LMFDB - Embedded newform 650.3.f.g.499.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [650,3,Mod(99,650)] 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("650.99"); 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([2, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	650.f (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,-4,0,0,0,-8,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == 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			499.2
Root			$1.22474 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	650.499
Dual form			650.3.f.g.99.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 - 1.00000i) q^{2} +0.449490i q^{3} +2.00000i q^{4} +(0.449490 - 0.449490i) q^{6} +(6.67423 - 6.67423i) q^{7} +(2.00000 - 2.00000i) q^{8} +8.79796 q^{9} +(-10.0227 - 10.0227i) q^{11} -0.898979 q^{12} +13.0000 q^{13} -13.3485 q^{14} -4.00000 q^{16} -11.6969 q^{17} +(-8.79796 - 8.79796i) q^{18} +(-6.00000 + 6.00000i) q^{19} +(3.00000 + 3.00000i) q^{21} +20.0454i q^{22} +33.3485 q^{23} +(0.898979 + 0.898979i) q^{24} +(-13.0000 - 13.0000i) q^{26} +8.00000i q^{27} +(13.3485 + 13.3485i) q^{28} -48.3939 q^{29} +(11.3258 - 11.3258i) q^{31} +(4.00000 + 4.00000i) q^{32} +(4.50510 - 4.50510i) q^{33} +(11.6969 + 11.6969i) q^{34} +17.5959i q^{36} +(-31.6969 + 31.6969i) q^{37} +12.0000 q^{38} +5.84337i q^{39} +(45.3939 - 45.3939i) q^{41} -6.00000i q^{42} +15.9546 q^{43} +(20.0454 - 20.0454i) q^{44} +(-33.3485 - 33.3485i) q^{46} +(59.4620 - 59.4620i) q^{47} -1.79796i q^{48} -40.0908i q^{49} -5.25765i q^{51} +26.0000i q^{52} -79.6969i q^{53} +(8.00000 - 8.00000i) q^{54} -26.6969i q^{56} +(-2.69694 - 2.69694i) q^{57} +(48.3939 + 48.3939i) q^{58} +(-53.4166 - 53.4166i) q^{59} -69.0908 q^{61} -22.6515 q^{62} +(58.7196 - 58.7196i) q^{63} -8.00000i q^{64} -9.01021 q^{66} +(58.7650 + 58.7650i) q^{67} -23.3939i q^{68} +14.9898i q^{69} +(-44.7878 + 44.7878i) q^{71} +(17.5959 - 17.5959i) q^{72} +(67.7878 - 67.7878i) q^{73} +63.3939 q^{74} +(-12.0000 - 12.0000i) q^{76} -133.788 q^{77} +(5.84337 - 5.84337i) q^{78} +74.7878 q^{79} +75.5857 q^{81} -90.7878 q^{82} +(5.41658 + 5.41658i) q^{83} +(-6.00000 + 6.00000i) q^{84} +(-15.9546 - 15.9546i) q^{86} -21.7526i q^{87} -40.0908 q^{88} +(-35.6969 - 35.6969i) q^{89} +(86.7650 - 86.7650i) q^{91} +66.6969i q^{92} +(5.09082 + 5.09082i) q^{93} -118.924 q^{94} +(-1.79796 + 1.79796i) q^{96} +(-61.3939 - 61.3939i) q^{97} +(-40.0908 + 40.0908i) q^{98} +(-88.1793 - 88.1793i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 8 q^{6} + 12 q^{7} + 8 q^{8} - 4 q^{9} + 4 q^{11} + 16 q^{12} + 52 q^{13} - 24 q^{14} - 16 q^{16} + 12 q^{17} + 4 q^{18} - 24 q^{19} + 12 q^{21} + 104 q^{23} - 16 q^{24} - 52 q^{26} + 24 q^{28}+ \cdots - 436 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 - 8 * q^6 + 12 * q^7 + 8 * q^8 - 4 * q^9 + 4 * q^11 + 16 * q^12 + 52 * q^13 - 24 * q^14 - 16 * q^16 + 12 * q^17 + 4 * q^18 - 24 * q^19 + 12 * q^21 + 104 * q^23 - 16 * q^24 - 52 * q^26 + 24 * q^28 - 76 * q^29 + 60 * q^31 + 16 * q^32 + 116 * q^33 - 12 * q^34 - 68 * q^37 + 48 * q^38 + 64 * q^41 + 152 * q^43 - 8 * q^44 - 104 * q^46 - 12 * q^47 + 32 * q^54 + 48 * q^57 + 76 * q^58 - 52 * q^59 - 100 * q^61 - 120 * q^62 + 132 * q^63 - 232 * q^66 + 44 * q^67 + 56 * q^71 - 8 * q^72 + 36 * q^73 + 136 * q^74 - 48 * q^76 - 300 * q^77 - 104 * q^78 + 64 * q^79 + 28 * q^81 - 128 * q^82 - 140 * q^83 - 24 * q^84 - 152 * q^86 + 16 * q^88 - 84 * q^89 + 156 * q^91 - 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
$3$			0.449490i			0.149830i	0.997190	+	0.0749150i	$0.0238685\pi$
$3$			0.449490i			0.149830i	−0.997190	+	0.0749150i	$0.976131\pi$
$4$			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	−0.0455022	−	0.998964i	$-0.514489\pi$
$7$	6.67423	−	6.67423i	0.953462	−	0.953462i	0.998964	+	0.0455022i	$0.0144888\pi$
$8$	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	$0.972844\pi$
$12$	−0.898979			−0.0749150
$13$	13.0000			1.00000
$13$	13.0000			1.00000
$14$	−13.3485			−0.953462
$15$		0			0
$16$	−4.00000			−0.250000
$17$	−11.6969			−0.688055			−0.344028	−	0.938960i	$-0.611791\pi$
$17$	−11.6969			−0.688055			−0.344028	+	0.938960i	$0.611791\pi$
$18$	−8.79796	−	8.79796i	−0.488775	−	0.488775i
$19$	−6.00000	+	6.00000i	−0.315789	+	0.315789i	−0.847147	−	0.531358i	$-0.821682\pi$
$19$	−6.00000	+	6.00000i	−0.315789	+	0.315789i	0.531358	+	0.847147i	$0.321682\pi$
$20$		0			0
$21$	3.00000	+	3.00000i	0.142857	+	0.142857i
$22$			20.0454i			0.911155i
$23$	33.3485			1.44993			0.724967	−	0.688784i	$-0.241855\pi$
$23$	33.3485			1.44993			0.724967	+	0.688784i	$0.241855\pi$
$24$	0.898979	+	0.898979i	0.0374575	+	0.0374575i
$25$		0			0
$26$	−13.0000	−	13.0000i	−0.500000	−	0.500000i
$27$			8.00000i			0.296296i
$28$	13.3485	+	13.3485i	0.476731	+	0.476731i
$29$	−48.3939			−1.66875			−0.834377	−	0.551194i	$-0.814172\pi$
$29$	−48.3939			−1.66875			−0.834377	+	0.551194i	$0.814172\pi$
$30$		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	−0.990945	−	0.134271i	$-0.957131\pi$
$37$	−31.6969	+	31.6969i	−0.856674	+	0.856674i	0.134271	+	0.990945i	$0.457131\pi$
$38$	12.0000			0.315789
$39$			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	$-0.0362531\pi$
$42$		−	6.00000i		−	0.142857i
$43$	15.9546			0.371037			0.185519	−	0.982641i	$-0.440604\pi$
$43$	15.9546			0.371037			0.185519	+	0.982641i	$0.440604\pi$
$44$	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	0.316584	−	0.948564i	$-0.397464\pi$
$47$	59.4620	−	59.4620i	1.26515	−	1.26515i	0.948564	−	0.316584i	$-0.102536\pi$
$48$		−	1.79796i		−	0.0374575i
$49$		−	40.0908i		−	0.818180i
$50$		0			0
$51$		−	5.25765i		−	0.103091i
$52$			26.0000i			0.500000i
$53$		−	79.6969i		−	1.50372i	−0.659325	−	0.751858i	$-0.729158\pi$
$53$		−	79.6969i		−	1.50372i	0.659325	−	0.751858i	$-0.270842\pi$
$54$	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	0.0905281	−	0.995894i	$-0.471144\pi$
$59$	−53.4166	−	53.4166i	−0.905366	−	0.905366i	−0.995894	+	0.0905281i	$0.971144\pi$
$60$		0			0
$61$	−69.0908			−1.13264			−0.566318	−	0.824187i	$-0.691633\pi$
$61$	−69.0908			−1.13264			−0.566318	+	0.824187i	$0.691633\pi$
$62$	−22.6515			−0.365347
$63$	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	$-0.0370529\pi$
$67$	58.7650	+	58.7650i	0.877090	+	0.877090i	−0.116142	+	0.993233i	$0.537053\pi$
$68$		−	23.3939i		−	0.344028i
$69$			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	$-0.521986\pi$
$73$	67.7878	−	67.7878i	0.928599	−	0.928599i	0.997616	+	0.0690162i	$0.0219860\pi$
$74$	63.3939			0.856674
$75$		0			0
$76$	−12.0000	−	12.0000i	−0.157895	−	0.157895i
$77$	−133.788			−1.73750
$78$	5.84337	−	5.84337i	0.0749150	−	0.0749150i
$79$	74.7878			0.946680			0.473340	−	0.880880i	$-0.343048\pi$
$79$	74.7878			0.946680			0.473340	+	0.880880i	$0.343048\pi$
$80$		0			0
$81$	75.5857			0.933157
$82$	−90.7878			−1.10717
$83$	5.41658	+	5.41658i	0.0652600	+	0.0652600i	0.738984	−	0.673724i	$-0.235306\pi$
$83$	5.41658	+	5.41658i	0.0652600	+	0.0652600i	−0.673724	+	0.738984i	$0.735306\pi$
$84$	−6.00000	+	6.00000i	−0.0714286	+	0.0714286i
$85$		0			0
$86$	−15.9546	−	15.9546i	−0.185519	−	0.185519i
$87$		−	21.7526i		−	0.250029i
$88$	−40.0908			−0.455577
$89$	−35.6969	−	35.6969i	−0.401089	−	0.401089i	0.477528	−	0.878617i	$-0.341533\pi$
$89$	−35.6969	−	35.6969i	−0.401089	−	0.401089i	−0.878617	+	0.477528i	$0.841533\pi$
$90$		0			0
$91$	86.7650	−	86.7650i	0.953462	−	0.953462i
$92$			66.6969i			0.724967i
$93$	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	$-0.397702\pi$
$97$	−61.3939	−	61.3939i	−0.632927	−	0.632927i	−0.948801	+	0.315874i	$0.897702\pi$
$98$	−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
$103$	−49.5755			−0.481316			−0.240658	−	0.970610i	$-0.577363\pi$
$103$	−49.5755			−0.481316			−0.240658	+	0.970610i	$0.577363\pi$
$104$	26.0000	−	26.0000i	0.250000	−	0.250000i
$105$		0			0
$106$	−79.6969	+	79.6969i	−0.751858	+	0.751858i
$107$		−	85.2577i		−	0.796801i	−0.917212	−	0.398400i	$-0.869566\pi$
$107$		−	85.2577i		−	0.796801i	0.917212	−	0.398400i	$-0.130434\pi$
$108$	−16.0000			−0.148148
$109$	107.182	−	107.182i	0.983318	−	0.983318i	−0.0165454	−	0.999863i	$-0.505267\pi$
$109$	107.182	−	107.182i	0.983318	−	0.983318i	0.999863	+	0.0165454i	$0.00526681\pi$
$110$		0			0
$111$	−14.2474	−	14.2474i	−0.128355	−	0.128355i
$112$	−26.6969	+	26.6969i	−0.238366	+	0.238366i
$113$			45.3939i			0.401716i	0.979620	+	0.200858i	$0.0643729\pi$
$113$			45.3939i			0.401716i	−0.979620	+	0.200858i	$0.935627\pi$
$114$			5.39388i			0.0473147i
$115$		0			0
$116$		−	96.7878i		−	0.834377i
$117$	114.373			0.977551
$118$			106.833i			0.905366i
$119$	−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
$127$	−170.788			−1.34479			−0.672393	−	0.740195i	$-0.734733\pi$
$127$	−170.788			−1.34479			−0.672393	+	0.740195i	$0.734733\pi$
$128$	−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
$133$			80.0908i			0.602187i
$134$		−	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	−0.318106	−	0.948055i	$-0.603047\pi$
$137$	86.3031	−	86.3031i	0.629949	−	0.629949i	0.948055	+	0.318106i	$0.103047\pi$
$138$	14.9898	−	14.9898i	0.108622	−	0.108622i
$139$	−21.6209			−0.155546			−0.0777731	−	0.996971i	$-0.524781\pi$
$139$	−21.6209			−0.155546			−0.0777731	+	0.996971i	$0.524781\pi$
$140$		0			0
$141$	26.7276	+	26.7276i	0.189557	+	0.189557i
$142$	89.5755			0.630813
$143$	−130.295	−	130.295i	−0.911155	−	0.911155i
$144$	−35.1918			−0.244388
$145$		0			0
$146$	−135.576			−0.928599
$147$	18.0204			0.122588
$148$	−63.3939	−	63.3939i	−0.428337	−	0.428337i
$149$	−55.9092	+	55.9092i	−0.375229	+	0.375229i	−0.869378	−	0.494148i	$-0.835480\pi$
$149$	−55.9092	+	55.9092i	−0.375229	+	0.375229i	0.494148	+	0.869378i	$0.335480\pi$
$150$		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	$0.638431\pi$
$152$			24.0000i			0.157895i
$153$	−102.909			−0.672609
$154$	133.788	+	133.788i	0.868752	+	0.868752i
$155$		0			0
$156$	−11.6867			−0.0749150
$157$		−	117.606i		−	0.749084i	−0.927210	−	0.374542i	$-0.877800\pi$
$157$		−	117.606i		−	0.749084i	0.927210	−	0.374542i	$-0.122200\pi$
$158$	−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	$-0.570424\pi$
$163$	123.258	−	123.258i	0.756182	−	0.756182i	0.975625	+	0.219443i	$0.0704241\pi$
$164$	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	−0.825432	−	0.564501i	$-0.809069\pi$
$167$	−43.5755	+	43.5755i	−0.260931	+	0.260931i	0.564501	+	0.825432i	$0.309069\pi$
$168$	12.0000			0.0714286
$169$	169.000			1.00000
$170$		0			0
$171$	−52.7878	+	52.7878i	−0.308700	+	0.308700i
$172$			31.9092i			0.185519i
$173$	−52.7276			−0.304784			−0.152392	−	0.988320i	$-0.548698\pi$
$173$	−52.7276			−0.304784			−0.152392	+	0.988320i	$0.548698\pi$
$174$	−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
$178$			71.3939i			0.401089i
$179$			140.000i			0.782123i	0.920365	+	0.391061i	$0.127892\pi$
$179$			140.000i			0.782123i	−0.920365	+	0.391061i	$0.872108\pi$
$180$		0			0
$181$			245.363i			1.35560i	0.735247	+	0.677799i	$0.237066\pi$
$181$			245.363i			1.35560i	−0.735247	+	0.677799i	$0.762934\pi$
$182$	−173.530			−0.953462
$183$		−	31.0556i		−	0.169703i
$184$	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	$0.464271\pi$
$192$	3.59592			0.0187287
$193$	−53.1214	+	53.1214i	−0.275241	+	0.275241i	−0.831206	−	0.555965i	$-0.812349\pi$
$193$	−53.1214	+	53.1214i	−0.275241	+	0.275241i	0.555965	+	0.831206i	$0.312349\pi$
$194$			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	$-0.0399540\pi$
$197$	170.788	+	170.788i	0.866943	+	0.866943i	−0.125190	+	0.992133i	$0.539954\pi$
$198$			176.359i			0.890700i
$199$			266.788i			1.34064i	0.742071	+	0.670321i	$0.233844\pi$
$199$			266.788i			1.34064i	−0.742071	+	0.670321i	$0.766156\pi$
$200$		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
$207$	293.398			1.41738
$208$	−52.0000			−0.250000
$209$	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	$0.449653\pi$
$212$	159.394			0.751858
$213$	−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
$217$		−	151.182i		−	0.696690i
$218$	−214.363			−0.983318
$219$	30.4699	+	30.4699i	0.139132	+	0.139132i
$220$		0			0
$221$	−152.060			−0.688055
$222$			28.4949i			0.128355i
$223$	211.439	+	211.439i	0.948158	+	0.948158i	0.998721	−	0.0505627i	$-0.0161015\pi$
$223$	211.439	+	211.439i	0.948158	+	0.948158i	−0.0505627	+	0.998721i	$0.516101\pi$
$224$	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	$-0.192196\pi$
$227$	57.9773	+	57.9773i	0.255407	+	0.255407i	−0.567776	+	0.823183i	$0.692196\pi$
$228$	5.39388	−	5.39388i	0.0236574	−	0.0236574i
$229$	−259.151	−	259.151i	−1.13166	−	1.13166i	−0.989901	−	0.141763i	$-0.954723\pi$
$229$	−259.151	−	259.151i	−1.13166	−	1.13166i	−0.141763	−	0.989901i	$-0.545277\pi$
$230$		0			0
$231$		−	60.1362i		−	0.260330i
$232$	−96.7878	+	96.7878i	−0.417189	+	0.417189i
$233$	−94.0000			−0.403433			−0.201717	−	0.979444i	$-0.564652\pi$
$233$	−94.0000			−0.403433			−0.201717	+	0.979444i	$0.564652\pi$
$234$	−114.373	−	114.373i	−0.488775	−	0.488775i
$235$		0			0
$236$	106.833	−	106.833i	0.452683	−	0.452683i
$237$			33.6163i			0.141841i
$238$	156.136			0.656035
$239$	−279.644	+	279.644i	−1.17006	+	1.17006i	−0.187861	+	0.982196i	$0.560156\pi$
$239$	−279.644	+	279.644i	−1.17006	+	1.17006i	−0.982196	+	0.187861i	$0.939844\pi$
$240$		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
$243$			105.975i			0.436111i
$244$		−	138.182i		−	0.566318i
$245$		0			0
$246$		−	40.8082i		−	0.165887i
$247$	−78.0000	+	78.0000i	−0.315789	+	0.315789i
$248$		−	45.3031i		−	0.182674i
$249$	−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
$257$	−318.212			−1.23818			−0.619090	−	0.785320i	$-0.712498\pi$
$257$	−318.212			−1.23818			−0.619090	+	0.785320i	$0.712498\pi$
$258$	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
$263$		−	80.4995i		−	0.306082i	−0.988220	−	0.153041i	$-0.951093\pi$
$263$		−	80.4995i		−	0.306082i	0.988220	−	0.153041i	$-0.0489066\pi$
$264$		−	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	$-0.473200\pi$
$269$	45.2429			0.168189			0.0840945	+	0.996458i	$0.473200\pi$
$270$		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	$0.541649\pi$
$272$	46.7878			0.172014
$273$	39.0000	+	39.0000i	0.142857	+	0.142857i
$274$	−172.606			−0.629949
$275$		0			0
$276$	−29.9796			−0.108622
$277$	297.151			1.07275			0.536374	−	0.843981i	$-0.319794\pi$
$277$	297.151			1.07275			0.536374	+	0.843981i	$0.319794\pi$
$278$	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	$0.925511\pi$
$282$		−	53.4551i		−	0.189557i
$283$	231.106			0.816628			0.408314	−	0.912842i	$-0.366117\pi$
$283$	231.106			0.816628			0.408314	+	0.912842i	$0.366117\pi$
$284$	−89.5755	−	89.5755i	−0.315407	−	0.315407i
$285$		0			0
$286$			260.590i			0.911155i
$287$		−	605.939i		−	2.11128i
$288$	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	$-0.727541\pi$
$293$	29.2122	−	29.2122i	0.0997005	−	0.0997005i	0.755198	+	0.655497i	$0.227541\pi$
$294$	−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
$298$	111.818			0.375229
$299$	433.530			1.44993
$300$		0			0
$301$	106.485	−	106.485i	0.353770	−	0.353770i
$302$		−	146.652i		−	0.485601i
$303$	−43.3689			−0.143132
$304$	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	−0.902439	−	0.430818i	$-0.858225\pi$
$307$	−144.788	+	144.788i	−0.471621	+	0.471621i	0.430818	+	0.902439i	$0.358225\pi$
$308$		−	267.576i		−	0.868752i
$309$		−	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
$313$			330.605i			1.05625i	0.849168	+	0.528123i	$0.177104\pi$
$313$			330.605i			1.05625i	−0.849168	+	0.528123i	$0.822896\pi$
$314$	−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	$-0.261556\pi$
$317$	−16.2724	−	16.2724i	−0.0513326	−	0.0513326i	−0.732307	+	0.680974i	$0.761556\pi$
$318$	−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
$322$	−445.151			−1.38246
$323$	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
$328$		−	181.576i		−	0.553584i
$329$		−	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
$337$	−345.454			−1.02509			−0.512543	−	0.858661i	$-0.671297\pi$
$337$	−345.454			−1.02509			−0.512543	+	0.858661i	$0.671297\pi$
$338$	−169.000	−	169.000i	−0.500000	−	0.500000i
$339$	−20.4041			−0.0601890
$340$		0			0
$341$	−227.030			−0.665776
$342$	105.576			0.308700
$343$	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
$347$			237.621i			0.684786i	0.939557	+	0.342393i	$0.111238\pi$
$347$			237.621i			0.684786i	−0.939557	+	0.342393i	$0.888762\pi$
$348$	43.5051			0.125015
$349$	−18.8786	−	18.8786i	−0.0540933	−	0.0540933i	0.679543	−	0.733636i	$-0.262178\pi$
$349$	−18.8786	−	18.8786i	−0.0540933	−	0.0540933i	−0.733636	+	0.679543i	$0.762178\pi$
$350$		0			0
$351$			104.000i			0.296296i
$352$		−	80.1816i		−	0.227789i
$353$	196.485	+	196.485i	0.556614	+	0.556614i	0.928342	−	0.371728i	$-0.121235\pi$
$353$	196.485	+	196.485i	0.556614	+	0.556614i	−0.371728	+	0.928342i	$0.621235\pi$
$354$	−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	$-0.999590\pi$
$359$	−359.462	−	359.462i	−1.00129	−	1.00129i	−0.00128770	−	0.999999i	$-0.500410\pi$
$360$		0			0
$361$			289.000i			0.800554i
$362$	245.363	−	245.363i	0.677799	−	0.677799i
$363$	−35.9184			−0.0989486
$364$	173.530	+	173.530i	0.476731	+	0.476731i
$365$		0			0
$366$	−31.0556	+	31.0556i	−0.0848514	+	0.0848514i
$367$			491.287i			1.33866i	0.742966	+	0.669329i	$0.233418\pi$
$367$			491.287i			1.33866i	−0.742966	+	0.669329i	$0.766582\pi$
$368$	−133.394			−0.362483
$369$	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
$373$		−	528.939i		−	1.41807i	−0.705175	−	0.709033i	$-0.749132\pi$
$373$		−	528.939i		−	1.41807i	0.705175	−	0.709033i	$-0.250868\pi$
$374$		−	234.470i		−	0.626925i
$375$		0			0
$376$		−	237.848i		−	0.632574i
$377$	−629.120			−1.66875
$378$		−	106.788i		−	0.282507i
$379$	−246.765	+	246.765i	−0.651095	+	0.651095i	−0.953257	−	0.302162i	$-0.902292\pi$
$379$	−246.765	+	246.765i	−0.651095	+	0.651095i	0.302162	+	0.953257i	$0.402292\pi$
$380$		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	0.996187	+	0.0872426i	$0.0278055\pi$
$383$	414.954	+	414.954i	1.08343	+	1.08343i	0.0872426	+	0.996187i	$0.472194\pi$
$384$	−3.59592	−	3.59592i	−0.00936437	−	0.00936437i
$385$		0			0
$386$	106.243			0.275241
$387$	140.368			0.362708
$388$	122.788	−	122.788i	0.316463	−	0.316463i
$389$		−	597.939i		−	1.53712i	−0.639779	−	0.768559i	$-0.720974\pi$
$389$		−	597.939i		−	1.53712i	0.639779	−	0.768559i	$-0.279026\pi$
$390$		0			0
$391$	−390.075			−0.997634
$392$	−80.1816	−	80.1816i	−0.204545	−	0.204545i
$393$			42.0408i			0.106974i
$394$		−	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	−1.00000		0.000228728i	$-0.999927\pi$
$397$	−396.909	+	396.909i	−0.999771	+	0.999771i	0.000228728		1.00000i	$0.499927\pi$
$398$	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	$0.822679\pi$
$402$	52.8286			0.131414
$403$	147.235	−	147.235i	0.365347	−	0.365347i
$404$	−192.969			−0.477647
$405$		0			0
$406$	645.984			1.59109
$407$	635.378			1.56113
$408$	−10.5153	−	10.5153i	−0.0257728	−	0.0257728i
$409$	−241.727	+	241.727i	−0.591018	+	0.591018i	−0.937907	−	0.346888i	$-0.887238\pi$
$409$	−241.727	+	241.727i	−0.591018	+	0.591018i	0.346888	+	0.937907i	$0.387238\pi$
$410$		0			0
$411$	38.7923	+	38.7923i	0.0943853	+	0.0943853i
$412$		−	99.1510i		−	0.240658i
$413$	−713.030			−1.72646
$414$	−293.398	−	293.398i	−0.708692	−	0.708692i
$415$		0			0
$416$	52.0000	+	52.0000i	0.125000	+	0.125000i
$417$		−	9.71838i		−	0.0233055i
$418$	−120.272	−	120.272i	−0.287733	−	0.287733i
$419$	−678.833			−1.62013			−0.810063	−	0.586342i	$-0.800567\pi$
$419$	−678.833			−1.62013			−0.810063	+	0.586342i	$0.800567\pi$
$420$		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
$428$	170.515			0.398400
$429$	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	$0.0976908\pi$
$432$		−	32.0000i		−	0.0740741i
$433$	−133.394			−0.308069			−0.154034	−	0.988065i	$-0.549227\pi$
$433$	−133.394			−0.308069			−0.154034	+	0.988065i	$0.549227\pi$
$434$	−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
$438$		−	60.9398i		−	0.139132i
$439$		−	782.302i		−	1.78201i	−0.453994	−	0.891005i	$-0.650001\pi$
$439$		−	782.302i		−	1.78201i	0.453994	−	0.891005i	$-0.349999\pi$
$440$		0			0
$441$		−	352.717i		−	0.799813i
$442$	152.060	+	152.060i	0.344028	+	0.344028i
$443$			354.742i			0.800773i	0.916346	+	0.400386i	$0.131124\pi$
$443$			354.742i			0.800773i	−0.916346	+	0.400386i	$0.868876\pi$
$444$	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	0.923446	−	0.383729i	$-0.125360\pi$
$449$	242.333	+	242.333i	0.539716	+	0.539716i	−0.383729	+	0.923446i	$0.625360\pi$
$450$		0			0
$451$	−909.939			−2.01760
$452$	−90.7878			−0.200858
$453$	−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	$-0.291203\pi$
$457$	−83.4245	−	83.4245i	−0.182548	−	0.182548i	−0.792465	+	0.609917i	$0.791203\pi$
$458$			518.302i			1.13166i
$459$		−	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	0.145402	−	0.989373i	$-0.453552\pi$
$463$	525.401	−	525.401i	1.13477	−	1.13477i	0.989373	−	0.145402i	$-0.0464476\pi$
$464$	193.576			0.417189
$465$		0			0
$466$	94.0000	+	94.0000i	0.201717	+	0.201717i
$467$	621.893			1.33168			0.665839	−	0.746096i	$-0.268074\pi$
$467$	621.893			1.33168			0.665839	+	0.746096i	$0.268074\pi$
$468$			228.747i			0.488775i
$469$	784.423			1.67254
$470$		0			0
$471$	52.8627			0.112235
$472$	−213.666			−0.452683
$473$	−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
$477$		−	701.170i		−	1.46996i
$478$	559.287			1.17006
$479$	358.007	+	358.007i	0.747405	+	0.747405i	0.973991	−	0.226586i	$-0.0727565\pi$
$479$	358.007	+	358.007i	0.747405	+	0.747405i	−0.226586	+	0.973991i	$0.572757\pi$
$480$		0			0
$481$	−412.060	+	412.060i	−0.856674	+	0.856674i
$482$		−	518.120i		−	1.07494i
$483$	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	$-0.204669\pi$
$487$	97.7503	+	97.7503i	0.200719	+	0.200719i	−0.599589	+	0.800308i	$0.704669\pi$
$488$	−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
$493$	566.060			1.14820
$494$	156.000			0.315789
$495$		0			0
$496$	−45.3031	+	45.3031i	−0.0913368	+	0.0913368i
$497$			597.848i			1.20291i
$498$	4.86939			0.00977790
$499$	−93.9773	+	93.9773i	−0.188331	+	0.188331i	−0.794974	−	0.606643i	$-0.792516\pi$
$499$	−93.9773	+	93.9773i	−0.188331	+	0.188331i	0.606643	+	0.794974i	$0.292516\pi$
$500$		0			0
$501$	−19.5867	−	19.5867i	−0.0390953	−	0.0390953i
$502$	67.1510	−	67.1510i	0.133767	−	0.133767i
$503$		−	68.7265i		−	0.136633i	−0.997664	−	0.0683166i	$-0.978237\pi$
$503$		−	68.7265i		−	0.136633i	0.997664	−	0.0683166i	$-0.0217628\pi$
$504$		−	234.879i		−	0.466029i
$505$		0			0
$506$			668.484i			1.32111i
$507$			75.9638i			0.149830i
$508$		−	341.576i		−	0.672393i
$509$	−488.545	+	488.545i	−0.959813	+	0.959813i	−0.999223	−	0.0394100i	$-0.987452\pi$
$509$	−488.545	+	488.545i	−0.959813	+	0.959813i	0.0394100	+	0.999223i	$0.487452\pi$
$510$		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
$517$	−1191.94			−2.30549
$518$	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
$523$			160.000i			0.305927i	0.988232	+	0.152964i	$0.0488817\pi$
$523$			160.000i			0.305927i	−0.988232	+	0.152964i	$0.951118\pi$
$524$			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
$532$	−160.182			−0.301093
$533$	590.120	−	590.120i	1.10717	−	1.10717i
$534$	−32.0908			−0.0600952
$535$		0			0
$536$	235.060			0.438545
$537$	−62.9286			−0.117185
$538$	−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	$0.790008\pi$
$542$		−	466.652i		−	0.860981i
$543$	−110.288			−0.203109
$544$	−46.7878	−	46.7878i	−0.0860069	−	0.0860069i
$545$		0			0
$546$		−	78.0000i		−	0.142857i
$547$		−	842.983i		−	1.54110i	−0.637378	−	0.770551i	$-0.719981\pi$
$547$		−	842.983i		−	1.54110i	0.637378	−	0.770551i	$-0.280019\pi$
$548$	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	−0.551266	−	0.834329i	$-0.685855\pi$
$557$	157.666	−	157.666i	0.283063	−	0.283063i	0.834329	+	0.551266i	$0.185855\pi$
$558$	−199.287			−0.357146
$559$	207.410			0.371037
$560$		0			0
$561$	−52.6959	+	52.6959i	−0.0939321	+	0.0939321i
$562$			416.363i			0.740860i
$563$	−100.486			−0.178483			−0.0892413	−	0.996010i	$-0.528444\pi$
$563$	−100.486			−0.178483			−0.0892413	+	0.996010i	$0.528444\pi$
$564$	−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
$568$			179.151i			0.315407i
$569$		−	692.212i		−	1.21654i	−0.793730	−	0.608271i	$-0.791863\pi$
$569$		−	692.212i		−	1.21654i	0.793730	−	0.608271i	$-0.208137\pi$
$570$		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
$573$			19.2327i			0.0335648i
$574$	−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	0.914030	+	0.405646i	$0.132953\pi$
$577$	761.453	+	761.453i	1.31968	+	1.31968i	0.405646	+	0.914030i	$0.367047\pi$
$578$	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
$582$	−55.1918			−0.0948313
$583$	−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	$-0.104136\pi$
$587$	367.235	+	367.235i	0.625613	+	0.625613i	−0.321348	+	0.946961i	$0.604136\pi$
$588$			36.0408i			0.0612939i
$589$			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	$-0.882599\pi$
$593$	−339.334	+	339.334i	−0.572232	+	0.572232i	0.360520	+	0.932752i	$0.382599\pi$
$594$	−160.363			−0.269972
$595$		0			0
$596$	−111.818	−	111.818i	−0.187615	−	0.187615i
$597$	−119.918			−0.200868
$598$	−433.530	−	433.530i	−0.724967	−	0.724967i
$599$	−931.741			−1.55549			−0.777747	−	0.628577i	$-0.783638\pi$
$599$	−931.741			−1.55549			−0.777747	+	0.628577i	$0.783638\pi$
$600$		0			0
$601$	−297.697			−0.495336			−0.247668	−	0.968845i	$-0.579664\pi$
$601$	−297.697			−0.495336			−0.247668	+	0.968845i	$0.579664\pi$
$602$	−212.969			−0.353770
$603$	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
$607$			219.650i			0.361862i	0.983496	+	0.180931i	$0.0579111\pi$
$607$			219.650i			0.361862i	−0.983496	+	0.180931i	$0.942089\pi$
$608$	−48.0000			−0.0789474
$609$	−145.182	−	145.182i	−0.238393	−	0.238393i
$610$		0			0
$611$	773.006	−	773.006i	1.26515	−	1.26515i
$612$		−	205.818i		−	0.336305i
$613$	392.363	+	392.363i	0.640071	+	0.640071i	0.950573	−	0.310502i	$-0.100497\pi$
$613$	392.363	+	392.363i	0.640071	+	0.640071i	−0.310502	+	0.950573i	$0.600497\pi$
$614$	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	$-0.0831984\pi$
$617$	436.605	+	436.605i	0.707626	+	0.707626i	−0.258410	+	0.966035i	$0.583198\pi$
$618$	−22.2837	+	22.2837i	−0.0360577	+	0.0360577i
$619$	282.363	+	282.363i	0.456160	+	0.456160i	0.897393	−	0.441232i	$-0.145459\pi$
$619$	282.363	+	282.363i	0.456160	+	0.456160i	−0.441232	+	0.897393i	$0.645459\pi$
$620$		0			0
$621$			266.788i			0.429610i
$622$	−311.773	+	311.773i	−0.501243	+	0.501243i
$623$	−476.499			−0.764847
$624$		−	23.3735i		−	0.0374575i
$625$		0			0
$626$	330.605	−	330.605i	0.528123	−	0.528123i
$627$			54.0612i			0.0862221i
$628$	235.212			0.374542
$629$	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
$633$			29.8775i			0.0471999i
$634$			32.5449i			0.0513326i
$635$		0			0
$636$			71.6459i			0.112651i
$637$		−	521.181i		−	0.818180i
$638$		−	970.075i		−	1.52049i
$639$	−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	0.991588	−	0.129436i	$-0.0413168\pi$
$643$	554.363	+	554.363i	0.862151	+	0.862151i	−0.129436	+	0.991588i	$0.541317\pi$
$644$	445.151	+	445.151i	0.691228	+	0.691228i
$645$		0			0
$646$	−140.363			−0.217281
$647$	−28.1362			−0.0434872			−0.0217436	−	0.999764i	$-0.506922\pi$
$647$	−28.1362			−0.0434872			−0.0217436	+	0.999764i	$0.506922\pi$
$648$	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
$653$			725.908i			1.11165i	0.831299	+	0.555826i	$0.187598\pi$
$653$			725.908i			1.11165i	−0.831299	+	0.555826i	$0.812402\pi$
$654$		−	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	$-0.111603\pi$
$659$	1237.82			1.87833			0.939163	+	0.343473i	$0.111603\pi$
$660$		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	$0.544637\pi$
$662$	−50.3020			−0.0759849
$663$		−	68.3495i		−	0.103091i
$664$	21.6663			0.0326300
$665$		0			0
$666$	557.737			0.837443
$667$	−1613.86			−2.41958
$668$	−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
$672$			24.0000i			0.0357143i
$673$	−711.272			−1.05687			−0.528434	−	0.848974i	$-0.677221\pi$
$673$	−711.272			−1.05687			−0.528434	+	0.848974i	$0.677221\pi$
$674$	345.454	+	345.454i	0.512543	+	0.512543i
$675$		0			0
$676$			338.000i			0.500000i
$677$			425.151i			0.627993i	0.949424	+	0.313996i	$0.101668\pi$
$677$			425.151i			0.627993i	−0.949424	+	0.313996i	$0.898332\pi$
$678$	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	$-0.773081\pi$
$683$	−69.9773	+	69.9773i	−0.102456	+	0.102456i	0.654021	+	0.756477i	$0.273081\pi$
$684$	−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
$688$	−63.8184			−0.0927593
$689$		−	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	$0.151494\pi$
$692$		−	105.455i		−	0.152392i
$693$	−1177.06			−1.69850
$694$	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
$698$			37.7571i			0.0540933i
$699$		−	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
$703$		−	380.363i		−	0.541057i
$704$	−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	0.990189	−	0.139738i	$-0.0446260\pi$
$709$	602.969	+	602.969i	0.850450	+	0.850450i	−0.139738	+	0.990189i	$0.544626\pi$
$710$		0			0
$711$	657.980			0.925428
$712$	−142.788			−0.200545
$713$	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
$718$			718.924i			1.00129i
$719$			749.589i			1.04254i	0.853391	+	0.521272i	$0.174542\pi$
$719$			749.589i			1.04254i	−0.853391	+	0.521272i	$0.825458\pi$
$720$		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
$727$	885.090			1.21745			0.608727	−	0.793379i	$-0.291680\pi$
$727$	885.090			1.21745			0.608727	+	0.793379i	$0.291680\pi$
$728$		−	347.060i		−	0.476731i
$729$	632.637			0.867814
$730$		0			0
$731$	−186.620			−0.255294
$732$	62.1112			0.0848514
$733$	−253.727	−	253.727i	−0.346148	−	0.346148i	0.512525	−	0.858673i	$-0.328710\pi$
$733$	−253.727	−	253.727i	−0.346148	−	0.346148i	−0.858673	+	0.512525i	$0.828710\pi$
$734$	491.287	−	491.287i	0.669329	−	0.669329i
$735$		0			0
$736$	133.394	+	133.394i	0.181242	+	0.181242i
$737$		−	1177.97i		−	1.59833i
$738$	−798.747			−1.08231
$739$	818.643	+	818.643i	1.10777	+	1.10777i	0.993443	+	0.114328i	$0.0364714\pi$
$739$	818.643	+	818.643i	1.10777	+	1.10777i	0.114328	+	0.993443i	$0.463529\pi$
$740$		0			0
$741$	−35.0602	−	35.0602i	−0.0473147	−	0.0473147i
$742$			1063.83i			1.43374i
$743$	223.705	+	223.705i	0.301083	+	0.301083i	0.841438	−	0.540354i	$-0.181710\pi$
$743$	223.705	+	223.705i	0.301083	+	0.301083i	−0.540354	+	0.841438i	$0.681710\pi$
$744$	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
$753$	−30.1837			−0.0400846
$754$	629.120	+	629.120i	0.834377	+	0.834377i
$755$		0			0
$756$	−106.788	+	106.788i	−0.141254	+	0.141254i
$757$		−	882.058i		−	1.16520i	−0.812758	−	0.582601i	$-0.802035\pi$
$757$		−	882.058i		−	1.16520i	0.812758	−	0.582601i	$-0.197965\pi$
$758$	493.530			0.651095
$759$	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
$763$		−	1430.71i		−	1.87511i
$764$			85.5755i			0.112010i
$765$		0			0
$766$		−	829.907i		−	1.08343i
$767$	−694.416	−	694.416i	−0.905366	−	0.905366i
$768$			7.19184i			0.00936437i
$769$	649.090	−	649.090i	0.844070	−	0.844070i	−0.145315	−	0.989385i	$-0.546420\pi$
$769$	649.090	−	649.090i	0.844070	−	0.844070i	0.989385	+	0.145315i	$0.0464197\pi$
$770$		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	0.196604	−	0.980483i	$-0.437009\pi$
$773$	−605.939	−	605.939i	−0.783879	−	0.783879i	−0.980483	+	0.196604i	$0.937009\pi$
$774$	−140.368	−	140.368i	−0.181354	−	0.181354i
$775$		0			0
$776$	−245.576			−0.316463
$777$	−190.182			−0.244764
$778$	−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
$783$		−	387.151i		−	0.494446i
$784$			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	0.229252	−	0.973367i	$-0.426372\pi$
$787$	946.461	−	946.461i	1.20262	−	1.20262i	0.973367	−	0.229252i	$-0.0736278\pi$
$788$	−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
$792$	−352.717			−0.445350
$793$	−898.181			−1.13264
$794$	793.818			0.999771
$795$		0			0
$796$	−533.576			−0.670321
$797$	832.878			1.04502			0.522508	−	0.852634i	$-0.324997\pi$
$797$	832.878			1.04502			0.522508	+	0.852634i	$0.324997\pi$
$798$	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
$802$			256.727i			0.320108i
$803$	−1358.83			−1.69220
$804$	−52.8286	−	52.8286i	−0.0657072	−	0.0657072i
$805$		0			0
$806$	−294.470			−0.365347
$807$			20.3362i			0.0251998i
$808$	192.969	+	192.969i	0.238823	+	0.238823i
$809$	−1194.00			−1.47590			−0.737948	−	0.674857i	$-0.764205\pi$
$809$	−1194.00			−1.47590			−0.737948	+	0.674857i	$0.764205\pi$
$810$		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
$818$	483.453			0.591018
$819$	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	$0.319224\pi$
$822$		−	77.5847i		−	0.0943853i
$823$	−1065.94			−1.29519			−0.647593	−	0.761986i	$-0.724224\pi$
$823$	−1065.94			−1.29519			−0.647593	+	0.761986i	$0.724224\pi$
$824$	−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	−0.775216	−	0.631697i	$-0.782359\pi$
$827$	−118.690	+	118.690i	−0.143519	+	0.143519i	0.631697	+	0.775216i	$0.282359\pi$
$828$			586.797i			0.708692i
$829$		−	1422.06i		−	1.71539i	−0.514157	−	0.857696i	$-0.671895\pi$
$829$		−	1422.06i		−	1.71539i	0.514157	−	0.857696i	$-0.328105\pi$
$830$		0			0
$831$			133.566i			0.160730i
$832$		−	104.000i		−	0.125000i
$833$			468.940i			0.562953i
$834$	−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	0.702360	−	0.711822i	$-0.252130\pi$
$839$	−7.93877	−	7.93877i	−0.00946218	−	0.00946218i	−0.711822	+	0.702360i	$0.752130\pi$
$840$		0			0
$841$	1500.97			1.78474
$842$	149.394			0.177427
$843$	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
$848$			318.788i			0.375929i
$849$			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	$-0.850281\pi$
$853$	−373.788	+	373.788i	−0.438204	+	0.438204i	0.453203	+	0.891407i	$0.350281\pi$
$854$	922.257			1.07993
$855$		0			0
$856$	−170.515	−	170.515i	−0.199200	−	0.199200i
$857$	181.031			0.211238			0.105619	−	0.994407i	$-0.466318\pi$
$857$	181.031			0.211238			0.105619	+	0.994407i	$0.466318\pi$
$858$	−117.133			−0.136518
$859$	1050.47			1.22290			0.611449	−	0.791284i	$-0.290587\pi$
$859$	1050.47			1.22290			0.611449	+	0.791284i	$0.290587\pi$
$860$		0			0
$861$	272.363			0.316334
$862$	−561.303			−0.651164
$863$	800.976	+	800.976i	0.928130	+	0.928130i	0.997585	−	0.0694550i	$-0.0221260\pi$
$863$	800.976	+	800.976i	0.928130	+	0.928130i	−0.0694550	+	0.997585i	$0.522126\pi$
$864$	−32.0000	+	32.0000i	−0.0370370	+	0.0370370i
$865$		0			0
$866$	133.394	+	133.394i	0.154034	+	0.154034i
$867$		−	68.4041i		−	0.0788974i
$868$	302.363			0.348345
$869$	−749.576	−	749.576i	−0.862573	−	0.862573i
$870$		0			0
$871$	763.946	+	763.946i	0.877090	+	0.877090i
$872$		−	428.727i		−	0.491659i
$873$	−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	$-0.438972\pi$
$877$	−693.817	−	693.817i	−0.791126	−	0.791126i	−0.981677	+	0.190551i	$0.938972\pi$
$878$	−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
$883$	1010.54			1.14444			0.572221	−	0.820099i	$-0.306082\pi$
$883$	1010.54			1.14444			0.572221	+	0.820099i	$0.306082\pi$
$884$		−	304.120i		−	0.344028i
$885$		0			0
$886$	354.742	−	354.742i	0.400386	−	0.400386i
$887$			338.424i			0.381538i	0.981635	+	0.190769i	$0.0610982\pi$
$887$			338.424i			0.381538i	−0.981635	+	0.190769i	$0.938902\pi$
$888$	−56.9898			−0.0641777
$889$	−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
$893$			713.544i			0.799041i
$894$			50.2612i			0.0562206i
$895$		0			0
$896$			106.788i			0.119183i
$897$			194.867i			0.217243i
$898$		−	484.665i		−	0.539716i
$899$	−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
$907$	−1255.39			−1.38411			−0.692057	−	0.721843i	$-0.743295\pi$
$907$	−1255.39			−1.38411			−0.692057	+	0.721843i	$0.743295\pi$
$908$	−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
$913$		−	108.578i		−	0.118924i
$914$			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	$-0.594019\pi$
$919$	−535.029			−0.582186			−0.291093	+	0.956695i	$0.594019\pi$
$920$		0			0
$921$	−65.0806	−	65.0806i	−0.0706630	−	0.0706630i
$922$	−448.908			−0.486885
$923$	−582.241	+	582.241i	−0.630813	+	0.630813i
$924$	120.272			0.130165
$925$		0			0
$926$	−1050.80			−1.13477
$927$	−436.163			−0.470511
$928$	−193.576	−	193.576i	−0.208594	−	0.208594i
$929$	−259.243	+	259.243i	−0.279056	+	0.279056i	−0.832732	−	0.553676i	$-0.813225\pi$
$929$	−259.243	+	259.243i	−0.279056	+	0.279056i	0.553676	+	0.832732i	$0.313225\pi$
$930$		0			0
$931$	240.545	+	240.545i	0.258373	+	0.258373i
$932$		−	188.000i		−	0.201717i
$933$	140.139			0.150202
$934$	−621.893	−	621.893i	−0.665839	−	0.665839i
$935$		0			0
$936$	228.747	−	228.747i	0.244388	−	0.244388i
$937$		−	74.3347i		−	0.0793327i	−0.999213	−	0.0396663i	$-0.987371\pi$
$937$		−	74.3347i		−	0.0793327i	0.999213	−	0.0396663i	$-0.0126295\pi$
$938$	−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	−0.631906	−	0.775045i	$-0.717727\pi$
$947$	135.553	−	135.553i	0.143139	−	0.143139i	0.775045	+	0.631906i	$0.217727\pi$
$948$	−67.2327			−0.0709205
$949$	881.241	−	881.241i	0.928599	−	0.928599i
$950$		0			0
$951$	7.31430	−	7.31430i	0.00769116	−	0.00769116i
$952$			312.272i			0.328017i
$953$	316.757			0.332379			0.166189	−	0.986094i	$-0.446854\pi$
$953$	316.757			0.332379			0.166189	+	0.986094i	$0.446854\pi$
$954$	−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
$958$		−	716.014i		−	0.747405i
$959$		−	1152.01i		−	1.20127i
$960$		0			0
$961$			704.454i			0.733043i
$962$	824.120			0.856674
$963$		−	750.093i		−	0.778913i
$964$	−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	−0.831853	−	0.554996i	$-0.812720\pi$
$967$	−1341.08	−	1341.08i	−1.38685	−	1.38685i	−0.554996	−	0.831853i	$-0.687280\pi$
$968$	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	$0.707885\pi$
$972$	−211.950			−0.218056
$973$	−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	$-0.322460\pi$
$977$	−311.817	−	311.817i	−0.319158	−	0.319158i	−0.848444	+	0.529286i	$0.822460\pi$
$978$		−	110.806i		−	0.113299i
$979$			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	$-0.733102\pi$
$983$	73.7661	−	73.7661i	0.0750418	−	0.0750418i	0.743631	+	0.668590i	$0.233102\pi$
$984$	81.6163			0.0829434
$985$		0			0
$986$	−566.060	−	566.060i	−0.574098	−	0.574098i
$987$	356.772			0.361471
$988$	−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	$0.317398\pi$
$992$	90.6061			0.0913368
$993$	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
$997$			662.362i			0.664355i	0.943217	+	0.332178i	$0.107783\pi$
$997$			662.362i			0.664355i	−0.943217	+	0.332178i	$0.892217\pi$
$998$	187.955			0.188331
$999$	−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.f.g.499.2		4
5.2	odd	4		650.3.k.g.551.2	yes	4
5.3	odd	4		650.3.k.f.551.1	yes	4
5.4	even	2		650.3.f.h.499.1		4
13.8	odd	4		650.3.f.h.99.2		4
65.8	even	4		650.3.k.f.151.1	✓	4
65.34	odd	4	inner	650.3.f.g.99.1		4
65.47	even	4		650.3.k.g.151.2	yes	4

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

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.f (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +0.449490i q^{3} +2.00000i q^{4} +(0.449490 - 0.449490i) q^{6} +(6.67423 - 6.67423i) q^{7} +(2.00000 - 2.00000i) q^{8} +8.79796 q^{9} +(-10.0227 - 10.0227i) q^{11} -0.898979 q^{12} +13.0000 q^{13} -13.3485 q^{14} -4.00000 q^{16} -11.6969 q^{17} +(-8.79796 - 8.79796i) q^{18} +(-6.00000 + 6.00000i) q^{19} +(3.00000 + 3.00000i) q^{21} +20.0454i q^{22} +33.3485 q^{23} +(0.898979 + 0.898979i) q^{24} +(-13.0000 - 13.0000i) q^{26} +8.00000i q^{27} +(13.3485 + 13.3485i) q^{28} -48.3939 q^{29} +(11.3258 - 11.3258i) q^{31} +(4.00000 + 4.00000i) q^{32} +(4.50510 - 4.50510i) q^{33} +(11.6969 + 11.6969i) q^{34} +17.5959i q^{36} +(-31.6969 + 31.6969i) q^{37} +12.0000 q^{38} +5.84337i q^{39} +(45.3939 - 45.3939i) q^{41} -6.00000i q^{42} +15.9546 q^{43} +(20.0454 - 20.0454i) q^{44} +(-33.3485 - 33.3485i) q^{46} +(59.4620 - 59.4620i) q^{47} -1.79796i q^{48} -40.0908i q^{49} -5.25765i q^{51} +26.0000i q^{52} -79.6969i q^{53} +(8.00000 - 8.00000i) q^{54} -26.6969i q^{56} +(-2.69694 - 2.69694i) q^{57} +(48.3939 + 48.3939i) q^{58} +(-53.4166 - 53.4166i) q^{59} -69.0908 q^{61} -22.6515 q^{62} +(58.7196 - 58.7196i) q^{63} -8.00000i q^{64} -9.01021 q^{66} +(58.7650 + 58.7650i) q^{67} -23.3939i q^{68} +14.9898i q^{69} +(-44.7878 + 44.7878i) q^{71} +(17.5959 - 17.5959i) q^{72} +(67.7878 - 67.7878i) q^{73} +63.3939 q^{74} +(-12.0000 - 12.0000i) q^{76} -133.788 q^{77} +(5.84337 - 5.84337i) q^{78} +74.7878 q^{79} +75.5857 q^{81} -90.7878 q^{82} +(5.41658 + 5.41658i) q^{83} +(-6.00000 + 6.00000i) q^{84} +(-15.9546 - 15.9546i) q^{86} -21.7526i q^{87} -40.0908 q^{88} +(-35.6969 - 35.6969i) q^{89} +(86.7650 - 86.7650i) q^{91} +66.6969i q^{92} +(5.09082 + 5.09082i) q^{93} -118.924 q^{94} +(-1.79796 + 1.79796i) q^{96} +(-61.3939 - 61.3939i) q^{97} +(-40.0908 + 40.0908i) q^{98} +(-88.1793 - 88.1793i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 8 q^{6} + 12 q^{7} + 8 q^{8} - 4 q^{9} + 4 q^{11} + 16 q^{12} + 52 q^{13} - 24 q^{14} - 16 q^{16} + 12 q^{17} + 4 q^{18} - 24 q^{19} + 12 q^{21} + 104 q^{23} - 16 q^{24} - 52 q^{26} + 24 q^{28}+ \cdots - 436 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 8 * q^6 + 12 * q^7 + 8 * q^8 - 4 * q^9 + 4 * q^11 + 16 * q^12 + 52 * q^13 - 24 * q^14 - 16 * q^16 + 12 * q^17 + 4 * q^18 - 24 * q^19 + 12 * q^21 + 104 * q^23 - 16 * q^24 - 52 * q^26 + 24 * q^28 - 76 * q^29 + 60 * q^31 + 16 * q^32 + 116 * q^33 - 12 * q^34 - 68 * q^37 + 48 * q^38 + 64 * q^41 + 152 * q^43 - 8 * q^44 - 104 * q^46 - 12 * q^47 + 32 * q^54 + 48 * q^57 + 76 * q^58 - 52 * q^59 - 100 * q^61 - 120 * q^62 + 132 * q^63 - 232 * q^66 + 44 * q^67 + 56 * q^71 - 8 * q^72 + 36 * q^73 + 136 * q^74 - 48 * q^76 - 300 * q^77 - 104 * q^78 + 64 * q^79 + 28 * q^81 - 128 * q^82 - 140 * q^83 - 24 * q^84 - 152 * q^86 + 16 * q^88 - 84 * q^89 + 156 * q^91 - 156 * q^93 + 24 * q^94 + 32 * q^96 - 128 * q^97 + 16 * q^98 - 436 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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