LMFDB - Embedded newform 504.2.bk.b.19.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(19,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 0, 5]))

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

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

chi := DirichletCharacter("504.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bk (of order $6$, degree $2$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.14
Character	$\chi$	$=$	504.19
Dual form			504.2.bk.b.451.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.28822 - 0.583515i) q^{2} +(1.31902 - 1.50339i) q^{4} +(0.245316 - 0.424900i) q^{5} +(-2.09582 - 1.61479i) q^{7} +(0.821939 - 2.70637i) q^{8} +O(q^{10})$	\(q+(1.28822 - 0.583515i) q^{2} +(1.31902 - 1.50339i) q^{4} +(0.245316 - 0.424900i) q^{5} +(-2.09582 - 1.61479i) q^{7} +(0.821939 - 2.70637i) q^{8} +(0.0680858 - 0.690511i) q^{10} +(-1.81586 - 3.14517i) q^{11} -0.540385 q^{13} +(-3.64213 - 0.857258i) q^{14} +(-0.520366 - 3.96601i) q^{16} +(5.14304 - 2.96933i) q^{17} +(5.91166 + 3.41310i) q^{19} +(-0.315214 - 0.929259i) q^{20} +(-4.17448 - 2.99208i) q^{22} +(-5.00278 - 2.88835i) q^{23} +(2.37964 + 4.12166i) q^{25} +(-0.696135 + 0.315323i) q^{26} +(-5.19209 + 1.02090i) q^{28} +7.49445i q^{29} +(3.22373 + 5.58367i) q^{31} +(-2.98457 - 4.80545i) q^{32} +(4.89271 - 6.82619i) q^{34} +(-1.20026 + 0.494381i) q^{35} +(0.156649 + 0.0904414i) q^{37} +(9.60711 + 0.947281i) q^{38} +(-0.948301 - 1.01316i) q^{40} -3.01371i q^{41} -2.87461 q^{43} +(-7.12357 - 1.41859i) q^{44} +(-8.13007 - 0.801642i) q^{46} +(3.88172 - 6.72333i) q^{47} +(1.78493 + 6.76861i) q^{49} +(5.47055 + 3.92105i) q^{50} +(-0.712780 + 0.812410i) q^{52} +(1.36638 - 0.788878i) q^{53} -1.78184 q^{55} +(-6.09284 + 4.34480i) q^{56} +(4.37312 + 9.65450i) q^{58} +(-3.98219 + 2.29912i) q^{59} +(-5.31955 + 9.21374i) q^{61} +(7.41103 + 5.31190i) q^{62} +(-6.64883 - 4.44894i) q^{64} +(-0.132565 + 0.229610i) q^{65} +(3.72223 + 6.44710i) q^{67} +(2.31971 - 11.6486i) q^{68} +(-1.25772 + 1.33724i) q^{70} -9.94014i q^{71} +(3.28414 - 1.89610i) q^{73} +(0.254572 + 0.0251014i) q^{74} +(12.9288 - 4.38558i) q^{76} +(-1.27305 + 9.52393i) q^{77} +(-3.76412 - 2.17322i) q^{79} +(-1.81281 - 0.751823i) q^{80} +(-1.75854 - 3.88232i) q^{82} +7.61195i q^{83} -2.91370i q^{85} +(-3.70313 + 1.67738i) q^{86} +(-10.0045 + 2.32925i) q^{88} +(8.57349 + 4.94991i) q^{89} +(1.13255 + 0.872607i) q^{91} +(-10.9411 + 3.71133i) q^{92} +(1.07734 - 10.9262i) q^{94} +(2.90045 - 1.67458i) q^{95} -8.12814i q^{97} +(6.24896 + 7.67792i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{4}+O(q^{10}) $ 32 * q + 2 * q^4	$ 32 q + 2 q^{4} + 18 q^{10} - 10 q^{16} - 12 q^{22} - 16 q^{25} - 6 q^{28} - 30 q^{40} + 16 q^{43} + 16 q^{46} + 8 q^{49} - 72 q^{52} - 38 q^{58} + 44 q^{64} + 16 q^{67} - 18 q^{70} - 24 q^{73} - 96 q^{82} - 30 q^{88} - 8 q^{91} - 72 q^{94}+O(q^{100}) $ 32 * q + 2 * q^4 + 18 * q^10 - 10 * q^16 - 12 * q^22 - 16 * q^25 - 6 * q^28 - 30 * q^40 + 16 * q^43 + 16 * q^46 + 8 * q^49 - 72 * q^52 - 38 * q^58 + 44 * q^64 + 16 * q^67 - 18 * q^70 - 24 * q^73 - 96 * q^82 - 30 * q^88 - 8 * q^91 - 72 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$1$

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 $

$2$	1.28822	−	0.583515i	0.910909	−	0.412607i
$2$	1.28822	−	0.583515i	0.910909	−	0.412607i
$3$		0			0
$3$		0			0
$4$	1.31902	−	1.50339i	0.659511	−	0.751695i
$5$	0.245316	−	0.424900i	0.109709	−	0.190021i	−0.805943	−	0.591992i	$-0.798342\pi$
$5$	0.245316	−	0.424900i	0.109709	−	0.190021i	0.915652	+	0.401971i	$0.131675\pi$
$6$		0			0
$7$	−2.09582	−	1.61479i	−0.792146	−	0.610332i
$7$	−2.09582	−	1.61479i	−0.792146	−	0.610332i
$8$	0.821939	−	2.70637i	0.290599	−	0.956845i
$9$		0			0
$10$	0.0680858	−	0.690511i	0.0215306	−	0.218359i
$11$	−1.81586	−	3.14517i	−0.547503	−	0.948303i	−0.998445	−	0.0557498i	$-0.982245\pi$
$11$	−1.81586	−	3.14517i	−0.547503	−	0.948303i	0.450942	−	0.892553i	$-0.351088\pi$
$12$		0			0
$13$	−0.540385			−0.149876			−0.0749380	−	0.997188i	$-0.523876\pi$
$13$	−0.540385			−0.149876			−0.0749380	+	0.997188i	$0.523876\pi$
$14$	−3.64213	−	0.857258i	−0.973400	−	0.229112i
$15$		0			0
$16$	−0.520366	−	3.96601i	−0.130092	−	0.991502i
$17$	5.14304	−	2.96933i	1.24737	−	0.720169i	0.276786	−	0.960932i	$-0.410731\pi$
$17$	5.14304	−	2.96933i	1.24737	−	0.720169i	0.970584	+	0.240762i	$0.0773975\pi$
$18$		0			0
$19$	5.91166	+	3.41310i	1.35623	+	0.783018i	0.989113	−	0.147158i	$-0.0470125\pi$
$19$	5.91166	+	3.41310i	1.35623	+	0.783018i	0.367114	+	0.930176i	$0.380346\pi$
$20$	−0.315214	−	0.929259i	−0.0704839	−	0.207789i
$21$		0			0
$22$	−4.17448	−	2.99208i	−0.890002	−	0.637914i
$23$	−5.00278	−	2.88835i	−1.04315	−	0.602264i	−0.122427	−	0.992478i	$-0.539068\pi$
$23$	−5.00278	−	2.88835i	−1.04315	−	0.602264i	−0.920724	+	0.390214i	$0.872401\pi$
$24$		0			0
$25$	2.37964	+	4.12166i	0.475928	+	0.824331i
$26$	−0.696135	+	0.315323i	−0.136523	+	0.0618399i
$27$		0			0
$28$	−5.19209	+	1.02090i	−0.981212	+	0.192932i
$29$			7.49445i			1.39168i	0.718195	+	0.695842i	$0.244969\pi$
$29$			7.49445i			1.39168i	−0.718195	+	0.695842i	$0.755031\pi$
$30$		0			0
$31$	3.22373	+	5.58367i	0.579000	+	1.00286i	0.995594	+	0.0937647i	$0.0298901\pi$
$31$	3.22373	+	5.58367i	0.579000	+	1.00286i	−0.416595	+	0.909092i	$0.636777\pi$
$32$	−2.98457	−	4.80545i	−0.527602	−	0.849491i
$33$		0			0
$34$	4.89271	−	6.82619i	0.839093	−	1.17068i
$35$	−1.20026	+	0.494381i	−0.202881	+	0.0835657i
$36$		0			0
$37$	0.156649	+	0.0904414i	0.0257530	+	0.0148685i	0.512821	−	0.858495i	$-0.328600\pi$
$37$	0.156649	+	0.0904414i	0.0257530	+	0.0148685i	−0.487068	+	0.873364i	$0.661934\pi$
$38$	9.60711	+	0.947281i	1.55848	+	0.153669i
$39$		0			0
$40$	−0.948301	−	1.01316i	−0.149940	−	0.160194i
$41$		−	3.01371i		−	0.470662i	−0.971915	−	0.235331i	$-0.924383\pi$
$41$		−	3.01371i		−	0.470662i	0.971915	−	0.235331i	$-0.0756174\pi$
$42$		0			0
$43$	−2.87461			−0.438374			−0.219187	−	0.975683i	$-0.570340\pi$
$43$	−2.87461			−0.438374			−0.219187	+	0.975683i	$0.570340\pi$
$44$	−7.12357	−	1.41859i	−1.07392	−	0.213861i
$45$		0			0
$46$	−8.13007	−	0.801642i	−1.19871	−	0.118196i
$47$	3.88172	−	6.72333i	0.566207	−	0.980699i	−0.430730	−	0.902481i	$-0.641744\pi$
$47$	3.88172	−	6.72333i	0.566207	−	0.980699i	0.996936	−	0.0782176i	$-0.0249229\pi$
$48$		0			0
$49$	1.78493	+	6.76861i	0.254990	+	0.966944i
$50$	5.47055	+	3.92105i	0.773652	+	0.554520i
$51$		0			0
$52$	−0.712780	+	0.812410i	−0.0988447	+	0.112661i
$53$	1.36638	−	0.788878i	0.187686	−	0.108361i	−0.403213	−	0.915106i	$-0.632107\pi$
$53$	1.36638	−	0.788878i	0.187686	−	0.108361i	0.590899	+	0.806746i	$0.298773\pi$
$54$		0			0
$55$	−1.78184			−0.240264
$56$	−6.09284	+	4.34480i	−0.814190	+	0.580598i
$57$		0			0
$58$	4.37312	+	9.65450i	0.574219	+	1.26770i
$59$	−3.98219	+	2.29912i	−0.518438	+	0.299320i	−0.736295	−	0.676661i	$-0.763426\pi$
$59$	−3.98219	+	2.29912i	−0.518438	+	0.299320i	0.217858	+	0.975981i	$0.430093\pi$
$60$		0			0
$61$	−5.31955	+	9.21374i	−0.681099	+	1.17970i	0.293547	+	0.955945i	$0.405164\pi$
$61$	−5.31955	+	9.21374i	−0.681099	+	1.17970i	−0.974646	+	0.223754i	$0.928169\pi$
$62$	7.41103	+	5.31190i	0.941202	+	0.674612i
$63$		0			0
$64$	−6.64883	−	4.44894i	−0.831104	−	0.556117i
$65$	−0.132565	+	0.229610i	−0.0164427	+	0.0284796i
$66$		0			0
$67$	3.72223	+	6.44710i	0.454743	+	0.787638i	0.998673	−	0.0514923i	$-0.0163978\pi$
$67$	3.72223	+	6.44710i	0.454743	+	0.787638i	−0.543930	+	0.839130i	$0.683064\pi$
$68$	2.31971	−	11.6486i	0.281306	−	1.41260i
$69$		0			0
$70$	−1.25772	+	1.33724i	−0.150327	+	0.159831i
$71$		−	9.94014i		−	1.17968i	−0.807521	−	0.589839i	$-0.799191\pi$
$71$		−	9.94014i		−	1.17968i	0.807521	−	0.589839i	$-0.200809\pi$
$72$		0			0
$73$	3.28414	−	1.89610i	0.384379	−	0.221921i	−0.295343	−	0.955391i	$-0.595434\pi$
$73$	3.28414	−	1.89610i	0.384379	−	0.221921i	0.679722	+	0.733470i	$0.262100\pi$
$74$	0.254572	+	0.0251014i	0.0295934	+	0.00291797i
$75$		0			0
$76$	12.9288	−	4.38558i	1.48304	−	0.503061i
$77$	−1.27305	+	9.52393i	−0.145078	+	1.08535i
$78$		0			0
$79$	−3.76412	−	2.17322i	−0.423497	−	0.244506i	0.273076	−	0.961993i	$-0.411959\pi$
$79$	−3.76412	−	2.17322i	−0.423497	−	0.244506i	−0.696572	+	0.717487i	$0.745292\pi$
$80$	−1.81281	−	0.751823i	−0.202679	−	0.0840563i
$81$		0			0
$82$	−1.75854	−	3.88232i	−0.194199	−	0.428730i
$83$			7.61195i			0.835520i	0.908557	+	0.417760i	$0.137185\pi$
$83$			7.61195i			0.835520i	−0.908557	+	0.417760i	$0.862815\pi$
$84$		0			0
$85$		−	2.91370i		−	0.316036i
$86$	−3.70313	+	1.67738i	−0.399319	+	0.180876i
$87$		0			0
$88$	−10.0045	+	2.32925i	−1.06648	+	0.248299i
$89$	8.57349	+	4.94991i	0.908788	+	0.524689i	0.880041	−	0.474898i	$-0.157515\pi$
$89$	8.57349	+	4.94991i	0.908788	+	0.524689i	0.0287469	+	0.999587i	$0.490848\pi$
$90$		0			0
$91$	1.13255	+	0.872607i	0.118724	+	0.0914741i
$92$	−10.9411	+	3.71133i	−1.14069	+	0.386933i
$93$		0			0
$94$	1.07734	−	10.9262i	0.111119	−	1.12695i
$95$	2.90045	−	1.67458i	0.297580	−	0.171808i
$96$		0			0
$97$		−	8.12814i		−	0.825288i	−0.910892	−	0.412644i	$-0.864605\pi$
$97$		−	8.12814i		−	0.825288i	0.910892	−	0.412644i	$-0.135395\pi$
$98$	6.24896	+	7.67792i	0.631240	+	0.775587i
$99$		0			0
$100$	9.33526	+	1.85903i	0.933526	+	0.185903i
$101$	8.88449	+	15.3884i	0.884040	+	1.53120i	0.846810	+	0.531896i	$0.178520\pi$
$101$	8.88449	+	15.3884i	0.884040	+	1.53120i	0.0372304	+	0.999307i	$0.488146\pi$
$102$		0			0
$103$	−2.44636	+	4.23721i	−0.241047	+	0.417505i	−0.961013	−	0.276504i	$-0.910824\pi$
$103$	−2.44636	+	4.23721i	−0.241047	+	0.417505i	0.719966	+	0.694009i	$0.244157\pi$
$104$	−0.444164	+	1.46248i	−0.0435538	+	0.143408i
$105$		0			0
$106$	1.29987	−	1.81355i	0.126255	−	0.176147i
$107$	−7.26995	+	12.5919i	−0.702813	+	1.21731i	0.264663	+	0.964341i	$0.414739\pi$
$107$	−7.26995	+	12.5919i	−0.702813	+	1.21731i	−0.967475	+	0.252966i	$0.918594\pi$
$108$		0			0
$109$	9.78810	−	5.65117i	0.937530	−	0.541283i	0.0483451	−	0.998831i	$-0.484605\pi$
$109$	9.78810	−	5.65117i	0.937530	−	0.541283i	0.889185	+	0.457547i	$0.151272\pi$
$110$	−2.29541	+	1.03973i	−0.218858	+	0.0991345i
$111$		0			0
$112$	−5.31366	+	9.15232i	−0.502094	+	0.864813i
$113$	1.09049			0.102584			0.0512922	−	0.998684i	$-0.483666\pi$
$113$	1.09049			0.102584			0.0512922	+	0.998684i	$0.483666\pi$
$114$		0			0
$115$	−2.45453	+	1.41712i	−0.228886	+	0.132147i
$116$	11.2671	+	9.88534i	1.04612	+	0.917831i
$117$		0			0
$118$	−3.78837	+	5.28544i	−0.348748	+	0.486564i
$119$	−15.5737	−	2.08172i	−1.42764	−	0.190831i
$120$		0			0
$121$	−1.09471	+	1.89610i	−0.0995193	+	0.172372i
$122$	−1.47640	+	14.9734i	−0.133667	+	1.35562i
$123$		0			0
$124$	12.6466	+	2.51845i	1.13570	+	0.226163i
$125$	4.78822			0.428272
$126$		0			0
$127$		−	2.47448i		−	0.219575i	−0.993955	−	0.109787i	$-0.964983\pi$
$127$		−	2.47448i		−	0.219575i	0.993955	−	0.109787i	$-0.0350170\pi$
$128$	−11.1612	−	1.85152i	−0.986518	−	0.163652i
$129$		0			0
$130$	−0.0367926	+	0.373142i	−0.00322692	+	0.0327267i
$131$	−18.3436	−	10.5907i	−1.60269	−	0.925313i	−0.990947	−	0.134255i	$-0.957136\pi$
$131$	−18.3436	−	10.5907i	−1.60269	−	0.925313i	−0.611742	−	0.791058i	$-0.709531\pi$
$132$		0			0
$133$	−6.87835	−	16.6993i	−0.596428	−	1.44801i
$134$	8.55703	+	6.13330i	0.739215	+	0.529836i
$135$		0			0
$136$	−3.80884	−	16.3596i	−0.326605	−	1.40282i
$137$	1.98785	+	3.44305i	0.169833	+	0.294160i	0.938361	−	0.345657i	$-0.112344\pi$
$137$	1.98785	+	3.44305i	0.169833	+	0.294160i	−0.768528	+	0.639816i	$0.779010\pi$
$138$		0			0
$139$		−	7.81321i		−	0.662708i	−0.943507	−	0.331354i	$-0.892495\pi$
$139$		−	7.81321i		−	0.662708i	0.943507	−	0.331354i	$-0.107505\pi$
$140$	−0.839923	+	2.45656i	−0.0709865	+	0.207617i
$141$		0			0
$142$	−5.80022	−	12.8051i	−0.486744	−	1.07458i
$143$	0.981265	+	1.69960i	0.0820575	+	0.142128i
$144$		0			0
$145$	3.18439	+	1.83851i	0.264450	+	0.152680i
$146$	3.12429	−	4.35893i	0.258568	−	0.360748i
$147$		0			0
$148$	0.342592	−	0.116211i	0.0281609	−	0.00955246i
$149$	−9.37513	−	5.41273i	−0.768040	−	0.443428i	0.0641348	−	0.997941i	$-0.479571\pi$
$149$	−9.37513	−	5.41273i	−0.768040	−	0.443428i	−0.832175	+	0.554513i	$0.812905\pi$
$150$		0			0
$151$	11.7571	−	6.78798i	0.956781	−	0.552398i	0.0616000	−	0.998101i	$-0.480380\pi$
$151$	11.7571	−	6.78798i	0.956781	−	0.552398i	0.895181	+	0.445703i	$0.147046\pi$
$152$	14.0961	−	13.1937i	1.14335	−	1.07015i
$153$		0			0
$154$	3.91739	+	13.0118i	0.315672	+	1.04852i
$155$	3.16334			0.254085
$156$		0			0
$157$	10.3258	+	17.8848i	0.824089	+	1.42736i	0.902613	+	0.430453i	$0.141646\pi$
$157$	10.3258	+	17.8848i	0.824089	+	1.42736i	−0.0785237	+	0.996912i	$0.525021\pi$
$158$	−6.11712	−	0.603160i	−0.486652	−	0.0479849i
$159$		0			0
$160$	−2.77400	+	0.0892896i	−0.219304	+	0.00705896i
$161$	5.82085	+	14.1319i	0.458747	+	1.11375i
$162$		0			0
$163$	4.75928	−	8.24331i	0.372776	−	0.645666i	−0.617216	−	0.786794i	$-0.711739\pi$
$163$	4.75928	−	8.24331i	0.372776	−	0.645666i	0.989991	+	0.141128i	$0.0450728\pi$
$164$	−4.53078	−	3.97514i	−0.353794	−	0.310407i
$165$		0			0
$166$	4.44168	+	9.80586i	0.344742	+	0.761083i
$167$	19.1794			1.48414			0.742072	−	0.670320i	$-0.233843\pi$
$167$	19.1794			1.48414			0.742072	+	0.670320i	$0.233843\pi$
$168$		0			0
$169$	−12.7080			−0.977537
$170$	−1.70019	−	3.75349i	−0.130399	−	0.287880i
$171$		0			0
$172$	−3.79167	+	4.32166i	−0.289112	+	0.329523i
$173$	8.34739	−	14.4581i	0.634640	−	1.09923i	−0.351951	−	0.936019i	$-0.614482\pi$
$173$	8.34739	−	14.4581i	0.634640	−	1.09923i	0.986591	−	0.163211i	$-0.0521851\pi$
$174$		0			0
$175$	1.66830	−	12.4809i	0.126112	−	0.943465i
$176$	−11.5288	+	8.83836i	−0.869019	+	0.666217i
$177$		0			0
$178$	13.9329	+	1.37381i	1.04431	+	0.102971i
$179$	2.84414	+	4.92620i	0.212581	+	0.368201i	0.952522	−	0.304471i	$-0.0984797\pi$
$179$	2.84414	+	4.92620i	0.212581	+	0.368201i	−0.739941	+	0.672672i	$0.765146\pi$
$180$		0			0
$181$	−13.9838			−1.03941			−0.519703	−	0.854347i	$-0.673957\pi$
$181$	−13.9838			−1.03941			−0.519703	+	0.854347i	$0.673957\pi$
$182$	1.96815	+	0.463250i	0.145889	+	0.0343384i
$183$		0			0
$184$	−11.9289	+	11.1653i	−0.879412	+	0.823116i
$185$	0.0768572	−	0.0443735i	0.00565065	−	0.00326241i
$186$		0			0
$187$	−18.6781	−	10.7838i	−1.36588	−	0.788590i
$188$	−4.98772	−	14.7040i	−0.363767	−	1.07240i
$189$		0			0
$190$	2.75928	−	3.84968i	0.200179	−	0.279285i
$191$	−13.7475	−	7.93711i	−0.994732	−	0.574309i	−0.0880469	−	0.996116i	$-0.528063\pi$
$191$	−13.7475	−	7.93711i	−0.994732	−	0.574309i	−0.906686	+	0.421807i	$0.861396\pi$
$192$		0			0
$193$	−6.27911	−	10.8757i	−0.451980	−	0.782852i	0.546529	−	0.837440i	$-0.315949\pi$
$193$	−6.27911	−	10.8757i	−0.451980	−	0.782852i	−0.998509	+	0.0545879i	$0.982615\pi$
$194$	−4.74289	−	10.4708i	−0.340520	−	0.751762i
$195$		0			0
$196$	12.5302	+	6.24449i	0.895015	+	0.446035i
$197$			15.6632i			1.11596i	0.829856	+	0.557978i	$0.188423\pi$
$197$			15.6632i			1.11596i	−0.829856	+	0.557978i	$0.811577\pi$
$198$		0			0
$199$	7.80247	+	13.5143i	0.553102	+	0.958001i	0.998048	+	0.0624441i	$0.0198895\pi$
$199$	7.80247	+	13.5143i	0.553102	+	0.958001i	−0.444946	+	0.895557i	$0.646777\pi$
$200$	13.1106	−	3.05243i	0.927062	−	0.215839i
$201$		0			0
$202$	20.4245	+	14.6394i	1.43707	+	1.03002i
$203$	12.1019	−	15.7070i	0.849389	−	1.10242i
$204$		0			0
$205$	−1.28053	−	0.739312i	−0.0894358	−	0.0516358i
$206$	−0.678969	+	6.88595i	−0.0473060	+	0.479767i
$207$		0			0
$208$	0.281198	+	2.14317i	0.0194976	+	0.148602i
$209$		−	24.7909i		−	1.71482i
$210$		0			0
$211$	−8.56986			−0.589973			−0.294987	−	0.955501i	$-0.595315\pi$
$211$	−8.56986			−0.589973			−0.294987	+	0.955501i	$0.595315\pi$
$212$	0.616288	−	3.09474i	0.0423268	−	0.212548i
$213$		0			0
$214$	−2.01772	+	20.4633i	−0.137929	+	1.39884i
$215$	−0.705189	+	1.22142i	−0.0480935	+	0.0833003i
$216$		0			0
$217$	2.26007	−	16.9080i	0.153424	−	1.14779i
$218$	9.31169	−	12.9914i	0.630668	−	0.879892i
$219$		0			0
$220$	−2.35029	+	2.67881i	−0.158456	+	0.180605i
$221$	−2.77922	+	1.60458i	−0.186951	+	0.107936i
$222$		0			0
$223$	−12.5152			−0.838082			−0.419041	−	0.907967i	$-0.637634\pi$
$223$	−12.5152			−0.838082			−0.419041	+	0.907967i	$0.637634\pi$
$224$	−1.50465	+	14.8908i	−0.100534	+	0.994934i
$225$		0			0
$226$	1.40479	−	0.636315i	0.0934450	−	0.0423270i
$227$	−3.12590	+	1.80474i	−0.207473	+	0.119785i	−0.600137	−	0.799898i	$-0.704887\pi$
$227$	−3.12590	+	1.80474i	−0.207473	+	0.119785i	0.392663	+	0.919682i	$0.371554\pi$
$228$		0			0
$229$	8.53993	−	14.7916i	0.564335	−	0.977456i	−0.432777	−	0.901501i	$-0.642466\pi$
$229$	8.53993	−	14.7916i	0.564335	−	0.977456i	0.997111	−	0.0759550i	$-0.0242005\pi$
$230$	−2.33506	+	3.25782i	−0.153969	+	0.214814i
$231$		0			0
$232$	20.2827	+	6.15998i	1.33163	+	0.404422i
$233$	6.71821	−	11.6363i	0.440124	−	0.762318i	−0.557574	−	0.830127i	$-0.688268\pi$
$233$	6.71821	−	11.6363i	0.440124	−	0.762318i	0.997698	+	0.0678096i	$0.0216010\pi$
$234$		0			0
$235$	−1.90450	−	3.29869i	−0.124236	−	0.215183i
$236$	−1.79612	+	9.01938i	−0.116918	+	0.587112i
$237$		0			0
$238$	−21.2771	+	6.40579i	−1.37919	+	0.415226i
$239$			0.107315i			0.00694166i	0.999994	+	0.00347083i	$0.00110480\pi$
$239$			0.107315i			0.00694166i	−0.999994	+	0.00347083i	$0.998895\pi$
$240$		0			0
$241$	−25.7173	+	14.8479i	−1.65660	+	0.956436i	−0.682326	+	0.731048i	$0.739032\pi$
$241$	−25.7173	+	14.8479i	−1.65660	+	0.956436i	−0.974269	+	0.225388i	$0.927635\pi$
$242$	−0.303830	+	3.08137i	−0.0195309	+	0.198078i
$243$		0			0
$244$	6.83524	+	20.1505i	0.437582	+	1.29000i
$245$	3.31385	+	0.902033i	0.211714	+	0.0576288i
$246$		0			0
$247$	−3.19457	−	1.84439i	−0.203266	−	0.117356i
$248$	17.7612	−	4.13517i	1.12784	−	0.262583i
$249$		0			0
$250$	6.16828	−	2.79400i	0.390116	−	0.176708i
$251$			5.63442i			0.355642i	0.984063	+	0.177821i	$0.0569048\pi$
$251$			5.63442i			0.355642i	−0.984063	+	0.177821i	$0.943095\pi$
$252$		0			0
$253$			20.9794i			1.31896i
$254$	−1.44390	−	3.18768i	−0.0905981	−	0.200013i
$255$		0			0
$256$	−15.4584	+	4.12755i	−0.966152	+	0.257972i
$257$	−5.46388	−	3.15457i	−0.340827	−	0.196777i	0.319811	−	0.947482i	$-0.396381\pi$
$257$	−5.46388	−	3.15457i	−0.340827	−	0.196777i	−0.660638	+	0.750705i	$0.729714\pi$
$258$		0			0
$259$	−0.182265	−	0.442504i	−0.0113254	−	0.0274959i
$260$	0.170337	+	0.502158i	0.0105638	+	0.0311425i
$261$		0			0
$262$	−29.8104	−	2.93937i	−1.84169	−	0.181595i
$263$	−2.76417	+	1.59589i	−0.170446	+	0.0984070i	−0.582796	−	0.812618i	$-0.698041\pi$
$263$	−2.76417	+	1.59589i	−0.170446	+	0.0984070i	0.412350	+	0.911025i	$0.364708\pi$
$264$		0			0
$265$		−	0.774098i		−	0.0475525i
$266$	−18.6051	−	17.4988i	−1.14075	−	1.07292i
$267$		0			0
$268$	14.6022	+	2.90789i	0.891972	+	0.177627i
$269$	−7.61144	−	13.1834i	−0.464078	−	0.803806i	0.535082	−	0.844800i	$-0.320281\pi$
$269$	−7.61144	−	13.1834i	−0.464078	−	0.803806i	−0.999159	+	0.0409940i	$0.986948\pi$
$270$		0			0
$271$	−6.21048	+	10.7569i	−0.377260	+	0.653433i	−0.990662	−	0.136337i	$-0.956467\pi$
$271$	−6.21048	+	10.7569i	−0.377260	+	0.653433i	0.613403	+	0.789770i	$0.289800\pi$
$272$	−14.4527	−	18.8522i	−0.876322	−	1.14308i
$273$		0			0
$274$	4.56986	+	3.27547i	0.276075	+	0.197878i
$275$	8.64220	−	14.9687i	0.521144	−	0.902648i
$276$		0			0
$277$	20.9137	−	12.0746i	1.25658	−	0.725490i	0.284176	−	0.958772i	$-0.408280\pi$
$277$	20.9137	−	12.0746i	1.25658	−	0.725490i	0.972409	+	0.233283i	$0.0749467\pi$
$278$	−4.55912	−	10.0651i	−0.273438	−	0.603667i
$279$		0			0
$280$	0.351434	+	3.65470i	0.0210022	+	0.218410i
$281$	−28.6773			−1.71074			−0.855371	−	0.518016i	$-0.826671\pi$
$281$	−28.6773			−1.71074			−0.855371	+	0.518016i	$0.826671\pi$
$282$		0			0
$283$	−0.943126	+	0.544514i	−0.0560630	+	0.0323680i	−0.527770	−	0.849388i	$-0.676972\pi$
$283$	−0.943126	+	0.544514i	−0.0560630	+	0.0323680i	0.471706	+	0.881756i	$0.343638\pi$
$284$	−14.9439	−	13.1113i	−0.886758	−	0.778010i
$285$		0			0
$286$	2.25583	+	1.61688i	0.133390	+	0.0956080i
$287$	−4.86649	+	6.31619i	−0.287260	+	0.372833i
$288$		0			0
$289$	9.13389	−	15.8204i	0.537288	−	0.930609i
$290$	5.17500	+	0.510265i	0.303886	+	0.0299638i
$291$		0			0
$292$	1.48127	−	7.43833i	0.0866849	−	0.435295i
$293$	−26.6388			−1.55626			−0.778128	−	0.628106i	$-0.783831\pi$
$293$	−26.6388			−1.55626			−0.778128	+	0.628106i	$0.783831\pi$
$294$		0			0
$295$			2.25605i			0.131352i
$296$	0.373524	−	0.349613i	0.0217106	−	0.0203208i
$297$		0			0
$298$	−15.2356	−	1.50226i	−0.882577	−	0.0870239i
$299$	2.70343	+	1.56082i	0.156343	+	0.0902648i
$300$		0			0
$301$	6.02466	+	4.64188i	0.347256	+	0.267554i
$302$	11.1849	−	15.6049i	0.643617	−	0.897959i
$303$		0			0
$304$	10.4601	−	25.2217i	0.599930	−	1.44657i
$305$	2.60995	+	4.52056i	0.149445	+	0.258847i
$306$		0			0
$307$		−	8.01723i		−	0.457568i	−0.973477	−	0.228784i	$-0.926525\pi$
$307$		−	8.01723i		−	0.457568i	0.973477	−	0.228784i	$-0.0734749\pi$
$308$	12.6390	+	14.4762i	0.720174	+	0.824856i
$309$		0			0
$310$	4.07508	−	1.84585i	0.231449	−	0.104837i
$311$	12.6299	+	21.8757i	0.716178	+	1.24046i	0.962504	+	0.271269i	$0.0874433\pi$
$311$	12.6299	+	21.8757i	0.716178	+	1.24046i	−0.246326	+	0.969187i	$0.579223\pi$
$312$		0			0
$313$	−14.1781	−	8.18573i	−0.801393	−	0.462685i	0.0425648	−	0.999094i	$-0.486447\pi$
$313$	−14.1781	−	8.18573i	−0.801393	−	0.462685i	−0.843958	+	0.536409i	$0.819780\pi$
$314$	23.7380	+	17.0143i	1.33961	+	0.960174i
$315$		0			0
$316$	−8.23215	+	2.79242i	−0.463094	+	0.157086i
$317$	−7.96228	−	4.59703i	−0.447206	−	0.258195i	0.259443	−	0.965758i	$-0.416461\pi$
$317$	−7.96228	−	4.59703i	−0.447206	−	0.258195i	−0.706650	+	0.707564i	$0.749794\pi$
$318$		0			0
$319$	23.5713	−	13.6089i	1.31974	−	0.761951i
$320$	−3.52142	+	1.73369i	−0.196853	+	0.0969165i
$321$		0			0
$322$	15.7447	+	14.8084i	0.877418	+	0.825242i
$323$	40.5385			2.25562
$324$		0			0
$325$	−1.28592	−	2.22728i	−0.0713301	−	0.123547i
$326$	1.32090	−	13.3963i	0.0731581	−	0.741953i
$327$		0			0
$328$	−8.15620	−	2.47708i	−0.450351	−	0.136774i
$329$	−18.9921	+	7.82275i	−1.04707	+	0.431282i
$330$		0			0
$331$	−10.3860	+	17.9891i	−0.570867	+	0.988770i	0.425611	+	0.904906i	$0.360059\pi$
$331$	−10.3860	+	17.9891i	−0.570867	+	0.988770i	−0.996477	+	0.0838636i	$0.973274\pi$
$332$	11.4437	+	10.0403i	0.628056	+	0.551034i
$333$		0			0
$334$	24.7072	−	11.1914i	1.35192	−	0.612368i
$335$	3.65250			0.199557
$336$		0			0
$337$	18.0768			0.984704			0.492352	−	0.870396i	$-0.336137\pi$
$337$	18.0768			0.984704			0.492352	+	0.870396i	$0.336137\pi$
$338$	−16.3707	+	7.41530i	−0.890447	+	0.403339i
$339$		0			0
$340$	−4.38044	−	3.84324i	−0.237562	−	0.208429i
$341$	11.7077	−	20.2784i	0.634008	−	1.09813i
$342$		0			0
$343$	7.18897	−	17.0681i	0.388168	−	0.921589i
$344$	−2.36275	+	7.77974i	−0.127391	+	0.419456i
$345$		0			0
$346$	2.31676	−	23.4960i	0.124550	−	1.26316i
$347$	−10.4646	−	18.1251i	−0.561767	−	0.973009i	−0.997342	−	0.0728567i	$-0.976788\pi$
$347$	−10.4646	−	18.1251i	−0.561767	−	0.973009i	0.435575	−	0.900152i	$-0.356545\pi$
$348$		0			0
$349$	−7.83482			−0.419388			−0.209694	−	0.977767i	$-0.567247\pi$
$349$	−7.83482			−0.419388			−0.209694	+	0.977767i	$0.567247\pi$
$350$	−5.13363	−	17.0516i	−0.274404	−	0.911445i
$351$		0			0
$352$	−9.69437	+	18.1130i	−0.516711	+	0.965426i
$353$	19.2573	−	11.1182i	1.02496	−	0.591761i	0.109424	−	0.993995i	$-0.465100\pi$
$353$	19.2573	−	11.1182i	1.02496	−	0.591761i	0.915537	+	0.402234i	$0.131766\pi$
$354$		0			0
$355$	−4.22357	−	2.43848i	−0.224164	−	0.129421i
$356$	18.7503	−	6.36027i	0.993761	−	0.337094i
$357$		0			0
$358$	6.53839	+	4.68643i	0.345564	+	0.247685i
$359$	17.8158	+	10.2860i	0.940284	+	0.542873i	0.890049	−	0.455864i	$-0.150670\pi$
$359$	17.8158	+	10.2860i	0.940284	+	0.542873i	0.0502349	+	0.998737i	$0.484003\pi$
$360$		0			0
$361$	13.7985	+	23.8996i	0.726235	+	1.25788i
$362$	−18.0142	+	8.15974i	−0.946805	+	0.428867i
$363$		0			0
$364$	2.80573	−	0.551679i	0.147060	−	0.0289158i
$365$		−	1.86057i		−	0.0973869i
$366$		0			0
$367$	4.03835	+	6.99463i	0.210800	+	0.365117i	0.951965	−	0.306206i	$-0.0990597\pi$
$367$	4.03835	+	6.99463i	0.210800	+	0.365117i	−0.741165	+	0.671323i	$0.765726\pi$
$368$	−8.85196	+	21.3441i	−0.461440	+	1.11264i
$369$		0			0
$370$	0.0731164	−	0.102010i	0.00380114	−	0.00530325i
$371$	−4.13755	−	0.553060i	−0.214811	−	0.0287135i
$372$		0			0
$373$	−26.0224	−	15.0240i	−1.34739	−	0.777914i	−0.359508	−	0.933142i	$-0.617055\pi$
$373$	−26.0224	−	15.0240i	−1.34739	−	0.777914i	−0.987879	+	0.155228i	$0.950389\pi$
$374$	−30.3540	−	2.99297i	−1.56957	−	0.154763i
$375$		0			0
$376$	−15.0053	−	16.0315i	−0.773837	−	0.826762i
$377$		−	4.04989i		−	0.208580i
$378$		0			0
$379$	29.5725			1.51904			0.759519	−	0.650485i	$-0.225434\pi$
$379$	29.5725			1.51904			0.759519	+	0.650485i	$0.225434\pi$
$380$	1.30821	−	6.56931i	0.0671100	−	0.336999i
$381$		0			0
$382$	−22.3412	−	2.20289i	−1.14307	−	0.112710i
$383$	−7.48736	+	12.9685i	−0.382586	+	0.662659i	−0.991431	−	0.130631i	$-0.958300\pi$
$383$	−7.48736	+	12.9685i	−0.382586	+	0.662659i	0.608845	+	0.793289i	$0.291633\pi$
$384$		0			0
$385$	3.73442	+	2.87730i	0.190324	+	0.146641i
$386$	−14.4350	−	10.3464i	−0.734723	−	0.526617i
$387$		0			0
$388$	−12.2198	−	10.7212i	−0.620365	−	0.544286i
$389$	28.1103	−	16.2295i	1.42525	−	0.822869i	0.428509	−	0.903537i	$-0.359039\pi$
$389$	28.1103	−	16.2295i	1.42525	−	0.822869i	0.996741	+	0.0806688i	$0.0257056\pi$
$390$		0			0
$391$	−34.3060			−1.73493
$392$	19.7854	+	0.732714i	0.999315	+	0.0370077i
$393$		0			0
$394$	9.13970	+	20.1776i	0.460452	+	1.01653i
$395$	−1.84680	+	1.06625i	−0.0929226	+	0.0536489i
$396$		0			0
$397$	−14.0866	+	24.3987i	−0.706985	+	1.22453i	0.258986	+	0.965881i	$0.416612\pi$
$397$	−14.0866	+	24.3987i	−0.706985	+	1.22453i	−0.965970	+	0.258652i	$0.916722\pi$
$398$	17.9371	+	12.8565i	0.899104	+	0.644438i
$399$		0			0
$400$	15.1082	−	11.5824i	0.755412	−	0.579122i
$401$	−17.4170	+	30.1671i	−0.869761	+	1.50647i	−0.00752102	+	0.999972i	$0.502394\pi$
$401$	−17.4170	+	30.1671i	−0.869761	+	1.50647i	−0.862240	+	0.506499i	$0.830939\pi$
$402$		0			0
$403$	−1.74206	−	3.01733i	−0.0867781	−	0.150304i
$404$	34.8536	+	6.94076i	1.73403	+	0.345315i
$405$		0			0
$406$	6.42468	−	27.2958i	0.318851	−	1.35467i
$407$		−	0.656917i		−	0.0325622i
$408$		0			0
$409$	10.8688	−	6.27510i	0.537427	−	0.310284i	−0.206609	−	0.978424i	$-0.566243\pi$
$409$	10.8688	−	6.27510i	0.537427	−	0.310284i	0.744035	+	0.668140i	$0.232909\pi$
$410$	−2.08100	−	0.205191i	−0.102773	−	0.0101336i
$411$		0			0
$412$	3.14339	+	9.26680i	0.154864	+	0.456543i
$413$	12.0586	+	1.61185i	0.593363	+	0.0793139i
$414$		0			0
$415$	3.23432	+	1.86734i	0.158767	+	0.0916639i
$416$	1.61282	+	2.59679i	0.0790749	+	0.127318i
$417$		0			0
$418$	−14.4658	−	31.9361i	−0.707547	−	1.56204i
$419$			29.2112i			1.42706i	0.700624	+	0.713531i	$0.252905\pi$
$419$			29.2112i			1.42706i	−0.700624	+	0.713531i	$0.747095\pi$
$420$		0			0
$421$		−	22.6705i		−	1.10489i	−0.833549	−	0.552446i	$-0.813695\pi$
$421$		−	22.6705i		−	1.10489i	0.833549	−	0.552446i	$-0.186305\pi$
$422$	−11.0399	+	5.00064i	−0.537412	+	0.243427i
$423$		0			0
$424$	−1.01191	−	4.34632i	−0.0491429	−	0.211076i
$425$	24.4772	+	14.1319i	1.18732	+	0.685497i
$426$		0			0
$427$	26.0271	−	10.7204i	1.25954	−	0.518796i
$428$	9.34136	+	27.5386i	0.451532	+	1.33113i
$429$		0			0
$430$	−0.195720	+	1.98495i	−0.00943846	+	0.0957227i
$431$	−20.2969	+	11.7184i	−0.977668	+	0.564457i	−0.901565	−	0.432643i	$-0.857581\pi$
$431$	−20.2969	+	11.7184i	−0.977668	+	0.564457i	−0.0761026	+	0.997100i	$0.524248\pi$
$432$		0			0
$433$			13.7501i			0.660789i	0.943843	+	0.330395i	$0.107182\pi$
$433$			13.7501i			0.660789i	−0.943843	+	0.330395i	$0.892818\pi$
$434$	−6.95461	−	23.1000i	−0.333832	−	1.10884i
$435$		0			0
$436$	4.41481	−	22.1694i	0.211431	−	1.06172i
$437$	−19.7165	−	34.1499i	−0.943166	−	1.63361i
$438$		0			0
$439$	2.87388	−	4.97770i	0.137163	−	0.237573i	−0.789259	−	0.614061i	$-0.789535\pi$
$439$	2.87388	−	4.97770i	0.137163	−	0.237573i	0.926422	+	0.376488i	$0.122868\pi$
$440$	−1.46457	+	4.82232i	−0.0698204	+	0.229895i
$441$		0			0
$442$	−2.64395	+	3.68877i	−0.125760	+	0.175457i
$443$	−5.00397	+	8.66713i	−0.237746	+	0.411788i	−0.960067	−	0.279770i	$-0.909742\pi$
$443$	−5.00397	+	8.66713i	−0.237746	+	0.411788i	0.722321	+	0.691558i	$0.243075\pi$
$444$		0			0
$445$	4.20643	−	2.42859i	0.199404	−	0.115126i
$446$	−16.1224	+	7.30283i	−0.763417	+	0.345799i
$447$		0			0
$448$	6.75068	+	20.0606i	0.318940	+	0.947775i
$449$	−38.6982			−1.82628			−0.913140	−	0.407645i	$-0.866350\pi$
$449$	−38.6982			−1.82628			−0.913140	+	0.407645i	$0.866350\pi$
$450$		0			0
$451$	−9.47861	+	5.47248i	−0.446330	+	0.257689i
$452$	1.43837	−	1.63943i	0.0676555	−	0.0771122i
$453$		0			0
$454$	−2.97376	+	4.14891i	−0.139565	+	0.194718i
$455$	0.648604	−	0.267156i	0.0304070	−	0.0125245i
$456$		0			0
$457$	−4.37461	+	7.57705i	−0.204636	+	0.354439i	−0.950017	−	0.312200i	$-0.898934\pi$
$457$	−4.37461	+	7.57705i	−0.204636	+	0.354439i	0.745381	+	0.666639i	$0.232268\pi$
$458$	2.37020	−	24.0380i	0.110752	−	1.12322i
$459$		0			0
$460$	−1.10709	+	5.55932i	−0.0516181	+	0.259205i
$461$	−15.6206			−0.727523			−0.363762	−	0.931492i	$-0.618508\pi$
$461$	−15.6206			−0.727523			−0.363762	+	0.931492i	$0.618508\pi$
$462$		0			0
$463$			32.6811i			1.51882i	0.650614	+	0.759409i	$0.274512\pi$
$463$			32.6811i			1.51882i	−0.650614	+	0.759409i	$0.725488\pi$
$464$	29.7230	−	3.89986i	1.37986	−	0.181046i
$465$		0			0
$466$	1.86459	−	18.9103i	0.0863755	−	0.876001i
$467$	−14.9379	−	8.62442i	−0.691245	−	0.399091i	0.112833	−	0.993614i	$-0.464007\pi$
$467$	−14.9379	−	8.62442i	−0.691245	−	0.399091i	−0.804078	+	0.594523i	$0.797341\pi$
$468$		0			0
$469$	2.60955	−	19.5226i	0.120498	−	0.901468i
$470$	−4.37824	−	3.13813i	−0.201953	−	0.144751i
$471$		0			0
$472$	2.94914	+	12.6670i	0.135745	+	0.583046i
$473$	5.21989	+	9.04112i	0.240011	+	0.415711i
$474$		0			0
$475$			32.4878i			1.49064i
$476$	−23.6717	+	20.6676i	−1.08499	+	0.947296i
$477$		0			0
$478$	0.0626201	+	0.138246i	0.00286418	+	0.00632322i
$479$	12.6733	+	21.9508i	0.579057	+	1.00296i	0.995588	+	0.0938341i	$0.0299123\pi$
$479$	12.6733	+	21.9508i	0.579057	+	1.00296i	−0.416531	+	0.909121i	$0.636754\pi$
$480$		0			0
$481$	−0.0846509	−	0.0488732i	−0.00385975	−	0.00222843i
$482$	−24.4656	+	34.1337i	−1.11438	+	1.55475i
$483$		0			0
$484$	1.40663	+	4.14677i	0.0639375	+	0.188490i
$485$	−3.45365	−	1.99397i	−0.156822	−	0.0905413i
$486$		0			0
$487$	−1.93649	+	1.11803i	−0.0877509	+	0.0506630i	−0.543233	−	0.839582i	$-0.682800\pi$
$487$	−1.93649	+	1.11803i	−0.0877509	+	0.0506630i	0.455482	+	0.890245i	$0.349467\pi$
$488$	20.5634	+	21.9698i	0.930861	+	0.994526i
$489$		0			0
$490$	4.79532	−	0.771666i	0.216631	−	0.0348603i
$491$	30.7996			1.38997			0.694984	−	0.719025i	$-0.255411\pi$
$491$	30.7996			1.38997			0.694984	+	0.719025i	$0.255411\pi$
$492$		0			0
$493$	22.2535	+	38.5442i	1.00225	+	1.73594i
$494$	−5.19154	−	0.511896i	−0.233578	−	0.0230313i
$495$		0			0
$496$	20.4674	−	15.6909i	0.919012	−	0.704543i
$497$	−16.0512	+	20.8328i	−0.719995	+	0.934477i
$498$		0			0
$499$	−1.62673	+	2.81758i	−0.0728224	+	0.126132i	−0.900137	−	0.435606i	$-0.856534\pi$
$499$	−1.62673	+	2.81758i	−0.0728224	+	0.126132i	0.827315	+	0.561739i	$0.189867\pi$
$500$	6.31577	−	7.19857i	0.282450	−	0.321930i
$501$		0			0
$502$	3.28777	+	7.25838i	0.146740	+	0.323957i
$503$	15.6206			0.696487			0.348244	−	0.937404i	$-0.386778\pi$
$503$	15.6206			0.696487			0.348244	+	0.937404i	$0.386778\pi$
$504$		0			0
$505$	8.71805			0.387948
$506$	12.2418	+	27.0261i	0.544214	+	1.20146i
$507$		0			0
$508$	−3.72011	−	3.26389i	−0.165053	−	0.144812i
$509$	2.86969	−	4.97045i	0.127197	−	0.220311i	−0.795393	−	0.606094i	$-0.792735\pi$
$509$	2.86969	−	4.97045i	0.127197	−	0.220311i	0.922590	+	0.385783i	$0.126069\pi$
$510$		0			0
$511$	−9.94475	−	1.32930i	−0.439930	−	0.0588048i
$512$	−17.5054	+	14.3374i	−0.773636	+	0.633630i
$513$		0			0
$514$	−8.87941	−	0.875528i	−0.391654	−	0.0386179i
$515$	1.20026	+	2.07892i	0.0528899	+	0.0916080i
$516$		0			0
$517$	−28.1947			−1.24000
$518$	−0.493005	−	0.463688i	−0.0216614	−	0.0203733i
$519$		0			0
$520$	0.512448	+	0.547496i	0.0224723	+	0.0240093i
$521$	−18.4368	+	10.6445i	−0.807729	+	0.466343i	−0.846167	−	0.532918i	$-0.821095\pi$
$521$	−18.4368	+	10.6445i	−0.807729	+	0.466343i	0.0384377	+	0.999261i	$0.487762\pi$
$522$		0			0
$523$	21.9585	+	12.6778i	0.960180	+	0.554360i	0.896228	−	0.443593i	$-0.146296\pi$
$523$	21.9585	+	12.6778i	0.960180	+	0.554360i	0.0639515	+	0.997953i	$0.479630\pi$
$524$	−40.1175	+	13.6083i	−1.75254	+	0.594480i
$525$		0			0
$526$	−2.62963	+	3.66880i	−0.114657	+	0.159967i
$527$	33.1596	+	19.1447i	1.44445	+	0.833956i
$528$		0			0
$529$	5.18518	+	8.98100i	0.225443	+	0.390478i
$530$	−0.451698	−	0.997209i	−0.0196205	−	0.0433160i
$531$		0			0
$532$	−34.1783	−	11.6859i	−1.48182	−	0.506648i
$533$			1.62856i			0.0705409i
$534$		0			0
$535$	3.56687	+	6.17801i	0.154209	+	0.267099i
$536$	20.5076	−	4.77460i	0.885795	−	0.206231i
$537$		0			0
$538$	−17.4979	−	12.5417i	−0.754389	−	0.540713i
$539$	18.0472	−	17.9048i	0.777348	−	0.771212i
$540$		0			0
$541$	25.6817	+	14.8274i	1.10414	+	0.637478i	0.937306	−	0.348507i	$-0.113311\pi$
$541$	25.6817	+	14.8274i	1.10414	+	0.637478i	0.166837	+	0.985984i	$0.446644\pi$
$542$	−1.72367	+	17.4811i	−0.0740381	+	0.750878i
$543$		0			0
$544$	−29.6187	−	15.8524i	−1.26989	−	0.679667i
$545$		−	5.54529i		−	0.237534i
$546$		0			0
$547$	−11.4301			−0.488718			−0.244359	−	0.969685i	$-0.578577\pi$
$547$	−11.4301			−0.488718			−0.244359	+	0.969685i	$0.578577\pi$
$548$	7.79826	+	1.55295i	0.333125	+	0.0663387i
$549$		0			0
$550$	2.39858	−	24.3259i	0.102276	−	1.03726i
$551$	−25.5793	+	44.3046i	−1.08971	+	1.88744i
$552$		0			0
$553$	4.37964	+	10.6329i	0.186241	+	0.452158i
$554$	19.8958	−	27.7582i	0.845292	−	1.17933i
$555$		0			0
$556$	−11.7463	−	10.3058i	−0.498154	−	0.437063i
$557$	−10.9990	+	6.35028i	−0.466043	+	0.269070i	−0.714582	−	0.699552i	$-0.753383\pi$
$557$	−10.9990	+	6.35028i	−0.466043	+	0.269070i	0.248539	+	0.968622i	$0.420050\pi$
$558$		0			0
$559$	1.55340			0.0657017
$560$	2.58530	+	4.50299i	0.109249	+	0.190286i
$561$		0			0
$562$	−36.9426	+	16.7336i	−1.55833	+	0.705864i
$563$	6.43843	−	3.71723i	0.271347	−	0.156662i	−0.358152	−	0.933663i	$-0.616593\pi$
$563$	6.43843	−	3.71723i	0.271347	−	0.156662i	0.629500	+	0.777001i	$0.283260\pi$
$564$		0			0
$565$	0.267514	−	0.463348i	0.0112544	−	0.0194932i
$566$	−0.897222	+	1.25178i	−0.0377130	+	0.0526163i
$567$		0			0
$568$	−26.9017	−	8.17019i	−1.12877	−	0.342814i
$569$	14.9396	−	25.8761i	0.626300	−	1.08478i	−0.361988	−	0.932183i	$-0.617902\pi$
$569$	14.9396	−	25.8761i	0.626300	−	1.08478i	0.988288	−	0.152600i	$-0.0487647\pi$
$570$		0			0
$571$	13.4302	+	23.2618i	0.562037	+	0.973477i	0.997319	+	0.0731823i	$0.0233155\pi$
$571$	13.4302	+	23.2618i	0.562037	+	0.973477i	−0.435282	+	0.900294i	$0.643351\pi$
$572$	3.84947	+	0.766585i	0.160955	+	0.0320525i
$573$		0			0
$574$	−2.58353	+	10.9763i	−0.107834	+	0.458142i
$575$		−	27.4930i		−	1.14654i
$576$		0			0
$577$	8.90026	−	5.13857i	0.370523	−	0.213921i	−0.303164	−	0.952938i	$-0.598043\pi$
$577$	8.90026	−	5.13857i	0.370523	−	0.213921i	0.673687	+	0.739017i	$0.264710\pi$
$578$	2.53505	−	25.7099i	0.105444	−	1.06939i
$579$		0			0
$580$	6.96428	−	2.36235i	0.289176	−	0.0980914i
$581$	12.2917	−	15.9533i	0.509945	−	0.661854i
$582$		0			0
$583$	−4.96230	−	2.86499i	−0.205518	−	0.118656i
$584$	−2.43217	−	10.4466i	−0.100644	−	0.432281i
$585$		0			0
$586$	−34.3167	+	15.5441i	−1.41761	+	0.642123i
$587$			33.9395i			1.40083i	0.713734	+	0.700417i	$0.247003\pi$
$587$			33.9395i			1.40083i	−0.713734	+	0.700417i	$0.752997\pi$
$588$		0			0
$589$			44.0117i			1.81347i
$590$	1.31644	+	2.90629i	0.0541968	+	0.119650i
$591$		0			0
$592$	0.277176	−	0.668334i	0.0113919	−	0.0274684i
$593$	8.72720	+	5.03865i	0.358383	+	0.206913i	0.668371	−	0.743828i	$-0.266992\pi$
$593$	8.72720	+	5.03865i	0.358383	+	0.206913i	−0.309988	+	0.950740i	$0.600325\pi$
$594$		0			0
$595$	−4.70501	+	6.10660i	−0.192887	+	0.250346i
$596$	−20.5034	+	6.95497i	−0.839854	+	0.284887i
$597$		0			0
$598$	4.39337	+	0.433196i	0.179658	+	0.0177147i
$599$	5.04612	−	2.91338i	0.206179	−	0.119037i	−0.393355	−	0.919386i	$-0.628686\pi$
$599$	5.04612	−	2.91338i	0.206179	−	0.119037i	0.599534	+	0.800349i	$0.295352\pi$
$600$		0			0
$601$			6.41352i			0.261613i	0.991408	+	0.130806i	$0.0417566\pi$
$601$			6.41352i			0.261613i	−0.991408	+	0.130806i	$0.958243\pi$
$602$	10.4697	+	2.46428i	0.426713	+	0.100437i
$603$		0			0
$604$	5.30291	−	26.6290i	0.215772	−	1.08352i
$605$	0.537102	+	0.930287i	0.0218363	+	0.0378216i
$606$		0			0
$607$	6.87499	−	11.9078i	0.279047	−	0.483324i	−0.692101	−	0.721801i	$-0.743315\pi$
$607$	6.87499	−	11.9078i	0.279047	−	0.483324i	0.971148	+	0.238477i	$0.0766481\pi$
$608$	−1.24229	−	38.5948i	−0.0503815	−	1.56523i
$609$		0			0
$610$	6.00000	+	4.30053i	0.242933	+	0.174124i
$611$	−2.09762	+	3.63319i	−0.0848607	+	0.146983i
$612$		0			0
$613$	8.85055	−	5.10987i	0.357470	−	0.206386i	−0.310500	−	0.950573i	$-0.600497\pi$
$613$	8.85055	−	5.10987i	0.357470	−	0.206386i	0.667971	+	0.744188i	$0.267163\pi$
$614$	−4.67817	−	10.3280i	−0.188796	−	0.416802i
$615$		0			0
$616$	24.7289	+	11.2734i	0.996355	+	0.454220i
$617$	−16.3216			−0.657084			−0.328542	−	0.944489i	$-0.606557\pi$
$617$	−16.3216			−0.657084			−0.328542	+	0.944489i	$0.606557\pi$
$618$		0			0
$619$	−17.1667	+	9.91120i	−0.689988	+	0.398365i	−0.803607	−	0.595160i	$-0.797089\pi$
$619$	−17.1667	+	9.91120i	−0.689988	+	0.398365i	0.113620	+	0.993524i	$0.463755\pi$
$620$	4.17251	−	4.75573i	0.167572	−	0.190995i
$621$		0			0
$622$	29.0349	+	20.8109i	1.16419	+	0.834443i
$623$	−9.97545	−	24.2185i	−0.399658	−	0.970292i
$624$		0			0
$625$	−10.7236	+	18.5738i	−0.428943	+	0.742951i
$626$	−23.0410	−	2.27189i	−0.920903	−	0.0908030i
$627$		0			0
$628$	40.5078	+	8.06674i	1.61644	+	0.321898i
$629$	1.07420			0.0428313
$630$		0			0
$631$		−	7.43503i		−	0.295984i	−0.988989	−	0.147992i	$-0.952719\pi$
$631$		−	7.43503i		−	0.295984i	0.988989	−	0.147992i	$-0.0472810\pi$
$632$	−8.97539	+	8.40083i	−0.357022	+	0.334167i
$633$		0			0
$634$	−12.9396	−	1.27587i	−0.513897	−	0.0506713i
$635$	−1.05141	−	0.607031i	−0.0417239	−	0.0240893i
$636$		0			0
$637$	−0.964549	−	3.65766i	−0.0382168	−	0.144922i
$638$	22.4240	−	31.2854i	0.887775	−	1.23860i
$639$		0			0
$640$	−3.52473	+	4.28818i	−0.139327	+	0.169505i
$641$	−8.43079	−	14.6026i	−0.332996	−	0.576767i	0.650102	−	0.759847i	$-0.274726\pi$
$641$	−8.43079	−	14.6026i	−0.332996	−	0.576767i	−0.983098	+	0.183081i	$0.941393\pi$
$642$		0			0
$643$		−	26.7506i		−	1.05494i	−0.849573	−	0.527470i	$-0.823141\pi$
$643$		−	26.7506i		−	1.05494i	0.849573	−	0.527470i	$-0.176859\pi$
$644$	28.9236	+	9.88926i	1.13975	+	0.389691i
$645$		0			0
$646$	52.2225	−	23.6548i	2.05467	−	0.930686i
$647$	−21.8338	−	37.8173i	−0.858377	−	1.48675i	−0.873476	−	0.486867i	$-0.838140\pi$
$647$	−21.8338	−	37.8173i	−0.858377	−	1.48675i	0.0150994	−	0.999886i	$-0.495194\pi$
$648$		0			0
$649$	14.4622	+	8.34977i	0.567692	+	0.327757i
$650$	−2.95620	−	2.11888i	−0.115952	−	0.0831091i
$651$		0			0
$652$	−6.11533	−	18.0282i	−0.239495	−	0.706037i
$653$	5.19811	+	3.00113i	0.203418	+	0.117443i	0.598249	−	0.801310i	$-0.295863\pi$
$653$	5.19811	+	3.00113i	0.203418	+	0.117443i	−0.394831	+	0.918754i	$0.629197\pi$
$654$		0			0
$655$	−8.99997	+	5.19614i	−0.351658	+	0.203030i
$656$	−11.9524	+	1.56823i	−0.466662	+	0.0612291i
$657$		0			0
$658$	−19.9013	+	21.1596i	−0.775835	+	0.824887i
$659$	4.22125			0.164436			0.0822182	−	0.996614i	$-0.473800\pi$
$659$	4.22125			0.164436			0.0822182	+	0.996614i	$0.473800\pi$
$660$		0			0
$661$	−19.5197	−	33.8091i	−0.759227	−	1.31502i	−0.943245	−	0.332097i	$-0.892244\pi$
$661$	−19.5197	−	33.8091i	−0.759227	−	1.31502i	0.184018	−	0.982923i	$-0.441090\pi$
$662$	−2.88256	+	29.2343i	−0.112034	+	1.13622i
$663$		0			0
$664$	20.6007	+	6.25656i	0.799463	+	0.242802i
$665$	−8.78291	−	1.17400i	−0.340587	−	0.0455257i
$666$		0			0
$667$	21.6466	−	37.4931i	0.838161	−	1.45174i
$668$	25.2980	−	28.8341i	0.978809	−	1.11562i
$669$		0			0
$670$	4.70522	−	2.13129i	0.181778	−	0.0823387i
$671$	38.6383			1.49162
$672$		0			0
$673$	−3.37885			−0.130245			−0.0651225	−	0.997877i	$-0.520744\pi$
$673$	−3.37885			−0.130245			−0.0651225	+	0.997877i	$0.520744\pi$
$674$	23.2869	−	10.5481i	0.896976	−	0.406296i
$675$		0			0
$676$	−16.7621	+	19.1051i	−0.644696	+	0.734810i
$677$	−9.17628	+	15.8938i	−0.352673	+	0.610848i	−0.986717	−	0.162449i	$-0.948061\pi$
$677$	−9.17628	+	15.8938i	−0.352673	+	0.610848i	0.634044	+	0.773297i	$0.281394\pi$
$678$		0			0
$679$	−13.1252	+	17.0351i	−0.503699	+	0.653748i
$680$	−7.88555	−	2.39489i	−0.302397	−	0.0918397i
$681$		0			0
$682$	3.24939	−	32.9546i	0.124426	−	1.26190i
$683$	−1.51296	−	2.62052i	−0.0578918	−	0.100272i	0.835627	−	0.549297i	$-0.185105\pi$
$683$	−1.51296	−	2.62052i	−0.0578918	−	0.100272i	−0.893519	+	0.449026i	$0.851771\pi$
$684$		0			0
$685$	1.95061			0.0745288
$686$	−0.698493	−	26.1823i	−0.0266686	−	0.999644i
$687$		0			0
$688$	1.49585	+	11.4007i	0.0570287	+	0.434648i
$689$	−0.738370	+	0.426298i	−0.0281296	+	0.0162407i
$690$		0			0
$691$	15.4571	+	8.92418i	0.588017	+	0.339492i	0.764313	−	0.644845i	$-0.223078\pi$
$691$	15.4571	+	8.92418i	0.588017	+	0.339492i	−0.176296	+	0.984337i	$0.556412\pi$
$692$	−10.7258	−	31.6199i	−0.407734	−	1.20201i
$693$		0			0
$694$	−24.0569	−	17.2430i	−0.913189	−	0.654534i
$695$	−3.31984	−	1.91671i	−0.125929	−	0.0727049i
$696$		0			0
$697$	−8.94870	−	15.4996i	−0.338956	−	0.587090i
$698$	−10.0930	+	4.57173i	−0.382025	+	0.173043i
$699$		0			0
$700$	−16.5631	−	18.9706i	−0.626026	−	0.717022i
$701$			5.67015i			0.214159i	0.994250	+	0.107079i	$0.0341499\pi$
$701$			5.67015i			0.214159i	−0.994250	+	0.107079i	$0.965850\pi$
$702$		0			0
$703$	0.617371	+	1.06932i	0.0232846	+	0.0403301i
$704$	−1.91927	+	28.9903i	−0.0723354	+	1.09261i
$705$		0			0
$706$	18.3200	−	25.5596i	0.689481	−	0.961947i
$707$	6.22867	−	46.5979i	0.234253	−	1.75249i
$708$		0			0
$709$	−21.1323	−	12.2008i	−0.793641	−	0.458209i	0.0476017	−	0.998866i	$-0.484842\pi$
$709$	−21.1323	−	12.2008i	−0.793641	−	0.458209i	−0.841243	+	0.540657i	$0.818176\pi$
$710$	−6.86378	−	0.676783i	−0.257593	−	0.0253992i
$711$		0			0
$712$	20.4431	−	19.1345i	0.766139	−	0.717095i
$713$		−	37.2452i		−	1.39484i
$714$		0			0
$715$	0.962882			0.0360097
$716$	11.1575	+	2.22190i	0.416974	+	0.0830364i
$717$		0			0
$718$	28.9527	+	2.85480i	1.08051	+	0.106540i
$719$	−20.4402	+	35.4035i	−0.762292	+	1.32033i	0.179375	+	0.983781i	$0.442592\pi$
$719$	−20.4402	+	35.4035i	−0.762292	+	1.32033i	−0.941667	+	0.336547i	$0.890741\pi$
$720$		0			0
$721$	11.9693	−	4.93010i	0.445761	−	0.183606i
$722$	31.7212	+	22.7364i	1.18054	+	0.846160i
$723$		0			0
$724$	−18.4449	+	21.0231i	−0.685500	+	0.781317i
$725$	−30.8895	+	17.8341i	−1.14721	+	0.662341i
$726$		0			0
$727$	41.3827			1.53480			0.767400	−	0.641168i	$-0.221550\pi$
$727$	41.3827			1.53480			0.767400	+	0.641168i	$0.221550\pi$
$728$	3.29248	−	2.34787i	0.122027	−	0.0870177i
$729$		0			0
$730$	−1.08567	−	2.39683i	−0.0401825	−	0.0887106i
$731$	−14.7842	+	8.53567i	−0.546814	+	0.315703i
$732$		0			0
$733$	0.977981	−	1.69391i	0.0361226	−	0.0625661i	−0.847399	−	0.530957i	$-0.821833\pi$
$733$	0.977981	−	1.69391i	0.0361226	−	0.0625661i	0.883521	+	0.468391i	$0.155166\pi$
$734$	9.28375	+	6.65418i	0.342670	+	0.245610i
$735$		0			0
$736$	1.05130	+	32.6611i	0.0387513	+	1.20390i
$737$	13.5181	−	23.4141i	0.497946	−	0.862469i
$738$		0			0
$739$	5.62673	+	9.74578i	0.206983	+	0.358504i	0.950763	−	0.309920i	$-0.100302\pi$
$739$	5.62673	+	9.74578i	0.206983	+	0.358504i	−0.743780	+	0.668424i	$0.766969\pi$
$740$	0.0346655	−	0.174076i	0.00127433	−	0.00639916i
$741$		0			0
$742$	−5.65279	+	1.70186i	−0.207521	+	0.0624772i
$743$		−	7.07525i		−	0.259566i	−0.991542	−	0.129783i	$-0.958572\pi$
$743$		−	7.07525i		−	0.259566i	0.991542	−	0.129783i	$-0.0414281\pi$
$744$		0			0
$745$	−4.59974	+	2.65566i	−0.168522	+	0.0972960i
$746$	−42.2893	−	4.16981i	−1.54832	−	0.152668i
$747$		0			0
$748$	−40.8491	+	13.8564i	−1.49359	+	0.506640i
$749$	35.5698	−	14.6510i	1.29969	−	0.535336i
$750$		0			0
$751$	−23.2134	−	13.4022i	−0.847067	−	0.489055i	0.0125930	−	0.999921i	$-0.495991\pi$
$751$	−23.2134	−	13.4022i	−0.847067	−	0.489055i	−0.859660	+	0.510866i	$0.829325\pi$
$752$	−28.6847	−	11.8963i	−1.04602	−	0.433814i
$753$		0			0
$754$	−2.36317	−	5.21715i	−0.0860616	−	0.189997i
$755$		−	6.66080i		−	0.242411i
$756$		0			0
$757$		−	51.1768i		−	1.86005i	−0.367494	−	0.930026i	$-0.619784\pi$
$757$		−	51.1768i		−	1.86005i	0.367494	−	0.930026i	$-0.380216\pi$
$758$	38.0959	−	17.2560i	1.38371	−	0.626766i
$759$		0			0
$760$	−2.14802	−	9.22608i	−0.0779170	−	0.334665i
$761$	26.1897	+	15.1207i	0.949377	+	0.548123i	0.892887	−	0.450280i	$-0.148676\pi$
$761$	26.1897	+	15.1207i	0.949377	+	0.548123i	0.0564899	+	0.998403i	$0.482009\pi$
$762$		0			0
$763$	−29.6395	−	3.96187i	−1.07302	−	0.143429i
$764$	−30.0658	+	10.1986i	−1.08774	+	0.368973i
$765$		0			0
$766$	−2.07806	+	21.0752i	−0.0750834	+	0.761479i
$767$	2.15192	−	1.24241i	0.0777013	−	0.0448609i
$768$		0			0
$769$		−	23.0956i		−	0.832850i	−0.909170	−	0.416425i	$-0.863283\pi$
$769$		−	23.0956i		−	0.832850i	0.909170	−	0.416425i	$-0.136717\pi$
$770$	6.48970	+	1.52750i	0.233873	+	0.0550473i
$771$		0			0
$772$	−24.6327	−	4.90537i	−0.886552	−	0.176548i
$773$	−6.39991	−	11.0850i	−0.230189	−	0.398699i	0.727675	−	0.685922i	$-0.240601\pi$
$773$	−6.39991	−	11.0850i	−0.230189	−	0.398699i	−0.957864	+	0.287224i	$0.907268\pi$
$774$		0			0
$775$	−15.3427	+	26.5743i	−0.551124	+	0.954575i
$776$	−21.9977	−	6.68084i	−0.789672	−	0.239828i
$777$		0			0
$778$	26.7421	−	37.3100i	0.958752	−	1.33763i
$779$	10.2861	−	17.8160i	0.368537	−	0.638325i
$780$		0			0
$781$	−31.2634	+	18.0499i	−1.11869	+	0.645877i
$782$	−44.1936	+	20.0180i	−1.58036	+	0.715843i
$783$		0			0
$784$	25.9155	−	10.6012i	0.925555	−	0.378614i
$785$	10.1324			0.361639
$786$		0			0
$787$	21.1326	−	12.2009i	0.753297	−	0.434916i	−0.0735872	−	0.997289i	$-0.523445\pi$
$787$	21.1326	−	12.2009i	0.753297	−	0.434916i	0.826884	+	0.562373i	$0.190111\pi$
$788$	23.5479	+	20.6601i	0.838859	+	0.735985i
$789$		0			0
$790$	−1.75691	+	2.45120i	−0.0625081	+	0.0872098i
$791$	−2.28546	−	1.76090i	−0.0812618	−	0.0626105i
$792$		0			0
$793$	2.87461	−	4.97897i	0.102080	−	0.176808i
$794$	−3.90963	+	39.6506i	−0.138747	+	1.40715i
$795$		0			0
$796$	30.6089	+	6.09546i	1.08490	+	0.216048i
$797$	−53.6746			−1.90125			−0.950625	−	0.310342i	$-0.899557\pi$
$797$	−53.6746			−1.90125			−0.950625	+	0.310342i	$0.899557\pi$
$798$		0			0
$799$		−	46.1045i		−	1.63106i
$800$	12.7042	−	23.7366i	0.449162	−	0.839216i
$801$		0			0
$802$	−4.83395	+	49.0249i	−0.170693	+	1.73113i
$803$	−11.9271	−	6.88610i	−0.420898	−	0.243005i
$804$		0			0
$805$	7.43259	+	0.993504i	0.261964	+	0.0350164i
$806$	−4.00481	−	2.87047i	−0.141064	−	0.101108i
$807$		0			0
$808$	48.9491	−	11.3964i	1.72202	−	0.400923i
$809$	5.82085	+	10.0820i	0.204650	+	0.354464i	0.950021	−	0.312185i	$-0.101061\pi$
$809$	5.82085	+	10.0820i	0.204650	+	0.354464i	−0.745371	+	0.666650i	$0.767728\pi$
$810$		0			0
$811$			11.8137i			0.414835i	0.978253	+	0.207417i	$0.0665058\pi$
$811$			11.8137i			0.414835i	−0.978253	+	0.207417i	$0.933494\pi$
$812$	−7.65107	−	38.9118i	−0.268500	−	1.36554i
$813$		0			0
$814$	−0.383321	−	0.846253i	−0.0134354	−	0.0296612i
$815$	−2.33506	−	4.04444i	−0.0817935	−	0.141671i
$816$		0			0
$817$	−16.9937	−	9.81132i	−0.594534	−	0.343255i
$818$	10.3398	−	14.4258i	0.361522	−	0.504386i
$819$		0			0
$820$	−2.80051	+	0.949962i	−0.0977982	+	0.0331741i
$821$	38.8983	+	22.4579i	1.35756	+	0.783788i	0.989294	−	0.145933i	$-0.0466184\pi$
$821$	38.8983	+	22.4579i	1.35756	+	0.783788i	0.368266	+	0.929721i	$0.379952\pi$
$822$		0			0
$823$	28.5336	−	16.4739i	0.994618	−	0.574243i	0.0879668	−	0.996123i	$-0.471963\pi$
$823$	28.5336	−	16.4739i	0.994618	−	0.574243i	0.906652	+	0.421880i	$0.138630\pi$
$824$	9.45670	+	10.1035i	0.329440	+	0.351971i
$825$		0			0
$826$	16.4746	−	4.95993i	0.573225	−	0.172578i
$827$	−8.21322			−0.285602			−0.142801	−	0.989751i	$-0.545611\pi$
$827$	−8.21322			−0.285602			−0.142801	+	0.989751i	$0.545611\pi$
$828$		0			0
$829$	10.1692	+	17.6135i	0.353190	+	0.611742i	0.986806	−	0.161905i	$-0.0517637\pi$
$829$	10.1692	+	17.6135i	0.353190	+	0.611742i	−0.633617	+	0.773647i	$0.718430\pi$
$830$	5.25613	+	0.518266i	0.182443	+	0.0179893i
$831$		0			0
$832$	3.59293	+	2.40414i	0.124562	+	0.0833485i
$833$	29.2782	+	29.5111i	1.01443	+	1.02250i
$834$		0			0
$835$	4.70501	−	8.14932i	0.162824	−	0.282019i
$836$	−37.2703	−	32.6997i	−1.28902	−	1.13094i
$837$		0			0
$838$	17.0452	+	37.6305i	0.588816	+	1.29992i
$839$	−53.3070			−1.84036			−0.920180	−	0.391495i	$-0.871958\pi$
$839$	−53.3070			−1.84036			−0.920180	+	0.391495i	$0.871958\pi$
$840$		0			0
$841$	−27.1668			−0.936785
$842$	−13.2286	−	29.2046i	−0.455886	−	1.00646i
$843$		0			0
$844$	−11.3038	+	12.8838i	−0.389094	+	0.443480i
$845$	−3.11748	+	5.39963i	−0.107244	+	0.185753i
$846$		0			0
$847$	5.35611	−	2.20615i	0.184038	−	0.0758043i
$848$	−3.83971	−	5.00855i	−0.131856	−	0.171994i
$849$		0			0
$850$	39.7781	+	3.92221i	1.36438	+	0.134531i
$851$	−0.522454	−	0.904916i	−0.0179095	−	0.0310201i
$852$		0			0
$853$	34.6193			1.18534			0.592670	−	0.805445i	$-0.298074\pi$
$853$	34.6193			1.18534			0.592670	+	0.805445i	$0.298074\pi$
$854$	27.2731	−	28.9974i	0.933265	−	0.992271i
$855$		0			0
$856$	28.1029	+	30.0249i	0.960537	+	1.02623i
$857$	20.2513	−	11.6921i	0.691772	−	0.399395i	−0.112504	−	0.993651i	$-0.535887\pi$
$857$	20.2513	−	11.6921i	0.691772	−	0.399395i	0.804275	+	0.594257i	$0.202554\pi$
$858$		0			0
$859$	−33.9371	−	19.5936i	−1.15792	−	0.668524i	−0.207114	−	0.978317i	$-0.566407\pi$
$859$	−33.9371	−	19.5936i	−1.15792	−	0.668524i	−0.950804	+	0.309793i	$0.899740\pi$
$860$	0.906116	+	2.67126i	0.0308983	+	0.0910891i
$861$		0			0
$862$	−19.3090	+	26.9395i	−0.657668	+	0.917562i
$863$	5.70797	+	3.29550i	0.194301	+	0.112180i	0.593995	−	0.804469i	$-0.297550\pi$
$863$	5.70797	+	3.29550i	0.194301	+	0.112180i	−0.399693	+	0.916649i	$0.630883\pi$
$864$		0			0
$865$	−4.09550	−	7.09362i	−0.139251	−	0.241190i
$866$	8.02340	+	17.7132i	0.272646	+	0.601919i
$867$		0			0
$868$	−22.4383	−	25.6998i	−0.761605	−	0.872308i
$869$			15.7850i			0.535471i
$870$		0			0
$871$	−2.01144	−	3.48392i	−0.0681550	−	0.118048i
$872$	−7.24890	−	31.1351i	−0.245479	−	1.05437i
$873$		0			0
$874$	−45.3261	−	32.4878i	−1.53318	−	1.09891i
$875$	−10.0353	−	7.73196i	−0.339253	−	0.261388i
$876$		0			0
$877$	40.6089	+	23.4456i	1.37126	+	0.791700i	0.991087	−	0.133213i	$-0.0425296\pi$
$877$	40.6089	+	23.4456i	1.37126	+	0.791700i	0.380177	+	0.924914i	$0.375863\pi$
$878$	0.797624	−	8.08933i	0.0269185	−	0.273002i
$879$		0			0
$880$	0.927211	+	7.06680i	0.0312563	+	0.238222i
$881$		−	47.5981i		−	1.60362i	−0.597579	−	0.801810i	$-0.703870\pi$
$881$		−	47.5981i		−	1.60362i	0.597579	−	0.801810i	$-0.296130\pi$
$882$		0			0
$883$	−36.2022			−1.21830			−0.609150	−	0.793055i	$-0.708489\pi$
$883$	−36.2022			−1.21830			−0.609150	+	0.793055i	$0.708489\pi$
$884$	−1.25354	+	6.29474i	−0.0421610	+	0.211715i
$885$		0			0
$886$	−1.38882	+	14.0851i	−0.0466582	+	0.473197i
$887$	21.5144	−	37.2641i	0.722384	−	1.25121i	−0.237658	−	0.971349i	$-0.576380\pi$
$887$	21.5144	−	37.2641i	0.722384	−	1.25121i	0.960042	−	0.279856i	$-0.0902868\pi$
$888$		0			0
$889$	−3.99576	+	5.18607i	−0.134013	+	0.173935i
$890$	4.00170	−	5.58307i	0.134137	−	0.187145i
$891$		0			0
$892$	−16.5079	+	18.8153i	−0.552724	+	0.629983i
$893$	45.8948	−	26.4973i	1.53581	−	0.886700i
$894$		0			0
$895$	2.79086			0.0932880
$896$	20.4020	+	21.9034i	0.681584	+	0.731740i
$897$		0			0
$898$	−49.8518	+	22.5810i	−1.66358	+	0.753537i
$899$	−41.8465	+	24.1601i	−1.39566	+	0.805785i
$900$		0			0
$901$	4.68488	−	8.11446i	0.156076	−	0.270332i
$902$	−9.01726	+	12.5807i	−0.300242	+	0.418890i
$903$		0			0
$904$	0.896313	−	2.95126i	0.0298109	−	0.0981573i
$905$	−3.43045	+	5.94171i	−0.114032	+	0.197509i
$906$		0			0
$907$	−24.4003	−	42.2626i	−0.810200	−	1.40331i	−0.912724	−	0.408576i	$-0.866025\pi$
$907$	−24.4003	−	42.2626i	−0.810200	−	1.40331i	0.102525	−	0.994730i	$-0.467308\pi$
$908$	−1.40990	+	7.07994i	−0.0467892	+	0.234956i
$909$		0			0
$910$	0.679655	−	0.722626i	0.0225303	−	0.0239548i
$911$		−	54.8706i		−	1.81794i	−0.416858	−	0.908971i	$-0.636869\pi$
$911$		−	54.8706i		−	1.81794i	0.416858	−	0.908971i	$-0.363131\pi$
$912$		0			0
$913$	23.9408	−	13.8223i	0.792326	−	0.457450i
$914$	−1.21414	+	12.3135i	−0.0401602	+	0.407296i
$915$		0			0
$916$	−10.9732	−	32.3493i	−0.362565	−	1.06885i
$917$	21.3432	+	51.8172i	0.704815	+	1.71115i
$918$		0			0
$919$	15.3943	+	8.88788i	0.507810	+	0.293184i	0.731933	−	0.681377i	$-0.238618\pi$
$919$	15.3943	+	8.88788i	0.507810	+	0.293184i	−0.224123	+	0.974561i	$0.571952\pi$
$920$	1.81778	+	7.80763i	0.0599304	+	0.257410i
$921$		0			0
$922$	−20.1227	+	9.11484i	−0.662707	+	0.300181i
$923$			5.37151i			0.176805i
$924$		0			0
$925$			0.860872i			0.0283053i
$926$	19.0699	+	42.1004i	0.626675	+	1.38350i
$927$		0			0
$928$	36.0142	−	22.3677i	1.18222	−	0.734256i
$929$	8.97118	+	5.17952i	0.294335	+	0.169934i	0.639895	−	0.768462i	$-0.278978\pi$
$929$	8.97118	+	5.17952i	0.294335	+	0.169934i	−0.345560	+	0.938397i	$0.612311\pi$
$930$		0			0
$931$	−12.5500	+	46.1058i	−0.411311	+	1.51106i
$932$	−8.63241	−	25.4486i	−0.282764	−	0.833596i
$933$		0			0
$934$	−24.2758	−	2.39365i	−0.794329	−	0.0783225i
$935$	−9.16408	+	5.29089i	−0.299698	+	0.173030i
$936$		0			0
$937$		−	39.4555i		−	1.28895i	−0.764624	−	0.644477i	$-0.777075\pi$
$937$		−	39.4555i		−	1.28895i	0.764624	−	0.644477i	$-0.222925\pi$
$938$	−8.03003	−	26.6721i	−0.262190	−	0.870874i
$939$		0			0
$940$	−7.47128	−	1.48783i	−0.243686	−	0.0485278i
$941$	−3.22053	−	5.57812i	−0.104986	−	0.181842i	0.808746	−	0.588158i	$-0.200147\pi$
$941$	−3.22053	−	5.57812i	−0.104986	−	0.181842i	−0.913733	+	0.406316i	$0.866813\pi$
$942$		0			0
$943$	−8.70466	+	15.0769i	−0.283463	+	0.490972i
$944$	11.1905	+	14.5970i	0.364221	+	0.475093i
$945$		0			0
$946$	12.0000	+	8.60107i	0.390154	+	0.279645i
$947$	−14.2748	+	24.7246i	−0.463868	+	0.803442i	−0.999150	−	0.0412311i	$-0.986872\pi$
$947$	−14.2748	+	24.7246i	−0.463868	+	0.803442i	0.535282	+	0.844673i	$0.320205\pi$
$948$		0			0
$949$	−1.77470	+	1.02462i	−0.0576092	+	0.0332607i
$950$	18.9571	+	41.8514i	0.615049	+	1.35784i
$951$		0			0
$952$	−18.4345	+	40.4372i	−0.597467	+	1.31058i
$953$	−19.9005			−0.644641			−0.322320	−	0.946631i	$-0.604463\pi$
$953$	−19.9005			−0.644641			−0.322320	+	0.946631i	$0.604463\pi$
$954$		0			0
$955$	−6.74496	+	3.89420i	−0.218262	+	0.126014i
$956$	0.161337	+	0.141551i	0.00521801	+	0.00457810i
$957$		0			0
$958$	29.1345	+	20.8824i	0.941295	+	0.674678i
$959$	1.39362	−	10.4260i	0.0450025	−	0.336672i
$960$		0			0
$961$	−5.28493	+	9.15376i	−0.170482	+	0.295283i
$962$	−0.137567	−	0.0135644i	−0.00443534	−	0.000437334i
$963$		0			0
$964$	−11.5995	+	58.2478i	−0.373594	+	1.87603i
$965$	−6.16147			−0.198345
$966$		0			0
$967$			24.1172i			0.775557i	0.921753	+	0.387778i	$0.126757\pi$
$967$			24.1172i			0.775557i	−0.921753	+	0.387778i	$0.873243\pi$
$968$	4.23175	+	4.52117i	0.136013	+	0.145316i
$969$		0			0
$970$	−5.61257	−	0.553411i	−0.180209	−	0.0177690i
$971$	−44.9204	−	25.9348i	−1.44156	−	0.832287i	−0.443609	−	0.896220i	$-0.646302\pi$
$971$	−44.9204	−	25.9348i	−1.44156	−	0.832287i	−0.997954	+	0.0639336i	$0.979635\pi$
$972$		0			0
$973$	−12.6167	+	16.3751i	−0.404472	+	0.524961i
$974$	−1.84224	+	2.57025i	−0.0590291	+	0.0823560i
$975$		0			0
$976$	39.3099	+	16.3029i	1.25828	+	0.521842i
$977$	24.5478	+	42.5181i	0.785355	+	1.36027i	0.928787	+	0.370615i	$0.120853\pi$
$977$	24.5478	+	42.5181i	0.785355	+	1.36027i	−0.143432	+	0.989660i	$0.545814\pi$
$978$		0			0
$979$		−	35.9534i		−	1.14908i
$980$	5.72715	−	3.79222i	0.182947	−	0.121138i
$981$		0			0
$982$	39.6767	−	17.9720i	1.26613	−	0.573511i
$983$	−8.32883	−	14.4260i	−0.265648	−	0.460116i	0.702085	−	0.712093i	$-0.252253\pi$
$983$	−8.32883	−	14.4260i	−0.265648	−	0.460116i	−0.967733	+	0.251977i	$0.918919\pi$
$984$		0			0
$985$	6.65530	+	3.84244i	0.212055	+	0.122430i
$986$	51.1586	+	36.6682i	1.62922	+	1.16775i
$987$		0			0
$988$	−6.98654	+	2.36990i	−0.222272	+	0.0753967i
$989$	14.3810	+	8.30289i	0.457290	+	0.264017i
$990$		0			0
$991$	−12.0877	+	6.97885i	−0.383979	+	0.221690i	−0.679548	−	0.733631i	$-0.737824\pi$
$991$	−12.0877	+	6.97885i	−0.383979	+	0.221690i	0.295569	+	0.955321i	$0.404491\pi$
$992$	17.2106	−	32.1564i	0.546437	−	1.02097i
$993$		0			0
$994$	−8.52127	+	36.2033i	−0.270278	+	1.14830i
$995$	7.65629			0.242721
$996$		0			0
$997$	−17.9524	−	31.0944i	−0.568557	−	0.984770i	−0.996709	−	0.0810634i	$-0.974168\pi$
$997$	−17.9524	−	31.0944i	−0.568557	−	0.984770i	0.428152	−	0.903707i	$-0.359165\pi$
$998$	−0.451487	+	4.57888i	−0.0142916	+	0.144942i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bk.b.19.14	yes	32
3.2	odd	2	inner	504.2.bk.b.19.3	✓	32
4.3	odd	2		2016.2.bs.b.271.9		32
7.3	odd	6	inner	504.2.bk.b.451.8	yes	32
8.3	odd	2	inner	504.2.bk.b.19.8	yes	32
8.5	even	2		2016.2.bs.b.271.7		32
12.11	even	2		2016.2.bs.b.271.8		32
21.17	even	6	inner	504.2.bk.b.451.9	yes	32
24.5	odd	2		2016.2.bs.b.271.10		32
24.11	even	2	inner	504.2.bk.b.19.9	yes	32
28.3	even	6		2016.2.bs.b.1711.7		32
56.3	even	6	inner	504.2.bk.b.451.14	yes	32
56.45	odd	6		2016.2.bs.b.1711.9		32
84.59	odd	6		2016.2.bs.b.1711.10		32
168.59	odd	6	inner	504.2.bk.b.451.3	yes	32
168.101	even	6		2016.2.bs.b.1711.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bk.b.19.3	✓	32	3.2	odd	2	inner
504.2.bk.b.19.8	yes	32	8.3	odd	2	inner
504.2.bk.b.19.9	yes	32	24.11	even	2	inner
504.2.bk.b.19.14	yes	32	1.1	even	1	trivial
504.2.bk.b.451.3	yes	32	168.59	odd	6	inner
504.2.bk.b.451.8	yes	32	7.3	odd	6	inner
504.2.bk.b.451.9	yes	32	21.17	even	6	inner
504.2.bk.b.451.14	yes	32	56.3	even	6	inner
2016.2.bs.b.271.7		32	8.5	even	2
2016.2.bs.b.271.8		32	12.11	even	2
2016.2.bs.b.271.9		32	4.3	odd	2
2016.2.bs.b.271.10		32	24.5	odd	2
2016.2.bs.b.1711.7		32	28.3	even	6
2016.2.bs.b.1711.8		32	168.101	even	6
2016.2.bs.b.1711.9		32	56.45	odd	6
2016.2.bs.b.1711.10		32	84.59	odd	6

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.28822 - 0.583515i) q^{2} +(1.31902 - 1.50339i) q^{4} +(0.245316 - 0.424900i) q^{5} +(-2.09582 - 1.61479i) q^{7} +(0.821939 - 2.70637i) q^{8} +O(q^{10})\)	\(q+(1.28822 - 0.583515i) q^{2} +(1.31902 - 1.50339i) q^{4} +(0.245316 - 0.424900i) q^{5} +(-2.09582 - 1.61479i) q^{7} +(0.821939 - 2.70637i) q^{8} +(0.0680858 - 0.690511i) q^{10} +(-1.81586 - 3.14517i) q^{11} -0.540385 q^{13} +(-3.64213 - 0.857258i) q^{14} +(-0.520366 - 3.96601i) q^{16} +(5.14304 - 2.96933i) q^{17} +(5.91166 + 3.41310i) q^{19} +(-0.315214 - 0.929259i) q^{20} +(-4.17448 - 2.99208i) q^{22} +(-5.00278 - 2.88835i) q^{23} +(2.37964 + 4.12166i) q^{25} +(-0.696135 + 0.315323i) q^{26} +(-5.19209 + 1.02090i) q^{28} +7.49445i q^{29} +(3.22373 + 5.58367i) q^{31} +(-2.98457 - 4.80545i) q^{32} +(4.89271 - 6.82619i) q^{34} +(-1.20026 + 0.494381i) q^{35} +(0.156649 + 0.0904414i) q^{37} +(9.60711 + 0.947281i) q^{38} +(-0.948301 - 1.01316i) q^{40} -3.01371i q^{41} -2.87461 q^{43} +(-7.12357 - 1.41859i) q^{44} +(-8.13007 - 0.801642i) q^{46} +(3.88172 - 6.72333i) q^{47} +(1.78493 + 6.76861i) q^{49} +(5.47055 + 3.92105i) q^{50} +(-0.712780 + 0.812410i) q^{52} +(1.36638 - 0.788878i) q^{53} -1.78184 q^{55} +(-6.09284 + 4.34480i) q^{56} +(4.37312 + 9.65450i) q^{58} +(-3.98219 + 2.29912i) q^{59} +(-5.31955 + 9.21374i) q^{61} +(7.41103 + 5.31190i) q^{62} +(-6.64883 - 4.44894i) q^{64} +(-0.132565 + 0.229610i) q^{65} +(3.72223 + 6.44710i) q^{67} +(2.31971 - 11.6486i) q^{68} +(-1.25772 + 1.33724i) q^{70} -9.94014i q^{71} +(3.28414 - 1.89610i) q^{73} +(0.254572 + 0.0251014i) q^{74} +(12.9288 - 4.38558i) q^{76} +(-1.27305 + 9.52393i) q^{77} +(-3.76412 - 2.17322i) q^{79} +(-1.81281 - 0.751823i) q^{80} +(-1.75854 - 3.88232i) q^{82} +7.61195i q^{83} -2.91370i q^{85} +(-3.70313 + 1.67738i) q^{86} +(-10.0045 + 2.32925i) q^{88} +(8.57349 + 4.94991i) q^{89} +(1.13255 + 0.872607i) q^{91} +(-10.9411 + 3.71133i) q^{92} +(1.07734 - 10.9262i) q^{94} +(2.90045 - 1.67458i) q^{95} -8.12814i q^{97} +(6.24896 + 7.67792i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{4}+O(q^{10}) \) 32 * q + 2 * q^4	\( 32 q + 2 q^{4} + 18 q^{10} - 10 q^{16} - 12 q^{22} - 16 q^{25} - 6 q^{28} - 30 q^{40} + 16 q^{43} + 16 q^{46} + 8 q^{49} - 72 q^{52} - 38 q^{58} + 44 q^{64} + 16 q^{67} - 18 q^{70} - 24 q^{73} - 96 q^{82} - 30 q^{88} - 8 q^{91} - 72 q^{94}+O(q^{100}) \) 32 * q + 2 * q^4 + 18 * q^10 - 10 * q^16 - 12 * q^22 - 16 * q^25 - 6 * q^28 - 30 * q^40 + 16 * q^43 + 16 * q^46 + 8 * q^49 - 72 * q^52 - 38 * q^58 + 44 * q^64 + 16 * q^67 - 18 * q^70 - 24 * q^73 - 96 * q^82 - 30 * q^88 - 8 * q^91 - 72 * q^94

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