LMFDB - Embedded newform 666.3.i.c.487.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [666,3,Mod(253,666)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(666, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("666.253");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	666.i (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$18.1471856064$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 74)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			487.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	666.487
Dual form			666.3.i.c.253.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} -2.00000i q^{4} +(6.00000 + 6.00000i) q^{5} +5.00000 q^{7} +(2.00000 + 2.00000i) q^{8} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} -2.00000i q^{4} +(6.00000 + 6.00000i) q^{5} +5.00000 q^{7} +(2.00000 + 2.00000i) q^{8} -12.0000 q^{10} -5.00000i q^{11} +(12.0000 + 12.0000i) q^{13} +(-5.00000 + 5.00000i) q^{14} -4.00000 q^{16} +(13.0000 + 13.0000i) q^{17} +(1.00000 + 1.00000i) q^{19} +(12.0000 - 12.0000i) q^{20} +(5.00000 + 5.00000i) q^{22} +(-17.0000 - 17.0000i) q^{23} +47.0000i q^{25} -24.0000 q^{26} -10.0000i q^{28} +(19.0000 - 19.0000i) q^{29} +(36.0000 - 36.0000i) q^{31} +(4.00000 - 4.00000i) q^{32} -26.0000 q^{34} +(30.0000 + 30.0000i) q^{35} +37.0000i q^{37} -2.00000 q^{38} +24.0000i q^{40} -25.0000i q^{41} +(-48.0000 - 48.0000i) q^{43} -10.0000 q^{44} +34.0000 q^{46} -55.0000 q^{47} -24.0000 q^{49} +(-47.0000 - 47.0000i) q^{50} +(24.0000 - 24.0000i) q^{52} +35.0000 q^{53} +(30.0000 - 30.0000i) q^{55} +(10.0000 + 10.0000i) q^{56} +38.0000i q^{58} +(54.0000 + 54.0000i) q^{59} +(6.00000 - 6.00000i) q^{61} +72.0000i q^{62} +8.00000i q^{64} +144.000i q^{65} +84.0000i q^{67} +(26.0000 - 26.0000i) q^{68} -60.0000 q^{70} -7.00000 q^{71} +109.000i q^{73} +(-37.0000 - 37.0000i) q^{74} +(2.00000 - 2.00000i) q^{76} -25.0000i q^{77} +(41.0000 + 41.0000i) q^{79} +(-24.0000 - 24.0000i) q^{80} +(25.0000 + 25.0000i) q^{82} +55.0000 q^{83} +156.000i q^{85} +96.0000 q^{86} +(10.0000 - 10.0000i) q^{88} +(19.0000 - 19.0000i) q^{89} +(60.0000 + 60.0000i) q^{91} +(-34.0000 + 34.0000i) q^{92} +(55.0000 - 55.0000i) q^{94} +12.0000i q^{95} +(-78.0000 - 78.0000i) q^{97} +(24.0000 - 24.0000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 12 q^{5} + 10 q^{7} + 4 q^{8}+O(q^{10}) $ 2 * q - 2 * q^2 + 12 * q^5 + 10 * q^7 + 4 * q^8	$ 2 q - 2 q^{2} + 12 q^{5} + 10 q^{7} + 4 q^{8} - 24 q^{10} + 24 q^{13} - 10 q^{14} - 8 q^{16} + 26 q^{17} + 2 q^{19} + 24 q^{20} + 10 q^{22} - 34 q^{23} - 48 q^{26} + 38 q^{29} + 72 q^{31} + 8 q^{32} - 52 q^{34} + 60 q^{35} - 4 q^{38} - 96 q^{43} - 20 q^{44} + 68 q^{46} - 110 q^{47} - 48 q^{49} - 94 q^{50} + 48 q^{52} + 70 q^{53} + 60 q^{55} + 20 q^{56} + 108 q^{59} + 12 q^{61} + 52 q^{68} - 120 q^{70} - 14 q^{71} - 74 q^{74} + 4 q^{76} + 82 q^{79} - 48 q^{80} + 50 q^{82} + 110 q^{83} + 192 q^{86} + 20 q^{88} + 38 q^{89} + 120 q^{91} - 68 q^{92} + 110 q^{94} - 156 q^{97} + 48 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 + 12 * q^5 + 10 * q^7 + 4 * q^8 - 24 * q^10 + 24 * q^13 - 10 * q^14 - 8 * q^16 + 26 * q^17 + 2 * q^19 + 24 * q^20 + 10 * q^22 - 34 * q^23 - 48 * q^26 + 38 * q^29 + 72 * q^31 + 8 * q^32 - 52 * q^34 + 60 * q^35 - 4 * q^38 - 96 * q^43 - 20 * q^44 + 68 * q^46 - 110 * q^47 - 48 * q^49 - 94 * q^50 + 48 * q^52 + 70 * q^53 + 60 * q^55 + 20 * q^56 + 108 * q^59 + 12 * q^61 + 52 * q^68 - 120 * q^70 - 14 * q^71 - 74 * q^74 + 4 * q^76 + 82 * q^79 - 48 * q^80 + 50 * q^82 + 110 * q^83 + 192 * q^86 + 20 * q^88 + 38 * q^89 + 120 * q^91 - 68 * q^92 + 110 * q^94 - 156 * q^97 + 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$		−	2.00000i		−	0.500000i
$5$	6.00000	+	6.00000i	1.20000	+	1.20000i	0.974166	+	0.225834i	$0.0725108\pi$
$5$	6.00000	+	6.00000i	1.20000	+	1.20000i	0.225834	+	0.974166i	$0.427489\pi$
$6$		0			0
$7$	5.00000			0.714286			0.357143	−	0.934050i	$-0.383751\pi$
$7$	5.00000			0.714286			0.357143	+	0.934050i	$0.383751\pi$
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$		0			0
$10$	−12.0000			−1.20000
$11$		−	5.00000i		−	0.454545i	−0.973831	−	0.227273i	$-0.927019\pi$
$11$		−	5.00000i		−	0.454545i	0.973831	−	0.227273i	$-0.0729809\pi$
$12$		0			0
$13$	12.0000	+	12.0000i	0.923077	+	0.923077i	0.997246	−	0.0741688i	$-0.0236304\pi$
$13$	12.0000	+	12.0000i	0.923077	+	0.923077i	−0.0741688	+	0.997246i	$0.523630\pi$
$14$	−5.00000	+	5.00000i	−0.357143	+	0.357143i
$15$		0			0
$16$	−4.00000			−0.250000
$17$	13.0000	+	13.0000i	0.764706	+	0.764706i	0.977169	−	0.212463i	$-0.0681486\pi$
$17$	13.0000	+	13.0000i	0.764706	+	0.764706i	−0.212463	+	0.977169i	$0.568149\pi$
$18$		0			0
$19$	1.00000	+	1.00000i	0.0526316	+	0.0526316i	0.732933	−	0.680301i	$-0.238151\pi$
$19$	1.00000	+	1.00000i	0.0526316	+	0.0526316i	−0.680301	+	0.732933i	$0.738151\pi$
$20$	12.0000	−	12.0000i	0.600000	−	0.600000i
$21$		0			0
$22$	5.00000	+	5.00000i	0.227273	+	0.227273i
$23$	−17.0000	−	17.0000i	−0.739130	−	0.739130i	0.233279	−	0.972410i	$-0.425054\pi$
$23$	−17.0000	−	17.0000i	−0.739130	−	0.739130i	−0.972410	+	0.233279i	$0.925054\pi$
$24$		0			0
$25$			47.0000i			1.88000i
$26$	−24.0000			−0.923077
$27$		0			0
$28$		−	10.0000i		−	0.357143i
$29$	19.0000	−	19.0000i	0.655172	−	0.655172i	−0.299061	−	0.954234i	$-0.596674\pi$
$29$	19.0000	−	19.0000i	0.655172	−	0.655172i	0.954234	+	0.299061i	$0.0966736\pi$
$30$		0			0
$31$	36.0000	−	36.0000i	1.16129	−	1.16129i	0.177097	−	0.984193i	$-0.443329\pi$
$31$	36.0000	−	36.0000i	1.16129	−	1.16129i	0.984193	−	0.177097i	$-0.0566706\pi$
$32$	4.00000	−	4.00000i	0.125000	−	0.125000i
$33$		0			0
$34$	−26.0000			−0.764706
$35$	30.0000	+	30.0000i	0.857143	+	0.857143i
$36$		0			0
$37$			37.0000i			1.00000i
$37$			37.0000i			1.00000i
$38$	−2.00000			−0.0526316
$39$		0			0
$40$			24.0000i			0.600000i
$41$		−	25.0000i		−	0.609756i	−0.952391	−	0.304878i	$-0.901384\pi$
$41$		−	25.0000i		−	0.609756i	0.952391	−	0.304878i	$-0.0986157\pi$
$42$		0			0
$43$	−48.0000	−	48.0000i	−1.11628	−	1.11628i	−0.992283	−	0.123996i	$-0.960429\pi$
$43$	−48.0000	−	48.0000i	−1.11628	−	1.11628i	−0.123996	−	0.992283i	$-0.539571\pi$
$44$	−10.0000			−0.227273
$45$		0			0
$46$	34.0000			0.739130
$47$	−55.0000			−1.17021			−0.585106	−	0.810957i	$-0.698947\pi$
$47$	−55.0000			−1.17021			−0.585106	+	0.810957i	$0.698947\pi$
$48$		0			0
$49$	−24.0000			−0.489796
$50$	−47.0000	−	47.0000i	−0.940000	−	0.940000i
$51$		0			0
$52$	24.0000	−	24.0000i	0.461538	−	0.461538i
$53$	35.0000			0.660377			0.330189	−	0.943915i	$-0.392888\pi$
$53$	35.0000			0.660377			0.330189	+	0.943915i	$0.392888\pi$
$54$		0			0
$55$	30.0000	−	30.0000i	0.545455	−	0.545455i
$56$	10.0000	+	10.0000i	0.178571	+	0.178571i
$57$		0			0
$58$			38.0000i			0.655172i
$59$	54.0000	+	54.0000i	0.915254	+	0.915254i	0.996679	−	0.0814252i	$-0.0259472\pi$
$59$	54.0000	+	54.0000i	0.915254	+	0.915254i	−0.0814252	+	0.996679i	$0.525947\pi$
$60$		0			0
$61$	6.00000	−	6.00000i	0.0983607	−	0.0983607i	−0.656214	−	0.754575i	$-0.727843\pi$
$61$	6.00000	−	6.00000i	0.0983607	−	0.0983607i	0.754575	+	0.656214i	$0.227843\pi$
$62$			72.0000i			1.16129i
$63$		0			0
$64$			8.00000i			0.125000i
$65$			144.000i			2.21538i
$66$		0			0
$67$			84.0000i			1.25373i	0.779127	+	0.626866i	$0.215663\pi$
$67$			84.0000i			1.25373i	−0.779127	+	0.626866i	$0.784337\pi$
$68$	26.0000	−	26.0000i	0.382353	−	0.382353i
$69$		0			0
$70$	−60.0000			−0.857143
$71$	−7.00000			−0.0985915			−0.0492958	−	0.998784i	$-0.515698\pi$
$71$	−7.00000			−0.0985915			−0.0492958	+	0.998784i	$0.515698\pi$
$72$		0			0
$73$			109.000i			1.49315i	0.665301	+	0.746575i	$0.268303\pi$
$73$			109.000i			1.49315i	−0.665301	+	0.746575i	$0.731697\pi$
$74$	−37.0000	−	37.0000i	−0.500000	−	0.500000i
$75$		0			0
$76$	2.00000	−	2.00000i	0.0263158	−	0.0263158i
$77$		−	25.0000i		−	0.324675i
$78$		0			0
$79$	41.0000	+	41.0000i	0.518987	+	0.518987i	0.917265	−	0.398278i	$-0.130392\pi$
$79$	41.0000	+	41.0000i	0.518987	+	0.518987i	−0.398278	+	0.917265i	$0.630392\pi$
$80$	−24.0000	−	24.0000i	−0.300000	−	0.300000i
$81$		0			0
$82$	25.0000	+	25.0000i	0.304878	+	0.304878i
$83$	55.0000			0.662651			0.331325	−	0.943517i	$-0.392504\pi$
$83$	55.0000			0.662651			0.331325	+	0.943517i	$0.392504\pi$
$84$		0			0
$85$			156.000i			1.83529i
$86$	96.0000			1.11628
$87$		0			0
$88$	10.0000	−	10.0000i	0.113636	−	0.113636i
$89$	19.0000	−	19.0000i	0.213483	−	0.213483i	−0.592262	−	0.805745i	$-0.701765\pi$
$89$	19.0000	−	19.0000i	0.213483	−	0.213483i	0.805745	+	0.592262i	$0.201765\pi$
$90$		0			0
$91$	60.0000	+	60.0000i	0.659341	+	0.659341i
$92$	−34.0000	+	34.0000i	−0.369565	+	0.369565i
$93$		0			0
$94$	55.0000	−	55.0000i	0.585106	−	0.585106i
$95$			12.0000i			0.126316i
$96$		0			0
$97$	−78.0000	−	78.0000i	−0.804124	−	0.804124i	0.179614	−	0.983737i	$-0.442515\pi$
$97$	−78.0000	−	78.0000i	−0.804124	−	0.804124i	−0.983737	+	0.179614i	$0.942515\pi$
$98$	24.0000	−	24.0000i	0.244898	−	0.244898i
$99$		0			0
$100$	94.0000			0.940000
$101$		−	35.0000i		−	0.346535i	−0.984875	−	0.173267i	$-0.944568\pi$
$101$		−	35.0000i		−	0.346535i	0.984875	−	0.173267i	$-0.0554325\pi$
$102$		0			0
$103$	−132.000	+	132.000i	−1.28155	+	1.28155i	−0.341770	+	0.939784i	$0.611026\pi$
$103$	−132.000	+	132.000i	−1.28155	+	1.28155i	−0.939784	+	0.341770i	$0.888974\pi$
$104$			48.0000i			0.461538i
$105$		0			0
$106$	−35.0000	+	35.0000i	−0.330189	+	0.330189i
$107$	−120.000			−1.12150			−0.560748	−	0.827987i	$-0.689486\pi$
$107$	−120.000			−1.12150			−0.560748	+	0.827987i	$0.689486\pi$
$108$		0			0
$109$	−19.0000	−	19.0000i	−0.174312	−	0.174312i	0.614559	−	0.788871i	$-0.289334\pi$
$109$	−19.0000	−	19.0000i	−0.174312	−	0.174312i	−0.788871	+	0.614559i	$0.789334\pi$
$110$			60.0000i			0.545455i
$111$		0			0
$112$	−20.0000			−0.178571
$113$	−43.0000	+	43.0000i	−0.380531	+	0.380531i	−0.871293	−	0.490762i	$-0.836718\pi$
$113$	−43.0000	+	43.0000i	−0.380531	+	0.380531i	0.490762	+	0.871293i	$0.336718\pi$
$114$		0			0
$115$		−	204.000i		−	1.77391i
$116$	−38.0000	−	38.0000i	−0.327586	−	0.327586i
$117$		0			0
$118$	−108.000			−0.915254
$119$	65.0000	+	65.0000i	0.546218	+	0.546218i
$120$		0			0
$121$	96.0000			0.793388
$122$			12.0000i			0.0983607i
$123$		0			0
$124$	−72.0000	−	72.0000i	−0.580645	−	0.580645i
$125$	−132.000	+	132.000i	−1.05600	+	1.05600i
$126$		0			0
$127$	−5.00000			−0.0393701			−0.0196850	−	0.999806i	$-0.506266\pi$
$127$	−5.00000			−0.0393701			−0.0196850	+	0.999806i	$0.506266\pi$
$128$	−8.00000	−	8.00000i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	−144.000	−	144.000i	−1.10769	−	1.10769i
$131$	−151.000	+	151.000i	−1.15267	+	1.15267i	−0.166657	+	0.986015i	$0.553297\pi$
$131$	−151.000	+	151.000i	−1.15267	+	1.15267i	−0.986015	+	0.166657i	$0.946703\pi$
$132$		0			0
$133$	5.00000	+	5.00000i	0.0375940	+	0.0375940i
$134$	−84.0000	−	84.0000i	−0.626866	−	0.626866i
$135$		0			0
$136$			52.0000i			0.382353i
$137$	180.000			1.31387			0.656934	−	0.753948i	$-0.271853\pi$
$137$	180.000			1.31387			0.656934	+	0.753948i	$0.271853\pi$
$138$		0			0
$139$		−	180.000i		−	1.29496i	−0.762081	−	0.647482i	$-0.775822\pi$
$139$		−	180.000i		−	1.29496i	0.762081	−	0.647482i	$-0.224178\pi$
$140$	60.0000	−	60.0000i	0.428571	−	0.428571i
$141$		0			0
$142$	7.00000	−	7.00000i	0.0492958	−	0.0492958i
$143$	60.0000	−	60.0000i	0.419580	−	0.419580i
$144$		0			0
$145$	228.000			1.57241
$146$	−109.000	−	109.000i	−0.746575	−	0.746575i
$147$		0			0
$148$	74.0000			0.500000
$149$	−47.0000			−0.315436			−0.157718	−	0.987484i	$-0.550414\pi$
$149$	−47.0000			−0.315436			−0.157718	+	0.987484i	$0.550414\pi$
$150$		0			0
$151$		−	180.000i		−	1.19205i	−0.802965	−	0.596026i	$-0.796745\pi$
$151$		−	180.000i		−	1.19205i	0.802965	−	0.596026i	$-0.203255\pi$
$152$			4.00000i			0.0263158i
$153$		0			0
$154$	25.0000	+	25.0000i	0.162338	+	0.162338i
$155$	432.000			2.78710
$156$		0			0
$157$	−95.0000			−0.605096			−0.302548	−	0.953134i	$-0.597837\pi$
$157$	−95.0000			−0.605096			−0.302548	+	0.953134i	$0.597837\pi$
$158$	−82.0000			−0.518987
$159$		0			0
$160$	48.0000			0.300000
$161$	−85.0000	−	85.0000i	−0.527950	−	0.527950i
$162$		0			0
$163$	−102.000	+	102.000i	−0.625767	+	0.625767i	−0.947000	−	0.321233i	$-0.895903\pi$
$163$	−102.000	+	102.000i	−0.625767	+	0.625767i	0.321233	+	0.947000i	$0.395903\pi$
$164$	−50.0000			−0.304878
$165$		0			0
$166$	−55.0000	+	55.0000i	−0.331325	+	0.331325i
$167$	−157.000	−	157.000i	−0.940120	−	0.940120i	0.0581860	−	0.998306i	$-0.481468\pi$
$167$	−157.000	−	157.000i	−0.940120	−	0.940120i	−0.998306	+	0.0581860i	$0.981468\pi$
$168$		0			0
$169$			119.000i			0.704142i
$170$	−156.000	−	156.000i	−0.917647	−	0.917647i
$171$		0			0
$172$	−96.0000	+	96.0000i	−0.558140	+	0.558140i
$173$			11.0000i			0.0635838i	0.999495	+	0.0317919i	$0.0101214\pi$
$173$			11.0000i			0.0635838i	−0.999495	+	0.0317919i	$0.989879\pi$
$174$		0			0
$175$			235.000i			1.34286i
$176$			20.0000i			0.113636i
$177$		0			0
$178$			38.0000i			0.213483i
$179$	229.000	−	229.000i	1.27933	−	1.27933i	0.338286	−	0.941043i	$-0.390153\pi$
$179$	229.000	−	229.000i	1.27933	−	1.27933i	0.941043	−	0.338286i	$-0.109847\pi$
$180$		0			0
$181$	97.0000			0.535912			0.267956	−	0.963431i	$-0.413652\pi$
$181$	97.0000			0.535912			0.267956	+	0.963431i	$0.413652\pi$
$182$	−120.000			−0.659341
$183$		0			0
$184$		−	68.0000i		−	0.369565i
$185$	−222.000	+	222.000i	−1.20000	+	1.20000i
$186$		0			0
$187$	65.0000	−	65.0000i	0.347594	−	0.347594i
$188$			110.000i			0.585106i
$189$		0			0
$190$	−12.0000	−	12.0000i	−0.0631579	−	0.0631579i
$191$	−6.00000	−	6.00000i	−0.0314136	−	0.0314136i	0.691226	−	0.722639i	$-0.257071\pi$
$191$	−6.00000	−	6.00000i	−0.0314136	−	0.0314136i	−0.722639	+	0.691226i	$0.757071\pi$
$192$		0			0
$193$	−198.000	−	198.000i	−1.02591	−	1.02591i	−0.999655	−	0.0262514i	$-0.991643\pi$
$193$	−198.000	−	198.000i	−1.02591	−	1.02591i	−0.0262514	−	0.999655i	$-0.508357\pi$
$194$	156.000			0.804124
$195$		0			0
$196$			48.0000i			0.244898i
$197$	155.000			0.786802			0.393401	−	0.919367i	$-0.371298\pi$
$197$	155.000			0.786802			0.393401	+	0.919367i	$0.371298\pi$
$198$		0			0
$199$	181.000	−	181.000i	0.909548	−	0.909548i	−0.0866878	−	0.996236i	$-0.527628\pi$
$199$	181.000	−	181.000i	0.909548	−	0.909548i	0.996236	+	0.0866878i	$0.0276283\pi$
$200$	−94.0000	+	94.0000i	−0.470000	+	0.470000i
$201$		0			0
$202$	35.0000	+	35.0000i	0.173267	+	0.173267i
$203$	95.0000	−	95.0000i	0.467980	−	0.467980i
$204$		0			0
$205$	150.000	−	150.000i	0.731707	−	0.731707i
$206$		−	264.000i		−	1.28155i
$207$		0			0
$208$	−48.0000	−	48.0000i	−0.230769	−	0.230769i
$209$	5.00000	−	5.00000i	0.0239234	−	0.0239234i
$210$		0			0
$211$	377.000			1.78673			0.893365	−	0.449332i	$-0.148338\pi$
$211$	377.000			1.78673			0.893365	+	0.449332i	$0.148338\pi$
$212$		−	70.0000i		−	0.330189i
$213$		0			0
$214$	120.000	−	120.000i	0.560748	−	0.560748i
$215$		−	576.000i		−	2.67907i
$216$		0			0
$217$	180.000	−	180.000i	0.829493	−	0.829493i
$218$	38.0000			0.174312
$219$		0			0
$220$	−60.0000	−	60.0000i	−0.272727	−	0.272727i
$221$			312.000i			1.41176i
$222$		0			0
$223$	−115.000			−0.515695			−0.257848	−	0.966186i	$-0.583013\pi$
$223$	−115.000			−0.515695			−0.257848	+	0.966186i	$0.583013\pi$
$224$	20.0000	−	20.0000i	0.0892857	−	0.0892857i
$225$		0			0
$226$		−	86.0000i		−	0.380531i
$227$	108.000	+	108.000i	0.475771	+	0.475771i	0.903776	−	0.428005i	$-0.140784\pi$
$227$	108.000	+	108.000i	0.475771	+	0.475771i	−0.428005	+	0.903776i	$0.640784\pi$
$228$		0			0
$229$	−263.000			−1.14847			−0.574236	−	0.818690i	$-0.694701\pi$
$229$	−263.000			−1.14847			−0.574236	+	0.818690i	$0.694701\pi$
$230$	204.000	+	204.000i	0.886957	+	0.886957i
$231$		0			0
$232$	76.0000			0.327586
$233$		−	84.0000i		−	0.360515i	−0.983619	−	0.180258i	$-0.942307\pi$
$233$		−	84.0000i		−	0.360515i	0.983619	−	0.180258i	$-0.0576931\pi$
$234$		0			0
$235$	−330.000	−	330.000i	−1.40426	−	1.40426i
$236$	108.000	−	108.000i	0.457627	−	0.457627i
$237$		0			0
$238$	−130.000			−0.546218
$239$	59.0000	+	59.0000i	0.246862	+	0.246862i	0.819681	−	0.572820i	$-0.194150\pi$
$239$	59.0000	+	59.0000i	0.246862	+	0.246862i	−0.572820	+	0.819681i	$0.694150\pi$
$240$		0			0
$241$	−139.000	−	139.000i	−0.576763	−	0.576763i	0.357247	−	0.934010i	$-0.383716\pi$
$241$	−139.000	−	139.000i	−0.576763	−	0.576763i	−0.934010	+	0.357247i	$0.883716\pi$
$242$	−96.0000	+	96.0000i	−0.396694	+	0.396694i
$243$		0			0
$244$	−12.0000	−	12.0000i	−0.0491803	−	0.0491803i
$245$	−144.000	−	144.000i	−0.587755	−	0.587755i
$246$		0			0
$247$			24.0000i			0.0971660i
$248$	144.000			0.580645
$249$		0			0
$250$		−	264.000i		−	1.05600i
$251$	54.0000	−	54.0000i	0.215139	−	0.215139i	−0.591307	−	0.806447i	$-0.701388\pi$
$251$	54.0000	−	54.0000i	0.215139	−	0.215139i	0.806447	+	0.591307i	$0.201388\pi$
$252$		0			0
$253$	−85.0000	+	85.0000i	−0.335968	+	0.335968i
$254$	5.00000	−	5.00000i	0.0196850	−	0.0196850i
$255$		0			0
$256$	16.0000			0.0625000
$257$	258.000	+	258.000i	1.00389	+	1.00389i	0.999992	+	0.00389865i	$0.00124098\pi$
$257$	258.000	+	258.000i	1.00389	+	1.00389i	0.00389865	+	0.999992i	$0.498759\pi$
$258$		0			0
$259$			185.000i			0.714286i
$260$	288.000			1.10769
$261$		0			0
$262$		−	302.000i		−	1.15267i
$263$			101.000i			0.384030i	0.981392	+	0.192015i	$0.0615023\pi$
$263$			101.000i			0.384030i	−0.981392	+	0.192015i	$0.938498\pi$
$264$		0			0
$265$	210.000	+	210.000i	0.792453	+	0.792453i
$266$	−10.0000			−0.0375940
$267$		0			0
$268$	168.000			0.626866
$269$	−502.000			−1.86617			−0.933086	−	0.359655i	$-0.882895\pi$
$269$	−502.000			−1.86617			−0.933086	+	0.359655i	$0.882895\pi$
$270$		0			0
$271$	17.0000			0.0627306			0.0313653	−	0.999508i	$-0.490014\pi$
$271$	17.0000			0.0627306			0.0313653	+	0.999508i	$0.490014\pi$
$272$	−52.0000	−	52.0000i	−0.191176	−	0.191176i
$273$		0			0
$274$	−180.000	+	180.000i	−0.656934	+	0.656934i
$275$	235.000			0.854545
$276$		0			0
$277$	348.000	−	348.000i	1.25632	−	1.25632i	0.303480	−	0.952838i	$-0.401852\pi$
$277$	348.000	−	348.000i	1.25632	−	1.25632i	0.952838	−	0.303480i	$-0.0981485\pi$
$278$	180.000	+	180.000i	0.647482	+	0.647482i
$279$		0			0
$280$			120.000i			0.428571i
$281$	−216.000	−	216.000i	−0.768683	−	0.768683i	0.209191	−	0.977875i	$-0.432917\pi$
$281$	−216.000	−	216.000i	−0.768683	−	0.768683i	−0.977875	+	0.209191i	$0.932917\pi$
$282$		0			0
$283$	138.000	−	138.000i	0.487633	−	0.487633i	−0.419926	−	0.907558i	$-0.637944\pi$
$283$	138.000	−	138.000i	0.487633	−	0.487633i	0.907558	+	0.419926i	$0.137944\pi$
$284$			14.0000i			0.0492958i
$285$		0			0
$286$			120.000i			0.419580i
$287$		−	125.000i		−	0.435540i
$288$		0			0
$289$			49.0000i			0.169550i
$290$	−228.000	+	228.000i	−0.786207	+	0.786207i
$291$		0			0
$292$	218.000			0.746575
$293$	180.000			0.614334			0.307167	−	0.951656i	$-0.400619\pi$
$293$	180.000			0.614334			0.307167	+	0.951656i	$0.400619\pi$
$294$		0			0
$295$			648.000i			2.19661i
$296$	−74.0000	+	74.0000i	−0.250000	+	0.250000i
$297$		0			0
$298$	47.0000	−	47.0000i	0.157718	−	0.157718i
$299$		−	408.000i		−	1.36455i
$300$		0			0
$301$	−240.000	−	240.000i	−0.797342	−	0.797342i
$302$	180.000	+	180.000i	0.596026	+	0.596026i
$303$		0			0
$304$	−4.00000	−	4.00000i	−0.0131579	−	0.0131579i
$305$	72.0000			0.236066
$306$		0			0
$307$		−	211.000i		−	0.687296i	−0.939098	−	0.343648i	$-0.888337\pi$
$307$		−	211.000i		−	0.687296i	0.939098	−	0.343648i	$-0.111663\pi$
$308$	−50.0000			−0.162338
$309$		0			0
$310$	−432.000	+	432.000i	−1.39355	+	1.39355i
$311$	−311.000	+	311.000i	−1.00000	+	1.00000i			1.00000i	$0.5\pi$
$311$	−311.000	+	311.000i	−1.00000	+	1.00000i	−1.00000			$\pi$
$312$		0			0
$313$	−228.000	−	228.000i	−0.728435	−	0.728435i	0.241873	−	0.970308i	$-0.422238\pi$
$313$	−228.000	−	228.000i	−0.728435	−	0.728435i	−0.970308	+	0.241873i	$0.922238\pi$
$314$	95.0000	−	95.0000i	0.302548	−	0.302548i
$315$		0			0
$316$	82.0000	−	82.0000i	0.259494	−	0.259494i
$317$		−	384.000i		−	1.21136i	−0.795710	−	0.605678i	$-0.792902\pi$
$317$		−	384.000i		−	1.21136i	0.795710	−	0.605678i	$-0.207098\pi$
$318$		0			0
$319$	−95.0000	−	95.0000i	−0.297806	−	0.297806i
$320$	−48.0000	+	48.0000i	−0.150000	+	0.150000i
$321$		0			0
$322$	170.000			0.527950
$323$			26.0000i			0.0804954i
$324$		0			0
$325$	−564.000	+	564.000i	−1.73538	+	1.73538i
$326$		−	204.000i		−	0.625767i
$327$		0			0
$328$	50.0000	−	50.0000i	0.152439	−	0.152439i
$329$	−275.000			−0.835866
$330$		0			0
$331$	−29.0000	−	29.0000i	−0.0876133	−	0.0876133i	0.661942	−	0.749555i	$-0.269733\pi$
$331$	−29.0000	−	29.0000i	−0.0876133	−	0.0876133i	−0.749555	+	0.661942i	$0.769733\pi$
$332$		−	110.000i		−	0.331325i
$333$		0			0
$334$	314.000			0.940120
$335$	−504.000	+	504.000i	−1.50448	+	1.50448i
$336$		0			0
$337$			599.000i			1.77745i	0.458443	+	0.888724i	$0.348407\pi$
$337$			599.000i			1.77745i	−0.458443	+	0.888724i	$0.651593\pi$
$338$	−119.000	−	119.000i	−0.352071	−	0.352071i
$339$		0			0
$340$	312.000			0.917647
$341$	−180.000	−	180.000i	−0.527859	−	0.527859i
$342$		0			0
$343$	−365.000			−1.06414
$344$		−	192.000i		−	0.558140i
$345$		0			0
$346$	−11.0000	−	11.0000i	−0.0317919	−	0.0317919i
$347$	277.000	−	277.000i	0.798271	−	0.798271i	−0.184552	−	0.982823i	$-0.559083\pi$
$347$	277.000	−	277.000i	0.798271	−	0.798271i	0.982823	+	0.184552i	$0.0590834\pi$
$348$		0			0
$349$	−228.000			−0.653295			−0.326648	−	0.945146i	$-0.605919\pi$
$349$	−228.000			−0.653295			−0.326648	+	0.945146i	$0.605919\pi$
$350$	−235.000	−	235.000i	−0.671429	−	0.671429i
$351$		0			0
$352$	−20.0000	−	20.0000i	−0.0568182	−	0.0568182i
$353$	287.000	−	287.000i	0.813031	−	0.813031i	−0.172056	−	0.985087i	$-0.555041\pi$
$353$	287.000	−	287.000i	0.813031	−	0.813031i	0.985087	+	0.172056i	$0.0550410\pi$
$354$		0			0
$355$	−42.0000	−	42.0000i	−0.118310	−	0.118310i
$356$	−38.0000	−	38.0000i	−0.106742	−	0.106742i
$357$		0			0
$358$			458.000i			1.27933i
$359$	−307.000			−0.855153			−0.427577	−	0.903979i	$-0.640633\pi$
$359$	−307.000			−0.855153			−0.427577	+	0.903979i	$0.640633\pi$
$360$		0			0
$361$		−	359.000i		−	0.994460i
$362$	−97.0000	+	97.0000i	−0.267956	+	0.267956i
$363$		0			0
$364$	120.000	−	120.000i	0.329670	−	0.329670i
$365$	−654.000	+	654.000i	−1.79178	+	1.79178i
$366$		0			0
$367$	−300.000			−0.817439			−0.408719	−	0.912660i	$-0.634025\pi$
$367$	−300.000			−0.817439			−0.408719	+	0.912660i	$0.634025\pi$
$368$	68.0000	+	68.0000i	0.184783	+	0.184783i
$369$		0			0
$370$		−	444.000i		−	1.20000i
$371$	175.000			0.471698
$372$		0			0
$373$		−	61.0000i		−	0.163539i	−0.996651	−	0.0817694i	$-0.973943\pi$
$373$		−	61.0000i		−	0.163539i	0.996651	−	0.0817694i	$-0.0260571\pi$
$374$			130.000i			0.347594i
$375$		0			0
$376$	−110.000	−	110.000i	−0.292553	−	0.292553i
$377$	456.000			1.20955
$378$		0			0
$379$	307.000			0.810026			0.405013	−	0.914311i	$-0.367267\pi$
$379$	307.000			0.810026			0.405013	+	0.914311i	$0.367267\pi$
$380$	24.0000			0.0631579
$381$		0			0
$382$	12.0000			0.0314136
$383$	−432.000	−	432.000i	−1.12794	−	1.12794i	−0.990512	−	0.137425i	$-0.956117\pi$
$383$	−432.000	−	432.000i	−1.12794	−	1.12794i	−0.137425	−	0.990512i	$-0.543883\pi$
$384$		0			0
$385$	150.000	−	150.000i	0.389610	−	0.389610i
$386$	396.000			1.02591
$387$		0			0
$388$	−156.000	+	156.000i	−0.402062	+	0.402062i
$389$	204.000	+	204.000i	0.524422	+	0.524422i	0.918904	−	0.394482i	$-0.129076\pi$
$389$	204.000	+	204.000i	0.524422	+	0.524422i	−0.394482	+	0.918904i	$0.629076\pi$
$390$		0			0
$391$		−	442.000i		−	1.13043i
$392$	−48.0000	−	48.0000i	−0.122449	−	0.122449i
$393$		0			0
$394$	−155.000	+	155.000i	−0.393401	+	0.393401i
$395$			492.000i			1.24557i
$396$		0			0
$397$			169.000i			0.425693i	0.977086	+	0.212846i	$0.0682734\pi$
$397$			169.000i			0.425693i	−0.977086	+	0.212846i	$0.931727\pi$
$398$			362.000i			0.909548i
$399$		0			0
$400$		−	188.000i		−	0.470000i
$401$	24.0000	−	24.0000i	0.0598504	−	0.0598504i	−0.676548	−	0.736398i	$-0.736525\pi$
$401$	24.0000	−	24.0000i	0.0598504	−	0.0598504i	0.736398	+	0.676548i	$0.236525\pi$
$402$		0			0
$403$	864.000			2.14392
$404$	−70.0000			−0.173267
$405$		0			0
$406$			190.000i			0.467980i
$407$	185.000			0.454545
$408$		0			0
$409$	−294.000	+	294.000i	−0.718826	+	0.718826i	−0.968365	−	0.249538i	$-0.919721\pi$
$409$	−294.000	+	294.000i	−0.718826	+	0.718826i	0.249538	+	0.968365i	$0.419721\pi$
$410$			300.000i			0.731707i
$411$		0			0
$412$	264.000	+	264.000i	0.640777	+	0.640777i
$413$	270.000	+	270.000i	0.653753	+	0.653753i
$414$		0			0
$415$	330.000	+	330.000i	0.795181	+	0.795181i
$416$	96.0000			0.230769
$417$		0			0
$418$			10.0000i			0.0239234i
$419$	463.000			1.10501			0.552506	−	0.833509i	$-0.313672\pi$
$419$	463.000			1.10501			0.552506	+	0.833509i	$0.313672\pi$
$420$		0			0
$421$	161.000	−	161.000i	0.382423	−	0.382423i	−0.489552	−	0.871974i	$-0.662840\pi$
$421$	161.000	−	161.000i	0.382423	−	0.382423i	0.871974	+	0.489552i	$0.162840\pi$
$422$	−377.000	+	377.000i	−0.893365	+	0.893365i
$423$		0			0
$424$	70.0000	+	70.0000i	0.165094	+	0.165094i
$425$	−611.000	+	611.000i	−1.43765	+	1.43765i
$426$		0			0
$427$	30.0000	−	30.0000i	0.0702576	−	0.0702576i
$428$			240.000i			0.560748i
$429$		0			0
$430$	576.000	+	576.000i	1.33953	+	1.33953i
$431$	324.000	−	324.000i	0.751740	−	0.751740i	−0.223064	−	0.974804i	$-0.571606\pi$
$431$	324.000	−	324.000i	0.751740	−	0.751740i	0.974804	+	0.223064i	$0.0716058\pi$
$432$		0			0
$433$	−25.0000			−0.0577367			−0.0288684	−	0.999583i	$-0.509190\pi$
$433$	−25.0000			−0.0577367			−0.0288684	+	0.999583i	$0.509190\pi$
$434$			360.000i			0.829493i
$435$		0			0
$436$	−38.0000	+	38.0000i	−0.0871560	+	0.0871560i
$437$		−	34.0000i		−	0.0778032i
$438$		0			0
$439$	−294.000	+	294.000i	−0.669704	+	0.669704i	−0.957647	−	0.287944i	$-0.907028\pi$
$439$	−294.000	+	294.000i	−0.669704	+	0.669704i	0.287944	+	0.957647i	$0.407028\pi$
$440$	120.000			0.272727
$441$		0			0
$442$	−312.000	−	312.000i	−0.705882	−	0.705882i
$443$			151.000i			0.340858i	0.985370	+	0.170429i	$0.0545153\pi$
$443$			151.000i			0.340858i	−0.985370	+	0.170429i	$0.945485\pi$
$444$		0			0
$445$	228.000			0.512360
$446$	115.000	−	115.000i	0.257848	−	0.257848i
$447$		0			0
$448$			40.0000i			0.0892857i
$449$	89.0000	+	89.0000i	0.198218	+	0.198218i	0.799236	−	0.601018i	$-0.205238\pi$
$449$	89.0000	+	89.0000i	0.198218	+	0.198218i	−0.601018	+	0.799236i	$0.705238\pi$
$450$		0			0
$451$	−125.000			−0.277162
$452$	86.0000	+	86.0000i	0.190265	+	0.190265i
$453$		0			0
$454$	−216.000			−0.475771
$455$			720.000i			1.58242i
$456$		0			0
$457$	42.0000	+	42.0000i	0.0919037	+	0.0919037i	0.751564	−	0.659660i	$-0.229300\pi$
$457$	42.0000	+	42.0000i	0.0919037	+	0.0919037i	−0.659660	+	0.751564i	$0.729300\pi$
$458$	263.000	−	263.000i	0.574236	−	0.574236i
$459$		0			0
$460$	−408.000			−0.886957
$461$	−156.000	−	156.000i	−0.338395	−	0.338395i	0.517368	−	0.855763i	$-0.326912\pi$
$461$	−156.000	−	156.000i	−0.338395	−	0.338395i	−0.855763	+	0.517368i	$0.826912\pi$
$462$		0			0
$463$	347.000	+	347.000i	0.749460	+	0.749460i	0.974378	−	0.224918i	$-0.0722113\pi$
$463$	347.000	+	347.000i	0.749460	+	0.749460i	−0.224918	+	0.974378i	$0.572211\pi$
$464$	−76.0000	+	76.0000i	−0.163793	+	0.163793i
$465$		0			0
$466$	84.0000	+	84.0000i	0.180258	+	0.180258i
$467$	−437.000	−	437.000i	−0.935760	−	0.935760i	0.0622975	−	0.998058i	$-0.480157\pi$
$467$	−437.000	−	437.000i	−0.935760	−	0.935760i	−0.998058	+	0.0622975i	$0.980157\pi$
$468$		0			0
$469$			420.000i			0.895522i
$470$	660.000			1.40426
$471$		0			0
$472$			216.000i			0.457627i
$473$	−240.000	+	240.000i	−0.507400	+	0.507400i
$474$		0			0
$475$	−47.0000	+	47.0000i	−0.0989474	+	0.0989474i
$476$	130.000	−	130.000i	0.273109	−	0.273109i
$477$		0			0
$478$	−118.000			−0.246862
$479$	349.000	+	349.000i	0.728601	+	0.728601i	0.970341	−	0.241740i	$-0.0777181\pi$
$479$	349.000	+	349.000i	0.728601	+	0.728601i	−0.241740	+	0.970341i	$0.577718\pi$
$480$		0			0
$481$	−444.000	+	444.000i	−0.923077	+	0.923077i
$482$	278.000			0.576763
$483$		0			0
$484$		−	192.000i		−	0.396694i
$485$		−	936.000i		−	1.92990i
$486$		0			0
$487$	257.000	+	257.000i	0.527721	+	0.527721i	0.919892	−	0.392171i	$-0.128276\pi$
$487$	257.000	+	257.000i	0.527721	+	0.527721i	−0.392171	+	0.919892i	$0.628276\pi$
$488$	24.0000			0.0491803
$489$		0			0
$490$	288.000			0.587755
$491$	−132.000			−0.268839			−0.134420	−	0.990925i	$-0.542917\pi$
$491$	−132.000			−0.268839			−0.134420	+	0.990925i	$0.542917\pi$
$492$		0			0
$493$	494.000			1.00203
$494$	−24.0000	−	24.0000i	−0.0485830	−	0.0485830i
$495$		0			0
$496$	−144.000	+	144.000i	−0.290323	+	0.290323i
$497$	−35.0000			−0.0704225
$498$		0			0
$499$	−264.000	+	264.000i	−0.529058	+	0.529058i	−0.920291	−	0.391233i	$-0.872049\pi$
$499$	−264.000	+	264.000i	−0.529058	+	0.529058i	0.391233	+	0.920291i	$0.372049\pi$
$500$	264.000	+	264.000i	0.528000	+	0.528000i
$501$		0			0
$502$			108.000i			0.215139i
$503$	−37.0000	−	37.0000i	−0.0735586	−	0.0735586i	0.669370	−	0.742929i	$-0.266564\pi$
$503$	−37.0000	−	37.0000i	−0.0735586	−	0.0735586i	−0.742929	+	0.669370i	$0.766564\pi$
$504$		0			0
$505$	210.000	−	210.000i	0.415842	−	0.415842i
$506$		−	170.000i		−	0.335968i
$507$		0			0
$508$			10.0000i			0.0196850i
$509$		−	695.000i		−	1.36542i	−0.730688	−	0.682711i	$-0.760801\pi$
$509$		−	695.000i		−	1.36542i	0.730688	−	0.682711i	$-0.239199\pi$
$510$		0			0
$511$			545.000i			1.06654i
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$		0			0
$514$	−516.000			−1.00389
$515$	−1584.00			−3.07573
$516$		0			0
$517$			275.000i			0.531915i
$518$	−185.000	−	185.000i	−0.357143	−	0.357143i
$519$		0			0
$520$	−288.000	+	288.000i	−0.553846	+	0.553846i
$521$		−	35.0000i		−	0.0671785i	−0.999436	−	0.0335893i	$-0.989306\pi$
$521$		−	35.0000i		−	0.0671785i	0.999436	−	0.0335893i	$-0.0106938\pi$
$522$		0			0
$523$	402.000	+	402.000i	0.768642	+	0.768642i	0.977868	−	0.209225i	$-0.0670941\pi$
$523$	402.000	+	402.000i	0.768642	+	0.768642i	−0.209225	+	0.977868i	$0.567094\pi$
$524$	302.000	+	302.000i	0.576336	+	0.576336i
$525$		0			0
$526$	−101.000	−	101.000i	−0.192015	−	0.192015i
$527$	936.000			1.77609
$528$		0			0
$529$			49.0000i			0.0926276i
$530$	−420.000			−0.792453
$531$		0			0
$532$	10.0000	−	10.0000i	0.0187970	−	0.0187970i
$533$	300.000	−	300.000i	0.562852	−	0.562852i
$534$		0			0
$535$	−720.000	−	720.000i	−1.34579	−	1.34579i
$536$	−168.000	+	168.000i	−0.313433	+	0.313433i
$537$		0			0
$538$	502.000	−	502.000i	0.933086	−	0.933086i
$539$			120.000i			0.222635i
$540$		0			0
$541$	−564.000	−	564.000i	−1.04251	−	1.04251i	−0.999055	−	0.0434586i	$-0.986162\pi$
$541$	−564.000	−	564.000i	−1.04251	−	1.04251i	−0.0434586	−	0.999055i	$-0.513838\pi$
$542$	−17.0000	+	17.0000i	−0.0313653	+	0.0313653i
$543$		0			0
$544$	104.000			0.191176
$545$		−	228.000i		−	0.418349i
$546$		0			0
$547$	408.000	−	408.000i	0.745887	−	0.745887i	−0.227817	−	0.973704i	$-0.573159\pi$
$547$	408.000	−	408.000i	0.745887	−	0.745887i	0.973704	+	0.227817i	$0.0731589\pi$
$548$		−	360.000i		−	0.656934i
$549$		0			0
$550$	−235.000	+	235.000i	−0.427273	+	0.427273i
$551$	38.0000			0.0689655
$552$		0			0
$553$	205.000	+	205.000i	0.370705	+	0.370705i
$554$			696.000i			1.25632i
$555$		0			0
$556$	−360.000			−0.647482
$557$	107.000	−	107.000i	0.192101	−	0.192101i	−0.604503	−	0.796603i	$-0.706628\pi$
$557$	107.000	−	107.000i	0.192101	−	0.192101i	0.796603	+	0.604503i	$0.206628\pi$
$558$		0			0
$559$		−	1152.00i		−	2.06082i
$560$	−120.000	−	120.000i	−0.214286	−	0.214286i
$561$		0			0
$562$	432.000			0.768683
$563$	−12.0000	−	12.0000i	−0.0213144	−	0.0213144i	0.696369	−	0.717684i	$-0.254798\pi$
$563$	−12.0000	−	12.0000i	−0.0213144	−	0.0213144i	−0.717684	+	0.696369i	$0.754798\pi$
$564$		0			0
$565$	−516.000			−0.913274
$566$			276.000i			0.487633i
$567$		0			0
$568$	−14.0000	−	14.0000i	−0.0246479	−	0.0246479i
$569$	−366.000	+	366.000i	−0.643234	+	0.643234i	−0.951349	−	0.308115i	$-0.900302\pi$
$569$	−366.000	+	366.000i	−0.643234	+	0.643234i	0.308115	+	0.951349i	$0.400302\pi$
$570$		0			0
$571$	437.000			0.765324			0.382662	−	0.923888i	$-0.375007\pi$
$571$	437.000			0.765324			0.382662	+	0.923888i	$0.375007\pi$
$572$	−120.000	−	120.000i	−0.209790	−	0.209790i
$573$		0			0
$574$	125.000	+	125.000i	0.217770	+	0.217770i
$575$	799.000	−	799.000i	1.38957	−	1.38957i
$576$		0			0
$577$	187.000	+	187.000i	0.324090	+	0.324090i	0.850334	−	0.526244i	$-0.176400\pi$
$577$	187.000	+	187.000i	0.324090	+	0.324090i	−0.526244	+	0.850334i	$0.676400\pi$
$578$	−49.0000	−	49.0000i	−0.0847751	−	0.0847751i
$579$		0			0
$580$		−	456.000i		−	0.786207i
$581$	275.000			0.473322
$582$		0			0
$583$		−	175.000i		−	0.300172i
$584$	−218.000	+	218.000i	−0.373288	+	0.373288i
$585$		0			0
$586$	−180.000	+	180.000i	−0.307167	+	0.307167i
$587$	−203.000	+	203.000i	−0.345826	+	0.345826i	−0.858552	−	0.512726i	$-0.828636\pi$
$587$	−203.000	+	203.000i	−0.345826	+	0.345826i	0.512726	+	0.858552i	$0.328636\pi$
$588$		0			0
$589$	72.0000			0.122241
$590$	−648.000	−	648.000i	−1.09831	−	1.09831i
$591$		0			0
$592$		−	148.000i		−	0.250000i
$593$	−995.000			−1.67791			−0.838954	−	0.544202i	$-0.816833\pi$
$593$	−995.000			−1.67791			−0.838954	+	0.544202i	$0.816833\pi$
$594$		0			0
$595$			780.000i			1.31092i
$596$			94.0000i			0.157718i
$597$		0			0
$598$	408.000	+	408.000i	0.682274	+	0.682274i
$599$	653.000			1.09015			0.545075	−	0.838387i	$-0.316501\pi$
$599$	653.000			1.09015			0.545075	+	0.838387i	$0.316501\pi$
$600$		0			0
$601$	−468.000			−0.778702			−0.389351	−	0.921089i	$-0.627301\pi$
$601$	−468.000			−0.778702			−0.389351	+	0.921089i	$0.627301\pi$
$602$	480.000			0.797342
$603$		0			0
$604$	−360.000			−0.596026
$605$	576.000	+	576.000i	0.952066	+	0.952066i
$606$		0			0
$607$	253.000	−	253.000i	0.416804	−	0.416804i	−0.467297	−	0.884101i	$-0.654772\pi$
$607$	253.000	−	253.000i	0.416804	−	0.416804i	0.884101	+	0.467297i	$0.154772\pi$
$608$	8.00000			0.0131579
$609$		0			0
$610$	−72.0000	+	72.0000i	−0.118033	+	0.118033i
$611$	−660.000	−	660.000i	−1.08020	−	1.08020i
$612$		0			0
$613$		−	731.000i		−	1.19250i	−0.802800	−	0.596248i	$-0.796658\pi$
$613$		−	731.000i		−	1.19250i	0.802800	−	0.596248i	$-0.203342\pi$
$614$	211.000	+	211.000i	0.343648	+	0.343648i
$615$		0			0
$616$	50.0000	−	50.0000i	0.0811688	−	0.0811688i
$617$			421.000i			0.682334i	0.940003	+	0.341167i	$0.110822\pi$
$617$			421.000i			0.682334i	−0.940003	+	0.341167i	$0.889178\pi$
$618$		0			0
$619$		−	65.0000i		−	0.105008i	−0.998621	−	0.0525040i	$-0.983280\pi$
$619$		−	65.0000i		−	0.105008i	0.998621	−	0.0525040i	$-0.0167202\pi$
$620$		−	864.000i		−	1.39355i
$621$		0			0
$622$		−	622.000i		−	1.00000i
$623$	95.0000	−	95.0000i	0.152488	−	0.152488i
$624$		0			0
$625$	−409.000			−0.654400
$626$	456.000			0.728435
$627$		0			0
$628$			190.000i			0.302548i
$629$	−481.000	+	481.000i	−0.764706	+	0.764706i
$630$		0			0
$631$	421.000	−	421.000i	0.667195	−	0.667195i	−0.289871	−	0.957066i	$-0.593612\pi$
$631$	421.000	−	421.000i	0.667195	−	0.667195i	0.957066	+	0.289871i	$0.0936124\pi$
$632$			164.000i			0.259494i
$633$		0			0
$634$	384.000	+	384.000i	0.605678	+	0.605678i
$635$	−30.0000	−	30.0000i	−0.0472441	−	0.0472441i
$636$		0			0
$637$	−288.000	−	288.000i	−0.452119	−	0.452119i
$638$	190.000			0.297806
$639$		0			0
$640$		−	96.0000i		−	0.150000i
$641$	443.000			0.691108			0.345554	−	0.938399i	$-0.387691\pi$
$641$	443.000			0.691108			0.345554	+	0.938399i	$0.387691\pi$
$642$		0			0
$643$	−277.000	+	277.000i	−0.430793	+	0.430793i	−0.888898	−	0.458105i	$-0.848528\pi$
$643$	−277.000	+	277.000i	−0.430793	+	0.430793i	0.458105	+	0.888898i	$0.348528\pi$
$644$	−170.000	+	170.000i	−0.263975	+	0.263975i
$645$		0			0
$646$	−26.0000	−	26.0000i	−0.0402477	−	0.0402477i
$647$	907.000	−	907.000i	1.40185	−	1.40185i	0.607649	−	0.794206i	$-0.292113\pi$
$647$	907.000	−	907.000i	1.40185	−	1.40185i	0.794206	−	0.607649i	$-0.207887\pi$
$648$		0			0
$649$	270.000	−	270.000i	0.416025	−	0.416025i
$650$		−	1128.00i		−	1.73538i
$651$		0			0
$652$	204.000	+	204.000i	0.312883	+	0.312883i
$653$	−708.000	+	708.000i	−1.08423	+	1.08423i	−0.0881165	+	0.996110i	$0.528085\pi$
$653$	−708.000	+	708.000i	−1.08423	+	1.08423i	−0.996110	+	0.0881165i	$0.971915\pi$
$654$		0			0
$655$	−1812.00			−2.76641
$656$			100.000i			0.152439i
$657$		0			0
$658$	275.000	−	275.000i	0.417933	−	0.417933i
$659$			365.000i			0.553869i	0.960889	+	0.276935i	$0.0893186\pi$
$659$			365.000i			0.553869i	−0.960889	+	0.276935i	$0.910681\pi$
$660$		0			0
$661$	−139.000	+	139.000i	−0.210287	+	0.210287i	−0.804390	−	0.594102i	$-0.797507\pi$
$661$	−139.000	+	139.000i	−0.210287	+	0.210287i	0.594102	+	0.804390i	$0.297507\pi$
$662$	58.0000			0.0876133
$663$		0			0
$664$	110.000	+	110.000i	0.165663	+	0.165663i
$665$			60.0000i			0.0902256i
$666$		0			0
$667$	−646.000			−0.968516
$668$	−314.000	+	314.000i	−0.470060	+	0.470060i
$669$		0			0
$670$		−	1008.00i		−	1.50448i
$671$	−30.0000	−	30.0000i	−0.0447094	−	0.0447094i
$672$		0			0
$673$	275.000			0.408618			0.204309	−	0.978906i	$-0.434505\pi$
$673$	275.000			0.408618			0.204309	+	0.978906i	$0.434505\pi$
$674$	−599.000	−	599.000i	−0.888724	−	0.888724i
$675$		0			0
$676$	238.000			0.352071
$677$			541.000i			0.799114i	0.916708	+	0.399557i	$0.130836\pi$
$677$			541.000i			0.799114i	−0.916708	+	0.399557i	$0.869164\pi$
$678$		0			0
$679$	−390.000	−	390.000i	−0.574374	−	0.574374i
$680$	−312.000	+	312.000i	−0.458824	+	0.458824i
$681$		0			0
$682$	360.000			0.527859
$683$	−852.000	−	852.000i	−1.24744	−	1.24744i	−0.956848	−	0.290590i	$-0.906148\pi$
$683$	−852.000	−	852.000i	−1.24744	−	1.24744i	−0.290590	−	0.956848i	$-0.593852\pi$
$684$		0			0
$685$	1080.00	+	1080.00i	1.57664	+	1.57664i
$686$	365.000	−	365.000i	0.532070	−	0.532070i
$687$		0			0
$688$	192.000	+	192.000i	0.279070	+	0.279070i
$689$	420.000	+	420.000i	0.609579	+	0.609579i
$690$		0			0
$691$		−	480.000i		−	0.694645i	−0.937746	−	0.347323i	$-0.887091\pi$
$691$		−	480.000i		−	0.694645i	0.937746	−	0.347323i	$-0.112909\pi$
$692$	22.0000			0.0317919
$693$		0			0
$694$			554.000i			0.798271i
$695$	1080.00	−	1080.00i	1.55396	−	1.55396i
$696$		0			0
$697$	325.000	−	325.000i	0.466284	−	0.466284i
$698$	228.000	−	228.000i	0.326648	−	0.326648i
$699$		0			0
$700$	470.000			0.671429
$701$	114.000	+	114.000i	0.162625	+	0.162625i	0.783728	−	0.621104i	$-0.213315\pi$
$701$	114.000	+	114.000i	0.162625	+	0.162625i	−0.621104	+	0.783728i	$0.713315\pi$
$702$		0			0
$703$	−37.0000	+	37.0000i	−0.0526316	+	0.0526316i
$704$	40.0000			0.0568182
$705$		0			0
$706$			574.000i			0.813031i
$707$		−	175.000i		−	0.247525i
$708$		0			0
$709$	−59.0000	−	59.0000i	−0.0832158	−	0.0832158i	0.664274	−	0.747489i	$-0.268741\pi$
$709$	−59.0000	−	59.0000i	−0.0832158	−	0.0832158i	−0.747489	+	0.664274i	$0.768741\pi$
$710$	84.0000			0.118310
$711$		0			0
$712$	76.0000			0.106742
$713$	−1224.00			−1.71669
$714$		0			0
$715$	720.000			1.00699
$716$	−458.000	−	458.000i	−0.639665	−	0.639665i
$717$		0			0
$718$	307.000	−	307.000i	0.427577	−	0.427577i
$719$	43.0000			0.0598053			0.0299026	−	0.999553i	$-0.490480\pi$
$719$	43.0000			0.0598053			0.0299026	+	0.999553i	$0.490480\pi$
$720$		0			0
$721$	−660.000	+	660.000i	−0.915395	+	0.915395i
$722$	359.000	+	359.000i	0.497230	+	0.497230i
$723$		0			0
$724$		−	194.000i		−	0.267956i
$725$	893.000	+	893.000i	1.23172	+	1.23172i
$726$		0			0
$727$	593.000	−	593.000i	0.815681	−	0.815681i	−0.169798	−	0.985479i	$-0.554312\pi$
$727$	593.000	−	593.000i	0.815681	−	0.815681i	0.985479	+	0.169798i	$0.0543115\pi$
$728$			240.000i			0.329670i
$729$		0			0
$730$		−	1308.00i		−	1.79178i
$731$		−	1248.00i		−	1.70725i
$732$		0			0
$733$			299.000i			0.407913i	0.978980	+	0.203956i	$0.0653801\pi$
$733$			299.000i			0.407913i	−0.978980	+	0.203956i	$0.934620\pi$
$734$	300.000	−	300.000i	0.408719	−	0.408719i
$735$		0			0
$736$	−136.000			−0.184783
$737$	420.000			0.569878
$738$		0			0
$739$			125.000i			0.169147i	0.996417	+	0.0845737i	$0.0269529\pi$
$739$			125.000i			0.169147i	−0.996417	+	0.0845737i	$0.973047\pi$
$740$	444.000	+	444.000i	0.600000	+	0.600000i
$741$		0			0
$742$	−175.000	+	175.000i	−0.235849	+	0.235849i
$743$			991.000i			1.33378i	0.745155	+	0.666891i	$0.232375\pi$
$743$			991.000i			1.33378i	−0.745155	+	0.666891i	$0.767625\pi$
$744$		0			0
$745$	−282.000	−	282.000i	−0.378523	−	0.378523i
$746$	61.0000	+	61.0000i	0.0817694	+	0.0817694i
$747$		0			0
$748$	−130.000	−	130.000i	−0.173797	−	0.173797i
$749$	−600.000			−0.801068
$750$		0			0
$751$		−	1085.00i		−	1.44474i	−0.691507	−	0.722370i	$-0.743053\pi$
$751$		−	1085.00i		−	1.44474i	0.691507	−	0.722370i	$-0.256947\pi$
$752$	220.000			0.292553
$753$		0			0
$754$	−456.000	+	456.000i	−0.604775	+	0.604775i
$755$	1080.00	−	1080.00i	1.43046	−	1.43046i
$756$		0			0
$757$	797.000	+	797.000i	1.05284	+	1.05284i	0.998524	+	0.0543164i	$0.0172980\pi$
$757$	797.000	+	797.000i	1.05284	+	1.05284i	0.0543164	+	0.998524i	$0.482702\pi$
$758$	−307.000	+	307.000i	−0.405013	+	0.405013i
$759$		0			0
$760$	−24.0000	+	24.0000i	−0.0315789	+	0.0315789i
$761$			695.000i			0.913272i	0.889654	+	0.456636i	$0.150946\pi$
$761$			695.000i			0.913272i	−0.889654	+	0.456636i	$0.849054\pi$
$762$		0			0
$763$	−95.0000	−	95.0000i	−0.124509	−	0.124509i
$764$	−12.0000	+	12.0000i	−0.0157068	+	0.0157068i
$765$		0			0
$766$	864.000			1.12794
$767$			1296.00i			1.68970i
$768$		0			0
$769$	211.000	−	211.000i	0.274382	−	0.274382i	−0.556479	−	0.830862i	$-0.687848\pi$
$769$	211.000	−	211.000i	0.274382	−	0.274382i	0.830862	+	0.556479i	$0.187848\pi$
$770$			300.000i			0.389610i
$771$		0			0
$772$	−396.000	+	396.000i	−0.512953	+	0.512953i
$773$	625.000			0.808538			0.404269	−	0.914640i	$-0.367526\pi$
$773$	625.000			0.808538			0.404269	+	0.914640i	$0.367526\pi$
$774$		0			0
$775$	1692.00	+	1692.00i	2.18323	+	2.18323i
$776$		−	312.000i		−	0.402062i
$777$		0			0
$778$	−408.000			−0.524422
$779$	25.0000	−	25.0000i	0.0320924	−	0.0320924i
$780$		0			0
$781$			35.0000i			0.0448143i
$782$	442.000	+	442.000i	0.565217	+	0.565217i
$783$		0			0
$784$	96.0000			0.122449
$785$	−570.000	−	570.000i	−0.726115	−	0.726115i
$786$		0			0
$787$	65.0000			0.0825921			0.0412961	−	0.999147i	$-0.486851\pi$
$787$	65.0000			0.0825921			0.0412961	+	0.999147i	$0.486851\pi$
$788$		−	310.000i		−	0.393401i
$789$		0			0
$790$	−492.000	−	492.000i	−0.622785	−	0.622785i
$791$	−215.000	+	215.000i	−0.271808	+	0.271808i
$792$		0			0
$793$	144.000			0.181589
$794$	−169.000	−	169.000i	−0.212846	−	0.212846i
$795$		0			0
$796$	−362.000	−	362.000i	−0.454774	−	0.454774i
$797$	222.000	−	222.000i	0.278545	−	0.278545i	−0.553983	−	0.832528i	$-0.686893\pi$
$797$	222.000	−	222.000i	0.278545	−	0.278545i	0.832528	+	0.553983i	$0.186893\pi$
$798$		0			0
$799$	−715.000	−	715.000i	−0.894869	−	0.894869i
$800$	188.000	+	188.000i	0.235000	+	0.235000i
$801$		0			0
$802$			48.0000i			0.0598504i
$803$	545.000			0.678705
$804$		0			0
$805$		−	1020.00i		−	1.26708i
$806$	−864.000	+	864.000i	−1.07196	+	1.07196i
$807$		0			0
$808$	70.0000	−	70.0000i	0.0866337	−	0.0866337i
$809$	179.000	−	179.000i	0.221261	−	0.221261i	−0.587768	−	0.809029i	$-0.699993\pi$
$809$	179.000	−	179.000i	0.221261	−	0.221261i	0.809029	+	0.587768i	$0.199993\pi$
$810$		0			0
$811$	−643.000			−0.792848			−0.396424	−	0.918067i	$-0.629749\pi$
$811$	−643.000			−0.792848			−0.396424	+	0.918067i	$0.629749\pi$
$812$	−190.000	−	190.000i	−0.233990	−	0.233990i
$813$		0			0
$814$	−185.000	+	185.000i	−0.227273	+	0.227273i
$815$	−1224.00			−1.50184
$816$		0			0
$817$		−	96.0000i		−	0.117503i
$818$		−	588.000i		−	0.718826i
$819$		0			0
$820$	−300.000	−	300.000i	−0.365854	−	0.365854i
$821$	−397.000			−0.483557			−0.241778	−	0.970332i	$-0.577731\pi$
$821$	−397.000			−0.483557			−0.241778	+	0.970332i	$0.577731\pi$
$822$		0			0
$823$	−540.000			−0.656136			−0.328068	−	0.944654i	$-0.606398\pi$
$823$	−540.000			−0.656136			−0.328068	+	0.944654i	$0.606398\pi$
$824$	−528.000			−0.640777
$825$		0			0
$826$	−540.000			−0.653753
$827$	−247.000	−	247.000i	−0.298670	−	0.298670i	0.541823	−	0.840493i	$-0.317734\pi$
$827$	−247.000	−	247.000i	−0.298670	−	0.298670i	−0.840493	+	0.541823i	$0.817734\pi$
$828$		0			0
$829$	306.000	−	306.000i	0.369119	−	0.369119i	−0.498037	−	0.867156i	$-0.665945\pi$
$829$	306.000	−	306.000i	0.369119	−	0.369119i	0.867156	+	0.498037i	$0.165945\pi$
$830$	−660.000			−0.795181
$831$		0			0
$832$	−96.0000	+	96.0000i	−0.115385	+	0.115385i
$833$	−312.000	−	312.000i	−0.374550	−	0.374550i
$834$		0			0
$835$		−	1884.00i		−	2.25629i
$836$	−10.0000	−	10.0000i	−0.0119617	−	0.0119617i
$837$		0			0
$838$	−463.000	+	463.000i	−0.552506	+	0.552506i
$839$			240.000i			0.286055i	0.989719	+	0.143027i	$0.0456837\pi$
$839$			240.000i			0.286055i	−0.989719	+	0.143027i	$0.954316\pi$
$840$		0			0
$841$			119.000i			0.141498i
$842$			322.000i			0.382423i
$843$		0			0
$844$		−	754.000i		−	0.893365i
$845$	−714.000	+	714.000i	−0.844970	+	0.844970i
$846$		0			0
$847$	480.000			0.566706
$848$	−140.000			−0.165094
$849$		0			0
$850$		−	1222.00i		−	1.43765i
$851$	629.000	−	629.000i	0.739130	−	0.739130i
$852$		0			0
$853$	−757.000	+	757.000i	−0.887456	+	0.887456i	−0.994278	−	0.106822i	$-0.965932\pi$
$853$	−757.000	+	757.000i	−0.887456	+	0.887456i	0.106822	+	0.994278i	$0.465932\pi$
$854$			60.0000i			0.0702576i
$855$		0			0
$856$	−240.000	−	240.000i	−0.280374	−	0.280374i
$857$	563.000	+	563.000i	0.656943	+	0.656943i	0.954656	−	0.297713i	$-0.0962237\pi$
$857$	563.000	+	563.000i	0.656943	+	0.656943i	−0.297713	+	0.954656i	$0.596224\pi$
$858$		0			0
$859$	−739.000	−	739.000i	−0.860303	−	0.860303i	0.131070	−	0.991373i	$-0.458159\pi$
$859$	−739.000	−	739.000i	−0.860303	−	0.860303i	−0.991373	+	0.131070i	$0.958159\pi$
$860$	−1152.00			−1.33953
$861$		0			0
$862$			648.000i			0.751740i
$863$	−480.000			−0.556199			−0.278100	−	0.960552i	$-0.589705\pi$
$863$	−480.000			−0.556199			−0.278100	+	0.960552i	$0.589705\pi$
$864$		0			0
$865$	−66.0000	+	66.0000i	−0.0763006	+	0.0763006i
$866$	25.0000	−	25.0000i	0.0288684	−	0.0288684i
$867$		0			0
$868$	−360.000	−	360.000i	−0.414747	−	0.414747i
$869$	205.000	−	205.000i	0.235903	−	0.235903i
$870$		0			0
$871$	−1008.00	+	1008.00i	−1.15729	+	1.15729i
$872$		−	76.0000i		−	0.0871560i
$873$		0			0
$874$	34.0000	+	34.0000i	0.0389016	+	0.0389016i
$875$	−660.000	+	660.000i	−0.754286	+	0.754286i
$876$		0			0
$877$	1380.00			1.57355			0.786773	−	0.617242i	$-0.211750\pi$
$877$	1380.00			1.57355			0.786773	+	0.617242i	$0.211750\pi$
$878$		−	588.000i		−	0.669704i
$879$		0			0
$880$	−120.000	+	120.000i	−0.136364	+	0.136364i
$881$		−	720.000i		−	0.817253i	−0.912702	−	0.408627i	$-0.866008\pi$
$881$		−	720.000i		−	0.817253i	0.912702	−	0.408627i	$-0.133992\pi$
$882$		0			0
$883$	−42.0000	+	42.0000i	−0.0475651	+	0.0475651i	−0.730489	−	0.682924i	$-0.760708\pi$
$883$	−42.0000	+	42.0000i	−0.0475651	+	0.0475651i	0.682924	+	0.730489i	$0.260708\pi$
$884$	624.000			0.705882
$885$		0			0
$886$	−151.000	−	151.000i	−0.170429	−	0.170429i
$887$			571.000i			0.643743i	0.946783	+	0.321871i	$0.104312\pi$
$887$			571.000i			0.643743i	−0.946783	+	0.321871i	$0.895688\pi$
$888$		0			0
$889$	−25.0000			−0.0281215
$890$	−228.000	+	228.000i	−0.256180	+	0.256180i
$891$		0			0
$892$			230.000i			0.257848i
$893$	−55.0000	−	55.0000i	−0.0615901	−	0.0615901i
$894$		0			0
$895$	2748.00			3.07039
$896$	−40.0000	−	40.0000i	−0.0446429	−	0.0446429i
$897$		0			0
$898$	−178.000			−0.198218
$899$		−	1368.00i		−	1.52169i
$900$		0			0
$901$	455.000	+	455.000i	0.504994	+	0.504994i
$902$	125.000	−	125.000i	0.138581	−	0.138581i
$903$		0			0
$904$	−172.000			−0.190265
$905$	582.000	+	582.000i	0.643094	+	0.643094i
$906$		0			0
$907$	42.0000	+	42.0000i	0.0463065	+	0.0463065i	0.729881	−	0.683574i	$-0.239576\pi$
$907$	42.0000	+	42.0000i	0.0463065	+	0.0463065i	−0.683574	+	0.729881i	$0.739576\pi$
$908$	216.000	−	216.000i	0.237885	−	0.237885i
$909$		0			0
$910$	−720.000	−	720.000i	−0.791209	−	0.791209i
$911$	144.000	+	144.000i	0.158068	+	0.158068i	0.781710	−	0.623642i	$-0.214348\pi$
$911$	144.000	+	144.000i	0.158068	+	0.158068i	−0.623642	+	0.781710i	$0.714348\pi$
$912$		0			0
$913$		−	275.000i		−	0.301205i
$914$	−84.0000			−0.0919037
$915$		0			0
$916$			526.000i			0.574236i
$917$	−755.000	+	755.000i	−0.823337	+	0.823337i
$918$		0			0
$919$	366.000	−	366.000i	0.398259	−	0.398259i	−0.479360	−	0.877619i	$-0.659131\pi$
$919$	366.000	−	366.000i	0.398259	−	0.398259i	0.877619	+	0.479360i	$0.159131\pi$
$920$	408.000	−	408.000i	0.443478	−	0.443478i
$921$		0			0
$922$	312.000			0.338395
$923$	−84.0000	−	84.0000i	−0.0910076	−	0.0910076i
$924$		0			0
$925$	−1739.00			−1.88000
$926$	−694.000			−0.749460
$927$		0			0
$928$		−	152.000i		−	0.163793i
$929$		−	1440.00i		−	1.55005i	−0.631928	−	0.775027i	$-0.717736\pi$
$929$		−	1440.00i		−	1.55005i	0.631928	−	0.775027i	$-0.282264\pi$
$930$		0			0
$931$	−24.0000	−	24.0000i	−0.0257787	−	0.0257787i
$932$	−168.000			−0.180258
$933$		0			0
$934$	874.000			0.935760
$935$	780.000			0.834225
$936$		0			0
$937$	35.0000			0.0373533			0.0186766	−	0.999826i	$-0.494055\pi$
$937$	35.0000			0.0373533			0.0186766	+	0.999826i	$0.494055\pi$
$938$	−420.000	−	420.000i	−0.447761	−	0.447761i
$939$		0			0
$940$	−660.000	+	660.000i	−0.702128	+	0.702128i
$941$	−132.000			−0.140276			−0.0701382	−	0.997537i	$-0.522344\pi$
$941$	−132.000			−0.140276			−0.0701382	+	0.997537i	$0.522344\pi$
$942$		0			0
$943$	−425.000	+	425.000i	−0.450689	+	0.450689i
$944$	−216.000	−	216.000i	−0.228814	−	0.228814i
$945$		0			0
$946$		−	480.000i		−	0.507400i
$947$	143.000	+	143.000i	0.151003	+	0.151003i	0.778566	−	0.627563i	$-0.215947\pi$
$947$	143.000	+	143.000i	0.151003	+	0.151003i	−0.627563	+	0.778566i	$0.715947\pi$
$948$		0			0
$949$	−1308.00	+	1308.00i	−1.37829	+	1.37829i
$950$		−	94.0000i		−	0.0989474i
$951$		0			0
$952$			260.000i			0.273109i
$953$			1571.00i			1.64848i	0.566242	+	0.824239i	$0.308397\pi$
$953$			1571.00i			1.64848i	−0.566242	+	0.824239i	$0.691603\pi$
$954$		0			0
$955$		−	72.0000i		−	0.0753927i
$956$	118.000	−	118.000i	0.123431	−	0.123431i
$957$		0			0
$958$	−698.000			−0.728601
$959$	900.000			0.938478
$960$		0			0
$961$		−	1631.00i		−	1.69719i
$962$		−	888.000i		−	0.923077i
$963$		0			0
$964$	−278.000	+	278.000i	−0.288382	+	0.288382i
$965$		−	2376.00i		−	2.46218i
$966$		0			0
$967$	−83.0000	−	83.0000i	−0.0858325	−	0.0858325i	0.662887	−	0.748719i	$-0.269331\pi$
$967$	−83.0000	−	83.0000i	−0.0858325	−	0.0858325i	−0.748719	+	0.662887i	$0.769331\pi$
$968$	192.000	+	192.000i	0.198347	+	0.198347i
$969$		0			0
$970$	936.000	+	936.000i	0.964948	+	0.964948i
$971$	−1512.00			−1.55716			−0.778579	−	0.627547i	$-0.784059\pi$
$971$	−1512.00			−1.55716			−0.778579	+	0.627547i	$0.784059\pi$
$972$		0			0
$973$		−	900.000i		−	0.924974i
$974$	−514.000			−0.527721
$975$		0			0
$976$	−24.0000	+	24.0000i	−0.0245902	+	0.0245902i
$977$	732.000	−	732.000i	0.749232	−	0.749232i	−0.225103	−	0.974335i	$-0.572272\pi$
$977$	732.000	−	732.000i	0.749232	−	0.749232i	0.974335	+	0.225103i	$0.0722718\pi$
$978$		0			0
$979$	−95.0000	−	95.0000i	−0.0970378	−	0.0970378i
$980$	−288.000	+	288.000i	−0.293878	+	0.293878i
$981$		0			0
$982$	132.000	−	132.000i	0.134420	−	0.134420i
$983$			571.000i			0.580875i	0.956894	+	0.290437i	$0.0938008\pi$
$983$			571.000i			0.580875i	−0.956894	+	0.290437i	$0.906199\pi$
$984$		0			0
$985$	930.000	+	930.000i	0.944162	+	0.944162i
$986$	−494.000	+	494.000i	−0.501014	+	0.501014i
$987$		0			0
$988$	48.0000			0.0485830
$989$			1632.00i			1.65015i
$990$		0			0
$991$	−834.000	+	834.000i	−0.841574	+	0.841574i	−0.989064	−	0.147489i	$-0.952881\pi$
$991$	−834.000	+	834.000i	−0.841574	+	0.841574i	0.147489	+	0.989064i	$0.452881\pi$
$992$		−	288.000i		−	0.290323i
$993$		0			0
$994$	35.0000	−	35.0000i	0.0352113	−	0.0352113i
$995$	2172.00			2.18291
$996$		0			0
$997$	247.000	+	247.000i	0.247743	+	0.247743i	0.820044	−	0.572301i	$-0.193949\pi$
$997$	247.000	+	247.000i	0.247743	+	0.247743i	−0.572301	+	0.820044i	$0.693949\pi$
$998$		−	528.000i		−	0.529058i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.3.i.c.487.1		2
3.2	odd	2		74.3.d.a.43.1	yes	2
12.11	even	2		592.3.k.a.561.1		2
37.31	odd	4	inner	666.3.i.c.253.1		2
111.68	even	4		74.3.d.a.31.1	✓	2
444.179	odd	4		592.3.k.a.401.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.3.d.a.31.1	✓	2	111.68	even	4
74.3.d.a.43.1	yes	2	3.2	odd	2
592.3.k.a.401.1		2	444.179	odd	4
592.3.k.a.561.1		2	12.11	even	2
666.3.i.c.253.1		2	37.31	odd	4	inner
666.3.i.c.487.1		2	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	666.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} -2.00000i q^{4} +(6.00000 + 6.00000i) q^{5} +5.00000 q^{7} +(2.00000 + 2.00000i) q^{8} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} -2.00000i q^{4} +(6.00000 + 6.00000i) q^{5} +5.00000 q^{7} +(2.00000 + 2.00000i) q^{8} -12.0000 q^{10} -5.00000i q^{11} +(12.0000 + 12.0000i) q^{13} +(-5.00000 + 5.00000i) q^{14} -4.00000 q^{16} +(13.0000 + 13.0000i) q^{17} +(1.00000 + 1.00000i) q^{19} +(12.0000 - 12.0000i) q^{20} +(5.00000 + 5.00000i) q^{22} +(-17.0000 - 17.0000i) q^{23} +47.0000i q^{25} -24.0000 q^{26} -10.0000i q^{28} +(19.0000 - 19.0000i) q^{29} +(36.0000 - 36.0000i) q^{31} +(4.00000 - 4.00000i) q^{32} -26.0000 q^{34} +(30.0000 + 30.0000i) q^{35} +37.0000i q^{37} -2.00000 q^{38} +24.0000i q^{40} -25.0000i q^{41} +(-48.0000 - 48.0000i) q^{43} -10.0000 q^{44} +34.0000 q^{46} -55.0000 q^{47} -24.0000 q^{49} +(-47.0000 - 47.0000i) q^{50} +(24.0000 - 24.0000i) q^{52} +35.0000 q^{53} +(30.0000 - 30.0000i) q^{55} +(10.0000 + 10.0000i) q^{56} +38.0000i q^{58} +(54.0000 + 54.0000i) q^{59} +(6.00000 - 6.00000i) q^{61} +72.0000i q^{62} +8.00000i q^{64} +144.000i q^{65} +84.0000i q^{67} +(26.0000 - 26.0000i) q^{68} -60.0000 q^{70} -7.00000 q^{71} +109.000i q^{73} +(-37.0000 - 37.0000i) q^{74} +(2.00000 - 2.00000i) q^{76} -25.0000i q^{77} +(41.0000 + 41.0000i) q^{79} +(-24.0000 - 24.0000i) q^{80} +(25.0000 + 25.0000i) q^{82} +55.0000 q^{83} +156.000i q^{85} +96.0000 q^{86} +(10.0000 - 10.0000i) q^{88} +(19.0000 - 19.0000i) q^{89} +(60.0000 + 60.0000i) q^{91} +(-34.0000 + 34.0000i) q^{92} +(55.0000 - 55.0000i) q^{94} +12.0000i q^{95} +(-78.0000 - 78.0000i) q^{97} +(24.0000 - 24.0000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 12 q^{5} + 10 q^{7} + 4 q^{8}+O(q^{10}) \) 2 * q - 2 * q^2 + 12 * q^5 + 10 * q^7 + 4 * q^8	\( 2 q - 2 q^{2} + 12 q^{5} + 10 q^{7} + 4 q^{8} - 24 q^{10} + 24 q^{13} - 10 q^{14} - 8 q^{16} + 26 q^{17} + 2 q^{19} + 24 q^{20} + 10 q^{22} - 34 q^{23} - 48 q^{26} + 38 q^{29} + 72 q^{31} + 8 q^{32} - 52 q^{34} + 60 q^{35} - 4 q^{38} - 96 q^{43} - 20 q^{44} + 68 q^{46} - 110 q^{47} - 48 q^{49} - 94 q^{50} + 48 q^{52} + 70 q^{53} + 60 q^{55} + 20 q^{56} + 108 q^{59} + 12 q^{61} + 52 q^{68} - 120 q^{70} - 14 q^{71} - 74 q^{74} + 4 q^{76} + 82 q^{79} - 48 q^{80} + 50 q^{82} + 110 q^{83} + 192 q^{86} + 20 q^{88} + 38 q^{89} + 120 q^{91} - 68 q^{92} + 110 q^{94} - 156 q^{97} + 48 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 + 12 * q^5 + 10 * q^7 + 4 * q^8 - 24 * q^10 + 24 * q^13 - 10 * q^14 - 8 * q^16 + 26 * q^17 + 2 * q^19 + 24 * q^20 + 10 * q^22 - 34 * q^23 - 48 * q^26 + 38 * q^29 + 72 * q^31 + 8 * q^32 - 52 * q^34 + 60 * q^35 - 4 * q^38 - 96 * q^43 - 20 * q^44 + 68 * q^46 - 110 * q^47 - 48 * q^49 - 94 * q^50 + 48 * q^52 + 70 * q^53 + 60 * q^55 + 20 * q^56 + 108 * q^59 + 12 * q^61 + 52 * q^68 - 120 * q^70 - 14 * q^71 - 74 * q^74 + 4 * q^76 + 82 * q^79 - 48 * q^80 + 50 * q^82 + 110 * q^83 + 192 * q^86 + 20 * q^88 + 38 * q^89 + 120 * q^91 - 68 * q^92 + 110 * q^94 - 156 * q^97 + 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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