LMFDB - Embedded newform 1045.2.a.j.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,2,Mod(1,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1045.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1045.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:	$8.34436701122$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 2x^{8} - 11x^{7} + 11x^{6} + 34x^{5} - 20x^{4} - 36x^{3} + 13x^{2} + 10x - 2 $ x^9 - 2x^8 - 11x^7 + 11x^6 + 34x^5 - 20x^4 - 36x^3 + 13x^2 + 10x - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$0.180277$ of defining polynomial
Character	$\chi$	$=$	1045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.287410 q^{2} -0.930455 q^{3} -1.91740 q^{4} -1.00000 q^{5} -0.267422 q^{6} +0.300889 q^{7} -1.12590 q^{8} -2.13425 q^{9} +O(q^{10})$	\(q+0.287410 q^{2} -0.930455 q^{3} -1.91740 q^{4} -1.00000 q^{5} -0.267422 q^{6} +0.300889 q^{7} -1.12590 q^{8} -2.13425 q^{9} -0.287410 q^{10} -1.00000 q^{11} +1.78405 q^{12} +0.796803 q^{13} +0.0864787 q^{14} +0.930455 q^{15} +3.51120 q^{16} -3.82150 q^{17} -0.613406 q^{18} +1.00000 q^{19} +1.91740 q^{20} -0.279964 q^{21} -0.287410 q^{22} +2.58740 q^{23} +1.04760 q^{24} +1.00000 q^{25} +0.229009 q^{26} +4.77719 q^{27} -0.576924 q^{28} +2.75028 q^{29} +0.267422 q^{30} -4.77493 q^{31} +3.26095 q^{32} +0.930455 q^{33} -1.09834 q^{34} -0.300889 q^{35} +4.09221 q^{36} +6.47899 q^{37} +0.287410 q^{38} -0.741390 q^{39} +1.12590 q^{40} +12.6694 q^{41} -0.0804645 q^{42} -6.23579 q^{43} +1.91740 q^{44} +2.13425 q^{45} +0.743646 q^{46} +12.4574 q^{47} -3.26701 q^{48} -6.90947 q^{49} +0.287410 q^{50} +3.55574 q^{51} -1.52779 q^{52} +1.49641 q^{53} +1.37301 q^{54} +1.00000 q^{55} -0.338771 q^{56} -0.930455 q^{57} +0.790457 q^{58} -0.530465 q^{59} -1.78405 q^{60} +6.48095 q^{61} -1.37236 q^{62} -0.642174 q^{63} -6.08516 q^{64} -0.796803 q^{65} +0.267422 q^{66} -4.09752 q^{67} +7.32734 q^{68} -2.40746 q^{69} -0.0864787 q^{70} +16.3846 q^{71} +2.40295 q^{72} +10.1800 q^{73} +1.86213 q^{74} -0.930455 q^{75} -1.91740 q^{76} -0.300889 q^{77} -0.213083 q^{78} +1.50592 q^{79} -3.51120 q^{80} +1.95780 q^{81} +3.64132 q^{82} -13.4051 q^{83} +0.536802 q^{84} +3.82150 q^{85} -1.79223 q^{86} -2.55901 q^{87} +1.12590 q^{88} -16.0559 q^{89} +0.613406 q^{90} +0.239750 q^{91} -4.96108 q^{92} +4.44286 q^{93} +3.58038 q^{94} -1.00000 q^{95} -3.03417 q^{96} +2.48228 q^{97} -1.98585 q^{98} +2.13425 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 3 q^{2} + 3 q^{3} + 9 q^{4} - 9 q^{5} + 6 q^{6} - 9 q^{7} + 15 q^{8} + 16 q^{9}+O(q^{10}) $ 9 * q + 3 * q^2 + 3 * q^3 + 9 * q^4 - 9 * q^5 + 6 * q^6 - 9 * q^7 + 15 * q^8 + 16 * q^9	\( 9 q + 3 q^{2} + 3 q^{3} + 9 q^{4} - 9 q^{5} + 6 q^{6} - 9 q^{7} + 15 q^{8} + 16 q^{9} - 3 q^{10} - 9 q^{11} + 13 q^{12} - 3 q^{13} + 4 q^{14} - 3 q^{15} + 17 q^{16} + 5 q^{17} + 17 q^{18} + 9 q^{19} - 9 q^{20} - q^{21} - 3 q^{22} + 4 q^{23} + 21 q^{24} + 9 q^{25} + 20 q^{26} + 24 q^{27} - 24 q^{28} + 3 q^{29} - 6 q^{30} - q^{31} + 38 q^{32} - 3 q^{33} + 28 q^{34} + 9 q^{35} + 17 q^{36} + 5 q^{37} + 3 q^{38} - 15 q^{40} - 5 q^{41} - 43 q^{42} - 11 q^{43} - 9 q^{44} - 16 q^{45} + 2 q^{46} + 30 q^{47} + 54 q^{48} + 12 q^{49} + 3 q^{50} + 40 q^{51} - 3 q^{52} - q^{53} + 65 q^{54} + 9 q^{55} - 16 q^{56} + 3 q^{57} - 15 q^{58} + 59 q^{59} - 13 q^{60} - 21 q^{61} - 10 q^{62} - 12 q^{63} + 19 q^{64} + 3 q^{65} - 6 q^{66} - 2 q^{67} - 9 q^{68} - 22 q^{69} - 4 q^{70} + 34 q^{71} + 32 q^{72} - 34 q^{73} - 21 q^{74} + 3 q^{75} + 9 q^{76} + 9 q^{77} - 65 q^{78} - 13 q^{79} - 17 q^{80} + 57 q^{81} + 10 q^{82} + 51 q^{83} - 95 q^{84} - 5 q^{85} - 14 q^{86} + 8 q^{87} - 15 q^{88} + 8 q^{89} - 17 q^{90} + 62 q^{91} + 57 q^{92} - 18 q^{93} + 2 q^{94} - 9 q^{95} + 81 q^{96} - 8 q^{97} - 20 q^{98} - 16 q^{99}+O(q^{100}) \) 9 * q + 3 * q^2 + 3 * q^3 + 9 * q^4 - 9 * q^5 + 6 * q^6 - 9 * q^7 + 15 * q^8 + 16 * q^9 - 3 * q^10 - 9 * q^11 + 13 * q^12 - 3 * q^13 + 4 * q^14 - 3 * q^15 + 17 * q^16 + 5 * q^17 + 17 * q^18 + 9 * q^19 - 9 * q^20 - q^21 - 3 * q^22 + 4 * q^23 + 21 * q^24 + 9 * q^25 + 20 * q^26 + 24 * q^27 - 24 * q^28 + 3 * q^29 - 6 * q^30 - q^31 + 38 * q^32 - 3 * q^33 + 28 * q^34 + 9 * q^35 + 17 * q^36 + 5 * q^37 + 3 * q^38 - 15 * q^40 - 5 * q^41 - 43 * q^42 - 11 * q^43 - 9 * q^44 - 16 * q^45 + 2 * q^46 + 30 * q^47 + 54 * q^48 + 12 * q^49 + 3 * q^50 + 40 * q^51 - 3 * q^52 - q^53 + 65 * q^54 + 9 * q^55 - 16 * q^56 + 3 * q^57 - 15 * q^58 + 59 * q^59 - 13 * q^60 - 21 * q^61 - 10 * q^62 - 12 * q^63 + 19 * q^64 + 3 * q^65 - 6 * q^66 - 2 * q^67 - 9 * q^68 - 22 * q^69 - 4 * q^70 + 34 * q^71 + 32 * q^72 - 34 * q^73 - 21 * q^74 + 3 * q^75 + 9 * q^76 + 9 * q^77 - 65 * q^78 - 13 * q^79 - 17 * q^80 + 57 * q^81 + 10 * q^82 + 51 * q^83 - 95 * q^84 - 5 * q^85 - 14 * q^86 + 8 * q^87 - 15 * q^88 + 8 * q^89 - 17 * q^90 + 62 * q^91 + 57 * q^92 - 18 * q^93 + 2 * q^94 - 9 * q^95 + 81 * q^96 - 8 * q^97 - 20 * q^98 - 16 * 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 $

$2$	0.287410	0.203230	0.101615	−	0.994824i	$-0.467599\pi$
$2$	0.287410	0.203230	0.101615	+	0.994824i	$0.467599\pi$
$3$	−0.930455	−0.537199	−0.268599	−	0.963252i	$-0.586561\pi$
$3$	−0.930455	−0.537199	−0.268599	+	0.963252i	$0.586561\pi$
$4$	−1.91740	−0.958698
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.267422	−0.109175
$7$	0.300889	0.113726	0.0568628	−	0.998382i	$-0.481890\pi$
$7$	0.300889	0.113726	0.0568628	+	0.998382i	$0.481890\pi$
$8$	−1.12590	−0.398065
$9$	−2.13425	−0.711418
$10$	−0.287410	−0.0908871
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.78405	0.515011
$13$	0.796803	0.220993	0.110497	−	0.993876i	$-0.464756\pi$
$13$	0.796803	0.220993	0.110497	+	0.993876i	$0.464756\pi$
$14$	0.0864787	0.0231124
$15$	0.930455	0.240242
$16$	3.51120	0.877799
$17$	−3.82150	−0.926851	−0.463425	−	0.886136i	$-0.653380\pi$
$17$	−3.82150	−0.926851	−0.463425	+	0.886136i	$0.653380\pi$
$18$	−0.613406	−0.144581
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	1.91740	0.428743
$21$	−0.279964	−0.0610932
$22$	−0.287410	−0.0612760
$23$	2.58740	0.539511	0.269756	−	0.962929i	$-0.413057\pi$
$23$	2.58740	0.539511	0.269756	+	0.962929i	$0.413057\pi$
$24$	1.04760	0.213840
$25$	1.00000	0.200000
$26$	0.229009	0.0449124
$27$	4.77719	0.919371
$28$	−0.576924	−0.109028
$29$	2.75028	0.510713	0.255357	−	0.966847i	$-0.417807\pi$
$29$	2.75028	0.510713	0.255357	+	0.966847i	$0.417807\pi$
$30$	0.267422	0.0488244
$31$	−4.77493	−0.857603	−0.428802	−	0.903399i	$-0.641064\pi$
$31$	−4.77493	−0.857603	−0.428802	+	0.903399i	$0.641064\pi$
$32$	3.26095	0.576460
$33$	0.930455	0.161971
$34$	−1.09834	−0.188364
$35$	−0.300889	−0.0508596
$36$	4.09221	0.682035
$37$	6.47899	1.06514	0.532570	−	0.846386i	$-0.321226\pi$
$37$	6.47899	1.06514	0.532570	+	0.846386i	$0.321226\pi$
$38$	0.287410	0.0466241
$39$	−0.741390	−0.118717
$40$	1.12590	0.178020
$41$	12.6694	1.97863	0.989317	−	0.145781i	$-0.0465694\pi$
$41$	12.6694	1.97863	0.989317	+	0.145781i	$0.0465694\pi$
$42$	−0.0804645	−0.0124159
$43$	−6.23579	−0.950949	−0.475474	−	0.879730i	$-0.657724\pi$
$43$	−6.23579	−0.950949	−0.475474	+	0.879730i	$0.657724\pi$
$44$	1.91740	0.289058
$45$	2.13425	0.318156
$46$	0.743646	0.109645
$47$	12.4574	1.81710	0.908549	−	0.417778i	$-0.137191\pi$
$47$	12.4574	1.81710	0.908549	+	0.417778i	$0.137191\pi$
$48$	−3.26701	−0.471552
$49$	−6.90947	−0.987067
$50$	0.287410	0.0406459
$51$	3.55574	0.497903
$52$	−1.52779	−0.211866
$53$	1.49641	0.205548	0.102774	−	0.994705i	$-0.467228\pi$
$53$	1.49641	0.205548	0.102774	+	0.994705i	$0.467228\pi$
$54$	1.37301	0.186843
$55$	1.00000	0.134840
$56$	−0.338771	−0.0452702
$57$	−0.930455	−0.123242
$58$	0.790457	0.103792
$59$	−0.530465	−0.0690607	−0.0345303	−	0.999404i	$-0.510994\pi$
$59$	−0.530465	−0.0690607	−0.0345303	+	0.999404i	$0.510994\pi$
$60$	−1.78405	−0.230320
$61$	6.48095	0.829801	0.414900	−	0.909867i	$-0.363816\pi$
$61$	6.48095	0.829801	0.414900	+	0.909867i	$0.363816\pi$
$62$	−1.37236	−0.174290
$63$	−0.642174	−0.0809064
$64$	−6.08516	−0.760645
$65$	−0.796803	−0.0988313
$66$	0.267422	0.0329174
$67$	−4.09752	−0.500592	−0.250296	−	0.968169i	$-0.580528\pi$
$67$	−4.09752	−0.500592	−0.250296	+	0.968169i	$0.580528\pi$
$68$	7.32734	0.888570
$69$	−2.40746	−0.289825
$70$	−0.0864787	−0.0103362
$71$	16.3846	1.94450	0.972249	−	0.233950i	$-0.0751652\pi$
$71$	16.3846	1.94450	0.972249	+	0.233950i	$0.0751652\pi$
$72$	2.40295	0.283191
$73$	10.1800	1.19148	0.595741	−	0.803177i	$-0.296859\pi$
$73$	10.1800	1.19148	0.595741	+	0.803177i	$0.296859\pi$
$74$	1.86213	0.216468
$75$	−0.930455	−0.107440
$76$	−1.91740	−0.219940
$77$	−0.300889	−0.0342895
$78$	−0.213083	−0.0241269
$79$	1.50592	0.169429	0.0847147	−	0.996405i	$-0.473002\pi$
$79$	1.50592	0.169429	0.0847147	+	0.996405i	$0.473002\pi$
$80$	−3.51120	−0.392564
$81$	1.95780	0.217533
$82$	3.64132	0.402117
$83$	−13.4051	−1.47140	−0.735700	−	0.677307i	$-0.763147\pi$
$83$	−13.4051	−1.47140	−0.735700	+	0.677307i	$0.763147\pi$
$84$	0.536802	0.0585699
$85$	3.82150	0.414500
$86$	−1.79223	−0.193261
$87$	−2.55901	−0.274355
$88$	1.12590	0.120021
$89$	−16.0559	−1.70193	−0.850963	−	0.525226i	$-0.823981\pi$
$89$	−16.0559	−1.70193	−0.850963	+	0.525226i	$0.823981\pi$
$90$	0.613406	0.0646587
$91$	0.239750	0.0251326
$92$	−4.96108	−0.517228
$93$	4.44286	0.460703
$94$	3.58038	0.369288
$95$	−1.00000	−0.102598
$96$	−3.03417	−0.309674
$97$	2.48228	0.252037	0.126019	−	0.992028i	$-0.459780\pi$
$97$	2.48228	0.252037	0.126019	+	0.992028i	$0.459780\pi$
$98$	−1.98585	−0.200601
$99$	2.13425	0.214501
$100$	−1.91740	−0.191740
$101$	−2.58271	−0.256990	−0.128495	−	0.991710i	$-0.541015\pi$
$101$	−2.58271	−0.256990	−0.128495	+	0.991710i	$0.541015\pi$
$102$	1.02196	0.101189
$103$	6.55810	0.646188	0.323094	−	0.946367i	$-0.395277\pi$
$103$	6.55810	0.646188	0.323094	+	0.946367i	$0.395277\pi$
$104$	−0.897120	−0.0879698
$105$	0.279964	0.0273217
$106$	0.430084	0.0417735
$107$	12.9662	1.25349	0.626745	−	0.779224i	$-0.284387\pi$
$107$	12.9662	1.25349	0.626745	+	0.779224i	$0.284387\pi$
$108$	−9.15977	−0.881399
$109$	19.5865	1.87605	0.938025	−	0.346567i	$-0.112653\pi$
$109$	19.5865	1.87605	0.938025	+	0.346567i	$0.112653\pi$
$110$	0.287410	0.0274035
$111$	−6.02841	−0.572191
$112$	1.05648	0.0998282
$113$	−8.89555	−0.836823	−0.418411	−	0.908258i	$-0.637413\pi$
$113$	−8.89555	−0.836823	−0.418411	+	0.908258i	$0.637413\pi$
$114$	−0.267422	−0.0250464
$115$	−2.58740	−0.241277
$116$	−5.27337	−0.489620
$117$	−1.70058	−0.157219
$118$	−0.152461	−0.0140352
$119$	−1.14985	−0.105407
$120$	−1.04760	−0.0956322
$121$	1.00000	0.0909091
$122$	1.86269	0.168640
$123$	−11.7883	−1.06292
$124$	9.15543	0.822182
$125$	−1.00000	−0.0894427
$126$	−0.184567	−0.0164426
$127$	−14.4276	−1.28024	−0.640122	−	0.768273i	$-0.721116\pi$
$127$	−14.4276	−1.28024	−0.640122	+	0.768273i	$0.721116\pi$
$128$	−8.27084	−0.731046
$129$	5.80212	0.510848
$130$	−0.229009	−0.0200854
$131$	21.1109	1.84447	0.922235	−	0.386630i	$-0.126361\pi$
$131$	21.1109	1.84447	0.922235	+	0.386630i	$0.126361\pi$
$132$	−1.78405	−0.155282
$133$	0.300889	0.0260904
$134$	−1.17767	−0.101735
$135$	−4.77719	−0.411155
$136$	4.30263	0.368947
$137$	−10.0358	−0.857420	−0.428710	−	0.903442i	$-0.641032\pi$
$137$	−10.0358	−0.857420	−0.428710	+	0.903442i	$0.641032\pi$
$138$	−0.691929	−0.0589009
$139$	−0.827999	−0.0702299	−0.0351150	−	0.999383i	$-0.511180\pi$
$139$	−0.827999	−0.0702299	−0.0351150	+	0.999383i	$0.511180\pi$
$140$	0.576924	0.0487590
$141$	−11.5910	−0.976142
$142$	4.70911	0.395179
$143$	−0.796803	−0.0666320
$144$	−7.49378	−0.624482
$145$	−2.75028	−0.228398
$146$	2.92584	0.242144
$147$	6.42895	0.530251
$148$	−12.4228	−1.02115
$149$	6.21556	0.509198	0.254599	−	0.967047i	$-0.418056\pi$
$149$	6.21556	0.509198	0.254599	+	0.967047i	$0.418056\pi$
$150$	−0.267422	−0.0218349
$151$	−7.97182	−0.648737	−0.324369	−	0.945931i	$-0.605152\pi$
$151$	−7.97182	−0.648737	−0.324369	+	0.945931i	$0.605152\pi$
$152$	−1.12590	−0.0913225
$153$	8.15606	0.659378
$154$	−0.0864787	−0.00696865
$155$	4.77493	0.383532
$156$	1.42154	0.113814
$157$	−19.9704	−1.59381	−0.796905	−	0.604104i	$-0.793531\pi$
$157$	−19.9704	−1.59381	−0.796905	+	0.604104i	$0.793531\pi$
$158$	0.432817	0.0344331
$159$	−1.39235	−0.110420
$160$	−3.26095	−0.257801
$161$	0.778523	0.0613562
$162$	0.562691	0.0442091
$163$	−18.7206	−1.46631	−0.733155	−	0.680062i	$-0.761953\pi$
$163$	−18.7206	−1.46631	−0.733155	+	0.680062i	$0.761953\pi$
$164$	−24.2923	−1.89691
$165$	−0.930455	−0.0724358
$166$	−3.85276	−0.299032
$167$	−6.43830	−0.498211	−0.249105	−	0.968476i	$-0.580137\pi$
$167$	−6.43830	−0.498211	−0.249105	+	0.968476i	$0.580137\pi$
$168$	0.315211	0.0243191
$169$	−12.3651	−0.951162
$170$	1.09834	0.0842388
$171$	−2.13425	−0.163210
$172$	11.9565	0.911672
$173$	−10.8623	−0.825844	−0.412922	−	0.910766i	$-0.635492\pi$
$173$	−10.8623	−0.825844	−0.412922	+	0.910766i	$0.635492\pi$
$174$	−0.735485	−0.0557570
$175$	0.300889	0.0227451
$176$	−3.51120	−0.264666
$177$	0.493574	0.0370993
$178$	−4.61464	−0.345882
$179$	17.8897	1.33714	0.668571	−	0.743648i	$-0.266906\pi$
$179$	17.8897	1.33714	0.668571	+	0.743648i	$0.266906\pi$
$180$	−4.09221	−0.305015
$181$	8.92287	0.663231	0.331616	−	0.943415i	$-0.392406\pi$
$181$	8.92287	0.663231	0.331616	+	0.943415i	$0.392406\pi$
$182$	0.0689065	0.00510769
$183$	−6.03023	−0.445768
$184$	−2.91316	−0.214761
$185$	−6.47899	−0.476345
$186$	1.27692	0.0936285
$187$	3.82150	0.279456
$188$	−23.8858	−1.74205
$189$	1.43741	0.104556
$190$	−0.287410	−0.0208509
$191$	8.56736	0.619912	0.309956	−	0.950751i	$-0.399686\pi$
$191$	8.56736	0.619912	0.309956	+	0.950751i	$0.399686\pi$
$192$	5.66197	0.408617
$193$	−3.27493	−0.235735	−0.117867	−	0.993029i	$-0.537606\pi$
$193$	−3.27493	−0.235735	−0.117867	+	0.993029i	$0.537606\pi$
$194$	0.713432	0.0512214
$195$	0.741390	0.0530920
$196$	13.2482	0.946298
$197$	−4.71636	−0.336027	−0.168013	−	0.985785i	$-0.553735\pi$
$197$	−4.71636	−0.336027	−0.168013	+	0.985785i	$0.553735\pi$
$198$	0.613406	0.0435929
$199$	20.2575	1.43601	0.718006	−	0.696036i	$-0.245055\pi$
$199$	20.2575	1.43601	0.718006	+	0.696036i	$0.245055\pi$
$200$	−1.12590	−0.0796131
$201$	3.81256	0.268917
$202$	−0.742298	−0.0522279
$203$	0.827529	0.0580812
$204$	−6.81776	−0.477338
$205$	−12.6694	−0.884872
$206$	1.88486	0.131325
$207$	−5.52218	−0.383818
$208$	2.79773	0.193988
$209$	−1.00000	−0.0691714
$210$	0.0804645	0.00555258
$211$	25.8874	1.78216	0.891080	−	0.453847i	$-0.149949\pi$
$211$	25.8874	1.78216	0.891080	+	0.453847i	$0.149949\pi$
$212$	−2.86922	−0.197059
$213$	−15.2452	−1.04458
$214$	3.72662	0.254746
$215$	6.23579	0.425277
$216$	−5.37864	−0.365970
$217$	−1.43673	−0.0975313
$218$	5.62937	0.381269
$219$	−9.47205	−0.640062
$220$	−1.91740	−0.129271
$221$	−3.04499	−0.204828
$222$	−1.73263	−0.116286
$223$	14.4668	0.968767	0.484384	−	0.874856i	$-0.339044\pi$
$223$	14.4668	0.968767	0.484384	+	0.874856i	$0.339044\pi$
$224$	0.981186	0.0655582
$225$	−2.13425	−0.142284
$226$	−2.55667	−0.170067
$227$	11.0768	0.735196	0.367598	−	0.929985i	$-0.380180\pi$
$227$	11.0768	0.735196	0.367598	+	0.929985i	$0.380180\pi$
$228$	1.78405	0.118152
$229$	−15.3259	−1.01276	−0.506382	−	0.862309i	$-0.669017\pi$
$229$	−15.3259	−1.01276	−0.506382	+	0.862309i	$0.669017\pi$
$230$	−0.743646	−0.0490346
$231$	0.279964	0.0184203
$232$	−3.09653	−0.203297
$233$	23.0652	1.51105	0.755527	−	0.655118i	$-0.227381\pi$
$233$	23.0652	1.51105	0.755527	+	0.655118i	$0.227381\pi$
$234$	−0.488764	−0.0319515
$235$	−12.4574	−0.812631
$236$	1.01711	0.0662083
$237$	−1.40119	−0.0910172
$238$	−0.330479	−0.0214217
$239$	22.7153	1.46933	0.734665	−	0.678430i	$-0.237339\pi$
$239$	22.7153	1.46933	0.734665	+	0.678430i	$0.237339\pi$
$240$	3.26701	0.210885
$241$	−21.3744	−1.37685	−0.688423	−	0.725310i	$-0.741697\pi$
$241$	−21.3744	−1.37685	−0.688423	+	0.725310i	$0.741697\pi$
$242$	0.287410	0.0184754
$243$	−16.1532	−1.03623
$244$	−12.4265	−0.795528
$245$	6.90947	0.441430
$246$	−3.38809	−0.216017
$247$	0.796803	0.0506994
$248$	5.37609	0.341382
$249$	12.4728	0.790434
$250$	−0.287410	−0.0181774
$251$	−17.3878	−1.09751	−0.548754	−	0.835984i	$-0.684898\pi$
$251$	−17.3878	−1.09751	−0.548754	+	0.835984i	$0.684898\pi$
$252$	1.23130	0.0775647
$253$	−2.58740	−0.162669
$254$	−4.14664	−0.260184
$255$	−3.55574	−0.222669
$256$	9.79320	0.612075
$257$	30.6254	1.91036	0.955179	−	0.296027i	$-0.0956619\pi$
$257$	30.6254	1.91036	0.955179	+	0.296027i	$0.0956619\pi$
$258$	1.66759	0.103820
$259$	1.94946	0.121133
$260$	1.52779	0.0947493
$261$	−5.86979	−0.363331
$262$	6.06749	0.374851
$263$	−0.894235	−0.0551409	−0.0275705	−	0.999620i	$-0.508777\pi$
$263$	−0.894235	−0.0551409	−0.0275705	+	0.999620i	$0.508777\pi$
$264$	−1.04760	−0.0644752
$265$	−1.49641	−0.0919240
$266$	0.0864787	0.00530235
$267$	14.9393	0.914272
$268$	7.85657	0.479917
$269$	12.8800	0.785305	0.392653	−	0.919687i	$-0.371558\pi$
$269$	12.8800	0.785305	0.392653	+	0.919687i	$0.371558\pi$
$270$	−1.37301	−0.0835589
$271$	7.66364	0.465533	0.232767	−	0.972533i	$-0.425222\pi$
$271$	7.66364	0.465533	0.232767	+	0.972533i	$0.425222\pi$
$272$	−13.4181	−0.813589
$273$	−0.223076	−0.0135012
$274$	−2.88440	−0.174253
$275$	−1.00000	−0.0603023
$276$	4.61606	0.277854
$277$	−30.4233	−1.82796	−0.913980	−	0.405759i	$-0.867007\pi$
$277$	−30.4233	−1.82796	−0.913980	+	0.405759i	$0.867007\pi$
$278$	−0.237975	−0.0142728
$279$	10.1909	0.610114
$280$	0.338771	0.0202454
$281$	1.27526	0.0760758	0.0380379	−	0.999276i	$-0.487889\pi$
$281$	1.27526	0.0760758	0.0380379	+	0.999276i	$0.487889\pi$
$282$	−3.33138	−0.198381
$283$	26.0339	1.54755	0.773777	−	0.633458i	$-0.218365\pi$
$283$	26.0339	1.54755	0.773777	+	0.633458i	$0.218365\pi$
$284$	−31.4158	−1.86419
$285$	0.930455	0.0551154
$286$	−0.229009	−0.0135416
$287$	3.81210	0.225021
$288$	−6.95970	−0.410104
$289$	−2.39610	−0.140947
$290$	−0.790457	−0.0464172
$291$	−2.30965	−0.135394
$292$	−19.5191	−1.14227
$293$	−9.93138	−0.580198	−0.290099	−	0.956997i	$-0.593688\pi$
$293$	−9.93138	−0.580198	−0.290099	+	0.956997i	$0.593688\pi$
$294$	1.84774	0.107763
$295$	0.530465	0.0308849
$296$	−7.29469	−0.423995
$297$	−4.77719	−0.277201
$298$	1.78641	0.103484
$299$	2.06165	0.119228
$300$	1.78405	0.103002
$301$	−1.87628	−0.108147
$302$	−2.29118	−0.131843
$303$	2.40310	0.138054
$304$	3.51120	0.201381
$305$	−6.48095	−0.371098
$306$	2.34413	0.134005
$307$	11.5960	0.661818	0.330909	−	0.943663i	$-0.392645\pi$
$307$	11.5960	0.661818	0.330909	+	0.943663i	$0.392645\pi$
$308$	0.576924	0.0328733
$309$	−6.10201	−0.347131
$310$	1.37236	0.0779450
$311$	31.2938	1.77451	0.887255	−	0.461279i	$-0.152609\pi$
$311$	31.2938	1.77451	0.887255	+	0.461279i	$0.152609\pi$
$312$	0.834730	0.0472573
$313$	9.84588	0.556522	0.278261	−	0.960505i	$-0.410242\pi$
$313$	9.84588	0.556522	0.278261	+	0.960505i	$0.410242\pi$
$314$	−5.73969	−0.323910
$315$	0.642174	0.0361824
$316$	−2.88745	−0.162432
$317$	16.2776	0.914240	0.457120	−	0.889405i	$-0.348881\pi$
$317$	16.2776	0.914240	0.457120	+	0.889405i	$0.348881\pi$
$318$	−0.400174	−0.0224407
$319$	−2.75028	−0.153986
$320$	6.08516	0.340171
$321$	−12.0645	−0.673373
$322$	0.223755	0.0124694
$323$	−3.82150	−0.212634
$324$	−3.75387	−0.208548
$325$	0.796803	0.0441987
$326$	−5.38049	−0.297998
$327$	−18.2244	−1.00781
$328$	−14.2645	−0.787626
$329$	3.74830	0.206650
$330$	−0.267422	−0.0147211
$331$	−9.52199	−0.523376	−0.261688	−	0.965153i	$-0.584279\pi$
$331$	−9.52199	−0.523376	−0.261688	+	0.965153i	$0.584279\pi$
$332$	25.7029	1.41063
$333$	−13.8278	−0.757759
$334$	−1.85043	−0.101251
$335$	4.09752	0.223872
$336$	−0.983009	−0.0536275
$337$	−22.4964	−1.22546	−0.612728	−	0.790294i	$-0.709928\pi$
$337$	−22.4964	−1.22546	−0.612728	+	0.790294i	$0.709928\pi$
$338$	−3.55386	−0.193304
$339$	8.27691	0.449540
$340$	−7.32734	−0.397381
$341$	4.77493	0.258577
$342$	−0.613406	−0.0331692
$343$	−4.18521	−0.225980
$344$	7.02087	0.378540
$345$	2.40746	0.129614
$346$	−3.12193	−0.167836
$347$	−12.7044	−0.682007	−0.341004	−	0.940062i	$-0.610767\pi$
$347$	−12.7044	−0.682007	−0.341004	+	0.940062i	$0.610767\pi$
$348$	4.90663	0.263023
$349$	−2.41972	−0.129525	−0.0647624	−	0.997901i	$-0.520629\pi$
$349$	−2.41972	−0.129525	−0.0647624	+	0.997901i	$0.520629\pi$
$350$	0.0864787	0.00462248
$351$	3.80648	0.203175
$352$	−3.26095	−0.173809
$353$	−10.6782	−0.568342	−0.284171	−	0.958774i	$-0.591718\pi$
$353$	−10.6782	−0.568342	−0.284171	+	0.958774i	$0.591718\pi$
$354$	0.141858	0.00753968
$355$	−16.3846	−0.869606
$356$	30.7856	1.63163
$357$	1.06988	0.0566243
$358$	5.14169	0.271747
$359$	3.51469	0.185498	0.0927492	−	0.995690i	$-0.470435\pi$
$359$	3.51469	0.185498	0.0927492	+	0.995690i	$0.470435\pi$
$360$	−2.40295	−0.126647
$361$	1.00000	0.0526316
$362$	2.56452	0.134788
$363$	−0.930455	−0.0488362
$364$	−0.459695	−0.0240946
$365$	−10.1800	−0.532847
$366$	−1.73315	−0.0905932
$367$	4.03280	0.210510	0.105255	−	0.994445i	$-0.466434\pi$
$367$	4.03280	0.210510	0.105255	+	0.994445i	$0.466434\pi$
$368$	9.08489	0.473582
$369$	−27.0398	−1.40764
$370$	−1.86213	−0.0968073
$371$	0.450255	0.0233761
$372$	−8.51872	−0.441675
$373$	7.90327	0.409216	0.204608	−	0.978844i	$-0.434408\pi$
$373$	7.90327	0.409216	0.204608	+	0.978844i	$0.434408\pi$
$374$	1.09834	0.0567938
$375$	0.930455	0.0480485
$376$	−14.0258	−0.723324
$377$	2.19143	0.112864
$378$	0.413125	0.0212489
$379$	18.3197	0.941018	0.470509	−	0.882395i	$-0.344070\pi$
$379$	18.3197	0.941018	0.470509	+	0.882395i	$0.344070\pi$
$380$	1.91740	0.0983603
$381$	13.4242	0.687745
$382$	2.46235	0.125985
$383$	−25.3807	−1.29690	−0.648448	−	0.761259i	$-0.724582\pi$
$383$	−25.3807	−1.29690	−0.648448	+	0.761259i	$0.724582\pi$
$384$	7.69565	0.392717
$385$	0.300889	0.0153347
$386$	−0.941248	−0.0479083
$387$	13.3088	0.676522
$388$	−4.75951	−0.241627
$389$	28.4425	1.44209	0.721047	−	0.692886i	$-0.243661\pi$
$389$	28.4425	1.44209	0.721047	+	0.692886i	$0.243661\pi$
$390$	0.213083	0.0107899
$391$	−9.88778	−0.500046
$392$	7.77936	0.392917
$393$	−19.6428	−0.990846
$394$	−1.35553	−0.0682905
$395$	−1.50592	−0.0757711
$396$	−4.09221	−0.205641
$397$	33.8266	1.69771	0.848853	−	0.528628i	$-0.177294\pi$
$397$	33.8266	1.69771	0.848853	+	0.528628i	$0.177294\pi$
$398$	5.82220	0.291840
$399$	−0.279964	−0.0140157
$400$	3.51120	0.175560
$401$	1.28065	0.0639528	0.0319764	−	0.999489i	$-0.489820\pi$
$401$	1.28065	0.0639528	0.0319764	+	0.999489i	$0.489820\pi$
$402$	1.09577	0.0546520
$403$	−3.80468	−0.189525
$404$	4.95208	0.246375
$405$	−1.95780	−0.0972837
$406$	0.237840	0.0118038
$407$	−6.47899	−0.321151
$408$	−4.00340	−0.198198
$409$	21.0388	1.04030	0.520151	−	0.854075i	$-0.325876\pi$
$409$	21.0388	1.04030	0.520151	+	0.854075i	$0.325876\pi$
$410$	−3.64132	−0.179832
$411$	9.33790	0.460605
$412$	−12.5745	−0.619499
$413$	−0.159611	−0.00785396
$414$	−1.58713	−0.0780032
$415$	13.4051	0.658030
$416$	2.59834	0.127394
$417$	0.770415	0.0377274
$418$	−0.287410	−0.0140577
$419$	14.5691	0.711745	0.355873	−	0.934535i	$-0.384184\pi$
$419$	14.5691	0.711745	0.355873	+	0.934535i	$0.384184\pi$
$420$	−0.536802	−0.0261933
$421$	28.8641	1.40675	0.703374	−	0.710820i	$-0.251676\pi$
$421$	28.8641	1.40675	0.703374	+	0.710820i	$0.251676\pi$
$422$	7.44029	0.362188
$423$	−26.5872	−1.29272
$424$	−1.68481	−0.0818216
$425$	−3.82150	−0.185370
$426$	−4.38161	−0.212290
$427$	1.95005	0.0943695
$428$	−24.8613	−1.20172
$429$	0.741390	0.0357946
$430$	1.79223	0.0864289
$431$	−10.3983	−0.500867	−0.250434	−	0.968134i	$-0.580573\pi$
$431$	−10.3983	−0.500867	−0.250434	+	0.968134i	$0.580573\pi$
$432$	16.7737	0.807023
$433$	−29.6374	−1.42428	−0.712141	−	0.702037i	$-0.752274\pi$
$433$	−29.6374	−1.42428	−0.712141	+	0.702037i	$0.752274\pi$
$434$	−0.412930	−0.0198213
$435$	2.55901	0.122695
$436$	−37.5551	−1.79856
$437$	2.58740	0.123772
$438$	−2.72236	−0.130080
$439$	−6.65353	−0.317556	−0.158778	−	0.987314i	$-0.550755\pi$
$439$	−6.65353	−0.317556	−0.158778	+	0.987314i	$0.550755\pi$
$440$	−1.12590	−0.0536751
$441$	14.7465	0.702217
$442$	−0.875160	−0.0416271
$443$	21.4180	1.01760	0.508799	−	0.860885i	$-0.330089\pi$
$443$	21.4180	1.01760	0.508799	+	0.860885i	$0.330089\pi$
$444$	11.5588	0.548558
$445$	16.0559	0.761124
$446$	4.15790	0.196882
$447$	−5.78330	−0.273541
$448$	−1.83096	−0.0865048
$449$	1.72255	0.0812921	0.0406461	−	0.999174i	$-0.487058\pi$
$449$	1.72255	0.0812921	0.0406461	+	0.999174i	$0.487058\pi$
$450$	−0.613406	−0.0289162
$451$	−12.6694	−0.596581
$452$	17.0563	0.802260
$453$	7.41742	0.348501
$454$	3.18360	0.149414
$455$	−0.239750	−0.0112396
$456$	1.04760	0.0490583
$457$	−34.5249	−1.61501	−0.807504	−	0.589862i	$-0.799182\pi$
$457$	−34.5249	−1.61501	−0.807504	+	0.589862i	$0.799182\pi$
$458$	−4.40482	−0.205824
$459$	−18.2561	−0.852120
$460$	4.96108	0.231311
$461$	−1.37915	−0.0642334	−0.0321167	−	0.999484i	$-0.510225\pi$
$461$	−1.37915	−0.0642334	−0.0321167	+	0.999484i	$0.510225\pi$
$462$	0.0804645	0.00374355
$463$	32.7479	1.52192	0.760961	−	0.648797i	$-0.224728\pi$
$463$	32.7479	1.52192	0.760961	+	0.648797i	$0.224728\pi$
$464$	9.65676	0.448304
$465$	−4.44286	−0.206033
$466$	6.62918	0.307091
$467$	4.35490	0.201521	0.100760	−	0.994911i	$-0.467872\pi$
$467$	4.35490	0.201521	0.100760	+	0.994911i	$0.467872\pi$
$468$	3.26068	0.150725
$469$	−1.23290	−0.0569301
$470$	−3.58038	−0.165151
$471$	18.5816	0.856193
$472$	0.597250	0.0274907
$473$	6.23579	0.286722
$474$	−0.402717	−0.0184974
$475$	1.00000	0.0458831
$476$	2.20472	0.101053
$477$	−3.19373	−0.146231
$478$	6.52861	0.298612
$479$	9.57735	0.437600	0.218800	−	0.975770i	$-0.429786\pi$
$479$	9.57735	0.437600	0.218800	+	0.975770i	$0.429786\pi$
$480$	3.03417	0.138490
$481$	5.16248	0.235389
$482$	−6.14322	−0.279816
$483$	−0.724381	−0.0329605
$484$	−1.91740	−0.0871543
$485$	−2.48228	−0.112714
$486$	−4.64260	−0.210593
$487$	−33.9216	−1.53713	−0.768567	−	0.639770i	$-0.779030\pi$
$487$	−33.9216	−1.53713	−0.768567	+	0.639770i	$0.779030\pi$
$488$	−7.29690	−0.330315
$489$	17.4187	0.787699
$490$	1.98585	0.0897116
$491$	10.9434	0.493871	0.246935	−	0.969032i	$-0.420576\pi$
$491$	10.9434	0.493871	0.246935	+	0.969032i	$0.420576\pi$
$492$	22.6029	1.01902
$493$	−10.5102	−0.473355
$494$	0.229009	0.0103036
$495$	−2.13425	−0.0959275
$496$	−16.7657	−0.752803
$497$	4.92996	0.221139
$498$	3.58482	0.160640
$499$	0.739013	0.0330828	0.0165414	−	0.999863i	$-0.494734\pi$
$499$	0.739013	0.0330828	0.0165414	+	0.999863i	$0.494734\pi$
$500$	1.91740	0.0857485
$501$	5.99055	0.267638
$502$	−4.99743	−0.223046
$503$	40.3204	1.79780	0.898898	−	0.438158i	$-0.144369\pi$
$503$	40.3204	1.79780	0.898898	+	0.438158i	$0.144369\pi$
$504$	0.723023	0.0322060
$505$	2.58271	0.114929
$506$	−0.743646	−0.0330591
$507$	11.5052	0.510963
$508$	27.6634	1.22737
$509$	23.4880	1.04109	0.520543	−	0.853835i	$-0.325729\pi$
$509$	23.4880	1.04109	0.520543	+	0.853835i	$0.325729\pi$
$510$	−1.02196	−0.0452529
$511$	3.06306	0.135502
$512$	19.3563	0.855438
$513$	4.77719	0.210918
$514$	8.80204	0.388242
$515$	−6.55810	−0.288984
$516$	−11.1250	−0.489749
$517$	−12.4574	−0.547876
$518$	0.560294	0.0246179
$519$	10.1069	0.443642
$520$	0.897120	0.0393413
$521$	−23.7116	−1.03882	−0.519412	−	0.854524i	$-0.673849\pi$
$521$	−23.7116	−1.03882	−0.519412	+	0.854524i	$0.673849\pi$
$522$	−1.68704	−0.0738396
$523$	−12.3608	−0.540498	−0.270249	−	0.962790i	$-0.587106\pi$
$523$	−12.3608	−0.540498	−0.270249	+	0.962790i	$0.587106\pi$
$524$	−40.4780	−1.76829
$525$	−0.279964	−0.0122186
$526$	−0.257012	−0.0112063
$527$	18.2474	0.794870
$528$	3.26701	0.142178
$529$	−16.3053	−0.708928
$530$	−0.430084	−0.0186817
$531$	1.13215	0.0491310
$532$	−0.576924	−0.0250128
$533$	10.0950	0.437265
$534$	4.29371	0.185807
$535$	−12.9662	−0.560578
$536$	4.61340	0.199268
$537$	−16.6456	−0.718311
$538$	3.70183	0.159597
$539$	6.90947	0.297612
$540$	9.15977	0.394174
$541$	27.8823	1.19875	0.599377	−	0.800467i	$-0.295415\pi$
$541$	27.8823	1.19875	0.599377	+	0.800467i	$0.295415\pi$
$542$	2.20261	0.0946101
$543$	−8.30233	−0.356287
$544$	−12.4617	−0.534293
$545$	−19.5865	−0.838995
$546$	−0.0641144	−0.00274384
$547$	38.8767	1.66225	0.831124	−	0.556088i	$-0.187698\pi$
$547$	38.8767	1.66225	0.831124	+	0.556088i	$0.187698\pi$
$548$	19.2427	0.822006
$549$	−13.8320	−0.590335
$550$	−0.287410	−0.0122552
$551$	2.75028	0.117166
$552$	2.71056	0.115369
$553$	0.453116	0.0192685
$554$	−8.74397	−0.371496
$555$	6.02841	0.255892
$556$	1.58760	0.0673293
$557$	2.12875	0.0901980	0.0450990	−	0.998983i	$-0.485640\pi$
$557$	2.12875	0.0901980	0.0450990	+	0.998983i	$0.485640\pi$
$558$	2.92897	0.123993
$559$	−4.96870	−0.210153
$560$	−1.05648	−0.0446445
$561$	−3.55574	−0.150123
$562$	0.366523	0.0154608
$563$	−27.4940	−1.15873	−0.579366	−	0.815067i	$-0.696700\pi$
$563$	−27.4940	−1.15873	−0.579366	+	0.815067i	$0.696700\pi$
$564$	22.2246	0.935825
$565$	8.89555	0.374239
$566$	7.48240	0.314509
$567$	0.589080	0.0247390
$568$	−18.4474	−0.774037
$569$	39.1968	1.64321	0.821607	−	0.570054i	$-0.193078\pi$
$569$	39.1968	1.64321	0.821607	+	0.570054i	$0.193078\pi$
$570$	0.267422	0.0112011
$571$	−14.1076	−0.590385	−0.295192	−	0.955438i	$-0.595384\pi$
$571$	−14.1076	−0.590385	−0.295192	+	0.955438i	$0.595384\pi$
$572$	1.52779	0.0638800
$573$	−7.97154	−0.333016
$574$	1.09564	0.0457310
$575$	2.58740	0.107902
$576$	12.9873	0.541137
$577$	10.5694	0.440012	0.220006	−	0.975499i	$-0.429392\pi$
$577$	10.5694	0.440012	0.220006	+	0.975499i	$0.429392\pi$
$578$	−0.688665	−0.0286447
$579$	3.04718	0.126636
$580$	5.27337	0.218965
$581$	−4.03345	−0.167336
$582$	−0.663816	−0.0275161
$583$	−1.49641	−0.0619751
$584$	−11.4617	−0.474287
$585$	1.70058	0.0703103
$586$	−2.85438	−0.117913
$587$	33.1988	1.37026	0.685130	−	0.728421i	$-0.259746\pi$
$587$	33.1988	1.37026	0.685130	+	0.728421i	$0.259746\pi$
$588$	−12.3268	−0.508350
$589$	−4.77493	−0.196748
$590$	0.152461	0.00627672
$591$	4.38836	0.180513
$592$	22.7490	0.934978
$593$	−3.95694	−0.162492	−0.0812460	−	0.996694i	$-0.525890\pi$
$593$	−3.95694	−0.162492	−0.0812460	+	0.996694i	$0.525890\pi$
$594$	−1.37301	−0.0563354
$595$	1.14985	0.0471393
$596$	−11.9177	−0.488167
$597$	−18.8487	−0.771424
$598$	0.592540	0.0242307
$599$	−14.9674	−0.611550	−0.305775	−	0.952104i	$-0.598915\pi$
$599$	−14.9674	−0.611550	−0.305775	+	0.952104i	$0.598915\pi$
$600$	1.04760	0.0427680
$601$	−21.4595	−0.875351	−0.437676	−	0.899133i	$-0.644198\pi$
$601$	−21.4595	−0.875351	−0.437676	+	0.899133i	$0.644198\pi$
$602$	−0.539263	−0.0219787
$603$	8.74515	0.356130
$604$	15.2851	0.621943
$605$	−1.00000	−0.0406558
$606$	0.690675	0.0280568
$607$	−31.9568	−1.29709	−0.648544	−	0.761177i	$-0.724622\pi$
$607$	−31.9568	−1.29709	−0.648544	+	0.761177i	$0.724622\pi$
$608$	3.26095	0.132249
$609$	−0.769979	−0.0312011
$610$	−1.86269	−0.0754182
$611$	9.92609	0.401567
$612$	−15.6384	−0.632144
$613$	21.0077	0.848491	0.424246	−	0.905547i	$-0.360539\pi$
$613$	21.0077	0.848491	0.424246	+	0.905547i	$0.360539\pi$
$614$	3.33280	0.134501
$615$	11.7883	0.475352
$616$	0.338771	0.0136495
$617$	−19.4358	−0.782455	−0.391227	−	0.920294i	$-0.627949\pi$
$617$	−19.4358	−0.782455	−0.391227	+	0.920294i	$0.627949\pi$
$618$	−1.75378	−0.0705474
$619$	−3.03667	−0.122054	−0.0610270	−	0.998136i	$-0.519438\pi$
$619$	−3.03667	−0.122054	−0.0610270	+	0.998136i	$0.519438\pi$
$620$	−9.15543	−0.367691
$621$	12.3605	0.496011
$622$	8.99416	0.360633
$623$	−4.83106	−0.193552
$624$	−2.60316	−0.104210
$625$	1.00000	0.0400000
$626$	2.82981	0.113102
$627$	0.930455	0.0371588
$628$	38.2911	1.52798
$629$	−24.7595	−0.987225
$630$	0.184567	0.00735334
$631$	−8.07984	−0.321653	−0.160827	−	0.986983i	$-0.551416\pi$
$631$	−8.07984	−0.321653	−0.160827	+	0.986983i	$0.551416\pi$
$632$	−1.69552	−0.0674440
$633$	−24.0870	−0.957373
$634$	4.67834	0.185801
$635$	14.4276	0.572542
$636$	2.66968	0.105860
$637$	−5.50548	−0.218135
$638$	−0.790457	−0.0312945
$639$	−34.9689	−1.38335
$640$	8.27084	0.326934
$641$	−24.0360	−0.949365	−0.474683	−	0.880157i	$-0.657437\pi$
$641$	−24.0360	−0.949365	−0.474683	+	0.880157i	$0.657437\pi$
$642$	−3.46745	−0.136849
$643$	16.2391	0.640408	0.320204	−	0.947349i	$-0.396249\pi$
$643$	16.2391	0.640408	0.320204	+	0.947349i	$0.396249\pi$
$644$	−1.49274	−0.0588220
$645$	−5.80212	−0.228458
$646$	−1.09834	−0.0432136
$647$	44.6801	1.75656	0.878278	−	0.478150i	$-0.158692\pi$
$647$	44.6801	1.75656	0.878278	+	0.478150i	$0.158692\pi$
$648$	−2.20428	−0.0865923
$649$	0.530465	0.0208226
$650$	0.229009	0.00898248
$651$	1.33681	0.0523937
$652$	35.8948	1.40575
$653$	3.66860	0.143564	0.0717818	−	0.997420i	$-0.477131\pi$
$653$	3.66860	0.143564	0.0717818	+	0.997420i	$0.477131\pi$
$654$	−5.23788	−0.204817
$655$	−21.1109	−0.824872
$656$	44.4849	1.73684
$657$	−21.7267	−0.847641
$658$	1.07730	0.0419975
$659$	19.2466	0.749741	0.374870	−	0.927077i	$-0.377687\pi$
$659$	19.2466	0.749741	0.374870	+	0.927077i	$0.377687\pi$
$660$	1.78405	0.0694441
$661$	16.0378	0.623799	0.311899	−	0.950115i	$-0.399035\pi$
$661$	16.0378	0.623799	0.311899	+	0.950115i	$0.399035\pi$
$662$	−2.73672	−0.106365
$663$	2.83322	0.110033
$664$	15.0928	0.585714
$665$	−0.300889	−0.0116680
$666$	−3.97425	−0.153999
$667$	7.11608	0.275536
$668$	12.3448	0.477634
$669$	−13.4607	−0.520420
$670$	1.17767	0.0454974
$671$	−6.48095	−0.250194
$672$	−0.912949	−0.0352178
$673$	−1.75279	−0.0675650	−0.0337825	−	0.999429i	$-0.510755\pi$
$673$	−1.75279	−0.0675650	−0.0337825	+	0.999429i	$0.510755\pi$
$674$	−6.46569	−0.249049
$675$	4.77719	0.183874
$676$	23.7088	0.911877
$677$	−22.6054	−0.868798	−0.434399	−	0.900721i	$-0.643039\pi$
$677$	−22.6054	−0.868798	−0.434399	+	0.900721i	$0.643039\pi$
$678$	2.37887	0.0913598
$679$	0.746891	0.0286630
$680$	−4.30263	−0.164998
$681$	−10.3065	−0.394946
$682$	1.37236	0.0525505
$683$	48.0446	1.83838	0.919188	−	0.393820i	$-0.128847\pi$
$683$	48.0446	1.83838	0.919188	+	0.393820i	$0.128847\pi$
$684$	4.09221	0.156469
$685$	10.0358	0.383450
$686$	−1.20287	−0.0459259
$687$	14.2601	0.544055
$688$	−21.8951	−0.834742
$689$	1.19235	0.0454248
$690$	0.691929	0.0263413
$691$	−4.66297	−0.177388	−0.0886939	−	0.996059i	$-0.528269\pi$
$691$	−4.66297	−0.177388	−0.0886939	+	0.996059i	$0.528269\pi$
$692$	20.8273	0.791735
$693$	0.642174	0.0243942
$694$	−3.65137	−0.138604
$695$	0.827999	0.0314078
$696$	2.88119	0.109211
$697$	−48.4163	−1.83390
$698$	−0.695453	−0.0263233
$699$	−21.4612	−0.811736
$700$	−0.576924	−0.0218057
$701$	−49.7904	−1.88056	−0.940279	−	0.340405i	$-0.889436\pi$
$701$	−49.7904	−1.88056	−0.940279	+	0.340405i	$0.889436\pi$
$702$	1.09402	0.0412912
$703$	6.47899	0.244360
$704$	6.08516	0.229343
$705$	11.5910	0.436544
$706$	−3.06902	−0.115504
$707$	−0.777111	−0.0292263
$708$	−0.946377	−0.0355670
$709$	0.658806	0.0247420	0.0123710	−	0.999923i	$-0.496062\pi$
$709$	0.658806	0.0247420	0.0123710	+	0.999923i	$0.496062\pi$
$710$	−4.70911	−0.176730
$711$	−3.21402	−0.120535
$712$	18.0774	0.677478
$713$	−12.3547	−0.462686
$714$	0.307496	0.0115077
$715$	0.796803	0.0297987
$716$	−34.3017	−1.28191
$717$	−21.1356	−0.789322
$718$	1.01016	0.0376988
$719$	39.3855	1.46883	0.734416	−	0.678700i	$-0.237456\pi$
$719$	39.3855	1.46883	0.734416	+	0.678700i	$0.237456\pi$
$720$	7.49378	0.279277
$721$	1.97326	0.0734881
$722$	0.287410	0.0106963
$723$	19.8879	0.739639
$724$	−17.1087	−0.635839
$725$	2.75028	0.102143
$726$	−0.267422	−0.00992497
$727$	27.4031	1.01633	0.508163	−	0.861261i	$-0.330325\pi$
$727$	27.4031	1.01633	0.508163	+	0.861261i	$0.330325\pi$
$728$	−0.269934	−0.0100044
$729$	9.15646	0.339128
$730$	−2.92584	−0.108290
$731$	23.8301	0.881388
$732$	11.5623	0.427357
$733$	−17.1385	−0.633025	−0.316513	−	0.948588i	$-0.602512\pi$
$733$	−17.1385	−0.633025	−0.316513	+	0.948588i	$0.602512\pi$
$734$	1.15907	0.0427820
$735$	−6.42895	−0.237135
$736$	8.43740	0.311007
$737$	4.09752	0.150934
$738$	−7.77151	−0.286073
$739$	28.1178	1.03433	0.517165	−	0.855886i	$-0.326987\pi$
$739$	28.1178	1.03433	0.517165	+	0.855886i	$0.326987\pi$
$740$	12.4228	0.456671
$741$	−0.741390	−0.0272356
$742$	0.129408	0.00475071
$743$	−17.3088	−0.634999	−0.317500	−	0.948258i	$-0.602843\pi$
$743$	−17.3088	−0.634999	−0.317500	+	0.948258i	$0.602843\pi$
$744$	−5.00221	−0.183390
$745$	−6.21556	−0.227720
$746$	2.27148	0.0831648
$747$	28.6099	1.04678
$748$	−7.32734	−0.267914
$749$	3.90139	0.142554
$750$	0.267422	0.00976488
$751$	−32.9928	−1.20392	−0.601961	−	0.798525i	$-0.705614\pi$
$751$	−32.9928	−1.20392	−0.601961	+	0.798525i	$0.705614\pi$
$752$	43.7404	1.59505
$753$	16.1786	0.589580
$754$	0.629839	0.0229374
$755$	7.97182	0.290124
$756$	−2.75608	−0.100238
$757$	−17.9339	−0.651819	−0.325910	−	0.945401i	$-0.605671\pi$
$757$	−17.9339	−0.651819	−0.325910	+	0.945401i	$0.605671\pi$
$758$	5.26526	0.191243
$759$	2.40746	0.0873854
$760$	1.12590	0.0408407
$761$	12.4428	0.451050	0.225525	−	0.974237i	$-0.427590\pi$
$761$	12.4428	0.451050	0.225525	+	0.974237i	$0.427590\pi$
$762$	3.85827	0.139770
$763$	5.89338	0.213355
$764$	−16.4270	−0.594308
$765$	−8.15606	−0.294883
$766$	−7.29468	−0.263568
$767$	−0.422676	−0.0152620
$768$	−9.11213	−0.328806
$769$	−39.5490	−1.42617	−0.713087	−	0.701076i	$-0.752703\pi$
$769$	−39.5490	−1.42617	−0.713087	+	0.701076i	$0.752703\pi$
$770$	0.0864787	0.00311647
$771$	−28.4955	−1.02624
$772$	6.27934	0.225998
$773$	36.4918	1.31252	0.656259	−	0.754535i	$-0.272138\pi$
$773$	36.4918	1.31252	0.656259	+	0.754535i	$0.272138\pi$
$774$	3.82507	0.137489
$775$	−4.77493	−0.171521
$776$	−2.79479	−0.100327
$777$	−1.81388	−0.0650727
$778$	8.17467	0.293076
$779$	12.6694	0.453930
$780$	−1.42154	−0.0508992
$781$	−16.3846	−0.586288
$782$	−2.84185	−0.101624
$783$	13.1386	0.469535
$784$	−24.2605	−0.866446
$785$	19.9704	0.712774
$786$	−5.64553	−0.201369
$787$	−31.5439	−1.12442	−0.562209	−	0.826995i	$-0.690048\pi$
$787$	−31.5439	−1.12442	−0.562209	+	0.826995i	$0.690048\pi$
$788$	9.04312	0.322148
$789$	0.832046	0.0296216
$790$	−0.432817	−0.0153989
$791$	−2.67658	−0.0951681
$792$	−2.40295	−0.0853852
$793$	5.16404	0.183381
$794$	9.72210	0.345024
$795$	1.39235	0.0493814
$796$	−38.8416	−1.37670
$797$	−16.4054	−0.581109	−0.290554	−	0.956859i	$-0.593840\pi$
$797$	−16.4054	−0.581109	−0.290554	+	0.956859i	$0.593840\pi$
$798$	−0.0804645	−0.00284841
$799$	−47.6060	−1.68418
$800$	3.26095	0.115292
$801$	34.2674	1.21078
$802$	0.368073	0.0129971
$803$	−10.1800	−0.359245
$804$	−7.31019	−0.257811
$805$	−0.778523	−0.0274393
$806$	−1.09350	−0.0385170
$807$	−11.9842	−0.421865
$808$	2.90788	0.102299
$809$	−21.2544	−0.747266	−0.373633	−	0.927577i	$-0.621888\pi$
$809$	−21.2544	−0.747266	−0.373633	+	0.927577i	$0.621888\pi$
$810$	−0.562691	−0.0197709
$811$	−13.9900	−0.491254	−0.245627	−	0.969364i	$-0.578994\pi$
$811$	−13.9900	−0.491254	−0.245627	+	0.969364i	$0.578994\pi$
$812$	−1.58670	−0.0556823
$813$	−7.13068	−0.250084
$814$	−1.86213	−0.0652675
$815$	18.7206	0.655754
$816$	12.4849	0.437059
$817$	−6.23579	−0.218163
$818$	6.04676	0.211420
$819$	−0.511686	−0.0178798
$820$	24.2923	0.848325
$821$	−11.9564	−0.417282	−0.208641	−	0.977992i	$-0.566904\pi$
$821$	−11.9564	−0.417282	−0.208641	+	0.977992i	$0.566904\pi$
$822$	2.68381	0.0936085
$823$	−26.3187	−0.917412	−0.458706	−	0.888588i	$-0.651687\pi$
$823$	−26.3187	−0.917412	−0.458706	+	0.888588i	$0.651687\pi$
$824$	−7.38375	−0.257225
$825$	0.930455	0.0323943
$826$	−0.0458739	−0.00159616
$827$	−42.1014	−1.46401	−0.732005	−	0.681299i	$-0.761415\pi$
$827$	−42.1014	−1.46401	−0.732005	+	0.681299i	$0.761415\pi$
$828$	10.5882	0.367965
$829$	16.8332	0.584641	0.292321	−	0.956320i	$-0.405573\pi$
$829$	16.8332	0.584641	0.292321	+	0.956320i	$0.405573\pi$
$830$	3.85276	0.133731
$831$	28.3075	0.981978
$832$	−4.84868	−0.168098
$833$	26.4046	0.914864
$834$	0.221425	0.00766733
$835$	6.43830	0.222807
$836$	1.91740	0.0663145
$837$	−22.8108	−0.788455
$838$	4.18729	0.144648
$839$	−13.4300	−0.463657	−0.231828	−	0.972757i	$-0.574471\pi$
$839$	−13.4300	−0.463657	−0.231828	+	0.972757i	$0.574471\pi$
$840$	−0.315211	−0.0108758
$841$	−21.4360	−0.739172
$842$	8.29582	0.285893
$843$	−1.18657	−0.0408678
$844$	−49.6363	−1.70855
$845$	12.3651	0.425373
$846$	−7.64144	−0.262718
$847$	0.300889	0.0103387
$848$	5.25420	0.180430
$849$	−24.2234	−0.831344
$850$	−1.09834	−0.0376727
$851$	16.7638	0.574654
$852$	29.2310	1.00144
$853$	−12.0280	−0.411832	−0.205916	−	0.978570i	$-0.566017\pi$
$853$	−12.0280	−0.411832	−0.205916	+	0.978570i	$0.566017\pi$
$854$	0.560464	0.0191787
$855$	2.13425	0.0729899
$856$	−14.5986	−0.498971
$857$	37.1067	1.26754	0.633770	−	0.773522i	$-0.281507\pi$
$857$	37.1067	1.26754	0.633770	+	0.773522i	$0.281507\pi$
$858$	0.213083	0.00727453
$859$	35.4839	1.21069	0.605347	−	0.795961i	$-0.293034\pi$
$859$	35.4839	1.21069	0.605347	+	0.795961i	$0.293034\pi$
$860$	−11.9565	−0.407712
$861$	−3.54699	−0.120881
$862$	−2.98857	−0.101791
$863$	−35.4855	−1.20794	−0.603969	−	0.797007i	$-0.706415\pi$
$863$	−35.4855	−1.20794	−0.603969	+	0.797007i	$0.706415\pi$
$864$	15.5782	0.529981
$865$	10.8623	0.369329
$866$	−8.51808	−0.289456
$867$	2.22947	0.0757167
$868$	2.75477	0.0935031
$869$	−1.50592	−0.0510849
$870$	0.735485	0.0249353
$871$	−3.26492	−0.110628
$872$	−22.0525	−0.746791
$873$	−5.29781	−0.179304
$874$	0.743646	0.0251542
$875$	−0.300889	−0.0101719
$876$	18.1617	0.613626
$877$	−15.1352	−0.511080	−0.255540	−	0.966799i	$-0.582253\pi$
$877$	−15.1352	−0.511080	−0.255540	+	0.966799i	$0.582253\pi$
$878$	−1.91229	−0.0645367
$879$	9.24071	0.311681
$880$	3.51120	0.118362
$881$	33.2511	1.12026	0.560129	−	0.828405i	$-0.310752\pi$
$881$	33.2511	1.12026	0.560129	+	0.828405i	$0.310752\pi$
$882$	4.23831	0.142711
$883$	−20.1355	−0.677614	−0.338807	−	0.940856i	$-0.610023\pi$
$883$	−20.1355	−0.677614	−0.338807	+	0.940856i	$0.610023\pi$
$884$	5.83844	0.196368
$885$	−0.493574	−0.0165913
$886$	6.15574	0.206806
$887$	−47.7828	−1.60439	−0.802195	−	0.597062i	$-0.796335\pi$
$887$	−47.7828	−1.60439	−0.802195	+	0.597062i	$0.796335\pi$
$888$	6.78738	0.227769
$889$	−4.34112	−0.145596
$890$	4.61464	0.154683
$891$	−1.95780	−0.0655887
$892$	−27.7385	−0.928755
$893$	12.4574	0.416871
$894$	−1.66218	−0.0555915
$895$	−17.8897	−0.597988
$896$	−2.48861	−0.0831386
$897$	−1.91827	−0.0640493
$898$	0.495078	0.0165210
$899$	−13.1324	−0.437989
$900$	4.09221	0.136407
$901$	−5.71855	−0.190513
$902$	−3.64132	−0.121243
$903$	1.74580	0.0580965
$904$	10.0155	0.333110
$905$	−8.92287	−0.296606
$906$	2.13184	0.0708257
$907$	−2.17460	−0.0722066	−0.0361033	−	0.999348i	$-0.511495\pi$
$907$	−2.17460	−0.0722066	−0.0361033	+	0.999348i	$0.511495\pi$
$908$	−21.2387	−0.704831
$909$	5.51217	0.182827
$910$	−0.0689065	−0.00228423
$911$	37.3731	1.23823	0.619113	−	0.785302i	$-0.287492\pi$
$911$	37.3731	1.23823	0.619113	+	0.785302i	$0.287492\pi$
$912$	−3.26701	−0.108182
$913$	13.4051	0.443644
$914$	−9.92282	−0.328218
$915$	6.03023	0.199353
$916$	29.3858	0.970934
$917$	6.35205	0.209763
$918$	−5.24698	−0.173176
$919$	17.5506	0.578940	0.289470	−	0.957187i	$-0.406521\pi$
$919$	17.5506	0.578940	0.289470	+	0.957187i	$0.406521\pi$
$920$	2.91316	0.0960439
$921$	−10.7895	−0.355528
$922$	−0.396382	−0.0130541
$923$	13.0553	0.429721
$924$	−0.536802	−0.0176595
$925$	6.47899	0.213028
$926$	9.41207	0.309300
$927$	−13.9966	−0.459710
$928$	8.96852	0.294406
$929$	−15.9227	−0.522405	−0.261203	−	0.965284i	$-0.584119\pi$
$929$	−15.9227	−0.522405	−0.261203	+	0.965284i	$0.584119\pi$
$930$	−1.27692	−0.0418719
$931$	−6.90947	−0.226449
$932$	−44.2252	−1.44864
$933$	−29.1175	−0.953264
$934$	1.25164	0.0409550
$935$	−3.82150	−0.124977
$936$	1.91468	0.0625833
$937$	−57.0024	−1.86219	−0.931094	−	0.364780i	$-0.881144\pi$
$937$	−57.0024	−1.86219	−0.931094	+	0.364780i	$0.881144\pi$
$938$	−0.354348	−0.0115699
$939$	−9.16115	−0.298963
$940$	23.8858	0.779067
$941$	−0.261201	−0.00851490	−0.00425745	−	0.999991i	$-0.501355\pi$
$941$	−0.261201	−0.00851490	−0.00425745	+	0.999991i	$0.501355\pi$
$942$	5.34053	0.174004
$943$	32.7810	1.06750
$944$	−1.86257	−0.0606214
$945$	−1.43741	−0.0467588
$946$	1.79223	0.0582704
$947$	−5.25839	−0.170875	−0.0854373	−	0.996344i	$-0.527229\pi$
$947$	−5.25839	−0.170875	−0.0854373	+	0.996344i	$0.527229\pi$
$948$	2.68664	0.0872580
$949$	8.11147	0.263309
$950$	0.287410	0.00932482
$951$	−15.1456	−0.491128
$952$	1.29462	0.0419587
$953$	−38.8454	−1.25833	−0.629164	−	0.777273i	$-0.716602\pi$
$953$	−38.8454	−1.25833	−0.629164	+	0.777273i	$0.716602\pi$
$954$	−0.917909	−0.0297184
$955$	−8.56736	−0.277233
$956$	−43.5542	−1.40864
$957$	2.55901	0.0827210
$958$	2.75263	0.0889333
$959$	−3.01968	−0.0975105
$960$	−5.66197	−0.182739
$961$	−8.20003	−0.264517
$962$	1.48375	0.0478380
$963$	−27.6732	−0.891755
$964$	40.9832	1.31998
$965$	3.27493	0.105424
$966$	−0.208194	−0.00669854
$967$	−32.3469	−1.04021	−0.520104	−	0.854103i	$-0.674107\pi$
$967$	−32.3469	−1.04021	−0.520104	+	0.854103i	$0.674107\pi$
$968$	−1.12590	−0.0361878
$969$	3.55574	0.114227
$970$	−0.713432	−0.0229069
$971$	27.4686	0.881510	0.440755	−	0.897627i	$-0.354711\pi$
$971$	27.4686	0.881510	0.440755	+	0.897627i	$0.354711\pi$
$972$	30.9721	0.993431
$973$	−0.249136	−0.00798693
$974$	−9.74940	−0.312391
$975$	−0.741390	−0.0237435
$976$	22.7559	0.728398
$977$	14.1760	0.453530	0.226765	−	0.973950i	$-0.427185\pi$
$977$	14.1760	0.453530	0.226765	+	0.973950i	$0.427185\pi$
$978$	5.00630	0.160084
$979$	16.0559	0.513150
$980$	−13.2482	−0.423198
$981$	−41.8026	−1.33466
$982$	3.14526	0.100369
$983$	−15.3640	−0.490037	−0.245018	−	0.969518i	$-0.578794\pi$
$983$	−15.3640	−0.490037	−0.245018	+	0.969518i	$0.578794\pi$
$984$	13.2725	0.423111
$985$	4.71636	0.150276
$986$	−3.02074	−0.0961998
$987$	−3.48762	−0.111012
$988$	−1.52779	−0.0486054
$989$	−16.1345	−0.513048
$990$	−0.613406	−0.0194953
$991$	−22.3817	−0.710977	−0.355489	−	0.934681i	$-0.615686\pi$
$991$	−22.3817	−0.710977	−0.355489	+	0.934681i	$0.615686\pi$
$992$	−15.5708	−0.494374
$993$	8.85978	0.281157
$994$	1.41692	0.0449420
$995$	−20.2575	−0.642205
$996$	−23.9154	−0.757787
$997$	52.2093	1.65348	0.826742	−	0.562581i	$-0.190192\pi$
$997$	52.2093	1.65348	0.826742	+	0.562581i	$0.190192\pi$
$998$	0.212400	0.00672340
$999$	30.9514	0.979258

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.2.a.j.1.5	✓	9
3.2	odd	2		9405.2.a.bi.1.5		9
5.4	even	2		5225.2.a.q.1.5		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.2.a.j.1.5	✓	9	1.1	even	1	trivial
5225.2.a.q.1.5		9	5.4	even	2
9405.2.a.bi.1.5		9	3.2	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:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1045.a (trivial)

\(f(q)\)	\(=\)	\(q+0.287410 q^{2} -0.930455 q^{3} -1.91740 q^{4} -1.00000 q^{5} -0.267422 q^{6} +0.300889 q^{7} -1.12590 q^{8} -2.13425 q^{9} +O(q^{10})\)	\(q+0.287410 q^{2} -0.930455 q^{3} -1.91740 q^{4} -1.00000 q^{5} -0.267422 q^{6} +0.300889 q^{7} -1.12590 q^{8} -2.13425 q^{9} -0.287410 q^{10} -1.00000 q^{11} +1.78405 q^{12} +0.796803 q^{13} +0.0864787 q^{14} +0.930455 q^{15} +3.51120 q^{16} -3.82150 q^{17} -0.613406 q^{18} +1.00000 q^{19} +1.91740 q^{20} -0.279964 q^{21} -0.287410 q^{22} +2.58740 q^{23} +1.04760 q^{24} +1.00000 q^{25} +0.229009 q^{26} +4.77719 q^{27} -0.576924 q^{28} +2.75028 q^{29} +0.267422 q^{30} -4.77493 q^{31} +3.26095 q^{32} +0.930455 q^{33} -1.09834 q^{34} -0.300889 q^{35} +4.09221 q^{36} +6.47899 q^{37} +0.287410 q^{38} -0.741390 q^{39} +1.12590 q^{40} +12.6694 q^{41} -0.0804645 q^{42} -6.23579 q^{43} +1.91740 q^{44} +2.13425 q^{45} +0.743646 q^{46} +12.4574 q^{47} -3.26701 q^{48} -6.90947 q^{49} +0.287410 q^{50} +3.55574 q^{51} -1.52779 q^{52} +1.49641 q^{53} +1.37301 q^{54} +1.00000 q^{55} -0.338771 q^{56} -0.930455 q^{57} +0.790457 q^{58} -0.530465 q^{59} -1.78405 q^{60} +6.48095 q^{61} -1.37236 q^{62} -0.642174 q^{63} -6.08516 q^{64} -0.796803 q^{65} +0.267422 q^{66} -4.09752 q^{67} +7.32734 q^{68} -2.40746 q^{69} -0.0864787 q^{70} +16.3846 q^{71} +2.40295 q^{72} +10.1800 q^{73} +1.86213 q^{74} -0.930455 q^{75} -1.91740 q^{76} -0.300889 q^{77} -0.213083 q^{78} +1.50592 q^{79} -3.51120 q^{80} +1.95780 q^{81} +3.64132 q^{82} -13.4051 q^{83} +0.536802 q^{84} +3.82150 q^{85} -1.79223 q^{86} -2.55901 q^{87} +1.12590 q^{88} -16.0559 q^{89} +0.613406 q^{90} +0.239750 q^{91} -4.96108 q^{92} +4.44286 q^{93} +3.58038 q^{94} -1.00000 q^{95} -3.03417 q^{96} +2.48228 q^{97} -1.98585 q^{98} +2.13425 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 3 q^{2} + 3 q^{3} + 9 q^{4} - 9 q^{5} + 6 q^{6} - 9 q^{7} + 15 q^{8} + 16 q^{9}+O(q^{10}) \) 9 * q + 3 * q^2 + 3 * q^3 + 9 * q^4 - 9 * q^5 + 6 * q^6 - 9 * q^7 + 15 * q^8 + 16 * q^9	\( 9 q + 3 q^{2} + 3 q^{3} + 9 q^{4} - 9 q^{5} + 6 q^{6} - 9 q^{7} + 15 q^{8} + 16 q^{9} - 3 q^{10} - 9 q^{11} + 13 q^{12} - 3 q^{13} + 4 q^{14} - 3 q^{15} + 17 q^{16} + 5 q^{17} + 17 q^{18} + 9 q^{19} - 9 q^{20} - q^{21} - 3 q^{22} + 4 q^{23} + 21 q^{24} + 9 q^{25} + 20 q^{26} + 24 q^{27} - 24 q^{28} + 3 q^{29} - 6 q^{30} - q^{31} + 38 q^{32} - 3 q^{33} + 28 q^{34} + 9 q^{35} + 17 q^{36} + 5 q^{37} + 3 q^{38} - 15 q^{40} - 5 q^{41} - 43 q^{42} - 11 q^{43} - 9 q^{44} - 16 q^{45} + 2 q^{46} + 30 q^{47} + 54 q^{48} + 12 q^{49} + 3 q^{50} + 40 q^{51} - 3 q^{52} - q^{53} + 65 q^{54} + 9 q^{55} - 16 q^{56} + 3 q^{57} - 15 q^{58} + 59 q^{59} - 13 q^{60} - 21 q^{61} - 10 q^{62} - 12 q^{63} + 19 q^{64} + 3 q^{65} - 6 q^{66} - 2 q^{67} - 9 q^{68} - 22 q^{69} - 4 q^{70} + 34 q^{71} + 32 q^{72} - 34 q^{73} - 21 q^{74} + 3 q^{75} + 9 q^{76} + 9 q^{77} - 65 q^{78} - 13 q^{79} - 17 q^{80} + 57 q^{81} + 10 q^{82} + 51 q^{83} - 95 q^{84} - 5 q^{85} - 14 q^{86} + 8 q^{87} - 15 q^{88} + 8 q^{89} - 17 q^{90} + 62 q^{91} + 57 q^{92} - 18 q^{93} + 2 q^{94} - 9 q^{95} + 81 q^{96} - 8 q^{97} - 20 q^{98} - 16 q^{99}+O(q^{100}) \) 9 * q + 3 * q^2 + 3 * q^3 + 9 * q^4 - 9 * q^5 + 6 * q^6 - 9 * q^7 + 15 * q^8 + 16 * q^9 - 3 * q^10 - 9 * q^11 + 13 * q^12 - 3 * q^13 + 4 * q^14 - 3 * q^15 + 17 * q^16 + 5 * q^17 + 17 * q^18 + 9 * q^19 - 9 * q^20 - q^21 - 3 * q^22 + 4 * q^23 + 21 * q^24 + 9 * q^25 + 20 * q^26 + 24 * q^27 - 24 * q^28 + 3 * q^29 - 6 * q^30 - q^31 + 38 * q^32 - 3 * q^33 + 28 * q^34 + 9 * q^35 + 17 * q^36 + 5 * q^37 + 3 * q^38 - 15 * q^40 - 5 * q^41 - 43 * q^42 - 11 * q^43 - 9 * q^44 - 16 * q^45 + 2 * q^46 + 30 * q^47 + 54 * q^48 + 12 * q^49 + 3 * q^50 + 40 * q^51 - 3 * q^52 - q^53 + 65 * q^54 + 9 * q^55 - 16 * q^56 + 3 * q^57 - 15 * q^58 + 59 * q^59 - 13 * q^60 - 21 * q^61 - 10 * q^62 - 12 * q^63 + 19 * q^64 + 3 * q^65 - 6 * q^66 - 2 * q^67 - 9 * q^68 - 22 * q^69 - 4 * q^70 + 34 * q^71 + 32 * q^72 - 34 * q^73 - 21 * q^74 + 3 * q^75 + 9 * q^76 + 9 * q^77 - 65 * q^78 - 13 * q^79 - 17 * q^80 + 57 * q^81 + 10 * q^82 + 51 * q^83 - 95 * q^84 - 5 * q^85 - 14 * q^86 + 8 * q^87 - 15 * q^88 + 8 * q^89 - 17 * q^90 + 62 * q^91 + 57 * q^92 - 18 * q^93 + 2 * q^94 - 9 * q^95 + 81 * q^96 - 8 * q^97 - 20 * q^98 - 16 * q^99

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