LMFDB - Embedded newform 460.2.e.b.91.14

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:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.14
Character	$\chi$	$=$	460.91
Dual form			460.2.e.b.91.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.151248 - 1.40610i) q^{2} -2.99817i q^{3} +(-1.95425 + 0.425339i) q^{4} +1.00000i q^{5} +(-4.21573 + 0.453465i) q^{6} -3.98264 q^{7} +(0.893646 + 2.68354i) q^{8} -5.98900 q^{9} +O(q^{10})$	\(q+(-0.151248 - 1.40610i) q^{2} -2.99817i q^{3} +(-1.95425 + 0.425339i) q^{4} +1.00000i q^{5} +(-4.21573 + 0.453465i) q^{6} -3.98264 q^{7} +(0.893646 + 2.68354i) q^{8} -5.98900 q^{9} +(1.40610 - 0.151248i) q^{10} +5.79526 q^{11} +(1.27524 + 5.85916i) q^{12} -5.59399 q^{13} +(0.602364 + 5.60000i) q^{14} +2.99817 q^{15} +(3.63817 - 1.66244i) q^{16} +1.88340i q^{17} +(0.905822 + 8.42115i) q^{18} -3.03292 q^{19} +(-0.425339 - 1.95425i) q^{20} +11.9406i q^{21} +(-0.876519 - 8.14873i) q^{22} +(-4.42059 - 1.85966i) q^{23} +(8.04570 - 2.67930i) q^{24} -1.00000 q^{25} +(0.846077 + 7.86572i) q^{26} +8.96151i q^{27} +(7.78306 - 1.69397i) q^{28} +1.45413 q^{29} +(-0.453465 - 4.21573i) q^{30} -4.43887i q^{31} +(-2.88782 - 4.86420i) q^{32} -17.3751i q^{33} +(2.64825 - 0.284859i) q^{34} -3.98264i q^{35} +(11.7040 - 2.54736i) q^{36} -4.01408i q^{37} +(0.458722 + 4.26460i) q^{38} +16.7717i q^{39} +(-2.68354 + 0.893646i) q^{40} -2.68576 q^{41} +(16.7897 - 1.80599i) q^{42} -4.78686 q^{43} +(-11.3254 + 2.46495i) q^{44} -5.98900i q^{45} +(-1.94627 + 6.49708i) q^{46} -6.45256i q^{47} +(-4.98426 - 10.9078i) q^{48} +8.86139 q^{49} +(0.151248 + 1.40610i) q^{50} +5.64674 q^{51} +(10.9320 - 2.37934i) q^{52} +8.62977i q^{53} +(12.6008 - 1.35541i) q^{54} +5.79526i q^{55} +(-3.55907 - 10.6876i) q^{56} +9.09320i q^{57} +(-0.219933 - 2.04465i) q^{58} -1.55268i q^{59} +(-5.85916 + 1.27524i) q^{60} +6.06982i q^{61} +(-6.24150 + 0.671368i) q^{62} +23.8520 q^{63} +(-6.40279 + 4.79627i) q^{64} -5.59399i q^{65} +(-24.4312 + 2.62795i) q^{66} -7.88582 q^{67} +(-0.801083 - 3.68063i) q^{68} +(-5.57557 + 13.2537i) q^{69} +(-5.60000 + 0.602364i) q^{70} -5.26340i q^{71} +(-5.35204 - 16.0717i) q^{72} +2.20605 q^{73} +(-5.64420 + 0.607119i) q^{74} +2.99817i q^{75} +(5.92708 - 1.29002i) q^{76} -23.0804 q^{77} +(23.5827 - 2.53668i) q^{78} -13.1166 q^{79} +(1.66244 + 3.63817i) q^{80} +8.90111 q^{81} +(0.406214 + 3.77645i) q^{82} +8.56752 q^{83} +(-5.07881 - 23.3349i) q^{84} -1.88340 q^{85} +(0.724001 + 6.73082i) q^{86} -4.35971i q^{87} +(5.17891 + 15.5518i) q^{88} -8.41278i q^{89} +(-8.42115 + 0.905822i) q^{90} +22.2788 q^{91} +(9.42993 + 1.75399i) q^{92} -13.3085 q^{93} +(-9.07296 + 0.975934i) q^{94} -3.03292i q^{95} +(-14.5837 + 8.65817i) q^{96} -2.87841i q^{97} +(-1.34026 - 12.4600i) q^{98} -34.7078 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{2} - 4 q^{4} - 16 q^{6} - 2 q^{8} - 52 q^{9}+O(q^{10}) $ 32 * q + 4 * q^2 - 4 * q^4 - 16 * q^6 - 2 * q^8 - 52 * q^9	$ 32 q + 4 q^{2} - 4 q^{4} - 16 q^{6} - 2 q^{8} - 52 q^{9} + 24 q^{12} - 4 q^{13} + 20 q^{16} - 56 q^{18} - 6 q^{24} - 32 q^{25} + 68 q^{26} + 8 q^{29} - 16 q^{32} + 8 q^{36} + 44 q^{41} - 4 q^{46} - 4 q^{48} - 12 q^{49} - 4 q^{50} + 16 q^{52} + 42 q^{54} - 10 q^{58} - 36 q^{62} - 22 q^{64} - 44 q^{69} - 42 q^{70} - 32 q^{72} - 8 q^{73} - 72 q^{77} + 122 q^{78} - 32 q^{81} + 20 q^{82} - 44 q^{85} + 64 q^{92} + 40 q^{93} - 26 q^{94} + 16 q^{96} + 62 q^{98}+O(q^{100}) $ 32 * q + 4 * q^2 - 4 * q^4 - 16 * q^6 - 2 * q^8 - 52 * q^9 + 24 * q^12 - 4 * q^13 + 20 * q^16 - 56 * q^18 - 6 * q^24 - 32 * q^25 + 68 * q^26 + 8 * q^29 - 16 * q^32 + 8 * q^36 + 44 * q^41 - 4 * q^46 - 4 * q^48 - 12 * q^49 - 4 * q^50 + 16 * q^52 + 42 * q^54 - 10 * q^58 - 36 * q^62 - 22 * q^64 - 44 * q^69 - 42 * q^70 - 32 * q^72 - 8 * q^73 - 72 * q^77 + 122 * q^78 - 32 * q^81 + 20 * q^82 - 44 * q^85 + 64 * q^92 + 40 * q^93 - 26 * q^94 + 16 * q^96 + 62 * 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 $

$2$	−0.151248	−	1.40610i	−0.106948	−	0.994265i
$2$	−0.151248	−	1.40610i	−0.106948	−	0.994265i
$3$		−	2.99817i		−	1.73099i	−0.500916	−	0.865496i	$-0.667003\pi$
$3$		−	2.99817i		−	1.73099i	0.500916	−	0.865496i	$-0.332997\pi$
$4$	−1.95425	+	0.425339i	−0.977124	+	0.212670i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	−4.21573	+	0.453465i	−1.72106	+	0.185126i
$7$	−3.98264			−1.50530			−0.752648	−	0.658424i	$-0.771224\pi$
$7$	−3.98264			−1.50530			−0.752648	+	0.658424i	$0.771224\pi$
$8$	0.893646	+	2.68354i	0.315952	+	0.948775i
$9$	−5.98900			−1.99633
$10$	1.40610	−	0.151248i	0.444649	−	0.0478287i
$11$	5.79526			1.74734			0.873668	−	0.486523i	$-0.161735\pi$
$11$	5.79526			1.74734			0.873668	+	0.486523i	$0.161735\pi$
$12$	1.27524	+	5.85916i	0.368129	+	1.69139i
$13$	−5.59399			−1.55149			−0.775747	−	0.631044i	$-0.782627\pi$
$13$	−5.59399			−1.55149			−0.775747	+	0.631044i	$0.782627\pi$
$14$	0.602364	+	5.60000i	0.160989	+	1.49666i
$15$	2.99817			0.774123
$16$	3.63817	−	1.66244i	0.909543	−	0.415609i
$17$			1.88340i			0.456791i	0.973568	+	0.228395i	$0.0733479\pi$
$17$			1.88340i			0.456791i	−0.973568	+	0.228395i	$0.926652\pi$
$18$	0.905822	+	8.42115i	0.213504	+	1.98488i
$19$	−3.03292			−0.695800			−0.347900	−	0.937532i	$-0.613105\pi$
$19$	−3.03292			−0.695800			−0.347900	+	0.937532i	$0.613105\pi$
$20$	−0.425339	−	1.95425i	−0.0951087	−	0.436983i
$21$			11.9406i			2.60565i
$22$	−0.876519	−	8.14873i	−0.186874	−	1.73731i
$23$	−4.42059	−	1.85966i	−0.921758	−	0.387766i
$23$	−4.42059	−	1.85966i	−0.921758	−	0.387766i
$24$	8.04570	−	2.67930i	1.64232	−	0.546910i
$25$	−1.00000			−0.200000
$26$	0.846077	+	7.86572i	0.165929	+	1.54259i
$27$			8.96151i			1.72464i
$28$	7.78306	−	1.69397i	1.47086	−	0.320131i
$29$	1.45413			0.270025			0.135012	−	0.990844i	$-0.456893\pi$
$29$	1.45413			0.270025			0.135012	+	0.990844i	$0.456893\pi$
$30$	−0.453465	−	4.21573i	−0.0827911	−	0.769683i
$31$		−	4.43887i		−	0.797244i	−0.917115	−	0.398622i	$-0.869489\pi$
$31$		−	4.43887i		−	0.797244i	0.917115	−	0.398622i	$-0.130511\pi$
$32$	−2.88782	−	4.86420i	−0.510500	−	0.859878i
$33$		−	17.3751i		−	3.02462i
$34$	2.64825	−	0.284859i	0.454171	−	0.0488530i
$35$		−	3.98264i		−	0.673188i
$36$	11.7040	−	2.54736i	1.95066	−	0.424559i
$37$		−	4.01408i		−	0.659910i	−0.943997	−	0.329955i	$-0.892966\pi$
$37$		−	4.01408i		−	0.659910i	0.943997	−	0.329955i	$-0.107034\pi$
$38$	0.458722	+	4.26460i	0.0744146	+	0.691809i
$39$			16.7717i			2.68562i
$40$	−2.68354	+	0.893646i	−0.424305	+	0.141298i
$41$	−2.68576			−0.419444			−0.209722	−	0.977761i	$-0.567256\pi$
$41$	−2.68576			−0.419444			−0.209722	+	0.977761i	$0.567256\pi$
$42$	16.7897	−	1.80599i	2.59071	−	0.278670i
$43$	−4.78686			−0.729989			−0.364995	−	0.931010i	$-0.618929\pi$
$43$	−4.78686			−0.729989			−0.364995	+	0.931010i	$0.618929\pi$
$44$	−11.3254	+	2.46495i	−1.70736	+	0.371605i
$45$		−	5.98900i		−	0.892787i
$46$	−1.94627	+	6.49708i	−0.286962	+	0.957942i
$47$		−	6.45256i		−	0.941203i	−0.882346	−	0.470601i	$-0.844037\pi$
$47$		−	6.45256i		−	0.941203i	0.882346	−	0.470601i	$-0.155963\pi$
$48$	−4.98426	−	10.9078i	−0.719416	−	1.57441i
$49$	8.86139			1.26591
$50$	0.151248	+	1.40610i	0.0213896	+	0.198853i
$51$	5.64674			0.790701
$52$	10.9320	−	2.37934i	1.51600	−	0.329955i
$53$			8.62977i			1.18539i	0.805427	+	0.592695i	$0.201936\pi$
$53$			8.62977i			1.18539i	−0.805427	+	0.592695i	$0.798064\pi$
$54$	12.6008	−	1.35541i	1.71475	−	0.184448i
$55$			5.79526i			0.781432i
$56$	−3.55907	−	10.6876i	−0.475600	−	1.42819i
$57$			9.09320i			1.20442i
$58$	−0.219933	−	2.04465i	−0.0288786	−	0.268476i
$59$		−	1.55268i		−	0.202142i	−0.994879	−	0.101071i	$-0.967773\pi$
$59$		−	1.55268i		−	0.202142i	0.994879	−	0.101071i	$-0.0322269\pi$
$60$	−5.85916	+	1.27524i	−0.756414	+	0.164632i
$61$			6.06982i			0.777161i	0.921415	+	0.388581i	$0.127035\pi$
$61$			6.06982i			0.777161i	−0.921415	+	0.388581i	$0.872965\pi$
$62$	−6.24150	+	0.671368i	−0.792671	+	0.0852638i
$63$	23.8520			3.00507
$64$	−6.40279	+	4.79627i	−0.800349	+	0.599534i
$65$		−	5.59399i		−	0.693849i
$66$	−24.4312	+	2.62795i	−3.00728	+	0.323478i
$67$	−7.88582			−0.963406			−0.481703	−	0.876335i	$-0.659982\pi$
$67$	−7.88582			−0.963406			−0.481703	+	0.876335i	$0.659982\pi$
$68$	−0.801083	−	3.68063i	−0.0971455	−	0.446341i
$69$	−5.57557	+	13.2537i	−0.671220	+	1.59556i
$70$	−5.60000	+	0.602364i	−0.669327	+	0.0719963i
$71$		−	5.26340i		−	0.624651i	−0.949975	−	0.312326i	$-0.898892\pi$
$71$		−	5.26340i		−	0.624651i	0.949975	−	0.312326i	$-0.101108\pi$
$72$	−5.35204	−	16.0717i	−0.630744	−	1.89407i
$73$	2.20605			0.258198			0.129099	−	0.991632i	$-0.458791\pi$
$73$	2.20605			0.258198			0.129099	+	0.991632i	$0.458791\pi$
$74$	−5.64420	+	0.607119i	−0.656125	+	0.0705762i
$75$			2.99817i			0.346198i
$76$	5.92708	−	1.29002i	0.679883	−	0.147976i
$77$	−23.0804			−2.63026
$78$	23.5827	−	2.53668i	2.67022	−	0.287222i
$79$	−13.1166			−1.47573			−0.737866	−	0.674947i	$-0.764166\pi$
$79$	−13.1166			−1.47573			−0.737866	+	0.674947i	$0.764166\pi$
$80$	1.66244	+	3.63817i	0.185866	+	0.406760i
$81$	8.90111			0.989012
$82$	0.406214	+	3.77645i	0.0448588	+	0.417039i
$83$	8.56752			0.940408			0.470204	−	0.882558i	$-0.344180\pi$
$83$	8.56752			0.940408			0.470204	+	0.882558i	$0.344180\pi$
$84$	−5.07881	−	23.3349i	−0.554143	−	2.54605i
$85$	−1.88340			−0.204283
$86$	0.724001	+	6.73082i	0.0780711	+	0.725803i
$87$		−	4.35971i		−	0.467410i
$88$	5.17891	+	15.5518i	0.552073	+	1.65783i
$89$		−	8.41278i		−	0.891753i	−0.895095	−	0.445876i	$-0.852892\pi$
$89$		−	8.41278i		−	0.891753i	0.895095	−	0.445876i	$-0.147108\pi$
$90$	−8.42115	+	0.905822i	−0.887667	+	0.0954820i
$91$	22.2788			2.33546
$92$	9.42993	+	1.75399i	0.983138	+	0.182866i
$93$	−13.3085			−1.38002
$94$	−9.07296	+	0.975934i	−0.935804	+	0.100660i
$95$		−	3.03292i		−	0.311171i
$96$	−14.5837	+	8.65817i	−1.48844	+	0.883671i
$97$		−	2.87841i		−	0.292259i	−0.989265	−	0.146129i	$-0.953318\pi$
$97$		−	2.87841i		−	0.292259i	0.989265	−	0.146129i	$-0.0466816\pi$
$98$	−1.34026	−	12.4600i	−0.135387	−	1.25865i
$99$	−34.7078			−3.48826
$100$	1.95425	−	0.425339i	0.195425	−	0.0425339i
$101$	−9.97313			−0.992363			−0.496182	−	0.868219i	$-0.665265\pi$
$101$	−9.97313			−0.992363			−0.496182	+	0.868219i	$0.665265\pi$
$102$	−0.854055	−	7.93989i	−0.0845641	−	0.786166i
$103$	7.70072			0.758774			0.379387	−	0.925238i	$-0.376135\pi$
$103$	7.70072			0.758774			0.379387	+	0.925238i	$0.376135\pi$
$104$	−4.99905	−	15.0117i	−0.490197	−	1.47202i
$105$	−11.9406			−1.16528
$106$	12.1343	−	1.30523i	1.17859	−	0.126775i
$107$	−4.39463			−0.424845			−0.212422	−	0.977178i	$-0.568135\pi$
$107$	−4.39463			−0.424845			−0.212422	+	0.977178i	$0.568135\pi$
$108$	−3.81168	−	17.5130i	−0.366779	−	1.68519i
$109$		−	3.05299i		−	0.292423i	−0.989253	−	0.146212i	$-0.953292\pi$
$109$		−	3.05299i		−	0.292423i	0.989253	−	0.146212i	$-0.0467080\pi$
$110$	8.14873	−	0.876519i	0.776951	−	0.0835728i
$111$	−12.0349			−1.14230
$112$	−14.4895	+	6.62088i	−1.36913	+	0.625615i
$113$			3.94010i			0.370653i	0.982677	+	0.185327i	$0.0593343\pi$
$113$			3.94010i			0.370653i	−0.982677	+	0.185327i	$0.940666\pi$
$114$	12.7860	−	1.37533i	1.19752	−	0.128811i
$115$	1.85966	−	4.42059i	0.173414	−	0.412223i
$116$	−2.84172	+	0.618497i	−0.263848	+	0.0574260i
$117$	33.5024			3.09730
$118$	−2.18323	+	0.234839i	−0.200982	+	0.0216187i
$119$		−	7.50089i		−	0.687605i
$120$	2.67930	+	8.04570i	0.244585	+	0.734469i
$121$	22.5850			2.05318
$122$	8.53479	−	0.918046i	0.772704	−	0.0831160i
$123$			8.05234i			0.726055i
$124$	1.88802	+	8.67465i	0.169550	+	0.779006i
$125$		−	1.00000i		−	0.0894427i
$126$	−3.60756	−	33.5384i	−0.321387	−	2.98783i
$127$			18.3409i			1.62749i	0.581222	+	0.813745i	$0.302575\pi$
$127$			18.3409i			1.62749i	−0.581222	+	0.813745i	$0.697425\pi$
$128$	7.71246	+	8.27756i	0.681691	+	0.731640i
$129$			14.3518i			1.26361i
$130$	−7.86572	+	0.846077i	−0.689869	+	0.0742059i
$131$		−	19.8204i		−	1.73172i	−0.500290	−	0.865858i	$-0.666773\pi$
$131$		−	19.8204i		−	1.73172i	0.500290	−	0.865858i	$-0.333227\pi$
$132$	7.39033	+	33.9553i	0.643246	+	2.95543i
$133$	12.0790			1.04738
$134$	1.19271	+	11.0883i	0.103035	+	0.957880i
$135$	−8.96151			−0.771284
$136$	−5.05418	+	1.68309i	−0.433392	+	0.144324i
$137$		−	10.6608i		−	0.910814i	−0.890283	−	0.455407i	$-0.849494\pi$
$137$		−	10.6608i		−	0.910814i	0.890283	−	0.455407i	$-0.150506\pi$
$138$	19.4793	+	5.83524i	1.65819	+	0.496729i
$139$		−	18.6904i		−	1.58530i	−0.609679	−	0.792649i	$-0.708701\pi$
$139$		−	18.6904i		−	1.58530i	0.609679	−	0.792649i	$-0.291299\pi$
$140$	1.69397	+	7.78306i	0.143167	+	0.657789i
$141$	−19.3458			−1.62921
$142$	−7.40089	+	0.796077i	−0.621069	+	0.0668053i
$143$	−32.4186			−2.71098
$144$	−21.7890	+	9.95633i	−1.81575	+	0.829694i
$145$			1.45413i			0.120759i
$146$	−0.333659	−	3.10193i	−0.0276138	−	0.256717i
$147$		−	26.5679i		−	2.19129i
$148$	1.70734	+	7.84450i	0.140343	+	0.644814i
$149$			4.09329i			0.335335i	0.985844	+	0.167668i	$0.0536235\pi$
$149$			4.09329i			0.335335i	−0.985844	+	0.167668i	$0.946376\pi$
$150$	4.21573	−	0.453465i	0.344213	−	0.0370253i
$151$			13.3803i			1.08887i	0.838803	+	0.544435i	$0.183256\pi$
$151$			13.3803i			1.08887i	−0.838803	+	0.544435i	$0.816744\pi$
$152$	−2.71036	−	8.13897i	−0.219839	−	0.660158i
$153$		−	11.2797i		−	0.911907i
$154$	3.49086	+	32.4534i	0.281301	+	2.61517i
$155$	4.43887			0.356538
$156$	−7.13366	−	32.7761i	−0.571150	−	2.62419i
$157$		−	16.7247i		−	1.33477i	−0.744711	−	0.667387i	$-0.767413\pi$
$157$		−	16.7247i		−	1.33477i	0.744711	−	0.667387i	$-0.232587\pi$
$158$	1.98385	+	18.4433i	0.157827	+	1.46727i
$159$	25.8735			2.05190
$160$	4.86420	−	2.88782i	0.384549	−	0.228302i
$161$	17.6056	+	7.40636i	1.38752	+	0.583703i
$162$	−1.34627	−	12.5159i	−0.105773	−	0.983339i
$163$		−	3.50306i		−	0.274381i	−0.990545	−	0.137190i	$-0.956193\pi$
$163$		−	3.50306i		−	0.274381i	0.990545	−	0.137190i	$-0.0438072\pi$
$164$	5.24863	−	1.14236i	0.409849	−	0.0892031i
$165$	17.3751			1.35265
$166$	−1.29582	−	12.0468i	−0.100575	−	0.935014i
$167$			0.0195683i			0.00151424i	1.00000		0.000757120i	$0.000240999\pi$
$167$			0.0195683i			0.00151424i	−1.00000		0.000757120i	$0.999759\pi$
$168$	−32.0431	+	10.6707i	−2.47218	+	0.823260i
$169$	18.2927			1.40713
$170$	0.284859	+	2.64825i	0.0218477	+	0.203111i
$171$	18.1642			1.38905
$172$	9.35472	−	2.03604i	0.713290	−	0.155247i
$173$	5.10225			0.387917			0.193959	−	0.981010i	$-0.437867\pi$
$173$	5.10225			0.387917			0.193959	+	0.981010i	$0.437867\pi$
$174$	−6.13020	+	0.659396i	−0.464730	+	0.0499887i
$175$	3.98264			0.301059
$176$	21.0842	−	9.63425i	1.58928	−	0.726209i
$177$	−4.65519			−0.349905
$178$	−11.8292	+	1.27241i	−0.886638	+	0.0953714i
$179$			7.08641i			0.529663i	0.964295	+	0.264832i	$0.0853163\pi$
$179$			7.08641i			0.529663i	−0.964295	+	0.264832i	$0.914684\pi$
$180$	2.54736	+	11.7040i	0.189869	+	0.872364i
$181$		−	21.0594i		−	1.56534i	−0.622439	−	0.782668i	$-0.713858\pi$
$181$		−	21.0594i		−	1.56534i	0.622439	−	0.782668i	$-0.286142\pi$
$182$	−3.36962	−	31.3263i	−0.249773	−	2.32206i
$183$	18.1983			1.34526
$184$	1.04003	−	13.5247i	0.0766723	−	0.997056i
$185$	4.01408			0.295121
$186$	2.01287	+	18.7131i	0.147591	+	1.37211i
$187$			10.9148i			0.798167i
$188$	2.74453	+	12.6099i	0.200165	+	0.919672i
$189$		−	35.6904i		−	2.59610i
$190$	−4.26460	+	0.458722i	−0.309387	+	0.0332792i
$191$	−20.2457			−1.46493			−0.732464	−	0.680805i	$-0.761630\pi$
$191$	−20.2457			−1.46493			−0.732464	+	0.680805i	$0.761630\pi$
$192$	14.3800	+	19.1966i	1.03779	+	1.38540i
$193$	12.0842			0.869841			0.434920	−	0.900469i	$-0.356776\pi$
$193$	12.0842			0.869841			0.434920	+	0.900469i	$0.356776\pi$
$194$	−4.04735	+	0.435353i	−0.290582	+	0.0312565i
$195$	−16.7717			−1.20105
$196$	−17.3174	+	3.76910i	−1.23695	+	0.269221i
$197$	−2.02719			−0.144431			−0.0722157	−	0.997389i	$-0.523007\pi$
$197$	−2.02719			−0.144431			−0.0722157	+	0.997389i	$0.523007\pi$
$198$	5.24947	+	48.8027i	0.373064	+	3.46826i
$199$	7.92307			0.561652			0.280826	−	0.959759i	$-0.409392\pi$
$199$	7.92307			0.561652			0.280826	+	0.959759i	$0.409392\pi$
$200$	−0.893646	−	2.68354i	−0.0631903	−	0.189755i
$201$			23.6430i			1.66765i
$202$	1.50841	+	14.0232i	0.106131	+	0.986671i
$203$	−5.79126			−0.406467
$204$	−11.0351	+	2.40178i	−0.772613	+	0.168158i
$205$		−	2.68576i		−	0.187581i
$206$	−1.16472	−	10.8280i	−0.0811496	−	0.754423i
$207$	26.4749	+	11.1375i	1.84014	+	0.774111i
$208$	−20.3519	+	9.29965i	−1.41115	+	0.644815i
$209$	−17.5766			−1.21580
$210$	1.80599	+	16.7897i	0.124625	+	1.15860i
$211$		−	23.3355i		−	1.60648i	−0.595653	−	0.803242i	$-0.703107\pi$
$211$		−	23.3355i		−	1.60648i	0.595653	−	0.803242i	$-0.296893\pi$
$212$	−3.67058	−	16.8647i	−0.252096	−	1.15827i
$213$	−15.7806			−1.08127
$214$	0.664677	+	6.17930i	0.0454364	+	0.422408i
$215$		−	4.78686i		−	0.326461i
$216$	−24.0486	+	8.00842i	−1.63630	+	0.544904i
$217$			17.6784i			1.20009i
$218$	−4.29281	+	0.461757i	−0.290746	+	0.0312741i
$219$		−	6.61409i		−	0.446939i
$220$	−2.46495	−	11.3254i	−0.166187	−	0.763556i
$221$		−	10.5357i		−	0.708708i
$222$	1.82024	+	16.9223i	0.122167	+	1.13575i
$223$		−	12.5908i		−	0.843140i	−0.906796	−	0.421570i	$-0.861479\pi$
$223$		−	12.5908i		−	0.843140i	0.906796	−	0.421570i	$-0.138521\pi$
$224$	11.5011	+	19.3724i	0.768453	+	1.29437i
$225$	5.98900			0.399267
$226$	5.54018	−	0.595930i	0.368527	−	0.0396407i
$227$	−1.21553			−0.0806778			−0.0403389	−	0.999186i	$-0.512844\pi$
$227$	−1.21553			−0.0806778			−0.0403389	+	0.999186i	$0.512844\pi$
$228$	−3.86770	−	17.7704i	−0.256144	−	1.17687i
$229$			14.2097i			0.939004i	0.882931	+	0.469502i	$0.155566\pi$
$229$			14.2097i			0.939004i	−0.882931	+	0.469502i	$0.844434\pi$
$230$	−6.49708	−	1.94627i	−0.428405	−	0.128333i
$231$			69.1989i			4.55295i
$232$	1.29947	+	3.90221i	0.0853147	+	0.256193i
$233$	11.2350			0.736029			0.368015	−	0.929820i	$-0.380038\pi$
$233$	11.2350			0.736029			0.368015	+	0.929820i	$0.380038\pi$
$234$	−5.06716	−	47.1078i	−0.331250	−	3.07953i
$235$	6.45256			0.420919
$236$	0.660415	+	3.03432i	0.0429894	+	0.197517i
$237$			39.3257i			2.55448i
$238$	−10.5470	+	1.13449i	−0.683661	+	0.0735381i
$239$		−	6.11790i		−	0.395734i	−0.980229	−	0.197867i	$-0.936599\pi$
$239$		−	6.11790i		−	0.395734i	0.980229	−	0.197867i	$-0.0634014\pi$
$240$	10.9078	−	4.98426i	0.704098	−	0.321733i
$241$			14.5518i			0.937363i	0.883367	+	0.468681i	$0.155271\pi$
$241$			14.5518i			0.937363i	−0.883367	+	0.468681i	$0.844729\pi$
$242$	−3.41593	−	31.7568i	−0.219584	−	2.04141i
$243$			0.197546i			0.0126726i
$244$	−2.58173	−	11.8619i	−0.165279	−	0.759383i
$245$			8.86139i			0.566134i
$246$	11.3224	−	1.21790i	0.721891	−	0.0776503i
$247$	16.9661			1.07953
$248$	11.9119	−	3.96677i	0.756405	−	0.251890i
$249$		−	25.6869i		−	1.62784i
$250$	−1.40610	+	0.151248i	−0.0889297	+	0.00956574i
$251$	−30.3294			−1.91437			−0.957187	−	0.289470i	$-0.906521\pi$
$251$	−30.3294			−1.91437			−0.957187	+	0.289470i	$0.906521\pi$
$252$	−46.6127	+	10.1452i	−2.93633	+	0.639087i
$253$	−25.6185	−	10.7772i	−1.61062	−	0.677558i
$254$	25.7892	−	2.77401i	1.61816	−	0.174057i
$255$			5.64674i			0.353612i
$256$	10.4726	−	12.0965i	0.654538	−	0.756029i
$257$	17.6265			1.09951			0.549754	−	0.835326i	$-0.314721\pi$
$257$	17.6265			1.09951			0.549754	+	0.835326i	$0.314721\pi$
$258$	20.1801	−	2.17068i	1.25636	−	0.135140i
$259$			15.9866i			0.993359i
$260$	2.37934	+	10.9320i	0.147561	+	0.677977i
$261$	−8.70876			−0.539059
$262$	−27.8695	+	2.99779i	−1.72178	+	0.185204i
$263$	19.3232			1.19152			0.595761	−	0.803162i	$-0.296851\pi$
$263$	19.3232			1.19152			0.595761	+	0.803162i	$0.296851\pi$
$264$	46.6269	−	15.5272i	2.86969	−	0.955635i
$265$	−8.62977			−0.530122
$266$	−1.82692	−	16.9844i	−0.112016	−	1.04138i
$267$	−25.2229			−1.54362
$268$	15.4108	−	3.35415i	0.941367	−	0.204887i
$269$	−1.94806			−0.118776			−0.0593878	−	0.998235i	$-0.518915\pi$
$269$	−1.94806			−0.118776			−0.0593878	+	0.998235i	$0.518915\pi$
$270$	1.35541	+	12.6008i	0.0824875	+	0.766861i
$271$			21.8168i			1.32528i	0.748939	+	0.662639i	$0.230564\pi$
$271$			21.8168i			1.32528i	−0.748939	+	0.662639i	$0.769436\pi$
$272$	3.13103	+	6.85212i	0.189847	+	0.415471i
$273$		−	66.7956i		−	4.04265i
$274$	−14.9902	+	1.61242i	−0.905590	+	0.0974099i
$275$	−5.79526			−0.349467
$276$	5.25875	−	28.2725i	0.316539	−	1.70180i
$277$	17.9387			1.07783			0.538917	−	0.842359i	$-0.318834\pi$
$277$	17.9387			1.07783			0.538917	+	0.842359i	$0.318834\pi$
$278$	−26.2806	+	2.82688i	−1.57621	+	0.169545i
$279$			26.5844i			1.59156i
$280$	10.6876	−	3.55907i	0.638705	−	0.212695i
$281$			12.9149i			0.770438i	0.922825	+	0.385219i	$0.125874\pi$
$281$			12.9149i			0.770438i	−0.922825	+	0.385219i	$0.874126\pi$
$282$	2.92601	+	27.2022i	0.174242	+	1.61987i
$283$	6.31080			0.375138			0.187569	−	0.982251i	$-0.439939\pi$
$283$	6.31080			0.375138			0.187569	+	0.982251i	$0.439939\pi$
$284$	2.23873	+	10.2860i	0.132844	+	0.610362i
$285$	−9.09320			−0.538635
$286$	4.90324	+	45.5839i	0.289934	+	2.69543i
$287$	10.6964			0.631388
$288$	17.2952	+	29.1317i	1.01913	+	1.71660i
$289$	13.4528			0.791342
$290$	2.04465	−	0.219933i	0.120066	−	0.0129149i
$291$	−8.62996			−0.505897
$292$	−4.31116	+	0.938318i	−0.252292	+	0.0549109i
$293$			0.368410i			0.0215227i	0.999942	+	0.0107614i	$0.00342552\pi$
$293$			0.368410i			0.0215227i	−0.999942	+	0.0107614i	$0.996574\pi$
$294$	−37.3572	+	4.01834i	−2.17872	+	0.234354i
$295$	1.55268			0.0904005
$296$	10.7719	−	3.58716i	0.626106	−	0.208500i
$297$			51.9343i			3.01353i
$298$	5.75558	−	0.619100i	0.333412	−	0.0358635i
$299$	24.7288	+	10.4029i	1.43010	+	0.601617i
$300$	−1.27524	−	5.85916i	−0.0736259	−	0.338279i
$301$	19.0643			1.09885
$302$	18.8140	−	2.02373i	1.08263	−	0.116453i
$303$			29.9011i			1.71777i
$304$	−11.0343	+	5.04204i	−0.632860	+	0.289181i
$305$	−6.06982			−0.347557
$306$	−15.8604	+	1.70602i	−0.906677	+	0.0975268i
$307$		−	13.5193i		−	0.771585i	−0.922586	−	0.385792i	$-0.873928\pi$
$307$		−	13.5193i		−	0.771585i	0.922586	−	0.385792i	$-0.126072\pi$
$308$	45.1048	−	9.81700i	2.57009	−	0.559376i
$309$		−	23.0880i		−	1.31343i
$310$	−0.671368	−	6.24150i	−0.0381311	−	0.354493i
$311$		−	7.98416i		−	0.452740i	−0.974041	−	0.226370i	$-0.927314\pi$
$311$		−	7.98416i		−	0.452740i	0.974041	−	0.226370i	$-0.0726859\pi$
$312$	−45.0076	+	14.9880i	−2.54805	+	0.848527i
$313$		−	15.1710i		−	0.857513i	−0.903420	−	0.428757i	$-0.858952\pi$
$313$		−	15.1710i		−	0.857513i	0.903420	−	0.428757i	$-0.141048\pi$
$314$	−23.5166	+	2.52957i	−1.32712	+	0.142752i
$315$			23.8520i			1.34391i
$316$	25.6331	−	5.57900i	1.44197	−	0.313843i
$317$	21.2389			1.19289			0.596447	−	0.802653i	$-0.296579\pi$
$317$	21.2389			1.19289			0.596447	+	0.802653i	$0.296579\pi$
$318$	−3.91330	−	36.3807i	−0.219447	−	2.04013i
$319$	8.42704			0.471824
$320$	−4.79627	−	6.40279i	−0.268120	−	0.357927i
$321$			13.1758i			0.735403i
$322$	7.75129	−	25.8755i	0.431962	−	1.44199i
$323$		−	5.71220i		−	0.317835i
$324$	−17.3950	+	3.78599i	−0.966387	+	0.210333i
$325$	5.59399			0.310299
$326$	−4.92566	+	0.529830i	−0.272807	+	0.0293445i
$327$	−9.15336			−0.506182
$328$	−2.40011	−	7.20734i	−0.132524	−	0.397959i
$329$			25.6982i			1.41679i
$330$	−2.62795	−	24.4312i	−0.144664	−	1.34490i
$331$			19.2611i			1.05869i	0.848407	+	0.529344i	$0.177562\pi$
$331$			19.2611i			1.05869i	−0.848407	+	0.529344i	$0.822438\pi$
$332$	−16.7431	+	3.64410i	−0.918895	+	0.199996i
$333$			24.0403i			1.31740i
$334$	0.0275150	−	0.00295966i	0.00150556	−	0.000161945i
$335$		−	7.88582i		−	0.430848i
$336$	19.8505	+	43.4420i	1.08293	+	2.36995i
$337$		−	11.9329i		−	0.650026i	−0.945710	−	0.325013i	$-0.894631\pi$
$337$		−	11.9329i		−	0.650026i	0.945710	−	0.325013i	$-0.105369\pi$
$338$	−2.76673	−	25.7214i	−0.150490	−	1.39906i
$339$	11.8131			0.641598
$340$	3.68063	−	0.801083i	0.199610	−	0.0434448i
$341$		−	25.7244i		−	1.39305i
$342$	−2.74729	−	25.5407i	−0.148556	−	1.38108i
$343$	−7.41326			−0.400278
$344$	−4.27776	−	12.8457i	−0.230641	−	0.692596i
$345$	−13.2537	−	5.57557i	−0.713554	−	0.300179i
$346$	−0.771704	−	7.17429i	−0.0414870	−	0.385692i
$347$			16.9785i			0.911451i	0.890120	+	0.455726i	$0.150620\pi$
$347$			16.9785i			0.911451i	−0.890120	+	0.455726i	$0.849380\pi$
$348$	1.85436	+	8.51996i	0.0994040	+	0.456718i
$349$	−20.3042			−1.08686			−0.543431	−	0.839454i	$-0.682875\pi$
$349$	−20.3042			−1.08686			−0.543431	+	0.839454i	$0.682875\pi$
$350$	−0.602364	−	5.60000i	−0.0321977	−	0.299332i
$351$		−	50.1306i		−	2.67577i
$352$	−16.7357	−	28.1893i	−0.892014	−	1.50250i
$353$	5.76510			0.306845			0.153423	−	0.988161i	$-0.450970\pi$
$353$	5.76510			0.306845			0.153423	+	0.988161i	$0.450970\pi$
$354$	0.704086	+	6.54567i	0.0374218	+	0.347899i
$355$	5.26340			0.279353
$356$	3.57829	+	16.4407i	0.189649	+	0.871353i
$357$	−22.4889			−1.19024
$358$	9.96422	−	1.07180i	0.526625	−	0.0566465i
$359$	23.2083			1.22489			0.612445	−	0.790513i	$-0.290186\pi$
$359$	23.2083			1.22489			0.612445	+	0.790513i	$0.290186\pi$
$360$	16.0717	−	5.35204i	0.847054	−	0.282077i
$361$	−9.80138			−0.515862
$362$	−29.6117	+	3.18519i	−1.55636	+	0.167410i
$363$		−	67.7136i		−	3.55404i
$364$	−43.5384	+	9.47606i	−2.28203	+	0.496680i
$365$			2.20605i			0.115470i
$366$	−2.75246	−	25.5887i	−0.143873	−	1.33754i
$367$	−14.6764			−0.766100			−0.383050	−	0.923728i	$-0.625126\pi$
$367$	−14.6764			−0.766100			−0.383050	+	0.923728i	$0.625126\pi$
$368$	−19.1745	+	0.583189i	−0.999538	+	0.0304008i
$369$	16.0850			0.837351
$370$	−0.607119	−	5.64420i	−0.0315626	−	0.293428i
$371$		−	34.3692i		−	1.78436i
$372$	26.0080	−	5.66061i	1.34845	−	0.293489i
$373$		−	7.41504i		−	0.383936i	−0.981401	−	0.191968i	$-0.938513\pi$
$373$		−	7.41504i		−	0.383936i	0.981401	−	0.191968i	$-0.0614870\pi$
$374$	15.3473	−	1.65083i	0.793589	−	0.0853625i
$375$	−2.99817			−0.154825
$376$	17.3157	−	5.76630i	0.892990	−	0.297374i
$377$	−8.13437			−0.418941
$378$	−50.1844	+	5.39809i	−2.58121	+	0.277648i
$379$	−23.2395			−1.19373			−0.596867	−	0.802340i	$-0.703588\pi$
$379$	−23.2395			−1.19373			−0.596867	+	0.802340i	$0.703588\pi$
$380$	1.29002	+	5.92708i	0.0661767	+	0.304053i
$381$	54.9890			2.81717
$382$	3.06212	+	28.4676i	0.156671	+	1.45653i
$383$	−31.3721			−1.60304			−0.801519	−	0.597969i	$-0.795975\pi$
$383$	−31.3721			−1.60304			−0.801519	+	0.597969i	$0.795975\pi$
$384$	24.8175	−	23.1232i	1.26646	−	1.18000i
$385$		−	23.0804i		−	1.17629i
$386$	−1.82771	−	16.9916i	−0.0930279	−	0.864852i
$387$	28.6685			1.45730
$388$	1.22430	+	5.62514i	0.0621545	+	0.285573i
$389$		−	24.7806i		−	1.25643i	−0.778041	−	0.628213i	$-0.783786\pi$
$389$		−	24.7806i		−	1.25643i	0.778041	−	0.628213i	$-0.216214\pi$
$390$	2.53668	+	23.5827i	0.128450	+	1.19416i
$391$	3.50248	−	8.32574i	0.177128	−	0.421051i
$392$	7.91895	+	23.7799i	0.399967	+	1.20107i
$393$	−59.4248			−2.99759
$394$	0.306608	+	2.85044i	0.0154467	+	0.143603i
$395$		−	13.1166i		−	0.659968i
$396$	67.8276	−	14.7626i	3.40847	−	0.741848i
$397$	2.92234			0.146668			0.0733339	−	0.997307i	$-0.476636\pi$
$397$	2.92234			0.146668			0.0733339	+	0.997307i	$0.476636\pi$
$398$	−1.19835	−	11.1407i	−0.0600677	−	0.558431i
$399$		−	36.2149i		−	1.81301i
$400$	−3.63817	+	1.66244i	−0.181909	+	0.0831218i
$401$			2.06852i			0.103297i	0.998665	+	0.0516485i	$0.0164476\pi$
$401$			2.06852i			0.103297i	−0.998665	+	0.0516485i	$0.983552\pi$
$402$	33.2445	−	3.57595i	1.65808	−	0.178352i
$403$			24.8310i			1.23692i
$404$	19.4900	−	4.24196i	0.969662	−	0.211045i
$405$			8.90111i			0.442300i
$406$	0.875914	+	8.14310i	0.0434709	+	0.404135i
$407$		−	23.2626i		−	1.15308i
$408$	5.04618	+	15.1533i	0.249823	+	0.750198i
$409$	−36.2807			−1.79396			−0.896982	−	0.442066i	$-0.854246\pi$
$409$	−36.2807			−1.79396			−0.896982	+	0.442066i	$0.854246\pi$
$410$	−3.77645	+	0.406214i	−0.186505	+	0.0200615i
$411$	−31.9628			−1.57661
$412$	−15.0491	+	3.27542i	−0.741417	+	0.161368i
$413$			6.18376i			0.304283i
$414$	11.6562	−	38.9110i	0.572872	−	1.91237i
$415$			8.56752i			0.420563i
$416$	16.1544	+	27.2103i	0.792037	+	1.33409i
$417$	−56.0369			−2.74414
$418$	2.65841	+	24.7145i	0.130027	+	1.20882i
$419$	−12.2063			−0.596318			−0.298159	−	0.954516i	$-0.596373\pi$
$419$	−12.2063			−0.596318			−0.298159	+	0.954516i	$0.596373\pi$
$420$	23.3349	−	5.07881i	1.13863	−	0.247820i
$421$			36.6749i			1.78742i	0.448642	+	0.893712i	$0.351908\pi$
$421$			36.6749i			1.78742i	−0.448642	+	0.893712i	$0.648092\pi$
$422$	−32.8121	+	3.52944i	−1.59727	+	0.171811i
$423$			38.6444i			1.87895i
$424$	−23.1583	+	7.71195i	−1.12467	+	0.374526i
$425$		−	1.88340i		−	0.0913582i
$426$	2.38677	+	22.1891i	0.115639	+	1.07506i
$427$		−	24.1739i		−	1.16986i
$428$	8.58819	−	1.86921i	0.415126	−	0.0903516i
$429$			97.1964i			4.69268i
$430$	−6.73082	+	0.724001i	−0.324589	+	0.0349144i
$431$	7.19412			0.346528			0.173264	−	0.984875i	$-0.444569\pi$
$431$	7.19412			0.346528			0.173264	+	0.984875i	$0.444569\pi$
$432$	14.8980	+	32.6035i	0.716778	+	1.56864i
$433$			1.56741i			0.0753250i	0.999291	+	0.0376625i	$0.0119912\pi$
$433$			1.56741i			0.0753250i	−0.999291	+	0.0376625i	$0.988009\pi$
$434$	24.8576	−	2.67381i	1.19320	−	0.128347i
$435$	4.35971			0.209032
$436$	1.29856	+	5.96629i	0.0621895	+	0.285734i
$437$	13.4073	+	5.64021i	0.641359	+	0.269808i
$438$	−9.30009	+	1.00037i	−0.444375	+	0.0477993i
$439$		−	32.2347i		−	1.53848i	−0.638960	−	0.769240i	$-0.720635\pi$
$439$		−	32.2347i		−	1.53848i	0.638960	−	0.769240i	$-0.279365\pi$
$440$	−15.5518	+	5.17891i	−0.741404	+	0.246895i
$441$	−53.0709			−2.52718
$442$	−14.8143	+	1.59350i	−0.704643	+	0.0757951i
$443$			30.2309i			1.43631i	0.695882	+	0.718156i	$0.255014\pi$
$443$			30.2309i			1.43631i	−0.695882	+	0.718156i	$0.744986\pi$
$444$	23.5191	−	5.11890i	1.11617	−	0.242932i
$445$	8.41278			0.398804
$446$	−17.7039	+	1.90432i	−0.838304	+	0.0901723i
$447$	12.2724			0.580462
$448$	25.5000	−	19.1018i	1.20476	−	0.902476i
$449$	14.1818			0.669279			0.334640	−	0.942346i	$-0.391385\pi$
$449$	14.1818			0.669279			0.334640	+	0.942346i	$0.391385\pi$
$450$	−0.905822	−	8.42115i	−0.0427008	−	0.396977i
$451$	−15.5646			−0.732910
$452$	−1.67588	−	7.69993i	−0.0788267	−	0.362174i
$453$	40.1163			1.88483
$454$	0.183846	+	1.70916i	0.00862834	+	0.0802151i
$455$			22.2788i			1.04445i
$456$	−24.4020	+	8.12611i	−1.14273	+	0.380540i
$457$		−	26.8756i		−	1.25719i	−0.777734	−	0.628593i	$-0.783631\pi$
$457$		−	26.8756i		−	1.25719i	0.777734	−	0.628593i	$-0.216369\pi$
$458$	19.9803	−	2.14918i	0.933618	−	0.100425i
$459$	−16.8781			−0.787802
$460$	−1.75399	+	9.42993i	−0.0817801	+	0.439673i
$461$	−33.8406			−1.57611			−0.788057	−	0.615602i	$-0.788913\pi$
$461$	−33.8406			−1.57611			−0.788057	+	0.615602i	$0.788913\pi$
$462$	97.3007	−	10.4662i	4.52684	−	0.486930i
$463$		−	21.3167i		−	0.990672i	−0.868701	−	0.495336i	$-0.835045\pi$
$463$		−	21.3167i		−	0.990672i	0.868701	−	0.495336i	$-0.164955\pi$
$464$	5.29037	−	2.41739i	0.245599	−	0.112225i
$465$		−	13.3085i		−	0.617165i
$466$	−1.69927	−	15.7976i	−0.0787170	−	0.731808i
$467$	13.8044			0.638792			0.319396	−	0.947621i	$-0.396520\pi$
$467$	13.8044			0.638792			0.319396	+	0.947621i	$0.396520\pi$
$468$	−65.4720	+	14.2499i	−3.02644	+	0.658701i
$469$	31.4063			1.45021
$470$	−0.975934	−	9.07296i	−0.0450165	−	0.418504i
$471$	−50.1433			−2.31048
$472$	4.16668	−	1.38755i	0.191787	−	0.0638670i
$473$	−27.7411			−1.27554
$474$	55.2960	−	5.94792i	2.53983	−	0.273197i
$475$	3.03292			0.139160
$476$	3.19042	+	14.6586i	0.146233	+	0.671876i
$477$		−	51.6837i		−	2.36643i
$478$	−8.60239	+	0.925317i	−0.393464	+	0.0423230i
$479$	14.7579			0.674305			0.337153	−	0.941450i	$-0.390536\pi$
$479$	14.7579			0.674305			0.337153	+	0.941450i	$0.390536\pi$
$480$	−8.65817	−	14.5837i	−0.395190	−	0.665651i
$481$			22.4547i			1.02385i
$482$	20.4613	−	2.20092i	0.931986	−	0.100249i
$483$	22.2055	−	52.7846i	1.01038	−	2.40178i
$484$	−44.1367	+	9.60629i	−2.00621	+	0.436650i
$485$	2.87841			0.130702
$486$	0.277770	−	0.0298784i	0.0125999	−	0.00135531i
$487$			6.98690i			0.316607i	0.987391	+	0.158303i	$0.0506024\pi$
$487$			6.98690i			0.316607i	−0.987391	+	0.158303i	$0.949398\pi$
$488$	−16.2886	+	5.42427i	−0.737352	+	0.245545i
$489$	−10.5028			−0.474951
$490$	12.4600	−	1.34026i	0.562887	−	0.0605470i
$491$			39.3615i			1.77636i	0.459497	+	0.888179i	$0.348030\pi$
$491$			39.3615i			1.77636i	−0.459497	+	0.888179i	$0.651970\pi$
$492$	−3.42498	−	15.7363i	−0.154410	−	0.709446i
$493$			2.73870i			0.123345i
$494$	−2.56609	−	23.8561i	−0.115454	−	1.07334i
$495$		−	34.7078i		−	1.56000i
$496$	−7.37933	−	16.1494i	−0.331342	−	0.725128i
$497$			20.9622i			0.940284i
$498$	−36.1183	+	3.88507i	−1.61850	+	0.174094i
$499$			29.8729i			1.33730i	0.743579	+	0.668648i	$0.233127\pi$
$499$			29.8729i			1.33730i	−0.743579	+	0.668648i	$0.766873\pi$
$500$	0.425339	+	1.95425i	0.0190217	+	0.0873966i
$501$	0.0586690			0.00262114
$502$	4.58725	+	42.6462i	0.204739	+	1.90339i
$503$	25.0359			1.11630			0.558148	−	0.829741i	$-0.311512\pi$
$503$	25.0359			1.11630			0.558148	+	0.829741i	$0.311512\pi$
$504$	21.3152	+	64.0079i	0.949457	+	2.85114i
$505$		−	9.97313i		−	0.443798i
$506$	−11.2791	+	37.6522i	−0.501419	+	1.67385i
$507$		−	54.8446i		−	2.43573i
$508$	−7.80110	−	35.8426i	−0.346118	−	1.59026i
$509$	−14.3139			−0.634454			−0.317227	−	0.948350i	$-0.602752\pi$
$509$	−14.3139			−0.634454			−0.317227	+	0.948350i	$0.602752\pi$
$510$	7.93989	−	0.854055i	0.351584	−	0.0378182i
$511$	−8.78588			−0.388664
$512$	−18.5928	−	12.8960i	−0.821695	−	0.569928i
$513$		−	27.1796i		−	1.20001i
$514$	−2.66596	−	24.7846i	−0.117590	−	1.09320i
$515$			7.70072i			0.339334i
$516$	−6.10439	−	28.0470i	−0.268731	−	1.23470i
$517$		−	37.3943i		−	1.64460i
$518$	22.4788	−	2.41794i	0.987662	−	0.106238i
$519$		−	15.2974i		−	0.671481i
$520$	15.0117	−	4.99905i	0.658307	−	0.219223i
$521$			1.85890i			0.0814399i	0.999171	+	0.0407200i	$0.0129652\pi$
$521$			1.85890i			0.0814399i	−0.999171	+	0.0407200i	$0.987035\pi$
$522$	1.31718	+	12.2454i	0.0576514	+	0.535967i
$523$	−40.9989			−1.79276			−0.896379	−	0.443289i	$-0.853812\pi$
$523$	−40.9989			−1.79276			−0.896379	+	0.443289i	$0.853812\pi$
$524$	8.43039	+	38.7340i	0.368283	+	1.69210i
$525$		−	11.9406i		−	0.521131i
$526$	−2.92259	−	27.1704i	−0.127431	−	1.18469i
$527$	8.36015			0.364174
$528$	−28.8851	−	63.2138i	−1.25706	−	2.75103i
$529$	16.0833	+	16.4416i	0.699275	+	0.714853i
$530$	1.30523	+	12.1343i	0.0566956	+	0.527082i
$531$			9.29899i			0.403542i
$532$	−23.6054	+	5.13768i	−1.02342	+	0.222747i
$533$	15.0241			0.650765
$534$	3.81490	+	35.4660i	0.165087	+	1.53476i
$535$		−	4.39463i		−	0.189996i
$536$	−7.04713	−	21.1619i	−0.304390	−	0.914056i
$537$	21.2462			0.916842
$538$	0.294640	+	2.73918i	0.0127028	+	0.118094i
$539$	51.3541			2.21198
$540$	17.5130	−	3.81168i	0.753640	−	0.164029i
$541$	5.47414			0.235351			0.117676	−	0.993052i	$-0.462456\pi$
$541$	5.47414			0.235351			0.117676	+	0.993052i	$0.462456\pi$
$542$	30.6767	−	3.29975i	1.31768	−	0.141736i
$543$	−63.1397			−2.70958
$544$	9.16123	−	5.43892i	0.392784	−	0.233192i
$545$	3.05299			0.130776
$546$	−93.9215	+	10.1027i	−4.01947	+	0.432355i
$547$			5.99189i			0.256195i	0.991762	+	0.128097i	$0.0408870\pi$
$547$			5.99189i			0.256195i	−0.991762	+	0.128097i	$0.959113\pi$
$548$	4.53446	+	20.8339i	0.193702	+	0.889978i
$549$		−	36.3522i		−	1.55147i
$550$	0.876519	+	8.14873i	0.0373749	+	0.347463i
$551$	−4.41025			−0.187883
$552$	−40.5494	−	3.11819i	−1.72590	−	0.132719i
$553$	52.2386			2.22141
$554$	−2.71319	−	25.2237i	−0.115272	−	1.07165i
$555$		−	12.0349i		−	0.510851i
$556$	7.94975	+	36.5256i	0.337145	+	1.54903i
$557$		−	0.922513i		−	0.0390881i	−0.999809	−	0.0195441i	$-0.993779\pi$
$557$		−	0.922513i		−	0.0390881i	0.999809	−	0.0195441i	$-0.00622146\pi$
$558$	37.3803	−	4.02082i	1.58244	−	0.170215i
$559$	26.7776			1.13257
$560$	−6.62088	−	14.4895i	−0.279783	−	0.612294i
$561$	32.7243			1.38162
$562$	18.1597	−	1.95335i	0.766019	−	0.0823969i
$563$	−7.93985			−0.334625			−0.167312	−	0.985904i	$-0.553509\pi$
$563$	−7.93985			−0.334625			−0.167312	+	0.985904i	$0.553509\pi$
$564$	37.8066	−	8.22855i	1.59194	−	0.346484i
$565$	−3.94010			−0.165761
$566$	−0.954493	−	8.87363i	−0.0401203	−	0.372987i
$567$	−35.4499			−1.48875
$568$	14.1246	−	4.70362i	0.592654	−	0.197360i
$569$			26.7516i			1.12148i	0.827990	+	0.560742i	$0.189484\pi$
$569$			26.7516i			1.12148i	−0.827990	+	0.560742i	$0.810516\pi$
$570$	1.37533	+	12.7860i	0.0576060	+	0.535546i
$571$	−7.93227			−0.331955			−0.165978	−	0.986130i	$-0.553078\pi$
$571$	−7.93227			−0.331955			−0.165978	+	0.986130i	$0.553078\pi$
$572$	63.3540	−	13.7889i	2.64896	−	0.576543i
$573$			60.7000i			2.53578i
$574$	−1.61780	−	15.0402i	−0.0675258	−	0.627766i
$575$	4.42059	+	1.85966i	0.184352	+	0.0775533i
$576$	38.3463	−	28.7249i	1.59776	−	1.19687i
$577$	10.9537			0.456007			0.228003	−	0.973660i	$-0.426780\pi$
$577$	10.9537			0.456007			0.228003	+	0.973660i	$0.426780\pi$
$578$	−2.03471	−	18.9160i	−0.0846326	−	0.786803i
$579$		−	36.2305i		−	1.50569i
$580$	−0.618497	−	2.84172i	−0.0256817	−	0.117996i
$581$	−34.1213			−1.41559
$582$	1.30526	+	12.1346i	0.0541048	+	0.502996i
$583$			50.0117i			2.07127i
$584$	1.97142	+	5.92002i	0.0815781	+	0.244972i
$585$			33.5024i			1.38515i
$586$	0.518022	−	0.0557211i	0.0213993	−	0.00230182i
$587$			29.1933i			1.20494i	0.798142	+	0.602469i	$0.205816\pi$
$587$			29.1933i			1.20494i	−0.798142	+	0.602469i	$0.794184\pi$
$588$	11.3004	+	51.9203i	0.466020	+	2.14116i
$589$			13.4627i			0.554722i
$590$	−0.234839	−	2.18323i	−0.00966817	−	0.0898820i
$591$			6.07785i			0.250010i
$592$	−6.67315	−	14.6039i	−0.274265	−	0.600217i
$593$	−25.8321			−1.06080			−0.530398	−	0.847749i	$-0.677957\pi$
$593$	−25.8321			−1.06080			−0.530398	+	0.847749i	$0.677957\pi$
$594$	73.0249	−	7.85493i	2.99625	−	0.322292i
$595$	7.50089			0.307506
$596$	−1.74104	−	7.99930i	−0.0713156	−	0.327664i
$597$		−	23.7547i		−	0.972215i
$598$	10.8874	−	36.3446i	0.445220	−	1.48624i
$599$		−	37.9945i		−	1.55241i	−0.630478	−	0.776207i	$-0.717141\pi$
$599$		−	37.9945i		−	1.55241i	0.630478	−	0.776207i	$-0.282859\pi$
$600$	−8.04570	+	2.67930i	−0.328464	+	0.109382i
$601$	3.77516			0.153992			0.0769960	−	0.997031i	$-0.475467\pi$
$601$	3.77516			0.153992			0.0769960	+	0.997031i	$0.475467\pi$
$602$	−2.88343	−	26.8064i	−0.117520	−	1.09255i
$603$	47.2281			1.92328
$604$	−5.69115	−	26.1484i	−0.231570	−	1.06396i
$605$			22.5850i			0.918211i
$606$	42.0440	−	4.52247i	1.70792	−	0.183713i
$607$			1.02324i			0.0415322i	0.999784	+	0.0207661i	$0.00661053\pi$
$607$			1.02324i			0.0415322i	−0.999784	+	0.0207661i	$0.993389\pi$
$608$	8.75854	+	14.7528i	0.355206	+	0.598303i
$609$			17.3632i			0.703591i
$610$	0.918046	+	8.53479i	0.0371706	+	0.345564i
$611$			36.0956i			1.46027i
$612$	4.79768	+	22.0433i	0.193935	+	0.891046i
$613$			18.5129i			0.747730i	0.927483	+	0.373865i	$0.121968\pi$
$613$			18.5129i			0.747730i	−0.927483	+	0.373865i	$0.878032\pi$
$614$	−19.0095	+	2.04475i	−0.767159	+	0.0825196i
$615$	−8.05234			−0.324702
$616$	−20.6257	−	61.9372i	−0.831034	−	2.49552i
$617$			24.7039i			0.994542i	0.867595	+	0.497271i	$0.165664\pi$
$617$			24.7039i			0.994542i	−0.867595	+	0.497271i	$0.834336\pi$
$618$	−32.4641	+	3.49201i	−1.30590	+	0.140469i
$619$	11.5886			0.465783			0.232892	−	0.972503i	$-0.425181\pi$
$619$	11.5886			0.465783			0.232892	+	0.972503i	$0.425181\pi$
$620$	−8.67465	+	1.88802i	−0.348382	+	0.0758249i
$621$	16.6654	−	39.6152i	0.668759	−	1.58970i
$622$	−11.2266	+	1.20759i	−0.450144	+	0.0484198i
$623$			33.5050i			1.34235i
$624$	27.8819	+	61.0184i	1.11617	+	2.44269i
$625$	1.00000			0.0400000
$626$	−21.3319	+	2.29457i	−0.852595	+	0.0917095i
$627$			52.6975i			2.10453i
$628$	7.11366	+	32.6841i	0.283866	+	1.30424i
$629$	7.56010			0.301441
$630$	33.5384	−	3.60756i	1.33620	−	0.143729i
$631$	38.3679			1.52740			0.763700	−	0.645571i	$-0.223381\pi$
$631$	38.3679			1.52740			0.763700	+	0.645571i	$0.223381\pi$
$632$	−11.7216	−	35.1989i	−0.466260	−	1.40014i
$633$	−69.9638			−2.78081
$634$	−3.21233	−	29.8640i	−0.127578	−	1.18605i
$635$	−18.3409			−0.727836
$636$	−50.5632	+	11.0050i	−2.00496	+	0.436377i
$637$	−49.5705			−1.96406
$638$	−1.27457	−	11.8493i	−0.0504607	−	0.469118i
$639$			31.5225i			1.24701i
$640$	−8.27756	+	7.71246i	−0.327199	+	0.304862i
$641$		−	38.4648i		−	1.51927i	−0.650350	−	0.759635i	$-0.725378\pi$
$641$		−	38.4648i		−	1.51927i	0.650350	−	0.759635i	$-0.274622\pi$
$642$	18.5266	−	1.99281i	0.731185	−	0.0786500i
$643$	−22.7495			−0.897154			−0.448577	−	0.893744i	$-0.648069\pi$
$643$	−22.7495			−0.897154			−0.448577	+	0.893744i	$0.648069\pi$
$644$	−37.5560	−	6.98550i	−1.47991	−	0.275267i
$645$	−14.3518			−0.565102
$646$	−8.03194	+	0.863956i	−0.316012	+	0.0339919i
$647$			41.0152i			1.61247i	0.591594	+	0.806236i	$0.298499\pi$
$647$			41.0152i			1.61247i	−0.591594	+	0.806236i	$0.701501\pi$
$648$	7.95444	+	23.8865i	0.312480	+	0.938350i
$649$		−	8.99818i		−	0.353209i
$650$	−0.846077	−	7.86572i	−0.0331859	−	0.308519i
$651$	53.0027			2.07734
$652$	1.48999	+	6.84585i	0.0583525	+	0.268104i
$653$	−34.9041			−1.36590			−0.682952	−	0.730464i	$-0.739304\pi$
$653$	−34.9041			−1.36590			−0.682952	+	0.730464i	$0.739304\pi$
$654$	1.38442	+	12.8706i	0.0541353	+	0.503279i
$655$	19.8204			0.774447
$656$	−9.77124	+	4.46490i	−0.381503	+	0.174325i
$657$	−13.2120			−0.515449
$658$	36.1343	−	3.88679i	1.40866	−	0.151523i
$659$	−28.7961			−1.12174			−0.560868	−	0.827905i	$-0.689533\pi$
$659$	−28.7961			−1.12174			−0.560868	+	0.827905i	$0.689533\pi$
$660$	−33.9553	+	7.39033i	−1.32171	+	0.287668i
$661$		−	19.6471i		−	0.764185i	−0.924124	−	0.382093i	$-0.875204\pi$
$661$		−	19.6471i		−	0.764185i	0.924124	−	0.382093i	$-0.124796\pi$
$662$	27.0831	−	2.91320i	1.05262	−	0.113225i
$663$	−31.5878			−1.22677
$664$	7.65633	+	22.9913i	0.297123	+	0.892236i
$665$			12.0790i			0.468405i
$666$	33.8031	−	3.63604i	1.30984	−	0.140894i
$667$	−6.42811	−	2.70418i	−0.248897	−	0.104706i
$668$	−0.00832317	−	0.0382413i	−0.000322033	−	0.00147960i
$669$	−37.7492			−1.45947
$670$	−11.0883	+	1.19271i	−0.428377	+	0.0460784i
$671$			35.1762i			1.35796i
$672$	58.0815	−	34.4823i	2.24054	−	1.33019i
$673$	−15.4460			−0.595399			−0.297699	−	0.954660i	$-0.596219\pi$
$673$	−15.4460			−0.595399			−0.297699	+	0.954660i	$0.596219\pi$
$674$	−16.7789	+	1.80482i	−0.646298	+	0.0695191i
$675$		−	8.96151i		−	0.344929i
$676$	−35.7485	+	7.78061i	−1.37494	+	0.299254i
$677$		−	1.18640i		−	0.0455969i	−0.999740	−	0.0227984i	$-0.992742\pi$
$677$		−	1.18640i		−	0.0455969i	0.999740	−	0.0227984i	$-0.00725760\pi$
$678$	−1.78670	−	16.6104i	−0.0686177	−	0.637918i
$679$			11.4637i			0.439936i
$680$	−1.68309	−	5.05418i	−0.0645436	−	0.193819i
$681$			3.64437i			0.139653i
$682$	−36.1711	+	3.89075i	−1.38506	+	0.148984i
$683$		−	1.67295i		−	0.0640136i	−0.999488	−	0.0320068i	$-0.989810\pi$
$683$		−	1.67295i		−	0.0640136i	0.999488	−	0.0320068i	$-0.0101898\pi$
$684$	−35.4973	+	7.72593i	−1.35727	+	0.295408i
$685$	10.6608			0.407328
$686$	1.12124	+	10.4238i	0.0428090	+	0.397982i
$687$	42.6031			1.62541
$688$	−17.4154	+	7.95786i	−0.663957	+	0.303390i
$689$		−	48.2748i		−	1.83912i
$690$	−5.83524	+	19.4793i	−0.222144	+	0.741565i
$691$			3.68019i			0.140001i	0.997547	+	0.0700006i	$0.0223001\pi$
$691$			3.68019i			0.140001i	−0.997547	+	0.0700006i	$0.977700\pi$
$692$	−9.97107	+	2.17019i	−0.379043	+	0.0824982i
$693$	138.229			5.25087
$694$	23.8734	−	2.56795i	0.906224	−	0.0974781i
$695$	18.6904			0.708967
$696$	11.6995	−	3.89604i	0.443467	−	0.147679i
$697$		−	5.05834i		−	0.191598i
$698$	3.07097	+	28.5498i	0.116238	+	1.08063i
$699$		−	33.6844i		−	1.27406i
$700$	−7.78306	+	1.69397i	−0.294172	+	0.0640261i
$701$		−	3.72654i		−	0.140750i	−0.997521	−	0.0703748i	$-0.977580\pi$
$701$		−	3.72654i		−	0.140750i	0.997521	−	0.0703748i	$-0.0224195\pi$
$702$	−70.4888	+	7.58213i	−2.66043	+	0.286169i
$703$			12.1744i			0.459165i
$704$	−37.1058	+	27.7956i	−1.39848	+	1.04759i
$705$		−	19.3458i		−	0.728607i
$706$	−0.871957	−	8.10632i	−0.0328165	−	0.305085i
$707$	39.7193			1.49380
$708$	9.09740	−	1.98003i	0.341901	−	0.0744143i
$709$			14.2628i			0.535653i	0.963467	+	0.267826i	$0.0863053\pi$
$709$			14.2628i			0.535653i	−0.963467	+	0.267826i	$0.913695\pi$
$710$	−0.796077	−	7.40089i	−0.0298763	−	0.277750i
$711$	78.5553			2.94605
$712$	22.5760	−	7.51805i	0.846073	−	0.281751i
$713$	−8.25479	+	19.6224i	−0.309144	+	0.734866i
$714$	3.40139	+	31.6217i	0.127294	+	1.18341i
$715$		−	32.4186i		−	1.21239i
$716$	−3.01413	−	13.8486i	−0.112643	−	0.517547i
$717$	−18.3425			−0.685012
$718$	−3.51021	−	32.6333i	−0.131000	−	1.21786i
$719$		−	6.87007i		−	0.256210i	−0.991761	−	0.128105i	$-0.959110\pi$
$719$		−	6.87007i		−	0.256210i	0.991761	−	0.128105i	$-0.0408895\pi$
$720$	−9.95633	−	21.7890i	−0.371051	−	0.812029i
$721$	−30.6692			−1.14218
$722$	1.48244	+	13.7817i	0.0551705	+	0.512903i
$723$	43.6286			1.62257
$724$	8.95741	+	41.1554i	0.332899	+	1.52953i
$725$	−1.45413			−0.0540049
$726$	−95.2123	+	10.2415i	−3.53366	+	0.380099i
$727$	−15.7302			−0.583399			−0.291700	−	0.956510i	$-0.594221\pi$
$727$	−15.7302			−0.583399			−0.291700	+	0.956510i	$0.594221\pi$
$728$	19.9094	+	59.7862i	0.737891	+	2.21582i
$729$	27.2956			1.01095
$730$	3.10193	−	0.333659i	0.114807	−	0.0123493i
$731$		−	9.01556i		−	0.333453i
$732$	−35.5641	+	7.74047i	−1.31449	+	0.286096i
$733$			30.3417i			1.12069i	0.828258	+	0.560347i	$0.189332\pi$
$733$			30.3417i			1.12069i	−0.828258	+	0.560347i	$0.810668\pi$
$734$	2.21976	+	20.6365i	0.0819330	+	0.761706i
$735$	26.5679			0.979973
$736$	3.72011	+	26.8730i	0.137125	+	0.990554i
$737$	−45.7003			−1.68339
$738$	−2.43281	−	22.6171i	−0.0895532	−	0.832548i
$739$			36.4285i			1.34004i	0.742342	+	0.670022i	$0.233715\pi$
$739$			36.4285i			1.34004i	−0.742342	+	0.670022i	$0.766285\pi$
$740$	−7.84450	+	1.70734i	−0.288370	+	0.0627632i
$741$		−	50.8673i		−	1.86866i
$742$	−48.3266	+	5.19826i	−1.77413	+	0.190834i
$743$	−45.4132			−1.66605			−0.833024	−	0.553237i	$-0.813393\pi$
$743$	−45.4132			−1.66605			−0.833024	+	0.553237i	$0.813393\pi$
$744$	−11.8930	−	35.7138i	−0.436020	−	1.30933i
$745$	−4.09329			−0.149966
$746$	−10.4263	+	1.12151i	−0.381734	+	0.0410613i
$747$	−51.3109			−1.87737
$748$	−4.64248	−	21.3302i	−0.169746	−	0.779908i
$749$	17.5022			0.639517
$750$	0.453465	+	4.21573i	0.0165582	+	0.153937i
$751$	31.8139			1.16091			0.580453	−	0.814294i	$-0.302876\pi$
$751$	31.8139			1.16091			0.580453	+	0.814294i	$0.302876\pi$
$752$	−10.7270	−	23.4755i	−0.391173	−	0.856065i
$753$			90.9325i			3.31377i
$754$	1.23030	+	11.4378i	0.0448050	+	0.416539i
$755$	−13.3803			−0.486958
$756$	15.1805	+	69.7480i	0.552111	+	2.53671i
$757$			37.0307i			1.34590i	0.739687	+	0.672951i	$0.234974\pi$
$757$			37.0307i			1.34590i	−0.739687	+	0.672951i	$0.765026\pi$
$758$	3.51492	+	32.6772i	0.127668	+	1.18689i
$759$	−32.3119	+	76.8085i	−1.17285	+	2.78797i
$760$	8.13897	−	2.71036i	0.295232	−	0.0983150i
$761$	3.82612			0.138697			0.0693484	−	0.997593i	$-0.477908\pi$
$761$	3.82612			0.138697			0.0693484	+	0.997593i	$0.477908\pi$
$762$	−8.31696	−	77.3202i	−0.301292	−	2.80102i
$763$			12.1589i			0.440183i
$764$	39.5652	−	8.61130i	1.43142	−	0.311546i
$765$	11.2797			0.407817
$766$	4.74495	+	44.1124i	0.171442	+	1.59384i
$767$			8.68567i			0.313621i
$768$	−36.2672	−	31.3986i	−1.30868	−	1.13300i
$769$			18.7353i			0.675613i	0.941216	+	0.337807i	$0.109685\pi$
$769$			18.7353i			0.675613i	−0.941216	+	0.337807i	$0.890315\pi$
$770$	−32.4534	+	3.49086i	−1.16954	+	0.125802i
$771$		−	52.8471i		−	1.90324i
$772$	−23.6156	+	5.13989i	−0.849943	+	0.184989i
$773$		−	35.5160i		−	1.27742i	−0.769447	−	0.638710i	$-0.779468\pi$
$773$		−	35.5160i		−	1.27742i	0.769447	−	0.638710i	$-0.220532\pi$
$774$	−4.33604	−	40.3109i	−0.155856	−	1.44894i
$775$			4.43887i			0.159449i
$776$	7.72434	−	2.57228i	0.277288	−	0.0923396i
$777$	47.9305			1.71950
$778$	−34.8441	+	3.74801i	−1.24922	+	0.134373i
$779$	8.14569			0.291850
$780$	32.7761	−	7.13366i	1.17357	−	0.255426i
$781$		−	30.5028i		−	1.09148i
$782$	−12.2366	−	3.66560i	−0.437579	−	0.131082i
$783$			13.0312i			0.465696i
$784$	32.2393	−	14.7315i	1.15140	−	0.526125i
$785$	16.7247			0.596929
$786$	8.98786	+	83.5574i	0.320586	+	2.98039i
$787$	−46.9898			−1.67501			−0.837503	−	0.546433i	$-0.815985\pi$
$787$	−46.9898			−1.67501			−0.837503	+	0.546433i	$0.815985\pi$
$788$	3.96163	−	0.862244i	0.141127	−	0.0307162i
$789$		−	57.9342i		−	2.06251i
$790$	−18.4433	+	1.98385i	−0.656182	+	0.0705823i
$791$		−	15.6920i		−	0.557943i
$792$	−31.0165	−	93.1398i	−1.10212	−	3.30958i
$793$		−	33.9545i		−	1.20576i
$794$	−0.441996	−	4.10910i	−0.0156859	−	0.145827i
$795$			25.8735i			0.917637i
$796$	−15.4837	+	3.36999i	−0.548804	+	0.119446i
$797$		−	40.1221i		−	1.42120i	−0.703597	−	0.710599i	$-0.748424\pi$
$797$		−	40.1221i		−	1.42120i	0.703597	−	0.710599i	$-0.251576\pi$
$798$	−50.9219	+	5.47742i	−1.80262	+	0.193899i
$799$	12.1527			0.429933
$800$	2.88782	+	4.86420i	0.102100	+	0.171976i
$801$			50.3841i			1.78024i
$802$	2.90855	−	0.312859i	0.102705	−	0.0110474i
$803$	12.7846			0.451159
$804$	−10.0563	−	46.2043i	−0.354658	−	1.62950i
$805$	−7.40636	+	17.6056i	−0.261040	+	0.620517i
$806$	34.9149	−	3.75562i	1.22982	−	0.132286i
$807$			5.84062i			0.205600i
$808$	−8.91244	−	26.7633i	−0.313539	−	0.941530i
$809$	2.62556			0.0923099			0.0461549	−	0.998934i	$-0.485303\pi$
$809$	2.62556			0.0923099			0.0461549	+	0.998934i	$0.485303\pi$
$810$	12.5159	−	1.34627i	0.439763	−	0.0473031i
$811$		−	41.5235i		−	1.45809i	−0.684467	−	0.729044i	$-0.739965\pi$
$811$		−	41.5235i		−	1.45809i	0.684467	−	0.729044i	$-0.260035\pi$
$812$	11.3176	−	2.46325i	0.397168	−	0.0864431i
$813$	65.4105			2.29405
$814$	−32.7096	+	3.51841i	−1.14647	+	0.123320i
$815$	3.50306			0.122707
$816$	20.5438	−	9.38734i	0.719177	−	0.328623i
$817$	14.5182			0.507927
$818$	5.48737	+	51.0144i	0.191861	+	1.78368i
$819$	−133.428			−4.66235
$820$	1.14236	+	5.24863i	0.0398928	+	0.183290i
$821$	2.74866			0.0959289			0.0479644	−	0.998849i	$-0.484727\pi$
$821$	2.74866			0.0959289			0.0479644	+	0.998849i	$0.484727\pi$
$822$	4.83430	+	44.9430i	0.168616	+	1.56757i
$823$		−	8.04460i		−	0.280417i	−0.990122	−	0.140209i	$-0.955223\pi$
$823$		−	8.04460i		−	0.280417i	0.990122	−	0.140209i	$-0.0447773\pi$
$824$	6.88172	+	20.6652i	0.239736	+	0.719907i
$825$			17.3751i			0.604925i
$826$	8.69500	−	0.935278i	0.302538	−	0.0325425i
$827$	−21.0973			−0.733626			−0.366813	−	0.930295i	$-0.619551\pi$
$827$	−21.0973			−0.733626			−0.366813	+	0.930295i	$0.619551\pi$
$828$	−56.4758	−	10.5046i	−1.96267	−	0.365061i
$829$	23.4109			0.813093			0.406546	−	0.913630i	$-0.366733\pi$
$829$	23.4109			0.813093			0.406546	+	0.913630i	$0.366733\pi$
$830$	12.0468	−	1.29582i	0.418151	−	0.0449785i
$831$		−	53.7833i		−	1.86572i
$832$	35.8172	−	26.8303i	1.24174	−	0.930173i
$833$			16.6895i			0.578258i
$834$	8.47544	+	78.7936i	0.293481	+	2.72840i
$835$	−0.0195683			−0.000677189
$836$	34.3490	−	7.47600i	1.18798	−	0.258563i
$837$	39.7789			1.37496
$838$	1.84618	+	17.1634i	0.0637752	+	0.592898i
$839$	2.04730			0.0706808			0.0353404	−	0.999375i	$-0.488748\pi$
$839$	2.04730			0.0706808			0.0353404	+	0.999375i	$0.488748\pi$
$840$	−10.6707	−	32.0431i	−0.368173	−	1.10559i
$841$	−26.8855			−0.927087
$842$	51.5686	−	5.54698i	1.77717	−	0.191162i
$843$	38.7210			1.33362
$844$	9.92552	+	45.6034i	0.341650	+	1.56973i
$845$			18.2927i			0.629288i
$846$	54.3379	−	5.84487i	1.86818	−	0.200951i
$847$	−89.9479			−3.09065
$848$	14.3464	+	31.3966i	0.492659	+	1.07816i
$849$		−	18.9208i		−	0.649361i
$850$	−2.64825	+	0.284859i	−0.0908342	+	0.00977059i
$851$	−7.46482	+	17.7446i	−0.255891	+	0.608277i
$852$	30.8391	−	6.71209i	1.05653	−	0.229952i
$853$	5.95932			0.204043			0.102022	−	0.994782i	$-0.467469\pi$
$853$	5.95932			0.204043			0.102022	+	0.994782i	$0.467469\pi$
$854$	−33.9910	+	3.65624i	−1.16315	+	0.125114i
$855$			18.1642i			0.621201i
$856$	−3.92724	−	11.7932i	−0.134230	−	0.403082i
$857$	35.6433			1.21755			0.608775	−	0.793343i	$-0.291661\pi$
$857$	35.6433			1.21755			0.608775	+	0.793343i	$0.291661\pi$
$858$	136.668	−	14.7007i	4.66577	−	0.501874i
$859$		−	4.58161i		−	0.156322i	−0.996941	−	0.0781612i	$-0.975095\pi$
$859$		−	4.58161i		−	0.156322i	0.996941	−	0.0781612i	$-0.0249049\pi$
$860$	2.03604	+	9.35472i	0.0694284	+	0.318993i
$861$		−	32.0695i		−	1.09293i
$862$	−1.08809	−	10.1157i	−0.0370606	−	0.344541i
$863$		−	33.8140i		−	1.15104i	−0.817788	−	0.575520i	$-0.804800\pi$
$863$		−	33.8140i		−	1.15104i	0.817788	−	0.575520i	$-0.195200\pi$
$864$	43.5906	−	25.8793i	1.48298	−	0.880430i
$865$			5.10225i			0.173482i
$866$	2.20394	−	0.237067i	0.0748930	−	0.00805588i
$867$		−	40.3338i		−	1.36981i
$868$	−7.51931	−	34.5480i	−0.255222	−	1.17263i
$869$	−76.0141			−2.57860
$870$	−0.659396	−	6.13020i	−0.0223556	−	0.207833i
$871$	44.1132			1.49472
$872$	8.19282	−	2.72829i	0.277444	−	0.0923915i
$873$			17.2388i			0.583446i
$874$	5.90289	−	19.7051i	0.199668	−	0.666536i
$875$			3.98264i			0.134638i
$876$	2.81323	+	12.9256i	0.0950503	+	0.436715i
$877$	−24.2787			−0.819832			−0.409916	−	0.912123i	$-0.634442\pi$
$877$	−24.2787			−0.819832			−0.409916	+	0.912123i	$0.634442\pi$
$878$	−45.3253	+	4.87543i	−1.52966	+	0.164538i
$879$	1.10455			0.0372557
$880$	9.63425	+	21.0842i	0.324771	+	0.710747i
$881$		−	33.0945i		−	1.11498i	−0.830183	−	0.557490i	$-0.811764\pi$
$881$		−	33.0945i		−	1.11498i	0.830183	−	0.557490i	$-0.188236\pi$
$882$	8.02684	+	74.6231i	0.270278	+	2.51269i
$883$		−	17.1091i		−	0.575767i	−0.957665	−	0.287884i	$-0.907048\pi$
$883$		−	17.1091i		−	0.575767i	0.957665	−	0.287884i	$-0.0929516\pi$
$884$	4.48125	+	20.5894i	0.150721	+	0.692496i
$885$		−	4.65519i		−	0.156482i
$886$	42.5077	−	4.57235i	1.42808	−	0.153611i
$887$		−	10.4384i		−	0.350487i	−0.984525	−	0.175243i	$-0.943929\pi$
$887$		−	10.4384i		−	0.350487i	0.984525	−	0.175243i	$-0.0560712\pi$
$888$	−10.7549	−	32.2961i	−0.360911	−	1.08378i
$889$		−	73.0451i		−	2.44985i
$890$	−1.27241	−	11.8292i	−0.0426514	−	0.396517i
$891$	51.5842			1.72814
$892$	5.35535	+	24.6055i	0.179310	+	0.823853i
$893$			19.5701i			0.654889i
$894$	−1.85616	−	17.2562i	−0.0620794	−	0.577133i
$895$	−7.08641			−0.236873
$896$	−30.7159	−	32.9665i	−1.02615	−	1.10133i
$897$	31.1897	−	74.1409i	1.04139	−	2.47549i
$898$	−2.14496	−	19.9410i	−0.0715782	−	0.665440i
$899$		−	6.45467i		−	0.215275i
$900$	−11.7040	+	2.54736i	−0.390133	+	0.0849119i
$901$	−16.2533			−0.541475
$902$	2.35411	+	21.8855i	0.0783834	+	0.728707i
$903$		−	57.1580i		−	1.90210i
$904$	−10.5734	+	3.52105i	−0.351667	+	0.117108i
$905$	21.0594			0.700040
$906$	−6.06749	−	56.4076i	−0.201579	−	1.87402i
$907$	9.34196			0.310195			0.155097	−	0.987899i	$-0.450431\pi$
$907$	9.34196			0.310195			0.155097	+	0.987899i	$0.450431\pi$
$908$	2.37545	−	0.517014i	0.0788322	−	0.0171577i
$909$	59.7290			1.98109
$910$	31.3263	−	3.36962i	1.03846	−	0.111702i
$911$	10.3085			0.341536			0.170768	−	0.985311i	$-0.445375\pi$
$911$	10.3085			0.341536			0.170768	+	0.985311i	$0.445375\pi$
$912$	15.1169	+	33.0827i	0.500570	+	1.09548i
$913$	49.6510			1.64321
$914$	−37.7898	+	4.06487i	−1.24998	+	0.134454i
$915$			18.1983i			0.601619i
$916$	−6.04395	−	27.7693i	−0.199698	−	0.917523i
$917$			78.9374i			2.60674i
$918$	2.55277	+	23.7323i	0.0842540	+	0.783283i
$919$	45.9326			1.51518			0.757588	−	0.652733i	$-0.226378\pi$
$919$	45.9326			1.51518			0.757588	+	0.652733i	$0.226378\pi$
$920$	13.5247	+	1.04003i	0.445897	+	0.0342889i
$921$	−40.5330			−1.33561
$922$	5.11831	+	47.5834i	0.168563	+	1.56707i
$923$			29.4434i			0.969142i
$924$	−29.4330	−	135.232i	−0.968275	−	4.44880i
$925$			4.01408i			0.131982i
$926$	−29.9735	+	3.22410i	−0.984990	+	0.105951i
$927$	−46.1196			−1.51477
$928$	−4.19926	−	7.07317i	−0.137847	−	0.232188i
$929$	16.4065			0.538279			0.269140	−	0.963101i	$-0.413261\pi$
$929$	16.4065			0.538279			0.269140	+	0.963101i	$0.413261\pi$
$930$	−18.7131	+	2.01287i	−0.613625	+	0.0660047i
$931$	−26.8759			−0.880823
$932$	−21.9560	+	4.77868i	−0.719192	+	0.156531i
$933$	−23.9378			−0.783690
$934$	−2.08788	−	19.4104i	−0.0683177	−	0.635128i
$935$	−10.9148			−0.356951
$936$	29.9393	+	89.9051i	0.978596	+	2.93864i
$937$		−	8.78310i		−	0.286931i	−0.989655	−	0.143466i	$-0.954175\pi$
$937$		−	8.78310i		−	0.286931i	0.989655	−	0.143466i	$-0.0458247\pi$
$938$	−4.75013	−	44.1605i	−0.155097	−	1.44189i
$939$	−45.4851			−1.48435
$940$	−12.6099	+	2.74453i	−0.411290	+	0.0895166i
$941$		−	30.1513i		−	0.982903i	−0.870905	−	0.491452i	$-0.836466\pi$
$941$		−	30.1513i		−	0.982903i	0.870905	−	0.491452i	$-0.163534\pi$
$942$	7.58406	+	70.5066i	0.247102	+	2.29723i
$943$	11.8726	+	4.99460i	0.386626	+	0.162646i
$944$	−2.58123	−	5.64892i	−0.0840119	−	0.183857i
$945$	35.6904			1.16101
$946$	4.19577	+	39.0068i	0.136416	+	1.26822i
$947$		−	18.5434i		−	0.602578i	−0.953533	−	0.301289i	$-0.902583\pi$
$947$		−	18.5434i		−	0.602578i	0.953533	−	0.301289i	$-0.0974169\pi$
$948$	−16.7268	−	76.8522i	−0.543260	−	2.49604i
$949$	−12.3406			−0.400593
$950$	−0.458722	−	4.26460i	−0.0148829	−	0.138362i
$951$		−	63.6776i		−	2.06489i
$952$	20.1289	−	6.70314i	0.652383	−	0.217250i
$953$		−	37.5153i		−	1.21524i	−0.794228	−	0.607619i	$-0.792125\pi$
$953$		−	37.5153i		−	1.21524i	0.794228	−	0.607619i	$-0.207875\pi$
$954$	−72.6725	+	7.81703i	−2.35286	+	0.253086i
$955$		−	20.2457i		−	0.655136i
$956$	2.60218	+	11.9559i	0.0841605	+	0.386681i
$957$		−	25.2657i		−	0.816723i
$958$	−2.23210	−	20.7511i	−0.0721157	−	0.670438i
$959$			42.4581i			1.37104i
$960$	−19.1966	+	14.3800i	−0.619569	+	0.464113i
$961$	11.2965			0.364402
$962$	31.5736	−	3.39622i	1.01797	−	0.109498i
$963$	26.3194			0.848131
$964$	−6.18944	−	28.4378i	−0.199349	−	0.915920i
$965$			12.0842i			0.389005i
$966$	−77.5790	−	23.2397i	−2.49606	−	0.747724i
$967$			23.8326i			0.766405i	0.923664	+	0.383203i	$0.125179\pi$
$967$			23.8326i			0.766405i	−0.923664	+	0.383203i	$0.874821\pi$
$968$	20.1830	+	60.6078i	0.648706	+	1.94801i
$969$	−17.1261			−0.550170
$970$	−0.435353	−	4.04735i	−0.0139783	−	0.129952i
$971$	−6.06680			−0.194693			−0.0973465	−	0.995251i	$-0.531036\pi$
$971$	−6.06680			−0.194693			−0.0973465	+	0.995251i	$0.531036\pi$
$972$	−0.0840241	−	0.386054i	−0.00269507	−	0.0123827i
$973$			74.4370i			2.38634i
$974$	9.82430	−	1.05675i	0.314791	−	0.0338605i
$975$		−	16.7717i		−	0.537124i
$976$	10.0907	+	22.0831i	0.322995	+	0.706862i
$977$			47.3845i			1.51597i	0.652274	+	0.757983i	$0.273815\pi$
$977$			47.3845i			1.51597i	−0.652274	+	0.757983i	$0.726185\pi$
$978$	1.58852	+	14.7680i	0.0507952	+	0.472227i
$979$		−	48.7542i		−	1.55819i
$980$	−3.76910	−	17.3174i	−0.120399	−	0.553183i
$981$			18.2843i			0.583774i
$982$	55.3463	−	5.95333i	1.76617	−	0.189978i
$983$	7.11365			0.226890			0.113445	−	0.993544i	$-0.463811\pi$
$983$	7.11365			0.226890			0.113445	+	0.993544i	$0.463811\pi$
$984$	−21.6088	+	7.19594i	−0.688863	+	0.229398i
$985$		−	2.02719i		−	0.0645917i
$986$	3.85089	−	0.414222i	0.122637	−	0.0131915i
$987$	77.0475			2.45245
$988$	−33.1560	+	7.21636i	−1.05483	+	0.229583i
$989$	21.1608	+	8.90194i	0.672873	+	0.283065i
$990$	−48.8027	+	5.24947i	−1.55105	+	0.166839i
$991$		−	26.6301i		−	0.845932i	−0.906145	−	0.422966i	$-0.860989\pi$
$991$		−	26.6301i		−	0.845932i	0.906145	−	0.422966i	$-0.139011\pi$
$992$	−21.5915	+	12.8187i	−0.685532	+	0.406993i
$993$	57.7481			1.83258
$994$	29.4750	−	3.17049i	0.934892	−	0.100562i
$995$			7.92307i			0.251178i
$996$	10.9256	+	50.1985i	0.346192	+	1.59060i
$997$	14.3787			0.455379			0.227689	−	0.973734i	$-0.426883\pi$
$997$	14.3787			0.455379			0.227689	+	0.973734i	$0.426883\pi$
$998$	42.0044	−	4.51821i	1.32963	−	0.143021i
$999$	35.9722			1.13811

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.e.b.91.14	yes	32
4.3	odd	2	inner	460.2.e.b.91.16	yes	32
23.22	odd	2	inner	460.2.e.b.91.13	✓	32
92.91	even	2	inner	460.2.e.b.91.15	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.e.b.91.13	✓	32	23.22	odd	2	inner
460.2.e.b.91.14	yes	32	1.1	even	1	trivial
460.2.e.b.91.15	yes	32	92.91	even	2	inner
460.2.e.b.91.16	yes	32	4.3	odd	2	inner

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)

\(f(q)\)	\(=\)	\(q+(-0.151248 - 1.40610i) q^{2} -2.99817i q^{3} +(-1.95425 + 0.425339i) q^{4} +1.00000i q^{5} +(-4.21573 + 0.453465i) q^{6} -3.98264 q^{7} +(0.893646 + 2.68354i) q^{8} -5.98900 q^{9} +O(q^{10})\)	\(q+(-0.151248 - 1.40610i) q^{2} -2.99817i q^{3} +(-1.95425 + 0.425339i) q^{4} +1.00000i q^{5} +(-4.21573 + 0.453465i) q^{6} -3.98264 q^{7} +(0.893646 + 2.68354i) q^{8} -5.98900 q^{9} +(1.40610 - 0.151248i) q^{10} +5.79526 q^{11} +(1.27524 + 5.85916i) q^{12} -5.59399 q^{13} +(0.602364 + 5.60000i) q^{14} +2.99817 q^{15} +(3.63817 - 1.66244i) q^{16} +1.88340i q^{17} +(0.905822 + 8.42115i) q^{18} -3.03292 q^{19} +(-0.425339 - 1.95425i) q^{20} +11.9406i q^{21} +(-0.876519 - 8.14873i) q^{22} +(-4.42059 - 1.85966i) q^{23} +(8.04570 - 2.67930i) q^{24} -1.00000 q^{25} +(0.846077 + 7.86572i) q^{26} +8.96151i q^{27} +(7.78306 - 1.69397i) q^{28} +1.45413 q^{29} +(-0.453465 - 4.21573i) q^{30} -4.43887i q^{31} +(-2.88782 - 4.86420i) q^{32} -17.3751i q^{33} +(2.64825 - 0.284859i) q^{34} -3.98264i q^{35} +(11.7040 - 2.54736i) q^{36} -4.01408i q^{37} +(0.458722 + 4.26460i) q^{38} +16.7717i q^{39} +(-2.68354 + 0.893646i) q^{40} -2.68576 q^{41} +(16.7897 - 1.80599i) q^{42} -4.78686 q^{43} +(-11.3254 + 2.46495i) q^{44} -5.98900i q^{45} +(-1.94627 + 6.49708i) q^{46} -6.45256i q^{47} +(-4.98426 - 10.9078i) q^{48} +8.86139 q^{49} +(0.151248 + 1.40610i) q^{50} +5.64674 q^{51} +(10.9320 - 2.37934i) q^{52} +8.62977i q^{53} +(12.6008 - 1.35541i) q^{54} +5.79526i q^{55} +(-3.55907 - 10.6876i) q^{56} +9.09320i q^{57} +(-0.219933 - 2.04465i) q^{58} -1.55268i q^{59} +(-5.85916 + 1.27524i) q^{60} +6.06982i q^{61} +(-6.24150 + 0.671368i) q^{62} +23.8520 q^{63} +(-6.40279 + 4.79627i) q^{64} -5.59399i q^{65} +(-24.4312 + 2.62795i) q^{66} -7.88582 q^{67} +(-0.801083 - 3.68063i) q^{68} +(-5.57557 + 13.2537i) q^{69} +(-5.60000 + 0.602364i) q^{70} -5.26340i q^{71} +(-5.35204 - 16.0717i) q^{72} +2.20605 q^{73} +(-5.64420 + 0.607119i) q^{74} +2.99817i q^{75} +(5.92708 - 1.29002i) q^{76} -23.0804 q^{77} +(23.5827 - 2.53668i) q^{78} -13.1166 q^{79} +(1.66244 + 3.63817i) q^{80} +8.90111 q^{81} +(0.406214 + 3.77645i) q^{82} +8.56752 q^{83} +(-5.07881 - 23.3349i) q^{84} -1.88340 q^{85} +(0.724001 + 6.73082i) q^{86} -4.35971i q^{87} +(5.17891 + 15.5518i) q^{88} -8.41278i q^{89} +(-8.42115 + 0.905822i) q^{90} +22.2788 q^{91} +(9.42993 + 1.75399i) q^{92} -13.3085 q^{93} +(-9.07296 + 0.975934i) q^{94} -3.03292i q^{95} +(-14.5837 + 8.65817i) q^{96} -2.87841i q^{97} +(-1.34026 - 12.4600i) q^{98} -34.7078 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{2} - 4 q^{4} - 16 q^{6} - 2 q^{8} - 52 q^{9}+O(q^{10}) \) 32 * q + 4 * q^2 - 4 * q^4 - 16 * q^6 - 2 * q^8 - 52 * q^9	\( 32 q + 4 q^{2} - 4 q^{4} - 16 q^{6} - 2 q^{8} - 52 q^{9} + 24 q^{12} - 4 q^{13} + 20 q^{16} - 56 q^{18} - 6 q^{24} - 32 q^{25} + 68 q^{26} + 8 q^{29} - 16 q^{32} + 8 q^{36} + 44 q^{41} - 4 q^{46} - 4 q^{48} - 12 q^{49} - 4 q^{50} + 16 q^{52} + 42 q^{54} - 10 q^{58} - 36 q^{62} - 22 q^{64} - 44 q^{69} - 42 q^{70} - 32 q^{72} - 8 q^{73} - 72 q^{77} + 122 q^{78} - 32 q^{81} + 20 q^{82} - 44 q^{85} + 64 q^{92} + 40 q^{93} - 26 q^{94} + 16 q^{96} + 62 q^{98}+O(q^{100}) \) 32 * q + 4 * q^2 - 4 * q^4 - 16 * q^6 - 2 * q^8 - 52 * q^9 + 24 * q^12 - 4 * q^13 + 20 * q^16 - 56 * q^18 - 6 * q^24 - 32 * q^25 + 68 * q^26 + 8 * q^29 - 16 * q^32 + 8 * q^36 + 44 * q^41 - 4 * q^46 - 4 * q^48 - 12 * q^49 - 4 * q^50 + 16 * q^52 + 42 * q^54 - 10 * q^58 - 36 * q^62 - 22 * q^64 - 44 * q^69 - 42 * q^70 - 32 * q^72 - 8 * q^73 - 72 * q^77 + 122 * q^78 - 32 * q^81 + 20 * q^82 - 44 * q^85 + 64 * q^92 + 40 * q^93 - 26 * q^94 + 16 * q^96 + 62 * q^98

Introduction

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