LMFDB - Embedded newform 1734.2.f.e.829.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1734,2,Mod(829,1734)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1734, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1734.829");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1734 = 2 \cdot 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1734.f (of order $4$, degree $2$, not 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:	$13.8460597105$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 102)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			829.1
Root			$-0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1734.829
Dual form			1734.2.f.e.1483.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-1.41421 - 1.41421i) q^{5} +(-0.707107 + 0.707107i) q^{6} +1.00000i q^{8} +1.00000i q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-1.41421 - 1.41421i) q^{5} +(-0.707107 + 0.707107i) q^{6} +1.00000i q^{8} +1.00000i q^{9} +(-1.41421 + 1.41421i) q^{10} +(2.82843 - 2.82843i) q^{11} +(0.707107 + 0.707107i) q^{12} +2.00000 q^{13} +2.00000i q^{15} +1.00000 q^{16} +1.00000 q^{18} -4.00000i q^{19} +(1.41421 + 1.41421i) q^{20} +(-2.82843 - 2.82843i) q^{22} +(0.707107 - 0.707107i) q^{24} -1.00000i q^{25} -2.00000i q^{26} +(0.707107 - 0.707107i) q^{27} +(-7.07107 - 7.07107i) q^{29} +2.00000 q^{30} +(-5.65685 - 5.65685i) q^{31} -1.00000i q^{32} -4.00000 q^{33} -1.00000i q^{36} +(1.41421 + 1.41421i) q^{37} -4.00000 q^{38} +(-1.41421 - 1.41421i) q^{39} +(1.41421 - 1.41421i) q^{40} +(7.07107 - 7.07107i) q^{41} +12.0000i q^{43} +(-2.82843 + 2.82843i) q^{44} +(1.41421 - 1.41421i) q^{45} +(-0.707107 - 0.707107i) q^{48} +7.00000i q^{49} -1.00000 q^{50} -2.00000 q^{52} -6.00000i q^{53} +(-0.707107 - 0.707107i) q^{54} -8.00000 q^{55} +(-2.82843 + 2.82843i) q^{57} +(-7.07107 + 7.07107i) q^{58} +12.0000i q^{59} -2.00000i q^{60} +(-7.07107 + 7.07107i) q^{61} +(-5.65685 + 5.65685i) q^{62} -1.00000 q^{64} +(-2.82843 - 2.82843i) q^{65} +4.00000i q^{66} -12.0000 q^{67} -1.00000 q^{72} +(7.07107 + 7.07107i) q^{73} +(1.41421 - 1.41421i) q^{74} +(-0.707107 + 0.707107i) q^{75} +4.00000i q^{76} +(-1.41421 + 1.41421i) q^{78} +(5.65685 - 5.65685i) q^{79} +(-1.41421 - 1.41421i) q^{80} -1.00000 q^{81} +(-7.07107 - 7.07107i) q^{82} -4.00000i q^{83} +12.0000 q^{86} +10.0000i q^{87} +(2.82843 + 2.82843i) q^{88} +6.00000 q^{89} +(-1.41421 - 1.41421i) q^{90} +8.00000i q^{93} +(-5.65685 + 5.65685i) q^{95} +(-0.707107 + 0.707107i) q^{96} +(-9.89949 - 9.89949i) q^{97} +7.00000 q^{98} +(2.82843 + 2.82843i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4}+O(q^{10}) $ 4 * q - 4 * q^4	$ 4 q - 4 q^{4} + 8 q^{13} + 4 q^{16} + 4 q^{18} + 8 q^{30} - 16 q^{33} - 16 q^{38} - 4 q^{50} - 8 q^{52} - 32 q^{55} - 4 q^{64} - 48 q^{67} - 4 q^{72} - 4 q^{81} + 48 q^{86} + 24 q^{89} + 28 q^{98}+O(q^{100}) $ 4 * q - 4 * q^4 + 8 * q^13 + 4 * q^16 + 4 * q^18 + 8 * q^30 - 16 * q^33 - 16 * q^38 - 4 * q^50 - 8 * q^52 - 32 * q^55 - 4 * q^64 - 48 * q^67 - 4 * q^72 - 4 * q^81 + 48 * q^86 + 24 * q^89 + 28 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1734\mathbb{Z}\right)^\times$.

$n$	$1157$	$1159$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$	−1.00000			−0.500000
$5$	−1.41421	−	1.41421i	−0.632456	−	0.632456i	0.316228	−	0.948683i	$-0.397584\pi$
$5$	−1.41421	−	1.41421i	−0.632456	−	0.632456i	−0.948683	+	0.316228i	$0.897584\pi$
$6$	−0.707107	+	0.707107i	−0.288675	+	0.288675i
$7$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$7$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$8$			1.00000i			0.353553i
$9$			1.00000i			0.333333i
$10$	−1.41421	+	1.41421i	−0.447214	+	0.447214i
$11$	2.82843	−	2.82843i	0.852803	−	0.852803i	−0.137675	−	0.990478i	$-0.543963\pi$
$11$	2.82843	−	2.82843i	0.852803	−	0.852803i	0.990478	+	0.137675i	$0.0439628\pi$
$12$	0.707107	+	0.707107i	0.204124	+	0.204124i
$13$	2.00000			0.554700			0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000			0.554700			0.277350	+	0.960769i	$0.410544\pi$
$14$		0			0
$15$			2.00000i			0.516398i
$16$	1.00000			0.250000
$17$		0			0
$17$		0			0
$18$	1.00000			0.235702
$19$		−	4.00000i		−	0.917663i	−0.888523	−	0.458831i	$-0.848268\pi$
$19$		−	4.00000i		−	0.917663i	0.888523	−	0.458831i	$-0.151732\pi$
$20$	1.41421	+	1.41421i	0.316228	+	0.316228i
$21$		0			0
$22$	−2.82843	−	2.82843i	−0.603023	−	0.603023i
$23$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$23$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$24$	0.707107	−	0.707107i	0.144338	−	0.144338i
$25$		−	1.00000i		−	0.200000i
$26$		−	2.00000i		−	0.392232i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$		0			0
$29$	−7.07107	−	7.07107i	−1.31306	−	1.31306i	−0.919145	−	0.393919i	$-0.871119\pi$
$29$	−7.07107	−	7.07107i	−1.31306	−	1.31306i	−0.393919	−	0.919145i	$-0.628881\pi$
$30$	2.00000			0.365148
$31$	−5.65685	−	5.65685i	−1.01600	−	1.01600i	−0.999870	−	0.0161311i	$-0.994865\pi$
$31$	−5.65685	−	5.65685i	−1.01600	−	1.01600i	−0.0161311	−	0.999870i	$-0.505135\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−4.00000			−0.696311
$34$		0			0
$35$		0			0
$36$		−	1.00000i		−	0.166667i
$37$	1.41421	+	1.41421i	0.232495	+	0.232495i	0.813733	−	0.581238i	$-0.197432\pi$
$37$	1.41421	+	1.41421i	0.232495	+	0.232495i	−0.581238	+	0.813733i	$0.697432\pi$
$38$	−4.00000			−0.648886
$39$	−1.41421	−	1.41421i	−0.226455	−	0.226455i
$40$	1.41421	−	1.41421i	0.223607	−	0.223607i
$41$	7.07107	−	7.07107i	1.10432	−	1.10432i	0.110432	−	0.993884i	$-0.464777\pi$
$41$	7.07107	−	7.07107i	1.10432	−	1.10432i	0.993884	−	0.110432i	$-0.0352233\pi$
$42$		0			0
$43$			12.0000i			1.82998i	0.403473	+	0.914991i	$0.367803\pi$
$43$			12.0000i			1.82998i	−0.403473	+	0.914991i	$0.632197\pi$
$44$	−2.82843	+	2.82843i	−0.426401	+	0.426401i
$45$	1.41421	−	1.41421i	0.210819	−	0.210819i
$46$		0			0
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$	−0.707107	−	0.707107i	−0.102062	−	0.102062i
$49$			7.00000i			1.00000i
$50$	−1.00000			−0.141421
$51$		0			0
$52$	−2.00000			−0.277350
$53$		−	6.00000i		−	0.824163i	−0.911147	−	0.412082i	$-0.864802\pi$
$53$		−	6.00000i		−	0.824163i	0.911147	−	0.412082i	$-0.135198\pi$
$54$	−0.707107	−	0.707107i	−0.0962250	−	0.0962250i
$55$	−8.00000			−1.07872
$56$		0			0
$57$	−2.82843	+	2.82843i	−0.374634	+	0.374634i
$58$	−7.07107	+	7.07107i	−0.928477	+	0.928477i
$59$			12.0000i			1.56227i	0.624364	+	0.781133i	$0.285358\pi$
$59$			12.0000i			1.56227i	−0.624364	+	0.781133i	$0.714642\pi$
$60$		−	2.00000i		−	0.258199i
$61$	−7.07107	+	7.07107i	−0.905357	+	0.905357i	−0.995893	−	0.0905357i	$-0.971142\pi$
$61$	−7.07107	+	7.07107i	−0.905357	+	0.905357i	0.0905357	+	0.995893i	$0.471142\pi$
$62$	−5.65685	+	5.65685i	−0.718421	+	0.718421i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−2.82843	−	2.82843i	−0.350823	−	0.350823i
$66$			4.00000i			0.492366i
$67$	−12.0000			−1.46603			−0.733017	−	0.680211i	$-0.761888\pi$
$67$	−12.0000			−1.46603			−0.733017	+	0.680211i	$0.761888\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$71$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$72$	−1.00000			−0.117851
$73$	7.07107	+	7.07107i	0.827606	+	0.827606i	0.987185	−	0.159579i	$-0.0510137\pi$
$73$	7.07107	+	7.07107i	0.827606	+	0.827606i	−0.159579	+	0.987185i	$0.551014\pi$
$74$	1.41421	−	1.41421i	0.164399	−	0.164399i
$75$	−0.707107	+	0.707107i	−0.0816497	+	0.0816497i
$76$			4.00000i			0.458831i
$77$		0			0
$78$	−1.41421	+	1.41421i	−0.160128	+	0.160128i
$79$	5.65685	−	5.65685i	0.636446	−	0.636446i	−0.313231	−	0.949677i	$-0.601411\pi$
$79$	5.65685	−	5.65685i	0.636446	−	0.636446i	0.949677	+	0.313231i	$0.101411\pi$
$80$	−1.41421	−	1.41421i	−0.158114	−	0.158114i
$81$	−1.00000			−0.111111
$82$	−7.07107	−	7.07107i	−0.780869	−	0.780869i
$83$		−	4.00000i		−	0.439057i	−0.975606	−	0.219529i	$-0.929548\pi$
$83$		−	4.00000i		−	0.439057i	0.975606	−	0.219529i	$-0.0704519\pi$
$84$		0			0
$85$		0			0
$86$	12.0000			1.29399
$87$			10.0000i			1.07211i
$88$	2.82843	+	2.82843i	0.301511	+	0.301511i
$89$	6.00000			0.635999			0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000			0.635999			0.317999	+	0.948091i	$0.396989\pi$
$90$	−1.41421	−	1.41421i	−0.149071	−	0.149071i
$91$		0			0
$92$		0			0
$93$			8.00000i			0.829561i
$94$		0			0
$95$	−5.65685	+	5.65685i	−0.580381	+	0.580381i
$96$	−0.707107	+	0.707107i	−0.0721688	+	0.0721688i
$97$	−9.89949	−	9.89949i	−1.00514	−	1.00514i	−0.999987	−	0.00515471i	$-0.998359\pi$
$97$	−9.89949	−	9.89949i	−1.00514	−	1.00514i	−0.00515471	−	0.999987i	$-0.501641\pi$
$98$	7.00000			0.707107
$99$	2.82843	+	2.82843i	0.284268	+	0.284268i
$100$			1.00000i			0.100000i
$101$	−10.0000			−0.995037			−0.497519	−	0.867453i	$-0.665755\pi$
$101$	−10.0000			−0.995037			−0.497519	+	0.867453i	$0.665755\pi$
$102$		0			0
$103$	−8.00000			−0.788263			−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000			−0.788263			−0.394132	+	0.919054i	$0.628955\pi$
$104$			2.00000i			0.196116i
$105$		0			0
$106$	−6.00000			−0.582772
$107$	−2.82843	−	2.82843i	−0.273434	−	0.273434i	0.557047	−	0.830481i	$-0.311934\pi$
$107$	−2.82843	−	2.82843i	−0.273434	−	0.273434i	−0.830481	+	0.557047i	$0.811934\pi$
$108$	−0.707107	+	0.707107i	−0.0680414	+	0.0680414i
$109$	−7.07107	+	7.07107i	−0.677285	+	0.677285i	−0.959385	−	0.282100i	$-0.908969\pi$
$109$	−7.07107	+	7.07107i	−0.677285	+	0.677285i	0.282100	+	0.959385i	$0.408969\pi$
$110$			8.00000i			0.762770i
$111$		−	2.00000i		−	0.189832i
$112$		0			0
$113$	−1.41421	+	1.41421i	−0.133038	+	0.133038i	−0.770490	−	0.637452i	$-0.779988\pi$
$113$	−1.41421	+	1.41421i	−0.133038	+	0.133038i	0.637452	+	0.770490i	$0.279988\pi$
$114$	2.82843	+	2.82843i	0.264906	+	0.264906i
$115$		0			0
$116$	7.07107	+	7.07107i	0.656532	+	0.656532i
$117$			2.00000i			0.184900i
$118$	12.0000			1.10469
$119$		0			0
$120$	−2.00000			−0.182574
$121$		−	5.00000i		−	0.454545i
$122$	7.07107	+	7.07107i	0.640184	+	0.640184i
$123$	−10.0000			−0.901670
$124$	5.65685	+	5.65685i	0.508001	+	0.508001i
$125$	−8.48528	+	8.48528i	−0.758947	+	0.758947i
$126$		0			0
$127$		0			0		1.00000			$0$
$127$		0			0		−1.00000			$\pi$
$128$			1.00000i			0.0883883i
$129$	8.48528	−	8.48528i	0.747087	−	0.747087i
$130$	−2.82843	+	2.82843i	−0.248069	+	0.248069i
$131$	−8.48528	−	8.48528i	−0.741362	−	0.741362i	0.231478	−	0.972840i	$-0.425644\pi$
$131$	−8.48528	−	8.48528i	−0.741362	−	0.741362i	−0.972840	+	0.231478i	$0.925644\pi$
$132$	4.00000			0.348155
$133$		0			0
$134$			12.0000i			1.03664i
$135$	−2.00000			−0.172133
$136$		0			0
$137$	10.0000			0.854358			0.427179	−	0.904167i	$-0.359507\pi$
$137$	10.0000			0.854358			0.427179	+	0.904167i	$0.359507\pi$
$138$		0			0
$139$	2.82843	+	2.82843i	0.239904	+	0.239904i	0.816810	−	0.576906i	$-0.195740\pi$
$139$	2.82843	+	2.82843i	0.239904	+	0.239904i	−0.576906	+	0.816810i	$0.695740\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	5.65685	−	5.65685i	0.473050	−	0.473050i
$144$			1.00000i			0.0833333i
$145$			20.0000i			1.66091i
$146$	7.07107	−	7.07107i	0.585206	−	0.585206i
$147$	4.94975	−	4.94975i	0.408248	−	0.408248i
$148$	−1.41421	−	1.41421i	−0.116248	−	0.116248i
$149$	10.0000			0.819232			0.409616	−	0.912258i	$-0.365663\pi$
$149$	10.0000			0.819232			0.409616	+	0.912258i	$0.365663\pi$
$150$	0.707107	+	0.707107i	0.0577350	+	0.0577350i
$151$		−	24.0000i		−	1.95309i	−0.215308	−	0.976546i	$-0.569076\pi$
$151$		−	24.0000i		−	1.95309i	0.215308	−	0.976546i	$-0.430924\pi$
$152$	4.00000			0.324443
$153$		0			0
$154$		0			0
$155$			16.0000i			1.28515i
$156$	1.41421	+	1.41421i	0.113228	+	0.113228i
$157$	2.00000			0.159617			0.0798087	−	0.996810i	$-0.474569\pi$
$157$	2.00000			0.159617			0.0798087	+	0.996810i	$0.474569\pi$
$158$	−5.65685	−	5.65685i	−0.450035	−	0.450035i
$159$	−4.24264	+	4.24264i	−0.336463	+	0.336463i
$160$	−1.41421	+	1.41421i	−0.111803	+	0.111803i
$161$		0			0
$162$			1.00000i			0.0785674i
$163$	2.82843	−	2.82843i	0.221540	−	0.221540i	−0.587607	−	0.809146i	$-0.699930\pi$
$163$	2.82843	−	2.82843i	0.221540	−	0.221540i	0.809146	+	0.587607i	$0.199930\pi$
$164$	−7.07107	+	7.07107i	−0.552158	+	0.552158i
$165$	5.65685	+	5.65685i	0.440386	+	0.440386i
$166$	−4.00000			−0.310460
$167$	−11.3137	−	11.3137i	−0.875481	−	0.875481i	0.117582	−	0.993063i	$-0.462486\pi$
$167$	−11.3137	−	11.3137i	−0.875481	−	0.875481i	−0.993063	+	0.117582i	$0.962486\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$		0			0
$171$	4.00000			0.305888
$172$		−	12.0000i		−	0.914991i
$173$	−4.24264	−	4.24264i	−0.322562	−	0.322562i	0.527187	−	0.849749i	$-0.323247\pi$
$173$	−4.24264	−	4.24264i	−0.322562	−	0.322562i	−0.849749	+	0.527187i	$0.823247\pi$
$174$	10.0000			0.758098
$175$		0			0
$176$	2.82843	−	2.82843i	0.213201	−	0.213201i
$177$	8.48528	−	8.48528i	0.637793	−	0.637793i
$178$		−	6.00000i		−	0.449719i
$179$		−	12.0000i		−	0.896922i	−0.893802	−	0.448461i	$-0.851972\pi$
$179$		−	12.0000i		−	0.896922i	0.893802	−	0.448461i	$-0.148028\pi$
$180$	−1.41421	+	1.41421i	−0.105409	+	0.105409i
$181$	−9.89949	+	9.89949i	−0.735824	+	0.735824i	−0.971767	−	0.235943i	$-0.924182\pi$
$181$	−9.89949	+	9.89949i	−0.735824	+	0.735824i	0.235943	+	0.971767i	$0.424182\pi$
$182$		0			0
$183$	10.0000			0.739221
$184$		0			0
$185$		−	4.00000i		−	0.294086i
$186$	8.00000			0.586588
$187$		0			0
$188$		0			0
$189$		0			0
$190$	5.65685	+	5.65685i	0.410391	+	0.410391i
$191$	16.0000			1.15772			0.578860	−	0.815427i	$-0.303498\pi$
$191$	16.0000			1.15772			0.578860	+	0.815427i	$0.303498\pi$
$192$	0.707107	+	0.707107i	0.0510310	+	0.0510310i
$193$	−12.7279	+	12.7279i	−0.916176	+	0.916176i	−0.996749	−	0.0805728i	$-0.974325\pi$
$193$	−12.7279	+	12.7279i	−0.916176	+	0.916176i	0.0805728	+	0.996749i	$0.474325\pi$
$194$	−9.89949	+	9.89949i	−0.710742	+	0.710742i
$195$			4.00000i			0.286446i
$196$		−	7.00000i		−	0.500000i
$197$	9.89949	−	9.89949i	0.705310	−	0.705310i	−0.260235	−	0.965545i	$-0.583800\pi$
$197$	9.89949	−	9.89949i	0.705310	−	0.705310i	0.965545	+	0.260235i	$0.0838002\pi$
$198$	2.82843	−	2.82843i	0.201008	−	0.201008i
$199$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$199$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$200$	1.00000			0.0707107
$201$	8.48528	+	8.48528i	0.598506	+	0.598506i
$202$			10.0000i			0.703598i
$203$		0			0
$204$		0			0
$205$	−20.0000			−1.39686
$206$			8.00000i			0.557386i
$207$		0			0
$208$	2.00000			0.138675
$209$	−11.3137	−	11.3137i	−0.782586	−	0.782586i
$210$		0			0
$211$	−19.7990	+	19.7990i	−1.36302	+	1.36302i	−0.492975	+	0.870043i	$0.664091\pi$
$211$	−19.7990	+	19.7990i	−1.36302	+	1.36302i	−0.870043	+	0.492975i	$0.835909\pi$
$212$			6.00000i			0.412082i
$213$		0			0
$214$	−2.82843	+	2.82843i	−0.193347	+	0.193347i
$215$	16.9706	−	16.9706i	1.15738	−	1.15738i
$216$	0.707107	+	0.707107i	0.0481125	+	0.0481125i
$217$		0			0
$218$	7.07107	+	7.07107i	0.478913	+	0.478913i
$219$		−	10.0000i		−	0.675737i
$220$	8.00000			0.539360
$221$		0			0
$222$	−2.00000			−0.134231
$223$		−	16.0000i		−	1.07144i	−0.844396	−	0.535720i	$-0.820040\pi$
$223$		−	16.0000i		−	1.07144i	0.844396	−	0.535720i	$-0.179960\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$	1.41421	+	1.41421i	0.0940721	+	0.0940721i
$227$	−2.82843	+	2.82843i	−0.187729	+	0.187729i	−0.794714	−	0.606984i	$-0.792379\pi$
$227$	−2.82843	+	2.82843i	−0.187729	+	0.187729i	0.606984	+	0.794714i	$0.292379\pi$
$228$	2.82843	−	2.82843i	0.187317	−	0.187317i
$229$		−	26.0000i		−	1.71813i	−0.511868	−	0.859064i	$-0.671046\pi$
$229$		−	26.0000i		−	1.71813i	0.511868	−	0.859064i	$-0.328954\pi$
$230$		0			0
$231$		0			0
$232$	7.07107	−	7.07107i	0.464238	−	0.464238i
$233$	18.3848	+	18.3848i	1.20443	+	1.20443i	0.972806	+	0.231621i	$0.0744028\pi$
$233$	18.3848	+	18.3848i	1.20443	+	1.20443i	0.231621	+	0.972806i	$0.425597\pi$
$234$	2.00000			0.130744
$235$		0			0
$236$		−	12.0000i		−	0.781133i
$237$	−8.00000			−0.519656
$238$		0			0
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$			2.00000i			0.129099i
$241$	−1.41421	−	1.41421i	−0.0910975	−	0.0910975i	0.660089	−	0.751187i	$-0.270518\pi$
$241$	−1.41421	−	1.41421i	−0.0910975	−	0.0910975i	−0.751187	+	0.660089i	$0.770518\pi$
$242$	−5.00000			−0.321412
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	7.07107	−	7.07107i	0.452679	−	0.452679i
$245$	9.89949	−	9.89949i	0.632456	−	0.632456i
$246$			10.0000i			0.637577i
$247$		−	8.00000i		−	0.509028i
$248$	5.65685	−	5.65685i	0.359211	−	0.359211i
$249$	−2.82843	+	2.82843i	−0.179244	+	0.179244i
$250$	8.48528	+	8.48528i	0.536656	+	0.536656i
$251$	−28.0000			−1.76734			−0.883672	−	0.468106i	$-0.844936\pi$
$251$	−28.0000			−1.76734			−0.883672	+	0.468106i	$0.844936\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	2.00000i		−	0.124757i	−0.998053	−	0.0623783i	$-0.980131\pi$
$257$		−	2.00000i		−	0.124757i	0.998053	−	0.0623783i	$-0.0198685\pi$
$258$	−8.48528	−	8.48528i	−0.528271	−	0.528271i
$259$		0			0
$260$	2.82843	+	2.82843i	0.175412	+	0.175412i
$261$	7.07107	−	7.07107i	0.437688	−	0.437688i
$262$	−8.48528	+	8.48528i	−0.524222	+	0.524222i
$263$		−	8.00000i		−	0.493301i	−0.969104	−	0.246651i	$-0.920670\pi$
$263$		−	8.00000i		−	0.493301i	0.969104	−	0.246651i	$-0.0793300\pi$
$264$		−	4.00000i		−	0.246183i
$265$	−8.48528	+	8.48528i	−0.521247	+	0.521247i
$266$		0			0
$267$	−4.24264	−	4.24264i	−0.259645	−	0.259645i
$268$	12.0000			0.733017
$269$	−4.24264	−	4.24264i	−0.258678	−	0.258678i	0.565838	−	0.824516i	$-0.308553\pi$
$269$	−4.24264	−	4.24264i	−0.258678	−	0.258678i	−0.824516	+	0.565838i	$0.808553\pi$
$270$			2.00000i			0.121716i
$271$	16.0000			0.971931			0.485965	−	0.873978i	$-0.338468\pi$
$271$	16.0000			0.971931			0.485965	+	0.873978i	$0.338468\pi$
$272$		0			0
$273$		0			0
$274$		−	10.0000i		−	0.604122i
$275$	−2.82843	−	2.82843i	−0.170561	−	0.170561i
$276$		0			0
$277$	21.2132	+	21.2132i	1.27458	+	1.27458i	0.943659	+	0.330919i	$0.107359\pi$
$277$	21.2132	+	21.2132i	1.27458	+	1.27458i	0.330919	+	0.943659i	$0.392641\pi$
$278$	2.82843	−	2.82843i	0.169638	−	0.169638i
$279$	5.65685	−	5.65685i	0.338667	−	0.338667i
$280$		0			0
$281$		−	6.00000i		−	0.357930i	−0.983855	−	0.178965i	$-0.942725\pi$
$281$		−	6.00000i		−	0.357930i	0.983855	−	0.178965i	$-0.0572749\pi$
$282$		0			0
$283$	−8.48528	+	8.48528i	−0.504398	+	0.504398i	−0.912801	−	0.408404i	$-0.866086\pi$
$283$	−8.48528	+	8.48528i	−0.504398	+	0.504398i	0.408404	+	0.912801i	$0.366086\pi$
$284$		0			0
$285$	8.00000			0.473879
$286$	−5.65685	−	5.65685i	−0.334497	−	0.334497i
$287$		0			0
$288$	1.00000			0.0589256
$289$		0			0
$290$	20.0000			1.17444
$291$			14.0000i			0.820695i
$292$	−7.07107	−	7.07107i	−0.413803	−	0.413803i
$293$	26.0000			1.51894			0.759468	−	0.650545i	$-0.225459\pi$
$293$	26.0000			1.51894			0.759468	+	0.650545i	$0.225459\pi$
$294$	−4.94975	−	4.94975i	−0.288675	−	0.288675i
$295$	16.9706	−	16.9706i	0.988064	−	0.988064i
$296$	−1.41421	+	1.41421i	−0.0821995	+	0.0821995i
$297$		−	4.00000i		−	0.232104i
$298$		−	10.0000i		−	0.579284i
$299$		0			0
$300$	0.707107	−	0.707107i	0.0408248	−	0.0408248i
$301$		0			0
$302$	−24.0000			−1.38104
$303$	7.07107	+	7.07107i	0.406222	+	0.406222i
$304$		−	4.00000i		−	0.229416i
$305$	20.0000			1.14520
$306$		0			0
$307$	−12.0000			−0.684876			−0.342438	−	0.939540i	$-0.611253\pi$
$307$	−12.0000			−0.684876			−0.342438	+	0.939540i	$0.611253\pi$
$308$		0			0
$309$	5.65685	+	5.65685i	0.321807	+	0.321807i
$310$	16.0000			0.908739
$311$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$311$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$312$	1.41421	−	1.41421i	0.0800641	−	0.0800641i
$313$	7.07107	−	7.07107i	0.399680	−	0.399680i	−0.478440	−	0.878120i	$-0.658798\pi$
$313$	7.07107	−	7.07107i	0.399680	−	0.399680i	0.878120	+	0.478440i	$0.158798\pi$
$314$		−	2.00000i		−	0.112867i
$315$		0			0
$316$	−5.65685	+	5.65685i	−0.318223	+	0.318223i
$317$	−4.24264	+	4.24264i	−0.238290	+	0.238290i	−0.816142	−	0.577851i	$-0.803891\pi$
$317$	−4.24264	+	4.24264i	−0.238290	+	0.238290i	0.577851	+	0.816142i	$0.303891\pi$
$318$	4.24264	+	4.24264i	0.237915	+	0.237915i
$319$	−40.0000			−2.23957
$320$	1.41421	+	1.41421i	0.0790569	+	0.0790569i
$321$			4.00000i			0.223258i
$322$		0			0
$323$		0			0
$324$	1.00000			0.0555556
$325$		−	2.00000i		−	0.110940i
$326$	−2.82843	−	2.82843i	−0.156652	−	0.156652i
$327$	10.0000			0.553001
$328$	7.07107	+	7.07107i	0.390434	+	0.390434i
$329$		0			0
$330$	5.65685	−	5.65685i	0.311400	−	0.311400i
$331$		−	20.0000i		−	1.09930i	−0.835395	−	0.549650i	$-0.814761\pi$
$331$		−	20.0000i		−	1.09930i	0.835395	−	0.549650i	$-0.185239\pi$
$332$			4.00000i			0.219529i
$333$	−1.41421	+	1.41421i	−0.0774984	+	0.0774984i
$334$	−11.3137	+	11.3137i	−0.619059	+	0.619059i
$335$	16.9706	+	16.9706i	0.927201	+	0.927201i
$336$		0			0
$337$	9.89949	+	9.89949i	0.539260	+	0.539260i	0.923312	−	0.384052i	$-0.125472\pi$
$337$	9.89949	+	9.89949i	0.539260	+	0.539260i	−0.384052	+	0.923312i	$0.625472\pi$
$338$			9.00000i			0.489535i
$339$	2.00000			0.108625
$340$		0			0
$341$	−32.0000			−1.73290
$342$		−	4.00000i		−	0.216295i
$343$		0			0
$344$	−12.0000			−0.646997
$345$		0			0
$346$	−4.24264	+	4.24264i	−0.228086	+	0.228086i
$347$	19.7990	−	19.7990i	1.06287	−	1.06287i	0.0649788	−	0.997887i	$-0.479302\pi$
$347$	19.7990	−	19.7990i	1.06287	−	1.06287i	0.997887	−	0.0649788i	$-0.0206980\pi$
$348$		−	10.0000i		−	0.536056i
$349$			14.0000i			0.749403i	0.927146	+	0.374701i	$0.122255\pi$
$349$			14.0000i			0.749403i	−0.927146	+	0.374701i	$0.877745\pi$
$350$		0			0
$351$	1.41421	−	1.41421i	0.0754851	−	0.0754851i
$352$	−2.82843	−	2.82843i	−0.150756	−	0.150756i
$353$	30.0000			1.59674			0.798369	−	0.602168i	$-0.205696\pi$
$353$	30.0000			1.59674			0.798369	+	0.602168i	$0.205696\pi$
$354$	−8.48528	−	8.48528i	−0.450988	−	0.450988i
$355$		0			0
$356$	−6.00000			−0.317999
$357$		0			0
$358$	−12.0000			−0.634220
$359$			24.0000i			1.26667i	0.773877	+	0.633336i	$0.218315\pi$
$359$			24.0000i			1.26667i	−0.773877	+	0.633336i	$0.781685\pi$
$360$	1.41421	+	1.41421i	0.0745356	+	0.0745356i
$361$	3.00000			0.157895
$362$	9.89949	+	9.89949i	0.520306	+	0.520306i
$363$	−3.53553	+	3.53553i	−0.185567	+	0.185567i
$364$		0			0
$365$		−	20.0000i		−	1.04685i
$366$		−	10.0000i		−	0.522708i
$367$	16.9706	−	16.9706i	0.885856	−	0.885856i	−0.108266	−	0.994122i	$-0.534530\pi$
$367$	16.9706	−	16.9706i	0.885856	−	0.885856i	0.994122	+	0.108266i	$0.0345298\pi$
$368$		0			0
$369$	7.07107	+	7.07107i	0.368105	+	0.368105i
$370$	−4.00000			−0.207950
$371$		0			0
$372$		−	8.00000i		−	0.414781i
$373$	6.00000			0.310668			0.155334	−	0.987862i	$-0.450355\pi$
$373$	6.00000			0.310668			0.155334	+	0.987862i	$0.450355\pi$
$374$		0			0
$375$	12.0000			0.619677
$376$		0			0
$377$	−14.1421	−	14.1421i	−0.728357	−	0.728357i
$378$		0			0
$379$	−2.82843	−	2.82843i	−0.145287	−	0.145287i	0.630722	−	0.776009i	$-0.282759\pi$
$379$	−2.82843	−	2.82843i	−0.145287	−	0.145287i	−0.776009	+	0.630722i	$0.782759\pi$
$380$	5.65685	−	5.65685i	0.290191	−	0.290191i
$381$		0			0
$382$		−	16.0000i		−	0.818631i
$383$		−	16.0000i		−	0.817562i	−0.912633	−	0.408781i	$-0.865954\pi$
$383$		−	16.0000i		−	0.817562i	0.912633	−	0.408781i	$-0.134046\pi$
$384$	0.707107	−	0.707107i	0.0360844	−	0.0360844i
$385$		0			0
$386$	12.7279	+	12.7279i	0.647834	+	0.647834i
$387$	−12.0000			−0.609994
$388$	9.89949	+	9.89949i	0.502571	+	0.502571i
$389$			26.0000i			1.31825i	0.752032	+	0.659126i	$0.229074\pi$
$389$			26.0000i			1.31825i	−0.752032	+	0.659126i	$0.770926\pi$
$390$	4.00000			0.202548
$391$		0			0
$392$	−7.00000			−0.353553
$393$			12.0000i			0.605320i
$394$	−9.89949	−	9.89949i	−0.498729	−	0.498729i
$395$	−16.0000			−0.805047
$396$	−2.82843	−	2.82843i	−0.142134	−	0.142134i
$397$	18.3848	−	18.3848i	0.922705	−	0.922705i	−0.0745145	−	0.997220i	$-0.523741\pi$
$397$	18.3848	−	18.3848i	0.922705	−	0.922705i	0.997220	+	0.0745145i	$0.0237407\pi$
$398$		0			0
$399$		0			0
$400$		−	1.00000i		−	0.0500000i
$401$	−9.89949	+	9.89949i	−0.494357	+	0.494357i	−0.909676	−	0.415319i	$-0.863670\pi$
$401$	−9.89949	+	9.89949i	−0.494357	+	0.494357i	0.415319	+	0.909676i	$0.363670\pi$
$402$	8.48528	−	8.48528i	0.423207	−	0.423207i
$403$	−11.3137	−	11.3137i	−0.563576	−	0.563576i
$404$	10.0000			0.497519
$405$	1.41421	+	1.41421i	0.0702728	+	0.0702728i
$406$		0			0
$407$	8.00000			0.396545
$408$		0			0
$409$	26.0000			1.28562			0.642809	−	0.766027i	$-0.277769\pi$
$409$	26.0000			1.28562			0.642809	+	0.766027i	$0.277769\pi$
$410$			20.0000i			0.987730i
$411$	−7.07107	−	7.07107i	−0.348790	−	0.348790i
$412$	8.00000			0.394132
$413$		0			0
$414$		0			0
$415$	−5.65685	+	5.65685i	−0.277684	+	0.277684i
$416$		−	2.00000i		−	0.0980581i
$417$		−	4.00000i		−	0.195881i
$418$	−11.3137	+	11.3137i	−0.553372	+	0.553372i
$419$	−2.82843	+	2.82843i	−0.138178	+	0.138178i	−0.772812	−	0.634635i	$-0.781151\pi$
$419$	−2.82843	+	2.82843i	−0.138178	+	0.138178i	0.634635	+	0.772812i	$0.281151\pi$
$420$		0			0
$421$	−22.0000			−1.07221			−0.536107	−	0.844150i	$-0.680106\pi$
$421$	−22.0000			−1.07221			−0.536107	+	0.844150i	$0.680106\pi$
$422$	19.7990	+	19.7990i	0.963800	+	0.963800i
$423$		0			0
$424$	6.00000			0.291386
$425$		0			0
$426$		0			0
$427$		0			0
$428$	2.82843	+	2.82843i	0.136717	+	0.136717i
$429$	−8.00000			−0.386244
$430$	−16.9706	−	16.9706i	−0.818393	−	0.818393i
$431$	5.65685	−	5.65685i	0.272481	−	0.272481i	−0.557617	−	0.830098i	$-0.688284\pi$
$431$	5.65685	−	5.65685i	0.272481	−	0.272481i	0.830098	+	0.557617i	$0.188284\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$		−	14.0000i		−	0.672797i	−0.941720	−	0.336399i	$-0.890791\pi$
$433$		−	14.0000i		−	0.672797i	0.941720	−	0.336399i	$-0.109209\pi$
$434$		0			0
$435$	14.1421	−	14.1421i	0.678064	−	0.678064i
$436$	7.07107	−	7.07107i	0.338643	−	0.338643i
$437$		0			0
$438$	−10.0000			−0.477818
$439$	−11.3137	−	11.3137i	−0.539974	−	0.539974i	0.383547	−	0.923521i	$-0.374702\pi$
$439$	−11.3137	−	11.3137i	−0.539974	−	0.539974i	−0.923521	+	0.383547i	$0.874702\pi$
$440$		−	8.00000i		−	0.381385i
$441$	−7.00000			−0.333333
$442$		0			0
$443$	−4.00000			−0.190046			−0.0950229	−	0.995475i	$-0.530292\pi$
$443$	−4.00000			−0.190046			−0.0950229	+	0.995475i	$0.530292\pi$
$444$			2.00000i			0.0949158i
$445$	−8.48528	−	8.48528i	−0.402241	−	0.402241i
$446$	−16.0000			−0.757622
$447$	−7.07107	−	7.07107i	−0.334450	−	0.334450i
$448$		0			0
$449$	1.41421	−	1.41421i	0.0667409	−	0.0667409i	−0.672948	−	0.739689i	$-0.734972\pi$
$449$	1.41421	−	1.41421i	0.0667409	−	0.0667409i	0.739689	+	0.672948i	$0.234972\pi$
$450$		−	1.00000i		−	0.0471405i
$451$		−	40.0000i		−	1.88353i
$452$	1.41421	−	1.41421i	0.0665190	−	0.0665190i
$453$	−16.9706	+	16.9706i	−0.797347	+	0.797347i
$454$	2.82843	+	2.82843i	0.132745	+	0.132745i
$455$		0			0
$456$	−2.82843	−	2.82843i	−0.132453	−	0.132453i
$457$		−	10.0000i		−	0.467780i	−0.972263	−	0.233890i	$-0.924854\pi$
$457$		−	10.0000i		−	0.467780i	0.972263	−	0.233890i	$-0.0751456\pi$
$458$	−26.0000			−1.21490
$459$		0			0
$460$		0			0
$461$		−	30.0000i		−	1.39724i	−0.715493	−	0.698620i	$-0.753798\pi$
$461$		−	30.0000i		−	1.39724i	0.715493	−	0.698620i	$-0.246202\pi$
$462$		0			0
$463$	−32.0000			−1.48717			−0.743583	−	0.668644i	$-0.766875\pi$
$463$	−32.0000			−1.48717			−0.743583	+	0.668644i	$0.766875\pi$
$464$	−7.07107	−	7.07107i	−0.328266	−	0.328266i
$465$	11.3137	−	11.3137i	0.524661	−	0.524661i
$466$	18.3848	−	18.3848i	0.851658	−	0.851658i
$467$		−	12.0000i		−	0.555294i	−0.960683	−	0.277647i	$-0.910445\pi$
$467$		−	12.0000i		−	0.555294i	0.960683	−	0.277647i	$-0.0895545\pi$
$468$		−	2.00000i		−	0.0924500i
$469$		0			0
$470$		0			0
$471$	−1.41421	−	1.41421i	−0.0651635	−	0.0651635i
$472$	−12.0000			−0.552345
$473$	33.9411	+	33.9411i	1.56061	+	1.56061i
$474$			8.00000i			0.367452i
$475$	−4.00000			−0.183533
$476$		0			0
$477$	6.00000			0.274721
$478$		0			0
$479$	−16.9706	−	16.9706i	−0.775405	−	0.775405i	0.203641	−	0.979046i	$-0.434723\pi$
$479$	−16.9706	−	16.9706i	−0.775405	−	0.775405i	−0.979046	+	0.203641i	$0.934723\pi$
$480$	2.00000			0.0912871
$481$	2.82843	+	2.82843i	0.128965	+	0.128965i
$482$	−1.41421	+	1.41421i	−0.0644157	+	0.0644157i
$483$		0			0
$484$			5.00000i			0.227273i
$485$			28.0000i			1.27141i
$486$	0.707107	−	0.707107i	0.0320750	−	0.0320750i
$487$	11.3137	−	11.3137i	0.512673	−	0.512673i	−0.402671	−	0.915345i	$-0.631918\pi$
$487$	11.3137	−	11.3137i	0.512673	−	0.512673i	0.915345	+	0.402671i	$0.131918\pi$
$488$	−7.07107	−	7.07107i	−0.320092	−	0.320092i
$489$	−4.00000			−0.180886
$490$	−9.89949	−	9.89949i	−0.447214	−	0.447214i
$491$		−	12.0000i		−	0.541552i	−0.962642	−	0.270776i	$-0.912720\pi$
$491$		−	12.0000i		−	0.541552i	0.962642	−	0.270776i	$-0.0872803\pi$
$492$	10.0000			0.450835
$493$		0			0
$494$	−8.00000			−0.359937
$495$		−	8.00000i		−	0.359573i
$496$	−5.65685	−	5.65685i	−0.254000	−	0.254000i
$497$		0			0
$498$	2.82843	+	2.82843i	0.126745	+	0.126745i
$499$	−2.82843	+	2.82843i	−0.126618	+	0.126618i	−0.767576	−	0.640958i	$-0.778537\pi$
$499$	−2.82843	+	2.82843i	−0.126618	+	0.126618i	0.640958	+	0.767576i	$0.278537\pi$
$500$	8.48528	−	8.48528i	0.379473	−	0.379473i
$501$			16.0000i			0.714827i
$502$			28.0000i			1.24970i
$503$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$503$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$504$		0			0
$505$	14.1421	+	14.1421i	0.629317	+	0.629317i
$506$		0			0
$507$	6.36396	+	6.36396i	0.282633	+	0.282633i
$508$		0			0
$509$	30.0000			1.32973			0.664863	−	0.746965i	$-0.268490\pi$
$509$	30.0000			1.32973			0.664863	+	0.746965i	$0.268490\pi$
$510$		0			0
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	−2.82843	−	2.82843i	−0.124878	−	0.124878i
$514$	−2.00000			−0.0882162
$515$	11.3137	+	11.3137i	0.498542	+	0.498542i
$516$	−8.48528	+	8.48528i	−0.373544	+	0.373544i
$517$		0			0
$518$		0			0
$519$			6.00000i			0.263371i
$520$	2.82843	−	2.82843i	0.124035	−	0.124035i
$521$	15.5563	−	15.5563i	0.681536	−	0.681536i	−0.278810	−	0.960346i	$-0.589940\pi$
$521$	15.5563	−	15.5563i	0.681536	−	0.681536i	0.960346	+	0.278810i	$0.0899400\pi$
$522$	−7.07107	−	7.07107i	−0.309492	−	0.309492i
$523$	4.00000			0.174908			0.0874539	−	0.996169i	$-0.472127\pi$
$523$	4.00000			0.174908			0.0874539	+	0.996169i	$0.472127\pi$
$524$	8.48528	+	8.48528i	0.370681	+	0.370681i
$525$		0			0
$526$	−8.00000			−0.348817
$527$		0			0
$528$	−4.00000			−0.174078
$529$			23.0000i			1.00000i
$530$	8.48528	+	8.48528i	0.368577	+	0.368577i
$531$	−12.0000			−0.520756
$532$		0			0
$533$	14.1421	−	14.1421i	0.612564	−	0.612564i
$534$	−4.24264	+	4.24264i	−0.183597	+	0.183597i
$535$			8.00000i			0.345870i
$536$		−	12.0000i		−	0.518321i
$537$	−8.48528	+	8.48528i	−0.366167	+	0.366167i
$538$	−4.24264	+	4.24264i	−0.182913	+	0.182913i
$539$	19.7990	+	19.7990i	0.852803	+	0.852803i
$540$	2.00000			0.0860663
$541$	7.07107	+	7.07107i	0.304009	+	0.304009i	0.842580	−	0.538571i	$-0.181036\pi$
$541$	7.07107	+	7.07107i	0.304009	+	0.304009i	−0.538571	+	0.842580i	$0.681036\pi$
$542$		−	16.0000i		−	0.687259i
$543$	14.0000			0.600798
$544$		0			0
$545$	20.0000			0.856706
$546$		0			0
$547$	8.48528	+	8.48528i	0.362804	+	0.362804i	0.864844	−	0.502040i	$-0.167417\pi$
$547$	8.48528	+	8.48528i	0.362804	+	0.362804i	−0.502040	+	0.864844i	$0.667417\pi$
$548$	−10.0000			−0.427179
$549$	−7.07107	−	7.07107i	−0.301786	−	0.301786i
$550$	−2.82843	+	2.82843i	−0.120605	+	0.120605i
$551$	−28.2843	+	28.2843i	−1.20495	+	1.20495i
$552$		0			0
$553$		0			0
$554$	21.2132	−	21.2132i	0.901263	−	0.901263i
$555$	−2.82843	+	2.82843i	−0.120060	+	0.120060i
$556$	−2.82843	−	2.82843i	−0.119952	−	0.119952i
$557$	34.0000			1.44063			0.720313	−	0.693649i	$-0.243998\pi$
$557$	34.0000			1.44063			0.720313	+	0.693649i	$0.243998\pi$
$558$	−5.65685	−	5.65685i	−0.239474	−	0.239474i
$559$			24.0000i			1.01509i
$560$		0			0
$561$		0			0
$562$	−6.00000			−0.253095
$563$		−	36.0000i		−	1.51722i	−0.651546	−	0.758610i	$-0.725879\pi$
$563$		−	36.0000i		−	1.51722i	0.651546	−	0.758610i	$-0.274121\pi$
$564$		0			0
$565$	4.00000			0.168281
$566$	8.48528	+	8.48528i	0.356663	+	0.356663i
$567$		0			0
$568$		0			0
$569$		−	6.00000i		−	0.251533i	−0.992060	−	0.125767i	$-0.959861\pi$
$569$		−	6.00000i		−	0.251533i	0.992060	−	0.125767i	$-0.0401390\pi$
$570$		−	8.00000i		−	0.335083i
$571$	19.7990	−	19.7990i	0.828562	−	0.828562i	−0.158756	−	0.987318i	$-0.550748\pi$
$571$	19.7990	−	19.7990i	0.828562	−	0.828562i	0.987318	+	0.158756i	$0.0507483\pi$
$572$	−5.65685	+	5.65685i	−0.236525	+	0.236525i
$573$	−11.3137	−	11.3137i	−0.472637	−	0.472637i
$574$		0			0
$575$		0			0
$576$		−	1.00000i		−	0.0416667i
$577$	2.00000			0.0832611			0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000			0.0832611			0.0416305	+	0.999133i	$0.486745\pi$
$578$		0			0
$579$	18.0000			0.748054
$580$		−	20.0000i		−	0.830455i
$581$		0			0
$582$	14.0000			0.580319
$583$	−16.9706	−	16.9706i	−0.702849	−	0.702849i
$584$	−7.07107	+	7.07107i	−0.292603	+	0.292603i
$585$	2.82843	−	2.82843i	0.116941	−	0.116941i
$586$		−	26.0000i		−	1.07405i
$587$		−	20.0000i		−	0.825488i	−0.910847	−	0.412744i	$-0.864570\pi$
$587$		−	20.0000i		−	0.825488i	0.910847	−	0.412744i	$-0.135430\pi$
$588$	−4.94975	+	4.94975i	−0.204124	+	0.204124i
$589$	−22.6274	+	22.6274i	−0.932346	+	0.932346i
$590$	−16.9706	−	16.9706i	−0.698667	−	0.698667i
$591$	−14.0000			−0.575883
$592$	1.41421	+	1.41421i	0.0581238	+	0.0581238i
$593$			14.0000i			0.574911i	0.957794	+	0.287456i	$0.0928094\pi$
$593$			14.0000i			0.574911i	−0.957794	+	0.287456i	$0.907191\pi$
$594$	−4.00000			−0.164122
$595$		0			0
$596$	−10.0000			−0.409616
$597$		0			0
$598$		0			0
$599$	8.00000			0.326871			0.163436	−	0.986554i	$-0.447742\pi$
$599$	8.00000			0.326871			0.163436	+	0.986554i	$0.447742\pi$
$600$	−0.707107	−	0.707107i	−0.0288675	−	0.0288675i
$601$	4.24264	−	4.24264i	0.173061	−	0.173061i	−0.615262	−	0.788323i	$-0.710950\pi$
$601$	4.24264	−	4.24264i	0.173061	−	0.173061i	0.788323	+	0.615262i	$0.210950\pi$
$602$		0			0
$603$		−	12.0000i		−	0.488678i
$604$			24.0000i			0.976546i
$605$	−7.07107	+	7.07107i	−0.287480	+	0.287480i
$606$	7.07107	−	7.07107i	0.287242	−	0.287242i
$607$	−16.9706	−	16.9706i	−0.688814	−	0.688814i	0.273156	−	0.961970i	$-0.411933\pi$
$607$	−16.9706	−	16.9706i	−0.688814	−	0.688814i	−0.961970	+	0.273156i	$0.911933\pi$
$608$	−4.00000			−0.162221
$609$		0			0
$610$		−	20.0000i		−	0.809776i
$611$		0			0
$612$		0			0
$613$	38.0000			1.53481			0.767403	−	0.641165i	$-0.221549\pi$
$613$	38.0000			1.53481			0.767403	+	0.641165i	$0.221549\pi$
$614$			12.0000i			0.484281i
$615$	14.1421	+	14.1421i	0.570266	+	0.570266i
$616$		0			0
$617$	−4.24264	−	4.24264i	−0.170802	−	0.170802i	0.616530	−	0.787332i	$-0.288538\pi$
$617$	−4.24264	−	4.24264i	−0.170802	−	0.170802i	−0.787332	+	0.616530i	$0.788538\pi$
$618$	5.65685	−	5.65685i	0.227552	−	0.227552i
$619$	−14.1421	+	14.1421i	−0.568420	+	0.568420i	−0.931686	−	0.363265i	$-0.881662\pi$
$619$	−14.1421	+	14.1421i	−0.568420	+	0.568420i	0.363265	+	0.931686i	$0.381662\pi$
$620$		−	16.0000i		−	0.642575i
$621$		0			0
$622$		0			0
$623$		0			0
$624$	−1.41421	−	1.41421i	−0.0566139	−	0.0566139i
$625$	19.0000			0.760000
$626$	−7.07107	−	7.07107i	−0.282617	−	0.282617i
$627$			16.0000i			0.638978i
$628$	−2.00000			−0.0798087
$629$		0			0
$630$		0			0
$631$			24.0000i			0.955425i	0.878516	+	0.477712i	$0.158534\pi$
$631$			24.0000i			0.955425i	−0.878516	+	0.477712i	$0.841466\pi$
$632$	5.65685	+	5.65685i	0.225018	+	0.225018i
$633$	28.0000			1.11290
$634$	4.24264	+	4.24264i	0.168497	+	0.168497i
$635$		0			0
$636$	4.24264	−	4.24264i	0.168232	−	0.168232i
$637$			14.0000i			0.554700i
$638$			40.0000i			1.58362i
$639$		0			0
$640$	1.41421	−	1.41421i	0.0559017	−	0.0559017i
$641$	1.41421	+	1.41421i	0.0558581	+	0.0558581i	0.734484	−	0.678626i	$-0.237424\pi$
$641$	1.41421	+	1.41421i	0.0558581	+	0.0558581i	−0.678626	+	0.734484i	$0.737424\pi$
$642$	4.00000			0.157867
$643$	19.7990	+	19.7990i	0.780796	+	0.780796i	0.979965	−	0.199169i	$-0.0638243\pi$
$643$	19.7990	+	19.7990i	0.780796	+	0.780796i	−0.199169	+	0.979965i	$0.563824\pi$
$644$		0			0
$645$	−24.0000			−0.944999
$646$		0			0
$647$	−40.0000			−1.57256			−0.786281	−	0.617869i	$-0.787996\pi$
$647$	−40.0000			−1.57256			−0.786281	+	0.617869i	$0.787996\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	33.9411	+	33.9411i	1.33231	+	1.33231i
$650$	−2.00000			−0.0784465
$651$		0			0
$652$	−2.82843	+	2.82843i	−0.110770	+	0.110770i
$653$	4.24264	−	4.24264i	0.166027	−	0.166027i	−0.619203	−	0.785231i	$-0.712544\pi$
$653$	4.24264	−	4.24264i	0.166027	−	0.166027i	0.785231	+	0.619203i	$0.212544\pi$
$654$		−	10.0000i		−	0.391031i
$655$			24.0000i			0.937758i
$656$	7.07107	−	7.07107i	0.276079	−	0.276079i
$657$	−7.07107	+	7.07107i	−0.275869	+	0.275869i
$658$		0			0
$659$	−36.0000			−1.40236			−0.701180	−	0.712984i	$-0.747343\pi$
$659$	−36.0000			−1.40236			−0.701180	+	0.712984i	$0.747343\pi$
$660$	−5.65685	−	5.65685i	−0.220193	−	0.220193i
$661$		−	6.00000i		−	0.233373i	−0.993169	−	0.116686i	$-0.962773\pi$
$661$		−	6.00000i		−	0.233373i	0.993169	−	0.116686i	$-0.0372273\pi$
$662$	−20.0000			−0.777322
$663$		0			0
$664$	4.00000			0.155230
$665$		0			0
$666$	1.41421	+	1.41421i	0.0547997	+	0.0547997i
$667$		0			0
$668$	11.3137	+	11.3137i	0.437741	+	0.437741i
$669$	−11.3137	+	11.3137i	−0.437413	+	0.437413i
$670$	16.9706	−	16.9706i	0.655630	−	0.655630i
$671$			40.0000i			1.54418i
$672$		0			0
$673$	−32.5269	+	32.5269i	−1.25382	+	1.25382i	−0.299827	+	0.953994i	$0.596929\pi$
$673$	−32.5269	+	32.5269i	−1.25382	+	1.25382i	−0.953994	+	0.299827i	$0.903071\pi$
$674$	9.89949	−	9.89949i	0.381314	−	0.381314i
$675$	−0.707107	−	0.707107i	−0.0272166	−	0.0272166i
$676$	9.00000			0.346154
$677$	−32.5269	−	32.5269i	−1.25011	−	1.25011i	−0.955670	−	0.294441i	$-0.904866\pi$
$677$	−32.5269	−	32.5269i	−1.25011	−	1.25011i	−0.294441	−	0.955670i	$-0.595134\pi$
$678$		−	2.00000i		−	0.0768095i
$679$		0			0
$680$		0			0
$681$	4.00000			0.153280
$682$			32.0000i			1.22534i
$683$	14.1421	+	14.1421i	0.541134	+	0.541134i	0.923861	−	0.382727i	$-0.125015\pi$
$683$	14.1421	+	14.1421i	0.541134	+	0.541134i	−0.382727	+	0.923861i	$0.625015\pi$
$684$	−4.00000			−0.152944
$685$	−14.1421	−	14.1421i	−0.540343	−	0.540343i
$686$		0			0
$687$	−18.3848	+	18.3848i	−0.701423	+	0.701423i
$688$			12.0000i			0.457496i
$689$		−	12.0000i		−	0.457164i
$690$		0			0
$691$	19.7990	−	19.7990i	0.753189	−	0.753189i	−0.221884	−	0.975073i	$-0.571221\pi$
$691$	19.7990	−	19.7990i	0.753189	−	0.753189i	0.975073	+	0.221884i	$0.0712206\pi$
$692$	4.24264	+	4.24264i	0.161281	+	0.161281i
$693$		0			0
$694$	−19.7990	−	19.7990i	−0.751559	−	0.751559i
$695$		−	8.00000i		−	0.303457i
$696$	−10.0000			−0.379049
$697$		0			0
$698$	14.0000			0.529908
$699$		−	26.0000i		−	0.983410i
$700$		0			0
$701$	−46.0000			−1.73740			−0.868698	−	0.495342i	$-0.835043\pi$
$701$	−46.0000			−1.73740			−0.868698	+	0.495342i	$0.835043\pi$
$702$	−1.41421	−	1.41421i	−0.0533761	−	0.0533761i
$703$	5.65685	−	5.65685i	0.213352	−	0.213352i
$704$	−2.82843	+	2.82843i	−0.106600	+	0.106600i
$705$		0			0
$706$		−	30.0000i		−	1.12906i
$707$		0			0
$708$	−8.48528	+	8.48528i	−0.318896	+	0.318896i
$709$	32.5269	+	32.5269i	1.22157	+	1.22157i	0.967072	+	0.254501i	$0.0819114\pi$
$709$	32.5269	+	32.5269i	1.22157	+	1.22157i	0.254501	+	0.967072i	$0.418089\pi$
$710$		0			0
$711$	5.65685	+	5.65685i	0.212149	+	0.212149i
$712$			6.00000i			0.224860i
$713$		0			0
$714$		0			0
$715$	−16.0000			−0.598366
$716$			12.0000i			0.448461i
$717$		0			0
$718$	24.0000			0.895672
$719$	28.2843	+	28.2843i	1.05483	+	1.05483i	0.998407	+	0.0564181i	$0.0179680\pi$
$719$	28.2843	+	28.2843i	1.05483	+	1.05483i	0.0564181	+	0.998407i	$0.482032\pi$
$720$	1.41421	−	1.41421i	0.0527046	−	0.0527046i
$721$		0			0
$722$		−	3.00000i		−	0.111648i
$723$			2.00000i			0.0743808i
$724$	9.89949	−	9.89949i	0.367912	−	0.367912i
$725$	−7.07107	+	7.07107i	−0.262613	+	0.262613i
$726$	3.53553	+	3.53553i	0.131216	+	0.131216i
$727$	8.00000			0.296704			0.148352	−	0.988935i	$-0.452603\pi$
$727$	8.00000			0.296704			0.148352	+	0.988935i	$0.452603\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$	−20.0000			−0.740233
$731$		0			0
$732$	−10.0000			−0.369611
$733$		−	46.0000i		−	1.69905i	−0.527549	−	0.849524i	$-0.676889\pi$
$733$		−	46.0000i		−	1.69905i	0.527549	−	0.849524i	$-0.323111\pi$
$734$	−16.9706	−	16.9706i	−0.626395	−	0.626395i
$735$	−14.0000			−0.516398
$736$		0			0
$737$	−33.9411	+	33.9411i	−1.25024	+	1.25024i
$738$	7.07107	−	7.07107i	0.260290	−	0.260290i
$739$			52.0000i			1.91285i	0.291977	+	0.956425i	$0.405687\pi$
$739$			52.0000i			1.91285i	−0.291977	+	0.956425i	$0.594313\pi$
$740$			4.00000i			0.147043i
$741$	−5.65685	+	5.65685i	−0.207810	+	0.207810i
$742$		0			0
$743$	−11.3137	−	11.3137i	−0.415060	−	0.415060i	0.468437	−	0.883497i	$-0.344817\pi$
$743$	−11.3137	−	11.3137i	−0.415060	−	0.415060i	−0.883497	+	0.468437i	$0.844817\pi$
$744$	−8.00000			−0.293294
$745$	−14.1421	−	14.1421i	−0.518128	−	0.518128i
$746$		−	6.00000i		−	0.219676i
$747$	4.00000			0.146352
$748$		0			0
$749$		0			0
$750$		−	12.0000i		−	0.438178i
$751$	−5.65685	−	5.65685i	−0.206422	−	0.206422i	0.596323	−	0.802745i	$-0.296628\pi$
$751$	−5.65685	−	5.65685i	−0.206422	−	0.206422i	−0.802745	+	0.596323i	$0.796628\pi$
$752$		0			0
$753$	19.7990	+	19.7990i	0.721515	+	0.721515i
$754$	−14.1421	+	14.1421i	−0.515026	+	0.515026i
$755$	−33.9411	+	33.9411i	−1.23524	+	1.23524i
$756$		0			0
$757$		−	10.0000i		−	0.363456i	−0.983349	−	0.181728i	$-0.941831\pi$
$757$		−	10.0000i		−	0.363456i	0.983349	−	0.181728i	$-0.0581691\pi$
$758$	−2.82843	+	2.82843i	−0.102733	+	0.102733i
$759$		0			0
$760$	−5.65685	−	5.65685i	−0.205196	−	0.205196i
$761$	6.00000			0.217500			0.108750	−	0.994069i	$-0.465315\pi$
$761$	6.00000			0.217500			0.108750	+	0.994069i	$0.465315\pi$
$762$		0			0
$763$		0			0
$764$	−16.0000			−0.578860
$765$		0			0
$766$	−16.0000			−0.578103
$767$			24.0000i			0.866590i
$768$	−0.707107	−	0.707107i	−0.0255155	−	0.0255155i
$769$	30.0000			1.08183			0.540914	−	0.841078i	$-0.318079\pi$
$769$	30.0000			1.08183			0.540914	+	0.841078i	$0.318079\pi$
$770$		0			0
$771$	−1.41421	+	1.41421i	−0.0509317	+	0.0509317i
$772$	12.7279	−	12.7279i	0.458088	−	0.458088i
$773$			38.0000i			1.36677i	0.730061	+	0.683383i	$0.239492\pi$
$773$			38.0000i			1.36677i	−0.730061	+	0.683383i	$0.760508\pi$
$774$			12.0000i			0.431331i
$775$	−5.65685	+	5.65685i	−0.203200	+	0.203200i
$776$	9.89949	−	9.89949i	0.355371	−	0.355371i
$777$		0			0
$778$	26.0000			0.932145
$779$	−28.2843	−	28.2843i	−1.01339	−	1.01339i
$780$		−	4.00000i		−	0.143223i
$781$		0			0
$782$		0			0
$783$	−10.0000			−0.357371
$784$			7.00000i			0.250000i
$785$	−2.82843	−	2.82843i	−0.100951	−	0.100951i
$786$	12.0000			0.428026
$787$	2.82843	+	2.82843i	0.100823	+	0.100823i	0.755719	−	0.654896i	$-0.227288\pi$
$787$	2.82843	+	2.82843i	0.100823	+	0.100823i	−0.654896	+	0.755719i	$0.727288\pi$
$788$	−9.89949	+	9.89949i	−0.352655	+	0.352655i
$789$	−5.65685	+	5.65685i	−0.201389	+	0.201389i
$790$			16.0000i			0.569254i
$791$		0			0
$792$	−2.82843	+	2.82843i	−0.100504	+	0.100504i
$793$	−14.1421	+	14.1421i	−0.502202	+	0.502202i
$794$	−18.3848	−	18.3848i	−0.652451	−	0.652451i
$795$	12.0000			0.425596
$796$		0			0
$797$		−	14.0000i		−	0.495905i	−0.968772	−	0.247953i	$-0.920242\pi$
$797$		−	14.0000i		−	0.495905i	0.968772	−	0.247953i	$-0.0797578\pi$
$798$		0			0
$799$		0			0
$800$	−1.00000			−0.0353553
$801$			6.00000i			0.212000i
$802$	9.89949	+	9.89949i	0.349563	+	0.349563i
$803$	40.0000			1.41157
$804$	−8.48528	−	8.48528i	−0.299253	−	0.299253i
$805$		0			0
$806$	−11.3137	+	11.3137i	−0.398508	+	0.398508i
$807$			6.00000i			0.211210i
$808$		−	10.0000i		−	0.351799i
$809$	−15.5563	+	15.5563i	−0.546932	+	0.546932i	−0.925552	−	0.378620i	$-0.876399\pi$
$809$	−15.5563	+	15.5563i	−0.546932	+	0.546932i	0.378620	+	0.925552i	$0.376399\pi$
$810$	1.41421	−	1.41421i	0.0496904	−	0.0496904i
$811$	−14.1421	−	14.1421i	−0.496598	−	0.496598i	0.413780	−	0.910377i	$-0.364208\pi$
$811$	−14.1421	−	14.1421i	−0.496598	−	0.496598i	−0.910377	+	0.413780i	$0.864208\pi$
$812$		0			0
$813$	−11.3137	−	11.3137i	−0.396789	−	0.396789i
$814$		−	8.00000i		−	0.280400i
$815$	−8.00000			−0.280228
$816$		0			0
$817$	48.0000			1.67931
$818$		−	26.0000i		−	0.909069i
$819$		0			0
$820$	20.0000			0.698430
$821$	−24.0416	−	24.0416i	−0.839059	−	0.839059i	0.149676	−	0.988735i	$-0.452177\pi$
$821$	−24.0416	−	24.0416i	−0.839059	−	0.839059i	−0.988735	+	0.149676i	$0.952177\pi$
$822$	−7.07107	+	7.07107i	−0.246632	+	0.246632i
$823$	22.6274	−	22.6274i	0.788742	−	0.788742i	−0.192546	−	0.981288i	$-0.561674\pi$
$823$	22.6274	−	22.6274i	0.788742	−	0.788742i	0.981288	+	0.192546i	$0.0616744\pi$
$824$		−	8.00000i		−	0.278693i
$825$			4.00000i			0.139262i
$826$		0			0
$827$	14.1421	−	14.1421i	0.491770	−	0.491770i	−0.417093	−	0.908864i	$-0.636951\pi$
$827$	14.1421	−	14.1421i	0.491770	−	0.491770i	0.908864	+	0.417093i	$0.136951\pi$
$828$		0			0
$829$	34.0000			1.18087			0.590434	−	0.807086i	$-0.298956\pi$
$829$	34.0000			1.18087			0.590434	+	0.807086i	$0.298956\pi$
$830$	5.65685	+	5.65685i	0.196352	+	0.196352i
$831$		−	30.0000i		−	1.04069i
$832$	−2.00000			−0.0693375
$833$		0			0
$834$	−4.00000			−0.138509
$835$			32.0000i			1.10741i
$836$	11.3137	+	11.3137i	0.391293	+	0.391293i
$837$	−8.00000			−0.276520
$838$	2.82843	+	2.82843i	0.0977064	+	0.0977064i
$839$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$839$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$840$		0			0
$841$			71.0000i			2.44828i
$842$			22.0000i			0.758170i
$843$	−4.24264	+	4.24264i	−0.146124	+	0.146124i
$844$	19.7990	−	19.7990i	0.681509	−	0.681509i
$845$	12.7279	+	12.7279i	0.437854	+	0.437854i
$846$		0			0
$847$		0			0
$848$		−	6.00000i		−	0.206041i
$849$	12.0000			0.411839
$850$		0			0
$851$		0			0
$852$		0			0
$853$	1.41421	+	1.41421i	0.0484218	+	0.0484218i	0.730903	−	0.682481i	$-0.239099\pi$
$853$	1.41421	+	1.41421i	0.0484218	+	0.0484218i	−0.682481	+	0.730903i	$0.739099\pi$
$854$		0			0
$855$	−5.65685	−	5.65685i	−0.193460	−	0.193460i
$856$	2.82843	−	2.82843i	0.0966736	−	0.0966736i
$857$	−4.24264	+	4.24264i	−0.144926	+	0.144926i	−0.775847	−	0.630921i	$-0.782677\pi$
$857$	−4.24264	+	4.24264i	−0.144926	+	0.144926i	0.630921	+	0.775847i	$0.282677\pi$
$858$			8.00000i			0.273115i
$859$		−	36.0000i		−	1.22830i	−0.789188	−	0.614152i	$-0.789498\pi$
$859$		−	36.0000i		−	1.22830i	0.789188	−	0.614152i	$-0.210502\pi$
$860$	−16.9706	+	16.9706i	−0.578691	+	0.578691i
$861$		0			0
$862$	−5.65685	−	5.65685i	−0.192673	−	0.192673i
$863$	32.0000			1.08929			0.544646	−	0.838666i	$-0.316664\pi$
$863$	32.0000			1.08929			0.544646	+	0.838666i	$0.316664\pi$
$864$	−0.707107	−	0.707107i	−0.0240563	−	0.0240563i
$865$			12.0000i			0.408012i
$866$	−14.0000			−0.475739
$867$		0			0
$868$		0			0
$869$		−	32.0000i		−	1.08553i
$870$	−14.1421	−	14.1421i	−0.479463	−	0.479463i
$871$	−24.0000			−0.813209
$872$	−7.07107	−	7.07107i	−0.239457	−	0.239457i
$873$	9.89949	−	9.89949i	0.335047	−	0.335047i
$874$		0			0
$875$		0			0
$876$			10.0000i			0.337869i
$877$	15.5563	−	15.5563i	0.525301	−	0.525301i	−0.393867	−	0.919167i	$-0.628863\pi$
$877$	15.5563	−	15.5563i	0.525301	−	0.525301i	0.919167	+	0.393867i	$0.128863\pi$
$878$	−11.3137	+	11.3137i	−0.381819	+	0.381819i
$879$	−18.3848	−	18.3848i	−0.620103	−	0.620103i
$880$	−8.00000			−0.269680
$881$	−1.41421	−	1.41421i	−0.0476461	−	0.0476461i	0.682882	−	0.730528i	$-0.260726\pi$
$881$	−1.41421	−	1.41421i	−0.0476461	−	0.0476461i	−0.730528	+	0.682882i	$0.760726\pi$
$882$			7.00000i			0.235702i
$883$	36.0000			1.21150			0.605748	−	0.795656i	$-0.292874\pi$
$883$	36.0000			1.21150			0.605748	+	0.795656i	$0.292874\pi$
$884$		0			0
$885$	−24.0000			−0.806751
$886$			4.00000i			0.134383i
$887$	33.9411	+	33.9411i	1.13963	+	1.13963i	0.988516	+	0.151115i	$0.0482865\pi$
$887$	33.9411	+	33.9411i	1.13963	+	1.13963i	0.151115	+	0.988516i	$0.451714\pi$
$888$	2.00000			0.0671156
$889$		0			0
$890$	−8.48528	+	8.48528i	−0.284427	+	0.284427i
$891$	−2.82843	+	2.82843i	−0.0947559	+	0.0947559i
$892$			16.0000i			0.535720i
$893$		0			0
$894$	−7.07107	+	7.07107i	−0.236492	+	0.236492i
$895$	−16.9706	+	16.9706i	−0.567263	+	0.567263i
$896$		0			0
$897$		0			0
$898$	−1.41421	−	1.41421i	−0.0471929	−	0.0471929i
$899$			80.0000i			2.66815i
$900$	−1.00000			−0.0333333
$901$		0			0
$902$	−40.0000			−1.33185
$903$		0			0
$904$	−1.41421	−	1.41421i	−0.0470360	−	0.0470360i
$905$	28.0000			0.930751
$906$	16.9706	+	16.9706i	0.563809	+	0.563809i
$907$	−19.7990	+	19.7990i	−0.657415	+	0.657415i	−0.954768	−	0.297353i	$-0.903896\pi$
$907$	−19.7990	+	19.7990i	−0.657415	+	0.657415i	0.297353	+	0.954768i	$0.403896\pi$
$908$	2.82843	−	2.82843i	0.0938647	−	0.0938647i
$909$		−	10.0000i		−	0.331679i
$910$		0			0
$911$	5.65685	−	5.65685i	0.187420	−	0.187420i	−0.607160	−	0.794580i	$-0.707691\pi$
$911$	5.65685	−	5.65685i	0.187420	−	0.187420i	0.794580	+	0.607160i	$0.207691\pi$
$912$	−2.82843	+	2.82843i	−0.0936586	+	0.0936586i
$913$	−11.3137	−	11.3137i	−0.374429	−	0.374429i
$914$	−10.0000			−0.330771
$915$	−14.1421	−	14.1421i	−0.467525	−	0.467525i
$916$			26.0000i			0.859064i
$917$		0			0
$918$		0			0
$919$	24.0000			0.791687			0.395843	−	0.918318i	$-0.370452\pi$
$919$	24.0000			0.791687			0.395843	+	0.918318i	$0.370452\pi$
$920$		0			0
$921$	8.48528	+	8.48528i	0.279600	+	0.279600i
$922$	−30.0000			−0.987997
$923$		0			0
$924$		0			0
$925$	1.41421	−	1.41421i	0.0464991	−	0.0464991i
$926$			32.0000i			1.05159i
$927$		−	8.00000i		−	0.262754i
$928$	−7.07107	+	7.07107i	−0.232119	+	0.232119i
$929$	−1.41421	+	1.41421i	−0.0463988	+	0.0463988i	−0.729926	−	0.683527i	$-0.760445\pi$
$929$	−1.41421	+	1.41421i	−0.0463988	+	0.0463988i	0.683527	+	0.729926i	$0.260445\pi$
$930$	−11.3137	−	11.3137i	−0.370991	−	0.370991i
$931$	28.0000			0.917663
$932$	−18.3848	−	18.3848i	−0.602213	−	0.602213i
$933$		0			0
$934$	−12.0000			−0.392652
$935$		0			0
$936$	−2.00000			−0.0653720
$937$			22.0000i			0.718709i	0.933201	+	0.359354i	$0.117003\pi$
$937$			22.0000i			0.718709i	−0.933201	+	0.359354i	$0.882997\pi$
$938$		0			0
$939$	−10.0000			−0.326338
$940$		0			0
$941$	7.07107	−	7.07107i	0.230510	−	0.230510i	−0.582395	−	0.812906i	$-0.697884\pi$
$941$	7.07107	−	7.07107i	0.230510	−	0.230510i	0.812906	+	0.582395i	$0.197884\pi$
$942$	−1.41421	+	1.41421i	−0.0460776	+	0.0460776i
$943$		0			0
$944$			12.0000i			0.390567i
$945$		0			0
$946$	33.9411	−	33.9411i	1.10352	−	1.10352i
$947$	−19.7990	−	19.7990i	−0.643381	−	0.643381i	0.308004	−	0.951385i	$-0.400339\pi$
$947$	−19.7990	−	19.7990i	−0.643381	−	0.643381i	−0.951385	+	0.308004i	$0.900339\pi$
$948$	8.00000			0.259828
$949$	14.1421	+	14.1421i	0.459073	+	0.459073i
$950$			4.00000i			0.129777i
$951$	6.00000			0.194563
$952$		0			0
$953$	−6.00000			−0.194359			−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000			−0.194359			−0.0971795	+	0.995267i	$0.530982\pi$
$954$		−	6.00000i		−	0.194257i
$955$	−22.6274	−	22.6274i	−0.732206	−	0.732206i
$956$		0			0
$957$	28.2843	+	28.2843i	0.914301	+	0.914301i
$958$	−16.9706	+	16.9706i	−0.548294	+	0.548294i
$959$		0			0
$960$		−	2.00000i		−	0.0645497i
$961$			33.0000i			1.06452i
$962$	2.82843	−	2.82843i	0.0911922	−	0.0911922i
$963$	2.82843	−	2.82843i	0.0911448	−	0.0911448i
$964$	1.41421	+	1.41421i	0.0455488	+	0.0455488i
$965$	36.0000			1.15888
$966$		0			0
$967$			8.00000i			0.257263i	0.991692	+	0.128631i	$0.0410584\pi$
$967$			8.00000i			0.257263i	−0.991692	+	0.128631i	$0.958942\pi$
$968$	5.00000			0.160706
$969$		0			0
$970$	28.0000			0.899026
$971$			4.00000i			0.128366i	0.997938	+	0.0641831i	$0.0204442\pi$
$971$			4.00000i			0.128366i	−0.997938	+	0.0641831i	$0.979556\pi$
$972$	−0.707107	−	0.707107i	−0.0226805	−	0.0226805i
$973$		0			0
$974$	−11.3137	−	11.3137i	−0.362515	−	0.362515i
$975$	−1.41421	+	1.41421i	−0.0452911	+	0.0452911i
$976$	−7.07107	+	7.07107i	−0.226339	+	0.226339i
$977$		−	46.0000i		−	1.47167i	−0.677161	−	0.735835i	$-0.736790\pi$
$977$		−	46.0000i		−	1.47167i	0.677161	−	0.735835i	$-0.263210\pi$
$978$			4.00000i			0.127906i
$979$	16.9706	−	16.9706i	0.542382	−	0.542382i
$980$	−9.89949	+	9.89949i	−0.316228	+	0.316228i
$981$	−7.07107	−	7.07107i	−0.225762	−	0.225762i
$982$	−12.0000			−0.382935
$983$	−33.9411	−	33.9411i	−1.08255	−	1.08255i	−0.996271	−	0.0862831i	$-0.972501\pi$
$983$	−33.9411	−	33.9411i	−1.08255	−	1.08255i	−0.0862831	−	0.996271i	$-0.527499\pi$
$984$		−	10.0000i		−	0.318788i
$985$	−28.0000			−0.892154
$986$		0			0
$987$		0			0
$988$			8.00000i			0.254514i
$989$		0			0
$990$	−8.00000			−0.254257
$991$	−28.2843	−	28.2843i	−0.898479	−	0.898479i	0.0968222	−	0.995302i	$-0.469132\pi$
$991$	−28.2843	−	28.2843i	−0.898479	−	0.898479i	−0.995302	+	0.0968222i	$0.969132\pi$
$992$	−5.65685	+	5.65685i	−0.179605	+	0.179605i
$993$	−14.1421	+	14.1421i	−0.448787	+	0.448787i
$994$		0			0
$995$		0			0
$996$	2.82843	−	2.82843i	0.0896221	−	0.0896221i
$997$	1.41421	−	1.41421i	0.0447886	−	0.0447886i	−0.684358	−	0.729146i	$-0.739917\pi$
$997$	1.41421	−	1.41421i	0.0447886	−	0.0447886i	0.729146	+	0.684358i	$0.239917\pi$
$998$	2.82843	+	2.82843i	0.0895323	+	0.0895323i
$999$	2.00000			0.0632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1734.2.f.e.829.1		4
17.2	even	8		1734.2.a.j.1.1		1
17.4	even	4	inner	1734.2.f.e.1483.1		4
17.8	even	8		1734.2.b.b.577.2		2
17.9	even	8		1734.2.b.b.577.1		2
17.13	even	4	inner	1734.2.f.e.1483.2		4
17.15	even	8		102.2.a.c.1.1	✓	1
17.16	even	2	inner	1734.2.f.e.829.2		4
51.2	odd	8		5202.2.a.c.1.1		1
51.32	odd	8		306.2.a.b.1.1		1
68.15	odd	8		816.2.a.b.1.1		1
85.32	odd	8		2550.2.d.m.2449.2		2
85.49	even	8		2550.2.a.c.1.1		1
85.83	odd	8		2550.2.d.m.2449.1		2
119.83	odd	8		4998.2.a.be.1.1		1
136.83	odd	8		3264.2.a.bc.1.1		1
136.117	even	8		3264.2.a.m.1.1		1
204.83	even	8		2448.2.a.p.1.1		1
255.134	odd	8		7650.2.a.ca.1.1		1
408.83	even	8		9792.2.a.l.1.1		1
408.389	odd	8		9792.2.a.k.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
102.2.a.c.1.1	✓	1	17.15	even	8
306.2.a.b.1.1		1	51.32	odd	8
816.2.a.b.1.1		1	68.15	odd	8
1734.2.a.j.1.1		1	17.2	even	8
1734.2.b.b.577.1		2	17.9	even	8
1734.2.b.b.577.2		2	17.8	even	8
1734.2.f.e.829.1		4	1.1	even	1	trivial
1734.2.f.e.829.2		4	17.16	even	2	inner
1734.2.f.e.1483.1		4	17.4	even	4	inner
1734.2.f.e.1483.2		4	17.13	even	4	inner
2448.2.a.p.1.1		1	204.83	even	8
2550.2.a.c.1.1		1	85.49	even	8
2550.2.d.m.2449.1		2	85.83	odd	8
2550.2.d.m.2449.2		2	85.32	odd	8
3264.2.a.m.1.1		1	136.117	even	8
3264.2.a.bc.1.1		1	136.83	odd	8
4998.2.a.be.1.1		1	119.83	odd	8
5202.2.a.c.1.1		1	51.2	odd	8
7650.2.a.ca.1.1		1	255.134	odd	8
9792.2.a.k.1.1		1	408.389	odd	8
9792.2.a.l.1.1		1	408.83	even	8

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:	\( N \)	\(=\)	\( 1734 = 2 \cdot 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1734.f (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-1.41421 - 1.41421i) q^{5} +(-0.707107 + 0.707107i) q^{6} +1.00000i q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-1.41421 - 1.41421i) q^{5} +(-0.707107 + 0.707107i) q^{6} +1.00000i q^{8} +1.00000i q^{9} +(-1.41421 + 1.41421i) q^{10} +(2.82843 - 2.82843i) q^{11} +(0.707107 + 0.707107i) q^{12} +2.00000 q^{13} +2.00000i q^{15} +1.00000 q^{16} +1.00000 q^{18} -4.00000i q^{19} +(1.41421 + 1.41421i) q^{20} +(-2.82843 - 2.82843i) q^{22} +(0.707107 - 0.707107i) q^{24} -1.00000i q^{25} -2.00000i q^{26} +(0.707107 - 0.707107i) q^{27} +(-7.07107 - 7.07107i) q^{29} +2.00000 q^{30} +(-5.65685 - 5.65685i) q^{31} -1.00000i q^{32} -4.00000 q^{33} -1.00000i q^{36} +(1.41421 + 1.41421i) q^{37} -4.00000 q^{38} +(-1.41421 - 1.41421i) q^{39} +(1.41421 - 1.41421i) q^{40} +(7.07107 - 7.07107i) q^{41} +12.0000i q^{43} +(-2.82843 + 2.82843i) q^{44} +(1.41421 - 1.41421i) q^{45} +(-0.707107 - 0.707107i) q^{48} +7.00000i q^{49} -1.00000 q^{50} -2.00000 q^{52} -6.00000i q^{53} +(-0.707107 - 0.707107i) q^{54} -8.00000 q^{55} +(-2.82843 + 2.82843i) q^{57} +(-7.07107 + 7.07107i) q^{58} +12.0000i q^{59} -2.00000i q^{60} +(-7.07107 + 7.07107i) q^{61} +(-5.65685 + 5.65685i) q^{62} -1.00000 q^{64} +(-2.82843 - 2.82843i) q^{65} +4.00000i q^{66} -12.0000 q^{67} -1.00000 q^{72} +(7.07107 + 7.07107i) q^{73} +(1.41421 - 1.41421i) q^{74} +(-0.707107 + 0.707107i) q^{75} +4.00000i q^{76} +(-1.41421 + 1.41421i) q^{78} +(5.65685 - 5.65685i) q^{79} +(-1.41421 - 1.41421i) q^{80} -1.00000 q^{81} +(-7.07107 - 7.07107i) q^{82} -4.00000i q^{83} +12.0000 q^{86} +10.0000i q^{87} +(2.82843 + 2.82843i) q^{88} +6.00000 q^{89} +(-1.41421 - 1.41421i) q^{90} +8.00000i q^{93} +(-5.65685 + 5.65685i) q^{95} +(-0.707107 + 0.707107i) q^{96} +(-9.89949 - 9.89949i) q^{97} +7.00000 q^{98} +(2.82843 + 2.82843i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4}+O(q^{10}) \) 4 * q - 4 * q^4	\( 4 q - 4 q^{4} + 8 q^{13} + 4 q^{16} + 4 q^{18} + 8 q^{30} - 16 q^{33} - 16 q^{38} - 4 q^{50} - 8 q^{52} - 32 q^{55} - 4 q^{64} - 48 q^{67} - 4 q^{72} - 4 q^{81} + 48 q^{86} + 24 q^{89} + 28 q^{98}+O(q^{100}) \) 4 * q - 4 * q^4 + 8 * q^13 + 4 * q^16 + 4 * q^18 + 8 * q^30 - 16 * q^33 - 16 * q^38 - 4 * q^50 - 8 * q^52 - 32 * q^55 - 4 * q^64 - 48 * q^67 - 4 * q^72 - 4 * q^81 + 48 * q^86 + 24 * q^89 + 28 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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