LMFDB - Embedded newform 650.3.k.g.551.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [650,3,Mod(151,650)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("650.151"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(650, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	650.k (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,4,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$17.7112171834$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			551.2
Root			$-1.22474 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	650.551
Dual form			650.3.k.g.151.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 - 1.00000i) q^{2} +0.449490 q^{3} -2.00000i q^{4} +(0.449490 - 0.449490i) q^{6} +(6.67423 + 6.67423i) q^{7} +(-2.00000 - 2.00000i) q^{8} -8.79796 q^{9} +(-10.0227 - 10.0227i) q^{11} -0.898979i q^{12} -13.0000i q^{13} +13.3485 q^{14} -4.00000 q^{16} -11.6969i q^{17} +(-8.79796 + 8.79796i) q^{18} +(6.00000 - 6.00000i) q^{19} +(3.00000 + 3.00000i) q^{21} -20.0454 q^{22} -33.3485i q^{23} +(-0.898979 - 0.898979i) q^{24} +(-13.0000 - 13.0000i) q^{26} -8.00000 q^{27} +(13.3485 - 13.3485i) q^{28} +48.3939 q^{29} +(11.3258 - 11.3258i) q^{31} +(-4.00000 + 4.00000i) q^{32} +(-4.50510 - 4.50510i) q^{33} +(-11.6969 - 11.6969i) q^{34} +17.5959i q^{36} +(-31.6969 - 31.6969i) q^{37} -12.0000i q^{38} -5.84337i q^{39} +(45.3939 - 45.3939i) q^{41} +6.00000 q^{42} -15.9546i q^{43} +(-20.0454 + 20.0454i) q^{44} +(-33.3485 - 33.3485i) q^{46} +(59.4620 + 59.4620i) q^{47} -1.79796 q^{48} +40.0908i q^{49} -5.25765i q^{51} -26.0000 q^{52} -79.6969 q^{53} +(-8.00000 + 8.00000i) q^{54} -26.6969i q^{56} +(2.69694 - 2.69694i) q^{57} +(48.3939 - 48.3939i) q^{58} +(53.4166 + 53.4166i) q^{59} -69.0908 q^{61} -22.6515i q^{62} +(-58.7196 - 58.7196i) q^{63} +8.00000i q^{64} -9.01021 q^{66} +(-58.7650 + 58.7650i) q^{67} -23.3939 q^{68} -14.9898i q^{69} +(-44.7878 + 44.7878i) q^{71} +(17.5959 + 17.5959i) q^{72} +(-67.7878 - 67.7878i) q^{73} -63.3939 q^{74} +(-12.0000 - 12.0000i) q^{76} -133.788i q^{77} +(-5.84337 - 5.84337i) q^{78} -74.7878 q^{79} +75.5857 q^{81} -90.7878i q^{82} +(5.41658 - 5.41658i) q^{83} +(6.00000 - 6.00000i) q^{84} +(-15.9546 - 15.9546i) q^{86} +21.7526 q^{87} +40.0908i q^{88} +(35.6969 + 35.6969i) q^{89} +(86.7650 - 86.7650i) q^{91} -66.6969 q^{92} +(5.09082 - 5.09082i) q^{93} +118.924 q^{94} +(-1.79796 + 1.79796i) q^{96} +(61.3939 - 61.3939i) q^{97} +(40.0908 + 40.0908i) q^{98} +(88.1793 + 88.1793i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 8 q^{3} - 8 q^{6} + 12 q^{7} - 8 q^{8} + 4 q^{9} + 4 q^{11} + 24 q^{14} - 16 q^{16} + 4 q^{18} + 24 q^{19} + 12 q^{21} + 8 q^{22} + 16 q^{24} - 52 q^{26} - 32 q^{27} + 24 q^{28} + 76 q^{29}+ \cdots + 436 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 - 8 * q^3 - 8 * q^6 + 12 * q^7 - 8 * q^8 + 4 * q^9 + 4 * q^11 + 24 * q^14 - 16 * q^16 + 4 * q^18 + 24 * q^19 + 12 * q^21 + 8 * q^22 + 16 * q^24 - 52 * q^26 - 32 * q^27 + 24 * q^28 + 76 * q^29 + 60 * q^31 - 16 * q^32 - 116 * q^33 + 12 * q^34 - 68 * q^37 + 64 * q^41 + 24 * q^42 + 8 * q^44 - 104 * q^46 - 12 * q^47 + 32 * q^48 - 104 * q^52 - 260 * q^53 - 32 * q^54 - 48 * q^57 + 76 * q^58 + 52 * q^59 - 100 * q^61 - 132 * q^63 - 232 * q^66 - 44 * q^67 + 24 * q^68 + 56 * q^71 - 8 * q^72 - 36 * q^73 - 136 * q^74 - 48 * q^76 + 104 * q^78 - 64 * q^79 + 28 * q^81 - 140 * q^83 + 24 * q^84 - 152 * q^86 + 136 * q^87 + 84 * q^89 + 156 * q^91 - 208 * q^92 - 156 * q^93 - 24 * q^94 + 32 * q^96 + 128 * q^97 - 16 * q^98 + 436 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	0.449490			0.149830			0.0749150	−	0.997190i	$-0.476131\pi$
$3$	0.449490			0.149830			0.0749150	+	0.997190i	$0.476131\pi$
$4$		−	2.00000i		−	0.500000i
$5$		0			0
$5$		0			0
$6$	0.449490	−	0.449490i	0.0749150	−	0.0749150i
$7$	6.67423	+	6.67423i	0.953462	+	0.953462i	0.998964	−	0.0455022i	$-0.0144888\pi$
$7$	6.67423	+	6.67423i	0.953462	+	0.953462i	−0.0455022	+	0.998964i	$0.514489\pi$
$8$	−2.00000	−	2.00000i	−0.250000	−	0.250000i
$9$	−8.79796			−0.977551
$10$		0			0
$11$	−10.0227	−	10.0227i	−0.911155	−	0.911155i	0.0852083	−	0.996363i	$-0.472844\pi$
$11$	−10.0227	−	10.0227i	−0.911155	−	0.911155i	−0.996363	+	0.0852083i	$0.972844\pi$
$12$		−	0.898979i		−	0.0749150i
$13$		−	13.0000i		−	1.00000i
$13$		−	13.0000i		−	1.00000i
$14$	13.3485			0.953462
$15$		0			0
$16$	−4.00000			−0.250000
$17$		−	11.6969i		−	0.688055i	−0.938960	−	0.344028i	$-0.888209\pi$
$17$		−	11.6969i		−	0.688055i	0.938960	−	0.344028i	$-0.111791\pi$
$18$	−8.79796	+	8.79796i	−0.488775	+	0.488775i
$19$	6.00000	−	6.00000i	0.315789	−	0.315789i	−0.531358	−	0.847147i	$-0.678318\pi$
$19$	6.00000	−	6.00000i	0.315789	−	0.315789i	0.847147	+	0.531358i	$0.178318\pi$
$20$		0			0
$21$	3.00000	+	3.00000i	0.142857	+	0.142857i
$22$	−20.0454			−0.911155
$23$		−	33.3485i		−	1.44993i	−0.688784	−	0.724967i	$-0.741855\pi$
$23$		−	33.3485i		−	1.44993i	0.688784	−	0.724967i	$-0.258145\pi$
$24$	−0.898979	−	0.898979i	−0.0374575	−	0.0374575i
$25$		0			0
$26$	−13.0000	−	13.0000i	−0.500000	−	0.500000i
$27$	−8.00000			−0.296296
$28$	13.3485	−	13.3485i	0.476731	−	0.476731i
$29$	48.3939			1.66875			0.834377	−	0.551194i	$-0.185828\pi$
$29$	48.3939			1.66875			0.834377	+	0.551194i	$0.185828\pi$
$30$		0			0
$31$	11.3258	−	11.3258i	0.365347	−	0.365347i	−0.500430	−	0.865777i	$-0.666825\pi$
$31$	11.3258	−	11.3258i	0.365347	−	0.365347i	0.865777	+	0.500430i	$0.166825\pi$
$32$	−4.00000	+	4.00000i	−0.125000	+	0.125000i
$33$	−4.50510	−	4.50510i	−0.136518	−	0.136518i
$34$	−11.6969	−	11.6969i	−0.344028	−	0.344028i
$35$		0			0
$36$			17.5959i			0.488775i
$37$	−31.6969	−	31.6969i	−0.856674	−	0.856674i	0.134271	−	0.990945i	$-0.457131\pi$
$37$	−31.6969	−	31.6969i	−0.856674	−	0.856674i	−0.990945	+	0.134271i	$0.957131\pi$
$38$		−	12.0000i		−	0.315789i
$39$		−	5.84337i		−	0.149830i
$40$		0			0
$41$	45.3939	−	45.3939i	1.10717	−	1.10717i	0.113646	−	0.993521i	$-0.463747\pi$
$41$	45.3939	−	45.3939i	1.10717	−	1.10717i	0.993521	−	0.113646i	$-0.0362531\pi$
$42$	6.00000			0.142857
$43$		−	15.9546i		−	0.371037i	−0.982641	−	0.185519i	$-0.940604\pi$
$43$		−	15.9546i		−	0.371037i	0.982641	−	0.185519i	$-0.0593965\pi$
$44$	−20.0454	+	20.0454i	−0.455577	+	0.455577i
$45$		0			0
$46$	−33.3485	−	33.3485i	−0.724967	−	0.724967i
$47$	59.4620	+	59.4620i	1.26515	+	1.26515i	0.948564	+	0.316584i	$0.102536\pi$
$47$	59.4620	+	59.4620i	1.26515	+	1.26515i	0.316584	+	0.948564i	$0.397464\pi$
$48$	−1.79796			−0.0374575
$49$			40.0908i			0.818180i
$50$		0			0
$51$		−	5.25765i		−	0.103091i
$52$	−26.0000			−0.500000
$53$	−79.6969			−1.50372			−0.751858	−	0.659325i	$-0.770842\pi$
$53$	−79.6969			−1.50372			−0.751858	+	0.659325i	$0.770842\pi$
$54$	−8.00000	+	8.00000i	−0.148148	+	0.148148i
$55$		0			0
$56$		−	26.6969i		−	0.476731i
$57$	2.69694	−	2.69694i	0.0473147	−	0.0473147i
$58$	48.3939	−	48.3939i	0.834377	−	0.834377i
$59$	53.4166	+	53.4166i	0.905366	+	0.905366i	0.995894	−	0.0905281i	$-0.0288555\pi$
$59$	53.4166	+	53.4166i	0.905366	+	0.905366i	−0.0905281	+	0.995894i	$0.528856\pi$
$60$		0			0
$61$	−69.0908			−1.13264			−0.566318	−	0.824187i	$-0.691633\pi$
$61$	−69.0908			−1.13264			−0.566318	+	0.824187i	$0.691633\pi$
$62$		−	22.6515i		−	0.365347i
$63$	−58.7196	−	58.7196i	−0.932058	−	0.932058i
$64$			8.00000i			0.125000i
$65$		0			0
$66$	−9.01021			−0.136518
$67$	−58.7650	+	58.7650i	−0.877090	+	0.877090i	−0.993233	−	0.116142i	$-0.962947\pi$
$67$	−58.7650	+	58.7650i	−0.877090	+	0.877090i	0.116142	+	0.993233i	$0.462947\pi$
$68$	−23.3939			−0.344028
$69$		−	14.9898i		−	0.217243i
$70$		0			0
$71$	−44.7878	+	44.7878i	−0.630813	+	0.630813i	−0.948272	−	0.317459i	$-0.897171\pi$
$71$	−44.7878	+	44.7878i	−0.630813	+	0.630813i	0.317459	+	0.948272i	$0.397171\pi$
$72$	17.5959	+	17.5959i	0.244388	+	0.244388i
$73$	−67.7878	−	67.7878i	−0.928599	−	0.928599i	0.0690162	−	0.997616i	$-0.478014\pi$
$73$	−67.7878	−	67.7878i	−0.928599	−	0.928599i	−0.997616	+	0.0690162i	$0.978014\pi$
$74$	−63.3939			−0.856674
$75$		0			0
$76$	−12.0000	−	12.0000i	−0.157895	−	0.157895i
$77$		−	133.788i		−	1.73750i
$78$	−5.84337	−	5.84337i	−0.0749150	−	0.0749150i
$79$	−74.7878			−0.946680			−0.473340	−	0.880880i	$-0.656952\pi$
$79$	−74.7878			−0.946680			−0.473340	+	0.880880i	$0.656952\pi$
$80$		0			0
$81$	75.5857			0.933157
$82$		−	90.7878i		−	1.10717i
$83$	5.41658	−	5.41658i	0.0652600	−	0.0652600i	−0.673724	−	0.738984i	$-0.735306\pi$
$83$	5.41658	−	5.41658i	0.0652600	−	0.0652600i	0.738984	+	0.673724i	$0.235306\pi$
$84$	6.00000	−	6.00000i	0.0714286	−	0.0714286i
$85$		0			0
$86$	−15.9546	−	15.9546i	−0.185519	−	0.185519i
$87$	21.7526			0.250029
$88$			40.0908i			0.455577i
$89$	35.6969	+	35.6969i	0.401089	+	0.401089i	0.878617	−	0.477528i	$-0.158467\pi$
$89$	35.6969	+	35.6969i	0.401089	+	0.401089i	−0.477528	+	0.878617i	$0.658467\pi$
$90$		0			0
$91$	86.7650	−	86.7650i	0.953462	−	0.953462i
$92$	−66.6969			−0.724967
$93$	5.09082	−	5.09082i	0.0547400	−	0.0547400i
$94$	118.924			1.26515
$95$		0			0
$96$	−1.79796	+	1.79796i	−0.0187287	+	0.0187287i
$97$	61.3939	−	61.3939i	0.632927	−	0.632927i	−0.315874	−	0.948801i	$-0.602298\pi$
$97$	61.3939	−	61.3939i	0.632927	−	0.632927i	0.948801	+	0.315874i	$0.102298\pi$
$98$	40.0908	+	40.0908i	0.409090	+	0.409090i
$99$	88.1793	+	88.1793i	0.890700	+	0.890700i
$100$		0			0
$101$			96.4847i			0.955294i	0.878552	+	0.477647i	$0.158510\pi$
$101$			96.4847i			0.955294i	−0.878552	+	0.477647i	$0.841490\pi$
$102$	−5.25765	−	5.25765i	−0.0515456	−	0.0515456i
$103$			49.5755i			0.481316i	0.970610	+	0.240658i	$0.0773632\pi$
$103$			49.5755i			0.481316i	−0.970610	+	0.240658i	$0.922637\pi$
$104$	−26.0000	+	26.0000i	−0.250000	+	0.250000i
$105$		0			0
$106$	−79.6969	+	79.6969i	−0.751858	+	0.751858i
$107$	85.2577			0.796801			0.398400	−	0.917212i	$-0.369566\pi$
$107$	85.2577			0.796801			0.398400	+	0.917212i	$0.369566\pi$
$108$			16.0000i			0.148148i
$109$	−107.182	+	107.182i	−0.983318	+	0.983318i	−0.999863	−	0.0165454i	$-0.994733\pi$
$109$	−107.182	+	107.182i	−0.983318	+	0.983318i	0.0165454	+	0.999863i	$0.494733\pi$
$110$		0			0
$111$	−14.2474	−	14.2474i	−0.128355	−	0.128355i
$112$	−26.6969	−	26.6969i	−0.238366	−	0.238366i
$113$	45.3939			0.401716			0.200858	−	0.979620i	$-0.435627\pi$
$113$	45.3939			0.401716			0.200858	+	0.979620i	$0.435627\pi$
$114$		−	5.39388i		−	0.0473147i
$115$		0			0
$116$		−	96.7878i		−	0.834377i
$117$			114.373i			0.977551i
$118$	106.833			0.905366
$119$	78.0681	−	78.0681i	0.656035	−	0.656035i
$120$		0			0
$121$			79.9092i			0.660406i
$122$	−69.0908	+	69.0908i	−0.566318	+	0.566318i
$123$	20.4041	−	20.4041i	0.165887	−	0.165887i
$124$	−22.6515	−	22.6515i	−0.182674	−	0.182674i
$125$		0			0
$126$	−117.439			−0.932058
$127$		−	170.788i		−	1.34479i	−0.740195	−	0.672393i	$-0.765267\pi$
$127$		−	170.788i		−	1.34479i	0.740195	−	0.672393i	$-0.234733\pi$
$128$	8.00000	+	8.00000i	0.0625000	+	0.0625000i
$129$		−	7.17143i		−	0.0555924i
$130$		0			0
$131$	93.5301			0.713970			0.356985	−	0.934110i	$-0.383805\pi$
$131$	93.5301			0.713970			0.356985	+	0.934110i	$0.383805\pi$
$132$	−9.01021	+	9.01021i	−0.0682591	+	0.0682591i
$133$	80.0908			0.602187
$134$			117.530i			0.877090i
$135$		0			0
$136$	−23.3939	+	23.3939i	−0.172014	+	0.172014i
$137$	86.3031	+	86.3031i	0.629949	+	0.629949i	0.948055	−	0.318106i	$-0.103047\pi$
$137$	86.3031	+	86.3031i	0.629949	+	0.629949i	−0.318106	+	0.948055i	$0.603047\pi$
$138$	−14.9898	−	14.9898i	−0.108622	−	0.108622i
$139$	21.6209			0.155546			0.0777731	−	0.996971i	$-0.475219\pi$
$139$	21.6209			0.155546			0.0777731	+	0.996971i	$0.475219\pi$
$140$		0			0
$141$	26.7276	+	26.7276i	0.189557	+	0.189557i
$142$			89.5755i			0.630813i
$143$	−130.295	+	130.295i	−0.911155	+	0.911155i
$144$	35.1918			0.244388
$145$		0			0
$146$	−135.576			−0.928599
$147$			18.0204i			0.122588i
$148$	−63.3939	+	63.3939i	−0.428337	+	0.428337i
$149$	55.9092	−	55.9092i	0.375229	−	0.375229i	−0.494148	−	0.869378i	$-0.664520\pi$
$149$	55.9092	−	55.9092i	0.375229	−	0.375229i	0.869378	+	0.494148i	$0.164520\pi$
$150$		0			0
$151$	73.3258	+	73.3258i	0.485601	+	0.485601i	0.906915	−	0.421314i	$-0.138431\pi$
$151$	73.3258	+	73.3258i	0.485601	+	0.485601i	−0.421314	+	0.906915i	$0.638431\pi$
$152$	−24.0000			−0.157895
$153$			102.909i			0.672609i
$154$	−133.788	−	133.788i	−0.868752	−	0.868752i
$155$		0			0
$156$	−11.6867			−0.0749150
$157$	117.606			0.749084			0.374542	−	0.927210i	$-0.377800\pi$
$157$	117.606			0.749084			0.374542	+	0.927210i	$0.377800\pi$
$158$	−74.7878	+	74.7878i	−0.473340	+	0.473340i
$159$	−35.8230			−0.225302
$160$		0			0
$161$	222.576	−	222.576i	1.38246	−	1.38246i
$162$	75.5857	−	75.5857i	0.466578	−	0.466578i
$163$	−123.258	−	123.258i	−0.756182	−	0.756182i	0.219443	−	0.975625i	$-0.429576\pi$
$163$	−123.258	−	123.258i	−0.756182	−	0.756182i	−0.975625	+	0.219443i	$0.929576\pi$
$164$	−90.7878	−	90.7878i	−0.553584	−	0.553584i
$165$		0			0
$166$		−	10.8332i		−	0.0652600i
$167$	−43.5755	−	43.5755i	−0.260931	−	0.260931i	0.564501	−	0.825432i	$-0.309069\pi$
$167$	−43.5755	−	43.5755i	−0.260931	−	0.260931i	−0.825432	+	0.564501i	$0.809069\pi$
$168$		−	12.0000i		−	0.0714286i
$169$	−169.000			−1.00000
$170$		0			0
$171$	−52.7878	+	52.7878i	−0.308700	+	0.308700i
$172$	−31.9092			−0.185519
$173$			52.7276i			0.304784i	0.988320	+	0.152392i	$0.0486975\pi$
$173$			52.7276i			0.304784i	−0.988320	+	0.152392i	$0.951302\pi$
$174$	21.7526	−	21.7526i	0.125015	−	0.125015i
$175$		0			0
$176$	40.0908	+	40.0908i	0.227789	+	0.227789i
$177$	24.0102	+	24.0102i	0.135651	+	0.135651i
$178$	71.3939			0.401089
$179$		−	140.000i		−	0.782123i	−0.920365	−	0.391061i	$-0.872108\pi$
$179$		−	140.000i		−	0.782123i	0.920365	−	0.391061i	$-0.127892\pi$
$180$		0			0
$181$			245.363i			1.35560i	0.735247	+	0.677799i	$0.237066\pi$
$181$			245.363i			1.35560i	−0.735247	+	0.677799i	$0.762934\pi$
$182$		−	173.530i		−	0.953462i
$183$	−31.0556			−0.169703
$184$	−66.6969	+	66.6969i	−0.362483	+	0.362483i
$185$		0			0
$186$		−	10.1816i		−	0.0547400i
$187$	−117.235	+	117.235i	−0.626925	+	0.626925i
$188$	118.924	−	118.924i	0.632574	−	0.632574i
$189$	−53.3939	−	53.3939i	−0.282507	−	0.282507i
$190$		0			0
$191$	42.7878			0.224020			0.112010	−	0.993707i	$-0.464271\pi$
$191$	42.7878			0.224020			0.112010	+	0.993707i	$0.464271\pi$
$192$			3.59592i			0.0187287i
$193$	53.1214	+	53.1214i	0.275241	+	0.275241i	0.831206	−	0.555965i	$-0.187651\pi$
$193$	53.1214	+	53.1214i	0.275241	+	0.275241i	−0.555965	+	0.831206i	$0.687651\pi$
$194$		−	122.788i		−	0.632927i
$195$		0			0
$196$	80.1816			0.409090
$197$	−170.788	+	170.788i	−0.866943	+	0.866943i	−0.992133	−	0.125190i	$-0.960046\pi$
$197$	−170.788	+	170.788i	−0.866943	+	0.866943i	0.125190	+	0.992133i	$0.460046\pi$
$198$	176.359			0.890700
$199$		−	266.788i		−	1.34064i	−0.742071	−	0.670321i	$-0.766156\pi$
$199$		−	266.788i		−	1.34064i	0.742071	−	0.670321i	$-0.233844\pi$
$200$		0			0
$201$	−26.4143	+	26.4143i	−0.131414	+	0.131414i
$202$	96.4847	+	96.4847i	0.477647	+	0.477647i
$203$	322.992	+	322.992i	1.59109	+	1.59109i
$204$	−10.5153			−0.0515456
$205$		0			0
$206$	49.5755	+	49.5755i	0.240658	+	0.240658i
$207$			293.398i			1.41738i
$208$			52.0000i			0.250000i
$209$	−120.272			−0.575466
$210$		0			0
$211$	66.4699			0.315023			0.157512	−	0.987517i	$-0.449653\pi$
$211$	66.4699			0.315023			0.157512	+	0.987517i	$0.449653\pi$
$212$			159.394i			0.751858i
$213$	−20.1316	+	20.1316i	−0.0945147	+	0.0945147i
$214$	85.2577	−	85.2577i	0.398400	−	0.398400i
$215$		0			0
$216$	16.0000	+	16.0000i	0.0740741	+	0.0740741i
$217$	151.182			0.696690
$218$			214.363i			0.983318i
$219$	−30.4699	−	30.4699i	−0.139132	−	0.139132i
$220$		0			0
$221$	−152.060			−0.688055
$222$	−28.4949			−0.128355
$223$	211.439	−	211.439i	0.948158	−	0.948158i	−0.0505627	−	0.998721i	$-0.516101\pi$
$223$	211.439	−	211.439i	0.948158	−	0.948158i	0.998721	+	0.0505627i	$0.0161015\pi$
$224$	−53.3939			−0.238366
$225$		0			0
$226$	45.3939	−	45.3939i	0.200858	−	0.200858i
$227$	−57.9773	+	57.9773i	−0.255407	+	0.255407i	−0.823183	−	0.567776i	$-0.807804\pi$
$227$	−57.9773	+	57.9773i	−0.255407	+	0.255407i	0.567776	+	0.823183i	$0.307804\pi$
$228$	−5.39388	−	5.39388i	−0.0236574	−	0.0236574i
$229$	259.151	+	259.151i	1.13166	+	1.13166i	0.989901	+	0.141763i	$0.0452772\pi$
$229$	259.151	+	259.151i	1.13166	+	1.13166i	0.141763	+	0.989901i	$0.454723\pi$
$230$		0			0
$231$		−	60.1362i		−	0.260330i
$232$	−96.7878	−	96.7878i	−0.417189	−	0.417189i
$233$			94.0000i			0.403433i	0.979444	+	0.201717i	$0.0646520\pi$
$233$			94.0000i			0.403433i	−0.979444	+	0.201717i	$0.935348\pi$
$234$	114.373	+	114.373i	0.488775	+	0.488775i
$235$		0			0
$236$	106.833	−	106.833i	0.452683	−	0.452683i
$237$	−33.6163			−0.141841
$238$		−	156.136i		−	0.656035i
$239$	279.644	−	279.644i	1.17006	−	1.17006i	0.187861	−	0.982196i	$-0.439844\pi$
$239$	279.644	−	279.644i	1.17006	−	1.17006i	0.982196	−	0.187861i	$-0.0601556\pi$
$240$		0			0
$241$	259.060	+	259.060i	1.07494	+	1.07494i	0.996955	+	0.0779840i	$0.0248483\pi$
$241$	259.060	+	259.060i	1.07494	+	1.07494i	0.0779840	+	0.996955i	$0.475152\pi$
$242$	79.9092	+	79.9092i	0.330203	+	0.330203i
$243$	105.975			0.436111
$244$			138.182i			0.566318i
$245$		0			0
$246$		−	40.8082i		−	0.165887i
$247$	−78.0000	−	78.0000i	−0.315789	−	0.315789i
$248$	−45.3031			−0.182674
$249$	2.43470	−	2.43470i	0.00977790	−	0.00977790i
$250$		0			0
$251$			67.1510i			0.267534i	0.991013	+	0.133767i	$0.0427074\pi$
$251$			67.1510i			0.267534i	−0.991013	+	0.133767i	$0.957293\pi$
$252$	−117.439	+	117.439i	−0.466029	+	0.466029i
$253$	−334.242	+	334.242i	−1.32111	+	1.32111i
$254$	−170.788	−	170.788i	−0.672393	−	0.672393i
$255$		0			0
$256$	16.0000			0.0625000
$257$		−	318.212i		−	1.23818i	−0.785320	−	0.619090i	$-0.787502\pi$
$257$		−	318.212i		−	1.23818i	0.785320	−	0.619090i	$-0.212498\pi$
$258$	−7.17143	−	7.17143i	−0.0277962	−	0.0277962i
$259$		−	423.106i		−	1.63361i
$260$		0			0
$261$	−425.767			−1.63129
$262$	93.5301	−	93.5301i	0.356985	−	0.356985i
$263$	−80.4995			−0.306082			−0.153041	−	0.988220i	$-0.548907\pi$
$263$	−80.4995			−0.306082			−0.153041	+	0.988220i	$0.548907\pi$
$264$			18.0204i			0.0682591i
$265$		0			0
$266$	80.0908	−	80.0908i	0.301093	−	0.301093i
$267$	16.0454	+	16.0454i	0.0600952	+	0.0600952i
$268$	117.530	+	117.530i	0.438545	+	0.438545i
$269$	−45.2429			−0.168189			−0.0840945	−	0.996458i	$-0.526800\pi$
$269$	−45.2429			−0.168189			−0.0840945	+	0.996458i	$0.526800\pi$
$270$		0			0
$271$	233.326	+	233.326i	0.860981	+	0.860981i	0.991452	−	0.130471i	$-0.0416491\pi$
$271$	233.326	+	233.326i	0.860981	+	0.860981i	−0.130471	+	0.991452i	$0.541649\pi$
$272$			46.7878i			0.172014i
$273$	39.0000	−	39.0000i	0.142857	−	0.142857i
$274$	172.606			0.629949
$275$		0			0
$276$	−29.9796			−0.108622
$277$			297.151i			1.07275i	0.843981	+	0.536374i	$0.180206\pi$
$277$			297.151i			1.07275i	−0.843981	+	0.536374i	$0.819794\pi$
$278$	21.6209	−	21.6209i	0.0777731	−	0.0777731i
$279$	−99.6436	+	99.6436i	−0.357146	+	0.357146i
$280$		0			0
$281$	−208.182	−	208.182i	−0.740860	−	0.740860i	0.231884	−	0.972744i	$-0.425511\pi$
$281$	−208.182	−	208.182i	−0.740860	−	0.740860i	−0.972744	+	0.231884i	$0.925511\pi$
$282$	53.4551			0.189557
$283$		−	231.106i		−	0.816628i	−0.912842	−	0.408314i	$-0.866117\pi$
$283$		−	231.106i		−	0.816628i	0.912842	−	0.408314i	$-0.133883\pi$
$284$	89.5755	+	89.5755i	0.315407	+	0.315407i
$285$		0			0
$286$			260.590i			0.911155i
$287$	605.939			2.11128
$288$	35.1918	−	35.1918i	0.122194	−	0.122194i
$289$	152.182			0.526580
$290$		0			0
$291$	27.5959	−	27.5959i	0.0948313	−	0.0948313i
$292$	−135.576	+	135.576i	−0.464300	+	0.464300i
$293$	−29.2122	−	29.2122i	−0.0997005	−	0.0997005i	0.655497	−	0.755198i	$-0.272459\pi$
$293$	−29.2122	−	29.2122i	−0.0997005	−	0.0997005i	−0.755198	+	0.655497i	$0.772459\pi$
$294$	18.0204	+	18.0204i	0.0612939	+	0.0612939i
$295$		0			0
$296$			126.788i			0.428337i
$297$	80.1816	+	80.1816i	0.269972	+	0.269972i
$298$		−	111.818i		−	0.375229i
$299$	−433.530			−1.44993
$300$		0			0
$301$	106.485	−	106.485i	0.353770	−	0.353770i
$302$	146.652			0.485601
$303$			43.3689i			0.143132i
$304$	−24.0000	+	24.0000i	−0.0789474	+	0.0789474i
$305$		0			0
$306$	102.909	+	102.909i	0.336305	+	0.336305i
$307$	−144.788	−	144.788i	−0.471621	−	0.471621i	0.430818	−	0.902439i	$-0.358225\pi$
$307$	−144.788	−	144.788i	−0.471621	−	0.471621i	−0.902439	+	0.430818i	$0.858225\pi$
$308$	−267.576			−0.868752
$309$			22.2837i			0.0721155i
$310$		0			0
$311$		−	311.773i		−	1.00249i	−0.865307	−	0.501243i	$-0.832876\pi$
$311$		−	311.773i		−	1.00249i	0.865307	−	0.501243i	$-0.167124\pi$
$312$	−11.6867	+	11.6867i	−0.0374575	+	0.0374575i
$313$	330.605			1.05625			0.528123	−	0.849168i	$-0.322896\pi$
$313$	330.605			1.05625			0.528123	+	0.849168i	$0.322896\pi$
$314$	117.606	−	117.606i	0.374542	−	0.374542i
$315$		0			0
$316$			149.576i			0.473340i
$317$	16.2724	−	16.2724i	0.0513326	−	0.0513326i	−0.680974	−	0.732307i	$-0.738444\pi$
$317$	16.2724	−	16.2724i	0.0513326	−	0.0513326i	0.732307	+	0.680974i	$0.238444\pi$
$318$	−35.8230	+	35.8230i	−0.112651	+	0.112651i
$319$	−485.037	−	485.037i	−1.52049	−	1.52049i
$320$		0			0
$321$	38.3224			0.119385
$322$		−	445.151i		−	1.38246i
$323$	−70.1816	−	70.1816i	−0.217281	−	0.217281i
$324$		−	151.171i		−	0.466578i
$325$		0			0
$326$	−246.515			−0.756182
$327$	−48.1770	+	48.1770i	−0.147330	+	0.147330i
$328$	−181.576			−0.553584
$329$			793.727i			2.41254i
$330$		0			0
$331$	25.1510	−	25.1510i	0.0759849	−	0.0759849i	−0.668093	−	0.744078i	$-0.732889\pi$
$331$	25.1510	−	25.1510i	0.0759849	−	0.0759849i	0.744078	+	0.668093i	$0.232889\pi$
$332$	−10.8332	−	10.8332i	−0.0326300	−	0.0326300i
$333$	278.868	+	278.868i	0.837443	+	0.837443i
$334$	−87.1510			−0.260931
$335$		0			0
$336$	−12.0000	−	12.0000i	−0.0357143	−	0.0357143i
$337$		−	345.454i		−	1.02509i	−0.858661	−	0.512543i	$-0.828703\pi$
$337$		−	345.454i		−	1.02509i	0.858661	−	0.512543i	$-0.171297\pi$
$338$	−169.000	+	169.000i	−0.500000	+	0.500000i
$339$	20.4041			0.0601890
$340$		0			0
$341$	−227.030			−0.665776
$342$			105.576i			0.308700i
$343$	59.4620	−	59.4620i	0.173359	−	0.173359i
$344$	−31.9092	+	31.9092i	−0.0927593	+	0.0927593i
$345$		0			0
$346$	52.7276	+	52.7276i	0.152392	+	0.152392i
$347$	−237.621			−0.684786			−0.342393	−	0.939557i	$-0.611238\pi$
$347$	−237.621			−0.684786			−0.342393	+	0.939557i	$0.611238\pi$
$348$		−	43.5051i		−	0.125015i
$349$	18.8786	+	18.8786i	0.0540933	+	0.0540933i	0.733636	−	0.679543i	$-0.237822\pi$
$349$	18.8786	+	18.8786i	0.0540933	+	0.0540933i	−0.679543	+	0.733636i	$0.737822\pi$
$350$		0			0
$351$			104.000i			0.296296i
$352$	80.1816			0.227789
$353$	196.485	−	196.485i	0.556614	−	0.556614i	−0.371728	−	0.928342i	$-0.621235\pi$
$353$	196.485	−	196.485i	0.556614	−	0.556614i	0.928342	+	0.371728i	$0.121235\pi$
$354$	48.0204			0.135651
$355$		0			0
$356$	71.3939	−	71.3939i	0.200545	−	0.200545i
$357$	35.0908	−	35.0908i	0.0982936	−	0.0982936i
$358$	−140.000	−	140.000i	−0.391061	−	0.391061i
$359$	359.462	+	359.462i	1.00129	+	1.00129i	0.999999	+	0.00128770i	$0.000409889\pi$
$359$	359.462	+	359.462i	1.00129	+	1.00129i	0.00128770	+	0.999999i	$0.499590\pi$
$360$		0			0
$361$			289.000i			0.800554i
$362$	245.363	+	245.363i	0.677799	+	0.677799i
$363$			35.9184i			0.0989486i
$364$	−173.530	−	173.530i	−0.476731	−	0.476731i
$365$		0			0
$366$	−31.0556	+	31.0556i	−0.0848514	+	0.0848514i
$367$	−491.287			−1.33866			−0.669329	−	0.742966i	$-0.733418\pi$
$367$	−491.287			−1.33866			−0.669329	+	0.742966i	$0.733418\pi$
$368$			133.394i			0.362483i
$369$	−399.373	+	399.373i	−1.08231	+	1.08231i
$370$		0			0
$371$	−531.916	−	531.916i	−1.43374	−	1.43374i
$372$	−10.1816	−	10.1816i	−0.0273700	−	0.0273700i
$373$	−528.939			−1.41807			−0.709033	−	0.705175i	$-0.750868\pi$
$373$	−528.939			−1.41807			−0.709033	+	0.705175i	$0.750868\pi$
$374$			234.470i			0.626925i
$375$		0			0
$376$		−	237.848i		−	0.632574i
$377$		−	629.120i		−	1.66875i
$378$	−106.788			−0.282507
$379$	246.765	−	246.765i	0.651095	−	0.651095i	−0.302162	−	0.953257i	$-0.597708\pi$
$379$	246.765	−	246.765i	0.651095	−	0.651095i	0.953257	+	0.302162i	$0.0977082\pi$
$380$		0			0
$381$		−	76.7673i		−	0.201489i
$382$	42.7878	−	42.7878i	0.112010	−	0.112010i
$383$	414.954	−	414.954i	1.08343	−	1.08343i	0.0872426	−	0.996187i	$-0.472194\pi$
$383$	414.954	−	414.954i	1.08343	−	1.08343i	0.996187	−	0.0872426i	$-0.0278055\pi$
$384$	3.59592	+	3.59592i	0.00936437	+	0.00936437i
$385$		0			0
$386$	106.243			0.275241
$387$			140.368i			0.362708i
$388$	−122.788	−	122.788i	−0.316463	−	0.316463i
$389$			597.939i			1.53712i	0.639779	+	0.768559i	$0.279026\pi$
$389$			597.939i			1.53712i	−0.639779	+	0.768559i	$0.720974\pi$
$390$		0			0
$391$	−390.075			−0.997634
$392$	80.1816	−	80.1816i	0.204545	−	0.204545i
$393$	42.0408			0.106974
$394$			341.576i			0.866943i
$395$		0			0
$396$	176.359	−	176.359i	0.445350	−	0.445350i
$397$	−396.909	−	396.909i	−0.999771	−	0.999771i	0.000228728	−	1.00000i	$-0.499927\pi$
$397$	−396.909	−	396.909i	−0.999771	−	0.999771i	−1.00000		0.000228728i	$0.999927\pi$
$398$	−266.788	−	266.788i	−0.670321	−	0.670321i
$399$	36.0000			0.0902256
$400$		0			0
$401$	−128.363	−	128.363i	−0.320108	−	0.320108i	0.528701	−	0.848808i	$-0.322679\pi$
$401$	−128.363	−	128.363i	−0.320108	−	0.320108i	−0.848808	+	0.528701i	$0.822679\pi$
$402$			52.8286i			0.131414i
$403$	−147.235	−	147.235i	−0.365347	−	0.365347i
$404$	192.969			0.477647
$405$		0			0
$406$	645.984			1.59109
$407$			635.378i			1.56113i
$408$	−10.5153	+	10.5153i	−0.0257728	+	0.0257728i
$409$	241.727	−	241.727i	0.591018	−	0.591018i	−0.346888	−	0.937907i	$-0.612762\pi$
$409$	241.727	−	241.727i	0.591018	−	0.591018i	0.937907	+	0.346888i	$0.112762\pi$
$410$		0			0
$411$	38.7923	+	38.7923i	0.0943853	+	0.0943853i
$412$	99.1510			0.240658
$413$			713.030i			1.72646i
$414$	293.398	+	293.398i	0.708692	+	0.708692i
$415$		0			0
$416$	52.0000	+	52.0000i	0.125000	+	0.125000i
$417$	9.71838			0.0233055
$418$	−120.272	+	120.272i	−0.287733	+	0.287733i
$419$	678.833			1.62013			0.810063	−	0.586342i	$-0.199433\pi$
$419$	678.833			1.62013			0.810063	+	0.586342i	$0.199433\pi$
$420$		0			0
$421$	−74.6969	+	74.6969i	−0.177427	+	0.177427i	−0.790233	−	0.612806i	$-0.790041\pi$
$421$	−74.6969	+	74.6969i	−0.177427	+	0.177427i	0.612806	+	0.790233i	$0.290041\pi$
$422$	66.4699	−	66.4699i	0.157512	−	0.157512i
$423$	−523.144	−	523.144i	−1.23675	−	1.23675i
$424$	159.394	+	159.394i	0.375929	+	0.375929i
$425$		0			0
$426$			40.2633i			0.0945147i
$427$	−461.128	−	461.128i	−1.07993	−	1.07993i
$428$		−	170.515i		−	0.398400i
$429$	−58.5663	+	58.5663i	−0.136518	+	0.136518i
$430$		0			0
$431$	280.652	−	280.652i	0.651164	−	0.651164i	−0.302110	−	0.953273i	$-0.597691\pi$
$431$	280.652	−	280.652i	0.651164	−	0.651164i	0.953273	+	0.302110i	$0.0976908\pi$
$432$	32.0000			0.0740741
$433$			133.394i			0.308069i	0.988065	+	0.154034i	$0.0492267\pi$
$433$			133.394i			0.308069i	−0.988065	+	0.154034i	$0.950773\pi$
$434$	151.182	−	151.182i	0.348345	−	0.348345i
$435$		0			0
$436$	214.363	+	214.363i	0.491659	+	0.491659i
$437$	−200.091	−	200.091i	−0.457874	−	0.457874i
$438$	−60.9398			−0.139132
$439$			782.302i			1.78201i	0.453994	+	0.891005i	$0.349999\pi$
$439$			782.302i			1.78201i	−0.453994	+	0.891005i	$0.650001\pi$
$440$		0			0
$441$		−	352.717i		−	0.799813i
$442$	−152.060	+	152.060i	−0.344028	+	0.344028i
$443$	354.742			0.800773			0.400386	−	0.916346i	$-0.368876\pi$
$443$	354.742			0.800773			0.400386	+	0.916346i	$0.368876\pi$
$444$	−28.4949	+	28.4949i	−0.0641777	+	0.0641777i
$445$		0			0
$446$		−	422.879i		−	0.948158i
$447$	25.1306	−	25.1306i	0.0562206	−	0.0562206i
$448$	−53.3939	+	53.3939i	−0.119183	+	0.119183i
$449$	−242.333	−	242.333i	−0.539716	−	0.539716i	0.383729	−	0.923446i	$-0.374640\pi$
$449$	−242.333	−	242.333i	−0.539716	−	0.539716i	−0.923446	+	0.383729i	$0.874640\pi$
$450$		0			0
$451$	−909.939			−2.01760
$452$		−	90.7878i		−	0.200858i
$453$	32.9592	+	32.9592i	0.0727576	+	0.0727576i
$454$			115.955i			0.255407i
$455$		0			0
$456$	−10.7878			−0.0236574
$457$	83.4245	−	83.4245i	0.182548	−	0.182548i	−0.609917	−	0.792465i	$-0.708797\pi$
$457$	83.4245	−	83.4245i	0.182548	−	0.182548i	0.792465	+	0.609917i	$0.208797\pi$
$458$	518.302			1.13166
$459$			93.5755i			0.203868i
$460$		0			0
$461$	224.454	−	224.454i	0.486885	−	0.486885i	−0.420437	−	0.907322i	$-0.638123\pi$
$461$	224.454	−	224.454i	0.486885	−	0.486885i	0.907322	+	0.420437i	$0.138123\pi$
$462$	−60.1362	−	60.1362i	−0.130165	−	0.130165i
$463$	−525.401	−	525.401i	−1.13477	−	1.13477i	−0.989373	−	0.145402i	$-0.953552\pi$
$463$	−525.401	−	525.401i	−1.13477	−	1.13477i	−0.145402	−	0.989373i	$-0.546448\pi$
$464$	−193.576			−0.417189
$465$		0			0
$466$	94.0000	+	94.0000i	0.201717	+	0.201717i
$467$			621.893i			1.33168i	0.746096	+	0.665839i	$0.231926\pi$
$467$			621.893i			1.33168i	−0.746096	+	0.665839i	$0.768074\pi$
$468$	228.747			0.488775
$469$	−784.423			−1.67254
$470$		0			0
$471$	52.8627			0.112235
$472$		−	213.666i		−	0.452683i
$473$	−159.908	+	159.908i	−0.338072	+	0.338072i
$474$	−33.6163	+	33.6163i	−0.0709205	+	0.0709205i
$475$		0			0
$476$	−156.136	−	156.136i	−0.328017	−	0.328017i
$477$	701.170			1.46996
$478$		−	559.287i		−	1.17006i
$479$	−358.007	−	358.007i	−0.747405	−	0.747405i	0.226586	−	0.973991i	$-0.427243\pi$
$479$	−358.007	−	358.007i	−0.747405	−	0.747405i	−0.973991	+	0.226586i	$0.927243\pi$
$480$		0			0
$481$	−412.060	+	412.060i	−0.856674	+	0.856674i
$482$	518.120			1.07494
$483$	100.045	−	100.045i	0.207133	−	0.207133i
$484$	159.818			0.330203
$485$		0			0
$486$	105.975	−	105.975i	0.218056	−	0.218056i
$487$	−97.7503	+	97.7503i	−0.200719	+	0.200719i	−0.800308	−	0.599589i	$-0.795331\pi$
$487$	−97.7503	+	97.7503i	−0.200719	+	0.200719i	0.599589	+	0.800308i	$0.295331\pi$
$488$	138.182	+	138.182i	0.283159	+	0.283159i
$489$	−55.4031	−	55.4031i	−0.113299	−	0.113299i
$490$		0			0
$491$			667.923i			1.36033i	0.733058	+	0.680166i	$0.238092\pi$
$491$			667.923i			1.36033i	−0.733058	+	0.680166i	$0.761908\pi$
$492$	−40.8082	−	40.8082i	−0.0829434	−	0.0829434i
$493$		−	566.060i		−	1.14820i
$494$	−156.000			−0.315789
$495$		0			0
$496$	−45.3031	+	45.3031i	−0.0913368	+	0.0913368i
$497$	−597.848			−1.20291
$498$		−	4.86939i		−	0.00977790i
$499$	93.9773	−	93.9773i	0.188331	−	0.188331i	−0.606643	−	0.794974i	$-0.707484\pi$
$499$	93.9773	−	93.9773i	0.188331	−	0.188331i	0.794974	+	0.606643i	$0.207484\pi$
$500$		0			0
$501$	−19.5867	−	19.5867i	−0.0390953	−	0.0390953i
$502$	67.1510	+	67.1510i	0.133767	+	0.133767i
$503$	−68.7265			−0.136633			−0.0683166	−	0.997664i	$-0.521763\pi$
$503$	−68.7265			−0.136633			−0.0683166	+	0.997664i	$0.521763\pi$
$504$			234.879i			0.466029i
$505$		0			0
$506$			668.484i			1.32111i
$507$	−75.9638			−0.149830
$508$	−341.576			−0.672393
$509$	488.545	−	488.545i	0.959813	−	0.959813i	−0.0394100	−	0.999223i	$-0.512548\pi$
$509$	488.545	−	488.545i	0.959813	−	0.959813i	0.999223	+	0.0394100i	$0.0125478\pi$
$510$		0			0
$511$		−	904.863i		−	1.77077i
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$	−48.0000	+	48.0000i	−0.0935673	+	0.0935673i
$514$	−318.212	−	318.212i	−0.619090	−	0.619090i
$515$		0			0
$516$	−14.3429			−0.0277962
$517$		−	1191.94i		−	2.30549i
$518$	−423.106	−	423.106i	−0.816806	−	0.816806i
$519$			23.7005i			0.0456657i
$520$		0			0
$521$	120.908			0.232069			0.116035	−	0.993245i	$-0.462982\pi$
$521$	120.908			0.232069			0.116035	+	0.993245i	$0.462982\pi$
$522$	−425.767	+	425.767i	−0.815646	+	0.815646i
$523$	160.000			0.305927			0.152964	−	0.988232i	$-0.451118\pi$
$523$	160.000			0.305927			0.152964	+	0.988232i	$0.451118\pi$
$524$		−	187.060i		−	0.356985i
$525$		0			0
$526$	−80.4995	+	80.4995i	−0.153041	+	0.153041i
$527$	−132.477	−	132.477i	−0.251379	−	0.251379i
$528$	18.0204	+	18.0204i	0.0341296	+	0.0341296i
$529$	−583.120			−1.10231
$530$		0			0
$531$	−469.957	−	469.957i	−0.885041	−	0.885041i
$532$		−	160.182i		−	0.301093i
$533$	−590.120	−	590.120i	−1.10717	−	1.10717i
$534$	32.0908			0.0600952
$535$		0			0
$536$	235.060			0.438545
$537$		−	62.9286i		−	0.117185i
$538$	−45.2429	+	45.2429i	−0.0840945	+	0.0840945i
$539$	401.818	−	401.818i	0.745489	−	0.745489i
$540$		0			0
$541$	−95.9092	−	95.9092i	−0.177281	−	0.177281i	0.612888	−	0.790170i	$-0.290008\pi$
$541$	−95.9092	−	95.9092i	−0.177281	−	0.177281i	−0.790170	+	0.612888i	$0.790008\pi$
$542$	466.652			0.860981
$543$			110.288i			0.203109i
$544$	46.7878	+	46.7878i	0.0860069	+	0.0860069i
$545$		0			0
$546$		−	78.0000i		−	0.142857i
$547$	842.983			1.54110			0.770551	−	0.637378i	$-0.219981\pi$
$547$	842.983			1.54110			0.770551	+	0.637378i	$0.219981\pi$
$548$	172.606	−	172.606i	0.314975	−	0.314975i
$549$	607.858			1.10721
$550$		0			0
$551$	290.363	−	290.363i	0.526975	−	0.526975i
$552$	−29.9796	+	29.9796i	−0.0543109	+	0.0543109i
$553$	−499.151	−	499.151i	−0.902624	−	0.902624i
$554$	297.151	+	297.151i	0.536374	+	0.536374i
$555$		0			0
$556$		−	43.2418i		−	0.0777731i
$557$	157.666	+	157.666i	0.283063	+	0.283063i	0.834329	−	0.551266i	$-0.185855\pi$
$557$	157.666	+	157.666i	0.283063	+	0.283063i	−0.551266	+	0.834329i	$0.685855\pi$
$558$			199.287i			0.357146i
$559$	−207.410			−0.371037
$560$		0			0
$561$	−52.6959	+	52.6959i	−0.0939321	+	0.0939321i
$562$	−416.363			−0.740860
$563$			100.486i			0.178483i	0.996010	+	0.0892413i	$0.0284442\pi$
$563$			100.486i			0.178483i	−0.996010	+	0.0892413i	$0.971556\pi$
$564$	53.4551	−	53.4551i	0.0947786	−	0.0947786i
$565$		0			0
$566$	−231.106	−	231.106i	−0.408314	−	0.408314i
$567$	504.477	+	504.477i	0.889730	+	0.889730i
$568$	179.151			0.315407
$569$			692.212i			1.21654i	0.793730	+	0.608271i	$0.208137\pi$
$569$			692.212i			1.21654i	−0.793730	+	0.608271i	$0.791863\pi$
$570$		0			0
$571$			243.637i			0.426684i	0.976978	+	0.213342i	$0.0684349\pi$
$571$			243.637i			0.426684i	−0.976978	+	0.213342i	$0.931565\pi$
$572$	260.590	+	260.590i	0.455577	+	0.455577i
$573$	19.2327			0.0335648
$574$	605.939	−	605.939i	1.05564	−	1.05564i
$575$		0			0
$576$		−	70.3837i		−	0.122194i
$577$	−761.453	+	761.453i	−1.31968	+	1.31968i	−0.405646	+	0.914030i	$0.632953\pi$
$577$	−761.453	+	761.453i	−1.31968	+	1.31968i	−0.914030	+	0.405646i	$0.867047\pi$
$578$	152.182	−	152.182i	0.263290	−	0.263290i
$579$	23.8775	+	23.8775i	0.0412393	+	0.0412393i
$580$		0			0
$581$	72.3031			0.124446
$582$		−	55.1918i		−	0.0948313i
$583$	798.779	+	798.779i	1.37012	+	1.37012i
$584$			271.151i			0.464300i
$585$		0			0
$586$	−58.4245			−0.0997005
$587$	−367.235	+	367.235i	−0.625613	+	0.625613i	−0.946961	−	0.321348i	$-0.895864\pi$
$587$	−367.235	+	367.235i	−0.625613	+	0.625613i	0.321348	+	0.946961i	$0.395864\pi$
$588$	36.0408			0.0612939
$589$		−	135.909i		−	0.230746i
$590$		0			0
$591$	−76.7673	+	76.7673i	−0.129894	+	0.129894i
$592$	126.788	+	126.788i	0.214169	+	0.214169i
$593$	339.334	+	339.334i	0.572232	+	0.572232i	0.932752	−	0.360520i	$-0.117401\pi$
$593$	339.334	+	339.334i	0.572232	+	0.572232i	−0.360520	+	0.932752i	$0.617401\pi$
$594$	160.363			0.269972
$595$		0			0
$596$	−111.818	−	111.818i	−0.187615	−	0.187615i
$597$		−	119.918i		−	0.200868i
$598$	−433.530	+	433.530i	−0.724967	+	0.724967i
$599$	931.741			1.55549			0.777747	−	0.628577i	$-0.216362\pi$
$599$	931.741			1.55549			0.777747	+	0.628577i	$0.216362\pi$
$600$		0			0
$601$	−297.697			−0.495336			−0.247668	−	0.968845i	$-0.579664\pi$
$601$	−297.697			−0.495336			−0.247668	+	0.968845i	$0.579664\pi$
$602$		−	212.969i		−	0.353770i
$603$	517.012	−	517.012i	0.857400	−	0.857400i
$604$	146.652	−	146.652i	0.242801	−	0.242801i
$605$		0			0
$606$	43.3689	+	43.3689i	0.0715658	+	0.0715658i
$607$	−219.650			−0.361862			−0.180931	−	0.983496i	$-0.557911\pi$
$607$	−219.650			−0.361862			−0.180931	+	0.983496i	$0.557911\pi$
$608$			48.0000i			0.0789474i
$609$	145.182	+	145.182i	0.238393	+	0.238393i
$610$		0			0
$611$	773.006	−	773.006i	1.26515	−	1.26515i
$612$	205.818			0.336305
$613$	392.363	−	392.363i	0.640071	−	0.640071i	−0.310502	−	0.950573i	$-0.600497\pi$
$613$	392.363	−	392.363i	0.640071	−	0.640071i	0.950573	+	0.310502i	$0.100497\pi$
$614$	−289.576			−0.471621
$615$		0			0
$616$	−267.576	+	267.576i	−0.434376	+	0.434376i
$617$	−436.605	+	436.605i	−0.707626	+	0.707626i	−0.966035	−	0.258410i	$-0.916802\pi$
$617$	−436.605	+	436.605i	−0.707626	+	0.707626i	0.258410	+	0.966035i	$0.416802\pi$
$618$	22.2837	+	22.2837i	0.0360577	+	0.0360577i
$619$	−282.363	−	282.363i	−0.456160	−	0.456160i	0.441232	−	0.897393i	$-0.354541\pi$
$619$	−282.363	−	282.363i	−0.456160	−	0.456160i	−0.897393	+	0.441232i	$0.854541\pi$
$620$		0			0
$621$			266.788i			0.429610i
$622$	−311.773	−	311.773i	−0.501243	−	0.501243i
$623$			476.499i			0.764847i
$624$			23.3735i			0.0374575i
$625$		0			0
$626$	330.605	−	330.605i	0.528123	−	0.528123i
$627$	−54.0612			−0.0862221
$628$		−	235.212i		−	0.374542i
$629$	−370.757	+	370.757i	−0.589439	+	0.589439i
$630$		0			0
$631$	−131.803	−	131.803i	−0.208879	−	0.208879i	0.594912	−	0.803791i	$-0.297187\pi$
$631$	−131.803	−	131.803i	−0.208879	−	0.208879i	−0.803791	+	0.594912i	$0.797187\pi$
$632$	149.576	+	149.576i	0.236670	+	0.236670i
$633$	29.8775			0.0471999
$634$		−	32.5449i		−	0.0513326i
$635$		0			0
$636$			71.6459i			0.112651i
$637$	521.181			0.818180
$638$	−970.075			−1.52049
$639$	394.041	−	394.041i	0.616652	−	0.616652i
$640$		0			0
$641$			911.938i			1.42268i	0.702848	+	0.711340i	$0.251911\pi$
$641$			911.938i			1.42268i	−0.702848	+	0.711340i	$0.748089\pi$
$642$	38.3224	−	38.3224i	0.0596923	−	0.0596923i
$643$	554.363	−	554.363i	0.862151	−	0.862151i	−0.129436	−	0.991588i	$-0.541317\pi$
$643$	554.363	−	554.363i	0.862151	−	0.862151i	0.991588	+	0.129436i	$0.0413168\pi$
$644$	−445.151	−	445.151i	−0.691228	−	0.691228i
$645$		0			0
$646$	−140.363			−0.217281
$647$		−	28.1362i		−	0.0434872i	−0.999764	−	0.0217436i	$-0.993078\pi$
$647$		−	28.1362i		−	0.0434872i	0.999764	−	0.0217436i	$-0.00692175\pi$
$648$	−151.171	−	151.171i	−0.233289	−	0.233289i
$649$		−	1070.76i		−	1.64986i
$650$		0			0
$651$	67.9546			0.104385
$652$	−246.515	+	246.515i	−0.378091	+	0.378091i
$653$	725.908			1.11165			0.555826	−	0.831299i	$-0.312402\pi$
$653$	725.908			1.11165			0.555826	+	0.831299i	$0.312402\pi$
$654$			96.3541i			0.147330i
$655$		0			0
$656$	−181.576	+	181.576i	−0.276792	+	0.276792i
$657$	596.394	+	596.394i	0.907753	+	0.907753i
$658$	793.727	+	793.727i	1.20627	+	1.20627i
$659$	−1237.82			−1.87833			−0.939163	−	0.343473i	$-0.888397\pi$
$659$	−1237.82			−1.87833			−0.939163	+	0.343473i	$0.888397\pi$
$660$		0			0
$661$	562.121	+	562.121i	0.850411	+	0.850411i	0.990184	−	0.139773i	$-0.0446373\pi$
$661$	562.121	+	562.121i	0.850411	+	0.850411i	−0.139773	+	0.990184i	$0.544637\pi$
$662$		−	50.3020i		−	0.0759849i
$663$	−68.3495			−0.103091
$664$	−21.6663			−0.0326300
$665$		0			0
$666$	557.737			0.837443
$667$		−	1613.86i		−	2.41958i
$668$	−87.1510	+	87.1510i	−0.130466	+	0.130466i
$669$	95.0398	−	95.0398i	0.142062	−	0.142062i
$670$		0			0
$671$	692.477	+	692.477i	1.03201	+	1.03201i
$672$	−24.0000			−0.0357143
$673$			711.272i			1.05687i	0.848974	+	0.528434i	$0.177221\pi$
$673$			711.272i			1.05687i	−0.848974	+	0.528434i	$0.822779\pi$
$674$	−345.454	−	345.454i	−0.512543	−	0.512543i
$675$		0			0
$676$			338.000i			0.500000i
$677$	−425.151			−0.627993			−0.313996	−	0.949424i	$-0.601668\pi$
$677$	−425.151			−0.627993			−0.313996	+	0.949424i	$0.601668\pi$
$678$	20.4041	−	20.4041i	0.0300945	−	0.0300945i
$679$	819.514			1.20694
$680$		0			0
$681$	−26.0602	+	26.0602i	−0.0382675	+	0.0382675i
$682$	−227.030	+	227.030i	−0.332888	+	0.332888i
$683$	69.9773	+	69.9773i	0.102456	+	0.102456i	0.756477	−	0.654021i	$-0.226919\pi$
$683$	69.9773	+	69.9773i	0.102456	+	0.102456i	−0.654021	+	0.756477i	$0.726919\pi$
$684$	105.576	+	105.576i	0.154350	+	0.154350i
$685$		0			0
$686$		−	118.924i		−	0.173359i
$687$	116.486	+	116.486i	0.169557	+	0.169557i
$688$			63.8184i			0.0927593i
$689$			1036.06i			1.50372i
$690$		0			0
$691$	297.614	−	297.614i	0.430700	−	0.430700i	−0.458166	−	0.888867i	$-0.651494\pi$
$691$	297.614	−	297.614i	0.430700	−	0.430700i	0.888867	+	0.458166i	$0.151494\pi$
$692$	105.455			0.152392
$693$			1177.06i			1.69850i
$694$	−237.621	+	237.621i	−0.342393	+	0.342393i
$695$		0			0
$696$	−43.5051	−	43.5051i	−0.0625073	−	0.0625073i
$697$	−530.969	−	530.969i	−0.761793	−	0.761793i
$698$	37.7571			0.0540933
$699$			42.2520i			0.0604464i
$700$		0			0
$701$			129.910i			0.185321i	0.995698	+	0.0926606i	$0.0295372\pi$
$701$			129.910i			0.185321i	−0.995698	+	0.0926606i	$0.970463\pi$
$702$	104.000	+	104.000i	0.148148	+	0.148148i
$703$	−380.363			−0.541057
$704$	80.1816	−	80.1816i	0.113894	−	0.113894i
$705$		0			0
$706$		−	392.969i		−	0.556614i
$707$	−643.961	+	643.961i	−0.910837	+	0.910837i
$708$	48.0204	−	48.0204i	0.0678254	−	0.0678254i
$709$	−602.969	−	602.969i	−0.850450	−	0.850450i	0.139738	−	0.990189i	$-0.455374\pi$
$709$	−602.969	−	602.969i	−0.850450	−	0.850450i	−0.990189	+	0.139738i	$0.955374\pi$
$710$		0			0
$711$	657.980			0.925428
$712$		−	142.788i		−	0.200545i
$713$	−377.697	−	377.697i	−0.529729	−	0.529729i
$714$		−	70.1816i		−	0.0982936i
$715$		0			0
$716$	−280.000			−0.391061
$717$	125.697	−	125.697i	0.175310	−	0.175310i
$718$	718.924			1.00129
$719$		−	749.589i		−	1.04254i	−0.853391	−	0.521272i	$-0.825458\pi$
$719$		−	749.589i		−	1.04254i	0.853391	−	0.521272i	$-0.174542\pi$
$720$		0			0
$721$	−330.879	+	330.879i	−0.458916	+	0.458916i
$722$	289.000	+	289.000i	0.400277	+	0.400277i
$723$	116.445	+	116.445i	0.161058	+	0.161058i
$724$	490.727			0.677799
$725$		0			0
$726$	35.9184	+	35.9184i	0.0494743	+	0.0494743i
$727$			885.090i			1.21745i	0.793379	+	0.608727i	$0.208320\pi$
$727$			885.090i			1.21745i	−0.793379	+	0.608727i	$0.791680\pi$
$728$	−347.060			−0.476731
$729$	−632.637			−0.867814
$730$		0			0
$731$	−186.620			−0.255294
$732$			62.1112i			0.0848514i
$733$	−253.727	+	253.727i	−0.346148	+	0.346148i	−0.858673	−	0.512525i	$-0.828710\pi$
$733$	−253.727	+	253.727i	−0.346148	+	0.346148i	0.512525	+	0.858673i	$0.328710\pi$
$734$	−491.287	+	491.287i	−0.669329	+	0.669329i
$735$		0			0
$736$	133.394	+	133.394i	0.181242	+	0.181242i
$737$	1177.97			1.59833
$738$			798.747i			1.08231i
$739$	−818.643	−	818.643i	−1.10777	−	1.10777i	−0.993443	−	0.114328i	$-0.963529\pi$
$739$	−818.643	−	818.643i	−1.10777	−	1.10777i	−0.114328	−	0.993443i	$-0.536471\pi$
$740$		0			0
$741$	−35.0602	−	35.0602i	−0.0473147	−	0.0473147i
$742$	−1063.83			−1.43374
$743$	223.705	−	223.705i	0.301083	−	0.301083i	−0.540354	−	0.841438i	$-0.681710\pi$
$743$	223.705	−	223.705i	0.301083	−	0.301083i	0.841438	+	0.540354i	$0.181710\pi$
$744$	−20.3633			−0.0273700
$745$		0			0
$746$	−528.939	+	528.939i	−0.709033	+	0.709033i
$747$	−47.6549	+	47.6549i	−0.0637950	+	0.0637950i
$748$	234.470	+	234.470i	0.313462	+	0.313462i
$749$	569.030	+	569.030i	0.759719	+	0.759719i
$750$		0			0
$751$			739.501i			0.984688i	0.870401	+	0.492344i	$0.163860\pi$
$751$			739.501i			0.984688i	−0.870401	+	0.492344i	$0.836140\pi$
$752$	−237.848	−	237.848i	−0.316287	−	0.316287i
$753$			30.1837i			0.0400846i
$754$	−629.120	−	629.120i	−0.834377	−	0.834377i
$755$		0			0
$756$	−106.788	+	106.788i	−0.141254	+	0.141254i
$757$	882.058			1.16520			0.582601	−	0.812758i	$-0.302035\pi$
$757$	882.058			1.16520			0.582601	+	0.812758i	$0.302035\pi$
$758$		−	493.530i		−	0.651095i
$759$	−150.238	+	150.238i	−0.197942	+	0.197942i
$760$		0			0
$761$	−638.393	−	638.393i	−0.838887	−	0.838887i	0.149826	−	0.988712i	$-0.452129\pi$
$761$	−638.393	−	638.393i	−0.838887	−	0.838887i	−0.988712	+	0.149826i	$0.952129\pi$
$762$	−76.7673	−	76.7673i	−0.100745	−	0.100745i
$763$	−1430.71			−1.87511
$764$		−	85.5755i		−	0.112010i
$765$		0			0
$766$		−	829.907i		−	1.08343i
$767$	694.416	−	694.416i	0.905366	−	0.905366i
$768$	7.19184			0.00936437
$769$	−649.090	+	649.090i	−0.844070	+	0.844070i	−0.989385	−	0.145315i	$-0.953580\pi$
$769$	−649.090	+	649.090i	−0.844070	+	0.844070i	0.145315	+	0.989385i	$0.453580\pi$
$770$		0			0
$771$		−	143.033i		−	0.185516i
$772$	106.243	−	106.243i	0.137620	−	0.137620i
$773$	−605.939	+	605.939i	−0.783879	+	0.783879i	−0.980483	−	0.196604i	$-0.937009\pi$
$773$	−605.939	+	605.939i	−0.783879	+	0.783879i	0.196604	+	0.980483i	$0.437009\pi$
$774$	140.368	+	140.368i	0.181354	+	0.181354i
$775$		0			0
$776$	−245.576			−0.316463
$777$		−	190.182i		−	0.244764i
$778$	597.939	+	597.939i	0.768559	+	0.768559i
$779$		−	544.727i		−	0.699264i
$780$		0			0
$781$	897.789			1.14954
$782$	−390.075	+	390.075i	−0.498817	+	0.498817i
$783$	−387.151			−0.494446
$784$		−	160.363i		−	0.204545i
$785$		0			0
$786$	42.0408	−	42.0408i	0.0534870	−	0.0534870i
$787$	946.461	+	946.461i	1.20262	+	1.20262i	0.973367	+	0.229252i	$0.0736278\pi$
$787$	946.461	+	946.461i	1.20262	+	1.20262i	0.229252	+	0.973367i	$0.426372\pi$
$788$	341.576	+	341.576i	0.433471	+	0.433471i
$789$	−36.1837			−0.0458602
$790$		0			0
$791$	302.969	+	302.969i	0.383021	+	0.383021i
$792$		−	352.717i		−	0.445350i
$793$			898.181i			1.13264i
$794$	−793.818			−0.999771
$795$		0			0
$796$	−533.576			−0.670321
$797$			832.878i			1.04502i	0.852634	+	0.522508i	$0.175003\pi$
$797$			832.878i			1.04502i	−0.852634	+	0.522508i	$0.824997\pi$
$798$	36.0000	−	36.0000i	0.0451128	−	0.0451128i
$799$	695.523	−	695.523i	0.870492	−	0.870492i
$800$		0			0
$801$	−314.060	−	314.060i	−0.392085	−	0.392085i
$802$	−256.727			−0.320108
$803$			1358.83i			1.69220i
$804$	52.8286	+	52.8286i	0.0657072	+	0.0657072i
$805$		0			0
$806$	−294.470			−0.365347
$807$	−20.3362			−0.0251998
$808$	192.969	−	192.969i	0.238823	−	0.238823i
$809$	1194.00			1.47590			0.737948	−	0.674857i	$-0.235795\pi$
$809$	1194.00			1.47590			0.737948	+	0.674857i	$0.235795\pi$
$810$		0			0
$811$	52.2656	−	52.2656i	0.0644458	−	0.0644458i	−0.674149	−	0.738595i	$-0.735490\pi$
$811$	52.2656	−	52.2656i	0.0644458	−	0.0644458i	0.738595	+	0.674149i	$0.235490\pi$
$812$	645.984	−	645.984i	0.795547	−	0.795547i
$813$	104.878	+	104.878i	0.129001	+	0.129001i
$814$	635.378	+	635.378i	0.780563	+	0.780563i
$815$		0			0
$816$			21.0306i			0.0257728i
$817$	−95.7276	−	95.7276i	−0.117170	−	0.117170i
$818$		−	483.453i		−	0.591018i
$819$	−763.355	+	763.355i	−0.932058	+	0.932058i
$820$		0			0
$821$	−250.515	+	250.515i	−0.305134	+	0.305134i	−0.843019	−	0.537884i	$-0.819224\pi$
$821$	−250.515	+	250.515i	−0.305134	+	0.305134i	0.537884	+	0.843019i	$0.319224\pi$
$822$	77.5847			0.0943853
$823$			1065.94i			1.29519i	0.761986	+	0.647593i	$0.224224\pi$
$823$			1065.94i			1.29519i	−0.761986	+	0.647593i	$0.775776\pi$
$824$	99.1510	−	99.1510i	0.120329	−	0.120329i
$825$		0			0
$826$	713.030	+	713.030i	0.863232	+	0.863232i
$827$	−118.690	−	118.690i	−0.143519	−	0.143519i	0.631697	−	0.775216i	$-0.282359\pi$
$827$	−118.690	−	118.690i	−0.143519	−	0.143519i	−0.775216	+	0.631697i	$0.782359\pi$
$828$	586.797			0.708692
$829$			1422.06i			1.71539i	0.514157	+	0.857696i	$0.328105\pi$
$829$			1422.06i			1.71539i	−0.514157	+	0.857696i	$0.671895\pi$
$830$		0			0
$831$			133.566i			0.160730i
$832$	104.000			0.125000
$833$	468.940			0.562953
$834$	9.71838	−	9.71838i	0.0116527	−	0.0116527i
$835$		0			0
$836$			240.545i			0.287733i
$837$	−90.6061	+	90.6061i	−0.108251	+	0.108251i
$838$	678.833	−	678.833i	0.810063	−	0.810063i
$839$	7.93877	+	7.93877i	0.00946218	+	0.00946218i	0.711822	−	0.702360i	$-0.247870\pi$
$839$	7.93877	+	7.93877i	0.00946218	+	0.00946218i	−0.702360	+	0.711822i	$0.747870\pi$
$840$		0			0
$841$	1500.97			1.78474
$842$			149.394i			0.177427i
$843$	−93.5755	−	93.5755i	−0.111003	−	0.111003i
$844$		−	132.940i		−	0.157512i
$845$		0			0
$846$	−1046.29			−1.23675
$847$	−533.333	+	533.333i	−0.629673	+	0.629673i
$848$	318.788			0.375929
$849$		−	103.880i		−	0.122355i
$850$		0			0
$851$	−1057.04	+	1057.04i	−1.24212	+	1.24212i
$852$	40.2633	+	40.2633i	0.0472574	+	0.0472574i
$853$	373.788	+	373.788i	0.438204	+	0.438204i	0.891407	−	0.453203i	$-0.149719\pi$
$853$	373.788	+	373.788i	0.438204	+	0.438204i	−0.453203	+	0.891407i	$0.649719\pi$
$854$	−922.257			−1.07993
$855$		0			0
$856$	−170.515	−	170.515i	−0.199200	−	0.199200i
$857$			181.031i			0.211238i	0.994407	+	0.105619i	$0.0336823\pi$
$857$			181.031i			0.211238i	−0.994407	+	0.105619i	$0.966318\pi$
$858$			117.133i			0.136518i
$859$	−1050.47			−1.22290			−0.611449	−	0.791284i	$-0.709413\pi$
$859$	−1050.47			−1.22290			−0.611449	+	0.791284i	$0.709413\pi$
$860$		0			0
$861$	272.363			0.316334
$862$		−	561.303i		−	0.651164i
$863$	800.976	−	800.976i	0.928130	−	0.928130i	−0.0694550	−	0.997585i	$-0.522126\pi$
$863$	800.976	−	800.976i	0.928130	−	0.928130i	0.997585	+	0.0694550i	$0.0221260\pi$
$864$	32.0000	−	32.0000i	0.0370370	−	0.0370370i
$865$		0			0
$866$	133.394	+	133.394i	0.154034	+	0.154034i
$867$	68.4041			0.0788974
$868$		−	302.363i		−	0.348345i
$869$	749.576	+	749.576i	0.862573	+	0.862573i
$870$		0			0
$871$	763.946	+	763.946i	0.877090	+	0.877090i
$872$	428.727			0.491659
$873$	−540.141	+	540.141i	−0.618718	+	0.618718i
$874$	−400.182			−0.457874
$875$		0			0
$876$	−60.9398	+	60.9398i	−0.0695660	+	0.0695660i
$877$	693.817	−	693.817i	0.791126	−	0.791126i	−0.190551	−	0.981677i	$-0.561028\pi$
$877$	693.817	−	693.817i	0.791126	−	0.791126i	0.981677	+	0.190551i	$0.0610276\pi$
$878$	782.302	+	782.302i	0.891005	+	0.891005i
$879$	−13.1306	−	13.1306i	−0.0149381	−	0.0149381i
$880$		0			0
$881$			1023.73i			1.16201i	0.813902	+	0.581003i	$0.197339\pi$
$881$			1023.73i			1.16201i	−0.813902	+	0.581003i	$0.802661\pi$
$882$	−352.717	−	352.717i	−0.399906	−	0.399906i
$883$		−	1010.54i		−	1.14444i	−0.820099	−	0.572221i	$-0.806082\pi$
$883$		−	1010.54i		−	1.14444i	0.820099	−	0.572221i	$-0.193918\pi$
$884$			304.120i			0.344028i
$885$		0			0
$886$	354.742	−	354.742i	0.400386	−	0.400386i
$887$	−338.424			−0.381538			−0.190769	−	0.981635i	$-0.561098\pi$
$887$	−338.424			−0.381538			−0.190769	+	0.981635i	$0.561098\pi$
$888$			56.9898i			0.0641777i
$889$	1139.88	−	1139.88i	1.28220	−	1.28220i
$890$		0			0
$891$	−757.573	−	757.573i	−0.850251	−	0.850251i
$892$	−422.879	−	422.879i	−0.474079	−	0.474079i
$893$	713.544			0.799041
$894$		−	50.2612i		−	0.0562206i
$895$		0			0
$896$			106.788i			0.119183i
$897$	−194.867			−0.217243
$898$	−484.665			−0.539716
$899$	548.098	−	548.098i	0.609675	−	0.609675i
$900$		0			0
$901$			932.210i			1.03464i
$902$	−909.939	+	909.939i	−1.00880	+	1.00880i
$903$	47.8638	−	47.8638i	0.0530053	−	0.0530053i
$904$	−90.7878	−	90.7878i	−0.100429	−	0.100429i
$905$		0			0
$906$	65.9184			0.0727576
$907$		−	1255.39i		−	1.38411i	−0.721843	−	0.692057i	$-0.756705\pi$
$907$		−	1255.39i		−	1.38411i	0.721843	−	0.692057i	$-0.243295\pi$
$908$	115.955	+	115.955i	0.127703	+	0.127703i
$909$		−	848.868i		−	0.933849i
$910$		0			0
$911$	1710.79			1.87792			0.938961	−	0.344022i	$-0.111790\pi$
$911$	1710.79			1.87792			0.938961	+	0.344022i	$0.111790\pi$
$912$	−10.7878	+	10.7878i	−0.0118287	+	0.0118287i
$913$	−108.578			−0.118924
$914$		−	166.849i		−	0.182548i
$915$		0			0
$916$	518.302	−	518.302i	0.565832	−	0.565832i
$917$	624.242	+	624.242i	0.680744	+	0.680744i
$918$	93.5755	+	93.5755i	0.101934	+	0.101934i
$919$	535.029			0.582186			0.291093	−	0.956695i	$-0.405981\pi$
$919$	535.029			0.582186			0.291093	+	0.956695i	$0.405981\pi$
$920$		0			0
$921$	−65.0806	−	65.0806i	−0.0706630	−	0.0706630i
$922$		−	448.908i		−	0.486885i
$923$	582.241	+	582.241i	0.630813	+	0.630813i
$924$	−120.272			−0.130165
$925$		0			0
$926$	−1050.80			−1.13477
$927$		−	436.163i		−	0.470511i
$928$	−193.576	+	193.576i	−0.208594	+	0.208594i
$929$	259.243	−	259.243i	0.279056	−	0.279056i	−0.553676	−	0.832732i	$-0.686775\pi$
$929$	259.243	−	259.243i	0.279056	−	0.279056i	0.832732	+	0.553676i	$0.186775\pi$
$930$		0			0
$931$	240.545	+	240.545i	0.258373	+	0.258373i
$932$	188.000			0.201717
$933$		−	140.139i		−	0.150202i
$934$	621.893	+	621.893i	0.665839	+	0.665839i
$935$		0			0
$936$	228.747	−	228.747i	0.244388	−	0.244388i
$937$	74.3347			0.0793327			0.0396663	−	0.999213i	$-0.487371\pi$
$937$	74.3347			0.0793327			0.0396663	+	0.999213i	$0.487371\pi$
$938$	−784.423	+	784.423i	−0.836272	+	0.836272i
$939$	148.604			0.158257
$940$		0			0
$941$	1033.57	−	1033.57i	1.09838	−	1.09838i	0.103778	−	0.994600i	$-0.466907\pi$
$941$	1033.57	−	1033.57i	1.09838	−	1.09838i	0.994600	−	0.103778i	$-0.0330933\pi$
$942$	52.8627	−	52.8627i	0.0561176	−	0.0561176i
$943$	−1513.82	−	1513.82i	−1.60532	−	1.60532i
$944$	−213.666	−	213.666i	−0.226341	−	0.226341i
$945$		0			0
$946$			319.816i			0.338072i
$947$	135.553	+	135.553i	0.143139	+	0.143139i	0.775045	−	0.631906i	$-0.217727\pi$
$947$	135.553	+	135.553i	0.143139	+	0.143139i	−0.631906	+	0.775045i	$0.717727\pi$
$948$			67.2327i			0.0709205i
$949$	−881.241	+	881.241i	−0.928599	+	0.928599i
$950$		0			0
$951$	7.31430	−	7.31430i	0.00769116	−	0.00769116i
$952$	−312.272			−0.328017
$953$		−	316.757i		−	0.332379i	−0.986094	−	0.166189i	$-0.946854\pi$
$953$		−	316.757i		−	0.332379i	0.986094	−	0.166189i	$-0.0531463\pi$
$954$	701.170	−	701.170i	0.734979	−	0.734979i
$955$		0			0
$956$	−559.287	−	559.287i	−0.585028	−	0.585028i
$957$	−218.019	−	218.019i	−0.227815	−	0.227815i
$958$	−716.014			−0.747405
$959$			1152.01i			1.20127i
$960$		0			0
$961$			704.454i			0.733043i
$962$			824.120i			0.856674i
$963$	−750.093			−0.778913
$964$	518.120	−	518.120i	0.537469	−	0.537469i
$965$		0			0
$966$		−	200.091i		−	0.207133i
$967$	1341.08	−	1341.08i	1.38685	−	1.38685i	0.554996	−	0.831853i	$-0.312720\pi$
$967$	1341.08	−	1341.08i	1.38685	−	1.38685i	0.831853	−	0.554996i	$-0.187280\pi$
$968$	159.818	−	159.818i	0.165102	−	0.165102i
$969$	−31.5459	−	31.5459i	−0.0325551	−	0.0325551i
$970$		0			0
$971$	−1180.05			−1.21529			−0.607644	−	0.794209i	$-0.707885\pi$
$971$	−1180.05			−1.21529			−0.607644	+	0.794209i	$0.707885\pi$
$972$		−	211.950i		−	0.218056i
$973$	144.303	+	144.303i	0.148307	+	0.148307i
$974$			195.501i			0.200719i
$975$		0			0
$976$	276.363			0.283159
$977$	311.817	−	311.817i	0.319158	−	0.319158i	−0.529286	−	0.848444i	$-0.677540\pi$
$977$	311.817	−	311.817i	0.319158	−	0.319158i	0.848444	+	0.529286i	$0.177540\pi$
$978$	−110.806			−0.113299
$979$		−	715.560i		−	0.730909i
$980$		0			0
$981$	942.980	−	942.980i	0.961243	−	0.961243i
$982$	667.923	+	667.923i	0.680166	+	0.680166i
$983$	−73.7661	−	73.7661i	−0.0750418	−	0.0750418i	0.668590	−	0.743631i	$-0.266898\pi$
$983$	−73.7661	−	73.7661i	−0.0750418	−	0.0750418i	−0.743631	+	0.668590i	$0.766898\pi$
$984$	−81.6163			−0.0829434
$985$		0			0
$986$	−566.060	−	566.060i	−0.574098	−	0.574098i
$987$			356.772i			0.361471i
$988$	−156.000	+	156.000i	−0.157895	+	0.157895i
$989$	−532.061			−0.537979
$990$		0			0
$991$	1075.65			1.08542			0.542710	−	0.839920i	$-0.317398\pi$
$991$	1075.65			1.08542			0.542710	+	0.839920i	$0.317398\pi$
$992$			90.6061i			0.0913368i
$993$	11.3051	−	11.3051i	0.0113848	−	0.0113848i
$994$	−597.848	+	597.848i	−0.601457	+	0.601457i
$995$		0			0
$996$	−4.86939	−	4.86939i	−0.00488895	−	0.00488895i
$997$	−662.362			−0.664355			−0.332178	−	0.943217i	$-0.607783\pi$
$997$	−662.362			−0.664355			−0.332178	+	0.943217i	$0.607783\pi$
$998$		−	187.955i		−	0.188331i
$999$	253.576	+	253.576i	0.253829	+	0.253829i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.3.k.g.551.2	yes	4
5.2	odd	4		650.3.f.h.499.1		4
5.3	odd	4		650.3.f.g.499.2		4
5.4	even	2		650.3.k.f.551.1	yes	4
13.8	odd	4	inner	650.3.k.g.151.2	yes	4
65.8	even	4		650.3.f.h.99.2		4
65.34	odd	4		650.3.k.f.151.1	✓	4
65.47	even	4		650.3.f.g.99.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
650.3.f.g.99.1		4	65.47	even	4
650.3.f.g.499.2		4	5.3	odd	4
650.3.f.h.99.2		4	65.8	even	4
650.3.f.h.499.1		4	5.2	odd	4
650.3.k.f.151.1	✓	4	65.34	odd	4
650.3.k.f.551.1	yes	4	5.4	even	2
650.3.k.g.151.2	yes	4	13.8	odd	4	inner
650.3.k.g.551.2	yes	4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	650.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.00000i) q^{2} +0.449490 q^{3} -2.00000i q^{4} +(0.449490 - 0.449490i) q^{6} +(6.67423 + 6.67423i) q^{7} +(-2.00000 - 2.00000i) q^{8} -8.79796 q^{9} +(-10.0227 - 10.0227i) q^{11} -0.898979i q^{12} -13.0000i q^{13} +13.3485 q^{14} -4.00000 q^{16} -11.6969i q^{17} +(-8.79796 + 8.79796i) q^{18} +(6.00000 - 6.00000i) q^{19} +(3.00000 + 3.00000i) q^{21} -20.0454 q^{22} -33.3485i q^{23} +(-0.898979 - 0.898979i) q^{24} +(-13.0000 - 13.0000i) q^{26} -8.00000 q^{27} +(13.3485 - 13.3485i) q^{28} +48.3939 q^{29} +(11.3258 - 11.3258i) q^{31} +(-4.00000 + 4.00000i) q^{32} +(-4.50510 - 4.50510i) q^{33} +(-11.6969 - 11.6969i) q^{34} +17.5959i q^{36} +(-31.6969 - 31.6969i) q^{37} -12.0000i q^{38} -5.84337i q^{39} +(45.3939 - 45.3939i) q^{41} +6.00000 q^{42} -15.9546i q^{43} +(-20.0454 + 20.0454i) q^{44} +(-33.3485 - 33.3485i) q^{46} +(59.4620 + 59.4620i) q^{47} -1.79796 q^{48} +40.0908i q^{49} -5.25765i q^{51} -26.0000 q^{52} -79.6969 q^{53} +(-8.00000 + 8.00000i) q^{54} -26.6969i q^{56} +(2.69694 - 2.69694i) q^{57} +(48.3939 - 48.3939i) q^{58} +(53.4166 + 53.4166i) q^{59} -69.0908 q^{61} -22.6515i q^{62} +(-58.7196 - 58.7196i) q^{63} +8.00000i q^{64} -9.01021 q^{66} +(-58.7650 + 58.7650i) q^{67} -23.3939 q^{68} -14.9898i q^{69} +(-44.7878 + 44.7878i) q^{71} +(17.5959 + 17.5959i) q^{72} +(-67.7878 - 67.7878i) q^{73} -63.3939 q^{74} +(-12.0000 - 12.0000i) q^{76} -133.788i q^{77} +(-5.84337 - 5.84337i) q^{78} -74.7878 q^{79} +75.5857 q^{81} -90.7878i q^{82} +(5.41658 - 5.41658i) q^{83} +(6.00000 - 6.00000i) q^{84} +(-15.9546 - 15.9546i) q^{86} +21.7526 q^{87} +40.0908i q^{88} +(35.6969 + 35.6969i) q^{89} +(86.7650 - 86.7650i) q^{91} -66.6969 q^{92} +(5.09082 - 5.09082i) q^{93} +118.924 q^{94} +(-1.79796 + 1.79796i) q^{96} +(61.3939 - 61.3939i) q^{97} +(40.0908 + 40.0908i) q^{98} +(88.1793 + 88.1793i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 8 q^{3} - 8 q^{6} + 12 q^{7} - 8 q^{8} + 4 q^{9} + 4 q^{11} + 24 q^{14} - 16 q^{16} + 4 q^{18} + 24 q^{19} + 12 q^{21} + 8 q^{22} + 16 q^{24} - 52 q^{26} - 32 q^{27} + 24 q^{28} + 76 q^{29}+ \cdots + 436 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 8 * q^3 - 8 * q^6 + 12 * q^7 - 8 * q^8 + 4 * q^9 + 4 * q^11 + 24 * q^14 - 16 * q^16 + 4 * q^18 + 24 * q^19 + 12 * q^21 + 8 * q^22 + 16 * q^24 - 52 * q^26 - 32 * q^27 + 24 * q^28 + 76 * q^29 + 60 * q^31 - 16 * q^32 - 116 * q^33 + 12 * q^34 - 68 * q^37 + 64 * q^41 + 24 * q^42 + 8 * q^44 - 104 * q^46 - 12 * q^47 + 32 * q^48 - 104 * q^52 - 260 * q^53 - 32 * q^54 - 48 * q^57 + 76 * q^58 + 52 * q^59 - 100 * q^61 - 132 * q^63 - 232 * q^66 - 44 * q^67 + 24 * q^68 + 56 * q^71 - 8 * q^72 - 36 * q^73 - 136 * q^74 - 48 * q^76 + 104 * q^78 - 64 * q^79 + 28 * q^81 - 140 * q^83 + 24 * q^84 - 152 * q^86 + 136 * q^87 + 84 * q^89 + 156 * q^91 - 208 * q^92 - 156 * q^93 - 24 * q^94 + 32 * q^96 + 128 * q^97 - 16 * q^98 + 436 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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