LMFDB - Embedded newform 83.2.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [83,2,Mod(1,83)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(83, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("83.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 83 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	83.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:	$0.662758336777$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.9059636.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 8x^{4} + 11x^{3} + 4x^{2} - 4x - 1 $ x^6 - x^5 - 8x^4 + 11x^3 + 4x^2 - 4x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.236470$ of defining polynomial
Character	$\chi$	$=$	83.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.429349 q^{2} +2.76735 q^{3} -1.81566 q^{4} +1.71413 q^{5} -1.18816 q^{6} -3.46533 q^{7} +1.63825 q^{8} +4.65821 q^{9} +O(q^{10})$	\(q-0.429349 q^{2} +2.76735 q^{3} -1.81566 q^{4} +1.71413 q^{5} -1.18816 q^{6} -3.46533 q^{7} +1.63825 q^{8} +4.65821 q^{9} -0.735961 q^{10} -4.04071 q^{11} -5.02456 q^{12} +4.06760 q^{13} +1.48784 q^{14} +4.74360 q^{15} +2.92794 q^{16} -4.60990 q^{17} -2.00000 q^{18} -2.09045 q^{19} -3.11228 q^{20} -9.58978 q^{21} +1.73487 q^{22} -3.55162 q^{23} +4.53361 q^{24} -2.06175 q^{25} -1.74642 q^{26} +4.58885 q^{27} +6.29187 q^{28} -0.181799 q^{29} -2.03666 q^{30} +10.0483 q^{31} -4.53361 q^{32} -11.1820 q^{33} +1.97926 q^{34} -5.94004 q^{35} -8.45773 q^{36} +8.34942 q^{37} +0.897532 q^{38} +11.2565 q^{39} +2.80818 q^{40} +5.35620 q^{41} +4.11737 q^{42} -3.68511 q^{43} +7.33654 q^{44} +7.98479 q^{45} +1.52489 q^{46} +12.0600 q^{47} +8.10262 q^{48} +5.00854 q^{49} +0.885213 q^{50} -12.7572 q^{51} -7.38537 q^{52} -3.24556 q^{53} -1.97022 q^{54} -6.92630 q^{55} -5.67708 q^{56} -5.78500 q^{57} +0.0780552 q^{58} +1.97056 q^{59} -8.61275 q^{60} +2.39757 q^{61} -4.31425 q^{62} -16.1423 q^{63} -3.90937 q^{64} +6.97240 q^{65} +4.80100 q^{66} -4.50274 q^{67} +8.37001 q^{68} -9.82857 q^{69} +2.55035 q^{70} -13.4130 q^{71} +7.63132 q^{72} +11.1047 q^{73} -3.58482 q^{74} -5.70559 q^{75} +3.79554 q^{76} +14.0024 q^{77} -4.83295 q^{78} +0.572829 q^{79} +5.01887 q^{80} -1.27569 q^{81} -2.29968 q^{82} +1.00000 q^{83} +17.4118 q^{84} -7.90197 q^{85} +1.58220 q^{86} -0.503100 q^{87} -6.61969 q^{88} -4.48566 q^{89} -3.42826 q^{90} -14.0956 q^{91} +6.44853 q^{92} +27.8073 q^{93} -5.17796 q^{94} -3.58330 q^{95} -12.5461 q^{96} +14.9833 q^{97} -2.15041 q^{98} -18.8225 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} + q^{3} + 7 q^{4} + 2 q^{5} - 7 q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 6 * q + q^2 + q^3 + 7 * q^4 + 2 * q^5 - 7 * q^6 + 3 * q^7 + 3 * q^8 + 3 * q^9	\( 6 q + q^{2} + q^{3} + 7 q^{4} + 2 q^{5} - 7 q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{9} - 6 q^{10} - 3 q^{11} - 9 q^{12} + 14 q^{13} - 15 q^{14} - 6 q^{15} + q^{16} - 5 q^{17} - 12 q^{18} - 4 q^{19} - 20 q^{20} - 2 q^{21} - q^{22} - 5 q^{23} - 17 q^{24} + 14 q^{25} - 2 q^{26} + 10 q^{27} + 9 q^{28} - q^{29} + 18 q^{30} + 3 q^{31} + 17 q^{32} + 2 q^{33} + 15 q^{34} - 10 q^{35} - 8 q^{36} + 39 q^{37} - 6 q^{38} - 8 q^{39} - 18 q^{40} - q^{41} + 17 q^{42} - 8 q^{43} + 27 q^{44} + 10 q^{45} - 12 q^{46} - 12 q^{47} + 7 q^{48} + 11 q^{49} + 35 q^{50} - 24 q^{51} + 36 q^{52} + 14 q^{53} + 19 q^{54} - 24 q^{55} - 23 q^{56} - 10 q^{57} + 25 q^{58} - 17 q^{59} - 5 q^{61} + 5 q^{62} - 11 q^{63} + 9 q^{64} - 8 q^{65} - 39 q^{66} + 16 q^{67} - 15 q^{68} + 8 q^{69} - 10 q^{70} - 26 q^{71} + 10 q^{72} - 6 q^{73} + 23 q^{74} - 45 q^{75} - 28 q^{76} + 6 q^{77} - 18 q^{78} - 12 q^{79} - 60 q^{80} - 34 q^{81} + 10 q^{82} + 6 q^{83} + 41 q^{84} + 18 q^{85} + 16 q^{86} - 3 q^{87} - 17 q^{88} - 22 q^{89} - 4 q^{90} - 2 q^{91} + 2 q^{92} + 34 q^{93} - 8 q^{94} - 4 q^{95} - 19 q^{96} + 6 q^{97} - 30 q^{98} - 18 q^{99}+O(q^{100}) \) 6 * q + q^2 + q^3 + 7 * q^4 + 2 * q^5 - 7 * q^6 + 3 * q^7 + 3 * q^8 + 3 * q^9 - 6 * q^10 - 3 * q^11 - 9 * q^12 + 14 * q^13 - 15 * q^14 - 6 * q^15 + q^16 - 5 * q^17 - 12 * q^18 - 4 * q^19 - 20 * q^20 - 2 * q^21 - q^22 - 5 * q^23 - 17 * q^24 + 14 * q^25 - 2 * q^26 + 10 * q^27 + 9 * q^28 - q^29 + 18 * q^30 + 3 * q^31 + 17 * q^32 + 2 * q^33 + 15 * q^34 - 10 * q^35 - 8 * q^36 + 39 * q^37 - 6 * q^38 - 8 * q^39 - 18 * q^40 - q^41 + 17 * q^42 - 8 * q^43 + 27 * q^44 + 10 * q^45 - 12 * q^46 - 12 * q^47 + 7 * q^48 + 11 * q^49 + 35 * q^50 - 24 * q^51 + 36 * q^52 + 14 * q^53 + 19 * q^54 - 24 * q^55 - 23 * q^56 - 10 * q^57 + 25 * q^58 - 17 * q^59 - 5 * q^61 + 5 * q^62 - 11 * q^63 + 9 * q^64 - 8 * q^65 - 39 * q^66 + 16 * q^67 - 15 * q^68 + 8 * q^69 - 10 * q^70 - 26 * q^71 + 10 * q^72 - 6 * q^73 + 23 * q^74 - 45 * q^75 - 28 * q^76 + 6 * q^77 - 18 * q^78 - 12 * q^79 - 60 * q^80 - 34 * q^81 + 10 * q^82 + 6 * q^83 + 41 * q^84 + 18 * q^85 + 16 * q^86 - 3 * q^87 - 17 * q^88 - 22 * q^89 - 4 * q^90 - 2 * q^91 + 2 * q^92 + 34 * q^93 - 8 * q^94 - 4 * q^95 - 19 * q^96 + 6 * q^97 - 30 * q^98 - 18 * 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 $

$2$	−0.429349	−0.303596	−0.151798	−	0.988412i	$-0.548506\pi$
$2$	−0.429349	−0.303596	−0.151798	+	0.988412i	$0.548506\pi$
$3$	2.76735	1.59773	0.798864	−	0.601511i	$-0.205434\pi$
$3$	2.76735	1.59773	0.798864	+	0.601511i	$0.205434\pi$
$4$	−1.81566	−0.907830
$5$	1.71413	0.766583	0.383291	−	0.923627i	$-0.374791\pi$
$5$	1.71413	0.766583	0.383291	+	0.923627i	$0.374791\pi$
$6$	−1.18816	−0.485064
$7$	−3.46533	−1.30977	−0.654887	−	0.755727i	$-0.727284\pi$
$7$	−3.46533	−1.30977	−0.654887	+	0.755727i	$0.727284\pi$
$8$	1.63825	0.579209
$9$	4.65821	1.55274
$10$	−0.735961	−0.232731
$11$	−4.04071	−1.21832	−0.609159	−	0.793048i	$-0.708493\pi$
$11$	−4.04071	−1.21832	−0.609159	+	0.793048i	$0.708493\pi$
$12$	−5.02456	−1.45047
$13$	4.06760	1.12815	0.564075	−	0.825724i	$-0.309233\pi$
$13$	4.06760	1.12815	0.564075	+	0.825724i	$0.309233\pi$
$14$	1.48784	0.397642
$15$	4.74360	1.22479
$16$	2.92794	0.731984
$17$	−4.60990	−1.11807	−0.559033	−	0.829146i	$-0.688827\pi$
$17$	−4.60990	−1.11807	−0.559033	+	0.829146i	$0.688827\pi$
$18$	−2.00000	−0.471405
$19$	−2.09045	−0.479582	−0.239791	−	0.970825i	$-0.577079\pi$
$19$	−2.09045	−0.479582	−0.239791	+	0.970825i	$0.577079\pi$
$20$	−3.11228	−0.695926
$21$	−9.58978	−2.09266
$22$	1.73487	0.369876
$23$	−3.55162	−0.740564	−0.370282	−	0.928919i	$-0.620739\pi$
$23$	−3.55162	−0.740564	−0.370282	+	0.928919i	$0.620739\pi$
$24$	4.53361	0.925419
$25$	−2.06175	−0.412351
$26$	−1.74642	−0.342501
$27$	4.58885	0.883125
$28$	6.29187	1.18905
$29$	−0.181799	−0.0337592	−0.0168796	−	0.999858i	$-0.505373\pi$
$29$	−0.181799	−0.0337592	−0.0168796	+	0.999858i	$0.505373\pi$
$30$	−2.03666	−0.371841
$31$	10.0483	1.80474	0.902368	−	0.430967i	$-0.141828\pi$
$31$	10.0483	1.80474	0.902368	+	0.430967i	$0.141828\pi$
$32$	−4.53361	−0.801436
$33$	−11.1820	−1.94654
$34$	1.97926	0.339440
$35$	−5.94004	−1.00405
$36$	−8.45773	−1.40962
$37$	8.34942	1.37264	0.686318	−	0.727301i	$-0.259226\pi$
$37$	8.34942	1.37264	0.686318	+	0.727301i	$0.259226\pi$
$38$	0.897532	0.145599
$39$	11.2565	1.80248
$40$	2.80818	0.444012
$41$	5.35620	0.836498	0.418249	−	0.908332i	$-0.362644\pi$
$41$	5.35620	0.836498	0.418249	+	0.908332i	$0.362644\pi$
$42$	4.11737	0.635323
$43$	−3.68511	−0.561974	−0.280987	−	0.959712i	$-0.590662\pi$
$43$	−3.68511	−0.561974	−0.280987	+	0.959712i	$0.590662\pi$
$44$	7.33654	1.10603
$45$	7.98479	1.19030
$46$	1.52489	0.224832
$47$	12.0600	1.75914	0.879568	−	0.475774i	$-0.157832\pi$
$47$	12.0600	1.75914	0.879568	+	0.475774i	$0.157832\pi$
$48$	8.10262	1.16951
$49$	5.00854	0.715505
$50$	0.885213	0.125188
$51$	−12.7572	−1.78637
$52$	−7.38537	−1.02417
$53$	−3.24556	−0.445812	−0.222906	−	0.974840i	$-0.571554\pi$
$53$	−3.24556	−0.445812	−0.222906	+	0.974840i	$0.571554\pi$
$54$	−1.97022	−0.268113
$55$	−6.92630	−0.933942
$56$	−5.67708	−0.758632
$57$	−5.78500	−0.766241
$58$	0.0780552	0.0102491
$59$	1.97056	0.256546	0.128273	−	0.991739i	$-0.459057\pi$
$59$	1.97056	0.256546	0.128273	+	0.991739i	$0.459057\pi$
$60$	−8.61275	−1.11190
$61$	2.39757	0.306978	0.153489	−	0.988150i	$-0.450949\pi$
$61$	2.39757	0.306978	0.153489	+	0.988150i	$0.450949\pi$
$62$	−4.31425	−0.547910
$63$	−16.1423	−2.03373
$64$	−3.90937	−0.488672
$65$	6.97240	0.864820
$66$	4.80100	0.590962
$67$	−4.50274	−0.550097	−0.275048	−	0.961430i	$-0.588694\pi$
$67$	−4.50274	−0.550097	−0.275048	+	0.961430i	$0.588694\pi$
$68$	8.37001	1.01501
$69$	−9.82857	−1.18322
$70$	2.55035	0.304825
$71$	−13.4130	−1.59184	−0.795918	−	0.605404i	$-0.793011\pi$
$71$	−13.4130	−1.59184	−0.795918	+	0.605404i	$0.793011\pi$
$72$	7.63132	0.899360
$73$	11.1047	1.29971	0.649853	−	0.760060i	$-0.274830\pi$
$73$	11.1047	1.29971	0.649853	+	0.760060i	$0.274830\pi$
$74$	−3.58482	−0.416727
$75$	−5.70559	−0.658825
$76$	3.79554	0.435378
$77$	14.0024	1.59572
$78$	−4.83295	−0.547224
$79$	0.572829	0.0644483	0.0322242	−	0.999481i	$-0.489741\pi$
$79$	0.572829	0.0644483	0.0322242	+	0.999481i	$0.489741\pi$
$80$	5.01887	0.561126
$81$	−1.27569	−0.141744
$82$	−2.29968	−0.253957
$83$	1.00000	0.109764
$83$	1.00000	0.109764
$84$	17.4118	1.89978
$85$	−7.90197	−0.857089
$86$	1.58220	0.170613
$87$	−0.503100	−0.0539380
$88$	−6.61969	−0.705661
$89$	−4.48566	−0.475479	−0.237739	−	0.971329i	$-0.576406\pi$
$89$	−4.48566	−0.475479	−0.237739	+	0.971329i	$0.576406\pi$
$90$	−3.42826	−0.361371
$91$	−14.0956	−1.47762
$92$	6.44853	0.672306
$93$	27.8073	2.88348
$94$	−5.17796	−0.534066
$95$	−3.58330	−0.367639
$96$	−12.5461	−1.28048
$97$	14.9833	1.52132	0.760662	−	0.649148i	$-0.224874\pi$
$97$	14.9833	1.52132	0.760662	+	0.649148i	$0.224874\pi$
$98$	−2.15041	−0.217224
$99$	−18.8225	−1.89173
$100$	3.74344	0.374344
$101$	−9.38428	−0.933771	−0.466886	−	0.884318i	$-0.654624\pi$
$101$	−9.38428	−0.933771	−0.466886	+	0.884318i	$0.654624\pi$
$102$	5.47729	0.542333
$103$	8.01355	0.789599	0.394799	−	0.918767i	$-0.370814\pi$
$103$	8.01355	0.789599	0.394799	+	0.918767i	$0.370814\pi$
$104$	6.66375	0.653434
$105$	−16.4381	−1.60420
$106$	1.39348	0.135347
$107$	−16.7545	−1.61972	−0.809859	−	0.586624i	$-0.800457\pi$
$107$	−16.7545	−1.61972	−0.809859	+	0.586624i	$0.800457\pi$
$108$	−8.33179	−0.801727
$109$	−6.59469	−0.631657	−0.315828	−	0.948816i	$-0.602282\pi$
$109$	−6.59469	−0.631657	−0.315828	+	0.948816i	$0.602282\pi$
$110$	2.97380	0.283541
$111$	23.1058	2.19310
$112$	−10.1463	−0.958733
$113$	0.0465998	0.00438374	0.00219187	−	0.999998i	$-0.499302\pi$
$113$	0.0465998	0.00438374	0.00219187	+	0.999998i	$0.499302\pi$
$114$	2.48378	0.232628
$115$	−6.08794	−0.567704
$116$	0.330085	0.0306476
$117$	18.9477	1.75172
$118$	−0.846060	−0.0778861
$119$	15.9748	1.46441
$120$	7.77120	0.709410
$121$	5.32730	0.484300
$122$	−1.02940	−0.0931972
$123$	14.8225	1.33650
$124$	−18.2444	−1.63839
$125$	−12.1048	−1.08268
$126$	6.93067	0.617433
$127$	3.92137	0.347965	0.173983	−	0.984749i	$-0.444336\pi$
$127$	3.92137	0.347965	0.173983	+	0.984749i	$0.444336\pi$
$128$	10.7457	0.949795
$129$	−10.1980	−0.897881
$130$	−2.99359	−0.262556
$131$	4.12336	0.360259	0.180130	−	0.983643i	$-0.442348\pi$
$131$	4.12336	0.360259	0.180130	+	0.983643i	$0.442348\pi$
$132$	20.3028	1.76713
$133$	7.24410	0.628143
$134$	1.93325	0.167007
$135$	7.86589	0.676988
$136$	−7.55217	−0.647593
$137$	−8.27752	−0.707196	−0.353598	−	0.935397i	$-0.615042\pi$
$137$	−8.27752	−0.707196	−0.353598	+	0.935397i	$0.615042\pi$
$138$	4.21989	0.359221
$139$	−14.8831	−1.26236	−0.631182	−	0.775635i	$-0.717430\pi$
$139$	−14.8831	−1.26236	−0.631182	+	0.775635i	$0.717430\pi$
$140$	10.7851	0.911506
$141$	33.3743	2.81062
$142$	5.75888	0.483275
$143$	−16.4360	−1.37444
$144$	13.6390	1.13658
$145$	−0.311627	−0.0258792
$146$	−4.76779	−0.394585
$147$	13.8604	1.14318
$148$	−15.1597	−1.24612
$149$	−10.2267	−0.837807	−0.418904	−	0.908031i	$-0.637585\pi$
$149$	−10.2267	−0.837807	−0.418904	+	0.908031i	$0.637585\pi$
$150$	2.44969	0.200016
$151$	−15.3926	−1.25263	−0.626315	−	0.779570i	$-0.715437\pi$
$151$	−15.3926	−1.25263	−0.626315	+	0.779570i	$0.715437\pi$
$152$	−3.42468	−0.277778
$153$	−21.4739	−1.73606
$154$	−6.01192	−0.484454
$155$	17.2242	1.38348
$156$	−20.4379	−1.63634
$157$	3.93240	0.313840	0.156920	−	0.987611i	$-0.449844\pi$
$157$	3.93240	0.313840	0.156920	+	0.987611i	$0.449844\pi$
$158$	−0.245944	−0.0195662
$159$	−8.98159	−0.712287
$160$	−7.77120	−0.614367
$161$	12.3075	0.969971
$162$	0.547717	0.0430327
$163$	14.2104	1.11305	0.556524	−	0.830832i	$-0.312135\pi$
$163$	14.2104	1.11305	0.556524	+	0.830832i	$0.312135\pi$
$164$	−9.72503	−0.759397
$165$	−19.1675	−1.49219
$166$	−0.429349	−0.0333240
$167$	−7.56693	−0.585546	−0.292773	−	0.956182i	$-0.594578\pi$
$167$	−7.56693	−0.585546	−0.292773	+	0.956182i	$0.594578\pi$
$168$	−15.7105	−1.21209
$169$	3.54537	0.272720
$170$	3.39271	0.260209
$171$	−9.73775	−0.744664
$172$	6.69090	0.510176
$173$	15.4381	1.17374	0.586870	−	0.809681i	$-0.300360\pi$
$173$	15.4381	1.17374	0.586870	+	0.809681i	$0.300360\pi$
$174$	0.216006	0.0163754
$175$	7.14467	0.540086
$176$	−11.8309	−0.891790
$177$	5.45323	0.409890
$178$	1.92591	0.144353
$179$	10.3698	0.775078	0.387539	−	0.921853i	$-0.373325\pi$
$179$	10.3698	0.775078	0.387539	+	0.921853i	$0.373325\pi$
$180$	−14.4977	−1.08059
$181$	−6.61431	−0.491638	−0.245819	−	0.969316i	$-0.579057\pi$
$181$	−6.61431	−0.491638	−0.245819	+	0.969316i	$0.579057\pi$
$182$	6.05193	0.448599
$183$	6.63492	0.490468
$184$	−5.81844	−0.428941
$185$	14.3120	1.05224
$186$	−11.9390	−0.875412
$187$	18.6273	1.36216
$188$	−21.8969	−1.59699
$189$	−15.9019	−1.15669
$190$	1.53849	0.111614
$191$	−10.3797	−0.751048	−0.375524	−	0.926813i	$-0.622537\pi$
$191$	−10.3797	−0.751048	−0.375524	+	0.926813i	$0.622537\pi$
$192$	−10.8186	−0.780765
$193$	−6.43728	−0.463365	−0.231683	−	0.972791i	$-0.574423\pi$
$193$	−6.43728	−0.463365	−0.231683	+	0.972791i	$0.574423\pi$
$194$	−6.43307	−0.461868
$195$	19.2950	1.38175
$196$	−9.09380	−0.649557
$197$	18.2710	1.30176	0.650878	−	0.759182i	$-0.274401\pi$
$197$	18.2710	1.30176	0.650878	+	0.759182i	$0.274401\pi$
$198$	8.08141	0.574321
$199$	2.30098	0.163112	0.0815559	−	0.996669i	$-0.474011\pi$
$199$	2.30098	0.163112	0.0815559	+	0.996669i	$0.474011\pi$
$200$	−3.37767	−0.238837
$201$	−12.4606	−0.878906
$202$	4.02913	0.283489
$203$	0.629994	0.0442169
$204$	23.1627	1.62172
$205$	9.18123	0.641245
$206$	−3.44061	−0.239719
$207$	−16.5442	−1.14990
$208$	11.9097	0.825787
$209$	8.44688	0.584283
$210$	7.05770	0.487028
$211$	5.42742	0.373639	0.186819	−	0.982394i	$-0.440182\pi$
$211$	5.42742	0.373639	0.186819	+	0.982394i	$0.440182\pi$
$212$	5.89283	0.404721
$213$	−37.1186	−2.54332
$214$	7.19353	0.491740
$215$	−6.31676	−0.430799
$216$	7.51769	0.511514
$217$	−34.8209	−2.36379
$218$	2.83142	0.191768
$219$	30.7306	2.07658
$220$	12.5758	0.847860
$221$	−18.7512	−1.26134
$222$	−9.92044	−0.665816
$223$	−11.3935	−0.762963	−0.381481	−	0.924376i	$-0.624586\pi$
$223$	−11.3935	−0.762963	−0.381481	+	0.924376i	$0.624586\pi$
$224$	15.7105	1.04970
$225$	−9.60409	−0.640273
$226$	−0.0200076	−0.00133089
$227$	0.821267	0.0545094	0.0272547	−	0.999629i	$-0.491323\pi$
$227$	0.821267	0.0545094	0.0272547	+	0.999629i	$0.491323\pi$
$228$	10.5036	0.695617
$229$	9.51560	0.628808	0.314404	−	0.949289i	$-0.398195\pi$
$229$	9.51560	0.628808	0.314404	+	0.949289i	$0.398195\pi$
$230$	2.61385	0.172352
$231$	38.7495	2.54953
$232$	−0.297832	−0.0195536
$233$	−15.4620	−1.01295	−0.506475	−	0.862255i	$-0.669052\pi$
$233$	−15.4620	−1.01295	−0.506475	+	0.862255i	$0.669052\pi$
$234$	−8.13520	−0.531815
$235$	20.6725	1.34852
$236$	−3.57787	−0.232900
$237$	1.58522	0.102971
$238$	−6.85879	−0.444589
$239$	−2.95569	−0.191188	−0.0955939	−	0.995420i	$-0.530475\pi$
$239$	−2.95569	−0.191188	−0.0955939	+	0.995420i	$0.530475\pi$
$240$	13.8890	0.896528
$241$	−7.75836	−0.499760	−0.249880	−	0.968277i	$-0.580391\pi$
$241$	−7.75836	−0.499760	−0.249880	+	0.968277i	$0.580391\pi$
$242$	−2.28727	−0.147031
$243$	−17.2968	−1.10959
$244$	−4.35318	−0.278684
$245$	8.58529	0.548494
$246$	−6.36401	−0.405755
$247$	−8.50311	−0.541040
$248$	16.4617	1.04532
$249$	2.76735	0.175374
$250$	5.19717	0.328698
$251$	28.9235	1.82563	0.912817	−	0.408368i	$-0.133902\pi$
$251$	28.9235	1.82563	0.912817	+	0.408368i	$0.133902\pi$
$252$	29.3088	1.84628
$253$	14.3510	0.902243
$254$	−1.68364	−0.105641
$255$	−21.8675	−1.36940
$256$	3.20509	0.200318
$257$	12.1661	0.758900	0.379450	−	0.925212i	$-0.376113\pi$
$257$	12.1661	0.758900	0.379450	+	0.925212i	$0.376113\pi$
$258$	4.37849	0.272593
$259$	−28.9335	−1.79784
$260$	−12.6595	−0.785109
$261$	−0.846858	−0.0524192
$262$	−1.77036	−0.109373
$263$	14.7570	0.909956	0.454978	−	0.890503i	$-0.349647\pi$
$263$	14.7570	0.909956	0.454978	+	0.890503i	$0.349647\pi$
$264$	−18.3190	−1.12745
$265$	−5.56332	−0.341752
$266$	−3.11025	−0.190702
$267$	−12.4134	−0.759687
$268$	8.17543	0.499394
$269$	−19.2591	−1.17425	−0.587124	−	0.809497i	$-0.699740\pi$
$269$	−19.2591	−1.17425	−0.587124	+	0.809497i	$0.699740\pi$
$270$	−3.37721	−0.205531
$271$	12.9576	0.787115	0.393558	−	0.919300i	$-0.371244\pi$
$271$	12.9576	0.787115	0.393558	+	0.919300i	$0.371244\pi$
$272$	−13.4975	−0.818406
$273$	−39.0074	−2.36084
$274$	3.55395	0.214702
$275$	8.33094	0.502375
$276$	17.8453	1.07416
$277$	9.76730	0.586860	0.293430	−	0.955981i	$-0.405203\pi$
$277$	9.76730	0.586860	0.293430	+	0.955981i	$0.405203\pi$
$278$	6.39003	0.383248
$279$	46.8073	2.80228
$280$	−9.73127	−0.581554
$281$	18.5973	1.10942	0.554711	−	0.832043i	$-0.312829\pi$
$281$	18.5973	1.10942	0.554711	+	0.832043i	$0.312829\pi$
$282$	−14.3292	−0.853293
$283$	14.8576	0.883194	0.441597	−	0.897214i	$-0.354412\pi$
$283$	14.8576	0.883194	0.441597	+	0.897214i	$0.354412\pi$
$284$	24.3535	1.44512
$285$	−9.91624	−0.587387
$286$	7.05677	0.417276
$287$	−18.5610	−1.09562
$288$	−21.1185	−1.24442
$289$	4.25119	0.250070
$290$	0.133797	0.00785682
$291$	41.4640	2.43066
$292$	−20.1624	−1.17991
$293$	7.02137	0.410193	0.205096	−	0.978742i	$-0.434249\pi$
$293$	7.02137	0.410193	0.205096	+	0.978742i	$0.434249\pi$
$294$	−5.95094	−0.347066
$295$	3.37780	0.196663
$296$	13.6784	0.795043
$297$	−18.5422	−1.07593
$298$	4.39084	0.254355
$299$	−14.4466	−0.835467
$300$	10.3594	0.598101
$301$	12.7701	0.736058
$302$	6.60878	0.380293
$303$	−25.9696	−1.49191
$304$	−6.12070	−0.351046
$305$	4.10976	0.235324
$306$	9.21980	0.527061
$307$	−29.5116	−1.68432	−0.842159	−	0.539229i	$-0.818716\pi$
$307$	−29.5116	−1.68432	−0.842159	+	0.539229i	$0.818716\pi$
$308$	−25.4236	−1.44864
$309$	22.1763	1.26156
$310$	−7.39518	−0.420018
$311$	3.36393	0.190751	0.0953754	−	0.995441i	$-0.469595\pi$
$311$	3.36393	0.190751	0.0953754	+	0.995441i	$0.469595\pi$
$312$	18.4409	1.04401
$313$	−15.1858	−0.858349	−0.429175	−	0.903222i	$-0.641196\pi$
$313$	−15.1858	−0.858349	−0.429175	+	0.903222i	$0.641196\pi$
$314$	−1.68837	−0.0952804
$315$	−27.6700	−1.55903
$316$	−1.04006	−0.0585081
$317$	−4.52517	−0.254159	−0.127080	−	0.991893i	$-0.540560\pi$
$317$	−4.52517	−0.254159	−0.127080	+	0.991893i	$0.540560\pi$
$318$	3.85624	0.216247
$319$	0.734595	0.0411294
$320$	−6.70118	−0.374607
$321$	−46.3655	−2.58787
$322$	−5.28424	−0.294479
$323$	9.63676	0.536204
$324$	2.31622	0.128679
$325$	−8.38639	−0.465193
$326$	−6.10124	−0.337916
$327$	−18.2498	−1.00922
$328$	8.77479	0.484507
$329$	−41.7920	−2.30407
$330$	8.22954	0.453021
$331$	7.18123	0.394716	0.197358	−	0.980331i	$-0.436764\pi$
$331$	7.18123	0.394716	0.197358	+	0.980331i	$0.436764\pi$
$332$	−1.81566	−0.0996472
$333$	38.8934	2.13134
$334$	3.24885	0.177769
$335$	−7.71828	−0.421695
$336$	−28.0783	−1.53180
$337$	18.1166	0.986875	0.493438	−	0.869781i	$-0.335740\pi$
$337$	18.1166	0.986875	0.493438	+	0.869781i	$0.335740\pi$
$338$	−1.52220	−0.0827968
$339$	0.128958	0.00700403
$340$	14.3473	0.778091
$341$	−40.6024	−2.19874
$342$	4.18090	0.226077
$343$	6.90108	0.372623
$344$	−6.03713	−0.325500
$345$	−16.8475	−0.907036
$346$	−6.62835	−0.356342
$347$	−1.40458	−0.0754018	−0.0377009	−	0.999289i	$-0.512003\pi$
$347$	−1.40458	−0.0754018	−0.0377009	+	0.999289i	$0.512003\pi$
$348$	0.913459	0.0489665
$349$	20.8308	1.11505	0.557524	−	0.830161i	$-0.311751\pi$
$349$	20.8308	1.11505	0.557524	+	0.830161i	$0.311751\pi$
$350$	−3.06756	−0.163968
$351$	18.6656	0.996297
$352$	18.3190	0.976405
$353$	−19.1109	−1.01717	−0.508586	−	0.861011i	$-0.669832\pi$
$353$	−19.1109	−1.01717	−0.508586	+	0.861011i	$0.669832\pi$
$354$	−2.34134	−0.124441
$355$	−22.9917	−1.22027
$356$	8.14443	0.431654
$357$	44.2080	2.33973
$358$	−4.45228	−0.235310
$359$	11.5137	0.607671	0.303836	−	0.952724i	$-0.401733\pi$
$359$	11.5137	0.607671	0.303836	+	0.952724i	$0.401733\pi$
$360$	13.0811	0.689433
$361$	−14.6300	−0.770001
$362$	2.83985	0.149259
$363$	14.7425	0.773780
$364$	25.5928	1.34143
$365$	19.0349	0.996333
$366$	−2.84870	−0.148904
$367$	−25.2997	−1.32063	−0.660316	−	0.750988i	$-0.729577\pi$
$367$	−25.2997	−1.32063	−0.660316	+	0.750988i	$0.729577\pi$
$368$	−10.3989	−0.542081
$369$	24.9503	1.29886
$370$	−6.14485	−0.319455
$371$	11.2470	0.583913
$372$	−50.4885	−2.61771
$373$	31.7473	1.64381	0.821905	−	0.569624i	$-0.192911\pi$
$373$	31.7473	1.64381	0.821905	+	0.569624i	$0.192911\pi$
$374$	−7.99760	−0.413546
$375$	−33.4981	−1.72984
$376$	19.7573	1.01891
$377$	−0.739485	−0.0380854
$378$	6.82747	0.351167
$379$	−27.5067	−1.41293	−0.706463	−	0.707750i	$-0.749710\pi$
$379$	−27.5067	−1.41293	−0.706463	+	0.707750i	$0.749710\pi$
$380$	6.50605	0.333754
$381$	10.8518	0.555954
$382$	4.45651	0.228015
$383$	19.7891	1.01118	0.505588	−	0.862775i	$-0.331276\pi$
$383$	19.7891	1.01118	0.505588	+	0.862775i	$0.331276\pi$
$384$	29.7371	1.51751
$385$	24.0019	1.22325
$386$	2.76384	0.140676
$387$	−17.1660	−0.872598
$388$	−27.2046	−1.38110
$389$	−29.8225	−1.51206	−0.756030	−	0.654537i	$-0.772864\pi$
$389$	−29.8225	−1.51206	−0.756030	+	0.654537i	$0.772864\pi$
$390$	−8.28431	−0.419493
$391$	16.3726	0.827999
$392$	8.20524	0.414427
$393$	11.4108	0.575597
$394$	−7.84465	−0.395208
$395$	0.981905	0.0494050
$396$	34.1752	1.71737
$397$	18.3473	0.920826	0.460413	−	0.887705i	$-0.347701\pi$
$397$	18.3473	0.920826	0.460413	+	0.887705i	$0.347701\pi$
$398$	−0.987922	−0.0495201
$399$	20.0469	1.00360
$400$	−6.03669	−0.301834
$401$	9.67281	0.483037	0.241519	−	0.970396i	$-0.422355\pi$
$401$	9.67281	0.483037	0.241519	+	0.970396i	$0.422355\pi$
$402$	5.34996	0.266832
$403$	40.8726	2.03601
$404$	17.0387	0.847705
$405$	−2.18670	−0.108658
$406$	−0.270487	−0.0134241
$407$	−33.7376	−1.67231
$408$	−20.8995	−1.03468
$409$	−2.22730	−0.110133	−0.0550664	−	0.998483i	$-0.517537\pi$
$409$	−2.22730	−0.110133	−0.0550664	+	0.998483i	$0.517537\pi$
$410$	−3.94195	−0.194679
$411$	−22.9068	−1.12991
$412$	−14.5499	−0.716821
$413$	−6.82866	−0.336016
$414$	7.10324	0.349105
$415$	1.71413	0.0841434
$416$	−18.4409	−0.904140
$417$	−41.1866	−2.01692
$418$	−3.62666	−0.177386
$419$	36.7487	1.79529	0.897646	−	0.440718i	$-0.145276\pi$
$419$	36.7487	1.79529	0.897646	+	0.440718i	$0.145276\pi$
$420$	29.8461	1.45634
$421$	27.2441	1.32780	0.663899	−	0.747822i	$-0.268900\pi$
$421$	27.2441	1.32780	0.663899	+	0.747822i	$0.268900\pi$
$422$	−2.33026	−0.113435
$423$	56.1781	2.73148
$424$	−5.31704	−0.258218
$425$	9.50449	0.461035
$426$	15.9368	0.772142
$427$	−8.30840	−0.402072
$428$	30.4205	1.47043
$429$	−45.4840	−2.19599
$430$	2.71209	0.130789
$431$	−24.0696	−1.15939	−0.579696	−	0.814833i	$-0.696829\pi$
$431$	−24.0696	−1.15939	−0.579696	+	0.814833i	$0.696829\pi$
$432$	13.4359	0.646434
$433$	7.84524	0.377018	0.188509	−	0.982071i	$-0.439635\pi$
$433$	7.84524	0.377018	0.188509	+	0.982071i	$0.439635\pi$
$434$	14.9503	0.717638
$435$	−0.862380	−0.0413480
$436$	11.9737	0.573437
$437$	7.42448	0.355161
$438$	−13.1941	−0.630441
$439$	−16.4035	−0.782895	−0.391447	−	0.920201i	$-0.628025\pi$
$439$	−16.4035	−0.782895	−0.391447	+	0.920201i	$0.628025\pi$
$440$	−11.3470	−0.540947
$441$	23.3308	1.11099
$442$	8.05083	0.382939
$443$	−19.0663	−0.905867	−0.452934	−	0.891544i	$-0.649623\pi$
$443$	−19.0663	−0.905867	−0.452934	+	0.891544i	$0.649623\pi$
$444$	−41.9522	−1.99096
$445$	−7.68901	−0.364494
$446$	4.89178	0.231632
$447$	−28.3009	−1.33859
$448$	13.5473	0.640049
$449$	−31.5603	−1.48942	−0.744712	−	0.667386i	$-0.767413\pi$
$449$	−31.5603	−1.48942	−0.744712	+	0.667386i	$0.767413\pi$
$450$	4.12351	0.194384
$451$	−21.6428	−1.01912
$452$	−0.0846094	−0.00397969
$453$	−42.5966	−2.00136
$454$	−0.352610	−0.0165488
$455$	−24.1617	−1.13272
$456$	−9.47727	−0.443814
$457$	−3.70070	−0.173111	−0.0865557	−	0.996247i	$-0.527586\pi$
$457$	−3.70070	−0.173111	−0.0865557	+	0.996247i	$0.527586\pi$
$458$	−4.08551	−0.190904
$459$	−21.1542	−0.987391
$460$	11.0536	0.515378
$461$	−3.91341	−0.182265	−0.0911327	−	0.995839i	$-0.529049\pi$
$461$	−3.91341	−0.182265	−0.0911327	+	0.995839i	$0.529049\pi$
$462$	−16.6371	−0.774026
$463$	15.5380	0.722113	0.361057	−	0.932544i	$-0.382416\pi$
$463$	15.5380	0.722113	0.361057	+	0.932544i	$0.382416\pi$
$464$	−0.532295	−0.0247112
$465$	47.6653	2.21042
$466$	6.63860	0.307527
$467$	22.7797	1.05412	0.527059	−	0.849829i	$-0.323295\pi$
$467$	22.7797	1.05412	0.527059	+	0.849829i	$0.323295\pi$
$468$	−34.4026	−1.59026
$469$	15.6035	0.720502
$470$	−8.87570	−0.409406
$471$	10.8823	0.501431
$472$	3.22828	0.148593
$473$	14.8904	0.684663
$474$	−0.680612	−0.0312616
$475$	4.30999	0.197756
$476$	−29.0049	−1.32944
$477$	−15.1185	−0.692229
$478$	1.26902	0.0580438
$479$	26.6747	1.21880	0.609399	−	0.792864i	$-0.291411\pi$
$479$	26.6747	1.21880	0.609399	+	0.792864i	$0.291411\pi$
$480$	−21.5056	−0.981592
$481$	33.9621	1.54854
$482$	3.33105	0.151725
$483$	34.0593	1.54975
$484$	−9.67256	−0.439662
$485$	25.6834	1.16622
$486$	7.42638	0.336868
$487$	10.6357	0.481952	0.240976	−	0.970531i	$-0.422533\pi$
$487$	10.6357	0.481952	0.240976	+	0.970531i	$0.422533\pi$
$488$	3.92783	0.177804
$489$	39.3252	1.77835
$490$	−3.68609	−0.166520
$491$	−5.75406	−0.259677	−0.129838	−	0.991535i	$-0.541446\pi$
$491$	−5.75406	−0.259677	−0.129838	+	0.991535i	$0.541446\pi$
$492$	−26.9125	−1.21331
$493$	0.838075	0.0377450
$494$	3.65080	0.164257
$495$	−32.2642	−1.45017
$496$	29.4209	1.32104
$497$	46.4807	2.08494
$498$	−1.18816	−0.0532427
$499$	−10.4173	−0.466340	−0.233170	−	0.972436i	$-0.574910\pi$
$499$	−10.4173	−0.466340	−0.233170	+	0.972436i	$0.574910\pi$
$500$	21.9781	0.982892
$501$	−20.9403	−0.935544
$502$	−12.4183	−0.554255
$503$	−12.8170	−0.571480	−0.285740	−	0.958307i	$-0.592239\pi$
$503$	−12.8170	−0.571480	−0.285740	+	0.958307i	$0.592239\pi$
$504$	−26.4451	−1.17796
$505$	−16.0859	−0.715813
$506$	−6.16161	−0.273917
$507$	9.81126	0.435733
$508$	−7.11987	−0.315893
$509$	−15.8462	−0.702372	−0.351186	−	0.936306i	$-0.614222\pi$
$509$	−15.8462	−0.702372	−0.351186	+	0.936306i	$0.614222\pi$
$510$	9.38880	0.415743
$511$	−38.4815	−1.70232
$512$	−22.8675	−1.01061
$513$	−9.59276	−0.423530
$514$	−5.22350	−0.230399
$515$	13.7363	0.605293
$516$	18.5160	0.815123
$517$	−48.7310	−2.14319
$518$	12.4226	0.545817
$519$	42.7227	1.87532
$520$	11.4225	0.500911
$521$	9.77072	0.428063	0.214032	−	0.976827i	$-0.431340\pi$
$521$	9.77072	0.428063	0.214032	+	0.976827i	$0.431340\pi$
$522$	0.363598	0.0159142
$523$	29.8312	1.30443	0.652214	−	0.758035i	$-0.273841\pi$
$523$	29.8312	1.30443	0.652214	+	0.758035i	$0.273841\pi$
$524$	−7.48661	−0.327054
$525$	19.7718	0.862911
$526$	−6.33591	−0.276259
$527$	−46.3219	−2.01781
$528$	−32.7403	−1.42484
$529$	−10.3860	−0.451565
$530$	2.38861	0.103754
$531$	9.17931	0.398348
$532$	−13.1528	−0.570247
$533$	21.7869	0.943694
$534$	5.32967	0.230638
$535$	−28.7194	−1.24165
$536$	−7.37661	−0.318621
$537$	28.6969	1.23836
$538$	8.26888	0.356497
$539$	−20.2380	−0.871714
$540$	−14.2818	−0.614590
$541$	−26.1476	−1.12417	−0.562087	−	0.827078i	$-0.690001\pi$
$541$	−26.1476	−1.12417	−0.562087	+	0.827078i	$0.690001\pi$
$542$	−5.56332	−0.238965
$543$	−18.3041	−0.785504
$544$	20.8995	0.896058
$545$	−11.3042	−0.484217
$546$	16.7478	0.716739
$547$	−20.1235	−0.860417	−0.430208	−	0.902730i	$-0.641560\pi$
$547$	−20.1235	−0.860417	−0.430208	+	0.902730i	$0.641560\pi$
$548$	15.0292	0.642014
$549$	11.1684	0.476656
$550$	−3.57688	−0.152519
$551$	0.380041	0.0161903
$552$	−16.1017	−0.685332
$553$	−1.98505	−0.0844127
$554$	−4.19358	−0.178168
$555$	39.6063	1.68119
$556$	27.0226	1.14601
$557$	32.5686	1.37997	0.689987	−	0.723822i	$-0.257616\pi$
$557$	32.5686	1.37997	0.689987	+	0.723822i	$0.257616\pi$
$558$	−20.0967	−0.850760
$559$	−14.9895	−0.633990
$560$	−17.3921	−0.734948
$561$	51.5481	2.17636
$562$	−7.98473	−0.336816
$563$	25.3791	1.06960	0.534800	−	0.844979i	$-0.320387\pi$
$563$	25.3791	1.06960	0.534800	+	0.844979i	$0.320387\pi$
$564$	−60.5963	−2.55156
$565$	0.0798782	0.00336050
$566$	−6.37911	−0.268134
$567$	4.42070	0.185652
$568$	−21.9739	−0.922006
$569$	−25.2508	−1.05857	−0.529284	−	0.848445i	$-0.677539\pi$
$569$	−25.2508	−1.05857	−0.529284	+	0.848445i	$0.677539\pi$
$570$	4.25753	0.178328
$571$	−36.1808	−1.51412	−0.757059	−	0.653346i	$-0.773365\pi$
$571$	−36.1808	−1.51412	−0.757059	+	0.653346i	$0.773365\pi$
$572$	29.8421	1.24776
$573$	−28.7242	−1.19997
$574$	7.96916	0.332626
$575$	7.32257	0.305372
$576$	−18.2107	−0.758779
$577$	14.0204	0.583675	0.291838	−	0.956468i	$-0.405733\pi$
$577$	14.0204	0.583675	0.291838	+	0.956468i	$0.405733\pi$
$578$	−1.82524	−0.0759202
$579$	−17.8142	−0.740332
$580$	0.565808	0.0234939
$581$	−3.46533	−0.143766
$582$	−17.8025	−0.737939
$583$	13.1144	0.543141
$584$	18.1923	0.752802
$585$	32.4789	1.34284
$586$	−3.01462	−0.124533
$587$	−22.3868	−0.924004	−0.462002	−	0.886879i	$-0.652869\pi$
$587$	−22.3868	−0.924004	−0.462002	+	0.886879i	$0.652869\pi$
$588$	−25.1657	−1.03782
$589$	−21.0055	−0.865518
$590$	−1.45026	−0.0597062
$591$	50.5623	2.07985
$592$	24.4466	1.00475
$593$	−35.7868	−1.46959	−0.734794	−	0.678290i	$-0.762721\pi$
$593$	−35.7868	−1.46959	−0.734794	+	0.678290i	$0.762721\pi$
$594$	7.96108	0.326647
$595$	27.3830	1.12259
$596$	18.5683	0.760586
$597$	6.36760	0.260609
$598$	6.20262	0.253644
$599$	−0.929895	−0.0379945	−0.0189972	−	0.999820i	$-0.506047\pi$
$599$	−0.929895	−0.0379945	−0.0189972	+	0.999820i	$0.506047\pi$
$600$	−9.34719	−0.381597
$601$	−19.0236	−0.775989	−0.387994	−	0.921662i	$-0.626832\pi$
$601$	−19.0236	−0.775989	−0.387994	+	0.921662i	$0.626832\pi$
$602$	−5.48284	−0.223464
$603$	−20.9747	−0.854156
$604$	27.9477	1.13717
$605$	9.13169	0.371256
$606$	11.1500	0.452938
$607$	29.2691	1.18800	0.593999	−	0.804466i	$-0.297548\pi$
$607$	29.2691	1.18800	0.593999	+	0.804466i	$0.297548\pi$
$608$	9.47727	0.384354
$609$	1.74341	0.0706466
$610$	−1.76452	−0.0714434
$611$	49.0553	1.98457
$612$	38.9893	1.57605
$613$	14.4807	0.584869	0.292434	−	0.956286i	$-0.405535\pi$
$613$	14.4807	0.584869	0.292434	+	0.956286i	$0.405535\pi$
$614$	12.6708	0.511352
$615$	25.4076	1.02454
$616$	22.9394	0.924256
$617$	23.8454	0.959978	0.479989	−	0.877274i	$-0.340641\pi$
$617$	23.8454	0.959978	0.479989	+	0.877274i	$0.340641\pi$
$618$	−9.52137	−0.383006
$619$	−24.2507	−0.974720	−0.487360	−	0.873201i	$-0.662040\pi$
$619$	−24.2507	−0.974720	−0.487360	+	0.873201i	$0.662040\pi$
$620$	−31.2732	−1.25596
$621$	−16.2979	−0.654010
$622$	−1.44430	−0.0579112
$623$	15.5443	0.622770
$624$	32.9582	1.31938
$625$	−10.4404	−0.417616
$626$	6.51999	0.260591
$627$	23.3755	0.933526
$628$	−7.13990	−0.284913
$629$	−38.4900	−1.53470
$630$	11.8801	0.473313
$631$	40.4397	1.60988	0.804940	−	0.593356i	$-0.202197\pi$
$631$	40.4397	1.60988	0.804940	+	0.593356i	$0.202197\pi$
$632$	0.938438	0.0373291
$633$	15.0195	0.596973
$634$	1.94288	0.0771616
$635$	6.72174	0.266744
$636$	16.3075	0.646635
$637$	20.3727	0.807197
$638$	−0.315398	−0.0124867
$639$	−62.4808	−2.47170
$640$	18.4195	0.728096
$641$	−25.3771	−1.00234	−0.501169	−	0.865350i	$-0.667096\pi$
$641$	−25.3771	−1.00234	−0.501169	+	0.865350i	$0.667096\pi$
$642$	19.9070	0.785667
$643$	22.2493	0.877427	0.438714	−	0.898627i	$-0.355434\pi$
$643$	22.2493	0.877427	0.438714	+	0.898627i	$0.355434\pi$
$644$	−22.3463	−0.880568
$645$	−17.4807	−0.688300
$646$	−4.13753	−0.162789
$647$	40.0408	1.57417	0.787083	−	0.616847i	$-0.211590\pi$
$647$	40.0408	1.57417	0.787083	+	0.616847i	$0.211590\pi$
$648$	−2.08990	−0.0820991
$649$	−7.96247	−0.312554
$650$	3.60069	0.141231
$651$	−96.3614	−3.77670
$652$	−25.8013	−1.01046
$653$	−6.54312	−0.256052	−0.128026	−	0.991771i	$-0.540864\pi$
$653$	−6.54312	−0.256052	−0.128026	+	0.991771i	$0.540864\pi$
$654$	7.83553	0.306394
$655$	7.06798	0.276169
$656$	15.6826	0.612303
$657$	51.7281	2.01810
$658$	17.9434	0.699505
$659$	44.4746	1.73248	0.866242	−	0.499625i	$-0.166529\pi$
$659$	44.4746	1.73248	0.866242	+	0.499625i	$0.166529\pi$
$660$	34.8016	1.35465
$661$	−13.0247	−0.506604	−0.253302	−	0.967387i	$-0.581517\pi$
$661$	−13.0247	−0.506604	−0.253302	+	0.967387i	$0.581517\pi$
$662$	−3.08325	−0.119834
$663$	−51.8912	−2.01529
$664$	1.63825	0.0635764
$665$	12.4173	0.481524
$666$	−16.6988	−0.647067
$667$	0.645680	0.0250008
$668$	13.7390	0.531576
$669$	−31.5297	−1.21901
$670$	3.31384	0.128025
$671$	−9.68789	−0.373997
$672$	43.4763	1.67714
$673$	−44.0963	−1.69979	−0.849894	−	0.526953i	$-0.823334\pi$
$673$	−44.0963	−1.69979	−0.849894	+	0.526953i	$0.823334\pi$
$674$	−7.77836	−0.299611
$675$	−9.46109	−0.364157
$676$	−6.43718	−0.247584
$677$	−35.4506	−1.36248	−0.681239	−	0.732061i	$-0.738559\pi$
$677$	−35.4506	−1.36248	−0.681239	+	0.732061i	$0.738559\pi$
$678$	−0.0553680	−0.00212639
$679$	−51.9222	−1.99259
$680$	−12.9454	−0.496434
$681$	2.27273	0.0870912
$682$	17.4326	0.667529
$683$	−6.82287	−0.261070	−0.130535	−	0.991444i	$-0.541669\pi$
$683$	−6.82287	−0.261070	−0.130535	+	0.991444i	$0.541669\pi$
$684$	17.6804	0.676028
$685$	−14.1888	−0.542124
$686$	−2.96297	−0.113127
$687$	26.3330	1.00467
$688$	−10.7898	−0.411356
$689$	−13.2016	−0.502942
$690$	7.23344	0.275372
$691$	−20.0352	−0.762175	−0.381087	−	0.924539i	$-0.624450\pi$
$691$	−20.0352	−0.762175	−0.381087	+	0.924539i	$0.624450\pi$
$692$	−28.0304	−1.06556
$693$	65.2261	2.47774
$694$	0.603055	0.0228917
$695$	−25.5115	−0.967707
$696$	−0.824204	−0.0312414
$697$	−24.6915	−0.935259
$698$	−8.94370	−0.338524
$699$	−42.7888	−1.61842
$700$	−12.9723	−0.490306
$701$	0.586341	0.0221458	0.0110729	−	0.999939i	$-0.496475\pi$
$701$	0.586341	0.0221458	0.0110729	+	0.999939i	$0.496475\pi$
$702$	−8.01406	−0.302471
$703$	−17.4540	−0.658291
$704$	15.7966	0.595358
$705$	57.2079	2.15457
$706$	8.20527	0.308809
$707$	32.5197	1.22303
$708$	−9.90122	−0.372110
$709$	−9.77413	−0.367075	−0.183538	−	0.983013i	$-0.558755\pi$
$709$	−9.77413	−0.367075	−0.183538	+	0.983013i	$0.558755\pi$
$710$	9.87148	0.370470
$711$	2.66836	0.100071
$712$	−7.34863	−0.275402
$713$	−35.6879	−1.33652
$714$	−18.9806	−0.710333
$715$	−28.1734	−1.05363
$716$	−18.8281	−0.703638
$717$	−8.17942	−0.305466
$718$	−4.94341	−0.184486
$719$	12.0344	0.448806	0.224403	−	0.974496i	$-0.427957\pi$
$719$	12.0344	0.448806	0.224403	+	0.974496i	$0.427957\pi$
$720$	23.3790	0.871282
$721$	−27.7696	−1.03420
$722$	6.28139	0.233769
$723$	−21.4701	−0.798481
$724$	12.0093	0.446324
$725$	0.374825	0.0139206
$726$	−6.32967	−0.234916
$727$	−28.8698	−1.07072	−0.535362	−	0.844623i	$-0.679825\pi$
$727$	−28.8698	−1.07072	−0.535362	+	0.844623i	$0.679825\pi$
$728$	−23.0921	−0.855850
$729$	−44.0393	−1.63108
$730$	−8.17262	−0.302482
$731$	16.9880	0.628323
$732$	−12.0468	−0.445261
$733$	7.90612	0.292019	0.146010	−	0.989283i	$-0.453357\pi$
$733$	7.90612	0.292019	0.146010	+	0.989283i	$0.453357\pi$
$734$	10.8624	0.400938
$735$	23.7585	0.876345
$736$	16.1017	0.593515
$737$	18.1942	0.670193
$738$	−10.7124	−0.394329
$739$	37.2389	1.36986	0.684928	−	0.728611i	$-0.259834\pi$
$739$	37.2389	1.36986	0.684928	+	0.728611i	$0.259834\pi$
$740$	−25.9857	−0.955254
$741$	−23.5310	−0.864435
$742$	−4.82887	−0.177273
$743$	−0.145574	−0.00534058	−0.00267029	−	0.999996i	$-0.500850\pi$
$743$	−0.145574	−0.00534058	−0.00267029	+	0.999996i	$0.500850\pi$
$744$	45.5552	1.67014
$745$	−17.5300	−0.642248
$746$	−13.6307	−0.499054
$747$	4.65821	0.170435
$748$	−33.8207	−1.23661
$749$	58.0599	2.12146
$750$	14.3824	0.525171
$751$	−13.3455	−0.486983	−0.243491	−	0.969903i	$-0.578293\pi$
$751$	−13.3455	−0.486983	−0.243491	+	0.969903i	$0.578293\pi$
$752$	35.3110	1.28766
$753$	80.0414	2.91687
$754$	0.317497	0.0115626
$755$	−26.3849	−0.960244
$756$	28.8724	1.05008
$757$	7.15825	0.260171	0.130086	−	0.991503i	$-0.458475\pi$
$757$	7.15825	0.260171	0.130086	+	0.991503i	$0.458475\pi$
$758$	11.8100	0.428958
$759$	39.7143	1.44154
$760$	−5.87035	−0.212940
$761$	22.2486	0.806512	0.403256	−	0.915087i	$-0.367878\pi$
$761$	22.2486	0.806512	0.403256	+	0.915087i	$0.367878\pi$
$762$	−4.65921	−0.168785
$763$	22.8528	0.827327
$764$	18.8460	0.681823
$765$	−36.8091	−1.33084
$766$	−8.49643	−0.306989
$767$	8.01546	0.289422
$768$	8.86959	0.320054
$769$	−16.7580	−0.604310	−0.302155	−	0.953259i	$-0.597706\pi$
$769$	−16.7580	−0.604310	−0.302155	+	0.953259i	$0.597706\pi$
$770$	−10.3052	−0.371374
$771$	33.6678	1.21252
$772$	11.6879	0.420657
$773$	−25.6083	−0.921068	−0.460534	−	0.887642i	$-0.652342\pi$
$773$	−25.6083	−0.921068	−0.460534	+	0.887642i	$0.652342\pi$
$774$	7.37021	0.264917
$775$	−20.7172	−0.744184
$776$	24.5464	0.881165
$777$	−80.0692	−2.87246
$778$	12.8043	0.459055
$779$	−11.1969	−0.401169
$780$	−35.0332	−1.25439
$781$	54.1982	1.93936
$782$	−7.02957	−0.251377
$783$	−0.834248	−0.0298136
$784$	14.6647	0.523739
$785$	6.74065	0.240584
$786$	−4.89920	−0.174749
$787$	−22.6847	−0.808621	−0.404310	−	0.914622i	$-0.632488\pi$
$787$	−22.6847	−0.808621	−0.404310	+	0.914622i	$0.632488\pi$
$788$	−33.1739	−1.18177
$789$	40.8378	1.45386
$790$	−0.421580	−0.0149991
$791$	−0.161484	−0.00574171
$792$	−30.8359	−1.09571
$793$	9.75237	0.346317
$794$	−7.87741	−0.279559
$795$	−15.3956	−0.546027
$796$	−4.17779	−0.148078
$797$	−16.8431	−0.596615	−0.298307	−	0.954470i	$-0.596422\pi$
$797$	−16.8431	−0.596615	−0.298307	+	0.954470i	$0.596422\pi$
$798$	−8.60714	−0.304689
$799$	−55.5955	−1.96683
$800$	9.34719	0.330473
$801$	−20.8952	−0.738294
$802$	−4.15301	−0.146648
$803$	−44.8708	−1.58346
$804$	22.6243	0.797896
$805$	21.0968	0.743563
$806$	−17.5486	−0.618124
$807$	−53.2967	−1.87613
$808$	−15.3738	−0.540849
$809$	43.5367	1.53067	0.765335	−	0.643632i	$-0.222573\pi$
$809$	43.5367	1.53067	0.765335	+	0.643632i	$0.222573\pi$
$810$	0.938859	0.0329881
$811$	17.4509	0.612786	0.306393	−	0.951905i	$-0.400878\pi$
$811$	17.4509	0.612786	0.306393	+	0.951905i	$0.400878\pi$
$812$	−1.14385	−0.0401414
$813$	35.8581	1.25760
$814$	14.4852	0.507706
$815$	24.3585	0.853243
$816$	−37.3523	−1.30759
$817$	7.70353	0.269512
$818$	0.956289	0.0334358
$819$	−65.6603	−2.29436
$820$	−16.6700	−0.582141
$821$	13.6110	0.475027	0.237514	−	0.971384i	$-0.423668\pi$
$821$	13.6110	0.475027	0.237514	+	0.971384i	$0.423668\pi$
$822$	9.83500	0.343035
$823$	−10.0913	−0.351762	−0.175881	−	0.984411i	$-0.556277\pi$
$823$	−10.0913	−0.351762	−0.175881	+	0.984411i	$0.556277\pi$
$824$	13.1282	0.457343
$825$	23.0546	0.802659
$826$	2.93188	0.102013
$827$	14.2921	0.496985	0.248492	−	0.968634i	$-0.420065\pi$
$827$	14.2921	0.496985	0.248492	+	0.968634i	$0.420065\pi$
$828$	30.0386	1.04391
$829$	10.7952	0.374934	0.187467	−	0.982271i	$-0.439972\pi$
$829$	10.7952	0.374934	0.187467	+	0.982271i	$0.439972\pi$
$830$	−0.735961	−0.0255456
$831$	27.0295	0.937643
$832$	−15.9018	−0.551294
$833$	−23.0889	−0.799982
$834$	17.6834	0.612327
$835$	−12.9707	−0.448870
$836$	−15.3367	−0.530430
$837$	46.1103	1.59381
$838$	−15.7780	−0.545043
$839$	42.9293	1.48209	0.741043	−	0.671458i	$-0.234332\pi$
$839$	42.9293	1.48209	0.741043	+	0.671458i	$0.234332\pi$
$840$	−26.9298	−0.929166
$841$	−28.9669	−0.998860
$842$	−11.6973	−0.403114
$843$	51.4652	1.77256
$844$	−9.85434	−0.339200
$845$	6.07722	0.209063
$846$	−24.1200	−0.829264
$847$	−18.4609	−0.634323
$848$	−9.50280	−0.326327
$849$	41.1162	1.41110
$850$	−4.08074	−0.139968
$851$	−29.6540	−1.01653
$852$	67.3947	2.30890
$853$	−35.7231	−1.22314	−0.611568	−	0.791192i	$-0.709461\pi$
$853$	−35.7231	−1.22314	−0.611568	+	0.791192i	$0.709461\pi$
$854$	3.56720	0.122067
$855$	−16.6918	−0.570847
$856$	−27.4481	−0.938155
$857$	27.6229	0.943579	0.471789	−	0.881711i	$-0.343608\pi$
$857$	27.6229	0.943579	0.471789	+	0.881711i	$0.343608\pi$
$858$	19.5285	0.666693
$859$	48.1035	1.64127	0.820636	−	0.571451i	$-0.193619\pi$
$859$	48.1035	1.64127	0.820636	+	0.571451i	$0.193619\pi$
$860$	11.4691	0.391092
$861$	−51.3648	−1.75051
$862$	10.3343	0.351986
$863$	8.84641	0.301135	0.150568	−	0.988600i	$-0.451890\pi$
$863$	8.84641	0.301135	0.150568	+	0.988600i	$0.451890\pi$
$864$	−20.8041	−0.707768
$865$	26.4630	0.899769
$866$	−3.36835	−0.114461
$867$	11.7645	0.399544
$868$	63.2228	2.14592
$869$	−2.31463	−0.0785186
$870$	0.370262	0.0125531
$871$	−18.3153	−0.620591
$872$	−10.8037	−0.365861
$873$	69.7955	2.36222
$874$	−3.18769	−0.107825
$875$	41.9471	1.41807
$876$	−55.7962	−1.88518
$877$	57.4804	1.94097	0.970487	−	0.241153i	$-0.0775255\pi$
$877$	57.4804	1.94097	0.970487	+	0.241153i	$0.0775255\pi$
$878$	7.04281	0.237683
$879$	19.4306	0.655377
$880$	−20.2798	−0.683631
$881$	5.79024	0.195078	0.0975391	−	0.995232i	$-0.468903\pi$
$881$	5.79024	0.195078	0.0975391	+	0.995232i	$0.468903\pi$
$882$	−10.0171	−0.337293
$883$	−5.84211	−0.196603	−0.0983013	−	0.995157i	$-0.531341\pi$
$883$	−5.84211	−0.196603	−0.0983013	+	0.995157i	$0.531341\pi$
$884$	34.0458	1.14509
$885$	9.34756	0.314215
$886$	8.18610	0.275017
$887$	18.9401	0.635947	0.317973	−	0.948100i	$-0.396998\pi$
$887$	18.9401	0.635947	0.317973	+	0.948100i	$0.396998\pi$
$888$	37.8530	1.27026
$889$	−13.5889	−0.455755
$890$	3.30127	0.110659
$891$	5.15469	0.172689
$892$	20.6867	0.692640
$893$	−25.2108	−0.843649
$894$	12.1510	0.406390
$895$	17.7752	0.594161
$896$	−37.2374	−1.24402
$897$	−39.9787	−1.33485
$898$	13.5504	0.452183
$899$	−1.82678	−0.0609264
$900$	17.4378	0.581259
$901$	14.9617	0.498447
$902$	9.29233	0.309401
$903$	35.3394	1.17602
$904$	0.0763422	0.00253910
$905$	−11.3378	−0.376881
$906$	18.2888	0.607605
$907$	25.4518	0.845112	0.422556	−	0.906337i	$-0.361133\pi$
$907$	25.4518	0.845112	0.422556	+	0.906337i	$0.361133\pi$
$908$	−1.49114	−0.0494852
$909$	−43.7140	−1.44990
$910$	10.3738	0.343888
$911$	8.07364	0.267492	0.133746	−	0.991016i	$-0.457299\pi$
$911$	8.07364	0.267492	0.133746	+	0.991016i	$0.457299\pi$
$912$	−16.9381	−0.560877
$913$	−4.04071	−0.133728
$914$	1.58889	0.0525559
$915$	11.3731	0.375984
$916$	−17.2771	−0.570851
$917$	−14.2888	−0.471858
$918$	9.08252	0.299768
$919$	16.1502	0.532746	0.266373	−	0.963870i	$-0.414175\pi$
$919$	16.1502	0.532746	0.266373	+	0.963870i	$0.414175\pi$
$920$	−9.97357	−0.328819
$921$	−81.6690	−2.69108
$922$	1.68022	0.0553350
$923$	−54.5589	−1.79583
$924$	−70.3559	−2.31454
$925$	−17.2145	−0.566008
$926$	−6.67124	−0.219231
$927$	37.3288	1.22604
$928$	0.824204	0.0270558
$929$	0.472594	0.0155053	0.00775265	−	0.999970i	$-0.497532\pi$
$929$	0.472594	0.0155053	0.00775265	+	0.999970i	$0.497532\pi$
$930$	−20.4650	−0.671075
$931$	−10.4701	−0.343143
$932$	28.0737	0.919586
$933$	9.30916	0.304768
$934$	−9.78044	−0.320026
$935$	31.9295	1.04421
$936$	31.0411	1.01461
$937$	−21.7412	−0.710256	−0.355128	−	0.934818i	$-0.615563\pi$
$937$	−21.7412	−0.710256	−0.355128	+	0.934818i	$0.615563\pi$
$938$	−6.69934	−0.218741
$939$	−42.0243	−1.37141
$940$	−37.5341	−1.22423
$941$	9.01349	0.293831	0.146916	−	0.989149i	$-0.453065\pi$
$941$	9.01349	0.293831	0.146916	+	0.989149i	$0.453065\pi$
$942$	−4.67232	−0.152232
$943$	−19.0232	−0.619480
$944$	5.76969	0.187787
$945$	−27.2579	−0.886701
$946$	−6.39320	−0.207861
$947$	−51.1752	−1.66297	−0.831485	−	0.555547i	$-0.812509\pi$
$947$	−51.1752	−1.66297	−0.831485	+	0.555547i	$0.812509\pi$
$948$	−2.87822	−0.0934801
$949$	45.1695	1.46626
$950$	−1.85049	−0.0600379
$951$	−12.5227	−0.406077
$952$	26.1708	0.848200
$953$	34.8923	1.13027	0.565136	−	0.824998i	$-0.308824\pi$
$953$	34.8923	1.13027	0.565136	+	0.824998i	$0.308824\pi$
$954$	6.49112	0.210158
$955$	−17.7921	−0.575740
$956$	5.36653	0.173566
$957$	2.03288	0.0657137
$958$	−11.4528	−0.370022
$959$	28.6844	0.926267
$960$	−18.5445	−0.598521
$961$	69.9692	2.25707
$962$	−14.5816	−0.470130
$963$	−78.0460	−2.51500
$964$	14.0865	0.453697
$965$	−11.0343	−0.355208
$966$	−14.6233	−0.470498
$967$	13.8871	0.446578	0.223289	−	0.974752i	$-0.428321\pi$
$967$	13.8871	0.446578	0.223289	+	0.974752i	$0.428321\pi$
$968$	8.72745	0.280511
$969$	26.6683	0.856708
$970$	−11.0271	−0.354060
$971$	−5.19291	−0.166648	−0.0833241	−	0.996522i	$-0.526554\pi$
$971$	−5.19291	−0.166648	−0.0833241	+	0.996522i	$0.526554\pi$
$972$	31.4052	1.00732
$973$	51.5748	1.65341
$974$	−4.56645	−0.146319
$975$	−23.2081	−0.743253
$976$	7.01995	0.224703
$977$	−39.6331	−1.26798	−0.633988	−	0.773343i	$-0.718583\pi$
$977$	−39.6331	−1.26798	−0.633988	+	0.773343i	$0.718583\pi$
$978$	−16.8842	−0.539899
$979$	18.1252	0.579285
$980$	−15.5880	−0.497939
$981$	−30.7195	−0.980797
$982$	2.47050	0.0788368
$983$	39.8963	1.27249	0.636246	−	0.771486i	$-0.280486\pi$
$983$	39.8963	1.27249	0.636246	+	0.771486i	$0.280486\pi$
$984$	24.2829	0.774111
$985$	31.3189	0.997904
$986$	−0.359827	−0.0114592
$987$	−115.653	−3.68128
$988$	15.4387	0.491172
$989$	13.0881	0.416177
$990$	13.8526	0.440264
$991$	−25.4030	−0.806952	−0.403476	−	0.914990i	$-0.632198\pi$
$991$	−25.4030	−0.806952	−0.403476	+	0.914990i	$0.632198\pi$
$992$	−45.5552	−1.44638
$993$	19.8730	0.630649
$994$	−19.9564	−0.632980
$995$	3.94417	0.125039
$996$	−5.02456	−0.159209
$997$	−11.5507	−0.365815	−0.182907	−	0.983130i	$-0.558551\pi$
$997$	−11.5507	−0.365815	−0.182907	+	0.983130i	$0.558551\pi$
$998$	4.47264	0.141579
$999$	38.3143	1.21221

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	83.2.a.b.1.3	✓	6
3.2	odd	2		747.2.a.j.1.4		6
4.3	odd	2		1328.2.a.l.1.1		6
5.4	even	2		2075.2.a.g.1.4		6
7.6	odd	2		4067.2.a.d.1.3		6
8.3	odd	2		5312.2.a.bo.1.6		6
8.5	even	2		5312.2.a.bn.1.1		6
83.82	odd	2		6889.2.a.e.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
83.2.a.b.1.3	✓	6	1.1	even	1	trivial
747.2.a.j.1.4		6	3.2	odd	2
1328.2.a.l.1.1		6	4.3	odd	2
2075.2.a.g.1.4		6	5.4	even	2
4067.2.a.d.1.3		6	7.6	odd	2
5312.2.a.bn.1.1		6	8.5	even	2
5312.2.a.bo.1.6		6	8.3	odd	2
6889.2.a.e.1.4		6	83.82	odd	2

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:	\( N \)	\(=\)	\( 83 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	83.a (trivial)

\(f(q)\)	\(=\)	\(q-0.429349 q^{2} +2.76735 q^{3} -1.81566 q^{4} +1.71413 q^{5} -1.18816 q^{6} -3.46533 q^{7} +1.63825 q^{8} +4.65821 q^{9} +O(q^{10})\)	\(q-0.429349 q^{2} +2.76735 q^{3} -1.81566 q^{4} +1.71413 q^{5} -1.18816 q^{6} -3.46533 q^{7} +1.63825 q^{8} +4.65821 q^{9} -0.735961 q^{10} -4.04071 q^{11} -5.02456 q^{12} +4.06760 q^{13} +1.48784 q^{14} +4.74360 q^{15} +2.92794 q^{16} -4.60990 q^{17} -2.00000 q^{18} -2.09045 q^{19} -3.11228 q^{20} -9.58978 q^{21} +1.73487 q^{22} -3.55162 q^{23} +4.53361 q^{24} -2.06175 q^{25} -1.74642 q^{26} +4.58885 q^{27} +6.29187 q^{28} -0.181799 q^{29} -2.03666 q^{30} +10.0483 q^{31} -4.53361 q^{32} -11.1820 q^{33} +1.97926 q^{34} -5.94004 q^{35} -8.45773 q^{36} +8.34942 q^{37} +0.897532 q^{38} +11.2565 q^{39} +2.80818 q^{40} +5.35620 q^{41} +4.11737 q^{42} -3.68511 q^{43} +7.33654 q^{44} +7.98479 q^{45} +1.52489 q^{46} +12.0600 q^{47} +8.10262 q^{48} +5.00854 q^{49} +0.885213 q^{50} -12.7572 q^{51} -7.38537 q^{52} -3.24556 q^{53} -1.97022 q^{54} -6.92630 q^{55} -5.67708 q^{56} -5.78500 q^{57} +0.0780552 q^{58} +1.97056 q^{59} -8.61275 q^{60} +2.39757 q^{61} -4.31425 q^{62} -16.1423 q^{63} -3.90937 q^{64} +6.97240 q^{65} +4.80100 q^{66} -4.50274 q^{67} +8.37001 q^{68} -9.82857 q^{69} +2.55035 q^{70} -13.4130 q^{71} +7.63132 q^{72} +11.1047 q^{73} -3.58482 q^{74} -5.70559 q^{75} +3.79554 q^{76} +14.0024 q^{77} -4.83295 q^{78} +0.572829 q^{79} +5.01887 q^{80} -1.27569 q^{81} -2.29968 q^{82} +1.00000 q^{83} +17.4118 q^{84} -7.90197 q^{85} +1.58220 q^{86} -0.503100 q^{87} -6.61969 q^{88} -4.48566 q^{89} -3.42826 q^{90} -14.0956 q^{91} +6.44853 q^{92} +27.8073 q^{93} -5.17796 q^{94} -3.58330 q^{95} -12.5461 q^{96} +14.9833 q^{97} -2.15041 q^{98} -18.8225 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} + q^{3} + 7 q^{4} + 2 q^{5} - 7 q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 6 * q + q^2 + q^3 + 7 * q^4 + 2 * q^5 - 7 * q^6 + 3 * q^7 + 3 * q^8 + 3 * q^9	\( 6 q + q^{2} + q^{3} + 7 q^{4} + 2 q^{5} - 7 q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{9} - 6 q^{10} - 3 q^{11} - 9 q^{12} + 14 q^{13} - 15 q^{14} - 6 q^{15} + q^{16} - 5 q^{17} - 12 q^{18} - 4 q^{19} - 20 q^{20} - 2 q^{21} - q^{22} - 5 q^{23} - 17 q^{24} + 14 q^{25} - 2 q^{26} + 10 q^{27} + 9 q^{28} - q^{29} + 18 q^{30} + 3 q^{31} + 17 q^{32} + 2 q^{33} + 15 q^{34} - 10 q^{35} - 8 q^{36} + 39 q^{37} - 6 q^{38} - 8 q^{39} - 18 q^{40} - q^{41} + 17 q^{42} - 8 q^{43} + 27 q^{44} + 10 q^{45} - 12 q^{46} - 12 q^{47} + 7 q^{48} + 11 q^{49} + 35 q^{50} - 24 q^{51} + 36 q^{52} + 14 q^{53} + 19 q^{54} - 24 q^{55} - 23 q^{56} - 10 q^{57} + 25 q^{58} - 17 q^{59} - 5 q^{61} + 5 q^{62} - 11 q^{63} + 9 q^{64} - 8 q^{65} - 39 q^{66} + 16 q^{67} - 15 q^{68} + 8 q^{69} - 10 q^{70} - 26 q^{71} + 10 q^{72} - 6 q^{73} + 23 q^{74} - 45 q^{75} - 28 q^{76} + 6 q^{77} - 18 q^{78} - 12 q^{79} - 60 q^{80} - 34 q^{81} + 10 q^{82} + 6 q^{83} + 41 q^{84} + 18 q^{85} + 16 q^{86} - 3 q^{87} - 17 q^{88} - 22 q^{89} - 4 q^{90} - 2 q^{91} + 2 q^{92} + 34 q^{93} - 8 q^{94} - 4 q^{95} - 19 q^{96} + 6 q^{97} - 30 q^{98} - 18 q^{99}+O(q^{100}) \) 6 * q + q^2 + q^3 + 7 * q^4 + 2 * q^5 - 7 * q^6 + 3 * q^7 + 3 * q^8 + 3 * q^9 - 6 * q^10 - 3 * q^11 - 9 * q^12 + 14 * q^13 - 15 * q^14 - 6 * q^15 + q^16 - 5 * q^17 - 12 * q^18 - 4 * q^19 - 20 * q^20 - 2 * q^21 - q^22 - 5 * q^23 - 17 * q^24 + 14 * q^25 - 2 * q^26 + 10 * q^27 + 9 * q^28 - q^29 + 18 * q^30 + 3 * q^31 + 17 * q^32 + 2 * q^33 + 15 * q^34 - 10 * q^35 - 8 * q^36 + 39 * q^37 - 6 * q^38 - 8 * q^39 - 18 * q^40 - q^41 + 17 * q^42 - 8 * q^43 + 27 * q^44 + 10 * q^45 - 12 * q^46 - 12 * q^47 + 7 * q^48 + 11 * q^49 + 35 * q^50 - 24 * q^51 + 36 * q^52 + 14 * q^53 + 19 * q^54 - 24 * q^55 - 23 * q^56 - 10 * q^57 + 25 * q^58 - 17 * q^59 - 5 * q^61 + 5 * q^62 - 11 * q^63 + 9 * q^64 - 8 * q^65 - 39 * q^66 + 16 * q^67 - 15 * q^68 + 8 * q^69 - 10 * q^70 - 26 * q^71 + 10 * q^72 - 6 * q^73 + 23 * q^74 - 45 * q^75 - 28 * q^76 + 6 * q^77 - 18 * q^78 - 12 * q^79 - 60 * q^80 - 34 * q^81 + 10 * q^82 + 6 * q^83 + 41 * q^84 + 18 * q^85 + 16 * q^86 - 3 * q^87 - 17 * q^88 - 22 * q^89 - 4 * q^90 - 2 * q^91 + 2 * q^92 + 34 * q^93 - 8 * q^94 - 4 * q^95 - 19 * q^96 + 6 * q^97 - 30 * q^98 - 18 * q^99

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