LMFDB - Embedded newform 6042.2.a.bd.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6042,2,Mod(1,6042)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6042, 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("6042.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6042 = 2 \cdot 3 \cdot 19 \cdot 53 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6042.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.2456129013$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 2 x^{10} - 35 x^{9} + 77 x^{8} + 394 x^{7} - 994 x^{6} - 1477 x^{5} + 4683 x^{4} + 563 x^{3} + \cdots + 1534 $ x^11 - 2x^10 - 35x^9 + 77x^8 + 394x^7 - 994x^6 - 1477x^5 + 4683x^4 + 563x^3 - 6194x^2 + 1258x + 1534
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$2.32043$ of defining polynomial
Character	$\chi$	$=$	6042.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.32043 q^{5} +1.00000 q^{6} -0.928685 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.32043 q^{5} +1.00000 q^{6} -0.928685 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.32043 q^{10} +6.48775 q^{11} -1.00000 q^{12} -4.80016 q^{13} +0.928685 q^{14} -2.32043 q^{15} +1.00000 q^{16} -0.708274 q^{17} -1.00000 q^{18} +1.00000 q^{19} +2.32043 q^{20} +0.928685 q^{21} -6.48775 q^{22} +3.31220 q^{23} +1.00000 q^{24} +0.384381 q^{25} +4.80016 q^{26} -1.00000 q^{27} -0.928685 q^{28} +0.356833 q^{29} +2.32043 q^{30} -7.07329 q^{31} -1.00000 q^{32} -6.48775 q^{33} +0.708274 q^{34} -2.15495 q^{35} +1.00000 q^{36} -10.2556 q^{37} -1.00000 q^{38} +4.80016 q^{39} -2.32043 q^{40} -6.64546 q^{41} -0.928685 q^{42} -2.77605 q^{43} +6.48775 q^{44} +2.32043 q^{45} -3.31220 q^{46} +3.23742 q^{47} -1.00000 q^{48} -6.13754 q^{49} -0.384381 q^{50} +0.708274 q^{51} -4.80016 q^{52} +1.00000 q^{53} +1.00000 q^{54} +15.0544 q^{55} +0.928685 q^{56} -1.00000 q^{57} -0.356833 q^{58} -2.56750 q^{59} -2.32043 q^{60} +0.142237 q^{61} +7.07329 q^{62} -0.928685 q^{63} +1.00000 q^{64} -11.1384 q^{65} +6.48775 q^{66} -7.24943 q^{67} -0.708274 q^{68} -3.31220 q^{69} +2.15495 q^{70} +7.50819 q^{71} -1.00000 q^{72} +0.749759 q^{73} +10.2556 q^{74} -0.384381 q^{75} +1.00000 q^{76} -6.02508 q^{77} -4.80016 q^{78} +5.37725 q^{79} +2.32043 q^{80} +1.00000 q^{81} +6.64546 q^{82} -14.8800 q^{83} +0.928685 q^{84} -1.64350 q^{85} +2.77605 q^{86} -0.356833 q^{87} -6.48775 q^{88} -5.61543 q^{89} -2.32043 q^{90} +4.45784 q^{91} +3.31220 q^{92} +7.07329 q^{93} -3.23742 q^{94} +2.32043 q^{95} +1.00000 q^{96} -16.5751 q^{97} +6.13754 q^{98} +6.48775 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 11 q^{2} - 11 q^{3} + 11 q^{4} + 2 q^{5} + 11 q^{6} - 2 q^{7} - 11 q^{8} + 11 q^{9}+O(q^{10}) $ 11 * q - 11 * q^2 - 11 * q^3 + 11 * q^4 + 2 * q^5 + 11 * q^6 - 2 * q^7 - 11 * q^8 + 11 * q^9	\( 11 q - 11 q^{2} - 11 q^{3} + 11 q^{4} + 2 q^{5} + 11 q^{6} - 2 q^{7} - 11 q^{8} + 11 q^{9} - 2 q^{10} - 6 q^{11} - 11 q^{12} - 7 q^{13} + 2 q^{14} - 2 q^{15} + 11 q^{16} - 16 q^{17} - 11 q^{18} + 11 q^{19} + 2 q^{20} + 2 q^{21} + 6 q^{22} - 11 q^{23} + 11 q^{24} + 19 q^{25} + 7 q^{26} - 11 q^{27} - 2 q^{28} - 7 q^{29} + 2 q^{30} + 12 q^{31} - 11 q^{32} + 6 q^{33} + 16 q^{34} - 5 q^{35} + 11 q^{36} + 3 q^{37} - 11 q^{38} + 7 q^{39} - 2 q^{40} + 11 q^{41} - 2 q^{42} + 7 q^{43} - 6 q^{44} + 2 q^{45} + 11 q^{46} - 37 q^{47} - 11 q^{48} + 23 q^{49} - 19 q^{50} + 16 q^{51} - 7 q^{52} + 11 q^{53} + 11 q^{54} - 11 q^{55} + 2 q^{56} - 11 q^{57} + 7 q^{58} - 16 q^{59} - 2 q^{60} + 24 q^{61} - 12 q^{62} - 2 q^{63} + 11 q^{64} - 7 q^{65} - 6 q^{66} - 28 q^{67} - 16 q^{68} + 11 q^{69} + 5 q^{70} + 4 q^{71} - 11 q^{72} - 7 q^{73} - 3 q^{74} - 19 q^{75} + 11 q^{76} - 13 q^{77} - 7 q^{78} + 5 q^{79} + 2 q^{80} + 11 q^{81} - 11 q^{82} - 11 q^{83} + 2 q^{84} - 11 q^{85} - 7 q^{86} + 7 q^{87} + 6 q^{88} - 10 q^{89} - 2 q^{90} - 24 q^{91} - 11 q^{92} - 12 q^{93} + 37 q^{94} + 2 q^{95} + 11 q^{96} - 24 q^{97} - 23 q^{98} - 6 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - 11 * q^3 + 11 * q^4 + 2 * q^5 + 11 * q^6 - 2 * q^7 - 11 * q^8 + 11 * q^9 - 2 * q^10 - 6 * q^11 - 11 * q^12 - 7 * q^13 + 2 * q^14 - 2 * q^15 + 11 * q^16 - 16 * q^17 - 11 * q^18 + 11 * q^19 + 2 * q^20 + 2 * q^21 + 6 * q^22 - 11 * q^23 + 11 * q^24 + 19 * q^25 + 7 * q^26 - 11 * q^27 - 2 * q^28 - 7 * q^29 + 2 * q^30 + 12 * q^31 - 11 * q^32 + 6 * q^33 + 16 * q^34 - 5 * q^35 + 11 * q^36 + 3 * q^37 - 11 * q^38 + 7 * q^39 - 2 * q^40 + 11 * q^41 - 2 * q^42 + 7 * q^43 - 6 * q^44 + 2 * q^45 + 11 * q^46 - 37 * q^47 - 11 * q^48 + 23 * q^49 - 19 * q^50 + 16 * q^51 - 7 * q^52 + 11 * q^53 + 11 * q^54 - 11 * q^55 + 2 * q^56 - 11 * q^57 + 7 * q^58 - 16 * q^59 - 2 * q^60 + 24 * q^61 - 12 * q^62 - 2 * q^63 + 11 * q^64 - 7 * q^65 - 6 * q^66 - 28 * q^67 - 16 * q^68 + 11 * q^69 + 5 * q^70 + 4 * q^71 - 11 * q^72 - 7 * q^73 - 3 * q^74 - 19 * q^75 + 11 * q^76 - 13 * q^77 - 7 * q^78 + 5 * q^79 + 2 * q^80 + 11 * q^81 - 11 * q^82 - 11 * q^83 + 2 * q^84 - 11 * q^85 - 7 * q^86 + 7 * q^87 + 6 * q^88 - 10 * q^89 - 2 * q^90 - 24 * q^91 - 11 * q^92 - 12 * q^93 + 37 * q^94 + 2 * q^95 + 11 * q^96 - 24 * q^97 - 23 * q^98 - 6 * 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
$5$	2.32043	1.03773	0.518863	−	0.854857i	$-0.326355\pi$
$5$	2.32043	1.03773	0.518863	+	0.854857i	$0.326355\pi$
$6$	1.00000	0.408248
$7$	−0.928685	−0.351010	−0.175505	−	0.984479i	$-0.556156\pi$
$7$	−0.928685	−0.351010	−0.175505	+	0.984479i	$0.556156\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−2.32043	−0.733783
$11$	6.48775	1.95613	0.978065	−	0.208298i	$-0.0667923\pi$
$11$	6.48775	1.95613	0.978065	+	0.208298i	$0.0667923\pi$
$12$	−1.00000	−0.288675
$13$	−4.80016	−1.33133	−0.665663	−	0.746253i	$-0.731851\pi$
$13$	−4.80016	−1.33133	−0.665663	+	0.746253i	$0.731851\pi$
$14$	0.928685	0.248202
$15$	−2.32043	−0.599132
$16$	1.00000	0.250000
$17$	−0.708274	−0.171782	−0.0858909	−	0.996305i	$-0.527374\pi$
$17$	−0.708274	−0.171782	−0.0858909	+	0.996305i	$0.527374\pi$
$18$	−1.00000	−0.235702
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	2.32043	0.518863
$21$	0.928685	0.202656
$22$	−6.48775	−1.38319
$23$	3.31220	0.690642	0.345321	−	0.938485i	$-0.387770\pi$
$23$	3.31220	0.690642	0.345321	+	0.938485i	$0.387770\pi$
$24$	1.00000	0.204124
$25$	0.384381	0.0768762
$26$	4.80016	0.941389
$27$	−1.00000	−0.192450
$28$	−0.928685	−0.175505
$29$	0.356833	0.0662622	0.0331311	−	0.999451i	$-0.489452\pi$
$29$	0.356833	0.0662622	0.0331311	+	0.999451i	$0.489452\pi$
$30$	2.32043	0.423650
$31$	−7.07329	−1.27040	−0.635201	−	0.772347i	$-0.719083\pi$
$31$	−7.07329	−1.27040	−0.635201	+	0.772347i	$0.719083\pi$
$32$	−1.00000	−0.176777
$33$	−6.48775	−1.12937
$34$	0.708274	0.121468
$35$	−2.15495	−0.364252
$36$	1.00000	0.166667
$37$	−10.2556	−1.68601	−0.843003	−	0.537909i	$-0.819215\pi$
$37$	−10.2556	−1.68601	−0.843003	+	0.537909i	$0.819215\pi$
$38$	−1.00000	−0.162221
$39$	4.80016	0.768641
$40$	−2.32043	−0.366892
$41$	−6.64546	−1.03785	−0.518923	−	0.854821i	$-0.673667\pi$
$41$	−6.64546	−1.03785	−0.518923	+	0.854821i	$0.673667\pi$
$42$	−0.928685	−0.143299
$43$	−2.77605	−0.423344	−0.211672	−	0.977341i	$-0.567891\pi$
$43$	−2.77605	−0.423344	−0.211672	+	0.977341i	$0.567891\pi$
$44$	6.48775	0.978065
$45$	2.32043	0.345909
$46$	−3.31220	−0.488358
$47$	3.23742	0.472227	0.236113	−	0.971726i	$-0.424126\pi$
$47$	3.23742	0.472227	0.236113	+	0.971726i	$0.424126\pi$
$48$	−1.00000	−0.144338
$49$	−6.13754	−0.876792
$50$	−0.384381	−0.0543597
$51$	0.708274	0.0991783
$52$	−4.80016	−0.665663
$53$	1.00000	0.137361
$53$	1.00000	0.137361
$54$	1.00000	0.136083
$55$	15.0544	2.02993
$56$	0.928685	0.124101
$57$	−1.00000	−0.132453
$58$	−0.356833	−0.0468544
$59$	−2.56750	−0.334260	−0.167130	−	0.985935i	$-0.553450\pi$
$59$	−2.56750	−0.334260	−0.167130	+	0.985935i	$0.553450\pi$
$60$	−2.32043	−0.299566
$61$	0.142237	0.0182116	0.00910580	−	0.999959i	$-0.497101\pi$
$61$	0.142237	0.0182116	0.00910580	+	0.999959i	$0.497101\pi$
$62$	7.07329	0.898309
$63$	−0.928685	−0.117003
$64$	1.00000	0.125000
$65$	−11.1384	−1.38155
$66$	6.48775	0.798587
$67$	−7.24943	−0.885659	−0.442829	−	0.896606i	$-0.646025\pi$
$67$	−7.24943	−0.885659	−0.442829	+	0.896606i	$0.646025\pi$
$68$	−0.708274	−0.0858909
$69$	−3.31220	−0.398743
$70$	2.15495	0.257565
$71$	7.50819	0.891058	0.445529	−	0.895268i	$-0.353016\pi$
$71$	7.50819	0.891058	0.445529	+	0.895268i	$0.353016\pi$
$72$	−1.00000	−0.117851
$73$	0.749759	0.0877526	0.0438763	−	0.999037i	$-0.486029\pi$
$73$	0.749759	0.0877526	0.0438763	+	0.999037i	$0.486029\pi$
$74$	10.2556	1.19219
$75$	−0.384381	−0.0443845
$76$	1.00000	0.114708
$77$	−6.02508	−0.686622
$78$	−4.80016	−0.543511
$79$	5.37725	0.604987	0.302494	−	0.953151i	$-0.402181\pi$
$79$	5.37725	0.604987	0.302494	+	0.953151i	$0.402181\pi$
$80$	2.32043	0.259432
$81$	1.00000	0.111111
$82$	6.64546	0.733869
$83$	−14.8800	−1.63329	−0.816645	−	0.577140i	$-0.804169\pi$
$83$	−14.8800	−1.63329	−0.816645	+	0.577140i	$0.804169\pi$
$84$	0.928685	0.101328
$85$	−1.64350	−0.178263
$86$	2.77605	0.299350
$87$	−0.356833	−0.0382565
$88$	−6.48775	−0.691597
$89$	−5.61543	−0.595235	−0.297617	−	0.954685i	$-0.596192\pi$
$89$	−5.61543	−0.595235	−0.297617	+	0.954685i	$0.596192\pi$
$90$	−2.32043	−0.244594
$91$	4.45784	0.467309
$92$	3.31220	0.345321
$93$	7.07329	0.733467
$94$	−3.23742	−0.333915
$95$	2.32043	0.238071
$96$	1.00000	0.102062
$97$	−16.5751	−1.68295	−0.841475	−	0.540296i	$-0.818312\pi$
$97$	−16.5751	−1.68295	−0.841475	+	0.540296i	$0.818312\pi$
$98$	6.13754	0.619985
$99$	6.48775	0.652044
$100$	0.384381	0.0384381
$101$	−11.9322	−1.18730	−0.593649	−	0.804724i	$-0.702313\pi$
$101$	−11.9322	−1.18730	−0.593649	+	0.804724i	$0.702313\pi$
$102$	−0.708274	−0.0701296
$103$	−2.99790	−0.295392	−0.147696	−	0.989033i	$-0.547186\pi$
$103$	−2.99790	−0.295392	−0.147696	+	0.989033i	$0.547186\pi$
$104$	4.80016	0.470695
$105$	2.15495	0.210301
$106$	−1.00000	−0.0971286
$107$	3.57968	0.346061	0.173031	−	0.984916i	$-0.444644\pi$
$107$	3.57968	0.346061	0.173031	+	0.984916i	$0.444644\pi$
$108$	−1.00000	−0.0962250
$109$	1.00660	0.0964145	0.0482072	−	0.998837i	$-0.484649\pi$
$109$	1.00660	0.0964145	0.0482072	+	0.998837i	$0.484649\pi$
$110$	−15.0544	−1.43538
$111$	10.2556	0.973416
$112$	−0.928685	−0.0877525
$113$	16.1312	1.51749	0.758747	−	0.651385i	$-0.225812\pi$
$113$	16.1312	1.51749	0.758747	+	0.651385i	$0.225812\pi$
$114$	1.00000	0.0936586
$115$	7.68573	0.716698
$116$	0.356833	0.0331311
$117$	−4.80016	−0.443775
$118$	2.56750	0.236358
$119$	0.657764	0.0602971
$120$	2.32043	0.211825
$121$	31.0909	2.82645
$122$	−0.142237	−0.0128775
$123$	6.64546	0.599201
$124$	−7.07329	−0.635201
$125$	−10.7102	−0.957950
$126$	0.928685	0.0827339
$127$	−13.0892	−1.16148	−0.580739	−	0.814090i	$-0.697236\pi$
$127$	−13.0892	−1.16148	−0.580739	+	0.814090i	$0.697236\pi$
$128$	−1.00000	−0.0883883
$129$	2.77605	0.244418
$130$	11.1384	0.976905
$131$	−20.6894	−1.80764	−0.903822	−	0.427909i	$-0.859250\pi$
$131$	−20.6894	−1.80764	−0.903822	+	0.427909i	$0.859250\pi$
$132$	−6.48775	−0.564686
$133$	−0.928685	−0.0805272
$134$	7.24943	0.626255
$135$	−2.32043	−0.199711
$136$	0.708274	0.0607340
$137$	20.6873	1.76744	0.883718	−	0.468020i	$-0.155032\pi$
$137$	20.6873	1.76744	0.883718	+	0.468020i	$0.155032\pi$
$138$	3.31220	0.281954
$139$	−5.39038	−0.457206	−0.228603	−	0.973520i	$-0.573416\pi$
$139$	−5.39038	−0.457206	−0.228603	+	0.973520i	$0.573416\pi$
$140$	−2.15495	−0.182126
$141$	−3.23742	−0.272640
$142$	−7.50819	−0.630073
$143$	−31.1423	−2.60425
$144$	1.00000	0.0833333
$145$	0.828004	0.0687620
$146$	−0.749759	−0.0620505
$147$	6.13754	0.506216
$148$	−10.2556	−0.843003
$149$	−6.63247	−0.543353	−0.271676	−	0.962389i	$-0.587578\pi$
$149$	−6.63247	−0.543353	−0.271676	+	0.962389i	$0.587578\pi$
$150$	0.384381	0.0313846
$151$	−15.8970	−1.29368	−0.646838	−	0.762627i	$-0.723909\pi$
$151$	−15.8970	−1.29368	−0.646838	+	0.762627i	$0.723909\pi$
$152$	−1.00000	−0.0811107
$153$	−0.708274	−0.0572606
$154$	6.02508	0.485515
$155$	−16.4131	−1.31833
$156$	4.80016	0.384321
$157$	−3.44330	−0.274805	−0.137403	−	0.990515i	$-0.543875\pi$
$157$	−3.44330	−0.274805	−0.137403	+	0.990515i	$0.543875\pi$
$158$	−5.37725	−0.427791
$159$	−1.00000	−0.0793052
$160$	−2.32043	−0.183446
$161$	−3.07600	−0.242422
$162$	−1.00000	−0.0785674
$163$	−6.74310	−0.528160	−0.264080	−	0.964501i	$-0.585068\pi$
$163$	−6.74310	−0.528160	−0.264080	+	0.964501i	$0.585068\pi$
$164$	−6.64546	−0.518923
$165$	−15.0544	−1.17198
$166$	14.8800	1.15491
$167$	−19.0088	−1.47094	−0.735471	−	0.677556i	$-0.763039\pi$
$167$	−19.0088	−1.47094	−0.735471	+	0.677556i	$0.763039\pi$
$168$	−0.928685	−0.0716496
$169$	10.0416	0.772428
$170$	1.64350	0.126051
$171$	1.00000	0.0764719
$172$	−2.77605	−0.211672
$173$	22.5020	1.71079	0.855396	−	0.517974i	$-0.173314\pi$
$173$	22.5020	1.71079	0.855396	+	0.517974i	$0.173314\pi$
$174$	0.356833	0.0270514
$175$	−0.356969	−0.0269843
$176$	6.48775	0.489033
$177$	2.56750	0.192985
$178$	5.61543	0.420895
$179$	10.8662	0.812181	0.406090	−	0.913833i	$-0.366892\pi$
$179$	10.8662	0.812181	0.406090	+	0.913833i	$0.366892\pi$
$180$	2.32043	0.172954
$181$	23.9515	1.78030	0.890151	−	0.455666i	$-0.150599\pi$
$181$	23.9515	1.78030	0.890151	+	0.455666i	$0.150599\pi$
$182$	−4.45784	−0.330437
$183$	−0.142237	−0.0105145
$184$	−3.31220	−0.244179
$185$	−23.7973	−1.74961
$186$	−7.07329	−0.518639
$187$	−4.59511	−0.336028
$188$	3.23742	0.236113
$189$	0.928685	0.0675519
$190$	−2.32043	−0.168341
$191$	−10.3073	−0.745813	−0.372906	−	0.927869i	$-0.621639\pi$
$191$	−10.3073	−0.745813	−0.372906	+	0.927869i	$0.621639\pi$
$192$	−1.00000	−0.0721688
$193$	20.4735	1.47372	0.736858	−	0.676047i	$-0.236309\pi$
$193$	20.4735	1.47372	0.736858	+	0.676047i	$0.236309\pi$
$194$	16.5751	1.19003
$195$	11.1384	0.797639
$196$	−6.13754	−0.438396
$197$	20.1739	1.43733	0.718664	−	0.695357i	$-0.244754\pi$
$197$	20.1739	1.43733	0.718664	+	0.695357i	$0.244754\pi$
$198$	−6.48775	−0.461064
$199$	22.8455	1.61948	0.809739	−	0.586790i	$-0.199609\pi$
$199$	22.8455	1.61948	0.809739	+	0.586790i	$0.199609\pi$
$200$	−0.384381	−0.0271798
$201$	7.24943	0.511335
$202$	11.9322	0.839546
$203$	−0.331385	−0.0232587
$204$	0.708274	0.0495891
$205$	−15.4203	−1.07700
$206$	2.99790	0.208874
$207$	3.31220	0.230214
$208$	−4.80016	−0.332831
$209$	6.48775	0.448767
$210$	−2.15495	−0.148705
$211$	10.9096	0.751048	0.375524	−	0.926813i	$-0.377463\pi$
$211$	10.9096	0.751048	0.375524	+	0.926813i	$0.377463\pi$
$212$	1.00000	0.0686803
$213$	−7.50819	−0.514452
$214$	−3.57968	−0.244702
$215$	−6.44163	−0.439315
$216$	1.00000	0.0680414
$217$	6.56887	0.445924
$218$	−1.00660	−0.0681753
$219$	−0.749759	−0.0506640
$220$	15.0544	1.01496
$221$	3.39983	0.228698
$222$	−10.2556	−0.688309
$223$	−18.1400	−1.21475	−0.607373	−	0.794417i	$-0.707777\pi$
$223$	−18.1400	−1.21475	−0.607373	+	0.794417i	$0.707777\pi$
$224$	0.928685	0.0620504
$225$	0.384381	0.0256254
$226$	−16.1312	−1.07303
$227$	12.5371	0.832114	0.416057	−	0.909339i	$-0.363412\pi$
$227$	12.5371	0.832114	0.416057	+	0.909339i	$0.363412\pi$
$228$	−1.00000	−0.0662266
$229$	27.8525	1.84054	0.920272	−	0.391280i	$-0.127967\pi$
$229$	27.8525	1.84054	0.920272	+	0.391280i	$0.127967\pi$
$230$	−7.68573	−0.506782
$231$	6.02508	0.396421
$232$	−0.356833	−0.0234272
$233$	−2.74466	−0.179808	−0.0899042	−	0.995950i	$-0.528656\pi$
$233$	−2.74466	−0.179808	−0.0899042	+	0.995950i	$0.528656\pi$
$234$	4.80016	0.313796
$235$	7.51220	0.490042
$236$	−2.56750	−0.167130
$237$	−5.37725	−0.349290
$238$	−0.657764	−0.0426365
$239$	9.42043	0.609357	0.304678	−	0.952455i	$-0.401451\pi$
$239$	9.42043	0.609357	0.304678	+	0.952455i	$0.401451\pi$
$240$	−2.32043	−0.149783
$241$	−19.9785	−1.28693	−0.643465	−	0.765475i	$-0.722504\pi$
$241$	−19.9785	−1.28693	−0.643465	+	0.765475i	$0.722504\pi$
$242$	−31.0909	−1.99860
$243$	−1.00000	−0.0641500
$244$	0.142237	0.00910580
$245$	−14.2417	−0.909870
$246$	−6.64546	−0.423699
$247$	−4.80016	−0.305427
$248$	7.07329	0.449155
$249$	14.8800	0.942980
$250$	10.7102	0.677373
$251$	1.33336	0.0841612	0.0420806	−	0.999114i	$-0.486601\pi$
$251$	1.33336	0.0841612	0.0420806	+	0.999114i	$0.486601\pi$
$252$	−0.928685	−0.0585017
$253$	21.4888	1.35099
$254$	13.0892	0.821289
$255$	1.64350	0.102920
$256$	1.00000	0.0625000
$257$	4.34905	0.271287	0.135643	−	0.990758i	$-0.456690\pi$
$257$	4.34905	0.271287	0.135643	+	0.990758i	$0.456690\pi$
$258$	−2.77605	−0.172830
$259$	9.52420	0.591805
$260$	−11.1384	−0.690776
$261$	0.356833	0.0220874
$262$	20.6894	1.27820
$263$	−29.6733	−1.82973	−0.914867	−	0.403755i	$-0.867705\pi$
$263$	−29.6733	−1.82973	−0.914867	+	0.403755i	$0.867705\pi$
$264$	6.48775	0.399294
$265$	2.32043	0.142543
$266$	0.928685	0.0569414
$267$	5.61543	0.343659
$268$	−7.24943	−0.442829
$269$	−20.1049	−1.22582	−0.612909	−	0.790154i	$-0.710001\pi$
$269$	−20.1049	−1.22582	−0.612909	+	0.790154i	$0.710001\pi$
$270$	2.32043	0.141217
$271$	24.5383	1.49059	0.745296	−	0.666733i	$-0.232308\pi$
$271$	24.5383	1.49059	0.745296	+	0.666733i	$0.232308\pi$
$272$	−0.708274	−0.0429454
$273$	−4.45784	−0.269801
$274$	−20.6873	−1.24977
$275$	2.49377	0.150380
$276$	−3.31220	−0.199371
$277$	−22.5599	−1.35549	−0.677747	−	0.735295i	$-0.737044\pi$
$277$	−22.5599	−1.35549	−0.677747	+	0.735295i	$0.737044\pi$
$278$	5.39038	0.323293
$279$	−7.07329	−0.423467
$280$	2.15495	0.128783
$281$	26.9567	1.60810	0.804050	−	0.594562i	$-0.202674\pi$
$281$	26.9567	1.60810	0.804050	+	0.594562i	$0.202674\pi$
$282$	3.23742	0.192786
$283$	−18.0782	−1.07464	−0.537318	−	0.843379i	$-0.680563\pi$
$283$	−18.0782	−1.07464	−0.537318	+	0.843379i	$0.680563\pi$
$284$	7.50819	0.445529
$285$	−2.32043	−0.137450
$286$	31.1423	1.84148
$287$	6.17154	0.364295
$288$	−1.00000	−0.0589256
$289$	−16.4983	−0.970491
$290$	−0.828004	−0.0486221
$291$	16.5751	0.971652
$292$	0.749759	0.0438763
$293$	−7.72353	−0.451214	−0.225607	−	0.974218i	$-0.572436\pi$
$293$	−7.72353	−0.451214	−0.225607	+	0.974218i	$0.572436\pi$
$294$	−6.13754	−0.357949
$295$	−5.95770	−0.346871
$296$	10.2556	0.596093
$297$	−6.48775	−0.376458
$298$	6.63247	0.384208
$299$	−15.8991	−0.919470
$300$	−0.384381	−0.0221922
$301$	2.57808	0.148598
$302$	15.8970	0.914768
$303$	11.9322	0.685486
$304$	1.00000	0.0573539
$305$	0.330051	0.0188987
$306$	0.708274	0.0404894
$307$	−17.9903	−1.02676	−0.513379	−	0.858162i	$-0.671607\pi$
$307$	−17.9903	−1.02676	−0.513379	+	0.858162i	$0.671607\pi$
$308$	−6.02508	−0.343311
$309$	2.99790	0.170545
$310$	16.4131	0.932199
$311$	−1.74113	−0.0987305	−0.0493652	−	0.998781i	$-0.515720\pi$
$311$	−1.74113	−0.0987305	−0.0493652	+	0.998781i	$0.515720\pi$
$312$	−4.80016	−0.271756
$313$	−5.18339	−0.292982	−0.146491	−	0.989212i	$-0.546798\pi$
$313$	−5.18339	−0.292982	−0.146491	+	0.989212i	$0.546798\pi$
$314$	3.44330	0.194317
$315$	−2.15495	−0.121417
$316$	5.37725	0.302494
$317$	10.6186	0.596401	0.298201	−	0.954503i	$-0.403614\pi$
$317$	10.6186	0.596401	0.298201	+	0.954503i	$0.403614\pi$
$318$	1.00000	0.0560772
$319$	2.31504	0.129617
$320$	2.32043	0.129716
$321$	−3.57968	−0.199798
$322$	3.07600	0.171419
$323$	−0.708274	−0.0394094
$324$	1.00000	0.0555556
$325$	−1.84509	−0.102347
$326$	6.74310	0.373466
$327$	−1.00660	−0.0556649
$328$	6.64546	0.366934
$329$	−3.00655	−0.165756
$330$	15.0544	0.828715
$331$	−0.966276	−0.0531113	−0.0265557	−	0.999647i	$-0.508454\pi$
$331$	−0.966276	−0.0531113	−0.0265557	+	0.999647i	$0.508454\pi$
$332$	−14.8800	−0.816645
$333$	−10.2556	−0.562002
$334$	19.0088	1.04011
$335$	−16.8218	−0.919071
$336$	0.928685	0.0506639
$337$	−26.3180	−1.43363	−0.716816	−	0.697263i	$-0.754401\pi$
$337$	−26.3180	−1.43363	−0.716816	+	0.697263i	$0.754401\pi$
$338$	−10.0416	−0.546189
$339$	−16.1312	−0.876126
$340$	−1.64350	−0.0891313
$341$	−45.8898	−2.48507
$342$	−1.00000	−0.0540738
$343$	12.2006	0.658773
$344$	2.77605	0.149675
$345$	−7.68573	−0.413786
$346$	−22.5020	−1.20971
$347$	−23.9061	−1.28335	−0.641674	−	0.766978i	$-0.721760\pi$
$347$	−23.9061	−1.28335	−0.641674	+	0.766978i	$0.721760\pi$
$348$	−0.356833	−0.0191282
$349$	16.1968	0.866994	0.433497	−	0.901155i	$-0.357279\pi$
$349$	16.1968	0.866994	0.433497	+	0.901155i	$0.357279\pi$
$350$	0.356969	0.0190808
$351$	4.80016	0.256214
$352$	−6.48775	−0.345798
$353$	−5.55863	−0.295856	−0.147928	−	0.988998i	$-0.547260\pi$
$353$	−5.55863	−0.295856	−0.147928	+	0.988998i	$0.547260\pi$
$354$	−2.56750	−0.136461
$355$	17.4222	0.924674
$356$	−5.61543	−0.297617
$357$	−0.657764	−0.0348126
$358$	−10.8662	−0.574299
$359$	−10.2345	−0.540158	−0.270079	−	0.962838i	$-0.587050\pi$
$359$	−10.2345	−0.540158	−0.270079	+	0.962838i	$0.587050\pi$
$360$	−2.32043	−0.122297
$361$	1.00000	0.0526316
$362$	−23.9515	−1.25886
$363$	−31.0909	−1.63185
$364$	4.45784	0.233654
$365$	1.73976	0.0910632
$366$	0.142237	0.00743485
$367$	−17.9873	−0.938928	−0.469464	−	0.882952i	$-0.655553\pi$
$367$	−17.9873	−0.938928	−0.469464	+	0.882952i	$0.655553\pi$
$368$	3.31220	0.172661
$369$	−6.64546	−0.345949
$370$	23.7973	1.23716
$371$	−0.928685	−0.0482149
$372$	7.07329	0.366733
$373$	20.4618	1.05947	0.529737	−	0.848162i	$-0.322291\pi$
$373$	20.4618	1.05947	0.529737	+	0.848162i	$0.322291\pi$
$374$	4.59511	0.237607
$375$	10.7102	0.553073
$376$	−3.23742	−0.166957
$377$	−1.71286	−0.0882165
$378$	−0.928685	−0.0477664
$379$	16.5718	0.851234	0.425617	−	0.904903i	$-0.360057\pi$
$379$	16.5718	0.851234	0.425617	+	0.904903i	$0.360057\pi$
$380$	2.32043	0.119035
$381$	13.0892	0.670580
$382$	10.3073	0.527369
$383$	−9.70200	−0.495749	−0.247874	−	0.968792i	$-0.579732\pi$
$383$	−9.70200	−0.495749	−0.247874	+	0.968792i	$0.579732\pi$
$384$	1.00000	0.0510310
$385$	−13.9808	−0.712526
$386$	−20.4735	−1.04207
$387$	−2.77605	−0.141115
$388$	−16.5751	−0.841475
$389$	−32.4457	−1.64506	−0.822530	−	0.568722i	$-0.807438\pi$
$389$	−32.4457	−1.64506	−0.822530	+	0.568722i	$0.807438\pi$
$390$	−11.1384	−0.564016
$391$	−2.34595	−0.118640
$392$	6.13754	0.309993
$393$	20.6894	1.04364
$394$	−20.1739	−1.01634
$395$	12.4775	0.627812
$396$	6.48775	0.326022
$397$	26.7674	1.34342	0.671708	−	0.740816i	$-0.265561\pi$
$397$	26.7674	1.34342	0.671708	+	0.740816i	$0.265561\pi$
$398$	−22.8455	−1.14514
$399$	0.928685	0.0464924
$400$	0.384381	0.0192190
$401$	−2.50288	−0.124988	−0.0624940	−	0.998045i	$-0.519905\pi$
$401$	−2.50288	−0.124988	−0.0624940	+	0.998045i	$0.519905\pi$
$402$	−7.24943	−0.361569
$403$	33.9530	1.69132
$404$	−11.9322	−0.593649
$405$	2.32043	0.115303
$406$	0.331385	0.0164464
$407$	−66.5356	−3.29805
$408$	−0.708274	−0.0350648
$409$	−17.0622	−0.843670	−0.421835	−	0.906673i	$-0.638614\pi$
$409$	−17.0622	−0.843670	−0.421835	+	0.906673i	$0.638614\pi$
$410$	15.4203	0.761555
$411$	−20.6873	−1.02043
$412$	−2.99790	−0.147696
$413$	2.38440	0.117329
$414$	−3.31220	−0.162786
$415$	−34.5279	−1.69491
$416$	4.80016	0.235347
$417$	5.39038	0.263968
$418$	−6.48775	−0.317326
$419$	24.5515	1.19942	0.599709	−	0.800218i	$-0.295283\pi$
$419$	24.5515	1.19942	0.599709	+	0.800218i	$0.295283\pi$
$420$	2.15495	0.105151
$421$	34.5061	1.68172	0.840862	−	0.541249i	$-0.182048\pi$
$421$	34.5061	1.68172	0.840862	+	0.541249i	$0.182048\pi$
$422$	−10.9096	−0.531071
$423$	3.23742	0.157409
$424$	−1.00000	−0.0485643
$425$	−0.272247	−0.0132059
$426$	7.50819	0.363773
$427$	−0.132094	−0.00639245
$428$	3.57968	0.173031
$429$	31.1423	1.50356
$430$	6.44163	0.310643
$431$	5.76807	0.277838	0.138919	−	0.990304i	$-0.455637\pi$
$431$	5.76807	0.277838	0.138919	+	0.990304i	$0.455637\pi$
$432$	−1.00000	−0.0481125
$433$	−28.0808	−1.34948	−0.674738	−	0.738057i	$-0.735744\pi$
$433$	−28.0808	−1.34948	−0.674738	+	0.738057i	$0.735744\pi$
$434$	−6.56887	−0.315316
$435$	−0.828004	−0.0396998
$436$	1.00660	0.0482072
$437$	3.31220	0.158444
$438$	0.749759	0.0358249
$439$	6.14117	0.293102	0.146551	−	0.989203i	$-0.453183\pi$
$439$	6.14117	0.293102	0.146551	+	0.989203i	$0.453183\pi$
$440$	−15.0544	−0.717688
$441$	−6.13754	−0.292264
$442$	−3.39983	−0.161714
$443$	5.09396	0.242021	0.121011	−	0.992651i	$-0.461386\pi$
$443$	5.09396	0.242021	0.121011	+	0.992651i	$0.461386\pi$
$444$	10.2556	0.486708
$445$	−13.0302	−0.617691
$446$	18.1400	0.858955
$447$	6.63247	0.313705
$448$	−0.928685	−0.0438763
$449$	1.46647	0.0692071	0.0346035	−	0.999401i	$-0.488983\pi$
$449$	1.46647	0.0692071	0.0346035	+	0.999401i	$0.488983\pi$
$450$	−0.384381	−0.0181199
$451$	−43.1141	−2.03016
$452$	16.1312	0.758747
$453$	15.8970	0.746905
$454$	−12.5371	−0.588393
$455$	10.3441	0.484939
$456$	1.00000	0.0468293
$457$	1.10625	0.0517483	0.0258741	−	0.999665i	$-0.491763\pi$
$457$	1.10625	0.0517483	0.0258741	+	0.999665i	$0.491763\pi$
$458$	−27.8525	−1.30146
$459$	0.708274	0.0330594
$460$	7.68573	0.358349
$461$	−1.68546	−0.0784999	−0.0392500	−	0.999229i	$-0.512497\pi$
$461$	−1.68546	−0.0784999	−0.0392500	+	0.999229i	$0.512497\pi$
$462$	−6.02508	−0.280312
$463$	−37.7007	−1.75210	−0.876050	−	0.482220i	$-0.839831\pi$
$463$	−37.7007	−1.75210	−0.876050	+	0.482220i	$0.839831\pi$
$464$	0.356833	0.0165655
$465$	16.4131	0.761138
$466$	2.74466	0.127144
$467$	6.90176	0.319375	0.159688	−	0.987168i	$-0.448951\pi$
$467$	6.90176	0.319375	0.159688	+	0.987168i	$0.448951\pi$
$468$	−4.80016	−0.221888
$469$	6.73244	0.310875
$470$	−7.51220	−0.346512
$471$	3.44330	0.158659
$472$	2.56750	0.118179
$473$	−18.0103	−0.828117
$474$	5.37725	0.246985
$475$	0.384381	0.0176366
$476$	0.657764	0.0301486
$477$	1.00000	0.0457869
$478$	−9.42043	−0.430880
$479$	−2.39586	−0.109470	−0.0547349	−	0.998501i	$-0.517431\pi$
$479$	−2.39586	−0.109470	−0.0547349	+	0.998501i	$0.517431\pi$
$480$	2.32043	0.105913
$481$	49.2284	2.24462
$482$	19.9785	0.909997
$483$	3.07600	0.139963
$484$	31.0909	1.41322
$485$	−38.4614	−1.74644
$486$	1.00000	0.0453609
$487$	39.7517	1.80132	0.900660	−	0.434524i	$-0.143084\pi$
$487$	39.7517	1.80132	0.900660	+	0.434524i	$0.143084\pi$
$488$	−0.142237	−0.00643877
$489$	6.74310	0.304934
$490$	14.2417	0.643375
$491$	−39.7767	−1.79510	−0.897548	−	0.440916i	$-0.854654\pi$
$491$	−39.7767	−1.79510	−0.897548	+	0.440916i	$0.854654\pi$
$492$	6.64546	0.299601
$493$	−0.252735	−0.0113826
$494$	4.80016	0.215970
$495$	15.0544	0.676643
$496$	−7.07329	−0.317600
$497$	−6.97274	−0.312770
$498$	−14.8800	−0.666788
$499$	40.4710	1.81173	0.905865	−	0.423566i	$-0.139222\pi$
$499$	40.4710	1.81173	0.905865	+	0.423566i	$0.139222\pi$
$500$	−10.7102	−0.478975
$501$	19.0088	0.849249
$502$	−1.33336	−0.0595109
$503$	−20.3642	−0.907993	−0.453997	−	0.891003i	$-0.650002\pi$
$503$	−20.3642	−0.907993	−0.453997	+	0.891003i	$0.650002\pi$
$504$	0.928685	0.0413669
$505$	−27.6878	−1.23209
$506$	−21.4888	−0.955292
$507$	−10.0416	−0.445962
$508$	−13.0892	−0.580739
$509$	16.6604	0.738458	0.369229	−	0.929338i	$-0.379622\pi$
$509$	16.6604	0.738458	0.369229	+	0.929338i	$0.379622\pi$
$510$	−1.64350	−0.0727754
$511$	−0.696290	−0.0308021
$512$	−1.00000	−0.0441942
$513$	−1.00000	−0.0441511
$514$	−4.34905	−0.191829
$515$	−6.95641	−0.306536
$516$	2.77605	0.122209
$517$	21.0036	0.923737
$518$	−9.52420	−0.418470
$519$	−22.5020	−0.987727
$520$	11.1384	0.488452
$521$	13.7249	0.601297	0.300648	−	0.953735i	$-0.402797\pi$
$521$	13.7249	0.601297	0.300648	+	0.953735i	$0.402797\pi$
$522$	−0.356833	−0.0156181
$523$	−36.2617	−1.58561	−0.792807	−	0.609472i	$-0.791381\pi$
$523$	−36.2617	−1.58561	−0.792807	+	0.609472i	$0.791381\pi$
$524$	−20.6894	−0.903822
$525$	0.356969	0.0155794
$526$	29.6733	1.29382
$527$	5.00983	0.218232
$528$	−6.48775	−0.282343
$529$	−12.0293	−0.523013
$530$	−2.32043	−0.100793
$531$	−2.56750	−0.111420
$532$	−0.928685	−0.0402636
$533$	31.8993	1.38171
$534$	−5.61543	−0.243004
$535$	8.30639	0.359117
$536$	7.24943	0.313128
$537$	−10.8662	−0.468913
$538$	20.1049	0.866784
$539$	−39.8189	−1.71512
$540$	−2.32043	−0.0998553
$541$	−34.2855	−1.47405	−0.737025	−	0.675865i	$-0.763770\pi$
$541$	−34.2855	−1.47405	−0.737025	+	0.675865i	$0.763770\pi$
$542$	−24.5383	−1.05401
$543$	−23.9515	−1.02786
$544$	0.708274	0.0303670
$545$	2.33573	0.100052
$546$	4.45784	0.190778
$547$	−17.8866	−0.764774	−0.382387	−	0.924002i	$-0.624898\pi$
$547$	−17.8866	−0.764774	−0.382387	+	0.924002i	$0.624898\pi$
$548$	20.6873	0.883718
$549$	0.142237	0.00607053
$550$	−2.49377	−0.106335
$551$	0.356833	0.0152016
$552$	3.31220	0.140977
$553$	−4.99377	−0.212357
$554$	22.5599	0.958480
$555$	23.7973	1.01014
$556$	−5.39038	−0.228603
$557$	−20.0329	−0.848821	−0.424410	−	0.905470i	$-0.639519\pi$
$557$	−20.0329	−0.848821	−0.424410	+	0.905470i	$0.639519\pi$
$558$	7.07329	0.299436
$559$	13.3255	0.563609
$560$	−2.15495	−0.0910631
$561$	4.59511	0.194006
$562$	−26.9567	−1.13710
$563$	−10.6784	−0.450042	−0.225021	−	0.974354i	$-0.572245\pi$
$563$	−10.6784	−0.450042	−0.225021	+	0.974354i	$0.572245\pi$
$564$	−3.23742	−0.136320
$565$	37.4313	1.57474
$566$	18.0782	0.759883
$567$	−0.928685	−0.0390011
$568$	−7.50819	−0.315037
$569$	28.4443	1.19245	0.596224	−	0.802818i	$-0.296667\pi$
$569$	28.4443	1.19245	0.596224	+	0.802818i	$0.296667\pi$
$570$	2.32043	0.0971920
$571$	7.17071	0.300085	0.150042	−	0.988680i	$-0.452059\pi$
$571$	7.17071	0.300085	0.150042	+	0.988680i	$0.452059\pi$
$572$	−31.1423	−1.30212
$573$	10.3073	0.430595
$574$	−6.17154	−0.257595
$575$	1.27315	0.0530940
$576$	1.00000	0.0416667
$577$	1.72629	0.0718665	0.0359332	−	0.999354i	$-0.488560\pi$
$577$	1.72629	0.0718665	0.0359332	+	0.999354i	$0.488560\pi$
$578$	16.4983	0.686241
$579$	−20.4735	−0.850851
$580$	0.828004	0.0343810
$581$	13.8188	0.573301
$582$	−16.5751	−0.687062
$583$	6.48775	0.268695
$584$	−0.749759	−0.0310252
$585$	−11.1384	−0.460517
$586$	7.72353	0.319056
$587$	−4.54058	−0.187410	−0.0937049	−	0.995600i	$-0.529871\pi$
$587$	−4.54058	−0.187410	−0.0937049	+	0.995600i	$0.529871\pi$
$588$	6.13754	0.253108
$589$	−7.07329	−0.291450
$590$	5.95770	0.245275
$591$	−20.1739	−0.829842
$592$	−10.2556	−0.421502
$593$	−9.15464	−0.375936	−0.187968	−	0.982175i	$-0.560190\pi$
$593$	−9.15464	−0.375936	−0.187968	+	0.982175i	$0.560190\pi$
$594$	6.48775	0.266196
$595$	1.52629	0.0625719
$596$	−6.63247	−0.271676
$597$	−22.8455	−0.935006
$598$	15.8991	0.650163
$599$	8.55358	0.349490	0.174745	−	0.984614i	$-0.444090\pi$
$599$	8.55358	0.349490	0.174745	+	0.984614i	$0.444090\pi$
$600$	0.384381	0.0156923
$601$	−30.8208	−1.25720	−0.628602	−	0.777727i	$-0.716373\pi$
$601$	−30.8208	−1.25720	−0.628602	+	0.777727i	$0.716373\pi$
$602$	−2.57808	−0.105075
$603$	−7.24943	−0.295220
$604$	−15.8970	−0.646838
$605$	72.1442	2.93308
$606$	−11.9322	−0.484712
$607$	38.6027	1.56683	0.783417	−	0.621496i	$-0.213475\pi$
$607$	38.6027	1.56683	0.783417	+	0.621496i	$0.213475\pi$
$608$	−1.00000	−0.0405554
$609$	0.331385	0.0134284
$610$	−0.330051	−0.0133634
$611$	−15.5402	−0.628688
$612$	−0.708274	−0.0286303
$613$	14.3724	0.580495	0.290248	−	0.956952i	$-0.406262\pi$
$613$	14.3724	0.580495	0.290248	+	0.956952i	$0.406262\pi$
$614$	17.9903	0.726028
$615$	15.4203	0.621807
$616$	6.02508	0.242757
$617$	−40.4819	−1.62974	−0.814869	−	0.579645i	$-0.803191\pi$
$617$	−40.4819	−1.62974	−0.814869	+	0.579645i	$0.803191\pi$
$618$	−2.99790	−0.120593
$619$	−29.8387	−1.19932	−0.599659	−	0.800255i	$-0.704697\pi$
$619$	−29.8387	−1.19932	−0.599659	+	0.800255i	$0.704697\pi$
$620$	−16.4131	−0.659165
$621$	−3.31220	−0.132914
$622$	1.74113	0.0698130
$623$	5.21497	0.208933
$624$	4.80016	0.192160
$625$	−26.7742	−1.07097
$626$	5.18339	0.207170
$627$	−6.48775	−0.259096
$628$	−3.44330	−0.137403
$629$	7.26376	0.289625
$630$	2.15495	0.0858551
$631$	9.44588	0.376034	0.188017	−	0.982166i	$-0.439794\pi$
$631$	9.44588	0.376034	0.188017	+	0.982166i	$0.439794\pi$
$632$	−5.37725	−0.213895
$633$	−10.9096	−0.433618
$634$	−10.6186	−0.421719
$635$	−30.3725	−1.20530
$636$	−1.00000	−0.0396526
$637$	29.4612	1.16730
$638$	−2.31504	−0.0916534
$639$	7.50819	0.297019
$640$	−2.32043	−0.0917229
$641$	−48.3650	−1.91030	−0.955152	−	0.296117i	$-0.904308\pi$
$641$	−48.3650	−1.91030	−0.955152	+	0.296117i	$0.904308\pi$
$642$	3.57968	0.141279
$643$	−16.3561	−0.645020	−0.322510	−	0.946566i	$-0.604527\pi$
$643$	−16.3561	−0.645020	−0.322510	+	0.946566i	$0.604527\pi$
$644$	−3.07600	−0.121211
$645$	6.44163	0.253639
$646$	0.708274	0.0278667
$647$	−27.8935	−1.09661	−0.548304	−	0.836279i	$-0.684726\pi$
$647$	−27.8935	−1.09661	−0.548304	+	0.836279i	$0.684726\pi$
$648$	−1.00000	−0.0392837
$649$	−16.6573	−0.653857
$650$	1.84509	0.0723704
$651$	−6.56887	−0.257454
$652$	−6.74310	−0.264080
$653$	7.48860	0.293052	0.146526	−	0.989207i	$-0.453191\pi$
$653$	7.48860	0.293052	0.146526	+	0.989207i	$0.453191\pi$
$654$	1.00660	0.0393610
$655$	−48.0083	−1.87584
$656$	−6.64546	−0.259462
$657$	0.749759	0.0292509
$658$	3.00655	0.117207
$659$	42.7645	1.66587	0.832935	−	0.553371i	$-0.186659\pi$
$659$	42.7645	1.66587	0.832935	+	0.553371i	$0.186659\pi$
$660$	−15.0544	−0.585990
$661$	−17.1265	−0.666145	−0.333072	−	0.942901i	$-0.608085\pi$
$661$	−17.1265	−0.666145	−0.333072	+	0.942901i	$0.608085\pi$
$662$	0.966276	0.0375554
$663$	−3.39983	−0.132039
$664$	14.8800	0.577455
$665$	−2.15495	−0.0835652
$666$	10.2556	0.397396
$667$	1.18190	0.0457635
$668$	−19.0088	−0.735471
$669$	18.1400	0.701334
$670$	16.8218	0.649882
$671$	0.922799	0.0356243
$672$	−0.928685	−0.0358248
$673$	0.822191	0.0316931	0.0158466	−	0.999874i	$-0.494956\pi$
$673$	0.822191	0.0316931	0.0158466	+	0.999874i	$0.494956\pi$
$674$	26.3180	1.01373
$675$	−0.384381	−0.0147948
$676$	10.0416	0.386214
$677$	26.6797	1.02538	0.512692	−	0.858573i	$-0.328648\pi$
$677$	26.6797	1.02538	0.512692	+	0.858573i	$0.328648\pi$
$678$	16.1312	0.619515
$679$	15.3931	0.590733
$680$	1.64350	0.0630253
$681$	−12.5371	−0.480421
$682$	45.8898	1.75721
$683$	−26.9076	−1.02959	−0.514796	−	0.857313i	$-0.672132\pi$
$683$	−26.9076	−1.02959	−0.514796	+	0.857313i	$0.672132\pi$
$684$	1.00000	0.0382360
$685$	48.0034	1.83412
$686$	−12.2006	−0.465823
$687$	−27.8525	−1.06264
$688$	−2.77605	−0.105836
$689$	−4.80016	−0.182872
$690$	7.68573	0.292591
$691$	−33.0837	−1.25856	−0.629281	−	0.777178i	$-0.716651\pi$
$691$	−33.0837	−1.25856	−0.629281	+	0.777178i	$0.716651\pi$
$692$	22.5020	0.855396
$693$	−6.02508	−0.228874
$694$	23.9061	0.907463
$695$	−12.5080	−0.474455
$696$	0.356833	0.0135257
$697$	4.70681	0.178283
$698$	−16.1968	−0.613057
$699$	2.74466	0.103812
$700$	−0.356969	−0.0134922
$701$	−47.0075	−1.77545	−0.887723	−	0.460377i	$-0.847714\pi$
$701$	−47.0075	−1.77545	−0.887723	+	0.460377i	$0.847714\pi$
$702$	−4.80016	−0.181170
$703$	−10.2556	−0.386796
$704$	6.48775	0.244516
$705$	−7.51220	−0.282926
$706$	5.55863	0.209202
$707$	11.0813	0.416753
$708$	2.56750	0.0964927
$709$	−23.0395	−0.865266	−0.432633	−	0.901570i	$-0.642415\pi$
$709$	−23.0395	−0.865266	−0.432633	+	0.901570i	$0.642415\pi$
$710$	−17.4222	−0.653843
$711$	5.37725	0.201662
$712$	5.61543	0.210447
$713$	−23.4282	−0.877393
$714$	0.657764	0.0246162
$715$	−72.2634	−2.70250
$716$	10.8662	0.406090
$717$	−9.42043	−0.351812
$718$	10.2345	0.381949
$719$	21.4179	0.798753	0.399377	−	0.916787i	$-0.369227\pi$
$719$	21.4179	0.798753	0.399377	+	0.916787i	$0.369227\pi$
$720$	2.32043	0.0864772
$721$	2.78411	0.103686
$722$	−1.00000	−0.0372161
$723$	19.9785	0.743010
$724$	23.9515	0.890151
$725$	0.137160	0.00509398
$726$	31.0909	1.15389
$727$	8.18334	0.303503	0.151752	−	0.988419i	$-0.451509\pi$
$727$	8.18334	0.303503	0.151752	+	0.988419i	$0.451509\pi$
$728$	−4.45784	−0.165219
$729$	1.00000	0.0370370
$730$	−1.73976	−0.0643914
$731$	1.96621	0.0727228
$732$	−0.142237	−0.00525723
$733$	−39.0982	−1.44412	−0.722062	−	0.691829i	$-0.756805\pi$
$733$	−39.0982	−1.44412	−0.722062	+	0.691829i	$0.756805\pi$
$734$	17.9873	0.663922
$735$	14.2417	0.525314
$736$	−3.31220	−0.122089
$737$	−47.0325	−1.73246
$738$	6.64546	0.244623
$739$	31.9365	1.17480	0.587401	−	0.809296i	$-0.300151\pi$
$739$	31.9365	1.17480	0.587401	+	0.809296i	$0.300151\pi$
$740$	−23.7973	−0.874807
$741$	4.80016	0.176338
$742$	0.928685	0.0340931
$743$	23.2360	0.852446	0.426223	−	0.904618i	$-0.359844\pi$
$743$	23.2360	0.852446	0.426223	+	0.904618i	$0.359844\pi$
$744$	−7.07329	−0.259320
$745$	−15.3902	−0.563852
$746$	−20.4618	−0.749161
$747$	−14.8800	−0.544430
$748$	−4.59511	−0.168014
$749$	−3.32440	−0.121471
$750$	−10.7102	−0.391081
$751$	−25.9048	−0.945278	−0.472639	−	0.881256i	$-0.656699\pi$
$751$	−25.9048	−0.945278	−0.472639	+	0.881256i	$0.656699\pi$
$752$	3.23742	0.118057
$753$	−1.33336	−0.0485905
$754$	1.71286	0.0623785
$755$	−36.8877	−1.34248
$756$	0.928685	0.0337760
$757$	−7.42098	−0.269720	−0.134860	−	0.990865i	$-0.543058\pi$
$757$	−7.42098	−0.269720	−0.134860	+	0.990865i	$0.543058\pi$
$758$	−16.5718	−0.601914
$759$	−21.4888	−0.779993
$760$	−2.32043	−0.0841707
$761$	13.9978	0.507422	0.253711	−	0.967280i	$-0.418349\pi$
$761$	13.9978	0.507422	0.253711	+	0.967280i	$0.418349\pi$
$762$	−13.0892	−0.474172
$763$	−0.934812	−0.0338425
$764$	−10.3073	−0.372906
$765$	−1.64350	−0.0594208
$766$	9.70200	0.350547
$767$	12.3244	0.445009
$768$	−1.00000	−0.0360844
$769$	−10.6443	−0.383845	−0.191922	−	0.981410i	$-0.561472\pi$
$769$	−10.6443	−0.383845	−0.191922	+	0.981410i	$0.561472\pi$
$770$	13.9808	0.503832
$771$	−4.34905	−0.156627
$772$	20.4735	0.736858
$773$	−14.7376	−0.530075	−0.265038	−	0.964238i	$-0.585384\pi$
$773$	−14.7376	−0.530075	−0.265038	+	0.964238i	$0.585384\pi$
$774$	2.77605	0.0997832
$775$	−2.71884	−0.0976636
$776$	16.5751	0.595013
$777$	−9.52420	−0.341679
$778$	32.4457	1.16323
$779$	−6.64546	−0.238098
$780$	11.1384	0.398820
$781$	48.7113	1.74303
$782$	2.34595	0.0838910
$783$	−0.356833	−0.0127522
$784$	−6.13754	−0.219198
$785$	−7.98992	−0.285173
$786$	−20.6894	−0.737967
$787$	4.33473	0.154516	0.0772582	−	0.997011i	$-0.475383\pi$
$787$	4.33473	0.154516	0.0772582	+	0.997011i	$0.475383\pi$
$788$	20.1739	0.718664
$789$	29.6733	1.05640
$790$	−12.4775	−0.443930
$791$	−14.9808	−0.532656
$792$	−6.48775	−0.230532
$793$	−0.682761	−0.0242456
$794$	−26.7674	−0.949938
$795$	−2.32043	−0.0822971
$796$	22.8455	0.809739
$797$	24.3759	0.863438	0.431719	−	0.902008i	$-0.357907\pi$
$797$	24.3759	0.863438	0.431719	+	0.902008i	$0.357907\pi$
$798$	−0.928685	−0.0328751
$799$	−2.29298	−0.0811200
$800$	−0.384381	−0.0135899
$801$	−5.61543	−0.198412
$802$	2.50288	0.0883799
$803$	4.86425	0.171656
$804$	7.24943	0.255668
$805$	−7.13762	−0.251568
$806$	−33.9530	−1.19594
$807$	20.1049	0.707726
$808$	11.9322	0.419773
$809$	16.0680	0.564922	0.282461	−	0.959279i	$-0.408849\pi$
$809$	16.0680	0.564922	0.282461	+	0.959279i	$0.408849\pi$
$810$	−2.32043	−0.0815315
$811$	−36.9396	−1.29713	−0.648563	−	0.761161i	$-0.724630\pi$
$811$	−36.9396	−1.29713	−0.648563	+	0.761161i	$0.724630\pi$
$812$	−0.331385	−0.0116293
$813$	−24.5383	−0.860594
$814$	66.5356	2.33207
$815$	−15.6469	−0.548086
$816$	0.708274	0.0247946
$817$	−2.77605	−0.0971218
$818$	17.0622	0.596565
$819$	4.45784	0.155770
$820$	−15.4203	−0.538501
$821$	13.7438	0.479660	0.239830	−	0.970815i	$-0.422908\pi$
$821$	13.7438	0.479660	0.239830	+	0.970815i	$0.422908\pi$
$822$	20.6873	0.721553
$823$	−53.2972	−1.85782	−0.928912	−	0.370301i	$-0.879254\pi$
$823$	−53.2972	−1.85782	−0.928912	+	0.370301i	$0.879254\pi$
$824$	2.99790	0.104437
$825$	−2.49377	−0.0868219
$826$	−2.38440	−0.0829640
$827$	−23.9406	−0.832498	−0.416249	−	0.909251i	$-0.636655\pi$
$827$	−23.9406	−0.832498	−0.416249	+	0.909251i	$0.636655\pi$
$828$	3.31220	0.115107
$829$	42.1312	1.46328	0.731638	−	0.681693i	$-0.238756\pi$
$829$	42.1312	1.46328	0.731638	+	0.681693i	$0.238756\pi$
$830$	34.5279	1.19848
$831$	22.5599	0.782595
$832$	−4.80016	−0.166416
$833$	4.34707	0.150617
$834$	−5.39038	−0.186654
$835$	−44.1085	−1.52644
$836$	6.48775	0.224384
$837$	7.07329	0.244489
$838$	−24.5515	−0.848116
$839$	9.36197	0.323211	0.161606	−	0.986855i	$-0.448333\pi$
$839$	9.36197	0.323211	0.161606	+	0.986855i	$0.448333\pi$
$840$	−2.15495	−0.0743527
$841$	−28.8727	−0.995609
$842$	−34.5061	−1.18916
$843$	−26.9567	−0.928437
$844$	10.9096	0.375524
$845$	23.3007	0.801569
$846$	−3.23742	−0.111305
$847$	−28.8737	−0.992112
$848$	1.00000	0.0343401
$849$	18.0782	0.620442
$850$	0.272247	0.00933800
$851$	−33.9686	−1.16443
$852$	−7.50819	−0.257226
$853$	−2.79261	−0.0956171	−0.0478085	−	0.998857i	$-0.515224\pi$
$853$	−2.79261	−0.0956171	−0.0478085	+	0.998857i	$0.515224\pi$
$854$	0.132094	0.00452015
$855$	2.32043	0.0793569
$856$	−3.57968	−0.122351
$857$	−11.4975	−0.392748	−0.196374	−	0.980529i	$-0.562917\pi$
$857$	−11.4975	−0.392748	−0.196374	+	0.980529i	$0.562917\pi$
$858$	−31.1423	−1.06318
$859$	16.5285	0.563944	0.281972	−	0.959423i	$-0.409011\pi$
$859$	16.5285	0.563944	0.281972	+	0.959423i	$0.409011\pi$
$860$	−6.44163	−0.219658
$861$	−6.17154	−0.210326
$862$	−5.76807	−0.196461
$863$	−8.40461	−0.286096	−0.143048	−	0.989716i	$-0.545690\pi$
$863$	−8.40461	−0.286096	−0.143048	+	0.989716i	$0.545690\pi$
$864$	1.00000	0.0340207
$865$	52.2142	1.77533
$866$	28.0808	0.954224
$867$	16.4983	0.560313
$868$	6.56887	0.222962
$869$	34.8862	1.18343
$870$	0.828004	0.0280720
$871$	34.7984	1.17910
$872$	−1.00660	−0.0340877
$873$	−16.5751	−0.560983
$874$	−3.31220	−0.112037
$875$	9.94641	0.336250
$876$	−0.749759	−0.0253320
$877$	−4.68297	−0.158133	−0.0790664	−	0.996869i	$-0.525194\pi$
$877$	−4.68297	−0.158133	−0.0790664	+	0.996869i	$0.525194\pi$
$878$	−6.14117	−0.207255
$879$	7.72353	0.260508
$880$	15.0544	0.507482
$881$	−2.37000	−0.0798475	−0.0399237	−	0.999203i	$-0.512712\pi$
$881$	−2.37000	−0.0798475	−0.0399237	+	0.999203i	$0.512712\pi$
$882$	6.13754	0.206662
$883$	0.0612644	0.00206171	0.00103086	−	0.999999i	$-0.499672\pi$
$883$	0.0612644	0.00206171	0.00103086	+	0.999999i	$0.499672\pi$
$884$	3.39983	0.114349
$885$	5.95770	0.200266
$886$	−5.09396	−0.171135
$887$	36.6727	1.23135	0.615674	−	0.788001i	$-0.288884\pi$
$887$	36.6727	1.23135	0.615674	+	0.788001i	$0.288884\pi$
$888$	−10.2556	−0.344155
$889$	12.1558	0.407691
$890$	13.0302	0.436773
$891$	6.48775	0.217348
$892$	−18.1400	−0.607373
$893$	3.23742	0.108336
$894$	−6.63247	−0.221823
$895$	25.2143	0.842821
$896$	0.928685	0.0310252
$897$	15.8991	0.530856
$898$	−1.46647	−0.0489368
$899$	−2.52398	−0.0841795
$900$	0.384381	0.0128127
$901$	−0.708274	−0.0235960
$902$	43.1141	1.43554
$903$	−2.57808	−0.0857931
$904$	−16.1312	−0.536515
$905$	55.5777	1.84747
$906$	−15.8970	−0.528141
$907$	17.9641	0.596489	0.298244	−	0.954490i	$-0.403599\pi$
$907$	17.9641	0.596489	0.298244	+	0.954490i	$0.403599\pi$
$908$	12.5371	0.416057
$909$	−11.9322	−0.395766
$910$	−10.3441	−0.342903
$911$	2.05664	0.0681394	0.0340697	−	0.999419i	$-0.489153\pi$
$911$	2.05664	0.0681394	0.0340697	+	0.999419i	$0.489153\pi$
$912$	−1.00000	−0.0331133
$913$	−96.5376	−3.19493
$914$	−1.10625	−0.0365916
$915$	−0.330051	−0.0109111
$916$	27.8525	0.920272
$917$	19.2140	0.634501
$918$	−0.708274	−0.0233765
$919$	−25.4136	−0.838318	−0.419159	−	0.907913i	$-0.637675\pi$
$919$	−25.4136	−0.838318	−0.419159	+	0.907913i	$0.637675\pi$
$920$	−7.68573	−0.253391
$921$	17.9903	0.592800
$922$	1.68546	0.0555078
$923$	−36.0405	−1.18629
$924$	6.02508	0.198211
$925$	−3.94205	−0.129614
$926$	37.7007	1.23892
$927$	−2.99790	−0.0984640
$928$	−0.356833	−0.0117136
$929$	51.4396	1.68768	0.843840	−	0.536595i	$-0.180290\pi$
$929$	51.4396	1.68768	0.843840	+	0.536595i	$0.180290\pi$
$930$	−16.4131	−0.538206
$931$	−6.13754	−0.201150
$932$	−2.74466	−0.0899042
$933$	1.74113	0.0570021
$934$	−6.90176	−0.225833
$935$	−10.6626	−0.348705
$936$	4.80016	0.156898
$937$	6.70772	0.219132	0.109566	−	0.993980i	$-0.465054\pi$
$937$	6.70772	0.219132	0.109566	+	0.993980i	$0.465054\pi$
$938$	−6.73244	−0.219822
$939$	5.18339	0.169153
$940$	7.51220	0.245021
$941$	−2.56104	−0.0834876	−0.0417438	−	0.999128i	$-0.513291\pi$
$941$	−2.56104	−0.0834876	−0.0417438	+	0.999128i	$0.513291\pi$
$942$	−3.44330	−0.112189
$943$	−22.0111	−0.716781
$944$	−2.56750	−0.0835651
$945$	2.15495	0.0701004
$946$	18.0103	0.585567
$947$	−10.1210	−0.328890	−0.164445	−	0.986386i	$-0.552583\pi$
$947$	−10.1210	−0.328890	−0.164445	+	0.986386i	$0.552583\pi$
$948$	−5.37725	−0.174645
$949$	−3.59896	−0.116827
$950$	−0.384381	−0.0124710
$951$	−10.6186	−0.344332
$952$	−0.657764	−0.0213183
$953$	44.7659	1.45011	0.725054	−	0.688692i	$-0.241815\pi$
$953$	44.7659	1.45011	0.725054	+	0.688692i	$0.241815\pi$
$954$	−1.00000	−0.0323762
$955$	−23.9174	−0.773950
$956$	9.42043	0.304678
$957$	−2.31504	−0.0748347
$958$	2.39586	0.0774069
$959$	−19.2120	−0.620388
$960$	−2.32043	−0.0748915
$961$	19.0315	0.613919
$962$	−49.2284	−1.58719
$963$	3.57968	0.115354
$964$	−19.9785	−0.643465
$965$	47.5073	1.52931
$966$	−3.07600	−0.0989686
$967$	60.8172	1.95575	0.977874	−	0.209194i	$-0.0670841\pi$
$967$	60.8172	1.95575	0.977874	+	0.209194i	$0.0670841\pi$
$968$	−31.0909	−0.999300
$969$	0.708274	0.0227531
$970$	38.4614	1.23492
$971$	−36.8038	−1.18109	−0.590546	−	0.807004i	$-0.701087\pi$
$971$	−36.8038	−1.18109	−0.590546	+	0.807004i	$0.701087\pi$
$972$	−1.00000	−0.0320750
$973$	5.00597	0.160484
$974$	−39.7517	−1.27373
$975$	1.84509	0.0590902
$976$	0.142237	0.00455290
$977$	−4.54247	−0.145326	−0.0726632	−	0.997357i	$-0.523150\pi$
$977$	−4.54247	−0.145326	−0.0726632	+	0.997357i	$0.523150\pi$
$978$	−6.74310	−0.215621
$979$	−36.4315	−1.16436
$980$	−14.2417	−0.454935
$981$	1.00660	0.0321382
$982$	39.7767	1.26933
$983$	−25.9561	−0.827872	−0.413936	−	0.910306i	$-0.635846\pi$
$983$	−25.9561	−0.827872	−0.413936	+	0.910306i	$0.635846\pi$
$984$	−6.64546	−0.211850
$985$	46.8120	1.49155
$986$	0.252735	0.00804874
$987$	3.00655	0.0956995
$988$	−4.80016	−0.152714
$989$	−9.19486	−0.292379
$990$	−15.0544	−0.478459
$991$	49.4258	1.57006	0.785032	−	0.619456i	$-0.212647\pi$
$991$	49.4258	1.57006	0.785032	+	0.619456i	$0.212647\pi$
$992$	7.07329	0.224577
$993$	0.966276	0.0306638
$994$	6.97274	0.221162
$995$	53.0114	1.68058
$996$	14.8800	0.471490
$997$	4.72009	0.149487	0.0747433	−	0.997203i	$-0.476186\pi$
$997$	4.72009	0.149487	0.0747433	+	0.997203i	$0.476186\pi$
$998$	−40.4710	−1.28109
$999$	10.2556	0.324472

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6042.2.a.bd.1.8	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6042.2.a.bd.1.8	✓	11	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:	\( N \)	\(=\)	\( 6042 = 2 \cdot 3 \cdot 19 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6042.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.32043 q^{5} +1.00000 q^{6} -0.928685 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.32043 q^{5} +1.00000 q^{6} -0.928685 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.32043 q^{10} +6.48775 q^{11} -1.00000 q^{12} -4.80016 q^{13} +0.928685 q^{14} -2.32043 q^{15} +1.00000 q^{16} -0.708274 q^{17} -1.00000 q^{18} +1.00000 q^{19} +2.32043 q^{20} +0.928685 q^{21} -6.48775 q^{22} +3.31220 q^{23} +1.00000 q^{24} +0.384381 q^{25} +4.80016 q^{26} -1.00000 q^{27} -0.928685 q^{28} +0.356833 q^{29} +2.32043 q^{30} -7.07329 q^{31} -1.00000 q^{32} -6.48775 q^{33} +0.708274 q^{34} -2.15495 q^{35} +1.00000 q^{36} -10.2556 q^{37} -1.00000 q^{38} +4.80016 q^{39} -2.32043 q^{40} -6.64546 q^{41} -0.928685 q^{42} -2.77605 q^{43} +6.48775 q^{44} +2.32043 q^{45} -3.31220 q^{46} +3.23742 q^{47} -1.00000 q^{48} -6.13754 q^{49} -0.384381 q^{50} +0.708274 q^{51} -4.80016 q^{52} +1.00000 q^{53} +1.00000 q^{54} +15.0544 q^{55} +0.928685 q^{56} -1.00000 q^{57} -0.356833 q^{58} -2.56750 q^{59} -2.32043 q^{60} +0.142237 q^{61} +7.07329 q^{62} -0.928685 q^{63} +1.00000 q^{64} -11.1384 q^{65} +6.48775 q^{66} -7.24943 q^{67} -0.708274 q^{68} -3.31220 q^{69} +2.15495 q^{70} +7.50819 q^{71} -1.00000 q^{72} +0.749759 q^{73} +10.2556 q^{74} -0.384381 q^{75} +1.00000 q^{76} -6.02508 q^{77} -4.80016 q^{78} +5.37725 q^{79} +2.32043 q^{80} +1.00000 q^{81} +6.64546 q^{82} -14.8800 q^{83} +0.928685 q^{84} -1.64350 q^{85} +2.77605 q^{86} -0.356833 q^{87} -6.48775 q^{88} -5.61543 q^{89} -2.32043 q^{90} +4.45784 q^{91} +3.31220 q^{92} +7.07329 q^{93} -3.23742 q^{94} +2.32043 q^{95} +1.00000 q^{96} -16.5751 q^{97} +6.13754 q^{98} +6.48775 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 11 q^{2} - 11 q^{3} + 11 q^{4} + 2 q^{5} + 11 q^{6} - 2 q^{7} - 11 q^{8} + 11 q^{9}+O(q^{10}) \) 11 * q - 11 * q^2 - 11 * q^3 + 11 * q^4 + 2 * q^5 + 11 * q^6 - 2 * q^7 - 11 * q^8 + 11 * q^9	\( 11 q - 11 q^{2} - 11 q^{3} + 11 q^{4} + 2 q^{5} + 11 q^{6} - 2 q^{7} - 11 q^{8} + 11 q^{9} - 2 q^{10} - 6 q^{11} - 11 q^{12} - 7 q^{13} + 2 q^{14} - 2 q^{15} + 11 q^{16} - 16 q^{17} - 11 q^{18} + 11 q^{19} + 2 q^{20} + 2 q^{21} + 6 q^{22} - 11 q^{23} + 11 q^{24} + 19 q^{25} + 7 q^{26} - 11 q^{27} - 2 q^{28} - 7 q^{29} + 2 q^{30} + 12 q^{31} - 11 q^{32} + 6 q^{33} + 16 q^{34} - 5 q^{35} + 11 q^{36} + 3 q^{37} - 11 q^{38} + 7 q^{39} - 2 q^{40} + 11 q^{41} - 2 q^{42} + 7 q^{43} - 6 q^{44} + 2 q^{45} + 11 q^{46} - 37 q^{47} - 11 q^{48} + 23 q^{49} - 19 q^{50} + 16 q^{51} - 7 q^{52} + 11 q^{53} + 11 q^{54} - 11 q^{55} + 2 q^{56} - 11 q^{57} + 7 q^{58} - 16 q^{59} - 2 q^{60} + 24 q^{61} - 12 q^{62} - 2 q^{63} + 11 q^{64} - 7 q^{65} - 6 q^{66} - 28 q^{67} - 16 q^{68} + 11 q^{69} + 5 q^{70} + 4 q^{71} - 11 q^{72} - 7 q^{73} - 3 q^{74} - 19 q^{75} + 11 q^{76} - 13 q^{77} - 7 q^{78} + 5 q^{79} + 2 q^{80} + 11 q^{81} - 11 q^{82} - 11 q^{83} + 2 q^{84} - 11 q^{85} - 7 q^{86} + 7 q^{87} + 6 q^{88} - 10 q^{89} - 2 q^{90} - 24 q^{91} - 11 q^{92} - 12 q^{93} + 37 q^{94} + 2 q^{95} + 11 q^{96} - 24 q^{97} - 23 q^{98} - 6 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - 11 * q^3 + 11 * q^4 + 2 * q^5 + 11 * q^6 - 2 * q^7 - 11 * q^8 + 11 * q^9 - 2 * q^10 - 6 * q^11 - 11 * q^12 - 7 * q^13 + 2 * q^14 - 2 * q^15 + 11 * q^16 - 16 * q^17 - 11 * q^18 + 11 * q^19 + 2 * q^20 + 2 * q^21 + 6 * q^22 - 11 * q^23 + 11 * q^24 + 19 * q^25 + 7 * q^26 - 11 * q^27 - 2 * q^28 - 7 * q^29 + 2 * q^30 + 12 * q^31 - 11 * q^32 + 6 * q^33 + 16 * q^34 - 5 * q^35 + 11 * q^36 + 3 * q^37 - 11 * q^38 + 7 * q^39 - 2 * q^40 + 11 * q^41 - 2 * q^42 + 7 * q^43 - 6 * q^44 + 2 * q^45 + 11 * q^46 - 37 * q^47 - 11 * q^48 + 23 * q^49 - 19 * q^50 + 16 * q^51 - 7 * q^52 + 11 * q^53 + 11 * q^54 - 11 * q^55 + 2 * q^56 - 11 * q^57 + 7 * q^58 - 16 * q^59 - 2 * q^60 + 24 * q^61 - 12 * q^62 - 2 * q^63 + 11 * q^64 - 7 * q^65 - 6 * q^66 - 28 * q^67 - 16 * q^68 + 11 * q^69 + 5 * q^70 + 4 * q^71 - 11 * q^72 - 7 * q^73 - 3 * q^74 - 19 * q^75 + 11 * q^76 - 13 * q^77 - 7 * q^78 + 5 * q^79 + 2 * q^80 + 11 * q^81 - 11 * q^82 - 11 * q^83 + 2 * q^84 - 11 * q^85 - 7 * q^86 + 7 * q^87 + 6 * q^88 - 10 * q^89 - 2 * q^90 - 24 * q^91 - 11 * q^92 - 12 * q^93 + 37 * q^94 + 2 * q^95 + 11 * q^96 - 24 * q^97 - 23 * q^98 - 6 * q^99

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