0.730797\pi$
$284$	−5.87217	−0.348449
$285$	−20.2010	−1.19660
$286$	6.43612	0.380575
$287$	6.05734	0.357553
$288$	1.00000	0.0589256
$289$	−15.7520	−0.926586
$290$	−6.33653	−0.372094
$291$	11.9593	0.701066
$292$	−7.77814	−0.455181
$293$	22.0617	1.28886	0.644429	−	0.764664i	$-0.277095\pi$
$293$	22.0617	1.28886	0.644429	+	0.764664i	$0.277095\pi$
$294$	−4.25958	−0.248424
$295$	−0.272214	−0.0158489
$296$	10.6804	0.620786
$297$	1.00000	0.0580259
$298$	−15.0404	−0.871265
$299$	−23.4555	−1.35647
$300$	8.22493	0.474866
$301$	−10.9987	−0.633954
$302$	−14.3901	−0.828058
$303$	1.24249	0.0713790
$304$	−5.55489	−0.318595
$305$	−3.63661	−0.208232
$306$	−1.11715	−0.0638635
$307$	−25.4026	−1.44980	−0.724902	−	0.688852i	$-0.758115\pi$
$307$	−25.4026	−1.44980	−0.724902	+	0.688852i	$0.758115\pi$
$308$	−1.65542	−0.0943264
$309$	−19.1188	−1.08763
$310$	7.24504	0.411490
$311$	−4.07486	−0.231064	−0.115532	−	0.993304i	$-0.536857\pi$
$311$	−4.07486	−0.231064	−0.115532	+	0.993304i	$0.536857\pi$
$312$	6.43612	0.364373
$313$	9.02954	0.510380	0.255190	−	0.966891i	$-0.417862\pi$
$313$	9.02954	0.510380	0.255190	+	0.966891i	$0.417862\pi$
$314$	−1.62798	−0.0918723
$315$	−6.02012	−0.339195
$316$	1.55257	0.0873387
$317$	16.4782	0.925509	0.462755	−	0.886486i	$-0.346861\pi$
$317$	16.4782	0.925509	0.462755	+	0.886486i	$0.346861\pi$
$318$	−7.64051	−0.428459
$319$	−1.74243	−0.0975573
$320$	3.63661	0.203293
$321$	−6.86786	−0.383327
$322$	6.03295	0.336203
$323$	6.20567	0.345293
$324$	1.00000	0.0555556
$325$	52.9366	2.93639
$326$	20.7016	1.14656
$327$	2.33976	0.129389
$328$	−3.65909	−0.202039
$329$	−18.5716	−1.02389
$330$	3.63661	0.200189
$331$	−28.0374	−1.54108	−0.770538	−	0.637394i	$-0.780012\pi$
$331$	−28.0374	−1.54108	−0.770538	+	0.637394i	$0.780012\pi$
$332$	15.0909	0.828222
$333$	10.6804	0.585282
$334$	1.30094	0.0711842
$335$	−50.8101	−2.77605
$336$	−1.65542	−0.0903106
$337$	1.51410	0.0824785	0.0412392	−	0.999149i	$-0.486869\pi$
$337$	1.51410	0.0824785	0.0412392	+	0.999149i	$0.486869\pi$
$338$	28.4236	1.54604
$339$	13.9624	0.758334
$340$	−4.06265	−0.220328
$341$	1.99225	0.107886
$342$	−5.55489	−0.300374
$343$	18.6393	1.00643
$344$	6.64405	0.358223
$345$	−13.2531	−0.713523
$346$	−24.3719	−1.31024
$347$	−35.7721	−1.92034	−0.960172	−	0.279409i	$-0.909861\pi$
$347$	−35.7721	−1.92034	−0.960172	+	0.279409i	$0.909861\pi$
$348$	−1.74243	−0.0934040
$349$	−20.5072	−1.09773	−0.548863	−	0.835912i	$-0.684939\pi$
$349$	−20.5072	−1.09773	−0.548863	+	0.835912i	$0.684939\pi$
$350$	−13.6157	−0.727791
$351$	6.43612	0.343534
$352$	1.00000	0.0533002
$353$	−9.01885	−0.480025	−0.240012	−	0.970770i	$-0.577152\pi$
$353$	−9.01885	−0.480025	−0.240012	+	0.970770i	$0.577152\pi$
$354$	−0.0748538	−0.00397844
$355$	−21.3548	−1.13339
$356$	−3.71513	−0.196902
$357$	1.84936	0.0978786
$358$	9.74345	0.514958
$359$	−35.2663	−1.86128	−0.930642	−	0.365930i	$-0.880751\pi$
$359$	−35.2663	−1.86128	−0.930642	+	0.365930i	$0.880751\pi$
$360$	3.63661	0.191666
$361$	11.8568	0.624042
$362$	11.1669	0.586920
$363$	1.00000	0.0524864
$364$	−10.6545	−0.558447
$365$	−28.2860	−1.48056
$366$	−1.00000	−0.0522708
$367$	13.8581	0.723387	0.361693	−	0.932297i	$-0.382199\pi$
$367$	13.8581	0.723387	0.361693	+	0.932297i	$0.382199\pi$
$368$	−3.64436	−0.189975
$369$	−3.65909	−0.190485
$370$	38.8404	2.01922
$371$	12.6483	0.656665
$372$	1.99225	0.103293
$373$	28.1145	1.45571	0.727856	−	0.685730i	$-0.240517\pi$
$373$	28.1145	1.45571	0.727856	+	0.685730i	$0.240517\pi$
$374$	−1.11715	−0.0577667
$375$	11.7278	0.605621
$376$	11.2187	0.578559
$377$	−11.2145	−0.577575
$378$	−1.65542	−0.0851457
$379$	31.8925	1.63821	0.819104	−	0.573645i	$-0.194471\pi$
$379$	31.8925	1.63821	0.819104	+	0.573645i	$0.194471\pi$
$380$	−20.2010	−1.03629
$381$	−9.26320	−0.474568
$382$	−24.2346	−1.23995
$383$	13.1481	0.671836	0.335918	−	0.941891i	$-0.390954\pi$
$383$	13.1481	0.671836	0.335918	+	0.941891i	$0.390954\pi$
$384$	1.00000	0.0510310
$385$	−6.02012	−0.306814
$386$	3.02708	0.154074
$387$	6.64405	0.337736
$388$	11.9593	0.607141
$389$	−20.7562	−1.05238	−0.526190	−	0.850367i	$-0.676380\pi$
$389$	−20.7562	−1.05238	−0.526190	+	0.850367i	$0.676380\pi$
$390$	23.4056	1.18519
$391$	4.07131	0.205895
$392$	−4.25958	−0.215141
$393$	−11.9435	−0.602472
$394$	−13.1681	−0.663401
$395$	5.64608	0.284085
$396$	1.00000	0.0502519
$397$	−7.09454	−0.356065	−0.178032	−	0.984025i	$-0.556973\pi$
$397$	−7.09454	−0.356065	−0.178032	+	0.984025i	$0.556973\pi$
$398$	−22.3693	−1.12127
$399$	9.19568	0.460360
$400$	8.22493	0.411246
$401$	−10.1912	−0.508923	−0.254462	−	0.967083i	$-0.581898\pi$
$401$	−10.1912	−0.508923	−0.254462	+	0.967083i	$0.581898\pi$
$402$	−13.9718	−0.696851
$403$	12.8224	0.638727
$404$	1.24249	0.0618161
$405$	3.63661	0.180705
$406$	2.88445	0.143153
$407$	10.6804	0.529408
$408$	−1.11715	−0.0553074
$409$	31.7800	1.57142	0.785710	−	0.618595i	$-0.212298\pi$
$409$	31.7800	1.57142	0.785710	+	0.618595i	$0.212298\pi$
$410$	−13.3067	−0.657170
$411$	19.9918	0.986123
$412$	−19.1188	−0.941918
$413$	0.123915	0.00609744
$414$	−3.64436	−0.179110
$415$	54.8798	2.69394
$416$	6.43612	0.315557
$417$	−2.90764	−0.142388
$418$	−5.55489	−0.271699
$419$	0.276412	0.0135036	0.00675180	−	0.999977i	$-0.497851\pi$
$419$	0.276412	0.0135036	0.00675180	+	0.999977i	$0.497851\pi$
$420$	−6.02012	−0.293752
$421$	15.1425	0.738002	0.369001	−	0.929429i	$-0.379700\pi$
$421$	15.1425	0.738002	0.369001	+	0.929429i	$0.379700\pi$
$422$	−3.82917	−0.186401
$423$	11.2187	0.545470
$424$	−7.64051	−0.371056
$425$	−9.18851	−0.445708
$426$	−5.87217	−0.284508
$427$	1.65542	0.0801115
$428$	−6.86786	−0.331971
$429$	6.43612	0.310739
$430$	24.1618	1.16519
$431$	−15.3738	−0.740532	−0.370266	−	0.928926i	$-0.620733\pi$
$431$	−15.3738	−0.740532	−0.370266	+	0.928926i	$0.620733\pi$
$432$	1.00000	0.0481125
$433$	36.5498	1.75647	0.878235	−	0.478229i	$-0.158721\pi$
$433$	36.5498	1.75647	0.878235	+	0.478229i	$0.158721\pi$
$434$	−3.29801	−0.158310
$435$	−6.33653	−0.303813
$436$	2.33976	0.112054
$437$	20.2440	0.968402
$438$	−7.77814	−0.371654
$439$	−26.9431	−1.28592	−0.642962	−	0.765898i	$-0.722295\pi$
$439$	−26.9431	−1.28592	−0.642962	+	0.765898i	$0.722295\pi$
$440$	3.63661	0.173369
$441$	−4.25958	−0.202837
$442$	−7.19014	−0.342000
$443$	29.1747	1.38613	0.693065	−	0.720875i	$-0.256260\pi$
$443$	29.1747	1.38613	0.693065	+	0.720875i	$0.256260\pi$
$444$	10.6804	0.506869
$445$	−13.5105	−0.640458
$446$	11.0856	0.524918
$447$	−15.0404	−0.711385
$448$	−1.65542	−0.0782113
$449$	−9.37976	−0.442658	−0.221329	−	0.975199i	$-0.571040\pi$
$449$	−9.37976	−0.442658	−0.221329	+	0.975199i	$0.571040\pi$
$450$	8.22493	0.387727
$451$	−3.65909	−0.172300
$452$	13.9624	0.656736
$453$	−14.3901	−0.676107
$454$	15.8836	0.745454
$455$	−38.7462	−1.81645
$456$	−5.55489	−0.260132
$457$	−14.1878	−0.663679	−0.331839	−	0.943336i	$-0.607669\pi$
$457$	−14.1878	−0.663679	−0.331839	+	0.943336i	$0.607669\pi$
$458$	15.1029	0.705713
$459$	−1.11715	−0.0521443
$460$	−13.2531	−0.617929
$461$	11.8385	0.551376	0.275688	−	0.961247i	$-0.411094\pi$
$461$	11.8385	0.551376	0.275688	+	0.961247i	$0.411094\pi$
$462$	−1.65542	−0.0770172
$463$	40.2318	1.86973	0.934865	−	0.355004i	$-0.115520\pi$
$463$	40.2318	1.86973	0.934865	+	0.355004i	$0.115520\pi$
$464$	−1.74243	−0.0808902
$465$	7.24504	0.335981
$466$	8.29255	0.384145
$467$	−24.7775	−1.14657	−0.573284	−	0.819357i	$-0.694331\pi$
$467$	−24.7775	−1.14657	−0.573284	+	0.819357i	$0.694331\pi$
$468$	6.43612	0.297510
$469$	23.1293	1.06801
$470$	40.7979	1.88187
$471$	−1.62798	−0.0750134
$472$	−0.0748538	−0.00344543
$473$	6.64405	0.305494
$474$	1.55257	0.0713118
$475$	−45.6886	−2.09633
$476$	1.84936	0.0847654
$477$	−7.64051	−0.349835
$478$	19.3939	0.887058
$479$	18.1197	0.827909	0.413955	−	0.910297i	$-0.364147\pi$
$479$	18.1197	0.827909	0.413955	+	0.910297i	$0.364147\pi$
$480$	3.63661	0.165988
$481$	68.7403	3.13429
$482$	−1.41796	−0.0645862
$483$	6.03295	0.274509
$484$	1.00000	0.0454545
$485$	43.4913	1.97484
$486$	1.00000	0.0453609
$487$	−25.4064	−1.15127	−0.575636	−	0.817706i	$-0.695246\pi$
$487$	−25.4064	−1.15127	−0.575636	+	0.817706i	$0.695246\pi$
$488$	−1.00000	−0.0452679
$489$	20.7016	0.936159
$490$	−15.4904	−0.699786
$491$	18.8016	0.848503	0.424251	−	0.905544i	$-0.360537\pi$
$491$	18.8016	0.848503	0.424251	+	0.905544i	$0.360537\pi$
$492$	−3.65909	−0.164965
$493$	1.94656	0.0876688
$494$	−35.7519	−1.60855
$495$	3.63661	0.163453
$496$	1.99225	0.0894547
$497$	9.72092	0.436043
$498$	15.0909	0.676241
$499$	20.5895	0.921711	0.460856	−	0.887475i	$-0.347543\pi$
$499$	20.5895	0.921711	0.460856	+	0.887475i	$0.347543\pi$
$500$	11.7278	0.524483
$501$	1.30094	0.0581217
$502$	7.12400	0.317959
$503$	−32.5168	−1.44985	−0.724927	−	0.688825i	$-0.758127\pi$
$503$	−32.5168	−1.44985	−0.724927	+	0.688825i	$0.758127\pi$
$504$	−1.65542	−0.0737383
$505$	4.51844	0.201068
$506$	−3.64436	−0.162011
$507$	28.4236	1.26234
$508$	−9.26320	−0.410988
$509$	35.6052	1.57817	0.789086	−	0.614283i	$-0.210555\pi$
$509$	35.6052	1.57817	0.789086	+	0.614283i	$0.210555\pi$
$510$	−4.06265	−0.179897
$511$	12.8761	0.569605
$512$	1.00000	0.0441942
$513$	−5.55489	−0.245254
$514$	−11.5558	−0.509703
$515$	−69.5277	−3.06376
$516$	6.64405	0.292488
$517$	11.2187	0.493396
$518$	−17.6806	−0.776839
$519$	−24.3719	−1.06981
$520$	23.4056	1.02641
$521$	−25.2607	−1.10669	−0.553345	−	0.832952i	$-0.686649\pi$
$521$	−25.2607	−1.10669	−0.553345	+	0.832952i	$0.686649\pi$
$522$	−1.74243	−0.0762640
$523$	−18.9119	−0.826961	−0.413480	−	0.910513i	$-0.635687\pi$
$523$	−18.9119	−0.826961	−0.413480	+	0.910513i	$0.635687\pi$
$524$	−11.9435	−0.521756
$525$	−13.6157	−0.594239
$526$	−0.693770	−0.0302498
$527$	−2.22565	−0.0969509
$528$	1.00000	0.0435194
$529$	−9.71865	−0.422550
$530$	−27.7856	−1.20693
$531$	−0.0748538	−0.00324838
$532$	9.19568	0.398683
$533$	−23.5503	−1.02008
$534$	−3.71513	−0.160769
$535$	−24.9757	−1.07979
$536$	−13.9718	−0.603491
$537$	9.74345	0.420461
$538$	8.18407	0.352840
$539$	−4.25958	−0.183473
$540$	3.63661	0.156495
$541$	−8.67386	−0.372918	−0.186459	−	0.982463i	$-0.559701\pi$
$541$	−8.67386	−0.372918	−0.186459	+	0.982463i	$0.559701\pi$
$542$	4.99753	0.214662
$543$	11.1669	0.479218
$544$	−1.11715	−0.0478976
$545$	8.50878	0.364476
$546$	−10.6545	−0.455970
$547$	32.4376	1.38693	0.693466	−	0.720489i	$-0.256083\pi$
$547$	32.4376	1.38693	0.693466	+	0.720489i	$0.256083\pi$
$548$	19.9918	0.854008
$549$	−1.00000	−0.0426790
$550$	8.22493	0.350712
$551$	9.67900	0.412339
$552$	−3.64436	−0.155114
$553$	−2.57015	−0.109294
$554$	−2.65986	−0.113007
$555$	38.8404	1.64869
$556$	−2.90764	−0.123311
$557$	28.9515	1.22672	0.613358	−	0.789805i	$-0.289818\pi$
$557$	28.9515	1.22672	0.613358	+	0.789805i	$0.289818\pi$
$558$	1.99225	0.0843387
$559$	42.7619	1.80863
$560$	−6.02012	−0.254397
$561$	−1.11715	−0.0471663
$562$	−22.2999	−0.940666
$563$	23.5430	0.992220	0.496110	−	0.868260i	$-0.334761\pi$
$563$	23.5430	0.992220	0.496110	+	0.868260i	$0.334761\pi$
$564$	11.2187	0.472391
$565$	50.7758	2.13615
$566$	−22.3131	−0.937891
$567$	−1.65542	−0.0695212
$568$	−5.87217	−0.246391
$569$	−21.4678	−0.899978	−0.449989	−	0.893034i	$-0.648572\pi$
$569$	−21.4678	−0.899978	−0.449989	+	0.893034i	$0.648572\pi$
$570$	−20.2010	−0.846125
$571$	16.5881	0.694192	0.347096	−	0.937830i	$-0.387168\pi$
$571$	16.5881	0.694192	0.347096	+	0.937830i	$0.387168\pi$
$572$	6.43612	0.269108
$573$	−24.2346	−1.01242
$574$	6.05734	0.252828
$575$	−29.9746	−1.25003
$576$	1.00000	0.0416667
$577$	−30.5258	−1.27081	−0.635404	−	0.772180i	$-0.719166\pi$
$577$	−30.5258	−1.27081	−0.635404	+	0.772180i	$0.719166\pi$
$578$	−15.7520	−0.655195
$579$	3.02708	0.125801
$580$	−6.33653	−0.263110
$581$	−24.9819	−1.03642
$582$	11.9593	0.495729
$583$	−7.64051	−0.316438
$584$	−7.77814	−0.321862
$585$	23.4056	0.967704
$586$	22.0617	0.911360
$587$	−22.4814	−0.927907	−0.463953	−	0.885860i	$-0.653570\pi$
$587$	−22.4814	−0.927907	−0.463953	+	0.885860i	$0.653570\pi$
$588$	−4.25958	−0.175662
$589$	−11.0667	−0.455997
$590$	−0.272214	−0.0112069
$591$	−13.1681	−0.541665
$592$	10.6804	0.438962
$593$	−22.6452	−0.929928	−0.464964	−	0.885329i	$-0.653933\pi$
$593$	−22.6452	−0.929928	−0.464964	+	0.885329i	$0.653933\pi$
$594$	1.00000	0.0410305
$595$	6.72541	0.275715
$596$	−15.0404	−0.616077
$597$	−22.3693	−0.915515
$598$	−23.4555	−0.959167
$599$	−32.8541	−1.34238	−0.671191	−	0.741284i	$-0.734217\pi$
$599$	−32.8541	−1.34238	−0.671191	+	0.741284i	$0.734217\pi$
$600$	8.22493	0.335781
$601$	−33.6150	−1.37118	−0.685592	−	0.727986i	$-0.740457\pi$
$601$	−33.6150	−1.37118	−0.685592	+	0.727986i	$0.740457\pi$
$602$	−10.9987	−0.448273
$603$	−13.9718	−0.568977
$604$	−14.3901	−0.585526
$605$	3.63661	0.147849
$606$	1.24249	0.0504726
$607$	17.9685	0.729318	0.364659	−	0.931141i	$-0.381186\pi$
$607$	17.9685	0.729318	0.364659	+	0.931141i	$0.381186\pi$
$608$	−5.55489	−0.225281
$609$	2.88445	0.116884
$610$	−3.63661	−0.147242
$611$	72.2046	2.92109
$612$	−1.11715	−0.0451583
$613$	−7.34476	−0.296652	−0.148326	−	0.988939i	$-0.547389\pi$
$613$	−7.34476	−0.296652	−0.148326	+	0.988939i	$0.547389\pi$
$614$	−25.4026	−1.02517
$615$	−13.3067	−0.536577
$616$	−1.65542	−0.0666988
$617$	−46.2309	−1.86119	−0.930593	−	0.366055i	$-0.880708\pi$
$617$	−46.2309	−1.86119	−0.930593	+	0.366055i	$0.880708\pi$
$618$	−19.1188	−0.769072
$619$	−19.5755	−0.786807	−0.393403	−	0.919366i	$-0.628702\pi$
$619$	−19.5755	−0.786807	−0.393403	+	0.919366i	$0.628702\pi$
$620$	7.24504	0.290968
$621$	−3.64436	−0.146243
$622$	−4.07486	−0.163387
$623$	6.15011	0.246399
$624$	6.43612	0.257651
$625$	1.52478	0.0609911
$626$	9.02954	0.360893
$627$	−5.55489	−0.221841
$628$	−1.62798	−0.0649635
$629$	−11.9317	−0.475746
$630$	−6.02012	−0.239847
$631$	33.1579	1.32000	0.659998	−	0.751267i	$-0.270557\pi$
$631$	33.1579	1.32000	0.659998	+	0.751267i	$0.270557\pi$
$632$	1.55257	0.0617578
$633$	−3.82917	−0.152196
$634$	16.4782	0.654434
$635$	−33.6867	−1.33681
$636$	−7.64051	−0.302966
$637$	−27.4151	−1.08623
$638$	−1.74243	−0.0689834
$639$	−5.87217	−0.232300
$640$	3.63661	0.143750
$641$	48.8512	1.92951	0.964754	−	0.263154i	$-0.0847627\pi$
$641$	48.8512	1.92951	0.964754	+	0.263154i	$0.0847627\pi$
$642$	−6.86786	−0.271053
$643$	5.83417	0.230077	0.115039	−	0.993361i	$-0.463301\pi$
$643$	5.83417	0.230077	0.115039	+	0.993361i	$0.463301\pi$
$644$	6.03295	0.237731
$645$	24.1618	0.951370
$646$	6.20567	0.244159
$647$	−15.7920	−0.620846	−0.310423	−	0.950599i	$-0.600471\pi$
$647$	−15.7920	−0.620846	−0.310423	+	0.950599i	$0.600471\pi$
$648$	1.00000	0.0392837
$649$	−0.0748538	−0.00293827
$650$	52.9366	2.07634
$651$	−3.29801	−0.129259
$652$	20.7016	0.810737
$653$	−21.1007	−0.825733	−0.412867	−	0.910791i	$-0.635472\pi$
$653$	−21.1007	−0.825733	−0.412867	+	0.910791i	$0.635472\pi$
$654$	2.33976	0.0914918
$655$	−43.4340	−1.69711
$656$	−3.65909	−0.142863
$657$	−7.77814	−0.303454
$658$	−18.5716	−0.723997
$659$	−34.4141	−1.34058	−0.670291	−	0.742098i	$-0.733831\pi$
$659$	−34.4141	−1.34058	−0.670291	+	0.742098i	$0.733831\pi$
$660$	3.63661	0.141555
$661$	−2.08847	−0.0812321	−0.0406161	−	0.999175i	$-0.512932\pi$
$661$	−2.08847	−0.0812321	−0.0406161	+	0.999175i	$0.512932\pi$
$662$	−28.0374	−1.08971
$663$	−7.19014	−0.279242
$664$	15.0909	0.585642
$665$	33.4411	1.29679
$666$	10.6804	0.413857
$667$	6.35004	0.245874
$668$	1.30094	0.0503349
$669$	11.0856	0.428594
$670$	−50.8101	−1.96296
$671$	−1.00000	−0.0386046
$672$	−1.65542	−0.0638593
$673$	39.0930	1.50693	0.753463	−	0.657491i	$-0.228382\pi$
$673$	39.0930	1.50693	0.753463	+	0.657491i	$0.228382\pi$
$674$	1.51410	0.0583211
$675$	8.22493	0.316578
$676$	28.4236	1.09321
$677$	−1.69822	−0.0652679	−0.0326340	−	0.999467i	$-0.510390\pi$
$677$	−1.69822	−0.0652679	−0.0326340	+	0.999467i	$0.510390\pi$
$678$	13.9624	0.536223
$679$	−19.7977	−0.759765
$680$	−4.06265	−0.155796
$681$	15.8836	0.608661
$682$	1.99225	0.0762872
$683$	28.3151	1.08345	0.541723	−	0.840557i	$-0.317772\pi$
$683$	28.3151	1.08345	0.541723	+	0.840557i	$0.317772\pi$
$684$	−5.55489	−0.212397
$685$	72.7024	2.77782
$686$	18.6393	0.711654
$687$	15.1029	0.576212
$688$	6.64405	0.253302
$689$	−49.1752	−1.87343
$690$	−13.2531	−0.504537
$691$	2.91790	0.111002	0.0555010	−	0.998459i	$-0.482324\pi$
$691$	2.91790	0.111002	0.0555010	+	0.998459i	$0.482324\pi$
$692$	−24.3719	−0.926482
$693$	−1.65542	−0.0628843
$694$	−35.7721	−1.35789
$695$	−10.5740	−0.401093
$696$	−1.74243	−0.0660466
$697$	4.08777	0.154835
$698$	−20.5072	−0.776210
$699$	8.29255	0.313653
$700$	−13.6157	−0.514626
$701$	1.03383	0.0390471	0.0195235	−	0.999809i	$-0.493785\pi$
$701$	1.03383	0.0390471	0.0195235	+	0.999809i	$0.493785\pi$
$702$	6.43612	0.242916
$703$	−59.3285	−2.23762
$704$	1.00000	0.0376889
$705$	40.7979	1.53654
$706$	−9.01885	−0.339429
$707$	−2.05684	−0.0773554
$708$	−0.0748538	−0.00281318
$709$	−13.8243	−0.519183	−0.259592	−	0.965718i	$-0.583588\pi$
$709$	−13.8243	−0.519183	−0.259592	+	0.965718i	$0.583588\pi$
$710$	−21.3548	−0.801431
$711$	1.55257	0.0582258
$712$	−3.71513	−0.139230
$713$	−7.26048	−0.271907
$714$	1.84936	0.0692106
$715$	23.4056	0.875321
$716$	9.74345	0.364130
$717$	19.3939	0.724280
$718$	−35.2663	−1.31613
$719$	−13.7830	−0.514018	−0.257009	−	0.966409i	$-0.582737\pi$
$719$	−13.7830	−0.514018	−0.257009	+	0.966409i	$0.582737\pi$
$720$	3.63661	0.135528
$721$	31.6497	1.17870
$722$	11.8568	0.441265
$723$	−1.41796	−0.0527344
$724$	11.1669	0.415015
$725$	−14.3313	−0.532253
$726$	1.00000	0.0371135
$727$	−11.8953	−0.441171	−0.220585	−	0.975368i	$-0.570797\pi$
$727$	−11.8953	−0.441171	−0.220585	+	0.975368i	$0.570797\pi$
$728$	−10.6545	−0.394881
$729$	1.00000	0.0370370
$730$	−28.2860	−1.04691
$731$	−7.42243	−0.274528
$732$	−1.00000	−0.0369611
$733$	33.4328	1.23487	0.617434	−	0.786623i	$-0.288172\pi$
$733$	33.4328	1.23487	0.617434	+	0.786623i	$0.288172\pi$
$734$	13.8581	0.511512
$735$	−15.4904	−0.571373
$736$	−3.64436	−0.134333
$737$	−13.9718	−0.514659
$738$	−3.65909	−0.134693
$739$	5.75440	0.211679	0.105839	−	0.994383i	$-0.466247\pi$
$739$	5.75440	0.211679	0.105839	+	0.994383i	$0.466247\pi$
$740$	38.8404	1.42780
$741$	−35.7519	−1.31338
$742$	12.6483	0.464333
$743$	−27.3948	−1.00502	−0.502508	−	0.864572i	$-0.667589\pi$
$743$	−27.3948	−1.00502	−0.502508	+	0.864572i	$0.667589\pi$
$744$	1.99225	0.0730395
$745$	−54.6959	−2.00390
$746$	28.1145	1.02934
$747$	15.0909	0.552148
$748$	−1.11715	−0.0408472
$749$	11.3692	0.415422
$750$	11.7278	0.428239
$751$	−14.6508	−0.534616	−0.267308	−	0.963611i	$-0.586134\pi$
$751$	−14.6508	−0.534616	−0.267308	+	0.963611i	$0.586134\pi$
$752$	11.2187	0.409103
$753$	7.12400	0.259613
$754$	−11.2145	−0.408407
$755$	−52.3312	−1.90453
$756$	−1.65542	−0.0602071
$757$	−51.4326	−1.86935	−0.934674	−	0.355505i	$-0.884309\pi$
$757$	−51.4326	−1.86935	−0.934674	+	0.355505i	$0.884309\pi$
$758$	31.8925	1.15839
$759$	−3.64436	−0.132282
$760$	−20.2010	−0.732766
$761$	−11.4916	−0.416570	−0.208285	−	0.978068i	$-0.566788\pi$
$761$	−11.4916	−0.416570	−0.208285	+	0.978068i	$0.566788\pi$
$762$	−9.26320	−0.335570
$763$	−3.87328	−0.140222
$764$	−24.2346	−0.876779
$765$	−4.06265	−0.146886
$766$	13.1481	0.475060
$767$	−0.481768	−0.0173956
$768$	1.00000	0.0360844
$769$	−3.07212	−0.110783	−0.0553917	−	0.998465i	$-0.517641\pi$
$769$	−3.07212	−0.110783	−0.0553917	+	0.998465i	$0.517641\pi$
$770$	−6.02012	−0.216950
$771$	−11.5558	−0.416171
$772$	3.02708	0.108947
$773$	10.5075	0.377929	0.188964	−	0.981984i	$-0.439487\pi$
$773$	10.5075	0.377929	0.188964	+	0.981984i	$0.439487\pi$
$774$	6.64405	0.238815
$775$	16.3861	0.588607
$776$	11.9593	0.429314
$777$	−17.6806	−0.634287
$778$	−20.7562	−0.744146
$779$	20.3258	0.728249
$780$	23.4056	0.838056
$781$	−5.87217	−0.210123
$782$	4.07131	0.145590
$783$	−1.74243	−0.0622693
$784$	−4.25958	−0.152128
$785$	−5.92033	−0.211306
$786$	−11.9435	−0.426012
$787$	8.30457	0.296026	0.148013	−	0.988985i	$-0.452712\pi$
$787$	8.30457	0.296026	0.148013	+	0.988985i	$0.452712\pi$
$788$	−13.1681	−0.469096
$789$	−0.693770	−0.0246989
$790$	5.64608	0.200878
$791$	−23.1137	−0.821827
$792$	1.00000	0.0355335
$793$	−6.43612	−0.228553
$794$	−7.09454	−0.251776
$795$	−27.7856	−0.985452
$796$	−22.3693	−0.792860
$797$	−8.69854	−0.308118	−0.154059	−	0.988062i	$-0.549235\pi$
$797$	−8.69854	−0.308118	−0.154059	+	0.988062i	$0.549235\pi$
$798$	9.19568	0.325524
$799$	−12.5330	−0.443385
$800$	8.22493	0.290795
$801$	−3.71513	−0.131268
$802$	−10.1912	−0.359863
$803$	−7.77814	−0.274484
$804$	−13.9718	−0.492748
$805$	21.9395	0.773265
$806$	12.8224	0.451648
$807$	8.18407	0.288093
$808$	1.24249	0.0437106
$809$	−14.4754	−0.508930	−0.254465	−	0.967082i	$-0.581899\pi$
$809$	−14.4754	−0.508930	−0.254465	+	0.967082i	$0.581899\pi$
$810$	3.63661	0.127777
$811$	−26.1680	−0.918884	−0.459442	−	0.888208i	$-0.651951\pi$
$811$	−26.1680	−0.918884	−0.459442	+	0.888208i	$0.651951\pi$
$812$	2.88445	0.101224
$813$	4.99753	0.175271
$814$	10.6804	0.374348
$815$	75.2836	2.63707
$816$	−1.11715	−0.0391082
$817$	−36.9069	−1.29121
$818$	31.7800	1.11116
$819$	−10.6545	−0.372298
$820$	−13.3067	−0.464689
$821$	41.7457	1.45694	0.728468	−	0.685080i	$-0.240233\pi$
$821$	41.7457	1.45694	0.728468	+	0.685080i	$0.240233\pi$
$822$	19.9918	0.697294
$823$	37.6219	1.31142	0.655709	−	0.755014i	$-0.272370\pi$
$823$	37.6219	1.31142	0.655709	+	0.755014i	$0.272370\pi$
$824$	−19.1188	−0.666036
$825$	8.22493	0.286355
$826$	0.123915	0.00431154
$827$	2.92736	0.101794	0.0508972	−	0.998704i	$-0.483792\pi$
$827$	2.92736	0.101794	0.0508972	+	0.998704i	$0.483792\pi$
$828$	−3.64436	−0.126650
$829$	5.38309	0.186963	0.0934813	−	0.995621i	$-0.470200\pi$
$829$	5.38309	0.186963	0.0934813	+	0.995621i	$0.470200\pi$
$830$	54.8798	1.90491
$831$	−2.65986	−0.0922695
$832$	6.43612	0.223132
$833$	4.75861	0.164876
$834$	−2.90764	−0.100683
$835$	4.73101	0.163723
$836$	−5.55489	−0.192120
$837$	1.99225	0.0688623
$838$	0.276412	0.00954849
$839$	−34.3874	−1.18719	−0.593593	−	0.804765i	$-0.702291\pi$
$839$	−34.3874	−1.18719	−0.593593	+	0.804765i	$0.702291\pi$
$840$	−6.02012	−0.207714
$841$	−25.9639	−0.895308
$842$	15.1425	0.521846
$843$	−22.2999	−0.768051
$844$	−3.82917	−0.131806
$845$	103.365	3.55588
$846$	11.2187	0.385706
$847$	−1.65542	−0.0568810
$848$	−7.64051	−0.262376
$849$	−22.3131	−0.765784
$850$	−9.18851	−0.315163
$851$	−38.9232	−1.33427
$852$	−5.87217	−0.201177
$853$	−44.0088	−1.50683	−0.753416	−	0.657544i	$-0.771595\pi$
$853$	−44.0088	−1.50683	−0.753416	+	0.657544i	$0.771595\pi$
$854$	1.65542	0.0566474
$855$	−20.2010	−0.690858
$856$	−6.86786	−0.234739
$857$	7.83848	0.267757	0.133879	−	0.990998i	$-0.457257\pi$
$857$	7.83848	0.267757	0.133879	+	0.990998i	$0.457257\pi$
$858$	6.43612	0.219725
$859$	27.0073	0.921477	0.460739	−	0.887536i	$-0.347585\pi$
$859$	27.0073	0.921477	0.460739	+	0.887536i	$0.347585\pi$
$860$	24.1618	0.823911
$861$	6.05734	0.206433
$862$	−15.3738	−0.523635
$863$	7.27400	0.247610	0.123805	−	0.992307i	$-0.460490\pi$
$863$	7.27400	0.247610	0.123805	+	0.992307i	$0.460490\pi$
$864$	1.00000	0.0340207
$865$	−88.6312	−3.01355
$866$	36.5498	1.24201
$867$	−15.7520	−0.534965
$868$	−3.29801	−0.111942
$869$	1.55257	0.0526672
$870$	−6.33653	−0.214829
$871$	−89.9243	−3.04697
$872$	2.33976	0.0792342
$873$	11.9593	0.404761
$874$	20.2440	0.684764
$875$	−19.4144	−0.656328
$876$	−7.77814	−0.262799
$877$	−0.103572	−0.00349739	−0.00174869	−	0.999998i	$-0.500557\pi$
$877$	−0.103572	−0.00349739	−0.00174869	+	0.999998i	$0.500557\pi$
$878$	−26.9431	−0.909285
$879$	22.0617	0.744122
$880$	3.63661	0.122590
$881$	−38.9913	−1.31365	−0.656825	−	0.754043i	$-0.728101\pi$
$881$	−38.9913	−1.31365	−0.656825	+	0.754043i	$0.728101\pi$
$882$	−4.25958	−0.143428
$883$	32.2663	1.08585	0.542924	−	0.839782i	$-0.317317\pi$
$883$	32.2663	1.08585	0.542924	+	0.839782i	$0.317317\pi$
$884$	−7.19014	−0.241830
$885$	−0.272214	−0.00915038
$886$	29.1747	0.980142
$887$	14.1216	0.474156	0.237078	−	0.971491i	$-0.423810\pi$
$887$	14.1216	0.474156	0.237078	+	0.971491i	$0.423810\pi$
$888$	10.6804	0.358411
$889$	15.3345	0.514303
$890$	−13.5105	−0.452872
$891$	1.00000	0.0335013
$892$	11.0856	0.371173
$893$	−62.3185	−2.08541
$894$	−15.0404	−0.503025
$895$	35.4331	1.18440
$896$	−1.65542	−0.0553037
$897$	−23.4555	−0.783157
$898$	−9.37976	−0.313007
$899$	−3.47135	−0.115776
$900$	8.22493	0.274164
$901$	8.53564	0.284363
$902$	−3.65909	−0.121834
$903$	−10.9987	−0.366014
$904$	13.9624	0.464383
$905$	40.6097	1.34991
$906$	−14.3901	−0.478080
$907$	8.71656	0.289429	0.144714	−	0.989473i	$-0.453774\pi$
$907$	8.71656	0.289429	0.144714	+	0.989473i	$0.453774\pi$
$908$	15.8836	0.527116
$909$	1.24249	0.0412107
$910$	−38.7462	−1.28442
$911$	−8.18041	−0.271029	−0.135515	−	0.990775i	$-0.543269\pi$
$911$	−8.18041	−0.271029	−0.135515	+	0.990775i	$0.543269\pi$
$912$	−5.55489	−0.183941
$913$	15.0909	0.499437
$914$	−14.1878	−0.469292
$915$	−3.63661	−0.120223
$916$	15.1029	0.499014
$917$	19.7716	0.652916
$918$	−1.11715	−0.0368716
$919$	42.4776	1.40121	0.700603	−	0.713552i	$-0.252915\pi$
$919$	42.4776	1.40121	0.700603	+	0.713552i	$0.252915\pi$
$920$	−13.2531	−0.436942
$921$	−25.4026	−0.837044
$922$	11.8385	0.389882
$923$	−37.7940	−1.24400
$924$	−1.65542	−0.0544594
$925$	87.8455	2.88834
$926$	40.2318	1.32210
$927$	−19.1188	−0.627945
$928$	−1.74243	−0.0571980
$929$	−24.5913	−0.806814	−0.403407	−	0.915021i	$-0.632174\pi$
$929$	−24.5913	−0.806814	−0.403407	+	0.915021i	$0.632174\pi$
$930$	7.24504	0.237574
$931$	23.6615	0.775474
$932$	8.29255	0.271631
$933$	−4.07486	−0.133405
$934$	−24.7775	−0.810746
$935$	−4.06265	−0.132863
$936$	6.43612	0.210371
$937$	9.18901	0.300192	0.150096	−	0.988671i	$-0.452042\pi$
$937$	9.18901	0.300192	0.150096	+	0.988671i	$0.452042\pi$
$938$	23.1293	0.755197
$939$	9.02954	0.294668
$940$	40.7979	1.33068
$941$	−24.9237	−0.812491	−0.406245	−	0.913764i	$-0.633162\pi$
$941$	−24.9237	−0.812491	−0.406245	+	0.913764i	$0.633162\pi$
$942$	−1.62798	−0.0530425
$943$	13.3350	0.434249
$944$	−0.0748538	−0.00243628
$945$	−6.02012	−0.195835
$946$	6.64405	0.216017
$947$	−5.98653	−0.194536	−0.0972681	−	0.995258i	$-0.531010\pi$
$947$	−5.98653	−0.194536	−0.0972681	+	0.995258i	$0.531010\pi$
$948$	1.55257	0.0504250
$949$	−50.0610	−1.62505
$950$	−45.6886	−1.48233
$951$	16.4782	0.534343
$952$	1.84936	0.0599382
$953$	−36.4885	−1.18198	−0.590990	−	0.806679i	$-0.701263\pi$
$953$	−36.4885	−1.18198	−0.590990	+	0.806679i	$0.701263\pi$
$954$	−7.64051	−0.247371
$955$	−88.1319	−2.85188
$956$	19.3939	0.627245
$957$	−1.74243	−0.0563247
$958$	18.1197	0.585420
$959$	−33.0949	−1.06869
$960$	3.63661	0.117371
$961$	−27.0309	−0.871966
$962$	68.7403	2.21628
$963$	−6.86786	−0.221314
$964$	−1.41796	−0.0456694
$965$	11.0083	0.354370
$966$	6.03295	0.194107
$967$	−2.75773	−0.0886826	−0.0443413	−	0.999016i	$-0.514119\pi$
$967$	−2.75773	−0.0886826	−0.0443413	+	0.999016i	$0.514119\pi$
$968$	1.00000	0.0321412
$969$	6.20567	0.199355
$970$	43.4913	1.39642
$971$	−24.8710	−0.798148	−0.399074	−	0.916919i	$-0.630668\pi$
$971$	−24.8710	−0.798148	−0.399074	+	0.916919i	$0.630668\pi$
$972$	1.00000	0.0320750
$973$	4.81337	0.154310
$974$	−25.4064	−0.814072
$975$	52.9366	1.69533
$976$	−1.00000	−0.0320092
$977$	−31.3795	−1.00392	−0.501959	−	0.864891i	$-0.667387\pi$
$977$	−31.3795	−1.00392	−0.501959	+	0.864891i	$0.667387\pi$
$978$	20.7016	0.661964
$979$	−3.71513	−0.118736
$980$	−15.4904	−0.494824
$981$	2.33976	0.0747027
$982$	18.8016	0.599982
$983$	19.4750	0.621155	0.310578	−	0.950548i	$-0.399478\pi$
$983$	19.4750	0.621155	0.310578	+	0.950548i	$0.399478\pi$
$984$	−3.65909	−0.116648
$985$	−47.8874	−1.52582
$986$	1.94656	0.0619912
$987$	−18.5716	−0.591141
$988$	−35.7519	−1.13742
$989$	−24.2133	−0.769938
$990$	3.63661	0.115579
$991$	−17.2807	−0.548939	−0.274469	−	0.961596i	$-0.588502\pi$
$991$	−17.2807	−0.548939	−0.274469	+	0.961596i	$0.588502\pi$
$992$	1.99225	0.0632540
$993$	−28.0374	−0.889741
$994$	9.72092	0.308329
$995$	−81.3485	−2.57892
$996$	15.0909	0.478174
$997$	19.2224	0.608781	0.304390	−	0.952547i	$-0.401547\pi$
$997$	19.2224	0.608781	0.304390	+	0.952547i	$0.401547\pi$
$998$	20.5895	0.651748
$999$	10.6804	0.337913

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.bc.1.8	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.bc.1.8	✓	9	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.63661 q^{5} +1.00000 q^{6} -1.65542 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.63661 q^{5} +1.00000 q^{6} -1.65542 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.63661 q^{10} +1.00000 q^{11} +1.00000 q^{12} +6.43612 q^{13} -1.65542 q^{14} +3.63661 q^{15} +1.00000 q^{16} -1.11715 q^{17} +1.00000 q^{18} -5.55489 q^{19} +3.63661 q^{20} -1.65542 q^{21} +1.00000 q^{22} -3.64436 q^{23} +1.00000 q^{24} +8.22493 q^{25} +6.43612 q^{26} +1.00000 q^{27} -1.65542 q^{28} -1.74243 q^{29} +3.63661 q^{30} +1.99225 q^{31} +1.00000 q^{32} +1.00000 q^{33} -1.11715 q^{34} -6.02012 q^{35} +1.00000 q^{36} +10.6804 q^{37} -5.55489 q^{38} +6.43612 q^{39} +3.63661 q^{40} -3.65909 q^{41} -1.65542 q^{42} +6.64405 q^{43} +1.00000 q^{44} +3.63661 q^{45} -3.64436 q^{46} +11.2187 q^{47} +1.00000 q^{48} -4.25958 q^{49} +8.22493 q^{50} -1.11715 q^{51} +6.43612 q^{52} -7.64051 q^{53} +1.00000 q^{54} +3.63661 q^{55} -1.65542 q^{56} -5.55489 q^{57} -1.74243 q^{58} -0.0748538 q^{59} +3.63661 q^{60} -1.00000 q^{61} +1.99225 q^{62} -1.65542 q^{63} +1.00000 q^{64} +23.4056 q^{65} +1.00000 q^{66} -13.9718 q^{67} -1.11715 q^{68} -3.64436 q^{69} -6.02012 q^{70} -5.87217 q^{71} +1.00000 q^{72} -7.77814 q^{73} +10.6804 q^{74} +8.22493 q^{75} -5.55489 q^{76} -1.65542 q^{77} +6.43612 q^{78} +1.55257 q^{79} +3.63661 q^{80} +1.00000 q^{81} -3.65909 q^{82} +15.0909 q^{83} -1.65542 q^{84} -4.06265 q^{85} +6.64405 q^{86} -1.74243 q^{87} +1.00000 q^{88} -3.71513 q^{89} +3.63661 q^{90} -10.6545 q^{91} -3.64436 q^{92} +1.99225 q^{93} +11.2187 q^{94} -20.2010 q^{95} +1.00000 q^{96} +11.9593 q^{97} -4.25958 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} + 9 q^{3} + 9 q^{4} + 8 q^{5} + 9 q^{6} + 9 q^{7} + 9 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q + 9 * q^2 + 9 * q^3 + 9 * q^4 + 8 * q^5 + 9 * q^6 + 9 * q^7 + 9 * q^8 + 9 * q^9	\( 9 q + 9 q^{2} + 9 q^{3} + 9 q^{4} + 8 q^{5} + 9 q^{6} + 9 q^{7} + 9 q^{8} + 9 q^{9} + 8 q^{10} + 9 q^{11} + 9 q^{12} + 8 q^{13} + 9 q^{14} + 8 q^{15} + 9 q^{16} + q^{17} + 9 q^{18} + 5 q^{19} + 8 q^{20} + 9 q^{21} + 9 q^{22} - q^{23} + 9 q^{24} + 23 q^{25} + 8 q^{26} + 9 q^{27} + 9 q^{28} - 14 q^{29} + 8 q^{30} + 25 q^{31} + 9 q^{32} + 9 q^{33} + q^{34} + 5 q^{35} + 9 q^{36} + 16 q^{37} + 5 q^{38} + 8 q^{39} + 8 q^{40} + 5 q^{41} + 9 q^{42} + 5 q^{43} + 9 q^{44} + 8 q^{45} - q^{46} + 8 q^{47} + 9 q^{48} + 30 q^{49} + 23 q^{50} + q^{51} + 8 q^{52} + q^{53} + 9 q^{54} + 8 q^{55} + 9 q^{56} + 5 q^{57} - 14 q^{58} + 4 q^{59} + 8 q^{60} - 9 q^{61} + 25 q^{62} + 9 q^{63} + 9 q^{64} - 14 q^{65} + 9 q^{66} - 4 q^{67} + q^{68} - q^{69} + 5 q^{70} + 20 q^{71} + 9 q^{72} + 15 q^{73} + 16 q^{74} + 23 q^{75} + 5 q^{76} + 9 q^{77} + 8 q^{78} - 2 q^{79} + 8 q^{80} + 9 q^{81} + 5 q^{82} + 21 q^{83} + 9 q^{84} - 16 q^{85} + 5 q^{86} - 14 q^{87} + 9 q^{88} + 10 q^{89} + 8 q^{90} - 19 q^{91} - q^{92} + 25 q^{93} + 8 q^{94} - 7 q^{95} + 9 q^{96} + 3 q^{97} + 30 q^{98} + 9 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 9 * q^3 + 9 * q^4 + 8 * q^5 + 9 * q^6 + 9 * q^7 + 9 * q^8 + 9 * q^9 + 8 * q^10 + 9 * q^11 + 9 * q^12 + 8 * q^13 + 9 * q^14 + 8 * q^15 + 9 * q^16 + q^17 + 9 * q^18 + 5 * q^19 + 8 * q^20 + 9 * q^21 + 9 * q^22 - q^23 + 9 * q^24 + 23 * q^25 + 8 * q^26 + 9 * q^27 + 9 * q^28 - 14 * q^29 + 8 * q^30 + 25 * q^31 + 9 * q^32 + 9 * q^33 + q^34 + 5 * q^35 + 9 * q^36 + 16 * q^37 + 5 * q^38 + 8 * q^39 + 8 * q^40 + 5 * q^41 + 9 * q^42 + 5 * q^43 + 9 * q^44 + 8 * q^45 - q^46 + 8 * q^47 + 9 * q^48 + 30 * q^49 + 23 * q^50 + q^51 + 8 * q^52 + q^53 + 9 * q^54 + 8 * q^55 + 9 * q^56 + 5 * q^57 - 14 * q^58 + 4 * q^59 + 8 * q^60 - 9 * q^61 + 25 * q^62 + 9 * q^63 + 9 * q^64 - 14 * q^65 + 9 * q^66 - 4 * q^67 + q^68 - q^69 + 5 * q^70 + 20 * q^71 + 9 * q^72 + 15 * q^73 + 16 * q^74 + 23 * q^75 + 5 * q^76 + 9 * q^77 + 8 * q^78 - 2 * q^79 + 8 * q^80 + 9 * q^81 + 5 * q^82 + 21 * q^83 + 9 * q^84 - 16 * q^85 + 5 * q^86 - 14 * q^87 + 9 * q^88 + 10 * q^89 + 8 * q^90 - 19 * q^91 - q^92 + 25 * q^93 + 8 * q^94 - 7 * q^95 + 9 * q^96 + 3 * q^97 + 30 * q^98 + 9 * q^99

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