LMFDB - Embedded newform 504.2.c.f.253.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(253,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("504.253");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.386672896.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} - 2x^{5} + 2x^{4} - 4x^{3} - 4x^{2} + 16 $ x^8 - x^6 - 2x^5 + 2x^4 - 4x^3 - 4x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			253.6
Root			$0.621372 - 1.27039i$ of defining polynomial
Character	$\chi$	$=$	504.253
Dual form			504.2.c.f.253.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.621372 + 1.27039i) q^{2} +(-1.22779 + 1.57877i) q^{4} +3.69833i q^{5} +1.00000 q^{7} +(-2.76858 - 0.578773i) q^{8} +O(q^{10})$	\(q+(0.621372 + 1.27039i) q^{2} +(-1.22779 + 1.57877i) q^{4} +3.69833i q^{5} +1.00000 q^{7} +(-2.76858 - 0.578773i) q^{8} +(-4.69833 + 2.29804i) q^{10} +3.21284i q^{11} -5.08157i q^{13} +(0.621372 + 1.27039i) q^{14} +(-0.985049 - 3.87681i) q^{16} -0.616762 q^{17} +4.48549i q^{19} +(-5.83882 - 4.54078i) q^{20} +(-4.08157 + 1.99637i) q^{22} -1.38324 q^{23} -8.67765 q^{25} +(6.45559 - 3.15755i) q^{26} +(-1.22779 + 1.57877i) q^{28} -5.67765i q^{29} +6.91117 q^{31} +(4.31299 - 3.66034i) q^{32} +(-0.383238 - 0.783529i) q^{34} +3.69833i q^{35} +6.91117i q^{37} +(-5.69833 + 2.78716i) q^{38} +(2.14049 - 10.2391i) q^{40} +0.616762 q^{41} +7.99274i q^{43} +(-5.07235 - 3.94470i) q^{44} +(-0.859506 - 1.75726i) q^{46} -4.97098 q^{47} +1.00000 q^{49} +(-5.39205 - 11.0240i) q^{50} +(8.02264 + 6.23912i) q^{52} +4.48549i q^{53} -11.8822 q^{55} +(-2.76858 - 0.578773i) q^{56} +(7.21284 - 3.52793i) q^{58} +4.00000i q^{59} -12.4782i q^{61} +(4.29441 + 8.77990i) q^{62} +(7.33004 + 3.20476i) q^{64} +18.7933 q^{65} +9.56706i q^{67} +(0.757255 - 0.973726i) q^{68} +(-4.69833 + 2.29804i) q^{70} +15.2056 q^{71} +15.5598 q^{73} +(-8.77990 + 4.29441i) q^{74} +(-7.08157 - 5.50725i) q^{76} +3.21284i q^{77} -5.23352 q^{79} +(14.3377 - 3.64304i) q^{80} +(0.383238 + 0.783529i) q^{82} -10.4257i q^{83} -2.28099i q^{85} +(-10.1539 + 4.96647i) q^{86} +(1.85951 - 8.89500i) q^{88} +14.1766 q^{89} -5.08157i q^{91} +(1.69833 - 2.18382i) q^{92} +(-3.08883 - 6.31509i) q^{94} -16.5888 q^{95} +9.73746 q^{97} +(0.621372 + 1.27039i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{4} + 8 q^{7} + 6 q^{8}+O(q^{10}) $ 8 * q + 2 * q^4 + 8 * q^7 + 6 * q^8	$ 8 q + 2 q^{4} + 8 q^{7} + 6 q^{8} - 4 q^{10} - 6 q^{16} - 4 q^{17} - 24 q^{20} - 12 q^{23} - 24 q^{25} + 28 q^{26} + 2 q^{28} + 8 q^{31} + 30 q^{32} - 4 q^{34} - 12 q^{38} + 28 q^{40} + 4 q^{41} - 16 q^{44} + 4 q^{46} + 8 q^{49} + 20 q^{50} - 12 q^{52} - 8 q^{55} + 6 q^{56} + 44 q^{58} - 12 q^{62} + 26 q^{64} + 16 q^{65} + 16 q^{68} - 4 q^{70} + 28 q^{71} - 8 q^{73} - 4 q^{74} - 24 q^{76} - 40 q^{79} + 4 q^{80} + 4 q^{82} - 24 q^{86} + 4 q^{88} - 20 q^{89} - 20 q^{92} - 72 q^{94} - 40 q^{95} + 40 q^{97}+O(q^{100}) $ 8 * q + 2 * q^4 + 8 * q^7 + 6 * q^8 - 4 * q^10 - 6 * q^16 - 4 * q^17 - 24 * q^20 - 12 * q^23 - 24 * q^25 + 28 * q^26 + 2 * q^28 + 8 * q^31 + 30 * q^32 - 4 * q^34 - 12 * q^38 + 28 * q^40 + 4 * q^41 - 16 * q^44 + 4 * q^46 + 8 * q^49 + 20 * q^50 - 12 * q^52 - 8 * q^55 + 6 * q^56 + 44 * q^58 - 12 * q^62 + 26 * q^64 + 16 * q^65 + 16 * q^68 - 4 * q^70 + 28 * q^71 - 8 * q^73 - 4 * q^74 - 24 * q^76 - 40 * q^79 + 4 * q^80 + 4 * q^82 - 24 * q^86 + 4 * q^88 - 20 * q^89 - 20 * q^92 - 72 * q^94 - 40 * q^95 + 40 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$1$	$-1$	$1$

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 $

$2$	0.621372	+	1.27039i	0.439377	+	0.898303i
$2$	0.621372	+	1.27039i	0.439377	+	0.898303i
$3$		0			0
$3$		0			0
$4$	−1.22779	+	1.57877i	−0.613897	+	0.789387i
$5$			3.69833i			1.65394i	0.562243	+	0.826972i	$0.309938\pi$
$5$			3.69833i			1.65394i	−0.562243	+	0.826972i	$0.690062\pi$
$6$		0			0
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	−2.76858	−	0.578773i	−0.978840	−	0.204627i
$9$		0			0
$10$	−4.69833	+	2.29804i	−1.48574	+	0.726704i
$11$			3.21284i			0.968708i	0.874872	+	0.484354i	$0.160945\pi$
$11$			3.21284i			0.968708i	−0.874872	+	0.484354i	$0.839055\pi$
$12$		0			0
$13$		−	5.08157i		−	1.40937i	−0.709518	−	0.704687i	$-0.751088\pi$
$13$		−	5.08157i		−	1.40937i	0.709518	−	0.704687i	$-0.248912\pi$
$14$	0.621372	+	1.27039i	0.166069	+	0.339527i
$15$		0			0
$16$	−0.985049	−	3.87681i	−0.246262	−	0.969203i
$17$	−0.616762			−0.149587			−0.0747933	−	0.997199i	$-0.523830\pi$
$17$	−0.616762			−0.149587			−0.0747933	+	0.997199i	$0.523830\pi$
$18$		0			0
$19$			4.48549i			1.02904i	0.857478	+	0.514521i	$0.172030\pi$
$19$			4.48549i			1.02904i	−0.857478	+	0.514521i	$0.827970\pi$
$20$	−5.83882	−	4.54078i	−1.30560	−	1.01535i
$21$		0			0
$22$	−4.08157	+	1.99637i	−0.870193	+	0.425628i
$23$	−1.38324			−0.288425			−0.144213	−	0.989547i	$-0.546065\pi$
$23$	−1.38324			−0.288425			−0.144213	+	0.989547i	$0.546065\pi$
$24$		0			0
$25$	−8.67765			−1.73553
$26$	6.45559	−	3.15755i	1.26604	−	0.619246i
$27$		0			0
$28$	−1.22779	+	1.57877i	−0.232031	+	0.298360i
$29$		−	5.67765i		−	1.05431i	−0.849768	−	0.527156i	$-0.823258\pi$
$29$		−	5.67765i		−	1.05431i	0.849768	−	0.527156i	$-0.176742\pi$
$30$		0			0
$31$	6.91117			1.24128			0.620642	−	0.784094i	$-0.286872\pi$
$31$	6.91117			1.24128			0.620642	+	0.784094i	$0.286872\pi$
$32$	4.31299	−	3.66034i	0.762436	−	0.647063i
$33$		0			0
$34$	−0.383238	−	0.783529i	−0.0657249	−	0.134374i
$35$			3.69833i			0.625132i
$36$		0			0
$37$			6.91117i			1.13619i	0.822963	+	0.568095i	$0.192319\pi$
$37$			6.91117i			1.13619i	−0.822963	+	0.568095i	$0.807681\pi$
$38$	−5.69833	+	2.78716i	−0.924391	+	0.452137i
$39$		0			0
$40$	2.14049	−	10.2391i	0.338442	−	1.61895i
$41$	0.616762			0.0963220			0.0481610	−	0.998840i	$-0.484664\pi$
$41$	0.616762			0.0963220			0.0481610	+	0.998840i	$0.484664\pi$
$42$		0			0
$43$			7.99274i			1.21888i	0.792832	+	0.609441i	$0.208606\pi$
$43$			7.99274i			1.21888i	−0.792832	+	0.609441i	$0.791394\pi$
$44$	−5.07235	−	3.94470i	−0.764685	−	0.594687i
$45$		0			0
$46$	−0.859506	−	1.75726i	−0.126727	−	0.259093i
$47$	−4.97098			−0.725092			−0.362546	−	0.931966i	$-0.618092\pi$
$47$	−4.97098			−0.725092			−0.362546	+	0.931966i	$0.618092\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$	−5.39205	−	11.0240i	−0.762551	−	1.55903i
$51$		0			0
$52$	8.02264	+	6.23912i	1.11254	+	0.865210i
$53$			4.48549i			0.616129i	0.951365	+	0.308065i	$0.0996813\pi$
$53$			4.48549i			0.616129i	−0.951365	+	0.308065i	$0.900319\pi$
$54$		0			0
$55$	−11.8822			−1.60219
$56$	−2.76858	−	0.578773i	−0.369967	−	0.0773418i
$57$		0			0
$58$	7.21284	−	3.52793i	0.947092	−	0.463240i
$59$			4.00000i			0.520756i	0.965507	+	0.260378i	$0.0838471\pi$
$59$			4.00000i			0.520756i	−0.965507	+	0.260378i	$0.916153\pi$
$60$		0			0
$61$		−	12.4782i		−	1.59767i	−0.601548	−	0.798837i	$-0.705449\pi$
$61$		−	12.4782i		−	1.59767i	0.601548	−	0.798837i	$-0.294551\pi$
$62$	4.29441	+	8.77990i	0.545391	+	1.11505i
$63$		0			0
$64$	7.33004	+	3.20476i	0.916255	+	0.400595i
$65$	18.7933			2.33102
$66$		0			0
$67$			9.56706i			1.16880i	0.811465	+	0.584401i	$0.198671\pi$
$67$			9.56706i			1.16880i	−0.811465	+	0.584401i	$0.801329\pi$
$68$	0.757255	−	0.973726i	0.0918307	−	0.118082i
$69$		0			0
$70$	−4.69833	+	2.29804i	−0.561558	+	0.274668i
$71$	15.2056			1.80457			0.902285	−	0.431139i	$-0.141888\pi$
$71$	15.2056			1.80457			0.902285	+	0.431139i	$0.141888\pi$
$72$		0			0
$73$	15.5598			1.82114			0.910568	−	0.413358i	$-0.135644\pi$
$73$	15.5598			1.82114			0.910568	+	0.413358i	$0.135644\pi$
$74$	−8.77990	+	4.29441i	−1.02064	+	0.499215i
$75$		0			0
$76$	−7.08157	−	5.50725i	−0.812312	−	0.631725i
$77$			3.21284i			0.366137i
$78$		0			0
$79$	−5.23352			−0.588817			−0.294409	−	0.955680i	$-0.595123\pi$
$79$	−5.23352			−0.588817			−0.294409	+	0.955680i	$0.595123\pi$
$80$	14.3377	−	3.64304i	1.60301	−	0.407304i
$81$		0			0
$82$	0.383238	+	0.783529i	0.0423216	+	0.0865263i
$83$		−	10.4257i		−	1.14437i	−0.820125	−	0.572184i	$-0.806096\pi$
$83$		−	10.4257i		−	1.14437i	0.820125	−	0.572184i	$-0.193904\pi$
$84$		0			0
$85$		−	2.28099i		−	0.247408i
$86$	−10.1539	+	4.96647i	−1.09492	+	0.535548i
$87$		0			0
$88$	1.85951	−	8.89500i	0.198224	−	0.948210i
$89$	14.1766			1.50271			0.751356	−	0.659897i	$-0.229400\pi$
$89$	14.1766			1.50271			0.751356	+	0.659897i	$0.229400\pi$
$90$		0			0
$91$		−	5.08157i		−	0.532693i
$92$	1.69833	−	2.18382i	0.177063	−	0.227679i
$93$		0			0
$94$	−3.08883	−	6.31509i	−0.318588	−	0.651352i
$95$	−16.5888			−1.70198
$96$		0			0
$97$	9.73746			0.988689			0.494344	−	0.869266i	$-0.335408\pi$
$97$	9.73746			0.988689			0.494344	+	0.869266i	$0.335408\pi$
$98$	0.621372	+	1.27039i	0.0627681	+	0.128329i
$99$		0			0
$100$	10.6544	−	13.7000i	1.06544	−	1.37000i
$101$		−	5.27265i		−	0.524648i	−0.964980	−	0.262324i	$-0.915511\pi$
$101$		−	5.27265i		−	0.524648i	0.964980	−	0.262324i	$-0.0844889\pi$
$102$		0			0
$103$	1.94019			0.191173			0.0955865	−	0.995421i	$-0.469527\pi$
$103$	1.94019			0.191173			0.0955865	+	0.995421i	$0.469527\pi$
$104$	−2.94108	+	14.0687i	−0.288396	+	1.37955i
$105$		0			0
$106$	−5.69833	+	2.78716i	−0.553471	+	0.270713i
$107$			4.78716i			0.462792i	0.972860	+	0.231396i	$0.0743293\pi$
$107$			4.78716i			0.462792i	−0.972860	+	0.231396i	$0.925671\pi$
$108$		0			0
$109$		−	0.970978i		−	0.0930028i	−0.998918	−	0.0465014i	$-0.985193\pi$
$109$		−	0.970978i		−	0.0930028i	0.998918	−	0.0465014i	$-0.0148072\pi$
$110$	−7.38324	−	15.0950i	−0.703964	−	1.43925i
$111$		0			0
$112$	−0.985049	−	3.87681i	−0.0930783	−	0.366324i
$113$	−15.5598			−1.46374			−0.731871	−	0.681443i	$-0.761353\pi$
$113$	−15.5598			−1.46374			−0.731871	+	0.681443i	$0.761353\pi$
$114$		0			0
$115$		−	5.11567i		−	0.477039i
$116$	8.96372	+	6.97098i	0.832260	+	0.647239i
$117$		0			0
$118$	−5.08157	+	2.48549i	−0.467796	+	0.228808i
$119$	−0.616762			−0.0565384
$120$		0			0
$121$	0.677649			0.0616045
$122$	15.8522	−	7.75363i	1.43520	−	0.701980i
$123$		0			0
$124$	−8.48549	+	10.9112i	−0.762019	+	0.979852i
$125$		−	13.6012i		−	1.21652i
$126$		0			0
$127$	−3.73746			−0.331646			−0.165823	−	0.986156i	$-0.553028\pi$
$127$	−3.73746			−0.331646			−0.165823	+	0.986156i	$0.553028\pi$
$128$	0.483388	+	11.3034i	0.0427259	+	0.999087i
$129$		0			0
$130$	11.6776	+	23.8749i	1.02420	+	2.09397i
$131$			3.39666i			0.296768i	0.988930	+	0.148384i	$0.0474071\pi$
$131$			3.39666i			0.296768i	−0.988930	+	0.148384i	$0.952593\pi$
$132$		0			0
$133$			4.48549i			0.388941i
$134$	−12.1539	+	5.94470i	−1.04994	+	0.513544i
$135$		0			0
$136$	1.70755	+	0.356965i	0.146421	+	0.0306095i
$137$	−13.0559			−1.11544			−0.557719	−	0.830030i	$-0.688323\pi$
$137$	−13.0559			−1.11544			−0.557719	+	0.830030i	$0.688323\pi$
$138$		0			0
$139$		−	2.80784i		−	0.238158i	−0.992885	−	0.119079i	$-0.962006\pi$
$139$		−	2.80784i		−	0.238158i	0.992885	−	0.119079i	$-0.0379942\pi$
$140$	−5.83882	−	4.54078i	−0.493471	−	0.383766i
$141$		0			0
$142$	9.44833	+	19.3171i	0.792886	+	1.62105i
$143$	16.3263			1.36527
$144$		0			0
$145$	20.9978			1.74377
$146$	9.66843	+	19.7670i	0.800165	+	1.63593i
$147$		0			0
$148$	−10.9112	−	8.48549i	−0.896893	−	0.697503i
$149$			12.4855i			1.02285i	0.859328	+	0.511426i	$0.170882\pi$
$149$			12.4855i			1.02285i	−0.859328	+	0.511426i	$0.829118\pi$
$150$		0			0
$151$	8.97098			0.730048			0.365024	−	0.930998i	$-0.381061\pi$
$151$	8.97098			0.730048			0.365024	+	0.930998i	$0.381061\pi$
$152$	2.59608	−	12.4184i	0.210570	−	1.00727i
$153$		0			0
$154$	−4.08157	+	1.99637i	−0.328902	+	0.160872i
$155$			25.5598i			2.05301i
$156$		0			0
$157$		−	15.1665i		−	1.21042i	−0.796068	−	0.605208i	$-0.793090\pi$
$157$		−	15.1665i		−	1.21042i	0.796068	−	0.605208i	$-0.206910\pi$
$158$	−3.25197	−	6.64863i	−0.258713	−	0.528936i
$159$		0			0
$160$	13.5372	+	15.9509i	1.07021	+	1.26103i
$161$	−1.38324			−0.109014
$162$		0			0
$163$			13.2263i			1.03596i	0.855392	+	0.517980i	$0.173316\pi$
$163$			13.2263i			1.03596i	−0.855392	+	0.517980i	$0.826684\pi$
$164$	−0.757255	+	0.973726i	−0.0591317	+	0.0760353i
$165$		0			0
$166$	13.2447	−	6.47823i	1.02799	−	0.502808i
$167$	−3.05587			−0.236470			−0.118235	−	0.992986i	$-0.537724\pi$
$167$	−3.05587			−0.236470			−0.118235	+	0.992986i	$0.537724\pi$
$168$		0			0
$169$	−12.8223			−0.986334
$170$	2.89775	−	1.41734i	0.222247	−	0.108705i
$171$		0			0
$172$	−12.6187	−	9.81343i	−0.962169	−	0.748267i
$173$		−	13.8615i		−	1.05387i	−0.849906	−	0.526934i	$-0.823342\pi$
$173$		−	13.8615i		−	1.05387i	0.849906	−	0.526934i	$-0.176658\pi$
$174$		0			0
$175$	−8.67765			−0.655969
$176$	12.4556	−	3.16480i	0.938875	−	0.238556i
$177$		0			0
$178$	8.80892	+	18.0098i	0.660257	+	1.34989i
$179$		−	18.3883i		−	1.37441i	−0.726465	−	0.687204i	$-0.758838\pi$
$179$		−	18.3883i		−	1.37441i	0.726465	−	0.687204i	$-0.241162\pi$
$180$		0			0
$181$			6.05255i			0.449882i	0.974372	+	0.224941i	$0.0722190\pi$
$181$			6.05255i			0.449882i	−0.974372	+	0.224941i	$0.927781\pi$
$182$	6.45559	−	3.15755i	0.478520	−	0.234053i
$183$		0			0
$184$	3.82960	+	0.800581i	0.282322	+	0.0590196i
$185$	−25.5598			−1.87919
$186$		0			0
$187$		−	1.98156i		−	0.144906i
$188$	6.10333	−	7.84805i	0.445131	−	0.572378i
$189$		0			0
$190$	−10.3078	−	21.0743i	−0.747809	−	1.52889i
$191$	15.2056			1.10024			0.550119	−	0.835086i	$-0.314582\pi$
$191$	15.2056			1.10024			0.550119	+	0.835086i	$0.314582\pi$
$192$		0			0
$193$	−19.4419			−1.39946			−0.699731	−	0.714406i	$-0.746697\pi$
$193$	−19.4419			−1.39946			−0.699731	+	0.714406i	$0.746697\pi$
$194$	6.05058	+	12.3704i	0.434407	+	0.888142i
$195$		0			0
$196$	−1.22779	+	1.57877i	−0.0876995	+	0.112770i
$197$		−	15.2520i		−	1.08666i	−0.839520	−	0.543329i	$-0.817164\pi$
$197$		−	15.2520i		−	1.08666i	0.839520	−	0.543329i	$-0.182836\pi$
$198$		0			0
$199$	−3.02902			−0.214722			−0.107361	−	0.994220i	$-0.534240\pi$
$199$	−3.02902			−0.214722			−0.107361	+	0.994220i	$0.534240\pi$
$200$	24.0247	+	5.02239i	1.69881	+	0.355137i
$201$		0			0
$202$	6.69833	−	3.27628i	0.471293	−	0.230518i
$203$		−	5.67765i		−	0.398493i
$204$		0			0
$205$			2.28099i			0.159311i
$206$	1.20558	+	2.46481i	0.0839969	+	0.171731i
$207$		0			0
$208$	−19.7003	+	5.00559i	−1.36597	+	0.347075i
$209$	−14.4112			−0.996841
$210$		0			0
$211$		−	0.963719i		−	0.0663452i	−0.999450	−	0.0331726i	$-0.989439\pi$
$211$		−	0.963719i		−	0.0663452i	0.999450	−	0.0331726i	$-0.0105611\pi$
$212$	−7.08157	−	5.50725i	−0.486364	−	0.378240i
$213$		0			0
$214$	−6.08157	+	2.97461i	−0.415728	+	0.203340i
$215$	−29.5598			−2.01596
$216$		0			0
$217$	6.91117			0.469161
$218$	1.23352	−	0.603339i	0.0835447	−	0.0408633i
$219$		0			0
$220$	14.5888	−	18.7592i	0.983578	−	1.26475i
$221$			3.13412i			0.210823i
$222$		0			0
$223$	−22.1486			−1.48318			−0.741591	−	0.670853i	$-0.765928\pi$
$223$	−22.1486			−1.48318			−0.741591	+	0.670853i	$0.765928\pi$
$224$	4.31299	−	3.66034i	0.288174	−	0.244567i
$225$		0			0
$226$	−9.66843	−	19.7670i	−0.643134	−	1.31488i
$227$			0.929615i			0.0617007i	0.999524	+	0.0308504i	$0.00982153\pi$
$227$			0.929615i			0.0617007i	−0.999524	+	0.0308504i	$0.990178\pi$
$228$		0			0
$229$		−	1.42236i		−	0.0939924i	−0.998895	−	0.0469962i	$-0.985035\pi$
$229$		−	1.42236i		−	0.0939924i	0.998895	−	0.0469962i	$-0.0149649\pi$
$230$	6.49891	−	3.17874i	0.428526	−	0.209600i
$231$		0			0
$232$	−3.28607	+	15.7190i	−0.215741	+	1.03200i
$233$	−10.9710			−0.718733			−0.359366	−	0.933197i	$-0.617007\pi$
$233$	−10.9710			−0.718733			−0.359366	+	0.933197i	$0.617007\pi$
$234$		0			0
$235$		−	18.3843i		−	1.19926i
$236$	−6.31509	−	4.91117i	−0.411077	−	0.319690i
$237$		0			0
$238$	−0.383238	−	0.783529i	−0.0248417	−	0.0507886i
$239$	4.82126			0.311862			0.155931	−	0.987768i	$-0.450162\pi$
$239$	4.82126			0.311862			0.155931	+	0.987768i	$0.450162\pi$
$240$		0			0
$241$	−0.204501			−0.0131731			−0.00658654	−	0.999978i	$-0.502097\pi$
$241$	−0.204501			−0.0131731			−0.00658654	+	0.999978i	$0.502097\pi$
$242$	0.421072	+	0.860880i	0.0270676	+	0.0553395i
$243$		0			0
$244$	19.7003	+	15.3207i	1.26118	+	0.980806i
$245$			3.69833i			0.236278i
$246$		0			0
$247$	22.7933			1.45030
$248$	−19.1341	−	4.00000i	−1.21502	−	0.254000i
$249$		0			0
$250$	17.2788	−	8.45138i	1.09281	−	0.534513i
$251$			3.10727i			0.196129i	0.995180	+	0.0980646i	$0.0312652\pi$
$251$			3.10727i			0.196129i	−0.995180	+	0.0980646i	$0.968735\pi$
$252$		0			0
$253$		−	4.44413i		−	0.279400i
$254$	−2.32235	−	4.74803i	−0.145717	−	0.297918i
$255$		0			0
$256$	−14.0594	+	7.63770i	−0.878710	+	0.477356i
$257$	14.1497			0.882635			0.441318	−	0.897351i	$-0.354511\pi$
$257$	14.1497			0.882635			0.441318	+	0.897351i	$0.354511\pi$
$258$		0			0
$259$			6.91117i			0.429439i
$260$	−23.0743	+	29.6704i	−1.43101	+	1.84008i
$261$		0			0
$262$	−4.31509	+	2.11059i	−0.266587	+	0.130393i
$263$	−2.94304			−0.181475			−0.0907377	−	0.995875i	$-0.528923\pi$
$263$	−2.94304			−0.181475			−0.0907377	+	0.995875i	$0.528923\pi$
$264$		0			0
$265$	−16.5888			−1.01904
$266$	−5.69833	+	2.78716i	−0.349387	+	0.170892i
$267$		0			0
$268$	−15.1042	−	11.7464i	−0.922637	−	0.717524i
$269$			0.642463i			0.0391717i	0.999808	+	0.0195858i	$0.00623476\pi$
$269$			0.642463i			0.0391717i	−0.999808	+	0.0195858i	$0.993765\pi$
$270$		0			0
$271$	−0.526852			−0.0320040			−0.0160020	−	0.999872i	$-0.505094\pi$
$271$	−0.526852			−0.0320040			−0.0160020	+	0.999872i	$0.505094\pi$
$272$	0.607540	+	2.39107i	0.0368375	+	0.144980i
$273$		0			0
$274$	−8.11255	−	16.5861i	−0.490097	−	1.00200i
$275$		−	27.8799i		−	1.68122i
$276$		0			0
$277$		−	21.7190i		−	1.30497i	−0.757802	−	0.652484i	$-0.773727\pi$
$277$		−	21.7190i		−	1.30497i	0.757802	−	0.652484i	$-0.226273\pi$
$278$	3.56706	−	1.74471i	0.213938	−	0.104641i
$279$		0			0
$280$	2.14049	−	10.2391i	0.127919	−	0.611904i
$281$	4.79332			0.285946			0.142973	−	0.989727i	$-0.454334\pi$
$281$	4.79332			0.285946			0.142973	+	0.989727i	$0.454334\pi$
$282$		0			0
$283$		−	22.6486i		−	1.34632i	−0.739496	−	0.673161i	$-0.764936\pi$
$283$		−	22.6486i		−	1.34632i	0.739496	−	0.673161i	$-0.235064\pi$
$284$	−18.6693	+	24.0062i	−1.10782	+	1.42450i
$285$		0			0
$286$	10.1447	+	20.7408i	0.599868	+	1.22643i
$287$	0.616762			0.0364063
$288$		0			0
$289$	−16.6196			−0.977624
$290$	13.0475	+	26.6755i	0.766174	+	1.56644i
$291$		0			0
$292$	−19.1042	+	24.5654i	−1.11799	+	1.43758i
$293$		−	24.3285i		−	1.42129i	−0.703552	−	0.710644i	$-0.748404\pi$
$293$		−	24.3285i		−	1.42129i	0.703552	−	0.710644i	$-0.251596\pi$
$294$		0			0
$295$	−14.7933			−0.861301
$296$	4.00000	−	19.1341i	0.232495	−	1.11215i
$297$		0			0
$298$	−15.8615	+	7.75814i	−0.918830	+	0.449417i
$299$			7.02902i			0.406499i
$300$		0			0
$301$			7.99274i			0.460694i
$302$	5.57432	+	11.3967i	0.320766	+	0.655804i
$303$		0			0
$304$	17.3894	−	4.41842i	0.997351	−	0.253414i
$305$	46.1486			2.64246
$306$		0			0
$307$			3.51451i			0.200584i	0.994958	+	0.100292i	$0.0319777\pi$
$307$			3.51451i			0.200584i	−0.994958	+	0.100292i	$0.968022\pi$
$308$	−5.07235	−	3.94470i	−0.289024	−	0.224770i
$309$		0			0
$310$	−32.4710	+	15.8822i	−1.84423	+	0.902046i
$311$	4.97098			0.281878			0.140939	−	0.990018i	$-0.454988\pi$
$311$	4.97098			0.281878			0.140939	+	0.990018i	$0.454988\pi$
$312$		0			0
$313$	−25.6447			−1.44952			−0.724762	−	0.689000i	$-0.758050\pi$
$313$	−25.6447			−1.44952			−0.724762	+	0.689000i	$0.758050\pi$
$314$	19.2674	−	9.42402i	1.08732	−	0.531828i
$315$		0			0
$316$	6.42568	−	8.26254i	0.361473	−	0.464804i
$317$		−	3.51451i		−	0.197395i	−0.995118	−	0.0986973i	$-0.968532\pi$
$317$		−	3.51451i		−	0.197395i	0.995118	−	0.0986973i	$-0.0314676\pi$
$318$		0			0
$319$	18.2414			1.02132
$320$	−11.8522	+	27.1089i	−0.662561	+	1.51543i
$321$		0			0
$322$	−0.859506	−	1.75726i	−0.0478984	−	0.0979280i
$323$		−	2.76648i		−	0.153931i
$324$		0			0
$325$			44.0961i			2.44601i
$326$	−16.8025	+	8.21843i	−0.930607	+	0.455177i
$327$		0			0
$328$	−1.70755	−	0.356965i	−0.0942838	−	0.0197101i
$329$	−4.97098			−0.274059
$330$		0			0
$331$		−	25.1849i		−	1.38429i	−0.721760	−	0.692144i	$-0.756666\pi$
$331$		−	25.1849i		−	1.38429i	0.721760	−	0.692144i	$-0.243334\pi$
$332$	16.4598	+	12.8006i	0.903348	+	0.702523i
$333$		0			0
$334$	−1.89883	−	3.88215i	−0.103899	−	0.212422i
$335$	−35.3821			−1.93313
$336$		0			0
$337$	21.7643			1.18558			0.592788	−	0.805358i	$-0.298027\pi$
$337$	21.7643			1.18558			0.592788	+	0.805358i	$0.298027\pi$
$338$	−7.96745	−	16.2894i	−0.433372	−	0.886027i
$339$		0			0
$340$	3.60116	+	2.80058i	0.195300	+	0.151883i
$341$			22.2045i			1.20244i
$342$		0			0
$343$	1.00000			0.0539949
$344$	4.62598	−	22.1285i	0.249416	−	1.19309i
$345$		0			0
$346$	17.6095	−	8.61313i	0.946693	−	0.463045i
$347$		−	31.9068i		−	1.71284i	−0.516276	−	0.856422i	$-0.672682\pi$
$347$		−	31.9068i		−	1.71284i	0.516276	−	0.856422i	$-0.327318\pi$
$348$		0			0
$349$			1.04021i			0.0556810i	0.999612	+	0.0278405i	$0.00886305\pi$
$349$			1.04021i			0.0556810i	−0.999612	+	0.0278405i	$0.991137\pi$
$350$	−5.39205	−	11.0240i	−0.288217	−	0.589259i
$351$		0			0
$352$	11.7601	+	13.8570i	0.626815	+	0.738578i
$353$	13.8503			0.737176			0.368588	−	0.929593i	$-0.379841\pi$
$353$	13.8503			0.737176			0.368588	+	0.929593i	$0.379841\pi$
$354$		0			0
$355$			56.2353i			2.98466i
$356$	−17.4059	+	22.3816i	−0.922510	+	1.18622i
$357$		0			0
$358$	23.3604	−	11.4260i	1.23463	−	0.603882i
$359$	−0.412260			−0.0217583			−0.0108791	−	0.999941i	$-0.503463\pi$
$359$	−0.412260			−0.0217583			−0.0108791	+	0.999941i	$0.503463\pi$
$360$		0			0
$361$	−1.11961			−0.0589269
$362$	−7.68911	+	3.76088i	−0.404131	+	0.197668i
$363$		0			0
$364$	8.02264	+	6.23912i	0.420501	+	0.327018i
$365$			57.5453i			3.01206i
$366$		0			0
$367$	4.97098			0.259483			0.129741	−	0.991548i	$-0.458585\pi$
$367$	4.97098			0.259483			0.129741	+	0.991548i	$0.458585\pi$
$368$	1.36256	+	5.36256i	0.0710282	+	0.279543i
$369$		0			0
$370$	−15.8822	−	32.4710i	−0.825674	−	1.68809i
$371$			4.48549i			0.232875i
$372$		0			0
$373$			2.16314i			0.112003i	0.998431	+	0.0560015i	$0.0178352\pi$
$373$			2.16314i			0.112003i	−0.998431	+	0.0560015i	$0.982165\pi$
$374$	2.51735	−	1.23128i	0.130169	−	0.0636682i
$375$		0			0
$376$	13.7625	+	2.87707i	0.709749	+	0.148373i
$377$	−28.8514			−1.48592
$378$		0			0
$379$			23.7570i			1.22032i	0.792279	+	0.610159i	$0.208894\pi$
$379$			23.7570i			1.22032i	−0.792279	+	0.610159i	$0.791106\pi$
$380$	20.3676	−	26.1900i	1.04484	−	1.34352i
$381$		0			0
$382$	9.44833	+	19.3171i	0.483418	+	0.988347i
$383$	37.5598			1.91922			0.959608	−	0.281340i	$-0.0907790\pi$
$383$	37.5598			1.91922			0.959608	+	0.281340i	$0.0907790\pi$
$384$		0			0
$385$	−11.8822			−0.605570
$386$	−12.0807	−	24.6989i	−0.614891	−	1.25714i
$387$		0			0
$388$	−11.9556	+	15.3732i	−0.606953	+	0.780458i
$389$			0.826283i			0.0418942i	0.999781	+	0.0209471i	$0.00666816\pi$
$389$			0.826283i			0.0418942i	−0.999781	+	0.0209471i	$0.993332\pi$
$390$		0			0
$391$	0.853128			0.0431446
$392$	−2.76858	−	0.578773i	−0.139834	−	0.0292325i
$393$		0			0
$394$	19.3760	−	9.47715i	0.976148	−	0.477452i
$395$		−	19.3553i		−	0.973871i
$396$		0			0
$397$		−	8.81902i		−	0.442614i	−0.975204	−	0.221307i	$-0.928968\pi$
$397$		−	8.81902i		−	0.442614i	0.975204	−	0.221307i	$-0.0710323\pi$
$398$	−1.88215	−	3.84805i	−0.0943437	−	0.192885i
$399$		0			0
$400$	8.54791	+	33.6416i	0.427395	+	1.68208i
$401$	8.64687			0.431804			0.215902	−	0.976415i	$-0.430731\pi$
$401$	8.64687			0.431804			0.215902	+	0.976415i	$0.430731\pi$
$402$		0			0
$403$		−	35.1196i		−	1.74943i
$404$	8.32431	+	6.47372i	0.414150	+	0.322080i
$405$		0			0
$406$	7.21284	−	3.52793i	0.357967	−	0.175088i
$407$	−22.2045			−1.10064
$408$		0			0
$409$	−18.7084			−0.925072			−0.462536	−	0.886600i	$-0.653060\pi$
$409$	−18.7084			−0.925072			−0.462536	+	0.886600i	$0.653060\pi$
$410$	−2.89775	+	1.41734i	−0.143110	+	0.0699976i
$411$		0			0
$412$	−2.38216	+	3.06313i	−0.117360	+	0.150909i
$413$			4.00000i			0.196827i
$414$		0			0
$415$	38.5576			1.89272
$416$	−18.6003	−	21.9168i	−0.911954	−	1.07456i
$417$		0			0
$418$	−8.95470	−	18.3078i	−0.437989	−	0.895465i
$419$		−	12.9710i		−	0.633674i	−0.948480	−	0.316837i	$-0.897379\pi$
$419$		−	12.9710i		−	0.633674i	0.948480	−	0.316837i	$-0.102621\pi$
$420$		0			0
$421$		−	3.54136i		−	0.172595i	−0.996269	−	0.0862976i	$-0.972496\pi$
$421$		−	3.54136i		−	0.172595i	0.996269	−	0.0862976i	$-0.0275036\pi$
$422$	1.22430	−	0.598828i	0.0595981	−	0.0291505i
$423$		0			0
$424$	2.59608	−	12.4184i	0.126077	−	0.603092i
$425$	5.35204			0.259612
$426$		0			0
$427$		−	12.4782i		−	0.603864i
$428$	−7.55784	−	5.87764i	−0.365322	−	0.284106i
$429$		0			0
$430$	−18.3676	−	37.5525i	−0.885766	−	1.81094i
$431$	−14.6168			−0.704065			−0.352032	−	0.935988i	$-0.614509\pi$
$431$	−14.6168			−0.704065			−0.352032	+	0.935988i	$0.614509\pi$
$432$		0			0
$433$	−2.97098			−0.142776			−0.0713880	−	0.997449i	$-0.522743\pi$
$433$	−2.97098			−0.142776			−0.0713880	+	0.997449i	$0.522743\pi$
$434$	4.29441	+	8.77990i	0.206138	+	0.421449i
$435$		0			0
$436$	1.53295	+	1.19216i	0.0734152	+	0.0570941i
$437$		−	6.20450i		−	0.296802i
$438$		0			0
$439$		0			0			−	1.00000i	$-0.5\pi$
$439$		0			0				1.00000i	$0.5\pi$
$440$	32.8967	+	6.87707i	1.56829	+	0.327851i
$441$		0			0
$442$	−3.98156	+	1.94745i	−0.189383	+	0.0926309i
$443$			27.1983i			1.29223i	0.763239	+	0.646116i	$0.223608\pi$
$443$			27.1983i			1.29223i	−0.763239	+	0.646116i	$0.776392\pi$
$444$		0			0
$445$			52.4296i			2.48540i
$446$	−13.7625	−	28.1374i	−0.651675	−	1.33235i
$447$		0			0
$448$	7.33004	+	3.20476i	0.346312	+	0.151410i
$449$	31.5598			1.48940			0.744700	−	0.667400i	$-0.232593\pi$
$449$	31.5598			1.48940			0.744700	+	0.667400i	$0.232593\pi$
$450$		0			0
$451$			1.98156i			0.0933079i
$452$	19.1042	−	24.5654i	0.898587	−	1.15546i
$453$		0			0
$454$	−1.18098	+	0.577637i	−0.0554259	+	0.0271099i
$455$	18.7933			0.881045
$456$		0			0
$457$	28.1117			1.31501			0.657506	−	0.753450i	$-0.271612\pi$
$457$	28.1117			1.31501			0.657506	+	0.753450i	$0.271612\pi$
$458$	1.80696	−	0.883817i	0.0844336	−	0.0412981i
$459$		0			0
$460$	8.07649	+	6.28099i	0.376568	+	0.292853i
$461$			5.19440i			0.241927i	0.992657	+	0.120964i	$0.0385984\pi$
$461$			5.19440i			0.241927i	−0.992657	+	0.120964i	$0.961402\pi$
$462$		0			0
$463$	−10.7665			−0.500361			−0.250180	−	0.968199i	$-0.580490\pi$
$463$	−10.7665			−0.500361			−0.250180	+	0.968199i	$0.580490\pi$
$464$	−22.0112	+	5.59276i	−1.02184	+	0.259637i
$465$		0			0
$466$	−6.81706	−	13.9374i	−0.315794	−	0.645640i
$467$			30.7520i			1.42303i	0.702670	+	0.711515i	$0.251991\pi$
$467$			30.7520i			1.42303i	−0.702670	+	0.711515i	$0.748009\pi$
$468$		0			0
$469$			9.56706i			0.441766i
$470$	23.3553	−	11.4235i	1.07730	−	0.526927i
$471$		0			0
$472$	2.31509	−	11.0743i	0.106561	−	0.509736i
$473$	−25.6794			−1.18074
$474$		0			0
$475$		−	38.9235i		−	1.78593i
$476$	0.757255	−	0.973726i	0.0347087	−	0.0446307i
$477$		0			0
$478$	2.99580	+	6.12489i	0.137025	+	0.280146i
$479$	−16.3263			−0.745967			−0.372983	−	0.927838i	$-0.621665\pi$
$479$	−16.3263			−0.745967			−0.372983	+	0.927838i	$0.621665\pi$
$480$		0			0
$481$	35.1196			1.60132
$482$	−0.127071	−	0.259797i	−0.00578794	−	0.0118334i
$483$		0			0
$484$	−0.832013	+	1.06985i	−0.0378188	+	0.0486297i
$485$			36.0123i			1.63524i
$486$		0			0
$487$	14.7933			0.670349			0.335175	−	0.942156i	$-0.391205\pi$
$487$	14.7933			0.670349			0.335175	+	0.942156i	$0.391205\pi$
$488$	−7.22206	+	34.5469i	−0.326927	+	1.56387i
$489$		0			0
$490$	−4.69833	+	2.29804i	−0.212249	+	0.103815i
$491$			14.0475i			0.633956i	0.948433	+	0.316978i	$0.102668\pi$
$491$			14.0475i			0.633956i	−0.948433	+	0.316978i	$0.897332\pi$
$492$		0			0
$493$			3.50176i			0.157711i
$494$	14.1631	+	28.9565i	0.637230	+	1.30281i
$495$		0			0
$496$	−6.80784	−	26.7933i	−0.305681	−	1.20306i
$497$	15.2056			0.682064
$498$		0			0
$499$		−	34.1414i		−	1.52838i	−0.644993	−	0.764189i	$-0.723140\pi$
$499$		−	34.1414i		−	1.52838i	0.644993	−	0.764189i	$-0.276860\pi$
$500$	21.4731	+	16.6994i	0.960308	+	0.746820i
$501$		0			0
$502$	−3.94745	+	1.93077i	−0.176183	+	0.0861746i
$503$	27.3821			1.22091			0.610455	−	0.792051i	$-0.290987\pi$
$503$	27.3821			1.22091			0.610455	+	0.792051i	$0.290987\pi$
$504$		0			0
$505$	19.5000			0.867738
$506$	5.64578	−	2.76146i	0.250986	−	0.122762i
$507$		0			0
$508$	4.58882	−	5.90059i	0.203596	−	0.261796i
$509$			2.49165i			0.110441i	0.998474	+	0.0552203i	$0.0175861\pi$
$509$			2.49165i			0.110441i	−0.998474	+	0.0552203i	$0.982414\pi$
$510$		0			0
$511$	15.5598			0.688325
$512$	−18.4390	−	13.1150i	−0.814895	−	0.579609i
$513$		0			0
$514$	8.79224	+	17.9757i	0.387809	+	0.792874i
$515$			7.17548i			0.316189i
$516$		0			0
$517$		−	15.9710i		−	0.702402i
$518$	−8.77990	+	4.29441i	−0.385767	+	0.188686i
$519$		0			0
$520$	−52.0308	−	10.8771i	−2.28170	−	0.476991i
$521$	3.00108			0.131480			0.0657399	−	0.997837i	$-0.479059\pi$
$521$	3.00108			0.131480			0.0657399	+	0.997837i	$0.479059\pi$
$522$		0			0
$523$			16.8514i			0.736859i	0.929656	+	0.368429i	$0.120104\pi$
$523$			16.8514i			0.736859i	−0.929656	+	0.368429i	$0.879896\pi$
$524$	−5.36256	−	4.17040i	−0.234264	−	0.182185i
$525$		0			0
$526$	−1.82872	−	3.73881i	−0.0797361	−	0.163020i
$527$	−4.26254			−0.185679
$528$		0			0
$529$	−21.0867			−0.916811
$530$	−10.3078	−	21.0743i	−0.447744	−	0.915410i
$531$		0			0
$532$	−7.08157	−	5.50725i	−0.307025	−	0.238770i
$533$		−	3.13412i		−	0.135754i
$534$		0			0
$535$	−17.7045			−0.765432
$536$	5.53716	−	26.4871i	0.239169	−	1.14407i
$537$		0			0
$538$	−0.816180	+	0.399209i	−0.0351880	+	0.0172111i
$539$			3.21284i			0.138387i
$540$		0			0
$541$			24.6319i			1.05901i	0.848307	+	0.529505i	$0.177622\pi$
$541$			24.6319i			1.05901i	−0.848307	+	0.529505i	$0.822378\pi$
$542$	−0.327371	−	0.669309i	−0.0140618	−	0.0287493i
$543$		0			0
$544$	−2.66009	+	2.25756i	−0.114050	+	0.0967920i
$545$	3.59100			0.153821
$546$		0			0
$547$		−	25.8564i		−	1.10554i	−0.833333	−	0.552771i	$-0.813570\pi$
$547$		−	25.8564i		−	1.10554i	0.833333	−	0.552771i	$-0.186430\pi$
$548$	16.0299	−	20.6123i	0.684764	−	0.880512i
$549$		0			0
$550$	35.4184	−	17.3238i	1.51025	−	0.738689i
$551$	25.4670			1.08493
$552$		0			0
$553$	−5.23352			−0.222552
$554$	27.5917	−	13.4956i	1.17226	−	0.573373i
$555$		0			0
$556$	4.43294	+	3.44745i	0.187999	+	0.146204i
$557$		−	27.2788i		−	1.15584i	−0.816093	−	0.577920i	$-0.803864\pi$
$557$		−	27.2788i		−	1.15584i	0.816093	−	0.577920i	$-0.196136\pi$
$558$		0			0
$559$	40.6157			1.71786
$560$	14.3377	−	3.64304i	0.605880	−	0.153946i
$561$		0			0
$562$	2.97844	+	6.08940i	0.125638	+	0.256866i
$563$		−	13.1776i		−	0.555371i	−0.960672	−	0.277686i	$-0.910433\pi$
$563$		−	13.1776i		−	0.555371i	0.960672	−	0.277686i	$-0.0895674\pi$
$564$		0			0
$565$		−	57.5453i		−	2.42095i
$566$	28.7726	−	14.0732i	1.20940	−	0.591542i
$567$		0			0
$568$	−42.0978	−	8.80058i	−1.76639	−	0.369264i
$569$	−17.4380			−0.731040			−0.365520	−	0.930803i	$-0.619109\pi$
$569$	−17.4380			−0.731040			−0.365520	+	0.930803i	$0.619109\pi$
$570$		0			0
$571$		−	4.71569i		−	0.197346i	−0.995120	−	0.0986728i	$-0.968540\pi$
$571$		−	4.71569i		−	0.197346i	0.995120	−	0.0986728i	$-0.0314597\pi$
$572$	−20.0453	+	25.7755i	−0.838136	+	1.07773i
$573$		0			0
$574$	0.383238	+	0.783529i	0.0159961	+	0.0327039i
$575$	12.0033			0.500570
$576$		0			0
$577$	−11.8223			−0.492171			−0.246085	−	0.969248i	$-0.579144\pi$
$577$	−11.8223			−0.492171			−0.246085	+	0.969248i	$0.579144\pi$
$578$	−10.3270	−	21.1134i	−0.429545	−	0.878202i
$579$		0			0
$580$	−25.7810	+	33.1508i	−1.07050	+	1.37651i
$581$		−	10.4257i		−	0.432530i
$582$		0			0
$583$	−14.4112			−0.596849
$584$	−43.0785	−	9.00559i	−1.78260	−	0.372654i
$585$		0			0
$586$	30.9068	−	15.1171i	1.27675	−	0.624480i
$587$			13.7810i			0.568802i	0.958705	+	0.284401i	$0.0917947\pi$
$587$			13.7810i			0.568802i	−0.958705	+	0.284401i	$0.908205\pi$
$588$		0			0
$589$			31.0000i			1.27733i
$590$	−9.19216	−	18.7933i	−0.378435	−	0.773709i
$591$		0			0
$592$	26.7933	−	6.80784i	1.10120	−	0.279800i
$593$	−36.8872			−1.51477			−0.757387	−	0.652966i	$-0.773524\pi$
$593$	−36.8872			−1.51477			−0.757387	+	0.652966i	$0.773524\pi$
$594$		0			0
$595$		−	2.28099i		−	0.0935114i
$596$	−19.7118	−	15.3296i	−0.807425	−	0.627925i
$597$		0			0
$598$	−8.92962	+	4.36764i	−0.365159	+	0.178606i
$599$	35.0895			1.43372			0.716859	−	0.697218i	$-0.245579\pi$
$599$	35.0895			1.43372			0.716859	+	0.697218i	$0.245579\pi$
$600$		0			0
$601$	18.3263			0.747544			0.373772	−	0.927521i	$-0.378064\pi$
$601$	18.3263			0.747544			0.373772	+	0.927521i	$0.378064\pi$
$602$	−10.1539	+	4.96647i	−0.413843	+	0.202418i
$603$		0			0
$604$	−11.0145	+	14.1631i	−0.448174	+	0.576290i
$605$			2.50617i			0.101890i
$606$		0			0
$607$	−12.4459			−0.505163			−0.252582	−	0.967576i	$-0.581280\pi$
$607$	−12.4459			−0.505163			−0.252582	+	0.967576i	$0.581280\pi$
$608$	16.4184	+	19.3459i	0.665855	+	0.784579i
$609$		0			0
$610$	28.6755	+	58.6269i	1.16104	+	2.37373i
$611$			25.2604i			1.02193i
$612$		0			0
$613$			14.2682i			0.576288i	0.957587	+	0.288144i	$0.0930383\pi$
$613$			14.2682i			0.576288i	−0.957587	+	0.288144i	$0.906962\pi$
$614$	−4.46481	+	2.18382i	−0.180185	+	0.0881318i
$615$		0			0
$616$	1.85951	−	8.89500i	0.0749216	−	0.358390i
$617$	−2.94413			−0.118526			−0.0592632	−	0.998242i	$-0.518875\pi$
$617$	−2.94413			−0.118526			−0.0592632	+	0.998242i	$0.518875\pi$
$618$		0			0
$619$			13.2604i			0.532979i	0.963838	+	0.266490i	$0.0858638\pi$
$619$			13.2604i			0.532979i	−0.963838	+	0.266490i	$0.914136\pi$
$620$	−40.3531	−	31.3821i	−1.62062	−	1.26034i
$621$		0			0
$622$	3.08883	+	6.31509i	0.123851	+	0.253212i
$623$	14.1766			0.567972
$624$		0			0
$625$	6.91335			0.276534
$626$	−15.9349	−	32.5788i	−0.636887	−	1.30211i
$627$		0			0
$628$	23.9444	+	18.6213i	0.955485	+	0.743070i
$629$		−	4.26254i		−	0.169959i
$630$		0			0
$631$	36.2335			1.44243			0.721217	−	0.692710i	$-0.243583\pi$
$631$	36.2335			1.44243			0.721217	+	0.692710i	$0.243583\pi$
$632$	14.4894	+	3.02902i	0.576358	+	0.120488i
$633$		0			0
$634$	4.46481	−	2.18382i	0.177320	−	0.0867306i
$635$		−	13.8223i		−	0.548523i
$636$		0			0
$637$		−	5.08157i		−	0.201339i
$638$	11.3347	+	23.1737i	0.448745	+	0.917456i
$639$		0			0
$640$	−41.8036	+	1.78773i	−1.65243	+	0.0706662i
$641$	−25.9441			−1.02473			−0.512366	−	0.858767i	$-0.671231\pi$
$641$	−25.9441			−1.02473			−0.512366	+	0.858767i	$0.671231\pi$
$642$		0			0
$643$			27.2643i			1.07520i	0.843200	+	0.537599i	$0.180669\pi$
$643$			27.2643i			1.07520i	−0.843200	+	0.537599i	$0.819331\pi$
$644$	1.69833	−	2.18382i	0.0669236	−	0.0860545i
$645$		0			0
$646$	3.51451	−	1.71901i	0.138277	−	0.0676336i
$647$	7.41118			0.291364			0.145682	−	0.989332i	$-0.453462\pi$
$647$	7.41118			0.291364			0.145682	+	0.989332i	$0.453462\pi$
$648$		0			0
$649$	−12.8514			−0.504460
$650$	−56.0193	+	27.4001i	−2.19726	+	1.07472i
$651$		0			0
$652$	−20.8813	−	16.2391i	−0.817774	−	0.635973i
$653$			17.7045i			0.692830i	0.938081	+	0.346415i	$0.112601\pi$
$653$			17.7045i			0.692830i	−0.938081	+	0.346415i	$0.887399\pi$
$654$		0			0
$655$	−12.5620			−0.490837
$656$	−0.607540	−	2.39107i	−0.0237205	−	0.0933556i
$657$		0			0
$658$	−3.08883	−	6.31509i	−0.120415	−	0.246188i
$659$		−	39.2252i		−	1.52800i	−0.645219	−	0.763998i	$-0.723234\pi$
$659$		−	39.2252i		−	1.52800i	0.645219	−	0.763998i	$-0.276766\pi$
$660$		0			0
$661$			8.35862i			0.325113i	0.986699	+	0.162556i	$0.0519739\pi$
$661$			8.35862i			0.325113i	−0.986699	+	0.162556i	$0.948026\pi$
$662$	31.9947	−	15.6492i	1.24351	−	0.608223i
$663$		0			0
$664$	−6.03410	+	28.8643i	−0.234169	+	1.12015i
$665$	−16.5888			−0.643287
$666$		0			0
$667$			7.85354i			0.304090i
$668$	3.75197	−	4.82452i	0.145168	−	0.186666i
$669$		0			0
$670$	−21.9855	−	44.9492i	−0.849373	−	1.73654i
$671$	40.0906			1.54768
$672$		0			0
$673$	37.9090			1.46128			0.730642	−	0.682761i	$-0.239221\pi$
$673$	37.9090			1.46128			0.730642	+	0.682761i	$0.239221\pi$
$674$	13.5237	+	27.6492i	0.520915	+	1.06501i
$675$		0			0
$676$	15.7432	−	20.2436i	0.605507	−	0.778599i
$677$		−	41.5844i		−	1.59822i	−0.601186	−	0.799109i	$-0.705305\pi$
$677$		−	41.5844i		−	1.59822i	0.601186	−	0.799109i	$-0.294695\pi$
$678$		0			0
$679$	9.73746			0.373689
$680$	−1.32017	+	6.31509i	−0.0506264	+	0.242173i
$681$		0			0
$682$	−28.2084	+	13.7973i	−1.08016	+	0.528324i
$683$			1.49559i			0.0572272i	0.999591	+	0.0286136i	$0.00910924\pi$
$683$			1.49559i			0.0572272i	−0.999591	+	0.0286136i	$0.990891\pi$
$684$		0			0
$685$		−	48.2849i		−	1.84487i
$686$	0.621372	+	1.27039i	0.0237241	+	0.0485038i
$687$		0			0
$688$	30.9864	−	7.87324i	1.18134	−	0.300164i
$689$	22.7933			0.868356
$690$		0			0
$691$			19.9028i			0.757137i	0.925573	+	0.378568i	$0.123583\pi$
$691$			19.9028i			0.757137i	−0.925573	+	0.378568i	$0.876417\pi$
$692$	21.8841	+	17.0190i	0.831909	+	0.646966i
$693$		0			0
$694$	40.5341	−	19.8260i	1.53865	−	0.752584i
$695$	10.3843			0.393900
$696$		0			0
$697$	−0.380395			−0.0144085
$698$	−1.32147	+	0.646355i	−0.0500184	+	0.0244649i
$699$		0			0
$700$	10.6544	−	13.7000i	0.402697	−	0.517813i
$701$		−	44.5347i		−	1.68205i	−0.540994	−	0.841026i	$-0.681952\pi$
$701$		−	44.5347i		−	1.68205i	0.540994	−	0.841026i	$-0.318048\pi$
$702$		0			0
$703$	−31.0000			−1.16919
$704$	−10.2964	+	23.5503i	−0.388059	+	0.887584i
$705$		0			0
$706$	8.60618	+	17.5953i	0.323898	+	0.662208i
$707$		−	5.27265i		−	0.198298i
$708$		0			0
$709$			35.3553i			1.32780i	0.747823	+	0.663898i	$0.231099\pi$
$709$			35.3553i			1.32780i	−0.747823	+	0.663898i	$0.768901\pi$
$710$	−71.4409	+	34.9430i	−2.68113	+	1.31139i
$711$		0			0
$712$	−39.2489	−	8.20501i	−1.47092	−	0.307496i
$713$	−9.55980			−0.358017
$714$		0			0
$715$			60.3800i			2.25808i
$716$	29.0310	+	22.5771i	1.08494	+	0.843744i
$717$		0			0
$718$	−0.256167	−	0.523732i	−0.00956007	−	0.0195455i
$719$	−11.0928			−0.413690			−0.206845	−	0.978374i	$-0.566320\pi$
$719$	−11.0928			−0.413690			−0.206845	+	0.978374i	$0.566320\pi$
$720$		0			0
$721$	1.94019			0.0722566
$722$	−0.695696	−	1.42235i	−0.0258911	−	0.0529342i
$723$		0			0
$724$	−9.55560	−	7.43128i	−0.355131	−	0.276181i
$725$			49.2686i			1.82979i
$726$		0			0
$727$	−38.1135			−1.41355			−0.706776	−	0.707438i	$-0.749851\pi$
$727$	−38.1135			−1.41355			−0.706776	+	0.707438i	$0.749851\pi$
$728$	−2.94108	+	14.0687i	−0.109003	+	0.521421i
$729$		0			0
$730$	−73.1051	+	35.7570i	−2.70574	+	1.32343i
$731$		−	4.92962i		−	0.182328i
$732$		0			0
$733$			27.9576i			1.03264i	0.856396	+	0.516319i	$0.172698\pi$
$733$			27.9576i			1.03264i	−0.856396	+	0.516319i	$0.827302\pi$
$734$	3.08883	+	6.31509i	0.114011	+	0.233094i
$735$		0			0
$736$	−5.96590	+	5.06313i	−0.219906	+	0.186629i
$737$	−30.7374			−1.13223
$738$		0			0
$739$		−	1.56706i		−	0.0576452i	−0.999585	−	0.0288226i	$-0.990824\pi$
$739$		−	1.56706i		−	0.0576452i	0.999585	−	0.0288226i	$-0.00917578\pi$
$740$	31.3821	−	40.3531i	1.15363	−	1.48341i
$741$		0			0
$742$	−5.69833	+	2.78716i	−0.209192	+	0.102320i
$743$	−44.0569			−1.61629			−0.808146	−	0.588982i	$-0.799529\pi$
$743$	−44.0569			−1.61629			−0.808146	+	0.588982i	$0.799529\pi$
$744$		0			0
$745$	−46.1755			−1.69174
$746$	−2.74803	+	1.34411i	−0.100613	+	0.0492115i
$747$		0			0
$748$	3.12843	+	2.43294i	0.114387	+	0.0889572i
$749$			4.78716i			0.174919i
$750$		0			0
$751$	−53.5039			−1.95239			−0.976193	−	0.216904i	$-0.930404\pi$
$751$	−53.5039			−1.95239			−0.976193	+	0.216904i	$0.930404\pi$
$752$	4.89665	+	19.2716i	0.178563	+	0.702761i
$753$		0			0
$754$	−17.9274	−	36.6526i	−0.652879	−	1.33481i
$755$			33.1776i			1.20746i
$756$		0			0
$757$		−	34.1486i		−	1.24115i	−0.784146	−	0.620576i	$-0.786899\pi$
$757$		−	34.1486i		−	1.24115i	0.784146	−	0.620576i	$-0.213101\pi$
$758$	−30.1808	+	14.7620i	−1.09621	+	0.536179i
$759$		0			0
$760$	45.9274	+	9.60116i	1.66596	+	0.348271i
$761$	8.23460			0.298504			0.149252	−	0.988799i	$-0.452313\pi$
$761$	8.23460			0.298504			0.149252	+	0.988799i	$0.452313\pi$
$762$		0			0
$763$		−	0.970978i		−	0.0351518i
$764$	−18.6693	+	24.0062i	−0.675432	+	0.868513i
$765$		0			0
$766$	23.3386	+	47.7157i	0.843259	+	1.72404i
$767$	20.3263			0.733939
$768$		0			0
$769$	17.4380			0.628831			0.314416	−	0.949285i	$-0.398191\pi$
$769$	17.4380			0.628831			0.314416	+	0.949285i	$0.398191\pi$
$770$	−7.38324	−	15.0950i	−0.266073	−	0.543986i
$771$		0			0
$772$	23.8707	−	30.6944i	0.859125	−	1.10472i
$773$			13.8470i			0.498040i	0.968498	+	0.249020i	$0.0801085\pi$
$773$			13.8470i			0.498040i	−0.968498	+	0.249020i	$0.919891\pi$
$774$		0			0
$775$	−59.9727			−2.15428
$776$	−26.9589	−	5.63578i	−0.967768	−	0.202313i
$777$		0			0
$778$	−1.04970	+	0.513429i	−0.0376337	+	0.0184073i
$779$			2.76648i			0.0991193i
$780$		0			0
$781$			48.8531i			1.74810i
$782$	0.530110	+	1.08381i	0.0189567	+	0.0387569i
$783$		0			0
$784$	−0.985049	−	3.87681i	−0.0351803	−	0.138458i
$785$	56.0906			2.00196
$786$		0			0
$787$		−	48.8368i		−	1.74085i	−0.492305	−	0.870423i	$-0.663845\pi$
$787$		−	48.8368i		−	1.74085i	0.492305	−	0.870423i	$-0.336155\pi$
$788$	24.0794	+	18.7263i	0.857793	+	0.667095i
$789$		0			0
$790$	24.5888	−	12.0268i	0.874831	−	0.427896i
$791$	−15.5598			−0.553243
$792$		0			0
$793$	−63.4090			−2.25172
$794$	11.2036	−	5.47990i	0.397602	−	0.194474i
$795$		0			0
$796$	3.71901	−	4.78214i	0.131817	−	0.169498i
$797$			44.7330i			1.58453i	0.610180	+	0.792263i	$0.291097\pi$
$797$			44.7330i			1.58453i	−0.610180	+	0.792263i	$0.708903\pi$
$798$		0			0
$799$	3.06591			0.108464
$800$	−37.4266	+	31.7632i	−1.32323	+	1.12300i
$801$		0			0
$802$	5.37292	+	10.9849i	0.189724	+	0.387891i
$803$			49.9912i			1.76415i
$804$		0			0
$805$		−	5.11567i		−	0.180304i
$806$	44.6157	−	21.8223i	1.57152	−	0.768659i
$807$		0			0
$808$	−3.05167	+	14.5977i	−0.107357	+	0.513546i
$809$	−7.79550			−0.274075			−0.137038	−	0.990566i	$-0.543758\pi$
$809$	−7.79550			−0.274075			−0.137038	+	0.990566i	$0.543758\pi$
$810$		0			0
$811$			9.53295i			0.334747i	0.985894	+	0.167374i	$0.0535286\pi$
$811$			9.53295i			0.334747i	−0.985894	+	0.167374i	$0.946471\pi$
$812$	8.96372	+	6.97098i	0.314565	+	0.244633i
$813$		0			0
$814$	−13.7973	−	28.2084i	−0.483594	−	0.988705i
$815$	−48.9151			−1.71342
$816$		0			0
$817$	−35.8514			−1.25428
$818$	−11.6249	−	23.7670i	−0.406455	−	0.830995i
$819$		0			0
$820$	−3.60116	−	2.80058i	−0.125758	−	0.0978005i
$821$		−	12.2498i		−	0.427521i	−0.976886	−	0.213760i	$-0.931429\pi$
$821$		−	12.2498i		−	0.427521i	0.976886	−	0.213760i	$-0.0685711\pi$
$822$		0			0
$823$	−49.7665			−1.73475			−0.867375	−	0.497655i	$-0.834194\pi$
$823$	−49.7665			−1.73475			−0.867375	+	0.497655i	$0.834194\pi$
$824$	−5.37158	−	1.12293i	−0.187128	−	0.0391192i
$825$		0			0
$826$	−5.08157	+	2.48549i	−0.176810	+	0.0864812i
$827$			13.1403i			0.456932i	0.973552	+	0.228466i	$0.0733710\pi$
$827$			13.1403i			0.456932i	−0.973552	+	0.228466i	$0.926629\pi$
$828$		0			0
$829$			0.961957i			0.0334102i	0.999860	+	0.0167051i	$0.00531764\pi$
$829$			0.961957i			0.0334102i	−0.999860	+	0.0167051i	$0.994682\pi$
$830$	23.9586	+	48.9833i	0.831616	+	1.70024i
$831$		0			0
$832$	16.2852	−	37.2481i	0.564587	−	1.29135i
$833$	−0.616762			−0.0213695
$834$		0			0
$835$		−	11.3016i		−	0.391108i
$836$	17.6939	−	22.7520i	0.611957	−	0.786893i
$837$		0			0
$838$	16.4782	−	8.05981i	0.569231	−	0.278421i
$839$	−51.4727			−1.77704			−0.888518	−	0.458842i	$-0.848264\pi$
$839$	−51.4727			−1.77704			−0.888518	+	0.458842i	$0.848264\pi$
$840$		0			0
$841$	−3.23570			−0.111576
$842$	4.49891	−	2.20050i	0.155043	−	0.0758343i
$843$		0			0
$844$	1.52149	+	1.18325i	0.0523720	+	0.0407291i
$845$		−	47.4213i		−	1.63134i
$846$		0			0
$847$	0.677649			0.0232843
$848$	17.3894	−	4.41842i	0.597155	−	0.151729i
$849$		0			0
$850$	3.32561	+	6.79919i	0.114067	+	0.233210i
$851$		−	9.55980i		−	0.327706i
$852$		0			0
$853$			3.72843i			0.127659i	0.997961	+	0.0638296i	$0.0203314\pi$
$853$			3.72843i			0.127659i	−0.997961	+	0.0638296i	$0.979669\pi$
$854$	15.8522	−	7.75363i	0.542453	−	0.265324i
$855$		0			0
$856$	2.77068	−	13.2536i	0.0946998	−	0.452999i
$857$	0.473828			0.0161857			0.00809283	−	0.999967i	$-0.497424\pi$
$857$	0.473828			0.0161857			0.00809283	+	0.999967i	$0.497424\pi$
$858$		0			0
$859$		−	41.3078i		−	1.40940i	−0.709503	−	0.704702i	$-0.751081\pi$
$859$		−	41.3078i		−	1.40940i	0.709503	−	0.704702i	$-0.248919\pi$
$860$	36.2933	−	46.6682i	1.23759	−	1.59137i
$861$		0			0
$862$	−9.08245	−	18.5690i	−0.309349	−	0.632463i
$863$	−29.9162			−1.01836			−0.509179	−	0.860660i	$-0.670051\pi$
$863$	−29.9162			−1.01836			−0.509179	+	0.860660i	$0.670051\pi$
$864$		0			0
$865$	51.2643			1.74304
$866$	−1.84608	−	3.77431i	−0.0627325	−	0.128256i
$867$		0			0
$868$	−8.48549	+	10.9112i	−0.288016	+	0.370349i
$869$		−	16.8145i		−	0.570392i
$870$		0			0
$871$	48.6157			1.64728
$872$	−0.561976	+	2.68823i	−0.0190309	+	0.0910349i
$873$		0			0
$874$	7.88215	−	3.85530i	0.266618	−	0.130408i
$875$		−	13.6012i		−	0.459803i
$876$		0			0
$877$		−	18.4670i		−	0.623588i	−0.950150	−	0.311794i	$-0.899070\pi$
$877$		−	18.4670i		−	0.623588i	0.950150	−	0.311794i	$-0.100930\pi$
$878$		0			0
$879$		0			0
$880$	11.7045	+	46.0649i	0.394558	+	1.55285i
$881$	50.5297			1.70239			0.851194	−	0.524851i	$-0.175879\pi$
$881$	50.5297			1.70239			0.851194	+	0.524851i	$0.175879\pi$
$882$		0			0
$883$		−	53.8688i		−	1.81283i	−0.422390	−	0.906414i	$-0.638809\pi$
$883$		−	53.8688i		−	1.81283i	0.422390	−	0.906414i	$-0.361191\pi$
$884$	−4.94806	−	3.84805i	−0.166421	−	0.129424i
$885$		0			0
$886$	−34.5525	+	16.9003i	−1.16082	+	0.567776i
$887$	−36.9978			−1.24227			−0.621133	−	0.783705i	$-0.713327\pi$
$887$	−36.9978			−1.24227			−0.621133	+	0.783705i	$0.713327\pi$
$888$		0			0
$889$	−3.73746			−0.125350
$890$	−66.6062	+	32.5783i	−2.23264	+	1.09203i
$891$		0			0
$892$	27.1939	−	34.9676i	0.910520	−	1.17080i
$893$		−	22.2973i		−	0.746150i
$894$		0			0
$895$	68.0061			2.27319
$896$	0.483388	+	11.3034i	0.0161489	+	0.377619i
$897$		0			0
$898$	19.6104	+	40.0933i	0.654407	+	1.33793i
$899$		−	39.2392i		−	1.30870i
$900$		0			0
$901$		−	2.76648i		−	0.0921647i
$902$	−2.51735	+	1.23128i	−0.0838187	+	0.0409973i
$903$		0			0
$904$	43.0785	+	9.00559i	1.43277	+	0.299522i
$905$	−22.3843			−0.744080
$906$		0			0
$907$			53.5112i			1.77681i	0.459061	+	0.888405i	$0.348186\pi$
$907$			53.5112i			1.77681i	−0.459061	+	0.888405i	$0.651814\pi$
$908$	−1.46765	−	1.14137i	−0.0487057	−	0.0378779i
$909$		0			0
$910$	11.6776	+	23.8749i	0.387110	+	0.791445i
$911$	11.0860			0.367295			0.183647	−	0.982992i	$-0.441210\pi$
$911$	11.0860			0.367295			0.183647	+	0.982992i	$0.441210\pi$
$912$		0			0
$913$	33.4961			1.10856
$914$	17.4679	+	35.7129i	0.577785	+	1.18128i
$915$		0			0
$916$	2.24559	+	1.74637i	0.0741963	+	0.0577016i
$917$			3.39666i			0.112168i
$918$		0			0
$919$	47.5286			1.56782			0.783912	−	0.620872i	$-0.213221\pi$
$919$	47.5286			1.56782			0.783912	+	0.620872i	$0.213221\pi$
$920$	−2.96081	+	14.1631i	−0.0976151	+	0.466945i
$921$		0			0
$922$	−6.59892	+	3.22766i	−0.217324	+	0.106297i
$923$		−	77.2682i		−	2.54331i
$924$		0			0
$925$		−	59.9727i		−	1.97189i
$926$	−6.68999	−	13.6776i	−0.219847	−	0.449475i
$927$		0			0
$928$	−20.7821	−	24.4877i	−0.682207	−	0.803847i
$929$	33.2425			1.09065			0.545325	−	0.838225i	$-0.316406\pi$
$929$	33.2425			1.09065			0.545325	+	0.838225i	$0.316406\pi$
$930$		0			0
$931$			4.48549i			0.147006i
$932$	13.4701	−	17.3207i	0.441227	−	0.567358i
$933$		0			0
$934$	−39.0671	+	19.1084i	−1.27831	+	0.625246i
$935$	7.32845			0.239666
$936$		0			0
$937$	−14.8514			−0.485173			−0.242586	−	0.970130i	$-0.577996\pi$
$937$	−14.8514			−0.485173			−0.242586	+	0.970130i	$0.577996\pi$
$938$	−12.1539	+	5.94470i	−0.396839	+	0.194101i
$939$		0			0
$940$	29.0247	+	22.5721i	0.946680	+	0.736222i
$941$			53.6258i			1.74815i	0.485791	+	0.874075i	$0.338532\pi$
$941$			53.6258i			1.74815i	−0.485791	+	0.874075i	$0.661468\pi$
$942$		0			0
$943$	−0.853128			−0.0277817
$944$	15.5073	−	3.94019i	0.504718	−	0.128242i
$945$		0			0
$946$	−15.9565	−	32.6229i	−0.518790	−	1.06066i
$947$		−	24.1324i		−	0.784198i	−0.919923	−	0.392099i	$-0.871749\pi$
$947$		−	24.1324i		−	0.784198i	0.919923	−	0.392099i	$-0.128251\pi$
$948$		0			0
$949$		−	79.0682i		−	2.56666i
$950$	49.4481	−	24.1860i	1.60431	−	0.784697i
$951$		0			0
$952$	1.70755	+	0.356965i	0.0553421	+	0.0115693i
$953$	−0.347434			−0.0112545			−0.00562725	−	0.999984i	$-0.501791\pi$
$953$	−0.347434			−0.0112545			−0.00562725	+	0.999984i	$0.501791\pi$
$954$		0			0
$955$			56.2353i			1.81973i
$956$	−5.91951	+	7.61168i	−0.191451	+	0.246179i
$957$		0			0
$958$	−10.1447	−	20.7408i	−0.327760	−	0.670104i
$959$	−13.0559			−0.421596
$960$		0			0
$961$	16.7643			0.540784
$962$	21.8223	+	44.6157i	0.703581	+	1.43847i
$963$		0			0
$964$	0.251085	−	0.322861i	0.00808690	−	0.0103986i
$965$		−	71.9028i		−	2.31463i
$966$		0			0
$967$	−8.14646			−0.261972			−0.130986	−	0.991384i	$-0.541814\pi$
$967$	−8.14646			−0.261972			−0.130986	+	0.991384i	$0.541814\pi$
$968$	−1.87612	−	0.392205i	−0.0603009	−	0.0126059i
$969$		0			0
$970$	−45.7498	+	22.3771i	−1.46894	+	0.718484i
$971$		−	3.02902i		−	0.0972059i	−0.998818	−	0.0486030i	$-0.984523\pi$
$971$		−	3.02902i		−	0.0972059i	0.998818	−	0.0486030i	$-0.0154769\pi$
$972$		0			0
$973$		−	2.80784i		−	0.0900152i
$974$	9.19216	+	18.7933i	0.294536	+	0.602177i
$975$		0			0
$976$	−48.3758	+	12.2917i	−1.54847	+	0.393447i
$977$	−18.7353			−0.599395			−0.299697	−	0.954034i	$-0.596886\pi$
$977$	−18.7353			−0.599395			−0.299697	+	0.954034i	$0.596886\pi$
$978$		0			0
$979$			45.5470i			1.45569i
$980$	−5.83882	−	4.54078i	−0.186514	−	0.145050i
$981$		0			0
$982$	−17.8459	+	8.72874i	−0.569485	+	0.278545i
$983$	−18.2313			−0.581490			−0.290745	−	0.956801i	$-0.593903\pi$
$983$	−18.2313			−0.581490			−0.290745	+	0.956801i	$0.593903\pi$
$984$		0			0
$985$	56.4068			1.79727
$986$	−4.44860	+	2.17589i	−0.141672	+	0.0692946i
$987$		0			0
$988$	−27.9855	+	35.9855i	−0.890337	+	1.14485i
$989$		−	11.0559i		−	0.351556i
$990$		0			0
$991$	−21.2973			−0.676530			−0.338265	−	0.941051i	$-0.609840\pi$
$991$	−21.2973			−0.676530			−0.338265	+	0.941051i	$0.609840\pi$
$992$	29.8078	−	25.2973i	0.946399	−	0.803189i
$993$		0			0
$994$	9.44833	+	19.3171i	0.299683	+	0.612700i
$995$		−	11.2023i		−	0.355138i
$996$		0			0
$997$		−	24.7900i		−	0.785107i	−0.919729	−	0.392553i	$-0.871592\pi$
$997$		−	24.7900i		−	0.785107i	0.919729	−	0.392553i	$-0.128408\pi$
$998$	43.3729	−	21.2145i	1.37295	−	0.671533i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.c.f.253.6		8
3.2	odd	2		168.2.c.b.85.3	✓	8
4.3	odd	2		2016.2.c.e.1009.7		8
8.3	odd	2		2016.2.c.e.1009.2		8
8.5	even	2	inner	504.2.c.f.253.5		8
12.11	even	2		672.2.c.b.337.1		8
21.20	even	2		1176.2.c.c.589.3		8
24.5	odd	2		168.2.c.b.85.4	yes	8
24.11	even	2		672.2.c.b.337.8		8
48.5	odd	4		5376.2.a.bp.1.4		4
48.11	even	4		5376.2.a.bl.1.4		4
48.29	odd	4		5376.2.a.bm.1.1		4
48.35	even	4		5376.2.a.bq.1.1		4
84.83	odd	2		4704.2.c.c.2353.8		8
168.83	odd	2		4704.2.c.c.2353.1		8
168.125	even	2		1176.2.c.c.589.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.c.b.85.3	✓	8	3.2	odd	2
168.2.c.b.85.4	yes	8	24.5	odd	2
504.2.c.f.253.5		8	8.5	even	2	inner
504.2.c.f.253.6		8	1.1	even	1	trivial
672.2.c.b.337.1		8	12.11	even	2
672.2.c.b.337.8		8	24.11	even	2
1176.2.c.c.589.3		8	21.20	even	2
1176.2.c.c.589.4		8	168.125	even	2
2016.2.c.e.1009.2		8	8.3	odd	2
2016.2.c.e.1009.7		8	4.3	odd	2
4704.2.c.c.2353.1		8	168.83	odd	2
4704.2.c.c.2353.8		8	84.83	odd	2
5376.2.a.bl.1.4		4	48.11	even	4
5376.2.a.bm.1.1		4	48.29	odd	4
5376.2.a.bp.1.4		4	48.5	odd	4
5376.2.a.bq.1.1		4	48.35	even	4

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.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.621372 + 1.27039i) q^{2} +(-1.22779 + 1.57877i) q^{4} +3.69833i q^{5} +1.00000 q^{7} +(-2.76858 - 0.578773i) q^{8} +O(q^{10})\)	\(q+(0.621372 + 1.27039i) q^{2} +(-1.22779 + 1.57877i) q^{4} +3.69833i q^{5} +1.00000 q^{7} +(-2.76858 - 0.578773i) q^{8} +(-4.69833 + 2.29804i) q^{10} +3.21284i q^{11} -5.08157i q^{13} +(0.621372 + 1.27039i) q^{14} +(-0.985049 - 3.87681i) q^{16} -0.616762 q^{17} +4.48549i q^{19} +(-5.83882 - 4.54078i) q^{20} +(-4.08157 + 1.99637i) q^{22} -1.38324 q^{23} -8.67765 q^{25} +(6.45559 - 3.15755i) q^{26} +(-1.22779 + 1.57877i) q^{28} -5.67765i q^{29} +6.91117 q^{31} +(4.31299 - 3.66034i) q^{32} +(-0.383238 - 0.783529i) q^{34} +3.69833i q^{35} +6.91117i q^{37} +(-5.69833 + 2.78716i) q^{38} +(2.14049 - 10.2391i) q^{40} +0.616762 q^{41} +7.99274i q^{43} +(-5.07235 - 3.94470i) q^{44} +(-0.859506 - 1.75726i) q^{46} -4.97098 q^{47} +1.00000 q^{49} +(-5.39205 - 11.0240i) q^{50} +(8.02264 + 6.23912i) q^{52} +4.48549i q^{53} -11.8822 q^{55} +(-2.76858 - 0.578773i) q^{56} +(7.21284 - 3.52793i) q^{58} +4.00000i q^{59} -12.4782i q^{61} +(4.29441 + 8.77990i) q^{62} +(7.33004 + 3.20476i) q^{64} +18.7933 q^{65} +9.56706i q^{67} +(0.757255 - 0.973726i) q^{68} +(-4.69833 + 2.29804i) q^{70} +15.2056 q^{71} +15.5598 q^{73} +(-8.77990 + 4.29441i) q^{74} +(-7.08157 - 5.50725i) q^{76} +3.21284i q^{77} -5.23352 q^{79} +(14.3377 - 3.64304i) q^{80} +(0.383238 + 0.783529i) q^{82} -10.4257i q^{83} -2.28099i q^{85} +(-10.1539 + 4.96647i) q^{86} +(1.85951 - 8.89500i) q^{88} +14.1766 q^{89} -5.08157i q^{91} +(1.69833 - 2.18382i) q^{92} +(-3.08883 - 6.31509i) q^{94} -16.5888 q^{95} +9.73746 q^{97} +(0.621372 + 1.27039i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{4} + 8 q^{7} + 6 q^{8}+O(q^{10}) \) 8 * q + 2 * q^4 + 8 * q^7 + 6 * q^8	\( 8 q + 2 q^{4} + 8 q^{7} + 6 q^{8} - 4 q^{10} - 6 q^{16} - 4 q^{17} - 24 q^{20} - 12 q^{23} - 24 q^{25} + 28 q^{26} + 2 q^{28} + 8 q^{31} + 30 q^{32} - 4 q^{34} - 12 q^{38} + 28 q^{40} + 4 q^{41} - 16 q^{44} + 4 q^{46} + 8 q^{49} + 20 q^{50} - 12 q^{52} - 8 q^{55} + 6 q^{56} + 44 q^{58} - 12 q^{62} + 26 q^{64} + 16 q^{65} + 16 q^{68} - 4 q^{70} + 28 q^{71} - 8 q^{73} - 4 q^{74} - 24 q^{76} - 40 q^{79} + 4 q^{80} + 4 q^{82} - 24 q^{86} + 4 q^{88} - 20 q^{89} - 20 q^{92} - 72 q^{94} - 40 q^{95} + 40 q^{97}+O(q^{100}) \) 8 * q + 2 * q^4 + 8 * q^7 + 6 * q^8 - 4 * q^10 - 6 * q^16 - 4 * q^17 - 24 * q^20 - 12 * q^23 - 24 * q^25 + 28 * q^26 + 2 * q^28 + 8 * q^31 + 30 * q^32 - 4 * q^34 - 12 * q^38 + 28 * q^40 + 4 * q^41 - 16 * q^44 + 4 * q^46 + 8 * q^49 + 20 * q^50 - 12 * q^52 - 8 * q^55 + 6 * q^56 + 44 * q^58 - 12 * q^62 + 26 * q^64 + 16 * q^65 + 16 * q^68 - 4 * q^70 + 28 * q^71 - 8 * q^73 - 4 * q^74 - 24 * q^76 - 40 * q^79 + 4 * q^80 + 4 * q^82 - 24 * q^86 + 4 * q^88 - 20 * q^89 - 20 * q^92 - 72 * q^94 - 40 * q^95 + 40 * q^97

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