LMFDB - Embedded newform 1334.2.a.k.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1334,2,Mod(1,1334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1334, 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("1334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1334 = 2 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1334.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:	$10.6520436296$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 5x^{9} - 8x^{8} + 60x^{7} + 13x^{6} - 241x^{5} + 6x^{4} + 346x^{3} + 16x^{2} - 64x - 12 $ x^10 - 5x^9 - 8x^8 + 60x^7 + 13x^6 - 241x^5 + 6x^4 + 346x^3 + 16x^2 - 64*x - 12
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$3.37864$ of defining polynomial
Character	$\chi$	$=$	1334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.37864 q^{3} +1.00000 q^{4} +0.983407 q^{5} -2.37864 q^{6} -3.11298 q^{7} +1.00000 q^{8} +2.65792 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.37864 q^{3} +1.00000 q^{4} +0.983407 q^{5} -2.37864 q^{6} -3.11298 q^{7} +1.00000 q^{8} +2.65792 q^{9} +0.983407 q^{10} +3.12835 q^{11} -2.37864 q^{12} -6.14646 q^{13} -3.11298 q^{14} -2.33917 q^{15} +1.00000 q^{16} +2.39472 q^{17} +2.65792 q^{18} +8.17601 q^{19} +0.983407 q^{20} +7.40466 q^{21} +3.12835 q^{22} +1.00000 q^{23} -2.37864 q^{24} -4.03291 q^{25} -6.14646 q^{26} +0.813682 q^{27} -3.11298 q^{28} +1.00000 q^{29} -2.33917 q^{30} +3.95395 q^{31} +1.00000 q^{32} -7.44120 q^{33} +2.39472 q^{34} -3.06133 q^{35} +2.65792 q^{36} -7.68657 q^{37} +8.17601 q^{38} +14.6202 q^{39} +0.983407 q^{40} +10.7996 q^{41} +7.40466 q^{42} +4.97550 q^{43} +3.12835 q^{44} +2.61382 q^{45} +1.00000 q^{46} +4.33800 q^{47} -2.37864 q^{48} +2.69065 q^{49} -4.03291 q^{50} -5.69618 q^{51} -6.14646 q^{52} +13.8445 q^{53} +0.813682 q^{54} +3.07644 q^{55} -3.11298 q^{56} -19.4478 q^{57} +1.00000 q^{58} -0.415747 q^{59} -2.33917 q^{60} +11.1106 q^{61} +3.95395 q^{62} -8.27406 q^{63} +1.00000 q^{64} -6.04447 q^{65} -7.44120 q^{66} -4.37578 q^{67} +2.39472 q^{68} -2.37864 q^{69} -3.06133 q^{70} +0.807253 q^{71} +2.65792 q^{72} -13.1142 q^{73} -7.68657 q^{74} +9.59284 q^{75} +8.17601 q^{76} -9.73848 q^{77} +14.6202 q^{78} +3.21669 q^{79} +0.983407 q^{80} -9.90922 q^{81} +10.7996 q^{82} +9.74943 q^{83} +7.40466 q^{84} +2.35499 q^{85} +4.97550 q^{86} -2.37864 q^{87} +3.12835 q^{88} +13.2910 q^{89} +2.61382 q^{90} +19.1338 q^{91} +1.00000 q^{92} -9.40501 q^{93} +4.33800 q^{94} +8.04035 q^{95} -2.37864 q^{96} -3.00992 q^{97} +2.69065 q^{98} +8.31489 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} + 5 q^{3} + 10 q^{4} - q^{5} + 5 q^{6} + 2 q^{7} + 10 q^{8} + 11 q^{9}+O(q^{10}) $ 10 * q + 10 * q^2 + 5 * q^3 + 10 * q^4 - q^5 + 5 * q^6 + 2 * q^7 + 10 * q^8 + 11 * q^9	\( 10 q + 10 q^{2} + 5 q^{3} + 10 q^{4} - q^{5} + 5 q^{6} + 2 q^{7} + 10 q^{8} + 11 q^{9} - q^{10} + q^{11} + 5 q^{12} + 9 q^{13} + 2 q^{14} + 5 q^{15} + 10 q^{16} + 11 q^{18} + 20 q^{19} - q^{20} + 14 q^{21} + q^{22} + 10 q^{23} + 5 q^{24} + 23 q^{25} + 9 q^{26} + 23 q^{27} + 2 q^{28} + 10 q^{29} + 5 q^{30} + 21 q^{31} + 10 q^{32} + q^{33} + 2 q^{35} + 11 q^{36} - 8 q^{37} + 20 q^{38} + 23 q^{39} - q^{40} - 4 q^{41} + 14 q^{42} - 3 q^{43} + q^{44} - 18 q^{45} + 10 q^{46} - q^{47} + 5 q^{48} + 18 q^{49} + 23 q^{50} - 6 q^{51} + 9 q^{52} - 13 q^{53} + 23 q^{54} + 13 q^{55} + 2 q^{56} - 22 q^{57} + 10 q^{58} + 14 q^{59} + 5 q^{60} + 12 q^{61} + 21 q^{62} - 26 q^{63} + 10 q^{64} - 25 q^{65} + q^{66} + 6 q^{67} + 5 q^{69} + 2 q^{70} + 8 q^{71} + 11 q^{72} + 16 q^{73} - 8 q^{74} + 8 q^{75} + 20 q^{76} - 16 q^{77} + 23 q^{78} + 7 q^{79} - q^{80} - 2 q^{81} - 4 q^{82} + 18 q^{83} + 14 q^{84} + 8 q^{85} - 3 q^{86} + 5 q^{87} + q^{88} + 2 q^{89} - 18 q^{90} + 8 q^{91} + 10 q^{92} - 41 q^{93} - q^{94} - 16 q^{95} + 5 q^{96} + 6 q^{97} + 18 q^{98} - 22 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 + 5 * q^3 + 10 * q^4 - q^5 + 5 * q^6 + 2 * q^7 + 10 * q^8 + 11 * q^9 - q^10 + q^11 + 5 * q^12 + 9 * q^13 + 2 * q^14 + 5 * q^15 + 10 * q^16 + 11 * q^18 + 20 * q^19 - q^20 + 14 * q^21 + q^22 + 10 * q^23 + 5 * q^24 + 23 * q^25 + 9 * q^26 + 23 * q^27 + 2 * q^28 + 10 * q^29 + 5 * q^30 + 21 * q^31 + 10 * q^32 + q^33 + 2 * q^35 + 11 * q^36 - 8 * q^37 + 20 * q^38 + 23 * q^39 - q^40 - 4 * q^41 + 14 * q^42 - 3 * q^43 + q^44 - 18 * q^45 + 10 * q^46 - q^47 + 5 * q^48 + 18 * q^49 + 23 * q^50 - 6 * q^51 + 9 * q^52 - 13 * q^53 + 23 * q^54 + 13 * q^55 + 2 * q^56 - 22 * q^57 + 10 * q^58 + 14 * q^59 + 5 * q^60 + 12 * q^61 + 21 * q^62 - 26 * q^63 + 10 * q^64 - 25 * q^65 + q^66 + 6 * q^67 + 5 * q^69 + 2 * q^70 + 8 * q^71 + 11 * q^72 + 16 * q^73 - 8 * q^74 + 8 * q^75 + 20 * q^76 - 16 * q^77 + 23 * q^78 + 7 * q^79 - q^80 - 2 * q^81 - 4 * q^82 + 18 * q^83 + 14 * q^84 + 8 * q^85 - 3 * q^86 + 5 * q^87 + q^88 + 2 * q^89 - 18 * q^90 + 8 * q^91 + 10 * q^92 - 41 * q^93 - q^94 - 16 * q^95 + 5 * q^96 + 6 * q^97 + 18 * q^98 - 22 * 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
$3$	−2.37864	−1.37331	−0.686654	−	0.726985i	$-0.740921\pi$
$3$	−2.37864	−1.37331	−0.686654	+	0.726985i	$0.740921\pi$
$4$	1.00000	0.500000
$5$	0.983407	0.439793	0.219897	−	0.975523i	$-0.429428\pi$
$5$	0.983407	0.439793	0.219897	+	0.975523i	$0.429428\pi$
$6$	−2.37864	−0.971075
$7$	−3.11298	−1.17660	−0.588298	−	0.808644i	$-0.700202\pi$
$7$	−3.11298	−1.17660	−0.588298	+	0.808644i	$0.700202\pi$
$8$	1.00000	0.353553
$9$	2.65792	0.885974
$10$	0.983407	0.310981
$11$	3.12835	0.943232	0.471616	−	0.881804i	$-0.343671\pi$
$11$	3.12835	0.943232	0.471616	+	0.881804i	$0.343671\pi$
$12$	−2.37864	−0.686654
$13$	−6.14646	−1.70472	−0.852360	−	0.522955i	$-0.824829\pi$
$13$	−6.14646	−1.70472	−0.852360	+	0.522955i	$0.824829\pi$
$14$	−3.11298	−0.831979
$15$	−2.33917	−0.603971
$16$	1.00000	0.250000
$17$	2.39472	0.580806	0.290403	−	0.956904i	$-0.406211\pi$
$17$	2.39472	0.580806	0.290403	+	0.956904i	$0.406211\pi$
$18$	2.65792	0.626478
$19$	8.17601	1.87571	0.937853	−	0.347034i	$-0.112811\pi$
$19$	8.17601	1.87571	0.937853	+	0.347034i	$0.112811\pi$
$20$	0.983407	0.219897
$21$	7.40466	1.61583
$22$	3.12835	0.666965
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−2.37864	−0.485538
$25$	−4.03291	−0.806582
$26$	−6.14646	−1.20542
$27$	0.813682	0.156593
$28$	−3.11298	−0.588298
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−2.33917	−0.427072
$31$	3.95395	0.710150	0.355075	−	0.934838i	$-0.384455\pi$
$31$	3.95395	0.710150	0.355075	+	0.934838i	$0.384455\pi$
$32$	1.00000	0.176777
$33$	−7.44120	−1.29535
$34$	2.39472	0.410692
$35$	−3.06133	−0.517459
$36$	2.65792	0.442987
$37$	−7.68657	−1.26366	−0.631832	−	0.775105i	$-0.717697\pi$
$37$	−7.68657	−1.26366	−0.631832	+	0.775105i	$0.717697\pi$
$38$	8.17601	1.32632
$39$	14.6202	2.34111
$40$	0.983407	0.155490
$41$	10.7996	1.68661	0.843306	−	0.537433i	$-0.180606\pi$
$41$	10.7996	1.68661	0.843306	+	0.537433i	$0.180606\pi$
$42$	7.40466	1.14256
$43$	4.97550	0.758757	0.379378	−	0.925242i	$-0.376138\pi$
$43$	4.97550	0.758757	0.379378	+	0.925242i	$0.376138\pi$
$44$	3.12835	0.471616
$45$	2.61382	0.389645
$46$	1.00000	0.147442
$47$	4.33800	0.632762	0.316381	−	0.948632i	$-0.397532\pi$
$47$	4.33800	0.632762	0.316381	+	0.948632i	$0.397532\pi$
$48$	−2.37864	−0.343327
$49$	2.69065	0.384379
$50$	−4.03291	−0.570340
$51$	−5.69618	−0.797625
$52$	−6.14646	−0.852360
$53$	13.8445	1.90169	0.950846	−	0.309663i	$-0.100216\pi$
$53$	13.8445	1.90169	0.950846	+	0.309663i	$0.100216\pi$
$54$	0.813682	0.110728
$55$	3.07644	0.414827
$56$	−3.11298	−0.415990
$57$	−19.4478	−2.57592
$58$	1.00000	0.131306
$59$	−0.415747	−0.0541257	−0.0270628	−	0.999634i	$-0.508615\pi$
$59$	−0.415747	−0.0541257	−0.0270628	+	0.999634i	$0.508615\pi$
$60$	−2.33917	−0.301986
$61$	11.1106	1.42257	0.711286	−	0.702903i	$-0.248113\pi$
$61$	11.1106	1.42257	0.711286	+	0.702903i	$0.248113\pi$
$62$	3.95395	0.502152
$63$	−8.27406	−1.04243
$64$	1.00000	0.125000
$65$	−6.04447	−0.749724
$66$	−7.44120	−0.915949
$67$	−4.37578	−0.534587	−0.267293	−	0.963615i	$-0.586129\pi$
$67$	−4.37578	−0.534587	−0.267293	+	0.963615i	$0.586129\pi$
$68$	2.39472	0.290403
$69$	−2.37864	−0.286354
$70$	−3.06133	−0.365899
$71$	0.807253	0.0958033	0.0479017	−	0.998852i	$-0.484747\pi$
$71$	0.807253	0.0958033	0.0479017	+	0.998852i	$0.484747\pi$
$72$	2.65792	0.313239
$73$	−13.1142	−1.53490	−0.767452	−	0.641107i	$-0.778475\pi$
$73$	−13.1142	−1.53490	−0.767452	+	0.641107i	$0.778475\pi$
$74$	−7.68657	−0.893546
$75$	9.59284	1.10769
$76$	8.17601	0.937853
$77$	−9.73848	−1.10980
$78$	14.6202	1.65541
$79$	3.21669	0.361906	0.180953	−	0.983492i	$-0.442082\pi$
$79$	3.21669	0.361906	0.180953	+	0.983492i	$0.442082\pi$
$80$	0.983407	0.109948
$81$	−9.90922	−1.10102
$82$	10.7996	1.19262
$83$	9.74943	1.07014	0.535069	−	0.844808i	$-0.320285\pi$
$83$	9.74943	1.07014	0.535069	+	0.844808i	$0.320285\pi$
$84$	7.40466	0.807914
$85$	2.35499	0.255434
$86$	4.97550	0.536522
$87$	−2.37864	−0.255017
$88$	3.12835	0.333483
$89$	13.2910	1.40884	0.704420	−	0.709784i	$-0.251207\pi$
$89$	13.2910	1.40884	0.704420	+	0.709784i	$0.251207\pi$
$90$	2.61382	0.275521
$91$	19.1338	2.00577
$92$	1.00000	0.104257
$93$	−9.40501	−0.975254
$94$	4.33800	0.447430
$95$	8.04035	0.824922
$96$	−2.37864	−0.242769
$97$	−3.00992	−0.305611	−0.152806	−	0.988256i	$-0.548831\pi$
$97$	−3.00992	−0.305611	−0.152806	+	0.988256i	$0.548831\pi$
$98$	2.69065	0.271797
$99$	8.31489	0.835678
$100$	−4.03291	−0.403291
$101$	−0.962893	−0.0958114	−0.0479057	−	0.998852i	$-0.515255\pi$
$101$	−0.962893	−0.0958114	−0.0479057	+	0.998852i	$0.515255\pi$
$102$	−5.69618	−0.564006
$103$	6.68681	0.658871	0.329436	−	0.944178i	$-0.393142\pi$
$103$	6.68681	0.658871	0.329436	+	0.944178i	$0.393142\pi$
$104$	−6.14646	−0.602710
$105$	7.28179	0.710630
$106$	13.8445	1.34470
$107$	12.2866	1.18779	0.593895	−	0.804543i	$-0.297590\pi$
$107$	12.2866	1.18779	0.593895	+	0.804543i	$0.297590\pi$
$108$	0.813682	0.0782966
$109$	−13.7038	−1.31259	−0.656295	−	0.754504i	$-0.727877\pi$
$109$	−13.7038	−1.31259	−0.656295	+	0.754504i	$0.727877\pi$
$110$	3.07644	0.293327
$111$	18.2836	1.73540
$112$	−3.11298	−0.294149
$113$	17.1459	1.61295	0.806476	−	0.591267i	$-0.201372\pi$
$113$	17.1459	1.61295	0.806476	+	0.591267i	$0.201372\pi$
$114$	−19.4478	−1.82145
$115$	0.983407	0.0917032
$116$	1.00000	0.0928477
$117$	−16.3368	−1.51034
$118$	−0.415747	−0.0382726
$119$	−7.45473	−0.683374
$120$	−2.33917	−0.213536
$121$	−1.21346	−0.110314
$122$	11.1106	1.00591
$123$	−25.6883	−2.31624
$124$	3.95395	0.355075
$125$	−8.88303	−0.794522
$126$	−8.27406	−0.737112
$127$	−2.67681	−0.237529	−0.118764	−	0.992922i	$-0.537893\pi$
$127$	−2.67681	−0.237529	−0.118764	+	0.992922i	$0.537893\pi$
$128$	1.00000	0.0883883
$129$	−11.8349	−1.04201
$130$	−6.04447	−0.530135
$131$	18.3171	1.60038	0.800188	−	0.599750i	$-0.204733\pi$
$131$	18.3171	1.60038	0.800188	+	0.599750i	$0.204733\pi$
$132$	−7.44120	−0.647674
$133$	−25.4518	−2.20695
$134$	−4.37578	−0.378010
$135$	0.800181	0.0688686
$136$	2.39472	0.205346
$137$	−3.51015	−0.299892	−0.149946	−	0.988694i	$-0.547910\pi$
$137$	−3.51015	−0.299892	−0.149946	+	0.988694i	$0.547910\pi$
$138$	−2.37864	−0.202483
$139$	−5.10163	−0.432714	−0.216357	−	0.976314i	$-0.569418\pi$
$139$	−5.10163	−0.432714	−0.216357	+	0.976314i	$0.569418\pi$
$140$	−3.06133	−0.258729
$141$	−10.3185	−0.868977
$142$	0.807253	0.0677432
$143$	−19.2282	−1.60795
$144$	2.65792	0.221493
$145$	0.983407	0.0816675
$146$	−13.1142	−1.08534
$147$	−6.40009	−0.527871
$148$	−7.68657	−0.631832
$149$	9.55292	0.782605	0.391303	−	0.920262i	$-0.372025\pi$
$149$	9.55292	0.782605	0.391303	+	0.920262i	$0.372025\pi$
$150$	9.59284	0.783252
$151$	−9.84887	−0.801489	−0.400745	−	0.916190i	$-0.631249\pi$
$151$	−9.84887	−0.801489	−0.400745	+	0.916190i	$0.631249\pi$
$152$	8.17601	0.663162
$153$	6.36498	0.514579
$154$	−9.73848	−0.784749
$155$	3.88834	0.312319
$156$	14.6202	1.17055
$157$	−18.7375	−1.49542	−0.747710	−	0.664026i	$-0.768846\pi$
$157$	−18.7375	−1.49542	−0.747710	+	0.664026i	$0.768846\pi$
$158$	3.21669	0.255906
$159$	−32.9311	−2.61161
$160$	0.983407	0.0777452
$161$	−3.11298	−0.245337
$162$	−9.90922	−0.778542
$163$	3.12416	0.244703	0.122352	−	0.992487i	$-0.460956\pi$
$163$	3.12416	0.244703	0.122352	+	0.992487i	$0.460956\pi$
$164$	10.7996	0.843306
$165$	−7.31773	−0.569685
$166$	9.74943	0.756702
$167$	10.9815	0.849776	0.424888	−	0.905246i	$-0.360313\pi$
$167$	10.9815	0.849776	0.424888	+	0.905246i	$0.360313\pi$
$168$	7.40466	0.571282
$169$	24.7789	1.90607
$170$	2.35499	0.180619
$171$	21.7312	1.66183
$172$	4.97550	0.379378
$173$	−3.98263	−0.302794	−0.151397	−	0.988473i	$-0.548377\pi$
$173$	−3.98263	−0.302794	−0.151397	+	0.988473i	$0.548377\pi$
$174$	−2.37864	−0.180324
$175$	12.5544	0.949022
$176$	3.12835	0.235808
$177$	0.988912	0.0743312
$178$	13.2910	0.996200
$179$	−20.9052	−1.56253	−0.781265	−	0.624199i	$-0.785425\pi$
$179$	−20.9052	−1.56253	−0.781265	+	0.624199i	$0.785425\pi$
$180$	2.61382	0.194823
$181$	−19.6091	−1.45753	−0.728766	−	0.684763i	$-0.759906\pi$
$181$	−19.6091	−1.45753	−0.728766	+	0.684763i	$0.759906\pi$
$182$	19.1338	1.41829
$183$	−26.4282	−1.95363
$184$	1.00000	0.0737210
$185$	−7.55903	−0.555751
$186$	−9.40501	−0.689609
$187$	7.49152	0.547834
$188$	4.33800	0.316381
$189$	−2.53298	−0.184247
$190$	8.04035	0.583308
$191$	−13.9575	−1.00993	−0.504966	−	0.863139i	$-0.668495\pi$
$191$	−13.9575	−1.00993	−0.504966	+	0.863139i	$0.668495\pi$
$192$	−2.37864	−0.171663
$193$	7.15327	0.514904	0.257452	−	0.966291i	$-0.417117\pi$
$193$	7.15327	0.514904	0.257452	+	0.966291i	$0.417117\pi$
$194$	−3.00992	−0.216100
$195$	14.3776	1.02960
$196$	2.69065	0.192190
$197$	−22.6127	−1.61109	−0.805544	−	0.592536i	$-0.798127\pi$
$197$	−22.6127	−1.61109	−0.805544	+	0.592536i	$0.798127\pi$
$198$	8.31489	0.590914
$199$	13.7438	0.974270	0.487135	−	0.873327i	$-0.338042\pi$
$199$	13.7438	0.974270	0.487135	+	0.873327i	$0.338042\pi$
$200$	−4.03291	−0.285170
$201$	10.4084	0.734152
$202$	−0.962893	−0.0677489
$203$	−3.11298	−0.218488
$204$	−5.69618	−0.398812
$205$	10.6204	0.741761
$206$	6.68681	0.465892
$207$	2.65792	0.184738
$208$	−6.14646	−0.426180
$209$	25.5774	1.76922
$210$	7.28179	0.502491
$211$	−22.4787	−1.54750	−0.773750	−	0.633491i	$-0.781621\pi$
$211$	−22.4787	−1.54750	−0.773750	+	0.633491i	$0.781621\pi$
$212$	13.8445	0.950846
$213$	−1.92016	−0.131567
$214$	12.2866	0.839894
$215$	4.89294	0.333696
$216$	0.813682	0.0553640
$217$	−12.3086	−0.835560
$218$	−13.7038	−0.928142
$219$	31.1940	2.10789
$220$	3.07644	0.207413
$221$	−14.7191	−0.990111
$222$	18.2836	1.22711
$223$	25.8466	1.73082	0.865408	−	0.501067i	$-0.167059\pi$
$223$	25.8466	1.73082	0.865408	+	0.501067i	$0.167059\pi$
$224$	−3.11298	−0.207995
$225$	−10.7192	−0.714611
$226$	17.1459	1.14053
$227$	−9.24216	−0.613423	−0.306712	−	0.951802i	$-0.599229\pi$
$227$	−9.24216	−0.613423	−0.306712	+	0.951802i	$0.599229\pi$
$228$	−19.4478	−1.28796
$229$	12.6821	0.838055	0.419027	−	0.907974i	$-0.362371\pi$
$229$	12.6821	0.838055	0.419027	+	0.907974i	$0.362371\pi$
$230$	0.983407	0.0648439
$231$	23.1643	1.52410
$232$	1.00000	0.0656532
$233$	−7.33914	−0.480803	−0.240402	−	0.970674i	$-0.577279\pi$
$233$	−7.33914	−0.480803	−0.240402	+	0.970674i	$0.577279\pi$
$234$	−16.3368	−1.06797
$235$	4.26602	0.278284
$236$	−0.415747	−0.0270628
$237$	−7.65135	−0.497008
$238$	−7.45473	−0.483218
$239$	−22.3329	−1.44460	−0.722298	−	0.691582i	$-0.756914\pi$
$239$	−22.3329	−1.44460	−0.722298	+	0.691582i	$0.756914\pi$
$240$	−2.33917	−0.150993
$241$	2.00939	0.129436	0.0647180	−	0.997904i	$-0.479385\pi$
$241$	2.00939	0.129436	0.0647180	+	0.997904i	$0.479385\pi$
$242$	−1.21346	−0.0780039
$243$	21.1294	1.35545
$244$	11.1106	0.711286
$245$	2.64601	0.169047
$246$	−25.6883	−1.63783
$247$	−50.2535	−3.19755
$248$	3.95395	0.251076
$249$	−23.1904	−1.46963
$250$	−8.88303	−0.561812
$251$	−0.837452	−0.0528595	−0.0264297	−	0.999651i	$-0.508414\pi$
$251$	−0.837452	−0.0528595	−0.0264297	+	0.999651i	$0.508414\pi$
$252$	−8.27406	−0.521217
$253$	3.12835	0.196677
$254$	−2.67681	−0.167958
$255$	−5.60166	−0.350790
$256$	1.00000	0.0625000
$257$	−10.8597	−0.677409	−0.338705	−	0.940893i	$-0.609989\pi$
$257$	−10.8597	−0.677409	−0.338705	+	0.940893i	$0.609989\pi$
$258$	−11.8349	−0.736810
$259$	23.9282	1.48682
$260$	−6.04447	−0.374862
$261$	2.65792	0.164521
$262$	18.3171	1.13164
$263$	8.32018	0.513044	0.256522	−	0.966538i	$-0.417423\pi$
$263$	8.32018	0.513044	0.256522	+	0.966538i	$0.417423\pi$
$264$	−7.44120	−0.457974
$265$	13.6148	0.836351
$266$	−25.4518	−1.56055
$267$	−31.6144	−1.93477
$268$	−4.37578	−0.267293
$269$	−15.2221	−0.928106	−0.464053	−	0.885807i	$-0.653605\pi$
$269$	−15.2221	−0.928106	−0.464053	+	0.885807i	$0.653605\pi$
$270$	0.800181	0.0486974
$271$	−15.1044	−0.917524	−0.458762	−	0.888559i	$-0.651707\pi$
$271$	−15.1044	−0.917524	−0.458762	+	0.888559i	$0.651707\pi$
$272$	2.39472	0.145201
$273$	−45.5124	−2.75454
$274$	−3.51015	−0.212056
$275$	−12.6163	−0.760794
$276$	−2.37864	−0.143177
$277$	−1.20726	−0.0725371	−0.0362685	−	0.999342i	$-0.511547\pi$
$277$	−1.20726	−0.0725371	−0.0362685	+	0.999342i	$0.511547\pi$
$278$	−5.10163	−0.305975
$279$	10.5093	0.629174
$280$	−3.06133	−0.182949
$281$	−17.9412	−1.07028	−0.535141	−	0.844762i	$-0.679742\pi$
$281$	−17.9412	−1.07028	−0.535141	+	0.844762i	$0.679742\pi$
$282$	−10.3185	−0.614459
$283$	7.65491	0.455037	0.227519	−	0.973774i	$-0.426939\pi$
$283$	7.65491	0.455037	0.227519	+	0.973774i	$0.426939\pi$
$284$	0.807253	0.0479017
$285$	−19.1251	−1.13287
$286$	−19.2282	−1.13699
$287$	−33.6189	−1.98446
$288$	2.65792	0.156620
$289$	−11.2653	−0.662665
$290$	0.983407	0.0577477
$291$	7.15951	0.419698
$292$	−13.1142	−0.767452
$293$	8.93694	0.522101	0.261051	−	0.965325i	$-0.415931\pi$
$293$	8.93694	0.522101	0.261051	+	0.965325i	$0.415931\pi$
$294$	−6.40009	−0.373261
$295$	−0.408849	−0.0238041
$296$	−7.68657	−0.446773
$297$	2.54548	0.147704
$298$	9.55292	0.553386
$299$	−6.14646	−0.355459
$300$	9.59284	0.553843
$301$	−15.4886	−0.892751
$302$	−9.84887	−0.566739
$303$	2.29037	0.131579
$304$	8.17601	0.468926
$305$	10.9263	0.625637
$306$	6.36498	0.363862
$307$	4.25203	0.242676	0.121338	−	0.992611i	$-0.461281\pi$
$307$	4.25203	0.242676	0.121338	+	0.992611i	$0.461281\pi$
$308$	−9.73848	−0.554901
$309$	−15.9055	−0.904833
$310$	3.88834	0.220843
$311$	21.8458	1.23876	0.619380	−	0.785091i	$-0.287384\pi$
$311$	21.8458	1.23876	0.619380	+	0.785091i	$0.287384\pi$
$312$	14.6202	0.827706
$313$	1.03903	0.0587297	0.0293648	−	0.999569i	$-0.490652\pi$
$313$	1.03903	0.0587297	0.0293648	+	0.999569i	$0.490652\pi$
$314$	−18.7375	−1.05742
$315$	−8.13677	−0.458455
$316$	3.21669	0.180953
$317$	−1.21906	−0.0684691	−0.0342345	−	0.999414i	$-0.510899\pi$
$317$	−1.21906	−0.0684691	−0.0342345	+	0.999414i	$0.510899\pi$
$318$	−32.9311	−1.84669
$319$	3.12835	0.175154
$320$	0.983407	0.0549741
$321$	−29.2254	−1.63120
$322$	−3.11298	−0.173480
$323$	19.5793	1.08942
$324$	−9.90922	−0.550512
$325$	24.7881	1.37500
$326$	3.12416	0.173031
$327$	32.5965	1.80259
$328$	10.7996	0.596308
$329$	−13.5041	−0.744505
$330$	−7.31773	−0.402828
$331$	22.8596	1.25648	0.628238	−	0.778021i	$-0.283776\pi$
$331$	22.8596	1.25648	0.628238	+	0.778021i	$0.283776\pi$
$332$	9.74943	0.535069
$333$	−20.4303	−1.11957
$334$	10.9815	0.600883
$335$	−4.30317	−0.235107
$336$	7.40466	0.403957
$337$	11.6218	0.633081	0.316540	−	0.948579i	$-0.397479\pi$
$337$	11.6218	0.633081	0.316540	+	0.948579i	$0.397479\pi$
$338$	24.7789	1.34780
$339$	−40.7839	−2.21508
$340$	2.35499	0.127717
$341$	12.3693	0.669836
$342$	21.7312	1.17509
$343$	13.4149	0.724337
$344$	4.97550	0.268261
$345$	−2.33917	−0.125937
$346$	−3.98263	−0.214108
$347$	3.28917	0.176572	0.0882860	−	0.996095i	$-0.471861\pi$
$347$	3.28917	0.176572	0.0882860	+	0.996095i	$0.471861\pi$
$348$	−2.37864	−0.127508
$349$	35.4617	1.89822	0.949112	−	0.314939i	$-0.101984\pi$
$349$	35.4617	1.89822	0.949112	+	0.314939i	$0.101984\pi$
$350$	12.5544	0.671060
$351$	−5.00126	−0.266948
$352$	3.12835	0.166741
$353$	30.0221	1.59792	0.798958	−	0.601386i	$-0.205385\pi$
$353$	30.0221	1.59792	0.798958	+	0.601386i	$0.205385\pi$
$354$	0.988912	0.0525601
$355$	0.793858	0.0421336
$356$	13.2910	0.704420
$357$	17.7321	0.938482
$358$	−20.9052	−1.10488
$359$	−26.6363	−1.40581	−0.702905	−	0.711284i	$-0.748114\pi$
$359$	−26.6363	−1.40581	−0.702905	+	0.711284i	$0.748114\pi$
$360$	2.61382	0.137760
$361$	47.8471	2.51827
$362$	−19.6091	−1.03063
$363$	2.88637	0.151495
$364$	19.1338	1.00288
$365$	−12.8966	−0.675040
$366$	−26.4282	−1.38142
$367$	−13.1616	−0.687029	−0.343515	−	0.939147i	$-0.611617\pi$
$367$	−13.1616	−0.687029	−0.343515	+	0.939147i	$0.611617\pi$
$368$	1.00000	0.0521286
$369$	28.7045	1.49429
$370$	−7.55903	−0.392975
$371$	−43.0978	−2.23752
$372$	−9.40501	−0.487627
$373$	−35.6818	−1.84753	−0.923766	−	0.382958i	$-0.874906\pi$
$373$	−35.6818	−1.84753	−0.923766	+	0.382958i	$0.874906\pi$
$374$	7.49152	0.387377
$375$	21.1295	1.09112
$376$	4.33800	0.223715
$377$	−6.14646	−0.316559
$378$	−2.53298	−0.130282
$379$	19.1841	0.985423	0.492711	−	0.870193i	$-0.336006\pi$
$379$	19.1841	0.985423	0.492711	+	0.870193i	$0.336006\pi$
$380$	8.04035	0.412461
$381$	6.36717	0.326200
$382$	−13.9575	−0.714130
$383$	12.7607	0.652039	0.326020	−	0.945363i	$-0.394292\pi$
$383$	12.7607	0.652039	0.326020	+	0.945363i	$0.394292\pi$
$384$	−2.37864	−0.121384
$385$	−9.57689	−0.488084
$386$	7.15327	0.364092
$387$	13.2245	0.672239
$388$	−3.00992	−0.152806
$389$	26.0270	1.31962	0.659811	−	0.751431i	$-0.270636\pi$
$389$	26.0270	1.31962	0.659811	+	0.751431i	$0.270636\pi$
$390$	14.3776	0.728038
$391$	2.39472	0.121106
$392$	2.69065	0.135899
$393$	−43.5698	−2.19781
$394$	−22.6127	−1.13921
$395$	3.16332	0.159164
$396$	8.31489	0.417839
$397$	3.55743	0.178543	0.0892713	−	0.996007i	$-0.471546\pi$
$397$	3.55743	0.178543	0.0892713	+	0.996007i	$0.471546\pi$
$398$	13.7438	0.688913
$399$	60.5405	3.03082
$400$	−4.03291	−0.201646
$401$	39.8222	1.98863	0.994313	−	0.106501i	$-0.0339648\pi$
$401$	39.8222	1.98863	0.994313	+	0.106501i	$0.0339648\pi$
$402$	10.4084	0.519124
$403$	−24.3028	−1.21061
$404$	−0.962893	−0.0479057
$405$	−9.74480	−0.484223
$406$	−3.11298	−0.154495
$407$	−24.0463	−1.19193
$408$	−5.69618	−0.282003
$409$	19.1029	0.944576	0.472288	−	0.881444i	$-0.343428\pi$
$409$	19.1029	0.944576	0.472288	+	0.881444i	$0.343428\pi$
$410$	10.6204	0.524504
$411$	8.34937	0.411844
$412$	6.68681	0.329436
$413$	1.29421	0.0636841
$414$	2.65792	0.130630
$415$	9.58766	0.470639
$416$	−6.14646	−0.301355
$417$	12.1349	0.594250
$418$	25.5774	1.25103
$419$	−30.4964	−1.48985	−0.744924	−	0.667150i	$-0.767514\pi$
$419$	−30.4964	−1.48985	−0.744924	+	0.667150i	$0.767514\pi$
$420$	7.28179	0.355315
$421$	18.0479	0.879601	0.439800	−	0.898096i	$-0.355049\pi$
$421$	18.0479	0.879601	0.439800	+	0.898096i	$0.355049\pi$
$422$	−22.4787	−1.09425
$423$	11.5301	0.560610
$424$	13.8445	0.672350
$425$	−9.65770	−0.468467
$426$	−1.92016	−0.0930322
$427$	−34.5872	−1.67379
$428$	12.2866	0.593895
$429$	45.7370	2.20820
$430$	4.89294	0.235959
$431$	−21.1838	−1.02039	−0.510195	−	0.860059i	$-0.670427\pi$
$431$	−21.1838	−1.02039	−0.510195	+	0.860059i	$0.670427\pi$
$432$	0.813682	0.0391483
$433$	−23.4132	−1.12517	−0.562583	−	0.826741i	$-0.690192\pi$
$433$	−23.4132	−1.12517	−0.562583	+	0.826741i	$0.690192\pi$
$434$	−12.3086	−0.590830
$435$	−2.33917	−0.112155
$436$	−13.7038	−0.656295
$437$	8.17601	0.391112
$438$	31.1940	1.49051
$439$	−26.5638	−1.26782	−0.633910	−	0.773407i	$-0.718551\pi$
$439$	−26.5638	−1.26782	−0.633910	+	0.773407i	$0.718551\pi$
$440$	3.07644	0.146663
$441$	7.15155	0.340550
$442$	−14.7191	−0.700114
$443$	38.7518	1.84115	0.920577	−	0.390561i	$-0.127719\pi$
$443$	38.7518	1.84115	0.920577	+	0.390561i	$0.127719\pi$
$444$	18.2836	0.867700
$445$	13.0704	0.619598
$446$	25.8466	1.22387
$447$	−22.7229	−1.07476
$448$	−3.11298	−0.147075
$449$	−24.3325	−1.14832	−0.574160	−	0.818743i	$-0.694671\pi$
$449$	−24.3325	−1.14832	−0.574160	+	0.818743i	$0.694671\pi$
$450$	−10.7192	−0.505306
$451$	33.7849	1.59087
$452$	17.1459	0.806476
$453$	23.4269	1.10069
$454$	−9.24216	−0.433756
$455$	18.8163	0.882123
$456$	−19.4478	−0.910725
$457$	35.5848	1.66459	0.832294	−	0.554334i	$-0.187027\pi$
$457$	35.5848	1.66459	0.832294	+	0.554334i	$0.187027\pi$
$458$	12.6821	0.592594
$459$	1.94854	0.0909502
$460$	0.983407	0.0458516
$461$	−12.3986	−0.577462	−0.288731	−	0.957410i	$-0.593233\pi$
$461$	−12.3986	−0.577462	−0.288731	+	0.957410i	$0.593233\pi$
$462$	23.1643	1.07770
$463$	27.6470	1.28486	0.642432	−	0.766343i	$-0.277926\pi$
$463$	27.6470	1.28486	0.642432	+	0.766343i	$0.277926\pi$
$464$	1.00000	0.0464238
$465$	−9.24895	−0.428910
$466$	−7.33914	−0.339979
$467$	0.518206	0.0239797	0.0119899	−	0.999928i	$-0.496183\pi$
$467$	0.518206	0.0239797	0.0119899	+	0.999928i	$0.496183\pi$
$468$	−16.3368	−0.755169
$469$	13.6217	0.628993
$470$	4.26602	0.196777
$471$	44.5699	2.05367
$472$	−0.415747	−0.0191363
$473$	15.5651	0.715683
$474$	−7.65135	−0.351438
$475$	−32.9731	−1.51291
$476$	−7.45473	−0.341687
$477$	36.7977	1.68485
$478$	−22.3329	−1.02148
$479$	4.50475	0.205827	0.102914	−	0.994690i	$-0.467183\pi$
$479$	4.50475	0.205827	0.102914	+	0.994690i	$0.467183\pi$
$480$	−2.33917	−0.106768
$481$	47.2452	2.15419
$482$	2.00939	0.0915251
$483$	7.40466	0.336924
$484$	−1.21346	−0.0551571
$485$	−2.95998	−0.134406
$486$	21.1294	0.958449
$487$	10.8435	0.491366	0.245683	−	0.969350i	$-0.420988\pi$
$487$	10.8435	0.491366	0.245683	+	0.969350i	$0.420988\pi$
$488$	11.1106	0.502955
$489$	−7.43126	−0.336053
$490$	2.64601	0.119534
$491$	7.96879	0.359626	0.179813	−	0.983701i	$-0.442451\pi$
$491$	7.96879	0.359626	0.179813	+	0.983701i	$0.442451\pi$
$492$	−25.6883	−1.15812
$493$	2.39472	0.107853
$494$	−50.2535	−2.26101
$495$	8.17693	0.367526
$496$	3.95395	0.177537
$497$	−2.51296	−0.112722
$498$	−23.1904	−1.03918
$499$	−38.5911	−1.72758	−0.863788	−	0.503856i	$-0.831914\pi$
$499$	−38.5911	−1.72758	−0.863788	+	0.503856i	$0.831914\pi$
$500$	−8.88303	−0.397261
$501$	−26.1211	−1.16700
$502$	−0.837452	−0.0373773
$503$	−22.6361	−1.00930	−0.504648	−	0.863325i	$-0.668378\pi$
$503$	−22.6361	−1.00930	−0.504648	+	0.863325i	$0.668378\pi$
$504$	−8.27406	−0.368556
$505$	−0.946916	−0.0421372
$506$	3.12835	0.139072
$507$	−58.9401	−2.61762
$508$	−2.67681	−0.118764
$509$	12.0951	0.536104	0.268052	−	0.963404i	$-0.413620\pi$
$509$	12.0951	0.536104	0.268052	+	0.963404i	$0.413620\pi$
$510$	−5.60166	−0.248046
$511$	40.8243	1.80596
$512$	1.00000	0.0441942
$513$	6.65267	0.293723
$514$	−10.8597	−0.479001
$515$	6.57586	0.289767
$516$	−11.8349	−0.521003
$517$	13.5708	0.596841
$518$	23.9282	1.05134
$519$	9.47324	0.415829
$520$	−6.04447	−0.265067
$521$	2.25208	0.0986653	0.0493327	−	0.998782i	$-0.484291\pi$
$521$	2.25208	0.0986653	0.0493327	+	0.998782i	$0.484291\pi$
$522$	2.65792	0.116334
$523$	−25.1841	−1.10122	−0.550612	−	0.834761i	$-0.685606\pi$
$523$	−25.1841	−1.10122	−0.550612	+	0.834761i	$0.685606\pi$
$524$	18.3171	0.800188
$525$	−29.8623	−1.30330
$526$	8.32018	0.362777
$527$	9.46861	0.412459
$528$	−7.44120	−0.323837
$529$	1.00000	0.0434783
$530$	13.6148	0.591390
$531$	−1.10502	−0.0479539
$532$	−25.4518	−1.10347
$533$	−66.3792	−2.87520
$534$	−31.6144	−1.36809
$535$	12.0827	0.522381
$536$	−4.37578	−0.189005
$537$	49.7260	2.14584
$538$	−15.2221	−0.656270
$539$	8.41729	0.362559
$540$	0.800181	0.0344343
$541$	−37.6776	−1.61989	−0.809944	−	0.586508i	$-0.800502\pi$
$541$	−37.6776	−1.61989	−0.809944	+	0.586508i	$0.800502\pi$
$542$	−15.1044	−0.648788
$543$	46.6429	2.00164
$544$	2.39472	0.102673
$545$	−13.4765	−0.577268
$546$	−45.5124	−1.94775
$547$	14.1080	0.603214	0.301607	−	0.953432i	$-0.402477\pi$
$547$	14.1080	0.603214	0.301607	+	0.953432i	$0.402477\pi$
$548$	−3.51015	−0.149946
$549$	29.5312	1.26036
$550$	−12.6163	−0.537962
$551$	8.17601	0.348310
$552$	−2.37864	−0.101242
$553$	−10.0135	−0.425817
$554$	−1.20726	−0.0512915
$555$	17.9802	0.763217
$556$	−5.10163	−0.216357
$557$	5.41214	0.229320	0.114660	−	0.993405i	$-0.463422\pi$
$557$	5.41214	0.229320	0.114660	+	0.993405i	$0.463422\pi$
$558$	10.5093	0.444893
$559$	−30.5817	−1.29347
$560$	−3.06133	−0.129365
$561$	−17.8196	−0.752345
$562$	−17.9412	−0.756804
$563$	25.2213	1.06295	0.531475	−	0.847074i	$-0.321638\pi$
$563$	25.2213	1.06295	0.531475	+	0.847074i	$0.321638\pi$
$564$	−10.3185	−0.434488
$565$	16.8614	0.709365
$566$	7.65491	0.321760
$567$	30.8472	1.29546
$568$	0.807253	0.0338716
$569$	0.774298	0.0324603	0.0162301	−	0.999868i	$-0.494834\pi$
$569$	0.774298	0.0324603	0.0162301	+	0.999868i	$0.494834\pi$
$570$	−19.1251	−0.801061
$571$	−20.8715	−0.873446	−0.436723	−	0.899596i	$-0.643861\pi$
$571$	−20.8715	−0.873446	−0.436723	+	0.899596i	$0.643861\pi$
$572$	−19.2282	−0.803973
$573$	33.1999	1.38695
$574$	−33.6189	−1.40323
$575$	−4.03291	−0.168184
$576$	2.65792	0.110747
$577$	−4.32961	−0.180244	−0.0901221	−	0.995931i	$-0.528726\pi$
$577$	−4.32961	−0.180244	−0.0901221	+	0.995931i	$0.528726\pi$
$578$	−11.2653	−0.468575
$579$	−17.0151	−0.707121
$580$	0.983407	0.0408338
$581$	−30.3498	−1.25912
$582$	7.15951	0.296771
$583$	43.3105	1.79374
$584$	−13.1142	−0.542670
$585$	−16.0657	−0.664236
$586$	8.93694	0.369181
$587$	11.1176	0.458873	0.229437	−	0.973324i	$-0.426312\pi$
$587$	11.1176	0.458873	0.229437	+	0.973324i	$0.426312\pi$
$588$	−6.40009	−0.263935
$589$	32.3275	1.33203
$590$	−0.408849	−0.0168320
$591$	53.7874	2.21252
$592$	−7.68657	−0.315916
$593$	36.7435	1.50887	0.754436	−	0.656373i	$-0.227910\pi$
$593$	36.7435	1.50887	0.754436	+	0.656373i	$0.227910\pi$
$594$	2.54548	0.104442
$595$	−7.33103	−0.300543
$596$	9.55292	0.391303
$597$	−32.6915	−1.33797
$598$	−6.14646	−0.251347
$599$	41.8026	1.70801	0.854005	−	0.520266i	$-0.174167\pi$
$599$	41.8026	1.70801	0.854005	+	0.520266i	$0.174167\pi$
$600$	9.59284	0.391626
$601$	27.6788	1.12904	0.564520	−	0.825419i	$-0.309061\pi$
$601$	27.6788	1.12904	0.564520	+	0.825419i	$0.309061\pi$
$602$	−15.4886	−0.631270
$603$	−11.6305	−0.473630
$604$	−9.84887	−0.400745
$605$	−1.19332	−0.0485154
$606$	2.29037	0.0930401
$607$	8.29577	0.336715	0.168357	−	0.985726i	$-0.446154\pi$
$607$	8.29577	0.336715	0.168357	+	0.985726i	$0.446154\pi$
$608$	8.17601	0.331581
$609$	7.40466	0.300052
$610$	10.9263	0.442392
$611$	−26.6633	−1.07868
$612$	6.36498	0.257289
$613$	4.69283	0.189542	0.0947708	−	0.995499i	$-0.469788\pi$
$613$	4.69283	0.189542	0.0947708	+	0.995499i	$0.469788\pi$
$614$	4.25203	0.171598
$615$	−25.2621	−1.01867
$616$	−9.73848	−0.392375
$617$	−13.9701	−0.562417	−0.281208	−	0.959647i	$-0.590735\pi$
$617$	−13.9701	−0.562417	−0.281208	+	0.959647i	$0.590735\pi$
$618$	−15.9055	−0.639814
$619$	−26.5729	−1.06806	−0.534028	−	0.845467i	$-0.679322\pi$
$619$	−26.5729	−1.06806	−0.534028	+	0.845467i	$0.679322\pi$
$620$	3.88834	0.156159
$621$	0.813682	0.0326519
$622$	21.8458	0.875936
$623$	−41.3745	−1.65764
$624$	14.6202	0.585276
$625$	11.4289	0.457157
$626$	1.03903	0.0415282
$627$	−60.8393	−2.42969
$628$	−18.7375	−0.747710
$629$	−18.4072	−0.733944
$630$	−8.13677	−0.324177
$631$	6.43284	0.256087	0.128044	−	0.991769i	$-0.459130\pi$
$631$	6.43284	0.256087	0.128044	+	0.991769i	$0.459130\pi$
$632$	3.21669	0.127953
$633$	53.4688	2.12519
$634$	−1.21906	−0.0484149
$635$	−2.63240	−0.104463
$636$	−32.9311	−1.30580
$637$	−16.5380	−0.655259
$638$	3.12835	0.123852
$639$	2.14561	0.0848792
$640$	0.983407	0.0388726
$641$	31.5444	1.24593	0.622964	−	0.782251i	$-0.285928\pi$
$641$	31.5444	1.24593	0.622964	+	0.782251i	$0.285928\pi$
$642$	−29.2254	−1.15343
$643$	4.62070	0.182223	0.0911114	−	0.995841i	$-0.470958\pi$
$643$	4.62070	0.182223	0.0911114	+	0.995841i	$0.470958\pi$
$644$	−3.11298	−0.122669
$645$	−11.6385	−0.458267
$646$	19.5793	0.770336
$647$	10.3043	0.405104	0.202552	−	0.979272i	$-0.435076\pi$
$647$	10.3043	0.405104	0.202552	+	0.979272i	$0.435076\pi$
$648$	−9.90922	−0.389271
$649$	−1.30060	−0.0510530
$650$	24.7881	0.972270
$651$	29.2776	1.14748
$652$	3.12416	0.122352
$653$	−24.7761	−0.969563	−0.484781	−	0.874635i	$-0.661101\pi$
$653$	−24.7761	−0.969563	−0.484781	+	0.874635i	$0.661101\pi$
$654$	32.5965	1.27462
$655$	18.0132	0.703834
$656$	10.7996	0.421653
$657$	−34.8566	−1.35988
$658$	−13.5041	−0.526445
$659$	−11.2164	−0.436929	−0.218464	−	0.975845i	$-0.570105\pi$
$659$	−11.2164	−0.436929	−0.218464	+	0.975845i	$0.570105\pi$
$660$	−7.31773	−0.284842
$661$	−10.4681	−0.407161	−0.203580	−	0.979058i	$-0.565258\pi$
$661$	−10.4681	−0.407161	−0.203580	+	0.979058i	$0.565258\pi$
$662$	22.8596	0.888463
$663$	35.0113	1.35973
$664$	9.74943	0.378351
$665$	−25.0294	−0.970600
$666$	−20.4303	−0.791658
$667$	1.00000	0.0387202
$668$	10.9815	0.424888
$669$	−61.4797	−2.37694
$670$	−4.30317	−0.166246
$671$	34.7579	1.34181
$672$	7.40466	0.285641
$673$	26.3035	1.01393	0.506963	−	0.861968i	$-0.330768\pi$
$673$	26.3035	1.01393	0.506963	+	0.861968i	$0.330768\pi$
$674$	11.6218	0.447656
$675$	−3.28151	−0.126305
$676$	24.7789	0.953035
$677$	−26.6780	−1.02532	−0.512660	−	0.858592i	$-0.671340\pi$
$677$	−26.6780	−1.02532	−0.512660	+	0.858592i	$0.671340\pi$
$678$	−40.7839	−1.56630
$679$	9.36983	0.359581
$680$	2.35499	0.0903096
$681$	21.9837	0.842419
$682$	12.3693	0.473645
$683$	−17.8239	−0.682012	−0.341006	−	0.940061i	$-0.610768\pi$
$683$	−17.8239	−0.682012	−0.341006	+	0.940061i	$0.610768\pi$
$684$	21.7312	0.830913
$685$	−3.45190	−0.131890
$686$	13.4149	0.512184
$687$	−30.1661	−1.15091
$688$	4.97550	0.189689
$689$	−85.0948	−3.24185
$690$	−2.33917	−0.0890507
$691$	9.96650	0.379143	0.189572	−	0.981867i	$-0.439290\pi$
$691$	9.96650	0.379143	0.189572	+	0.981867i	$0.439290\pi$
$692$	−3.98263	−0.151397
$693$	−25.8841	−0.983256
$694$	3.28917	0.124855
$695$	−5.01697	−0.190305
$696$	−2.37864	−0.0901621
$697$	25.8620	0.979594
$698$	35.4617	1.34225
$699$	17.4572	0.660291
$700$	12.5544	0.474511
$701$	−23.8288	−0.900003	−0.450001	−	0.893028i	$-0.648577\pi$
$701$	−23.8288	−0.900003	−0.450001	+	0.893028i	$0.648577\pi$
$702$	−5.00126	−0.188760
$703$	−62.8455	−2.37026
$704$	3.12835	0.117904
$705$	−10.1473	−0.382170
$706$	30.0221	1.12990
$707$	2.99747	0.112731
$708$	0.988912	0.0371656
$709$	−35.7366	−1.34212	−0.671058	−	0.741405i	$-0.734160\pi$
$709$	−35.7366	−1.34212	−0.671058	+	0.741405i	$0.734160\pi$
$710$	0.793858	0.0297930
$711$	8.54971	0.320639
$712$	13.2910	0.498100
$713$	3.95395	0.148076
$714$	17.7321	0.663607
$715$	−18.9092	−0.707163
$716$	−20.9052	−0.781265
$717$	53.1219	1.98387
$718$	−26.6363	−0.994058
$719$	14.4113	0.537451	0.268725	−	0.963217i	$-0.413398\pi$
$719$	14.4113	0.537451	0.268725	+	0.963217i	$0.413398\pi$
$720$	2.61382	0.0974113
$721$	−20.8159	−0.775226
$722$	47.8471	1.78069
$723$	−4.77961	−0.177755
$724$	−19.6091	−0.728766
$725$	−4.03291	−0.149779
$726$	2.88637	0.107123
$727$	11.6046	0.430391	0.215195	−	0.976571i	$-0.430961\pi$
$727$	11.6046	0.430391	0.215195	+	0.976571i	$0.430961\pi$
$728$	19.1338	0.709146
$729$	−20.5316	−0.760428
$730$	−12.8966	−0.477325
$731$	11.9149	0.440690
$732$	−26.4282	−0.976814
$733$	16.5691	0.611995	0.305997	−	0.952032i	$-0.401010\pi$
$733$	16.5691	0.611995	0.305997	+	0.952032i	$0.401010\pi$
$734$	−13.1616	−0.485803
$735$	−6.29390	−0.232154
$736$	1.00000	0.0368605
$737$	−13.6889	−0.504239
$738$	28.7045	1.05663
$739$	−50.4282	−1.85503	−0.927516	−	0.373782i	$-0.878061\pi$
$739$	−50.4282	−1.85503	−0.927516	+	0.373782i	$0.878061\pi$
$740$	−7.55903	−0.277875
$741$	119.535	4.39122
$742$	−43.0978	−1.58217
$743$	−12.1849	−0.447021	−0.223510	−	0.974702i	$-0.571752\pi$
$743$	−12.1849	−0.447021	−0.223510	+	0.974702i	$0.571752\pi$
$744$	−9.40501	−0.344804
$745$	9.39440	0.344184
$746$	−35.6818	−1.30640
$747$	25.9132	0.948115
$748$	7.49152	0.273917
$749$	−38.2479	−1.39755
$750$	21.1295	0.771541
$751$	15.9111	0.580605	0.290303	−	0.956935i	$-0.406244\pi$
$751$	15.9111	0.580605	0.290303	+	0.956935i	$0.406244\pi$
$752$	4.33800	0.158190
$753$	1.99199	0.0725923
$754$	−6.14646	−0.223841
$755$	−9.68545	−0.352489
$756$	−2.53298	−0.0921235
$757$	33.9797	1.23501	0.617507	−	0.786565i	$-0.288143\pi$
$757$	33.9797	1.23501	0.617507	+	0.786565i	$0.288143\pi$
$758$	19.1841	0.696799
$759$	−7.44120	−0.270099
$760$	8.04035	0.291654
$761$	12.7076	0.460649	0.230325	−	0.973114i	$-0.426021\pi$
$761$	12.7076	0.460649	0.230325	+	0.973114i	$0.426021\pi$
$762$	6.36717	0.230658
$763$	42.6598	1.54439
$764$	−13.9575	−0.504966
$765$	6.25937	0.226308
$766$	12.7607	0.461061
$767$	2.55537	0.0922691
$768$	−2.37864	−0.0858317
$769$	−42.9525	−1.54891	−0.774454	−	0.632630i	$-0.781975\pi$
$769$	−42.9525	−1.54891	−0.774454	+	0.632630i	$0.781975\pi$
$770$	−9.57689	−0.345127
$771$	25.8313	0.930291
$772$	7.15327	0.257452
$773$	−18.8710	−0.678742	−0.339371	−	0.940653i	$-0.610214\pi$
$773$	−18.8710	−0.678742	−0.339371	+	0.940653i	$0.610214\pi$
$774$	13.2245	0.475345
$775$	−15.9459	−0.572794
$776$	−3.00992	−0.108050
$777$	−56.9164	−2.04187
$778$	26.0270	0.933114
$779$	88.2976	3.16359
$780$	14.3776	0.514801
$781$	2.52537	0.0903647
$782$	2.39472	0.0856351
$783$	0.813682	0.0290786
$784$	2.69065	0.0960948
$785$	−18.4266	−0.657675
$786$	−43.5698	−1.55408
$787$	−14.5906	−0.520098	−0.260049	−	0.965595i	$-0.583739\pi$
$787$	−14.5906	−0.520098	−0.260049	+	0.965595i	$0.583739\pi$
$788$	−22.6127	−0.805544
$789$	−19.7907	−0.704567
$790$	3.16332	0.112546
$791$	−53.3749	−1.89779
$792$	8.31489	0.295457
$793$	−68.2910	−2.42509
$794$	3.55743	0.126249
$795$	−32.3847	−1.14857
$796$	13.7438	0.487135
$797$	5.60560	0.198561	0.0992803	−	0.995060i	$-0.468346\pi$
$797$	5.60560	0.198561	0.0992803	+	0.995060i	$0.468346\pi$
$798$	60.5405	2.14311
$799$	10.3883	0.367512
$800$	−4.03291	−0.142585
$801$	35.3263	1.24819
$802$	39.8222	1.40617
$803$	−41.0258	−1.44777
$804$	10.4084	0.367076
$805$	−3.06133	−0.107898
$806$	−24.3028	−0.856028
$807$	36.2078	1.27458
$808$	−0.962893	−0.0338745
$809$	51.1066	1.79681	0.898407	−	0.439165i	$-0.144726\pi$
$809$	51.1066	1.79681	0.898407	+	0.439165i	$0.144726\pi$
$810$	−9.74480	−0.342397
$811$	−20.5516	−0.721665	−0.360833	−	0.932631i	$-0.617507\pi$
$811$	−20.5516	−0.721665	−0.360833	+	0.932631i	$0.617507\pi$
$812$	−3.11298	−0.109244
$813$	35.9278	1.26004
$814$	−24.0463	−0.842821
$815$	3.07232	0.107619
$816$	−5.69618	−0.199406
$817$	40.6797	1.42320
$818$	19.1029	0.667916
$819$	50.8561	1.77706
$820$	10.6204	0.370880
$821$	9.01469	0.314615	0.157307	−	0.987550i	$-0.449719\pi$
$821$	9.01469	0.314615	0.157307	+	0.987550i	$0.449719\pi$
$822$	8.34937	0.291218
$823$	23.5033	0.819273	0.409637	−	0.912249i	$-0.365655\pi$
$823$	23.5033	0.819273	0.409637	+	0.912249i	$0.365655\pi$
$824$	6.68681	0.232946
$825$	30.0097	1.04480
$826$	1.29421	0.0450314
$827$	32.8451	1.14214	0.571068	−	0.820903i	$-0.306529\pi$
$827$	32.8451	1.14214	0.571068	+	0.820903i	$0.306529\pi$
$828$	2.65792	0.0923691
$829$	−35.5452	−1.23454	−0.617268	−	0.786753i	$-0.711761\pi$
$829$	−35.5452	−1.23454	−0.617268	+	0.786753i	$0.711761\pi$
$830$	9.58766	0.332792
$831$	2.87163	0.0996157
$832$	−6.14646	−0.213090
$833$	6.44337	0.223250
$834$	12.1349	0.420198
$835$	10.7993	0.373726
$836$	25.5774	0.884612
$837$	3.21726	0.111205
$838$	−30.4964	−1.05348
$839$	−20.6260	−0.712087	−0.356044	−	0.934469i	$-0.615875\pi$
$839$	−20.6260	−0.712087	−0.356044	+	0.934469i	$0.615875\pi$
$840$	7.28179	0.251246
$841$	1.00000	0.0344828
$842$	18.0479	0.621972
$843$	42.6757	1.46983
$844$	−22.4787	−0.773750
$845$	24.3678	0.838277
$846$	11.5301	0.396411
$847$	3.77747	0.129795
$848$	13.8445	0.475423
$849$	−18.2083	−0.624906
$850$	−9.65770	−0.331256
$851$	−7.68657	−0.263492
$852$	−1.92016	−0.0657837
$853$	−35.0692	−1.20075	−0.600373	−	0.799720i	$-0.704981\pi$
$853$	−35.0692	−1.20075	−0.600373	+	0.799720i	$0.704981\pi$
$854$	−34.5872	−1.18355
$855$	21.3706	0.730859
$856$	12.2866	0.419947
$857$	−45.8137	−1.56497	−0.782483	−	0.622671i	$-0.786047\pi$
$857$	−45.8137	−1.56497	−0.782483	+	0.622671i	$0.786047\pi$
$858$	45.7370	1.56144
$859$	−40.7709	−1.39109	−0.695543	−	0.718485i	$-0.744836\pi$
$859$	−40.7709	−1.39109	−0.695543	+	0.718485i	$0.744836\pi$
$860$	4.89294	0.166848
$861$	79.9673	2.72528
$862$	−21.1838	−0.721524
$863$	−36.4713	−1.24150	−0.620749	−	0.784010i	$-0.713171\pi$
$863$	−36.4713	−1.24150	−0.620749	+	0.784010i	$0.713171\pi$
$864$	0.813682	0.0276820
$865$	−3.91655	−0.133167
$866$	−23.4132	−0.795612
$867$	26.7961	0.910043
$868$	−12.3086	−0.417780
$869$	10.0629	0.341361
$870$	−2.33917	−0.0793053
$871$	26.8955	0.911321
$872$	−13.7038	−0.464071
$873$	−8.00013	−0.270763
$874$	8.17601	0.276558
$875$	27.6527	0.934832
$876$	31.1940	1.05395
$877$	31.1039	1.05031	0.525153	−	0.851008i	$-0.324008\pi$
$877$	31.1039	1.05031	0.525153	+	0.851008i	$0.324008\pi$
$878$	−26.5638	−0.896484
$879$	−21.2577	−0.717006
$880$	3.07644	0.103707
$881$	−23.6818	−0.797860	−0.398930	−	0.916981i	$-0.630618\pi$
$881$	−23.6818	−0.797860	−0.398930	+	0.916981i	$0.630618\pi$
$882$	7.15155	0.240805
$883$	−36.9127	−1.24221	−0.621106	−	0.783727i	$-0.713316\pi$
$883$	−36.9127	−1.24221	−0.621106	+	0.783727i	$0.713316\pi$
$884$	−14.7191	−0.495056
$885$	0.972503	0.0326903
$886$	38.7518	1.30189
$887$	17.4984	0.587539	0.293769	−	0.955876i	$-0.405090\pi$
$887$	17.4984	0.587539	0.293769	+	0.955876i	$0.405090\pi$
$888$	18.2836	0.613557
$889$	8.33287	0.279475
$890$	13.0704	0.438122
$891$	−30.9995	−1.03852
$892$	25.8466	0.865408
$893$	35.4675	1.18687
$894$	−22.7229	−0.759969
$895$	−20.5584	−0.687190
$896$	−3.11298	−0.103997
$897$	14.6202	0.488154
$898$	−24.3325	−0.811985
$899$	3.95395	0.131872
$900$	−10.7192	−0.357305
$901$	33.1538	1.10451
$902$	33.7849	1.12491
$903$	36.8419	1.22602
$904$	17.1459	0.570265
$905$	−19.2837	−0.641012
$906$	23.4269	0.778306
$907$	−10.7055	−0.355471	−0.177736	−	0.984078i	$-0.556877\pi$
$907$	−10.7055	−0.355471	−0.177736	+	0.984078i	$0.556877\pi$
$908$	−9.24216	−0.306712
$909$	−2.55929	−0.0848864
$910$	18.8163	0.623755
$911$	−16.6335	−0.551093	−0.275547	−	0.961288i	$-0.588859\pi$
$911$	−16.6335	−0.551093	−0.275547	+	0.961288i	$0.588859\pi$
$912$	−19.4478	−0.643980
$913$	30.4996	1.00939
$914$	35.5848	1.17704
$915$	−25.9897	−0.859192
$916$	12.6821	0.419027
$917$	−57.0209	−1.88300
$918$	1.94854	0.0643115
$919$	−6.18369	−0.203981	−0.101991	−	0.994785i	$-0.532521\pi$
$919$	−6.18369	−0.203981	−0.101991	+	0.994785i	$0.532521\pi$
$920$	0.983407	0.0324220
$921$	−10.1140	−0.333269
$922$	−12.3986	−0.408327
$923$	−4.96175	−0.163318
$924$	23.1643	0.762050
$925$	30.9993	1.01925
$926$	27.6470	0.908536
$927$	17.7730	0.583743
$928$	1.00000	0.0328266
$929$	−0.258796	−0.00849084	−0.00424542	−	0.999991i	$-0.501351\pi$
$929$	−0.258796	−0.00849084	−0.00424542	+	0.999991i	$0.501351\pi$
$930$	−9.24895	−0.303285
$931$	21.9988	0.720982
$932$	−7.33914	−0.240402
$933$	−51.9632	−1.70120
$934$	0.518206	0.0169562
$935$	7.36721	0.240934
$936$	−16.3368	−0.533985
$937$	−25.7682	−0.841812	−0.420906	−	0.907104i	$-0.638288\pi$
$937$	−25.7682	−0.841812	−0.420906	+	0.907104i	$0.638288\pi$
$938$	13.6217	0.444765
$939$	−2.47149	−0.0806539
$940$	4.26602	0.139142
$941$	−44.4078	−1.44765	−0.723827	−	0.689982i	$-0.757619\pi$
$941$	−44.4078	−1.44765	−0.723827	+	0.689982i	$0.757619\pi$
$942$	44.5699	1.45216
$943$	10.7996	0.351683
$944$	−0.415747	−0.0135314
$945$	−2.49095	−0.0810305
$946$	15.5651	0.506065
$947$	−40.9488	−1.33066	−0.665329	−	0.746550i	$-0.731709\pi$
$947$	−40.9488	−1.33066	−0.665329	+	0.746550i	$0.731709\pi$
$948$	−7.65135	−0.248504
$949$	80.6060	2.61658
$950$	−32.9731	−1.06979
$951$	2.89970	0.0940291
$952$	−7.45473	−0.241609
$953$	−26.6855	−0.864428	−0.432214	−	0.901771i	$-0.642268\pi$
$953$	−26.6855	−0.864428	−0.432214	+	0.901771i	$0.642268\pi$
$954$	36.7977	1.19137
$955$	−13.7259	−0.444161
$956$	−22.3329	−0.722298
$957$	−7.44120	−0.240540
$958$	4.50475	0.145542
$959$	10.9270	0.352852
$960$	−2.33917	−0.0754964
$961$	−15.3663	−0.495687
$962$	47.2452	1.52325
$963$	32.6568	1.05235
$964$	2.00939	0.0647180
$965$	7.03458	0.226451
$966$	7.40466	0.238241
$967$	31.7301	1.02037	0.510185	−	0.860065i	$-0.329577\pi$
$967$	31.7301	1.02037	0.510185	+	0.860065i	$0.329577\pi$
$968$	−1.21346	−0.0390020
$969$	−46.5720	−1.49611
$970$	−2.95998	−0.0950391
$971$	28.1594	0.903680	0.451840	−	0.892099i	$-0.350768\pi$
$971$	28.1594	0.903680	0.451840	+	0.892099i	$0.350768\pi$
$972$	21.1294	0.677726
$973$	15.8813	0.509130
$974$	10.8435	0.347448
$975$	−58.9619	−1.88829
$976$	11.1106	0.355643
$977$	−8.77864	−0.280854	−0.140427	−	0.990091i	$-0.544847\pi$
$977$	−8.77864	−0.280854	−0.140427	+	0.990091i	$0.544847\pi$
$978$	−7.43126	−0.237625
$979$	41.5787	1.32886
$980$	2.64601	0.0845236
$981$	−36.4237	−1.16292
$982$	7.96879	0.254294
$983$	37.3193	1.19030	0.595151	−	0.803614i	$-0.297092\pi$
$983$	37.3193	1.19030	0.595151	+	0.803614i	$0.297092\pi$
$984$	−25.6883	−0.818914
$985$	−22.2375	−0.708545
$986$	2.39472	0.0762635
$987$	32.1214	1.02243
$988$	−50.2535	−1.59878
$989$	4.97550	0.158212
$990$	8.17693	0.259880
$991$	12.8401	0.407880	0.203940	−	0.978983i	$-0.434625\pi$
$991$	12.8401	0.407880	0.203940	+	0.978983i	$0.434625\pi$
$992$	3.95395	0.125538
$993$	−54.3747	−1.72553
$994$	−2.51296	−0.0797064
$995$	13.5157	0.428477
$996$	−23.1904	−0.734815
$997$	46.1807	1.46256	0.731279	−	0.682078i	$-0.238924\pi$
$997$	46.1807	1.46256	0.731279	+	0.682078i	$0.238924\pi$
$998$	−38.5911	−1.22158
$999$	−6.25442	−0.197881

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1334.2.a.k.1.1	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1334.2.a.k.1.1	✓	10	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:	\( N \)	\(=\)	\( 1334 = 2 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1334.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.37864 q^{3} +1.00000 q^{4} +0.983407 q^{5} -2.37864 q^{6} -3.11298 q^{7} +1.00000 q^{8} +2.65792 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.37864 q^{3} +1.00000 q^{4} +0.983407 q^{5} -2.37864 q^{6} -3.11298 q^{7} +1.00000 q^{8} +2.65792 q^{9} +0.983407 q^{10} +3.12835 q^{11} -2.37864 q^{12} -6.14646 q^{13} -3.11298 q^{14} -2.33917 q^{15} +1.00000 q^{16} +2.39472 q^{17} +2.65792 q^{18} +8.17601 q^{19} +0.983407 q^{20} +7.40466 q^{21} +3.12835 q^{22} +1.00000 q^{23} -2.37864 q^{24} -4.03291 q^{25} -6.14646 q^{26} +0.813682 q^{27} -3.11298 q^{28} +1.00000 q^{29} -2.33917 q^{30} +3.95395 q^{31} +1.00000 q^{32} -7.44120 q^{33} +2.39472 q^{34} -3.06133 q^{35} +2.65792 q^{36} -7.68657 q^{37} +8.17601 q^{38} +14.6202 q^{39} +0.983407 q^{40} +10.7996 q^{41} +7.40466 q^{42} +4.97550 q^{43} +3.12835 q^{44} +2.61382 q^{45} +1.00000 q^{46} +4.33800 q^{47} -2.37864 q^{48} +2.69065 q^{49} -4.03291 q^{50} -5.69618 q^{51} -6.14646 q^{52} +13.8445 q^{53} +0.813682 q^{54} +3.07644 q^{55} -3.11298 q^{56} -19.4478 q^{57} +1.00000 q^{58} -0.415747 q^{59} -2.33917 q^{60} +11.1106 q^{61} +3.95395 q^{62} -8.27406 q^{63} +1.00000 q^{64} -6.04447 q^{65} -7.44120 q^{66} -4.37578 q^{67} +2.39472 q^{68} -2.37864 q^{69} -3.06133 q^{70} +0.807253 q^{71} +2.65792 q^{72} -13.1142 q^{73} -7.68657 q^{74} +9.59284 q^{75} +8.17601 q^{76} -9.73848 q^{77} +14.6202 q^{78} +3.21669 q^{79} +0.983407 q^{80} -9.90922 q^{81} +10.7996 q^{82} +9.74943 q^{83} +7.40466 q^{84} +2.35499 q^{85} +4.97550 q^{86} -2.37864 q^{87} +3.12835 q^{88} +13.2910 q^{89} +2.61382 q^{90} +19.1338 q^{91} +1.00000 q^{92} -9.40501 q^{93} +4.33800 q^{94} +8.04035 q^{95} -2.37864 q^{96} -3.00992 q^{97} +2.69065 q^{98} +8.31489 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} + 5 q^{3} + 10 q^{4} - q^{5} + 5 q^{6} + 2 q^{7} + 10 q^{8} + 11 q^{9}+O(q^{10}) \) 10 * q + 10 * q^2 + 5 * q^3 + 10 * q^4 - q^5 + 5 * q^6 + 2 * q^7 + 10 * q^8 + 11 * q^9	\( 10 q + 10 q^{2} + 5 q^{3} + 10 q^{4} - q^{5} + 5 q^{6} + 2 q^{7} + 10 q^{8} + 11 q^{9} - q^{10} + q^{11} + 5 q^{12} + 9 q^{13} + 2 q^{14} + 5 q^{15} + 10 q^{16} + 11 q^{18} + 20 q^{19} - q^{20} + 14 q^{21} + q^{22} + 10 q^{23} + 5 q^{24} + 23 q^{25} + 9 q^{26} + 23 q^{27} + 2 q^{28} + 10 q^{29} + 5 q^{30} + 21 q^{31} + 10 q^{32} + q^{33} + 2 q^{35} + 11 q^{36} - 8 q^{37} + 20 q^{38} + 23 q^{39} - q^{40} - 4 q^{41} + 14 q^{42} - 3 q^{43} + q^{44} - 18 q^{45} + 10 q^{46} - q^{47} + 5 q^{48} + 18 q^{49} + 23 q^{50} - 6 q^{51} + 9 q^{52} - 13 q^{53} + 23 q^{54} + 13 q^{55} + 2 q^{56} - 22 q^{57} + 10 q^{58} + 14 q^{59} + 5 q^{60} + 12 q^{61} + 21 q^{62} - 26 q^{63} + 10 q^{64} - 25 q^{65} + q^{66} + 6 q^{67} + 5 q^{69} + 2 q^{70} + 8 q^{71} + 11 q^{72} + 16 q^{73} - 8 q^{74} + 8 q^{75} + 20 q^{76} - 16 q^{77} + 23 q^{78} + 7 q^{79} - q^{80} - 2 q^{81} - 4 q^{82} + 18 q^{83} + 14 q^{84} + 8 q^{85} - 3 q^{86} + 5 q^{87} + q^{88} + 2 q^{89} - 18 q^{90} + 8 q^{91} + 10 q^{92} - 41 q^{93} - q^{94} - 16 q^{95} + 5 q^{96} + 6 q^{97} + 18 q^{98} - 22 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 + 5 * q^3 + 10 * q^4 - q^5 + 5 * q^6 + 2 * q^7 + 10 * q^8 + 11 * q^9 - q^10 + q^11 + 5 * q^12 + 9 * q^13 + 2 * q^14 + 5 * q^15 + 10 * q^16 + 11 * q^18 + 20 * q^19 - q^20 + 14 * q^21 + q^22 + 10 * q^23 + 5 * q^24 + 23 * q^25 + 9 * q^26 + 23 * q^27 + 2 * q^28 + 10 * q^29 + 5 * q^30 + 21 * q^31 + 10 * q^32 + q^33 + 2 * q^35 + 11 * q^36 - 8 * q^37 + 20 * q^38 + 23 * q^39 - q^40 - 4 * q^41 + 14 * q^42 - 3 * q^43 + q^44 - 18 * q^45 + 10 * q^46 - q^47 + 5 * q^48 + 18 * q^49 + 23 * q^50 - 6 * q^51 + 9 * q^52 - 13 * q^53 + 23 * q^54 + 13 * q^55 + 2 * q^56 - 22 * q^57 + 10 * q^58 + 14 * q^59 + 5 * q^60 + 12 * q^61 + 21 * q^62 - 26 * q^63 + 10 * q^64 - 25 * q^65 + q^66 + 6 * q^67 + 5 * q^69 + 2 * q^70 + 8 * q^71 + 11 * q^72 + 16 * q^73 - 8 * q^74 + 8 * q^75 + 20 * q^76 - 16 * q^77 + 23 * q^78 + 7 * q^79 - q^80 - 2 * q^81 - 4 * q^82 + 18 * q^83 + 14 * q^84 + 8 * q^85 - 3 * q^86 + 5 * q^87 + q^88 + 2 * q^89 - 18 * q^90 + 8 * q^91 + 10 * q^92 - 41 * q^93 - q^94 - 16 * q^95 + 5 * q^96 + 6 * q^97 + 18 * q^98 - 22 * q^99

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