LMFDB - Embedded newform 4026.2.a.y.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4026, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4026 = 2 \cdot 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4026.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.1477718538$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 2x^{6} - 21x^{5} + 39x^{4} + 89x^{3} - 100x^{2} - 96x + 8 $ x^7 - 2x^6 - 21x^5 + 39x^4 + 89x^3 - 100x^2 - 96x + 8
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			1.2
Root			$3.01987$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.01987 q^{5} +1.00000 q^{6} +4.36357 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.01987 q^{5} +1.00000 q^{6} +4.36357 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.01987 q^{10} -1.00000 q^{11} -1.00000 q^{12} +0.0368976 q^{13} -4.36357 q^{14} +3.01987 q^{15} +1.00000 q^{16} -0.558875 q^{17} -1.00000 q^{18} +2.94619 q^{19} -3.01987 q^{20} -4.36357 q^{21} +1.00000 q^{22} +0.521977 q^{23} +1.00000 q^{24} +4.11962 q^{25} -0.0368976 q^{26} -1.00000 q^{27} +4.36357 q^{28} -10.5536 q^{29} -3.01987 q^{30} -2.62382 q^{31} -1.00000 q^{32} +1.00000 q^{33} +0.558875 q^{34} -13.1774 q^{35} +1.00000 q^{36} -8.18081 q^{37} -2.94619 q^{38} -0.0368976 q^{39} +3.01987 q^{40} +0.597641 q^{41} +4.36357 q^{42} +3.12983 q^{43} -1.00000 q^{44} -3.01987 q^{45} -0.521977 q^{46} +10.3693 q^{47} -1.00000 q^{48} +12.0408 q^{49} -4.11962 q^{50} +0.558875 q^{51} +0.0368976 q^{52} -0.0266868 q^{53} +1.00000 q^{54} +3.01987 q^{55} -4.36357 q^{56} -2.94619 q^{57} +10.5536 q^{58} +2.47353 q^{59} +3.01987 q^{60} -1.00000 q^{61} +2.62382 q^{62} +4.36357 q^{63} +1.00000 q^{64} -0.111426 q^{65} -1.00000 q^{66} -5.64725 q^{67} -0.558875 q^{68} -0.521977 q^{69} +13.1774 q^{70} +0.263712 q^{71} -1.00000 q^{72} -1.59228 q^{73} +8.18081 q^{74} -4.11962 q^{75} +2.94619 q^{76} -4.36357 q^{77} +0.0368976 q^{78} +16.9297 q^{79} -3.01987 q^{80} +1.00000 q^{81} -0.597641 q^{82} -3.93936 q^{83} -4.36357 q^{84} +1.68773 q^{85} -3.12983 q^{86} +10.5536 q^{87} +1.00000 q^{88} -1.68773 q^{89} +3.01987 q^{90} +0.161005 q^{91} +0.521977 q^{92} +2.62382 q^{93} -10.3693 q^{94} -8.89711 q^{95} +1.00000 q^{96} -17.9409 q^{97} -12.0408 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} - 2 q^{5} + 7 q^{6} + q^{7} - 7 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 - 2 * q^5 + 7 * q^6 + q^7 - 7 * q^8 + 7 * q^9	$ 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} - 2 q^{5} + 7 q^{6} + q^{7} - 7 q^{8} + 7 q^{9} + 2 q^{10} - 7 q^{11} - 7 q^{12} - q^{14} + 2 q^{15} + 7 q^{16} + 3 q^{17} - 7 q^{18} - 5 q^{19} - 2 q^{20} - q^{21} + 7 q^{22} - 3 q^{23} + 7 q^{24} + 11 q^{25} - 7 q^{27} + q^{28} - 14 q^{29} - 2 q^{30} + 5 q^{31} - 7 q^{32} + 7 q^{33} - 3 q^{34} - 9 q^{35} + 7 q^{36} + 14 q^{37} + 5 q^{38} + 2 q^{40} - 7 q^{41} + q^{42} + q^{43} - 7 q^{44} - 2 q^{45} + 3 q^{46} - 7 q^{48} - 11 q^{50} - 3 q^{51} - 3 q^{53} + 7 q^{54} + 2 q^{55} - q^{56} + 5 q^{57} + 14 q^{58} - 14 q^{59} + 2 q^{60} - 7 q^{61} - 5 q^{62} + q^{63} + 7 q^{64} - 10 q^{65} - 7 q^{66} + 3 q^{68} + 3 q^{69} + 9 q^{70} - 22 q^{71} - 7 q^{72} + q^{73} - 14 q^{74} - 11 q^{75} - 5 q^{76} - q^{77} + 10 q^{79} - 2 q^{80} + 7 q^{81} + 7 q^{82} - 17 q^{83} - q^{84} + 18 q^{85} - q^{86} + 14 q^{87} + 7 q^{88} - 18 q^{89} + 2 q^{90} + 21 q^{91} - 3 q^{92} - 5 q^{93} - 41 q^{95} + 7 q^{96} + 25 q^{97} - 7 q^{99}+O(q^{100}) $ 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 - 2 * q^5 + 7 * q^6 + q^7 - 7 * q^8 + 7 * q^9 + 2 * q^10 - 7 * q^11 - 7 * q^12 - q^14 + 2 * q^15 + 7 * q^16 + 3 * q^17 - 7 * q^18 - 5 * q^19 - 2 * q^20 - q^21 + 7 * q^22 - 3 * q^23 + 7 * q^24 + 11 * q^25 - 7 * q^27 + q^28 - 14 * q^29 - 2 * q^30 + 5 * q^31 - 7 * q^32 + 7 * q^33 - 3 * q^34 - 9 * q^35 + 7 * q^36 + 14 * q^37 + 5 * q^38 + 2 * q^40 - 7 * q^41 + q^42 + q^43 - 7 * q^44 - 2 * q^45 + 3 * q^46 - 7 * q^48 - 11 * q^50 - 3 * q^51 - 3 * q^53 + 7 * q^54 + 2 * q^55 - q^56 + 5 * q^57 + 14 * q^58 - 14 * q^59 + 2 * q^60 - 7 * q^61 - 5 * q^62 + q^63 + 7 * q^64 - 10 * q^65 - 7 * q^66 + 3 * q^68 + 3 * q^69 + 9 * q^70 - 22 * q^71 - 7 * q^72 + q^73 - 14 * q^74 - 11 * q^75 - 5 * q^76 - q^77 + 10 * q^79 - 2 * q^80 + 7 * q^81 + 7 * q^82 - 17 * q^83 - q^84 + 18 * q^85 - q^86 + 14 * q^87 + 7 * q^88 - 18 * q^89 + 2 * q^90 + 21 * q^91 - 3 * q^92 - 5 * q^93 - 41 * q^95 + 7 * q^96 + 25 * q^97 - 7 * 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
$5$	−3.01987	−1.35053	−0.675264	−	0.737576i	$-0.735970\pi$
$5$	−3.01987	−1.35053	−0.675264	+	0.737576i	$0.735970\pi$
$6$	1.00000	0.408248
$7$	4.36357	1.64928	0.824638	−	0.565661i	$-0.191379\pi$
$7$	4.36357	1.64928	0.824638	+	0.565661i	$0.191379\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	3.01987	0.954967
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−1.00000	−0.288675
$13$	0.0368976	0.0102335	0.00511677	−	0.999987i	$-0.498371\pi$
$13$	0.0368976	0.0102335	0.00511677	+	0.999987i	$0.498371\pi$
$14$	−4.36357	−1.16621
$15$	3.01987	0.779727
$16$	1.00000	0.250000
$17$	−0.558875	−0.135547	−0.0677735	−	0.997701i	$-0.521590\pi$
$17$	−0.558875	−0.135547	−0.0677735	+	0.997701i	$0.521590\pi$
$18$	−1.00000	−0.235702
$19$	2.94619	0.675903	0.337951	−	0.941164i	$-0.390266\pi$
$19$	2.94619	0.675903	0.337951	+	0.941164i	$0.390266\pi$
$20$	−3.01987	−0.675264
$21$	−4.36357	−0.952210
$22$	1.00000	0.213201
$23$	0.521977	0.108840	0.0544199	−	0.998518i	$-0.482669\pi$
$23$	0.521977	0.108840	0.0544199	+	0.998518i	$0.482669\pi$
$24$	1.00000	0.204124
$25$	4.11962	0.823924
$26$	−0.0368976	−0.00723621
$27$	−1.00000	−0.192450
$28$	4.36357	0.824638
$29$	−10.5536	−1.95976	−0.979878	−	0.199598i	$-0.936036\pi$
$29$	−10.5536	−1.95976	−0.979878	+	0.199598i	$0.936036\pi$
$30$	−3.01987	−0.551350
$31$	−2.62382	−0.471253	−0.235626	−	0.971844i	$-0.575714\pi$
$31$	−2.62382	−0.471253	−0.235626	+	0.971844i	$0.575714\pi$
$32$	−1.00000	−0.176777
$33$	1.00000	0.174078
$34$	0.558875	0.0958462
$35$	−13.1774	−2.22739
$36$	1.00000	0.166667
$37$	−8.18081	−1.34492	−0.672459	−	0.740135i	$-0.734762\pi$
$37$	−8.18081	−1.34492	−0.672459	+	0.740135i	$0.734762\pi$
$38$	−2.94619	−0.477935
$39$	−0.0368976	−0.00590834
$40$	3.01987	0.477483
$41$	0.597641	0.0933359	0.0466679	−	0.998910i	$-0.485140\pi$
$41$	0.597641	0.0933359	0.0466679	+	0.998910i	$0.485140\pi$
$42$	4.36357	0.673314
$43$	3.12983	0.477294	0.238647	−	0.971106i	$-0.423296\pi$
$43$	3.12983	0.477294	0.238647	+	0.971106i	$0.423296\pi$
$44$	−1.00000	−0.150756
$45$	−3.01987	−0.450176
$46$	−0.521977	−0.0769613
$47$	10.3693	1.51253	0.756263	−	0.654268i	$-0.227023\pi$
$47$	10.3693	1.51253	0.756263	+	0.654268i	$0.227023\pi$
$48$	−1.00000	−0.144338
$49$	12.0408	1.72011
$50$	−4.11962	−0.582602
$51$	0.558875	0.0782581
$52$	0.0368976	0.00511677
$53$	−0.0266868	−0.00366571	−0.00183285	−	0.999998i	$-0.500583\pi$
$53$	−0.0266868	−0.00366571	−0.00183285	+	0.999998i	$0.500583\pi$
$54$	1.00000	0.136083
$55$	3.01987	0.407199
$56$	−4.36357	−0.583107
$57$	−2.94619	−0.390233
$58$	10.5536	1.38576
$59$	2.47353	0.322027	0.161013	−	0.986952i	$-0.448524\pi$
$59$	2.47353	0.322027	0.161013	+	0.986952i	$0.448524\pi$
$60$	3.01987	0.389864
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	2.62382	0.333226
$63$	4.36357	0.549759
$64$	1.00000	0.125000
$65$	−0.111426	−0.0138207
$66$	−1.00000	−0.123091
$67$	−5.64725	−0.689921	−0.344960	−	0.938617i	$-0.612108\pi$
$67$	−5.64725	−0.689921	−0.344960	+	0.938617i	$0.612108\pi$
$68$	−0.558875	−0.0677735
$69$	−0.521977	−0.0628387
$70$	13.1774	1.57500
$71$	0.263712	0.0312968	0.0156484	−	0.999878i	$-0.495019\pi$
$71$	0.263712	0.0312968	0.0156484	+	0.999878i	$0.495019\pi$
$72$	−1.00000	−0.117851
$73$	−1.59228	−0.186362	−0.0931809	−	0.995649i	$-0.529703\pi$
$73$	−1.59228	−0.186362	−0.0931809	+	0.995649i	$0.529703\pi$
$74$	8.18081	0.951000
$75$	−4.11962	−0.475693
$76$	2.94619	0.337951
$77$	−4.36357	−0.497276
$78$	0.0368976	0.00417783
$79$	16.9297	1.90474	0.952371	−	0.304941i	$-0.0986369\pi$
$79$	16.9297	1.90474	0.952371	+	0.304941i	$0.0986369\pi$
$80$	−3.01987	−0.337632
$81$	1.00000	0.111111
$82$	−0.597641	−0.0659984
$83$	−3.93936	−0.432401	−0.216201	−	0.976349i	$-0.569366\pi$
$83$	−3.93936	−0.432401	−0.216201	+	0.976349i	$0.569366\pi$
$84$	−4.36357	−0.476105
$85$	1.68773	0.183060
$86$	−3.12983	−0.337498
$87$	10.5536	1.13147
$88$	1.00000	0.106600
$89$	−1.68773	−0.178899	−0.0894495	−	0.995991i	$-0.528511\pi$
$89$	−1.68773	−0.178899	−0.0894495	+	0.995991i	$0.528511\pi$
$90$	3.01987	0.318322
$91$	0.161005	0.0168779
$92$	0.521977	0.0544199
$93$	2.62382	0.272078
$94$	−10.3693	−1.06952
$95$	−8.89711	−0.912825
$96$	1.00000	0.102062
$97$	−17.9409	−1.82162	−0.910809	−	0.412828i	$-0.864541\pi$
$97$	−17.9409	−1.82162	−0.910809	+	0.412828i	$0.864541\pi$
$98$	−12.0408	−1.21630
$99$	−1.00000	−0.100504
$100$	4.11962	0.411962
$101$	3.16007	0.314438	0.157219	−	0.987564i	$-0.449747\pi$
$101$	3.16007	0.314438	0.157219	+	0.987564i	$0.449747\pi$
$102$	−0.558875	−0.0553368
$103$	−2.29864	−0.226492	−0.113246	−	0.993567i	$-0.536125\pi$
$103$	−2.29864	−0.226492	−0.113246	+	0.993567i	$0.536125\pi$
$104$	−0.0368976	−0.00361810
$105$	13.1774	1.28599
$106$	0.0266868	0.00259205
$107$	−2.19728	−0.212419	−0.106210	−	0.994344i	$-0.533871\pi$
$107$	−2.19728	−0.212419	−0.106210	+	0.994344i	$0.533871\pi$
$108$	−1.00000	−0.0962250
$109$	1.27730	0.122344	0.0611718	−	0.998127i	$-0.480516\pi$
$109$	1.27730	0.122344	0.0611718	+	0.998127i	$0.480516\pi$
$110$	−3.01987	−0.287933
$111$	8.18081	0.776488
$112$	4.36357	0.412319
$113$	−2.87511	−0.270468	−0.135234	−	0.990814i	$-0.543179\pi$
$113$	−2.87511	−0.270468	−0.135234	+	0.990814i	$0.543179\pi$
$114$	2.94619	0.275936
$115$	−1.57630	−0.146991
$116$	−10.5536	−0.979878
$117$	0.0368976	0.00341118
$118$	−2.47353	−0.227707
$119$	−2.43869	−0.223554
$120$	−3.01987	−0.275675
$121$	1.00000	0.0909091
$122$	1.00000	0.0905357
$123$	−0.597641	−0.0538875
$124$	−2.62382	−0.235626
$125$	2.65864	0.237796
$126$	−4.36357	−0.388738
$127$	−4.10279	−0.364064	−0.182032	−	0.983293i	$-0.558267\pi$
$127$	−4.10279	−0.364064	−0.182032	+	0.983293i	$0.558267\pi$
$128$	−1.00000	−0.0883883
$129$	−3.12983	−0.275566
$130$	0.111426	0.00977270
$131$	12.0757	1.05506	0.527529	−	0.849537i	$-0.323119\pi$
$131$	12.0757	1.05506	0.527529	+	0.849537i	$0.323119\pi$
$132$	1.00000	0.0870388
$133$	12.8559	1.11475
$134$	5.64725	0.487848
$135$	3.01987	0.259909
$136$	0.558875	0.0479231
$137$	−6.38845	−0.545802	−0.272901	−	0.962042i	$-0.587983\pi$
$137$	−6.38845	−0.545802	−0.272901	+	0.962042i	$0.587983\pi$
$138$	0.521977	0.0444336
$139$	0.678777	0.0575731	0.0287866	−	0.999586i	$-0.490836\pi$
$139$	0.678777	0.0575731	0.0287866	+	0.999586i	$0.490836\pi$
$140$	−13.1774	−1.11370
$141$	−10.3693	−0.873257
$142$	−0.263712	−0.0221302
$143$	−0.0368976	−0.00308553
$144$	1.00000	0.0833333
$145$	31.8705	2.64670
$146$	1.59228	0.131778
$147$	−12.0408	−0.993107
$148$	−8.18081	−0.672459
$149$	−11.1377	−0.912435	−0.456218	−	0.889868i	$-0.650796\pi$
$149$	−11.1377	−0.912435	−0.456218	+	0.889868i	$0.650796\pi$
$150$	4.11962	0.336365
$151$	1.65723	0.134863	0.0674315	−	0.997724i	$-0.478520\pi$
$151$	1.65723	0.134863	0.0674315	+	0.997724i	$0.478520\pi$
$152$	−2.94619	−0.238968
$153$	−0.558875	−0.0451823
$154$	4.36357	0.351627
$155$	7.92361	0.636440
$156$	−0.0368976	−0.00295417
$157$	−13.2564	−1.05798	−0.528988	−	0.848629i	$-0.677428\pi$
$157$	−13.2564	−1.05798	−0.528988	+	0.848629i	$0.677428\pi$
$158$	−16.9297	−1.34686
$159$	0.0266868	0.00211640
$160$	3.01987	0.238742
$161$	2.27769	0.179507
$162$	−1.00000	−0.0785674
$163$	7.43775	0.582570	0.291285	−	0.956636i	$-0.405917\pi$
$163$	7.43775	0.582570	0.291285	+	0.956636i	$0.405917\pi$
$164$	0.597641	0.0466679
$165$	−3.01987	−0.235097
$166$	3.93936	0.305754
$167$	16.1212	1.24750	0.623748	−	0.781625i	$-0.285609\pi$
$167$	16.1212	1.24750	0.623748	+	0.781625i	$0.285609\pi$
$168$	4.36357	0.336657
$169$	−12.9986	−0.999895
$170$	−1.68773	−0.129443
$171$	2.94619	0.225301
$172$	3.12983	0.238647
$173$	−4.75521	−0.361532	−0.180766	−	0.983526i	$-0.557858\pi$
$173$	−4.75521	−0.361532	−0.180766	+	0.983526i	$0.557858\pi$
$174$	−10.5536	−0.800067
$175$	17.9763	1.35888
$176$	−1.00000	−0.0753778
$177$	−2.47353	−0.185922
$178$	1.68773	0.126501
$179$	−1.19452	−0.0892827	−0.0446414	−	0.999003i	$-0.514215\pi$
$179$	−1.19452	−0.0892827	−0.0446414	+	0.999003i	$0.514215\pi$
$180$	−3.01987	−0.225088
$181$	−25.6174	−1.90412	−0.952062	−	0.305905i	$-0.901041\pi$
$181$	−25.6174	−1.90412	−0.952062	+	0.305905i	$0.901041\pi$
$182$	−0.161005	−0.0119345
$183$	1.00000	0.0739221
$184$	−0.521977	−0.0384807
$185$	24.7050	1.81635
$186$	−2.62382	−0.192388
$187$	0.558875	0.0408690
$188$	10.3693	0.756263
$189$	−4.36357	−0.317403
$190$	8.89711	0.645465
$191$	−13.7299	−0.993460	−0.496730	−	0.867905i	$-0.665466\pi$
$191$	−13.7299	−0.993460	−0.496730	+	0.867905i	$0.665466\pi$
$192$	−1.00000	−0.0721688
$193$	7.81154	0.562287	0.281143	−	0.959666i	$-0.409286\pi$
$193$	7.81154	0.562287	0.281143	+	0.959666i	$0.409286\pi$
$194$	17.9409	1.28808
$195$	0.111426	0.00797937
$196$	12.0408	0.860056
$197$	13.8614	0.987583	0.493792	−	0.869580i	$-0.335611\pi$
$197$	13.8614	0.987583	0.493792	+	0.869580i	$0.335611\pi$
$198$	1.00000	0.0710669
$199$	−12.0082	−0.851240	−0.425620	−	0.904902i	$-0.639944\pi$
$199$	−12.0082	−0.851240	−0.425620	+	0.904902i	$0.639944\pi$
$200$	−4.11962	−0.291301
$201$	5.64725	0.398326
$202$	−3.16007	−0.222341
$203$	−46.0515	−3.23218
$204$	0.558875	0.0391291
$205$	−1.80480	−0.126053
$206$	2.29864	0.160154
$207$	0.521977	0.0362799
$208$	0.0368976	0.00255839
$209$	−2.94619	−0.203792
$210$	−13.1774	−0.909329
$211$	4.32770	0.297931	0.148966	−	0.988842i	$-0.452406\pi$
$211$	4.32770	0.297931	0.148966	+	0.988842i	$0.452406\pi$
$212$	−0.0266868	−0.00183285
$213$	−0.263712	−0.0180692
$214$	2.19728	0.150203
$215$	−9.45168	−0.644599
$216$	1.00000	0.0680414
$217$	−11.4493	−0.777226
$218$	−1.27730	−0.0865099
$219$	1.59228	0.107596
$220$	3.01987	0.203600
$221$	−0.0206211	−0.00138713
$222$	−8.18081	−0.549060
$223$	25.7527	1.72453	0.862264	−	0.506459i	$-0.169046\pi$
$223$	25.7527	1.72453	0.862264	+	0.506459i	$0.169046\pi$
$224$	−4.36357	−0.291554
$225$	4.11962	0.274641
$226$	2.87511	0.191250
$227$	−26.8452	−1.78178	−0.890890	−	0.454220i	$-0.849918\pi$
$227$	−26.8452	−1.78178	−0.890890	+	0.454220i	$0.849918\pi$
$228$	−2.94619	−0.195116
$229$	−21.8780	−1.44574	−0.722871	−	0.690983i	$-0.757178\pi$
$229$	−21.8780	−1.44574	−0.722871	+	0.690983i	$0.757178\pi$
$230$	1.57630	0.103938
$231$	4.36357	0.287102
$232$	10.5536	0.692878
$233$	−22.9287	−1.50211	−0.751056	−	0.660239i	$-0.770455\pi$
$233$	−22.9287	−1.50211	−0.751056	+	0.660239i	$0.770455\pi$
$234$	−0.0368976	−0.00241207
$235$	−31.3141	−2.04271
$236$	2.47353	0.161013
$237$	−16.9297	−1.09970
$238$	2.43869	0.158077
$239$	7.85316	0.507979	0.253989	−	0.967207i	$-0.418257\pi$
$239$	7.85316	0.507979	0.253989	+	0.967207i	$0.418257\pi$
$240$	3.01987	0.194932
$241$	−3.39353	−0.218597	−0.109298	−	0.994009i	$-0.534860\pi$
$241$	−3.39353	−0.218597	−0.109298	+	0.994009i	$0.534860\pi$
$242$	−1.00000	−0.0642824
$243$	−1.00000	−0.0641500
$244$	−1.00000	−0.0640184
$245$	−36.3616	−2.32306
$246$	0.597641	0.0381042
$247$	0.108707	0.00691688
$248$	2.62382	0.166613
$249$	3.93936	0.249647
$250$	−2.65864	−0.168147
$251$	10.4106	0.657109	0.328554	−	0.944485i	$-0.393439\pi$
$251$	10.4106	0.657109	0.328554	+	0.944485i	$0.393439\pi$
$252$	4.36357	0.274879
$253$	−0.521977	−0.0328164
$254$	4.10279	0.257432
$255$	−1.68773	−0.105690
$256$	1.00000	0.0625000
$257$	−12.5273	−0.781430	−0.390715	−	0.920512i	$-0.627772\pi$
$257$	−12.5273	−0.781430	−0.390715	+	0.920512i	$0.627772\pi$
$258$	3.12983	0.194855
$259$	−35.6976	−2.21814
$260$	−0.111426	−0.00691034
$261$	−10.5536	−0.653252
$262$	−12.0757	−0.746038
$263$	−3.97968	−0.245398	−0.122699	−	0.992444i	$-0.539155\pi$
$263$	−3.97968	−0.245398	−0.122699	+	0.992444i	$0.539155\pi$
$264$	−1.00000	−0.0615457
$265$	0.0805906	0.00495064
$266$	−12.8559	−0.788247
$267$	1.68773	0.103287
$268$	−5.64725	−0.344960
$269$	−13.1793	−0.803557	−0.401778	−	0.915737i	$-0.631608\pi$
$269$	−13.1793	−0.803557	−0.401778	+	0.915737i	$0.631608\pi$
$270$	−3.01987	−0.183783
$271$	−15.8240	−0.961242	−0.480621	−	0.876929i	$-0.659589\pi$
$271$	−15.8240	−0.961242	−0.480621	+	0.876929i	$0.659589\pi$
$272$	−0.558875	−0.0338868
$273$	−0.161005	−0.00974449
$274$	6.38845	0.385940
$275$	−4.11962	−0.248422
$276$	−0.521977	−0.0314193
$277$	28.2720	1.69870	0.849351	−	0.527828i	$-0.176994\pi$
$277$	28.2720	1.69870	0.849351	+	0.527828i	$0.176994\pi$
$278$	−0.678777	−0.0407104
$279$	−2.62382	−0.157084
$280$	13.1774	0.787502
$281$	−9.66940	−0.576828	−0.288414	−	0.957506i	$-0.593128\pi$
$281$	−9.66940	−0.576828	−0.288414	+	0.957506i	$0.593128\pi$
$282$	10.3693	0.617486
$283$	−28.1590	−1.67388	−0.836940	−	0.547295i	$-0.815658\pi$
$283$	−28.1590	−1.67388	−0.836940	+	0.547295i	$0.815658\pi$
$284$	0.263712	0.0156484
$285$	8.89711	0.527020
$286$	0.0368976	0.00218180
$287$	2.60785	0.153937
$288$	−1.00000	−0.0589256
$289$	−16.6877	−0.981627
$290$	−31.8705	−1.87150
$291$	17.9409	1.05171
$292$	−1.59228	−0.0931809
$293$	−20.3060	−1.18629	−0.593144	−	0.805097i	$-0.702113\pi$
$293$	−20.3060	−1.18629	−0.593144	+	0.805097i	$0.702113\pi$
$294$	12.0408	0.702233
$295$	−7.46975	−0.434906
$296$	8.18081	0.475500
$297$	1.00000	0.0580259
$298$	11.1377	0.645189
$299$	0.0192597	0.00111382
$300$	−4.11962	−0.237846
$301$	13.6572	0.787190
$302$	−1.65723	−0.0953626
$303$	−3.16007	−0.181541
$304$	2.94619	0.168976
$305$	3.01987	0.172917
$306$	0.558875	0.0319487
$307$	−3.69771	−0.211039	−0.105520	−	0.994417i	$-0.533651\pi$
$307$	−3.69771	−0.211039	−0.105520	+	0.994417i	$0.533651\pi$
$308$	−4.36357	−0.248638
$309$	2.29864	0.130765
$310$	−7.92361	−0.450031
$311$	22.0417	1.24987	0.624934	−	0.780677i	$-0.285126\pi$
$311$	22.0417	1.24987	0.624934	+	0.780677i	$0.285126\pi$
$312$	0.0368976	0.00208891
$313$	−30.9471	−1.74923	−0.874616	−	0.484817i	$-0.838886\pi$
$313$	−30.9471	−1.74923	−0.874616	+	0.484817i	$0.838886\pi$
$314$	13.2564	0.748102
$315$	−13.1774	−0.742464
$316$	16.9297	0.952371
$317$	−15.5934	−0.875812	−0.437906	−	0.899021i	$-0.644280\pi$
$317$	−15.5934	−0.875812	−0.437906	+	0.899021i	$0.644280\pi$
$318$	−0.0266868	−0.00149652
$319$	10.5536	0.590889
$320$	−3.01987	−0.168816
$321$	2.19728	0.122640
$322$	−2.27769	−0.126930
$323$	−1.64655	−0.0916166
$324$	1.00000	0.0555556
$325$	0.152004	0.00843166
$326$	−7.43775	−0.411939
$327$	−1.27730	−0.0706351
$328$	−0.597641	−0.0329992
$329$	45.2474	2.49457
$330$	3.01987	0.166238
$331$	−10.4075	−0.572046	−0.286023	−	0.958223i	$-0.592333\pi$
$331$	−10.4075	−0.572046	−0.286023	+	0.958223i	$0.592333\pi$
$332$	−3.93936	−0.216201
$333$	−8.18081	−0.448306
$334$	−16.1212	−0.882113
$335$	17.0540	0.931757
$336$	−4.36357	−0.238053
$337$	−2.60953	−0.142150	−0.0710752	−	0.997471i	$-0.522643\pi$
$337$	−2.60953	−0.142150	−0.0710752	+	0.997471i	$0.522643\pi$
$338$	12.9986	0.707033
$339$	2.87511	0.156155
$340$	1.68773	0.0915300
$341$	2.62382	0.142088
$342$	−2.94619	−0.159312
$343$	21.9958	1.18766
$344$	−3.12983	−0.168749
$345$	1.57630	0.0848653
$346$	4.75521	0.255642
$347$	22.8189	1.22499	0.612493	−	0.790476i	$-0.290167\pi$
$347$	22.8189	1.22499	0.612493	+	0.790476i	$0.290167\pi$
$348$	10.5536	0.565733
$349$	−10.7297	−0.574346	−0.287173	−	0.957879i	$-0.592715\pi$
$349$	−10.7297	−0.574346	−0.287173	+	0.957879i	$0.592715\pi$
$350$	−17.9763	−0.960872
$351$	−0.0368976	−0.00196945
$352$	1.00000	0.0533002
$353$	11.4209	0.607873	0.303936	−	0.952692i	$-0.401699\pi$
$353$	11.4209	0.607873	0.303936	+	0.952692i	$0.401699\pi$
$354$	2.47353	0.131467
$355$	−0.796376	−0.0422672
$356$	−1.68773	−0.0894495
$357$	2.43869	0.129069
$358$	1.19452	0.0631324
$359$	−18.2671	−0.964103	−0.482052	−	0.876143i	$-0.660108\pi$
$359$	−18.2671	−0.964103	−0.482052	+	0.876143i	$0.660108\pi$
$360$	3.01987	0.159161
$361$	−10.3200	−0.543156
$362$	25.6174	1.34642
$363$	−1.00000	−0.0524864
$364$	0.161005	0.00843897
$365$	4.80847	0.251687
$366$	−1.00000	−0.0522708
$367$	14.4878	0.756257	0.378129	−	0.925753i	$-0.376568\pi$
$367$	14.4878	0.756257	0.378129	+	0.925753i	$0.376568\pi$
$368$	0.521977	0.0272099
$369$	0.597641	0.0311120
$370$	−24.7050	−1.28435
$371$	−0.116450	−0.00604577
$372$	2.62382	0.136039
$373$	18.3953	0.952474	0.476237	−	0.879317i	$-0.342000\pi$
$373$	18.3953	0.952474	0.476237	+	0.879317i	$0.342000\pi$
$374$	−0.558875	−0.0288987
$375$	−2.65864	−0.137292
$376$	−10.3693	−0.534758
$377$	−0.389402	−0.0200552
$378$	4.36357	0.224438
$379$	−32.4183	−1.66522	−0.832609	−	0.553862i	$-0.813154\pi$
$379$	−32.4183	−1.66522	−0.832609	+	0.553862i	$0.813154\pi$
$380$	−8.89711	−0.456412
$381$	4.10279	0.210193
$382$	13.7299	0.702483
$383$	−8.22539	−0.420298	−0.210149	−	0.977669i	$-0.567395\pi$
$383$	−8.22539	−0.420298	−0.210149	+	0.977669i	$0.567395\pi$
$384$	1.00000	0.0510310
$385$	13.1774	0.671584
$386$	−7.81154	−0.397597
$387$	3.12983	0.159098
$388$	−17.9409	−0.910809
$389$	12.0485	0.610883	0.305441	−	0.952211i	$-0.401196\pi$
$389$	12.0485	0.610883	0.305441	+	0.952211i	$0.401196\pi$
$390$	−0.111426	−0.00564227
$391$	−0.291720	−0.0147529
$392$	−12.0408	−0.608152
$393$	−12.0757	−0.609138
$394$	−13.8614	−0.698327
$395$	−51.1256	−2.57241
$396$	−1.00000	−0.0502519
$397$	11.5044	0.577391	0.288696	−	0.957421i	$-0.406778\pi$
$397$	11.5044	0.577391	0.288696	+	0.957421i	$0.406778\pi$
$398$	12.0082	0.601918
$399$	−12.8559	−0.643601
$400$	4.11962	0.205981
$401$	12.4755	0.622997	0.311499	−	0.950247i	$-0.399169\pi$
$401$	12.4755	0.622997	0.311499	+	0.950247i	$0.399169\pi$
$402$	−5.64725	−0.281659
$403$	−0.0968128	−0.00482259
$404$	3.16007	0.157219
$405$	−3.01987	−0.150059
$406$	46.0515	2.28550
$407$	8.18081	0.405508
$408$	−0.558875	−0.0276684
$409$	20.9291	1.03488	0.517439	−	0.855720i	$-0.326885\pi$
$409$	20.9291	1.03488	0.517439	+	0.855720i	$0.326885\pi$
$410$	1.80480	0.0891327
$411$	6.38845	0.315119
$412$	−2.29864	−0.113246
$413$	10.7934	0.531111
$414$	−0.521977	−0.0256538
$415$	11.8964	0.583969
$416$	−0.0368976	−0.00180905
$417$	−0.678777	−0.0332399
$418$	2.94619	0.144103
$419$	−5.98387	−0.292331	−0.146166	−	0.989260i	$-0.546693\pi$
$419$	−5.98387	−0.292331	−0.146166	+	0.989260i	$0.546693\pi$
$420$	13.1774	0.642993
$421$	−23.1469	−1.12811	−0.564054	−	0.825738i	$-0.690759\pi$
$421$	−23.1469	−1.12811	−0.564054	+	0.825738i	$0.690759\pi$
$422$	−4.32770	−0.210669
$423$	10.3693	0.504175
$424$	0.0266868	0.00129602
$425$	−2.30235	−0.111680
$426$	0.263712	0.0127769
$427$	−4.36357	−0.211168
$428$	−2.19728	−0.106210
$429$	0.0368976	0.00178143
$430$	9.45168	0.455800
$431$	9.11986	0.439288	0.219644	−	0.975580i	$-0.429510\pi$
$431$	9.11986	0.439288	0.219644	+	0.975580i	$0.429510\pi$
$432$	−1.00000	−0.0481125
$433$	−6.28250	−0.301918	−0.150959	−	0.988540i	$-0.548236\pi$
$433$	−6.28250	−0.301918	−0.150959	+	0.988540i	$0.548236\pi$
$434$	11.4493	0.549582
$435$	−31.8705	−1.52807
$436$	1.27730	0.0611718
$437$	1.53784	0.0735651
$438$	−1.59228	−0.0760819
$439$	−39.3641	−1.87875	−0.939374	−	0.342895i	$-0.888593\pi$
$439$	−39.3641	−1.87875	−0.939374	+	0.342895i	$0.888593\pi$
$440$	−3.01987	−0.143967
$441$	12.0408	0.573371
$442$	0.0206211	0.000980847 0
$443$	−2.55043	−0.121175	−0.0605873	−	0.998163i	$-0.519297\pi$
$443$	−2.55043	−0.121175	−0.0605873	+	0.998163i	$0.519297\pi$
$444$	8.18081	0.388244
$445$	5.09672	0.241608
$446$	−25.7527	−1.21943
$447$	11.1377	0.526795
$448$	4.36357	0.206160
$449$	−14.6680	−0.692226	−0.346113	−	0.938193i	$-0.612499\pi$
$449$	−14.6680	−0.692226	−0.346113	+	0.938193i	$0.612499\pi$
$450$	−4.11962	−0.194201
$451$	−0.597641	−0.0281418
$452$	−2.87511	−0.135234
$453$	−1.65723	−0.0778632
$454$	26.8452	1.25991
$455$	−0.486215	−0.0227941
$456$	2.94619	0.137968
$457$	−11.6782	−0.546282	−0.273141	−	0.961974i	$-0.588062\pi$
$457$	−11.6782	−0.546282	−0.273141	+	0.961974i	$0.588062\pi$
$458$	21.8780	1.02229
$459$	0.558875	0.0260860
$460$	−1.57630	−0.0734955
$461$	9.75494	0.454333	0.227166	−	0.973856i	$-0.427054\pi$
$461$	9.75494	0.454333	0.227166	+	0.973856i	$0.427054\pi$
$462$	−4.36357	−0.203012
$463$	15.0533	0.699586	0.349793	−	0.936827i	$-0.386252\pi$
$463$	15.0533	0.699586	0.349793	+	0.936827i	$0.386252\pi$
$464$	−10.5536	−0.489939
$465$	−7.92361	−0.367449
$466$	22.9287	1.06215
$467$	−7.57885	−0.350707	−0.175354	−	0.984506i	$-0.556107\pi$
$467$	−7.57885	−0.350707	−0.175354	+	0.984506i	$0.556107\pi$
$468$	0.0368976	0.00170559
$469$	−24.6422	−1.13787
$470$	31.3141	1.44441
$471$	13.2564	0.610823
$472$	−2.47353	−0.113854
$473$	−3.12983	−0.143910
$474$	16.9297	0.777608
$475$	12.1372	0.556892
$476$	−2.43869	−0.111777
$477$	−0.0266868	−0.00122190
$478$	−7.85316	−0.359195
$479$	−39.4629	−1.80310	−0.901552	−	0.432671i	$-0.857571\pi$
$479$	−39.4629	−1.80310	−0.901552	+	0.432671i	$0.857571\pi$
$480$	−3.01987	−0.137838
$481$	−0.301852	−0.0137633
$482$	3.39353	0.154571
$483$	−2.27769	−0.103638
$484$	1.00000	0.0454545
$485$	54.1791	2.46015
$486$	1.00000	0.0453609
$487$	−32.8898	−1.49038	−0.745189	−	0.666853i	$-0.767641\pi$
$487$	−32.8898	−1.49038	−0.745189	+	0.666853i	$0.767641\pi$
$488$	1.00000	0.0452679
$489$	−7.43775	−0.336347
$490$	36.3616	1.64265
$491$	0.0114984	0.000518915 0	0.000259457	−	1.00000i	$-0.499917\pi$
$491$	0.0114984	0.000518915 0	0.000259457		1.00000i	$0.499917\pi$
$492$	−0.597641	−0.0269437
$493$	5.89814	0.265639
$494$	−0.108707	−0.00489097
$495$	3.01987	0.135733
$496$	−2.62382	−0.117813
$497$	1.15073	0.0516171
$498$	−3.93936	−0.176527
$499$	−22.9248	−1.02625	−0.513127	−	0.858313i	$-0.671513\pi$
$499$	−22.9248	−1.02625	−0.513127	+	0.858313i	$0.671513\pi$
$500$	2.65864	0.118898
$501$	−16.1212	−0.720243
$502$	−10.4106	−0.464646
$503$	−22.4873	−1.00266	−0.501328	−	0.865257i	$-0.667155\pi$
$503$	−22.4873	−1.00266	−0.501328	+	0.865257i	$0.667155\pi$
$504$	−4.36357	−0.194369
$505$	−9.54299	−0.424658
$506$	0.521977	0.0232047
$507$	12.9986	0.577290
$508$	−4.10279	−0.182032
$509$	8.96966	0.397573	0.198786	−	0.980043i	$-0.436300\pi$
$509$	8.96966	0.397573	0.198786	+	0.980043i	$0.436300\pi$
$510$	1.68773	0.0747339
$511$	−6.94801	−0.307362
$512$	−1.00000	−0.0441942
$513$	−2.94619	−0.130078
$514$	12.5273	0.552555
$515$	6.94160	0.305883
$516$	−3.12983	−0.137783
$517$	−10.3693	−0.456043
$518$	35.6976	1.56846
$519$	4.75521	0.208731
$520$	0.111426	0.00488635
$521$	13.5637	0.594237	0.297119	−	0.954841i	$-0.403974\pi$
$521$	13.5637	0.594237	0.297119	+	0.954841i	$0.403974\pi$
$522$	10.5536	0.461919
$523$	−25.4475	−1.11274	−0.556371	−	0.830934i	$-0.687807\pi$
$523$	−25.4475	−1.11274	−0.556371	+	0.830934i	$0.687807\pi$
$524$	12.0757	0.527529
$525$	−17.9763	−0.784548
$526$	3.97968	0.173522
$527$	1.46639	0.0638769
$528$	1.00000	0.0435194
$529$	−22.7275	−0.988154
$530$	−0.0805906	−0.00350063
$531$	2.47353	0.107342
$532$	12.8559	0.557375
$533$	0.0220515	0.000955157 0
$534$	−1.68773	−0.0730352
$535$	6.63551	0.286878
$536$	5.64725	0.243924
$537$	1.19452	0.0515474
$538$	13.1793	0.568200
$539$	−12.0408	−0.518633
$540$	3.01987	0.129955
$541$	−18.2594	−0.785031	−0.392516	−	0.919745i	$-0.628395\pi$
$541$	−18.2594	−0.785031	−0.392516	+	0.919745i	$0.628395\pi$
$542$	15.8240	0.679700
$543$	25.6174	1.09935
$544$	0.558875	0.0239616
$545$	−3.85729	−0.165228
$546$	0.161005	0.00689039
$547$	37.8612	1.61883	0.809415	−	0.587237i	$-0.199784\pi$
$547$	37.8612	1.61883	0.809415	+	0.587237i	$0.199784\pi$
$548$	−6.38845	−0.272901
$549$	−1.00000	−0.0426790
$550$	4.11962	0.175661
$551$	−31.0929	−1.32460
$552$	0.521977	0.0222168
$553$	73.8741	3.14145
$554$	−28.2720	−1.20116
$555$	−24.7050	−1.04867
$556$	0.678777	0.0287866
$557$	4.51615	0.191355	0.0956777	−	0.995412i	$-0.469498\pi$
$557$	4.51615	0.191355	0.0956777	+	0.995412i	$0.469498\pi$
$558$	2.62382	0.111075
$559$	0.115483	0.00488441
$560$	−13.1774	−0.556848
$561$	−0.558875	−0.0235957
$562$	9.66940	0.407879
$563$	33.9896	1.43249	0.716245	−	0.697849i	$-0.245859\pi$
$563$	33.9896	1.43249	0.716245	+	0.697849i	$0.245859\pi$
$564$	−10.3693	−0.436628
$565$	8.68247	0.365274
$566$	28.1590	1.18361
$567$	4.36357	0.183253
$568$	−0.263712	−0.0110651
$569$	−19.6460	−0.823604	−0.411802	−	0.911273i	$-0.635101\pi$
$569$	−19.6460	−0.823604	−0.411802	+	0.911273i	$0.635101\pi$
$570$	−8.89711	−0.372659
$571$	0.418250	0.0175032	0.00875161	−	0.999962i	$-0.497214\pi$
$571$	0.418250	0.0175032	0.00875161	+	0.999962i	$0.497214\pi$
$572$	−0.0368976	−0.00154277
$573$	13.7299	0.573575
$574$	−2.60785	−0.108850
$575$	2.15035	0.0896756
$576$	1.00000	0.0416667
$577$	45.1863	1.88113	0.940566	−	0.339611i	$-0.110295\pi$
$577$	45.1863	1.88113	0.940566	+	0.339611i	$0.110295\pi$
$578$	16.6877	0.694115
$579$	−7.81154	−0.324636
$580$	31.8705	1.32335
$581$	−17.1897	−0.713149
$582$	−17.9409	−0.743673
$583$	0.0266868	0.00110525
$584$	1.59228	0.0658888
$585$	−0.111426	−0.00460689
$586$	20.3060	0.838832
$587$	30.0626	1.24082	0.620408	−	0.784279i	$-0.286967\pi$
$587$	30.0626	1.24082	0.620408	+	0.784279i	$0.286967\pi$
$588$	−12.0408	−0.496554
$589$	−7.73029	−0.318521
$590$	7.46975	0.307525
$591$	−13.8614	−0.570181
$592$	−8.18081	−0.336229
$593$	−15.4674	−0.635169	−0.317585	−	0.948230i	$-0.602872\pi$
$593$	−15.4674	−0.635169	−0.317585	+	0.948230i	$0.602872\pi$
$594$	−1.00000	−0.0410305
$595$	7.36453	0.301916
$596$	−11.1377	−0.456218
$597$	12.0082	0.491464
$598$	−0.0192597	−0.000787587 0
$599$	19.6813	0.804156	0.402078	−	0.915605i	$-0.368288\pi$
$599$	19.6813	0.804156	0.402078	+	0.915605i	$0.368288\pi$
$600$	4.11962	0.168183
$601$	−18.8203	−0.767695	−0.383848	−	0.923396i	$-0.625401\pi$
$601$	−18.8203	−0.767695	−0.383848	+	0.923396i	$0.625401\pi$
$602$	−13.6572	−0.556628
$603$	−5.64725	−0.229974
$604$	1.65723	0.0674315
$605$	−3.01987	−0.122775
$606$	3.16007	0.128369
$607$	17.8869	0.726006	0.363003	−	0.931788i	$-0.381752\pi$
$607$	17.8869	0.726006	0.363003	+	0.931788i	$0.381752\pi$
$608$	−2.94619	−0.119484
$609$	46.0515	1.86610
$610$	−3.01987	−0.122271
$611$	0.382604	0.0154785
$612$	−0.558875	−0.0225912
$613$	12.9145	0.521612	0.260806	−	0.965391i	$-0.416012\pi$
$613$	12.9145	0.521612	0.260806	+	0.965391i	$0.416012\pi$
$614$	3.69771	0.149227
$615$	1.80480	0.0727765
$616$	4.36357	0.175813
$617$	10.4735	0.421649	0.210825	−	0.977524i	$-0.432385\pi$
$617$	10.4735	0.421649	0.210825	+	0.977524i	$0.432385\pi$
$618$	−2.29864	−0.0924649
$619$	40.8113	1.64034	0.820172	−	0.572117i	$-0.193878\pi$
$619$	40.8113	1.64034	0.820172	+	0.572117i	$0.193878\pi$
$620$	7.92361	0.318220
$621$	−0.521977	−0.0209462
$622$	−22.0417	−0.883790
$623$	−7.36453	−0.295054
$624$	−0.0368976	−0.00147709
$625$	−28.6268	−1.14507
$626$	30.9471	1.23689
$627$	2.94619	0.117660
$628$	−13.2564	−0.528988
$629$	4.57205	0.182300
$630$	13.1774	0.525001
$631$	37.4232	1.48979	0.744897	−	0.667180i	$-0.232499\pi$
$631$	37.4232	1.48979	0.744897	+	0.667180i	$0.232499\pi$
$632$	−16.9297	−0.673428
$633$	−4.32770	−0.172011
$634$	15.5934	0.619292
$635$	12.3899	0.491679
$636$	0.0266868	0.00105820
$637$	0.444276	0.0176028
$638$	−10.5536	−0.417821
$639$	0.263712	0.0104323
$640$	3.01987	0.119371
$641$	−43.2870	−1.70973	−0.854867	−	0.518848i	$-0.826361\pi$
$641$	−43.2870	−1.70973	−0.854867	+	0.518848i	$0.826361\pi$
$642$	−2.19728	−0.0867199
$643$	−30.2574	−1.19323	−0.596617	−	0.802526i	$-0.703489\pi$
$643$	−30.2574	−1.19323	−0.596617	+	0.802526i	$0.703489\pi$
$644$	2.27769	0.0897534
$645$	9.45168	0.372159
$646$	1.64655	0.0647827
$647$	−41.8188	−1.64407	−0.822033	−	0.569440i	$-0.807160\pi$
$647$	−41.8188	−1.64407	−0.822033	+	0.569440i	$0.807160\pi$
$648$	−1.00000	−0.0392837
$649$	−2.47353	−0.0970947
$650$	−0.152004	−0.00596208
$651$	11.4493	0.448732
$652$	7.43775	0.291285
$653$	33.5936	1.31462	0.657310	−	0.753620i	$-0.271694\pi$
$653$	33.5936	1.31462	0.657310	+	0.753620i	$0.271694\pi$
$654$	1.27730	0.0499465
$655$	−36.4670	−1.42488
$656$	0.597641	0.0233340
$657$	−1.59228	−0.0621206
$658$	−45.2474	−1.76393
$659$	−9.71213	−0.378331	−0.189165	−	0.981945i	$-0.560578\pi$
$659$	−9.71213	−0.378331	−0.189165	+	0.981945i	$0.560578\pi$
$660$	−3.01987	−0.117548
$661$	16.8434	0.655134	0.327567	−	0.944828i	$-0.393771\pi$
$661$	16.8434	0.655134	0.327567	+	0.944828i	$0.393771\pi$
$662$	10.4075	0.404498
$663$	0.0206211	0.000800858 0
$664$	3.93936	0.152877
$665$	−38.8232	−1.50550
$666$	8.18081	0.317000
$667$	−5.50874	−0.213299
$668$	16.1212	0.623748
$669$	−25.7527	−0.995657
$670$	−17.0540	−0.658852
$671$	1.00000	0.0386046
$672$	4.36357	0.168329
$673$	30.9257	1.19210	0.596049	−	0.802948i	$-0.296736\pi$
$673$	30.9257	1.19210	0.596049	+	0.802948i	$0.296736\pi$
$674$	2.60953	0.100515
$675$	−4.11962	−0.158564
$676$	−12.9986	−0.499948
$677$	−4.39489	−0.168909	−0.0844547	−	0.996427i	$-0.526915\pi$
$677$	−4.39489	−0.168909	−0.0844547	+	0.996427i	$0.526915\pi$
$678$	−2.87511	−0.110418
$679$	−78.2863	−3.00435
$680$	−1.68773	−0.0647215
$681$	26.8452	1.02871
$682$	−2.62382	−0.100471
$683$	−13.9972	−0.535588	−0.267794	−	0.963476i	$-0.586295\pi$
$683$	−13.9972	−0.535588	−0.267794	+	0.963476i	$0.586295\pi$
$684$	2.94619	0.112650
$685$	19.2923	0.737121
$686$	−21.9958	−0.839805
$687$	21.8780	0.834699
$688$	3.12983	0.119324
$689$	−0.000984677 0	−3.75132e−5 0
$690$	−1.57630	−0.0600088
$691$	27.7348	1.05508	0.527542	−	0.849529i	$-0.323114\pi$
$691$	27.7348	1.05508	0.527542	+	0.849529i	$0.323114\pi$
$692$	−4.75521	−0.180766
$693$	−4.36357	−0.165759
$694$	−22.8189	−0.866195
$695$	−2.04982	−0.0777541
$696$	−10.5536	−0.400033
$697$	−0.334006	−0.0126514
$698$	10.7297	0.406124
$699$	22.9287	0.867244
$700$	17.9763	0.679439
$701$	−38.4711	−1.45303	−0.726517	−	0.687149i	$-0.758862\pi$
$701$	−38.4711	−1.45303	−0.726517	+	0.687149i	$0.758862\pi$
$702$	0.0368976	0.00139261
$703$	−24.1022	−0.909033
$704$	−1.00000	−0.0376889
$705$	31.3141	1.17936
$706$	−11.4209	−0.429831
$707$	13.7892	0.518596
$708$	−2.47353	−0.0929611
$709$	15.7584	0.591821	0.295910	−	0.955216i	$-0.404377\pi$
$709$	15.7584	0.591821	0.295910	+	0.955216i	$0.404377\pi$
$710$	0.796376	0.0298875
$711$	16.9297	0.634914
$712$	1.68773	0.0632503
$713$	−1.36958	−0.0512910
$714$	−2.43869	−0.0912657
$715$	0.111426	0.00416709
$716$	−1.19452	−0.0446414
$717$	−7.85316	−0.293282
$718$	18.2671	0.681724
$719$	−30.3245	−1.13091	−0.565457	−	0.824778i	$-0.691300\pi$
$719$	−30.3245	−1.13091	−0.565457	+	0.824778i	$0.691300\pi$
$720$	−3.01987	−0.112544
$721$	−10.0303	−0.373548
$722$	10.3200	0.384069
$723$	3.39353	0.126207
$724$	−25.6174	−0.952062
$725$	−43.4768	−1.61469
$726$	1.00000	0.0371135
$727$	7.92309	0.293851	0.146926	−	0.989148i	$-0.453062\pi$
$727$	7.92309	0.293851	0.146926	+	0.989148i	$0.453062\pi$
$728$	−0.161005	−0.00596725
$729$	1.00000	0.0370370
$730$	−4.80847	−0.177969
$731$	−1.74918	−0.0646958
$732$	1.00000	0.0369611
$733$	28.1511	1.03978	0.519892	−	0.854232i	$-0.325972\pi$
$733$	28.1511	1.03978	0.519892	+	0.854232i	$0.325972\pi$
$734$	−14.4878	−0.534755
$735$	36.3616	1.34122
$736$	−0.521977	−0.0192403
$737$	5.64725	0.208019
$738$	−0.597641	−0.0219995
$739$	12.0793	0.444345	0.222172	−	0.975007i	$-0.428685\pi$
$739$	12.0793	0.444345	0.222172	+	0.975007i	$0.428685\pi$
$740$	24.7050	0.908174
$741$	−0.108707	−0.00399346
$742$	0.116450	0.00427500
$743$	−0.709415	−0.0260259	−0.0130130	−	0.999915i	$-0.504142\pi$
$743$	−0.709415	−0.0260259	−0.0130130	+	0.999915i	$0.504142\pi$
$744$	−2.62382	−0.0961941
$745$	33.6344	1.23227
$746$	−18.3953	−0.673501
$747$	−3.93936	−0.144134
$748$	0.558875	0.0204345
$749$	−9.58801	−0.350338
$750$	2.65864	0.0970798
$751$	−18.0215	−0.657614	−0.328807	−	0.944397i	$-0.606647\pi$
$751$	−18.0215	−0.657614	−0.328807	+	0.944397i	$0.606647\pi$
$752$	10.3693	0.378131
$753$	−10.4106	−0.379382
$754$	0.389402	0.0141812
$755$	−5.00461	−0.182136
$756$	−4.36357	−0.158702
$757$	−7.91121	−0.287538	−0.143769	−	0.989611i	$-0.545922\pi$
$757$	−7.91121	−0.287538	−0.143769	+	0.989611i	$0.545922\pi$
$758$	32.4183	1.17749
$759$	0.521977	0.0189466
$760$	8.89711	0.322732
$761$	−15.0075	−0.544021	−0.272010	−	0.962294i	$-0.587689\pi$
$761$	−15.0075	−0.544021	−0.272010	+	0.962294i	$0.587689\pi$
$762$	−4.10279	−0.148629
$763$	5.57361	0.201778
$764$	−13.7299	−0.496730
$765$	1.68773	0.0610200
$766$	8.22539	0.297195
$767$	0.0912674	0.00329547
$768$	−1.00000	−0.0360844
$769$	14.7641	0.532407	0.266203	−	0.963917i	$-0.414231\pi$
$769$	14.7641	0.532407	0.266203	+	0.963917i	$0.414231\pi$
$770$	−13.1774	−0.474882
$771$	12.5273	0.451159
$772$	7.81154	0.281143
$773$	13.1082	0.471468	0.235734	−	0.971818i	$-0.424251\pi$
$773$	13.1082	0.471468	0.235734	+	0.971818i	$0.424251\pi$
$774$	−3.12983	−0.112499
$775$	−10.8092	−0.388276
$776$	17.9409	0.644039
$777$	35.6976	1.28064
$778$	−12.0485	−0.431959
$779$	1.76076	0.0630859
$780$	0.111426	0.00398969
$781$	−0.263712	−0.00943635
$782$	0.291720	0.0104319
$783$	10.5536	0.377155
$784$	12.0408	0.430028
$785$	40.0326	1.42882
$786$	12.0757	0.430725
$787$	−39.5122	−1.40846	−0.704229	−	0.709973i	$-0.748707\pi$
$787$	−39.5122	−1.40846	−0.704229	+	0.709973i	$0.748707\pi$
$788$	13.8614	0.493792
$789$	3.97968	0.141680
$790$	51.1256	1.81897
$791$	−12.5458	−0.446076
$792$	1.00000	0.0355335
$793$	−0.0368976	−0.00131027
$794$	−11.5044	−0.408277
$795$	−0.0805906	−0.00285825
$796$	−12.0082	−0.425620
$797$	−42.1962	−1.49467	−0.747333	−	0.664450i	$-0.768666\pi$
$797$	−42.1962	−1.49467	−0.747333	+	0.664450i	$0.768666\pi$
$798$	12.8559	0.455095
$799$	−5.79517	−0.205018
$800$	−4.11962	−0.145650
$801$	−1.68773	−0.0596330
$802$	−12.4755	−0.440526
$803$	1.59228	0.0561902
$804$	5.64725	0.199163
$805$	−6.87832	−0.242429
$806$	0.0968128	0.00341008
$807$	13.1793	0.463934
$808$	−3.16007	−0.111171
$809$	17.3040	0.608377	0.304188	−	0.952612i	$-0.401615\pi$
$809$	17.3040	0.608377	0.304188	+	0.952612i	$0.401615\pi$
$810$	3.01987	0.106107
$811$	−35.0396	−1.23041	−0.615203	−	0.788369i	$-0.710926\pi$
$811$	−35.0396	−1.23041	−0.615203	+	0.788369i	$0.710926\pi$
$812$	−46.0515	−1.61609
$813$	15.8240	0.554973
$814$	−8.18081	−0.286737
$815$	−22.4610	−0.786776
$816$	0.558875	0.0195645
$817$	9.22107	0.322605
$818$	−20.9291	−0.731769
$819$	0.161005	0.00562598
$820$	−1.80480	−0.0630263
$821$	14.7682	0.515413	0.257707	−	0.966223i	$-0.417033\pi$
$821$	14.7682	0.515413	0.257707	+	0.966223i	$0.417033\pi$
$822$	−6.38845	−0.222823
$823$	11.2801	0.393201	0.196600	−	0.980484i	$-0.437010\pi$
$823$	11.2801	0.393201	0.196600	+	0.980484i	$0.437010\pi$
$824$	2.29864	0.0800770
$825$	4.11962	0.143427
$826$	−10.7934	−0.375552
$827$	−29.5061	−1.02603	−0.513014	−	0.858380i	$-0.671471\pi$
$827$	−29.5061	−1.02603	−0.513014	+	0.858380i	$0.671471\pi$
$828$	0.521977	0.0181400
$829$	−24.0402	−0.834952	−0.417476	−	0.908688i	$-0.637085\pi$
$829$	−24.0402	−0.834952	−0.417476	+	0.908688i	$0.637085\pi$
$830$	−11.8964	−0.412929
$831$	−28.2720	−0.980746
$832$	0.0368976	0.00127919
$833$	−6.72929	−0.233156
$834$	0.678777	0.0235041
$835$	−48.6840	−1.68478
$836$	−2.94619	−0.101896
$837$	2.62382	0.0906926
$838$	5.98387	0.206709
$839$	−13.9205	−0.480589	−0.240294	−	0.970700i	$-0.577244\pi$
$839$	−13.9205	−0.480589	−0.240294	+	0.970700i	$0.577244\pi$
$840$	−13.1774	−0.454665
$841$	82.3786	2.84064
$842$	23.1469	0.797693
$843$	9.66940	0.333032
$844$	4.32770	0.148966
$845$	39.2542	1.35039
$846$	−10.3693	−0.356506
$847$	4.36357	0.149934
$848$	−0.0266868	−0.000916427 0
$849$	28.1590	0.966415
$850$	2.30235	0.0789700
$851$	−4.27020	−0.146380
$852$	−0.263712	−0.00903462
$853$	9.87189	0.338007	0.169003	−	0.985615i	$-0.445945\pi$
$853$	9.87189	0.338007	0.169003	+	0.985615i	$0.445945\pi$
$854$	4.36357	0.149318
$855$	−8.89711	−0.304275
$856$	2.19728	0.0751016
$857$	2.67362	0.0913292	0.0456646	−	0.998957i	$-0.485459\pi$
$857$	2.67362	0.0913292	0.0456646	+	0.998957i	$0.485459\pi$
$858$	−0.0368976	−0.00125966
$859$	0.308608	0.0105296	0.00526478	−	0.999986i	$-0.498324\pi$
$859$	0.308608	0.0105296	0.00526478	+	0.999986i	$0.498324\pi$
$860$	−9.45168	−0.322300
$861$	−2.60785	−0.0888754
$862$	−9.11986	−0.310624
$863$	−22.5262	−0.766802	−0.383401	−	0.923582i	$-0.625247\pi$
$863$	−22.5262	−0.766802	−0.383401	+	0.923582i	$0.625247\pi$
$864$	1.00000	0.0340207
$865$	14.3601	0.488259
$866$	6.28250	0.213488
$867$	16.6877	0.566743
$868$	−11.4493	−0.388613
$869$	−16.9297	−0.574301
$870$	31.8705	1.08051
$871$	−0.208370	−0.00706034
$872$	−1.27730	−0.0432550
$873$	−17.9409	−0.607206
$874$	−1.53784	−0.0520183
$875$	11.6012	0.392191
$876$	1.59228	0.0537980
$877$	−33.9287	−1.14569	−0.572845	−	0.819663i	$-0.694160\pi$
$877$	−33.9287	−1.14569	−0.572845	+	0.819663i	$0.694160\pi$
$878$	39.3641	1.32848
$879$	20.3060	0.684903
$880$	3.01987	0.101800
$881$	14.6970	0.495154	0.247577	−	0.968868i	$-0.420366\pi$
$881$	14.6970	0.495154	0.247577	+	0.968868i	$0.420366\pi$
$882$	−12.0408	−0.405434
$883$	56.8438	1.91295	0.956473	−	0.291819i	$-0.0942606\pi$
$883$	56.8438	1.91295	0.956473	+	0.291819i	$0.0942606\pi$
$884$	−0.0206211	−0.000693563 0
$885$	7.46975	0.251093
$886$	2.55043	0.0856834
$887$	35.8302	1.20306	0.601531	−	0.798850i	$-0.294558\pi$
$887$	35.8302	1.20306	0.601531	+	0.798850i	$0.294558\pi$
$888$	−8.18081	−0.274530
$889$	−17.9029	−0.600442
$890$	−5.09672	−0.170843
$891$	−1.00000	−0.0335013
$892$	25.7527	0.862264
$893$	30.5501	1.02232
$894$	−11.1377	−0.372500
$895$	3.60730	0.120579
$896$	−4.36357	−0.145777
$897$	−0.0192597	−0.000643062 0
$898$	14.6680	0.489478
$899$	27.6908	0.923540
$900$	4.11962	0.137321
$901$	0.0149146	0.000496876 0
$902$	0.597641	0.0198993
$903$	−13.6572	−0.454485
$904$	2.87511	0.0956249
$905$	77.3611	2.57157
$906$	1.65723	0.0550576
$907$	−27.9889	−0.929356	−0.464678	−	0.885480i	$-0.653830\pi$
$907$	−27.9889	−0.929356	−0.464678	+	0.885480i	$0.653830\pi$
$908$	−26.8452	−0.890890
$909$	3.16007	0.104813
$910$	0.486215	0.0161179
$911$	1.10994	0.0367738	0.0183869	−	0.999831i	$-0.494147\pi$
$911$	1.10994	0.0367738	0.0183869	+	0.999831i	$0.494147\pi$
$912$	−2.94619	−0.0975581
$913$	3.93936	0.130374
$914$	11.6782	0.386279
$915$	−3.01987	−0.0998338
$916$	−21.8780	−0.722871
$917$	52.6931	1.74008
$918$	−0.558875	−0.0184456
$919$	8.86028	0.292274	0.146137	−	0.989264i	$-0.453316\pi$
$919$	8.86028	0.292274	0.146137	+	0.989264i	$0.453316\pi$
$920$	1.57630	0.0519692
$921$	3.69771	0.121844
$922$	−9.75494	−0.321262
$923$	0.00973033	0.000320278 0
$924$	4.36357	0.143551
$925$	−33.7018	−1.10811
$926$	−15.0533	−0.494682
$927$	−2.29864	−0.0754973
$928$	10.5536	0.346439
$929$	−24.1576	−0.792584	−0.396292	−	0.918124i	$-0.629703\pi$
$929$	−24.1576	−0.792584	−0.396292	+	0.918124i	$0.629703\pi$
$930$	7.92361	0.259825
$931$	35.4745	1.16263
$932$	−22.9287	−0.751056
$933$	−22.0417	−0.721612
$934$	7.57885	0.247987
$935$	−1.68773	−0.0551946
$936$	−0.0368976	−0.00120603
$937$	34.2494	1.11888	0.559440	−	0.828871i	$-0.311016\pi$
$937$	34.2494	1.11888	0.559440	+	0.828871i	$0.311016\pi$
$938$	24.6422	0.804596
$939$	30.9471	1.00992
$940$	−31.3141	−1.02135
$941$	9.08233	0.296076	0.148038	−	0.988982i	$-0.452704\pi$
$941$	9.08233	0.296076	0.148038	+	0.988982i	$0.452704\pi$
$942$	−13.2564	−0.431917
$943$	0.311955	0.0101587
$944$	2.47353	0.0805067
$945$	13.1774	0.428662
$946$	3.12983	0.101760
$947$	0.172057	0.00559112	0.00279556	−	0.999996i	$-0.499110\pi$
$947$	0.172057	0.00559112	0.00279556	+	0.999996i	$0.499110\pi$
$948$	−16.9297	−0.549852
$949$	−0.0587511	−0.00190714
$950$	−12.1372	−0.393782
$951$	15.5934	0.505650
$952$	2.43869	0.0790384
$953$	38.1546	1.23595	0.617975	−	0.786198i	$-0.287953\pi$
$953$	38.1546	1.23595	0.617975	+	0.786198i	$0.287953\pi$
$954$	0.0266868	0.000864016 0
$955$	41.4625	1.34170
$956$	7.85316	0.253989
$957$	−10.5536	−0.341150
$958$	39.4629	1.27499
$959$	−27.8765	−0.900179
$960$	3.01987	0.0974659
$961$	−24.1155	−0.777921
$962$	0.301852	0.00973210
$963$	−2.19728	−0.0708065
$964$	−3.39353	−0.109298
$965$	−23.5898	−0.759384
$966$	2.27769	0.0732833
$967$	19.3363	0.621812	0.310906	−	0.950441i	$-0.399368\pi$
$967$	19.3363	0.621812	0.310906	+	0.950441i	$0.399368\pi$
$968$	−1.00000	−0.0321412
$969$	1.64655	0.0528948
$970$	−54.1791	−1.73959
$971$	15.6928	0.503605	0.251803	−	0.967779i	$-0.418977\pi$
$971$	15.6928	0.503605	0.251803	+	0.967779i	$0.418977\pi$
$972$	−1.00000	−0.0320750
$973$	2.96190	0.0949540
$974$	32.8898	1.05386
$975$	−0.152004	−0.00486802
$976$	−1.00000	−0.0320092
$977$	0.484623	0.0155045	0.00775223	−	0.999970i	$-0.497532\pi$
$977$	0.484623	0.0155045	0.00775223	+	0.999970i	$0.497532\pi$
$978$	7.43775	0.237833
$979$	1.68773	0.0539401
$980$	−36.3616	−1.16153
$981$	1.27730	0.0407812
$982$	−0.0114984	−0.000366928 0
$983$	−20.0980	−0.641027	−0.320514	−	0.947244i	$-0.603856\pi$
$983$	−20.0980	−0.641027	−0.320514	+	0.947244i	$0.603856\pi$
$984$	0.597641	0.0190521
$985$	−41.8596	−1.33376
$986$	−5.89814	−0.187835
$987$	−45.2474	−1.44024
$988$	0.108707	0.00345844
$989$	1.63370	0.0519486
$990$	−3.01987	−0.0959778
$991$	40.6534	1.29140	0.645699	−	0.763592i	$-0.276566\pi$
$991$	40.6534	1.29140	0.645699	+	0.763592i	$0.276566\pi$
$992$	2.62382	0.0833065
$993$	10.4075	0.330271
$994$	−1.15073	−0.0364988
$995$	36.2633	1.14962
$996$	3.93936	0.124823
$997$	14.8395	0.469973	0.234986	−	0.971999i	$-0.424495\pi$
$997$	14.8395	0.469973	0.234986	+	0.971999i	$0.424495\pi$
$998$	22.9248	0.725671
$999$	8.18081	0.258829

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.y.1.2	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.y.1.2	✓	7	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.01987 q^{5} +1.00000 q^{6} +4.36357 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.01987 q^{5} +1.00000 q^{6} +4.36357 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.01987 q^{10} -1.00000 q^{11} -1.00000 q^{12} +0.0368976 q^{13} -4.36357 q^{14} +3.01987 q^{15} +1.00000 q^{16} -0.558875 q^{17} -1.00000 q^{18} +2.94619 q^{19} -3.01987 q^{20} -4.36357 q^{21} +1.00000 q^{22} +0.521977 q^{23} +1.00000 q^{24} +4.11962 q^{25} -0.0368976 q^{26} -1.00000 q^{27} +4.36357 q^{28} -10.5536 q^{29} -3.01987 q^{30} -2.62382 q^{31} -1.00000 q^{32} +1.00000 q^{33} +0.558875 q^{34} -13.1774 q^{35} +1.00000 q^{36} -8.18081 q^{37} -2.94619 q^{38} -0.0368976 q^{39} +3.01987 q^{40} +0.597641 q^{41} +4.36357 q^{42} +3.12983 q^{43} -1.00000 q^{44} -3.01987 q^{45} -0.521977 q^{46} +10.3693 q^{47} -1.00000 q^{48} +12.0408 q^{49} -4.11962 q^{50} +0.558875 q^{51} +0.0368976 q^{52} -0.0266868 q^{53} +1.00000 q^{54} +3.01987 q^{55} -4.36357 q^{56} -2.94619 q^{57} +10.5536 q^{58} +2.47353 q^{59} +3.01987 q^{60} -1.00000 q^{61} +2.62382 q^{62} +4.36357 q^{63} +1.00000 q^{64} -0.111426 q^{65} -1.00000 q^{66} -5.64725 q^{67} -0.558875 q^{68} -0.521977 q^{69} +13.1774 q^{70} +0.263712 q^{71} -1.00000 q^{72} -1.59228 q^{73} +8.18081 q^{74} -4.11962 q^{75} +2.94619 q^{76} -4.36357 q^{77} +0.0368976 q^{78} +16.9297 q^{79} -3.01987 q^{80} +1.00000 q^{81} -0.597641 q^{82} -3.93936 q^{83} -4.36357 q^{84} +1.68773 q^{85} -3.12983 q^{86} +10.5536 q^{87} +1.00000 q^{88} -1.68773 q^{89} +3.01987 q^{90} +0.161005 q^{91} +0.521977 q^{92} +2.62382 q^{93} -10.3693 q^{94} -8.89711 q^{95} +1.00000 q^{96} -17.9409 q^{97} -12.0408 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} - 2 q^{5} + 7 q^{6} + q^{7} - 7 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 - 2 * q^5 + 7 * q^6 + q^7 - 7 * q^8 + 7 * q^9	\( 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} - 2 q^{5} + 7 q^{6} + q^{7} - 7 q^{8} + 7 q^{9} + 2 q^{10} - 7 q^{11} - 7 q^{12} - q^{14} + 2 q^{15} + 7 q^{16} + 3 q^{17} - 7 q^{18} - 5 q^{19} - 2 q^{20} - q^{21} + 7 q^{22} - 3 q^{23} + 7 q^{24} + 11 q^{25} - 7 q^{27} + q^{28} - 14 q^{29} - 2 q^{30} + 5 q^{31} - 7 q^{32} + 7 q^{33} - 3 q^{34} - 9 q^{35} + 7 q^{36} + 14 q^{37} + 5 q^{38} + 2 q^{40} - 7 q^{41} + q^{42} + q^{43} - 7 q^{44} - 2 q^{45} + 3 q^{46} - 7 q^{48} - 11 q^{50} - 3 q^{51} - 3 q^{53} + 7 q^{54} + 2 q^{55} - q^{56} + 5 q^{57} + 14 q^{58} - 14 q^{59} + 2 q^{60} - 7 q^{61} - 5 q^{62} + q^{63} + 7 q^{64} - 10 q^{65} - 7 q^{66} + 3 q^{68} + 3 q^{69} + 9 q^{70} - 22 q^{71} - 7 q^{72} + q^{73} - 14 q^{74} - 11 q^{75} - 5 q^{76} - q^{77} + 10 q^{79} - 2 q^{80} + 7 q^{81} + 7 q^{82} - 17 q^{83} - q^{84} + 18 q^{85} - q^{86} + 14 q^{87} + 7 q^{88} - 18 q^{89} + 2 q^{90} + 21 q^{91} - 3 q^{92} - 5 q^{93} - 41 q^{95} + 7 q^{96} + 25 q^{97} - 7 q^{99}+O(q^{100}) \) 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 - 2 * q^5 + 7 * q^6 + q^7 - 7 * q^8 + 7 * q^9 + 2 * q^10 - 7 * q^11 - 7 * q^12 - q^14 + 2 * q^15 + 7 * q^16 + 3 * q^17 - 7 * q^18 - 5 * q^19 - 2 * q^20 - q^21 + 7 * q^22 - 3 * q^23 + 7 * q^24 + 11 * q^25 - 7 * q^27 + q^28 - 14 * q^29 - 2 * q^30 + 5 * q^31 - 7 * q^32 + 7 * q^33 - 3 * q^34 - 9 * q^35 + 7 * q^36 + 14 * q^37 + 5 * q^38 + 2 * q^40 - 7 * q^41 + q^42 + q^43 - 7 * q^44 - 2 * q^45 + 3 * q^46 - 7 * q^48 - 11 * q^50 - 3 * q^51 - 3 * q^53 + 7 * q^54 + 2 * q^55 - q^56 + 5 * q^57 + 14 * q^58 - 14 * q^59 + 2 * q^60 - 7 * q^61 - 5 * q^62 + q^63 + 7 * q^64 - 10 * q^65 - 7 * q^66 + 3 * q^68 + 3 * q^69 + 9 * q^70 - 22 * q^71 - 7 * q^72 + q^73 - 14 * q^74 - 11 * q^75 - 5 * q^76 - q^77 + 10 * q^79 - 2 * q^80 + 7 * q^81 + 7 * q^82 - 17 * q^83 - q^84 + 18 * q^85 - q^86 + 14 * q^87 + 7 * q^88 - 18 * q^89 + 2 * q^90 + 21 * q^91 - 3 * q^92 - 5 * q^93 - 41 * q^95 + 7 * q^96 + 25 * q^97 - 7 * q^99

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