LMFDB - Embedded newform 504.2.bk.b.19.9

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			19.9
Character	$\chi$	$=$	504.19
Dual form			504.2.bk.b.451.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.138771 + 1.40739i) q^{2} +(-1.96148 + 0.390611i) q^{4} +(0.245316 - 0.424900i) q^{5} +(2.09582 + 1.61479i) q^{7} +(-0.821939 - 2.70637i) q^{8} +O(q^{10})$	\(q+(0.138771 + 1.40739i) q^{2} +(-1.96148 + 0.390611i) q^{4} +(0.245316 - 0.424900i) q^{5} +(2.09582 + 1.61479i) q^{7} +(-0.821939 - 2.70637i) q^{8} +(0.632043 + 0.286291i) q^{10} +(1.81586 + 3.14517i) q^{11} +0.540385 q^{13} +(-1.98179 + 3.17372i) q^{14} +(3.69485 - 1.53235i) q^{16} +(-5.14304 + 2.96933i) q^{17} +(5.91166 + 3.41310i) q^{19} +(-0.315214 + 0.929259i) q^{20} +(-4.17448 + 2.99208i) q^{22} +(-5.00278 - 2.88835i) q^{23} +(2.37964 + 4.12166i) q^{25} +(0.0749900 + 0.760532i) q^{26} +(-4.74167 - 2.34873i) q^{28} +7.49445i q^{29} +(-3.22373 - 5.58367i) q^{31} +(2.66936 + 4.98744i) q^{32} +(-4.89271 - 6.82619i) q^{34} +(1.20026 - 0.494381i) q^{35} +(-0.156649 - 0.0904414i) q^{37} +(-3.98318 + 8.79364i) q^{38} +(-1.35157 - 0.314674i) q^{40} +3.01371i q^{41} -2.87461 q^{43} +(-4.79032 - 5.45990i) q^{44} +(3.37079 - 7.44167i) q^{46} +(3.88172 - 6.72333i) q^{47} +(1.78493 + 6.76861i) q^{49} +(-5.47055 + 3.92105i) q^{50} +(-1.05996 + 0.211080i) q^{52} +(1.36638 - 0.788878i) q^{53} +1.78184 q^{55} +(2.64757 - 6.99931i) q^{56} +(-10.5476 + 1.04002i) q^{58} +(3.98219 - 2.29912i) q^{59} +(5.31955 - 9.21374i) q^{61} +(7.41103 - 5.31190i) q^{62} +(-6.64883 + 4.44894i) q^{64} +(0.132565 - 0.229610i) q^{65} +(3.72223 + 6.44710i) q^{67} +(8.92814 - 7.83323i) q^{68} +(0.862349 + 1.62063i) q^{70} -9.94014i q^{71} +(3.28414 - 1.89610i) q^{73} +(0.105548 - 0.233017i) q^{74} +(-12.9288 - 4.38558i) q^{76} +(-1.27305 + 9.52393i) q^{77} +(3.76412 + 2.17322i) q^{79} +(0.255309 - 1.94585i) q^{80} +(-4.24146 + 0.418216i) q^{82} -7.61195i q^{83} +2.91370i q^{85} +(-0.398914 - 4.04569i) q^{86} +(7.01944 - 7.49952i) q^{88} +(-8.57349 - 4.94991i) q^{89} +(1.13255 + 0.872607i) q^{91} +(10.9411 + 3.71133i) q^{92} +(10.0010 + 4.53008i) q^{94} +(2.90045 - 1.67458i) q^{95} -8.12814i q^{97} +(-9.27836 + 3.45138i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.138771	+	1.40739i	0.0981262	+	0.995174i
$2$	0.138771	+	1.40739i	0.0981262	+	0.995174i
$3$		0			0
$3$		0			0
$4$	−1.96148	+	0.390611i	−0.980742	+	0.195305i
$5$	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
$10$	0.632043	+	0.286291i	0.199869	+	0.0905333i
$11$	1.81586	+	3.14517i	0.547503	+	0.948303i	0.998445	+	0.0557498i	$0.0177549\pi$
$11$	1.81586	+	3.14517i	0.547503	+	0.948303i	−0.450942	+	0.892553i	$0.648912\pi$
$12$		0			0
$13$	0.540385			0.149876			0.0749380	−	0.997188i	$-0.476124\pi$
$13$	0.540385			0.149876			0.0749380	+	0.997188i	$0.476124\pi$
$14$	−1.98179	+	3.17372i	−0.529656	+	0.848212i
$15$		0			0
$16$	3.69485	−	1.53235i	0.923712	−	0.383088i
$17$	−5.14304	+	2.96933i	−1.24737	+	0.720169i	−0.970584	−	0.240762i	$-0.922603\pi$
$17$	−5.14304	+	2.96933i	−1.24737	+	0.720169i	−0.276786	+	0.960932i	$0.589269\pi$
$18$		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
$26$	0.0749900	+	0.760532i	0.0147068	+	0.149153i
$27$		0			0
$28$	−4.74167	−	2.34873i	−0.896092	−	0.443868i
$29$			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	$-0.970110\pi$
$31$	−3.22373	−	5.58367i	−0.579000	−	1.00286i	0.416595	−	0.909092i	$-0.363223\pi$
$32$	2.66936	+	4.98744i	0.471880	+	0.881663i
$33$		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	0.487068	−	0.873364i	$-0.338066\pi$
$37$	−0.156649	−	0.0904414i	−0.0257530	−	0.0148685i	−0.512821	+	0.858495i	$0.671400\pi$
$38$	−3.98318	+	8.79364i	−0.646158	+	1.42652i
$39$		0			0
$40$	−1.35157	−	0.314674i	−0.213702	−	0.0497543i
$41$			3.01371i			0.470662i	0.971915	+	0.235331i	$0.0756174\pi$
$41$			3.01371i			0.470662i	−0.971915	+	0.235331i	$0.924383\pi$
$42$		0			0
$43$	−2.87461			−0.438374			−0.219187	−	0.975683i	$-0.570340\pi$
$43$	−2.87461			−0.438374			−0.219187	+	0.975683i	$0.570340\pi$
$44$	−4.79032	−	5.45990i	−0.722168	−	0.823111i
$45$		0			0
$46$	3.37079	−	7.44167i	0.496997	−	1.09721i
$47$	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
$52$	−1.05996	+	0.211080i	−0.146990	+	0.0292716i
$53$	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
$56$	2.64757	−	6.99931i	0.353796	−	0.935323i
$57$		0			0
$58$	−10.5476	+	1.04002i	−1.38497	+	0.136561i
$59$	3.98219	−	2.29912i	0.518438	−	0.299320i	−0.217858	−	0.975981i	$-0.569907\pi$
$59$	3.98219	−	2.29912i	0.518438	−	0.299320i	0.736295	+	0.676661i	$0.236574\pi$
$60$		0			0
$61$	5.31955	−	9.21374i	0.681099	−	1.17970i	−0.293547	−	0.955945i	$-0.594836\pi$
$61$	5.31955	−	9.21374i	0.681099	−	1.17970i	0.974646	−	0.223754i	$-0.0718311\pi$
$62$	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	$0.683064\pi$
$68$	8.92814	−	7.83323i	1.08270	−	0.949919i
$69$		0			0
$70$	0.862349	+	1.62063i	0.103070	+	0.193702i
$71$		−	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	$0.262100\pi$
$74$	0.105548	−	0.233017i	0.0122697	−	0.0270877i
$75$		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	0.696572	−	0.717487i	$-0.254708\pi$
$79$	3.76412	+	2.17322i	0.423497	+	0.244506i	−0.273076	+	0.961993i	$0.588041\pi$
$80$	0.255309	−	1.94585i	0.0285444	−	0.217553i
$81$		0			0
$82$	−4.24146	+	0.418216i	−0.468391	+	0.0461843i
$83$		−	7.61195i		−	0.835520i	−0.908557	−	0.417760i	$-0.862815\pi$
$83$		−	7.61195i		−	0.835520i	0.908557	−	0.417760i	$-0.137185\pi$
$84$		0			0
$85$			2.91370i			0.316036i
$86$	−0.398914	−	4.04569i	−0.0430160	−	0.436258i
$87$		0			0
$88$	7.01944	−	7.49952i	0.748275	−	0.799452i
$89$	−8.57349	−	4.94991i	−0.908788	−	0.524689i	−0.0287469	−	0.999587i	$-0.509152\pi$
$89$	−8.57349	−	4.94991i	−0.908788	−	0.524689i	−0.880041	+	0.474898i	$0.842485\pi$
$90$		0			0
$91$	1.13255	+	0.872607i	0.118724	+	0.0914741i
$92$	10.9411	+	3.71133i	1.14069	+	0.386933i
$93$		0			0
$94$	10.0010	+	4.53008i	1.03153	+	0.467242i
$95$	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	$-0.135395\pi$
$98$	−9.27836	+	3.45138i	−0.937256	+	0.348642i
$99$		0			0
$100$	−6.27759	−	7.15506i	−0.627759	−	0.715506i
$101$	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	−0.719966	−	0.694009i	$-0.755843\pi$
$103$	2.44636	−	4.23721i	0.241047	−	0.417505i	0.961013	+	0.276504i	$0.0891760\pi$
$104$	−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	$-0.585261\pi$
$107$	7.26995	−	12.5919i	0.702813	−	1.21731i	0.967475	−	0.252966i	$-0.0814061\pi$
$108$		0			0
$109$	−9.78810	+	5.65117i	−0.937530	+	0.541283i	−0.889185	−	0.457547i	$-0.848728\pi$
$109$	−9.78810	+	5.65117i	−0.937530	+	0.541283i	−0.0483451	+	0.998831i	$0.515395\pi$
$110$	0.247269	+	2.50774i	0.0235762	+	0.239104i
$111$		0			0
$112$	10.2182	+	2.75485i	0.965525	+	0.260309i
$113$	−1.09049			−0.102584			−0.0512922	−	0.998684i	$-0.516334\pi$
$113$	−1.09049			−0.102584			−0.0512922	+	0.998684i	$0.516334\pi$
$114$		0			0
$115$	−2.45453	+	1.41712i	−0.228886	+	0.132147i
$116$	−2.92741	−	14.7002i	−0.271803	−	1.36488i
$117$		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
$122$	13.7055	+	6.20808i	1.24084	+	0.562053i
$123$		0			0
$124$	8.50435	+	9.69306i	0.763713	+	0.870463i
$125$	4.78822			0.428272
$126$		0			0
$127$			2.47448i			0.219575i	0.993955	+	0.109787i	$0.0350170\pi$
$127$			2.47448i			0.219575i	−0.993955	+	0.109787i	$0.964983\pi$
$128$	−7.18405	−	8.74011i	−0.634986	−	0.772524i
$129$		0			0
$130$	0.341547	+	0.154708i	0.0299556	+	0.0135688i
$131$	18.3436	+	10.5907i	1.60269	+	0.925313i	0.990947	+	0.134255i	$0.0428642\pi$
$131$	18.3436	+	10.5907i	1.60269	+	0.925313i	0.611742	+	0.791058i	$0.290469\pi$
$132$		0			0
$133$	6.87835	+	16.6993i	0.596428	+	1.44801i
$134$	−8.55703	+	6.13330i	−0.739215	+	0.529836i
$135$		0			0
$136$	12.2634	+	11.4783i	1.05158	+	0.984259i
$137$	−1.98785	−	3.44305i	−0.169833	−	0.294160i	0.768528	−	0.639816i	$-0.220990\pi$
$137$	−1.98785	−	3.44305i	−0.169833	−	0.294160i	−0.938361	+	0.345657i	$0.887656\pi$
$138$		0			0
$139$		−	7.81321i		−	0.662708i	−0.943507	−	0.331354i	$-0.892495\pi$
$139$		−	7.81321i		−	0.662708i	0.943507	−	0.331354i	$-0.107505\pi$
$140$	−2.16119	+	1.43856i	−0.182654	+	0.121580i
$141$		0			0
$142$	13.9896	−	1.37941i	1.17398	−	0.115757i
$143$	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	−0.895181	−	0.445703i	$-0.852954\pi$
$151$	−11.7571	+	6.78798i	−0.956781	+	0.552398i	−0.0616000	+	0.998101i	$0.519620\pi$
$152$	4.37807	−	18.8045i	0.355108	−	1.52524i
$153$		0			0
$154$	−13.5805	−	0.470027i	−1.09435	−	0.0378758i
$155$	−3.16334			−0.254085
$156$		0			0
$157$	−10.3258	−	17.8848i	−0.824089	−	1.42736i	−0.902613	−	0.430453i	$-0.858354\pi$
$157$	−10.3258	−	17.8848i	−0.824089	−	1.42736i	0.0785237	−	0.996912i	$-0.474979\pi$
$158$	−2.53621	+	5.59916i	−0.201770	+	0.445445i
$159$		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	$0.0450728\pi$
$164$	−1.17719	−	5.91134i	−0.0919228	−	0.461598i
$165$		0			0
$166$	10.7130	−	1.05632i	0.831488	−	0.0819864i
$167$	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
$170$	−4.10071	+	0.404339i	−0.314510	+	0.0310114i
$171$		0			0
$172$	5.63850	−	1.12285i	0.429932	−	0.0856167i
$173$	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
$178$	5.77669	−	12.7531i	0.432981	−	0.955888i
$179$	−2.84414	−	4.92620i	−0.212581	−	0.368201i	0.739941	−	0.672672i	$-0.234854\pi$
$179$	−2.84414	−	4.92620i	−0.212581	−	0.368201i	−0.952522	+	0.304471i	$0.901520\pi$
$180$		0			0
$181$	13.9838			1.03941			0.519703	−	0.854347i	$-0.326043\pi$
$181$	13.9838			1.03941			0.519703	+	0.854347i	$0.326043\pi$
$182$	−1.07093	+	1.71503i	−0.0793827	+	0.127127i
$183$		0			0
$184$	−3.70497	+	15.9134i	−0.273134	+	1.17315i
$185$	−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	$0.982615\pi$
$194$	11.4395	−	1.12795i	0.821305	−	0.0809824i
$195$		0			0
$196$	−6.14500	−	12.5793i	−0.438928	−	0.898522i
$197$			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	$-0.980110\pi$
$199$	−7.80247	−	13.5143i	−0.553102	−	0.958001i	0.444946	−	0.895557i	$-0.353223\pi$
$200$	9.19879	−	9.82793i	0.650453	−	0.694939i
$201$		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
$206$	6.30289	+	2.85497i	0.439143	+	0.198915i
$207$		0			0
$208$	1.99664	−	0.828061i	0.138442	−	0.0574157i
$209$			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	$0.595315\pi$
$212$	−2.37198	+	2.08109i	−0.162908	+	0.142930i
$213$		0			0
$214$	18.7306	+	8.48425i	1.28040	+	0.579971i
$215$	−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
$220$	−3.49506	+	0.696007i	−0.235637	+	0.0469248i
$221$	−2.77922	+	1.60458i	−0.186951	+	0.107936i
$222$		0			0
$223$	12.5152			0.838082			0.419041	−	0.907967i	$-0.362366\pi$
$223$	12.5152			0.838082			0.419041	+	0.907967i	$0.362366\pi$
$224$	−2.45916	+	14.7632i	−0.164309	+	0.986409i
$225$		0			0
$226$	−0.151328	−	1.53474i	−0.0100662	−	0.102089i
$227$	3.12590	−	1.80474i	0.207473	−	0.119785i	−0.392663	−	0.919682i	$-0.628446\pi$
$227$	3.12590	−	1.80474i	0.207473	−	0.119785i	0.600137	+	0.799898i	$0.295113\pi$
$228$		0			0
$229$	−8.53993	+	14.7916i	−0.564335	+	0.977456i	0.432777	+	0.901501i	$0.357534\pi$
$229$	−8.53993	+	14.7916i	−0.564335	+	0.977456i	−0.997111	+	0.0759550i	$0.975799\pi$
$230$	−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	−0.997698	−	0.0678096i	$-0.978399\pi$
$233$	−6.71821	+	11.6363i	−0.440124	+	0.762318i	0.557574	+	0.830127i	$0.311732\pi$
$234$		0			0
$235$	−1.90450	−	3.29869i	−0.124236	−	0.215183i
$236$	−6.91295	+	6.06518i	−0.449995	+	0.394809i
$237$		0			0
$238$	0.768597	−	22.2072i	0.0498208	−	1.43948i
$239$			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	$0.927635\pi$
$242$	−2.82046	−	1.27756i	−0.181306	−	0.0821248i
$243$		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
$248$	−12.4617	+	13.3140i	−0.791322	+	0.845443i
$249$		0			0
$250$	0.664468	+	6.73889i	0.0420247	+	0.426205i
$251$		−	5.63442i		−	0.355642i	−0.984063	−	0.177821i	$-0.943095\pi$
$251$		−	5.63442i		−	0.355642i	0.984063	−	0.177821i	$-0.0569048\pi$
$252$		0			0
$253$		−	20.9794i		−	1.31896i
$254$	−3.48256	+	0.343387i	−0.218515	+	0.0215460i
$255$		0			0
$256$	11.3038	−	11.3236i	0.706487	−	0.707727i
$257$	5.46388	+	3.15457i	0.340827	+	0.196777i	0.660638	−	0.750705i	$-0.270286\pi$
$257$	5.46388	+	3.15457i	0.340827	+	0.196777i	−0.319811	+	0.947482i	$0.603619\pi$
$258$		0			0
$259$	−0.182265	−	0.442504i	−0.0113254	−	0.0274959i
$260$	−0.170337	+	0.502158i	−0.0105638	+	0.0311425i
$261$		0			0
$262$	−12.3596	+	27.2863i	−0.763581	+	1.68575i
$263$	−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
$266$	−22.5479	+	11.9979i	−1.38250	+	0.735638i
$267$		0			0
$268$	−9.81941	−	11.1919i	−0.599816	−	0.683656i
$269$	−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	−0.613403	−	0.789770i	$-0.710200\pi$
$271$	6.21048	−	10.7569i	0.377260	−	0.653433i	0.990662	+	0.136337i	$0.0435331\pi$
$272$	−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	−0.972409	−	0.233283i	$-0.925053\pi$
$277$	−20.9137	+	12.0746i	−1.25658	+	0.725490i	−0.284176	+	0.958772i	$0.591720\pi$
$278$	10.9962	−	1.08425i	0.659510	−	0.0650290i
$279$		0			0
$280$	−2.32452	−	2.84200i	−0.138917	−	0.169842i
$281$	28.6773			1.71074			0.855371	−	0.518016i	$-0.173329\pi$
$281$	28.6773			1.71074			0.855371	+	0.518016i	$0.173329\pi$
$282$		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	$0.343638\pi$
$284$	3.88273	+	19.4974i	0.230397	+	1.15696i
$285$		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
$290$	−2.14560	+	4.73681i	−0.125994	+	0.278155i
$291$		0			0
$292$	−5.70115	+	5.00198i	−0.333635	+	0.292719i
$293$	−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
$296$	−0.116012	+	0.498287i	−0.00674303	+	0.0289624i
$297$		0			0
$298$	6.31682	−	13.9456i	0.365923	−	0.807846i
$299$	−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
$304$	27.0727	+	3.55212i	1.55273	+	0.203728i
$305$	−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	$-0.0734749\pi$
$308$	−1.22308	−	19.1783i	−0.0696915	−	1.09279i
$309$		0			0
$310$	−0.438981	−	4.45205i	−0.0249324	−	0.252859i
$311$	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
$320$	0.259287	+	3.91649i	0.0144946	+	0.218938i
$321$		0			0
$322$	19.0813	−	10.1533i	1.06336	−	0.565821i
$323$	−40.5385			−2.25562
$324$		0			0
$325$	1.28592	+	2.22728i	0.0713301	+	0.123547i
$326$	12.2620	+	5.55422i	0.679129	+	0.307620i
$327$		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	$0.973274\pi$
$332$	2.97331	+	14.9307i	0.163181	+	0.819430i
$333$		0			0
$334$	2.66155	+	26.9928i	0.145633	+	1.47698i
$335$	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	$0.336137\pi$
$338$	−1.76350	−	17.8851i	−0.0959220	−	0.972820i
$339$		0			0
$340$	−1.13812	−	5.71519i	−0.0617234	−	0.309950i
$341$	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
$346$	21.5066	+	9.74165i	1.15620	+	0.523714i
$347$	10.4646	+	18.1251i	0.561767	+	0.973009i	0.997342	+	0.0728567i	$0.0232116\pi$
$347$	10.4646	+	18.1251i	0.561767	+	0.973009i	−0.435575	+	0.900152i	$0.643455\pi$
$348$		0			0
$349$	7.83482			0.419388			0.209694	−	0.977767i	$-0.432753\pi$
$349$	7.83482			0.419388			0.209694	+	0.977767i	$0.432753\pi$
$350$	−17.7969	−	0.615958i	−0.951286	−	0.0329243i
$351$		0			0
$352$	−10.8391	+	17.4521i	−0.577728	+	0.930198i
$353$	−19.2573	+	11.1182i	−1.02496	+	0.591761i	−0.915537	−	0.402234i	$-0.868234\pi$
$353$	−19.2573	+	11.1182i	−1.02496	+	0.591761i	−0.109424	+	0.993995i	$0.534900\pi$
$354$		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
$362$	1.94055	+	19.6806i	0.101993	+	1.03439i
$363$		0			0
$364$	−2.56233	−	1.26922i	−0.134303	−	0.0665252i
$365$		−	1.86057i		−	0.0973869i
$366$		0			0
$367$	−4.03835	−	6.99463i	−0.210800	−	0.365117i	0.741165	−	0.671323i	$-0.234274\pi$
$367$	−4.03835	−	6.99463i	−0.210800	−	0.365117i	−0.951965	+	0.306206i	$0.900940\pi$
$368$	−22.9105	−	3.00600i	−1.19429	−	0.156699i
$369$		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	0.987879	−	0.155228i	$-0.0496112\pi$
$373$	26.0224	+	15.0240i	1.34739	+	0.777914i	0.359508	+	0.933142i	$0.382945\pi$
$374$	12.5850	−	27.7838i	0.650756	−	1.43667i
$375$		0			0
$376$	−21.3863	−	4.97918i	−1.10292	−	0.256782i
$377$			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	$0.225434\pi$
$380$	−5.03508	+	4.41760i	−0.258294	+	0.226618i
$381$		0			0
$382$	9.26284	−	20.4495i	0.473928	−	1.04629i
$383$	−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
$388$	3.17494	+	15.9432i	0.161183	+	0.809395i
$389$	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
$392$	16.8512	−	10.3940i	0.851115	−	0.524979i
$393$		0			0
$394$	−22.0442	+	2.17360i	−1.11057	+	0.109505i
$395$	1.84680	−	1.06625i	0.0929226	−	0.0536489i
$396$		0			0
$397$	14.0866	−	24.3987i	0.706985	−	1.22453i	−0.258986	−	0.965881i	$-0.583388\pi$
$397$	14.0866	−	24.3987i	0.706985	−	1.22453i	0.965970	−	0.258652i	$-0.0832784\pi$
$398$	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	$-0.497606\pi$
$401$	17.4170	−	30.1671i	0.869761	−	1.50647i	0.862240	−	0.506499i	$-0.169061\pi$
$402$		0			0
$403$	−1.74206	−	3.01733i	−0.0867781	−	0.150304i
$404$	−23.4377	−	26.7137i	−1.16607	−	1.32906i
$405$		0			0
$406$	−23.7853	−	14.8524i	−1.18044	−	0.737114i
$407$		−	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	$0.232909\pi$
$410$	−0.862798	+	1.90479i	−0.0426106	+	0.0940710i
$411$		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
$416$	1.44248	+	2.69514i	0.0707234	+	0.132140i
$417$		0			0
$418$	−34.8904	+	3.44026i	−1.70654	+	0.168269i
$419$		−	29.2112i		−	1.42706i	−0.700624	−	0.713531i	$-0.747095\pi$
$419$		−	29.2112i		−	1.42706i	0.700624	−	0.713531i	$-0.252905\pi$
$420$		0			0
$421$			22.6705i			1.10489i	0.833549	+	0.552446i	$0.186305\pi$
$421$			22.6705i			1.10489i	−0.833549	+	0.552446i	$0.813695\pi$
$422$	−1.18925	−	12.0611i	−0.0578918	−	0.587126i
$423$		0			0
$424$	−3.25807	−	3.04950i	−0.158226	−	0.148097i
$425$	−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
$430$	−1.81688	−	0.822976i	−0.0876175	−	0.0396874i
$431$	−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	$0.892818\pi$
$434$	24.1098	+	0.834447i	1.15731	+	0.0400548i
$435$		0			0
$436$	16.9918	−	14.9080i	0.813760	−	0.713964i
$437$	−19.7165	−	34.1499i	−0.943166	−	1.63361i
$438$		0			0
$439$	−2.87388	+	4.97770i	−0.137163	+	0.237573i	−0.926422	−	0.376488i	$-0.877132\pi$
$439$	−2.87388	+	4.97770i	−0.137163	+	0.237573i	0.789259	+	0.614061i	$0.210465\pi$
$440$	−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	−0.722321	−	0.691558i	$-0.756925\pi$
$443$	5.00397	−	8.66713i	0.237746	−	0.411788i	0.960067	+	0.279770i	$0.0902581\pi$
$444$		0			0
$445$	−4.20643	+	2.42859i	−0.199404	+	0.115126i
$446$	1.73676	+	17.6138i	0.0822379	+	0.834038i
$447$		0			0
$448$	−21.1188	−	1.41228i	−0.997771	−	0.0667238i
$449$	38.6982			1.82628			0.913140	−	0.407645i	$-0.133650\pi$
$449$	38.6982			1.82628			0.913140	+	0.407645i	$0.133650\pi$
$450$		0			0
$451$	−9.47861	+	5.47248i	−0.446330	+	0.257689i
$452$	2.13897	−	0.425956i	0.100609	−	0.0200353i
$453$		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	$0.232268\pi$
$458$	−22.0026	−	9.96635i	−1.02811	−	0.465697i
$459$		0			0
$460$	4.26097	−	3.73843i	0.198669	−	0.174305i
$461$	−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	$-0.725488\pi$
$463$		−	32.6811i		−	1.51882i	0.650614	−	0.759409i	$-0.274512\pi$
$464$	11.4841	+	27.6908i	0.533138	+	1.28551i
$465$		0			0
$466$	−17.3091	−	7.84034i	−0.801826	−	0.363197i
$467$	14.9379	+	8.62442i	0.691245	+	0.399091i	0.804078	−	0.594523i	$-0.202659\pi$
$467$	14.9379	+	8.62442i	0.691245	+	0.399091i	−0.112833	+	0.993614i	$0.535993\pi$
$468$		0			0
$469$	−2.60955	+	19.5226i	−0.120498	+	0.901468i
$470$	4.37824	−	3.13813i	0.201953	−	0.144751i
$471$		0			0
$472$	−9.49538	−	8.88754i	−0.437060	−	0.409082i
$473$	−5.21989	−	9.04112i	−0.240011	−	0.415711i
$474$		0			0
$475$			32.4878i			1.49064i
$476$	31.3608	−	2.00000i	1.43742	−	0.0916701i
$477$		0			0
$478$	−0.151034	+	0.0148923i	−0.00690815	+	0.000681158i
$479$	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	−0.455482	−	0.890245i	$-0.650533\pi$
$487$	1.93649	−	1.11803i	0.0877509	−	0.0506630i	0.543233	+	0.839582i	$0.317200\pi$
$488$	−29.3081	−	6.82353i	−1.32672	−	0.308887i
$489$		0			0
$490$	−0.809643	+	4.78906i	−0.0365759	+	0.216348i
$491$	−30.7996			−1.38997			−0.694984	−	0.719025i	$-0.744589\pi$
$491$	−30.7996			−1.38997			−0.694984	+	0.719025i	$0.744589\pi$
$492$		0			0
$493$	−22.2535	−	38.5442i	−1.00225	−	1.73594i
$494$	−2.15245	+	4.75195i	−0.0968435	+	0.213800i
$495$		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	$0.189867\pi$
$500$	−9.39202	+	1.87033i	−0.420024	+	0.0836437i
$501$		0			0
$502$	7.92982	−	0.781897i	0.353925	−	0.0348978i
$503$	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
$506$	29.5262	−	2.91134i	1.31260	−	0.129425i
$507$		0			0
$508$	−0.966559	−	4.85366i	−0.0428841	−	0.215346i
$509$	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
$514$	−3.68148	+	8.12756i	−0.162383	+	0.358491i
$515$	−1.20026	−	2.07892i	−0.0528899	−	0.0916080i
$516$		0			0
$517$	28.1947			1.24000
$518$	0.597482	−	0.317924i	0.0262518	−	0.0139688i
$519$		0			0
$520$	−0.730369	−	0.170045i	−0.0320288	−	0.00745696i
$521$	18.4368	−	10.6445i	0.807729	−	0.466343i	−0.0384377	−	0.999261i	$-0.512238\pi$
$521$	18.4368	−	10.6445i	0.807729	−	0.466343i	0.846167	+	0.532918i	$0.178905\pi$
$522$		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
$530$	1.08946	−	0.107423i	0.0473230	−	0.00466615i
$531$		0			0
$532$	−20.0147	−	30.0687i	−0.867747	−	1.30364i
$533$			1.62856i			0.0705409i
$534$		0			0
$535$	−3.56687	−	6.17801i	−0.154209	−	0.267099i
$536$	14.3888	−	15.3728i	0.621499	−	0.664006i
$537$		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	−0.166837	−	0.985984i	$-0.553356\pi$
$541$	−25.6817	−	14.8274i	−1.10414	−	0.637478i	−0.937306	+	0.348507i	$0.886689\pi$
$542$	16.0009	+	7.24781i	0.687298	+	0.311320i
$543$		0			0
$544$	−28.5380	−	17.7244i	−1.22356	−	0.759926i
$545$			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	$0.578577\pi$
$548$	5.24402	+	5.97702i	0.224014	+	0.255326i
$549$		0			0
$550$	−22.2661	−	10.0857i	−0.949430	−	0.430056i
$551$	−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
$556$	3.05192	+	15.3255i	0.129430	+	0.649946i
$557$	−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
$560$	3.67722	−	3.66589i	0.155391	−	0.154912i
$561$		0			0
$562$	3.97958	+	40.3600i	0.167869	+	1.70249i
$563$	−6.43843	+	3.71723i	−0.271347	+	0.156662i	−0.629500	−	0.777001i	$-0.716740\pi$
$563$	−6.43843	+	3.71723i	−0.271347	+	0.156662i	0.358152	+	0.933663i	$0.383407\pi$
$564$		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	$0.382098\pi$
$569$	−14.9396	+	25.8761i	−0.626300	+	1.08478i	−0.988288	+	0.152600i	$0.951235\pi$
$570$		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	$0.643351\pi$
$572$	−2.58862	−	2.95045i	−0.108236	−	0.123365i
$573$		0			0
$574$	−9.56466	−	5.97254i	−0.399221	−	0.249289i
$575$		−	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	$0.264710\pi$
$578$	23.5329	+	10.6595i	0.978840	+	0.443377i
$579$		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
$584$	−7.83089	−	7.32960i	−0.324045	−	0.303301i
$585$		0			0
$586$	−3.69671	−	37.4912i	−0.152710	−	1.54875i
$587$		−	33.9395i		−	1.40083i	−0.713734	−	0.700417i	$-0.752997\pi$
$587$		−	33.9395i		−	1.40083i	0.713734	−	0.700417i	$-0.247003\pi$
$588$		0			0
$589$		−	44.0117i		−	1.81347i
$590$	3.17514	−	0.313075i	0.130718	−	0.0128891i
$591$		0			0
$592$	−0.717383	−	0.0941253i	−0.0294843	−	0.00386853i
$593$	−8.72720	−	5.03865i	−0.358383	−	0.206913i	0.309988	−	0.950740i	$-0.399675\pi$
$593$	−8.72720	−	5.03865i	−0.358383	−	0.206913i	−0.668371	+	0.743828i	$0.733008\pi$
$594$		0			0
$595$	−4.70501	+	6.10660i	−0.192887	+	0.250346i
$596$	20.5034	+	6.95497i	0.839854	+	0.284887i
$597$		0			0
$598$	1.82153	−	4.02137i	0.0744878	−	0.164446i
$599$	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	$0.958243\pi$
$602$	5.69688	−	9.12320i	0.232187	−	0.371834i
$603$		0			0
$604$	20.4100	−	17.9070i	0.830469	−	0.728624i
$605$	0.537102	+	0.930287i	0.0218363	+	0.0378216i
$606$		0			0
$607$	−6.87499	+	11.9078i	−0.279047	+	0.483324i	−0.971148	−	0.238477i	$-0.923352\pi$
$607$	−6.87499	+	11.9078i	−0.279047	+	0.483324i	0.692101	+	0.721801i	$0.256685\pi$
$608$	−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	−0.667971	−	0.744188i	$-0.732837\pi$
$613$	−8.85055	+	5.10987i	−0.357470	+	0.206386i	0.310500	+	0.950573i	$0.399503\pi$
$614$	11.2834	−	1.11256i	0.455359	−	0.0448994i
$615$		0			0
$616$	26.8216	−	4.38275i	1.08067	−	0.176586i
$617$	16.3216			0.657084			0.328542	−	0.944489i	$-0.393443\pi$
$617$	16.3216			0.657084			0.328542	+	0.944489i	$0.393443\pi$
$618$		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	$0.463755\pi$
$620$	6.20484	−	1.23563i	0.249192	−	0.0496242i
$621$		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
$626$	9.55298	−	21.0900i	0.381814	−	0.842927i
$627$		0			0
$628$	27.2399	+	31.0475i	1.08699	+	1.23893i
$629$	1.07420			0.0428313
$630$		0			0
$631$			7.43503i			0.295984i	0.988989	+	0.147992i	$0.0472810\pi$
$631$			7.43503i			0.295984i	−0.988989	+	0.147992i	$0.952719\pi$
$632$	2.78764	−	11.9733i	0.110886	−	0.476274i
$633$		0			0
$634$	5.36486	−	11.8440i	0.213066	−	0.470384i
$635$	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
$640$	−5.47604	+	0.908414i	−0.216459	+	0.0359082i
$641$	8.43079	+	14.6026i	0.332996	+	0.576767i	0.983098	−	0.183081i	$-0.0586070\pi$
$641$	8.43079	+	14.6026i	0.332996	+	0.576767i	−0.650102	+	0.759847i	$0.725274\pi$
$642$		0			0
$643$		−	26.7506i		−	1.05494i	−0.849573	−	0.527470i	$-0.823141\pi$
$643$		−	26.7506i		−	1.05494i	0.849573	−	0.527470i	$-0.176859\pi$
$644$	16.9376	+	25.4458i	0.667434	+	1.00271i
$645$		0			0
$646$	−5.62558	−	57.0534i	−0.221336	−	2.24474i
$647$	−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
$656$	4.61807	+	11.1352i	0.180305	+	0.434756i
$657$		0			0
$658$	13.6452	+	25.6437i	0.531946	+	0.999697i
$659$	−4.22125			−0.164436			−0.0822182	−	0.996614i	$-0.526200\pi$
$659$	−4.22125			−0.164436			−0.0822182	+	0.996614i	$0.526200\pi$
$660$		0			0
$661$	19.5197	+	33.8091i	0.759227	+	1.31502i	0.943245	+	0.332097i	$0.107756\pi$
$661$	19.5197	+	33.8091i	0.759227	+	1.31502i	−0.184018	+	0.982923i	$0.558910\pi$
$662$	−26.7589	−	12.1208i	−1.04002	−	0.471087i
$663$		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
$668$	−37.6200	+	7.49166i	−1.45556	+	0.289861i
$669$		0			0
$670$	0.506862	+	5.14048i	0.0195818	+	0.198594i
$671$	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	$0.520744\pi$
$674$	2.50854	+	25.4410i	0.0966253	+	0.979952i
$675$		0			0
$676$	24.9265	−	4.96387i	0.958712	−	0.190918i
$677$	−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
$682$	30.1642	+	13.6632i	1.15505	+	0.523193i
$683$	1.51296	+	2.62052i	0.0578918	+	0.100272i	0.893519	−	0.449026i	$-0.148229\pi$
$683$	1.51296	+	2.62052i	0.0578918	+	0.100272i	−0.835627	+	0.549297i	$0.814895\pi$
$684$		0			0
$685$	−1.95061			−0.0745288
$686$	−25.0190	−	7.74911i	−0.955231	−	0.295862i
$687$		0			0
$688$	−10.6212	+	4.40492i	−0.404931	+	0.167936i
$689$	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
$698$	1.08725	+	11.0266i	0.0411530	+	0.417364i
$699$		0			0
$700$	−1.60281	−	25.1327i	−0.0605807	−	0.949926i
$701$			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
$704$	−26.0660	−	12.8330i	−0.982399	−	0.483663i
$705$		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	0.841243	−	0.540657i	$-0.181824\pi$
$709$	21.1323	+	12.2008i	0.793641	+	0.458209i	−0.0476017	+	0.998866i	$0.515158\pi$
$710$	2.84578	−	6.28260i	0.106800	−	0.235782i
$711$		0			0
$712$	−6.34937	+	27.2715i	−0.237953	+	1.02204i
$713$			37.2452i			1.39484i
$714$		0			0
$715$	0.962882			0.0360097
$716$	7.50296	+	8.55171i	0.280399	+	0.319592i
$717$		0			0
$718$	−12.0040	+	26.5012i	−0.447987	+	0.989017i
$719$	−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
$724$	−27.4290	+	5.46221i	−1.01939	+	0.203002i
$725$	−30.8895	+	17.8341i	−1.14721	+	0.662341i
$726$		0			0
$727$	−41.3827			−1.53480			−0.767400	−	0.641168i	$-0.778450\pi$
$727$	−41.3827			−1.53480			−0.767400	+	0.641168i	$0.778450\pi$
$728$	1.43071	−	3.78233i	0.0530255	−	0.140182i
$729$		0			0
$730$	2.61855	−	0.258195i	0.0969169	−	0.00955621i
$731$	14.7842	−	8.53567i	0.546814	−	0.315703i
$732$		0			0
$733$	−0.977981	+	1.69391i	−0.0361226	+	0.0625661i	−0.883521	−	0.468391i	$-0.844834\pi$
$733$	−0.977981	+	1.69391i	−0.0361226	+	0.0625661i	0.847399	+	0.530957i	$0.178167\pi$
$734$	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	$0.766969\pi$
$740$	0.133421	−	0.117059i	0.00490467	−	0.00430318i
$741$		0			0
$742$	−0.204197	+	5.89989i	−0.00749631	+	0.216592i
$743$		−	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
$746$	−17.5335	+	38.7085i	−0.641946	+	1.41722i
$747$		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	0.859660	−	0.510866i	$-0.170675\pi$
$751$	23.2134	+	13.4022i	0.847067	+	0.489055i	−0.0125930	+	0.999921i	$0.504009\pi$
$752$	4.03983	−	30.7898i	0.147317	−	1.12279i
$753$		0			0
$754$	−5.69977	+	0.562009i	−0.207573	+	0.0204672i
$755$			6.66080i			0.242411i
$756$		0			0
$757$			51.1768i			1.86005i	0.367494	+	0.930026i	$0.380216\pi$
$757$			51.1768i			1.86005i	−0.367494	+	0.930026i	$0.619784\pi$
$758$	4.10382	+	41.6200i	0.149058	+	1.51171i
$759$		0			0
$760$	−6.91601	−	6.47328i	−0.250870	−	0.234811i
$761$	−26.1897	−	15.1207i	−0.949377	−	0.548123i	−0.0564899	−	0.998403i	$-0.517991\pi$
$761$	−26.1897	−	15.1207i	−0.949377	−	0.548123i	−0.892887	+	0.450280i	$0.851324\pi$
$762$		0			0
$763$	−29.6395	−	3.96187i	−1.07302	−	0.143429i
$764$	30.0658	+	10.1986i	1.08774	+	0.368973i
$765$		0			0
$766$	−19.2907	−	8.73797i	−0.697002	−	0.315716i
$767$	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	$-0.136717\pi$
$770$	−3.53124	+	5.65507i	−0.127257	+	0.203795i
$771$		0			0
$772$	16.5645	+	18.8799i	0.596171	+	0.679502i
$773$	−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
$782$	4.76069	+	48.2818i	0.170242	+	1.72655i
$783$		0			0
$784$	16.9669	+	22.2738i	0.605962	+	0.795494i
$785$	−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	$0.190111\pi$
$788$	−6.11821	−	30.7231i	−0.217952	−	1.09447i
$789$		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
$794$	36.2932	+	16.4394i	1.28800	+	0.583414i
$795$		0			0
$796$	20.5832	+	23.4603i	0.729554	+	0.831529i
$797$	−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
$800$	−14.2044	+	22.8705i	−0.502201	+	0.808593i
$801$		0			0
$802$	44.8737	+	20.3261i	1.58455	+	0.717740i
$803$	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
$808$	34.3441	−	36.6930i	1.20822	−	1.29086i
$809$	−5.82085	−	10.0820i	−0.204650	−	0.354464i	0.745371	−	0.666650i	$-0.232272\pi$
$809$	−5.82085	−	10.0820i	−0.204650	−	0.354464i	−0.950021	+	0.312185i	$0.898939\pi$
$810$		0			0
$811$			11.8137i			0.414835i	0.978253	+	0.207417i	$0.0665058\pi$
$811$			11.8137i			0.414835i	−0.978253	+	0.207417i	$0.933494\pi$
$812$	17.6024	−	35.5362i	0.617725	−	1.24708i
$813$		0			0
$814$	0.924537	−	0.0911613i	0.0324050	−	0.00319520i
$815$	−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	−0.906652	−	0.421880i	$-0.861370\pi$
$823$	−28.5336	+	16.4739i	−0.994618	+	0.574243i	−0.0879668	+	0.996123i	$0.528037\pi$
$824$	−13.4782	−	3.13800i	−0.469536	−	0.109318i
$825$		0			0
$826$	−0.595116	+	17.1947i	−0.0207067	+	0.598282i
$827$	8.21322			0.285602			0.142801	−	0.989751i	$-0.454389\pi$
$827$	8.21322			0.285602			0.142801	+	0.989751i	$0.454389\pi$
$828$		0			0
$829$	−10.1692	−	17.6135i	−0.353190	−	0.611742i	0.633617	−	0.773647i	$-0.281570\pi$
$829$	−10.1692	−	17.6135i	−0.353190	−	0.611742i	−0.986806	+	0.161905i	$0.948236\pi$
$830$	2.17924	−	4.81108i	0.0756424	−	0.166995i
$831$		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
$836$	−9.68357	−	48.6269i	−0.334913	−	1.68180i
$837$		0			0
$838$	41.1115	−	4.05368i	1.42017	−	0.140032i
$839$	−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
$842$	−31.9062	+	3.14602i	−1.09956	+	0.108419i
$843$		0			0
$844$	16.8096	−	3.34748i	0.578612	−	0.115225i
$845$	−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
$850$	16.4923	−	36.4100i	0.565682	−	1.24885i
$851$	0.522454	+	0.904916i	0.0179095	+	0.0310201i
$852$		0			0
$853$	−34.6193			−1.18534			−0.592670	−	0.805445i	$-0.701926\pi$
$853$	−34.6193			−1.18534			−0.592670	+	0.805445i	$0.701926\pi$
$854$	18.6996	+	35.1425i	0.639886	+	1.20255i
$855$		0			0
$856$	−40.0538	−	9.32535i	−1.36901	−	0.318734i
$857$	−20.2513	+	11.6921i	−0.691772	+	0.399395i	−0.804275	−	0.594257i	$-0.797446\pi$
$857$	−20.2513	+	11.6921i	−0.691772	+	0.399395i	0.112504	+	0.993651i	$0.464113\pi$
$858$		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
$866$	−19.3518	+	1.90813i	−0.657600	+	0.0648407i
$867$		0			0
$868$	2.17136	+	34.0476i	0.0737007	+	1.15565i
$869$			15.7850i			0.535471i
$870$		0			0
$871$	2.01144	+	3.48392i	0.0681550	+	0.118048i
$872$	23.3393	+	21.8453i	0.790370	+	0.739775i
$873$		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	−0.380177	−	0.924914i	$-0.624137\pi$
$877$	−40.6089	−	23.4456i	−1.37126	−	0.791700i	−0.991087	+	0.133213i	$0.957470\pi$
$878$	−7.40437	−	3.35390i	−0.249886	−	0.113189i
$879$		0			0
$880$	6.58364	−	2.73041i	0.221934	−	0.0920422i
$881$			47.5981i			1.60362i	0.597579	+	0.801810i	$0.296130\pi$
$881$			47.5981i			1.60362i	−0.597579	+	0.801810i	$0.703870\pi$
$882$		0			0
$883$	−36.2022			−1.21830			−0.609150	−	0.793055i	$-0.708489\pi$
$883$	−36.2022			−1.21830			−0.609150	+	0.793055i	$0.708489\pi$
$884$	4.82463	−	4.23296i	0.162270	−	0.142370i
$885$		0			0
$886$	12.8924	+	5.83978i	0.433130	+	0.196191i
$887$	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
$892$	−24.5485	+	4.88859i	−0.821943	+	0.163682i
$893$	45.8948	−	26.4973i	1.53581	−	0.886700i
$894$		0			0
$895$	−2.79086			−0.0932880
$896$	−0.943069	−	29.9184i	−0.0315057	−	0.999504i
$897$		0			0
$898$	5.37020	+	54.4634i	0.179206	+	1.81747i
$899$	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	$-0.467308\pi$
$908$	−5.42646	+	4.76098i	−0.180083	+	0.157999i
$909$		0			0
$910$	0.466001	+	0.875764i	0.0154478	+	0.0290313i
$911$		−	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
$914$	−11.2709	−	5.10530i	−0.372809	−	0.168868i
$915$		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	0.224123	−	0.974561i	$-0.428048\pi$
$919$	−15.3943	−	8.88788i	−0.507810	−	0.293184i	−0.731933	+	0.681377i	$0.761382\pi$
$920$	5.85272	+	5.47806i	0.192958	+	0.180606i
$921$		0			0
$922$	−2.16769	−	21.9842i	−0.0713891	−	0.724012i
$923$		−	5.37151i		−	0.176805i
$924$		0			0
$925$		−	0.860872i		−	0.0283053i
$926$	45.9950	−	4.53520i	1.51149	−	0.149036i
$927$		0			0
$928$	−37.3781	+	20.0054i	−1.22700	+	0.656708i
$929$	−8.97118	−	5.17952i	−0.294335	−	0.169934i	0.345560	−	0.938397i	$-0.387689\pi$
$929$	−8.97118	−	5.17952i	−0.294335	−	0.169934i	−0.639895	+	0.768462i	$0.721022\pi$
$930$		0			0
$931$	−12.5500	+	46.1058i	−0.411311	+	1.51106i
$932$	8.63241	−	25.4486i	0.282764	−	0.833596i
$933$		0			0
$934$	−10.0650	+	22.2203i	−0.329335	+	0.727071i
$935$	−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	$-0.222925\pi$
$938$	−27.8380	−	0.963481i	−0.908942	−	0.0314588i
$939$		0			0
$940$	5.02414	+	5.72641i	0.163870	+	0.186775i
$941$	−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	−0.535282	−	0.844673i	$-0.679795\pi$
$947$	14.2748	−	24.7246i	0.463868	−	0.803442i	0.999150	+	0.0412311i	$0.0131280\pi$
$948$		0			0
$949$	1.77470	−	1.02462i	0.0576092	−	0.0332607i
$950$	−45.7229	+	4.50837i	−1.48345	+	0.146271i
$951$		0			0
$952$	7.16676	+	43.8592i	0.232276	+	1.42149i
$953$	19.9005			0.644641			0.322320	−	0.946631i	$-0.395537\pi$
$953$	19.9005			0.644641			0.322320	+	0.946631i	$0.395537\pi$
$954$		0			0
$955$	−6.74496	+	3.89420i	−0.218262	+	0.126014i
$956$	−0.0419185	−	0.210498i	−0.00135574	−	0.00680798i
$957$		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
$962$	0.0570365	−	0.125919i	0.00183893	−	0.00405979i
$963$		0			0
$964$	44.6443	−	39.1693i	1.43790	−	1.26156i
$965$	−6.16147			−0.198345
$966$		0			0
$967$		−	24.1172i		−	0.775557i	−0.921753	−	0.387778i	$-0.873243\pi$
$967$		−	24.1172i		−	0.775557i	0.921753	−	0.387778i	$-0.126757\pi$
$968$	6.03132	+	1.40422i	0.193854	+	0.0451332i
$969$		0			0
$970$	2.32702	−	5.13733i	0.0747160	−	0.164950i
$971$	44.9204	+	25.9348i	1.44156	+	0.832287i	0.997954	−	0.0639336i	$-0.0203646\pi$
$971$	44.9204	+	25.9348i	1.44156	+	0.832287i	0.443609	+	0.896220i	$0.353698\pi$
$972$		0			0
$973$	12.6167	−	16.3751i	0.404472	−	0.524961i
$974$	1.84224	+	2.57025i	0.0590291	+	0.0823560i
$975$		0			0
$976$	5.53623	−	42.1948i	0.177210	−	1.35062i
$977$	−24.5478	−	42.5181i	−0.785355	−	1.36027i	−0.928787	−	0.370615i	$-0.879147\pi$
$977$	−24.5478	−	42.5181i	−0.785355	−	1.36027i	0.143432	−	0.989660i	$-0.454186\pi$
$978$		0			0
$979$		−	35.9534i		−	1.14908i
$980$	−6.85242	−	0.474898i	−0.218893	−	0.0151701i
$981$		0			0
$982$	−4.27411	−	43.3471i	−0.136392	−	1.38326i
$983$	−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	−0.295569	−	0.955321i	$-0.595509\pi$
$991$	12.0877	−	6.97885i	0.383979	−	0.221690i	0.679548	+	0.733631i	$0.262176\pi$
$992$	19.2429	−	30.9830i	0.610963	−	0.983711i
$993$		0			0
$994$	31.5472	+	19.6993i	1.00062	+	0.624824i
$995$	−7.65629			−0.242721
$996$		0			0
$997$	17.9524	+	31.0944i	0.568557	+	0.984770i	0.996709	+	0.0810634i	$0.0258316\pi$
$997$	17.9524	+	31.0944i	0.568557	+	0.984770i	−0.428152	+	0.903707i	$0.640835\pi$
$998$	−4.19117	−	1.89844i	−0.132669	−	0.0600941i
$999$		0			0

Twists

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

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

\(f(q)\)	\(=\)	\(q+(0.138771 + 1.40739i) q^{2} +(-1.96148 + 0.390611i) q^{4} +(0.245316 - 0.424900i) q^{5} +(2.09582 + 1.61479i) q^{7} +(-0.821939 - 2.70637i) q^{8} +O(q^{10})\)	\(q+(0.138771 + 1.40739i) q^{2} +(-1.96148 + 0.390611i) q^{4} +(0.245316 - 0.424900i) q^{5} +(2.09582 + 1.61479i) q^{7} +(-0.821939 - 2.70637i) q^{8} +(0.632043 + 0.286291i) q^{10} +(1.81586 + 3.14517i) q^{11} +0.540385 q^{13} +(-1.98179 + 3.17372i) q^{14} +(3.69485 - 1.53235i) q^{16} +(-5.14304 + 2.96933i) q^{17} +(5.91166 + 3.41310i) q^{19} +(-0.315214 + 0.929259i) q^{20} +(-4.17448 + 2.99208i) q^{22} +(-5.00278 - 2.88835i) q^{23} +(2.37964 + 4.12166i) q^{25} +(0.0749900 + 0.760532i) q^{26} +(-4.74167 - 2.34873i) q^{28} +7.49445i q^{29} +(-3.22373 - 5.58367i) q^{31} +(2.66936 + 4.98744i) q^{32} +(-4.89271 - 6.82619i) q^{34} +(1.20026 - 0.494381i) q^{35} +(-0.156649 - 0.0904414i) q^{37} +(-3.98318 + 8.79364i) q^{38} +(-1.35157 - 0.314674i) q^{40} +3.01371i q^{41} -2.87461 q^{43} +(-4.79032 - 5.45990i) q^{44} +(3.37079 - 7.44167i) q^{46} +(3.88172 - 6.72333i) q^{47} +(1.78493 + 6.76861i) q^{49} +(-5.47055 + 3.92105i) q^{50} +(-1.05996 + 0.211080i) q^{52} +(1.36638 - 0.788878i) q^{53} +1.78184 q^{55} +(2.64757 - 6.99931i) q^{56} +(-10.5476 + 1.04002i) q^{58} +(3.98219 - 2.29912i) q^{59} +(5.31955 - 9.21374i) q^{61} +(7.41103 - 5.31190i) q^{62} +(-6.64883 + 4.44894i) q^{64} +(0.132565 - 0.229610i) q^{65} +(3.72223 + 6.44710i) q^{67} +(8.92814 - 7.83323i) q^{68} +(0.862349 + 1.62063i) q^{70} -9.94014i q^{71} +(3.28414 - 1.89610i) q^{73} +(0.105548 - 0.233017i) q^{74} +(-12.9288 - 4.38558i) q^{76} +(-1.27305 + 9.52393i) q^{77} +(3.76412 + 2.17322i) q^{79} +(0.255309 - 1.94585i) q^{80} +(-4.24146 + 0.418216i) q^{82} -7.61195i q^{83} +2.91370i q^{85} +(-0.398914 - 4.04569i) q^{86} +(7.01944 - 7.49952i) q^{88} +(-8.57349 - 4.94991i) q^{89} +(1.13255 + 0.872607i) q^{91} +(10.9411 + 3.71133i) q^{92} +(10.0010 + 4.53008i) q^{94} +(2.90045 - 1.67458i) q^{95} -8.12814i q^{97} +(-9.27836 + 3.45138i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{4}+O(q^{10}) \) 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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