LMFDB - Embedded newform 6422.2.a.bf.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6422,2,Mod(1,6422)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6422, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6422.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6422 = 2 \cdot 13^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6422.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:	$51.2799281781$
Analytic rank:	$0$
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} - 16x^{5} + 29x^{4} + 60x^{3} - 79x^{2} - 47x - 2 $ x^7 - 2x^6 - 16x^5 + 29x^4 + 60x^3 - 79x^2 - 47x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 494)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-0.0462763$ of defining polynomial
Character	$\chi$	$=$	6422.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.0462763 q^{3} +1.00000 q^{4} +2.81822 q^{5} -0.0462763 q^{6} -4.11903 q^{7} +1.00000 q^{8} -2.99786 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.0462763 q^{3} +1.00000 q^{4} +2.81822 q^{5} -0.0462763 q^{6} -4.11903 q^{7} +1.00000 q^{8} -2.99786 q^{9} +2.81822 q^{10} +5.30670 q^{11} -0.0462763 q^{12} -4.11903 q^{14} -0.130417 q^{15} +1.00000 q^{16} -2.26337 q^{17} -2.99786 q^{18} +1.00000 q^{19} +2.81822 q^{20} +0.190614 q^{21} +5.30670 q^{22} -2.21961 q^{23} -0.0462763 q^{24} +2.94234 q^{25} +0.277559 q^{27} -4.11903 q^{28} -6.69167 q^{29} -0.130417 q^{30} +5.06112 q^{31} +1.00000 q^{32} -0.245575 q^{33} -2.26337 q^{34} -11.6083 q^{35} -2.99786 q^{36} +6.62546 q^{37} +1.00000 q^{38} +2.81822 q^{40} +11.8017 q^{41} +0.190614 q^{42} +9.97189 q^{43} +5.30670 q^{44} -8.44861 q^{45} -2.21961 q^{46} -5.50401 q^{47} -0.0462763 q^{48} +9.96643 q^{49} +2.94234 q^{50} +0.104740 q^{51} +13.8276 q^{53} +0.277559 q^{54} +14.9554 q^{55} -4.11903 q^{56} -0.0462763 q^{57} -6.69167 q^{58} -10.0539 q^{59} -0.130417 q^{60} -1.36970 q^{61} +5.06112 q^{62} +12.3483 q^{63} +1.00000 q^{64} -0.245575 q^{66} +7.27220 q^{67} -2.26337 q^{68} +0.102715 q^{69} -11.6083 q^{70} +5.96350 q^{71} -2.99786 q^{72} +15.8898 q^{73} +6.62546 q^{74} -0.136161 q^{75} +1.00000 q^{76} -21.8585 q^{77} +8.52674 q^{79} +2.81822 q^{80} +8.98073 q^{81} +11.8017 q^{82} +6.81888 q^{83} +0.190614 q^{84} -6.37866 q^{85} +9.97189 q^{86} +0.309666 q^{87} +5.30670 q^{88} -14.8045 q^{89} -8.44861 q^{90} -2.21961 q^{92} -0.234210 q^{93} -5.50401 q^{94} +2.81822 q^{95} -0.0462763 q^{96} +3.19810 q^{97} +9.96643 q^{98} -15.9087 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 7 q^{2} + 2 q^{3} + 7 q^{4} + 2 q^{5} + 2 q^{6} + q^{7} + 7 q^{8} + 15 q^{9}+O(q^{10}) $ 7 * q + 7 * q^2 + 2 * q^3 + 7 * q^4 + 2 * q^5 + 2 * q^6 + q^7 + 7 * q^8 + 15 * q^9	\( 7 q + 7 q^{2} + 2 q^{3} + 7 q^{4} + 2 q^{5} + 2 q^{6} + q^{7} + 7 q^{8} + 15 q^{9} + 2 q^{10} + 5 q^{11} + 2 q^{12} + q^{14} + 13 q^{15} + 7 q^{16} + 16 q^{17} + 15 q^{18} + 7 q^{19} + 2 q^{20} - 3 q^{21} + 5 q^{22} + 3 q^{23} + 2 q^{24} + 7 q^{25} + 5 q^{27} + q^{28} - 7 q^{29} + 13 q^{30} + 11 q^{31} + 7 q^{32} + 6 q^{33} + 16 q^{34} + q^{35} + 15 q^{36} - 3 q^{37} + 7 q^{38} + 2 q^{40} + 15 q^{41} - 3 q^{42} + 23 q^{43} + 5 q^{44} - 38 q^{45} + 3 q^{46} - q^{47} + 2 q^{48} + 14 q^{49} + 7 q^{50} - 16 q^{51} + 21 q^{53} + 5 q^{54} + 8 q^{55} + q^{56} + 2 q^{57} - 7 q^{58} + 8 q^{59} + 13 q^{60} - 6 q^{61} + 11 q^{62} - 22 q^{63} + 7 q^{64} + 6 q^{66} + 28 q^{67} + 16 q^{68} + 48 q^{69} + q^{70} + 4 q^{71} + 15 q^{72} + 12 q^{73} - 3 q^{74} + 5 q^{75} + 7 q^{76} - 26 q^{77} - 4 q^{79} + 2 q^{80} + 51 q^{81} + 15 q^{82} + 13 q^{83} - 3 q^{84} - 39 q^{85} + 23 q^{86} - 16 q^{87} + 5 q^{88} - 15 q^{89} - 38 q^{90} + 3 q^{92} + 6 q^{93} - q^{94} + 2 q^{95} + 2 q^{96} - 37 q^{97} + 14 q^{98} - 15 q^{99}+O(q^{100}) \) 7 * q + 7 * q^2 + 2 * q^3 + 7 * q^4 + 2 * q^5 + 2 * q^6 + q^7 + 7 * q^8 + 15 * q^9 + 2 * q^10 + 5 * q^11 + 2 * q^12 + q^14 + 13 * q^15 + 7 * q^16 + 16 * q^17 + 15 * q^18 + 7 * q^19 + 2 * q^20 - 3 * q^21 + 5 * q^22 + 3 * q^23 + 2 * q^24 + 7 * q^25 + 5 * q^27 + q^28 - 7 * q^29 + 13 * q^30 + 11 * q^31 + 7 * q^32 + 6 * q^33 + 16 * q^34 + q^35 + 15 * q^36 - 3 * q^37 + 7 * q^38 + 2 * q^40 + 15 * q^41 - 3 * q^42 + 23 * q^43 + 5 * q^44 - 38 * q^45 + 3 * q^46 - q^47 + 2 * q^48 + 14 * q^49 + 7 * q^50 - 16 * q^51 + 21 * q^53 + 5 * q^54 + 8 * q^55 + q^56 + 2 * q^57 - 7 * q^58 + 8 * q^59 + 13 * q^60 - 6 * q^61 + 11 * q^62 - 22 * q^63 + 7 * q^64 + 6 * q^66 + 28 * q^67 + 16 * q^68 + 48 * q^69 + q^70 + 4 * q^71 + 15 * q^72 + 12 * q^73 - 3 * q^74 + 5 * q^75 + 7 * q^76 - 26 * q^77 - 4 * q^79 + 2 * q^80 + 51 * q^81 + 15 * q^82 + 13 * q^83 - 3 * q^84 - 39 * q^85 + 23 * q^86 - 16 * q^87 + 5 * q^88 - 15 * q^89 - 38 * q^90 + 3 * q^92 + 6 * q^93 - q^94 + 2 * q^95 + 2 * q^96 - 37 * q^97 + 14 * q^98 - 15 * 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
$3$	−0.0462763	−0.0267177	−0.0133588	−	0.999911i	$-0.504252\pi$
$3$	−0.0462763	−0.0267177	−0.0133588	+	0.999911i	$0.504252\pi$
$4$	1.00000	0.500000
$5$	2.81822	1.26034	0.630172	−	0.776455i	$-0.282984\pi$
$5$	2.81822	1.26034	0.630172	+	0.776455i	$0.282984\pi$
$6$	−0.0462763	−0.0188922
$7$	−4.11903	−1.55685	−0.778424	−	0.627739i	$-0.783981\pi$
$7$	−4.11903	−1.55685	−0.778424	+	0.627739i	$0.783981\pi$
$8$	1.00000	0.353553
$9$	−2.99786	−0.999286
$10$	2.81822	0.891198
$11$	5.30670	1.60003	0.800015	−	0.599981i	$-0.204825\pi$
$11$	5.30670	1.60003	0.800015	+	0.599981i	$0.204825\pi$
$12$	−0.0462763	−0.0133588
$13$	0	0
$13$	0	0
$14$	−4.11903	−1.10086
$15$	−0.130417	−0.0336735
$16$	1.00000	0.250000
$17$	−2.26337	−0.548948	−0.274474	−	0.961595i	$-0.588504\pi$
$17$	−2.26337	−0.548948	−0.274474	+	0.961595i	$0.588504\pi$
$18$	−2.99786	−0.706602
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	2.81822	0.630172
$21$	0.190614	0.0415953
$22$	5.30670	1.13139
$23$	−2.21961	−0.462820	−0.231410	−	0.972856i	$-0.574334\pi$
$23$	−2.21961	−0.462820	−0.231410	+	0.972856i	$0.574334\pi$
$24$	−0.0462763	−0.00944612
$25$	2.94234	0.588468
$26$	0	0
$27$	0.277559	0.0534162
$28$	−4.11903	−0.778424
$29$	−6.69167	−1.24261	−0.621306	−	0.783568i	$-0.713398\pi$
$29$	−6.69167	−1.24261	−0.621306	+	0.783568i	$0.713398\pi$
$30$	−0.130417	−0.0238107
$31$	5.06112	0.909004	0.454502	−	0.890746i	$-0.349817\pi$
$31$	5.06112	0.909004	0.454502	+	0.890746i	$0.349817\pi$
$32$	1.00000	0.176777
$33$	−0.245575	−0.0427490
$34$	−2.26337	−0.388165
$35$	−11.6083	−1.96216
$36$	−2.99786	−0.499643
$37$	6.62546	1.08922	0.544609	−	0.838690i	$-0.316678\pi$
$37$	6.62546	1.08922	0.544609	+	0.838690i	$0.316678\pi$
$38$	1.00000	0.162221
$39$	0	0
$40$	2.81822	0.445599
$41$	11.8017	1.84312	0.921561	−	0.388233i	$-0.126915\pi$
$41$	11.8017	1.84312	0.921561	+	0.388233i	$0.126915\pi$
$42$	0.190614	0.0294123
$43$	9.97189	1.52070	0.760349	−	0.649514i	$-0.225028\pi$
$43$	9.97189	1.52070	0.760349	+	0.649514i	$0.225028\pi$
$44$	5.30670	0.800015
$45$	−8.44861	−1.25944
$46$	−2.21961	−0.327263
$47$	−5.50401	−0.802842	−0.401421	−	0.915894i	$-0.631484\pi$
$47$	−5.50401	−0.802842	−0.401421	+	0.915894i	$0.631484\pi$
$48$	−0.0462763	−0.00667941
$49$	9.96643	1.42378
$50$	2.94234	0.416110
$51$	0.104740	0.0146666
$52$	0	0
$53$	13.8276	1.89936	0.949680	−	0.313220i	$-0.101408\pi$
$53$	13.8276	1.89936	0.949680	+	0.313220i	$0.101408\pi$
$54$	0.277559	0.0377710
$55$	14.9554	2.01659
$56$	−4.11903	−0.550429
$57$	−0.0462763	−0.00612945
$58$	−6.69167	−0.878660
$59$	−10.0539	−1.30891	−0.654454	−	0.756102i	$-0.727101\pi$
$59$	−10.0539	−1.30891	−0.654454	+	0.756102i	$0.727101\pi$
$60$	−0.130417	−0.0168367
$61$	−1.36970	−0.175372	−0.0876859	−	0.996148i	$-0.527947\pi$
$61$	−1.36970	−0.175372	−0.0876859	+	0.996148i	$0.527947\pi$
$62$	5.06112	0.642763
$63$	12.3483	1.55574
$64$	1.00000	0.125000
$65$	0	0
$66$	−0.245575	−0.0302281
$67$	7.27220	0.888440	0.444220	−	0.895918i	$-0.353481\pi$
$67$	7.27220	0.888440	0.444220	+	0.895918i	$0.353481\pi$
$68$	−2.26337	−0.274474
$69$	0.102715	0.0123655
$70$	−11.6083	−1.38746
$71$	5.96350	0.707737	0.353868	−	0.935295i	$-0.384866\pi$
$71$	5.96350	0.707737	0.353868	+	0.935295i	$0.384866\pi$
$72$	−2.99786	−0.353301
$73$	15.8898	1.85976	0.929879	−	0.367866i	$-0.119912\pi$
$73$	15.8898	1.85976	0.929879	+	0.367866i	$0.119912\pi$
$74$	6.62546	0.770194
$75$	−0.136161	−0.0157225
$76$	1.00000	0.114708
$77$	−21.8585	−2.49100
$78$	0	0
$79$	8.52674	0.959333	0.479667	−	0.877451i	$-0.340758\pi$
$79$	8.52674	0.959333	0.479667	+	0.877451i	$0.340758\pi$
$80$	2.81822	0.315086
$81$	8.98073	0.997859
$82$	11.8017	1.30328
$83$	6.81888	0.748469	0.374235	−	0.927334i	$-0.377905\pi$
$83$	6.81888	0.748469	0.374235	+	0.927334i	$0.377905\pi$
$84$	0.190614	0.0207977
$85$	−6.37866	−0.691863
$86$	9.97189	1.07530
$87$	0.309666	0.0331997
$88$	5.30670	0.565696
$89$	−14.8045	−1.56928	−0.784639	−	0.619953i	$-0.787152\pi$
$89$	−14.8045	−1.56928	−0.784639	+	0.619953i	$0.787152\pi$
$90$	−8.44861	−0.890562
$91$	0	0
$92$	−2.21961	−0.231410
$93$	−0.234210	−0.0242865
$94$	−5.50401	−0.567695
$95$	2.81822	0.289143
$96$	−0.0462763	−0.00472306
$97$	3.19810	0.324718	0.162359	−	0.986732i	$-0.448090\pi$
$97$	3.19810	0.324718	0.162359	+	0.986732i	$0.448090\pi$
$98$	9.96643	1.00676
$99$	−15.9087	−1.59889
$100$	2.94234	0.294234
$101$	−4.96682	−0.494217	−0.247108	−	0.968988i	$-0.579480\pi$
$101$	−4.96682	−0.494217	−0.247108	+	0.968988i	$0.579480\pi$
$102$	0.104740	0.0103709
$103$	−8.01176	−0.789422	−0.394711	−	0.918805i	$-0.629155\pi$
$103$	−8.01176	−0.789422	−0.394711	+	0.918805i	$0.629155\pi$
$104$	0	0
$105$	0.537191	0.0524244
$106$	13.8276	1.34305
$107$	6.13949	0.593527	0.296764	−	0.954951i	$-0.404093\pi$
$107$	6.13949	0.593527	0.296764	+	0.954951i	$0.404093\pi$
$108$	0.277559	0.0267081
$109$	−9.79838	−0.938514	−0.469257	−	0.883062i	$-0.655478\pi$
$109$	−9.79838	−0.938514	−0.469257	+	0.883062i	$0.655478\pi$
$110$	14.9554	1.42594
$111$	−0.306602	−0.0291014
$112$	−4.11903	−0.389212
$113$	−10.1455	−0.954409	−0.477205	−	0.878792i	$-0.658350\pi$
$113$	−10.1455	−0.954409	−0.477205	+	0.878792i	$0.658350\pi$
$114$	−0.0462763	−0.00433418
$115$	−6.25533	−0.583312
$116$	−6.69167	−0.621306
$117$	0	0
$118$	−10.0539	−0.925537
$119$	9.32289	0.854628
$120$	−0.130417	−0.0119054
$121$	17.1610	1.56009
$122$	−1.36970	−0.124007
$123$	−0.546141	−0.0492439
$124$	5.06112	0.454502
$125$	−5.79893	−0.518672
$126$	12.3483	1.10007
$127$	4.27692	0.379515	0.189757	−	0.981831i	$-0.439230\pi$
$127$	4.27692	0.379515	0.189757	+	0.981831i	$0.439230\pi$
$128$	1.00000	0.0883883
$129$	−0.461463	−0.0406295
$130$	0	0
$131$	−11.4400	−0.999517	−0.499759	−	0.866165i	$-0.666578\pi$
$131$	−11.4400	−0.999517	−0.499759	+	0.866165i	$0.666578\pi$
$132$	−0.245575	−0.0213745
$133$	−4.11903	−0.357165
$134$	7.27220	0.628222
$135$	0.782221	0.0673229
$136$	−2.26337	−0.194082
$137$	22.0740	1.88591	0.942955	−	0.332920i	$-0.108034\pi$
$137$	22.0740	1.88591	0.942955	+	0.332920i	$0.108034\pi$
$138$	0.102715	0.00874370
$139$	18.6086	1.57836	0.789178	−	0.614164i	$-0.210507\pi$
$139$	18.6086	1.57836	0.789178	+	0.614164i	$0.210507\pi$
$140$	−11.6083	−0.981082
$141$	0.254705	0.0214501
$142$	5.96350	0.500446
$143$	0	0
$144$	−2.99786	−0.249822
$145$	−18.8586	−1.56612
$146$	15.8898	1.31505
$147$	−0.461210	−0.0380399
$148$	6.62546	0.544609
$149$	−3.63944	−0.298155	−0.149077	−	0.988826i	$-0.547630\pi$
$149$	−3.63944	−0.298155	−0.149077	+	0.988826i	$0.547630\pi$
$150$	−0.136161	−0.0111175
$151$	7.85053	0.638867	0.319433	−	0.947609i	$-0.396507\pi$
$151$	7.85053	0.638867	0.319433	+	0.947609i	$0.396507\pi$
$152$	1.00000	0.0811107
$153$	6.78526	0.548556
$154$	−21.8585	−1.76140
$155$	14.2633	1.14566
$156$	0	0
$157$	4.65357	0.371395	0.185698	−	0.982607i	$-0.440545\pi$
$157$	4.65357	0.371395	0.185698	+	0.982607i	$0.440545\pi$
$158$	8.52674	0.678351
$159$	−0.639889	−0.0507465
$160$	2.81822	0.222800
$161$	9.14263	0.720540
$162$	8.98073	0.705593
$163$	−8.07276	−0.632307	−0.316154	−	0.948708i	$-0.602391\pi$
$163$	−8.07276	−0.632307	−0.316154	+	0.948708i	$0.602391\pi$
$164$	11.8017	0.921561
$165$	−0.692082	−0.0538785
$166$	6.81888	0.529248
$167$	−16.1610	−1.25058	−0.625289	−	0.780393i	$-0.715019\pi$
$167$	−16.1610	−1.25058	−0.625289	+	0.780393i	$0.715019\pi$
$168$	0.190614	0.0147062
$169$	0	0
$170$	−6.37866	−0.489221
$171$	−2.99786	−0.229252
$172$	9.97189	0.760349
$173$	−2.78298	−0.211586	−0.105793	−	0.994388i	$-0.533738\pi$
$173$	−2.78298	−0.211586	−0.105793	+	0.994388i	$0.533738\pi$
$174$	0.309666	0.0234757
$175$	−12.1196	−0.916155
$176$	5.30670	0.400007
$177$	0.465258	0.0349709
$178$	−14.8045	−1.10965
$179$	0.586051	0.0438035	0.0219017	−	0.999760i	$-0.493028\pi$
$179$	0.586051	0.0438035	0.0219017	+	0.999760i	$0.493028\pi$
$180$	−8.44861	−0.629722
$181$	0.442224	0.0328703	0.0164351	−	0.999865i	$-0.494768\pi$
$181$	0.442224	0.0328703	0.0164351	+	0.999865i	$0.494768\pi$
$182$	0	0
$183$	0.0633846	0.00468553
$184$	−2.21961	−0.163632
$185$	18.6720	1.37279
$186$	−0.234210	−0.0171731
$187$	−12.0110	−0.878332
$188$	−5.50401	−0.401421
$189$	−1.14327	−0.0831610
$190$	2.81822	0.204455
$191$	15.8325	1.14560	0.572799	−	0.819696i	$-0.305857\pi$
$191$	15.8325	1.14560	0.572799	+	0.819696i	$0.305857\pi$
$192$	−0.0462763	−0.00333971
$193$	−5.25735	−0.378432	−0.189216	−	0.981935i	$-0.560595\pi$
$193$	−5.25735	−0.378432	−0.189216	+	0.981935i	$0.560595\pi$
$194$	3.19810	0.229610
$195$	0	0
$196$	9.96643	0.711888
$197$	−4.88043	−0.347717	−0.173858	−	0.984771i	$-0.555623\pi$
$197$	−4.88043	−0.347717	−0.173858	+	0.984771i	$0.555623\pi$
$198$	−15.9087	−1.13058
$199$	11.0642	0.784319	0.392160	−	0.919897i	$-0.371728\pi$
$199$	11.0642	0.784319	0.392160	+	0.919897i	$0.371728\pi$
$200$	2.94234	0.208055
$201$	−0.336531	−0.0237370
$202$	−4.96682	−0.349464
$203$	27.5632	1.93456
$204$	0.104740	0.00733330
$205$	33.2598	2.32297
$206$	−8.01176	−0.558206
$207$	6.65407	0.462489
$208$	0	0
$209$	5.30670	0.367072
$210$	0.537191	0.0370697
$211$	1.11115	0.0764950	0.0382475	−	0.999268i	$-0.487822\pi$
$211$	1.11115	0.0764950	0.0382475	+	0.999268i	$0.487822\pi$
$212$	13.8276	0.949680
$213$	−0.275969	−0.0189091
$214$	6.13949	0.419687
$215$	28.1029	1.91660
$216$	0.277559	0.0188855
$217$	−20.8469	−1.41518
$218$	−9.79838	−0.663630
$219$	−0.735321	−0.0496884
$220$	14.9554	1.00829
$221$	0	0
$222$	−0.306602	−0.0205778
$223$	14.3383	0.960167	0.480083	−	0.877223i	$-0.340606\pi$
$223$	14.3383	0.960167	0.480083	+	0.877223i	$0.340606\pi$
$224$	−4.11903	−0.275214
$225$	−8.82072	−0.588048
$226$	−10.1455	−0.674869
$227$	−11.2444	−0.746317	−0.373159	−	0.927768i	$-0.621725\pi$
$227$	−11.2444	−0.746317	−0.373159	+	0.927768i	$0.621725\pi$
$228$	−0.0462763	−0.00306473
$229$	8.90916	0.588734	0.294367	−	0.955692i	$-0.404891\pi$
$229$	8.90916	0.588734	0.294367	+	0.955692i	$0.404891\pi$
$230$	−6.25533	−0.412464
$231$	1.01153	0.0665537
$232$	−6.69167	−0.439330
$233$	−10.5997	−0.694407	−0.347203	−	0.937790i	$-0.612869\pi$
$233$	−10.5997	−0.694407	−0.347203	+	0.937790i	$0.612869\pi$
$234$	0	0
$235$	−15.5115	−1.01186
$236$	−10.0539	−0.654454
$237$	−0.394586	−0.0256311
$238$	9.32289	0.604313
$239$	0.528678	0.0341974	0.0170987	−	0.999854i	$-0.494557\pi$
$239$	0.528678	0.0341974	0.0170987	+	0.999854i	$0.494557\pi$
$240$	−0.130417	−0.00841836
$241$	1.14353	0.0736614	0.0368307	−	0.999322i	$-0.488274\pi$
$241$	1.14353	0.0736614	0.0368307	+	0.999322i	$0.488274\pi$
$242$	17.1610	1.10315
$243$	−1.24827	−0.0800767
$244$	−1.36970	−0.0876859
$245$	28.0875	1.79445
$246$	−0.546141	−0.0348207
$247$	0	0
$248$	5.06112	0.321382
$249$	−0.315553	−0.0199973
$250$	−5.79893	−0.366757
$251$	22.4247	1.41544	0.707719	−	0.706494i	$-0.249724\pi$
$251$	22.4247	1.41544	0.707719	+	0.706494i	$0.249724\pi$
$252$	12.3483	0.777868
$253$	−11.7788	−0.740525
$254$	4.27692	0.268358
$255$	0.295181	0.0184850
$256$	1.00000	0.0625000
$257$	−11.3945	−0.710772	−0.355386	−	0.934720i	$-0.615651\pi$
$257$	−11.3945	−0.710772	−0.355386	+	0.934720i	$0.615651\pi$
$258$	−0.461463	−0.0287294
$259$	−27.2905	−1.69575
$260$	0	0
$261$	20.0607	1.24173
$262$	−11.4400	−0.706766
$263$	1.69504	0.104521	0.0522603	−	0.998633i	$-0.483357\pi$
$263$	1.69504	0.104521	0.0522603	+	0.998633i	$0.483357\pi$
$264$	−0.245575	−0.0151141
$265$	38.9690	2.39385
$266$	−4.11903	−0.252554
$267$	0.685100	0.0419274
$268$	7.27220	0.444220
$269$	−24.4071	−1.48813	−0.744065	−	0.668108i	$-0.767105\pi$
$269$	−24.4071	−1.48813	−0.744065	+	0.668108i	$0.767105\pi$
$270$	0.782221	0.0476045
$271$	−12.0963	−0.734796	−0.367398	−	0.930064i	$-0.619751\pi$
$271$	−12.0963	−0.734796	−0.367398	+	0.930064i	$0.619751\pi$
$272$	−2.26337	−0.137237
$273$	0	0
$274$	22.0740	1.33354
$275$	15.6141	0.941566
$276$	0.102715	0.00618273
$277$	−31.9226	−1.91804	−0.959021	−	0.283334i	$-0.908559\pi$
$277$	−31.9226	−1.91804	−0.959021	+	0.283334i	$0.908559\pi$
$278$	18.6086	1.11607
$279$	−15.1725	−0.908355
$280$	−11.6083	−0.693730
$281$	5.06348	0.302062	0.151031	−	0.988529i	$-0.451741\pi$
$281$	5.06348	0.302062	0.151031	+	0.988529i	$0.451741\pi$
$282$	0.254705	0.0151675
$283$	25.4293	1.51161	0.755807	−	0.654794i	$-0.227245\pi$
$283$	25.4293	1.51161	0.755807	+	0.654794i	$0.227245\pi$
$284$	5.96350	0.353868
$285$	−0.130417	−0.00772522
$286$	0	0
$287$	−48.6117	−2.86946
$288$	−2.99786	−0.176651
$289$	−11.8772	−0.698656
$290$	−18.8586	−1.10741
$291$	−0.147996	−0.00867571
$292$	15.8898	0.929879
$293$	6.99131	0.408436	0.204218	−	0.978925i	$-0.434535\pi$
$293$	6.99131	0.408436	0.204218	+	0.978925i	$0.434535\pi$
$294$	−0.461210	−0.0268983
$295$	−28.3341	−1.64967
$296$	6.62546	0.385097
$297$	1.47292	0.0854676
$298$	−3.63944	−0.210827
$299$	0	0
$300$	−0.136161	−0.00786124
$301$	−41.0745	−2.36750
$302$	7.85053	0.451747
$303$	0.229846	0.0132043
$304$	1.00000	0.0573539
$305$	−3.86010	−0.221029
$306$	6.78526	0.387888
$307$	−14.9269	−0.851926	−0.425963	−	0.904741i	$-0.640065\pi$
$307$	−14.9269	−0.851926	−0.425963	+	0.904741i	$0.640065\pi$
$308$	−21.8585	−1.24550
$309$	0.370755	0.0210915
$310$	14.2633	0.810103
$311$	−20.1499	−1.14260	−0.571299	−	0.820742i	$-0.693560\pi$
$311$	−20.1499	−1.14260	−0.571299	+	0.820742i	$0.693560\pi$
$312$	0	0
$313$	−15.2363	−0.861205	−0.430603	−	0.902542i	$-0.641699\pi$
$313$	−15.2363	−0.861205	−0.430603	+	0.902542i	$0.641699\pi$
$314$	4.65357	0.262616
$315$	34.8001	1.96076
$316$	8.52674	0.479667
$317$	4.33507	0.243482	0.121741	−	0.992562i	$-0.461152\pi$
$317$	4.33507	0.243482	0.121741	+	0.992562i	$0.461152\pi$
$318$	−0.639889	−0.0358832
$319$	−35.5107	−1.98822
$320$	2.81822	0.157543
$321$	−0.284113	−0.0158577
$322$	9.14263	0.509499
$323$	−2.26337	−0.125937
$324$	8.98073	0.498930
$325$	0	0
$326$	−8.07276	−0.447109
$327$	0.453433	0.0250749
$328$	11.8017	0.651642
$329$	22.6712	1.24990
$330$	−0.692082	−0.0380979
$331$	7.18468	0.394905	0.197453	−	0.980312i	$-0.436733\pi$
$331$	7.18468	0.394905	0.197453	+	0.980312i	$0.436733\pi$
$332$	6.81888	0.374235
$333$	−19.8622	−1.08844
$334$	−16.1610	−0.884292
$335$	20.4946	1.11974
$336$	0.190614	0.0103988
$337$	23.9676	1.30560	0.652799	−	0.757531i	$-0.273594\pi$
$337$	23.9676	1.30560	0.652799	+	0.757531i	$0.273594\pi$
$338$	0	0
$339$	0.469497	0.0254996
$340$	−6.37866	−0.345932
$341$	26.8578	1.45443
$342$	−2.99786	−0.162106
$343$	−12.2188	−0.659754
$344$	9.97189	0.537648
$345$	0.289474	0.0155847
$346$	−2.78298	−0.149614
$347$	32.5767	1.74881	0.874403	−	0.485200i	$-0.161253\pi$
$347$	32.5767	1.74881	0.874403	+	0.485200i	$0.161253\pi$
$348$	0.309666	0.0165998
$349$	14.7032	0.787047	0.393523	−	0.919315i	$-0.371256\pi$
$349$	14.7032	0.787047	0.393523	+	0.919315i	$0.371256\pi$
$350$	−12.1196	−0.647819
$351$	0	0
$352$	5.30670	0.282848
$353$	10.0572	0.535292	0.267646	−	0.963517i	$-0.413754\pi$
$353$	10.0572	0.535292	0.267646	+	0.963517i	$0.413754\pi$
$354$	0.465258	0.0247282
$355$	16.8064	0.891992
$356$	−14.8045	−0.784639
$357$	−0.431429	−0.0228337
$358$	0.586051	0.0309737
$359$	−1.13000	−0.0596393	−0.0298196	−	0.999555i	$-0.509493\pi$
$359$	−1.13000	−0.0596393	−0.0298196	+	0.999555i	$0.509493\pi$
$360$	−8.44861	−0.445281
$361$	1.00000	0.0526316
$362$	0.442224	0.0232428
$363$	−0.794150	−0.0416820
$364$	0	0
$365$	44.7808	2.34393
$366$	0.0633846	0.00331317
$367$	1.59357	0.0831834	0.0415917	−	0.999135i	$-0.486757\pi$
$367$	1.59357	0.0831834	0.0415917	+	0.999135i	$0.486757\pi$
$368$	−2.21961	−0.115705
$369$	−35.3799	−1.84181
$370$	18.6720	0.970710
$371$	−56.9562	−2.95702
$372$	−0.234210	−0.0121432
$373$	9.28269	0.480639	0.240320	−	0.970694i	$-0.422748\pi$
$373$	9.28269	0.480639	0.240320	+	0.970694i	$0.422748\pi$
$374$	−12.0110	−0.621075
$375$	0.268353	0.0138577
$376$	−5.50401	−0.283848
$377$	0	0
$378$	−1.14327	−0.0588037
$379$	−22.9148	−1.17705	−0.588526	−	0.808478i	$-0.700292\pi$
$379$	−22.9148	−1.17705	−0.588526	+	0.808478i	$0.700292\pi$
$380$	2.81822	0.144571
$381$	−0.197920	−0.0101397
$382$	15.8325	0.810060
$383$	−25.4393	−1.29989	−0.649943	−	0.759983i	$-0.725207\pi$
$383$	−25.4393	−1.29989	−0.649943	+	0.759983i	$0.725207\pi$
$384$	−0.0462763	−0.00236153
$385$	−61.6018	−3.13952
$386$	−5.25735	−0.267592
$387$	−29.8943	−1.51961
$388$	3.19810	0.162359
$389$	−19.3964	−0.983438	−0.491719	−	0.870754i	$-0.663631\pi$
$389$	−19.3964	−0.983438	−0.491719	+	0.870754i	$0.663631\pi$
$390$	0	0
$391$	5.02379	0.254064
$392$	9.96643	0.503381
$393$	0.529401	0.0267048
$394$	−4.88043	−0.245873
$395$	24.0302	1.20909
$396$	−15.9087	−0.799443
$397$	23.4750	1.17818	0.589088	−	0.808069i	$-0.299487\pi$
$397$	23.4750	1.17818	0.589088	+	0.808069i	$0.299487\pi$
$398$	11.0642	0.554597
$399$	0.190614	0.00954262
$400$	2.94234	0.147117
$401$	−21.4822	−1.07277	−0.536385	−	0.843973i	$-0.680211\pi$
$401$	−21.4822	−1.07277	−0.536385	+	0.843973i	$0.680211\pi$
$402$	−0.336531	−0.0167846
$403$	0	0
$404$	−4.96682	−0.247108
$405$	25.3096	1.25765
$406$	27.5632	1.36794
$407$	35.1593	1.74278
$408$	0.104740	0.00518543
$409$	−14.0288	−0.693681	−0.346840	−	0.937924i	$-0.612745\pi$
$409$	−14.0288	−0.693681	−0.346840	+	0.937924i	$0.612745\pi$
$410$	33.2598	1.64259
$411$	−1.02150	−0.0503871
$412$	−8.01176	−0.394711
$413$	41.4124	2.03777
$414$	6.65407	0.327029
$415$	19.2171	0.943329
$416$	0	0
$417$	−0.861136	−0.0421700
$418$	5.30670	0.259559
$419$	36.1851	1.76776	0.883879	−	0.467716i	$-0.154923\pi$
$419$	36.1851	1.76776	0.883879	+	0.467716i	$0.154923\pi$
$420$	0.537191	0.0262122
$421$	9.60899	0.468313	0.234157	−	0.972199i	$-0.424767\pi$
$421$	9.60899	0.468313	0.234157	+	0.972199i	$0.424767\pi$
$422$	1.11115	0.0540901
$423$	16.5002	0.802269
$424$	13.8276	0.671525
$425$	−6.65960	−0.323038
$426$	−0.275969	−0.0133707
$427$	5.64183	0.273027
$428$	6.13949	0.296764
$429$	0	0
$430$	28.1029	1.35524
$431$	21.3702	1.02937	0.514683	−	0.857381i	$-0.327910\pi$
$431$	21.3702	1.02937	0.514683	+	0.857381i	$0.327910\pi$
$432$	0.277559	0.0133541
$433$	10.5155	0.505343	0.252671	−	0.967552i	$-0.418691\pi$
$433$	10.5155	0.505343	0.252671	+	0.967552i	$0.418691\pi$
$434$	−20.8469	−1.00068
$435$	0.872706	0.0418431
$436$	−9.79838	−0.469257
$437$	−2.21961	−0.106178
$438$	−0.735321	−0.0351350
$439$	−4.96595	−0.237012	−0.118506	−	0.992953i	$-0.537810\pi$
$439$	−4.96595	−0.237012	−0.118506	+	0.992953i	$0.537810\pi$
$440$	14.9554	0.712971
$441$	−29.8779	−1.42276
$442$	0	0
$443$	−0.354569	−0.0168461	−0.00842304	−	0.999965i	$-0.502681\pi$
$443$	−0.354569	−0.0168461	−0.00842304	+	0.999965i	$0.502681\pi$
$444$	−0.306602	−0.0145507
$445$	−41.7224	−1.97783
$446$	14.3383	0.678940
$447$	0.168420	0.00796600
$448$	−4.11903	−0.194606
$449$	−15.2664	−0.720468	−0.360234	−	0.932862i	$-0.617303\pi$
$449$	−15.2664	−0.720468	−0.360234	+	0.932862i	$0.617303\pi$
$450$	−8.82072	−0.415813
$451$	62.6282	2.94905
$452$	−10.1455	−0.477205
$453$	−0.363294	−0.0170690
$454$	−11.2444	−0.527726
$455$	0	0
$456$	−0.0462763	−0.00216709
$457$	−36.1193	−1.68959	−0.844794	−	0.535091i	$-0.820277\pi$
$457$	−36.1193	−1.68959	−0.844794	+	0.535091i	$0.820277\pi$
$458$	8.90916	0.416298
$459$	−0.628219	−0.0293227
$460$	−6.25533	−0.291656
$461$	−22.5295	−1.04930	−0.524652	−	0.851317i	$-0.675805\pi$
$461$	−22.5295	−1.04930	−0.524652	+	0.851317i	$0.675805\pi$
$462$	1.01153	0.0470606
$463$	−9.65334	−0.448629	−0.224314	−	0.974517i	$-0.572014\pi$
$463$	−9.65334	−0.448629	−0.224314	+	0.974517i	$0.572014\pi$
$464$	−6.69167	−0.310653
$465$	−0.660055	−0.0306093
$466$	−10.5997	−0.491020
$467$	−7.52061	−0.348012	−0.174006	−	0.984745i	$-0.555671\pi$
$467$	−7.52061	−0.348012	−0.174006	+	0.984745i	$0.555671\pi$
$468$	0	0
$469$	−29.9544	−1.38317
$470$	−15.5115	−0.715491
$471$	−0.215350	−0.00992281
$472$	−10.0539	−0.462769
$473$	52.9178	2.43316
$474$	−0.394586	−0.0181240
$475$	2.94234	0.135004
$476$	9.32289	0.427314
$477$	−41.4531	−1.89801
$478$	0.528678	0.0241812
$479$	−0.277934	−0.0126991	−0.00634956	−	0.999980i	$-0.502021\pi$
$479$	−0.277934	−0.0126991	−0.00634956	+	0.999980i	$0.502021\pi$
$480$	−0.130417	−0.00595268
$481$	0	0
$482$	1.14353	0.0520865
$483$	−0.423087	−0.0192511
$484$	17.1610	0.780047
$485$	9.01294	0.409257
$486$	−1.24827	−0.0566228
$487$	5.59670	0.253611	0.126805	−	0.991928i	$-0.459528\pi$
$487$	5.59670	0.253611	0.126805	+	0.991928i	$0.459528\pi$
$488$	−1.36970	−0.0620033
$489$	0.373578	0.0168938
$490$	28.0875	1.26887
$491$	4.81057	0.217098	0.108549	−	0.994091i	$-0.465380\pi$
$491$	4.81057	0.217098	0.108549	+	0.994091i	$0.465380\pi$
$492$	−0.546141	−0.0246220
$493$	15.1457	0.682129
$494$	0	0
$495$	−44.8342	−2.01515
$496$	5.06112	0.227251
$497$	−24.5638	−1.10184
$498$	−0.315553	−0.0141403
$499$	−26.7880	−1.19920	−0.599598	−	0.800301i	$-0.704673\pi$
$499$	−26.7880	−1.19920	−0.599598	+	0.800301i	$0.704673\pi$
$500$	−5.79893	−0.259336
$501$	0.747873	0.0334125
$502$	22.4247	1.00087
$503$	14.7294	0.656752	0.328376	−	0.944547i	$-0.393499\pi$
$503$	14.7294	0.656752	0.328376	+	0.944547i	$0.393499\pi$
$504$	12.3483	0.550036
$505$	−13.9976	−0.622884
$506$	−11.7788	−0.523630
$507$	0	0
$508$	4.27692	0.189757
$509$	1.79988	0.0797781	0.0398890	−	0.999204i	$-0.487300\pi$
$509$	1.79988	0.0797781	0.0398890	+	0.999204i	$0.487300\pi$
$510$	0.295181	0.0130708
$511$	−65.4505	−2.89536
$512$	1.00000	0.0441942
$513$	0.277559	0.0122545
$514$	−11.3945	−0.502592
$515$	−22.5789	−0.994944
$516$	−0.461463	−0.0203148
$517$	−29.2081	−1.28457
$518$	−27.2905	−1.19908
$519$	0.128786	0.00565309
$520$	0	0
$521$	30.4378	1.33351	0.666753	−	0.745279i	$-0.267684\pi$
$521$	30.4378	1.33351	0.666753	+	0.745279i	$0.267684\pi$
$522$	20.0607	0.878033
$523$	6.74067	0.294749	0.147374	−	0.989081i	$-0.452918\pi$
$523$	6.74067	0.294749	0.147374	+	0.989081i	$0.452918\pi$
$524$	−11.4400	−0.499759
$525$	0.560850	0.0244775
$526$	1.69504	0.0739072
$527$	−11.4552	−0.498996
$528$	−0.245575	−0.0106873
$529$	−18.0733	−0.785798
$530$	38.9690	1.69271
$531$	30.1402	1.30797
$532$	−4.11903	−0.178583
$533$	0	0
$534$	0.685100	0.0296472
$535$	17.3024	0.748049
$536$	7.27220	0.314111
$537$	−0.0271203	−0.00117033
$538$	−24.4071	−1.05227
$539$	52.8888	2.27808
$540$	0.782221	0.0336614
$541$	−26.4161	−1.13572	−0.567858	−	0.823126i	$-0.692228\pi$
$541$	−26.4161	−1.13572	−0.567858	+	0.823126i	$0.692228\pi$
$542$	−12.0963	−0.519579
$543$	−0.0204645	−0.000878217 0
$544$	−2.26337	−0.0970412
$545$	−27.6139	−1.18285
$546$	0	0
$547$	26.9158	1.15084	0.575418	−	0.817859i	$-0.304839\pi$
$547$	26.9158	1.15084	0.575418	+	0.817859i	$0.304839\pi$
$548$	22.0740	0.942955
$549$	4.10616	0.175247
$550$	15.6141	0.665788
$551$	−6.69167	−0.285075
$552$	0.102715	0.00437185
$553$	−35.1219	−1.49354
$554$	−31.9226	−1.35626
$555$	−0.864071	−0.0366778
$556$	18.6086	0.789178
$557$	6.10712	0.258767	0.129383	−	0.991595i	$-0.458700\pi$
$557$	6.10712	0.258767	0.129383	+	0.991595i	$0.458700\pi$
$558$	−15.1725	−0.642304
$559$	0	0
$560$	−11.6083	−0.490541
$561$	0.555826	0.0234670
$562$	5.06348	0.213590
$563$	22.3933	0.943766	0.471883	−	0.881661i	$-0.343575\pi$
$563$	22.3933	0.943766	0.471883	+	0.881661i	$0.343575\pi$
$564$	0.254705	0.0107250
$565$	−28.5922	−1.20288
$566$	25.4293	1.06887
$567$	−36.9919	−1.55351
$568$	5.96350	0.250223
$569$	−20.3718	−0.854031	−0.427015	−	0.904244i	$-0.640435\pi$
$569$	−20.3718	−0.854031	−0.427015	+	0.904244i	$0.640435\pi$
$570$	−0.130417	−0.00546256
$571$	1.94161	0.0812536	0.0406268	−	0.999174i	$-0.487065\pi$
$571$	1.94161	0.0812536	0.0406268	+	0.999174i	$0.487065\pi$
$572$	0	0
$573$	−0.732670	−0.0306077
$574$	−48.6117	−2.02902
$575$	−6.53083	−0.272355
$576$	−2.99786	−0.124911
$577$	−4.03188	−0.167849	−0.0839246	−	0.996472i	$-0.526745\pi$
$577$	−4.03188	−0.167849	−0.0839246	+	0.996472i	$0.526745\pi$
$578$	−11.8772	−0.494025
$579$	0.243291	0.0101108
$580$	−18.8586	−0.783060
$581$	−28.0872	−1.16525
$582$	−0.147996	−0.00613465
$583$	73.3786	3.03903
$584$	15.8898	0.657524
$585$	0	0
$586$	6.99131	0.288808
$587$	−23.5415	−0.971661	−0.485831	−	0.874053i	$-0.661483\pi$
$587$	−23.5415	−0.971661	−0.485831	+	0.874053i	$0.661483\pi$
$588$	−0.461210	−0.0190200
$589$	5.06112	0.208540
$590$	−28.3341	−1.16650
$591$	0.225849	0.00929017
$592$	6.62546	0.272305
$593$	13.8571	0.569044	0.284522	−	0.958669i	$-0.408165\pi$
$593$	13.8571	0.569044	0.284522	+	0.958669i	$0.408165\pi$
$594$	1.47292	0.0604347
$595$	26.2739	1.07713
$596$	−3.63944	−0.149077
$597$	−0.512010	−0.0209552
$598$	0	0
$599$	25.4638	1.04042	0.520211	−	0.854038i	$-0.325853\pi$
$599$	25.4638	1.04042	0.520211	+	0.854038i	$0.325853\pi$
$600$	−0.136161	−0.00555874
$601$	−9.72793	−0.396810	−0.198405	−	0.980120i	$-0.563576\pi$
$601$	−9.72793	−0.396810	−0.198405	+	0.980120i	$0.563576\pi$
$602$	−41.0745	−1.67407
$603$	−21.8010	−0.887806
$604$	7.85053	0.319433
$605$	48.3635	1.96625
$606$	0.229846	0.00933686
$607$	−10.5850	−0.429631	−0.214815	−	0.976655i	$-0.568915\pi$
$607$	−10.5850	−0.429631	−0.214815	+	0.976655i	$0.568915\pi$
$608$	1.00000	0.0405554
$609$	−1.27553	−0.0516869
$610$	−3.86010	−0.156291
$611$	0	0
$612$	6.78526	0.274278
$613$	10.9614	0.442726	0.221363	−	0.975192i	$-0.428950\pi$
$613$	10.9614	0.442726	0.221363	+	0.975192i	$0.428950\pi$
$614$	−14.9269	−0.602402
$615$	−1.53914	−0.0620643
$616$	−21.8585	−0.880702
$617$	14.1917	0.571338	0.285669	−	0.958328i	$-0.407784\pi$
$617$	14.1917	0.571338	0.285669	+	0.958328i	$0.407784\pi$
$618$	0.370755	0.0149140
$619$	2.35729	0.0947476	0.0473738	−	0.998877i	$-0.484915\pi$
$619$	2.35729	0.0947476	0.0473738	+	0.998877i	$0.484915\pi$
$620$	14.2633	0.572829
$621$	−0.616072	−0.0247221
$622$	−20.1499	−0.807939
$623$	60.9804	2.44313
$624$	0	0
$625$	−31.0543	−1.24217
$626$	−15.2363	−0.608964
$627$	−0.245575	−0.00980730
$628$	4.65357	0.185698
$629$	−14.9959	−0.597924
$630$	34.8001	1.38647
$631$	−22.3437	−0.889488	−0.444744	−	0.895658i	$-0.646705\pi$
$631$	−22.3437	−0.889488	−0.444744	+	0.895658i	$0.646705\pi$
$632$	8.52674	0.339175
$633$	−0.0514201	−0.00204377
$634$	4.33507	0.172168
$635$	12.0533	0.478319
$636$	−0.639889	−0.0253732
$637$	0	0
$638$	−35.5107	−1.40588
$639$	−17.8777	−0.707232
$640$	2.81822	0.111400
$641$	4.96712	0.196190	0.0980948	−	0.995177i	$-0.468725\pi$
$641$	4.96712	0.196190	0.0980948	+	0.995177i	$0.468725\pi$
$642$	−0.284113	−0.0112131
$643$	−13.6576	−0.538601	−0.269301	−	0.963056i	$-0.586793\pi$
$643$	−13.6576	−0.538601	−0.269301	+	0.963056i	$0.586793\pi$
$644$	9.14263	0.360270
$645$	−1.30050	−0.0512072
$646$	−2.26337	−0.0890511
$647$	−44.7472	−1.75919	−0.879597	−	0.475720i	$-0.842187\pi$
$647$	−44.7472	−1.75919	−0.879597	+	0.475720i	$0.842187\pi$
$648$	8.98073	0.352796
$649$	−53.3530	−2.09429
$650$	0	0
$651$	0.964719	0.0378103
$652$	−8.07276	−0.316154
$653$	0.948387	0.0371133	0.0185566	−	0.999828i	$-0.494093\pi$
$653$	0.948387	0.0371133	0.0185566	+	0.999828i	$0.494093\pi$
$654$	0.453433	0.0177306
$655$	−32.2404	−1.25974
$656$	11.8017	0.460781
$657$	−47.6353	−1.85843
$658$	22.6712	0.883815
$659$	−10.2267	−0.398374	−0.199187	−	0.979961i	$-0.563830\pi$
$659$	−10.2267	−0.398374	−0.199187	+	0.979961i	$0.563830\pi$
$660$	−0.692082	−0.0269393
$661$	−29.3099	−1.14002	−0.570011	−	0.821637i	$-0.693061\pi$
$661$	−29.3099	−1.14002	−0.570011	+	0.821637i	$0.693061\pi$
$662$	7.18468	0.279240
$663$	0	0
$664$	6.81888	0.264624
$665$	−11.6083	−0.450151
$666$	−19.8622	−0.769644
$667$	14.8529	0.575106
$668$	−16.1610	−0.625289
$669$	−0.663526	−0.0256534
$670$	20.4946	0.791776
$671$	−7.26857	−0.280600
$672$	0.190614	0.00735309
$673$	−18.4268	−0.710302	−0.355151	−	0.934809i	$-0.615571\pi$
$673$	−18.4268	−0.710302	−0.355151	+	0.934809i	$0.615571\pi$
$674$	23.9676	0.923198
$675$	0.816673	0.0314337
$676$	0	0
$677$	−21.4531	−0.824508	−0.412254	−	0.911069i	$-0.635258\pi$
$677$	−21.4531	−0.824508	−0.412254	+	0.911069i	$0.635258\pi$
$678$	0.469497	0.0180309
$679$	−13.1731	−0.505537
$680$	−6.37866	−0.244611
$681$	0.520350	0.0199398
$682$	26.8578	1.02844
$683$	10.2397	0.391811	0.195905	−	0.980623i	$-0.437235\pi$
$683$	10.2397	0.391811	0.195905	+	0.980623i	$0.437235\pi$
$684$	−2.99786	−0.114626
$685$	62.2093	2.37690
$686$	−12.2188	−0.466516
$687$	−0.412283	−0.0157296
$688$	9.97189	0.380175
$689$	0	0
$690$	0.289474	0.0110201
$691$	42.3797	1.61220	0.806100	−	0.591779i	$-0.201574\pi$
$691$	42.3797	1.61220	0.806100	+	0.591779i	$0.201574\pi$
$692$	−2.78298	−0.105793
$693$	65.5286	2.48922
$694$	32.5767	1.23659
$695$	52.4429	1.98927
$696$	0.309666	0.0117379
$697$	−26.7117	−1.01178
$698$	14.7032	0.556526
$699$	0.490513	0.0185529
$700$	−12.1196	−0.458077
$701$	39.8502	1.50512	0.752560	−	0.658524i	$-0.228819\pi$
$701$	39.8502	1.50512	0.752560	+	0.658524i	$0.228819\pi$
$702$	0	0
$703$	6.62546	0.249884
$704$	5.30670	0.200004
$705$	0.717815	0.0270345
$706$	10.0572	0.378509
$707$	20.4585	0.769421
$708$	0.465258	0.0174855
$709$	−40.8003	−1.53229	−0.766143	−	0.642670i	$-0.777827\pi$
$709$	−40.8003	−1.53229	−0.766143	+	0.642670i	$0.777827\pi$
$710$	16.8064	0.630734
$711$	−25.5620	−0.958648
$712$	−14.8045	−0.554824
$713$	−11.2337	−0.420705
$714$	−0.431429	−0.0161458
$715$	0	0
$716$	0.586051	0.0219017
$717$	−0.0244653	−0.000913673 0
$718$	−1.13000	−0.0421713
$719$	21.9349	0.818033	0.409017	−	0.912527i	$-0.365872\pi$
$719$	21.9349	0.818033	0.409017	+	0.912527i	$0.365872\pi$
$720$	−8.44861	−0.314861
$721$	33.0007	1.22901
$722$	1.00000	0.0372161
$723$	−0.0529185	−0.00196806
$724$	0.442224	0.0164351
$725$	−19.6892	−0.731238
$726$	−0.794150	−0.0294737
$727$	41.3420	1.53329	0.766645	−	0.642072i	$-0.221925\pi$
$727$	41.3420	1.53329	0.766645	+	0.642072i	$0.221925\pi$
$728$	0	0
$729$	−26.8844	−0.995720
$730$	44.7808	1.65741
$731$	−22.5701	−0.834784
$732$	0.0633846	0.00234276
$733$	−29.7154	−1.09756	−0.548782	−	0.835965i	$-0.684908\pi$
$733$	−29.7154	−1.09756	−0.548782	+	0.835965i	$0.684908\pi$
$734$	1.59357	0.0588196
$735$	−1.29979	−0.0479434
$736$	−2.21961	−0.0818158
$737$	38.5913	1.42153
$738$	−35.3799	−1.30235
$739$	10.5609	0.388488	0.194244	−	0.980953i	$-0.437775\pi$
$739$	10.5609	0.388488	0.194244	+	0.980953i	$0.437775\pi$
$740$	18.6720	0.686395
$741$	0	0
$742$	−56.9562	−2.09093
$743$	−4.00318	−0.146862	−0.0734311	−	0.997300i	$-0.523395\pi$
$743$	−4.00318	−0.146862	−0.0734311	+	0.997300i	$0.523395\pi$
$744$	−0.234210	−0.00858656
$745$	−10.2567	−0.375778
$746$	9.28269	0.339863
$747$	−20.4420	−0.747935
$748$	−12.0110	−0.439166
$749$	−25.2888	−0.924031
$750$	0.268353	0.00979888
$751$	18.5075	0.675347	0.337674	−	0.941263i	$-0.390360\pi$
$751$	18.5075	0.675347	0.337674	+	0.941263i	$0.390360\pi$
$752$	−5.50401	−0.200711
$753$	−1.03774	−0.0378172
$754$	0	0
$755$	22.1245	0.805192
$756$	−1.14327	−0.0415805
$757$	16.7827	0.609979	0.304989	−	0.952356i	$-0.401347\pi$
$757$	16.7827	0.609979	0.304989	+	0.952356i	$0.401347\pi$
$758$	−22.9148	−0.832302
$759$	0.545079	0.0197851
$760$	2.81822	0.102227
$761$	−46.9636	−1.70243	−0.851215	−	0.524817i	$-0.824134\pi$
$761$	−46.9636	−1.70243	−0.851215	+	0.524817i	$0.824134\pi$
$762$	−0.197920	−0.00716989
$763$	40.3598	1.46112
$764$	15.8325	0.572799
$765$	19.1223	0.691369
$766$	−25.4393	−0.919158
$767$	0	0
$768$	−0.0462763	−0.00166985
$769$	6.41061	0.231173	0.115586	−	0.993297i	$-0.463125\pi$
$769$	6.41061	0.231173	0.115586	+	0.993297i	$0.463125\pi$
$770$	−61.6018	−2.21998
$771$	0.527298	0.0189902
$772$	−5.25735	−0.189216
$773$	−22.1481	−0.796613	−0.398306	−	0.917252i	$-0.630402\pi$
$773$	−22.1481	−0.796613	−0.398306	+	0.917252i	$0.630402\pi$
$774$	−29.8943	−1.07453
$775$	14.8915	0.534920
$776$	3.19810	0.114805
$777$	1.26290	0.0453064
$778$	−19.3964	−0.695396
$779$	11.8017	0.422841
$780$	0	0
$781$	31.6465	1.13240
$782$	5.02379	0.179650
$783$	−1.85733	−0.0663757
$784$	9.96643	0.355944
$785$	13.1148	0.468086
$786$	0.529401	0.0188831
$787$	45.1147	1.60816	0.804082	−	0.594518i	$-0.202657\pi$
$787$	45.1147	1.60816	0.804082	+	0.594518i	$0.202657\pi$
$788$	−4.88043	−0.173858
$789$	−0.0784402	−0.00279254
$790$	24.0302	0.854956
$791$	41.7897	1.48587
$792$	−15.9087	−0.565292
$793$	0	0
$794$	23.4750	0.833096
$795$	−1.80334	−0.0639580
$796$	11.0642	0.392160
$797$	−14.3603	−0.508667	−0.254334	−	0.967117i	$-0.581856\pi$
$797$	−14.3603	−0.508667	−0.254334	+	0.967117i	$0.581856\pi$
$798$	0.190614	0.00674765
$799$	12.4576	0.440719
$800$	2.94234	0.104027
$801$	44.3819	1.56816
$802$	−21.4822	−0.758563
$803$	84.3222	2.97567
$804$	−0.336531	−0.0118685
$805$	25.7659	0.908129
$806$	0	0
$807$	1.12947	0.0397593
$808$	−4.96682	−0.174732
$809$	−23.3734	−0.821766	−0.410883	−	0.911688i	$-0.634779\pi$
$809$	−23.3734	−0.821766	−0.410883	+	0.911688i	$0.634779\pi$
$810$	25.3096	0.889290
$811$	−11.2209	−0.394019	−0.197009	−	0.980402i	$-0.563123\pi$
$811$	−11.2209	−0.394019	−0.197009	+	0.980402i	$0.563123\pi$
$812$	27.5632	0.967279
$813$	0.559771	0.0196320
$814$	35.1593	1.23233
$815$	−22.7508	−0.796925
$816$	0.104740	0.00366665
$817$	9.97189	0.348872
$818$	−14.0288	−0.490506
$819$	0	0
$820$	33.2598	1.16148
$821$	−4.64104	−0.161973	−0.0809866	−	0.996715i	$-0.525807\pi$
$821$	−4.64104	−0.161973	−0.0809866	+	0.996715i	$0.525807\pi$
$822$	−1.02150	−0.0356291
$823$	−40.6527	−1.41706	−0.708532	−	0.705678i	$-0.750642\pi$
$823$	−40.6527	−1.41706	−0.708532	+	0.705678i	$0.750642\pi$
$824$	−8.01176	−0.279103
$825$	−0.722564	−0.0251564
$826$	41.4124	1.44092
$827$	32.7555	1.13902	0.569510	−	0.821985i	$-0.307133\pi$
$827$	32.7555	1.13902	0.569510	+	0.821985i	$0.307133\pi$
$828$	6.65407	0.231245
$829$	−19.3842	−0.673242	−0.336621	−	0.941640i	$-0.609284\pi$
$829$	−19.3842	−0.673242	−0.336621	+	0.941640i	$0.609284\pi$
$830$	19.2171	0.667034
$831$	1.47726	0.0512456
$832$	0	0
$833$	−22.5577	−0.781578
$834$	−0.861136	−0.0298187
$835$	−45.5453	−1.57616
$836$	5.30670	0.183536
$837$	1.40476	0.0485556
$838$	36.1851	1.24999
$839$	−2.29328	−0.0791727	−0.0395864	−	0.999216i	$-0.512604\pi$
$839$	−2.29328	−0.0791727	−0.0395864	+	0.999216i	$0.512604\pi$
$840$	0.537191	0.0185348
$841$	15.7785	0.544086
$842$	9.60899	0.331148
$843$	−0.234319	−0.00807039
$844$	1.11115	0.0382475
$845$	0	0
$846$	16.5002	0.567290
$847$	−70.6868	−2.42883
$848$	13.8276	0.474840
$849$	−1.17678	−0.0403868
$850$	−6.65960	−0.228422
$851$	−14.7059	−0.504112
$852$	−0.275969	−0.00945454
$853$	26.3173	0.901086	0.450543	−	0.892755i	$-0.351230\pi$
$853$	26.3173	0.901086	0.450543	+	0.892755i	$0.351230\pi$
$854$	5.64183	0.193059
$855$	−8.44861	−0.288936
$856$	6.13949	0.209844
$857$	6.39962	0.218607	0.109303	−	0.994008i	$-0.465138\pi$
$857$	6.39962	0.218607	0.109303	+	0.994008i	$0.465138\pi$
$858$	0	0
$859$	9.95427	0.339635	0.169818	−	0.985476i	$-0.445682\pi$
$859$	9.95427	0.339635	0.169818	+	0.985476i	$0.445682\pi$
$860$	28.1029	0.958302
$861$	2.24957	0.0766653
$862$	21.3702	0.727871
$863$	33.1437	1.12822	0.564112	−	0.825698i	$-0.309219\pi$
$863$	33.1437	1.12822	0.564112	+	0.825698i	$0.309219\pi$
$864$	0.277559	0.00944275
$865$	−7.84305	−0.266672
$866$	10.5155	0.357331
$867$	0.549631	0.0186665
$868$	−20.8469	−0.707591
$869$	45.2488	1.53496
$870$	0.872706	0.0295875
$871$	0	0
$872$	−9.79838	−0.331815
$873$	−9.58746	−0.324486
$874$	−2.21961	−0.0750793
$875$	23.8860	0.807494
$876$	−0.735321	−0.0248442
$877$	28.2911	0.955323	0.477661	−	0.878544i	$-0.341485\pi$
$877$	28.2911	0.955323	0.477661	+	0.878544i	$0.341485\pi$
$878$	−4.96595	−0.167593
$879$	−0.323532	−0.0109125
$880$	14.9554	0.504147
$881$	−48.0750	−1.61969	−0.809843	−	0.586646i	$-0.800448\pi$
$881$	−48.0750	−1.61969	−0.809843	+	0.586646i	$0.800448\pi$
$882$	−29.8779	−1.00604
$883$	20.7062	0.696820	0.348410	−	0.937342i	$-0.386722\pi$
$883$	20.7062	0.696820	0.348410	+	0.937342i	$0.386722\pi$
$884$	0	0
$885$	1.31120	0.0440754
$886$	−0.354569	−0.0119120
$887$	42.4965	1.42689	0.713447	−	0.700710i	$-0.247133\pi$
$887$	42.4965	1.42689	0.713447	+	0.700710i	$0.247133\pi$
$888$	−0.306602	−0.0102889
$889$	−17.6168	−0.590847
$890$	−41.7224	−1.39854
$891$	47.6580	1.59660
$892$	14.3383	0.480083
$893$	−5.50401	−0.184185
$894$	0.168420	0.00563281
$895$	1.65162	0.0552075
$896$	−4.11903	−0.137607
$897$	0	0
$898$	−15.2664	−0.509448
$899$	−33.8674	−1.12954
$900$	−8.82072	−0.294024
$901$	−31.2969	−1.04265
$902$	62.6282	2.08529
$903$	1.90078	0.0632540
$904$	−10.1455	−0.337435
$905$	1.24628	0.0414279
$906$	−0.363294	−0.0120696
$907$	44.9409	1.49224	0.746119	−	0.665812i	$-0.231915\pi$
$907$	44.9409	1.49224	0.746119	+	0.665812i	$0.231915\pi$
$908$	−11.2444	−0.373159
$909$	14.8898	0.493864
$910$	0	0
$911$	28.5002	0.944255	0.472127	−	0.881530i	$-0.343486\pi$
$911$	28.5002	0.944255	0.472127	+	0.881530i	$0.343486\pi$
$912$	−0.0462763	−0.00153236
$913$	36.1857	1.19757
$914$	−36.1193	−1.19472
$915$	0.178632	0.00590538
$916$	8.90916	0.294367
$917$	47.1217	1.55610
$918$	−0.628219	−0.0207343
$919$	−53.2809	−1.75757	−0.878787	−	0.477213i	$-0.841647\pi$
$919$	−53.2809	−1.75757	−0.878787	+	0.477213i	$0.841647\pi$
$920$	−6.25533	−0.206232
$921$	0.690764	0.0227615
$922$	−22.5295	−0.741970
$923$	0	0
$924$	1.01153	0.0332769
$925$	19.4944	0.640970
$926$	−9.65334	−0.317228
$927$	24.0181	0.788859
$928$	−6.69167	−0.219665
$929$	−3.24777	−0.106556	−0.0532779	−	0.998580i	$-0.516967\pi$
$929$	−3.24777	−0.106556	−0.0532779	+	0.998580i	$0.516967\pi$
$930$	−0.660055	−0.0216441
$931$	9.96643	0.326636
$932$	−10.5997	−0.347203
$933$	0.932465	0.0305275
$934$	−7.52061	−0.246082
$935$	−33.8496	−1.10700
$936$	0	0
$937$	33.8520	1.10590	0.552949	−	0.833215i	$-0.313502\pi$
$937$	33.8520	1.10590	0.552949	+	0.833215i	$0.313502\pi$
$938$	−29.9544	−0.978046
$939$	0.705079	0.0230094
$940$	−15.5115	−0.505929
$941$	−14.6036	−0.476065	−0.238032	−	0.971257i	$-0.576502\pi$
$941$	−14.6036	−0.476065	−0.238032	+	0.971257i	$0.576502\pi$
$942$	−0.215350	−0.00701649
$943$	−26.1952	−0.853034
$944$	−10.0539	−0.327227
$945$	−3.22199	−0.104811
$946$	52.9178	1.72051
$947$	−22.3116	−0.725030	−0.362515	−	0.931978i	$-0.618082\pi$
$947$	−22.3116	−0.725030	−0.362515	+	0.931978i	$0.618082\pi$
$948$	−0.394586	−0.0128156
$949$	0	0
$950$	2.94234	0.0954621
$951$	−0.200611	−0.00650526
$952$	9.32289	0.302157
$953$	16.0880	0.521141	0.260571	−	0.965455i	$-0.416089\pi$
$953$	16.0880	0.521141	0.260571	+	0.965455i	$0.416089\pi$
$954$	−41.4531	−1.34209
$955$	44.6194	1.44385
$956$	0.528678	0.0170987
$957$	1.64330	0.0531205
$958$	−0.277934	−0.00897963
$959$	−90.9236	−2.93608
$960$	−0.130417	−0.00420918
$961$	−5.38505	−0.173711
$962$	0	0
$963$	−18.4053	−0.593103
$964$	1.14353	0.0368307
$965$	−14.8163	−0.476955
$966$	−0.423087	−0.0136126
$967$	−11.2495	−0.361758	−0.180879	−	0.983505i	$-0.557894\pi$
$967$	−11.2495	−0.361758	−0.180879	+	0.983505i	$0.557894\pi$
$968$	17.1610	0.551576
$969$	0.104740	0.00336475
$970$	9.01294	0.289388
$971$	38.3534	1.23082	0.615410	−	0.788207i	$-0.288991\pi$
$971$	38.3534	1.23082	0.615410	+	0.788207i	$0.288991\pi$
$972$	−1.24827	−0.0400384
$973$	−76.6492	−2.45726
$974$	5.59670	0.179330
$975$	0	0
$976$	−1.36970	−0.0438430
$977$	−27.4302	−0.877570	−0.438785	−	0.898592i	$-0.644591\pi$
$977$	−27.4302	−0.877570	−0.438785	+	0.898592i	$0.644591\pi$
$978$	0.373578	0.0119457
$979$	−78.5632	−2.51089
$980$	28.0875	0.897224
$981$	29.3741	0.937844
$982$	4.81057	0.153511
$983$	5.01605	0.159987	0.0799936	−	0.996795i	$-0.474510\pi$
$983$	5.01605	0.159987	0.0799936	+	0.996795i	$0.474510\pi$
$984$	−0.546141	−0.0174104
$985$	−13.7541	−0.438243
$986$	15.1457	0.482338
$987$	−1.04914	−0.0333945
$988$	0	0
$989$	−22.1337	−0.703810
$990$	−44.8342	−1.42492
$991$	−5.85548	−0.186005	−0.0930027	−	0.995666i	$-0.529647\pi$
$991$	−5.85548	−0.186005	−0.0930027	+	0.995666i	$0.529647\pi$
$992$	5.06112	0.160691
$993$	−0.332481	−0.0105510
$994$	−24.5638	−0.779118
$995$	31.1812	0.988512
$996$	−0.315553	−0.00999867
$997$	−15.7727	−0.499528	−0.249764	−	0.968307i	$-0.580353\pi$
$997$	−15.7727	−0.499528	−0.249764	+	0.968307i	$0.580353\pi$
$998$	−26.7880	−0.847960
$999$	1.83896	0.0581820

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6422.2.a.bf.1.4		7
13.5	odd	4		494.2.d.c.77.4	✓	14
13.8	odd	4		494.2.d.c.77.11	yes	14
13.12	even	2		6422.2.a.be.1.4		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
494.2.d.c.77.4	✓	14	13.5	odd	4
494.2.d.c.77.11	yes	14	13.8	odd	4
6422.2.a.be.1.4		7	13.12	even	2
6422.2.a.bf.1.4		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:	\( N \)	\(=\)	\( 6422 = 2 \cdot 13^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6422.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.0462763 q^{3} +1.00000 q^{4} +2.81822 q^{5} -0.0462763 q^{6} -4.11903 q^{7} +1.00000 q^{8} -2.99786 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.0462763 q^{3} +1.00000 q^{4} +2.81822 q^{5} -0.0462763 q^{6} -4.11903 q^{7} +1.00000 q^{8} -2.99786 q^{9} +2.81822 q^{10} +5.30670 q^{11} -0.0462763 q^{12} -4.11903 q^{14} -0.130417 q^{15} +1.00000 q^{16} -2.26337 q^{17} -2.99786 q^{18} +1.00000 q^{19} +2.81822 q^{20} +0.190614 q^{21} +5.30670 q^{22} -2.21961 q^{23} -0.0462763 q^{24} +2.94234 q^{25} +0.277559 q^{27} -4.11903 q^{28} -6.69167 q^{29} -0.130417 q^{30} +5.06112 q^{31} +1.00000 q^{32} -0.245575 q^{33} -2.26337 q^{34} -11.6083 q^{35} -2.99786 q^{36} +6.62546 q^{37} +1.00000 q^{38} +2.81822 q^{40} +11.8017 q^{41} +0.190614 q^{42} +9.97189 q^{43} +5.30670 q^{44} -8.44861 q^{45} -2.21961 q^{46} -5.50401 q^{47} -0.0462763 q^{48} +9.96643 q^{49} +2.94234 q^{50} +0.104740 q^{51} +13.8276 q^{53} +0.277559 q^{54} +14.9554 q^{55} -4.11903 q^{56} -0.0462763 q^{57} -6.69167 q^{58} -10.0539 q^{59} -0.130417 q^{60} -1.36970 q^{61} +5.06112 q^{62} +12.3483 q^{63} +1.00000 q^{64} -0.245575 q^{66} +7.27220 q^{67} -2.26337 q^{68} +0.102715 q^{69} -11.6083 q^{70} +5.96350 q^{71} -2.99786 q^{72} +15.8898 q^{73} +6.62546 q^{74} -0.136161 q^{75} +1.00000 q^{76} -21.8585 q^{77} +8.52674 q^{79} +2.81822 q^{80} +8.98073 q^{81} +11.8017 q^{82} +6.81888 q^{83} +0.190614 q^{84} -6.37866 q^{85} +9.97189 q^{86} +0.309666 q^{87} +5.30670 q^{88} -14.8045 q^{89} -8.44861 q^{90} -2.21961 q^{92} -0.234210 q^{93} -5.50401 q^{94} +2.81822 q^{95} -0.0462763 q^{96} +3.19810 q^{97} +9.96643 q^{98} -15.9087 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 7 q^{2} + 2 q^{3} + 7 q^{4} + 2 q^{5} + 2 q^{6} + q^{7} + 7 q^{8} + 15 q^{9}+O(q^{10}) \) 7 * q + 7 * q^2 + 2 * q^3 + 7 * q^4 + 2 * q^5 + 2 * q^6 + q^7 + 7 * q^8 + 15 * q^9	\( 7 q + 7 q^{2} + 2 q^{3} + 7 q^{4} + 2 q^{5} + 2 q^{6} + q^{7} + 7 q^{8} + 15 q^{9} + 2 q^{10} + 5 q^{11} + 2 q^{12} + q^{14} + 13 q^{15} + 7 q^{16} + 16 q^{17} + 15 q^{18} + 7 q^{19} + 2 q^{20} - 3 q^{21} + 5 q^{22} + 3 q^{23} + 2 q^{24} + 7 q^{25} + 5 q^{27} + q^{28} - 7 q^{29} + 13 q^{30} + 11 q^{31} + 7 q^{32} + 6 q^{33} + 16 q^{34} + q^{35} + 15 q^{36} - 3 q^{37} + 7 q^{38} + 2 q^{40} + 15 q^{41} - 3 q^{42} + 23 q^{43} + 5 q^{44} - 38 q^{45} + 3 q^{46} - q^{47} + 2 q^{48} + 14 q^{49} + 7 q^{50} - 16 q^{51} + 21 q^{53} + 5 q^{54} + 8 q^{55} + q^{56} + 2 q^{57} - 7 q^{58} + 8 q^{59} + 13 q^{60} - 6 q^{61} + 11 q^{62} - 22 q^{63} + 7 q^{64} + 6 q^{66} + 28 q^{67} + 16 q^{68} + 48 q^{69} + q^{70} + 4 q^{71} + 15 q^{72} + 12 q^{73} - 3 q^{74} + 5 q^{75} + 7 q^{76} - 26 q^{77} - 4 q^{79} + 2 q^{80} + 51 q^{81} + 15 q^{82} + 13 q^{83} - 3 q^{84} - 39 q^{85} + 23 q^{86} - 16 q^{87} + 5 q^{88} - 15 q^{89} - 38 q^{90} + 3 q^{92} + 6 q^{93} - q^{94} + 2 q^{95} + 2 q^{96} - 37 q^{97} + 14 q^{98} - 15 q^{99}+O(q^{100}) \) 7 * q + 7 * q^2 + 2 * q^3 + 7 * q^4 + 2 * q^5 + 2 * q^6 + q^7 + 7 * q^8 + 15 * q^9 + 2 * q^10 + 5 * q^11 + 2 * q^12 + q^14 + 13 * q^15 + 7 * q^16 + 16 * q^17 + 15 * q^18 + 7 * q^19 + 2 * q^20 - 3 * q^21 + 5 * q^22 + 3 * q^23 + 2 * q^24 + 7 * q^25 + 5 * q^27 + q^28 - 7 * q^29 + 13 * q^30 + 11 * q^31 + 7 * q^32 + 6 * q^33 + 16 * q^34 + q^35 + 15 * q^36 - 3 * q^37 + 7 * q^38 + 2 * q^40 + 15 * q^41 - 3 * q^42 + 23 * q^43 + 5 * q^44 - 38 * q^45 + 3 * q^46 - q^47 + 2 * q^48 + 14 * q^49 + 7 * q^50 - 16 * q^51 + 21 * q^53 + 5 * q^54 + 8 * q^55 + q^56 + 2 * q^57 - 7 * q^58 + 8 * q^59 + 13 * q^60 - 6 * q^61 + 11 * q^62 - 22 * q^63 + 7 * q^64 + 6 * q^66 + 28 * q^67 + 16 * q^68 + 48 * q^69 + q^70 + 4 * q^71 + 15 * q^72 + 12 * q^73 - 3 * q^74 + 5 * q^75 + 7 * q^76 - 26 * q^77 - 4 * q^79 + 2 * q^80 + 51 * q^81 + 15 * q^82 + 13 * q^83 - 3 * q^84 - 39 * q^85 + 23 * q^86 - 16 * q^87 + 5 * q^88 - 15 * q^89 - 38 * q^90 + 3 * q^92 + 6 * q^93 - q^94 + 2 * q^95 + 2 * q^96 - 37 * q^97 + 14 * q^98 - 15 * q^99

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