LMFDB - Embedded newform 675.2.r.a.496.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(46,675)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("675.46"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([20, 18])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.r (of order $15$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 225)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			496.20
Character	$\chi$	$=$	675.496
Dual form			675.2.r.a.181.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.16617 - 0.247876i) q^{2} +(-0.528590 + 0.235343i) q^{4} +(-0.918757 + 2.03860i) q^{5} +(0.157578 + 0.272934i) q^{7} +(-2.48714 + 1.80701i) q^{8} +(-0.566103 + 2.60508i) q^{10} +(2.82788 - 0.601085i) q^{11} +(-6.38538 - 1.35725i) q^{13} +(0.251417 + 0.279226i) q^{14} +(-1.67816 + 1.86379i) q^{16} +(-0.794350 + 0.577129i) q^{17} +(-5.88399 + 4.27497i) q^{19} +(0.00587474 - 1.29381i) q^{20} +(3.14879 - 1.40193i) q^{22} +(0.876336 + 0.973270i) q^{23} +(-3.31177 - 3.74595i) q^{25} -7.78284 q^{26} +(-0.147528 - 0.107185i) q^{28} +(-0.450873 + 4.28977i) q^{29} +(0.905916 + 8.61921i) q^{31} +(1.57924 - 2.73533i) q^{32} +(-0.783287 + 0.869928i) q^{34} +(-0.701179 + 0.0704794i) q^{35} +(0.00738727 + 0.0227357i) q^{37} +(-5.80205 + 6.44383i) q^{38} +(-1.39870 - 6.73048i) q^{40} +(4.48136 + 0.952542i) q^{41} +(-1.34599 - 2.33132i) q^{43} +(-1.35333 + 0.983252i) q^{44} +(1.26320 + 0.917772i) q^{46} +(-0.544941 + 5.18477i) q^{47} +(3.45034 - 5.97616i) q^{49} +(-4.79061 - 3.54749i) q^{50} +(3.69467 - 0.785326i) q^{52} +(3.44104 + 2.50006i) q^{53} +(-1.37277 + 6.31717i) q^{55} +(-0.885114 - 0.394078i) q^{56} +(0.537539 + 5.11434i) q^{58} +(5.06713 + 1.07705i) q^{59} +(7.24968 - 1.54097i) q^{61} +(3.19295 + 9.82688i) q^{62} +(2.71365 - 8.35176i) q^{64} +(8.63350 - 11.7702i) q^{65} +(0.260529 + 2.47877i) q^{67} +(0.284062 - 0.492010i) q^{68} +(-0.800221 + 0.255996i) q^{70} +(-9.63629 - 7.00118i) q^{71} +(-0.283594 + 0.872814i) q^{73} +(0.0142504 + 0.0246825i) q^{74} +(2.10413 - 3.64447i) q^{76} +(0.609670 + 0.677108i) q^{77} +(1.18974 - 11.3196i) q^{79} +(-2.25770 - 5.13348i) q^{80} +5.46212 q^{82} +(9.08283 + 4.04394i) q^{83} +(-0.446720 - 2.14960i) q^{85} +(-2.14753 - 2.38507i) q^{86} +(-5.94717 + 6.60500i) q^{88} +(-3.78718 + 11.6557i) q^{89} +(-0.635757 - 1.95666i) q^{91} +(-0.692276 - 0.308221i) q^{92} +(0.649689 + 6.18138i) q^{94} +(-3.30899 - 15.9228i) q^{95} +(0.772754 - 7.35226i) q^{97} +(2.54232 - 7.82445i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28}+ \cdots - 146 q^{98}+O(q^{100}) $ 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.16617	−	0.247876i	0.824604	−	0.175275i	0.223763	−	0.974644i	$-0.428166\pi$
$2$	1.16617	−	0.247876i	0.824604	−	0.175275i	0.600841	+	0.799369i	$0.294832\pi$
$3$		0			0
$3$		0			0
$4$	−0.528590	+	0.235343i	−0.264295	+	0.117672i
$5$	−0.918757	+	2.03860i	−0.410881	+	0.911689i
$5$	−0.918757	+	2.03860i	−0.410881	+	0.911689i
$6$		0			0
$7$	0.157578	+	0.272934i	0.0595591	+	0.103159i	0.894268	−	0.447533i	$-0.147697\pi$
$7$	0.157578	+	0.272934i	0.0595591	+	0.103159i	−0.834708	+	0.550692i	$0.814364\pi$
$8$	−2.48714	+	1.80701i	−0.879336	+	0.638875i
$9$		0			0
$10$	−0.566103	+	2.60508i	−0.179017	+	0.823800i
$11$	2.82788	−	0.601085i	0.852639	−	0.181234i	0.239195	−	0.970972i	$-0.423117\pi$
$11$	2.82788	−	0.601085i	0.852639	−	0.181234i	0.613445	+	0.789738i	$0.289783\pi$
$12$		0			0
$13$	−6.38538	−	1.35725i	−1.77098	−	0.376434i	−0.797166	−	0.603761i	$-0.793668\pi$
$13$	−6.38538	−	1.35725i	−1.77098	−	0.376434i	−0.973819	+	0.227326i	$0.927002\pi$
$14$	0.251417	+	0.279226i	0.0671939	+	0.0746264i
$15$		0			0
$16$	−1.67816	+	1.86379i	−0.419541	+	0.465948i
$17$	−0.794350	+	0.577129i	−0.192658	+	0.139974i	−0.679933	−	0.733274i	$-0.737991\pi$
$17$	−0.794350	+	0.577129i	−0.192658	+	0.139974i	0.487275	+	0.873249i	$0.337991\pi$
$18$		0			0
$19$	−5.88399	+	4.27497i	−1.34988	+	0.980746i	−0.350863	+	0.936427i	$0.614112\pi$
$19$	−5.88399	+	4.27497i	−1.34988	+	0.980746i	−0.999017	+	0.0443190i	$0.985888\pi$
$20$	0.00587474	−	1.29381i	0.00131363	−	0.289304i
$21$		0			0
$22$	3.14879	−	1.40193i	0.671324	−	0.298893i
$23$	0.876336	+	0.973270i	0.182729	+	0.202941i	0.827549	−	0.561393i	$-0.189734\pi$
$23$	0.876336	+	0.973270i	0.182729	+	0.202941i	−0.644820	+	0.764334i	$0.723068\pi$
$24$		0			0
$25$	−3.31177	−	3.74595i	−0.662354	−	0.749191i
$26$	−7.78284			−1.52634
$27$		0			0
$28$	−0.147528	−	0.107185i	−0.0278801	−	0.0202561i
$29$	−0.450873	+	4.28977i	−0.0837249	+	0.796589i	0.869420	+	0.494074i	$0.164493\pi$
$29$	−0.450873	+	4.28977i	−0.0837249	+	0.796589i	−0.953145	+	0.302515i	$0.902174\pi$
$30$		0			0
$31$	0.905916	+	8.61921i	0.162707	+	1.54806i	0.705817	+	0.708394i	$0.250580\pi$
$31$	0.905916	+	8.61921i	0.162707	+	1.54806i	−0.543110	+	0.839662i	$0.682753\pi$
$32$	1.57924	−	2.73533i	0.279173	−	0.483542i
$33$		0			0
$34$	−0.783287	+	0.869928i	−0.134333	+	0.149191i
$35$	−0.701179	+	0.0704794i	−0.118521	+	0.0119132i
$36$		0			0
$37$	0.00738727	+	0.0227357i	0.00121446	+	0.00373772i	0.951662	−	0.307148i	$-0.0993745\pi$
$37$	0.00738727	+	0.0227357i	0.00121446	+	0.00373772i	−0.950447	+	0.310885i	$0.899375\pi$
$38$	−5.80205	+	6.44383i	−0.941217	+	1.04533i
$39$		0			0
$40$	−1.39870	−	6.73048i	−0.221153	−	1.06418i
$41$	4.48136	+	0.952542i	0.699871	+	0.148762i	0.544087	−	0.839029i	$-0.316876\pi$
$41$	4.48136	+	0.952542i	0.699871	+	0.148762i	0.155784	+	0.987791i	$0.450210\pi$
$42$		0			0
$43$	−1.34599	−	2.33132i	−0.205261	−	0.355523i	0.744955	−	0.667115i	$-0.232471\pi$
$43$	−1.34599	−	2.33132i	−0.205261	−	0.355523i	−0.950216	+	0.311592i	$0.899138\pi$
$44$	−1.35333	+	0.983252i	−0.204022	+	0.148231i
$45$		0			0
$46$	1.26320	+	0.917772i	0.186249	+	0.135318i
$47$	−0.544941	+	5.18477i	−0.0794878	+	0.756276i	0.880085	+	0.474816i	$0.157485\pi$
$47$	−0.544941	+	5.18477i	−0.0794878	+	0.756276i	−0.959573	+	0.281460i	$0.909181\pi$
$48$		0			0
$49$	3.45034	−	5.97616i	0.492905	−	0.853737i
$50$	−4.79061	−	3.54749i	−0.677494	−	0.501691i
$51$		0			0
$52$	3.69467	−	0.785326i	0.512358	−	0.108905i
$53$	3.44104	+	2.50006i	0.472663	+	0.343410i	0.798478	−	0.602024i	$-0.205639\pi$
$53$	3.44104	+	2.50006i	0.472663	+	0.343410i	−0.325815	+	0.945433i	$0.605639\pi$
$54$		0			0
$55$	−1.37277	+	6.31717i	−0.185104	+	0.851808i
$56$	−0.885114	−	0.394078i	−0.118278	−	0.0526609i
$57$		0			0
$58$	0.537539	+	5.11434i	0.0705823	+	0.671546i
$59$	5.06713	+	1.07705i	0.659684	+	0.140220i	0.525576	−	0.850747i	$-0.323850\pi$
$59$	5.06713	+	1.07705i	0.659684	+	0.140220i	0.134108	+	0.990967i	$0.457183\pi$
$60$		0			0
$61$	7.24968	−	1.54097i	0.928226	−	0.197301i	0.281096	−	0.959680i	$-0.409302\pi$
$61$	7.24968	−	1.54097i	0.928226	−	0.197301i	0.647131	+	0.762379i	$0.275969\pi$
$62$	3.19295	+	9.82688i	0.405505	+	1.24801i
$63$		0			0
$64$	2.71365	−	8.35176i	0.339207	−	1.04397i
$65$	8.63350	−	11.7702i	1.07085	−	1.45992i
$66$		0			0
$67$	0.260529	+	2.47877i	0.0318287	+	0.302830i	0.998842	+	0.0481052i	$0.0153183\pi$
$67$	0.260529	+	2.47877i	0.0318287	+	0.302830i	−0.967014	+	0.254725i	$0.918015\pi$
$68$	0.284062	−	0.492010i	0.0344476	−	0.0596649i
$69$		0			0
$70$	−0.800221	+	0.255996i	−0.0956447	+	0.0305974i
$71$	−9.63629	−	7.00118i	−1.14362	−	0.830887i	−0.155999	−	0.987757i	$-0.549860\pi$
$71$	−9.63629	−	7.00118i	−1.14362	−	0.830887i	−0.987619	+	0.156870i	$0.949860\pi$
$72$		0			0
$73$	−0.283594	+	0.872814i	−0.0331922	+	0.102155i	−0.966280	−	0.257493i	$-0.917103\pi$
$73$	−0.283594	+	0.872814i	−0.0331922	+	0.102155i	0.933088	+	0.359649i	$0.117103\pi$
$74$	0.0142504	+	0.0246825i	0.00165658	+	0.00286928i
$75$		0			0
$76$	2.10413	−	3.64447i	0.241361	−	0.418049i
$77$	0.609670	+	0.677108i	0.0694784	+	0.0771636i
$78$		0			0
$79$	1.18974	−	11.3196i	0.133857	−	1.27356i	−0.696999	−	0.717072i	$-0.745482\pi$
$79$	1.18974	−	11.3196i	0.133857	−	1.27356i	0.830856	−	0.556488i	$-0.187851\pi$
$80$	−2.25770	−	5.13348i	−0.252418	−	0.573940i
$81$		0			0
$82$	5.46212			0.603191
$83$	9.08283	+	4.04394i	0.996970	+	0.443880i	0.839333	−	0.543617i	$-0.182946\pi$
$83$	9.08283	+	4.04394i	0.996970	+	0.443880i	0.157637	+	0.987497i	$0.449612\pi$
$84$		0			0
$85$	−0.446720	−	2.14960i	−0.0484536	−	0.233157i
$86$	−2.14753	−	2.38507i	−0.231574	−	0.257189i
$87$		0			0
$88$	−5.94717	+	6.60500i	−0.633971	+	0.704096i
$89$	−3.78718	+	11.6557i	−0.401440	+	1.23551i	0.522391	+	0.852706i	$0.325040\pi$
$89$	−3.78718	+	11.6557i	−0.401440	+	1.23551i	−0.923831	+	0.382800i	$0.874960\pi$
$90$		0			0
$91$	−0.635757	−	1.95666i	−0.0666455	−	0.205114i
$92$	−0.692276	−	0.308221i	−0.0721747	−	0.0321343i
$93$		0			0
$94$	0.649689	+	6.18138i	0.0670103	+	0.637561i
$95$	−3.30899	−	15.9228i	−0.339496	−	1.63364i
$96$		0			0
$97$	0.772754	−	7.35226i	0.0784612	−	0.746509i	−0.882591	−	0.470142i	$-0.844203\pi$
$97$	0.772754	−	7.35226i	0.0784612	−	0.746509i	0.961052	−	0.276367i	$-0.0891306\pi$
$98$	2.54232	−	7.82445i	0.256813	−	0.790389i
$99$		0			0
$100$	2.63216	+	1.20067i	0.263216	+	0.120067i
$101$	5.77262	+	9.99848i	0.574397	+	0.994885i	0.996107	+	0.0881544i	$0.0280969\pi$
$101$	5.77262	+	9.99848i	0.574397	+	0.994885i	−0.421709	+	0.906731i	$0.638570\pi$
$102$		0			0
$103$	−14.9529	+	6.65745i	−1.47335	+	0.655978i	−0.977212	−	0.212265i	$-0.931916\pi$
$103$	−14.9529	+	6.65745i	−1.47335	+	0.655978i	−0.496139	+	0.868243i	$0.665249\pi$
$104$	18.3339	−	8.16277i	1.79779	−	0.800426i
$105$		0			0
$106$	4.63253	+	2.06253i	0.449951	+	0.200331i
$107$	10.1611			0.982314			0.491157	−	0.871071i	$-0.336574\pi$
$107$	10.1611			0.982314			0.491157	+	0.871071i	$0.336574\pi$
$108$		0			0
$109$	3.42411	+	10.5383i	0.327970	+	1.00939i	0.970082	+	0.242777i	$0.0780584\pi$
$109$	3.42411	+	10.5383i	0.327970	+	1.00939i	−0.642112	+	0.766611i	$0.721942\pi$
$110$	−0.0349956	+	7.70715i	−0.00333670	+	0.734848i
$111$		0			0
$112$	−0.773134	−	0.164335i	−0.0730543	−	0.0155282i
$113$	−14.3476	−	3.04967i	−1.34970	−	0.286888i	−0.524349	−	0.851503i	$-0.675691\pi$
$113$	−14.3476	−	3.04967i	−1.34970	−	0.286888i	−0.825355	+	0.564615i	$0.809025\pi$
$114$		0			0
$115$	−2.78925	+	0.892300i	−0.260099	+	0.0832074i
$116$	−0.771242	−	2.37364i	−0.0716080	−	0.220387i
$117$		0			0
$118$	6.17609			0.568555
$119$	−0.282690	−	0.125862i	−0.0259142	−	0.0115377i
$120$		0			0
$121$	−2.41337	+	1.07450i	−0.219397	+	0.0976820i
$122$	8.07236	−	3.59405i	0.730837	−	0.325390i
$123$		0			0
$124$	−2.50733	−	4.34283i	−0.225165	−	0.389998i
$125$	10.6792	−	3.30976i	0.955178	−	0.296034i
$126$		0			0
$127$	4.75644	−	14.6388i	0.422066	−	1.29899i	−0.483710	−	0.875228i	$-0.660711\pi$
$127$	4.75644	−	14.6388i	0.422066	−	1.29899i	0.905776	−	0.423757i	$-0.139289\pi$
$128$	0.434062	−	4.12983i	0.0383660	−	0.365029i
$129$		0			0
$130$	7.15054	−	15.8661i	0.627144	−	1.39155i
$131$	0.348937	+	3.31991i	0.0304868	+	0.290062i	0.999134	+	0.0416200i	$0.0132519\pi$
$131$	0.348937	+	3.31991i	0.0304868	+	0.290062i	−0.968647	+	0.248442i	$0.920081\pi$
$132$		0			0
$133$	−2.09398	−	0.932298i	−0.181571	−	0.0808405i
$134$	0.918249	+	2.82608i	0.0793247	+	0.244136i
$135$		0			0
$136$	0.932779	−	2.87080i	0.0799851	−	0.246169i
$137$	5.65113	−	6.27621i	0.482808	−	0.536213i	−0.451693	−	0.892174i	$-0.649180\pi$
$137$	5.65113	−	6.27621i	0.482808	−	0.536213i	0.934501	+	0.355961i	$0.115846\pi$
$138$		0			0
$139$	−0.957106	−	1.06297i	−0.0811807	−	0.0901603i	0.701186	−	0.712978i	$-0.252654\pi$
$139$	−0.957106	−	1.06297i	−0.0811807	−	0.0901603i	−0.782367	+	0.622818i	$0.785988\pi$
$140$	0.354049	−	0.202273i	0.0299226	−	0.0170952i
$141$		0			0
$142$	−12.9729	−	5.77593i	−1.08867	−	0.484705i
$143$	−18.8729			−1.57823
$144$		0			0
$145$	−8.33087	−	4.86040i	−0.691841	−	0.403634i
$146$	−0.114368	+	1.08814i	−0.00946519	+	0.0900553i
$147$		0			0
$148$	−0.00925554	−	0.0102793i	−0.000760800	−	0.000844954i
$149$	−10.3534	+	17.9326i	−0.848181	+	1.46909i	0.0346486	+	0.999400i	$0.488969\pi$
$149$	−10.3534	+	17.9326i	−0.848181	+	1.46909i	−0.882830	+	0.469693i	$0.844365\pi$
$150$		0			0
$151$	10.6562	+	18.4570i	0.867186	+	1.50201i	0.864860	+	0.502014i	$0.167407\pi$
$151$	10.6562	+	18.4570i	0.867186	+	1.50201i	0.00232675	+	0.999997i	$0.499259\pi$
$152$	6.90938	−	21.2649i	0.560425	−	1.72481i
$153$		0			0
$154$	0.878816	+	0.638497i	0.0708170	+	0.0514516i
$155$	−18.4034	−	6.07216i	−1.47820	−	0.487728i
$156$		0			0
$157$	−6.98186	+	12.0929i	−0.557213	+	0.965122i	0.440514	+	0.897746i	$0.354796\pi$
$157$	−6.98186	+	12.0929i	−0.557213	+	0.965122i	−0.997728	+	0.0673760i	$0.978537\pi$
$158$	−1.41843	−	13.4955i	−0.112845	−	1.07364i
$159$		0			0
$160$	4.12530	+	5.73254i	0.326133	+	0.453197i
$161$	−0.127547	+	0.392548i	−0.0100521	+	0.0309371i
$162$		0			0
$163$	−0.190245	−	0.585515i	−0.0149012	−	0.0458611i	0.943329	−	0.331858i	$-0.107675\pi$
$163$	−0.190245	−	0.585515i	−0.0149012	−	0.0458611i	−0.958231	+	0.285997i	$0.907675\pi$
$164$	−2.59298	+	0.551154i	−0.202477	+	0.0430379i
$165$		0			0
$166$	11.5945	+	2.46448i	0.899907	+	0.191281i
$167$	−0.564465	−	5.37053i	−0.0436796	−	0.415584i	−0.994412	−	0.105571i	$-0.966333\pi$
$167$	−0.564465	−	5.37053i	−0.0436796	−	0.415584i	0.950732	−	0.310013i	$-0.100334\pi$
$168$		0			0
$169$	27.0548	+	12.0456i	2.08114	+	0.926582i
$170$	−1.05378	−	2.39606i	−0.0808216	−	0.183769i
$171$		0			0
$172$	1.26014	+	0.915544i	0.0960846	+	0.0698096i
$173$	−0.355757	+	0.0756186i	−0.0270477	+	0.00574917i	−0.221416	−	0.975180i	$-0.571068\pi$
$173$	−0.355757	+	0.0756186i	−0.0270477	+	0.00574917i	0.194368	+	0.980929i	$0.437734\pi$
$174$		0			0
$175$	0.500534	−	1.49418i	0.0378368	−	0.112949i
$176$	−3.62536	+	6.27931i	−0.273272	+	0.473321i
$177$		0			0
$178$	−1.52730	+	14.5313i	−0.114476	+	1.08917i
$179$	−12.2855	−	8.92591i	−0.918259	−	0.667154i	0.0248313	−	0.999692i	$-0.492095\pi$
$179$	−12.2855	−	8.92591i	−0.918259	−	0.667154i	−0.943090	+	0.332538i	$0.892095\pi$
$180$		0			0
$181$	0.0462635	−	0.0336124i	0.00343874	−	0.00249839i	−0.586065	−	0.810264i	$-0.699324\pi$
$181$	0.0462635	−	0.0336124i	0.00343874	−	0.00249839i	0.589503	+	0.807766i	$0.299324\pi$
$182$	−1.22641	−	2.12420i	−0.0909074	−	0.157456i
$183$		0			0
$184$	−3.93828	−	0.837107i	−0.290334	−	0.0617124i
$185$	−0.0531361	−	0.00582888i	−0.00390664	−	0.000428548i
$186$		0			0
$187$	−1.89943	+	2.10953i	−0.138900	+	0.154264i
$188$	−0.932151	−	2.86887i	−0.0679841	−	0.209234i
$189$		0			0
$190$	−7.80571	−	17.7484i	−0.566286	−	1.28760i
$191$	−1.60360	+	1.78098i	−0.116033	+	0.128867i	−0.798363	−	0.602177i	$-0.794300\pi$
$191$	−1.60360	+	1.78098i	−0.116033	+	0.128867i	0.682330	+	0.731044i	$0.260967\pi$
$192$		0			0
$193$	2.94773	−	5.10562i	0.212182	−	0.367511i	−0.740215	−	0.672370i	$-0.765276\pi$
$193$	2.94773	−	5.10562i	0.212182	−	0.367511i	0.952397	+	0.304860i	$0.0986095\pi$
$194$	−0.921292	−	8.76550i	−0.0661449	−	0.629326i
$195$		0			0
$196$	−0.417364	+	3.97095i	−0.0298117	+	0.283640i
$197$	12.8434	+	9.33130i	0.915057	+	0.664828i	0.942289	−	0.334801i	$-0.108669\pi$
$197$	12.8434	+	9.33130i	0.915057	+	0.664828i	−0.0272318	+	0.999629i	$0.508669\pi$
$198$		0			0
$199$	4.61006			0.326798			0.163399	−	0.986560i	$-0.447754\pi$
$199$	4.61006			0.326798			0.163399	+	0.986560i	$0.447754\pi$
$200$	15.0058	+	3.33229i	1.06107	+	0.235629i
$201$		0			0
$202$	9.21022	+	10.2290i	0.648029	+	0.719709i
$203$	−1.24187	+	0.552916i	−0.0871622	+	0.0388071i
$204$		0			0
$205$	−6.05913	+	8.26054i	−0.423188	+	0.576941i
$206$	−15.7873	+	11.4702i	−1.09995	+	0.799164i
$207$		0			0
$208$	13.2453	−	9.62331i	0.918400	−	0.667256i
$209$	−14.0696	+	15.6259i	−0.973217	+	1.08087i
$210$		0			0
$211$	0.0990841	+	0.110044i	0.00682123	+	0.00757575i	0.746546	−	0.665334i	$-0.231711\pi$
$211$	0.0990841	+	0.110044i	0.00682123	+	0.00757575i	−0.739725	+	0.672910i	$0.765044\pi$
$212$	−2.40727	−	0.511681i	−0.165332	−	0.0351424i
$213$		0			0
$214$	11.8496	−	2.51870i	0.810020	−	0.172175i
$215$	5.98927	−	0.602015i	0.408465	−	0.0410571i
$216$		0			0
$217$	−2.20972	+	1.60546i	−0.150006	+	0.108986i
$218$	6.60528	+	11.4407i	0.447366	+	0.774861i
$219$		0			0
$220$	−0.761075	−	3.66227i	−0.0513117	−	0.246910i
$221$	5.85553	−	2.60705i	0.393886	−	0.175369i
$222$		0			0
$223$	1.61074	−	0.342372i	0.107863	−	0.0229270i	−0.153664	−	0.988123i	$-0.549107\pi$
$223$	1.61074	−	0.342372i	0.107863	−	0.0229270i	0.261527	+	0.965196i	$0.415774\pi$
$224$	0.995419			0.0665092
$225$		0			0
$226$	−17.4876			−1.16326
$227$	−3.58225	+	0.761432i	−0.237763	+	0.0505380i	−0.325252	−	0.945627i	$-0.605449\pi$
$227$	−3.58225	+	0.761432i	−0.237763	+	0.0505380i	0.0874891	+	0.996165i	$0.472116\pi$
$228$		0			0
$229$	−0.773433	+	0.344355i	−0.0511099	+	0.0227556i	−0.432132	−	0.901810i	$-0.642239\pi$
$229$	−0.773433	+	0.344355i	−0.0511099	+	0.0227556i	0.381023	+	0.924566i	$0.375572\pi$
$230$	−3.03155	+	1.73196i	−0.199894	+	0.114202i
$231$		0			0
$232$	−6.63027	−	11.4840i	−0.435299	−	0.753960i
$233$	−9.04329	+	6.57033i	−0.592445	+	0.430437i	−0.843189	−	0.537617i	$-0.819325\pi$
$233$	−9.04329	+	6.57033i	−0.592445	+	0.430437i	0.250744	+	0.968053i	$0.419325\pi$
$234$		0			0
$235$	−10.0690	−	5.87446i	−0.656829	−	0.383207i
$236$	−2.93191	+	0.623197i	−0.190851	+	0.0405667i
$237$		0			0
$238$	−0.360862	−	0.0767036i	−0.0233912	−	0.00497196i
$239$	10.9299	+	12.1389i	0.706996	+	0.785199i	0.984473	−	0.175533i	$-0.0561650\pi$
$239$	10.9299	+	12.1389i	0.706996	+	0.785199i	−0.277477	+	0.960732i	$0.589498\pi$
$240$		0			0
$241$	1.40222	−	1.55732i	0.0903247	−	0.100316i	−0.696288	−	0.717763i	$-0.745166\pi$
$241$	1.40222	−	1.55732i	0.0903247	−	0.100316i	0.786613	+	0.617447i	$0.211833\pi$
$242$	−2.54805	+	1.85127i	−0.163795	+	0.119004i
$243$		0			0
$244$	−3.46945	+	2.52070i	−0.222109	+	0.161372i
$245$	9.01297	+	12.5245i	0.575818	+	0.800161i
$246$		0			0
$247$	43.3737	−	19.3112i	2.75980	−	1.22874i
$248$	−17.8282	−	19.8002i	−1.13209	−	1.25731i
$249$		0			0
$250$	11.6333	−	6.50685i	0.735756	−	0.411529i
$251$	15.8673			1.00154			0.500769	−	0.865581i	$-0.333051\pi$
$251$	15.8673			1.00154			0.500769	+	0.865581i	$0.333051\pi$
$252$		0			0
$253$	3.06320	+	2.22554i	0.192582	+	0.139919i
$254$	1.91818	−	18.2503i	0.120358	−	1.14513i
$255$		0			0
$256$	1.31835	+	12.5433i	0.0823968	+	0.783953i
$257$	1.09760	−	1.90109i	0.0684661	−	0.118587i	−0.829760	−	0.558120i	$-0.811523\pi$
$257$	1.09760	−	1.90109i	0.0684661	−	0.118587i	0.898226	+	0.439533i	$0.144856\pi$
$258$		0			0
$259$	−0.00504127	+	0.00559889i	−0.000313249	+	0.000347898i
$260$	−1.79354	+	8.25347i	−0.111230	+	0.511858i
$261$		0			0
$262$	1.22985	+	3.78508i	0.0759801	+	0.233843i
$263$	19.8482	−	22.0437i	1.22389	−	1.35927i	0.311346	−	0.950297i	$-0.399220\pi$
$263$	19.8482	−	22.0437i	1.22389	−	1.35927i	0.912546	−	0.408973i	$-0.134113\pi$
$264$		0			0
$265$	−8.25810	+	4.71795i	−0.507291	+	0.289821i
$266$	−2.67302	−	0.568167i	−0.163893	−	0.0348366i
$267$		0			0
$268$	−0.721076	−	1.24894i	−0.0440467	−	0.0762912i
$269$	20.4742	−	14.8754i	1.24833	−	0.906968i	0.250210	−	0.968192i	$-0.419500\pi$
$269$	20.4742	−	14.8754i	1.24833	−	0.906968i	0.998124	+	0.0612238i	$0.0195003\pi$
$270$		0			0
$271$	−15.2201	−	11.0580i	−0.924555	−	0.671728i	0.0200987	−	0.999798i	$-0.493602\pi$
$271$	−15.2201	−	11.0580i	−0.924555	−	0.671728i	−0.944654	+	0.328070i	$0.893602\pi$
$272$	0.257402	−	2.44902i	0.0156073	−	0.148494i
$273$		0			0
$274$	5.03443	−	8.71989i	0.304141	−	0.526788i
$275$	−11.6169	−	8.60247i	−0.700528	−	0.518748i
$276$		0			0
$277$	−22.1401	+	4.70603i	−1.33027	+	0.282758i	−0.817580	−	0.575814i	$-0.804685\pi$
$277$	−22.1401	+	4.70603i	−1.33027	+	0.282758i	−0.512692	+	0.858573i	$0.671352\pi$
$278$	−1.37963	−	1.00236i	−0.0827447	−	0.0601176i
$279$		0			0
$280$	1.61657	−	1.44233i	0.0966087	−	0.0861958i
$281$	0.856636	+	0.381399i	0.0511026	+	0.0227523i	0.432129	−	0.901812i	$-0.357763\pi$
$281$	0.856636	+	0.381399i	0.0511026	+	0.0227523i	−0.381026	+	0.924564i	$0.624429\pi$
$282$		0			0
$283$	−1.21199	−	11.5313i	−0.0720454	−	0.685466i	−0.969622	−	0.244608i	$-0.921341\pi$
$283$	−1.21199	−	11.5313i	−0.0720454	−	0.685466i	0.897577	−	0.440858i	$-0.145326\pi$
$284$	6.74133	+	1.43291i	0.400024	+	0.0850278i
$285$		0			0
$286$	−22.0090	+	4.67815i	−1.30142	+	0.276625i
$287$	0.446185	+	1.37322i	0.0263375	+	0.0810583i
$288$		0			0
$289$	−4.95538	+	15.2511i	−0.291493	+	0.897122i
$290$	−10.9200	−	3.60301i	−0.641242	−	0.211576i
$291$		0			0
$292$	−0.0555058	−	0.528103i	−0.00324823	−	0.0309049i
$293$	−11.8547	+	20.5330i	−0.692561	+	1.19955i	0.278435	+	0.960455i	$0.410184\pi$
$293$	−11.8547	+	20.5330i	−0.692561	+	1.19955i	−0.970996	+	0.239096i	$0.923149\pi$
$294$		0			0
$295$	−6.85114	+	9.34030i	−0.398889	+	0.543813i
$296$	−0.0594568	−	0.0431979i	−0.00345586	−	0.00251083i
$297$		0			0
$298$	−7.62869	+	23.4787i	−0.441918	+	1.36008i
$299$	−4.27476	−	7.40411i	−0.247216	−	0.428190i
$300$		0			0
$301$	0.424198	−	0.734732i	0.0244504	−	0.0423493i
$302$	17.0019	+	18.8825i	0.978350	+	1.08657i
$303$		0			0
$304$	1.90666	−	18.1406i	0.109354	−	1.04044i
$305$	−3.51928	+	16.1950i	−0.201513	+	0.927321i
$306$		0			0
$307$	−12.6269			−0.720652			−0.360326	−	0.932826i	$-0.617335\pi$
$307$	−12.6269			−0.720652			−0.360326	+	0.932826i	$0.617335\pi$
$308$	−0.481619	−	0.214430i	−0.0274428	−	0.0122183i
$309$		0			0
$310$	−22.9666	−	2.51937i	−1.30442	−	0.143091i
$311$	9.47726	+	10.5256i	0.537406	+	0.596850i	0.949296	−	0.314384i	$-0.101798\pi$
$311$	9.47726	+	10.5256i	0.537406	+	0.596850i	−0.411890	+	0.911234i	$0.635131\pi$
$312$		0			0
$313$	1.87423	−	2.08155i	0.105938	−	0.117656i	−0.687844	−	0.725859i	$-0.741443\pi$
$313$	1.87423	−	2.08155i	0.105938	−	0.117656i	0.793782	+	0.608203i	$0.208109\pi$
$314$	−5.14446	+	15.8330i	−0.290319	+	0.893509i
$315$		0			0
$316$	2.03512	+	6.26345i	0.114484	+	0.352347i
$317$	−27.2462	−	12.1308i	−1.53030	−	0.681332i	−0.542929	−	0.839778i	$-0.682685\pi$
$317$	−27.2462	−	12.1308i	−1.53030	−	0.681332i	−0.987368	+	0.158446i	$0.949351\pi$
$318$		0			0
$319$	1.30350	+	12.4020i	0.0729820	+	0.694377i
$320$	14.5327	+	13.2053i	0.812403	+	0.738198i
$321$		0			0
$322$	−0.0514372	+	0.489392i	−0.00286648	+	0.0272728i
$323$	2.20674	−	6.79164i	0.122786	−	0.377897i
$324$		0			0
$325$	16.0627	+	28.4142i	0.890998	+	1.57614i
$326$	−0.366993	−	0.635650i	−0.0203259	−	0.0352054i
$327$		0			0
$328$	−12.8670	+	5.72877i	−0.710462	+	0.316318i
$329$	−1.50097	+	0.668275i	−0.0827512	+	0.0368432i
$330$		0			0
$331$	−18.6133	−	8.28716i	−1.02308	−	0.455504i	−0.174547	−	0.984649i	$-0.555846\pi$
$331$	−18.6133	−	8.28716i	−1.02308	−	0.455504i	−0.848531	+	0.529145i	$0.822513\pi$
$332$	−5.75281			−0.315726
$333$		0			0
$334$	−1.98949	−	6.12301i	−0.108860	−	0.335036i
$335$	−5.29259	−	1.74627i	−0.289165	−	0.0954091i
$336$		0			0
$337$	−25.9922	−	5.52480i	−1.41588	−	0.300955i	−0.564471	−	0.825453i	$-0.690920\pi$
$337$	−25.9922	−	5.52480i	−1.41588	−	0.300955i	−0.851412	+	0.524498i	$0.824253\pi$
$338$	34.5362	+	7.34089i	1.87852	+	0.399292i
$339$		0			0
$340$	0.742026	+	1.03113i	0.0402420	+	0.0559206i
$341$	7.74271	+	23.8296i	0.419291	+	1.29045i
$342$		0			0
$343$	4.38089			0.236546
$344$	7.56039	+	3.36610i	0.407629	+	0.181488i
$345$		0			0
$346$	−0.396128	+	0.176368i	−0.0212960	+	0.00948158i
$347$	−18.7081	+	8.32938i	−1.00430	+	0.447144i	−0.841931	−	0.539585i	$-0.818581\pi$
$347$	−18.7081	+	8.32938i	−1.00430	+	0.447144i	−0.162372	+	0.986730i	$0.551914\pi$
$348$		0			0
$349$	2.88806	+	5.00227i	0.154594	+	0.267766i	0.932911	−	0.360106i	$-0.117260\pi$
$349$	2.88806	+	5.00227i	0.154594	+	0.267766i	−0.778317	+	0.627872i	$0.783926\pi$
$350$	0.213335	−	1.86653i	0.0114032	−	0.0997701i
$351$		0			0
$352$	2.82175	−	8.68445i	0.150400	−	0.462883i
$353$	1.44559	−	13.7539i	0.0769411	−	0.732045i	−0.886246	−	0.463214i	$-0.846696\pi$
$353$	1.44559	−	13.7539i	0.0769411	−	0.732045i	0.963187	−	0.268831i	$-0.0866373\pi$
$354$		0			0
$355$	23.1260	−	13.2122i	1.22740	−	0.701229i
$356$	−0.741236	−	7.05239i	−0.0392854	−	0.373776i
$357$		0			0
$358$	−16.5394	−	7.36382i	−0.874135	−	0.389190i
$359$	−0.158269	−	0.487102i	−0.00835313	−	0.0257083i	0.946793	−	0.321843i	$-0.104302\pi$
$359$	−0.158269	−	0.487102i	−0.00835313	−	0.0257083i	−0.955146	+	0.296135i	$0.904302\pi$
$360$		0			0
$361$	10.4747	−	32.2377i	0.551299	−	1.69672i
$362$	0.0456192	−	0.0506652i	0.00239769	−	0.00266291i
$363$		0			0
$364$	0.796542	+	0.884650i	0.0417501	+	0.0463682i
$365$	−1.51876	−	1.38004i	−0.0794957	−	0.0722345i
$366$		0			0
$367$	−17.8610	−	7.95224i	−0.932337	−	0.415103i	−0.116373	−	0.993206i	$-0.537127\pi$
$367$	−17.8610	−	7.95224i	−0.932337	−	0.415103i	−0.815964	+	0.578102i	$0.803793\pi$
$368$	−3.28461			−0.171222
$369$		0			0
$370$	−0.0634103	+	0.00637373i	−0.00329655	+	0.000331354i
$371$	−0.140118	+	1.33313i	−0.00727455	+	0.0692127i
$372$		0			0
$373$	16.5937	+	18.4292i	0.859191	+	0.954228i	0.999355	−	0.0359001i	$-0.0114298\pi$
$373$	16.5937	+	18.4292i	0.859191	+	0.954228i	−0.140165	+	0.990128i	$0.544763\pi$
$374$	−1.69214	+	2.93088i	−0.0874987	+	0.151552i
$375$		0			0
$376$	−8.01359	−	13.8800i	−0.413270	−	0.715804i
$377$	8.70129	−	26.7798i	0.448139	−	1.37923i
$378$		0			0
$379$	15.1691	+	11.0210i	0.779184	+	0.566110i	0.904734	−	0.425977i	$-0.140070\pi$
$379$	15.1691	+	11.0210i	0.779184	+	0.566110i	−0.125550	+	0.992087i	$0.540070\pi$
$380$	5.49642	+	7.63786i	0.281960	+	0.391814i
$381$		0			0
$382$	−1.42861	+	2.47442i	−0.0730938	+	0.126602i
$383$	0.573056	+	5.45227i	0.0292818	+	0.278598i	0.999359	+	0.0358009i	$0.0113982\pi$
$383$	0.573056	+	5.45227i	0.0292818	+	0.278598i	−0.970077	+	0.242797i	$0.921935\pi$
$384$		0			0
$385$	−1.94049	+	0.620776i	−0.0988965	+	0.0316377i
$386$	2.17198	−	6.68468i	0.110551	−	0.340241i
$387$		0			0
$388$	1.32184	+	4.06819i	0.0671061	+	0.206531i
$389$	−1.53381	+	0.326022i	−0.0777673	+	0.0165300i	−0.246631	−	0.969109i	$-0.579324\pi$
$389$	−1.53381	+	0.326022i	−0.0777673	+	0.0165300i	0.168864	+	0.985639i	$0.445990\pi$
$390$		0			0
$391$	−1.25782	−	0.267358i	−0.0636107	−	0.0135209i
$392$	2.21753	+	21.0983i	0.112002	+	1.06563i
$393$		0			0
$394$	17.2906	+	7.69827i	0.871087	+	0.387833i
$395$	21.9831	+	12.8254i	1.10609	+	0.645317i
$396$		0			0
$397$	7.83333	+	5.69125i	0.393143	+	0.285635i	0.766742	−	0.641955i	$-0.221876\pi$
$397$	7.83333	+	5.69125i	0.393143	+	0.285635i	−0.373599	+	0.927590i	$0.621876\pi$
$398$	5.37609	−	1.14272i	0.269479	−	0.0572796i
$399$		0			0
$400$	12.5394	+	0.113877i	0.626969	+	0.00569383i
$401$	0.505309	−	0.875221i	0.0252339	−	0.0437064i	−0.853133	−	0.521694i	$-0.825300\pi$
$401$	0.505309	−	0.875221i	0.0252339	−	0.0437064i	0.878367	+	0.477988i	$0.158634\pi$
$402$		0			0
$403$	5.91384	−	56.2665i	0.294590	−	2.80283i
$404$	−5.40443	−	3.92655i	−0.268880	−	0.195353i
$405$		0			0
$406$	−1.31117	+	0.952622i	−0.0650724	+	0.0472779i
$407$	0.0345565	+	0.0598535i	0.00171290	+	0.00296683i
$408$		0			0
$409$	−7.84185	−	1.66684i	−0.387754	−	0.0824197i	0.00990955	−	0.999951i	$-0.496846\pi$
$409$	−7.84185	−	1.66684i	−0.387754	−	0.0824197i	−0.397664	+	0.917531i	$0.630179\pi$
$410$	−5.01836	+	11.1351i	−0.247839	+	0.549922i
$411$		0			0
$412$	6.33716	−	7.03812i	0.312209	−	0.346744i
$413$	0.504507	+	1.55271i	0.0248251	+	0.0764040i
$414$		0			0
$415$	−16.5889	+	14.8009i	−0.814316	+	0.726546i
$416$	−13.7966	+	15.3227i	−0.676434	+	0.751256i
$417$		0			0
$418$	−12.5342	+	21.7099i	−0.613070	+	1.06187i
$419$	2.61646	+	24.8939i	0.127822	+	1.21615i	0.850880	+	0.525360i	$0.176069\pi$
$419$	2.61646	+	24.8939i	0.127822	+	1.21615i	−0.723058	+	0.690788i	$0.757264\pi$
$420$		0			0
$421$	−3.44840	+	32.8093i	−0.168065	+	1.59903i	0.507450	+	0.861681i	$0.330588\pi$
$421$	−3.44840	+	32.8093i	−0.168065	+	1.59903i	−0.675515	+	0.737346i	$0.736079\pi$
$422$	0.142826	+	0.103769i	0.00695265	+	0.00505140i
$423$		0			0
$424$	−13.0760			−0.635026
$425$	4.79260	+	1.06428i	0.232475	+	0.0516250i
$426$		0			0
$427$	1.56298	+	1.73586i	0.0756377	+	0.0840042i
$428$	−5.37108	+	2.39136i	−0.259621	+	0.115591i
$429$		0			0
$430$	6.83526	−	2.18665i	0.329625	−	0.105449i
$431$	−4.71468	+	3.42542i	−0.227098	+	0.164997i	−0.695516	−	0.718511i	$-0.744824\pi$
$431$	−4.71468	+	3.42542i	−0.227098	+	0.164997i	0.468418	+	0.883507i	$0.344824\pi$
$432$		0			0
$433$	−1.68629	+	1.22516i	−0.0810381	+	0.0588776i	−0.627567	−	0.778563i	$-0.715949\pi$
$433$	−1.68629	+	1.22516i	−0.0810381	+	0.0588776i	0.546529	+	0.837440i	$0.315949\pi$
$434$	−2.17895	+	2.41997i	−0.104593	+	0.116162i
$435$		0			0
$436$	−4.29007	−	4.76461i	−0.205457	−	0.228183i
$437$	−9.31706	−	1.98040i	−0.445695	−	0.0947355i
$438$		0			0
$439$	−22.2890	+	4.73767i	−1.06380	+	0.226117i	−0.706383	−	0.707830i	$-0.749674\pi$
$439$	−22.2890	+	4.73767i	−1.06380	+	0.226117i	−0.357413	+	0.933946i	$0.616341\pi$
$440$	−8.00095	−	18.1923i	−0.381430	−	0.867284i
$441$		0			0
$442$	6.18230	−	4.49170i	0.294062	−	0.213648i
$443$	−4.50211	−	7.79787i	−0.213901	−	0.370488i	0.739031	−	0.673672i	$-0.235284\pi$
$443$	−4.50211	−	7.79787i	−0.213901	−	0.370488i	−0.952932	+	0.303184i	$0.901950\pi$
$444$		0			0
$445$	−20.2819	−	18.4293i	−0.961453	−	0.873634i
$446$	1.79352	−	0.798526i	0.0849256	−	0.0378113i
$447$		0			0
$448$	2.70709	−	0.575410i	0.127898	−	0.0271856i
$449$	2.14345			0.101156			0.0505779	−	0.998720i	$-0.483894\pi$
$449$	2.14345			0.101156			0.0505779	+	0.998720i	$0.483894\pi$
$450$		0			0
$451$	13.2453			0.623698
$452$	8.30169	−	1.76458i	0.390479	−	0.0829988i
$453$		0			0
$454$	−3.98876	+	1.77591i	−0.187202	+	0.0833477i
$455$	4.57295	+	0.501640i	0.214383	+	0.0235173i
$456$		0			0
$457$	9.78295	+	16.9446i	0.457627	+	0.792634i	0.998835	−	0.0482552i	$-0.0153661\pi$
$457$	9.78295	+	16.9446i	0.457627	+	0.792634i	−0.541208	+	0.840889i	$0.682033\pi$
$458$	−0.816594	+	0.593290i	−0.0381569	+	0.0277226i
$459$		0			0
$460$	1.26437	−	1.12809i	0.0589516	−	0.0525976i
$461$	−3.73066	+	0.792976i	−0.173754	+	0.0369326i	−0.293967	−	0.955816i	$-0.594976\pi$
$461$	−3.73066	+	0.792976i	−0.173754	+	0.0369326i	0.120213	+	0.992748i	$0.461642\pi$
$462$		0			0
$463$	−8.85242	−	1.88164i	−0.411407	−	0.0874473i	−0.00244131	−	0.999997i	$-0.500777\pi$
$463$	−8.85242	−	1.88164i	−0.411407	−	0.0874473i	−0.408966	+	0.912550i	$0.634110\pi$
$464$	−7.23859	−	8.03927i	−0.336043	−	0.373214i
$465$		0			0
$466$	−8.91735	+	9.90372i	−0.413088	+	0.458781i
$467$	−24.8972	+	18.0889i	−1.15211	+	0.837053i	−0.988759	−	0.149515i	$-0.952229\pi$
$467$	−24.8972	+	18.0889i	−1.15211	+	0.837053i	−0.163346	+	0.986569i	$0.552229\pi$
$468$		0			0
$469$	−0.635487	+	0.461708i	−0.0293441	+	0.0213197i
$470$	−13.1983	−	4.35473i	−0.608790	−	0.200869i
$471$		0			0
$472$	−14.5489	+	6.47759i	−0.669667	+	0.298155i
$473$	−5.20763	−	5.78365i	−0.239447	−	0.265933i
$474$		0			0
$475$	35.5003	+	7.88343i	1.62886	+	0.361717i
$476$	0.179048			0.00820666
$477$		0			0
$478$	15.7550	+	11.4467i	0.720617	+	0.523559i
$479$	1.28729	−	12.2478i	0.0588179	−	0.559615i	−0.924940	−	0.380113i	$-0.875885\pi$
$479$	1.28729	−	12.2478i	0.0588179	−	0.559615i	0.983758	−	0.179501i	$-0.0574484\pi$
$480$		0			0
$481$	−0.0163124	−	0.155202i	−0.000743782	−	0.00707662i
$482$	1.24920	−	2.16367i	0.0568993	−	0.0985524i
$483$		0			0
$484$	1.02281	−	1.13594i	0.0464912	−	0.0516338i
$485$	14.2783	+	8.33027i	0.648346	+	0.378258i
$486$		0			0
$487$	1.53444	+	4.72251i	0.0695320	+	0.213997i	0.979784	−	0.200056i	$-0.0641125\pi$
$487$	1.53444	+	4.72251i	0.0695320	+	0.213997i	−0.910252	+	0.414054i	$0.864113\pi$
$488$	−15.2464	+	16.9329i	−0.690173	+	0.766514i
$489$		0			0
$490$	13.6152	+	12.3715i	0.615070	+	0.558889i
$491$	−18.6448	−	3.96308i	−0.841430	−	0.178852i	−0.233018	−	0.972472i	$-0.574860\pi$
$491$	−18.6448	−	3.96308i	−0.841430	−	0.178852i	−0.608412	+	0.793621i	$0.708193\pi$
$492$		0			0
$493$	−2.11760	−	3.66778i	−0.0953718	−	0.165189i
$494$	45.7942	−	33.2714i	2.06038	−	1.49695i
$495$		0			0
$496$	−17.5847	−	12.7760i	−0.789576	−	0.573660i
$497$	0.392386	−	3.73331i	0.0176009	−	0.167462i
$498$		0			0
$499$	−2.50922	+	4.34610i	−0.112328	+	0.194558i	−0.916709	−	0.399557i	$-0.869164\pi$
$499$	−2.50922	+	4.34610i	−0.112328	+	0.194558i	0.804380	+	0.594115i	$0.202497\pi$
$500$	−4.86600	+	4.26279i	−0.217614	+	0.190638i
$501$		0			0
$502$	18.5039	−	3.93313i	0.825871	−	0.175544i
$503$	5.48055	+	3.98186i	0.244366	+	0.177542i	0.703226	−	0.710966i	$-0.251742\pi$
$503$	5.48055	+	3.98186i	0.244366	+	0.177542i	−0.458860	+	0.888508i	$0.651742\pi$
$504$		0			0
$505$	−25.6865	+	2.58190i	−1.14304	+	0.114893i
$506$	4.12386	+	1.83606i	0.183328	+	0.0816228i
$507$		0			0
$508$	0.930943	+	8.85733i	0.0413039	+	0.392981i
$509$	−9.72702	−	2.06754i	−0.431143	−	0.0916422i	−0.0127717	−	0.999918i	$-0.504065\pi$
$509$	−9.72702	−	2.06754i	−0.431143	−	0.0916422i	−0.418371	+	0.908276i	$0.637399\pi$
$510$		0			0
$511$	−0.282909	+	0.0601341i	−0.0125152	+	0.00266018i
$512$	7.21302	+	22.1994i	0.318774	+	0.981084i
$513$		0			0
$514$	0.808743	−	2.48906i	0.0356721	−	0.109788i
$515$	0.166186	−	36.5995i	0.00732303	−	1.61277i
$516$		0			0
$517$	1.57546	+	14.9895i	0.0692886	+	0.659237i
$518$	−0.00449112	+	0.00777885i	−0.000197329	+	0.000341783i
$519$		0			0
$520$	−0.203763	+	44.8750i	−0.00893558	+	1.96790i
$521$	−15.4969	−	11.2591i	−0.678930	−	0.493272i	0.194072	−	0.980987i	$-0.437830\pi$
$521$	−15.4969	−	11.2591i	−0.678930	−	0.493272i	−0.873003	+	0.487715i	$0.837830\pi$
$522$		0			0
$523$	0.0808887	−	0.248950i	0.00353702	−	0.0108858i	−0.949272	−	0.314455i	$-0.898178\pi$
$523$	0.0808887	−	0.248950i	0.00353702	−	0.0108858i	0.952809	+	0.303569i	$0.0981783\pi$
$524$	−0.965764	−	1.67275i	−0.0421896	−	0.0730745i
$525$		0			0
$526$	17.6822	−	30.6265i	0.770980	−	1.33538i
$527$	−5.69401	−	6.32384i	−0.248035	−	0.275471i
$528$		0			0
$529$	2.22487	−	21.1682i	0.0967333	−	0.920356i
$530$	−8.46084	+	7.54890i	−0.367516	+	0.327903i
$531$		0			0
$532$	1.32626			0.0575009
$533$	−27.3223	−	12.1647i	−1.18346	−	0.526911i
$534$		0			0
$535$	−9.33561	+	20.7145i	−0.403614	+	0.895565i
$536$	−5.12714	−	5.69427i	−0.221459	−	0.245955i
$537$		0			0
$538$	20.1891	−	22.4222i	0.870412	−	0.966691i
$539$	6.16497	−	18.9738i	0.265544	−	0.817261i
$540$		0			0
$541$	6.23922	+	19.2023i	0.268245	+	0.825573i	0.990928	+	0.134394i	$0.0429087\pi$
$541$	6.23922	+	19.2023i	0.268245	+	0.825573i	−0.722683	+	0.691180i	$0.757091\pi$
$542$	−20.4902	−	9.12282i	−0.880129	−	0.391859i
$543$		0			0
$544$	0.324166	+	3.08423i	0.0138985	+	0.132235i
$545$	−24.6293	−	2.70177i	−1.05500	−	0.115731i
$546$		0			0
$547$	0.785409	−	7.47267i	0.0335817	−	0.319508i	−0.964816	−	0.262925i	$-0.915313\pi$
$547$	0.785409	−	7.47267i	0.0335817	−	0.319508i	0.998398	−	0.0565830i	$-0.0180206\pi$
$548$	−1.51006	+	4.64750i	−0.0645067	+	0.198531i
$549$		0			0
$550$	−15.6796	−	7.15234i	−0.668582	−	0.304977i
$551$	−15.6857	−	27.1684i	−0.668233	−	1.15741i
$552$		0			0
$553$	3.27699	−	1.45901i	0.139352	−	0.0620435i
$554$	−24.6526	+	10.9760i	−1.04739	+	0.466327i
$555$		0			0
$556$	0.756081	+	0.336629i	0.0320650	+	0.0142762i
$557$	−17.2753			−0.731980			−0.365990	−	0.930619i	$-0.619270\pi$
$557$	−17.2753			−0.731980			−0.365990	+	0.930619i	$0.619270\pi$
$558$		0			0
$559$	5.43045	+	16.7132i	0.229684	+	0.706894i
$560$	1.04534	−	1.42513i	0.0441735	−	0.0602226i
$561$		0			0
$562$	1.09352	+	0.232435i	0.0461273	+	0.00980467i
$563$	2.64361	+	0.561918i	0.111415	+	0.0236820i	0.263282	−	0.964719i	$-0.415195\pi$
$563$	2.64361	+	0.561918i	0.111415	+	0.0236820i	−0.151867	+	0.988401i	$0.548528\pi$
$564$		0			0
$565$	19.3990	−	26.4470i	0.816120	−	1.11263i
$566$	−4.27172	−	13.1470i	−0.179554	−	0.552610i
$567$		0			0
$568$	36.6180			1.53646
$569$	39.0521	+	17.3871i	1.63715	+	0.728906i	0.999154	−	0.0411349i	$-0.0130973\pi$
$569$	39.0521	+	17.3871i	1.63715	+	0.728906i	0.637995	+	0.770040i	$0.279764\pi$
$570$		0			0
$571$	27.6907	−	12.3287i	1.15882	−	0.515941i	0.264949	−	0.964262i	$-0.414645\pi$
$571$	27.6907	−	12.3287i	1.15882	−	0.515941i	0.893872	+	0.448322i	$0.147978\pi$
$572$	9.97604	−	4.44162i	0.417119	−	0.185714i
$573$		0			0
$574$	0.860713	+	1.49080i	0.0359255	+	0.0622247i
$575$	0.743598	−	6.50596i	0.0310102	−	0.271317i
$576$		0			0
$577$	11.8163	−	36.3667i	0.491917	−	1.51396i	−0.329790	−	0.944054i	$-0.606978\pi$
$577$	11.8163	−	36.3667i	0.491917	−	1.51396i	0.821707	−	0.569910i	$-0.193022\pi$
$578$	−1.99841	+	19.0136i	−0.0831229	+	0.790862i
$579$		0			0
$580$	5.54748	+	0.608543i	0.230346	+	0.0252684i
$581$	0.327531	+	3.11625i	0.0135883	+	0.129284i
$582$		0			0
$583$	11.2336	+	5.00152i	0.465248	+	0.207142i
$584$	−0.871846	−	2.68327i	−0.0360773	−	0.111034i
$585$		0			0
$586$	−8.73494	+	26.8834i	−0.360837	+	1.11054i
$587$	−12.5219	+	13.9069i	−0.516832	+	0.574000i	−0.943905	−	0.330217i	$-0.892878\pi$
$587$	−12.5219	+	13.9069i	−0.516832	+	0.574000i	0.427073	+	0.904217i	$0.359545\pi$
$588$		0			0
$589$	−42.1773	−	46.8426i	−1.73789	−	1.93012i
$590$	−5.67432	+	12.5906i	−0.233608	+	0.518346i
$591$		0			0
$592$	−0.0547716	−	0.0243859i	−0.00225110	−	0.00100225i
$593$	42.4830			1.74457			0.872284	−	0.489000i	$-0.162638\pi$
$593$	42.4830			1.74457			0.872284	+	0.489000i	$0.162638\pi$
$594$		0			0
$595$	0.516306	−	0.460656i	0.0211665	−	0.0188851i
$596$	1.25238	−	11.9156i	0.0512994	−	0.488081i
$597$		0			0
$598$	−6.82039	−	7.57481i	−0.278906	−	0.309757i
$599$	22.9566	−	39.7621i	0.937983	−	1.62463i	0.168757	−	0.985658i	$-0.446025\pi$
$599$	22.9566	−	39.7621i	0.937983	−	1.62463i	0.769226	−	0.638977i	$-0.220642\pi$
$600$		0			0
$601$	13.8303	+	23.9548i	0.564150	+	0.977136i	0.997128	+	0.0757320i	$0.0241293\pi$
$601$	13.8303	+	23.9548i	0.564150	+	0.977136i	−0.432978	+	0.901404i	$0.642537\pi$
$602$	0.312563	−	0.961968i	0.0127391	−	0.0392069i
$603$		0			0
$604$	−9.97648	−	7.24834i	−0.405937	−	0.294931i
$605$	0.0268222	−	5.90710i	0.00109048	−	0.240158i
$606$		0			0
$607$	−7.77177	+	13.4611i	−0.315446	+	0.546369i	−0.979532	−	0.201287i	$-0.935488\pi$
$607$	−7.77177	+	13.4611i	−0.315446	+	0.546369i	0.664086	+	0.747656i	$0.268821\pi$
$608$	2.40120	+	22.8459i	0.0973814	+	0.926523i
$609$		0			0
$610$	−0.0897161	+	19.7584i	−0.00363250	+	0.799993i
$611$	10.5167	−	32.3671i	0.425460	−	1.30943i
$612$		0			0
$613$	−12.9646	−	39.9011i	−0.523637	−	1.61159i	−0.766996	−	0.641652i	$-0.778249\pi$
$613$	−12.9646	−	39.9011i	−0.523637	−	1.61159i	0.243359	−	0.969936i	$-0.421751\pi$
$614$	−14.7250	+	3.12990i	−0.594253	+	0.126312i
$615$		0			0
$616$	−2.73988	−	0.582379i	−0.110393	−	0.0234647i
$617$	−0.968484	−	9.21451i	−0.0389897	−	0.370962i	−0.996567	−	0.0827867i	$-0.973618\pi$
$617$	−0.968484	−	9.21451i	−0.0389897	−	0.370962i	0.957578	−	0.288176i	$-0.0930487\pi$
$618$		0			0
$619$	9.46155	+	4.21255i	0.380292	+	0.169317i	0.587975	−	0.808879i	$-0.299926\pi$
$619$	9.46155	+	4.21255i	0.380292	+	0.169317i	−0.207683	+	0.978196i	$0.566592\pi$
$620$	11.1569	−	1.12144i	0.448073	−	0.0450383i
$621$		0			0
$622$	13.6611	+	9.92537i	0.547760	+	0.397971i
$623$	−3.77802	+	0.803044i	−0.151363	+	0.0321733i
$624$		0			0
$625$	−3.06433	+	24.8115i	−0.122573	+	0.992459i
$626$	1.66970	−	2.89201i	0.0667347	−	0.115588i
$627$		0			0
$628$	0.844549	−	8.03534i	0.0337012	−	0.320645i
$629$	−0.0189895	−	0.0137967i	−0.000757161	−	0.000550110i
$630$		0			0
$631$	29.6450	−	21.5383i	1.18015	−	0.857428i	0.187960	−	0.982177i	$-0.439813\pi$
$631$	29.6450	−	21.5383i	1.18015	−	0.857428i	0.992188	+	0.124749i	$0.0398126\pi$
$632$	17.4957	+	30.3034i	0.695941	+	1.20541i
$633$		0			0
$634$	−34.7805	−	7.39282i	−1.38131	−	0.293606i
$635$	25.4727	+	23.1460i	1.01085	+	0.918521i
$636$		0			0
$637$	−30.1429	+	33.4770i	−1.19430	+	1.32641i
$638$	4.59425	+	14.1397i	0.181888	+	0.559794i
$639$		0			0
$640$	8.02026	+	4.67918i	0.317029	+	0.184961i
$641$	17.6253	−	19.5749i	0.696157	−	0.773161i	−0.286603	−	0.958050i	$-0.592526\pi$
$641$	17.6253	−	19.5749i	0.696157	−	0.773161i	0.982759	+	0.184889i	$0.0591926\pi$
$642$		0			0
$643$	24.3415	−	42.1606i	0.959934	−	1.66265i	0.237282	−	0.971441i	$-0.423743\pi$
$643$	24.3415	−	42.1606i	0.959934	−	1.66265i	0.722651	−	0.691213i	$-0.242923\pi$
$644$	−0.0249638	−	0.237514i	−0.000983711	−	0.00935938i
$645$		0			0
$646$	0.889937	−	8.46718i	0.0350141	−	0.333137i
$647$	−10.6167	−	7.71348i	−0.417386	−	0.303248i	0.359199	−	0.933261i	$-0.383050\pi$
$647$	−10.6167	−	7.71348i	−0.417386	−	0.303248i	−0.776585	+	0.630012i	$0.783050\pi$
$648$		0			0
$649$	14.9767			0.587885
$650$	25.7750	+	29.1542i	1.01098	+	1.14352i
$651$		0			0
$652$	0.238359	+	0.264724i	0.00933485	+	0.0103674i
$653$	44.1587	−	19.6607i	1.72806	−	0.769383i	0.731943	−	0.681366i	$-0.238614\pi$
$653$	44.1587	−	19.6607i	1.72806	−	0.769383i	0.996119	−	0.0880168i	$-0.0280529\pi$
$654$		0			0
$655$	−7.08856	−	2.33885i	−0.276973	−	0.0913864i
$656$	−9.29580	+	6.75379i	−0.362940	+	0.263691i
$657$		0			0
$658$	−1.58473	+	1.15137i	−0.0617792	+	0.0448853i
$659$	−20.0735	+	22.2938i	−0.781951	+	0.868444i	−0.994064	−	0.108801i	$-0.965299\pi$
$659$	−20.0735	+	22.2938i	−0.781951	+	0.868444i	0.212113	+	0.977245i	$0.431966\pi$
$660$		0			0
$661$	8.02224	+	8.90960i	0.312029	+	0.346543i	0.878677	−	0.477417i	$-0.158427\pi$
$661$	8.02224	+	8.90960i	0.312029	+	0.346543i	−0.566648	+	0.823960i	$0.691760\pi$
$662$	−23.7604	−	5.05042i	−0.923473	−	0.196290i
$663$		0			0
$664$	−29.8977	+	6.35495i	−1.16026	+	0.246620i
$665$	3.82444	−	3.41222i	0.148305	−	0.132320i
$666$		0			0
$667$	−4.57022	+	3.32046i	−0.176959	+	0.128569i
$668$	1.56229	+	2.70596i	0.0604468	+	0.104697i
$669$		0			0
$670$	−6.60489	−	0.724539i	−0.255169	−	0.0279914i
$671$	19.5750	−	8.71535i	0.755685	−	0.336452i
$672$		0			0
$673$	25.3929	−	5.39742i	0.978824	−	0.208055i	0.309397	−	0.950933i	$-0.399873\pi$
$673$	25.3929	−	5.39742i	0.978824	−	0.208055i	0.669427	+	0.742878i	$0.266540\pi$
$674$	−31.6806			−1.22029
$675$		0			0
$676$	−17.1357			−0.659067
$677$	38.4473	−	8.17223i	1.47765	−	0.314084i	0.602572	−	0.798065i	$-0.294143\pi$
$677$	38.4473	−	8.17223i	1.47765	−	0.314084i	0.875079	+	0.483980i	$0.160809\pi$
$678$		0			0
$679$	2.12845	−	0.947647i	0.0816824	−	0.0363674i
$680$	4.99541	+	4.53913i	0.191565	+	0.174068i
$681$		0			0
$682$	14.9361	+	25.8700i	0.571932	+	0.990615i
$683$	26.3578	−	19.1501i	1.00855	−	0.732757i	0.0446482	−	0.999003i	$-0.485783\pi$
$683$	26.3578	−	19.1501i	1.00855	−	0.732757i	0.963905	+	0.266246i	$0.0857833\pi$
$684$		0			0
$685$	7.60267	+	17.2867i	0.290483	+	0.660491i
$686$	5.10885	−	1.08592i	0.195057	−	0.0414606i
$687$		0			0
$688$	6.60389	+	1.40370i	0.251771	+	0.0535156i
$689$	−18.5791	−	20.6342i	−0.707807	−	0.786100i
$690$		0			0
$691$	22.3344	−	24.8048i	0.849639	−	0.943620i	−0.149340	−	0.988786i	$-0.547715\pi$
$691$	22.3344	−	24.8048i	0.849639	−	0.943620i	0.998979	+	0.0451661i	$0.0143817\pi$
$692$	0.170254	−	0.123696i	0.00647207	−	0.00470223i
$693$		0			0
$694$	−19.7521	+	14.3507i	−0.749779	+	0.544746i
$695$	3.04632	−	0.974541i	0.115554	−	0.0369664i
$696$		0			0
$697$	−4.10951	+	1.82967i	−0.155659	+	0.0693037i
$698$	4.60791	+	5.11760i	0.174412	+	0.193704i
$699$		0			0
$700$	0.0870675	+	0.907604i	0.00329084	+	0.0343042i
$701$	47.0156			1.77575			0.887877	−	0.460081i	$-0.152180\pi$
$701$	47.0156			1.77575			0.887877	+	0.460081i	$0.152180\pi$
$702$		0			0
$703$	−0.140661	−	0.102196i	−0.00530513	−	0.00385441i
$704$	2.65377	−	25.2490i	0.100018	−	0.951606i
$705$		0			0
$706$	−1.72346	−	16.3976i	−0.0648633	−	0.617133i
$707$	−1.81928	+	3.15109i	−0.0684211	+	0.118509i
$708$		0			0
$709$	−1.96106	+	2.17797i	−0.0736490	+	0.0817955i	−0.778843	−	0.627219i	$-0.784193\pi$
$709$	−1.96106	+	2.17797i	−0.0736490	+	0.0817955i	0.705194	+	0.709014i	$0.250860\pi$
$710$	23.6938	−	21.1400i	0.889212	−	0.793369i
$711$		0			0
$712$	−11.6428	−	35.8329i	−0.436333	−	1.34289i
$713$	−7.59494	+	8.43503i	−0.284433	+	0.315894i
$714$		0			0
$715$	17.3396	−	38.4743i	0.648465	−	1.43886i
$716$	8.59463	+	1.82684i	0.321196	+	0.0682724i
$717$		0			0
$718$	−0.305309	−	0.528811i	−0.0113940	−	0.0197351i
$719$	−13.9385	+	10.1269i	−0.519820	+	0.377671i	−0.816536	−	0.577295i	$-0.804108\pi$
$719$	−13.9385	+	10.1269i	−0.519820	+	0.377671i	0.296716	+	0.954966i	$0.404108\pi$
$720$		0			0
$721$	−4.17330	−	3.03208i	−0.155422	−	0.112920i
$722$	4.22424	−	40.1910i	0.157210	−	1.49575i
$723$		0			0
$724$	−0.0165440	+	0.0286550i	−0.000614851	+	0.00106495i
$725$	17.5624	−	12.5178i	0.652253	−	0.464899i
$726$		0			0
$727$	0.169906	−	0.0361146i	0.00630145	−	0.00133942i	−0.204760	−	0.978812i	$-0.565641\pi$
$727$	0.169906	−	0.0361146i	0.00630145	−	0.00133942i	0.211061	+	0.977473i	$0.432308\pi$
$728$	5.11692	+	3.71766i	0.189646	+	0.137786i
$729$		0			0
$730$	−2.11321	−	1.23289i	−0.0782134	−	0.0456313i
$731$	2.41466	+	1.07508i	0.0893094	+	0.0397631i
$732$		0			0
$733$	5.54047	+	52.7141i	0.204642	+	1.94704i	0.305630	+	0.952150i	$0.401133\pi$
$733$	5.54047	+	52.7141i	0.204642	+	1.94704i	−0.100988	+	0.994888i	$0.532200\pi$
$734$	−22.8001	−	4.84631i	−0.841566	−	0.178880i
$735$		0			0
$736$	4.04616	−	0.860038i	0.149144	−	0.0317014i
$737$	2.22670	+	6.85308i	0.0820216	+	0.252436i
$738$		0			0
$739$	−1.32714	+	4.08451i	−0.0488195	+	0.150251i	−0.972494	−	0.232926i	$-0.925170\pi$
$739$	−1.32714	+	4.08451i	−0.0488195	+	0.150251i	0.923675	+	0.383177i	$0.125170\pi$
$740$	0.0294590	−	0.00942414i	0.00108293	−	0.000346438i
$741$		0			0
$742$	0.167051	+	1.58938i	0.00613264	+	0.0583481i
$743$	15.1680	−	26.2718i	0.556461	−	0.963820i	−0.441327	−	0.897346i	$-0.645492\pi$
$743$	15.1680	−	26.2718i	0.556461	−	0.963820i	0.997788	−	0.0664731i	$-0.0211746\pi$
$744$		0			0
$745$	−27.0451	−	37.5820i	−0.990855	−	1.37690i
$746$	23.9192	+	17.3783i	0.875745	+	0.636266i
$747$		0			0
$748$	0.507554	−	1.56209i	0.0185580	−	0.0571157i
$749$	1.60118	+	2.77332i	0.0585057	+	0.101335i
$750$		0			0
$751$	13.8299	−	23.9541i	0.504661	−	0.874099i	−0.495324	−	0.868708i	$-0.664951\pi$
$751$	13.8299	−	23.9541i	0.504661	−	0.874099i	0.999985	−	0.00539081i	$-0.00171596\pi$
$752$	−8.74882	−	9.71655i	−0.319037	−	0.354326i
$753$		0			0
$754$	3.50907	−	33.3866i	0.127793	−	1.21587i
$755$	−47.4169	+	4.76614i	−1.72568	+	0.173457i
$756$		0			0
$757$	31.2908			1.13729			0.568643	−	0.822585i	$-0.307469\pi$
$757$	31.2908			1.13729			0.568643	+	0.822585i	$0.307469\pi$
$758$	20.4215	+	9.09225i	0.741743	+	0.330245i
$759$		0			0
$760$	37.0026	+	33.6227i	1.34222	+	1.21962i
$761$	12.3374	+	13.7021i	0.447230	+	0.496699i	0.924034	−	0.382311i	$-0.124872\pi$
$761$	12.3374	+	13.7021i	0.447230	+	0.496699i	−0.476804	+	0.879010i	$0.658205\pi$
$762$		0			0
$763$	−2.33670	+	2.59517i	−0.0845942	+	0.0939514i
$764$	0.428507	−	1.31881i	0.0155028	−	0.0477128i
$765$		0			0
$766$	2.01977	+	6.21620i	0.0729771	+	0.224601i
$767$	−30.8937	−	13.7548i	−1.11551	−	0.496656i
$768$		0			0
$769$	1.71866	+	16.3520i	0.0619765	+	0.589667i	0.980802	+	0.195004i	$0.0624719\pi$
$769$	1.71866	+	16.3520i	0.0619765	+	0.589667i	−0.918826	+	0.394663i	$0.870861\pi$
$770$	−2.10906	+	1.20493i	−0.0760052	+	0.0434227i
$771$		0			0
$772$	−0.356567	+	3.39251i	−0.0128331	+	0.122099i
$773$	−11.8001	+	36.3171i	−0.424421	+	1.30623i	0.479126	+	0.877746i	$0.340954\pi$
$773$	−11.8001	+	36.3171i	−0.424421	+	1.30623i	−0.903547	+	0.428489i	$0.859046\pi$
$774$		0			0
$775$	29.2870	−	31.9384i	1.05202	−	1.14726i
$776$	11.3637	+	19.6825i	0.407932	+	0.706559i
$777$		0			0
$778$	−1.70787	+	0.760391i	−0.0612299	+	0.0272613i
$779$	−30.4404	+	13.5529i	−1.09064	+	0.485584i
$780$		0			0
$781$	−31.4586	−	14.0063i	−1.12568	−	0.501184i
$782$	−1.53310			−0.0548235
$783$		0			0
$784$	5.34808	+	16.4597i	0.191003	+	0.587846i
$785$	−18.2380	−	25.3437i	−0.650943	−	0.904555i
$786$		0			0
$787$	12.3966	+	2.63498i	0.441891	+	0.0939267i	0.423483	−	0.905904i	$-0.360807\pi$
$787$	12.3966	+	2.63498i	0.441891	+	0.0939267i	0.0184071	+	0.999831i	$0.494140\pi$
$788$	−8.98497	−	1.90982i	−0.320076	−	0.0680344i
$789$		0			0
$790$	28.8151	+	9.50746i	1.02520	+	0.338260i
$791$	−1.42851	−	4.39650i	−0.0507919	−	0.156321i
$792$		0			0
$793$	−48.3834			−1.71814
$794$	10.5457	+	4.69524i	0.374252	+	0.166628i
$795$		0			0
$796$	−2.43683	+	1.08495i	−0.0863712	+	0.0384549i
$797$	−19.2212	+	8.55785i	−0.680851	+	0.303134i	−0.717867	−	0.696180i	$-0.754881\pi$
$797$	−19.2212	+	8.55785i	−0.680851	+	0.303134i	0.0370159	+	0.999315i	$0.488215\pi$
$798$		0			0
$799$	−2.55941	−	4.43302i	−0.0905452	−	0.156829i
$800$	−15.4765	+	3.14302i	−0.547177	+	0.111122i
$801$		0			0
$802$	0.372328	−	1.14591i	0.0131473	−	0.0404634i
$803$	−0.277337	+	2.63868i	−0.00978699	+	0.0931170i
$804$		0			0
$805$	−0.683064	−	0.620673i	−0.0240749	−	0.0218758i
$806$	−7.05060	−	67.0819i	−0.248347	−	2.36286i
$807$		0			0
$808$	−32.4247	−	14.4364i	−1.14070	−	0.507871i
$809$	11.6292	+	35.7910i	0.408861	+	1.25834i	0.917628	+	0.397441i	$0.130102\pi$
$809$	11.6292	+	35.7910i	0.408861	+	1.25834i	−0.508767	+	0.860904i	$0.669898\pi$
$810$		0			0
$811$	8.42021	−	25.9147i	0.295673	−	0.909989i	−0.687321	−	0.726354i	$-0.741213\pi$
$811$	8.42021	−	25.9147i	0.295673	−	0.909989i	0.982994	−	0.183636i	$-0.0587866\pi$
$812$	0.526315	−	0.584532i	0.0184700	−	0.0205131i
$813$		0			0
$814$	0.0551348	+	0.0612334i	0.00193247	+	0.00214623i
$815$	1.36842	+	0.150112i	0.0479336	+	0.00525819i
$816$		0			0
$817$	17.8861	+	7.96342i	0.625756	+	0.278605i
$818$	−9.55806			−0.334190
$819$		0			0
$820$	1.25873	−	5.79242i	0.0439568	−	0.202280i
$821$	−2.10819	+	20.0581i	−0.0735763	+	0.700032i	0.894105	+	0.447857i	$0.147813\pi$
$821$	−2.10819	+	20.0581i	−0.0735763	+	0.700032i	−0.967682	+	0.252175i	$0.918854\pi$
$822$		0			0
$823$	−32.2377	−	35.8036i	−1.12374	−	1.24804i	−0.965435	−	0.260645i	$-0.916065\pi$
$823$	−32.2377	−	35.8036i	−1.12374	−	1.24804i	−0.158301	−	0.987391i	$-0.550602\pi$
$824$	25.1598	−	43.5780i	0.876483	−	1.51811i
$825$		0			0
$826$	0.973219	+	1.68566i	0.0338626	+	0.0586518i
$827$	6.10623	−	18.7930i	0.212334	−	0.653498i	−0.786998	−	0.616956i	$-0.788366\pi$
$827$	6.10623	−	18.7930i	0.212334	−	0.653498i	0.999332	−	0.0365422i	$-0.0116343\pi$
$828$		0			0
$829$	21.1194	+	15.3441i	0.733507	+	0.532924i	0.890671	−	0.454648i	$-0.150235\pi$
$829$	21.1194	+	15.3441i	0.733507	+	0.532924i	−0.157164	+	0.987573i	$0.550235\pi$
$830$	−15.6766	+	21.3723i	−0.544143	+	0.741842i
$831$		0			0
$832$	−28.6631	+	49.6460i	−0.993716	+	1.72117i
$833$	0.708240	+	6.73845i	0.0245390	+	0.233473i
$834$		0			0
$835$	11.4670	+	3.78349i	0.396830	+	0.130933i
$836$	3.75961	−	11.5709i	0.130029	−	0.400188i
$837$		0			0
$838$	9.22184	+	28.3819i	0.318563	+	0.980436i
$839$	−2.91824	+	0.620290i	−0.100749	+	0.0214148i	−0.258010	−	0.966142i	$-0.583067\pi$
$839$	−2.91824	+	0.620290i	−0.100749	+	0.0214148i	0.157261	+	0.987557i	$0.449733\pi$
$840$		0			0
$841$	10.1675	+	2.16116i	0.350603	+	0.0745229i
$842$	4.11124	+	39.1159i	0.141683	+	1.34802i
$843$		0			0
$844$	−0.0782730	−	0.0348494i	−0.00269427	−	0.00119957i
$845$	−49.4129	+	44.0869i	−1.69985	+	1.51664i
$846$		0			0
$847$	−0.673564	−	0.489373i	−0.0231439	−	0.0168150i
$848$	−10.4342	+	2.21786i	−0.358313	+	0.0761617i
$849$		0			0
$850$	5.85278	+	0.0531521i	0.200749	+	0.00182310i
$851$	−0.0156542	+	0.0271139i	−0.000536620	+	0.000929453i
$852$		0			0
$853$	−2.84812	+	27.0980i	−0.0975177	+	0.927819i	0.830935	+	0.556369i	$0.187806\pi$
$853$	−2.84812	+	27.0980i	−0.0975177	+	0.927819i	−0.928453	+	0.371450i	$0.878861\pi$
$854$	2.25297	+	1.63688i	0.0770950	+	0.0560128i
$855$		0			0
$856$	−25.2722	+	18.3613i	−0.863784	+	0.627576i
$857$	25.6908	+	44.4978i	0.877582	+	1.52002i	0.853986	+	0.520296i	$0.174178\pi$
$857$	25.6908	+	44.4978i	0.877582	+	1.52002i	0.0235962	+	0.999722i	$0.492488\pi$
$858$		0			0
$859$	−47.3418	−	10.0628i	−1.61528	−	0.343339i	−0.690351	−	0.723474i	$-0.742544\pi$
$859$	−47.3418	−	10.0628i	−1.61528	−	0.343339i	−0.924931	+	0.380135i	$0.875877\pi$
$860$	−3.02419	+	1.72775i	−0.103124	+	0.0589159i
$861$		0			0
$862$	−4.64902	+	5.16326i	−0.158346	+	0.175861i
$863$	−0.728582	−	2.24234i	−0.0248012	−	0.0763303i	0.937890	−	0.346933i	$-0.112777\pi$
$863$	−0.728582	−	2.24234i	−0.0248012	−	0.0763303i	−0.962691	+	0.270603i	$0.912777\pi$
$864$		0			0
$865$	0.172699	−	0.794722i	0.00587193	−	0.0270214i
$866$	−1.66281	+	1.84674i	−0.0565045	+	0.0627547i
$867$		0			0
$868$	0.790204	−	1.36867i	0.0268213	−	0.0464558i
$869$	−3.43962	−	32.7258i	−0.116681	−	1.11015i
$870$		0			0
$871$	1.70074	−	16.1815i	0.0576275	−	0.548289i
$872$	−27.5591	−	20.0229i	−0.933269	−	0.678060i
$873$		0			0
$874$	−11.3561			−0.384127
$875$	2.58616	+	2.39317i	0.0874281	+	0.0809040i
$876$		0			0
$877$	18.3361	+	20.3643i	0.619165	+	0.687652i	0.968405	−	0.249381i	$-0.0802271\pi$
$877$	18.3361	+	20.3643i	0.619165	+	0.687652i	−0.349241	+	0.937033i	$0.613560\pi$
$878$	−24.8183	+	11.0498i	−0.837578	+	0.372914i
$879$		0			0
$880$	−9.47017	−	13.1598i	−0.319239	−	0.443617i
$881$	34.8348	−	25.3090i	1.17362	−	0.852682i	0.182179	−	0.983265i	$-0.441685\pi$
$881$	34.8348	−	25.3090i	1.17362	−	0.852682i	0.991437	+	0.130584i	$0.0416851\pi$
$882$		0			0
$883$	11.2465	−	8.17107i	0.378475	−	0.274979i	−0.382241	−	0.924063i	$-0.624848\pi$
$883$	11.2465	−	8.17107i	0.378475	−	0.274979i	0.760717	+	0.649084i	$0.224848\pi$
$884$	−2.48162	+	2.75612i	−0.0834660	+	0.0926984i
$885$		0			0
$886$	−7.18311	−	7.97765i	−0.241321	−	0.268014i
$887$	−5.62735	−	1.19613i	−0.188948	−	0.0401621i	0.112466	−	0.993656i	$-0.464125\pi$
$887$	−5.62735	−	1.19613i	−0.188948	−	0.0401621i	−0.301414	+	0.953493i	$0.597459\pi$
$888$		0			0
$889$	4.74494	−	1.00857i	0.159140	−	0.0338263i
$890$	−28.2202	−	16.4643i	−0.945944	−	0.551883i
$891$		0			0
$892$	−0.770844	+	0.560051i	−0.0258098	+	0.0187519i
$893$	−18.9583	−	32.8368i	−0.634416	−	1.09884i
$894$		0			0
$895$	29.4837	−	16.8444i	0.985532	−	0.563046i
$896$	1.19557	−	0.532301i	0.0399411	−	0.0177829i
$897$		0			0
$898$	2.49962	−	0.531311i	0.0834134	−	0.0177301i
$899$	−37.3829			−1.24679
$900$		0			0
$901$	−4.17624			−0.139131
$902$	15.4463	−	3.28320i	0.514304	−	0.109319i
$903$		0			0
$904$	41.1951	−	18.3413i	1.37013	−	0.610021i
$905$	0.0260173	+	0.125194i	0.000864844	+	0.00416160i
$906$		0			0
$907$	−9.88602	−	17.1231i	−0.328260	−	0.568563i	0.653907	−	0.756575i	$-0.273129\pi$
$907$	−9.88602	−	17.1231i	−0.328260	−	0.568563i	−0.982167	+	0.188012i	$0.939796\pi$
$908$	1.71435	−	1.24555i	0.0568926	−	0.0413349i
$909$		0			0
$910$	5.45716	−	0.548530i	0.180903	−	0.0181836i
$911$	−20.7570	+	4.41203i	−0.687709	+	0.146177i	−0.538496	−	0.842628i	$-0.681007\pi$
$911$	−20.7570	+	4.41203i	−0.687709	+	0.146177i	−0.149213	+	0.988805i	$0.547674\pi$
$912$		0			0
$913$	28.1160	+	5.97623i	0.930502	+	0.197784i
$914$	15.6087	+	17.3352i	0.516290	+	0.573398i
$915$		0			0
$916$	0.327787	−	0.364045i	0.0108304	−	0.0120284i
$917$	−0.851132	+	0.618383i	−0.0281068	+	0.0204208i
$918$		0			0
$919$	−0.706640	+	0.513404i	−0.0233099	+	0.0169356i	−0.599379	−	0.800465i	$-0.704586\pi$
$919$	−0.706640	+	0.513404i	−0.0233099	+	0.0169356i	0.576069	+	0.817401i	$0.304586\pi$
$920$	5.32485	−	7.25948i	0.175555	−	0.239338i
$921$		0			0
$922$	−4.15401	+	1.84948i	−0.136805	+	0.0609095i
$923$	52.0290	+	57.7840i	1.71255	+	1.90198i
$924$		0			0
$925$	0.0607019	−	0.102968i	0.00199587	−	0.00338556i
$926$	−10.7898			−0.354575
$927$		0			0
$928$	11.0219	+	8.00787i	0.361811	+	0.262871i
$929$	1.35255	−	12.8687i	0.0443759	−	0.422208i	−0.949671	−	0.313251i	$-0.898582\pi$
$929$	1.35255	−	12.8687i	0.0443759	−	0.422208i	0.994046	−	0.108958i	$-0.0347513\pi$
$930$		0			0
$931$	5.24615	+	49.9138i	0.171936	+	1.63586i
$932$	3.23391	−	5.60129i	0.105930	−	0.183476i
$933$		0			0
$934$	−24.5505	+	27.2661i	−0.803316	+	0.892173i
$935$	−2.55537	−	5.81031i	−0.0835694	−	0.190017i
$936$		0			0
$937$	−0.517445	−	1.59253i	−0.0169042	−	0.0520257i	0.942249	−	0.334914i	$-0.108707\pi$
$937$	−0.517445	−	1.59253i	−0.0169042	−	0.0520257i	−0.959153	+	0.282889i	$0.908707\pi$
$938$	−0.626637	+	0.695951i	−0.0204604	+	0.0227236i
$939$		0			0
$940$	6.70489	+	0.735508i	0.218689	+	0.0239896i
$941$	−9.83792	−	2.09111i	−0.320707	−	0.0681684i	0.0447453	−	0.998998i	$-0.485752\pi$
$941$	−9.83792	−	2.09111i	−0.320707	−	0.0681684i	−0.365452	+	0.930830i	$0.619086\pi$
$942$		0			0
$943$	3.00010	+	5.19632i	0.0976966	+	0.169216i
$944$	−10.5109	+	7.63660i	−0.342100	+	0.248550i
$945$		0			0
$946$	−7.50659	−	5.45386i	−0.244060	−	0.177320i
$947$	−4.26952	+	40.6218i	−0.138741	+	1.32003i	0.674575	+	0.738207i	$0.264327\pi$
$947$	−4.26952	+	40.6218i	−0.138741	+	1.32003i	−0.813315	+	0.581823i	$0.802340\pi$
$948$		0			0
$949$	2.99549	−	5.18833i	0.0972376	−	0.168420i
$950$	43.3534	+	0.393714i	1.40657	+	0.0127738i
$951$		0			0
$952$	0.930524	−	0.197789i	0.0301585	−	0.00641038i
$953$	28.0837	+	20.4040i	0.909720	+	0.660951i	0.940944	−	0.338562i	$-0.109940\pi$
$953$	28.0837	+	20.4040i	0.909720	+	0.660951i	−0.0312237	+	0.999512i	$0.509940\pi$
$954$		0			0
$955$	−2.15739	−	4.90540i	−0.0698114	−	0.158735i
$956$	−8.63424	−	3.84421i	−0.279251	−	0.124331i
$957$		0			0
$958$	−1.53473	−	14.6020i	−0.0495850	−	0.471770i
$959$	2.60349	+	0.553388i	0.0840710	+	0.0178698i
$960$		0			0
$961$	−43.1476	+	9.17130i	−1.39186	+	0.295848i
$962$	−0.0574940	−	0.176948i	−0.00185368	−	0.00570504i
$963$		0			0
$964$	−0.374693	+	1.15319i	−0.0120680	+	0.0371416i
$965$	7.70007	+	10.7001i	0.247874	+	0.344448i
$966$		0			0
$967$	2.19986	+	20.9302i	0.0707426	+	0.673071i	0.971223	+	0.238174i	$0.0765487\pi$
$967$	2.19986	+	20.9302i	0.0707426	+	0.673071i	−0.900480	+	0.434897i	$0.856785\pi$
$968$	4.06075	−	7.03343i	0.130517	−	0.226063i
$969$		0			0
$970$	18.7158	+	6.17522i	0.600928	+	0.198274i
$971$	−27.0192	−	19.6306i	−0.867089	−	0.629977i	0.0627155	−	0.998031i	$-0.480024\pi$
$971$	−27.0192	−	19.6306i	−0.867089	−	0.629977i	−0.929804	+	0.368055i	$0.880024\pi$
$972$		0			0
$973$	0.139302	−	0.428728i	0.00446583	−	0.0137444i
$974$	2.96001	+	5.12688i	0.0948448	+	0.164276i
$975$		0			0
$976$	−9.29412	+	16.0979i	−0.297497	+	0.515281i
$977$	−5.17890	−	5.75176i	−0.165688	−	0.184015i	0.654583	−	0.755990i	$-0.272844\pi$
$977$	−5.17890	−	5.75176i	−0.165688	−	0.184015i	−0.820271	+	0.571975i	$0.806177\pi$
$978$		0			0
$979$	−3.70361	+	35.2375i	−0.118368	+	1.12620i
$980$	−7.71173	−	4.49918i	−0.246342	−	0.143721i
$981$		0			0
$982$	−22.7253			−0.725195
$983$	43.9585	+	19.5716i	1.40206	+	0.624236i	0.961829	−	0.273650i	$-0.0882311\pi$
$983$	43.9585	+	19.5716i	1.40206	+	0.624236i	0.440228	+	0.897886i	$0.354898\pi$
$984$		0			0
$985$	−30.8228	+	17.6094i	−0.982095	+	0.561083i
$986$	−3.37863	−	3.75234i	−0.107597	−	0.119499i
$987$		0			0
$988$	−18.3822	+	20.4154i	−0.584814	+	0.649502i
$989$	1.08947	−	3.35303i	0.0346430	−	0.106620i
$990$		0			0
$991$	−15.7450	−	48.4581i	−0.500157	−	1.53932i	−0.808763	−	0.588134i	$-0.799863\pi$
$991$	−15.7450	−	48.4581i	−0.500157	−	1.53932i	0.308607	−	0.951190i	$-0.400137\pi$
$992$	25.0070	+	11.1339i	0.793974	+	0.353500i
$993$		0			0
$994$	−0.467810	−	4.45092i	−0.0148380	−	0.141175i
$995$	−4.23552	+	9.39806i	−0.134275	+	0.297939i
$996$		0			0
$997$	−1.58042	+	15.0367i	−0.0500525	+	0.476218i	0.940571	+	0.339597i	$0.110291\pi$
$997$	−1.58042	+	15.0367i	−0.0500525	+	0.476218i	−0.990623	+	0.136620i	$0.956376\pi$
$998$	−1.84887	+	5.69025i	−0.0585251	+	0.180122i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.r.a.496.20		224
3.2	odd	2		225.2.q.a.121.9	yes	224
9.2	odd	6		225.2.q.a.196.20	yes	224
9.7	even	3	inner	675.2.r.a.46.9		224
25.6	even	5	inner	675.2.r.a.631.9		224
75.56	odd	10		225.2.q.a.31.20	✓	224
225.56	odd	30		225.2.q.a.106.9	yes	224
225.106	even	15	inner	675.2.r.a.181.20		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.20	✓	224	75.56	odd	10
225.2.q.a.106.9	yes	224	225.56	odd	30
225.2.q.a.121.9	yes	224	3.2	odd	2
225.2.q.a.196.20	yes	224	9.2	odd	6
675.2.r.a.46.9		224	9.7	even	3	inner
675.2.r.a.181.20		224	225.106	even	15	inner
675.2.r.a.496.20		224	1.1	even	1	trivial
675.2.r.a.631.9		224	25.6	even	5	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.r (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.16617 - 0.247876i) q^{2} +(-0.528590 + 0.235343i) q^{4} +(-0.918757 + 2.03860i) q^{5} +(0.157578 + 0.272934i) q^{7} +(-2.48714 + 1.80701i) q^{8} +(-0.566103 + 2.60508i) q^{10} +(2.82788 - 0.601085i) q^{11} +(-6.38538 - 1.35725i) q^{13} +(0.251417 + 0.279226i) q^{14} +(-1.67816 + 1.86379i) q^{16} +(-0.794350 + 0.577129i) q^{17} +(-5.88399 + 4.27497i) q^{19} +(0.00587474 - 1.29381i) q^{20} +(3.14879 - 1.40193i) q^{22} +(0.876336 + 0.973270i) q^{23} +(-3.31177 - 3.74595i) q^{25} -7.78284 q^{26} +(-0.147528 - 0.107185i) q^{28} +(-0.450873 + 4.28977i) q^{29} +(0.905916 + 8.61921i) q^{31} +(1.57924 - 2.73533i) q^{32} +(-0.783287 + 0.869928i) q^{34} +(-0.701179 + 0.0704794i) q^{35} +(0.00738727 + 0.0227357i) q^{37} +(-5.80205 + 6.44383i) q^{38} +(-1.39870 - 6.73048i) q^{40} +(4.48136 + 0.952542i) q^{41} +(-1.34599 - 2.33132i) q^{43} +(-1.35333 + 0.983252i) q^{44} +(1.26320 + 0.917772i) q^{46} +(-0.544941 + 5.18477i) q^{47} +(3.45034 - 5.97616i) q^{49} +(-4.79061 - 3.54749i) q^{50} +(3.69467 - 0.785326i) q^{52} +(3.44104 + 2.50006i) q^{53} +(-1.37277 + 6.31717i) q^{55} +(-0.885114 - 0.394078i) q^{56} +(0.537539 + 5.11434i) q^{58} +(5.06713 + 1.07705i) q^{59} +(7.24968 - 1.54097i) q^{61} +(3.19295 + 9.82688i) q^{62} +(2.71365 - 8.35176i) q^{64} +(8.63350 - 11.7702i) q^{65} +(0.260529 + 2.47877i) q^{67} +(0.284062 - 0.492010i) q^{68} +(-0.800221 + 0.255996i) q^{70} +(-9.63629 - 7.00118i) q^{71} +(-0.283594 + 0.872814i) q^{73} +(0.0142504 + 0.0246825i) q^{74} +(2.10413 - 3.64447i) q^{76} +(0.609670 + 0.677108i) q^{77} +(1.18974 - 11.3196i) q^{79} +(-2.25770 - 5.13348i) q^{80} +5.46212 q^{82} +(9.08283 + 4.04394i) q^{83} +(-0.446720 - 2.14960i) q^{85} +(-2.14753 - 2.38507i) q^{86} +(-5.94717 + 6.60500i) q^{88} +(-3.78718 + 11.6557i) q^{89} +(-0.635757 - 1.95666i) q^{91} +(-0.692276 - 0.308221i) q^{92} +(0.649689 + 6.18138i) q^{94} +(-3.30899 - 15.9228i) q^{95} +(0.772754 - 7.35226i) q^{97} +(2.54232 - 7.82445i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28}+ \cdots - 146 q^{98}+O(q^{100}) \) 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Introduction

L-functions

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