LMFDB - Embedded newform 1530.2.n.o.829.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1530,2,Mod(829,1530)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1530, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 1]))

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

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

chi := DirichletCharacter("1530.829");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1530.n (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:	$12.2171115093$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 170)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			829.1
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1530.829
Dual form			1530.2.n.o.1279.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{4} +(-2.12132 + 0.707107i) q^{5} +(1.00000 + 1.00000i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{4} +(-2.12132 + 0.707107i) q^{5} +(1.00000 + 1.00000i) q^{7} +1.00000 q^{8} +(-2.12132 + 0.707107i) q^{10} +(4.41421 - 4.41421i) q^{11} +3.00000i q^{13} +(1.00000 + 1.00000i) q^{14} +1.00000 q^{16} +(-2.12132 - 3.53553i) q^{17} -1.24264i q^{19} +(-2.12132 + 0.707107i) q^{20} +(4.41421 - 4.41421i) q^{22} +(2.82843 + 2.82843i) q^{23} +(4.00000 - 3.00000i) q^{25} +3.00000i q^{26} +(1.00000 + 1.00000i) q^{28} +(0.707107 + 0.707107i) q^{29} +(7.36396 + 7.36396i) q^{31} +1.00000 q^{32} +(-2.12132 - 3.53553i) q^{34} +(-2.82843 - 1.41421i) q^{35} +(-3.24264 + 3.24264i) q^{37} -1.24264i q^{38} +(-2.12132 + 0.707107i) q^{40} +(-1.58579 + 1.58579i) q^{41} +12.2426 q^{43} +(4.41421 - 4.41421i) q^{44} +(2.82843 + 2.82843i) q^{46} +4.41421i q^{47} -5.00000i q^{49} +(4.00000 - 3.00000i) q^{50} +3.00000i q^{52} +3.00000 q^{53} +(-6.24264 + 12.4853i) q^{55} +(1.00000 + 1.00000i) q^{56} +(0.707107 + 0.707107i) q^{58} +6.89949i q^{59} +(1.87868 - 1.87868i) q^{61} +(7.36396 + 7.36396i) q^{62} +1.00000 q^{64} +(-2.12132 - 6.36396i) q^{65} -2.48528i q^{67} +(-2.12132 - 3.53553i) q^{68} +(-2.82843 - 1.41421i) q^{70} +(-2.29289 - 2.29289i) q^{71} +(4.36396 - 4.36396i) q^{73} +(-3.24264 + 3.24264i) q^{74} -1.24264i q^{76} +8.82843 q^{77} +(8.24264 - 8.24264i) q^{79} +(-2.12132 + 0.707107i) q^{80} +(-1.58579 + 1.58579i) q^{82} +4.24264 q^{83} +(7.00000 + 6.00000i) q^{85} +12.2426 q^{86} +(4.41421 - 4.41421i) q^{88} +5.48528 q^{89} +(-3.00000 + 3.00000i) q^{91} +(2.82843 + 2.82843i) q^{92} +4.41421i q^{94} +(0.878680 + 2.63604i) q^{95} +(-4.12132 + 4.12132i) q^{97} -5.00000i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{4} + 4 q^{7} + 4 q^{8}+O(q^{10}) $ 4 * q + 4 * q^2 + 4 * q^4 + 4 * q^7 + 4 * q^8	$ 4 q + 4 q^{2} + 4 q^{4} + 4 q^{7} + 4 q^{8} + 12 q^{11} + 4 q^{14} + 4 q^{16} + 12 q^{22} + 16 q^{25} + 4 q^{28} + 4 q^{31} + 4 q^{32} + 4 q^{37} - 12 q^{41} + 32 q^{43} + 12 q^{44} + 16 q^{50} + 12 q^{53} - 8 q^{55} + 4 q^{56} + 16 q^{61} + 4 q^{62} + 4 q^{64} - 12 q^{71} - 8 q^{73} + 4 q^{74} + 24 q^{77} + 16 q^{79} - 12 q^{82} + 28 q^{85} + 32 q^{86} + 12 q^{88} - 12 q^{89} - 12 q^{91} + 12 q^{95} - 8 q^{97}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^4 + 4 * q^7 + 4 * q^8 + 12 * q^11 + 4 * q^14 + 4 * q^16 + 12 * q^22 + 16 * q^25 + 4 * q^28 + 4 * q^31 + 4 * q^32 + 4 * q^37 - 12 * q^41 + 32 * q^43 + 12 * q^44 + 16 * q^50 + 12 * q^53 - 8 * q^55 + 4 * q^56 + 16 * q^61 + 4 * q^62 + 4 * q^64 - 12 * q^71 - 8 * q^73 + 4 * q^74 + 24 * q^77 + 16 * q^79 - 12 * q^82 + 28 * q^85 + 32 * q^86 + 12 * q^88 - 12 * q^89 - 12 * q^91 + 12 * q^95 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1530\mathbb{Z}\right)^\times$.

$n$	$307$	$1261$	$1361$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−2.12132	+	0.707107i	−0.948683	+	0.316228i
$5$	−2.12132	+	0.707107i	−0.948683	+	0.316228i
$6$		0			0
$7$	1.00000	+	1.00000i	0.377964	+	0.377964i	0.870367	−	0.492403i	$-0.163881\pi$
$7$	1.00000	+	1.00000i	0.377964	+	0.377964i	−0.492403	+	0.870367i	$0.663881\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	−2.12132	+	0.707107i	−0.670820	+	0.223607i
$11$	4.41421	−	4.41421i	1.33094	−	1.33094i	0.426401	−	0.904534i	$-0.359781\pi$
$11$	4.41421	−	4.41421i	1.33094	−	1.33094i	0.904534	−	0.426401i	$-0.140219\pi$
$12$		0			0
$13$			3.00000i			0.832050i	0.909353	+	0.416025i	$0.136577\pi$
$13$			3.00000i			0.832050i	−0.909353	+	0.416025i	$0.863423\pi$
$14$	1.00000	+	1.00000i	0.267261	+	0.267261i
$15$		0			0
$16$	1.00000			0.250000
$17$	−2.12132	−	3.53553i	−0.514496	−	0.857493i
$17$	−2.12132	−	3.53553i	−0.514496	−	0.857493i
$18$		0			0
$19$		−	1.24264i		−	0.285081i	−0.989789	−	0.142541i	$-0.954473\pi$
$19$		−	1.24264i		−	0.285081i	0.989789	−	0.142541i	$-0.0455272\pi$
$20$	−2.12132	+	0.707107i	−0.474342	+	0.158114i
$21$		0			0
$22$	4.41421	−	4.41421i	0.941113	−	0.941113i
$23$	2.82843	+	2.82843i	0.589768	+	0.589768i	0.937568	−	0.347801i	$-0.113071\pi$
$23$	2.82843	+	2.82843i	0.589768	+	0.589768i	−0.347801	+	0.937568i	$0.613071\pi$
$24$		0			0
$25$	4.00000	−	3.00000i	0.800000	−	0.600000i
$26$			3.00000i			0.588348i
$27$		0			0
$28$	1.00000	+	1.00000i	0.188982	+	0.188982i
$29$	0.707107	+	0.707107i	0.131306	+	0.131306i	0.769706	−	0.638399i	$-0.220403\pi$
$29$	0.707107	+	0.707107i	0.131306	+	0.131306i	−0.638399	+	0.769706i	$0.720403\pi$
$30$		0			0
$31$	7.36396	+	7.36396i	1.32261	+	1.32261i	0.911659	+	0.410947i	$0.134802\pi$
$31$	7.36396	+	7.36396i	1.32261	+	1.32261i	0.410947	+	0.911659i	$0.365198\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−2.12132	−	3.53553i	−0.363803	−	0.606339i
$35$	−2.82843	−	1.41421i	−0.478091	−	0.239046i
$36$		0			0
$37$	−3.24264	+	3.24264i	−0.533087	+	0.533087i	−0.921490	−	0.388403i	$-0.873027\pi$
$37$	−3.24264	+	3.24264i	−0.533087	+	0.533087i	0.388403	+	0.921490i	$0.373027\pi$
$38$		−	1.24264i		−	0.201583i
$39$		0			0
$40$	−2.12132	+	0.707107i	−0.335410	+	0.111803i
$41$	−1.58579	+	1.58579i	−0.247658	+	0.247658i	−0.820009	−	0.572351i	$-0.806032\pi$
$41$	−1.58579	+	1.58579i	−0.247658	+	0.247658i	0.572351	+	0.820009i	$0.306032\pi$
$42$		0			0
$43$	12.2426			1.86699			0.933493	−	0.358597i	$-0.116745\pi$
$43$	12.2426			1.86699			0.933493	+	0.358597i	$0.116745\pi$
$44$	4.41421	−	4.41421i	0.665468	−	0.665468i
$45$		0			0
$46$	2.82843	+	2.82843i	0.417029	+	0.417029i
$47$			4.41421i			0.643879i	0.946760	+	0.321940i	$0.104335\pi$
$47$			4.41421i			0.643879i	−0.946760	+	0.321940i	$0.895665\pi$
$48$		0			0
$49$		−	5.00000i		−	0.714286i
$50$	4.00000	−	3.00000i	0.565685	−	0.424264i
$51$		0			0
$52$			3.00000i			0.416025i
$53$	3.00000			0.412082			0.206041	−	0.978543i	$-0.433942\pi$
$53$	3.00000			0.412082			0.206041	+	0.978543i	$0.433942\pi$
$54$		0			0
$55$	−6.24264	+	12.4853i	−0.841757	+	1.68351i
$56$	1.00000	+	1.00000i	0.133631	+	0.133631i
$57$		0			0
$58$	0.707107	+	0.707107i	0.0928477	+	0.0928477i
$59$			6.89949i			0.898238i	0.893472	+	0.449119i	$0.148262\pi$
$59$			6.89949i			0.898238i	−0.893472	+	0.449119i	$0.851738\pi$
$60$		0			0
$61$	1.87868	−	1.87868i	0.240540	−	0.240540i	−0.576533	−	0.817074i	$-0.695595\pi$
$61$	1.87868	−	1.87868i	0.240540	−	0.240540i	0.817074	+	0.576533i	$0.195595\pi$
$62$	7.36396	+	7.36396i	0.935224	+	0.935224i
$63$		0			0
$64$	1.00000			0.125000
$65$	−2.12132	−	6.36396i	−0.263117	−	0.789352i
$66$		0			0
$67$		−	2.48528i		−	0.303625i	−0.988409	−	0.151813i	$-0.951489\pi$
$67$		−	2.48528i		−	0.303625i	0.988409	−	0.151813i	$-0.0485111\pi$
$68$	−2.12132	−	3.53553i	−0.257248	−	0.428746i
$69$		0			0
$70$	−2.82843	−	1.41421i	−0.338062	−	0.169031i
$71$	−2.29289	−	2.29289i	−0.272116	−	0.272116i	0.557835	−	0.829952i	$-0.311632\pi$
$71$	−2.29289	−	2.29289i	−0.272116	−	0.272116i	−0.829952	+	0.557835i	$0.811632\pi$
$72$		0			0
$73$	4.36396	−	4.36396i	0.510763	−	0.510763i	−0.403997	−	0.914760i	$-0.632379\pi$
$73$	4.36396	−	4.36396i	0.510763	−	0.510763i	0.914760	+	0.403997i	$0.132379\pi$
$74$	−3.24264	+	3.24264i	−0.376949	+	0.376949i
$75$		0			0
$76$		−	1.24264i		−	0.142541i
$77$	8.82843			1.00609
$78$		0			0
$79$	8.24264	−	8.24264i	0.927370	−	0.927370i	−0.0701658	−	0.997535i	$-0.522353\pi$
$79$	8.24264	−	8.24264i	0.927370	−	0.927370i	0.997535	+	0.0701658i	$0.0223528\pi$
$80$	−2.12132	+	0.707107i	−0.237171	+	0.0790569i
$81$		0			0
$82$	−1.58579	+	1.58579i	−0.175121	+	0.175121i
$83$	4.24264			0.465690			0.232845	−	0.972514i	$-0.425196\pi$
$83$	4.24264			0.465690			0.232845	+	0.972514i	$0.425196\pi$
$84$		0			0
$85$	7.00000	+	6.00000i	0.759257	+	0.650791i
$86$	12.2426			1.32016
$87$		0			0
$88$	4.41421	−	4.41421i	0.470557	−	0.470557i
$89$	5.48528			0.581439			0.290719	−	0.956808i	$-0.406105\pi$
$89$	5.48528			0.581439			0.290719	+	0.956808i	$0.406105\pi$
$90$		0			0
$91$	−3.00000	+	3.00000i	−0.314485	+	0.314485i
$92$	2.82843	+	2.82843i	0.294884	+	0.294884i
$93$		0			0
$94$			4.41421i			0.455291i
$95$	0.878680	+	2.63604i	0.0901506	+	0.270452i
$96$		0			0
$97$	−4.12132	+	4.12132i	−0.418457	+	0.418457i	−0.884672	−	0.466215i	$-0.845617\pi$
$97$	−4.12132	+	4.12132i	−0.418457	+	0.418457i	0.466215	+	0.884672i	$0.345617\pi$
$98$		−	5.00000i		−	0.505076i
$99$		0			0
$100$	4.00000	−	3.00000i	0.400000	−	0.300000i
$101$		0			0			−	1.00000i	$-0.5\pi$
$101$		0			0				1.00000i	$0.5\pi$
$102$		0			0
$103$		0			0		1.00000			$0$
$103$		0			0		−1.00000			$\pi$
$104$			3.00000i			0.294174i
$105$		0			0
$106$	3.00000			0.291386
$107$	−2.82843	+	2.82843i	−0.273434	+	0.273434i	−0.830481	−	0.557047i	$-0.811934\pi$
$107$	−2.82843	+	2.82843i	−0.273434	+	0.273434i	0.557047	+	0.830481i	$0.311934\pi$
$108$		0			0
$109$	−12.6066	+	12.6066i	−1.20749	+	1.20749i	−0.235657	+	0.971836i	$0.575724\pi$
$109$	−12.6066	+	12.6066i	−1.20749	+	1.20749i	−0.971836	+	0.235657i	$0.924276\pi$
$110$	−6.24264	+	12.4853i	−0.595212	+	1.19042i
$111$		0			0
$112$	1.00000	+	1.00000i	0.0944911	+	0.0944911i
$113$	−9.53553	−	9.53553i	−0.897028	−	0.897028i	0.0981446	−	0.995172i	$-0.468709\pi$
$113$	−9.53553	−	9.53553i	−0.897028	−	0.897028i	−0.995172	+	0.0981446i	$0.968709\pi$
$114$		0			0
$115$	−8.00000	−	4.00000i	−0.746004	−	0.373002i
$116$	0.707107	+	0.707107i	0.0656532	+	0.0656532i
$117$		0			0
$118$			6.89949i			0.635150i
$119$	1.41421	−	5.65685i	0.129641	−	0.518563i
$120$		0			0
$121$		−	27.9706i		−	2.54278i
$122$	1.87868	−	1.87868i	0.170088	−	0.170088i
$123$		0			0
$124$	7.36396	+	7.36396i	0.661303	+	0.661303i
$125$	−6.36396	+	9.19239i	−0.569210	+	0.822192i
$126$		0			0
$127$	−7.72792			−0.685742			−0.342871	−	0.939382i	$-0.611399\pi$
$127$	−7.72792			−0.685742			−0.342871	+	0.939382i	$0.611399\pi$
$128$	1.00000			0.0883883
$129$		0			0
$130$	−2.12132	−	6.36396i	−0.186052	−	0.558156i
$131$	−10.4142	−	10.4142i	−0.909894	−	0.909894i	0.0863691	−	0.996263i	$-0.472474\pi$
$131$	−10.4142	−	10.4142i	−0.909894	−	0.909894i	−0.996263	+	0.0863691i	$0.972474\pi$
$132$		0			0
$133$	1.24264	−	1.24264i	0.107751	−	0.107751i
$134$		−	2.48528i		−	0.214696i
$135$		0			0
$136$	−2.12132	−	3.53553i	−0.181902	−	0.303170i
$137$			7.41421i			0.633439i	0.948519	+	0.316720i	$0.102581\pi$
$137$			7.41421i			0.633439i	−0.948519	+	0.316720i	$0.897419\pi$
$138$		0			0
$139$	−11.0000	−	11.0000i	−0.933008	−	0.933008i	0.0648849	−	0.997893i	$-0.479332\pi$
$139$	−11.0000	−	11.0000i	−0.933008	−	0.933008i	−0.997893	+	0.0648849i	$0.979332\pi$
$140$	−2.82843	−	1.41421i	−0.239046	−	0.119523i
$141$		0			0
$142$	−2.29289	−	2.29289i	−0.192415	−	0.192415i
$143$	13.2426	+	13.2426i	1.10741	+	1.10741i
$144$		0			0
$145$	−2.00000	−	1.00000i	−0.166091	−	0.0830455i
$146$	4.36396	−	4.36396i	0.361164	−	0.361164i
$147$		0			0
$148$	−3.24264	+	3.24264i	−0.266543	+	0.266543i
$149$	−12.7279			−1.04271			−0.521356	−	0.853339i	$-0.674574\pi$
$149$	−12.7279			−1.04271			−0.521356	+	0.853339i	$0.674574\pi$
$150$		0			0
$151$		−	12.0000i		−	0.976546i	−0.872691	−	0.488273i	$-0.837627\pi$
$151$		−	12.0000i		−	0.976546i	0.872691	−	0.488273i	$-0.162373\pi$
$152$		−	1.24264i		−	0.100791i
$153$		0			0
$154$	8.82843			0.711415
$155$	−20.8284	−	10.4142i	−1.67298	−	0.836490i
$156$		0			0
$157$		−	12.0000i		−	0.957704i	−0.877896	−	0.478852i	$-0.841053\pi$
$157$		−	12.0000i		−	0.957704i	0.877896	−	0.478852i	$-0.158947\pi$
$158$	8.24264	−	8.24264i	0.655749	−	0.655749i
$159$		0			0
$160$	−2.12132	+	0.707107i	−0.167705	+	0.0559017i
$161$			5.65685i			0.445823i
$162$		0			0
$163$	12.4853	+	12.4853i	0.977923	+	0.977923i	0.999762	−	0.0218388i	$-0.00695206\pi$
$163$	12.4853	+	12.4853i	0.977923	+	0.977923i	−0.0218388	+	0.999762i	$0.506952\pi$
$164$	−1.58579	+	1.58579i	−0.123829	+	0.123829i
$165$		0			0
$166$	4.24264			0.329293
$167$	−13.0711	+	13.0711i	−1.01147	+	1.01147i	−0.0115361	+	0.999933i	$0.503672\pi$
$167$	−13.0711	+	13.0711i	−1.01147	+	1.01147i	−0.999933	+	0.0115361i	$0.996328\pi$
$168$		0			0
$169$	4.00000			0.307692
$170$	7.00000	+	6.00000i	0.536875	+	0.460179i
$171$		0			0
$172$	12.2426			0.933493
$173$	−6.34315	+	6.34315i	−0.482260	+	0.482260i	−0.905853	−	0.423592i	$-0.860769\pi$
$173$	−6.34315	+	6.34315i	−0.482260	+	0.482260i	0.423592	+	0.905853i	$0.360769\pi$
$174$		0			0
$175$	7.00000	+	1.00000i	0.529150	+	0.0755929i
$176$	4.41421	−	4.41421i	0.332734	−	0.332734i
$177$		0			0
$178$	5.48528			0.411139
$179$		−	23.3137i		−	1.74255i	−0.490797	−	0.871274i	$-0.663294\pi$
$179$		−	23.3137i		−	1.74255i	0.490797	−	0.871274i	$-0.336706\pi$
$180$		0			0
$181$	−14.0000	+	14.0000i	−1.04061	+	1.04061i	−0.0414721	+	0.999140i	$0.513205\pi$
$181$	−14.0000	+	14.0000i	−1.04061	+	1.04061i	−0.999140	+	0.0414721i	$0.986795\pi$
$182$	−3.00000	+	3.00000i	−0.222375	+	0.222375i
$183$		0			0
$184$	2.82843	+	2.82843i	0.208514	+	0.208514i
$185$	4.58579	−	9.17157i	0.337154	−	0.674307i
$186$		0			0
$187$	−24.9706	−	6.24264i	−1.82603	−	0.456507i
$188$			4.41421i			0.321940i
$189$		0			0
$190$	0.878680	+	2.63604i	0.0637461	+	0.191238i
$191$	21.2132			1.53493			0.767467	−	0.641089i	$-0.221517\pi$
$191$	21.2132			1.53493			0.767467	+	0.641089i	$0.221517\pi$
$192$		0			0
$193$	1.51472	+	1.51472i	0.109032	+	0.109032i	0.759518	−	0.650486i	$-0.225435\pi$
$193$	1.51472	+	1.51472i	0.109032	+	0.109032i	−0.650486	+	0.759518i	$0.725435\pi$
$194$	−4.12132	+	4.12132i	−0.295894	+	0.295894i
$195$		0			0
$196$		−	5.00000i		−	0.357143i
$197$	−14.6569	−	14.6569i	−1.04426	−	1.04426i	−0.998974	−	0.0452834i	$-0.985581\pi$
$197$	−14.6569	−	14.6569i	−1.04426	−	1.04426i	−0.0452834	−	0.998974i	$-0.514419\pi$
$198$		0			0
$199$	−2.87868	−	2.87868i	−0.204064	−	0.204064i	0.597675	−	0.801739i	$-0.296091\pi$
$199$	−2.87868	−	2.87868i	−0.204064	−	0.204064i	−0.801739	+	0.597675i	$0.796091\pi$
$200$	4.00000	−	3.00000i	0.282843	−	0.212132i
$201$		0			0
$202$		0			0
$203$			1.41421i			0.0992583i
$204$		0			0
$205$	2.24264	−	4.48528i	0.156633	−	0.313266i
$206$		0			0
$207$		0			0
$208$			3.00000i			0.208013i
$209$	−5.48528	−	5.48528i	−0.379425	−	0.379425i
$210$		0			0
$211$	−8.00000	+	8.00000i	−0.550743	+	0.550743i	−0.926655	−	0.375912i	$-0.877329\pi$
$211$	−8.00000	+	8.00000i	−0.550743	+	0.550743i	0.375912	+	0.926655i	$0.377329\pi$
$212$	3.00000			0.206041
$213$		0			0
$214$	−2.82843	+	2.82843i	−0.193347	+	0.193347i
$215$	−25.9706	+	8.65685i	−1.77118	+	0.590393i
$216$		0			0
$217$			14.7279i			0.999796i
$218$	−12.6066	+	12.6066i	−0.853827	+	0.853827i
$219$		0			0
$220$	−6.24264	+	12.4853i	−0.420879	+	0.841757i
$221$	10.6066	−	6.36396i	0.713477	−	0.428086i
$222$		0			0
$223$	−14.7574			−0.988226			−0.494113	−	0.869398i	$-0.664507\pi$
$223$	−14.7574			−0.988226			−0.494113	+	0.869398i	$0.664507\pi$
$224$	1.00000	+	1.00000i	0.0668153	+	0.0668153i
$225$		0			0
$226$	−9.53553	−	9.53553i	−0.634294	−	0.634294i
$227$	13.9497	+	13.9497i	0.925877	+	0.925877i	0.997436	−	0.0715591i	$-0.0227975\pi$
$227$	13.9497	+	13.9497i	0.925877	+	0.925877i	−0.0715591	+	0.997436i	$0.522797\pi$
$228$		0			0
$229$			16.2426i			1.07334i	0.843791	+	0.536672i	$0.180319\pi$
$229$			16.2426i			1.07334i	−0.843791	+	0.536672i	$0.819681\pi$
$230$	−8.00000	−	4.00000i	−0.527504	−	0.263752i
$231$		0			0
$232$	0.707107	+	0.707107i	0.0464238	+	0.0464238i
$233$	1.05025	−	1.05025i	0.0688043	−	0.0688043i	−0.671867	−	0.740672i	$-0.734507\pi$
$233$	1.05025	−	1.05025i	0.0688043	−	0.0688043i	0.740672	+	0.671867i	$0.234507\pi$
$234$		0			0
$235$	−3.12132	−	9.36396i	−0.203612	−	0.610837i
$236$			6.89949i			0.449119i
$237$		0			0
$238$	1.41421	−	5.65685i	0.0916698	−	0.366679i
$239$	−13.7574			−0.889890			−0.444945	−	0.895558i	$-0.646777\pi$
$239$	−13.7574			−0.889890			−0.444945	+	0.895558i	$0.646777\pi$
$240$		0			0
$241$	11.2426	+	11.2426i	0.724202	+	0.724202i	0.969458	−	0.245256i	$-0.0788721\pi$
$241$	11.2426	+	11.2426i	0.724202	+	0.724202i	−0.245256	+	0.969458i	$0.578872\pi$
$242$		−	27.9706i		−	1.79802i
$243$		0			0
$244$	1.87868	−	1.87868i	0.120270	−	0.120270i
$245$	3.53553	+	10.6066i	0.225877	+	0.677631i
$246$		0			0
$247$	3.72792			0.237202
$248$	7.36396	+	7.36396i	0.467612	+	0.467612i
$249$		0			0
$250$	−6.36396	+	9.19239i	−0.402492	+	0.581378i
$251$	−3.51472			−0.221847			−0.110924	−	0.993829i	$-0.535381\pi$
$251$	−3.51472			−0.221847			−0.110924	+	0.993829i	$0.535381\pi$
$252$		0			0
$253$	24.9706			1.56989
$254$	−7.72792			−0.484893
$255$		0			0
$256$	1.00000			0.0625000
$257$	18.7279			1.16822			0.584108	−	0.811676i	$-0.301445\pi$
$257$	18.7279			1.16822			0.584108	+	0.811676i	$0.301445\pi$
$258$		0			0
$259$	−6.48528			−0.402976
$260$	−2.12132	−	6.36396i	−0.131559	−	0.394676i
$261$		0			0
$262$	−10.4142	−	10.4142i	−0.643392	−	0.643392i
$263$	−13.2426			−0.816576			−0.408288	−	0.912853i	$-0.633874\pi$
$263$	−13.2426			−0.816576			−0.408288	+	0.912853i	$0.633874\pi$
$264$		0			0
$265$	−6.36396	+	2.12132i	−0.390935	+	0.130312i
$266$	1.24264	−	1.24264i	0.0761912	−	0.0761912i
$267$		0			0
$268$		−	2.48528i		−	0.151813i
$269$	12.7071	+	12.7071i	0.774766	+	0.774766i	0.978936	−	0.204170i	$-0.0654494\pi$
$269$	12.7071	+	12.7071i	0.774766	+	0.774766i	−0.204170	+	0.978936i	$0.565449\pi$
$270$		0			0
$271$	10.4853			0.636935			0.318468	−	0.947934i	$-0.396832\pi$
$271$	10.4853			0.636935			0.318468	+	0.947934i	$0.396832\pi$
$272$	−2.12132	−	3.53553i	−0.128624	−	0.214373i
$273$		0			0
$274$			7.41421i			0.447909i
$275$	4.41421	−	30.8995i	0.266187	−	1.86331i
$276$		0			0
$277$	−0.242641	+	0.242641i	−0.0145789	+	0.0145789i	−0.714359	−	0.699780i	$-0.753281\pi$
$277$	−0.242641	+	0.242641i	−0.0145789	+	0.0145789i	0.699780	+	0.714359i	$0.253281\pi$
$278$	−11.0000	−	11.0000i	−0.659736	−	0.659736i
$279$		0			0
$280$	−2.82843	−	1.41421i	−0.169031	−	0.0845154i
$281$			14.6569i			0.874355i	0.899375	+	0.437177i	$0.144022\pi$
$281$			14.6569i			0.874355i	−0.899375	+	0.437177i	$0.855978\pi$
$282$		0			0
$283$	−14.8787	−	14.8787i	−0.884446	−	0.884446i	0.109537	−	0.993983i	$-0.465063\pi$
$283$	−14.8787	−	14.8787i	−0.884446	−	0.884446i	−0.993983	+	0.109537i	$0.965063\pi$
$284$	−2.29289	−	2.29289i	−0.136058	−	0.136058i
$285$		0			0
$286$	13.2426	+	13.2426i	0.783054	+	0.783054i
$287$	−3.17157			−0.187212
$288$		0			0
$289$	−8.00000	+	15.0000i	−0.470588	+	0.882353i
$290$	−2.00000	−	1.00000i	−0.117444	−	0.0587220i
$291$		0			0
$292$	4.36396	−	4.36396i	0.255382	−	0.255382i
$293$		−	9.34315i		−	0.545832i	−0.962038	−	0.272916i	$-0.912012\pi$
$293$		−	9.34315i		−	0.545832i	0.962038	−	0.272916i	$-0.0879882\pi$
$294$		0			0
$295$	−4.87868	−	14.6360i	−0.284048	−	0.852143i
$296$	−3.24264	+	3.24264i	−0.188475	+	0.188475i
$297$		0			0
$298$	−12.7279			−0.737309
$299$	−8.48528	+	8.48528i	−0.490716	+	0.490716i
$300$		0			0
$301$	12.2426	+	12.2426i	0.705654	+	0.705654i
$302$		−	12.0000i		−	0.690522i
$303$		0			0
$304$		−	1.24264i		−	0.0712703i
$305$	−2.65685	+	5.31371i	−0.152131	+	0.304262i
$306$		0			0
$307$		−	9.21320i		−	0.525825i	−0.964820	−	0.262913i	$-0.915317\pi$
$307$		−	9.21320i		−	0.525825i	0.964820	−	0.262913i	$-0.0846831\pi$
$308$	8.82843			0.503046
$309$		0			0
$310$	−20.8284	−	10.4142i	−1.18298	−	0.591488i
$311$	−1.41421	−	1.41421i	−0.0801927	−	0.0801927i	0.665873	−	0.746065i	$-0.268059\pi$
$311$	−1.41421	−	1.41421i	−0.0801927	−	0.0801927i	−0.746065	+	0.665873i	$0.768059\pi$
$312$		0			0
$313$	−5.51472	−	5.51472i	−0.311710	−	0.311710i	0.533862	−	0.845572i	$-0.320740\pi$
$313$	−5.51472	−	5.51472i	−0.311710	−	0.311710i	−0.845572	+	0.533862i	$0.820740\pi$
$314$		−	12.0000i		−	0.677199i
$315$		0			0
$316$	8.24264	−	8.24264i	0.463685	−	0.463685i
$317$	−14.1421	−	14.1421i	−0.794301	−	0.794301i	0.187889	−	0.982190i	$-0.439836\pi$
$317$	−14.1421	−	14.1421i	−0.794301	−	0.794301i	−0.982190	+	0.187889i	$0.939836\pi$
$318$		0			0
$319$	6.24264			0.349521
$320$	−2.12132	+	0.707107i	−0.118585	+	0.0395285i
$321$		0			0
$322$			5.65685i			0.315244i
$323$	−4.39340	+	2.63604i	−0.244455	+	0.146673i
$324$		0			0
$325$	9.00000	+	12.0000i	0.499230	+	0.665640i
$326$	12.4853	+	12.4853i	0.691496	+	0.691496i
$327$		0			0
$328$	−1.58579	+	1.58579i	−0.0875604	+	0.0875604i
$329$	−4.41421	+	4.41421i	−0.243363	+	0.243363i
$330$		0			0
$331$			9.72792i			0.534695i	0.963600	+	0.267347i	$0.0861472\pi$
$331$			9.72792i			0.534695i	−0.963600	+	0.267347i	$0.913853\pi$
$332$	4.24264			0.232845
$333$		0			0
$334$	−13.0711	+	13.0711i	−0.715217	+	0.715217i
$335$	1.75736	+	5.27208i	0.0960148	+	0.288044i
$336$		0			0
$337$	−16.8492	+	16.8492i	−0.917837	+	0.917837i	−0.996872	−	0.0790351i	$-0.974816\pi$
$337$	−16.8492	+	16.8492i	−0.917837	+	0.917837i	0.0790351	+	0.996872i	$0.474816\pi$
$338$	4.00000			0.217571
$339$		0			0
$340$	7.00000	+	6.00000i	0.379628	+	0.325396i
$341$	65.0122			3.52061
$342$		0			0
$343$	12.0000	−	12.0000i	0.647939	−	0.647939i
$344$	12.2426			0.660079
$345$		0			0
$346$	−6.34315	+	6.34315i	−0.341010	+	0.341010i
$347$	−14.2929	−	14.2929i	−0.767283	−	0.767283i	0.210345	−	0.977627i	$-0.432541\pi$
$347$	−14.2929	−	14.2929i	−0.767283	−	0.767283i	−0.977627	+	0.210345i	$0.932541\pi$
$348$		0			0
$349$		−	22.9706i		−	1.22959i	−0.788688	−	0.614793i	$-0.789240\pi$
$349$		−	22.9706i		−	1.22959i	0.788688	−	0.614793i	$-0.210760\pi$
$350$	7.00000	+	1.00000i	0.374166	+	0.0534522i
$351$		0			0
$352$	4.41421	−	4.41421i	0.235278	−	0.235278i
$353$		−	11.3137i		−	0.602168i	−0.953598	−	0.301084i	$-0.902652\pi$
$353$		−	11.3137i		−	0.602168i	0.953598	−	0.301084i	$-0.0973484\pi$
$354$		0			0
$355$	6.48528	+	3.24264i	0.344203	+	0.172101i
$356$	5.48528			0.290719
$357$		0			0
$358$		−	23.3137i		−	1.23217i
$359$		−	7.07107i		−	0.373197i	−0.982436	−	0.186598i	$-0.940254\pi$
$359$		−	7.07107i		−	0.373197i	0.982436	−	0.186598i	$-0.0597463\pi$
$360$		0			0
$361$	17.4558			0.918729
$362$	−14.0000	+	14.0000i	−0.735824	+	0.735824i
$363$		0			0
$364$	−3.00000	+	3.00000i	−0.157243	+	0.157243i
$365$	−6.17157	+	12.3431i	−0.323035	+	0.646070i
$366$		0			0
$367$	−9.75736	−	9.75736i	−0.509330	−	0.509330i	0.404991	−	0.914321i	$-0.367275\pi$
$367$	−9.75736	−	9.75736i	−0.509330	−	0.509330i	−0.914321	+	0.404991i	$0.867275\pi$
$368$	2.82843	+	2.82843i	0.147442	+	0.147442i
$369$		0			0
$370$	4.58579	−	9.17157i	0.238404	−	0.476807i
$371$	3.00000	+	3.00000i	0.155752	+	0.155752i
$372$		0			0
$373$		−	15.5147i		−	0.803322i	−0.915788	−	0.401661i	$-0.868433\pi$
$373$		−	15.5147i		−	0.803322i	0.915788	−	0.401661i	$-0.131567\pi$
$374$	−24.9706	−	6.24264i	−1.29120	−	0.322799i
$375$		0			0
$376$			4.41421i			0.227646i
$377$	−2.12132	+	2.12132i	−0.109254	+	0.109254i
$378$		0			0
$379$	−16.4853	−	16.4853i	−0.846792	−	0.846792i	0.142939	−	0.989731i	$-0.454345\pi$
$379$	−16.4853	−	16.4853i	−0.846792	−	0.846792i	−0.989731	+	0.142939i	$0.954345\pi$
$380$	0.878680	+	2.63604i	0.0450753	+	0.135226i
$381$		0			0
$382$	21.2132			1.08536
$383$	4.75736			0.243090			0.121545	−	0.992586i	$-0.461215\pi$
$383$	4.75736			0.243090			0.121545	+	0.992586i	$0.461215\pi$
$384$		0			0
$385$	−18.7279	+	6.24264i	−0.954463	+	0.318154i
$386$	1.51472	+	1.51472i	0.0770971	+	0.0770971i
$387$		0			0
$388$	−4.12132	+	4.12132i	−0.209228	+	0.209228i
$389$			28.6274i			1.45147i	0.687976	+	0.725734i	$0.258500\pi$
$389$			28.6274i			1.45147i	−0.687976	+	0.725734i	$0.741500\pi$
$390$		0			0
$391$	4.00000	−	16.0000i	0.202289	−	0.809155i
$392$		−	5.00000i		−	0.252538i
$393$		0			0
$394$	−14.6569	−	14.6569i	−0.738402	−	0.738402i
$395$	−11.6569	+	23.3137i	−0.586520	+	1.17304i
$396$		0			0
$397$	−20.7279	−	20.7279i	−1.04030	−	1.04030i	−0.999153	−	0.0411517i	$-0.986897\pi$
$397$	−20.7279	−	20.7279i	−1.04030	−	1.04030i	−0.0411517	−	0.999153i	$-0.513103\pi$
$398$	−2.87868	−	2.87868i	−0.144295	−	0.144295i
$399$		0			0
$400$	4.00000	−	3.00000i	0.200000	−	0.150000i
$401$	21.8995	−	21.8995i	1.09361	−	1.09361i	0.0984684	−	0.995140i	$-0.468606\pi$
$401$	21.8995	−	21.8995i	1.09361	−	1.09361i	0.995140	−	0.0984684i	$-0.0313943\pi$
$402$		0			0
$403$	−22.0919	+	22.0919i	−1.10048	+	1.10048i
$404$		0			0
$405$		0			0
$406$			1.41421i			0.0701862i
$407$			28.6274i			1.41901i
$408$		0			0
$409$	8.51472			0.421026			0.210513	−	0.977591i	$-0.432487\pi$
$409$	8.51472			0.421026			0.210513	+	0.977591i	$0.432487\pi$
$410$	2.24264	−	4.48528i	0.110756	−	0.221512i
$411$		0			0
$412$		0			0
$413$	−6.89949	+	6.89949i	−0.339502	+	0.339502i
$414$		0			0
$415$	−9.00000	+	3.00000i	−0.441793	+	0.147264i
$416$			3.00000i			0.147087i
$417$		0			0
$418$	−5.48528	−	5.48528i	−0.268294	−	0.268294i
$419$	−11.3137	+	11.3137i	−0.552711	+	0.552711i	−0.927222	−	0.374511i	$-0.877810\pi$
$419$	−11.3137	+	11.3137i	−0.552711	+	0.552711i	0.374511	+	0.927222i	$0.377810\pi$
$420$		0			0
$421$	23.2132			1.13134			0.565671	−	0.824631i	$-0.308617\pi$
$421$	23.2132			1.13134			0.565671	+	0.824631i	$0.308617\pi$
$422$	−8.00000	+	8.00000i	−0.389434	+	0.389434i
$423$		0			0
$424$	3.00000			0.145693
$425$	−19.0919	−	7.77817i	−0.926092	−	0.377297i
$426$		0			0
$427$	3.75736			0.181831
$428$	−2.82843	+	2.82843i	−0.136717	+	0.136717i
$429$		0			0
$430$	−25.9706	+	8.65685i	−1.25241	+	0.417471i
$431$	−6.34315	+	6.34315i	−0.305539	+	0.305539i	−0.843176	−	0.537638i	$-0.819317\pi$
$431$	−6.34315	+	6.34315i	−0.305539	+	0.305539i	0.537638	+	0.843176i	$0.319317\pi$
$432$		0			0
$433$	−14.2426			−0.684458			−0.342229	−	0.939617i	$-0.611182\pi$
$433$	−14.2426			−0.684458			−0.342229	+	0.939617i	$0.611182\pi$
$434$			14.7279i			0.706963i
$435$		0			0
$436$	−12.6066	+	12.6066i	−0.603747	+	0.603747i
$437$	3.51472	−	3.51472i	0.168132	−	0.168132i
$438$		0			0
$439$	−12.9706	−	12.9706i	−0.619051	−	0.619051i	0.326237	−	0.945288i	$-0.394219\pi$
$439$	−12.9706	−	12.9706i	−0.619051	−	0.619051i	−0.945288	+	0.326237i	$0.894219\pi$
$440$	−6.24264	+	12.4853i	−0.297606	+	0.595212i
$441$		0			0
$442$	10.6066	−	6.36396i	0.504505	−	0.302703i
$443$		−	1.79899i		−	0.0854726i	−0.999086	−	0.0427363i	$-0.986392\pi$
$443$		−	1.79899i		−	0.0854726i	0.999086	−	0.0427363i	$-0.0136075\pi$
$444$		0			0
$445$	−11.6360	+	3.87868i	−0.551601	+	0.183867i
$446$	−14.7574			−0.698781
$447$		0			0
$448$	1.00000	+	1.00000i	0.0472456	+	0.0472456i
$449$	−10.7990	+	10.7990i	−0.509636	+	0.509636i	−0.914415	−	0.404779i	$-0.867349\pi$
$449$	−10.7990	+	10.7990i	−0.509636	+	0.509636i	0.404779	+	0.914415i	$0.367349\pi$
$450$		0			0
$451$			14.0000i			0.659234i
$452$	−9.53553	−	9.53553i	−0.448514	−	0.448514i
$453$		0			0
$454$	13.9497	+	13.9497i	0.654694	+	0.654694i
$455$	4.24264	−	8.48528i	0.198898	−	0.397796i
$456$		0			0
$457$	6.24264			0.292018			0.146009	−	0.989283i	$-0.453357\pi$
$457$	6.24264			0.292018			0.146009	+	0.989283i	$0.453357\pi$
$458$			16.2426i			0.758969i
$459$		0			0
$460$	−8.00000	−	4.00000i	−0.373002	−	0.186501i
$461$		−	16.2843i		−	0.758434i	−0.925308	−	0.379217i	$-0.876193\pi$
$461$		−	16.2843i		−	0.758434i	0.925308	−	0.379217i	$-0.123807\pi$
$462$		0			0
$463$			16.7574i			0.778781i	0.921073	+	0.389390i	$0.127314\pi$
$463$			16.7574i			0.778781i	−0.921073	+	0.389390i	$0.872686\pi$
$464$	0.707107	+	0.707107i	0.0328266	+	0.0328266i
$465$		0			0
$466$	1.05025	−	1.05025i	0.0486520	−	0.0486520i
$467$	−6.72792			−0.311331			−0.155666	−	0.987810i	$-0.549752\pi$
$467$	−6.72792			−0.311331			−0.155666	+	0.987810i	$0.549752\pi$
$468$		0			0
$469$	2.48528	−	2.48528i	0.114760	−	0.114760i
$470$	−3.12132	−	9.36396i	−0.143976	−	0.431927i
$471$		0			0
$472$			6.89949i			0.317575i
$473$	54.0416	−	54.0416i	2.48484	−	2.48484i
$474$		0			0
$475$	−3.72792	−	4.97056i	−0.171049	−	0.228065i
$476$	1.41421	−	5.65685i	0.0648204	−	0.259281i
$477$		0			0
$478$	−13.7574			−0.629247
$479$	19.9497	+	19.9497i	0.911527	+	0.911527i	0.996392	−	0.0848652i	$-0.0270460\pi$
$479$	19.9497	+	19.9497i	0.911527	+	0.911527i	−0.0848652	+	0.996392i	$0.527046\pi$
$480$		0			0
$481$	−9.72792	−	9.72792i	−0.443555	−	0.443555i
$482$	11.2426	+	11.2426i	0.512088	+	0.512088i
$483$		0			0
$484$		−	27.9706i		−	1.27139i
$485$	5.82843	−	11.6569i	0.264655	−	0.529310i
$486$		0			0
$487$	2.75736	+	2.75736i	0.124948	+	0.124948i	0.766815	−	0.641868i	$-0.221840\pi$
$487$	2.75736	+	2.75736i	0.124948	+	0.124948i	−0.641868	+	0.766815i	$0.721840\pi$
$488$	1.87868	−	1.87868i	0.0850438	−	0.0850438i
$489$		0			0
$490$	3.53553	+	10.6066i	0.159719	+	0.479157i
$491$			12.8995i			0.582146i	0.956701	+	0.291073i	$0.0940123\pi$
$491$			12.8995i			0.582146i	−0.956701	+	0.291073i	$0.905988\pi$
$492$		0			0
$493$	1.00000	−	4.00000i	0.0450377	−	0.180151i
$494$	3.72792			0.167727
$495$		0			0
$496$	7.36396	+	7.36396i	0.330652	+	0.330652i
$497$		−	4.58579i		−	0.205701i
$498$		0			0
$499$	−25.4853	+	25.4853i	−1.14088	+	1.14088i	−0.152588	+	0.988290i	$0.548761\pi$
$499$	−25.4853	+	25.4853i	−1.14088	+	1.14088i	−0.988290	+	0.152588i	$0.951239\pi$
$500$	−6.36396	+	9.19239i	−0.284605	+	0.411096i
$501$		0			0
$502$	−3.51472			−0.156870
$503$	1.07107	+	1.07107i	0.0477566	+	0.0477566i	0.730582	−	0.682825i	$-0.239249\pi$
$503$	1.07107	+	1.07107i	0.0477566	+	0.0477566i	−0.682825	+	0.730582i	$0.739249\pi$
$504$		0			0
$505$		0			0
$506$	24.9706			1.11008
$507$		0			0
$508$	−7.72792			−0.342871
$509$		0			0			−	1.00000i	$-0.5\pi$
$509$		0			0				1.00000i	$0.5\pi$
$510$		0			0
$511$	8.72792			0.386101
$512$	1.00000			0.0441942
$513$		0			0
$514$	18.7279			0.826053
$515$		0			0
$516$		0			0
$517$	19.4853	+	19.4853i	0.856962	+	0.856962i
$518$	−6.48528			−0.284947
$519$		0			0
$520$	−2.12132	−	6.36396i	−0.0930261	−	0.279078i
$521$	−11.3137	+	11.3137i	−0.495663	+	0.495663i	−0.910085	−	0.414422i	$-0.863984\pi$
$521$	−11.3137	+	11.3137i	−0.495663	+	0.495663i	0.414422	+	0.910085i	$0.363984\pi$
$522$		0			0
$523$			9.51472i			0.416050i	0.978124	+	0.208025i	$0.0667035\pi$
$523$			9.51472i			0.416050i	−0.978124	+	0.208025i	$0.933297\pi$
$524$	−10.4142	−	10.4142i	−0.454947	−	0.454947i
$525$		0			0
$526$	−13.2426			−0.577407
$527$	10.4142	−	41.6569i	0.453650	−	1.81460i
$528$		0			0
$529$		−	7.00000i		−	0.304348i
$530$	−6.36396	+	2.12132i	−0.276433	+	0.0921443i
$531$		0			0
$532$	1.24264	−	1.24264i	0.0538753	−	0.0538753i
$533$	−4.75736	−	4.75736i	−0.206064	−	0.206064i
$534$		0			0
$535$	4.00000	−	8.00000i	0.172935	−	0.345870i
$536$		−	2.48528i		−	0.107348i
$537$		0			0
$538$	12.7071	+	12.7071i	0.547842	+	0.547842i
$539$	−22.0711	−	22.0711i	−0.950668	−	0.950668i
$540$		0			0
$541$	−12.9706	−	12.9706i	−0.557648	−	0.557648i	0.370989	−	0.928637i	$-0.379019\pi$
$541$	−12.9706	−	12.9706i	−0.557648	−	0.557648i	−0.928637	+	0.370989i	$0.879019\pi$
$542$	10.4853			0.450381
$543$		0			0
$544$	−2.12132	−	3.53553i	−0.0909509	−	0.151585i
$545$	17.8284	−	35.6569i	0.763686	−	1.52737i
$546$		0			0
$547$	23.6066	−	23.6066i	1.00935	−	1.00935i	0.00938949	−	0.999956i	$-0.497011\pi$
$547$	23.6066	−	23.6066i	1.00935	−	1.00935i	0.999956	−	0.00938949i	$-0.00298881\pi$
$548$			7.41421i			0.316720i
$549$		0			0
$550$	4.41421	−	30.8995i	0.188223	−	1.31756i
$551$	0.878680	−	0.878680i	0.0374330	−	0.0374330i
$552$		0			0
$553$	16.4853			0.701025
$554$	−0.242641	+	0.242641i	−0.0103088	+	0.0103088i
$555$		0			0
$556$	−11.0000	−	11.0000i	−0.466504	−	0.466504i
$557$		−	4.79899i		−	0.203340i	−0.994818	−	0.101670i	$-0.967581\pi$
$557$		−	4.79899i		−	0.203340i	0.994818	−	0.101670i	$-0.0324185\pi$
$558$		0			0
$559$			36.7279i			1.55343i
$560$	−2.82843	−	1.41421i	−0.119523	−	0.0597614i
$561$		0			0
$562$			14.6569i			0.618262i
$563$	−21.9411			−0.924708			−0.462354	−	0.886695i	$-0.652995\pi$
$563$	−21.9411			−0.924708			−0.462354	+	0.886695i	$0.652995\pi$
$564$		0			0
$565$	26.9706	+	13.4853i	1.13466	+	0.567330i
$566$	−14.8787	−	14.8787i	−0.625398	−	0.625398i
$567$		0			0
$568$	−2.29289	−	2.29289i	−0.0962077	−	0.0962077i
$569$		−	2.31371i		−	0.0969957i	−0.998823	−	0.0484979i	$-0.984557\pi$
$569$		−	2.31371i		−	0.0969957i	0.998823	−	0.0484979i	$-0.0154434\pi$
$570$		0			0
$571$	22.2132	−	22.2132i	0.929594	−	0.929594i	−0.0680858	−	0.997679i	$-0.521689\pi$
$571$	22.2132	−	22.2132i	0.929594	−	0.929594i	0.997679	+	0.0680858i	$0.0216892\pi$
$572$	13.2426	+	13.2426i	0.553703	+	0.553703i
$573$		0			0
$574$	−3.17157			−0.132379
$575$	19.7990	+	2.82843i	0.825675	+	0.117954i
$576$		0			0
$577$			28.9706i			1.20606i	0.797718	+	0.603030i	$0.206040\pi$
$577$			28.9706i			1.20606i	−0.797718	+	0.603030i	$0.793960\pi$
$578$	−8.00000	+	15.0000i	−0.332756	+	0.623918i
$579$		0			0
$580$	−2.00000	−	1.00000i	−0.0830455	−	0.0415227i
$581$	4.24264	+	4.24264i	0.176014	+	0.176014i
$582$		0			0
$583$	13.2426	−	13.2426i	0.548454	−	0.548454i
$584$	4.36396	−	4.36396i	0.180582	−	0.180582i
$585$		0			0
$586$		−	9.34315i		−	0.385962i
$587$	−24.0000			−0.990586			−0.495293	−	0.868726i	$-0.664939\pi$
$587$	−24.0000			−0.990586			−0.495293	+	0.868726i	$0.664939\pi$
$588$		0			0
$589$	9.15076	−	9.15076i	0.377050	−	0.377050i
$590$	−4.87868	−	14.6360i	−0.200852	−	0.602556i
$591$		0			0
$592$	−3.24264	+	3.24264i	−0.133272	+	0.133272i
$593$	−18.0000			−0.739171			−0.369586	−	0.929197i	$-0.620500\pi$
$593$	−18.0000			−0.739171			−0.369586	+	0.929197i	$0.620500\pi$
$594$		0			0
$595$	1.00000	+	13.0000i	0.0409960	+	0.532948i
$596$	−12.7279			−0.521356
$597$		0			0
$598$	−8.48528	+	8.48528i	−0.346989	+	0.346989i
$599$	12.0000			0.490307			0.245153	−	0.969484i	$-0.421162\pi$
$599$	12.0000			0.490307			0.245153	+	0.969484i	$0.421162\pi$
$600$		0			0
$601$	3.27208	−	3.27208i	0.133471	−	0.133471i	−0.637215	−	0.770686i	$-0.719914\pi$
$601$	3.27208	−	3.27208i	0.133471	−	0.133471i	0.770686	+	0.637215i	$0.219914\pi$
$602$	12.2426	+	12.2426i	0.498973	+	0.498973i
$603$		0			0
$604$		−	12.0000i		−	0.488273i
$605$	19.7782	+	59.3345i	0.804097	+	2.41229i
$606$		0			0
$607$	−24.4558	+	24.4558i	−0.992632	+	0.992632i	−0.999973	−	0.00734096i	$-0.997663\pi$
$607$	−24.4558	+	24.4558i	−0.992632	+	0.992632i	0.00734096	+	0.999973i	$0.497663\pi$
$608$		−	1.24264i		−	0.0503957i
$609$		0			0
$610$	−2.65685	+	5.31371i	−0.107573	+	0.215146i
$611$	−13.2426			−0.535740
$612$		0			0
$613$		−	37.9706i		−	1.53362i	−0.641876	−	0.766808i	$-0.721844\pi$
$613$		−	37.9706i		−	1.53362i	0.641876	−	0.766808i	$-0.278156\pi$
$614$		−	9.21320i		−	0.371815i
$615$		0			0
$616$	8.82843			0.355707
$617$	−7.43503	+	7.43503i	−0.299323	+	0.299323i	−0.840749	−	0.541426i	$-0.817885\pi$
$617$	−7.43503	+	7.43503i	−0.299323	+	0.299323i	0.541426	+	0.840749i	$0.317885\pi$
$618$		0			0
$619$	14.2426	−	14.2426i	0.572460	−	0.572460i	−0.360355	−	0.932815i	$-0.617344\pi$
$619$	14.2426	−	14.2426i	0.572460	−	0.572460i	0.932815	+	0.360355i	$0.117344\pi$
$620$	−20.8284	−	10.4142i	−0.836490	−	0.418245i
$621$		0			0
$622$	−1.41421	−	1.41421i	−0.0567048	−	0.0567048i
$623$	5.48528	+	5.48528i	0.219763	+	0.219763i
$624$		0			0
$625$	7.00000	−	24.0000i	0.280000	−	0.960000i
$626$	−5.51472	−	5.51472i	−0.220412	−	0.220412i
$627$		0			0
$628$		−	12.0000i		−	0.478852i
$629$	18.3431	+	4.58579i	0.731389	+	0.182847i
$630$		0			0
$631$			14.4853i			0.576650i	0.957533	+	0.288325i	$0.0930983\pi$
$631$			14.4853i			0.576650i	−0.957533	+	0.288325i	$0.906902\pi$
$632$	8.24264	−	8.24264i	0.327875	−	0.327875i
$633$		0			0
$634$	−14.1421	−	14.1421i	−0.561656	−	0.561656i
$635$	16.3934	−	5.46447i	0.650552	−	0.216851i
$636$		0			0
$637$	15.0000			0.594322
$638$	6.24264			0.247149
$639$		0			0
$640$	−2.12132	+	0.707107i	−0.0838525	+	0.0279508i
$641$	27.5563	+	27.5563i	1.08841	+	1.08841i	0.995692	+	0.0927179i	$0.0295555\pi$
$641$	27.5563	+	27.5563i	1.08841	+	1.08841i	0.0927179	+	0.995692i	$0.470445\pi$
$642$		0			0
$643$	−12.2426	+	12.2426i	−0.482803	+	0.482803i	−0.906026	−	0.423223i	$-0.860899\pi$
$643$	−12.2426	+	12.2426i	−0.482803	+	0.482803i	0.423223	+	0.906026i	$0.360899\pi$
$644$			5.65685i			0.222911i
$645$		0			0
$646$	−4.39340	+	2.63604i	−0.172856	+	0.103714i
$647$		−	17.5269i		−	0.689054i	−0.938776	−	0.344527i	$-0.888039\pi$
$647$		−	17.5269i		−	0.689054i	0.938776	−	0.344527i	$-0.111961\pi$
$648$		0			0
$649$	30.4558	+	30.4558i	1.19550	+	1.19550i
$650$	9.00000	+	12.0000i	0.353009	+	0.470679i
$651$		0			0
$652$	12.4853	+	12.4853i	0.488961	+	0.488961i
$653$	34.7990	+	34.7990i	1.36179	+	1.36179i	0.871636	+	0.490154i	$0.163059\pi$
$653$	34.7990	+	34.7990i	1.36179	+	1.36179i	0.490154	+	0.871636i	$0.336941\pi$
$654$		0			0
$655$	29.4558	+	14.7279i	1.15094	+	0.575468i
$656$	−1.58579	+	1.58579i	−0.0619146	+	0.0619146i
$657$		0			0
$658$	−4.41421	+	4.41421i	−0.172084	+	0.172084i
$659$	12.2132			0.475759			0.237879	−	0.971295i	$-0.423548\pi$
$659$	12.2132			0.475759			0.237879	+	0.971295i	$0.423548\pi$
$660$		0			0
$661$		−	12.0000i		−	0.466746i	−0.972387	−	0.233373i	$-0.925024\pi$
$661$		−	12.0000i		−	0.466746i	0.972387	−	0.233373i	$-0.0749763\pi$
$662$			9.72792i			0.378086i
$663$		0			0
$664$	4.24264			0.164646
$665$	−1.75736	+	3.51472i	−0.0681475	+	0.136295i
$666$		0			0
$667$			4.00000i			0.154881i
$668$	−13.0711	+	13.0711i	−0.505735	+	0.505735i
$669$		0			0
$670$	1.75736	+	5.27208i	0.0678927	+	0.203678i
$671$		−	16.5858i		−	0.640287i
$672$		0			0
$673$	30.1213	+	30.1213i	1.16109	+	1.16109i	0.984237	+	0.176855i	$0.0565922\pi$
$673$	30.1213	+	30.1213i	1.16109	+	1.16109i	0.176855	+	0.984237i	$0.443408\pi$
$674$	−16.8492	+	16.8492i	−0.649009	+	0.649009i
$675$		0			0
$676$	4.00000			0.153846
$677$	−19.5858	+	19.5858i	−0.752743	+	0.752743i	−0.974990	−	0.222247i	$-0.928661\pi$
$677$	−19.5858	+	19.5858i	−0.752743	+	0.752743i	0.222247	+	0.974990i	$0.428661\pi$
$678$		0			0
$679$	−8.24264			−0.316324
$680$	7.00000	+	6.00000i	0.268438	+	0.230089i
$681$		0			0
$682$	65.0122			2.48945
$683$	−17.4645	+	17.4645i	−0.668259	+	0.668259i	−0.957313	−	0.289054i	$-0.906659\pi$
$683$	−17.4645	+	17.4645i	−0.668259	+	0.668259i	0.289054	+	0.957313i	$0.406659\pi$
$684$		0			0
$685$	−5.24264	−	15.7279i	−0.200311	−	0.600933i
$686$	12.0000	−	12.0000i	0.458162	−	0.458162i
$687$		0			0
$688$	12.2426			0.466746
$689$			9.00000i			0.342873i
$690$		0			0
$691$	−7.48528	+	7.48528i	−0.284754	+	0.284754i	−0.835001	−	0.550248i	$-0.814533\pi$
$691$	−7.48528	+	7.48528i	−0.284754	+	0.284754i	0.550248	+	0.835001i	$0.314533\pi$
$692$	−6.34315	+	6.34315i	−0.241130	+	0.241130i
$693$		0			0
$694$	−14.2929	−	14.2929i	−0.542551	−	0.542551i
$695$	31.1127	+	15.5563i	1.18017	+	0.590086i
$696$		0			0
$697$	8.97056	+	2.24264i	0.339784	+	0.0849461i
$698$		−	22.9706i		−	0.869449i
$699$		0			0
$700$	7.00000	+	1.00000i	0.264575	+	0.0377964i
$701$	12.0000			0.453234			0.226617	−	0.973984i	$-0.427233\pi$
$701$	12.0000			0.453234			0.226617	+	0.973984i	$0.427233\pi$
$702$		0			0
$703$	4.02944	+	4.02944i	0.151973	+	0.151973i
$704$	4.41421	−	4.41421i	0.166367	−	0.166367i
$705$		0			0
$706$		−	11.3137i		−	0.425797i
$707$		0			0
$708$		0			0
$709$	−18.6066	−	18.6066i	−0.698786	−	0.698786i	0.265363	−	0.964149i	$-0.414508\pi$
$709$	−18.6066	−	18.6066i	−0.698786	−	0.698786i	−0.964149	+	0.265363i	$0.914508\pi$
$710$	6.48528	+	3.24264i	0.243388	+	0.121694i
$711$		0			0
$712$	5.48528			0.205570
$713$			41.6569i			1.56006i
$714$		0			0
$715$	−37.4558	−	18.7279i	−1.40077	−	0.700385i
$716$		−	23.3137i		−	0.871274i
$717$		0			0
$718$		−	7.07107i		−	0.263890i
$719$	−21.7487	−	21.7487i	−0.811091	−	0.811091i	0.173706	−	0.984797i	$-0.444426\pi$
$719$	−21.7487	−	21.7487i	−0.811091	−	0.811091i	−0.984797	+	0.173706i	$0.944426\pi$
$720$		0			0
$721$		0			0
$722$	17.4558			0.649639
$723$		0			0
$724$	−14.0000	+	14.0000i	−0.520306	+	0.520306i
$725$	4.94975	+	0.707107i	0.183829	+	0.0262613i
$726$		0			0
$727$			25.2426i			0.936198i	0.883676	+	0.468099i	$0.155061\pi$
$727$			25.2426i			0.936198i	−0.883676	+	0.468099i	$0.844939\pi$
$728$	−3.00000	+	3.00000i	−0.111187	+	0.111187i
$729$		0			0
$730$	−6.17157	+	12.3431i	−0.228420	+	0.456840i
$731$	−25.9706	−	43.2843i	−0.960556	−	1.60093i
$732$		0			0
$733$	0.970563			0.0358486			0.0179243	−	0.999839i	$-0.494294\pi$
$733$	0.970563			0.0358486			0.0179243	+	0.999839i	$0.494294\pi$
$734$	−9.75736	−	9.75736i	−0.360151	−	0.360151i
$735$		0			0
$736$	2.82843	+	2.82843i	0.104257	+	0.104257i
$737$	−10.9706	−	10.9706i	−0.404106	−	0.404106i
$738$		0			0
$739$			41.1838i			1.51497i	0.652853	+	0.757485i	$0.273572\pi$
$739$			41.1838i			1.51497i	−0.652853	+	0.757485i	$0.726428\pi$
$740$	4.58579	−	9.17157i	0.168577	−	0.337154i
$741$		0			0
$742$	3.00000	+	3.00000i	0.110133	+	0.110133i
$743$	12.1716	−	12.1716i	0.446532	−	0.446532i	−0.447668	−	0.894200i	$-0.647745\pi$
$743$	12.1716	−	12.1716i	0.446532	−	0.446532i	0.894200	+	0.447668i	$0.147745\pi$
$744$		0			0
$745$	27.0000	−	9.00000i	0.989203	−	0.329734i
$746$		−	15.5147i		−	0.568034i
$747$		0			0
$748$	−24.9706	−	6.24264i	−0.913014	−	0.228254i
$749$	−5.65685			−0.206697
$750$		0			0
$751$	6.63604	+	6.63604i	0.242153	+	0.242153i	0.817740	−	0.575588i	$-0.195227\pi$
$751$	6.63604	+	6.63604i	0.242153	+	0.242153i	−0.575588	+	0.817740i	$0.695227\pi$
$752$			4.41421i			0.160970i
$753$		0			0
$754$	−2.12132	+	2.12132i	−0.0772539	+	0.0772539i
$755$	8.48528	+	25.4558i	0.308811	+	0.926433i
$756$		0			0
$757$	−34.9411			−1.26996			−0.634978	−	0.772530i	$-0.718991\pi$
$757$	−34.9411			−1.26996			−0.634978	+	0.772530i	$0.718991\pi$
$758$	−16.4853	−	16.4853i	−0.598772	−	0.598772i
$759$		0			0
$760$	0.878680	+	2.63604i	0.0318731	+	0.0956192i
$761$	−3.51472			−0.127408			−0.0637042	−	0.997969i	$-0.520291\pi$
$761$	−3.51472			−0.127408			−0.0637042	+	0.997969i	$0.520291\pi$
$762$		0			0
$763$	−25.2132			−0.912779
$764$	21.2132			0.767467
$765$		0			0
$766$	4.75736			0.171890
$767$	−20.6985			−0.747379
$768$		0			0
$769$	36.4558			1.31463			0.657316	−	0.753615i	$-0.271692\pi$
$769$	36.4558			1.31463			0.657316	+	0.753615i	$0.271692\pi$
$770$	−18.7279	+	6.24264i	−0.674907	+	0.224969i
$771$		0			0
$772$	1.51472	+	1.51472i	0.0545159	+	0.0545159i
$773$	15.5147			0.558026			0.279013	−	0.960287i	$-0.409993\pi$
$773$	15.5147			0.558026			0.279013	+	0.960287i	$0.409993\pi$
$774$		0			0
$775$	51.5477	+	7.36396i	1.85165	+	0.264521i
$776$	−4.12132	+	4.12132i	−0.147947	+	0.147947i
$777$		0			0
$778$			28.6274i			1.02634i
$779$	1.97056	+	1.97056i	0.0706027	+	0.0706027i
$780$		0			0
$781$	−20.2426			−0.724339
$782$	4.00000	−	16.0000i	0.143040	−	0.572159i
$783$		0			0
$784$		−	5.00000i		−	0.178571i
$785$	8.48528	+	25.4558i	0.302853	+	0.908558i
$786$		0			0
$787$	−11.3640	+	11.3640i	−0.405081	+	0.405081i	−0.880019	−	0.474938i	$-0.842471\pi$
$787$	−11.3640	+	11.3640i	−0.405081	+	0.405081i	0.474938	+	0.880019i	$0.342471\pi$
$788$	−14.6569	−	14.6569i	−0.522129	−	0.522129i
$789$		0			0
$790$	−11.6569	+	23.3137i	−0.414732	+	0.829465i
$791$		−	19.0711i		−	0.678089i
$792$		0			0
$793$	5.63604	+	5.63604i	0.200142	+	0.200142i
$794$	−20.7279	−	20.7279i	−0.735606	−	0.735606i
$795$		0			0
$796$	−2.87868	−	2.87868i	−0.102032	−	0.102032i
$797$	−4.97056			−0.176066			−0.0880332	−	0.996118i	$-0.528058\pi$
$797$	−4.97056			−0.176066			−0.0880332	+	0.996118i	$0.528058\pi$
$798$		0			0
$799$	15.6066	−	9.36396i	0.552122	−	0.331273i
$800$	4.00000	−	3.00000i	0.141421	−	0.106066i
$801$		0			0
$802$	21.8995	−	21.8995i	0.773298	−	0.773298i
$803$		−	38.5269i		−	1.35959i
$804$		0			0
$805$	−4.00000	−	12.0000i	−0.140981	−	0.422944i
$806$	−22.0919	+	22.0919i	−0.778153	+	0.778153i
$807$		0			0
$808$		0			0
$809$	−6.85786	+	6.85786i	−0.241110	+	0.241110i	−0.817309	−	0.576199i	$-0.804535\pi$
$809$	−6.85786	+	6.85786i	−0.241110	+	0.241110i	0.576199	+	0.817309i	$0.304535\pi$
$810$		0			0
$811$	−7.48528	−	7.48528i	−0.262844	−	0.262844i	0.563365	−	0.826208i	$-0.309507\pi$
$811$	−7.48528	−	7.48528i	−0.262844	−	0.262844i	−0.826208	+	0.563365i	$0.809507\pi$
$812$			1.41421i			0.0496292i
$813$		0			0
$814$			28.6274i			1.00339i
$815$	−35.3137	−	17.6569i	−1.23699	−	0.618493i
$816$		0			0
$817$		−	15.2132i		−	0.532243i
$818$	8.51472			0.297710
$819$		0			0
$820$	2.24264	−	4.48528i	0.0783164	−	0.156633i
$821$	−6.02082	−	6.02082i	−0.210128	−	0.210128i	0.594194	−	0.804322i	$-0.297471\pi$
$821$	−6.02082	−	6.02082i	−0.210128	−	0.210128i	−0.804322	+	0.594194i	$0.797471\pi$
$822$		0			0
$823$	−14.7279	−	14.7279i	−0.513383	−	0.513383i	0.402178	−	0.915561i	$-0.368253\pi$
$823$	−14.7279	−	14.7279i	−0.513383	−	0.513383i	−0.915561	+	0.402178i	$0.868253\pi$
$824$		0			0
$825$		0			0
$826$	−6.89949	+	6.89949i	−0.240064	+	0.240064i
$827$	17.3137	+	17.3137i	0.602057	+	0.602057i	0.940858	−	0.338801i	$-0.110021\pi$
$827$	17.3137	+	17.3137i	0.602057	+	0.602057i	−0.338801	+	0.940858i	$0.610021\pi$
$828$		0			0
$829$	14.0000			0.486240			0.243120	−	0.969996i	$-0.421829\pi$
$829$	14.0000			0.486240			0.243120	+	0.969996i	$0.421829\pi$
$830$	−9.00000	+	3.00000i	−0.312395	+	0.104132i
$831$		0			0
$832$			3.00000i			0.104006i
$833$	−17.6777	+	10.6066i	−0.612495	+	0.367497i
$834$		0			0
$835$	18.4853	−	36.9706i	0.639710	−	1.27942i
$836$	−5.48528	−	5.48528i	−0.189712	−	0.189712i
$837$		0			0
$838$	−11.3137	+	11.3137i	−0.390826	+	0.390826i
$839$	27.0208	−	27.0208i	0.932862	−	0.932862i	−0.0650217	−	0.997884i	$-0.520712\pi$
$839$	27.0208	−	27.0208i	0.932862	−	0.932862i	0.997884	+	0.0650217i	$0.0207117\pi$
$840$		0			0
$841$		−	28.0000i		−	0.965517i
$842$	23.2132			0.799980
$843$		0			0
$844$	−8.00000	+	8.00000i	−0.275371	+	0.275371i
$845$	−8.48528	+	2.82843i	−0.291903	+	0.0973009i
$846$		0			0
$847$	27.9706	−	27.9706i	0.961080	−	0.961080i
$848$	3.00000			0.103020
$849$		0			0
$850$	−19.0919	−	7.77817i	−0.654846	−	0.266789i
$851$	−18.3431			−0.628795
$852$		0			0
$853$	−25.4853	+	25.4853i	−0.872599	+	0.872599i	−0.992755	−	0.120156i	$-0.961661\pi$
$853$	−25.4853	+	25.4853i	−0.872599	+	0.872599i	0.120156	+	0.992755i	$0.461661\pi$
$854$	3.75736			0.128574
$855$		0			0
$856$	−2.82843	+	2.82843i	−0.0966736	+	0.0966736i
$857$	1.43503	+	1.43503i	0.0490197	+	0.0490197i	0.731192	−	0.682172i	$-0.238964\pi$
$857$	1.43503	+	1.43503i	0.0490197	+	0.0490197i	−0.682172	+	0.731192i	$0.738964\pi$
$858$		0			0
$859$		−	20.2721i		−	0.691674i	−0.938295	−	0.345837i	$-0.887595\pi$
$859$		−	20.2721i		−	0.691674i	0.938295	−	0.345837i	$-0.112405\pi$
$860$	−25.9706	+	8.65685i	−0.885589	+	0.295196i
$861$		0			0
$862$	−6.34315	+	6.34315i	−0.216048	+	0.216048i
$863$			7.11270i			0.242119i	0.992645	+	0.121060i	$0.0386292\pi$
$863$			7.11270i			0.242119i	−0.992645	+	0.121060i	$0.961371\pi$
$864$		0			0
$865$	8.97056	−	17.9411i	0.305008	−	0.610017i
$866$	−14.2426			−0.483985
$867$		0			0
$868$			14.7279i			0.499898i
$869$		−	72.7696i		−	2.46854i
$870$		0			0
$871$	7.45584			0.252632
$872$	−12.6066	+	12.6066i	−0.426913	+	0.426913i
$873$		0			0
$874$	3.51472	−	3.51472i	0.118887	−	0.118887i
$875$	−15.5563	+	2.82843i	−0.525901	+	0.0956183i
$876$		0			0
$877$	−25.4853	−	25.4853i	−0.860577	−	0.860577i	0.130828	−	0.991405i	$-0.458236\pi$
$877$	−25.4853	−	25.4853i	−0.860577	−	0.860577i	−0.991405	+	0.130828i	$0.958236\pi$
$878$	−12.9706	−	12.9706i	−0.437735	−	0.437735i
$879$		0			0
$880$	−6.24264	+	12.4853i	−0.210439	+	0.420879i
$881$	39.5563	+	39.5563i	1.33269	+	1.33269i	0.902958	+	0.429730i	$0.141391\pi$
$881$	39.5563	+	39.5563i	1.33269	+	1.33269i	0.429730	+	0.902958i	$0.358609\pi$
$882$		0			0
$883$			6.72792i			0.226413i	0.993572	+	0.113206i	$0.0361121\pi$
$883$			6.72792i			0.226413i	−0.993572	+	0.113206i	$0.963888\pi$
$884$	10.6066	−	6.36396i	0.356739	−	0.214043i
$885$		0			0
$886$		−	1.79899i		−	0.0604382i
$887$	22.4142	−	22.4142i	0.752596	−	0.752596i	−0.222367	−	0.974963i	$-0.571378\pi$
$887$	22.4142	−	22.4142i	0.752596	−	0.752596i	0.974963	+	0.222367i	$0.0713784\pi$
$888$		0			0
$889$	−7.72792	−	7.72792i	−0.259186	−	0.259186i
$890$	−11.6360	+	3.87868i	−0.390041	+	0.130014i
$891$		0			0
$892$	−14.7574			−0.494113
$893$	5.48528			0.183558
$894$		0			0
$895$	16.4853	+	49.4558i	0.551042	+	1.65313i
$896$	1.00000	+	1.00000i	0.0334077	+	0.0334077i
$897$		0			0
$898$	−10.7990	+	10.7990i	−0.360367	+	0.360367i
$899$			10.4142i			0.347333i
$900$		0			0
$901$	−6.36396	−	10.6066i	−0.212014	−	0.353357i
$902$			14.0000i			0.466149i
$903$		0			0
$904$	−9.53553	−	9.53553i	−0.317147	−	0.317147i
$905$	19.7990	−	39.5980i	0.658141	−	1.31628i
$906$		0			0
$907$	21.8492	+	21.8492i	0.725492	+	0.725492i	0.969718	−	0.244226i	$-0.0785339\pi$
$907$	21.8492	+	21.8492i	0.725492	+	0.725492i	−0.244226	+	0.969718i	$0.578534\pi$
$908$	13.9497	+	13.9497i	0.462939	+	0.462939i
$909$		0			0
$910$	4.24264	−	8.48528i	0.140642	−	0.281284i
$911$	12.6863	−	12.6863i	0.420316	−	0.420316i	−0.464997	−	0.885312i	$-0.653945\pi$
$911$	12.6863	−	12.6863i	0.420316	−	0.420316i	0.885312	+	0.464997i	$0.153945\pi$
$912$		0			0
$913$	18.7279	−	18.7279i	0.619804	−	0.619804i
$914$	6.24264			0.206488
$915$		0			0
$916$			16.2426i			0.536672i
$917$		−	20.8284i		−	0.687815i
$918$		0			0
$919$	11.2132			0.369889			0.184945	−	0.982749i	$-0.440789\pi$
$919$	11.2132			0.369889			0.184945	+	0.982749i	$0.440789\pi$
$920$	−8.00000	−	4.00000i	−0.263752	−	0.131876i
$921$		0			0
$922$		−	16.2843i		−	0.536294i
$923$	6.87868	−	6.87868i	0.226414	−	0.226414i
$924$		0			0
$925$	−3.24264	+	22.6985i	−0.106617	+	0.746322i
$926$			16.7574i			0.550681i
$927$		0			0
$928$	0.707107	+	0.707107i	0.0232119	+	0.0232119i
$929$	26.6569	−	26.6569i	0.874583	−	0.874583i	−0.118385	−	0.992968i	$-0.537772\pi$
$929$	26.6569	−	26.6569i	0.874583	−	0.874583i	0.992968	+	0.118385i	$0.0377716\pi$
$930$		0			0
$931$	−6.21320			−0.203630
$932$	1.05025	−	1.05025i	0.0344022	−	0.0344022i
$933$		0			0
$934$	−6.72792			−0.220144
$935$	57.3848	−	4.41421i	1.87668	−	0.144360i
$936$		0			0
$937$	4.78680			0.156378			0.0781889	−	0.996939i	$-0.475086\pi$
$937$	4.78680			0.156378			0.0781889	+	0.996939i	$0.475086\pi$
$938$	2.48528	−	2.48528i	0.0811473	−	0.0811473i
$939$		0			0
$940$	−3.12132	−	9.36396i	−0.101806	−	0.305419i
$941$	−33.1924	+	33.1924i	−1.08204	+	1.08204i	−0.0857218	+	0.996319i	$0.527320\pi$
$941$	−33.1924	+	33.1924i	−1.08204	+	1.08204i	−0.996319	+	0.0857218i	$0.972680\pi$
$942$		0			0
$943$	−8.97056			−0.292122
$944$			6.89949i			0.224559i
$945$		0			0
$946$	54.0416	−	54.0416i	1.75704	−	1.75704i
$947$	−27.7071	+	27.7071i	−0.900360	+	0.900360i	−0.995467	−	0.0951071i	$-0.969681\pi$
$947$	−27.7071	+	27.7071i	−0.900360	+	0.900360i	0.0951071	+	0.995467i	$0.469681\pi$
$948$		0			0
$949$	13.0919	+	13.0919i	0.424981	+	0.424981i
$950$	−3.72792	−	4.97056i	−0.120950	−	0.161266i
$951$		0			0
$952$	1.41421	−	5.65685i	0.0458349	−	0.183340i
$953$			7.41421i			0.240170i	0.992764	+	0.120085i	$0.0383167\pi$
$953$			7.41421i			0.240170i	−0.992764	+	0.120085i	$0.961683\pi$
$954$		0			0
$955$	−45.0000	+	15.0000i	−1.45617	+	0.485389i
$956$	−13.7574			−0.444945
$957$		0			0
$958$	19.9497	+	19.9497i	0.644547	+	0.644547i
$959$	−7.41421	+	7.41421i	−0.239417	+	0.239417i
$960$		0			0
$961$			77.4558i			2.49858i
$962$	−9.72792	−	9.72792i	−0.313641	−	0.313641i
$963$		0			0
$964$	11.2426	+	11.2426i	0.362101	+	0.362101i
$965$	−4.28427	−	2.14214i	−0.137916	−	0.0689578i
$966$		0			0
$967$	−2.97056			−0.0955269			−0.0477634	−	0.998859i	$-0.515209\pi$
$967$	−2.97056			−0.0955269			−0.0477634	+	0.998859i	$0.515209\pi$
$968$		−	27.9706i		−	0.899008i
$969$		0			0
$970$	5.82843	−	11.6569i	0.187140	−	0.374279i
$971$		−	0.556349i		−	0.0178541i	−0.999960	−	0.00892705i	$-0.997158\pi$
$971$		−	0.556349i		−	0.0178541i	0.999960	−	0.00892705i	$-0.00284161\pi$
$972$		0			0
$973$		−	22.0000i		−	0.705288i
$974$	2.75736	+	2.75736i	0.0883515	+	0.0883515i
$975$		0			0
$976$	1.87868	−	1.87868i	0.0601351	−	0.0601351i
$977$	24.7279			0.791116			0.395558	−	0.918441i	$-0.370551\pi$
$977$	24.7279			0.791116			0.395558	+	0.918441i	$0.370551\pi$
$978$		0			0
$979$	24.2132	−	24.2132i	0.773857	−	0.773857i
$980$	3.53553	+	10.6066i	0.112938	+	0.338815i
$981$		0			0
$982$			12.8995i			0.411639i
$983$	−38.0122	+	38.0122i	−1.21240	+	1.21240i	−0.242166	+	0.970235i	$0.577858\pi$
$983$	−38.0122	+	38.0122i	−1.21240	+	1.21240i	−0.970235	+	0.242166i	$0.922142\pi$
$984$		0			0
$985$	41.4558	+	20.7279i	1.32089	+	0.660447i
$986$	1.00000	−	4.00000i	0.0318465	−	0.127386i
$987$		0			0
$988$	3.72792			0.118601
$989$	34.6274	+	34.6274i	1.10109	+	1.10109i
$990$		0			0
$991$	16.8787	+	16.8787i	0.536169	+	0.536169i	0.922401	−	0.386233i	$-0.126224\pi$
$991$	16.8787	+	16.8787i	0.536169	+	0.536169i	−0.386233	+	0.922401i	$0.626224\pi$
$992$	7.36396	+	7.36396i	0.233806	+	0.233806i
$993$		0			0
$994$		−	4.58579i		−	0.145452i
$995$	8.14214	+	4.07107i	0.258123	+	0.129062i
$996$		0			0
$997$	−28.6985	−	28.6985i	−0.908890	−	0.908890i	0.0872926	−	0.996183i	$-0.472178\pi$
$997$	−28.6985	−	28.6985i	−0.908890	−	0.908890i	−0.996183	+	0.0872926i	$0.972178\pi$
$998$	−25.4853	+	25.4853i	−0.806722	+	0.806722i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1530.2.n.o.829.1		4
3.2	odd	2		170.2.g.e.149.1	yes	4
5.4	even	2		1530.2.n.j.829.2		4
15.2	even	4		850.2.h.k.251.2		4
15.8	even	4		850.2.h.h.251.1		4
15.14	odd	2		170.2.g.f.149.2	yes	4
17.4	even	4		1530.2.n.j.1279.2		4
51.38	odd	4		170.2.g.f.89.2	yes	4
85.4	even	4	inner	1530.2.n.o.1279.1		4
255.38	even	4		850.2.h.h.701.1		4
255.89	odd	4		170.2.g.e.89.1	✓	4
255.242	even	4		850.2.h.k.701.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.g.e.89.1	✓	4	255.89	odd	4
170.2.g.e.149.1	yes	4	3.2	odd	2
170.2.g.f.89.2	yes	4	51.38	odd	4
170.2.g.f.149.2	yes	4	15.14	odd	2
850.2.h.h.251.1		4	15.8	even	4
850.2.h.h.701.1		4	255.38	even	4
850.2.h.k.251.2		4	15.2	even	4
850.2.h.k.701.2		4	255.242	even	4
1530.2.n.j.829.2		4	5.4	even	2
1530.2.n.j.1279.2		4	17.4	even	4
1530.2.n.o.829.1		4	1.1	even	1	trivial
1530.2.n.o.1279.1		4	85.4	even	4	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:	\( N \)	\(=\)	\( 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1530.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(-2.12132 + 0.707107i) q^{5} +(1.00000 + 1.00000i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(-2.12132 + 0.707107i) q^{5} +(1.00000 + 1.00000i) q^{7} +1.00000 q^{8} +(-2.12132 + 0.707107i) q^{10} +(4.41421 - 4.41421i) q^{11} +3.00000i q^{13} +(1.00000 + 1.00000i) q^{14} +1.00000 q^{16} +(-2.12132 - 3.53553i) q^{17} -1.24264i q^{19} +(-2.12132 + 0.707107i) q^{20} +(4.41421 - 4.41421i) q^{22} +(2.82843 + 2.82843i) q^{23} +(4.00000 - 3.00000i) q^{25} +3.00000i q^{26} +(1.00000 + 1.00000i) q^{28} +(0.707107 + 0.707107i) q^{29} +(7.36396 + 7.36396i) q^{31} +1.00000 q^{32} +(-2.12132 - 3.53553i) q^{34} +(-2.82843 - 1.41421i) q^{35} +(-3.24264 + 3.24264i) q^{37} -1.24264i q^{38} +(-2.12132 + 0.707107i) q^{40} +(-1.58579 + 1.58579i) q^{41} +12.2426 q^{43} +(4.41421 - 4.41421i) q^{44} +(2.82843 + 2.82843i) q^{46} +4.41421i q^{47} -5.00000i q^{49} +(4.00000 - 3.00000i) q^{50} +3.00000i q^{52} +3.00000 q^{53} +(-6.24264 + 12.4853i) q^{55} +(1.00000 + 1.00000i) q^{56} +(0.707107 + 0.707107i) q^{58} +6.89949i q^{59} +(1.87868 - 1.87868i) q^{61} +(7.36396 + 7.36396i) q^{62} +1.00000 q^{64} +(-2.12132 - 6.36396i) q^{65} -2.48528i q^{67} +(-2.12132 - 3.53553i) q^{68} +(-2.82843 - 1.41421i) q^{70} +(-2.29289 - 2.29289i) q^{71} +(4.36396 - 4.36396i) q^{73} +(-3.24264 + 3.24264i) q^{74} -1.24264i q^{76} +8.82843 q^{77} +(8.24264 - 8.24264i) q^{79} +(-2.12132 + 0.707107i) q^{80} +(-1.58579 + 1.58579i) q^{82} +4.24264 q^{83} +(7.00000 + 6.00000i) q^{85} +12.2426 q^{86} +(4.41421 - 4.41421i) q^{88} +5.48528 q^{89} +(-3.00000 + 3.00000i) q^{91} +(2.82843 + 2.82843i) q^{92} +4.41421i q^{94} +(0.878680 + 2.63604i) q^{95} +(-4.12132 + 4.12132i) q^{97} -5.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{4} + 4 q^{7} + 4 q^{8}+O(q^{10}) \) 4 * q + 4 * q^2 + 4 * q^4 + 4 * q^7 + 4 * q^8	\( 4 q + 4 q^{2} + 4 q^{4} + 4 q^{7} + 4 q^{8} + 12 q^{11} + 4 q^{14} + 4 q^{16} + 12 q^{22} + 16 q^{25} + 4 q^{28} + 4 q^{31} + 4 q^{32} + 4 q^{37} - 12 q^{41} + 32 q^{43} + 12 q^{44} + 16 q^{50} + 12 q^{53} - 8 q^{55} + 4 q^{56} + 16 q^{61} + 4 q^{62} + 4 q^{64} - 12 q^{71} - 8 q^{73} + 4 q^{74} + 24 q^{77} + 16 q^{79} - 12 q^{82} + 28 q^{85} + 32 q^{86} + 12 q^{88} - 12 q^{89} - 12 q^{91} + 12 q^{95} - 8 q^{97}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^4 + 4 * q^7 + 4 * q^8 + 12 * q^11 + 4 * q^14 + 4 * q^16 + 12 * q^22 + 16 * q^25 + 4 * q^28 + 4 * q^31 + 4 * q^32 + 4 * q^37 - 12 * q^41 + 32 * q^43 + 12 * q^44 + 16 * q^50 + 12 * q^53 - 8 * q^55 + 4 * q^56 + 16 * q^61 + 4 * q^62 + 4 * q^64 - 12 * q^71 - 8 * q^73 + 4 * q^74 + 24 * q^77 + 16 * q^79 - 12 * q^82 + 28 * q^85 + 32 * q^86 + 12 * q^88 - 12 * q^89 - 12 * q^91 + 12 * q^95 - 8 * q^97

Introduction

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