LMFDB - Embedded newform 350.2.g.b.307.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(293,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 2]))

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

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

chi := DirichletCharacter("350.293");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.g (of order $4$, 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:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 22 x^{14} - 52 x^{13} + 72 x^{12} - 32 x^{11} + 148 x^{10} + 268 x^{9} - 461 x^{8} + \cdots + 81 $ x^16 - 4x^15 + 22x^14 - 52x^13 + 72x^12 - 32x^11 + 148x^10 + 268x^9 - 461x^8 - 1548x^7 - 840x^6 + 1800x^5 + 2772x^4 + 1296x^3 + 54x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.5
Root			$-0.847914 - 0.111630i$ of defining polynomial
Character	$\chi$	$=$	350.307
Dual form			350.2.g.b.293.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(-2.28737 - 2.28737i) q^{3} +1.00000i q^{4} -3.23483i q^{6} +(-2.51027 - 0.835798i) q^{7} +(-0.707107 + 0.707107i) q^{8} +7.46410i q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(-2.28737 - 2.28737i) q^{3} +1.00000i q^{4} -3.23483i q^{6} +(-2.51027 - 0.835798i) q^{7} +(-0.707107 + 0.707107i) q^{8} +7.46410i q^{9} -1.73205 q^{11} +(2.28737 - 2.28737i) q^{12} +(1.67447 + 1.67447i) q^{13} +(-1.18403 - 2.36603i) q^{14} -1.00000 q^{16} +(-3.96184 + 3.96184i) q^{17} +(-5.27792 + 5.27792i) q^{18} -5.60288 q^{19} +(3.83013 + 7.65368i) q^{21} +(-1.22474 - 1.22474i) q^{22} +(-1.55291 + 1.55291i) q^{23} +3.23483 q^{24} +2.36806i q^{26} +(10.2110 - 10.2110i) q^{27} +(0.835798 - 2.51027i) q^{28} -1.26795i q^{29} +4.10160i q^{31} +(-0.707107 - 0.707107i) q^{32} +(3.96184 + 3.96184i) q^{33} -5.60288 q^{34} -7.46410 q^{36} +(-5.79555 - 5.79555i) q^{37} +(-3.96184 - 3.96184i) q^{38} -7.66025i q^{39} -9.70448i q^{41} +(-2.70366 + 8.12028i) q^{42} +(2.44949 - 2.44949i) q^{43} -1.73205i q^{44} -2.19615 q^{46} +(-2.90027 + 2.90027i) q^{47} +(2.28737 + 2.28737i) q^{48} +(5.60288 + 4.19615i) q^{49} +18.1244 q^{51} +(-1.67447 + 1.67447i) q^{52} +(-2.68973 + 2.68973i) q^{53} +14.4406 q^{54} +(2.36603 - 1.18403i) q^{56} +(12.8159 + 12.8159i) q^{57} +(0.896575 - 0.896575i) q^{58} -11.2058i q^{61} +(-2.90027 + 2.90027i) q^{62} +(6.23848 - 18.7369i) q^{63} -1.00000i q^{64} +5.60288i q^{66} +(-2.77766 - 2.77766i) q^{67} +(-3.96184 - 3.96184i) q^{68} +7.10417 q^{69} -2.19615 q^{71} +(-5.27792 - 5.27792i) q^{72} +(5.18763 + 5.18763i) q^{73} -8.19615i q^{74} -5.60288i q^{76} +(4.34791 + 1.44764i) q^{77} +(5.41662 - 5.41662i) q^{78} -2.00000i q^{79} -24.3205 q^{81} +(6.86210 - 6.86210i) q^{82} +(6.86210 + 6.86210i) q^{83} +(-7.65368 + 3.83013i) q^{84} +3.46410 q^{86} +(-2.90027 + 2.90027i) q^{87} +(1.22474 - 1.22474i) q^{88} -9.70448 q^{89} +(-2.80385 - 5.60288i) q^{91} +(-1.55291 - 1.55291i) q^{92} +(9.38186 - 9.38186i) q^{93} -4.10160 q^{94} +3.23483i q^{96} +(-3.34894 + 3.34894i) q^{97} +(0.994709 + 6.92896i) q^{98} -12.9282i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 16 q^{16} - 8 q^{21} - 64 q^{36} + 48 q^{46} + 96 q^{51} + 24 q^{56} + 48 q^{71} - 112 q^{81} - 128 q^{91}+O(q^{100}) $ 16 * q - 16 * q^16 - 8 * q^21 - 64 * q^36 + 48 * q^46 + 96 * q^51 + 24 * q^56 + 48 * q^71 - 112 * q^81 - 128 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	−2.28737	−	2.28737i	−1.32061	−	1.32061i	−0.913280	−	0.407332i	$-0.866459\pi$
$3$	−2.28737	−	2.28737i	−1.32061	−	1.32061i	−0.407332	−	0.913280i	$-0.633541\pi$
$4$			1.00000i			0.500000i
$5$		0			0
$5$		0			0
$6$		−	3.23483i		−	1.32061i
$7$	−2.51027	−	0.835798i	−0.948792	−	0.315902i
$7$	−2.51027	−	0.835798i	−0.948792	−	0.315902i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$			7.46410i			2.48803i
$10$		0			0
$11$	−1.73205			−0.522233			−0.261116	−	0.965307i	$-0.584091\pi$
$11$	−1.73205			−0.522233			−0.261116	+	0.965307i	$0.584091\pi$
$12$	2.28737	−	2.28737i	0.660306	−	0.660306i
$13$	1.67447	+	1.67447i	0.464414	+	0.464414i	0.900099	−	0.435685i	$-0.143494\pi$
$13$	1.67447	+	1.67447i	0.464414	+	0.464414i	−0.435685	+	0.900099i	$0.643494\pi$
$14$	−1.18403	−	2.36603i	−0.316445	−	0.632347i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−3.96184	+	3.96184i	−0.960887	+	0.960887i	−0.999263	−	0.0383767i	$-0.987781\pi$
$17$	−3.96184	+	3.96184i	−0.960887	+	0.960887i	0.0383767	+	0.999263i	$0.487781\pi$
$18$	−5.27792	+	5.27792i	−1.24402	+	1.24402i
$19$	−5.60288			−1.28539			−0.642695	−	0.766122i	$-0.722184\pi$
$19$	−5.60288			−1.28539			−0.642695	+	0.766122i	$0.722184\pi$
$20$		0			0
$21$	3.83013	+	7.65368i	0.835802	+	1.67017i
$22$	−1.22474	−	1.22474i	−0.261116	−	0.261116i
$23$	−1.55291	+	1.55291i	−0.323805	+	0.323805i	−0.850225	−	0.526420i	$-0.823534\pi$
$23$	−1.55291	+	1.55291i	−0.323805	+	0.323805i	0.526420	+	0.850225i	$0.323534\pi$
$24$	3.23483			0.660306
$25$		0			0
$26$			2.36806i			0.464414i
$27$	10.2110	−	10.2110i	1.96512	−	1.96512i
$28$	0.835798	−	2.51027i	0.157951	−	0.474396i
$29$		−	1.26795i		−	0.235452i	−0.993046	−	0.117726i	$-0.962440\pi$
$29$		−	1.26795i		−	0.235452i	0.993046	−	0.117726i	$-0.0375605\pi$
$30$		0			0
$31$			4.10160i			0.736668i	0.929693	+	0.368334i	$0.120072\pi$
$31$			4.10160i			0.736668i	−0.929693	+	0.368334i	$0.879928\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	3.96184	+	3.96184i	0.689667	+	0.689667i
$34$	−5.60288			−0.960887
$35$		0			0
$36$	−7.46410			−1.24402
$37$	−5.79555	−	5.79555i	−0.952783	−	0.952783i	0.0461511	−	0.998934i	$-0.485304\pi$
$37$	−5.79555	−	5.79555i	−0.952783	−	0.952783i	−0.998934	+	0.0461511i	$0.985304\pi$
$38$	−3.96184	−	3.96184i	−0.642695	−	0.642695i
$39$		−	7.66025i		−	1.22662i
$40$		0			0
$41$		−	9.70448i		−	1.51559i	−0.652496	−	0.757793i	$-0.726278\pi$
$41$		−	9.70448i		−	1.51559i	0.652496	−	0.757793i	$-0.273722\pi$
$42$	−2.70366	+	8.12028i	−0.417184	+	1.25299i
$43$	2.44949	−	2.44949i	0.373544	−	0.373544i	−0.495222	−	0.868766i	$-0.664913\pi$
$43$	2.44949	−	2.44949i	0.373544	−	0.373544i	0.868766	+	0.495222i	$0.164913\pi$
$44$		−	1.73205i		−	0.261116i
$45$		0			0
$46$	−2.19615			−0.323805
$47$	−2.90027	+	2.90027i	−0.423047	+	0.423047i	−0.886252	−	0.463204i	$-0.846700\pi$
$47$	−2.90027	+	2.90027i	−0.423047	+	0.423047i	0.463204	+	0.886252i	$0.346700\pi$
$48$	2.28737	+	2.28737i	0.330153	+	0.330153i
$49$	5.60288	+	4.19615i	0.800412	+	0.599450i
$50$		0			0
$51$	18.1244			2.53792
$52$	−1.67447	+	1.67447i	−0.232207	+	0.232207i
$53$	−2.68973	+	2.68973i	−0.369462	+	0.369462i	−0.867281	−	0.497819i	$-0.834134\pi$
$53$	−2.68973	+	2.68973i	−0.369462	+	0.369462i	0.497819	+	0.867281i	$0.334134\pi$
$54$	14.4406			1.96512
$55$		0			0
$56$	2.36603	−	1.18403i	0.316173	−	0.158222i
$57$	12.8159	+	12.8159i	1.69750	+	1.69750i
$58$	0.896575	−	0.896575i	0.117726	−	0.117726i
$59$		0			0			−	1.00000i	$-0.5\pi$
$59$		0			0				1.00000i	$0.5\pi$
$60$		0			0
$61$		−	11.2058i		−	1.43475i	−0.696686	−	0.717376i	$-0.745343\pi$
$61$		−	11.2058i		−	1.43475i	0.696686	−	0.717376i	$-0.254657\pi$
$62$	−2.90027	+	2.90027i	−0.368334	+	0.368334i
$63$	6.23848	−	18.7369i	0.785975	−	2.36063i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$			5.60288i			0.689667i
$67$	−2.77766	−	2.77766i	−0.339345	−	0.339345i	0.516776	−	0.856121i	$-0.327132\pi$
$67$	−2.77766	−	2.77766i	−0.339345	−	0.339345i	−0.856121	+	0.516776i	$0.827132\pi$
$68$	−3.96184	−	3.96184i	−0.480443	−	0.480443i
$69$	7.10417			0.855242
$70$		0			0
$71$	−2.19615			−0.260635			−0.130318	−	0.991472i	$-0.541600\pi$
$71$	−2.19615			−0.260635			−0.130318	+	0.991472i	$0.541600\pi$
$72$	−5.27792	−	5.27792i	−0.622008	−	0.622008i
$73$	5.18763	+	5.18763i	0.607167	+	0.607167i	0.942205	−	0.335038i	$-0.108749\pi$
$73$	5.18763	+	5.18763i	0.607167	+	0.607167i	−0.335038	+	0.942205i	$0.608749\pi$
$74$		−	8.19615i		−	0.952783i
$75$		0			0
$76$		−	5.60288i		−	0.642695i
$77$	4.34791	+	1.44764i	0.495490	+	0.164974i
$78$	5.41662	−	5.41662i	0.613311	−	0.613311i
$79$		−	2.00000i		−	0.225018i	−0.993651	−	0.112509i	$-0.964111\pi$
$79$		−	2.00000i		−	0.225018i	0.993651	−	0.112509i	$-0.0358886\pi$
$80$		0			0
$81$	−24.3205			−2.70228
$82$	6.86210	−	6.86210i	0.757793	−	0.757793i
$83$	6.86210	+	6.86210i	0.753214	+	0.753214i	0.975078	−	0.221864i	$-0.0712141\pi$
$83$	6.86210	+	6.86210i	0.753214	+	0.753214i	−0.221864	+	0.975078i	$0.571214\pi$
$84$	−7.65368	+	3.83013i	−0.835085	+	0.417901i
$85$		0			0
$86$	3.46410			0.373544
$87$	−2.90027	+	2.90027i	−0.310941	+	0.310941i
$88$	1.22474	−	1.22474i	0.130558	−	0.130558i
$89$	−9.70448			−1.02867			−0.514336	−	0.857589i	$-0.671962\pi$
$89$	−9.70448			−1.02867			−0.514336	+	0.857589i	$0.671962\pi$
$90$		0			0
$91$	−2.80385	−	5.60288i	−0.293923	−	0.587342i
$92$	−1.55291	−	1.55291i	−0.161903	−	0.161903i
$93$	9.38186	−	9.38186i	0.972853	−	0.972853i
$94$	−4.10160			−0.423047
$95$		0			0
$96$			3.23483i			0.330153i
$97$	−3.34894	+	3.34894i	−0.340033	+	0.340033i	−0.856380	−	0.516347i	$-0.827292\pi$
$97$	−3.34894	+	3.34894i	−0.340033	+	0.340033i	0.516347	+	0.856380i	$0.327292\pi$
$98$	0.994709	+	6.92896i	0.100481	+	0.699931i
$99$		−	12.9282i		−	1.29933i
$100$		0			0
$101$			7.10417i			0.706892i	0.935455	+	0.353446i	$0.114990\pi$
$101$			7.10417i			0.706892i	−0.935455	+	0.353446i	$0.885010\pi$
$102$	12.8159	+	12.8159i	1.26896	+	1.26896i
$103$	−3.34894	−	3.34894i	−0.329981	−	0.329981i	0.522598	−	0.852579i	$-0.324963\pi$
$103$	−3.34894	−	3.34894i	−0.329981	−	0.329981i	−0.852579	+	0.522598i	$0.824963\pi$
$104$	−2.36806			−0.232207
$105$		0			0
$106$	−3.80385			−0.369462
$107$	9.46979	+	9.46979i	0.915479	+	0.915479i	0.996696	−	0.0812173i	$-0.0258808\pi$
$107$	9.46979	+	9.46979i	0.915479	+	0.915479i	−0.0812173	+	0.996696i	$0.525881\pi$
$108$	10.2110	+	10.2110i	0.982558	+	0.982558i
$109$			2.00000i			0.191565i	0.995402	+	0.0957826i	$0.0305354\pi$
$109$			2.00000i			0.191565i	−0.995402	+	0.0957826i	$0.969465\pi$
$110$		0			0
$111$			26.5131i			2.51651i
$112$	2.51027	+	0.835798i	0.237198	+	0.0789755i
$113$	−7.91688	+	7.91688i	−0.744757	+	0.744757i	−0.973489	−	0.228732i	$-0.926542\pi$
$113$	−7.91688	+	7.91688i	−0.744757	+	0.744757i	0.228732	+	0.973489i	$0.426542\pi$
$114$			18.1244i			1.69750i
$115$		0			0
$116$	1.26795			0.117726
$117$	−12.4984	+	12.4984i	−1.15548	+	1.15548i
$118$		0			0
$119$	13.2566	−	6.63397i	1.21523	−	0.608135i
$120$		0			0
$121$	−8.00000			−0.727273
$122$	7.92367	−	7.92367i	0.717376	−	0.717376i
$123$	−22.1977	+	22.1977i	−2.00150	+	2.00150i
$124$	−4.10160			−0.368334
$125$		0			0
$126$	17.6603	−	8.83771i	1.57330	−	0.787326i
$127$	−12.7279	−	12.7279i	−1.12942	−	1.12942i	−0.990271	−	0.139149i	$-0.955563\pi$
$127$	−12.7279	−	12.7279i	−1.12942	−	1.12942i	−0.139149	−	0.990271i	$-0.544437\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−11.2058			−0.986613
$130$		0			0
$131$		0			0		1.00000			$0$
$131$		0			0		−1.00000			$\pi$
$132$	−3.96184	+	3.96184i	−0.344834	+	0.344834i
$133$	14.0647	+	4.68288i	1.21957	+	0.406057i
$134$		−	3.92820i		−	0.339345i
$135$		0			0
$136$		−	5.60288i		−	0.480443i
$137$	0.568406	+	0.568406i	0.0485622	+	0.0485622i	0.730971	−	0.682409i	$-0.239068\pi$
$137$	0.568406	+	0.568406i	0.0485622	+	0.0485622i	−0.682409	+	0.730971i	$0.739068\pi$
$138$	5.02341	+	5.02341i	0.427621	+	0.427621i
$139$	2.60031			0.220555			0.110278	−	0.993901i	$-0.464826\pi$
$139$	2.60031			0.220555			0.110278	+	0.993901i	$0.464826\pi$
$140$		0			0
$141$	13.2679			1.11736
$142$	−1.55291	−	1.55291i	−0.130318	−	0.130318i
$143$	−2.90027	−	2.90027i	−0.242532	−	0.242532i
$144$		−	7.46410i		−	0.622008i
$145$		0			0
$146$			7.33642i			0.607167i
$147$	−3.21771	−	22.4140i	−0.265392	−	1.84868i
$148$	5.79555	−	5.79555i	0.476392	−	0.476392i
$149$			16.3923i			1.34291i	0.741045	+	0.671455i	$0.234330\pi$
$149$			16.3923i			1.34291i	−0.741045	+	0.671455i	$0.765670\pi$
$150$		0			0
$151$	−16.5885			−1.34995			−0.674975	−	0.737841i	$-0.735845\pi$
$151$	−16.5885			−1.34995			−0.674975	+	0.737841i	$0.735845\pi$
$152$	3.96184	−	3.96184i	0.321347	−	0.321347i
$153$	−29.5716	−	29.5716i	−2.39072	−	2.39072i
$154$	2.05080	+	4.09808i	0.165258	+	0.330232i
$155$		0			0
$156$	7.66025			0.613311
$157$	15.3987	−	15.3987i	1.22895	−	1.22895i	0.264586	−	0.964362i	$-0.414765\pi$
$157$	15.3987	−	15.3987i	1.22895	−	1.22895i	0.964362	−	0.264586i	$-0.0852353\pi$
$158$	1.41421	−	1.41421i	0.112509	−	0.112509i
$159$	12.3048			0.975833
$160$		0			0
$161$	5.19615	−	2.60031i	0.409514	−	0.204933i
$162$	−17.1972	−	17.1972i	−1.35114	−	1.35114i
$163$	2.77766	−	2.77766i	0.217563	−	0.217563i	−0.589908	−	0.807471i	$-0.700836\pi$
$163$	2.77766	−	2.77766i	0.217563	−	0.217563i	0.807471	+	0.589908i	$0.200836\pi$
$164$	9.70448			0.757793
$165$		0			0
$166$			9.70448i			0.753214i
$167$	−15.8473	+	15.8473i	−1.22630	+	1.22630i	−0.260953	+	0.965351i	$0.584037\pi$
$167$	−15.8473	+	15.8473i	−1.22630	+	1.22630i	−0.965351	+	0.260953i	$0.915963\pi$
$168$	−8.12028	−	2.70366i	−0.626493	−	0.208592i
$169$		−	7.39230i		−	0.568639i
$170$		0			0
$171$		−	41.8205i		−	3.19809i
$172$	2.44949	+	2.44949i	0.186772	+	0.186772i
$173$	−10.8239	−	10.8239i	−0.822929	−	0.822929i	0.163598	−	0.986527i	$-0.447690\pi$
$173$	−10.8239	−	10.8239i	−0.822929	−	0.822929i	−0.986527	+	0.163598i	$0.947690\pi$
$174$	−4.10160			−0.310941
$175$		0			0
$176$	1.73205			0.130558
$177$		0			0
$178$	−6.86210	−	6.86210i	−0.514336	−	0.514336i
$179$			6.80385i			0.508543i	0.967133	+	0.254272i	$0.0818358\pi$
$179$			6.80385i			0.508543i	−0.967133	+	0.254272i	$0.918164\pi$
$180$		0			0
$181$		−	3.00258i		−	0.223180i	−0.993754	−	0.111590i	$-0.964406\pi$
$181$		−	3.00258i		−	0.223180i	0.993754	−	0.111590i	$-0.0355943\pi$
$182$	1.97922	−	5.94446i	0.146709	−	0.440632i
$183$	−25.6317	+	25.6317i	−1.89475	+	1.89475i
$184$		−	2.19615i		−	0.161903i
$185$		0			0
$186$	13.2679			0.972853
$187$	6.86210	−	6.86210i	0.501807	−	0.501807i
$188$	−2.90027	−	2.90027i	−0.211524	−	0.211524i
$189$	−34.1668	+	17.0981i	−2.48527	+	1.24370i
$190$		0			0
$191$	12.9282			0.935452			0.467726	−	0.883874i	$-0.345073\pi$
$191$	12.9282			0.935452			0.467726	+	0.883874i	$0.345073\pi$
$192$	−2.28737	+	2.28737i	−0.165077	+	0.165077i
$193$	4.33057	−	4.33057i	0.311721	−	0.311721i	−0.533855	−	0.845576i	$-0.679257\pi$
$193$	4.33057	−	4.33057i	0.311721	−	0.311721i	0.845576	+	0.533855i	$0.179257\pi$
$194$	−4.73611			−0.340033
$195$		0			0
$196$	−4.19615	+	5.60288i	−0.299725	+	0.400206i
$197$	15.8338	+	15.8338i	1.12811	+	1.12811i	0.990485	+	0.137623i	$0.0439464\pi$
$197$	15.8338	+	15.8338i	1.12811	+	1.12811i	0.137623	+	0.990485i	$0.456054\pi$
$198$	9.14162	−	9.14162i	0.649667	−	0.649667i
$199$	15.3074			1.08511			0.542555	−	0.840020i	$-0.317457\pi$
$199$	15.3074			1.08511			0.542555	+	0.840020i	$0.317457\pi$
$200$		0			0
$201$			12.7071i			0.896287i
$202$	−5.02341	+	5.02341i	−0.353446	+	0.353446i
$203$	−1.05975	+	3.18289i	−0.0743798	+	0.223395i
$204$			18.1244i			1.26896i
$205$		0			0
$206$		−	4.73611i		−	0.329981i
$207$	−11.5911	−	11.5911i	−0.805638	−	0.805638i
$208$	−1.67447	−	1.67447i	−0.116104	−	0.116104i
$209$	9.70448			0.671273
$210$		0			0
$211$	9.19615			0.633089			0.316545	−	0.948578i	$-0.397477\pi$
$211$	9.19615			0.633089			0.316545	+	0.948578i	$0.397477\pi$
$212$	−2.68973	−	2.68973i	−0.184731	−	0.184731i
$213$	5.02341	+	5.02341i	0.344198	+	0.344198i
$214$			13.3923i			0.915479i
$215$		0			0
$216$			14.4406i			0.982558i
$217$	3.42811	−	10.2961i	0.232715	−	0.698945i
$218$	−1.41421	+	1.41421i	−0.0957826	+	0.0957826i
$219$		−	23.7321i		−	1.60366i
$220$		0			0
$221$	−13.2679			−0.892499
$222$	−18.7476	+	18.7476i	−1.25826	+	1.25826i
$223$	12.0497	+	12.0497i	0.806910	+	0.806910i	0.984165	−	0.177255i	$-0.0567217\pi$
$223$	12.0497	+	12.0497i	0.806910	+	0.806910i	−0.177255	+	0.984165i	$0.556722\pi$
$224$	1.18403	+	2.36603i	0.0791112	+	0.158087i
$225$		0			0
$226$	−11.1962			−0.744757
$227$	7.92367	−	7.92367i	0.525913	−	0.525913i	−0.393438	−	0.919351i	$-0.628715\pi$
$227$	7.92367	−	7.92367i	0.525913	−	0.525913i	0.919351	+	0.393438i	$0.128715\pi$
$228$	−12.8159	+	12.8159i	−0.848751	+	0.848751i
$229$	−4.10160			−0.271041			−0.135521	−	0.990775i	$-0.543271\pi$
$229$	−4.10160			−0.271041			−0.135521	+	0.990775i	$0.543271\pi$
$230$		0			0
$231$	−6.63397	−	13.2566i	−0.436483	−	0.872218i
$232$	0.896575	+	0.896575i	0.0588631	+	0.0588631i
$233$	−7.34847	+	7.34847i	−0.481414	+	0.481414i	−0.905583	−	0.424169i	$-0.860566\pi$
$233$	−7.34847	+	7.34847i	−0.481414	+	0.481414i	0.424169	+	0.905583i	$0.360566\pi$
$234$	−17.6754			−1.15548
$235$		0			0
$236$		0			0
$237$	−4.57474	+	4.57474i	−0.297161	+	0.297161i
$238$	14.0647	+	4.68288i	0.911681	+	0.303546i
$239$			25.8564i			1.67251i	0.548339	+	0.836256i	$0.315260\pi$
$239$			25.8564i			1.67251i	−0.548339	+	0.836256i	$0.684740\pi$
$240$		0			0
$241$			1.50129i			0.0967065i	0.998830	+	0.0483532i	$0.0153973\pi$
$241$			1.50129i			0.0967065i	−0.998830	+	0.0483532i	$0.984603\pi$
$242$	−5.65685	−	5.65685i	−0.363636	−	0.363636i
$243$	24.9968	+	24.9968i	1.60355	+	1.60355i
$244$	11.2058			0.717376
$245$		0			0
$246$	−31.3923			−2.00150
$247$	−9.38186	−	9.38186i	−0.596953	−	0.596953i
$248$	−2.90027	−	2.90027i	−0.184167	−	0.184167i
$249$		−	31.3923i		−	1.98941i
$250$		0			0
$251$			16.8087i			1.06095i	0.847700	+	0.530476i	$0.177987\pi$
$251$			16.8087i			1.06095i	−0.847700	+	0.530476i	$0.822013\pi$
$252$	18.7369	+	6.23848i	1.18031	+	0.392987i
$253$	2.68973	−	2.68973i	0.169102	−	0.169102i
$254$		−	18.0000i		−	1.12942i
$255$		0			0
$256$	1.00000			0.0625000
$257$	13.7242	−	13.7242i	0.856092	−	0.856092i	−0.134783	−	0.990875i	$-0.543034\pi$
$257$	13.7242	−	13.7242i	0.856092	−	0.856092i	0.990875	+	0.134783i	$0.0430336\pi$
$258$	−7.92367	−	7.92367i	−0.493306	−	0.493306i
$259$	9.70448	+	19.3923i	0.603007	+	1.20498i
$260$		0			0
$261$	9.46410			0.585813
$262$		0			0
$263$	15.8338	−	15.8338i	0.976351	−	0.976351i	−0.0233759	−	0.999727i	$-0.507441\pi$
$263$	15.8338	−	15.8338i	0.976351	−	0.976351i	0.999727	+	0.0233759i	$0.00744144\pi$
$264$	−5.60288			−0.344834
$265$		0			0
$266$	6.63397	+	13.2566i	0.406755	+	0.812812i
$267$	22.1977	+	22.1977i	1.35848	+	1.35848i
$268$	2.77766	−	2.77766i	0.169673	−	0.169673i
$269$	−12.3048			−0.750236			−0.375118	−	0.926977i	$-0.622398\pi$
$269$	−12.3048			−0.750236			−0.375118	+	0.926977i	$0.622398\pi$
$270$		0			0
$271$			19.4090i			1.17901i	0.807765	+	0.589505i	$0.200677\pi$
$271$			19.4090i			1.17901i	−0.807765	+	0.589505i	$0.799323\pi$
$272$	3.96184	−	3.96184i	0.240222	−	0.240222i
$273$	−6.40242	+	19.2293i	−0.387492	+	1.16381i
$274$			0.803848i			0.0485622i
$275$		0			0
$276$			7.10417i			0.427621i
$277$	14.9372	+	14.9372i	0.897488	+	0.897488i	0.995213	−	0.0977255i	$-0.0311567\pi$
$277$	14.9372	+	14.9372i	0.897488	+	0.897488i	−0.0977255	+	0.995213i	$0.531157\pi$
$278$	1.83869	+	1.83869i	0.110278	+	0.110278i
$279$	−30.6147			−1.83286
$280$		0			0
$281$	−13.8564			−0.826604			−0.413302	−	0.910594i	$-0.635625\pi$
$281$	−13.8564			−0.826604			−0.413302	+	0.910594i	$0.635625\pi$
$282$	9.38186	+	9.38186i	0.558681	+	0.558681i
$283$	−10.2110	−	10.2110i	−0.606983	−	0.606983i	0.335173	−	0.942157i	$-0.391205\pi$
$283$	−10.2110	−	10.2110i	−0.606983	−	0.606983i	−0.942157	+	0.335173i	$0.891205\pi$
$284$		−	2.19615i		−	0.130318i
$285$		0			0
$286$		−	4.10160i		−	0.242532i
$287$	−8.11098	+	24.3608i	−0.478776	+	1.43797i
$288$	5.27792	−	5.27792i	0.311004	−	0.311004i
$289$		−	14.3923i		−	0.846606i
$290$		0			0
$291$	15.3205			0.898104
$292$	−5.18763	+	5.18763i	−0.303583	+	0.303583i
$293$	2.12314	+	2.12314i	0.124035	+	0.124035i	0.766400	−	0.642364i	$-0.222046\pi$
$293$	2.12314	+	2.12314i	0.124035	+	0.124035i	−0.642364	+	0.766400i	$0.722046\pi$
$294$	13.5738	−	18.1244i	0.791642	−	1.05703i
$295$		0			0
$296$	8.19615			0.476392
$297$	−17.6860	+	17.6860i	−1.02625	+	1.02625i
$298$	−11.5911	+	11.5911i	−0.671455	+	0.671455i
$299$	−5.20061			−0.300759
$300$		0			0
$301$	−8.19615	+	4.10160i	−0.472418	+	0.236412i
$302$	−11.7298	−	11.7298i	−0.674975	−	0.674975i
$303$	16.2499	−	16.2499i	0.933530	−	0.933530i
$304$	5.60288			0.321347
$305$		0			0
$306$		−	41.8205i		−	2.39072i
$307$	−3.51316	+	3.51316i	−0.200507	+	0.200507i	−0.800217	−	0.599710i	$-0.795282\pi$
$307$	−3.51316	+	3.51316i	−0.200507	+	0.200507i	0.599710	+	0.800217i	$0.295282\pi$
$308$	−1.44764	+	4.34791i	−0.0824872	+	0.247745i
$309$			15.3205i			0.871553i
$310$		0			0
$311$			19.4090i			1.10058i	0.834973	+	0.550291i	$0.185483\pi$
$311$			19.4090i			1.10058i	−0.834973	+	0.550291i	$0.814517\pi$
$312$	5.41662	+	5.41662i	0.306656	+	0.306656i
$313$	−20.4221	−	20.4221i	−1.15432	−	1.15432i	−0.985676	−	0.168648i	$-0.946060\pi$
$313$	−20.4221	−	20.4221i	−1.15432	−	1.15432i	−0.168648	−	0.985676i	$-0.553940\pi$
$314$	21.7770			1.22895
$315$		0			0
$316$	2.00000			0.112509
$317$	11.5911	+	11.5911i	0.651022	+	0.651022i	0.953239	−	0.302217i	$-0.0977269\pi$
$317$	11.5911	+	11.5911i	0.651022	+	0.651022i	−0.302217	+	0.953239i	$0.597727\pi$
$318$	8.70080	+	8.70080i	0.487917	+	0.487917i
$319$			2.19615i			0.122961i
$320$		0			0
$321$		−	43.3218i		−	2.41799i
$322$	5.51293	+	1.83554i	0.307224	+	0.102291i
$323$	22.1977	−	22.1977i	1.23511	−	1.23511i
$324$		−	24.3205i		−	1.35114i
$325$		0			0
$326$	3.92820			0.217563
$327$	4.57474	−	4.57474i	0.252983	−	0.252983i
$328$	6.86210	+	6.86210i	0.378896	+	0.378896i
$329$	9.70448	−	4.85641i	0.535025	−	0.267742i
$330$		0			0
$331$	−23.5885			−1.29654			−0.648269	−	0.761411i	$-0.724507\pi$
$331$	−23.5885			−1.29654			−0.648269	+	0.761411i	$0.724507\pi$
$332$	−6.86210	+	6.86210i	−0.376607	+	0.376607i
$333$	43.2586	−	43.2586i	2.37056	−	2.37056i
$334$	−22.4115			−1.22630
$335$		0			0
$336$	−3.83013	−	7.65368i	−0.208951	−	0.417543i
$337$	−18.1953	−	18.1953i	−0.991162	−	0.991162i	0.00879972	−	0.999961i	$-0.497199\pi$
$337$	−18.1953	−	18.1953i	−0.991162	−	0.991162i	−0.999961	+	0.00879972i	$0.997199\pi$
$338$	5.22715	−	5.22715i	0.284319	−	0.284319i
$339$	36.2176			1.96707
$340$		0			0
$341$		−	7.10417i		−	0.384712i
$342$	29.5716	−	29.5716i	1.59905	−	1.59905i
$343$	−10.5576	−	15.2163i	−0.570057	−	0.821605i
$344$			3.46410i			0.186772i
$345$		0			0
$346$		−	15.3074i		−	0.822929i
$347$	−21.0609	−	21.0609i	−1.13061	−	1.13061i	−0.990076	−	0.140532i	$-0.955119\pi$
$347$	−21.0609	−	21.0609i	−1.13061	−	1.13061i	−0.140532	−	0.990076i	$-0.544881\pi$
$348$	−2.90027	−	2.90027i	−0.155471	−	0.155471i
$349$	7.10417			0.380278			0.190139	−	0.981757i	$-0.439106\pi$
$349$	7.10417			0.380278			0.190139	+	0.981757i	$0.439106\pi$
$350$		0			0
$351$	34.1962			1.82526
$352$	1.22474	+	1.22474i	0.0652791	+	0.0652791i
$353$	19.5247	+	19.5247i	1.03920	+	1.03920i	0.999200	+	0.0399971i	$0.0127349\pi$
$353$	19.5247	+	19.5247i	1.03920	+	1.03920i	0.0399971	+	0.999200i	$0.487265\pi$
$354$		0			0
$355$		0			0
$356$		−	9.70448i		−	0.514336i
$357$	−45.4970	−	15.1483i	−2.40796	−	0.801733i
$358$	−4.81105	+	4.81105i	−0.254272	+	0.254272i
$359$			10.3923i			0.548485i	0.961661	+	0.274242i	$0.0884271\pi$
$359$			10.3923i			0.548485i	−0.961661	+	0.274242i	$0.911573\pi$
$360$		0			0
$361$	12.3923			0.652227
$362$	2.12314	−	2.12314i	0.111590	−	0.111590i
$363$	18.2989	+	18.2989i	0.960445	+	0.960445i
$364$	5.60288	−	2.80385i	0.293671	−	0.146962i
$365$		0			0
$366$	−36.2487			−1.89475
$367$	−3.34894	+	3.34894i	−0.174813	+	0.174813i	−0.789090	−	0.614277i	$-0.789448\pi$
$367$	−3.34894	+	3.34894i	−0.174813	+	0.174813i	0.614277	+	0.789090i	$0.289448\pi$
$368$	1.55291	−	1.55291i	0.0809513	−	0.0809513i
$369$	72.4352			3.77083
$370$		0			0
$371$	9.00000	−	4.50386i	0.467257	−	0.233829i
$372$	9.38186	+	9.38186i	0.486427	+	0.486427i
$373$	−9.38186	+	9.38186i	−0.485774	+	0.485774i	−0.906970	−	0.421196i	$-0.861611\pi$
$373$	−9.38186	+	9.38186i	−0.485774	+	0.485774i	0.421196	+	0.906970i	$0.361611\pi$
$374$	9.70448			0.501807
$375$		0			0
$376$		−	4.10160i		−	0.211524i
$377$	2.12314	−	2.12314i	0.109347	−	0.109347i
$378$	−36.2497	−	12.0694i	−1.86449	−	0.620784i
$379$		−	33.9808i		−	1.74547i	−0.488190	−	0.872737i	$-0.662343\pi$
$379$		−	33.9808i		−	1.74547i	0.488190	−	0.872737i	$-0.337657\pi$
$380$		0			0
$381$			58.2269i			2.98305i
$382$	9.14162	+	9.14162i	0.467726	+	0.467726i
$383$	−13.7242	−	13.7242i	−0.701274	−	0.701274i	0.263410	−	0.964684i	$-0.415153\pi$
$383$	−13.7242	−	13.7242i	−0.701274	−	0.701274i	−0.964684	+	0.263410i	$0.915153\pi$
$384$	−3.23483			−0.165077
$385$		0			0
$386$	6.12436			0.311721
$387$	18.2832	+	18.2832i	0.929389	+	0.929389i
$388$	−3.34894	−	3.34894i	−0.170017	−	0.170017i
$389$		−	0.339746i		−	0.0172258i	−0.999963	−	0.00861290i	$-0.997258\pi$
$389$		−	0.339746i		−	0.0172258i	0.999963	−	0.00861290i	$-0.00274161\pi$
$390$		0			0
$391$		−	12.3048i		−	0.622280i
$392$	−6.92896	+	0.994709i	−0.349966	+	0.0502404i
$393$		0			0
$394$			22.3923i			1.12811i
$395$		0			0
$396$	12.9282			0.649667
$397$	8.37235	−	8.37235i	0.420196	−	0.420196i	−0.465075	−	0.885271i	$-0.653973\pi$
$397$	8.37235	−	8.37235i	0.420196	−	0.420196i	0.885271	+	0.465075i	$0.153973\pi$
$398$	10.8239	+	10.8239i	0.542555	+	0.542555i
$399$	−21.4598	−	42.8827i	−1.07433	−	2.14682i
$400$		0			0
$401$	14.0718			0.702712			0.351356	−	0.936242i	$-0.385721\pi$
$401$	14.0718			0.702712			0.351356	+	0.936242i	$0.385721\pi$
$402$	−8.98525	+	8.98525i	−0.448143	+	0.448143i
$403$	−6.86800	+	6.86800i	−0.342119	+	0.342119i
$404$	−7.10417			−0.353446
$405$		0			0
$406$	−3.00000	+	1.50129i	−0.148888	+	0.0745077i
$407$	10.0382	+	10.0382i	0.497575	+	0.497575i
$408$	−12.8159	+	12.8159i	−0.634479	+	0.634479i
$409$	−35.1186			−1.73650			−0.868251	−	0.496125i	$-0.834756\pi$
$409$	−35.1186			−1.73650			−0.868251	+	0.496125i	$0.834756\pi$
$410$		0			0
$411$		−	2.60031i		−	0.128264i
$412$	3.34894	−	3.34894i	0.164990	−	0.164990i
$413$		0			0
$414$		−	16.3923i		−	0.805638i
$415$		0			0
$416$		−	2.36806i		−	0.116104i
$417$	−5.94786	−	5.94786i	−0.291268	−	0.291268i
$418$	6.86210	+	6.86210i	0.335636	+	0.335636i
$419$	−36.2176			−1.76935			−0.884673	−	0.466212i	$-0.845618\pi$
$419$	−36.2176			−1.76935			−0.884673	+	0.466212i	$0.845618\pi$
$420$		0			0
$421$	29.1769			1.42200			0.710998	−	0.703194i	$-0.248244\pi$
$421$	29.1769			1.42200			0.710998	+	0.703194i	$0.248244\pi$
$422$	6.50266	+	6.50266i	0.316545	+	0.316545i
$423$	−21.6479	−	21.6479i	−1.05256	−	1.05256i
$424$		−	3.80385i		−	0.184731i
$425$		0			0
$426$			7.10417i			0.344198i
$427$	−9.36576	+	28.1295i	−0.453241	+	1.36128i
$428$	−9.46979	+	9.46979i	−0.457740	+	0.457740i
$429$			13.2679i			0.640583i
$430$		0			0
$431$	7.51666			0.362065			0.181032	−	0.983477i	$-0.442056\pi$
$431$	7.51666			0.362065			0.181032	+	0.983477i	$0.442056\pi$
$432$	−10.2110	+	10.2110i	−0.491279	+	0.491279i
$433$	15.2344	+	15.2344i	0.732121	+	0.732121i	0.971040	−	0.238919i	$-0.0767929\pi$
$433$	15.2344	+	15.2344i	0.732121	+	0.732121i	−0.238919	+	0.971040i	$0.576793\pi$
$434$	9.70448	−	4.85641i	0.465830	−	0.233115i
$435$		0			0
$436$	−2.00000			−0.0957826
$437$	8.70080	−	8.70080i	0.416216	−	0.416216i
$438$	16.7811	−	16.7811i	0.801832	−	0.801832i
$439$	−8.20319			−0.391517			−0.195758	−	0.980652i	$-0.562717\pi$
$439$	−8.20319			−0.391517			−0.195758	+	0.980652i	$0.562717\pi$
$440$		0			0
$441$	−31.3205	+	41.8205i	−1.49145	+	1.99145i
$442$	−9.38186	−	9.38186i	−0.446249	−	0.446249i
$443$	10.6066	−	10.6066i	0.503935	−	0.503935i	−0.408723	−	0.912658i	$-0.634026\pi$
$443$	10.6066	−	10.6066i	0.503935	−	0.503935i	0.912658	+	0.408723i	$0.134026\pi$
$444$	−26.5131			−1.25826
$445$		0			0
$446$			17.0409i			0.806910i
$447$	37.4952	−	37.4952i	1.77346	−	1.77346i
$448$	−0.835798	+	2.51027i	−0.0394877	+	0.118599i
$449$		−	1.14359i		−	0.0539695i	−0.999636	−	0.0269848i	$-0.991409\pi$
$449$		−	1.14359i		−	0.0539695i	0.999636	−	0.0269848i	$-0.00859056\pi$
$450$		0			0
$451$			16.8087i			0.791488i
$452$	−7.91688	−	7.91688i	−0.372378	−	0.372378i
$453$	37.9439	+	37.9439i	1.78276	+	1.78276i
$454$	11.2058			0.525913
$455$		0			0
$456$	−18.1244			−0.848751
$457$	9.05369	+	9.05369i	0.423514	+	0.423514i	0.886412	−	0.462898i	$-0.153190\pi$
$457$	9.05369	+	9.05369i	0.423514	+	0.423514i	−0.462898	+	0.886412i	$0.653190\pi$
$458$	−2.90027	−	2.90027i	−0.135521	−	0.135521i
$459$			80.9090i			3.77651i
$460$		0			0
$461$		−	26.5131i		−	1.23484i	−0.786634	−	0.617420i	$-0.788178\pi$
$461$		−	26.5131i		−	1.23484i	0.786634	−	0.617420i	$-0.211822\pi$
$462$	4.68288	−	14.0647i	0.217867	−	0.654351i
$463$	−26.2880	+	26.2880i	−1.22171	+	1.22171i	−0.254685	+	0.967024i	$0.581972\pi$
$463$	−26.2880	+	26.2880i	−1.22171	+	1.22171i	−0.967024	+	0.254685i	$0.918028\pi$
$464$			1.26795i			0.0588631i
$465$		0			0
$466$	−10.3923			−0.481414
$467$	5.80053	−	5.80053i	0.268417	−	0.268417i	−0.560045	−	0.828462i	$-0.689216\pi$
$467$	5.80053	−	5.80053i	0.268417	−	0.268417i	0.828462	+	0.560045i	$0.189216\pi$
$468$	−12.4984	−	12.4984i	−0.577739	−	0.577739i
$469$	4.65111	+	9.29423i	0.214768	+	0.429168i
$470$		0			0
$471$	−70.4449			−3.24593
$472$		0			0
$473$	−4.24264	+	4.24264i	−0.195077	+	0.195077i
$474$	−6.46965			−0.297161
$475$		0			0
$476$	6.63397	+	13.2566i	0.304068	+	0.607614i
$477$	−20.0764	−	20.0764i	−0.919235	−	0.919235i
$478$	−18.2832	+	18.2832i	−0.836256	+	0.836256i
$479$	−19.4090			−0.886818			−0.443409	−	0.896319i	$-0.646231\pi$
$479$	−19.4090			−0.886818			−0.443409	+	0.896319i	$0.646231\pi$
$480$		0			0
$481$		−	19.4090i		−	0.884972i
$482$	−1.06157	+	1.06157i	−0.0483532	+	0.0483532i
$483$	−17.8334	−	5.93765i	−0.811446	−	0.270173i
$484$		−	8.00000i		−	0.363636i
$485$		0			0
$486$			35.3508i			1.60355i
$487$	14.5211	+	14.5211i	0.658013	+	0.658013i	0.954910	−	0.296897i	$-0.0959518\pi$
$487$	14.5211	+	14.5211i	0.658013	+	0.658013i	−0.296897	+	0.954910i	$0.595952\pi$
$488$	7.92367	+	7.92367i	0.358688	+	0.358688i
$489$	−12.7071			−0.574633
$490$		0			0
$491$	−18.9282			−0.854218			−0.427109	−	0.904200i	$-0.640468\pi$
$491$	−18.9282			−0.854218			−0.427109	+	0.904200i	$0.640468\pi$
$492$	−22.1977	−	22.1977i	−1.00075	−	1.00075i
$493$	5.02341	+	5.02341i	0.226243	+	0.226243i
$494$		−	13.2679i		−	0.596953i
$495$		0			0
$496$		−	4.10160i		−	0.184167i
$497$	5.51293	+	1.83554i	0.247289	+	0.0823352i
$498$	22.1977	−	22.1977i	0.994703	−	0.994703i
$499$		−	24.7846i		−	1.10951i	−0.832013	−	0.554756i	$-0.812812\pi$
$499$		−	24.7846i		−	1.10951i	0.832013	−	0.554756i	$-0.187188\pi$
$500$		0			0
$501$	72.4974			3.23895
$502$	−11.8855	+	11.8855i	−0.530476	+	0.530476i
$503$	12.9471	+	12.9471i	0.577282	+	0.577282i	0.934153	−	0.356872i	$-0.116157\pi$
$503$	12.9471	+	12.9471i	0.577282	+	0.577282i	−0.356872	+	0.934153i	$0.616157\pi$
$504$	8.83771	+	17.6603i	0.393663	+	0.786650i
$505$		0			0
$506$	3.80385			0.169102
$507$	−16.9089	+	16.9089i	−0.750951	+	0.750951i
$508$	12.7279	−	12.7279i	0.564710	−	0.564710i
$509$	−33.6173			−1.49006			−0.745030	−	0.667031i	$-0.767565\pi$
$509$	−33.6173			−1.49006			−0.745030	+	0.667031i	$0.767565\pi$
$510$		0			0
$511$	−8.68653	−	17.3582i	−0.384270	−	0.767880i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−57.2113	+	57.2113i	−2.52594	+	2.52594i
$514$	19.4090			0.856092
$515$		0			0
$516$		−	11.2058i		−	0.493306i
$517$	5.02341	−	5.02341i	0.220929	−	0.220929i
$518$	−6.85033	+	20.5745i	−0.300986	+	0.903993i
$519$			49.5167i			2.17354i
$520$		0			0
$521$		−	29.1134i		−	1.27548i	−0.770251	−	0.637741i	$-0.779869\pi$
$521$		−	29.1134i		−	1.27548i	0.770251	−	0.637741i	$-0.220131\pi$
$522$	6.69213	+	6.69213i	0.292907	+	0.292907i
$523$	−23.9352	−	23.9352i	−1.04662	−	1.04662i	−0.998859	−	0.0477563i	$-0.984793\pi$
$523$	−23.9352	−	23.9352i	−1.04662	−	1.04662i	−0.0477563	−	0.998859i	$-0.515207\pi$
$524$		0			0
$525$		0			0
$526$	22.3923			0.976351
$527$	−16.2499	−	16.2499i	−0.707855	−	0.707855i
$528$	−3.96184	−	3.96184i	−0.172417	−	0.172417i
$529$			18.1769i			0.790301i
$530$		0			0
$531$		0			0
$532$	−4.68288	+	14.0647i	−0.203029	+	0.609784i
$533$	16.2499	−	16.2499i	0.703859	−	0.703859i
$534$			31.3923i			1.35848i
$535$		0			0
$536$	3.92820			0.169673
$537$	15.5629	−	15.5629i	0.671589	−	0.671589i
$538$	−8.70080	−	8.70080i	−0.375118	−	0.375118i
$539$	−9.70448	−	7.26795i	−0.418002	−	0.313053i
$540$		0			0
$541$	44.5885			1.91701			0.958504	−	0.285080i	$-0.0920201\pi$
$541$	44.5885			1.91701			0.958504	+	0.285080i	$0.0920201\pi$
$542$	−13.7242	+	13.7242i	−0.589505	+	0.589505i
$543$	−6.86800	+	6.86800i	−0.294734	+	0.294734i
$544$	5.60288			0.240222
$545$		0			0
$546$	−18.1244	+	9.06996i	−0.775651	+	0.388158i
$547$	5.22715	+	5.22715i	0.223497	+	0.223497i	0.809969	−	0.586472i	$-0.199484\pi$
$547$	5.22715	+	5.22715i	0.223497	+	0.223497i	−0.586472	+	0.809969i	$0.699484\pi$
$548$	−0.568406	+	0.568406i	−0.0242811	+	0.0242811i
$549$	83.6410			3.56971
$550$		0			0
$551$			7.10417i			0.302648i
$552$	−5.02341	+	5.02341i	−0.213810	+	0.213810i
$553$	−1.67160	+	5.02053i	−0.0710835	+	0.213495i
$554$			21.1244i			0.897488i
$555$		0			0
$556$			2.60031i			0.110278i
$557$	−23.1822	−	23.1822i	−0.982262	−	0.982262i	0.0175832	−	0.999845i	$-0.494403\pi$
$557$	−23.1822	−	23.1822i	−0.982262	−	0.982262i	−0.999845	+	0.0175832i	$0.994403\pi$
$558$	−21.6479	−	21.6479i	−0.916428	−	0.916428i
$559$	8.20319			0.346958
$560$		0			0
$561$	−31.3923			−1.32538
$562$	−9.79796	−	9.79796i	−0.413302	−	0.413302i
$563$	−13.7242	−	13.7242i	−0.578406	−	0.578406i	0.356058	−	0.934464i	$-0.384121\pi$
$563$	−13.7242	−	13.7242i	−0.578406	−	0.578406i	−0.934464	+	0.356058i	$0.884121\pi$
$564$			13.2679i			0.558681i
$565$		0			0
$566$		−	14.4406i		−	0.606983i
$567$	61.0510	+	20.3270i	2.56390	+	0.853655i
$568$	1.55291	−	1.55291i	0.0651588	−	0.0651588i
$569$		−	16.1769i		−	0.678172i	−0.940755	−	0.339086i	$-0.889882\pi$
$569$		−	16.1769i		−	0.678172i	0.940755	−	0.339086i	$-0.110118\pi$
$570$		0			0
$571$	9.60770			0.402070			0.201035	−	0.979584i	$-0.435570\pi$
$571$	9.60770			0.402070			0.201035	+	0.979584i	$0.435570\pi$
$572$	2.90027	−	2.90027i	0.121266	−	0.121266i
$573$	−29.5716	−	29.5716i	−1.23537	−	1.23537i
$574$	−22.9610	+	11.4904i	−0.958375	+	0.479599i
$575$		0			0
$576$	7.46410			0.311004
$577$	−12.2140	+	12.2140i	−0.508474	+	0.508474i	−0.914058	−	0.405584i	$-0.867068\pi$
$577$	−12.2140	+	12.2140i	−0.508474	+	0.508474i	0.405584	+	0.914058i	$0.367068\pi$
$578$	10.1769	−	10.1769i	0.423303	−	0.423303i
$579$	−19.8112			−0.823327
$580$		0			0
$581$	−11.4904	−	22.9610i	−0.476701	−	0.952585i
$582$	10.8332	+	10.8332i	0.449052	+	0.449052i
$583$	4.65874	−	4.65874i	0.192945	−	0.192945i
$584$	−7.33642			−0.303583
$585$		0			0
$586$			3.00258i			0.124035i
$587$	−3.18471	+	3.18471i	−0.131447	+	0.131447i	−0.769769	−	0.638322i	$-0.779629\pi$
$587$	−3.18471	+	3.18471i	−0.131447	+	0.131447i	0.638322	+	0.769769i	$0.279629\pi$
$588$	22.4140	−	3.21771i	0.924338	−	0.132696i
$589$		−	22.9808i		−	0.946906i
$590$		0			0
$591$		−	72.4352i		−	2.97959i
$592$	5.79555	+	5.79555i	0.238196	+	0.238196i
$593$	−14.0087	−	14.0087i	−0.575266	−	0.575266i	0.358329	−	0.933595i	$-0.383347\pi$
$593$	−14.0087	−	14.0087i	−0.575266	−	0.575266i	−0.933595	+	0.358329i	$0.883347\pi$
$594$	−25.0118			−1.02625
$595$		0			0
$596$	−16.3923			−0.671455
$597$	−35.0136	−	35.0136i	−1.43301	−	1.43301i
$598$	−3.67739	−	3.67739i	−0.150380	−	0.150380i
$599$			22.7321i			0.928806i	0.885624	+	0.464403i	$0.153731\pi$
$599$			22.7321i			0.928806i	−0.885624	+	0.464403i	$0.846269\pi$
$600$		0			0
$601$			12.7071i			0.518332i	0.965833	+	0.259166i	$0.0834476\pi$
$601$			12.7071i			0.518332i	−0.965833	+	0.259166i	$0.916552\pi$
$602$	−8.69582	−	2.89529i	−0.354415	−	0.118003i
$603$	20.7327	−	20.7327i	0.844302	−	0.844302i
$604$		−	16.5885i		−	0.674975i
$605$		0			0
$606$	22.9808			0.933530
$607$	3.34894	−	3.34894i	0.135929	−	0.135929i	−0.635868	−	0.771798i	$-0.719358\pi$
$607$	3.34894	−	3.34894i	0.135929	−	0.135929i	0.771798	+	0.635868i	$0.219358\pi$
$608$	3.96184	+	3.96184i	0.160674	+	0.160674i
$609$	9.70448	−	4.85641i	0.393245	−	0.196792i
$610$		0			0
$611$	−9.71281			−0.392938
$612$	29.5716	−	29.5716i	1.19536	−	1.19536i
$613$	4.24264	−	4.24264i	0.171359	−	0.171359i	−0.616217	−	0.787576i	$-0.711336\pi$
$613$	4.24264	−	4.24264i	0.171359	−	0.171359i	0.787576	+	0.616217i	$0.211336\pi$
$614$	−4.96836			−0.200507
$615$		0			0
$616$	−4.09808	+	2.05080i	−0.165116	+	0.0826290i
$617$	8.48528	+	8.48528i	0.341605	+	0.341605i	0.856970	−	0.515366i	$-0.172344\pi$
$617$	8.48528	+	8.48528i	0.341605	+	0.341605i	−0.515366	+	0.856970i	$0.672344\pi$
$618$	−10.8332	+	10.8332i	−0.435777	+	0.435777i
$619$	−47.0211			−1.88994			−0.944969	−	0.327160i	$-0.893908\pi$
$619$	−47.0211			−1.88994			−0.944969	+	0.327160i	$0.893908\pi$
$620$		0			0
$621$			31.7137i			1.27263i
$622$	−13.7242	+	13.7242i	−0.550291	+	0.550291i
$623$	24.3608	+	8.11098i	0.975996	+	0.324960i
$624$			7.66025i			0.306656i
$625$		0			0
$626$		−	28.8812i		−	1.15432i
$627$	−22.1977	−	22.1977i	−0.886491	−	0.886491i
$628$	15.3987	+	15.3987i	0.614474	+	0.614474i
$629$	45.9221			1.83103
$630$		0			0
$631$	36.9808			1.47218			0.736090	−	0.676883i	$-0.236670\pi$
$631$	36.9808			1.47218			0.736090	+	0.676883i	$0.236670\pi$
$632$	1.41421	+	1.41421i	0.0562544	+	0.0562544i
$633$	−21.0350	−	21.0350i	−0.836065	−	0.836065i
$634$			16.3923i			0.651022i
$635$		0			0
$636$			12.3048i			0.487917i
$637$	2.35553	+	16.4082i	0.0933294	+	0.650116i
$638$	−1.55291	+	1.55291i	−0.0614805	+	0.0614805i
$639$		−	16.3923i		−	0.648470i
$640$		0			0
$641$	−36.0000			−1.42191			−0.710957	−	0.703235i	$-0.751738\pi$
$641$	−36.0000			−1.42191			−0.710957	+	0.703235i	$0.751738\pi$
$642$	30.6331	−	30.6331i	1.20899	−	1.20899i
$643$	−20.4221	−	20.4221i	−0.805368	−	0.805368i	0.178561	−	0.983929i	$-0.442856\pi$
$643$	−20.4221	−	20.4221i	−0.805368	−	0.805368i	−0.983929	+	0.178561i	$0.942856\pi$
$644$	2.60031	+	5.19615i	0.102466	+	0.204757i
$645$		0			0
$646$	31.3923			1.23511
$647$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$647$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$648$	17.1972	−	17.1972i	0.675570	−	0.675570i
$649$		0			0
$650$		0			0
$651$	−31.3923	+	15.7096i	−1.23036	+	0.615709i
$652$	2.77766	+	2.77766i	0.108782	+	0.108782i
$653$	−35.1894	+	35.1894i	−1.37707	+	1.37707i	−0.527537	+	0.849532i	$0.676884\pi$
$653$	−35.1894	+	35.1894i	−1.37707	+	1.37707i	−0.849532	+	0.527537i	$0.823116\pi$
$654$	6.46965			0.252983
$655$		0			0
$656$			9.70448i			0.378896i
$657$	−38.7210	+	38.7210i	−1.51065	+	1.51065i
$658$	10.2961	+	3.42811i	0.401384	+	0.133641i
$659$		−	11.8756i		−	0.462609i	−0.972881	−	0.231305i	$-0.925701\pi$
$659$		−	11.8756i		−	0.462609i	0.972881	−	0.231305i	$-0.0742994\pi$
$660$		0			0
$661$			26.5131i			1.03124i	0.856817	+	0.515621i	$0.172439\pi$
$661$			26.5131i			1.03124i	−0.856817	+	0.515621i	$0.827561\pi$
$662$	−16.6796	−	16.6796i	−0.648269	−	0.648269i
$663$	30.3487	+	30.3487i	1.17864	+	1.17864i
$664$	−9.70448			−0.376607
$665$		0			0
$666$	61.1769			2.37056
$667$	1.96902	+	1.96902i	0.0762406	+	0.0762406i
$668$	−15.8473	−	15.8473i	−0.613152	−	0.613152i
$669$		−	55.1244i		−	2.13123i
$670$		0			0
$671$			19.4090i			0.749275i
$672$	2.70366	−	8.12028i	0.104296	−	0.313247i
$673$	−1.13681	+	1.13681i	−0.0438209	+	0.0438209i	−0.728678	−	0.684857i	$-0.759865\pi$
$673$	−1.13681	+	1.13681i	−0.0438209	+	0.0438209i	0.684857	+	0.728678i	$0.259865\pi$
$674$		−	25.7321i		−	0.991162i
$675$		0			0
$676$	7.39230			0.284319
$677$	−33.2489	+	33.2489i	−1.27786	+	1.27786i	−0.335998	+	0.941863i	$0.609074\pi$
$677$	−33.2489	+	33.2489i	−1.27786	+	1.27786i	−0.941863	+	0.335998i	$0.890926\pi$
$678$	25.6097	+	25.6097i	0.983535	+	0.983535i
$679$	11.2058	−	5.60770i	0.430038	−	0.215204i
$680$		0			0
$681$	−36.2487			−1.38905
$682$	5.02341	−	5.02341i	0.192356	−	0.192356i
$683$	0.152304	−	0.152304i	0.00582775	−	0.00582775i	−0.704187	−	0.710015i	$-0.748688\pi$
$683$	0.152304	−	0.152304i	0.00582775	−	0.00582775i	0.710015	+	0.704187i	$0.248688\pi$
$684$	41.8205			1.59905
$685$		0			0
$686$	3.29423	−	18.2249i	0.125774	−	0.695831i
$687$	9.38186	+	9.38186i	0.357940	+	0.357940i
$688$	−2.44949	+	2.44949i	−0.0933859	+	0.0933859i
$689$	−9.00773			−0.343167
$690$		0			0
$691$			16.8087i			0.639431i	0.947514	+	0.319716i	$0.103587\pi$
$691$			16.8087i			0.639431i	−0.947514	+	0.319716i	$0.896413\pi$
$692$	10.8239	−	10.8239i	0.411464	−	0.411464i
$693$	−10.8054	+	32.4532i	−0.410462	+	1.23280i
$694$		−	29.7846i		−	1.13061i
$695$		0			0
$696$		−	4.10160i		−	0.155471i
$697$	38.4476	+	38.4476i	1.45631	+	1.45631i
$698$	5.02341	+	5.02341i	0.190139	+	0.190139i
$699$	33.6173			1.27152
$700$		0			0
$701$	−18.9282			−0.714908			−0.357454	−	0.933931i	$-0.616355\pi$
$701$	−18.9282			−0.714908			−0.357454	+	0.933931i	$0.616355\pi$
$702$	24.1803	+	24.1803i	0.912628	+	0.912628i
$703$	32.4718	+	32.4718i	1.22470	+	1.22470i
$704$			1.73205i			0.0652791i
$705$		0			0
$706$			27.6121i			1.03920i
$707$	5.93765	−	17.8334i	0.223308	−	0.670693i
$708$		0			0
$709$		−	0.392305i		−	0.0147333i	−0.999973	−	0.00736666i	$-0.997655\pi$
$709$		−	0.392305i		−	0.0147333i	0.999973	−	0.00736666i	$-0.00234490\pi$
$710$		0			0
$711$	14.9282			0.559851
$712$	6.86210	−	6.86210i	0.257168	−	0.257168i
$713$	−6.36943	−	6.36943i	−0.238537	−	0.238537i
$714$	−21.4598	−	42.8827i	−0.803111	−	1.60484i
$715$		0			0
$716$	−6.80385			−0.254272
$717$	59.1431	−	59.1431i	2.20874	−	2.20874i
$718$	−7.34847	+	7.34847i	−0.274242	+	0.274242i
$719$	26.5131			0.988773			0.494386	−	0.869242i	$-0.335393\pi$
$719$	26.5131			0.988773			0.494386	+	0.869242i	$0.335393\pi$
$720$		0			0
$721$	5.60770	+	11.2058i	0.208841	+	0.417325i
$722$	8.76268	+	8.76268i	0.326113	+	0.326113i
$723$	3.43400	−	3.43400i	0.127712	−	0.127712i
$724$	3.00258			0.111590
$725$		0			0
$726$			25.8786i			0.960445i
$727$	−25.4455	+	25.4455i	−0.943721	+	0.943721i	−0.998499	−	0.0547775i	$-0.982555\pi$
$727$	−25.4455	+	25.4455i	−0.943721	+	0.943721i	0.0547775	+	0.998499i	$0.482555\pi$
$728$	5.94446	+	1.97922i	0.220316	+	0.0733547i
$729$		−	41.3923i		−	1.53305i
$730$		0			0
$731$			19.4090i			0.717866i
$732$	−25.6317	−	25.6317i	−0.947375	−	0.947375i
$733$	3.34894	+	3.34894i	0.123696	+	0.123696i	0.766245	−	0.642549i	$-0.222123\pi$
$733$	3.34894	+	3.34894i	0.123696	+	0.123696i	−0.642549	+	0.766245i	$0.722123\pi$
$734$	−4.73611			−0.174813
$735$		0			0
$736$	2.19615			0.0809513
$737$	4.81105	+	4.81105i	0.177217	+	0.177217i
$738$	51.2194	+	51.2194i	1.88541	+	1.88541i
$739$			16.7846i			0.617432i	0.951154	+	0.308716i	$0.0998992\pi$
$739$			16.7846i			0.617432i	−0.951154	+	0.308716i	$0.900101\pi$
$740$		0			0
$741$			42.9195i			1.57669i
$742$	9.54867	+	3.17925i	0.350543	+	0.116714i
$743$	4.65874	−	4.65874i	0.170913	−	0.170913i	−0.616468	−	0.787380i	$-0.711437\pi$
$743$	4.65874	−	4.65874i	0.170913	−	0.170913i	0.787380	+	0.616468i	$0.211437\pi$
$744$			13.2679i			0.486427i
$745$		0			0
$746$	−13.2679			−0.485774
$747$	−51.2194	+	51.2194i	−1.87402	+	1.87402i
$748$	6.86210	+	6.86210i	0.250903	+	0.250903i
$749$	−15.8569	−	31.6865i	−0.579398	−	1.15780i
$750$		0			0
$751$	−13.8038			−0.503710			−0.251855	−	0.967765i	$-0.581041\pi$
$751$	−13.8038			−0.503710			−0.251855	+	0.967765i	$0.581041\pi$
$752$	2.90027	−	2.90027i	0.105762	−	0.105762i
$753$	38.4476	−	38.4476i	1.40111	−	1.40111i
$754$	3.00258			0.109347
$755$		0			0
$756$	−17.0981	−	34.1668i	−0.621851	−	1.24263i
$757$	−28.8019	−	28.8019i	−1.04682	−	1.04682i	−0.998849	−	0.0479746i	$-0.984723\pi$
$757$	−28.8019	−	28.8019i	−1.04682	−	1.04682i	−0.0479746	−	0.998849i	$-0.515277\pi$
$758$	24.0280	−	24.0280i	0.872737	−	0.872737i
$759$	−12.3048			−0.446635
$760$		0			0
$761$		−	29.1134i		−	1.05536i	−0.849443	−	0.527681i	$-0.823062\pi$
$761$		−	29.1134i		−	1.05536i	0.849443	−	0.527681i	$-0.176938\pi$
$762$	−41.1726	+	41.1726i	−1.49153	+	1.49153i
$763$	1.67160	−	5.02053i	0.0605158	−	0.181756i
$764$			12.9282i			0.467726i
$765$		0			0
$766$		−	19.4090i		−	0.701274i
$767$		0			0
$768$	−2.28737	−	2.28737i	−0.0825383	−	0.0825383i
$769$	1.50129			0.0541378			0.0270689	−	0.999634i	$-0.491383\pi$
$769$	1.50129			0.0541378			0.0270689	+	0.999634i	$0.491383\pi$
$770$		0			0
$771$	−62.7846			−2.26113
$772$	4.33057	+	4.33057i	0.155861	+	0.155861i
$773$	11.6011	+	11.6011i	0.417261	+	0.417261i	0.884259	−	0.466997i	$-0.154664\pi$
$773$	11.6011	+	11.6011i	0.417261	+	0.417261i	−0.466997	+	0.884259i	$0.654664\pi$
$774$			25.8564i			0.929389i
$775$		0			0
$776$		−	4.73611i		−	0.170017i
$777$	22.1596	−	66.5550i	0.794972	−	2.38765i
$778$	0.240237	−	0.240237i	0.00861290	−	0.00861290i
$779$			54.3731i			1.94812i
$780$		0			0
$781$	3.80385			0.136112
$782$	8.70080	−	8.70080i	0.311140	−	0.311140i
$783$	−12.9471	−	12.9471i	−0.462691	−	0.462691i
$784$	−5.60288	−	4.19615i	−0.200103	−	0.149863i
$785$		0			0
$786$		0			0
$787$	−10.3753	+	10.3753i	−0.369838	+	0.369838i	−0.867418	−	0.497580i	$-0.834222\pi$
$787$	−10.3753	+	10.3753i	−0.369838	+	0.369838i	0.497580	+	0.867418i	$0.334222\pi$
$788$	−15.8338	+	15.8338i	−0.564054	+	0.564054i
$789$	−72.4352			−2.57876
$790$		0			0
$791$	26.4904	−	13.2566i	0.941890	−	0.471349i
$792$	9.14162	+	9.14162i	0.324833	+	0.324833i
$793$	18.7637	−	18.7637i	0.666319	−	0.666319i
$794$	11.8403			0.420196
$795$		0			0
$796$			15.3074i			0.542555i
$797$	25.3253	−	25.3253i	0.897067	−	0.897067i	−0.0981086	−	0.995176i	$-0.531279\pi$
$797$	25.3253	−	25.3253i	0.897067	−	0.897067i	0.995176	+	0.0981086i	$0.0312793\pi$
$798$	15.1483	−	45.4970i	0.536244	−	1.61058i
$799$		−	22.9808i		−	0.813001i
$800$		0			0
$801$		−	72.4352i		−	2.55937i
$802$	9.95026	+	9.95026i	0.351356	+	0.351356i
$803$	−8.98525	−	8.98525i	−0.317082	−	0.317082i
$804$	−12.7071			−0.448143
$805$		0			0
$806$	−9.71281			−0.342119
$807$	28.1456	+	28.1456i	0.990771	+	0.990771i
$808$	−5.02341	−	5.02341i	−0.176723	−	0.176723i
$809$		−	51.0333i		−	1.79424i	−0.441791	−	0.897118i	$-0.645657\pi$
$809$		−	51.0333i		−	1.79424i	0.441791	−	0.897118i	$-0.354343\pi$
$810$		0			0
$811$			41.8205i			1.46852i	0.678870	+	0.734258i	$0.262470\pi$
$811$			41.8205i			1.46852i	−0.678870	+	0.734258i	$0.737530\pi$
$812$	−3.18289	−	1.05975i	−0.111698	−	0.0371899i
$813$	44.3954	−	44.3954i	1.55702	−	1.55702i
$814$			14.1962i			0.497575i
$815$		0			0
$816$	−18.1244			−0.634479
$817$	−13.7242	+	13.7242i	−0.480149	+	0.480149i
$818$	−24.8326	−	24.8326i	−0.868251	−	0.868251i
$819$	41.8205	−	20.9282i	1.46133	−	0.731291i
$820$		0			0
$821$	−33.1244			−1.15605			−0.578024	−	0.816020i	$-0.696176\pi$
$821$	−33.1244			−1.15605			−0.578024	+	0.816020i	$0.696176\pi$
$822$	1.83869	−	1.83869i	0.0641319	−	0.0641319i
$823$	−0.896575	+	0.896575i	−0.0312527	+	0.0312527i	−0.722560	−	0.691308i	$-0.757035\pi$
$823$	−0.896575	+	0.896575i	−0.0312527	+	0.0312527i	0.691308	+	0.722560i	$0.257035\pi$
$824$	4.73611			0.164990
$825$		0			0
$826$		0			0
$827$	−19.9241	−	19.9241i	−0.692828	−	0.692828i	0.270025	−	0.962853i	$-0.412968\pi$
$827$	−19.9241	−	19.9241i	−0.692828	−	0.692828i	−0.962853	+	0.270025i	$0.912968\pi$
$828$	11.5911	−	11.5911i	0.402819	−	0.402819i
$829$	14.2083			0.493476			0.246738	−	0.969082i	$-0.420641\pi$
$829$	14.2083			0.493476			0.246738	+	0.969082i	$0.420641\pi$
$830$		0			0
$831$		−	68.3336i		−	2.37047i
$832$	1.67447	−	1.67447i	0.0580518	−	0.0580518i
$833$	−38.8222	+	5.57324i	−1.34511	+	0.193101i
$834$		−	8.41154i		−	0.291268i
$835$		0			0
$836$			9.70448i			0.335636i
$837$	41.8816	+	41.8816i	1.44764	+	1.44764i
$838$	−25.6097	−	25.6097i	−0.884673	−	0.884673i
$839$	21.3125			0.735790			0.367895	−	0.929867i	$-0.380079\pi$
$839$	21.3125			0.735790			0.367895	+	0.929867i	$0.380079\pi$
$840$		0			0
$841$	27.3923			0.944562
$842$	20.6312	+	20.6312i	0.710998	+	0.710998i
$843$	31.6947	+	31.6947i	1.09162	+	1.09162i
$844$			9.19615i			0.316545i
$845$		0			0
$846$		−	30.6147i		−	1.05256i
$847$	20.0821	+	6.68638i	0.690030	+	0.229747i
$848$	2.68973	−	2.68973i	0.0923656	−	0.0923656i
$849$			46.7128i			1.60318i
$850$		0			0
$851$	18.0000			0.617032
$852$	−5.02341	+	5.02341i	−0.172099	+	0.172099i
$853$	−7.02633	−	7.02633i	−0.240577	−	0.240577i	0.576512	−	0.817089i	$-0.304413\pi$
$853$	−7.02633	−	7.02633i	−0.240577	−	0.240577i	−0.817089	+	0.576512i	$0.804413\pi$
$854$	−26.5131	+	13.2679i	−0.907261	+	0.454020i
$855$		0			0
$856$	−13.3923			−0.457740
$857$	−15.5629	+	15.5629i	−0.531619	+	0.531619i	−0.921054	−	0.389435i	$-0.872670\pi$
$857$	−15.5629	+	15.5629i	−0.531619	+	0.531619i	0.389435	+	0.921054i	$0.372670\pi$
$858$	−9.38186	+	9.38186i	−0.320291	+	0.320291i
$859$	36.2176			1.23573			0.617864	−	0.786285i	$-0.287998\pi$
$859$	36.2176			1.23573			0.617864	+	0.786285i	$0.287998\pi$
$860$		0			0
$861$	74.2750	−	37.1694i	2.53128	−	1.26673i
$862$	5.31508	+	5.31508i	0.181032	+	0.181032i
$863$	−22.3500	+	22.3500i	−0.760803	+	0.760803i	−0.976468	−	0.215664i	$-0.930808\pi$
$863$	−22.3500	+	22.3500i	−0.760803	+	0.760803i	0.215664	+	0.976468i	$0.430808\pi$
$864$	−14.4406			−0.491279
$865$		0			0
$866$			21.5448i			0.732121i
$867$	−32.9205	+	32.9205i	−1.11804	+	1.11804i
$868$	10.2961	+	3.42811i	0.349472	+	0.116357i
$869$			3.46410i			0.117512i
$870$		0			0
$871$		−	9.30221i		−	0.315193i
$872$	−1.41421	−	1.41421i	−0.0478913	−	0.0478913i
$873$	−24.9968	−	24.9968i	−0.846014	−	0.846014i
$874$	12.3048			0.416216
$875$		0			0
$876$	23.7321			0.801832
$877$	−1.31268	−	1.31268i	−0.0443260	−	0.0443260i	0.684596	−	0.728922i	$-0.259978\pi$
$877$	−1.31268	−	1.31268i	−0.0443260	−	0.0443260i	−0.728922	+	0.684596i	$0.759978\pi$
$878$	−5.80053	−	5.80053i	−0.195758	−	0.195758i
$879$		−	9.71281i		−	0.327605i
$880$		0			0
$881$			53.0263i			1.78650i	0.449560	+	0.893250i	$0.351581\pi$
$881$			53.0263i			1.78650i	−0.449560	+	0.893250i	$0.648419\pi$
$882$	−51.7185	+	7.42461i	−1.74145	+	0.250000i
$883$	−12.3998	+	12.3998i	−0.417285	+	0.417285i	−0.884267	−	0.466982i	$-0.845341\pi$
$883$	−12.3998	+	12.3998i	−0.417285	+	0.417285i	0.466982	+	0.884267i	$0.345341\pi$
$884$		−	13.2679i		−	0.446249i
$885$		0			0
$886$	15.0000			0.503935
$887$	8.70080	−	8.70080i	0.292144	−	0.292144i	−0.545783	−	0.837927i	$-0.683768\pi$
$887$	8.70080	−	8.70080i	0.292144	−	0.292144i	0.837927	+	0.545783i	$0.183768\pi$
$888$	−18.7476	−	18.7476i	−0.629129	−	0.629129i
$889$	21.3125	+	42.5885i	0.714799	+	1.42837i
$890$		0			0
$891$	42.1244			1.41122
$892$	−12.0497	+	12.0497i	−0.403455	+	0.403455i
$893$	16.2499	−	16.2499i	0.543781	−	0.543781i
$894$	53.0263			1.77346
$895$		0			0
$896$	−2.36603	+	1.18403i	−0.0790434	+	0.0395556i
$897$	11.8957	+	11.8957i	0.397186	+	0.397186i
$898$	0.808643	−	0.808643i	0.0269848	−	0.0269848i
$899$	5.20061			0.173450
$900$		0			0
$901$		−	21.3125i		−	0.710023i
$902$	−11.8855	+	11.8855i	−0.395744	+	0.395744i
$903$	28.1295	+	9.36576i	0.936090	+	0.311673i
$904$		−	11.1962i		−	0.372378i
$905$		0			0
$906$			53.6608i			1.78276i
$907$	31.6675	+	31.6675i	1.05150	+	1.05150i	0.998600	+	0.0529024i	$0.0168472\pi$
$907$	31.6675	+	31.6675i	1.05150	+	1.05150i	0.0529024	+	0.998600i	$0.483153\pi$
$908$	7.92367	+	7.92367i	0.262956	+	0.262956i
$909$	−53.0263			−1.75877
$910$		0			0
$911$	−24.0000			−0.795155			−0.397578	−	0.917568i	$-0.630149\pi$
$911$	−24.0000			−0.795155			−0.397578	+	0.917568i	$0.630149\pi$
$912$	−12.8159	−	12.8159i	−0.424375	−	0.424375i
$913$	−11.8855	−	11.8855i	−0.393353	−	0.393353i
$914$			12.8038i			0.423514i
$915$		0			0
$916$		−	4.10160i		−	0.135521i
$917$		0			0
$918$	−57.2113	+	57.2113i	−1.88825	+	1.88825i
$919$		−	9.60770i		−	0.316929i	−0.987365	−	0.158464i	$-0.949346\pi$
$919$		−	9.60770i		−	0.316929i	0.987365	−	0.158464i	$-0.0506543\pi$
$920$		0			0
$921$	16.0718			0.529584
$922$	18.7476	−	18.7476i	0.617420	−	0.617420i
$923$	−3.67739	−	3.67739i	−0.121043	−	0.121043i
$924$	13.2566	−	6.63397i	0.436109	−	0.218242i
$925$		0			0
$926$	−37.1769			−1.22171
$927$	24.9968	−	24.9968i	0.821003	−	0.821003i
$928$	−0.896575	+	0.896575i	−0.0294315	+	0.0294315i
$929$	38.8179			1.27357			0.636787	−	0.771040i	$-0.280263\pi$
$929$	38.8179			1.27357			0.636787	+	0.771040i	$0.280263\pi$
$930$		0			0
$931$	−31.3923	−	23.5106i	−1.02884	−	0.770527i
$932$	−7.34847	−	7.34847i	−0.240707	−	0.240707i
$933$	44.3954	−	44.3954i	1.45344	−	1.45344i
$934$	8.20319			0.268417
$935$		0			0
$936$		−	17.6754i		−	0.577739i
$937$	35.9850	−	35.9850i	1.17558	−	1.17558i	0.194719	−	0.980859i	$-0.437620\pi$
$937$	35.9850	−	35.9850i	1.17558	−	1.17558i	0.980859	−	0.194719i	$-0.0623795\pi$
$938$	−3.28318	+	9.86084i	−0.107200	+	0.321968i
$939$			93.4256i			3.04883i
$940$		0			0
$941$			14.2083i			0.463179i	0.972814	+	0.231589i	$0.0743926\pi$
$941$			14.2083i			0.463179i	−0.972814	+	0.231589i	$0.925607\pi$
$942$	−49.8120	−	49.8120i	−1.62296	−	1.62296i
$943$	15.0702	+	15.0702i	0.490754	+	0.490754i
$944$		0			0
$945$		0			0
$946$	−6.00000			−0.195077
$947$	5.07484	+	5.07484i	0.164910	+	0.164910i	0.784738	−	0.619828i	$-0.212798\pi$
$947$	5.07484	+	5.07484i	0.164910	+	0.164910i	−0.619828	+	0.784738i	$0.712798\pi$
$948$	−4.57474	−	4.57474i	−0.148580	−	0.148580i
$949$			17.3731i			0.563954i
$950$		0			0
$951$		−	53.0263i		−	1.71949i
$952$	−4.68288	+	14.0647i	−0.151773	+	0.455841i
$953$	−3.67423	+	3.67423i	−0.119020	+	0.119020i	−0.764108	−	0.645088i	$-0.776821\pi$
$953$	−3.67423	+	3.67423i	−0.119020	+	0.119020i	0.645088	+	0.764108i	$0.276821\pi$
$954$		−	28.3923i		−	0.919235i
$955$		0			0
$956$	−25.8564			−0.836256
$957$	5.02341	−	5.02341i	0.162384	−	0.162384i
$958$	−13.7242	−	13.7242i	−0.443409	−	0.443409i
$959$	−0.951779	−	1.90192i	−0.0307345	−	0.0614163i
$960$		0			0
$961$	14.1769			0.457320
$962$	13.7242	−	13.7242i	0.442486	−	0.442486i
$963$	−70.6835	+	70.6835i	−2.27774	+	2.27774i
$964$	−1.50129			−0.0483532
$965$		0			0
$966$	−8.41154	−	16.8087i	−0.270637	−	0.540809i
$967$	−14.2808	−	14.2808i	−0.459241	−	0.459241i	0.439165	−	0.898406i	$-0.355274\pi$
$967$	−14.2808	−	14.2808i	−0.459241	−	0.459241i	−0.898406	+	0.439165i	$0.855274\pi$
$968$	5.65685	−	5.65685i	0.181818	−	0.181818i
$969$	−101.549			−3.26221
$970$		0			0
$971$		−	11.6080i		−	0.372520i	−0.982501	−	0.186260i	$-0.940363\pi$
$971$		−	11.6080i		−	0.372520i	0.982501	−	0.186260i	$-0.0596366\pi$
$972$	−24.9968	+	24.9968i	−0.801773	+	0.801773i
$973$	−6.52747	−	2.17333i	−0.209261	−	0.0696738i
$974$			20.5359i			0.658013i
$975$		0			0
$976$			11.2058i			0.358688i
$977$	−36.4785	−	36.4785i	−1.16705	−	1.16705i	−0.982897	−	0.184155i	$-0.941045\pi$
$977$	−36.4785	−	36.4785i	−1.16705	−	1.16705i	−0.184155	−	0.982897i	$-0.558955\pi$
$978$	−8.98525	−	8.98525i	−0.287316	−	0.287316i
$979$	16.8087			0.537207
$980$		0			0
$981$	−14.9282			−0.476621
$982$	−13.3843	−	13.3843i	−0.427109	−	0.427109i
$983$	26.6713	+	26.6713i	0.850682	+	0.850682i	0.990217	−	0.139535i	$-0.0445608\pi$
$983$	26.6713	+	26.6713i	0.850682	+	0.850682i	−0.139535	+	0.990217i	$0.544561\pi$
$984$		−	31.3923i		−	1.00075i
$985$		0			0
$986$			7.10417i			0.226243i
$987$	−33.3061	−	11.0893i	−1.06014	−	0.352977i
$988$	9.38186	−	9.38186i	0.298477	−	0.298477i
$989$			7.60770i			0.241911i
$990$		0			0
$991$	−4.19615			−0.133295			−0.0666476	−	0.997777i	$-0.521230\pi$
$991$	−4.19615			−0.133295			−0.0666476	+	0.997777i	$0.521230\pi$
$992$	2.90027	−	2.90027i	0.0920835	−	0.0920835i
$993$	53.9555	+	53.9555i	1.71223	+	1.71223i
$994$	2.60031	+	5.19615i	0.0824767	+	0.164812i
$995$		0			0
$996$	31.3923			0.994703
$997$	−8.37235	+	8.37235i	−0.265155	+	0.265155i	−0.827144	−	0.561989i	$-0.810036\pi$
$997$	−8.37235	+	8.37235i	−0.265155	+	0.265155i	0.561989	+	0.827144i	$0.310036\pi$
$998$	17.5254	−	17.5254i	0.554756	−	0.554756i
$999$	−118.357			−3.74466

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.g.b.307.5	yes	16
5.2	odd	4	inner	350.2.g.b.293.1	✓	16
5.3	odd	4	inner	350.2.g.b.293.8	yes	16
5.4	even	2	inner	350.2.g.b.307.4	yes	16
7.6	odd	2	inner	350.2.g.b.307.8	yes	16
35.13	even	4	inner	350.2.g.b.293.5	yes	16
35.27	even	4	inner	350.2.g.b.293.4	yes	16
35.34	odd	2	inner	350.2.g.b.307.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.g.b.293.1	✓	16	5.2	odd	4	inner
350.2.g.b.293.4	yes	16	35.27	even	4	inner
350.2.g.b.293.5	yes	16	35.13	even	4	inner
350.2.g.b.293.8	yes	16	5.3	odd	4	inner
350.2.g.b.307.1	yes	16	35.34	odd	2	inner
350.2.g.b.307.4	yes	16	5.4	even	2	inner
350.2.g.b.307.5	yes	16	1.1	even	1	trivial
350.2.g.b.307.8	yes	16	7.6	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-2.28737 - 2.28737i) q^{3} +1.00000i q^{4} -3.23483i q^{6} +(-2.51027 - 0.835798i) q^{7} +(-0.707107 + 0.707107i) q^{8} +7.46410i q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(-2.28737 - 2.28737i) q^{3} +1.00000i q^{4} -3.23483i q^{6} +(-2.51027 - 0.835798i) q^{7} +(-0.707107 + 0.707107i) q^{8} +7.46410i q^{9} -1.73205 q^{11} +(2.28737 - 2.28737i) q^{12} +(1.67447 + 1.67447i) q^{13} +(-1.18403 - 2.36603i) q^{14} -1.00000 q^{16} +(-3.96184 + 3.96184i) q^{17} +(-5.27792 + 5.27792i) q^{18} -5.60288 q^{19} +(3.83013 + 7.65368i) q^{21} +(-1.22474 - 1.22474i) q^{22} +(-1.55291 + 1.55291i) q^{23} +3.23483 q^{24} +2.36806i q^{26} +(10.2110 - 10.2110i) q^{27} +(0.835798 - 2.51027i) q^{28} -1.26795i q^{29} +4.10160i q^{31} +(-0.707107 - 0.707107i) q^{32} +(3.96184 + 3.96184i) q^{33} -5.60288 q^{34} -7.46410 q^{36} +(-5.79555 - 5.79555i) q^{37} +(-3.96184 - 3.96184i) q^{38} -7.66025i q^{39} -9.70448i q^{41} +(-2.70366 + 8.12028i) q^{42} +(2.44949 - 2.44949i) q^{43} -1.73205i q^{44} -2.19615 q^{46} +(-2.90027 + 2.90027i) q^{47} +(2.28737 + 2.28737i) q^{48} +(5.60288 + 4.19615i) q^{49} +18.1244 q^{51} +(-1.67447 + 1.67447i) q^{52} +(-2.68973 + 2.68973i) q^{53} +14.4406 q^{54} +(2.36603 - 1.18403i) q^{56} +(12.8159 + 12.8159i) q^{57} +(0.896575 - 0.896575i) q^{58} -11.2058i q^{61} +(-2.90027 + 2.90027i) q^{62} +(6.23848 - 18.7369i) q^{63} -1.00000i q^{64} +5.60288i q^{66} +(-2.77766 - 2.77766i) q^{67} +(-3.96184 - 3.96184i) q^{68} +7.10417 q^{69} -2.19615 q^{71} +(-5.27792 - 5.27792i) q^{72} +(5.18763 + 5.18763i) q^{73} -8.19615i q^{74} -5.60288i q^{76} +(4.34791 + 1.44764i) q^{77} +(5.41662 - 5.41662i) q^{78} -2.00000i q^{79} -24.3205 q^{81} +(6.86210 - 6.86210i) q^{82} +(6.86210 + 6.86210i) q^{83} +(-7.65368 + 3.83013i) q^{84} +3.46410 q^{86} +(-2.90027 + 2.90027i) q^{87} +(1.22474 - 1.22474i) q^{88} -9.70448 q^{89} +(-2.80385 - 5.60288i) q^{91} +(-1.55291 - 1.55291i) q^{92} +(9.38186 - 9.38186i) q^{93} -4.10160 q^{94} +3.23483i q^{96} +(-3.34894 + 3.34894i) q^{97} +(0.994709 + 6.92896i) q^{98} -12.9282i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 16 q^{16} - 8 q^{21} - 64 q^{36} + 48 q^{46} + 96 q^{51} + 24 q^{56} + 48 q^{71} - 112 q^{81} - 128 q^{91}+O(q^{100}) \) 16 * q - 16 * q^16 - 8 * q^21 - 64 * q^36 + 48 * q^46 + 96 * q^51 + 24 * q^56 + 48 * q^71 - 112 * q^81 - 128 * q^91

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