LMFDB - Embedded newform 1470.2.d.e.1469.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,2,Mod(1469,1470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1470, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1470.1469");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1470.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.7380090971$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.3317760000.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81 $ x^8 - 4x^6 + 7x^4 - 36*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1469.6
Root			$-1.01575 - 1.40294i$ of defining polynomial
Character	$\chi$	$=$	1470.1469
Dual form			1470.2.d.e.1469.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(0.707107 - 1.58114i) q^{3} +1.00000 q^{4} +(1.41421 + 1.73205i) q^{5} +(-0.707107 + 1.58114i) q^{6} -1.00000 q^{8} +(-2.00000 - 2.23607i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(0.707107 - 1.58114i) q^{3} +1.00000 q^{4} +(1.41421 + 1.73205i) q^{5} +(-0.707107 + 1.58114i) q^{6} -1.00000 q^{8} +(-2.00000 - 2.23607i) q^{9} +(-1.41421 - 1.73205i) q^{10} -4.68556i q^{11} +(0.707107 - 1.58114i) q^{12} -1.04456 q^{13} +(3.73861 - 1.01132i) q^{15} +1.00000 q^{16} -3.16228i q^{17} +(2.00000 + 2.23607i) q^{18} +1.43023i q^{19} +(1.41421 + 1.73205i) q^{20} +4.68556i q^{22} -4.47723 q^{23} +(-0.707107 + 1.58114i) q^{24} +(-1.00000 + 4.89898i) q^{25} +1.04456 q^{26} +(-4.94975 + 1.58114i) q^{27} -6.92163i q^{29} +(-3.73861 + 1.01132i) q^{30} -6.62638i q^{31} -1.00000 q^{32} +(-7.40852 - 3.31319i) q^{33} +3.16228i q^{34} +(-2.00000 - 2.23607i) q^{36} +2.66291i q^{37} -1.43023i q^{38} +(-0.738613 + 1.65159i) q^{39} +(-1.41421 - 1.73205i) q^{40} -1.04456 q^{41} +6.92163i q^{43} -4.68556i q^{44} +(1.04456 - 6.62638i) q^{45} +4.47723 q^{46} -11.2189i q^{47} +(0.707107 - 1.58114i) q^{48} +(1.00000 - 4.89898i) q^{50} +(-5.00000 - 2.23607i) q^{51} -1.04456 q^{52} -5.00000 q^{53} +(4.94975 - 1.58114i) q^{54} +(8.11562 - 6.62638i) q^{55} +(2.26139 + 1.01132i) q^{57} +6.92163i q^{58} +10.5744 q^{59} +(3.73861 - 1.01132i) q^{60} -3.46410i q^{61} +6.62638i q^{62} +1.00000 q^{64} +(-1.47723 - 1.80922i) q^{65} +(7.40852 + 3.31319i) q^{66} -14.2701i q^{67} -3.16228i q^{68} +(-3.16588 + 7.07912i) q^{69} +6.92163i q^{71} +(2.00000 + 2.23607i) q^{72} +3.50333 q^{73} -2.66291i q^{74} +(7.03886 + 5.04524i) q^{75} +1.43023i q^{76} +(0.738613 - 1.65159i) q^{78} +11.4772 q^{79} +(1.41421 + 1.73205i) q^{80} +(-1.00000 + 8.94427i) q^{81} +1.04456 q^{82} -4.06775i q^{83} +(5.47723 - 4.47214i) q^{85} -6.92163i q^{86} +(-10.9441 - 4.89433i) q^{87} +4.68556i q^{88} +4.91754 q^{89} +(-1.04456 + 6.62638i) q^{90} -4.47723 q^{92} +(-10.4772 - 4.68556i) q^{93} +11.2189i q^{94} +(-2.47723 + 2.02265i) q^{95} +(-0.707107 + 1.58114i) q^{96} +11.9886 q^{97} +(-10.4772 + 9.37112i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 8 q^{4} - 8 q^{8} - 16 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 + 8 * q^4 - 8 * q^8 - 16 * q^9	$ 8 q - 8 q^{2} + 8 q^{4} - 8 q^{8} - 16 q^{9} + 8 q^{15} + 8 q^{16} + 16 q^{18} + 8 q^{23} - 8 q^{25} - 8 q^{30} - 8 q^{32} - 16 q^{36} + 16 q^{39} - 8 q^{46} + 8 q^{50} - 40 q^{51} - 40 q^{53} + 40 q^{57} + 8 q^{60} + 8 q^{64} + 32 q^{65} + 16 q^{72} - 16 q^{78} + 48 q^{79} - 8 q^{81} + 8 q^{92} - 40 q^{93} + 24 q^{95} - 40 q^{99}+O(q^{100}) $ 8 * q - 8 * q^2 + 8 * q^4 - 8 * q^8 - 16 * q^9 + 8 * q^15 + 8 * q^16 + 16 * q^18 + 8 * q^23 - 8 * q^25 - 8 * q^30 - 8 * q^32 - 16 * q^36 + 16 * q^39 - 8 * q^46 + 8 * q^50 - 40 * q^51 - 40 * q^53 + 40 * q^57 + 8 * q^60 + 8 * q^64 + 32 * q^65 + 16 * q^72 - 16 * q^78 + 48 * q^79 - 8 * q^81 + 8 * q^92 - 40 * q^93 + 24 * q^95 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

$n$	$491$	$1081$	$1177$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	0.707107	−	1.58114i	0.408248	−	0.912871i
$3$	0.707107	−	1.58114i	0.408248	−	0.912871i
$4$	1.00000			0.500000
$5$	1.41421	+	1.73205i	0.632456	+	0.774597i
$5$	1.41421	+	1.73205i	0.632456	+	0.774597i
$6$	−0.707107	+	1.58114i	−0.288675	+	0.645497i
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	−2.00000	−	2.23607i	−0.666667	−	0.745356i
$10$	−1.41421	−	1.73205i	−0.447214	−	0.547723i
$11$		−	4.68556i		−	1.41275i	−0.707838	−	0.706374i	$-0.750330\pi$
$11$		−	4.68556i		−	1.41275i	0.707838	−	0.706374i	$-0.249670\pi$
$12$	0.707107	−	1.58114i	0.204124	−	0.456435i
$13$	−1.04456			−0.289708			−0.144854	−	0.989453i	$-0.546271\pi$
$13$	−1.04456			−0.289708			−0.144854	+	0.989453i	$0.546271\pi$
$14$		0			0
$15$	3.73861	−	1.01132i	0.965306	−	0.261123i
$16$	1.00000			0.250000
$17$		−	3.16228i		−	0.766965i	−0.923548	−	0.383482i	$-0.874725\pi$
$17$		−	3.16228i		−	0.766965i	0.923548	−	0.383482i	$-0.125275\pi$
$18$	2.00000	+	2.23607i	0.471405	+	0.527046i
$19$			1.43023i			0.328117i	0.986451	+	0.164058i	$0.0524585\pi$
$19$			1.43023i			0.328117i	−0.986451	+	0.164058i	$0.947541\pi$
$20$	1.41421	+	1.73205i	0.316228	+	0.387298i
$21$		0			0
$22$			4.68556i			0.998964i
$23$	−4.47723			−0.933566			−0.466783	−	0.884372i	$-0.654587\pi$
$23$	−4.47723			−0.933566			−0.466783	+	0.884372i	$0.654587\pi$
$24$	−0.707107	+	1.58114i	−0.144338	+	0.322749i
$25$	−1.00000	+	4.89898i	−0.200000	+	0.979796i
$26$	1.04456			0.204854
$27$	−4.94975	+	1.58114i	−0.952579	+	0.304290i
$28$		0			0
$29$		−	6.92163i		−	1.28531i	−0.766154	−	0.642657i	$-0.777832\pi$
$29$		−	6.92163i		−	1.28531i	0.766154	−	0.642657i	$-0.222168\pi$
$30$	−3.73861	+	1.01132i	−0.682574	+	0.184641i
$31$		−	6.62638i		−	1.19013i	−0.803677	−	0.595066i	$-0.797126\pi$
$31$		−	6.62638i		−	1.19013i	0.803677	−	0.595066i	$-0.202874\pi$
$32$	−1.00000			−0.176777
$33$	−7.40852	−	3.31319i	−1.28966	−	0.576752i
$34$			3.16228i			0.542326i
$35$		0			0
$36$	−2.00000	−	2.23607i	−0.333333	−	0.372678i
$37$			2.66291i			0.437780i	0.975750	+	0.218890i	$0.0702436\pi$
$37$			2.66291i			0.437780i	−0.975750	+	0.218890i	$0.929756\pi$
$38$		−	1.43023i		−	0.232013i
$39$	−0.738613	+	1.65159i	−0.118273	+	0.264466i
$40$	−1.41421	−	1.73205i	−0.223607	−	0.273861i
$41$	−1.04456			−0.163132			−0.0815661	−	0.996668i	$-0.525992\pi$
$41$	−1.04456			−0.163132			−0.0815661	+	0.996668i	$0.525992\pi$
$42$		0			0
$43$			6.92163i			1.05554i	0.849388	+	0.527769i	$0.176971\pi$
$43$			6.92163i			1.05554i	−0.849388	+	0.527769i	$0.823029\pi$
$44$		−	4.68556i		−	0.706374i
$45$	1.04456	−	6.62638i	0.155713	−	0.987802i
$46$	4.47723			0.660131
$47$		−	11.2189i		−	1.63644i	−0.574904	−	0.818221i	$-0.694960\pi$
$47$		−	11.2189i		−	1.63644i	0.574904	−	0.818221i	$-0.305040\pi$
$48$	0.707107	−	1.58114i	0.102062	−	0.228218i
$49$		0			0
$50$	1.00000	−	4.89898i	0.141421	−	0.692820i
$51$	−5.00000	−	2.23607i	−0.700140	−	0.313112i
$52$	−1.04456			−0.144854
$53$	−5.00000			−0.686803			−0.343401	−	0.939189i	$-0.611579\pi$
$53$	−5.00000			−0.686803			−0.343401	+	0.939189i	$0.611579\pi$
$54$	4.94975	−	1.58114i	0.673575	−	0.215166i
$55$	8.11562	−	6.62638i	1.09431	−	0.893501i
$56$		0			0
$57$	2.26139	+	1.01132i	0.299528	+	0.133953i
$58$			6.92163i			0.908854i
$59$	10.5744			1.37667			0.688334	−	0.725394i	$-0.258342\pi$
$59$	10.5744			1.37667			0.688334	+	0.725394i	$0.258342\pi$
$60$	3.73861	−	1.01132i	0.482653	−	0.130561i
$61$		−	3.46410i		−	0.443533i	−0.975100	−	0.221766i	$-0.928818\pi$
$61$		−	3.46410i		−	0.443533i	0.975100	−	0.221766i	$-0.0711822\pi$
$62$			6.62638i			0.841551i
$63$		0			0
$64$	1.00000			0.125000
$65$	−1.47723	−	1.80922i	−0.183227	−	0.224407i
$66$	7.40852	+	3.31319i	0.911925	+	0.407825i
$67$		−	14.2701i		−	1.74337i	−0.490067	−	0.871685i	$-0.663028\pi$
$67$		−	14.2701i		−	1.74337i	0.490067	−	0.871685i	$-0.336972\pi$
$68$		−	3.16228i		−	0.383482i
$69$	−3.16588	+	7.07912i	−0.381127	+	0.852225i
$70$		0			0
$71$			6.92163i			0.821446i	0.911760	+	0.410723i	$0.134724\pi$
$71$			6.92163i			0.821446i	−0.911760	+	0.410723i	$0.865276\pi$
$72$	2.00000	+	2.23607i	0.235702	+	0.263523i
$73$	3.50333			0.410033			0.205017	−	0.978758i	$-0.434275\pi$
$73$	3.50333			0.410033			0.205017	+	0.978758i	$0.434275\pi$
$74$		−	2.66291i		−	0.309557i
$75$	7.03886	+	5.04524i	0.812778	+	0.582574i
$76$			1.43023i			0.164058i
$77$		0			0
$78$	0.738613	−	1.65159i	0.0836314	−	0.187006i
$79$	11.4772			1.29129			0.645644	−	0.763638i	$-0.276589\pi$
$79$	11.4772			1.29129			0.645644	+	0.763638i	$0.276589\pi$
$80$	1.41421	+	1.73205i	0.158114	+	0.193649i
$81$	−1.00000	+	8.94427i	−0.111111	+	0.993808i
$82$	1.04456			0.115352
$83$		−	4.06775i		−	0.446494i	−0.974762	−	0.223247i	$-0.928334\pi$
$83$		−	4.06775i		−	0.446494i	0.974762	−	0.223247i	$-0.0716656\pi$
$84$		0			0
$85$	5.47723	−	4.47214i	0.594089	−	0.485071i
$86$		−	6.92163i		−	0.746378i
$87$	−10.9441	−	4.89433i	−1.17333	−	0.524727i
$88$			4.68556i			0.499482i
$89$	4.91754			0.521258			0.260629	−	0.965439i	$-0.416070\pi$
$89$	4.91754			0.521258			0.260629	+	0.965439i	$0.416070\pi$
$90$	−1.04456	+	6.62638i	−0.110106	+	0.698482i
$91$		0			0
$92$	−4.47723			−0.466783
$93$	−10.4772	−	4.68556i	−1.08644	−	0.485870i
$94$			11.2189i			1.15714i
$95$	−2.47723	+	2.02265i	−0.254158	+	0.207519i
$96$	−0.707107	+	1.58114i	−0.0721688	+	0.161374i
$97$	11.9886			1.21726			0.608629	−	0.793455i	$-0.291720\pi$
$97$	11.9886			1.21726			0.608629	+	0.793455i	$0.291720\pi$
$98$		0			0
$99$	−10.4772	+	9.37112i	−1.05300	+	0.941833i
$100$	−1.00000	+	4.89898i	−0.100000	+	0.489898i
$101$	−11.3137			−1.12576			−0.562878	−	0.826540i	$-0.690306\pi$
$101$	−11.3137			−1.12576			−0.562878	+	0.826540i	$0.690306\pi$
$102$	5.00000	+	2.23607i	0.495074	+	0.221404i
$103$	−4.91754			−0.484540			−0.242270	−	0.970209i	$-0.577892\pi$
$103$	−4.91754			−0.484540			−0.242270	+	0.970209i	$0.577892\pi$
$104$	1.04456			0.102427
$105$		0			0
$106$	5.00000			0.485643
$107$	5.47723			0.529503			0.264752	−	0.964317i	$-0.414710\pi$
$107$	5.47723			0.529503			0.264752	+	0.964317i	$0.414710\pi$
$108$	−4.94975	+	1.58114i	−0.476290	+	0.152145i
$109$	−20.4317			−1.95700			−0.978500	−	0.206248i	$-0.933875\pi$
$109$	−20.4317			−1.95700			−0.978500	+	0.206248i	$0.933875\pi$
$110$	−8.11562	+	6.62638i	−0.773794	+	0.631800i
$111$	4.21043	+	1.88296i	0.399637	+	0.178723i
$112$		0			0
$113$	−17.4772			−1.64412			−0.822060	−	0.569402i	$-0.807175\pi$
$113$	−17.4772			−1.64412			−0.822060	+	0.569402i	$0.807175\pi$
$114$	−2.26139	−	1.01132i	−0.211798	−	0.0947191i
$115$	−6.33175	−	7.75478i	−0.590439	−	0.723137i
$116$		−	6.92163i		−	0.642657i
$117$	2.08911	+	2.33570i	0.193139	+	0.215935i
$118$	−10.5744			−0.973452
$119$		0			0
$120$	−3.73861	+	1.01132i	−0.341287	+	0.0923207i
$121$	−10.9545			−0.995859
$122$			3.46410i			0.313625i
$123$	−0.738613	+	1.65159i	−0.0665985	+	0.148919i
$124$		−	6.62638i		−	0.595066i
$125$	−9.89949	+	5.19615i	−0.885438	+	0.464758i
$126$		0			0
$127$		−	8.73085i		−	0.774738i	−0.921925	−	0.387369i	$-0.873384\pi$
$127$		−	8.73085i		−	0.774738i	0.921925	−	0.387369i	$-0.126616\pi$
$128$	−1.00000			−0.0883883
$129$	10.9441	+	4.89433i	0.963570	+	0.430922i
$130$	1.47723	+	1.80922i	0.129561	+	0.158679i
$131$	13.7725			1.20331			0.601654	−	0.798757i	$-0.294509\pi$
$131$	13.7725			1.20331			0.601654	+	0.798757i	$0.294509\pi$
$132$	−7.40852	−	3.31319i	−0.644829	−	0.288376i
$133$		0			0
$134$			14.2701i			1.23275i
$135$	−9.73861	−	6.33715i	−0.838166	−	0.545415i
$136$			3.16228i			0.271163i
$137$	3.47723			0.297079			0.148540	−	0.988906i	$-0.452543\pi$
$137$	3.47723			0.297079			0.148540	+	0.988906i	$0.452543\pi$
$138$	3.16588	−	7.07912i	0.269497	−	0.602614i
$139$		−	20.1810i		−	1.71173i	−0.517202	−	0.855863i	$-0.673026\pi$
$139$		−	20.1810i		−	1.71173i	0.517202	−	0.855863i	$-0.326974\pi$
$140$		0			0
$141$	−17.7386	−	7.93295i	−1.49386	−	0.668075i
$142$		−	6.92163i		−	0.580850i
$143$			4.89433i			0.409284i
$144$	−2.00000	−	2.23607i	−0.166667	−	0.186339i
$145$	11.9886	−	9.78866i	0.995600	−	0.812904i
$146$	−3.50333			−0.289937
$147$		0			0
$148$			2.66291i			0.218890i
$149$			2.44949i			0.200670i	0.994954	+	0.100335i	$0.0319915\pi$
$149$			2.44949i			0.200670i	−0.994954	+	0.100335i	$0.968009\pi$
$150$	−7.03886	−	5.04524i	−0.574721	−	0.411942i
$151$	−2.00000			−0.162758			−0.0813788	−	0.996683i	$-0.525932\pi$
$151$	−2.00000			−0.162758			−0.0813788	+	0.996683i	$0.525932\pi$
$152$		−	1.43023i		−	0.116007i
$153$	−7.07107	+	6.32456i	−0.571662	+	0.511310i
$154$		0			0
$155$	11.4772	−	9.37112i	0.921873	−	0.752706i
$156$	−0.738613	+	1.65159i	−0.0591364	+	0.132233i
$157$	14.4474			1.15303			0.576513	−	0.817088i	$-0.304413\pi$
$157$	14.4474			1.15303			0.576513	+	0.817088i	$0.304413\pi$
$158$	−11.4772			−0.913079
$159$	−3.53553	+	7.90569i	−0.280386	+	0.626962i
$160$	−1.41421	−	1.73205i	−0.111803	−	0.136931i
$161$		0			0
$162$	1.00000	−	8.94427i	0.0785674	−	0.702728i
$163$			14.6969i			1.15115i	0.817748	+	0.575577i	$0.195222\pi$
$163$			14.6969i			1.15115i	−0.817748	+	0.575577i	$0.804778\pi$
$164$	−1.04456			−0.0815661
$165$	−4.73861	−	17.5175i	−0.368901	−	1.36373i
$166$			4.06775i			0.315719i
$167$		−	4.29068i		−	0.332023i	−0.986124	−	0.166011i	$-0.946911\pi$
$167$		−	4.29068i		−	0.332023i	0.986124	−	0.166011i	$-0.0530889\pi$
$168$		0			0
$169$	−11.9089			−0.916069
$170$	−5.47723	+	4.47214i	−0.420084	+	0.342997i
$171$	3.19808	−	2.86045i	0.244564	−	0.218744i
$172$			6.92163i			0.527769i
$173$			1.12840i			0.0857909i	0.999080	+	0.0428954i	$0.0136582\pi$
$173$			1.12840i			0.0857909i	−0.999080	+	0.0428954i	$0.986342\pi$
$174$	10.9441	+	4.89433i	0.829666	+	0.371038i
$175$		0			0
$176$		−	4.68556i		−	0.353187i
$177$	7.47723	−	16.7196i	0.562023	−	1.25672i
$178$	−4.91754			−0.368585
$179$			19.3825i			1.44872i	0.689424	+	0.724358i	$0.257864\pi$
$179$			19.3825i			1.44872i	−0.689424	+	0.724358i	$0.742136\pi$
$180$	1.04456	−	6.62638i	0.0778566	−	0.493901i
$181$		−	3.16228i		−	0.235050i	−0.993070	−	0.117525i	$-0.962504\pi$
$181$		−	3.16228i		−	0.235050i	0.993070	−	0.117525i	$-0.0374961\pi$
$182$		0			0
$183$	−5.47723	−	2.44949i	−0.404888	−	0.181071i
$184$	4.47723			0.330065
$185$	−4.61230	+	3.76593i	−0.339103	+	0.276876i
$186$	10.4772	+	4.68556i	0.768227	+	0.343562i
$187$	−14.8170			−1.08353
$188$		−	11.2189i		−	0.818221i
$189$		0			0
$190$	2.47723	−	2.02265i	0.179717	−	0.146738i
$191$			16.2927i			1.17890i	0.807804	+	0.589451i	$0.200656\pi$
$191$			16.2927i			1.17890i	−0.807804	+	0.589451i	$0.799344\pi$
$192$	0.707107	−	1.58114i	0.0510310	−	0.114109i
$193$		−	7.34847i		−	0.528954i	−0.964392	−	0.264477i	$-0.914801\pi$
$193$		−	7.34847i		−	0.528954i	0.964392	−	0.264477i	$-0.0851994\pi$
$194$	−11.9886			−0.860732
$195$	−3.90519	+	1.05638i	−0.279657	+	0.0756492i
$196$		0			0
$197$	−9.00000			−0.641223			−0.320612	−	0.947211i	$-0.603888\pi$
$197$	−9.00000			−0.641223			−0.320612	+	0.947211i	$0.603888\pi$
$198$	10.4772	−	9.37112i	0.744584	−	0.665976i
$199$			15.5096i			1.09944i	0.835348	+	0.549722i	$0.185266\pi$
$199$			15.5096i			1.09944i	−0.835348	+	0.549722i	$0.814734\pi$
$200$	1.00000	−	4.89898i	0.0707107	−	0.346410i
$201$	−22.5630	−	10.0905i	−1.59147	−	0.711728i
$202$	11.3137			0.796030
$203$		0			0
$204$	−5.00000	−	2.23607i	−0.350070	−	0.156556i
$205$	−1.47723	−	1.80922i	−0.103174	−	0.126362i
$206$	4.91754			0.342621
$207$	8.95445	+	10.0114i	0.622377	+	0.695839i
$208$	−1.04456			−0.0724269
$209$	6.70141			0.463546
$210$		0			0
$211$	24.4772			1.68508			0.842541	−	0.538632i	$-0.181059\pi$
$211$	24.4772			1.68508			0.842541	+	0.538632i	$0.181059\pi$
$212$	−5.00000			−0.343401
$213$	10.9441	+	4.89433i	0.749874	+	0.335354i
$214$	−5.47723			−0.374415
$215$	−11.9886	+	9.78866i	−0.817616	+	0.667581i
$216$	4.94975	−	1.58114i	0.336788	−	0.107583i
$217$		0			0
$218$	20.4317			1.38381
$219$	2.47723	−	5.53924i	0.167395	−	0.374307i
$220$	8.11562	−	6.62638i	0.547155	−	0.446750i
$221$			3.30318i			0.222196i
$222$	−4.21043	−	1.88296i	−0.282586	−	0.126376i
$223$	21.8881			1.46574			0.732868	−	0.680371i	$-0.238181\pi$
$223$	21.8881			1.46574			0.732868	+	0.680371i	$0.238181\pi$
$224$		0			0
$225$	12.9545	−	7.56189i	0.863630	−	0.504126i
$226$	17.4772			1.16257
$227$		−	10.3923i		−	0.689761i	−0.938647	−	0.344881i	$-0.887919\pi$
$227$		−	10.3923i		−	0.689761i	0.938647	−	0.344881i	$-0.112081\pi$
$228$	2.26139	+	1.01132i	0.149764	+	0.0669765i
$229$			13.5546i			0.895712i	0.894106	+	0.447856i	$0.147812\pi$
$229$			13.5546i			0.895712i	−0.894106	+	0.447856i	$0.852188\pi$
$230$	6.33175	+	7.75478i	0.417503	+	0.511335i
$231$		0			0
$232$			6.92163i			0.454427i
$233$	4.00000			0.262049			0.131024	−	0.991379i	$-0.458173\pi$
$233$	4.00000			0.262049			0.131024	+	0.991379i	$0.458173\pi$
$234$	−2.08911	−	2.33570i	−0.136570	−	0.152689i
$235$	19.4317	−	15.8659i	1.26758	−	1.03498i
$236$	10.5744			0.688334
$237$	8.11562	−	18.1471i	0.527166	−	1.17878i
$238$		0			0
$239$		0			0		1.00000			$0$
$239$		0			0		−1.00000			$\pi$
$240$	3.73861	−	1.01132i	0.241326	−	0.0652806i
$241$		−	21.3094i		−	1.37266i	−0.727292	−	0.686328i	$-0.759221\pi$
$241$		−	21.3094i		−	1.37266i	0.727292	−	0.686328i	$-0.240779\pi$
$242$	10.9545			0.704179
$243$	13.4350	+	7.90569i	0.861858	+	0.507151i
$244$		−	3.46410i		−	0.221766i
$245$		0			0
$246$	0.738613	−	1.65159i	0.0470922	−	0.105301i
$247$		−	1.49395i		−	0.0950579i
$248$			6.62638i			0.420776i
$249$	−6.43168	−	2.87633i	−0.407591	−	0.182280i
$250$	9.89949	−	5.19615i	0.626099	−	0.328634i
$251$	−8.85494			−0.558919			−0.279459	−	0.960158i	$-0.590155\pi$
$251$	−8.85494			−0.558919			−0.279459	+	0.960158i	$0.590155\pi$
$252$		0			0
$253$			20.9783i			1.31889i
$254$			8.73085i			0.547822i
$255$	−3.19808	−	11.8225i	−0.200272	−	0.740356i
$256$	1.00000			0.0625000
$257$		−	10.9960i		−	0.685909i	−0.939352	−	0.342954i	$-0.888572\pi$
$257$		−	10.9960i		−	0.685909i	0.939352	−	0.342954i	$-0.111428\pi$
$258$	−10.9441	−	4.89433i	−0.681347	−	0.304708i
$259$		0			0
$260$	−1.47723	−	1.80922i	−0.0916136	−	0.112203i
$261$	−15.4772	+	13.8433i	−0.958016	+	0.856876i
$262$	−13.7725			−0.850867
$263$	2.00000			0.123325			0.0616626	−	0.998097i	$-0.480360\pi$
$263$	2.00000			0.123325			0.0616626	+	0.998097i	$0.480360\pi$
$264$	7.40852	+	3.31319i	0.455963	+	0.203913i
$265$	−7.07107	−	8.66025i	−0.434372	−	0.531995i
$266$		0			0
$267$	3.47723	−	7.77531i	0.212803	−	0.475841i
$268$		−	14.2701i		−	0.871685i
$269$	−17.5810			−1.07194			−0.535968	−	0.844239i	$-0.680053\pi$
$269$	−17.5810			−1.07194			−0.535968	+	0.844239i	$0.680053\pi$
$270$	9.73861	+	6.33715i	0.592673	+	0.385666i
$271$			6.32456i			0.384189i	0.981376	+	0.192095i	$0.0615281\pi$
$271$			6.32456i			0.384189i	−0.981376	+	0.192095i	$0.938472\pi$
$272$		−	3.16228i		−	0.191741i
$273$		0			0
$274$	−3.47723			−0.210067
$275$	22.9545	+	4.68556i	1.38421	+	0.282550i
$276$	−3.16588	+	7.07912i	−0.190563	+	0.426113i
$277$			9.79796i			0.588702i	0.955697	+	0.294351i	$0.0951035\pi$
$277$			9.79796i			0.588702i	−0.955697	+	0.294351i	$0.904896\pi$
$278$			20.1810i			1.21037i
$279$	−14.8170	+	13.2528i	−0.887073	+	0.793422i
$280$		0			0
$281$			1.80922i			0.107929i	0.998543	+	0.0539646i	$0.0171858\pi$
$281$			1.80922i			0.107929i	−0.998543	+	0.0539646i	$0.982814\pi$
$282$	17.7386	+	7.93295i	1.05632	+	0.472400i
$283$	9.22460			0.548345			0.274173	−	0.961680i	$-0.411596\pi$
$283$	9.22460			0.548345			0.274173	+	0.961680i	$0.411596\pi$
$284$			6.92163i			0.410723i
$285$	1.44642	+	5.34706i	0.0856786	+	0.316733i
$286$		−	4.89433i		−	0.289408i
$287$		0			0
$288$	2.00000	+	2.23607i	0.117851	+	0.131762i
$289$	7.00000			0.411765
$290$	−11.9886	+	9.78866i	−0.703995	+	0.574810i
$291$	8.47723	−	18.9557i	0.496944	−	1.11120i
$292$	3.50333			0.205017
$293$			8.05661i			0.470672i	0.971914	+	0.235336i	$0.0756190\pi$
$293$			8.05661i			0.470672i	−0.971914	+	0.235336i	$0.924381\pi$
$294$		0			0
$295$	14.9545	+	18.3154i	0.870682	+	1.06636i
$296$		−	2.66291i		−	0.154779i
$297$	7.40852	+	23.1923i	0.429886	+	1.34576i
$298$		−	2.44949i		−	0.141895i
$299$	4.67671			0.270461
$300$	7.03886	+	5.04524i	0.406389	+	0.291287i
$301$		0			0
$302$	2.00000			0.115087
$303$	−8.00000	+	17.8885i	−0.459588	+	1.02767i
$304$			1.43023i			0.0820291i
$305$	6.00000	−	4.89898i	0.343559	−	0.280515i
$306$	7.07107	−	6.32456i	0.404226	−	0.361551i
$307$	−11.9886			−0.684226			−0.342113	−	0.939659i	$-0.611143\pi$
$307$	−11.9886			−0.684226			−0.342113	+	0.939659i	$0.611143\pi$
$308$		0			0
$309$	−3.47723	+	7.77531i	−0.197812	+	0.442322i
$310$	−11.4772	+	9.37112i	−0.651863	+	0.532244i
$311$	−17.5810			−0.996930			−0.498465	−	0.866910i	$-0.666103\pi$
$311$	−17.5810			−0.996930			−0.498465	+	0.866910i	$0.666103\pi$
$312$	0.738613	−	1.65159i	0.0418157	−	0.0935028i
$313$	23.2379			1.31348			0.656742	−	0.754115i	$-0.271934\pi$
$313$	23.2379			1.31348			0.656742	+	0.754115i	$0.271934\pi$
$314$	−14.4474			−0.815313
$315$		0			0
$316$	11.4772			0.645644
$317$	9.90890			0.556539			0.278270	−	0.960503i	$-0.410239\pi$
$317$	9.90890			0.556539			0.278270	+	0.960503i	$0.410239\pi$
$318$	3.53553	−	7.90569i	0.198263	−	0.443329i
$319$	−32.4317			−1.81583
$320$	1.41421	+	1.73205i	0.0790569	+	0.0968246i
$321$	3.87298	−	8.66025i	0.216169	−	0.483368i
$322$		0			0
$323$	4.52277			0.251654
$324$	−1.00000	+	8.94427i	−0.0555556	+	0.496904i
$325$	1.04456	−	5.11726i	0.0579416	−	0.283854i
$326$		−	14.6969i		−	0.813988i
$327$	−14.4474	+	32.3053i	−0.798942	+	1.78649i
$328$	1.04456			0.0576760
$329$		0			0
$330$	4.73861	+	17.5175i	0.260852	+	0.964306i
$331$	21.4317			1.17799			0.588996	−	0.808136i	$-0.299523\pi$
$331$	21.4317			1.17799			0.588996	+	0.808136i	$0.299523\pi$
$332$		−	4.06775i		−	0.223247i
$333$	5.95445	−	5.32582i	0.326302	−	0.291853i
$334$			4.29068i			0.234776i
$335$	24.7165	−	20.1810i	1.35041	−	1.10260i
$336$		0			0
$337$			17.1464i			0.934025i	0.884251	+	0.467013i	$0.154670\pi$
$337$			17.1464i			0.934025i	−0.884251	+	0.467013i	$0.845330\pi$
$338$	11.9089			0.647759
$339$	−12.3583	+	27.6339i	−0.671209	+	1.50087i
$340$	5.47723	−	4.47214i	0.297044	−	0.242536i
$341$	−31.0483			−1.68136
$342$	−3.19808	+	2.86045i	−0.172933	+	0.154676i
$343$		0			0
$344$		−	6.92163i		−	0.373189i
$345$	−16.7386	+	4.52792i	−0.901177	+	0.243775i
$346$		−	1.12840i		−	0.0606633i
$347$	17.4772			0.938227			0.469113	−	0.883138i	$-0.344574\pi$
$347$	17.4772			0.938227			0.469113	+	0.883138i	$0.344574\pi$
$348$	−10.9441	−	4.89433i	−0.586663	−	0.262364i
$349$			11.7436i			0.628623i	0.949320	+	0.314311i	$0.101774\pi$
$349$			11.7436i			0.628623i	−0.949320	+	0.314311i	$0.898226\pi$
$350$		0			0
$351$	5.17029	−	1.65159i	0.275970	−	0.0881553i
$352$			4.68556i			0.249741i
$353$		−	0.603648i		−	0.0321289i	−0.999871	−	0.0160645i	$-0.994886\pi$
$353$		−	0.603648i		−	0.0321289i	0.999871	−	0.0160645i	$-0.00511370\pi$
$354$	−7.47723	+	16.7196i	−0.397410	+	0.888636i
$355$	−11.9886	+	9.78866i	−0.636289	+	0.519528i
$356$	4.91754			0.260629
$357$		0			0
$358$		−	19.3825i		−	1.02440i
$359$		−	11.3938i		−	0.601340i	−0.953728	−	0.300670i	$-0.902790\pi$
$359$		−	11.3938i		−	0.601340i	0.953728	−	0.300670i	$-0.0972102\pi$
$360$	−1.04456	+	6.62638i	−0.0550529	+	0.349241i
$361$	16.9545			0.892340
$362$			3.16228i			0.166206i
$363$	−7.74597	+	17.3205i	−0.406558	+	0.909091i
$364$		0			0
$365$	4.95445	+	6.06794i	0.259328	+	0.317610i
$366$	5.47723	+	2.44949i	0.286299	+	0.128037i
$367$	0.369657			0.0192960			0.00964798	−	0.999953i	$-0.496929\pi$
$367$	0.369657			0.0192960			0.00964798	+	0.999953i	$0.496929\pi$
$368$	−4.47723			−0.233392
$369$	2.08911	+	2.33570i	0.108755	+	0.121592i
$370$	4.61230	−	3.76593i	0.239782	−	0.195781i
$371$		0			0
$372$	−10.4772	−	4.68556i	−0.543219	−	0.242935i
$373$		−	23.2144i		−	1.20199i	−0.799251	−	0.600997i	$-0.794770\pi$
$373$		−	23.2144i		−	1.20199i	0.799251	−	0.600997i	$-0.205230\pi$
$374$	14.8170			0.766171
$375$	1.21584	+	19.3267i	0.0627856	+	0.998027i
$376$			11.2189i			0.578570i
$377$			7.23003i			0.372365i
$378$		0			0
$379$	−20.4772			−1.05184			−0.525922	−	0.850533i	$-0.676280\pi$
$379$	−20.4772			−1.05184			−0.525922	+	0.850533i	$0.676280\pi$
$380$	−2.47723	+	2.02265i	−0.127079	+	0.103760i
$381$	−13.8047	−	6.17364i	−0.707235	−	0.316285i
$382$		−	16.2927i		−	0.833609i
$383$			18.1471i			0.927273i	0.886026	+	0.463636i	$0.153456\pi$
$383$			18.1471i			0.927273i	−0.886026	+	0.463636i	$0.846544\pi$
$384$	−0.707107	+	1.58114i	−0.0360844	+	0.0806872i
$385$		0			0
$386$			7.34847i			0.374027i
$387$	15.4772	−	13.8433i	0.786752	−	0.703692i
$388$	11.9886			0.608629
$389$			7.34847i			0.372582i	0.982495	+	0.186291i	$0.0596468\pi$
$389$			7.34847i			0.372582i	−0.982495	+	0.186291i	$0.940353\pi$
$390$	3.90519	−	1.05638i	0.197747	−	0.0534921i
$391$			14.1582i			0.716012i
$392$		0			0
$393$	9.73861	−	21.7762i	0.491248	−	1.09846i
$394$	9.00000			0.453413
$395$	16.2312	+	19.8791i	0.816683	+	1.00023i
$396$	−10.4772	+	9.37112i	−0.526500	+	0.470916i
$397$	14.8815			0.746879			0.373439	−	0.927655i	$-0.378178\pi$
$397$	14.8815			0.746879			0.373439	+	0.927655i	$0.378178\pi$
$398$		−	15.5096i		−	0.777424i
$399$		0			0
$400$	−1.00000	+	4.89898i	−0.0500000	+	0.244949i
$401$			0.955537i			0.0477173i	0.999715	+	0.0238586i	$0.00759516\pi$
$401$			0.955537i			0.0477173i	−0.999715	+	0.0238586i	$0.992405\pi$
$402$	22.5630	+	10.0905i	1.12534	+	0.503267i
$403$			6.92163i			0.344791i
$404$	−11.3137			−0.562878
$405$	−16.9061	+	10.9171i	−0.840073	+	0.542473i
$406$		0			0
$407$	12.4772			0.618473
$408$	5.00000	+	2.23607i	0.247537	+	0.110702i
$409$			15.5096i			0.766899i	0.923562	+	0.383449i	$0.125264\pi$
$409$			15.5096i			0.766899i	−0.923562	+	0.383449i	$0.874736\pi$
$410$	1.47723	+	1.80922i	0.0729550	+	0.0893512i
$411$	2.45877	−	5.49798i	0.121282	−	0.271195i
$412$	−4.91754			−0.242270
$413$		0			0
$414$	−8.95445	−	10.0114i	−0.440087	−	0.492033i
$415$	7.04555	−	5.75267i	0.345852	−	0.282387i
$416$	1.04456			0.0512136
$417$	−31.9089	−	14.2701i	−1.56259	−	0.698810i
$418$	−6.70141			−0.327777
$419$	8.85494			0.432592			0.216296	−	0.976328i	$-0.430602\pi$
$419$	8.85494			0.432592			0.216296	+	0.976328i	$0.430602\pi$
$420$		0			0
$421$	18.9545			0.923783			0.461892	−	0.886936i	$-0.347171\pi$
$421$	18.9545			0.923783			0.461892	+	0.886936i	$0.347171\pi$
$422$	−24.4772			−1.19153
$423$	−25.0862	+	22.4378i	−1.21973	+	1.09096i
$424$	5.00000			0.242821
$425$	15.4919	+	3.16228i	0.751469	+	0.153393i
$426$	−10.9441	−	4.89433i	−0.530241	−	0.237131i
$427$		0			0
$428$	5.47723			0.264752
$429$	7.73861	+	3.46081i	0.373624	+	0.167090i
$430$	11.9886	−	9.78866i	0.578142	−	0.472051i
$431$			7.66374i			0.369149i	0.982818	+	0.184575i	$0.0590908\pi$
$431$			7.66374i			0.369149i	−0.982818	+	0.184575i	$0.940909\pi$
$432$	−4.94975	+	1.58114i	−0.238145	+	0.0760726i
$433$		0			0			−	1.00000i	$-0.5\pi$
$433$		0			0				1.00000i	$0.5\pi$
$434$		0			0
$435$	−7.00000	−	25.8773i	−0.335624	−	1.24072i
$436$	−20.4317			−0.978500
$437$		−	6.40345i		−	0.306318i
$438$	−2.47723	+	5.53924i	−0.118366	+	0.264675i
$439$			8.88319i			0.423971i	0.977273	+	0.211986i	$0.0679930\pi$
$439$			8.88319i			0.423971i	−0.977273	+	0.211986i	$0.932007\pi$
$440$	−8.11562	+	6.62638i	−0.386897	+	0.315900i
$441$		0			0
$442$		−	3.30318i		−	0.157116i
$443$	15.0455			0.714836			0.357418	−	0.933945i	$-0.383657\pi$
$443$	15.0455			0.714836			0.357418	+	0.933945i	$0.383657\pi$
$444$	4.21043	+	1.88296i	0.199818	+	0.0893615i
$445$	6.95445	+	8.51743i	0.329673	+	0.403765i
$446$	−21.8881			−1.03643
$447$	3.87298	+	1.73205i	0.183186	+	0.0819232i
$448$		0			0
$449$			25.8773i			1.22122i	0.791930	+	0.610612i	$0.209077\pi$
$449$			25.8773i			1.22122i	−0.791930	+	0.610612i	$0.790923\pi$
$450$	−12.9545	+	7.56189i	−0.610679	+	0.356471i
$451$			4.89433i			0.230465i
$452$	−17.4772			−0.822060
$453$	−1.41421	+	3.16228i	−0.0664455	+	0.148577i
$454$			10.3923i			0.487735i
$455$		0			0
$456$	−2.26139	−	1.01132i	−0.105899	−	0.0473595i
$457$			11.0785i			0.518230i	0.965846	+	0.259115i	$0.0834308\pi$
$457$			11.0785i			0.518230i	−0.965846	+	0.259115i	$0.916569\pi$
$458$		−	13.5546i		−	0.633364i
$459$	5.00000	+	15.6525i	0.233380	+	0.730595i
$460$	−6.33175	−	7.75478i	−0.295220	−	0.361569i
$461$	31.7876			1.48050			0.740248	−	0.672334i	$-0.234708\pi$
$461$	31.7876			1.48050			0.740248	+	0.672334i	$0.234708\pi$
$462$		0			0
$463$		−	22.5741i		−	1.04911i	−0.851377	−	0.524554i	$-0.824232\pi$
$463$		−	22.5741i		−	1.04911i	0.851377	−	0.524554i	$-0.175768\pi$
$464$		−	6.92163i		−	0.321328i
$465$	−6.70141	−	24.7735i	−0.310770	−	1.14884i
$466$	−4.00000			−0.185296
$467$		−	28.0146i		−	1.29636i	−0.761486	−	0.648181i	$-0.775530\pi$
$467$		−	28.0146i		−	1.29636i	0.761486	−	0.648181i	$-0.224470\pi$
$468$	2.08911	+	2.33570i	0.0965693	+	0.107968i
$469$		0			0
$470$	−19.4317	+	15.8659i	−0.896316	+	0.731839i
$471$	10.2158	−	22.8433i	0.470721	−	1.05256i
$472$	−10.5744			−0.486726
$473$	32.4317			1.49121
$474$	−8.11562	+	18.1471i	−0.372763	+	0.833523i
$475$	−7.00665	−	1.43023i	−0.321487	−	0.0656233i
$476$		0			0
$477$	10.0000	+	11.1803i	0.457869	+	0.511913i
$478$		0			0
$479$	42.3620			1.93557			0.967784	−	0.251780i	$-0.0810161\pi$
$479$	42.3620			1.93557			0.967784	+	0.251780i	$0.0810161\pi$
$480$	−3.73861	+	1.01132i	−0.170644	+	0.0461604i
$481$		−	2.78156i		−	0.126828i
$482$			21.3094i			0.970615i
$483$		0			0
$484$	−10.9545			−0.497930
$485$	16.9545	+	20.7649i	0.769862	+	0.942884i
$486$	−13.4350	−	7.90569i	−0.609425	−	0.358610i
$487$			17.0349i			0.771923i	0.922515	+	0.385962i	$0.126130\pi$
$487$			17.0349i			0.771923i	−0.922515	+	0.385962i	$0.873870\pi$
$488$			3.46410i			0.156813i
$489$	23.2379	+	10.3923i	1.05085	+	0.469956i
$490$		0			0
$491$		−	13.8433i		−	0.624737i	−0.949961	−	0.312369i	$-0.898878\pi$
$491$		−	13.8433i		−	0.624737i	0.949961	−	0.312369i	$-0.101122\pi$
$492$	−0.738613	+	1.65159i	−0.0332992	+	0.0744594i
$493$	−21.8881			−0.985791
$494$			1.49395i			0.0672161i
$495$	−31.0483	−	4.89433i	−1.39552	−	0.219984i
$496$		−	6.62638i		−	0.297533i
$497$		0			0
$498$	6.43168	+	2.87633i	0.288210	+	0.128892i
$499$	1.90890			0.0854542			0.0427271	−	0.999087i	$-0.486395\pi$
$499$	1.90890			0.0854542			0.0427271	+	0.999087i	$0.486395\pi$
$500$	−9.89949	+	5.19615i	−0.442719	+	0.232379i
$501$	−6.78416	−	3.03397i	−0.303094	−	0.135548i
$502$	8.85494			0.395215
$503$			15.5096i			0.691537i	0.938320	+	0.345769i	$0.112382\pi$
$503$			15.5096i			0.691537i	−0.938320	+	0.345769i	$0.887618\pi$
$504$		0			0
$505$	−16.0000	−	19.5959i	−0.711991	−	0.872007i
$506$		−	20.9783i		−	0.932599i
$507$	−8.42087	+	18.8296i	−0.373984	+	0.836253i
$508$		−	8.73085i		−	0.387369i
$509$	24.7165			1.09554			0.547770	−	0.836629i	$-0.315477\pi$
$509$	24.7165			1.09554			0.547770	+	0.836629i	$0.315477\pi$
$510$	3.19808	+	11.8225i	0.141614	+	0.523511i
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	−2.26139	−	7.07926i	−0.0998427	−	0.312557i
$514$			10.9960i			0.485011i
$515$	−6.95445	−	8.51743i	−0.306450	−	0.375323i
$516$	10.9441	+	4.89433i	0.481785	+	0.215461i
$517$	−52.5667			−2.31188
$518$		0			0
$519$	1.78416	+	0.797901i	0.0783160	+	0.0350240i
$520$	1.47723	+	1.80922i	0.0647806	+	0.0793397i
$521$	35.5962			1.55950			0.779748	−	0.626093i	$-0.215347\pi$
$521$	35.5962			1.55950			0.779748	+	0.626093i	$0.215347\pi$
$522$	15.4772	−	13.8433i	0.677420	−	0.605903i
$523$	−16.9061			−0.739254			−0.369627	−	0.929180i	$-0.620515\pi$
$523$	−16.9061			−0.739254			−0.369627	+	0.929180i	$0.620515\pi$
$524$	13.7725			0.601654
$525$		0			0
$526$	−2.00000			−0.0872041
$527$	−20.9545			−0.912790
$528$	−7.40852	−	3.31319i	−0.322414	−	0.144188i
$529$	−2.95445			−0.128454
$530$	7.07107	+	8.66025i	0.307148	+	0.376177i
$531$	−21.1488	−	23.6451i	−0.917779	−	1.02611i
$532$		0			0
$533$	1.09110			0.0472607
$534$	−3.47723	+	7.77531i	−0.150474	+	0.336471i
$535$	7.74597	+	9.48683i	0.334887	+	0.410152i
$536$			14.2701i			0.616374i
$537$	30.6464	+	13.7055i	1.32249	+	0.591436i
$538$	17.5810			0.757973
$539$		0			0
$540$	−9.73861	−	6.33715i	−0.419083	−	0.272707i
$541$	8.52277			0.366423			0.183211	−	0.983074i	$-0.441351\pi$
$541$	8.52277			0.366423			0.183211	+	0.983074i	$0.441351\pi$
$542$		−	6.32456i		−	0.271663i
$543$	−5.00000	−	2.23607i	−0.214571	−	0.0959589i
$544$			3.16228i			0.135582i
$545$	−28.8948	−	35.3887i	−1.23772	−	1.51589i
$546$		0			0
$547$			3.61845i			0.154714i	0.997003	+	0.0773569i	$0.0246481\pi$
$547$			3.61845i			0.154714i	−0.997003	+	0.0773569i	$0.975352\pi$
$548$	3.47723			0.148540
$549$	−7.74597	+	6.92820i	−0.330590	+	0.295689i
$550$	−22.9545	−	4.68556i	−0.978781	−	0.199793i
$551$	9.89949			0.421733
$552$	3.16588	−	7.07912i	0.134749	−	0.301307i
$553$		0			0
$554$		−	9.79796i		−	0.416275i
$555$	2.69306	+	9.95560i	0.114314	+	0.422591i
$556$		−	20.1810i		−	0.855863i
$557$	−27.8634			−1.18061			−0.590304	−	0.807181i	$-0.700992\pi$
$557$	−27.8634			−1.18061			−0.590304	+	0.807181i	$0.700992\pi$
$558$	14.8170	−	13.2528i	0.627255	−	0.561034i
$559$		−	7.23003i		−	0.305798i
$560$		0			0
$561$	−10.4772	+	23.4278i	−0.442349	+	0.989122i
$562$		−	1.80922i		−	0.0763175i
$563$		−	10.3923i		−	0.437983i	−0.975727	−	0.218992i	$-0.929723\pi$
$563$		−	10.3923i		−	0.437983i	0.975727	−	0.218992i	$-0.0702768\pi$
$564$	−17.7386	−	7.93295i	−0.746930	−	0.334037i
$565$	−24.7165	−	30.2714i	−1.03983	−	1.27353i
$566$	−9.22460			−0.387739
$567$		0			0
$568$		−	6.92163i		−	0.290425i
$569$			7.56189i			0.317011i	0.987358	+	0.158505i	$0.0506676\pi$
$569$			7.56189i			0.317011i	−0.987358	+	0.158505i	$0.949332\pi$
$570$	−1.44642	−	5.34706i	−0.0605839	−	0.223964i
$571$	14.9545			0.625824			0.312912	−	0.949782i	$-0.398695\pi$
$571$	14.9545			0.625824			0.312912	+	0.949782i	$0.398695\pi$
$572$			4.89433i			0.204642i
$573$	25.7611	+	11.5207i	1.07618	+	0.481284i
$574$		0			0
$575$	4.47723	−	21.9338i	0.186713	−	0.914704i
$576$	−2.00000	−	2.23607i	−0.0833333	−	0.0931695i
$577$	−0.674899			−0.0280964			−0.0140482	−	0.999901i	$-0.504472\pi$
$577$	−0.674899			−0.0280964			−0.0140482	+	0.999901i	$0.504472\pi$
$578$	−7.00000			−0.291162
$579$	−11.6190	−	5.19615i	−0.482867	−	0.215945i
$580$	11.9886	−	9.78866i	0.497800	−	0.406452i
$581$		0			0
$582$	−8.47723	+	18.9557i	−0.351392	+	0.785737i
$583$			23.4278i			0.970280i
$584$	−3.50333			−0.144969
$585$	−1.09110	+	6.92163i	−0.0451113	+	0.286174i
$586$		−	8.05661i		−	0.332815i
$587$		−	21.0864i		−	0.870330i	−0.900351	−	0.435165i	$-0.856690\pi$
$587$		−	21.0864i		−	0.870330i	0.900351	−	0.435165i	$-0.143310\pi$
$588$		0			0
$589$	9.47723			0.390502
$590$	−14.9545	−	18.3154i	−0.615665	−	0.754033i
$591$	−6.36396	+	14.2302i	−0.261778	+	0.585354i
$592$			2.66291i			0.109445i
$593$		−	1.65316i		−	0.0678871i	−0.999424	−	0.0339435i	$-0.989193\pi$
$593$		−	1.65316i		−	0.0678871i	0.999424	−	0.0339435i	$-0.0108066\pi$
$594$	−7.40852	−	23.1923i	−0.303975	−	0.951593i
$595$		0			0
$596$			2.44949i			0.100335i
$597$	24.5228	+	10.9669i	1.00365	+	0.448846i
$598$	−4.67671			−0.191245
$599$		−	23.6412i		−	0.965954i	−0.875633	−	0.482977i	$-0.839556\pi$
$599$		−	23.6412i		−	0.965954i	0.875633	−	0.482977i	$-0.160444\pi$
$600$	−7.03886	−	5.04524i	−0.287360	−	0.205971i
$601$			4.06775i			0.165927i	0.996553	+	0.0829635i	$0.0264385\pi$
$601$			4.06775i			0.165927i	−0.996553	+	0.0829635i	$0.973562\pi$
$602$		0			0
$603$	−31.9089	+	28.5402i	−1.29943	+	1.16225i
$604$	−2.00000			−0.0813788
$605$	−15.4919	−	18.9737i	−0.629837	−	0.771389i
$606$	8.00000	−	17.8885i	0.324978	−	0.726672i
$607$	12.2938			0.498992			0.249496	−	0.968376i	$-0.419735\pi$
$607$	12.2938			0.498992			0.249496	+	0.968376i	$0.419735\pi$
$608$		−	1.43023i		−	0.0580034i
$609$		0			0
$610$	−6.00000	+	4.89898i	−0.242933	+	0.198354i
$611$			11.7188i			0.474090i
$612$	−7.07107	+	6.32456i	−0.285831	+	0.255655i
$613$		−	5.85452i		−	0.236462i	−0.992986	−	0.118231i	$-0.962278\pi$
$613$		−	5.85452i		−	0.236462i	0.992986	−	0.118231i	$-0.0377223\pi$
$614$	11.9886			0.483821
$615$	−3.90519	+	1.05638i	−0.157473	+	0.0425975i
$616$		0			0
$617$	−14.5228			−0.584665			−0.292332	−	0.956317i	$-0.594431\pi$
$617$	−14.5228			−0.584665			−0.292332	+	0.956317i	$0.594431\pi$
$618$	3.47723	−	7.77531i	0.139875	−	0.312769i
$619$			30.1925i			1.21354i	0.794877	+	0.606771i	$0.207535\pi$
$619$			30.1925i			1.21354i	−0.794877	+	0.606771i	$0.792465\pi$
$620$	11.4772	−	9.37112i	0.460936	−	0.376353i
$621$	22.1611	−	7.07912i	0.889296	−	0.284075i
$622$	17.5810			0.704936
$623$		0			0
$624$	−0.738613	+	1.65159i	−0.0295682	+	0.0661165i
$625$	−23.0000	−	9.79796i	−0.920000	−	0.391918i
$626$	−23.2379			−0.928773
$627$	4.73861	−	10.5959i	0.189242	−	0.423158i
$628$	14.4474			0.576513
$629$	8.42087			0.335762
$630$		0			0
$631$	3.47723			0.138426			0.0692131	−	0.997602i	$-0.477951\pi$
$631$	3.47723			0.138426			0.0692131	+	0.997602i	$0.477951\pi$
$632$	−11.4772			−0.456540
$633$	17.3080	−	38.7019i	0.687932	−	1.53826i
$634$	−9.90890			−0.393533
$635$	15.1223	−	12.3473i	0.600109	−	0.489987i
$636$	−3.53553	+	7.90569i	−0.140193	+	0.313481i
$637$		0			0
$638$	32.4317			1.28398
$639$	15.4772	−	13.8433i	0.612270	−	0.547631i
$640$	−1.41421	−	1.73205i	−0.0559017	−	0.0684653i
$641$			16.0793i			0.635095i	0.948242	+	0.317547i	$0.102859\pi$
$641$			16.0793i			0.635095i	−0.948242	+	0.317547i	$0.897141\pi$
$642$	−3.87298	+	8.66025i	−0.152854	+	0.341793i
$643$	26.0663			1.02796			0.513978	−	0.857803i	$-0.328171\pi$
$643$	26.0663			1.02796			0.513978	+	0.857803i	$0.328171\pi$
$644$		0			0
$645$	7.00000	+	25.8773i	0.275625	+	1.01892i
$646$	−4.52277			−0.177946
$647$		−	20.4039i		−	0.802160i	−0.916043	−	0.401080i	$-0.868635\pi$
$647$		−	20.4039i		−	0.802160i	0.916043	−	0.401080i	$-0.131365\pi$
$648$	1.00000	−	8.94427i	0.0392837	−	0.351364i
$649$		−	49.5469i		−	1.94489i
$650$	−1.04456	+	5.11726i	−0.0409709	+	0.200715i
$651$		0			0
$652$			14.6969i			0.575577i
$653$	−39.8634			−1.55997			−0.779987	−	0.625796i	$-0.784774\pi$
$653$	−39.8634			−1.55997			−0.779987	+	0.625796i	$0.784774\pi$
$654$	14.4474	−	32.3053i	0.564937	−	1.26324i
$655$	19.4772	+	23.8546i	0.761038	+	0.932078i
$656$	−1.04456			−0.0407831
$657$	−7.00665	−	7.83368i	−0.273356	−	0.305621i
$658$		0			0
$659$			34.2929i			1.33586i	0.744224	+	0.667930i	$0.232819\pi$
$659$			34.2929i			1.33586i	−0.744224	+	0.667930i	$0.767181\pi$
$660$	−4.73861	−	17.5175i	−0.184450	−	0.681867i
$661$			0.603648i			0.0234792i	0.999931	+	0.0117396i	$0.00373691\pi$
$661$			0.603648i			0.0234792i	−0.999931	+	0.0117396i	$0.996263\pi$
$662$	−21.4317			−0.832966
$663$	5.22278	+	2.33570i	0.202836	+	0.0907110i
$664$			4.06775i			0.157859i
$665$		0			0
$666$	−5.95445	+	5.32582i	−0.230730	+	0.206371i
$667$			30.9897i			1.19993i
$668$		−	4.29068i		−	0.166011i
$669$	15.4772	−	34.6081i	0.598384	−	1.33803i
$670$	−24.7165	+	20.1810i	−0.954883	+	0.779659i
$671$	−16.2312			−0.626600
$672$		0			0
$673$		−	14.1585i		−	0.545771i	−0.962047	−	0.272885i	$-0.912022\pi$
$673$		−	14.1585i		−	0.545771i	0.962047	−	0.272885i	$-0.0879780\pi$
$674$		−	17.1464i		−	0.660456i
$675$	−2.79622	−	25.8299i	−0.107627	−	0.994191i
$676$	−11.9089			−0.458035
$677$		−	32.9090i		−	1.26479i	−0.774644	−	0.632397i	$-0.782071\pi$
$677$		−	32.9090i		−	1.26479i	0.774644	−	0.632397i	$-0.217929\pi$
$678$	12.3583	−	27.6339i	0.474616	−	1.06127i
$679$		0			0
$680$	−5.47723	+	4.47214i	−0.210042	+	0.171499i
$681$	−16.4317	−	7.34847i	−0.629663	−	0.281594i
$682$	31.0483			1.18890
$683$	18.9545			0.725272			0.362636	−	0.931931i	$-0.381877\pi$
$683$	18.9545			0.725272			0.362636	+	0.931931i	$0.381877\pi$
$684$	3.19808	−	2.86045i	0.122282	−	0.109372i
$685$	4.91754	+	6.02273i	0.187890	+	0.230117i
$686$		0			0
$687$	21.4317	+	9.58454i	0.817669	+	0.365673i
$688$			6.92163i			0.263885i
$689$	5.22278			0.198972
$690$	16.7386	−	4.52792i	0.637228	−	0.172375i
$691$		−	3.46410i		−	0.131781i	−0.997827	−	0.0658903i	$-0.979011\pi$
$691$		−	3.46410i		−	0.131781i	0.997827	−	0.0658903i	$-0.0209887\pi$
$692$			1.12840i			0.0428954i
$693$		0			0
$694$	−17.4772			−0.663426
$695$	34.9545	−	28.5402i	1.32590	−	1.08259i
$696$	10.9441	+	4.89433i	0.414833	+	0.185519i
$697$			3.30318i			0.125117i
$698$		−	11.7436i		−	0.444503i
$699$	2.82843	−	6.32456i	0.106981	−	0.239217i
$700$		0			0
$701$		−	51.7546i		−	1.95474i	−0.211531	−	0.977371i	$-0.567845\pi$
$701$		−	51.7546i		−	1.95474i	0.211531	−	0.977371i	$-0.432155\pi$
$702$	−5.17029	+	1.65159i	−0.195140	+	0.0623352i
$703$	−3.80857			−0.143643
$704$		−	4.68556i		−	0.176594i
$705$	−11.3459	−	41.9431i	−0.427312	−	1.57967i
$706$			0.603648i			0.0227186i
$707$		0			0
$708$	7.47723	−	16.7196i	0.281011	−	0.628360i
$709$	−22.4317			−0.842439			−0.421220	−	0.906959i	$-0.638398\pi$
$709$	−22.4317			−0.842439			−0.421220	+	0.906959i	$0.638398\pi$
$710$	11.9886	−	9.78866i	0.449924	−	0.367362i
$711$	−22.9545	−	25.6639i	−0.860859	−	0.962470i
$712$	−4.91754			−0.184293
$713$			29.6678i			1.11107i
$714$		0			0
$715$	−8.47723	+	6.92163i	−0.317030	+	0.258854i
$716$			19.3825i			0.724358i
$717$		0			0
$718$			11.3938i			0.425211i
$719$	−0.803730			−0.0299741			−0.0149870	−	0.999888i	$-0.504771\pi$
$719$	−0.803730			−0.0299741			−0.0149870	+	0.999888i	$0.504771\pi$
$720$	1.04456	−	6.62638i	0.0389283	−	0.246951i
$721$		0			0
$722$	−16.9545			−0.630979
$723$	−33.6931	−	15.0680i	−1.25306	−	0.560385i
$724$		−	3.16228i		−	0.117525i
$725$	33.9089	+	6.92163i	1.25935	+	0.257063i
$726$	7.74597	−	17.3205i	0.287480	−	0.642824i
$727$	15.1223			0.560854			0.280427	−	0.959875i	$-0.409524\pi$
$727$	15.1223			0.560854			0.280427	+	0.959875i	$0.409524\pi$
$728$		0			0
$729$	22.0000	−	15.6525i	0.814815	−	0.579721i
$730$	−4.95445	−	6.06794i	−0.183372	−	0.224584i
$731$	21.8881			0.809561
$732$	−5.47723	−	2.44949i	−0.202444	−	0.0905357i
$733$	2.39435			0.0884375			0.0442187	−	0.999022i	$-0.485920\pi$
$733$	2.39435			0.0884375			0.0442187	+	0.999022i	$0.485920\pi$
$734$	−0.369657			−0.0136443
$735$		0			0
$736$	4.47723			0.165033
$737$	−66.8634			−2.46294
$738$	−2.08911	−	2.33570i	−0.0769013	−	0.0859783i
$739$	6.47723			0.238269			0.119134	−	0.992878i	$-0.461988\pi$
$739$	6.47723			0.238269			0.119134	+	0.992878i	$0.461988\pi$
$740$	−4.61230	+	3.76593i	−0.169551	+	0.138438i
$741$	−2.36215	−	1.05638i	−0.0867756	−	0.0388072i
$742$		0			0
$743$	−13.4317			−0.492760			−0.246380	−	0.969173i	$-0.579241\pi$
$743$	−13.4317			−0.492760			−0.246380	+	0.969173i	$0.579241\pi$
$744$	10.4772	+	4.68556i	0.384114	+	0.171781i
$745$	−4.24264	+	3.46410i	−0.155438	+	0.126915i
$746$			23.2144i			0.849938i
$747$	−9.09576	+	8.13550i	−0.332797	+	0.297662i
$748$	−14.8170			−0.541764
$749$		0			0
$750$	−1.21584	−	19.3267i	−0.0443961	−	0.705712i
$751$	−32.0000			−1.16770			−0.583848	−	0.811863i	$-0.698454\pi$
$751$	−32.0000			−1.16770			−0.583848	+	0.811863i	$0.698454\pi$
$752$		−	11.2189i		−	0.409111i
$753$	−6.26139	+	14.0009i	−0.228178	+	0.510221i
$754$		−	7.23003i		−	0.263302i
$755$	−2.82843	−	3.46410i	−0.102937	−	0.126072i
$756$		0			0
$757$		−	48.1361i		−	1.74954i	−0.484541	−	0.874768i	$-0.661014\pi$
$757$		−	48.1361i		−	1.74954i	0.484541	−	0.874768i	$-0.338986\pi$
$758$	20.4772			0.743766
$759$	33.1696	+	14.8339i	1.20398	+	0.538436i
$760$	2.47723	−	2.02265i	0.0898584	−	0.0733691i
$761$	1.78387			0.0646653			0.0323326	−	0.999477i	$-0.489706\pi$
$761$	1.78387			0.0646653			0.0323326	+	0.999477i	$0.489706\pi$
$762$	13.8047	+	6.17364i	0.500091	+	0.223648i
$763$		0			0
$764$			16.2927i			0.589451i
$765$	−20.9545	−	3.30318i	−0.757610	−	0.119427i
$766$		−	18.1471i		−	0.655681i
$767$	−11.0455			−0.398832
$768$	0.707107	−	1.58114i	0.0255155	−	0.0570544i
$769$			16.1921i			0.583902i	0.956433	+	0.291951i	$0.0943045\pi$
$769$			16.1921i			0.583902i	−0.956433	+	0.291951i	$0.905696\pi$
$770$		0			0
$771$	−17.3861	−	7.77531i	−0.626146	−	0.280021i
$772$		−	7.34847i		−	0.264477i
$773$			16.1921i			0.582390i	0.956664	+	0.291195i	$0.0940528\pi$
$773$			16.1921i			0.582390i	−0.956664	+	0.291195i	$0.905947\pi$
$774$	−15.4772	+	13.8433i	−0.556317	+	0.497585i
$775$	32.4625	+	6.62638i	1.16609	+	0.238027i
$776$	−11.9886			−0.430366
$777$		0			0
$778$		−	7.34847i		−	0.263455i
$779$		−	1.49395i		−	0.0535264i
$780$	−3.90519	+	1.05638i	−0.139828	+	0.0378246i
$781$	32.4317			1.16050
$782$		−	14.1582i		−	0.506297i
$783$	10.9441	+	34.2603i	0.391108	+	1.22436i
$784$		0			0
$785$	20.4317	+	25.0236i	0.729238	+	0.893130i
$786$	−9.73861	+	21.7762i	−0.347365	+	0.776731i
$787$	−50.1724			−1.78845			−0.894226	−	0.447616i	$-0.852273\pi$
$787$	−50.1724			−1.78845			−0.894226	+	0.447616i	$0.852273\pi$
$788$	−9.00000			−0.320612
$789$	1.41421	−	3.16228i	0.0503473	−	0.112580i
$790$	−16.2312	−	19.8791i	−0.577482	−	0.707268i
$791$		0			0
$792$	10.4772	−	9.37112i	0.372292	−	0.332988i
$793$			3.61845i			0.128495i
$794$	−14.8815			−0.528123
$795$	−18.6931	+	5.05662i	−0.662975	+	0.179340i
$796$			15.5096i			0.549722i
$797$			54.2183i			1.92051i	0.279121	+	0.960256i	$0.409957\pi$
$797$			54.2183i			1.92051i	−0.279121	+	0.960256i	$0.590043\pi$
$798$		0			0
$799$	−35.4772			−1.25509
$800$	1.00000	−	4.89898i	0.0353553	−	0.173205i
$801$	−9.83508	−	10.9960i	−0.347505	−	0.388523i
$802$		−	0.955537i		−	0.0337412i
$803$		−	16.4150i		−	0.579274i
$804$	−22.5630	−	10.0905i	−0.795736	−	0.355864i
$805$		0			0
$806$		−	6.92163i		−	0.243804i
$807$	−12.4317	+	27.7981i	−0.437616	+	0.978539i
$808$	11.3137			0.398015
$809$			8.84242i			0.310883i	0.987845	+	0.155441i	$0.0496800\pi$
$809$			8.84242i			0.310883i	−0.987845	+	0.155441i	$0.950320\pi$
$810$	16.9061	−	10.9171i	0.594021	−	0.383586i
$811$			38.3280i			1.34588i	0.739697	+	0.672940i	$0.234969\pi$
$811$			38.3280i			1.34588i	−0.739697	+	0.672940i	$0.765031\pi$
$812$		0			0
$813$	10.0000	+	4.47214i	0.350715	+	0.156845i
$814$	−12.4772			−0.437327
$815$	−25.4558	+	20.7846i	−0.891679	+	0.728053i
$816$	−5.00000	−	2.23607i	−0.175035	−	0.0782780i
$817$	−9.89949			−0.346339
$818$		−	15.5096i		−	0.542279i
$819$		0			0
$820$	−1.47723	−	1.80922i	−0.0515870	−	0.0631809i
$821$		−	11.7090i		−	0.408648i	−0.978903	−	0.204324i	$-0.934500\pi$
$821$		−	11.7090i		−	0.408648i	0.978903	−	0.204324i	$-0.0654996\pi$
$822$	−2.45877	+	5.49798i	−0.0857594	+	0.191764i
$823$			3.19161i			0.111252i	0.998452	+	0.0556262i	$0.0177155\pi$
$823$			3.19161i			0.111252i	−0.998452	+	0.0556262i	$0.982284\pi$
$824$	4.91754			0.171311
$825$	23.6398	−	32.9810i	0.823031	−	1.14825i
$826$		0			0
$827$	3.90890			0.135926			0.0679629	−	0.997688i	$-0.478350\pi$
$827$	3.90890			0.135926			0.0679629	+	0.997688i	$0.478350\pi$
$828$	8.95445	+	10.0114i	0.311189	+	0.347920i
$829$		−	50.4524i		−	1.75228i	−0.482053	−	0.876142i	$-0.660109\pi$
$829$		−	50.4524i		−	1.75228i	0.482053	−	0.876142i	$-0.339891\pi$
$830$	−7.04555	+	5.75267i	−0.244555	+	0.199678i
$831$	15.4919	+	6.92820i	0.537409	+	0.240337i
$832$	−1.04456			−0.0362135
$833$		0			0
$834$	31.9089	+	14.2701i	1.10491	+	0.494133i
$835$	7.43168	−	6.06794i	0.257184	−	0.209990i
$836$	6.70141			0.231773
$837$	10.4772	+	32.7989i	0.362146	+	1.13370i
$838$	−8.85494			−0.305889
$839$	−40.1440			−1.38593			−0.692963	−	0.720973i	$-0.743695\pi$
$839$	−40.1440			−1.38593			−0.692963	+	0.720973i	$0.743695\pi$
$840$		0			0
$841$	−18.9089			−0.652031
$842$	−18.9545			−0.653214
$843$	2.86064	+	1.27931i	0.0985255	+	0.0440619i
$844$	24.4772			0.842541
$845$	−16.8417	−	20.6268i	−0.579373	−	0.709584i
$846$	25.0862	−	22.4378i	0.862481	−	0.771426i
$847$		0			0
$848$	−5.00000			−0.171701
$849$	6.52277	−	14.5854i	0.223861	−	0.500569i
$850$	−15.4919	−	3.16228i	−0.531369	−	0.108465i
$851$		−	11.9225i		−	0.408697i
$852$	10.9441	+	4.89433i	0.374937	+	0.167677i
$853$	−31.2891			−1.07132			−0.535659	−	0.844434i	$-0.679937\pi$
$853$	−31.2891			−1.07132			−0.535659	+	0.844434i	$0.679937\pi$
$854$		0			0
$855$	9.47723	+	1.49395i	0.324114	+	0.0510921i
$856$	−5.47723			−0.187208
$857$		−	15.0637i		−	0.514566i	−0.966336	−	0.257283i	$-0.917173\pi$
$857$		−	15.0637i		−	0.514566i	0.966336	−	0.257283i	$-0.0828273\pi$
$858$	−7.73861	−	3.46081i	−0.264192	−	0.118150i
$859$			30.5733i			1.04315i	0.853207	+	0.521573i	$0.174655\pi$
$859$			30.5733i			1.04315i	−0.853207	+	0.521573i	$0.825345\pi$
$860$	−11.9886	+	9.78866i	−0.408808	+	0.333790i
$861$		0			0
$862$		−	7.66374i		−	0.261028i
$863$	26.4772			0.901295			0.450648	−	0.892702i	$-0.351193\pi$
$863$	26.4772			0.901295			0.450648	+	0.892702i	$0.351193\pi$
$864$	4.94975	−	1.58114i	0.168394	−	0.0537914i
$865$	−1.95445	+	1.59580i	−0.0664533	+	0.0542589i
$866$		0			0
$867$	4.94975	−	11.0680i	0.168102	−	0.375888i
$868$		0			0
$869$		−	53.7772i		−	1.82427i
$870$	7.00000	+	25.8773i	0.237322	+	0.877322i
$871$			14.9059i			0.505068i
$872$	20.4317			0.691904
$873$	−23.9772	−	26.8073i	−0.811506	−	0.907291i
$874$			6.40345i			0.216600i
$875$		0			0
$876$	2.47723	−	5.53924i	0.0836977	−	0.187154i
$877$		−	55.6980i		−	1.88079i	−0.340087	−	0.940394i	$-0.610457\pi$
$877$		−	55.6980i		−	1.88079i	0.340087	−	0.940394i	$-0.389543\pi$
$878$		−	8.88319i		−	0.299793i
$879$	12.7386	+	5.69688i	0.429663	+	0.192151i
$880$	8.11562	−	6.62638i	0.273578	−	0.223375i
$881$	−18.7544			−0.631853			−0.315926	−	0.948784i	$-0.602315\pi$
$881$	−18.7544			−0.631853			−0.315926	+	0.948784i	$0.602315\pi$
$882$		0			0
$883$			24.3833i			0.820564i	0.911959	+	0.410282i	$0.134570\pi$
$883$			24.3833i			0.820564i	−0.911959	+	0.410282i	$0.865430\pi$
$884$			3.30318i			0.111098i
$885$	39.5336	−	10.6941i	1.32891	−	0.359479i
$886$	−15.0455			−0.505465
$887$			3.46410i			0.116313i	0.998307	+	0.0581566i	$0.0185223\pi$
$887$			3.46410i			0.116313i	−0.998307	+	0.0581566i	$0.981478\pi$
$888$	−4.21043	−	1.88296i	−0.141293	−	0.0631881i
$889$		0			0
$890$	−6.95445	−	8.51743i	−0.233114	−	0.285505i
$891$	41.9089	+	4.68556i	1.40400	+	0.156972i
$892$	21.8881			0.732868
$893$	16.0455			0.536944
$894$	−3.87298	−	1.73205i	−0.129532	−	0.0579284i
$895$	−33.5715	+	27.4110i	−1.12217	+	0.916248i
$896$		0			0
$897$	3.30694	−	7.39453i	0.110415	−	0.246896i
$898$		−	25.8773i		−	0.863536i
$899$	−45.8653			−1.52969
$900$	12.9545	−	7.56189i	0.431815	−	0.252063i
$901$			15.8114i			0.526754i
$902$		−	4.89433i		−	0.162963i
$903$		0			0
$904$	17.4772			0.581284
$905$	5.47723	−	4.47214i	0.182069	−	0.148659i
$906$	1.41421	−	3.16228i	0.0469841	−	0.105060i
$907$			9.79796i			0.325336i	0.986681	+	0.162668i	$0.0520099\pi$
$907$			9.79796i			0.325336i	−0.986681	+	0.162668i	$0.947990\pi$
$908$		−	10.3923i		−	0.344881i
$909$	22.6274	+	25.2982i	0.750504	+	0.839089i
$910$		0			0
$911$			24.0681i			0.797410i	0.917079	+	0.398705i	$0.130540\pi$
$911$			24.0681i			0.797410i	−0.917079	+	0.398705i	$0.869460\pi$
$912$	2.26139	+	1.01132i	0.0748820	+	0.0334883i
$913$	−19.0597			−0.630783
$914$		−	11.0785i		−	0.366444i
$915$	−3.50333	−	12.9509i	−0.115816	−	0.428145i
$916$			13.5546i			0.447856i
$917$		0			0
$918$	−5.00000	−	15.6525i	−0.165025	−	0.516609i
$919$	0.431677			0.0142397			0.00711985	−	0.999975i	$-0.497734\pi$
$919$	0.431677			0.0142397			0.00711985	+	0.999975i	$0.497734\pi$
$920$	6.33175	+	7.75478i	0.208752	+	0.255668i
$921$	−8.47723	+	18.9557i	−0.279334	+	0.624610i
$922$	−31.7876			−1.04687
$923$		−	7.23003i		−	0.237979i
$924$		0			0
$925$	−13.0455	−	2.66291i	−0.428935	−	0.0875560i
$926$			22.5741i			0.741831i
$927$	9.83508	+	10.9960i	0.323026	+	0.361154i
$928$			6.92163i			0.227213i
$929$	−15.9260			−0.522515			−0.261258	−	0.965269i	$-0.584137\pi$
$929$	−15.9260			−0.522515			−0.261258	+	0.965269i	$0.584137\pi$
$930$	6.70141	+	24.7735i	0.219748	+	0.812354i
$931$		0			0
$932$	4.00000			0.131024
$933$	−12.4317	+	27.7981i	−0.406995	+	0.910068i
$934$			28.0146i			0.916667i
$935$	−20.9545	−	25.6639i	−0.685284	−	0.839298i
$936$	−2.08911	−	2.33570i	−0.0682848	−	0.0763447i
$937$	53.6757			1.75351			0.876754	−	0.480938i	$-0.159704\pi$
$937$	53.6757			1.75351			0.876754	+	0.480938i	$0.159704\pi$
$938$		0			0
$939$	16.4317	−	36.7423i	0.536228	−	1.19904i
$940$	19.4317	−	15.8659i	0.633791	−	0.517489i
$941$	20.4739			0.667430			0.333715	−	0.942674i	$-0.391698\pi$
$941$	20.4739			0.667430			0.333715	+	0.942674i	$0.391698\pi$
$942$	−10.2158	+	22.8433i	−0.332850	+	0.744275i
$943$	4.67671			0.152295
$944$	10.5744			0.344167
$945$		0			0
$946$	−32.4317			−1.05444
$947$	−32.8634			−1.06792			−0.533958	−	0.845511i	$-0.679296\pi$
$947$	−32.8634			−1.06792			−0.533958	+	0.845511i	$0.679296\pi$
$948$	8.11562	−	18.1471i	0.263583	−	0.589390i
$949$	−3.65942			−0.118790
$950$	7.00665	+	1.43023i	0.227326	+	0.0464027i
$951$	7.00665	−	15.6674i	0.227206	−	0.508049i
$952$		0			0
$953$	−46.9545			−1.52100			−0.760502	−	0.649336i	$-0.775047\pi$
$953$	−46.9545			−1.52100			−0.760502	+	0.649336i	$0.775047\pi$
$954$	−10.0000	−	11.1803i	−0.323762	−	0.361977i
$955$	−28.2199	+	23.0414i	−0.913173	+	0.745603i
$956$		0			0
$957$	−22.9327	+	51.2790i	−0.741308	+	1.65761i
$958$	−42.3620			−1.36865
$959$		0			0
$960$	3.73861	−	1.01132i	0.120663	−	0.0326403i
$961$	−12.9089			−0.416416
$962$			2.78156i			0.0896811i
$963$	−10.9545	−	12.2474i	−0.353002	−	0.394669i
$964$		−	21.3094i		−	0.686328i
$965$	12.7279	−	10.3923i	0.409726	−	0.334540i
$966$		0			0
$967$			7.23690i			0.232723i	0.993207	+	0.116361i	$0.0371231\pi$
$967$			7.23690i			0.232723i	−0.993207	+	0.116361i	$0.962877\pi$
$968$	10.9545			0.352089
$969$	3.19808	−	7.15113i	0.102737	−	0.229728i
$970$	−16.9545	−	20.7649i	−0.544375	−	0.666720i
$971$	37.7497			1.21145			0.605723	−	0.795676i	$-0.292884\pi$
$971$	37.7497			1.21145			0.605723	+	0.795676i	$0.292884\pi$
$972$	13.4350	+	7.90569i	0.430929	+	0.253575i
$973$		0			0
$974$		−	17.0349i		−	0.545832i
$975$	−7.35248	−	5.27004i	−0.235468	−	0.168776i
$976$		−	3.46410i		−	0.110883i
$977$	−3.90890			−0.125057			−0.0625284	−	0.998043i	$-0.519916\pi$
$977$	−3.90890			−0.125057			−0.0625284	+	0.998043i	$0.519916\pi$
$978$	−23.2379	−	10.3923i	−0.743066	−	0.332309i
$979$		−	23.0414i		−	0.736407i
$980$		0			0
$981$	40.8634	+	45.6866i	1.30467	+	1.45866i
$982$			13.8433i			0.441756i
$983$			52.7881i			1.68368i	0.539728	+	0.841840i	$0.318527\pi$
$983$			52.7881i			1.68368i	−0.539728	+	0.841840i	$0.681473\pi$
$984$	0.738613	−	1.65159i	0.0235461	−	0.0526507i
$985$	−12.7279	−	15.5885i	−0.405545	−	0.496690i
$986$	21.8881			0.697059
$987$		0			0
$988$		−	1.49395i		−	0.0475290i
$989$		−	30.9897i		−	0.985414i
$990$	31.0483	+	4.89433i	0.986779	+	0.155552i
$991$	10.5228			0.334267			0.167133	−	0.985934i	$-0.446549\pi$
$991$	10.5228			0.334267			0.167133	+	0.985934i	$0.446549\pi$
$992$			6.62638i			0.210388i
$993$	15.1545	−	33.8865i	0.480913	−	1.07535i
$994$		0			0
$995$	−26.8634	+	21.9338i	−0.851626	+	0.695349i
$996$	−6.43168	−	2.87633i	−0.203795	−	0.0911401i
$997$	15.4919			0.490634			0.245317	−	0.969443i	$-0.421108\pi$
$997$	15.4919			0.490634			0.245317	+	0.969443i	$0.421108\pi$
$998$	−1.90890			−0.0604252
$999$	−4.21043	−	13.1807i	−0.133212	−	0.417020i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.d.e.1469.6		8
3.2	odd	2		1470.2.d.f.1469.7		8
5.4	even	2		1470.2.d.f.1469.3		8
7.4	even	3		210.2.t.f.89.1	yes	8
7.5	odd	6		210.2.t.f.59.2	yes	8
7.6	odd	2	inner	1470.2.d.e.1469.3		8
15.14	odd	2	inner	1470.2.d.e.1469.2		8
21.5	even	6		210.2.t.e.59.4	yes	8
21.11	odd	6		210.2.t.e.89.3	yes	8
21.20	even	2		1470.2.d.f.1469.2		8
35.4	even	6		210.2.t.e.89.4	yes	8
35.12	even	12		1050.2.s.i.101.1		16
35.18	odd	12		1050.2.s.i.551.2		16
35.19	odd	6		210.2.t.e.59.3	✓	8
35.32	odd	12		1050.2.s.i.551.7		16
35.33	even	12		1050.2.s.i.101.8		16
35.34	odd	2		1470.2.d.f.1469.6		8
105.32	even	12		1050.2.s.i.551.1		16
105.47	odd	12		1050.2.s.i.101.7		16
105.53	even	12		1050.2.s.i.551.8		16
105.68	odd	12		1050.2.s.i.101.2		16
105.74	odd	6		210.2.t.f.89.2	yes	8
105.89	even	6		210.2.t.f.59.1	yes	8
105.104	even	2	inner	1470.2.d.e.1469.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.t.e.59.3	✓	8	35.19	odd	6
210.2.t.e.59.4	yes	8	21.5	even	6
210.2.t.e.89.3	yes	8	21.11	odd	6
210.2.t.e.89.4	yes	8	35.4	even	6
210.2.t.f.59.1	yes	8	105.89	even	6
210.2.t.f.59.2	yes	8	7.5	odd	6
210.2.t.f.89.1	yes	8	7.4	even	3
210.2.t.f.89.2	yes	8	105.74	odd	6
1050.2.s.i.101.1		16	35.12	even	12
1050.2.s.i.101.2		16	105.68	odd	12
1050.2.s.i.101.7		16	105.47	odd	12
1050.2.s.i.101.8		16	35.33	even	12
1050.2.s.i.551.1		16	105.32	even	12
1050.2.s.i.551.2		16	35.18	odd	12
1050.2.s.i.551.7		16	35.32	odd	12
1050.2.s.i.551.8		16	105.53	even	12
1470.2.d.e.1469.2		8	15.14	odd	2	inner
1470.2.d.e.1469.3		8	7.6	odd	2	inner
1470.2.d.e.1469.6		8	1.1	even	1	trivial
1470.2.d.e.1469.7		8	105.104	even	2	inner
1470.2.d.f.1469.2		8	21.20	even	2
1470.2.d.f.1469.3		8	5.4	even	2
1470.2.d.f.1469.6		8	35.34	odd	2
1470.2.d.f.1469.7		8	3.2	odd	2

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:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(0.707107 - 1.58114i) q^{3} +1.00000 q^{4} +(1.41421 + 1.73205i) q^{5} +(-0.707107 + 1.58114i) q^{6} -1.00000 q^{8} +(-2.00000 - 2.23607i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(0.707107 - 1.58114i) q^{3} +1.00000 q^{4} +(1.41421 + 1.73205i) q^{5} +(-0.707107 + 1.58114i) q^{6} -1.00000 q^{8} +(-2.00000 - 2.23607i) q^{9} +(-1.41421 - 1.73205i) q^{10} -4.68556i q^{11} +(0.707107 - 1.58114i) q^{12} -1.04456 q^{13} +(3.73861 - 1.01132i) q^{15} +1.00000 q^{16} -3.16228i q^{17} +(2.00000 + 2.23607i) q^{18} +1.43023i q^{19} +(1.41421 + 1.73205i) q^{20} +4.68556i q^{22} -4.47723 q^{23} +(-0.707107 + 1.58114i) q^{24} +(-1.00000 + 4.89898i) q^{25} +1.04456 q^{26} +(-4.94975 + 1.58114i) q^{27} -6.92163i q^{29} +(-3.73861 + 1.01132i) q^{30} -6.62638i q^{31} -1.00000 q^{32} +(-7.40852 - 3.31319i) q^{33} +3.16228i q^{34} +(-2.00000 - 2.23607i) q^{36} +2.66291i q^{37} -1.43023i q^{38} +(-0.738613 + 1.65159i) q^{39} +(-1.41421 - 1.73205i) q^{40} -1.04456 q^{41} +6.92163i q^{43} -4.68556i q^{44} +(1.04456 - 6.62638i) q^{45} +4.47723 q^{46} -11.2189i q^{47} +(0.707107 - 1.58114i) q^{48} +(1.00000 - 4.89898i) q^{50} +(-5.00000 - 2.23607i) q^{51} -1.04456 q^{52} -5.00000 q^{53} +(4.94975 - 1.58114i) q^{54} +(8.11562 - 6.62638i) q^{55} +(2.26139 + 1.01132i) q^{57} +6.92163i q^{58} +10.5744 q^{59} +(3.73861 - 1.01132i) q^{60} -3.46410i q^{61} +6.62638i q^{62} +1.00000 q^{64} +(-1.47723 - 1.80922i) q^{65} +(7.40852 + 3.31319i) q^{66} -14.2701i q^{67} -3.16228i q^{68} +(-3.16588 + 7.07912i) q^{69} +6.92163i q^{71} +(2.00000 + 2.23607i) q^{72} +3.50333 q^{73} -2.66291i q^{74} +(7.03886 + 5.04524i) q^{75} +1.43023i q^{76} +(0.738613 - 1.65159i) q^{78} +11.4772 q^{79} +(1.41421 + 1.73205i) q^{80} +(-1.00000 + 8.94427i) q^{81} +1.04456 q^{82} -4.06775i q^{83} +(5.47723 - 4.47214i) q^{85} -6.92163i q^{86} +(-10.9441 - 4.89433i) q^{87} +4.68556i q^{88} +4.91754 q^{89} +(-1.04456 + 6.62638i) q^{90} -4.47723 q^{92} +(-10.4772 - 4.68556i) q^{93} +11.2189i q^{94} +(-2.47723 + 2.02265i) q^{95} +(-0.707107 + 1.58114i) q^{96} +11.9886 q^{97} +(-10.4772 + 9.37112i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 8 q^{4} - 8 q^{8} - 16 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 + 8 * q^4 - 8 * q^8 - 16 * q^9	\( 8 q - 8 q^{2} + 8 q^{4} - 8 q^{8} - 16 q^{9} + 8 q^{15} + 8 q^{16} + 16 q^{18} + 8 q^{23} - 8 q^{25} - 8 q^{30} - 8 q^{32} - 16 q^{36} + 16 q^{39} - 8 q^{46} + 8 q^{50} - 40 q^{51} - 40 q^{53} + 40 q^{57} + 8 q^{60} + 8 q^{64} + 32 q^{65} + 16 q^{72} - 16 q^{78} + 48 q^{79} - 8 q^{81} + 8 q^{92} - 40 q^{93} + 24 q^{95} - 40 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + 8 * q^4 - 8 * q^8 - 16 * q^9 + 8 * q^15 + 8 * q^16 + 16 * q^18 + 8 * q^23 - 8 * q^25 - 8 * q^30 - 8 * q^32 - 16 * q^36 + 16 * q^39 - 8 * q^46 + 8 * q^50 - 40 * q^51 - 40 * q^53 + 40 * q^57 + 8 * q^60 + 8 * q^64 + 32 * q^65 + 16 * q^72 - 16 * q^78 + 48 * q^79 - 8 * q^81 + 8 * q^92 - 40 * q^93 + 24 * q^95 - 40 * q^99

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