LMFDB - Embedded newform 6762.2.a.ch.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6762,2,Mod(1,6762)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6762, 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("6762.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6762.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:	$53.9948418468$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.138768.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 11x^{2} + 12x + 8 $ x^4 - 2x^3 - 11x^2 + 12*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 966)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$3.89728$ of defining polynomial
Character	$\chi$	$=$	6762.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.89728 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.89728 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +3.89728 q^{10} +4.02636 q^{11} +1.00000 q^{12} +0.619394 q^{13} -3.89728 q^{15} +1.00000 q^{16} +1.25153 q^{17} -1.00000 q^{18} +8.41395 q^{19} -3.89728 q^{20} -4.02636 q^{22} +1.00000 q^{23} -1.00000 q^{24} +10.1888 q^{25} -0.619394 q^{26} +1.00000 q^{27} -9.41395 q^{29} +3.89728 q^{30} -5.18878 q^{31} -1.00000 q^{32} +4.02636 q^{33} -1.25153 q^{34} +1.00000 q^{36} +1.38061 q^{37} -8.41395 q^{38} +0.619394 q^{39} +3.89728 q^{40} +4.41395 q^{41} +2.00000 q^{43} +4.02636 q^{44} -3.89728 q^{45} -1.00000 q^{46} +6.13607 q^{47} +1.00000 q^{48} -10.1888 q^{50} +1.25153 q^{51} +0.619394 q^{52} -1.89728 q^{53} -1.00000 q^{54} -15.6918 q^{55} +8.41395 q^{57} +9.41395 q^{58} -11.0197 q^{59} -3.89728 q^{60} +0.205443 q^{61} +5.18878 q^{62} +1.00000 q^{64} -2.41395 q^{65} -4.02636 q^{66} +12.0527 q^{67} +1.25153 q^{68} +1.00000 q^{69} +0.483327 q^{71} -1.00000 q^{72} -3.15544 q^{73} -1.38061 q^{74} +10.1888 q^{75} +8.41395 q^{76} -0.619394 q^{78} +15.4737 q^{79} -3.89728 q^{80} +1.00000 q^{81} -4.41395 q^{82} -7.13607 q^{83} -4.87755 q^{85} -2.00000 q^{86} -9.41395 q^{87} -4.02636 q^{88} -10.2085 q^{89} +3.89728 q^{90} +1.00000 q^{92} -5.18878 q^{93} -6.13607 q^{94} -32.7915 q^{95} -1.00000 q^{96} -12.0531 q^{97} +4.02636 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} - 2 q^{5} - 4 q^{6} - 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 - 2 * q^5 - 4 * q^6 - 4 * q^8 + 4 * q^9	$ 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} - 2 q^{5} - 4 q^{6} - 4 q^{8} + 4 q^{9} + 2 q^{10} + 6 q^{11} + 4 q^{12} + 2 q^{13} - 2 q^{15} + 4 q^{16} + 2 q^{17} - 4 q^{18} + 6 q^{19} - 2 q^{20} - 6 q^{22} + 4 q^{23} - 4 q^{24} + 6 q^{25} - 2 q^{26} + 4 q^{27} - 10 q^{29} + 2 q^{30} + 14 q^{31} - 4 q^{32} + 6 q^{33} - 2 q^{34} + 4 q^{36} + 6 q^{37} - 6 q^{38} + 2 q^{39} + 2 q^{40} - 10 q^{41} + 8 q^{43} + 6 q^{44} - 2 q^{45} - 4 q^{46} + 10 q^{47} + 4 q^{48} - 6 q^{50} + 2 q^{51} + 2 q^{52} + 6 q^{53} - 4 q^{54} - 22 q^{55} + 6 q^{57} + 10 q^{58} - 24 q^{59} - 2 q^{60} + 28 q^{61} - 14 q^{62} + 4 q^{64} + 18 q^{65} - 6 q^{66} + 28 q^{67} + 2 q^{68} + 4 q^{69} + 16 q^{71} - 4 q^{72} - 6 q^{73} - 6 q^{74} + 6 q^{75} + 6 q^{76} - 2 q^{78} - 4 q^{79} - 2 q^{80} + 4 q^{81} + 10 q^{82} - 14 q^{83} - 26 q^{85} - 8 q^{86} - 10 q^{87} - 6 q^{88} + 14 q^{89} + 2 q^{90} + 4 q^{92} + 14 q^{93} - 10 q^{94} - 34 q^{95} - 4 q^{96} + 6 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 - 2 * q^5 - 4 * q^6 - 4 * q^8 + 4 * q^9 + 2 * q^10 + 6 * q^11 + 4 * q^12 + 2 * q^13 - 2 * q^15 + 4 * q^16 + 2 * q^17 - 4 * q^18 + 6 * q^19 - 2 * q^20 - 6 * q^22 + 4 * q^23 - 4 * q^24 + 6 * q^25 - 2 * q^26 + 4 * q^27 - 10 * q^29 + 2 * q^30 + 14 * q^31 - 4 * q^32 + 6 * q^33 - 2 * q^34 + 4 * q^36 + 6 * q^37 - 6 * q^38 + 2 * q^39 + 2 * q^40 - 10 * q^41 + 8 * q^43 + 6 * q^44 - 2 * q^45 - 4 * q^46 + 10 * q^47 + 4 * q^48 - 6 * q^50 + 2 * q^51 + 2 * q^52 + 6 * q^53 - 4 * q^54 - 22 * q^55 + 6 * q^57 + 10 * q^58 - 24 * q^59 - 2 * q^60 + 28 * q^61 - 14 * q^62 + 4 * q^64 + 18 * q^65 - 6 * q^66 + 28 * q^67 + 2 * q^68 + 4 * q^69 + 16 * q^71 - 4 * q^72 - 6 * q^73 - 6 * q^74 + 6 * q^75 + 6 * q^76 - 2 * q^78 - 4 * q^79 - 2 * q^80 + 4 * q^81 + 10 * q^82 - 14 * q^83 - 26 * q^85 - 8 * q^86 - 10 * q^87 - 6 * q^88 + 14 * q^89 + 2 * q^90 + 4 * q^92 + 14 * q^93 - 10 * q^94 - 34 * q^95 - 4 * q^96 + 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
$5$	−3.89728	−1.74292	−0.871458	−	0.490470i	$-0.836825\pi$
$5$	−3.89728	−1.74292	−0.871458	+	0.490470i	$0.836825\pi$
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	3.89728	1.23243
$11$	4.02636	1.21399	0.606996	−	0.794705i	$-0.292374\pi$
$11$	4.02636	1.21399	0.606996	+	0.794705i	$0.292374\pi$
$12$	1.00000	0.288675
$13$	0.619394	0.171789	0.0858945	−	0.996304i	$-0.472625\pi$
$13$	0.619394	0.171789	0.0858945	+	0.996304i	$0.472625\pi$
$14$	0	0
$15$	−3.89728	−1.00627
$16$	1.00000	0.250000
$17$	1.25153	0.303540	0.151770	−	0.988416i	$-0.451503\pi$
$17$	1.25153	0.303540	0.151770	+	0.988416i	$0.451503\pi$
$18$	−1.00000	−0.235702
$19$	8.41395	1.93029	0.965146	−	0.261710i	$-0.0842865\pi$
$19$	8.41395	1.93029	0.965146	+	0.261710i	$0.0842865\pi$
$20$	−3.89728	−0.871458
$21$	0	0
$22$	−4.02636	−0.858422
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−1.00000	−0.204124
$25$	10.1888	2.03776
$26$	−0.619394	−0.121473
$27$	1.00000	0.192450
$28$	0	0
$29$	−9.41395	−1.74813	−0.874063	−	0.485812i	$-0.838524\pi$
$29$	−9.41395	−1.74813	−0.874063	+	0.485812i	$0.838524\pi$
$30$	3.89728	0.711542
$31$	−5.18878	−0.931933	−0.465966	−	0.884802i	$-0.654293\pi$
$31$	−5.18878	−0.931933	−0.465966	+	0.884802i	$0.654293\pi$
$32$	−1.00000	−0.176777
$33$	4.02636	0.700899
$34$	−1.25153	−0.214635
$35$	0	0
$36$	1.00000	0.166667
$37$	1.38061	0.226970	0.113485	−	0.993540i	$-0.463799\pi$
$37$	1.38061	0.226970	0.113485	+	0.993540i	$0.463799\pi$
$38$	−8.41395	−1.36492
$39$	0.619394	0.0991824
$40$	3.89728	0.616214
$41$	4.41395	0.689343	0.344672	−	0.938723i	$-0.387990\pi$
$41$	4.41395	0.689343	0.344672	+	0.938723i	$0.387990\pi$
$42$	0	0
$43$	2.00000	0.304997	0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000	0.304997	0.152499	+	0.988304i	$0.451268\pi$
$44$	4.02636	0.606996
$45$	−3.89728	−0.580972
$46$	−1.00000	−0.147442
$47$	6.13607	0.895037	0.447519	−	0.894275i	$-0.352308\pi$
$47$	6.13607	0.895037	0.447519	+	0.894275i	$0.352308\pi$
$48$	1.00000	0.144338
$49$	0	0
$50$	−10.1888	−1.44091
$51$	1.25153	0.175249
$52$	0.619394	0.0858945
$53$	−1.89728	−0.260611	−0.130306	−	0.991474i	$-0.541596\pi$
$53$	−1.89728	−0.260611	−0.130306	+	0.991474i	$0.541596\pi$
$54$	−1.00000	−0.136083
$55$	−15.6918	−2.11589
$56$	0	0
$57$	8.41395	1.11446
$58$	9.41395	1.23611
$59$	−11.0197	−1.43465	−0.717323	−	0.696741i	$-0.754633\pi$
$59$	−11.0197	−1.43465	−0.717323	+	0.696741i	$0.754633\pi$
$60$	−3.89728	−0.503137
$61$	0.205443	0.0263042	0.0131521	−	0.999914i	$-0.495813\pi$
$61$	0.205443	0.0263042	0.0131521	+	0.999914i	$0.495813\pi$
$62$	5.18878	0.658976
$63$	0	0
$64$	1.00000	0.125000
$65$	−2.41395	−0.299414
$66$	−4.02636	−0.495610
$67$	12.0527	1.47247	0.736237	−	0.676724i	$-0.236601\pi$
$67$	12.0527	1.47247	0.736237	+	0.676724i	$0.236601\pi$
$68$	1.25153	0.151770
$69$	1.00000	0.120386
$70$	0	0
$71$	0.483327	0.0573604	0.0286802	−	0.999589i	$-0.490870\pi$
$71$	0.483327	0.0573604	0.0286802	+	0.999589i	$0.490870\pi$
$72$	−1.00000	−0.117851
$73$	−3.15544	−0.369316	−0.184658	−	0.982803i	$-0.559118\pi$
$73$	−3.15544	−0.369316	−0.184658	+	0.982803i	$0.559118\pi$
$74$	−1.38061	−0.160492
$75$	10.1888	1.17650
$76$	8.41395	0.965146
$77$	0	0
$78$	−0.619394	−0.0701326
$79$	15.4737	1.74092	0.870461	−	0.492237i	$-0.163821\pi$
$79$	15.4737	1.74092	0.870461	+	0.492237i	$0.163821\pi$
$80$	−3.89728	−0.435729
$81$	1.00000	0.111111
$82$	−4.41395	−0.487439
$83$	−7.13607	−0.783285	−0.391643	−	0.920117i	$-0.628093\pi$
$83$	−7.13607	−0.783285	−0.391643	+	0.920117i	$0.628093\pi$
$84$	0	0
$85$	−4.87755	−0.529045
$86$	−2.00000	−0.215666
$87$	−9.41395	−1.00928
$88$	−4.02636	−0.429211
$89$	−10.2085	−1.08210	−0.541050	−	0.840990i	$-0.681973\pi$
$89$	−10.2085	−1.08210	−0.541050	+	0.840990i	$0.681973\pi$
$90$	3.89728	0.410809
$91$	0	0
$92$	1.00000	0.104257
$93$	−5.18878	−0.538052
$94$	−6.13607	−0.632887
$95$	−32.7915	−3.36434
$96$	−1.00000	−0.102062
$97$	−12.0531	−1.22380	−0.611902	−	0.790934i	$-0.709595\pi$
$97$	−12.0531	−1.22380	−0.611902	+	0.790934i	$0.709595\pi$
$98$	0	0
$99$	4.02636	0.404664
$100$	10.1888	1.01888
$101$	10.1888	1.01382	0.506911	−	0.861999i	$-0.330787\pi$
$101$	10.1888	1.01382	0.506911	+	0.861999i	$0.330787\pi$
$102$	−1.25153	−0.123920
$103$	−6.95698	−0.685492	−0.342746	−	0.939428i	$-0.611357\pi$
$103$	−6.95698	−0.685492	−0.342746	+	0.939428i	$0.611357\pi$
$104$	−0.619394	−0.0607366
$105$	0	0
$106$	1.89728	0.184280
$107$	11.1361	1.07656	0.538282	−	0.842765i	$-0.319073\pi$
$107$	11.1361	1.07656	0.538282	+	0.842765i	$0.319073\pi$
$108$	1.00000	0.0962250
$109$	1.36787	0.131018	0.0655089	−	0.997852i	$-0.479133\pi$
$109$	1.36787	0.131018	0.0655089	+	0.997852i	$0.479133\pi$
$110$	15.6918	1.49616
$111$	1.38061	0.131041
$112$	0	0
$113$	19.7582	1.85869	0.929346	−	0.369210i	$-0.120372\pi$
$113$	19.7582	1.85869	0.929346	+	0.369210i	$0.120372\pi$
$114$	−8.41395	−0.788039
$115$	−3.89728	−0.363423
$116$	−9.41395	−0.874063
$117$	0.619394	0.0572630
$118$	11.0197	1.01445
$119$	0	0
$120$	3.89728	0.355771
$121$	5.21155	0.473777
$122$	−0.205443	−0.0185999
$123$	4.41395	0.397993
$124$	−5.18878	−0.465966
$125$	−20.2221	−1.80872
$126$	0	0
$127$	−15.4337	−1.36952	−0.684759	−	0.728770i	$-0.740092\pi$
$127$	−15.4337	−1.36952	−0.684759	+	0.728770i	$0.740092\pi$
$128$	−1.00000	−0.0883883
$129$	2.00000	0.176090
$130$	2.41395	0.211718
$131$	−20.8942	−1.82554	−0.912769	−	0.408476i	$-0.866060\pi$
$131$	−20.8942	−1.82554	−0.912769	+	0.408476i	$0.866060\pi$
$132$	4.02636	0.350449
$133$	0	0
$134$	−12.0527	−1.04120
$135$	−3.89728	−0.335424
$136$	−1.25153	−0.107318
$137$	6.37398	0.544566	0.272283	−	0.962217i	$-0.412221\pi$
$137$	6.37398	0.544566	0.272283	+	0.962217i	$0.412221\pi$
$138$	−1.00000	−0.0851257
$139$	2.13607	0.181179	0.0905894	−	0.995888i	$-0.471125\pi$
$139$	2.13607	0.181179	0.0905894	+	0.995888i	$0.471125\pi$
$140$	0	0
$141$	6.13607	0.516750
$142$	−0.483327	−0.0405599
$143$	2.49390	0.208551
$144$	1.00000	0.0833333
$145$	36.6888	3.04684
$146$	3.15544	0.261146
$147$	0	0
$148$	1.38061	0.113485
$149$	11.8218	0.968479	0.484240	−	0.874935i	$-0.339096\pi$
$149$	11.8218	0.968479	0.484240	+	0.874935i	$0.339096\pi$
$150$	−10.1888	−0.831911
$151$	9.43368	0.767702	0.383851	−	0.923395i	$-0.374598\pi$
$151$	9.43368	0.767702	0.383851	+	0.923395i	$0.374598\pi$
$152$	−8.41395	−0.682462
$153$	1.25153	0.101180
$154$	0	0
$155$	20.2221	1.62428
$156$	0.619394	0.0495912
$157$	−3.78182	−0.301822	−0.150911	−	0.988547i	$-0.548221\pi$
$157$	−3.78182	−0.301822	−0.150911	+	0.988547i	$0.548221\pi$
$158$	−15.4737	−1.23102
$159$	−1.89728	−0.150464
$160$	3.89728	0.308107
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	4.48333	0.351161	0.175581	−	0.984465i	$-0.443820\pi$
$163$	4.48333	0.351161	0.175581	+	0.984465i	$0.443820\pi$
$164$	4.41395	0.344672
$165$	−15.6918	−1.22161
$166$	7.13607	0.553866
$167$	−17.1388	−1.32624	−0.663119	−	0.748514i	$-0.730768\pi$
$167$	−17.1388	−1.32624	−0.663119	+	0.748514i	$0.730768\pi$
$168$	0	0
$169$	−12.6164	−0.970489
$170$	4.87755	0.374091
$171$	8.41395	0.643431
$172$	2.00000	0.152499
$173$	2.84456	0.216268	0.108134	−	0.994136i	$-0.465512\pi$
$173$	2.84456	0.216268	0.108134	+	0.994136i	$0.465512\pi$
$174$	9.41395	0.713670
$175$	0	0
$176$	4.02636	0.303498
$177$	−11.0197	−0.828293
$178$	10.2085	0.765160
$179$	13.2782	0.992463	0.496231	−	0.868190i	$-0.334717\pi$
$179$	13.2782	0.992463	0.496231	+	0.868190i	$0.334717\pi$
$180$	−3.89728	−0.290486
$181$	−14.5066	−1.07827	−0.539135	−	0.842219i	$-0.681249\pi$
$181$	−14.5066	−1.07827	−0.539135	+	0.842219i	$0.681249\pi$
$182$	0	0
$183$	0.205443	0.0151868
$184$	−1.00000	−0.0737210
$185$	−5.38061	−0.395590
$186$	5.18878	0.380460
$187$	5.03910	0.368495
$188$	6.13607	0.447519
$189$	0	0
$190$	32.7915	2.37895
$191$	−15.2419	−1.10286	−0.551431	−	0.834221i	$-0.685918\pi$
$191$	−15.2419	−1.10286	−0.551431	+	0.834221i	$0.685918\pi$
$192$	1.00000	0.0721688
$193$	11.9500	0.860179	0.430090	−	0.902786i	$-0.358482\pi$
$193$	11.9500	0.860179	0.430090	+	0.902786i	$0.358482\pi$
$194$	12.0531	0.865360
$195$	−2.41395	−0.172867
$196$	0	0
$197$	−18.5391	−1.32086	−0.660428	−	0.750889i	$-0.729625\pi$
$197$	−18.5391	−1.32086	−0.660428	+	0.750889i	$0.729625\pi$
$198$	−4.02636	−0.286141
$199$	8.91753	0.632147	0.316073	−	0.948735i	$-0.397635\pi$
$199$	8.91753	0.632147	0.316073	+	0.948735i	$0.397635\pi$
$200$	−10.1888	−0.720456
$201$	12.0527	0.850133
$202$	−10.1888	−0.716880
$203$	0	0
$204$	1.25153	0.0876244
$205$	−17.2024	−1.20147
$206$	6.95698	0.484716
$207$	1.00000	0.0695048
$208$	0.619394	0.0429473
$209$	33.8776	2.34336
$210$	0	0
$211$	17.1694	1.18199	0.590996	−	0.806675i	$-0.298735\pi$
$211$	17.1694	1.18199	0.590996	+	0.806675i	$0.298735\pi$
$212$	−1.89728	−0.130306
$213$	0.483327	0.0331170
$214$	−11.1361	−0.761246
$215$	−7.79456	−0.531584
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	−1.36787	−0.0926436
$219$	−3.15544	−0.213225
$220$	−15.6918	−1.05794
$221$	0.775189	0.0521448
$222$	−1.38061	−0.0926602
$223$	9.39422	0.629084	0.314542	−	0.949244i	$-0.398149\pi$
$223$	9.39422	0.629084	0.314542	+	0.949244i	$0.398149\pi$
$224$	0	0
$225$	10.1888	0.679252
$226$	−19.7582	−1.31429
$227$	−25.3179	−1.68041	−0.840203	−	0.542272i	$-0.817564\pi$
$227$	−25.3179	−1.68041	−0.840203	+	0.542272i	$0.817564\pi$
$228$	8.41395	0.557228
$229$	11.9600	0.790341	0.395170	−	0.918608i	$-0.370686\pi$
$229$	11.9600	0.790341	0.395170	+	0.918608i	$0.370686\pi$
$230$	3.89728	0.256979
$231$	0	0
$232$	9.41395	0.618056
$233$	−8.86429	−0.580719	−0.290360	−	0.956918i	$-0.593775\pi$
$233$	−8.86429	−0.580719	−0.290360	+	0.956918i	$0.593775\pi$
$234$	−0.619394	−0.0404911
$235$	−23.9140	−1.55997
$236$	−11.0197	−0.717323
$237$	15.4737	1.00512
$238$	0	0
$239$	9.93062	0.642359	0.321179	−	0.947018i	$-0.395921\pi$
$239$	9.93062	0.642359	0.321179	+	0.947018i	$0.395921\pi$
$240$	−3.89728	−0.251568
$241$	12.2840	0.791282	0.395641	−	0.918405i	$-0.370523\pi$
$241$	12.2840	0.791282	0.395641	+	0.918405i	$0.370523\pi$
$242$	−5.21155	−0.335011
$243$	1.00000	0.0641500
$244$	0.205443	0.0131521
$245$	0	0
$246$	−4.41395	−0.281423
$247$	5.21155	0.331603
$248$	5.18878	0.329488
$249$	−7.13607	−0.452230
$250$	20.2221	1.27896
$251$	−6.81481	−0.430147	−0.215073	−	0.976598i	$-0.568999\pi$
$251$	−6.81481	−0.430147	−0.215073	+	0.976598i	$0.568999\pi$
$252$	0	0
$253$	4.02636	0.253135
$254$	15.4337	0.968395
$255$	−4.87755	−0.305444
$256$	1.00000	0.0625000
$257$	23.5000	1.46589	0.732945	−	0.680288i	$-0.238145\pi$
$257$	23.5000	1.46589	0.732945	+	0.680288i	$0.238145\pi$
$258$	−2.00000	−0.124515
$259$	0	0
$260$	−2.41395	−0.149707
$261$	−9.41395	−0.582709
$262$	20.8942	1.29085
$263$	18.8534	1.16255	0.581275	−	0.813707i	$-0.302554\pi$
$263$	18.8534	1.16255	0.581275	+	0.813707i	$0.302554\pi$
$264$	−4.02636	−0.247805
$265$	7.39422	0.454224
$266$	0	0
$267$	−10.2085	−0.624751
$268$	12.0527	0.736237
$269$	26.7976	1.63388	0.816940	−	0.576723i	$-0.195669\pi$
$269$	26.7976	1.63388	0.816940	+	0.576723i	$0.195669\pi$
$270$	3.89728	0.237181
$271$	28.4803	1.73005	0.865027	−	0.501725i	$-0.167301\pi$
$271$	28.4803	1.73005	0.865027	+	0.501725i	$0.167301\pi$
$272$	1.25153	0.0758850
$273$	0	0
$274$	−6.37398	−0.385066
$275$	41.0237	2.47382
$276$	1.00000	0.0601929
$277$	19.3969	1.16545	0.582724	−	0.812670i	$-0.301987\pi$
$277$	19.3969	1.16545	0.582724	+	0.812670i	$0.301987\pi$
$278$	−2.13607	−0.128113
$279$	−5.18878	−0.310644
$280$	0	0
$281$	22.3903	1.33569	0.667847	−	0.744299i	$-0.267216\pi$
$281$	22.3903	1.33569	0.667847	+	0.744299i	$0.267216\pi$
$282$	−6.13607	−0.365397
$283$	10.0395	0.596784	0.298392	−	0.954443i	$-0.403550\pi$
$283$	10.0395	0.596784	0.298392	+	0.954443i	$0.403550\pi$
$284$	0.483327	0.0286802
$285$	−32.7915	−1.94240
$286$	−2.49390	−0.147468
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	−15.4337	−0.907863
$290$	−36.6888	−2.15444
$291$	−12.0531	−0.706564
$292$	−3.15544	−0.184658
$293$	25.0228	1.46185	0.730924	−	0.682459i	$-0.239090\pi$
$293$	25.0228	1.46185	0.730924	+	0.682459i	$0.239090\pi$
$294$	0	0
$295$	42.9469	2.50047
$296$	−1.38061	−0.0802461
$297$	4.02636	0.233633
$298$	−11.8218	−0.684818
$299$	0.619394	0.0358205
$300$	10.1888	0.588250
$301$	0	0
$302$	−9.43368	−0.542847
$303$	10.1888	0.585330
$304$	8.41395	0.482573
$305$	−0.800667	−0.0458461
$306$	−1.25153	−0.0715451
$307$	27.6221	1.57648	0.788238	−	0.615370i	$-0.210993\pi$
$307$	27.6221	1.57648	0.788238	+	0.615370i	$0.210993\pi$
$308$	0	0
$309$	−6.95698	−0.395769
$310$	−20.2221	−1.14854
$311$	−12.8337	−0.727730	−0.363865	−	0.931452i	$-0.618543\pi$
$311$	−12.8337	−0.727730	−0.363865	+	0.931452i	$0.618543\pi$
$312$	−0.619394	−0.0350663
$313$	11.3306	0.640443	0.320222	−	0.947343i	$-0.396243\pi$
$313$	11.3306	0.640443	0.320222	+	0.947343i	$0.396243\pi$
$314$	3.78182	0.213420
$315$	0	0
$316$	15.4737	0.870461
$317$	29.0197	1.62991	0.814955	−	0.579524i	$-0.196762\pi$
$317$	29.0197	1.62991	0.814955	+	0.579524i	$0.196762\pi$
$318$	1.89728	0.106394
$319$	−37.9039	−2.12221
$320$	−3.89728	−0.217865
$321$	11.1361	0.621555
$322$	0	0
$323$	10.5303	0.585921
$324$	1.00000	0.0555556
$325$	6.31087	0.350064
$326$	−4.48333	−0.248309
$327$	1.36787	0.0756432
$328$	−4.41395	−0.243720
$329$	0	0
$330$	15.6918	0.863807
$331$	29.1024	1.59961	0.799806	−	0.600259i	$-0.204936\pi$
$331$	29.1024	1.59961	0.799806	+	0.600259i	$0.204936\pi$
$332$	−7.13607	−0.391643
$333$	1.38061	0.0756567
$334$	17.1388	0.937792
$335$	−46.9728	−2.56640
$336$	0	0
$337$	2.54215	0.138480	0.0692399	−	0.997600i	$-0.477943\pi$
$337$	2.54215	0.138480	0.0692399	+	0.997600i	$0.477943\pi$
$338$	12.6164	0.686239
$339$	19.7582	1.07312
$340$	−4.87755	−0.264522
$341$	−20.8919	−1.13136
$342$	−8.41395	−0.454974
$343$	0	0
$344$	−2.00000	−0.107833
$345$	−3.89728	−0.209822
$346$	−2.84456	−0.152925
$347$	20.3776	1.09392	0.546962	−	0.837157i	$-0.315784\pi$
$347$	20.3776	1.09392	0.546962	+	0.837157i	$0.315784\pi$
$348$	−9.41395	−0.504641
$349$	−5.63876	−0.301836	−0.150918	−	0.988546i	$-0.548223\pi$
$349$	−5.63876	−0.301836	−0.150918	+	0.988546i	$0.548223\pi$
$350$	0	0
$351$	0.619394	0.0330608
$352$	−4.02636	−0.214606
$353$	4.69759	0.250027	0.125014	−	0.992155i	$-0.460103\pi$
$353$	4.69759	0.250027	0.125014	+	0.992155i	$0.460103\pi$
$354$	11.0197	0.585692
$355$	−1.88366	−0.0999743
$356$	−10.2085	−0.541050
$357$	0	0
$358$	−13.2782	−0.701777
$359$	−28.4303	−1.50049	−0.750246	−	0.661158i	$-0.770065\pi$
$359$	−28.4303	−1.50049	−0.750246	+	0.661158i	$0.770065\pi$
$360$	3.89728	0.205405
$361$	51.7946	2.72603
$362$	14.5066	0.762452
$363$	5.21155	0.273536
$364$	0	0
$365$	12.2976	0.643686
$366$	−0.205443	−0.0107387
$367$	6.27177	0.327384	0.163692	−	0.986511i	$-0.447660\pi$
$367$	6.27177	0.327384	0.163692	+	0.986511i	$0.447660\pi$
$368$	1.00000	0.0521286
$369$	4.41395	0.229781
$370$	5.38061	0.279724
$371$	0	0
$372$	−5.18878	−0.269026
$373$	−6.27396	−0.324853	−0.162427	−	0.986721i	$-0.551932\pi$
$373$	−6.27396	−0.324853	−0.162427	+	0.986721i	$0.551932\pi$
$374$	−5.03910	−0.260565
$375$	−20.2221	−1.04427
$376$	−6.13607	−0.316443
$377$	−5.83095	−0.300309
$378$	0	0
$379$	−28.2248	−1.44981	−0.724906	−	0.688848i	$-0.758117\pi$
$379$	−28.2248	−1.44981	−0.724906	+	0.688848i	$0.758117\pi$
$380$	−32.7915	−1.68217
$381$	−15.4337	−0.790691
$382$	15.2419	0.779841
$383$	−9.44658	−0.482698	−0.241349	−	0.970438i	$-0.577590\pi$
$383$	−9.44658	−0.482698	−0.241349	+	0.970438i	$0.577590\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−11.9500	−0.608239
$387$	2.00000	0.101666
$388$	−12.0531	−0.611902
$389$	5.64183	0.286052	0.143026	−	0.989719i	$-0.454317\pi$
$389$	5.64183	0.286052	0.143026	+	0.989719i	$0.454317\pi$
$390$	2.41395	0.122235
$391$	1.25153	0.0632925
$392$	0	0
$393$	−20.8942	−1.05397
$394$	18.5391	0.933987
$395$	−60.3051	−3.03428
$396$	4.02636	0.202332
$397$	32.7388	1.64311	0.821557	−	0.570127i	$-0.193106\pi$
$397$	32.7388	1.64311	0.821557	+	0.570127i	$0.193106\pi$
$398$	−8.91753	−0.446995
$399$	0	0
$400$	10.1888	0.509439
$401$	−9.88490	−0.493628	−0.246814	−	0.969063i	$-0.579384\pi$
$401$	−9.88490	−0.493628	−0.246814	+	0.969063i	$0.579384\pi$
$402$	−12.0527	−0.601135
$403$	−3.21390	−0.160096
$404$	10.1888	0.506911
$405$	−3.89728	−0.193657
$406$	0	0
$407$	5.55881	0.275540
$408$	−1.25153	−0.0619598
$409$	25.1061	1.24142	0.620710	−	0.784041i	$-0.286845\pi$
$409$	25.1061	1.24142	0.620710	+	0.784041i	$0.286845\pi$
$410$	17.2024	0.849566
$411$	6.37398	0.314405
$412$	−6.95698	−0.342746
$413$	0	0
$414$	−1.00000	−0.0491473
$415$	27.8112	1.36520
$416$	−0.619394	−0.0303683
$417$	2.13607	0.104604
$418$	−33.8776	−1.65701
$419$	1.66548	0.0813640	0.0406820	−	0.999172i	$-0.487047\pi$
$419$	1.66548	0.0813640	0.0406820	+	0.999172i	$0.487047\pi$
$420$	0	0
$421$	4.61887	0.225110	0.112555	−	0.993645i	$-0.464097\pi$
$421$	4.61887	0.225110	0.112555	+	0.993645i	$0.464097\pi$
$422$	−17.1694	−0.835794
$423$	6.13607	0.298346
$424$	1.89728	0.0921400
$425$	12.7515	0.618540
$426$	−0.483327	−0.0234173
$427$	0	0
$428$	11.1361	0.538282
$429$	2.49390	0.120407
$430$	7.79456	0.375887
$431$	−32.8674	−1.58316	−0.791582	−	0.611062i	$-0.790742\pi$
$431$	−32.8674	−1.58316	−0.791582	+	0.611062i	$0.790742\pi$
$432$	1.00000	0.0481125
$433$	−21.0079	−1.00957	−0.504787	−	0.863244i	$-0.668429\pi$
$433$	−21.0079	−1.00957	−0.504787	+	0.863244i	$0.668429\pi$
$434$	0	0
$435$	36.6888	1.75909
$436$	1.36787	0.0655089
$437$	8.41395	0.402494
$438$	3.15544	0.150773
$439$	7.87004	0.375617	0.187808	−	0.982206i	$-0.439862\pi$
$439$	7.87004	0.375617	0.187808	+	0.982206i	$0.439862\pi$
$440$	15.6918	0.748079
$441$	0	0
$442$	−0.775189	−0.0368720
$443$	16.5561	0.786605	0.393303	−	0.919409i	$-0.371332\pi$
$443$	16.5561	0.786605	0.393303	+	0.919409i	$0.371332\pi$
$444$	1.38061	0.0655207
$445$	39.7854	1.88601
$446$	−9.39422	−0.444829
$447$	11.8218	0.559152
$448$	0	0
$449$	−10.4272	−0.492090	−0.246045	−	0.969258i	$-0.579131\pi$
$449$	−10.4272	−0.492090	−0.246045	+	0.969258i	$0.579131\pi$
$450$	−10.1888	−0.480304
$451$	17.7721	0.836858
$452$	19.7582	0.929346
$453$	9.43368	0.443233
$454$	25.3179	1.18823
$455$	0	0
$456$	−8.41395	−0.394019
$457$	25.8082	1.20726	0.603628	−	0.797266i	$-0.293721\pi$
$457$	25.8082	1.20726	0.603628	+	0.797266i	$0.293721\pi$
$458$	−11.9600	−0.558855
$459$	1.25153	0.0584163
$460$	−3.89728	−0.181712
$461$	19.1660	0.892650	0.446325	−	0.894871i	$-0.352733\pi$
$461$	19.1660	0.892650	0.446325	+	0.894871i	$0.352733\pi$
$462$	0	0
$463$	11.6891	0.543240	0.271620	−	0.962405i	$-0.412441\pi$
$463$	11.6891	0.543240	0.271620	+	0.962405i	$0.412441\pi$
$464$	−9.41395	−0.437032
$465$	20.2221	0.937779
$466$	8.86429	0.410630
$467$	−0.837576	−0.0387584	−0.0193792	−	0.999812i	$-0.506169\pi$
$467$	−0.837576	−0.0387584	−0.0193792	+	0.999812i	$0.506169\pi$
$468$	0.619394	0.0286315
$469$	0	0
$470$	23.9140	1.10307
$471$	−3.78182	−0.174257
$472$	11.0197	0.507224
$473$	8.05271	0.370264
$474$	−15.4737	−0.710728
$475$	85.7279	3.93347
$476$	0	0
$477$	−1.89728	−0.0868704
$478$	−9.93062	−0.454216
$479$	−3.58605	−0.163851	−0.0819254	−	0.996638i	$-0.526107\pi$
$479$	−3.58605	−0.163851	−0.0819254	+	0.996638i	$0.526107\pi$
$480$	3.89728	0.177886
$481$	0.855139	0.0389910
$482$	−12.2840	−0.559521
$483$	0	0
$484$	5.21155	0.236889
$485$	46.9742	2.13299
$486$	−1.00000	−0.0453609
$487$	−15.0361	−0.681349	−0.340674	−	0.940181i	$-0.610655\pi$
$487$	−15.0361	−0.681349	−0.340674	+	0.940181i	$0.610655\pi$
$488$	−0.205443	−0.00929995
$489$	4.48333	0.202743
$490$	0	0
$491$	−6.13302	−0.276779	−0.138390	−	0.990378i	$-0.544193\pi$
$491$	−6.13302	−0.276779	−0.138390	+	0.990378i	$0.544193\pi$
$492$	4.41395	0.198996
$493$	−11.7818	−0.530626
$494$	−5.21155	−0.234479
$495$	−15.6918	−0.705296
$496$	−5.18878	−0.232983
$497$	0	0
$498$	7.13607	0.319775
$499$	−21.4925	−0.962137	−0.481068	−	0.876683i	$-0.659751\pi$
$499$	−21.4925	−0.962137	−0.481068	+	0.876683i	$0.659751\pi$
$500$	−20.2221	−0.904361
$501$	−17.1388	−0.765704
$502$	6.81481	0.304160
$503$	14.0922	0.628339	0.314169	−	0.949367i	$-0.398274\pi$
$503$	14.0922	0.628339	0.314169	+	0.949367i	$0.398274\pi$
$504$	0	0
$505$	−39.7085	−1.76701
$506$	−4.02636	−0.178993
$507$	−12.6164	−0.560312
$508$	−15.4337	−0.684759
$509$	−11.9575	−0.530007	−0.265003	−	0.964247i	$-0.585373\pi$
$509$	−11.9575	−0.530007	−0.265003	+	0.964247i	$0.585373\pi$
$510$	4.87755	0.215982
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	8.41395	0.371485
$514$	−23.5000	−1.03654
$515$	27.1133	1.19475
$516$	2.00000	0.0880451
$517$	24.7060	1.08657
$518$	0	0
$519$	2.84456	0.124863
$520$	2.41395	0.105859
$521$	−22.3776	−0.980379	−0.490189	−	0.871616i	$-0.663072\pi$
$521$	−22.3776	−0.980379	−0.490189	+	0.871616i	$0.663072\pi$
$522$	9.41395	0.412037
$523$	−15.2660	−0.667537	−0.333768	−	0.942655i	$-0.608320\pi$
$523$	−15.2660	−0.667537	−0.333768	+	0.942655i	$0.608320\pi$
$524$	−20.8942	−0.912769
$525$	0	0
$526$	−18.8534	−0.822046
$527$	−6.49390	−0.282879
$528$	4.02636	0.175225
$529$	1.00000	0.0434783
$530$	−7.39422	−0.321185
$531$	−11.0197	−0.478215
$532$	0	0
$533$	2.73398	0.118422
$534$	10.2085	0.441765
$535$	−43.4004	−1.87636
$536$	−12.0527	−0.520598
$537$	13.2782	0.572999
$538$	−26.7976	−1.15533
$539$	0	0
$540$	−3.89728	−0.167712
$541$	4.79151	0.206003	0.103002	−	0.994681i	$-0.467155\pi$
$541$	4.79151	0.206003	0.103002	+	0.994681i	$0.467155\pi$
$542$	−28.4803	−1.22333
$543$	−14.5066	−0.622540
$544$	−1.25153	−0.0536588
$545$	−5.33096	−0.228353
$546$	0	0
$547$	20.5888	0.880312	0.440156	−	0.897921i	$-0.354923\pi$
$547$	20.5888	0.880312	0.440156	+	0.897921i	$0.354923\pi$
$548$	6.37398	0.272283
$549$	0.205443	0.00876808
$550$	−41.0237	−1.74926
$551$	−79.2085	−3.37440
$552$	−1.00000	−0.0425628
$553$	0	0
$554$	−19.3969	−0.824097
$555$	−5.38061	−0.228394
$556$	2.13607	0.0905894
$557$	26.6979	1.13123	0.565614	−	0.824670i	$-0.308639\pi$
$557$	26.6979	1.13123	0.565614	+	0.824670i	$0.308639\pi$
$558$	5.18878	0.219659
$559$	1.23879	0.0523952
$560$	0	0
$561$	5.03910	0.212751
$562$	−22.3903	−0.944478
$563$	−21.0070	−0.885339	−0.442670	−	0.896685i	$-0.645969\pi$
$563$	−21.0070	−0.885339	−0.442670	+	0.896685i	$0.645969\pi$
$564$	6.13607	0.258375
$565$	−77.0031	−3.23954
$566$	−10.0395	−0.421990
$567$	0	0
$568$	−0.483327	−0.0202800
$569$	−16.3381	−0.684929	−0.342465	−	0.939531i	$-0.611262\pi$
$569$	−16.3381	−0.684929	−0.342465	+	0.939531i	$0.611262\pi$
$570$	32.7915	1.37349
$571$	−3.04967	−0.127625	−0.0638124	−	0.997962i	$-0.520326\pi$
$571$	−3.04967	−0.127625	−0.0638124	+	0.997962i	$0.520326\pi$
$572$	2.49390	0.104275
$573$	−15.2419	−0.636738
$574$	0	0
$575$	10.1888	0.424902
$576$	1.00000	0.0416667
$577$	−3.89388	−0.162104	−0.0810521	−	0.996710i	$-0.525828\pi$
$577$	−3.89388	−0.162104	−0.0810521	+	0.996710i	$0.525828\pi$
$578$	15.4337	0.641956
$579$	11.9500	0.496625
$580$	36.6888	1.52342
$581$	0	0
$582$	12.0531	0.499616
$583$	−7.63912	−0.316380
$584$	3.15544	0.130573
$585$	−2.41395	−0.0998046
$586$	−25.0228	−1.03368
$587$	36.4701	1.50528	0.752641	−	0.658431i	$-0.228780\pi$
$587$	36.4701	1.50528	0.752641	+	0.658431i	$0.228780\pi$
$588$	0	0
$589$	−43.6582	−1.79890
$590$	−42.9469	−1.76810
$591$	−18.5391	−0.762597
$592$	1.38061	0.0567426
$593$	26.9466	1.10656	0.553282	−	0.832994i	$-0.313375\pi$
$593$	26.9466	1.10656	0.553282	+	0.832994i	$0.313375\pi$
$594$	−4.02636	−0.165203
$595$	0	0
$596$	11.8218	0.484240
$597$	8.91753	0.364970
$598$	−0.619394	−0.0253289
$599$	−39.2507	−1.60374	−0.801869	−	0.597499i	$-0.796161\pi$
$599$	−39.2507	−1.60374	−0.801869	+	0.597499i	$0.796161\pi$
$600$	−10.1888	−0.415955
$601$	7.94999	0.324287	0.162143	−	0.986767i	$-0.448159\pi$
$601$	7.94999	0.324287	0.162143	+	0.986767i	$0.448159\pi$
$602$	0	0
$603$	12.0527	0.490824
$604$	9.43368	0.383851
$605$	−20.3109	−0.825754
$606$	−10.1888	−0.413891
$607$	−18.1221	−0.735554	−0.367777	−	0.929914i	$-0.619881\pi$
$607$	−18.1221	−0.735554	−0.367777	+	0.929914i	$0.619881\pi$
$608$	−8.41395	−0.341231
$609$	0	0
$610$	0.800667	0.0324181
$611$	3.80064	0.153758
$612$	1.25153	0.0505900
$613$	−38.6655	−1.56168	−0.780842	−	0.624728i	$-0.785210\pi$
$613$	−38.6655	−1.56168	−0.780842	+	0.624728i	$0.785210\pi$
$614$	−27.6221	−1.11474
$615$	−17.2024	−0.693668
$616$	0	0
$617$	11.9509	0.481124	0.240562	−	0.970634i	$-0.422668\pi$
$617$	11.9509	0.481124	0.240562	+	0.970634i	$0.422668\pi$
$618$	6.95698	0.279851
$619$	14.9303	0.600098	0.300049	−	0.953924i	$-0.402997\pi$
$619$	14.9303	0.600098	0.300049	+	0.953924i	$0.402997\pi$
$620$	20.2221	0.812140
$621$	1.00000	0.0401286
$622$	12.8337	0.514583
$623$	0	0
$624$	0.619394	0.0247956
$625$	27.8674	1.11469
$626$	−11.3306	−0.452862
$627$	33.8776	1.35294
$628$	−3.78182	−0.150911
$629$	1.72787	0.0688945
$630$	0	0
$631$	27.8917	1.11035	0.555176	−	0.831733i	$-0.312651\pi$
$631$	27.8917	1.11035	0.555176	+	0.831733i	$0.312651\pi$
$632$	−15.4737	−0.615509
$633$	17.1694	0.682423
$634$	−29.0197	−1.15252
$635$	60.1493	2.38695
$636$	−1.89728	−0.0752320
$637$	0	0
$638$	37.9039	1.50063
$639$	0.483327	0.0191201
$640$	3.89728	0.154053
$641$	25.9539	1.02512	0.512559	−	0.858652i	$-0.328697\pi$
$641$	25.9539	1.02512	0.512559	+	0.858652i	$0.328697\pi$
$642$	−11.1361	−0.439506
$643$	−49.0759	−1.93536	−0.967682	−	0.252175i	$-0.918854\pi$
$643$	−49.0759	−1.93536	−0.967682	+	0.252175i	$0.918854\pi$
$644$	0	0
$645$	−7.79456	−0.306910
$646$	−10.5303	−0.414309
$647$	−18.3143	−0.720008	−0.360004	−	0.932951i	$-0.617225\pi$
$647$	−18.3143	−0.720008	−0.360004	+	0.932951i	$0.617225\pi$
$648$	−1.00000	−0.0392837
$649$	−44.3694	−1.74165
$650$	−6.31087	−0.247533
$651$	0	0
$652$	4.48333	0.175581
$653$	−1.16905	−0.0457486	−0.0228743	−	0.999738i	$-0.507282\pi$
$653$	−1.16905	−0.0457486	−0.0228743	+	0.999738i	$0.507282\pi$
$654$	−1.36787	−0.0534878
$655$	81.4307	3.18176
$656$	4.41395	0.172336
$657$	−3.15544	−0.123105
$658$	0	0
$659$	−4.40121	−0.171447	−0.0857234	−	0.996319i	$-0.527320\pi$
$659$	−4.40121	−0.171447	−0.0857234	+	0.996319i	$0.527320\pi$
$660$	−15.6918	−0.610804
$661$	−11.2818	−0.438812	−0.219406	−	0.975634i	$-0.570412\pi$
$661$	−11.2818	−0.438812	−0.219406	+	0.975634i	$0.570412\pi$
$662$	−29.1024	−1.13110
$663$	0.775189	0.0301058
$664$	7.13607	0.276933
$665$	0	0
$666$	−1.38061	−0.0534974
$667$	−9.41395	−0.364510
$668$	−17.1388	−0.663119
$669$	9.39422	0.363202
$670$	46.9728	1.81472
$671$	0.827185	0.0319331
$672$	0	0
$673$	6.54966	0.252471	0.126235	−	0.992000i	$-0.459711\pi$
$673$	6.54966	0.252471	0.126235	+	0.992000i	$0.459711\pi$
$674$	−2.54215	−0.0979200
$675$	10.1888	0.392166
$676$	−12.6164	−0.485244
$677$	−4.75066	−0.182583	−0.0912913	−	0.995824i	$-0.529099\pi$
$677$	−4.75066	−0.182583	−0.0912913	+	0.995824i	$0.529099\pi$
$678$	−19.7582	−0.758808
$679$	0	0
$680$	4.87755	0.187046
$681$	−25.3179	−0.970182
$682$	20.8919	0.799992
$683$	18.3894	0.703652	0.351826	−	0.936065i	$-0.385561\pi$
$683$	18.3894	0.703652	0.351826	+	0.936065i	$0.385561\pi$
$684$	8.41395	0.321715
$685$	−24.8412	−0.949132
$686$	0	0
$687$	11.9600	0.456303
$688$	2.00000	0.0762493
$689$	−1.17516	−0.0447702
$690$	3.89728	0.148367
$691$	32.4500	1.23446	0.617228	−	0.786784i	$-0.288256\pi$
$691$	32.4500	1.23446	0.617228	+	0.786784i	$0.288256\pi$
$692$	2.84456	0.108134
$693$	0	0
$694$	−20.3776	−0.773522
$695$	−8.32485	−0.315779
$696$	9.41395	0.356835
$697$	5.52418	0.209243
$698$	5.63876	0.213430
$699$	−8.86429	−0.335278
$700$	0	0
$701$	−33.9894	−1.28376	−0.641882	−	0.766804i	$-0.721846\pi$
$701$	−33.9894	−1.28376	−0.641882	+	0.766804i	$0.721846\pi$
$702$	−0.619394	−0.0233775
$703$	11.6164	0.438119
$704$	4.02636	0.151749
$705$	−23.9140	−0.900652
$706$	−4.69759	−0.176796
$707$	0	0
$708$	−11.0197	−0.414147
$709$	−16.6624	−0.625771	−0.312885	−	0.949791i	$-0.601296\pi$
$709$	−16.6624	−0.625771	−0.312885	+	0.949791i	$0.601296\pi$
$710$	1.88366	0.0706925
$711$	15.4737	0.580307
$712$	10.2085	0.382580
$713$	−5.18878	−0.194321
$714$	0	0
$715$	−9.71943	−0.363486
$716$	13.2782	0.496231
$717$	9.93062	0.370866
$718$	28.4303	1.06101
$719$	33.1932	1.23790	0.618950	−	0.785431i	$-0.287559\pi$
$719$	33.1932	1.23790	0.618950	+	0.785431i	$0.287559\pi$
$720$	−3.89728	−0.145243
$721$	0	0
$722$	−51.7946	−1.92759
$723$	12.2840	0.456847
$724$	−14.5066	−0.539135
$725$	−95.9167	−3.56226
$726$	−5.21155	−0.193419
$727$	−27.3991	−1.01618	−0.508089	−	0.861305i	$-0.669648\pi$
$727$	−27.3991	−1.01618	−0.508089	+	0.861305i	$0.669648\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−12.2976	−0.455155
$731$	2.50305	0.0925788
$732$	0.205443	0.00759338
$733$	1.09880	0.0405851	0.0202925	−	0.999794i	$-0.493540\pi$
$733$	1.09880	0.0405851	0.0202925	+	0.999794i	$0.493540\pi$
$734$	−6.27177	−0.231495
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	48.5285	1.78757
$738$	−4.41395	−0.162480
$739$	−49.5137	−1.82139	−0.910695	−	0.413080i	$-0.864453\pi$
$739$	−49.5137	−1.82139	−0.910695	+	0.413080i	$0.864453\pi$
$740$	−5.38061	−0.197795
$741$	5.21155	0.191451
$742$	0	0
$743$	10.6054	0.389075	0.194538	−	0.980895i	$-0.437679\pi$
$743$	10.6054	0.389075	0.194538	+	0.980895i	$0.437679\pi$
$744$	5.18878	0.190230
$745$	−46.0728	−1.68798
$746$	6.27396	0.229706
$747$	−7.13607	−0.261095
$748$	5.03910	0.184248
$749$	0	0
$750$	20.2221	0.738408
$751$	−4.17857	−0.152478	−0.0762390	−	0.997090i	$-0.524291\pi$
$751$	−4.17857	−0.152478	−0.0762390	+	0.997090i	$0.524291\pi$
$752$	6.13607	0.223759
$753$	−6.81481	−0.248345
$754$	5.83095	0.212351
$755$	−36.7657	−1.33804
$756$	0	0
$757$	−18.0758	−0.656978	−0.328489	−	0.944508i	$-0.606539\pi$
$757$	−18.0758	−0.656978	−0.328489	+	0.944508i	$0.606539\pi$
$758$	28.2248	1.02517
$759$	4.02636	0.146148
$760$	32.7915	1.18947
$761$	3.81769	0.138391	0.0691955	−	0.997603i	$-0.477957\pi$
$761$	3.81769	0.138391	0.0691955	+	0.997603i	$0.477957\pi$
$762$	15.4337	0.559103
$763$	0	0
$764$	−15.2419	−0.551431
$765$	−4.87755	−0.176348
$766$	9.44658	0.341319
$767$	−6.82555	−0.246456
$768$	1.00000	0.0360844
$769$	−11.4105	−0.411475	−0.205737	−	0.978607i	$-0.565959\pi$
$769$	−11.4105	−0.411475	−0.205737	+	0.978607i	$0.565959\pi$
$770$	0	0
$771$	23.5000	0.846332
$772$	11.9500	0.430090
$773$	−25.6558	−0.922775	−0.461388	−	0.887199i	$-0.652648\pi$
$773$	−25.6558	−0.922775	−0.461388	+	0.887199i	$0.652648\pi$
$774$	−2.00000	−0.0718885
$775$	−52.8674	−1.89905
$776$	12.0531	0.432680
$777$	0	0
$778$	−5.64183	−0.202269
$779$	37.1388	1.33063
$780$	−2.41395	−0.0864333
$781$	1.94605	0.0696351
$782$	−1.25153	−0.0447545
$783$	−9.41395	−0.336427
$784$	0	0
$785$	14.7388	0.526050
$786$	20.8942	0.745273
$787$	−35.6303	−1.27008	−0.635042	−	0.772478i	$-0.719017\pi$
$787$	−35.6303	−1.27008	−0.635042	+	0.772478i	$0.719017\pi$
$788$	−18.5391	−0.660428
$789$	18.8534	0.671198
$790$	60.3051	2.14556
$791$	0	0
$792$	−4.02636	−0.143070
$793$	0.127250	0.00451878
$794$	−32.7388	−1.16186
$795$	7.39422	0.262246
$796$	8.91753	0.316073
$797$	−37.7840	−1.33838	−0.669189	−	0.743092i	$-0.733358\pi$
$797$	−37.7840	−1.33838	−0.669189	+	0.743092i	$0.733358\pi$
$798$	0	0
$799$	7.67946	0.271680
$800$	−10.1888	−0.360228
$801$	−10.2085	−0.360700
$802$	9.88490	0.349048
$803$	−12.7049	−0.448347
$804$	12.0527	0.425066
$805$	0	0
$806$	3.21390	0.113205
$807$	26.7976	0.943321
$808$	−10.1888	−0.358440
$809$	13.5800	0.477446	0.238723	−	0.971088i	$-0.423271\pi$
$809$	13.5800	0.477446	0.238723	+	0.971088i	$0.423271\pi$
$810$	3.89728	0.136936
$811$	−46.7245	−1.64072	−0.820359	−	0.571848i	$-0.806227\pi$
$811$	−46.7245	−1.64072	−0.820359	+	0.571848i	$0.806227\pi$
$812$	0	0
$813$	28.4803	0.998847
$814$	−5.55881	−0.194836
$815$	−17.4728	−0.612045
$816$	1.25153	0.0438122
$817$	16.8279	0.588734
$818$	−25.1061	−0.877816
$819$	0	0
$820$	−17.2024	−0.600734
$821$	34.5922	1.20728	0.603638	−	0.797259i	$-0.293717\pi$
$821$	34.5922	1.20728	0.603638	+	0.797259i	$0.293717\pi$
$822$	−6.37398	−0.222318
$823$	41.4242	1.44396	0.721978	−	0.691916i	$-0.243233\pi$
$823$	41.4242	1.44396	0.721978	+	0.691916i	$0.243233\pi$
$824$	6.95698	0.242358
$825$	41.0237	1.42826
$826$	0	0
$827$	50.4046	1.75274	0.876370	−	0.481638i	$-0.159958\pi$
$827$	50.4046	1.75274	0.876370	+	0.481638i	$0.159958\pi$
$828$	1.00000	0.0347524
$829$	44.7157	1.55304	0.776520	−	0.630093i	$-0.216983\pi$
$829$	44.7157	1.55304	0.776520	+	0.630093i	$0.216983\pi$
$830$	−27.8112	−0.965342
$831$	19.3969	0.672872
$832$	0.619394	0.0214736
$833$	0	0
$834$	−2.13607	−0.0739659
$835$	66.7946	2.31152
$836$	33.8776	1.17168
$837$	−5.18878	−0.179351
$838$	−1.66548	−0.0575330
$839$	−24.1691	−0.834408	−0.417204	−	0.908813i	$-0.636990\pi$
$839$	−24.1691	−0.834408	−0.417204	+	0.908813i	$0.636990\pi$
$840$	0	0
$841$	59.6225	2.05595
$842$	−4.61887	−0.159177
$843$	22.3903	0.771163
$844$	17.1694	0.590996
$845$	49.1694	1.69148
$846$	−6.13607	−0.210962
$847$	0	0
$848$	−1.89728	−0.0651528
$849$	10.0395	0.344553
$850$	−12.7515	−0.437374
$851$	1.38061	0.0473266
$852$	0.483327	0.0165585
$853$	17.3969	0.595660	0.297830	−	0.954619i	$-0.403737\pi$
$853$	17.3969	0.595660	0.297830	+	0.954619i	$0.403737\pi$
$854$	0	0
$855$	−32.7915	−1.12145
$856$	−11.1361	−0.380623
$857$	34.9837	1.19502	0.597510	−	0.801861i	$-0.296157\pi$
$857$	34.9837	1.19502	0.597510	+	0.801861i	$0.296157\pi$
$858$	−2.49390	−0.0851404
$859$	−26.9269	−0.918733	−0.459366	−	0.888247i	$-0.651923\pi$
$859$	−26.9269	−0.918733	−0.459366	+	0.888247i	$0.651923\pi$
$860$	−7.79456	−0.265792
$861$	0	0
$862$	32.8674	1.11947
$863$	55.7160	1.89660	0.948298	−	0.317382i	$-0.102804\pi$
$863$	55.7160	1.89660	0.948298	+	0.317382i	$0.102804\pi$
$864$	−1.00000	−0.0340207
$865$	−11.0861	−0.376937
$866$	21.0079	0.713876
$867$	−15.4337	−0.524155
$868$	0	0
$869$	62.3025	2.11347
$870$	−36.6888	−1.24387
$871$	7.46538	0.252955
$872$	−1.36787	−0.0463218
$873$	−12.0531	−0.407935
$874$	−8.41395	−0.284606
$875$	0	0
$876$	−3.15544	−0.106612
$877$	−22.6976	−0.766443	−0.383222	−	0.923656i	$-0.625185\pi$
$877$	−22.6976	−0.766443	−0.383222	+	0.923656i	$0.625185\pi$
$878$	−7.87004	−0.265601
$879$	25.0228	0.843998
$880$	−15.6918	−0.528972
$881$	−1.80423	−0.0607861	−0.0303930	−	0.999538i	$-0.509676\pi$
$881$	−1.80423	−0.0607861	−0.0303930	+	0.999538i	$0.509676\pi$
$882$	0	0
$883$	−36.5861	−1.23122	−0.615610	−	0.788051i	$-0.711090\pi$
$883$	−36.5861	−1.23122	−0.615610	+	0.788051i	$0.711090\pi$
$884$	0.775189	0.0260724
$885$	42.9469	1.44365
$886$	−16.5561	−0.556214
$887$	19.3408	0.649401	0.324701	−	0.945817i	$-0.394736\pi$
$887$	19.3408	0.649401	0.324701	+	0.945817i	$0.394736\pi$
$888$	−1.38061	−0.0463301
$889$	0	0
$890$	−39.7854	−1.33361
$891$	4.02636	0.134888
$892$	9.39422	0.314542
$893$	51.6286	1.72768
$894$	−11.8218	−0.395380
$895$	−51.7490	−1.72978
$896$	0	0
$897$	0.619394	0.0206810
$898$	10.4272	0.347961
$899$	48.8469	1.62914
$900$	10.1888	0.339626
$901$	−2.37450	−0.0791059
$902$	−17.7721	−0.591748
$903$	0	0
$904$	−19.7582	−0.657147
$905$	56.5364	1.87933
$906$	−9.43368	−0.313413
$907$	−5.58677	−0.185506	−0.0927528	−	0.995689i	$-0.529567\pi$
$907$	−5.58677	−0.185506	−0.0927528	+	0.995689i	$0.529567\pi$
$908$	−25.3179	−0.840203
$909$	10.1888	0.337941
$910$	0	0
$911$	−29.3170	−0.971315	−0.485657	−	0.874149i	$-0.661420\pi$
$911$	−29.3170	−0.971315	−0.485657	+	0.874149i	$0.661420\pi$
$912$	8.41395	0.278614
$913$	−28.7324	−0.950902
$914$	−25.8082	−0.853659
$915$	−0.800667	−0.0264692
$916$	11.9600	0.395170
$917$	0	0
$918$	−1.25153	−0.0413066
$919$	−25.5135	−0.841612	−0.420806	−	0.907151i	$-0.638253\pi$
$919$	−25.5135	−0.841612	−0.420806	+	0.907151i	$0.638253\pi$
$920$	3.89728	0.128489
$921$	27.6221	0.910179
$922$	−19.1660	−0.631199
$923$	0.299370	0.00985388
$924$	0	0
$925$	14.0667	0.462510
$926$	−11.6891	−0.384129
$927$	−6.95698	−0.228497
$928$	9.41395	0.309028
$929$	5.12173	0.168039	0.0840193	−	0.996464i	$-0.473224\pi$
$929$	5.12173	0.168039	0.0840193	+	0.996464i	$0.473224\pi$
$930$	−20.2221	−0.663110
$931$	0	0
$932$	−8.86429	−0.290360
$933$	−12.8337	−0.420155
$934$	0.837576	0.0274063
$935$	−19.6388	−0.642256
$936$	−0.619394	−0.0202455
$937$	39.6816	1.29634	0.648171	−	0.761494i	$-0.275534\pi$
$937$	39.6816	1.29634	0.648171	+	0.761494i	$0.275534\pi$
$938$	0	0
$939$	11.3306	0.369760
$940$	−23.9140	−0.779987
$941$	10.3003	0.335781	0.167890	−	0.985806i	$-0.446305\pi$
$941$	10.3003	0.335781	0.167890	+	0.985806i	$0.446305\pi$
$942$	3.78182	0.123218
$943$	4.41395	0.143738
$944$	−11.0197	−0.358662
$945$	0	0
$946$	−8.05271	−0.261816
$947$	20.2309	0.657417	0.328708	−	0.944431i	$-0.393387\pi$
$947$	20.2309	0.657417	0.328708	+	0.944431i	$0.393387\pi$
$948$	15.4737	0.502561
$949$	−1.95446	−0.0634444
$950$	−85.7279	−2.78138
$951$	29.0197	0.941029
$952$	0	0
$953$	−29.4213	−0.953049	−0.476525	−	0.879161i	$-0.658104\pi$
$953$	−29.4213	−0.953049	−0.476525	+	0.879161i	$0.658104\pi$
$954$	1.89728	0.0614267
$955$	59.4018	1.92220
$956$	9.93062	0.321179
$957$	−37.9039	−1.22526
$958$	3.58605	0.115860
$959$	0	0
$960$	−3.89728	−0.125784
$961$	−4.07655	−0.131502
$962$	−0.855139	−0.0275708
$963$	11.1361	0.358855
$964$	12.2840	0.395641
$965$	−46.5725	−1.49922
$966$	0	0
$967$	−8.05542	−0.259045	−0.129522	−	0.991576i	$-0.541344\pi$
$967$	−8.05542	−0.259045	−0.129522	+	0.991576i	$0.541344\pi$
$968$	−5.21155	−0.167506
$969$	10.5303	0.338282
$970$	−46.9742	−1.50825
$971$	45.1658	1.44944	0.724721	−	0.689043i	$-0.241969\pi$
$971$	45.1658	1.44944	0.724721	+	0.689043i	$0.241969\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	15.0361	0.481786
$975$	6.31087	0.202110
$976$	0.205443	0.00657606
$977$	20.3898	0.652327	0.326163	−	0.945313i	$-0.394244\pi$
$977$	20.3898	0.652327	0.326163	+	0.945313i	$0.394244\pi$
$978$	−4.48333	−0.143361
$979$	−41.1031	−1.31366
$980$	0	0
$981$	1.36787	0.0436726
$982$	6.13302	0.195713
$983$	49.4534	1.57732	0.788660	−	0.614830i	$-0.210775\pi$
$983$	49.4534	1.57732	0.788660	+	0.614830i	$0.210775\pi$
$984$	−4.41395	−0.140712
$985$	72.2521	2.30214
$986$	11.7818	0.375210
$987$	0	0
$988$	5.21155	0.165802
$989$	2.00000	0.0635963
$990$	15.6918	0.498719
$991$	−58.8518	−1.86949	−0.934744	−	0.355322i	$-0.884371\pi$
$991$	−58.8518	−1.86949	−0.934744	+	0.355322i	$0.884371\pi$
$992$	5.18878	0.164744
$993$	29.1024	0.923536
$994$	0	0
$995$	−34.7541	−1.10178
$996$	−7.13607	−0.226115
$997$	50.3419	1.59434	0.797172	−	0.603752i	$-0.206328\pi$
$997$	50.3419	1.59434	0.797172	+	0.603752i	$0.206328\pi$
$998$	21.4925	0.680333
$999$	1.38061	0.0436804

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6762.2.a.ch.1.1		4
7.3	odd	6		966.2.i.n.415.1	yes	8
7.5	odd	6		966.2.i.n.277.1	✓	8
7.6	odd	2		6762.2.a.cg.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.i.n.277.1	✓	8	7.5	odd	6
966.2.i.n.415.1	yes	8	7.3	odd	6
6762.2.a.cg.1.4		4	7.6	odd	2
6762.2.a.ch.1.1		4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6762.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.89728 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.89728 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +3.89728 q^{10} +4.02636 q^{11} +1.00000 q^{12} +0.619394 q^{13} -3.89728 q^{15} +1.00000 q^{16} +1.25153 q^{17} -1.00000 q^{18} +8.41395 q^{19} -3.89728 q^{20} -4.02636 q^{22} +1.00000 q^{23} -1.00000 q^{24} +10.1888 q^{25} -0.619394 q^{26} +1.00000 q^{27} -9.41395 q^{29} +3.89728 q^{30} -5.18878 q^{31} -1.00000 q^{32} +4.02636 q^{33} -1.25153 q^{34} +1.00000 q^{36} +1.38061 q^{37} -8.41395 q^{38} +0.619394 q^{39} +3.89728 q^{40} +4.41395 q^{41} +2.00000 q^{43} +4.02636 q^{44} -3.89728 q^{45} -1.00000 q^{46} +6.13607 q^{47} +1.00000 q^{48} -10.1888 q^{50} +1.25153 q^{51} +0.619394 q^{52} -1.89728 q^{53} -1.00000 q^{54} -15.6918 q^{55} +8.41395 q^{57} +9.41395 q^{58} -11.0197 q^{59} -3.89728 q^{60} +0.205443 q^{61} +5.18878 q^{62} +1.00000 q^{64} -2.41395 q^{65} -4.02636 q^{66} +12.0527 q^{67} +1.25153 q^{68} +1.00000 q^{69} +0.483327 q^{71} -1.00000 q^{72} -3.15544 q^{73} -1.38061 q^{74} +10.1888 q^{75} +8.41395 q^{76} -0.619394 q^{78} +15.4737 q^{79} -3.89728 q^{80} +1.00000 q^{81} -4.41395 q^{82} -7.13607 q^{83} -4.87755 q^{85} -2.00000 q^{86} -9.41395 q^{87} -4.02636 q^{88} -10.2085 q^{89} +3.89728 q^{90} +1.00000 q^{92} -5.18878 q^{93} -6.13607 q^{94} -32.7915 q^{95} -1.00000 q^{96} -12.0531 q^{97} +4.02636 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} - 2 q^{5} - 4 q^{6} - 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 - 2 * q^5 - 4 * q^6 - 4 * q^8 + 4 * q^9	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} - 2 q^{5} - 4 q^{6} - 4 q^{8} + 4 q^{9} + 2 q^{10} + 6 q^{11} + 4 q^{12} + 2 q^{13} - 2 q^{15} + 4 q^{16} + 2 q^{17} - 4 q^{18} + 6 q^{19} - 2 q^{20} - 6 q^{22} + 4 q^{23} - 4 q^{24} + 6 q^{25} - 2 q^{26} + 4 q^{27} - 10 q^{29} + 2 q^{30} + 14 q^{31} - 4 q^{32} + 6 q^{33} - 2 q^{34} + 4 q^{36} + 6 q^{37} - 6 q^{38} + 2 q^{39} + 2 q^{40} - 10 q^{41} + 8 q^{43} + 6 q^{44} - 2 q^{45} - 4 q^{46} + 10 q^{47} + 4 q^{48} - 6 q^{50} + 2 q^{51} + 2 q^{52} + 6 q^{53} - 4 q^{54} - 22 q^{55} + 6 q^{57} + 10 q^{58} - 24 q^{59} - 2 q^{60} + 28 q^{61} - 14 q^{62} + 4 q^{64} + 18 q^{65} - 6 q^{66} + 28 q^{67} + 2 q^{68} + 4 q^{69} + 16 q^{71} - 4 q^{72} - 6 q^{73} - 6 q^{74} + 6 q^{75} + 6 q^{76} - 2 q^{78} - 4 q^{79} - 2 q^{80} + 4 q^{81} + 10 q^{82} - 14 q^{83} - 26 q^{85} - 8 q^{86} - 10 q^{87} - 6 q^{88} + 14 q^{89} + 2 q^{90} + 4 q^{92} + 14 q^{93} - 10 q^{94} - 34 q^{95} - 4 q^{96} + 6 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 - 2 * q^5 - 4 * q^6 - 4 * q^8 + 4 * q^9 + 2 * q^10 + 6 * q^11 + 4 * q^12 + 2 * q^13 - 2 * q^15 + 4 * q^16 + 2 * q^17 - 4 * q^18 + 6 * q^19 - 2 * q^20 - 6 * q^22 + 4 * q^23 - 4 * q^24 + 6 * q^25 - 2 * q^26 + 4 * q^27 - 10 * q^29 + 2 * q^30 + 14 * q^31 - 4 * q^32 + 6 * q^33 - 2 * q^34 + 4 * q^36 + 6 * q^37 - 6 * q^38 + 2 * q^39 + 2 * q^40 - 10 * q^41 + 8 * q^43 + 6 * q^44 - 2 * q^45 - 4 * q^46 + 10 * q^47 + 4 * q^48 - 6 * q^50 + 2 * q^51 + 2 * q^52 + 6 * q^53 - 4 * q^54 - 22 * q^55 + 6 * q^57 + 10 * q^58 - 24 * q^59 - 2 * q^60 + 28 * q^61 - 14 * q^62 + 4 * q^64 + 18 * q^65 - 6 * q^66 + 28 * q^67 + 2 * q^68 + 4 * q^69 + 16 * q^71 - 4 * q^72 - 6 * q^73 - 6 * q^74 + 6 * q^75 + 6 * q^76 - 2 * q^78 - 4 * q^79 - 2 * q^80 + 4 * q^81 + 10 * q^82 - 14 * q^83 - 26 * q^85 - 8 * q^86 - 10 * q^87 - 6 * q^88 + 14 * q^89 + 2 * q^90 + 4 * q^92 + 14 * q^93 - 10 * q^94 - 34 * q^95 - 4 * q^96 + 6 * q^99

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