LMFDB - Embedded newform 460.2.e.a.91.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(91,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("460.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.e (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	16.0.7465802011608416256.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{14} + x^{12} + 8x^{10} - 20x^{8} + 32x^{6} + 16x^{4} - 64x^{2} + 256 $ x^16 - x^14 + x^12 + 8x^10 - 20x^8 + 32x^6 + 16x^4 - 64*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.8
Root			$1.37379 + 0.335728i$ of defining polynomial
Character	$\chi$	$=$	460.91
Dual form			460.2.e.a.91.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.637910 + 1.26217i) q^{2} -2.87247i q^{3} +(-1.18614 - 1.61030i) q^{4} +1.00000i q^{5} +(3.62554 + 1.83238i) q^{6} -2.68161 q^{7} +(2.78912 - 0.469882i) q^{8} -5.25109 q^{9} +O(q^{10})$	\(q+(-0.637910 + 1.26217i) q^{2} -2.87247i q^{3} +(-1.18614 - 1.61030i) q^{4} +1.00000i q^{5} +(3.62554 + 1.83238i) q^{6} -2.68161 q^{7} +(2.78912 - 0.469882i) q^{8} -5.25109 q^{9} +(-1.26217 - 0.637910i) q^{10} -4.89140 q^{11} +(-4.62554 + 3.40715i) q^{12} +0.727591 q^{13} +(1.71063 - 3.38465i) q^{14} +2.87247 q^{15} +(-1.18614 + 3.82009i) q^{16} +6.34755i q^{17} +(3.34972 - 6.62776i) q^{18} +2.68161 q^{19} +(1.61030 - 1.18614i) q^{20} +7.70285i q^{21} +(3.12027 - 6.17377i) q^{22} +(2.20979 + 4.25639i) q^{23} +(-1.34972 - 8.01167i) q^{24} -1.00000 q^{25} +(-0.464138 + 0.918342i) q^{26} +6.46618i q^{27} +(3.18077 + 4.31821i) q^{28} -4.27582 q^{29} +(-1.83238 + 3.62554i) q^{30} -6.13645i q^{31} +(-4.06494 - 3.93398i) q^{32} +14.0504i q^{33} +(-8.01167 - 4.04917i) q^{34} -2.68161i q^{35} +(6.22853 + 8.45583i) q^{36} +3.87539i q^{37} +(-1.71063 + 3.38465i) q^{38} -2.08998i q^{39} +(0.469882 + 2.78912i) q^{40} -8.07172 q^{41} +(-9.72230 - 4.91373i) q^{42} -11.1319 q^{43} +(5.80189 + 7.87663i) q^{44} -5.25109i q^{45} +(-6.78193 + 0.0739292i) q^{46} +9.80928i q^{47} +(10.9731 + 3.40715i) q^{48} +0.191051 q^{49} +(0.637910 - 1.26217i) q^{50} +18.2331 q^{51} +(-0.863025 - 1.17164i) q^{52} -11.1565i q^{53} +(-8.16141 - 4.12484i) q^{54} -4.89140i q^{55} +(-7.47935 + 1.26004i) q^{56} -7.70285i q^{57} +(2.72759 - 5.39681i) q^{58} +1.87953i q^{59} +(-3.40715 - 4.62554i) q^{60} -6.93356i q^{61} +(7.74524 + 3.91451i) q^{62} +14.0814 q^{63} +(7.55842 - 2.62112i) q^{64} +0.727591i q^{65} +(-17.7340 - 8.96290i) q^{66} -10.5224 q^{67} +(10.2215 - 7.52908i) q^{68} +(12.2263 - 6.34755i) q^{69} +(3.38465 + 1.71063i) q^{70} -7.24866i q^{71} +(-14.6459 + 2.46739i) q^{72} +7.90882 q^{73} +(-4.89140 - 2.47215i) q^{74} +2.87247i q^{75} +(-3.18077 - 4.31821i) q^{76} +13.1168 q^{77} +(2.63791 + 1.33322i) q^{78} -3.67993 q^{79} +(-3.82009 - 1.18614i) q^{80} +2.82064 q^{81} +(5.14904 - 10.1879i) q^{82} +4.75372 q^{83} +(12.4039 - 9.13667i) q^{84} -6.34755 q^{85} +(7.10119 - 14.0504i) q^{86} +12.2822i q^{87} +(-13.6427 + 2.29838i) q^{88} +8.12461i q^{89} +(6.62776 + 3.34972i) q^{90} -1.95112 q^{91} +(4.23295 - 8.60710i) q^{92} -17.6268 q^{93} +(-12.3810 - 6.25744i) q^{94} +2.68161i q^{95} +(-11.3003 + 11.6764i) q^{96} +2.68434i q^{97} +(-0.121873 + 0.241138i) q^{98} +25.6852 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} + 14 q^{6} + 4 q^{9}+O(q^{10}) $ 16 * q + 4 * q^4 + 14 * q^6 + 4 * q^9	$ 16 q + 4 q^{4} + 14 q^{6} + 4 q^{9} - 30 q^{12} + 4 q^{13} + 4 q^{16} + 30 q^{18} + 2 q^{24} - 16 q^{25} - 54 q^{26} - 48 q^{29} + 34 q^{36} - 36 q^{41} - 40 q^{46} + 18 q^{48} + 68 q^{49} + 34 q^{52} - 40 q^{54} + 36 q^{58} + 6 q^{62} + 52 q^{64} + 40 q^{69} + 42 q^{70} - 78 q^{72} + 8 q^{73} + 72 q^{77} + 32 q^{78} + 40 q^{81} - 42 q^{82} + 12 q^{85} - 120 q^{93} + 20 q^{94} - 22 q^{96} - 18 q^{98}+O(q^{100}) $ 16 * q + 4 * q^4 + 14 * q^6 + 4 * q^9 - 30 * q^12 + 4 * q^13 + 4 * q^16 + 30 * q^18 + 2 * q^24 - 16 * q^25 - 54 * q^26 - 48 * q^29 + 34 * q^36 - 36 * q^41 - 40 * q^46 + 18 * q^48 + 68 * q^49 + 34 * q^52 - 40 * q^54 + 36 * q^58 + 6 * q^62 + 52 * q^64 + 40 * q^69 + 42 * q^70 - 78 * q^72 + 8 * q^73 + 72 * q^77 + 32 * q^78 + 40 * q^81 - 42 * q^82 + 12 * q^85 - 120 * q^93 + 20 * q^94 - 22 * q^96 - 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−0.637910	+	1.26217i	−0.451071	+	0.892488i
$2$	−0.637910	+	1.26217i	−0.451071	+	0.892488i
$3$		−	2.87247i		−	1.65842i	−0.558936	−	0.829211i	$-0.688790\pi$
$3$		−	2.87247i		−	1.65842i	0.558936	−	0.829211i	$-0.311210\pi$
$4$	−1.18614	−	1.61030i	−0.593070	−	0.805151i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	3.62554	+	1.83238i	1.48012	+	0.748065i
$7$	−2.68161			−1.01355			−0.506777	−	0.862077i	$-0.669163\pi$
$7$	−2.68161			−1.01355			−0.506777	+	0.862077i	$0.669163\pi$
$8$	2.78912	−	0.469882i	0.986104	−	0.166128i
$9$	−5.25109			−1.75036
$10$	−1.26217	−	0.637910i	−0.399133	−	0.201725i
$11$	−4.89140			−1.47481			−0.737406	−	0.675449i	$-0.763950\pi$
$11$	−4.89140			−1.47481			−0.737406	+	0.675449i	$0.763950\pi$
$12$	−4.62554	+	3.40715i	−1.33528	+	0.983561i
$13$	0.727591			0.201797			0.100899	−	0.994897i	$-0.467828\pi$
$13$	0.727591			0.201797			0.100899	+	0.994897i	$0.467828\pi$
$14$	1.71063	−	3.38465i	0.457185	−	0.904586i
$15$	2.87247			0.741669
$16$	−1.18614	+	3.82009i	−0.296535	+	0.955022i
$17$			6.34755i			1.53951i	0.638342	+	0.769753i	$0.279621\pi$
$17$			6.34755i			1.53951i	−0.638342	+	0.769753i	$0.720379\pi$
$18$	3.34972	−	6.62776i	0.789537	−	1.56218i
$19$	2.68161			0.615204			0.307602	−	0.951515i	$-0.400473\pi$
$19$	2.68161			0.615204			0.307602	+	0.951515i	$0.400473\pi$
$20$	1.61030	−	1.18614i	0.360074	−	0.265229i
$21$			7.70285i			1.68090i
$22$	3.12027	−	6.17377i	0.665245	−	1.31625i
$23$	2.20979	+	4.25639i	0.460772	+	0.887518i
$23$	2.20979	+	4.25639i	0.460772	+	0.887518i
$24$	−1.34972	−	8.01167i	−0.275511	−	1.63538i
$25$	−1.00000			−0.200000
$26$	−0.464138	+	0.918342i	−0.0910249	+	0.180102i
$27$			6.46618i			1.24442i
$28$	3.18077	+	4.31821i	0.601109	+	0.816064i
$29$	−4.27582			−0.794000			−0.397000	−	0.917819i	$-0.629949\pi$
$29$	−4.27582			−0.794000			−0.397000	+	0.917819i	$0.629949\pi$
$30$	−1.83238	+	3.62554i	−0.334545	+	0.661930i
$31$		−	6.13645i		−	1.10214i	−0.834459	−	0.551070i	$-0.814220\pi$
$31$		−	6.13645i		−	1.10214i	0.834459	−	0.551070i	$-0.185780\pi$
$32$	−4.06494	−	3.93398i	−0.718587	−	0.695437i
$33$			14.0504i			2.44586i
$34$	−8.01167	−	4.04917i	−1.37399	−	0.694426i
$35$		−	2.68161i		−	0.453275i
$36$	6.22853	+	8.45583i	1.03809	+	1.40930i
$37$			3.87539i			0.637111i	0.947904	+	0.318555i	$0.103198\pi$
$37$			3.87539i			0.637111i	−0.947904	+	0.318555i	$0.896802\pi$
$38$	−1.71063	+	3.38465i	−0.277501	+	0.549063i
$39$		−	2.08998i		−	0.334665i
$40$	0.469882	+	2.78912i	0.0742949	+	0.440999i
$41$	−8.07172			−1.26059			−0.630296	−	0.776355i	$-0.717066\pi$
$41$	−8.07172			−1.26059			−0.630296	+	0.776355i	$0.717066\pi$
$42$	−9.72230	−	4.91373i	−1.50018	−	0.758205i
$43$	−11.1319			−1.69761			−0.848803	−	0.528709i	$-0.822676\pi$
$43$	−11.1319			−1.69761			−0.848803	+	0.528709i	$0.822676\pi$
$44$	5.80189	+	7.87663i	0.874668	+	1.18745i
$45$		−	5.25109i		−	0.782786i
$46$	−6.78193	+	0.0739292i	−0.999941	+	0.0109003i
$47$			9.80928i			1.43083i	0.698699	+	0.715416i	$0.253763\pi$
$47$			9.80928i			1.43083i	−0.698699	+	0.715416i	$0.746237\pi$
$48$	10.9731	+	3.40715i	1.58383	+	0.491780i
$49$	0.191051			0.0272930
$50$	0.637910	−	1.26217i	0.0902142	−	0.178498i
$51$	18.2331			2.55315
$52$	−0.863025	−	1.17164i	−0.119680	−	0.162477i
$53$		−	11.1565i		−	1.53246i	−0.642565	−	0.766231i	$-0.722130\pi$
$53$		−	11.1565i		−	1.53246i	0.642565	−	0.766231i	$-0.277870\pi$
$54$	−8.16141	−	4.12484i	−1.11063	−	0.561320i
$55$		−	4.89140i		−	0.659556i
$56$	−7.47935	+	1.26004i	−0.999470	+	0.168380i
$57$		−	7.70285i		−	1.02027i
$58$	2.72759	−	5.39681i	0.358150	−	0.708636i
$59$			1.87953i			0.244694i	0.992487	+	0.122347i	$0.0390420\pi$
$59$			1.87953i			0.244694i	−0.992487	+	0.122347i	$0.960958\pi$
$60$	−3.40715	−	4.62554i	−0.439862	−	0.597155i
$61$		−	6.93356i		−	0.887751i	−0.896088	−	0.443875i	$-0.853603\pi$
$61$		−	6.93356i		−	0.887751i	0.896088	−	0.443875i	$-0.146397\pi$
$62$	7.74524	+	3.91451i	0.983646	+	0.497143i
$63$	14.0814			1.77409
$64$	7.55842	−	2.62112i	0.944803	−	0.327640i
$65$			0.727591i			0.0902465i
$66$	−17.7340	−	8.96290i	−2.18290	−	1.10326i
$67$	−10.5224			−1.28552			−0.642761	−	0.766067i	$-0.722211\pi$
$67$	−10.5224			−1.28552			−0.642761	+	0.766067i	$0.722211\pi$
$68$	10.2215	−	7.52908i	1.23953	−	0.913035i
$69$	12.2263	−	6.34755i	1.47188	−	0.764155i
$70$	3.38465	+	1.71063i	0.404543	+	0.204459i
$71$		−	7.24866i		−	0.860258i	−0.902767	−	0.430129i	$-0.858468\pi$
$71$		−	7.24866i		−	0.860258i	0.902767	−	0.430129i	$-0.141532\pi$
$72$	−14.6459	+	2.46739i	−1.72604	+	0.290785i
$73$	7.90882			0.925657			0.462829	−	0.886448i	$-0.346834\pi$
$73$	7.90882			0.925657			0.462829	+	0.886448i	$0.346834\pi$
$74$	−4.89140	−	2.47215i	−0.568614	−	0.287382i
$75$			2.87247i			0.331684i
$76$	−3.18077	−	4.31821i	−0.364859	−	0.495332i
$77$	13.1168			1.49480
$78$	2.63791	+	1.33322i	0.298685	+	0.150958i
$79$	−3.67993			−0.414024			−0.207012	−	0.978338i	$-0.566374\pi$
$79$	−3.67993			−0.414024			−0.207012	+	0.978338i	$0.566374\pi$
$80$	−3.82009	−	1.18614i	−0.427099	−	0.132615i
$81$	2.82064			0.313404
$82$	5.14904	−	10.1879i	0.568616	−	1.12506i
$83$	4.75372			0.521789			0.260894	−	0.965367i	$-0.415983\pi$
$83$	4.75372			0.521789			0.260894	+	0.965367i	$0.415983\pi$
$84$	12.4039	−	9.13667i	1.35338	−	0.996892i
$85$	−6.34755			−0.688488
$86$	7.10119	−	14.0504i	0.765741	−	1.51509i
$87$			12.2822i			1.31679i
$88$	−13.6427	+	2.29838i	−1.45432	+	0.245008i
$89$			8.12461i			0.861207i	0.902541	+	0.430603i	$0.141699\pi$
$89$			8.12461i			0.861207i	−0.902541	+	0.430603i	$0.858301\pi$
$90$	6.62776	+	3.34972i	0.698627	+	0.353092i
$91$	−1.95112			−0.204533
$92$	4.23295	−	8.60710i	0.441316	−	0.897352i
$93$	−17.6268			−1.82781
$94$	−12.3810	−	6.25744i	−1.27700	−	0.645406i
$95$			2.68161i			0.275128i
$96$	−11.3003	+	11.6764i	−1.15333	+	1.19172i
$97$			2.68434i			0.272554i	0.990671	+	0.136277i	$0.0435137\pi$
$97$			2.68434i			0.272554i	−0.990671	+	0.136277i	$0.956486\pi$
$98$	−0.121873	+	0.241138i	−0.0123111	+	0.0243587i
$99$	25.6852			2.58146
$100$	1.18614	+	1.61030i	0.118614	+	0.161030i
$101$	1.53860			0.153096			0.0765480	−	0.997066i	$-0.475610\pi$
$101$	1.53860			0.153096			0.0765480	+	0.997066i	$0.475610\pi$
$102$	−11.6311	+	23.0133i	−1.15165	+	2.27866i
$103$	−18.1121			−1.78464			−0.892321	−	0.451401i	$-0.850924\pi$
$103$	−18.1121			−1.78464			−0.892321	+	0.451401i	$0.850924\pi$
$104$	2.02934	−	0.341882i	0.198993	−	0.0335243i
$105$	−7.70285			−0.751722
$106$	14.0814	+	7.11684i	1.36770	+	0.691249i
$107$	11.1319			1.07617			0.538083	−	0.842892i	$-0.319149\pi$
$107$	11.1319			1.07617			0.538083	+	0.842892i	$0.319149\pi$
$108$	10.4125	−	7.66979i	1.00194	−	0.738026i
$109$		−	10.6447i		−	1.01958i	−0.860300	−	0.509788i	$-0.829724\pi$
$109$		−	10.6447i		−	1.01958i	0.860300	−	0.509788i	$-0.170276\pi$
$110$	6.17377	+	3.12027i	0.588646	+	0.297507i
$111$	11.1319			1.05660
$112$	3.18077	−	10.2440i	0.300555	−	0.967967i
$113$			5.41399i			0.509305i	0.967033	+	0.254653i	$0.0819611\pi$
$113$			5.41399i			0.509305i	−0.967033	+	0.254653i	$0.918039\pi$
$114$	9.72230	+	4.91373i	0.910577	+	0.460213i
$115$	−4.25639	+	2.20979i	−0.396910	+	0.206064i
$116$	5.07172	+	6.88536i	0.470898	+	0.639290i
$117$	−3.82064			−0.353218
$118$	−2.37228	−	1.19897i	−0.218386	−	0.110374i
$119$		−	17.0217i		−	1.56037i
$120$	8.01167	−	1.34972i	0.731362	−	0.123212i
$121$	12.9258			1.17507
$122$	8.75132	+	4.42299i	0.792307	+	0.400439i
$123$			23.1858i			2.09059i
$124$	−9.88154	+	7.27870i	−0.887388	+	0.653646i
$125$		−	1.00000i		−	0.0894427i
$126$	−8.98266	+	17.7731i	−0.800239	+	1.58335i
$127$		−	3.05353i		−	0.270957i	−0.990780	−	0.135478i	$-0.956743\pi$
$127$		−	3.05353i		−	0.270957i	0.990780	−	0.135478i	$-0.0432571\pi$
$128$	−1.51330	+	11.2120i	−0.133758	+	0.991014i
$129$			31.9762i			2.81535i
$130$	−0.918342	−	0.464138i	−0.0805439	−	0.0407076i
$131$		−	3.09691i		−	0.270578i	−0.990806	−	0.135289i	$-0.956804\pi$
$131$		−	3.09691i		−	0.270578i	0.990806	−	0.135289i	$-0.0431963\pi$
$132$	22.6254	−	16.6658i	1.96929	−	1.45057i
$133$	−7.19105			−0.623543
$134$	6.71238	−	13.2811i	0.579861	−	1.14731i
$135$	−6.46618			−0.556520
$136$	2.98260	+	17.7041i	0.255756	+	1.51811i
$137$		−	5.92579i		−	0.506275i	−0.967430	−	0.253137i	$-0.918538\pi$
$137$		−	5.92579i		−	0.506275i	0.967430	−	0.253137i	$-0.0814625\pi$
$138$	0.212359	+	19.4809i	0.0180772	+	1.65832i
$139$		−	3.32470i		−	0.281997i	−0.990010	−	0.140999i	$-0.954969\pi$
$139$		−	3.32470i		−	0.281997i	0.990010	−	0.140999i	$-0.0450313\pi$
$140$	−4.31821	+	3.18077i	−0.364955	+	0.268824i
$141$	28.1769			2.37292
$142$	9.14904	+	4.62400i	0.767770	+	0.388037i
$143$	−3.55894			−0.297613
$144$	6.22853	−	20.0596i	0.519044	−	1.67163i
$145$		−	4.27582i		−	0.355088i
$146$	−5.04512	+	9.98227i	−0.417537	+	0.826138i
$147$		−	0.548788i		−	0.0452633i
$148$	6.24055	−	4.59676i	0.512970	−	0.377851i
$149$		−	14.4242i		−	1.18168i	−0.806789	−	0.590839i	$-0.798797\pi$
$149$		−	14.4242i		−	1.18168i	0.806789	−	0.590839i	$-0.201203\pi$
$150$	−3.62554	−	1.83238i	−0.296024	−	0.149613i
$151$		−	13.3082i		−	1.08300i	−0.840700	−	0.541501i	$-0.817856\pi$
$151$		−	13.3082i		−	1.08300i	0.840700	−	0.541501i	$-0.182144\pi$
$152$	7.47935	−	1.26004i	0.606656	−	0.102203i
$153$		−	33.3315i		−	2.69469i
$154$	−8.36737	+	16.5557i	−0.674262	+	1.33409i
$155$	6.13645			0.492892
$156$	−3.36550	+	2.47901i	−0.269456	+	0.198480i
$157$			3.66320i			0.292356i	0.989258	+	0.146178i	$0.0466971\pi$
$157$			3.66320i			0.292356i	−0.989258	+	0.146178i	$0.953303\pi$
$158$	2.34746	−	4.64469i	0.186754	−	0.369512i
$159$	−32.0467			−2.54147
$160$	3.93398	−	4.06494i	0.311009	−	0.321362i
$161$	−5.92579	−	11.4140i	−0.467018	−	0.899548i
$162$	−1.79932	+	3.56012i	−0.141368	+	0.279710i
$163$			16.6589i			1.30483i	0.757864	+	0.652413i	$0.226243\pi$
$163$			16.6589i			1.30483i	−0.757864	+	0.652413i	$0.773757\pi$
$164$	9.57420	+	12.9979i	0.747620	+	1.01497i
$165$	−14.0504			−1.09382
$166$	−3.03245	+	6.00000i	−0.235364	+	0.465690i
$167$		−	1.87953i		−	0.145442i	−0.997352	−	0.0727211i	$-0.976832\pi$
$167$		−	1.87953i		−	0.145442i	0.997352	−	0.0727211i	$-0.0231683\pi$
$168$	3.61943	+	21.4842i	0.279245	+	1.65754i
$169$	−12.4706			−0.959278
$170$	4.04917	−	8.01167i	0.310557	−	0.614467i
$171$	−14.0814			−1.07683
$172$	13.2041	+	17.9258i	1.00680	+	1.36683i
$173$	6.34755			0.482595			0.241297	−	0.970451i	$-0.422427\pi$
$173$	6.34755			0.482595			0.241297	+	0.970451i	$0.422427\pi$
$174$	−15.5022	−	7.83492i	−1.17522	−	0.593964i
$175$	2.68161			0.202711
$176$	5.80189	−	18.6856i	0.437334	−	1.40848i
$177$	5.39889			0.405805
$178$	−10.2546	−	5.18277i	−0.768617	−	0.388465i
$179$			3.09691i			0.231474i	0.993280	+	0.115737i	$0.0369229\pi$
$179$			3.09691i			0.231474i	−0.993280	+	0.115737i	$0.963077\pi$
$180$	−8.45583	+	6.22853i	−0.630260	+	0.464247i
$181$			10.7610i			0.799860i	0.916546	+	0.399930i	$0.130966\pi$
$181$			10.7610i			0.799860i	−0.916546	+	0.399930i	$0.869034\pi$
$182$	1.24464	−	2.46264i	0.0922587	−	0.182543i
$183$	−19.9164			−1.47227
$184$	8.16337	+	10.8333i	0.601811	+	0.798638i
$185$	−3.87539			−0.284925
$186$	11.2443	−	22.2480i	0.824472	−	1.63130i
$187$		−	31.0484i		−	2.27048i
$188$	15.7959	−	11.6352i	1.15203	−	0.848584i
$189$		−	17.3398i		−	1.26128i
$190$	−3.38465	−	1.71063i	−0.245548	−	0.124102i
$191$	−4.75372			−0.343967			−0.171984	−	0.985100i	$-0.555018\pi$
$191$	−4.75372			−0.343967			−0.171984	+	0.985100i	$0.555018\pi$
$192$	−7.52908	−	21.7113i	−0.543365	−	1.56688i
$193$	21.3640			1.53781			0.768907	−	0.639360i	$-0.220801\pi$
$193$	21.3640			1.53781			0.768907	+	0.639360i	$0.220801\pi$
$194$	−3.38809	−	1.71237i	−0.243251	−	0.122941i
$195$	2.08998			0.149667
$196$	−0.226613	−	0.307650i	−0.0161867	−	0.0219750i
$197$	20.4988			1.46048			0.730238	−	0.683193i	$-0.239409\pi$
$197$	20.4988			1.46048			0.730238	+	0.683193i	$0.239409\pi$
$198$	−16.3848	+	32.4190i	−1.16442	+	2.30392i
$199$	−15.2762			−1.08290			−0.541449	−	0.840733i	$-0.682124\pi$
$199$	−15.2762			−1.08290			−0.541449	+	0.840733i	$0.682124\pi$
$200$	−2.78912	+	0.469882i	−0.197221	+	0.0332257i
$201$			30.2254i			2.13194i
$202$	−0.981487	+	1.94197i	−0.0690572	+	0.136636i
$203$	11.4661			0.804762
$204$	−21.6271	−	29.3608i	−1.51420	−	2.05567i
$205$		−	8.07172i		−	0.563754i
$206$	11.5539	−	22.8606i	0.805000	−	1.59277i
$207$	−11.6038	−	22.3507i	−0.806518	−	1.55348i
$208$	−0.863025	+	2.77946i	−0.0598400	+	0.192721i
$209$	−13.1168			−0.907311
$210$	4.91373	−	9.72230i	0.339080	−	0.670903i
$211$			26.0740i			1.79501i	0.441008	+	0.897503i	$0.354621\pi$
$211$			26.0740i			1.79501i	−0.441008	+	0.897503i	$0.645379\pi$
$212$	−17.9653	+	13.2332i	−1.23386	+	0.908858i
$213$	−20.8216			−1.42667
$214$	−7.10119	+	14.0504i	−0.485427	+	0.960466i
$215$		−	11.1319i		−	0.759193i
$216$	3.03834	+	18.0350i	0.206733	+	1.22712i
$217$			16.4556i			1.11708i
$218$	13.4354	+	6.79036i	0.909960	+	0.459901i
$219$		−	22.7179i		−	1.53513i
$220$	−7.87663	+	5.80189i	−0.531042	+	0.391163i
$221$			4.61841i			0.310668i
$222$	−7.10119	+	14.0504i	−0.476600	+	0.943001i
$223$			1.47929i			0.0990606i	0.998773	+	0.0495303i	$0.0157724\pi$
$223$			1.47929i			0.0990606i	−0.998773	+	0.0495303i	$0.984228\pi$
$224$	10.9006	+	10.5494i	0.728328	+	0.704863i
$225$	5.25109			0.350072
$226$	−6.83337	−	3.45364i	−0.454549	−	0.229733i
$227$	2.20064			0.146062			0.0730308	−	0.997330i	$-0.476733\pi$
$227$	2.20064			0.146062			0.0730308	+	0.997330i	$0.476733\pi$
$228$	−12.4039	+	9.13667i	−0.821469	+	0.605091i
$229$		−	17.4140i		−	1.15075i	−0.817890	−	0.575374i	$-0.804856\pi$
$229$		−	17.4140i		−	1.15075i	0.817890	−	0.575374i	$-0.195144\pi$
$230$	−0.0739292	−	6.78193i	−0.00487475	−	0.447187i
$231$		−	37.6777i		−	2.47901i
$232$	−11.9258	+	2.00913i	−0.782967	+	0.131906i
$233$	−26.7931			−1.75527			−0.877637	−	0.479326i	$-0.840881\pi$
$233$	−26.7931			−1.75527			−0.877637	+	0.479326i	$0.840881\pi$
$234$	2.43723	−	4.82229i	0.159326	−	0.315243i
$235$	−9.80928			−0.639887
$236$	3.02661	−	2.22938i	0.197015	−	0.145121i
$237$			10.5705i			0.686627i
$238$	21.4842	+	10.8583i	1.39261	+	0.703839i
$239$			23.5866i			1.52569i	0.646583	+	0.762844i	$0.276198\pi$
$239$			23.5866i			1.52569i	−0.646583	+	0.762844i	$0.723802\pi$
$240$	−3.40715	+	10.9731i	−0.219931	+	0.708310i
$241$			0.212188i			0.0136683i	0.999977	+	0.00683413i	$0.00217539\pi$
$241$			0.212188i			0.0136683i	−0.999977	+	0.00683413i	$0.997825\pi$
$242$	−8.24550	+	16.3145i	−0.530041	+	1.04874i
$243$			11.2963i			0.724659i
$244$	−11.1651	+	8.22417i	−0.714773	+	0.526499i
$245$			0.191051i			0.0122058i
$246$	−29.2644	−	14.7905i	−1.86583	−	0.943005i
$247$	1.95112			0.124147
$248$	−2.88341	−	17.1153i	−0.183097	−	1.08682i
$249$		−	13.6549i		−	0.865346i
$250$	1.26217	+	0.637910i	0.0798266	+	0.0403450i
$251$	−11.1153			−0.701589			−0.350795	−	0.936452i	$-0.614088\pi$
$251$	−11.1153			−0.701589			−0.350795	+	0.936452i	$0.614088\pi$
$252$	−16.7025	−	22.6753i	−1.05216	−	1.42841i
$253$	−10.8089	−	20.8197i	−0.679553	−	1.30892i
$254$	3.85407	+	1.94788i	0.241826	+	0.122221i
$255$			18.2331i			1.14180i
$256$	−13.1861	−	9.06232i	−0.824134	−	0.566395i
$257$	1.25450			0.0782533			0.0391267	−	0.999234i	$-0.487542\pi$
$257$	1.25450			0.0782533			0.0391267	+	0.999234i	$0.487542\pi$
$258$	−40.3594	−	20.3979i	−2.51266	−	1.26992i
$259$		−	10.3923i		−	0.645746i
$260$	1.17164	−	0.863025i	0.0726620	−	0.0535225i
$261$	22.4527			1.38979
$262$	3.90882	+	1.97555i	0.241488	+	0.122050i
$263$	−25.6760			−1.58325			−0.791625	−	0.611007i	$-0.790765\pi$
$263$	−25.6760			−1.58325			−0.791625	+	0.611007i	$0.790765\pi$
$264$	6.60203	+	39.1883i	0.406327	+	2.41187i
$265$	11.1565			0.685338
$266$	4.58725	−	9.07632i	0.281262	−	0.556505i
$267$	23.3377			1.42824
$268$	12.4811	+	16.9443i	0.762404	+	1.03504i
$269$	20.4193			1.24498			0.622492	−	0.782626i	$-0.286120\pi$
$269$	20.4193			1.24498			0.622492	+	0.782626i	$0.286120\pi$
$270$	4.12484	−	8.16141i	0.251030	−	0.496687i
$271$		−	3.08711i		−	0.187529i	−0.995594	−	0.0937643i	$-0.970110\pi$
$271$		−	3.08711i		−	0.187529i	0.995594	−	0.0937643i	$-0.0298900\pi$
$272$	−24.2482	−	7.52908i	−1.47026	−	0.456518i
$273$			5.60452i			0.339201i
$274$	7.47935	+	3.78012i	0.451844	+	0.228366i
$275$	4.89140			0.294963
$276$	−24.7236	−	12.1590i	−1.48819	−	0.731887i
$277$	2.96451			0.178120			0.0890602	−	0.996026i	$-0.471614\pi$
$277$	2.96451			0.178120			0.0890602	+	0.996026i	$0.471614\pi$
$278$	4.19633	+	2.12086i	0.251679	+	0.127201i
$279$			32.2230i			1.92914i
$280$	−1.26004	−	7.47935i	−0.0753019	−	0.446977i
$281$		−	8.93603i		−	0.533079i	−0.963824	−	0.266539i	$-0.914120\pi$
$281$		−	8.93603i		−	0.533079i	0.963824	−	0.266539i	$-0.0858802\pi$
$282$	−17.9743	+	35.5640i	−1.07036	+	2.11780i
$283$	17.2348			1.02450			0.512252	−	0.858835i	$-0.328811\pi$
$283$	17.2348			1.02450			0.512252	+	0.858835i	$0.328811\pi$
$284$	−11.6725	+	8.59793i	−0.692637	+	0.510194i
$285$	7.70285			0.456278
$286$	2.27028	−	4.49198i	0.134245	−	0.265616i
$287$	21.6452			1.27768
$288$	21.3454	+	20.6577i	1.25779	+	1.21727i
$289$	−23.2913			−1.37008
$290$	5.39681	+	2.72759i	0.316911	+	0.160170i
$291$	7.71069			0.452009
$292$	−9.38097	−	12.7356i	−0.548980	−	0.745294i
$293$			20.3500i			1.18886i	0.804147	+	0.594430i	$0.202622\pi$
$293$			20.3500i			1.18886i	−0.804147	+	0.594430i	$0.797378\pi$
$294$	0.692663	+	0.350078i	0.0403969	+	0.0204169i
$295$	−1.87953			−0.109430
$296$	1.82098	+	10.8089i	0.105842	+	0.628257i
$297$		−	31.6286i		−	1.83528i
$298$	18.2058	+	9.20136i	1.05463	+	0.533021i
$299$	1.60782	+	3.09691i	0.0929826	+	0.179099i
$300$	4.62554	−	3.40715i	0.267056	−	0.196712i
$301$	29.8516			1.72062
$302$	16.7971	+	8.48941i	0.966567	+	0.488511i
$303$		−	4.41957i		−	0.253898i
$304$	−3.18077	+	10.2440i	−0.182430	+	0.587534i
$305$	6.93356			0.397014
$306$	42.0700	+	21.2625i	2.40498	+	1.21550i
$307$		−	32.9240i		−	1.87907i	−0.342449	−	0.939537i	$-0.611256\pi$
$307$		−	32.9240i		−	1.87907i	0.342449	−	0.939537i	$-0.388744\pi$
$308$	−15.5584	−	21.1221i	−0.886523	−	1.20354i
$309$			52.0266i			2.95969i
$310$	−3.91451	+	7.74524i	−0.222329	+	0.439900i
$311$			31.6677i			1.79571i	0.440291	+	0.897855i	$0.354875\pi$
$311$			31.6677i			1.79571i	−0.440291	+	0.897855i	$0.645125\pi$
$312$	−0.982045	−	5.82922i	−0.0555973	−	0.330015i
$313$			5.92579i			0.334946i	0.985877	+	0.167473i	$0.0535606\pi$
$313$			5.92579i			0.334946i	−0.985877	+	0.167473i	$0.946439\pi$
$314$	−4.62358	−	2.33680i	−0.260924	−	0.131873i
$315$			14.0814i			0.793396i
$316$	4.36491	+	5.92579i	0.245546	+	0.333352i
$317$	14.3079			0.803611			0.401806	−	0.915725i	$-0.368383\pi$
$317$	14.3079			0.803611			0.401806	+	0.915725i	$0.368383\pi$
$318$	20.4429	−	40.4483i	1.14638	−	2.26823i
$319$	20.9147			1.17100
$320$	2.62112	+	7.55842i	0.146525	+	0.422529i
$321$		−	31.9762i		−	1.78474i
$322$	18.1865	−	0.198249i	1.01349	−	0.0110480i
$323$			17.0217i			0.947111i
$324$	−3.34568	−	4.54208i	−0.185871	−	0.252338i
$325$	−0.727591			−0.0403595
$326$	−21.0263	−	10.6269i	−1.16454	−	0.588569i
$327$	−30.5766			−1.69089
$328$	−22.5130	+	3.79276i	−1.24307	+	0.209420i
$329$		−	26.3047i		−	1.45023i
$330$	8.96290	−	17.7340i	0.493391	−	0.976223i
$331$			15.1629i			0.833430i	0.909037	+	0.416715i	$0.136819\pi$
$331$			15.1629i			0.833430i	−0.909037	+	0.416715i	$0.863181\pi$
$332$	−5.63858	−	7.65492i	−0.309457	−	0.420119i
$333$		−	20.3500i		−	1.11517i
$334$	2.37228	+	1.19897i	0.129805	+	0.0656047i
$335$		−	10.5224i		−	0.574903i
$336$	−29.4256	−	9.13667i	−1.60530	−	0.498446i
$337$		−	11.5520i		−	0.629276i	−0.949212	−	0.314638i	$-0.898117\pi$
$337$		−	11.5520i		−	0.629276i	0.949212	−	0.314638i	$-0.101883\pi$
$338$	7.95513	−	15.7400i	0.432702	−	0.856144i
$339$	15.5515			0.844643
$340$	7.52908	+	10.2215i	0.408322	+	0.554337i
$341$			30.0158i			1.62545i
$342$	8.98266	−	17.7731i	0.485727	−	0.961058i
$343$	18.2590			0.985892
$344$	−31.0484	+	5.23070i	−1.67402	+	0.282021i
$345$	6.34755	+	12.2263i	0.341740	+	0.658245i
$346$	−4.04917	+	8.01167i	−0.217684	+	0.430710i
$347$			3.94249i			0.211644i	0.994385	+	0.105822i	$0.0337474\pi$
$347$			3.94249i			0.211644i	−0.994385	+	0.105822i	$0.966253\pi$
$348$	19.7780	−	14.5684i	1.06021	−	0.780947i
$349$	−14.2826			−0.764532			−0.382266	−	0.924052i	$-0.624856\pi$
$349$	−14.2826			−0.764532			−0.382266	+	0.924052i	$0.624856\pi$
$350$	−1.71063	+	3.38465i	−0.0914370	+	0.180917i
$351$			4.70473i			0.251120i
$352$	19.8833	+	19.2427i	1.05978	+	1.02564i
$353$	−24.2520			−1.29080			−0.645402	−	0.763843i	$-0.723310\pi$
$353$	−24.2520			−1.29080			−0.645402	+	0.763843i	$0.723310\pi$
$354$	−3.44401	+	6.81431i	−0.183047	+	0.362176i
$355$	7.24866			0.384719
$356$	13.0831	−	9.63693i	0.693401	−	0.510756i
$357$	−48.8942			−2.58776
$358$	−3.90882	−	1.97555i	−0.206588	−	0.104411i
$359$	35.2093			1.85828			0.929138	−	0.369734i	$-0.120551\pi$
$359$	35.2093			1.85828			0.929138	+	0.369734i	$0.120551\pi$
$360$	−2.46739	−	14.6459i	−0.130043	−	0.771908i
$361$	−11.8089			−0.621524
$362$	−13.5822	−	6.86457i	−0.713866	−	0.360794i
$363$		−	37.1290i		−	1.94876i
$364$	2.31430	+	3.14189i	0.121302	+	0.164680i
$365$			7.90882i			0.413967i
$366$	12.7049	−	25.1379i	0.664096	−	1.31398i
$367$	4.51174			0.235511			0.117755	−	0.993043i	$-0.462430\pi$
$367$	4.51174			0.235511			0.117755	+	0.993043i	$0.462430\pi$
$368$	−18.8809	+	3.39290i	−0.984235	+	0.176867i
$369$	42.3853			2.20649
$370$	2.47215	−	4.89140i	0.128521	−	0.254292i
$371$			29.9174i			1.55323i
$372$	20.9078	+	28.3844i	1.08402	+	1.47166i
$373$			1.05569i			0.0546617i	0.999626	+	0.0273309i	$0.00870077\pi$
$373$			1.05569i			0.0546617i	−0.999626	+	0.0273309i	$0.991299\pi$
$374$	39.1883	+	19.8061i	2.02638	+	1.02415i
$375$	−2.87247			−0.148334
$376$	4.60921	+	27.3593i	0.237702	+	1.41095i
$377$	−3.11105			−0.160227
$378$	21.8857	+	11.0612i	1.12568	+	0.568928i
$379$	6.48253			0.332985			0.166493	−	0.986043i	$-0.446756\pi$
$379$	6.48253			0.332985			0.166493	+	0.986043i	$0.446756\pi$
$380$	4.31821	−	3.18077i	0.221519	−	0.163170i
$381$	−8.77117			−0.449361
$382$	3.03245	−	6.00000i	0.155154	−	0.306987i
$383$	−1.34915			−0.0689383			−0.0344692	−	0.999406i	$-0.510974\pi$
$383$	−1.34915			−0.0689383			−0.0344692	+	0.999406i	$0.510974\pi$
$384$	32.2063	+	4.34692i	1.64352	+	0.221828i
$385$			13.1168i			0.668496i
$386$	−13.6283	+	26.9650i	−0.693663	+	1.37248i
$387$	58.4548			2.97143
$388$	4.32260	−	3.18401i	0.219447	−	0.161643i
$389$			10.3846i			0.526519i	0.964725	+	0.263259i	$0.0847975\pi$
$389$			10.3846i			0.526519i	−0.964725	+	0.263259i	$0.915203\pi$
$390$	−1.33322	+	2.63791i	−0.0675103	+	0.133576i
$391$	−27.0176	+	14.0267i	−1.36634	+	0.709362i
$392$	0.532865	−	0.0897714i	0.0269137	−	0.00453414i
$393$	−8.89578			−0.448733
$394$	−13.0764	+	25.8729i	−0.658778	+	1.30346i
$395$		−	3.67993i		−	0.185157i
$396$	−30.4662	−	41.3608i	−1.53098	−	2.07846i
$397$	−23.4623			−1.17754			−0.588770	−	0.808300i	$-0.700388\pi$
$397$	−23.4623			−1.17754			−0.588770	+	0.808300i	$0.700388\pi$
$398$	9.74483	−	19.2811i	0.488464	−	0.966474i
$399$			20.6561i			1.03410i
$400$	1.18614	−	3.82009i	0.0593070	−	0.191004i
$401$			26.3500i			1.31586i	0.753080	+	0.657929i	$0.228567\pi$
$401$			26.3500i			1.31586i	−0.753080	+	0.657929i	$0.771433\pi$
$402$	−38.1496	−	19.2811i	−1.90273	−	0.961654i
$403$		−	4.46482i		−	0.222409i
$404$	−1.82499	−	2.47760i	−0.0907967	−	0.123265i
$405$			2.82064i			0.140159i
$406$	−7.31434	+	14.4722i	−0.363005	+	0.718241i
$407$		−	18.9561i		−	0.939619i
$408$	50.8545	−	8.56742i	2.51767	−	0.424151i
$409$	18.3538			0.907535			0.453768	−	0.891120i	$-0.350080\pi$
$409$	18.3538			0.907535			0.453768	+	0.891120i	$0.350080\pi$
$410$	10.1879	+	5.14904i	0.503144	+	0.254293i
$411$	−17.0217			−0.839617
$412$	21.4836	+	29.1660i	1.05842	+	1.43691i
$413$		−	5.04017i		−	0.248010i
$414$	35.6125	−	0.388208i	1.75026	−	0.0190794i
$415$			4.75372i			0.233351i
$416$	−2.95762	−	2.86233i	−0.145009	−	0.140337i
$417$	−9.55010			−0.467670
$418$	8.36737	−	16.5557i	0.409261	−	0.809764i
$419$	−20.3386			−0.993606			−0.496803	−	0.867863i	$-0.665493\pi$
$419$	−20.3386			−0.993606			−0.496803	+	0.867863i	$0.665493\pi$
$420$	9.13667	+	12.4039i	0.445824	+	0.605249i
$421$		−	9.22242i		−	0.449473i	−0.974420	−	0.224737i	$-0.927848\pi$
$421$		−	9.22242i		−	0.449473i	0.974420	−	0.224737i	$-0.0721522\pi$
$422$	−32.9098	−	16.6329i	−1.60202	−	0.809675i
$423$		−	51.5094i		−	2.50447i
$424$	−5.24224	−	31.1168i	−0.254585	−	1.51117i
$425$		−	6.34755i		−	0.307901i
$426$	13.2823	−	26.2803i	0.643529	−	1.27329i
$427$			18.5931i			0.899784i
$428$	−13.2041	−	17.9258i	−0.638242	−	0.866476i
$429$			10.2229i			0.493568i
$430$	14.0504	+	7.10119i	0.677570	+	0.342450i
$431$	10.2805			0.495192			0.247596	−	0.968863i	$-0.420359\pi$
$431$	10.2805			0.495192			0.247596	+	0.968863i	$0.420359\pi$
$432$	−24.7014	−	7.66979i	−1.18844	−	0.369013i
$433$			17.8095i			0.855868i	0.903810	+	0.427934i	$0.140758\pi$
$433$			17.8095i			0.855868i	−0.903810	+	0.427934i	$0.859242\pi$
$434$	−20.7697	−	10.4972i	−0.996979	−	0.503881i
$435$	−12.2822			−0.588885
$436$	−17.1412	+	12.6261i	−0.820913	+	0.604681i
$437$	5.92579	+	11.4140i	0.283469	+	0.546005i
$438$	28.6738	+	14.4920i	1.37009	+	0.692452i
$439$		−	14.9756i		−	0.714746i	−0.933962	−	0.357373i	$-0.883672\pi$
$439$		−	14.9756i		−	0.714746i	0.933962	−	0.357373i	$-0.116328\pi$
$440$	−2.29838	−	13.6427i	−0.109571	−	0.650391i
$441$	−1.00322			−0.0477726
$442$	−5.82922	−	2.94613i	−0.277268	−	0.140133i
$443$		−	14.0082i		−	0.665548i	−0.943007	−	0.332774i	$-0.892015\pi$
$443$		−	14.0082i		−	0.665548i	0.943007	−	0.332774i	$-0.107985\pi$
$444$	−13.2041	−	17.9258i	−0.626637	−	0.850720i
$445$	−8.12461			−0.385143
$446$	−1.86711	−	0.943654i	−0.0884104	−	0.0446833i
$447$	−41.4332			−1.95972
$448$	−20.2688	+	7.02882i	−0.957609	+	0.332081i
$449$	−28.3872			−1.33967			−0.669837	−	0.742508i	$-0.733636\pi$
$449$	−28.3872			−1.33967			−0.669837	+	0.742508i	$0.733636\pi$
$450$	−3.34972	+	6.62776i	−0.157907	+	0.312435i
$451$	39.4820			1.85914
$452$	8.71815	−	6.42175i	0.410067	−	0.302054i
$453$	−38.2273			−1.79607
$454$	−1.40381	+	2.77758i	−0.0658841	+	0.130358i
$455$		−	1.95112i		−	0.0914698i
$456$	−3.61943	−	21.4842i	−0.169495	−	1.00609i
$457$		−	35.6394i		−	1.66714i	−0.552413	−	0.833570i	$-0.686293\pi$
$457$		−	35.6394i		−	1.66714i	0.552413	−	0.833570i	$-0.313707\pi$
$458$	21.9794	+	11.1086i	1.02703	+	0.519069i
$459$	−41.0443			−1.91579
$460$	8.60710	+	4.23295i	0.401308	+	0.197362i
$461$	−1.09286			−0.0508997			−0.0254498	−	0.999676i	$-0.508102\pi$
$461$	−1.09286			−0.0508997			−0.0254498	+	0.999676i	$0.508102\pi$
$462$	47.5557	+	24.0350i	2.21249	+	1.11821i
$463$		−	20.3766i		−	0.946980i	−0.880799	−	0.473490i	$-0.842994\pi$
$463$		−	20.3766i		−	0.946980i	0.880799	−	0.473490i	$-0.157006\pi$
$464$	5.07172	−	16.3340i	0.235449	−	0.758287i
$465$		−	17.6268i		−	0.817422i
$466$	17.0916	−	33.8174i	0.791753	−	1.56656i
$467$	−30.8277			−1.42654			−0.713268	−	0.700892i	$-0.752786\pi$
$467$	−30.8277			−1.42654			−0.713268	+	0.700892i	$0.752786\pi$
$468$	4.53182	+	6.15238i	0.209483	+	0.284394i
$469$	28.2171			1.30295
$470$	6.25744	−	12.3810i	0.288634	−	0.571092i
$471$	10.5224			0.484849
$472$	0.883156	+	5.24224i	0.0406506	+	0.241293i
$473$	54.4508			2.50365
$474$	−13.3417	−	6.74302i	−0.612806	−	0.309717i
$475$	−2.68161			−0.123041
$476$	−27.4100	+	20.1901i	−1.25634	+	0.925411i
$477$			58.5837i			2.68236i
$478$	−29.7702	−	15.0461i	−1.36166	−	0.688193i
$479$	−14.5699			−0.665715			−0.332858	−	0.942977i	$-0.608013\pi$
$479$	−14.5699			−0.665715			−0.332858	+	0.942977i	$0.608013\pi$
$480$	−11.6764	−	11.3003i	−0.532954	−	0.515784i
$481$			2.81970i			0.128567i
$482$	−0.267818	−	0.135357i	−0.0121988	−	0.00616535i
$483$	−32.7863	+	17.0217i	−1.49183	+	0.774513i
$484$	−15.3318	−	20.8144i	−0.696900	−	0.946110i
$485$	−2.68434			−0.121890
$486$	−14.2579	−	7.20604i	−0.646750	−	0.326873i
$487$			2.18374i			0.0989549i	0.998775	+	0.0494774i	$0.0157556\pi$
$487$			2.18374i			0.0989549i	−0.998775	+	0.0494774i	$0.984244\pi$
$488$	−3.25795	−	19.3385i	−0.147481	−	0.875415i
$489$	47.8522			2.16395
$490$	−0.241138	−	0.121873i	−0.0108935	−	0.00550568i
$491$		−	7.55568i		−	0.340983i	−0.985359	−	0.170491i	$-0.945464\pi$
$491$		−	7.55568i		−	0.340983i	0.985359	−	0.170491i	$-0.0545355\pi$
$492$	37.3361	−	27.5016i	1.68324	−	1.23987i
$493$		−	27.1410i		−	1.22237i
$494$	−1.24464	+	2.46264i	−0.0559989	+	0.110799i
$495$			25.6852i			1.15446i
$496$	23.4418	+	7.27870i	1.05257	+	0.326823i
$497$			19.4381i			0.871919i
$498$	17.2348	+	8.71062i	0.772311	+	0.390332i
$499$			10.0079i			0.448015i	0.974587	+	0.224007i	$0.0719140\pi$
$499$			10.0079i			0.448015i	−0.974587	+	0.224007i	$0.928086\pi$
$500$	−1.61030	+	1.18614i	−0.0720149	+	0.0530458i
$501$	−5.39889			−0.241204
$502$	7.09054	−	14.0293i	0.316466	−	0.626160i
$503$	32.7697			1.46113			0.730563	−	0.682845i	$-0.239258\pi$
$503$	32.7697			1.46113			0.730563	+	0.682845i	$0.239258\pi$
$504$	39.2747	−	6.61659i	1.74943	−	0.294726i
$505$			1.53860i			0.0684666i
$506$	33.1731	−	0.361617i	1.47472	−	0.0160758i
$507$			35.8215i			1.59089i
$508$	−4.91710	+	3.62191i	−0.218161	+	0.160696i
$509$	−4.89723			−0.217066			−0.108533	−	0.994093i	$-0.534615\pi$
$509$	−4.89723			−0.217066			−0.108533	+	0.994093i	$0.534615\pi$
$510$	−23.0133	−	11.6311i	−1.01905	−	0.515034i
$511$	−21.2084			−0.938204
$512$	19.8498	−	10.8622i	0.877244	−	0.480045i
$513$			17.3398i			0.765570i
$514$	−0.800256	+	1.58339i	−0.0352978	+	0.0698402i
$515$		−	18.1121i		−	0.798116i
$516$	51.4913	−	37.9283i	2.26678	−	1.66970i
$517$		−	47.9811i		−	2.11021i
$518$	13.1168	+	6.62936i	0.576321	+	0.291277i
$519$		−	18.2331i		−	0.800346i
$520$	0.341882	+	2.02934i	0.0149925	+	0.0889924i
$521$		−	31.5065i		−	1.38033i	−0.723654	−	0.690163i	$-0.757539\pi$
$521$		−	31.5065i		−	1.38033i	0.723654	−	0.690163i	$-0.242461\pi$
$522$	−14.3228	+	28.3391i	−0.626892	+	1.24037i
$523$	−29.1444			−1.27440			−0.637198	−	0.770700i	$-0.719906\pi$
$523$	−29.1444			−1.27440			−0.637198	+	0.770700i	$0.719906\pi$
$524$	−4.98696	+	3.67337i	−0.217856	+	0.160472i
$525$		−	7.70285i		−	0.336180i
$526$	16.3790	−	32.4075i	0.714158	−	1.41303i
$527$	38.9514			1.69675
$528$	−53.6738	−	16.6658i	−2.33585	−	0.725284i
$529$	−13.2337	+	18.8114i	−0.575378	+	0.817888i
$530$	−7.11684	+	14.0814i	−0.309136	+	0.611656i
$531$		−	9.86956i		−	0.428302i
$532$	8.52960	+	11.5798i	0.369805	+	0.502046i
$533$	−5.87291			−0.254384
$534$	−14.8874	+	29.4561i	−0.644239	+	1.27469i
$535$			11.1319i			0.481276i
$536$	−29.3484	+	4.94431i	−1.26766	+	0.213562i
$537$	8.89578			0.383881
$538$	−13.0257	+	25.7726i	−0.561576	+	1.11113i
$539$	−0.934506			−0.0402520
$540$	7.66979	+	10.4125i	0.330055	+	0.448082i
$541$	10.0459			0.431906			0.215953	−	0.976404i	$-0.430714\pi$
$541$	10.0459			0.431906			0.215953	+	0.976404i	$0.430714\pi$
$542$	3.89645	+	1.96930i	0.167367	+	0.0845886i
$543$	30.9107			1.32651
$544$	24.9711	−	25.8024i	1.07063	−	1.10627i
$545$	10.6447			0.455968
$546$	−7.07386	−	3.57518i	−0.302733	−	0.153004i
$547$			40.9194i			1.74959i	0.484495	+	0.874794i	$0.339003\pi$
$547$			40.9194i			1.74959i	−0.484495	+	0.874794i	$0.660997\pi$
$548$	−9.54231	+	7.02882i	−0.407627	+	0.300256i
$549$			36.4087i			1.55389i
$550$	−3.12027	+	6.17377i	−0.133049	+	0.263251i
$551$	−11.4661			−0.488472
$552$	31.1182	−	23.4490i	1.32448	−	0.998057i
$553$	9.86814			0.419636
$554$	−1.89109	+	3.74172i	−0.0803449	+	0.158970i
$555$			11.1319i			0.472525i
$556$	−5.35377	+	3.94356i	−0.227050	+	0.167244i
$557$		−	5.20180i		−	0.220407i	−0.993909	−	0.110204i	$-0.964850\pi$
$557$		−	5.20180i		−	0.220407i	0.993909	−	0.110204i	$-0.0351503\pi$
$558$	−40.6709	−	20.5554i	−1.72174	−	0.870180i
$559$	−8.09950			−0.342572
$560$	10.2440	+	3.18077i	0.432888	+	0.134412i
$561$	−89.1856			−3.76542
$562$	11.2788	+	5.70038i	0.475766	+	0.240456i
$563$	22.2639			0.938311			0.469156	−	0.883115i	$-0.344558\pi$
$563$	22.2639			0.938311			0.469156	+	0.883115i	$0.344558\pi$
$564$	−33.4217	−	45.3733i	−1.40731	−	1.91056i
$565$	−5.41399			−0.227768
$566$	−10.9943	+	21.7533i	−0.462124	+	0.914358i
$567$	−7.56387			−0.317652
$568$	−3.40602	−	20.2174i	−0.142913	−	0.848304i
$569$			33.1614i			1.39020i	0.718913	+	0.695100i	$0.244640\pi$
$569$			33.1614i			1.39020i	−0.718913	+	0.695100i	$0.755360\pi$
$570$	−4.91373	+	9.72230i	−0.205814	+	0.407222i
$571$	−3.20810			−0.134255			−0.0671274	−	0.997744i	$-0.521383\pi$
$571$	−3.20810			−0.134255			−0.0671274	+	0.997744i	$0.521383\pi$
$572$	4.22140	+	5.73096i	0.176506	+	0.239623i
$573$			13.6549i			0.570443i
$574$	−13.8077	+	27.3200i	−0.576323	+	1.14031i
$575$	−2.20979	−	4.25639i	−0.0921545	−	0.177504i
$576$	−39.6899	+	13.7637i	−1.65375	+	0.573488i
$577$	12.3249			0.513091			0.256545	−	0.966532i	$-0.417416\pi$
$577$	12.3249			0.513091			0.256545	+	0.966532i	$0.417416\pi$
$578$	14.8578	−	29.3976i	0.618002	−	1.22278i
$579$		−	61.3675i		−	2.55034i
$580$	−6.88536	+	5.07172i	−0.285899	+	0.210592i
$581$	−12.7476			−0.528861
$582$	−4.91873	+	9.73219i	−0.203888	+	0.403412i
$583$			54.5709i			2.26009i
$584$	22.0587	−	3.71621i	0.912795	−	0.153778i
$585$		−	3.82064i		−	0.157964i
$586$	−25.6852	−	12.9815i	−1.06104	−	0.536260i
$587$		−	8.83980i		−	0.364857i	−0.983219	−	0.182429i	$-0.941604\pi$
$587$		−	8.83980i		−	0.364857i	0.983219	−	0.182429i	$-0.0583959\pi$
$588$	−0.883714	+	0.650940i	−0.0364438	+	0.0268443i
$589$		−	16.4556i		−	0.678041i
$590$	1.19897	−	2.37228i	0.0493608	−	0.0976653i
$591$		−	58.8821i		−	2.42208i
$592$	−14.8043	−	4.59676i	−0.608455	−	0.188926i
$593$	2.38210			0.0978212			0.0489106	−	0.998803i	$-0.484425\pi$
$593$	2.38210			0.0978212			0.0489106	+	0.998803i	$0.484425\pi$
$594$	39.9207	+	20.1762i	1.63797	+	0.827841i
$595$	17.0217			0.697820
$596$	−23.2273	+	17.1092i	−0.951429	+	0.700818i
$597$			43.8803i			1.79590i
$598$	−4.93447	+	0.0537902i	−0.201785	+	0.00219964i
$599$		−	8.38036i		−	0.342412i	−0.985235	−	0.171206i	$-0.945234\pi$
$599$		−	8.38036i		−	0.342412i	0.985235	−	0.171206i	$-0.0547664\pi$
$600$	1.34972	+	8.01167i	0.0551022	+	0.327075i
$601$	29.2981			1.19509			0.597547	−	0.801834i	$-0.296142\pi$
$601$	29.2981			1.19509			0.597547	+	0.801834i	$0.296142\pi$
$602$	−19.0426	+	37.6777i	−0.776120	+	1.53563i
$603$	55.2543			2.25013
$604$	−21.4301	+	15.7853i	−0.871980	+	0.642297i
$605$			12.9258i			0.525508i
$606$	5.57825	+	2.81929i	0.226601	+	0.114526i
$607$		−	6.58224i		−	0.267165i	−0.991038	−	0.133582i	$-0.957352\pi$
$607$		−	6.58224i		−	0.267165i	0.991038	−	0.133582i	$-0.0426481\pi$
$608$	−10.9006	−	10.5494i	−0.442078	−	0.427836i
$609$		−	32.9360i		−	1.33464i
$610$	−4.42299	+	8.75132i	−0.179082	+	0.354331i
$611$			7.13714i			0.288738i
$612$	−53.6738	+	39.5359i	−2.16963	+	1.59814i
$613$			31.7187i			1.28111i	0.767914	+	0.640553i	$0.221295\pi$
$613$			31.7187i			1.28111i	−0.767914	+	0.640553i	$0.778705\pi$
$614$	41.5557	+	21.0026i	1.67705	+	0.847595i
$615$	−23.1858			−0.934941
$616$	36.5845	−	6.16337i	1.47403	−	0.248329i
$617$			41.9737i			1.68980i	0.534925	+	0.844899i	$0.320340\pi$
$617$			41.9737i			1.68980i	−0.534925	+	0.844899i	$0.679660\pi$
$618$	−65.6663	−	33.1883i	−2.64149	−	1.33503i
$619$	40.4232			1.62474			0.812372	−	0.583139i	$-0.198176\pi$
$619$	40.4232			1.62474			0.812372	+	0.583139i	$0.198176\pi$
$620$	−7.27870	−	9.88154i	−0.292319	−	0.396852i
$621$	−27.5226	+	14.2889i	−1.10444	+	0.573392i
$622$	−39.9700	−	20.2011i	−1.60265	−	0.809992i
$623$		−	21.7871i		−	0.872880i
$624$	7.98391	+	2.47901i	0.319612	+	0.0992399i
$625$	1.00000			0.0400000
$626$	−7.47935	−	3.78012i	−0.298935	−	0.151084i
$627$			37.6777i			1.50470i
$628$	5.89886	−	4.34508i	0.235390	−	0.173387i
$629$	−24.5992			−0.980836
$630$	−17.7731	−	8.98266i	−0.708096	−	0.357878i
$631$	3.27191			0.130253			0.0651263	−	0.997877i	$-0.479255\pi$
$631$	3.27191			0.130253			0.0651263	+	0.997877i	$0.479255\pi$
$632$	−10.2638	+	1.72913i	−0.408271	+	0.0687812i
$633$	74.8967			2.97688
$634$	−9.12715	+	18.0590i	−0.362486	+	0.717214i
$635$	3.05353			0.121176
$636$	38.0119	+	51.6048i	1.50727	+	2.04627i
$637$	0.139007			0.00550765
$638$	−13.3417	+	26.3979i	−0.528204	+	1.04510i
$639$			38.0633i			1.50576i
$640$	−11.2120	−	1.51330i	−0.443195	−	0.0598185i
$641$		−	2.70337i		−	0.106777i	−0.998574	−	0.0533884i	$-0.982998\pi$
$641$		−	2.70337i		−	0.106777i	0.998574	−	0.0533884i	$-0.0170021\pi$
$642$	40.3594	+	20.3979i	1.59286	+	0.805043i
$643$	−3.81007			−0.150254			−0.0751272	−	0.997174i	$-0.523936\pi$
$643$	−3.81007			−0.150254			−0.0751272	+	0.997174i	$0.523936\pi$
$644$	−11.3511	+	23.0809i	−0.447297	+	0.909515i
$645$	−31.9762			−1.25906
$646$	−21.4842	−	10.8583i	−0.845285	−	0.427214i
$647$			5.11436i			0.201066i	0.994934	+	0.100533i	$0.0320548\pi$
$647$			5.11436i			0.201066i	−0.994934	+	0.100533i	$0.967945\pi$
$648$	7.86711	−	1.32537i	0.309049	−	0.0520654i
$649$		−	9.19352i		−	0.360877i
$650$	0.464138	−	0.918342i	0.0182050	−	0.0360203i
$651$	47.2682			1.85259
$652$	26.8258	−	19.7598i	1.05058	−	0.773853i
$653$	−27.5197			−1.07693			−0.538465	−	0.842648i	$-0.680996\pi$
$653$	−27.5197			−1.07693			−0.538465	+	0.842648i	$0.680996\pi$
$654$	19.5051	−	38.5928i	0.762710	−	1.50910i
$655$	3.09691			0.121006
$656$	9.57420	−	30.8347i	0.373810	−	1.20389i
$657$	−41.5299			−1.62024
$658$	33.2010	+	16.7800i	1.29431	+	0.654154i
$659$	31.4372			1.22462			0.612310	−	0.790618i	$-0.290241\pi$
$659$	31.4372			1.22462			0.612310	+	0.790618i	$0.290241\pi$
$660$	16.6658	+	22.6254i	0.648713	+	0.880692i
$661$			0.251685i			0.00978943i	0.999988	+	0.00489471i	$0.00155804\pi$
$661$			0.251685i			0.00978943i	−0.999988	+	0.00489471i	$0.998442\pi$
$662$	−19.1382	−	9.67259i	−0.743826	−	0.375936i
$663$	13.2663			0.515219
$664$	13.2587	−	2.23369i	0.514538	−	0.0866839i
$665$		−	7.19105i		−	0.278857i
$666$	25.6852	+	12.9815i	0.995280	+	0.503022i
$667$	−9.44865	−	18.1996i	−0.365853	−	0.704690i
$668$	−3.02661	+	2.22938i	−0.117103	+	0.0862575i
$669$	4.24921			0.164284
$670$	13.2811	+	6.71238i	0.513094	+	0.259322i
$671$			33.9148i			1.30927i
$672$	30.3029	−	31.3117i	1.16896	−	1.20787i
$673$	−9.56375			−0.368655			−0.184328	−	0.982865i	$-0.559011\pi$
$673$	−9.56375			−0.368655			−0.184328	+	0.982865i	$0.559011\pi$
$674$	14.5805	+	7.36912i	0.561621	+	0.283848i
$675$		−	6.46618i		−	0.248883i
$676$	14.7919	+	20.0814i	0.568919	+	0.772363i
$677$		−	48.6951i		−	1.87150i	−0.352658	−	0.935752i	$-0.614722\pi$
$677$		−	48.6951i		−	1.87150i	0.352658	−	0.935752i	$-0.385278\pi$
$678$	−9.92048	+	19.6286i	−0.380994	+	0.753834i
$679$		−	7.19837i		−	0.276248i
$680$	−17.7041	+	2.98260i	−0.678921	+	0.114377i
$681$		−	6.32127i		−	0.242232i
$682$	−37.8851	−	19.1474i	−1.45069	−	0.733193i
$683$			23.9040i			0.914662i	0.889297	+	0.457331i	$0.151195\pi$
$683$			23.9040i			0.914662i	−0.889297	+	0.457331i	$0.848805\pi$
$684$	16.7025	+	22.6753i	0.638636	+	0.867010i
$685$	5.92579			0.226413
$686$	−11.6476	+	23.0459i	−0.444707	+	0.879897i
$687$	−50.0212			−1.90843
$688$	13.2041	−	42.5250i	0.503400	−	1.62125i
$689$		−	8.11736i		−	0.309247i
$690$	−19.4809	+	0.212359i	−0.741625	+	0.00808438i
$691$		−	32.6562i		−	1.24230i	−0.783691	−	0.621150i	$-0.786666\pi$
$691$		−	32.6562i		−	1.24230i	0.783691	−	0.621150i	$-0.213334\pi$
$692$	−7.52908	−	10.2215i	−0.286213	−	0.388562i
$693$	−68.8777			−2.61645
$694$	−4.97609	−	2.51495i	−0.188890	−	0.0954664i
$695$	3.32470			0.126113
$696$	5.77117	+	34.2565i	0.218756	+	1.29849i
$697$		−	51.2356i		−	1.94069i
$698$	9.11105	−	18.0271i	0.344858	−	0.682336i
$699$			76.9624i			2.91098i
$700$	−3.18077	−	4.31821i	−0.120222	−	0.163213i
$701$		−	6.51180i		−	0.245947i	−0.992410	−	0.122974i	$-0.960757\pi$
$701$		−	6.51180i		−	0.245947i	0.992410	−	0.122974i	$-0.0392431\pi$
$702$	−5.93816	−	3.00119i	−0.224121	−	0.113273i
$703$			10.3923i			0.391953i
$704$	−36.9713	+	12.8209i	−1.39341	+	0.483207i
$705$			28.1769i			1.06120i
$706$	15.4706	−	30.6101i	0.582244	−	1.15203i
$707$	−4.12592			−0.155171
$708$	−6.40384	−	8.69384i	−0.240671	−	0.326734i
$709$		−	8.35583i		−	0.313810i	−0.987614	−	0.156905i	$-0.949848\pi$
$709$		−	8.35583i		−	0.313810i	0.987614	−	0.156905i	$-0.0501516\pi$
$710$	−4.62400	+	9.14904i	−0.173536	+	0.343357i
$711$	19.3236			0.724692
$712$	3.81761	+	22.6605i	0.143071	+	0.849239i
$713$	26.1191	−	13.5602i	0.978169	−	0.507835i
$714$	31.1901	−	61.7128i	1.16726	−	2.30954i
$715$		−	3.55894i		−	0.133097i
$716$	4.98696	−	3.67337i	0.186371	−	0.137280i
$717$	67.7517			2.53023
$718$	−22.4604	+	44.4401i	−0.838214	+	1.65849i
$719$			3.98961i			0.148787i	0.997229	+	0.0743937i	$0.0237021\pi$
$719$			3.98961i			0.148787i	−0.997229	+	0.0743937i	$0.976298\pi$
$720$	20.0596	+	6.22853i	0.747577	+	0.232123i
$721$	48.5698			1.80883
$722$	7.53305	−	14.9049i	0.280351	−	0.554703i
$723$	0.609505			0.0226677
$724$	17.3285	−	12.7641i	0.644008	−	0.474373i
$725$	4.27582			0.158800
$726$	46.8630	+	23.6849i	1.73925	+	0.879031i
$727$	26.1403			0.969490			0.484745	−	0.874656i	$-0.338912\pi$
$727$	26.1403			0.969490			0.484745	+	0.874656i	$0.338912\pi$
$728$	−5.44191	+	0.916794i	−0.201690	+	0.0339787i
$729$	40.9103			1.51520
$730$	−9.98227	−	5.04512i	−0.369460	−	0.186728i
$731$		−	70.6606i		−	2.61348i
$732$	23.6237	+	32.0715i	0.873157	+	1.18540i
$733$		−	46.1008i		−	1.70277i	−0.524540	−	0.851386i	$-0.675763\pi$
$733$		−	46.1008i		−	1.70277i	0.524540	−	0.851386i	$-0.324237\pi$
$734$	−2.87808	+	5.69458i	−0.106232	+	0.210191i
$735$	0.548788			0.0202424
$736$	7.76190	−	25.9952i	0.286108	−	0.958198i
$737$	51.4695			1.89590
$738$	−27.0380	+	53.4974i	−0.995284	+	1.96927i
$739$		−	32.2296i		−	1.18559i	−0.805355	−	0.592793i	$-0.798025\pi$
$739$		−	32.2296i		−	1.18559i	0.805355	−	0.592793i	$-0.201975\pi$
$740$	4.59676	+	6.24055i	0.168980	+	0.229407i
$741$		−	5.60452i		−	0.205887i
$742$	−37.7608	−	19.0846i	−1.38624	−	0.700619i
$743$	−33.3792			−1.22456			−0.612281	−	0.790640i	$-0.709748\pi$
$743$	−33.3792			−1.22456			−0.612281	+	0.790640i	$0.709748\pi$
$744$	−49.1633	+	8.28250i	−1.80241	+	0.303651i
$745$	14.4242			0.528463
$746$	−1.33246	−	0.673438i	−0.0487850	−	0.0246563i
$747$	−24.9622			−0.913319
$748$	−49.9973	+	36.8278i	−1.82808	+	1.34656i
$749$	−29.8516			−1.09075
$750$	1.83238	−	3.62554i	0.0669090	−	0.132386i
$751$	−1.95865			−0.0714723			−0.0357362	−	0.999361i	$-0.511378\pi$
$751$	−1.95865			−0.0714723			−0.0357362	+	0.999361i	$0.511378\pi$
$752$	−37.4723	−	11.6352i	−1.36648	−	0.424292i
$753$			31.9283i			1.16353i
$754$	1.98457	−	3.92667i	0.0722737	−	0.143001i
$755$	13.3082			0.484333
$756$	−27.9223	+	20.5674i	−1.01552	+	0.748030i
$757$			16.8031i			0.610721i	0.952237	+	0.305360i	$0.0987769\pi$
$757$			16.8031i			0.610721i	−0.952237	+	0.305360i	$0.901223\pi$
$758$	−4.13528	+	8.18205i	−0.150200	+	0.297186i
$759$	−59.8040	+	31.0484i	−2.17075	+	1.12698i
$760$	1.26004	+	7.47935i	0.0457065	+	0.271305i
$761$	−44.9975			−1.63116			−0.815579	−	0.578646i	$-0.803581\pi$
$761$	−44.9975			−1.63116			−0.815579	+	0.578646i	$0.803581\pi$
$762$	5.59522	−	11.0707i	0.202693	−	0.401049i
$763$			28.5449i			1.03340i
$764$	5.63858	+	7.65492i	0.203997	+	0.276945i
$765$	33.3315			1.20510
$766$	0.860637	−	1.70285i	0.0310961	−	0.0615266i
$767$			1.36753i			0.0493785i
$768$	−26.0313	+	37.8768i	−0.939322	+	1.36676i
$769$		−	19.8146i		−	0.714531i	−0.934003	−	0.357266i	$-0.883709\pi$
$769$		−	19.8146i		−	0.714531i	0.934003	−	0.357266i	$-0.116291\pi$
$770$	−16.5557	−	8.36737i	−0.596625	−	0.301539i
$771$		−	3.60350i		−	0.129777i
$772$	−25.3407	−	34.4025i	−0.912032	−	1.23817i
$773$		−	47.4024i		−	1.70494i	−0.522772	−	0.852472i	$-0.675102\pi$
$773$		−	47.4024i		−	1.70494i	0.522772	−	0.852472i	$-0.324898\pi$
$774$	−37.2889	+	73.7798i	−1.34032	+	2.65196i
$775$			6.13645i			0.220428i
$776$	1.26132	+	7.48696i	0.0452789	+	0.268766i
$777$	−29.8516			−1.07092
$778$	−13.1071	−	6.62443i	−0.469912	−	0.237497i
$779$	−21.6452			−0.775521
$780$	−2.47901	−	3.36550i	−0.0887629	−	0.120504i
$781$			35.4561i			1.26872i
$782$	−0.469269	−	43.0486i	−0.0167810	−	1.53941i
$783$		−	27.6482i		−	0.988066i
$784$	−0.226613	+	0.729831i	−0.00809333	+	0.0260654i
$785$	−3.66320			−0.130745
$786$	5.67471	−	11.2280i	0.202410	−	0.400488i
$787$	28.8128			1.02706			0.513532	−	0.858070i	$-0.328337\pi$
$787$	28.8128			1.02706			0.513532	+	0.858070i	$0.328337\pi$
$788$	−24.3144	−	33.0092i	−0.866165	−	1.17590i
$789$			73.7536i			2.62570i
$790$	4.64469	+	2.34746i	0.165251	+	0.0835190i
$791$		−	14.5182i		−	0.516209i
$792$	71.6391	−	12.0690i	2.54558	−	0.428853i
$793$		−	5.04479i		−	0.179146i
$794$	14.9669	−	29.6134i	0.531154	−	1.05094i
$795$		−	32.0467i		−	1.13658i
$796$	18.1197	+	24.5992i	0.642235	+	0.871897i
$797$			29.1492i			1.03252i	0.856432	+	0.516260i	$0.172676\pi$
$797$			29.1492i			1.03252i	−0.856432	+	0.516260i	$0.827324\pi$
$798$	−26.0715	−	13.1767i	−0.922920	−	0.466451i
$799$	−62.2649			−2.20277
$800$	4.06494	+	3.93398i	0.143717	+	0.139087i
$801$		−	42.6630i		−	1.50742i
$802$	−33.2582	−	16.8089i	−1.17439	−	0.593545i
$803$	−38.6852			−1.36517
$804$	48.6720	−	35.8516i	1.71653	−	1.26439i
$805$	11.4140	−	5.92579i	0.402290	−	0.208857i
$806$	5.63536	+	2.84816i	0.198497	+	0.100322i
$807$		−	58.6537i		−	2.06471i
$808$	4.29134	−	0.722959i	0.150969	−	0.0254336i
$809$	−39.3289			−1.38273			−0.691365	−	0.722506i	$-0.742990\pi$
$809$	−39.3289			−1.38273			−0.691365	+	0.722506i	$0.742990\pi$
$810$	−3.56012	−	1.79932i	−0.125090	−	0.0632215i
$811$			25.2461i			0.886510i	0.896396	+	0.443255i	$0.146176\pi$
$811$			25.2461i			0.886510i	−0.896396	+	0.443255i	$0.853824\pi$
$812$	−13.6004	−	18.4639i	−0.477281	−	0.647955i
$813$	−8.86763			−0.311001
$814$	23.9258	+	12.0923i	0.838599	+	0.423835i
$815$	−16.6589			−0.583536
$816$	−21.6271	+	69.6522i	−0.757099	+	2.43831i
$817$	−29.8516			−1.04437
$818$	−11.7081	+	23.1656i	−0.409363	+	0.809965i
$819$	10.2455			0.358006
$820$	−12.9979	+	9.57420i	−0.453907	+	0.334346i
$821$	11.0606			0.386019			0.193009	−	0.981197i	$-0.438175\pi$
$821$	11.0606			0.386019			0.193009	+	0.981197i	$0.438175\pi$
$822$	10.8583	−	21.4842i	0.378727	−	0.749348i
$823$			9.36041i			0.326283i	0.986603	+	0.163142i	$0.0521628\pi$
$823$			9.36041i			0.326283i	−0.986603	+	0.163142i	$0.947837\pi$
$824$	−50.5170	+	8.51057i	−1.75984	+	0.296480i
$825$		−	14.0504i		−	0.489172i
$826$	6.36154	+	3.21517i	0.221346	+	0.111870i
$827$	−50.8347			−1.76770			−0.883848	−	0.467775i	$-0.845056\pi$
$827$	−50.8347			−1.76770			−0.883848	+	0.467775i	$0.845056\pi$
$828$	−22.2276	+	45.1966i	−0.772462	+	1.57069i
$829$	6.23369			0.216505			0.108252	−	0.994123i	$-0.465475\pi$
$829$	6.23369			0.216505			0.108252	+	0.994123i	$0.465475\pi$
$830$	−6.00000	−	3.03245i	−0.208263	−	0.105258i
$831$		−	8.51548i		−	0.295399i
$832$	5.49944	−	1.90710i	0.190659	−	0.0661168i
$833$			1.21270i			0.0420177i
$834$	6.09211	−	12.0538i	0.210952	−	0.417390i
$835$	1.87953			0.0650437
$836$	15.5584	+	21.1221i	0.538099	+	0.730522i
$837$	39.6794			1.37152
$838$	12.9742	−	25.6708i	0.448187	−	0.886782i
$839$	−14.6079			−0.504320			−0.252160	−	0.967686i	$-0.581141\pi$
$839$	−14.6079			−0.504320			−0.252160	+	0.967686i	$0.581141\pi$
$840$	−21.4842	+	3.61943i	−0.741276	+	0.124882i
$841$	−10.7174			−0.369564
$842$	11.6403	+	5.88308i	0.401150	+	0.202744i
$843$	−25.6685			−0.884069
$844$	41.9869	−	30.9274i	1.44525	−	1.06456i
$845$		−	12.4706i		−	0.429002i
$846$	65.0135	+	32.8584i	2.23521	+	1.12969i
$847$	−34.6620			−1.19100
$848$	42.6188	+	13.2332i	1.46354	+	0.454429i
$849$		−	49.5065i		−	1.69906i
$850$	8.01167	+	4.04917i	0.274798	+	0.138885i
$851$	−16.4952	+	8.56379i	−0.565447	+	0.293563i
$852$	24.6973	+	33.5290i	0.846116	+	1.14868i
$853$	33.5602			1.14908			0.574541	−	0.818476i	$-0.305181\pi$
$853$	33.5602			1.14908			0.574541	+	0.818476i	$0.305181\pi$
$854$	−23.4677	−	11.8607i	−0.803047	−	0.405866i
$855$		−	14.0814i		−	0.481573i
$856$	31.0484	−	5.23070i	1.06121	−	0.178782i
$857$	−51.6052			−1.76280			−0.881400	−	0.472372i	$-0.843398\pi$
$857$	−51.6052			−1.76280			−0.881400	+	0.472372i	$0.843398\pi$
$858$	−12.9031	−	6.52132i	−0.440504	−	0.222634i
$859$		−	27.1505i		−	0.926365i	−0.886263	−	0.463182i	$-0.846708\pi$
$859$		−	27.1505i		−	0.926365i	0.886263	−	0.463182i	$-0.153292\pi$
$860$	−17.9258	+	13.2041i	−0.611264	+	0.450255i
$861$		−	62.1753i		−	2.11893i
$862$	−6.55801	+	12.9757i	−0.223367	+	0.441953i
$863$		−	8.73671i		−	0.297401i	−0.988882	−	0.148701i	$-0.952491\pi$
$863$		−	8.73671i		−	0.297401i	0.988882	−	0.148701i	$-0.0475091\pi$
$864$	25.4378	−	26.2846i	0.865412	−	0.894222i
$865$			6.34755i			0.215823i
$866$	−22.4786	−	11.3608i	−0.763852	−	0.386057i
$867$			66.9037i			2.27217i
$868$	26.4985	−	19.5186i	0.899417	−	0.662506i
$869$	18.0000			0.610608
$870$	7.83492	−	15.5022i	0.265629	−	0.525573i
$871$	−7.65603			−0.259415
$872$	−5.00175	−	29.6894i	−0.169381	−	1.00541i
$873$		−	14.0957i		−	0.477067i
$874$	−18.1865	+	0.198249i	−0.615168	+	0.00670589i
$875$			2.68161i			0.0906551i
$876$	−36.5826	+	26.9466i	−1.23601	+	0.910440i
$877$	15.0426			0.507954			0.253977	−	0.967210i	$-0.418261\pi$
$877$	15.0426			0.507954			0.253977	+	0.967210i	$0.418261\pi$
$878$	18.9017	+	9.55309i	0.637903	+	0.322401i
$879$	58.4548			1.97163
$880$	18.6856	+	5.80189i	0.629891	+	0.195582i
$881$		−	18.6951i		−	0.629854i	−0.949116	−	0.314927i	$-0.898020\pi$
$881$		−	18.6951i		−	0.629854i	0.949116	−	0.314927i	$-0.101980\pi$
$882$	0.639967	−	1.26624i	0.0215488	−	0.0426365i
$883$			0.220695i			0.00742699i	0.999993	+	0.00371350i	$0.00118205\pi$
$883$			0.220695i			0.00742699i	−0.999993	+	0.00371350i	$0.998818\pi$
$884$	7.43704	−	5.47809i	0.250135	−	0.184248i
$885$			5.39889i			0.181482i
$886$	17.6807	+	8.93595i	0.593994	+	0.300209i
$887$			36.1252i			1.21297i	0.795096	+	0.606483i	$0.207420\pi$
$887$			36.1252i			1.21297i	−0.795096	+	0.606483i	$0.792580\pi$
$888$	31.0484	−	5.23070i	1.04192	−	0.175531i
$889$			8.18838i			0.274630i
$890$	5.18277	−	10.2546i	0.173727	−	0.343736i
$891$	−13.7969			−0.462213
$892$	2.38210	−	1.75465i	0.0797587	−	0.0587499i
$893$			26.3047i			0.880254i
$894$	26.4306	−	52.2956i	0.883973	−	1.74903i
$895$	−3.09691			−0.103518
$896$	4.05809	−	30.0664i	0.135571	−	1.00445i
$897$	8.89578	−	4.61841i	0.297021	−	0.154204i
$898$	18.1085	−	35.8294i	0.604288	−	1.19564i
$899$			26.2384i			0.875099i
$900$	−6.22853	−	8.45583i	−0.207618	−	0.281861i
$901$	70.8164			2.35924
$902$	−25.1860	+	49.8330i	−0.838602	+	1.65926i
$903$		−	85.7478i		−	2.85351i
$904$	2.54394	+	15.1003i	0.0846100	+	0.502228i
$905$	−10.7610			−0.357708
$906$	24.3856	−	48.2493i	0.810157	−	1.60298i
$907$	17.3062			0.574642			0.287321	−	0.957834i	$-0.407235\pi$
$907$	17.3062			0.574642			0.287321	+	0.957834i	$0.407235\pi$
$908$	−2.61027	−	3.54369i	−0.0866248	−	0.117602i
$909$	−8.07930			−0.267974
$910$	2.46264	+	1.24464i	0.0816357	+	0.0412593i
$911$	36.3949			1.20582			0.602909	−	0.797810i	$-0.294008\pi$
$911$	36.3949			1.20582			0.602909	+	0.797810i	$0.294008\pi$
$912$	29.4256	+	9.13667i	0.974378	+	0.302545i
$913$	−23.2524			−0.769541
$914$	44.9829	+	22.7347i	1.48790	+	0.751998i
$915$		−	19.9164i		−	0.658417i
$916$	−28.0418	+	20.6554i	−0.926526	+	0.682475i
$917$			8.30471i			0.274246i
$918$	26.1826	−	51.8049i	0.864155	−	1.70982i
$919$	11.5400			0.380668			0.190334	−	0.981719i	$-0.439043\pi$
$919$	11.5400			0.380668			0.190334	+	0.981719i	$0.439043\pi$
$920$	−10.8333	+	8.16337i	−0.357162	+	0.269138i
$921$	−94.5733			−3.11630
$922$	0.697148	−	1.37938i	0.0229594	−	0.0454274i
$923$		−	5.27406i		−	0.173598i
$924$	−60.6725	+	44.6911i	−1.99598	+	1.47023i
$925$		−	3.87539i		−	0.127422i
$926$	25.7187	+	12.9984i	0.845169	+	0.427155i
$927$	95.1084			3.12377
$928$	17.3810	+	16.8210i	0.570558	+	0.552177i
$929$	14.6414			0.480368			0.240184	−	0.970727i	$-0.422792\pi$
$929$	14.6414			0.480368			0.240184	+	0.970727i	$0.422792\pi$
$930$	22.2480	+	11.2443i	0.729540	+	0.368715i
$931$	0.512325			0.0167908
$932$	31.7804	+	43.1450i	1.04100	+	1.41326i
$933$	90.9645			2.97804
$934$	19.6653	−	38.9098i	0.643468	−	1.27317i
$935$	31.0484			1.01539
$936$	−10.6562	+	1.79525i	−0.348310	+	0.0586796i
$937$		−	10.9207i		−	0.356762i	−0.983961	−	0.178381i	$-0.942914\pi$
$937$		−	10.9207i		−	0.356762i	0.983961	−	0.178381i	$-0.0570860\pi$
$938$	−18.0000	+	35.6148i	−0.587721	+	1.16286i
$939$	17.0217			0.555481
$940$	11.6352	+	15.7959i	0.379498	+	0.515206i
$941$		−	24.4113i		−	0.795786i	−0.917432	−	0.397893i	$-0.869741\pi$
$941$		−	24.4113i		−	0.795786i	0.917432	−	0.397893i	$-0.130259\pi$
$942$	−6.71238	+	13.2811i	−0.218701	+	0.432722i
$943$	−17.8368	−	34.3564i	−0.580846	−	1.11880i
$944$	−7.17996	−	2.22938i	−0.233688	−	0.0725603i
$945$	17.3398			0.564063
$946$	−34.7347	+	68.7261i	−1.12932	+	2.23448i
$947$			11.9194i			0.387327i	0.981068	+	0.193664i	$0.0620371\pi$
$947$			11.9194i			0.387327i	−0.981068	+	0.193664i	$0.937963\pi$
$948$	17.0217	−	12.5381i	0.552838	−	0.407218i
$949$	5.75438			0.186795
$950$	1.71063	−	3.38465i	0.0555001	−	0.109813i
$951$		−	41.0990i		−	1.33273i
$952$	−7.99817	−	47.4755i	−0.259222	−	1.53869i
$953$			56.4533i			1.82870i	0.404923	+	0.914351i	$0.367298\pi$
$953$			56.4533i			1.82870i	−0.404923	+	0.914351i	$0.632702\pi$
$954$	−73.9425	−	37.3712i	−2.39398	−	1.20994i
$955$		−	4.75372i		−	0.153827i
$956$	37.9815	−	27.9770i	1.22841	−	0.904840i
$957$		−	60.0770i		−	1.94201i
$958$	9.29429	−	18.3897i	0.300285	−	0.594143i
$959$			15.8907i			0.513137i
$960$	21.7113	−	7.52908i	0.700731	−	0.243000i
$961$	−6.65605			−0.214711
$962$	−3.55894	−	1.79872i	−0.114745	−	0.0579929i
$963$	−58.4548			−1.88368
$964$	0.341687	−	0.251685i	0.0110050	−	0.00810624i
$965$			21.3640i			0.687732i
$966$	−0.569466	−	52.2402i	−0.0183223	−	1.68080i
$967$			23.1460i			0.744324i	0.928168	+	0.372162i	$0.121383\pi$
$967$			23.1460i			0.744324i	−0.928168	+	0.372162i	$0.878617\pi$
$968$	36.0516	−	6.07360i	1.15874	−	0.195213i
$969$	48.8942			1.57071
$970$	1.71237	−	3.38809i	0.0549809	−	0.108785i
$971$	−9.18083			−0.294627			−0.147313	−	0.989090i	$-0.547063\pi$
$971$	−9.18083			−0.294627			−0.147313	+	0.989090i	$0.547063\pi$
$972$	18.1905	−	13.3990i	0.583460	−	0.429774i
$973$			8.91556i			0.285820i
$974$	−2.75625	−	1.39303i	−0.0883161	−	0.0446356i
$975$			2.08998i			0.0669330i
$976$	26.4868	+	8.22417i	0.847822	+	0.263249i
$977$			56.3849i			1.80391i	0.431827	+	0.901956i	$0.357869\pi$
$977$			56.3849i			1.80391i	−0.431827	+	0.901956i	$0.642131\pi$
$978$	−30.5254	+	60.3975i	−0.976095	+	1.93130i
$979$		−	39.7407i		−	1.27012i
$980$	0.307650	−	0.226613i	0.00982750	−	0.00723889i
$981$			55.8962i			1.78463i
$982$	9.53654	+	4.81984i	0.304323	+	0.153807i
$983$	−22.0549			−0.703441			−0.351721	−	0.936105i	$-0.614403\pi$
$983$	−22.0549			−0.703441			−0.351721	+	0.936105i	$0.614403\pi$
$984$	10.8946	+	64.6680i	0.347307	+	2.06154i
$985$			20.4988i			0.653145i
$986$	34.2565	+	17.3135i	1.09095	+	0.551374i
$987$	−75.5595			−2.40509
$988$	−2.31430	−	3.14189i	−0.0736276	−	0.0999567i
$989$	−24.5992	−	47.3819i	−0.782210	−	1.50666i
$990$	−32.4190	−	16.3848i	−1.03034	−	0.520744i
$991$			14.4702i			0.459661i	0.973231	+	0.229830i	$0.0738171\pi$
$991$			14.4702i			0.459661i	−0.973231	+	0.229830i	$0.926183\pi$
$992$	−24.1407	+	24.9443i	−0.766468	+	0.791984i
$993$	43.5550			1.38218
$994$	−24.5342	−	12.3998i	−0.778177	−	0.393297i
$995$		−	15.2762i		−	0.484287i
$996$	−21.9885	+	16.1967i	−0.696734	+	0.513211i
$997$	−33.2358			−1.05259			−0.526294	−	0.850303i	$-0.676419\pi$
$997$	−33.2358			−1.05259			−0.526294	+	0.850303i	$0.676419\pi$
$998$	−12.6316	−	6.38414i	−0.399848	−	0.202086i
$999$	−25.0590			−0.792831

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.e.a.91.8	yes	16
4.3	odd	2	inner	460.2.e.a.91.6	yes	16
23.22	odd	2	inner	460.2.e.a.91.7	yes	16
92.91	even	2	inner	460.2.e.a.91.5	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.e.a.91.5	✓	16	92.91	even	2	inner
460.2.e.a.91.6	yes	16	4.3	odd	2	inner
460.2.e.a.91.7	yes	16	23.22	odd	2	inner
460.2.e.a.91.8	yes	16	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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.637910 + 1.26217i) q^{2} -2.87247i q^{3} +(-1.18614 - 1.61030i) q^{4} +1.00000i q^{5} +(3.62554 + 1.83238i) q^{6} -2.68161 q^{7} +(2.78912 - 0.469882i) q^{8} -5.25109 q^{9} +O(q^{10})\)	\(q+(-0.637910 + 1.26217i) q^{2} -2.87247i q^{3} +(-1.18614 - 1.61030i) q^{4} +1.00000i q^{5} +(3.62554 + 1.83238i) q^{6} -2.68161 q^{7} +(2.78912 - 0.469882i) q^{8} -5.25109 q^{9} +(-1.26217 - 0.637910i) q^{10} -4.89140 q^{11} +(-4.62554 + 3.40715i) q^{12} +0.727591 q^{13} +(1.71063 - 3.38465i) q^{14} +2.87247 q^{15} +(-1.18614 + 3.82009i) q^{16} +6.34755i q^{17} +(3.34972 - 6.62776i) q^{18} +2.68161 q^{19} +(1.61030 - 1.18614i) q^{20} +7.70285i q^{21} +(3.12027 - 6.17377i) q^{22} +(2.20979 + 4.25639i) q^{23} +(-1.34972 - 8.01167i) q^{24} -1.00000 q^{25} +(-0.464138 + 0.918342i) q^{26} +6.46618i q^{27} +(3.18077 + 4.31821i) q^{28} -4.27582 q^{29} +(-1.83238 + 3.62554i) q^{30} -6.13645i q^{31} +(-4.06494 - 3.93398i) q^{32} +14.0504i q^{33} +(-8.01167 - 4.04917i) q^{34} -2.68161i q^{35} +(6.22853 + 8.45583i) q^{36} +3.87539i q^{37} +(-1.71063 + 3.38465i) q^{38} -2.08998i q^{39} +(0.469882 + 2.78912i) q^{40} -8.07172 q^{41} +(-9.72230 - 4.91373i) q^{42} -11.1319 q^{43} +(5.80189 + 7.87663i) q^{44} -5.25109i q^{45} +(-6.78193 + 0.0739292i) q^{46} +9.80928i q^{47} +(10.9731 + 3.40715i) q^{48} +0.191051 q^{49} +(0.637910 - 1.26217i) q^{50} +18.2331 q^{51} +(-0.863025 - 1.17164i) q^{52} -11.1565i q^{53} +(-8.16141 - 4.12484i) q^{54} -4.89140i q^{55} +(-7.47935 + 1.26004i) q^{56} -7.70285i q^{57} +(2.72759 - 5.39681i) q^{58} +1.87953i q^{59} +(-3.40715 - 4.62554i) q^{60} -6.93356i q^{61} +(7.74524 + 3.91451i) q^{62} +14.0814 q^{63} +(7.55842 - 2.62112i) q^{64} +0.727591i q^{65} +(-17.7340 - 8.96290i) q^{66} -10.5224 q^{67} +(10.2215 - 7.52908i) q^{68} +(12.2263 - 6.34755i) q^{69} +(3.38465 + 1.71063i) q^{70} -7.24866i q^{71} +(-14.6459 + 2.46739i) q^{72} +7.90882 q^{73} +(-4.89140 - 2.47215i) q^{74} +2.87247i q^{75} +(-3.18077 - 4.31821i) q^{76} +13.1168 q^{77} +(2.63791 + 1.33322i) q^{78} -3.67993 q^{79} +(-3.82009 - 1.18614i) q^{80} +2.82064 q^{81} +(5.14904 - 10.1879i) q^{82} +4.75372 q^{83} +(12.4039 - 9.13667i) q^{84} -6.34755 q^{85} +(7.10119 - 14.0504i) q^{86} +12.2822i q^{87} +(-13.6427 + 2.29838i) q^{88} +8.12461i q^{89} +(6.62776 + 3.34972i) q^{90} -1.95112 q^{91} +(4.23295 - 8.60710i) q^{92} -17.6268 q^{93} +(-12.3810 - 6.25744i) q^{94} +2.68161i q^{95} +(-11.3003 + 11.6764i) q^{96} +2.68434i q^{97} +(-0.121873 + 0.241138i) q^{98} +25.6852 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} + 14 q^{6} + 4 q^{9}+O(q^{10}) \) 16 * q + 4 * q^4 + 14 * q^6 + 4 * q^9	\( 16 q + 4 q^{4} + 14 q^{6} + 4 q^{9} - 30 q^{12} + 4 q^{13} + 4 q^{16} + 30 q^{18} + 2 q^{24} - 16 q^{25} - 54 q^{26} - 48 q^{29} + 34 q^{36} - 36 q^{41} - 40 q^{46} + 18 q^{48} + 68 q^{49} + 34 q^{52} - 40 q^{54} + 36 q^{58} + 6 q^{62} + 52 q^{64} + 40 q^{69} + 42 q^{70} - 78 q^{72} + 8 q^{73} + 72 q^{77} + 32 q^{78} + 40 q^{81} - 42 q^{82} + 12 q^{85} - 120 q^{93} + 20 q^{94} - 22 q^{96} - 18 q^{98}+O(q^{100}) \) 16 * q + 4 * q^4 + 14 * q^6 + 4 * q^9 - 30 * q^12 + 4 * q^13 + 4 * q^16 + 30 * q^18 + 2 * q^24 - 16 * q^25 - 54 * q^26 - 48 * q^29 + 34 * q^36 - 36 * q^41 - 40 * q^46 + 18 * q^48 + 68 * q^49 + 34 * q^52 - 40 * q^54 + 36 * q^58 + 6 * q^62 + 52 * q^64 + 40 * q^69 + 42 * q^70 - 78 * q^72 + 8 * q^73 + 72 * q^77 + 32 * q^78 + 40 * q^81 - 42 * q^82 + 12 * q^85 - 120 * q^93 + 20 * q^94 - 22 * q^96 - 18 * q^98

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