LMFDB - Embedded newform 1350.3.k.b.899.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1350,3,Mod(449,1350)] 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("1350.449"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1350, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 1350 = 2 \cdot 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1350.k (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,-32,0,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$36.7848356886$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			899.6
Character	$\chi$	$=$	1350.899
Dual form			1350.3.k.b.449.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(0.860641 + 0.496891i) q^{7} +2.82843 q^{8} +(-4.31820 - 2.49311i) q^{11} +(1.22998 - 0.710132i) q^{13} +(-1.21713 + 0.702710i) q^{14} +(-2.00000 + 3.46410i) q^{16} -24.1344 q^{17} +27.5702 q^{19} +(6.10686 - 3.52579i) q^{22} +(3.01971 + 5.23030i) q^{23} +2.00856i q^{26} -1.98756i q^{28} +(16.5910 + 9.57883i) q^{29} +(-13.6022 - 23.5597i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(17.0656 - 29.5585i) q^{34} +63.1320i q^{37} +(-19.4951 + 33.7664i) q^{38} +(-58.1104 + 33.5501i) q^{41} +(23.9528 + 13.8292i) q^{43} +9.97245i q^{44} -8.54104 q^{46} +(3.37944 - 5.85337i) q^{47} +(-24.0062 - 41.5800i) q^{49} +(-2.45997 - 1.42026i) q^{52} +87.8018 q^{53} +(2.43426 + 1.40542i) q^{56} +(-23.4633 + 13.5465i) q^{58} +(89.2923 - 51.5529i) q^{59} +(36.0064 - 62.3649i) q^{61} +38.4728 q^{62} +8.00000 q^{64} +(-17.2928 + 9.98403i) q^{67} +(24.1344 + 41.8020i) q^{68} +55.1081i q^{71} +132.751i q^{73} +(-77.3206 - 44.6411i) q^{74} +(-27.5702 - 47.7530i) q^{76} +(-2.47761 - 4.29135i) q^{77} +(-19.7946 + 34.2853i) q^{79} -94.8939i q^{82} +(-60.5938 + 104.952i) q^{83} +(-33.8744 + 19.5574i) q^{86} +(-12.2137 - 7.05159i) q^{88} +74.0513i q^{89} +1.41143 q^{91} +(6.03943 - 10.4606i) q^{92} +(4.77926 + 8.27791i) q^{94} +(1.98117 + 1.14383i) q^{97} +67.8998 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{4} - 72 q^{14} - 64 q^{16} - 160 q^{19} - 144 q^{29} - 32 q^{31} + 96 q^{34} - 216 q^{41} + 48 q^{46} + 168 q^{49} + 144 q^{56} + 288 q^{59} - 152 q^{61} + 256 q^{64} - 576 q^{74} + 160 q^{76}+ \cdots + 168 q^{94}+O(q^{100}) $ 32 * q - 32 * q^4 - 72 * q^14 - 64 * q^16 - 160 * q^19 - 144 * q^29 - 32 * q^31 + 96 * q^34 - 216 * q^41 + 48 * q^46 + 168 * q^49 + 144 * q^56 + 288 * q^59 - 152 * q^61 + 256 * q^64 - 576 * q^74 + 160 * q^76 - 160 * q^79 + 432 * q^86 - 1312 * q^91 + 168 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times$.

$n$	$1001$	$1027$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.707107	+	1.22474i	−0.353553	+	0.612372i
$2$	−0.707107	+	1.22474i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−1.00000	−	1.73205i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.860641	+	0.496891i	0.122949	+	0.0709844i	0.560213	−	0.828349i	$-0.310719\pi$
$7$	0.860641	+	0.496891i	0.122949	+	0.0709844i	−0.437264	+	0.899333i	$0.644053\pi$
$8$	2.82843			0.353553
$9$		0			0
$10$		0			0
$11$	−4.31820	−	2.49311i	−0.392564	−	0.226647i	0.290707	−	0.956812i	$-0.406110\pi$
$11$	−4.31820	−	2.49311i	−0.392564	−	0.226647i	−0.683270	+	0.730166i	$0.739443\pi$
$12$		0			0
$13$	1.22998	−	0.710132i	0.0946142	−	0.0546255i	−0.451946	−	0.892045i	$-0.649270\pi$
$13$	1.22998	−	0.710132i	0.0946142	−	0.0546255i	0.546561	+	0.837420i	$0.315937\pi$
$14$	−1.21713	+	0.702710i	−0.0869378	+	0.0501936i
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	−24.1344			−1.41967			−0.709835	−	0.704368i	$-0.751231\pi$
$17$	−24.1344			−1.41967			−0.709835	+	0.704368i	$0.751231\pi$
$18$		0			0
$19$	27.5702			1.45106			0.725531	−	0.688189i	$-0.241594\pi$
$19$	27.5702			1.45106			0.725531	+	0.688189i	$0.241594\pi$
$20$		0			0
$21$		0			0
$22$	6.10686	−	3.52579i	0.277584	−	0.160263i
$23$	3.01971	+	5.23030i	0.131292	+	0.227404i	0.924175	−	0.381970i	$-0.124754\pi$
$23$	3.01971	+	5.23030i	0.131292	+	0.227404i	−0.792883	+	0.609374i	$0.791421\pi$
$24$		0			0
$25$		0			0
$26$			2.00856i			0.0772522i
$27$		0			0
$28$		−	1.98756i		−	0.0709844i
$29$	16.5910	+	9.57883i	0.572104	+	0.330305i	0.757989	−	0.652267i	$-0.226182\pi$
$29$	16.5910	+	9.57883i	0.572104	+	0.330305i	−0.185885	+	0.982572i	$0.559515\pi$
$30$		0			0
$31$	−13.6022	−	23.5597i	−0.438780	−	0.759990i	0.558815	−	0.829292i	$-0.311256\pi$
$31$	−13.6022	−	23.5597i	−0.438780	−	0.759990i	−0.997596	+	0.0693023i	$0.977923\pi$
$32$	−2.82843	−	4.89898i	−0.0883883	−	0.153093i
$33$		0			0
$34$	17.0656	−	29.5585i	0.501929	−	0.869367i
$35$		0			0
$36$		0			0
$37$			63.1320i			1.70627i	0.521689	+	0.853136i	$0.325302\pi$
$37$			63.1320i			1.70627i	−0.521689	+	0.853136i	$0.674698\pi$
$38$	−19.4951	+	33.7664i	−0.513028	+	0.888591i
$39$		0			0
$40$		0			0
$41$	−58.1104	+	33.5501i	−1.41733	+	0.818294i	−0.996063	−	0.0886435i	$-0.971747\pi$
$41$	−58.1104	+	33.5501i	−1.41733	+	0.818294i	−0.421264	+	0.906938i	$0.638413\pi$
$42$		0			0
$43$	23.9528	+	13.8292i	0.557042	+	0.321609i	0.751958	−	0.659212i	$-0.229110\pi$
$43$	23.9528	+	13.8292i	0.557042	+	0.321609i	−0.194915	+	0.980820i	$0.562443\pi$
$44$			9.97245i			0.226647i
$45$		0			0
$46$	−8.54104			−0.185675
$47$	3.37944	−	5.85337i	0.0719031	−	0.124540i	−0.827832	−	0.560976i	$-0.810426\pi$
$47$	3.37944	−	5.85337i	0.0719031	−	0.124540i	0.899735	+	0.436436i	$0.143759\pi$
$48$		0			0
$49$	−24.0062	−	41.5800i	−0.489922	−	0.848571i
$50$		0			0
$51$		0			0
$52$	−2.45997	−	1.42026i	−0.0473071	−	0.0273128i
$53$	87.8018			1.65664			0.828319	−	0.560257i	$-0.189298\pi$
$53$	87.8018			1.65664			0.828319	+	0.560257i	$0.189298\pi$
$54$		0			0
$55$		0			0
$56$	2.43426	+	1.40542i	0.0434689	+	0.0250968i
$57$		0			0
$58$	−23.4633	+	13.5465i	−0.404539	+	0.233561i
$59$	89.2923	−	51.5529i	1.51343	−	0.873778i	0.513552	−	0.858058i	$-0.328329\pi$
$59$	89.2923	−	51.5529i	1.51343	−	0.873778i	0.999876	−	0.0157198i	$-0.00500398\pi$
$60$		0			0
$61$	36.0064	−	62.3649i	0.590269	−	1.02238i	−0.403927	−	0.914791i	$-0.632355\pi$
$61$	36.0064	−	62.3649i	0.590269	−	1.02238i	0.994196	−	0.107585i	$-0.0343117\pi$
$62$	38.4728			0.620529
$63$		0			0
$64$	8.00000			0.125000
$65$		0			0
$66$		0			0
$67$	−17.2928	+	9.98403i	−0.258102	+	0.149015i	−0.623469	−	0.781848i	$-0.714277\pi$
$67$	−17.2928	+	9.98403i	−0.258102	+	0.149015i	0.365366	+	0.930864i	$0.380944\pi$
$68$	24.1344	+	41.8020i	0.354918	+	0.614735i
$69$		0			0
$70$		0			0
$71$			55.1081i			0.776170i	0.921624	+	0.388085i	$0.126863\pi$
$71$			55.1081i			0.776170i	−0.921624	+	0.388085i	$0.873137\pi$
$72$		0			0
$73$			132.751i			1.81851i	0.416241	+	0.909254i	$0.363347\pi$
$73$			132.751i			1.81851i	−0.416241	+	0.909254i	$0.636653\pi$
$74$	−77.3206	−	44.6411i	−1.04487	−	0.603258i
$75$		0			0
$76$	−27.5702	−	47.7530i	−0.362766	−	0.628328i
$77$	−2.47761	−	4.29135i	−0.0321768	−	0.0557318i
$78$		0			0
$79$	−19.7946	+	34.2853i	−0.250565	+	0.433992i	−0.963682	−	0.267054i	$-0.913950\pi$
$79$	−19.7946	+	34.2853i	−0.250565	+	0.433992i	0.713116	+	0.701046i	$0.247283\pi$
$80$		0			0
$81$		0			0
$82$		−	94.8939i		−	1.15724i
$83$	−60.5938	+	104.952i	−0.730046	+	1.26448i	0.226817	+	0.973937i	$0.427168\pi$
$83$	−60.5938	+	104.952i	−0.730046	+	1.26448i	−0.956863	+	0.290540i	$0.906165\pi$
$84$		0			0
$85$		0			0
$86$	−33.8744	+	19.5574i	−0.393888	+	0.227412i
$87$		0			0
$88$	−12.2137	−	7.05159i	−0.138792	−	0.0801317i
$89$			74.0513i			0.832037i	0.909356	+	0.416018i	$0.136575\pi$
$89$			74.0513i			0.832037i	−0.909356	+	0.416018i	$0.863425\pi$
$90$		0			0
$91$	1.41143			0.0155103
$92$	6.03943	−	10.4606i	0.0656460	−	0.113702i
$93$		0			0
$94$	4.77926	+	8.27791i	0.0508431	+	0.0880629i
$95$		0			0
$96$		0			0
$97$	1.98117	+	1.14383i	0.0204245	+	0.0117921i	0.510177	−	0.860069i	$-0.329580\pi$
$97$	1.98117	+	1.14383i	0.0204245	+	0.0117921i	−0.489753	+	0.871861i	$0.662913\pi$
$98$	67.8998			0.692855
$99$		0			0
$100$		0			0
$101$	98.4221	+	56.8240i	0.974476	+	0.562614i	0.900598	−	0.434653i	$-0.143129\pi$
$101$	98.4221	+	56.8240i	0.974476	+	0.562614i	0.0738781	+	0.997267i	$0.476462\pi$
$102$		0			0
$103$	−49.1412	+	28.3717i	−0.477099	+	0.275453i	−0.719207	−	0.694796i	$-0.755495\pi$
$103$	−49.1412	+	28.3717i	−0.477099	+	0.275453i	0.242108	+	0.970249i	$0.422161\pi$
$104$	3.47892	−	2.00856i	0.0334512	−	0.0193130i
$105$		0			0
$106$	−62.0852	+	107.535i	−0.585710	+	1.01448i
$107$	93.1862			0.870899			0.435450	−	0.900213i	$-0.356589\pi$
$107$	93.1862			0.870899			0.435450	+	0.900213i	$0.356589\pi$
$108$		0			0
$109$	21.7553			0.199590			0.0997950	−	0.995008i	$-0.468181\pi$
$109$	21.7553			0.199590			0.0997950	+	0.995008i	$0.468181\pi$
$110$		0			0
$111$		0			0
$112$	−3.44256	+	1.98756i	−0.0307372	+	0.0177461i
$113$	71.6214	+	124.052i	0.633817	+	1.09780i	0.986764	+	0.162161i	$0.0518463\pi$
$113$	71.6214	+	124.052i	0.633817	+	1.09780i	−0.352947	+	0.935643i	$0.614820\pi$
$114$		0			0
$115$		0			0
$116$		−	38.3153i		−	0.330305i
$117$		0			0
$118$			145.814i			1.23571i
$119$	−20.7710	−	11.9922i	−0.174547	−	0.100775i
$120$		0			0
$121$	−48.0688	−	83.2576i	−0.397263	−	0.688079i
$122$	50.9208	+	88.1973i	0.417383	+	0.722929i
$123$		0			0
$124$	−27.2044	+	47.1194i	−0.219390	+	0.379995i
$125$		0			0
$126$		0			0
$127$			165.052i			1.29962i	0.760096	+	0.649811i	$0.225152\pi$
$127$			165.052i			1.29962i	−0.760096	+	0.649811i	$0.774848\pi$
$128$	−5.65685	+	9.79796i	−0.0441942	+	0.0765466i
$129$		0			0
$130$		0			0
$131$	−45.4381	+	26.2337i	−0.346856	+	0.200257i	−0.663300	−	0.748354i	$-0.730844\pi$
$131$	−45.4381	+	26.2337i	−0.346856	+	0.200257i	0.316444	+	0.948611i	$0.397511\pi$
$132$		0			0
$133$	23.7280	+	13.6994i	0.178406	+	0.103003i
$134$		−	28.2391i		−	0.210740i
$135$		0			0
$136$	−68.2624			−0.501929
$137$	−60.1866	+	104.246i	−0.439318	+	0.760921i	−0.997637	−	0.0687051i	$-0.978113\pi$
$137$	−60.1866	+	104.246i	−0.439318	+	0.760921i	0.558319	+	0.829626i	$0.311447\pi$
$138$		0			0
$139$	−33.1992	−	57.5027i	−0.238843	−	0.413689i	0.721539	−	0.692373i	$-0.243435\pi$
$139$	−33.1992	−	57.5027i	−0.238843	−	0.413689i	−0.960383	+	0.278685i	$0.910102\pi$
$140$		0			0
$141$		0			0
$142$	−67.4933	−	38.9673i	−0.475305	−	0.274418i
$143$	−7.08176			−0.0495228
$144$		0			0
$145$		0			0
$146$	−162.586	−	93.8692i	−1.11360	−	0.642940i
$147$		0			0
$148$	109.348	−	63.1320i	0.738837	−	0.426568i
$149$	82.8092	−	47.8099i	0.555766	−	0.320872i	−0.195678	−	0.980668i	$-0.562691\pi$
$149$	82.8092	−	47.8099i	0.555766	−	0.320872i	0.751444	+	0.659796i	$0.229357\pi$
$150$		0			0
$151$	−135.262	+	234.281i	−0.895776	+	1.55153i	−0.0629346	+	0.998018i	$0.520046\pi$
$151$	−135.262	+	234.281i	−0.895776	+	1.55153i	−0.832841	+	0.553512i	$0.813287\pi$
$152$	77.9803			0.513028
$153$		0			0
$154$	7.00774			0.0455048
$155$		0			0
$156$		0			0
$157$	−31.4759	+	18.1726i	−0.200483	+	0.115749i	−0.596881	−	0.802330i	$-0.703594\pi$
$157$	−31.4759	+	18.1726i	−0.200483	+	0.115749i	0.396398	+	0.918079i	$0.370260\pi$
$158$	−27.9939	−	48.4868i	−0.177176	−	0.306878i
$159$		0			0
$160$		0			0
$161$			6.00188i			0.0372787i
$162$		0			0
$163$			93.3260i			0.572552i	0.958147	+	0.286276i	$0.0924175\pi$
$163$			93.3260i			0.572552i	−0.958147	+	0.286276i	$0.907583\pi$
$164$	116.221	+	67.1001i	0.708664	+	0.409147i
$165$		0			0
$166$	−85.6926	−	148.424i	−0.516221	−	0.894120i
$167$	28.4639	+	49.3009i	0.170443	+	0.295215i	0.938575	−	0.345076i	$-0.112147\pi$
$167$	28.4639	+	49.3009i	0.170443	+	0.295215i	−0.768132	+	0.640291i	$0.778814\pi$
$168$		0			0
$169$	−83.4914	+	144.611i	−0.494032	+	0.855689i
$170$		0			0
$171$		0			0
$172$		−	55.3167i		−	0.321609i
$173$	108.820	−	188.482i	0.629017	−	1.08949i	−0.358732	−	0.933441i	$-0.616791\pi$
$173$	108.820	−	188.482i	0.629017	−	1.08949i	0.987749	−	0.156049i	$-0.0498758\pi$
$174$		0			0
$175$		0			0
$176$	17.2728	−	9.97245i	0.0981409	−	0.0566617i
$177$		0			0
$178$	−90.6939	−	52.3622i	−0.509516	−	0.294169i
$179$			56.2638i			0.314323i	0.987573	+	0.157161i	$0.0502343\pi$
$179$			56.2638i			0.314323i	−0.987573	+	0.157161i	$0.949766\pi$
$180$		0			0
$181$	−130.959			−0.723528			−0.361764	−	0.932270i	$-0.617825\pi$
$181$	−130.959			−0.723528			−0.361764	+	0.932270i	$0.617825\pi$
$182$	−0.998034	+	1.72865i	−0.00548370	+	0.00949805i
$183$		0			0
$184$	8.54104	+	14.7935i	0.0464187	+	0.0803996i
$185$		0			0
$186$		0			0
$187$	104.217	+	60.1698i	0.557311	+	0.321764i
$188$	−13.5178			−0.0719031
$189$		0			0
$190$		0			0
$191$	29.4446	+	16.9999i	0.154160	+	0.0890045i	0.575096	−	0.818086i	$-0.304965\pi$
$191$	29.4446	+	16.9999i	0.154160	+	0.0890045i	−0.420935	+	0.907091i	$0.638298\pi$
$192$		0			0
$193$	−158.577	+	91.5542i	−0.821640	+	0.474374i	−0.850982	−	0.525195i	$-0.823992\pi$
$193$	−158.577	+	91.5542i	−0.821640	+	0.474374i	0.0293415	+	0.999569i	$0.490659\pi$
$194$	−2.80180	+	1.61762i	−0.0144423	+	0.00833825i
$195$		0			0
$196$	−48.0124	+	83.1599i	−0.244961	+	0.424285i
$197$	−30.9351			−0.157031			−0.0785154	−	0.996913i	$-0.525018\pi$
$197$	−30.9351			−0.157031			−0.0785154	+	0.996913i	$0.525018\pi$
$198$		0			0
$199$	332.873			1.67273			0.836363	−	0.548176i	$-0.184678\pi$
$199$	332.873			1.67273			0.836363	+	0.548176i	$0.184678\pi$
$200$		0			0
$201$		0			0
$202$	−139.190	+	80.3613i	−0.689059	+	0.397828i
$203$	9.51927	+	16.4879i	0.0468930	+	0.0812210i
$204$		0			0
$205$		0			0
$206$		−	80.2473i		−	0.389550i
$207$		0			0
$208$			5.68105i			0.0273128i
$209$	−119.054	−	68.7356i	−0.569634	−	0.328878i
$210$		0			0
$211$	80.3859	+	139.232i	0.380976	+	0.659869i	0.991202	−	0.132358i	$-0.0422548\pi$
$211$	80.3859	+	139.232i	0.380976	+	0.659869i	−0.610226	+	0.792227i	$0.708921\pi$
$212$	−87.8018	−	152.077i	−0.414159	−	0.717345i
$213$		0			0
$214$	−65.8926	+	114.129i	−0.307909	+	0.533315i
$215$		0			0
$216$		0			0
$217$		−	27.0352i		−	0.124586i
$218$	−15.3833	+	26.6447i	−0.0705657	+	0.122223i
$219$		0			0
$220$		0			0
$221$	−29.6849	+	17.1386i	−0.134321	+	0.0775502i
$222$		0			0
$223$	−338.964	−	195.701i	−1.52002	−	0.877582i	−0.999722	−	0.0235946i	$-0.992489\pi$
$223$	−338.964	−	195.701i	−1.52002	−	0.877582i	−0.520294	−	0.853987i	$-0.674178\pi$
$224$		−	5.62168i		−	0.0250968i
$225$		0			0
$226$	−202.576			−0.896353
$227$	−170.350	+	295.054i	−0.750439	+	1.29980i	0.197172	+	0.980369i	$0.436824\pi$
$227$	−170.350	+	295.054i	−0.750439	+	1.29980i	−0.947610	+	0.319429i	$0.896509\pi$
$228$		0			0
$229$	−47.2232	−	81.7931i	−0.206215	−	0.357175i	0.744304	−	0.667841i	$-0.232781\pi$
$229$	−47.2232	−	81.7931i	−0.206215	−	0.357175i	−0.950519	+	0.310666i	$0.899448\pi$
$230$		0			0
$231$		0			0
$232$	46.9265	+	27.0930i	0.202269	+	0.116780i
$233$	117.982			0.506362			0.253181	−	0.967419i	$-0.418523\pi$
$233$	117.982			0.506362			0.253181	+	0.967419i	$0.418523\pi$
$234$		0			0
$235$		0			0
$236$	−178.585	−	103.106i	−0.756714	−	0.436889i
$237$		0			0
$238$	29.3747	−	16.9595i	0.123423	−	0.0712583i
$239$	−319.661	+	184.556i	−1.33749	+	0.772203i	−0.986435	−	0.164151i	$-0.947512\pi$
$239$	−319.661	+	184.556i	−1.33749	+	0.772203i	−0.351059	+	0.936353i	$0.614178\pi$
$240$		0			0
$241$	187.815	−	325.306i	0.779316	−	1.34982i	−0.153020	−	0.988223i	$-0.548900\pi$
$241$	187.815	−	325.306i	0.779316	−	1.34982i	0.932336	−	0.361592i	$-0.117767\pi$
$242$	135.959			0.561814
$243$		0			0
$244$	−144.026			−0.590269
$245$		0			0
$246$		0			0
$247$	33.9109	−	19.5785i	0.137291	−	0.0792650i
$248$	−38.4728	−	66.6368i	−0.155132	−	0.268697i
$249$		0			0
$250$		0			0
$251$			240.639i			0.958722i	0.877618	+	0.479361i	$0.159131\pi$
$251$			240.639i			0.958722i	−0.877618	+	0.479361i	$0.840869\pi$
$252$		0			0
$253$		−	30.1140i		−	0.119028i
$254$	−202.146	−	116.709i	−0.795852	−	0.459485i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−62.6094	−	108.443i	−0.243616	−	0.421956i	0.718125	−	0.695914i	$-0.245000\pi$
$257$	−62.6094	−	108.443i	−0.243616	−	0.421956i	−0.961742	+	0.273958i	$0.911667\pi$
$258$		0			0
$259$	−31.3697	+	54.3340i	−0.121119	+	0.209784i
$260$		0			0
$261$		0			0
$262$		−	74.2001i		−	0.283207i
$263$	−46.6216	+	80.7510i	−0.177269	+	0.307038i	−0.940944	−	0.338562i	$-0.890059\pi$
$263$	−46.6216	+	80.7510i	−0.177269	+	0.307038i	0.763675	+	0.645600i	$0.223393\pi$
$264$		0			0
$265$		0			0
$266$	−33.5565	+	19.3738i	−0.126152	+	0.0728340i
$267$		0			0
$268$	34.5857	+	19.9681i	0.129051	+	0.0745077i
$269$		−	76.3366i		−	0.283779i	−0.989882	−	0.141890i	$-0.954682\pi$
$269$		−	76.3366i		−	0.283779i	0.989882	−	0.141890i	$-0.0453178\pi$
$270$		0			0
$271$	529.738			1.95475			0.977377	−	0.211506i	$-0.0678368\pi$
$271$	529.738			1.95475			0.977377	+	0.211506i	$0.0678368\pi$
$272$	48.2688	−	83.6040i	0.177459	−	0.307368i
$273$		0			0
$274$	−85.1167	−	147.426i	−0.310645	−	0.538053i
$275$		0			0
$276$		0			0
$277$	−73.5785	−	42.4806i	−0.265626	−	0.153359i	0.361272	−	0.932460i	$-0.382343\pi$
$277$	−73.5785	−	42.4806i	−0.265626	−	0.153359i	−0.626898	+	0.779101i	$0.715676\pi$
$278$	93.9016			0.337775
$279$		0			0
$280$		0			0
$281$	185.539	+	107.121i	0.660282	+	0.381214i	0.792384	−	0.610022i	$-0.208839\pi$
$281$	185.539	+	107.121i	0.660282	+	0.381214i	−0.132102	+	0.991236i	$0.542173\pi$
$282$		0			0
$283$	327.494	−	189.079i	1.15722	−	0.668123i	0.206586	−	0.978428i	$-0.433765\pi$
$283$	327.494	−	189.079i	1.15722	−	0.668123i	0.950637	+	0.310305i	$0.100431\pi$
$284$	95.4500	−	55.1081i	0.336091	−	0.194042i
$285$		0			0
$286$	5.00756	−	8.67334i	0.0175089	−	0.0303264i
$287$	−66.6829			−0.232345
$288$		0			0
$289$	293.469			1.01546
$290$		0			0
$291$		0			0
$292$	229.932	−	132.751i	0.787437	−	0.454627i
$293$	25.0000	+	43.3012i	0.0853242	+	0.147786i	0.905529	−	0.424284i	$-0.139474\pi$
$293$	25.0000	+	43.3012i	0.0853242	+	0.147786i	−0.820205	+	0.572070i	$0.806141\pi$
$294$		0			0
$295$		0			0
$296$			178.564i			0.603258i
$297$		0			0
$298$			135.227i			0.453781i
$299$	7.42840	+	4.28879i	0.0248442	+	0.0143438i
$300$		0			0
$301$	13.7432	+	23.8039i	0.0456584	+	0.0790827i
$302$	−191.290	−	331.323i	−0.633409	−	1.09710i
$303$		0			0
$304$	−55.1404	+	95.5059i	−0.181383	+	0.314164i
$305$		0			0
$306$		0			0
$307$		−	145.083i		−	0.472583i	−0.971682	−	0.236292i	$-0.924068\pi$
$307$		−	145.083i		−	0.472583i	0.971682	−	0.236292i	$-0.0759320\pi$
$308$	−4.95522	+	8.58270i	−0.0160884	+	0.0278659i
$309$		0			0
$310$		0			0
$311$	−90.5772	+	52.2947i	−0.291245	+	0.168150i	−0.638503	−	0.769619i	$-0.720446\pi$
$311$	−90.5772	+	52.2947i	−0.291245	+	0.168150i	0.347258	+	0.937770i	$0.387113\pi$
$312$		0			0
$313$	−50.0335	−	28.8869i	−0.159852	−	0.0922903i	0.417940	−	0.908474i	$-0.362752\pi$
$313$	−50.0335	−	28.8869i	−0.159852	−	0.0922903i	−0.577792	+	0.816184i	$0.696085\pi$
$314$		−	51.3999i		−	0.163694i
$315$		0			0
$316$	79.1786			0.250565
$317$	−49.1500	+	85.1303i	−0.155047	+	0.268550i	−0.933076	−	0.359679i	$-0.882886\pi$
$317$	−49.1500	+	85.1303i	−0.155047	+	0.268550i	0.778029	+	0.628228i	$0.216220\pi$
$318$		0			0
$319$	−47.7622	−	82.7266i	−0.149725	−	0.259331i
$320$		0			0
$321$		0			0
$322$	−7.35077	−	4.24397i	−0.0228285	−	0.0131800i
$323$	−665.390			−2.06003
$324$		0			0
$325$		0			0
$326$	−114.301	−	65.9915i	−0.350615	−	0.202428i
$327$		0			0
$328$	−164.361	+	94.8939i	−0.501101	+	0.289311i
$329$	5.81697	−	3.35843i	0.0176808	−	0.0102080i
$330$		0			0
$331$	106.537	−	184.528i	0.321865	−	0.557487i	−0.659008	−	0.752136i	$-0.729024\pi$
$331$	106.537	−	184.528i	0.321865	−	0.557487i	0.980873	+	0.194649i	$0.0623569\pi$
$332$	242.375			0.730046
$333$		0			0
$334$	−80.5081			−0.241042
$335$		0			0
$336$		0			0
$337$	−142.921	+	82.5154i	−0.424097	+	0.244853i	−0.696829	−	0.717237i	$-0.745406\pi$
$337$	−142.921	+	82.5154i	−0.424097	+	0.244853i	0.272731	+	0.962090i	$0.412073\pi$
$338$	−118.075	−	204.511i	−0.349333	−	0.605063i
$339$		0			0
$340$		0			0
$341$			135.647i			0.397792i
$342$		0			0
$343$		−	96.4092i		−	0.281076i
$344$	67.7488	+	39.1148i	0.196944	+	0.113706i
$345$		0			0
$346$	153.895	+	266.553i	0.444782	+	0.770385i
$347$	−45.1789	−	78.2522i	−0.130199	−	0.225511i	0.793554	−	0.608499i	$-0.208228\pi$
$347$	−45.1789	−	78.2522i	−0.130199	−	0.225511i	−0.923753	+	0.382989i	$0.874895\pi$
$348$		0			0
$349$	−177.488	+	307.418i	−0.508561	+	0.880853i	0.491390	+	0.870939i	$0.336489\pi$
$349$	−177.488	+	307.418i	−0.508561	+	0.880853i	−0.999951	+	0.00991327i	$0.996844\pi$
$350$		0			0
$351$		0			0
$352$			28.2064i			0.0801317i
$353$	180.548	−	312.718i	0.511467	−	0.885887i	−0.488445	−	0.872595i	$-0.662436\pi$
$353$	180.548	−	312.718i	0.511467	−	0.885887i	0.999912	−	0.0132919i	$-0.00423108\pi$
$354$		0			0
$355$		0			0
$356$	128.261	−	74.0513i	0.360283	−	0.208009i
$357$		0			0
$358$	−68.9088	−	39.7845i	−0.192483	−	0.111130i
$359$			229.312i			0.638753i	0.947628	+	0.319377i	$0.103473\pi$
$359$			229.312i			0.638753i	−0.947628	+	0.319377i	$0.896527\pi$
$360$		0			0
$361$	399.115			1.10558
$362$	92.6017	−	160.391i	0.255806	−	0.443069i
$363$		0			0
$364$	−1.41143	−	2.44467i	−0.00387756	−	0.00671614i
$365$		0			0
$366$		0			0
$367$	356.434	+	205.787i	0.971210	+	0.560728i	0.899605	−	0.436705i	$-0.143854\pi$
$367$	356.434	+	205.787i	0.971210	+	0.560728i	0.0716052	+	0.997433i	$0.477188\pi$
$368$	−24.1577			−0.0656460
$369$		0			0
$370$		0			0
$371$	75.5658	+	43.6279i	0.203681	+	0.117596i
$372$		0			0
$373$	594.984	−	343.514i	1.59513	−	0.920949i	0.602723	−	0.797950i	$-0.294082\pi$
$373$	594.984	−	343.514i	1.59513	−	0.920949i	0.992407	−	0.122999i	$-0.0392511\pi$
$374$	−147.385	+	85.0929i	−0.394078	+	0.227521i
$375$		0			0
$376$	9.55851	−	16.5558i	0.0254216	−	0.0440315i
$377$	27.2089			0.0721722
$378$		0			0
$379$	154.733			0.408267			0.204134	−	0.978943i	$-0.434562\pi$
$379$	154.733			0.408267			0.204134	+	0.978943i	$0.434562\pi$
$380$		0			0
$381$		0			0
$382$	−41.6410	+	24.0414i	−0.109008	+	0.0629357i
$383$	−81.5612	−	141.268i	−0.212954	−	0.368846i	0.739684	−	0.672954i	$-0.234975\pi$
$383$	−81.5612	−	141.268i	−0.212954	−	0.368846i	−0.952638	+	0.304108i	$0.901642\pi$
$384$		0			0
$385$		0			0
$386$		−	258.954i		−	0.670866i
$387$		0			0
$388$		−	4.57532i		−	0.0117921i
$389$	268.744	+	155.159i	0.690858	+	0.398867i	0.803933	−	0.594719i	$-0.202737\pi$
$389$	268.744	+	155.159i	0.690858	+	0.398867i	−0.113075	+	0.993586i	$0.536070\pi$
$390$		0			0
$391$	−72.8790	−	126.230i	−0.186391	−	0.322839i
$392$	−67.8998	−	117.606i	−0.173214	−	0.300015i
$393$		0			0
$394$	21.8744	−	37.8876i	0.0555188	−	0.0961614i
$395$		0			0
$396$		0			0
$397$			270.057i			0.680244i	0.940381	+	0.340122i	$0.110468\pi$
$397$			270.057i			0.680244i	−0.940381	+	0.340122i	$0.889532\pi$
$398$	−235.376	+	407.684i	−0.591398	+	1.02433i
$399$		0			0
$400$		0			0
$401$	525.394	−	303.336i	1.31021	−	0.756449i	0.328078	−	0.944651i	$-0.393599\pi$
$401$	525.394	−	303.336i	1.31021	−	0.756449i	0.982130	+	0.188201i	$0.0602658\pi$
$402$		0			0
$403$	−33.4610	−	19.3187i	−0.0830297	−	0.0479372i
$404$		−	227.296i		−	0.562614i
$405$		0			0
$406$	−26.9246			−0.0663167
$407$	157.395	−	272.617i	0.386721	−	0.669820i
$408$		0			0
$409$	−332.949	−	576.684i	−0.814055	−	1.40998i	−0.910004	−	0.414599i	$-0.863922\pi$
$409$	−332.949	−	576.684i	−0.814055	−	1.40998i	0.0959493	−	0.995386i	$-0.469411\pi$
$410$		0			0
$411$		0			0
$412$	98.2825	+	56.7434i	0.238550	+	0.137727i
$413$	102.465			0.248099
$414$		0			0
$415$		0			0
$416$	−6.95784	−	4.01711i	−0.0167256	−	0.00965652i
$417$		0			0
$418$	168.367	−	97.2068i	0.402792	−	0.232552i
$419$	187.245	−	108.106i	0.446886	−	0.258010i	−0.259628	−	0.965709i	$-0.583600\pi$
$419$	187.245	−	108.106i	0.446886	−	0.258010i	0.706514	+	0.707699i	$0.250267\pi$
$420$		0			0
$421$	−157.752	+	273.234i	−0.374708	+	0.649013i	−0.990283	−	0.139065i	$-0.955590\pi$
$421$	−157.752	+	273.234i	−0.374708	+	0.649013i	0.615576	+	0.788078i	$0.288924\pi$
$422$	−227.366			−0.538781
$423$		0			0
$424$	248.341			0.585710
$425$		0			0
$426$		0			0
$427$	61.9772	−	35.7825i	0.145146	−	0.0837999i
$428$	−93.1862	−	161.403i	−0.217725	−	0.377110i
$429$		0			0
$430$		0			0
$431$		−	705.119i		−	1.63601i	−0.575213	−	0.818003i	$-0.695081\pi$
$431$		−	705.119i		−	1.63601i	0.575213	−	0.818003i	$-0.304919\pi$
$432$		0			0
$433$			152.735i			0.352737i	0.984324	+	0.176369i	$0.0564351\pi$
$433$			152.735i			0.352737i	−0.984324	+	0.176369i	$0.943565\pi$
$434$	33.1113	+	19.1168i	0.0762932	+	0.0440479i
$435$		0			0
$436$	−21.7553	−	37.6813i	−0.0498975	−	0.0864250i
$437$	83.2541	+	144.200i	0.190513	+	0.329978i
$438$		0			0
$439$	81.1173	−	140.499i	0.184778	−	0.320044i	−0.758724	−	0.651412i	$-0.774177\pi$
$439$	81.1173	−	140.499i	0.184778	−	0.320044i	0.943502	+	0.331368i	$0.107510\pi$
$440$		0			0
$441$		0			0
$442$		−	48.4753i		−	0.109673i
$443$	193.783	−	335.641i	0.437433	−	0.757655i	−0.560058	−	0.828453i	$-0.689221\pi$
$443$	193.783	−	335.641i	0.437433	−	0.757655i	0.997491	+	0.0707979i	$0.0225545\pi$
$444$		0			0
$445$		0			0
$446$	479.367	−	276.763i	1.07481	−	0.620544i
$447$		0			0
$448$	6.88513	+	3.97513i	0.0153686	+	0.00887306i
$449$			111.025i			0.247272i	0.992328	+	0.123636i	$0.0394554\pi$
$449$			111.025i			0.247272i	−0.992328	+	0.123636i	$0.960545\pi$
$450$		0			0
$451$	334.577			0.741855
$452$	143.243	−	248.104i	0.316909	−	0.548902i
$453$		0			0
$454$	−240.911	−	417.269i	−0.530640	−	0.919096i
$455$		0			0
$456$		0			0
$457$	−258.768	−	149.400i	−0.566232	−	0.326914i	0.189411	−	0.981898i	$-0.439342\pi$
$457$	−258.768	−	149.400i	−0.566232	−	0.326914i	−0.755643	+	0.654984i	$0.772675\pi$
$458$	133.567			0.291632
$459$		0			0
$460$		0			0
$461$	180.036	+	103.944i	0.390534	+	0.225475i	0.682392	−	0.730987i	$-0.260940\pi$
$461$	180.036	+	103.944i	0.390534	+	0.225475i	−0.291857	+	0.956462i	$0.594273\pi$
$462$		0			0
$463$	749.220	−	432.563i	1.61819	−	0.934261i	0.630798	−	0.775947i	$-0.282728\pi$
$463$	749.220	−	432.563i	1.61819	−	0.934261i	0.987389	−	0.158313i	$-0.0506056\pi$
$464$	−66.3641	+	38.3153i	−0.143026	+	0.0825762i
$465$		0			0
$466$	−83.4262	+	144.498i	−0.179026	+	0.310082i
$467$	−854.726			−1.83025			−0.915124	−	0.403172i	$-0.867908\pi$
$467$	−854.726			−1.83025			−0.915124	+	0.403172i	$0.867908\pi$
$468$		0			0
$469$	−19.8439			−0.0423111
$470$		0			0
$471$		0			0
$472$	252.557	−	145.814i	0.535078	−	0.308927i
$473$	−68.9554	−	119.434i	−0.145783	−	0.252504i
$474$		0			0
$475$		0			0
$476$			47.9687i			0.100775i
$477$		0			0
$478$		−	522.004i		−	1.09206i
$479$	263.392	+	152.069i	0.549879	+	0.317473i	0.749073	−	0.662487i	$-0.230499\pi$
$479$	263.392	+	152.069i	0.549879	+	0.317473i	−0.199194	+	0.979960i	$0.563832\pi$
$480$		0			0
$481$	44.8321	+	77.6514i	0.0932060	+	0.161437i
$482$	265.611	+	460.051i	0.551060	+	0.954464i
$483$		0			0
$484$	−96.1375	+	166.515i	−0.198631	+	0.344039i
$485$		0			0
$486$		0			0
$487$		−	907.378i		−	1.86320i	−0.363486	−	0.931600i	$-0.618413\pi$
$487$		−	907.378i		−	1.86320i	0.363486	−	0.931600i	$-0.381587\pi$
$488$	101.842	−	176.395i	0.208692	−	0.361465i
$489$		0			0
$490$		0			0
$491$	−56.6785	+	32.7234i	−0.115435	+	0.0666464i	−0.556606	−	0.830777i	$-0.687897\pi$
$491$	−56.6785	+	32.7234i	−0.115435	+	0.0666464i	0.441171	+	0.897423i	$0.354563\pi$
$492$		0			0
$493$	−400.414	−	231.179i	−0.812200	−	0.468924i
$494$			55.3763i			0.112098i
$495$		0			0
$496$	108.818			0.219390
$497$	−27.3827	+	47.4282i	−0.0550960	+	0.0954291i
$498$		0			0
$499$	358.642	+	621.186i	0.718721	+	1.24486i	0.961507	+	0.274782i	$0.0886057\pi$
$499$	358.642	+	621.186i	0.718721	+	1.24486i	−0.242785	+	0.970080i	$0.578061\pi$
$500$		0			0
$501$		0			0
$502$	−294.722	−	170.158i	−0.587095	−	0.338959i
$503$	−623.374			−1.23931			−0.619657	−	0.784873i	$-0.712728\pi$
$503$	−623.374			−1.23931			−0.619657	+	0.784873i	$0.712728\pi$
$504$		0			0
$505$		0			0
$506$	36.8819	+	21.2938i	0.0728892	+	0.0420826i
$507$		0			0
$508$	285.878	−	165.052i	0.562753	−	0.324905i
$509$	577.161	−	333.224i	1.13391	−	0.654664i	0.188996	−	0.981978i	$-0.439477\pi$
$509$	577.161	−	333.224i	1.13391	−	0.654664i	0.944916	+	0.327313i	$0.106143\pi$
$510$		0			0
$511$	−65.9628	+	114.251i	−0.129086	+	0.223583i
$512$	22.6274			0.0441942
$513$		0			0
$514$	177.086			0.344526
$515$		0			0
$516$		0			0
$517$	−29.1862	+	16.8507i	−0.0564530	+	0.0325932i
$518$	−44.3635	−	76.8399i	−0.0856439	−	0.148340i
$519$		0			0
$520$		0			0
$521$		−	896.544i		−	1.72081i	−0.509608	−	0.860407i	$-0.670210\pi$
$521$		−	896.544i		−	1.72081i	0.509608	−	0.860407i	$-0.329790\pi$
$522$		0			0
$523$			354.070i			0.676999i	0.940967	+	0.338499i	$0.109919\pi$
$523$			354.070i			0.676999i	−0.940967	+	0.338499i	$0.890081\pi$
$524$	90.8762	+	52.4674i	0.173428	+	0.100129i
$525$		0			0
$526$	−65.9329	−	114.199i	−0.125348	−	0.217109i
$527$	328.281	+	568.599i	0.622923	+	1.07893i
$528$		0			0
$529$	246.263	−	426.539i	0.465525	−	0.806313i
$530$		0			0
$531$		0			0
$532$		−	54.7975i		−	0.103003i
$533$	−47.6500	+	82.5321i	−0.0893995	+	0.154845i
$534$		0			0
$535$		0			0
$536$	−48.9116	+	28.2391i	−0.0912529	+	0.0526849i
$537$		0			0
$538$	93.4928	+	53.9781i	0.173779	+	0.100331i
$539$			239.401i			0.444157i
$540$		0			0
$541$	−392.737			−0.725947			−0.362974	−	0.931799i	$-0.618238\pi$
$541$	−392.737			−0.725947			−0.362974	+	0.931799i	$0.618238\pi$
$542$	−374.581	+	648.794i	−0.691110	+	1.19704i
$543$		0			0
$544$	68.2624	+	118.234i	0.125482	+	0.217342i
$545$		0			0
$546$		0			0
$547$	234.742	+	135.528i	0.429145	+	0.247767i	0.698982	−	0.715139i	$-0.253637\pi$
$547$	234.742	+	135.528i	0.429145	+	0.247767i	−0.269837	+	0.962906i	$0.586970\pi$
$548$	240.746			0.439318
$549$		0			0
$550$		0			0
$551$	457.418	+	264.090i	0.830159	+	0.479293i
$552$		0			0
$553$	−34.0722	+	19.6716i	−0.0616133	+	0.0355725i
$554$	104.056	−	60.0766i	0.187826	−	0.108442i
$555$		0			0
$556$	−66.3984	+	115.005i	−0.119422	+	0.206844i
$557$	122.363			0.219682			0.109841	−	0.993949i	$-0.464966\pi$
$557$	122.363			0.219682			0.109841	+	0.993949i	$0.464966\pi$
$558$		0			0
$559$	39.2821			0.0702722
$560$		0			0
$561$		0			0
$562$	−262.392	+	151.492i	−0.466890	+	0.269559i
$563$	−26.4560	−	45.8232i	−0.0469911	−	0.0813911i	0.841573	−	0.540143i	$-0.181630\pi$
$563$	−26.4560	−	45.8232i	−0.0469911	−	0.0813911i	−0.888564	+	0.458752i	$0.848297\pi$
$564$		0			0
$565$		0			0
$566$			534.796i			0.944869i
$567$		0			0
$568$			155.869i			0.274418i
$569$	−631.466	−	364.577i	−1.10978	−	0.640733i	−0.171009	−	0.985269i	$-0.554703\pi$
$569$	−631.466	−	364.577i	−1.10978	−	0.640733i	−0.938773	+	0.344536i	$0.888036\pi$
$570$		0			0
$571$	198.741	+	344.229i	0.348057	+	0.602853i	0.985904	−	0.167310i	$-0.0535081\pi$
$571$	198.741	+	344.229i	0.348057	+	0.602853i	−0.637847	+	0.770163i	$0.720175\pi$
$572$	7.08176	+	12.2660i	0.0123807	+	0.0214440i
$573$		0			0
$574$	47.1520	−	81.6696i	0.0821463	−	0.142282i
$575$		0			0
$576$		0			0
$577$			82.2138i			0.142485i	0.997459	+	0.0712425i	$0.0226964\pi$
$577$			82.2138i			0.142485i	−0.997459	+	0.0712425i	$0.977304\pi$
$578$	−207.514	+	359.425i	−0.359021	+	0.621842i
$579$		0			0
$580$		0			0
$581$	−104.299	+	60.2171i	−0.179516	+	0.103644i
$582$		0			0
$583$	−379.146	−	218.900i	−0.650335	−	0.375471i
$584$			375.477i			0.642940i
$585$		0			0
$586$	−70.7106			−0.120667
$587$	430.684	−	745.966i	0.733703	−	1.27081i	−0.221587	−	0.975141i	$-0.571124\pi$
$587$	430.684	−	745.966i	0.733703	−	1.27081i	0.955290	−	0.295671i	$-0.0955431\pi$
$588$		0			0
$589$	−375.015	−	649.545i	−0.636698	−	1.10279i
$590$		0			0
$591$		0			0
$592$	−218.696	−	126.264i	−0.369419	−	0.213284i
$593$	377.445			0.636500			0.318250	−	0.948007i	$-0.396905\pi$
$593$	377.445			0.636500			0.318250	+	0.948007i	$0.396905\pi$
$594$		0			0
$595$		0			0
$596$	−165.618	−	95.6198i	−0.277883	−	0.160436i
$597$		0			0
$598$	−10.5053	+	6.06527i	−0.0175675	+	0.0101426i
$599$	−268.405	+	154.964i	−0.448089	+	0.258704i	−0.707023	−	0.707191i	$-0.749962\pi$
$599$	−268.405	+	154.964i	−0.448089	+	0.258704i	0.258934	+	0.965895i	$0.416629\pi$
$600$		0			0
$601$	−208.891	+	361.810i	−0.347573	+	0.602014i	−0.985818	−	0.167820i	$-0.946327\pi$
$601$	−208.891	+	361.810i	−0.347573	+	0.602014i	0.638245	+	0.769833i	$0.279661\pi$
$602$	−38.8716			−0.0645708
$603$		0			0
$604$	541.049			0.895776
$605$		0			0
$606$		0			0
$607$	−741.461	+	428.083i	−1.22152	+	0.705244i	−0.965241	−	0.261360i	$-0.915829\pi$
$607$	−741.461	+	428.083i	−1.22152	+	0.705244i	−0.256277	+	0.966603i	$0.582496\pi$
$608$	−77.9803	−	135.066i	−0.128257	−	0.222148i
$609$		0			0
$610$		0			0
$611$		−	9.59940i		−	0.0157110i
$612$		0			0
$613$		−	1022.92i		−	1.66870i	−0.551231	−	0.834352i	$-0.685842\pi$
$613$		−	1022.92i		−	1.66870i	0.551231	−	0.834352i	$-0.314158\pi$
$614$	177.690	+	102.589i	0.289397	+	0.167083i
$615$		0			0
$616$	−7.00774	−	12.1378i	−0.0113762	−	0.0197042i
$617$	−292.984	−	507.463i	−0.474852	−	0.822468i	0.524733	−	0.851267i	$-0.324165\pi$
$617$	−292.984	−	507.463i	−0.474852	−	0.822468i	−0.999585	+	0.0287987i	$0.990832\pi$
$618$		0			0
$619$	−455.788	+	789.447i	−0.736329	+	1.27536i	0.217809	+	0.975991i	$0.430109\pi$
$619$	−455.788	+	789.447i	−0.736329	+	1.27536i	−0.954138	+	0.299367i	$0.903224\pi$
$620$		0			0
$621$		0			0
$622$		−	147.912i		−	0.237800i
$623$	−36.7954	+	63.7315i	−0.0590617	+	0.102298i
$624$		0			0
$625$		0			0
$626$	70.7581	−	40.8522i	0.113032	−	0.0652591i
$627$		0			0
$628$	62.9518	+	36.3452i	0.100242	+	0.0578746i
$629$		−	1523.65i		−	2.42234i
$630$		0			0
$631$	463.111			0.733932			0.366966	−	0.930234i	$-0.380396\pi$
$631$	463.111			0.733932			0.366966	+	0.930234i	$0.380396\pi$
$632$	−55.9877	+	96.9736i	−0.0885882	+	0.153439i
$633$		0			0
$634$	−69.5086	−	120.392i	−0.109635	−	0.189893i
$635$		0			0
$636$		0			0
$637$	−59.0545	−	34.0951i	−0.0927072	−	0.0535245i
$638$	135.092			0.211743
$639$		0			0
$640$		0			0
$641$	512.450	+	295.863i	0.799454	+	0.461565i	0.843280	−	0.537474i	$-0.180622\pi$
$641$	512.450	+	295.863i	0.799454	+	0.461565i	−0.0438265	+	0.999039i	$0.513955\pi$
$642$		0			0
$643$	−647.010	+	373.551i	−1.00624	+	0.580950i	−0.910087	−	0.414417i	$-0.863986\pi$
$643$	−647.010	+	373.551i	−1.00624	+	0.580950i	−0.0961484	+	0.995367i	$0.530652\pi$
$644$	10.3956	−	6.00188i	0.0161422	−	0.00931969i
$645$		0			0
$646$	470.502	−	814.933i	0.728331	−	1.26151i
$647$	−86.2103			−0.133246			−0.0666231	−	0.997778i	$-0.521223\pi$
$647$	−86.2103			−0.133246			−0.0666231	+	0.997778i	$0.521223\pi$
$648$		0			0
$649$	−514.109			−0.792156
$650$		0			0
$651$		0			0
$652$	161.645	−	93.3260i	0.247922	−	0.143138i
$653$	85.7737	+	148.564i	0.131353	+	0.227511i	0.924198	−	0.381913i	$-0.124734\pi$
$653$	85.7737	+	148.564i	0.131353	+	0.227511i	−0.792845	+	0.609423i	$0.791401\pi$
$654$		0			0
$655$		0			0
$656$		−	268.401i		−	0.409147i
$657$		0			0
$658$			9.49908i			0.0144363i
$659$	81.6071	+	47.1159i	0.123835	+	0.0714960i	0.560638	−	0.828061i	$-0.310556\pi$
$659$	81.6071	+	47.1159i	0.123835	+	0.0714960i	−0.436803	+	0.899557i	$0.643889\pi$
$660$		0			0
$661$	−422.390	−	731.602i	−0.639017	−	1.10681i	−0.985649	−	0.168809i	$-0.946008\pi$
$661$	−422.390	−	731.602i	−0.639017	−	1.10681i	0.346631	−	0.938001i	$-0.387325\pi$
$662$	150.667	+	260.962i	0.227593	+	0.394203i
$663$		0			0
$664$	−171.385	+	296.848i	−0.258110	+	0.447060i
$665$		0			0
$666$		0			0
$667$			115.701i			0.173465i
$668$	56.9278	−	98.6019i	0.0852213	−	0.147608i
$669$		0			0
$670$		0			0
$671$	−310.966	+	179.536i	−0.463436	+	0.267565i
$672$		0			0
$673$	609.933	+	352.145i	0.906290	+	0.523247i	0.879235	−	0.476387i	$-0.158054\pi$
$673$	609.933	+	352.145i	0.906290	+	0.523247i	0.0270541	+	0.999634i	$0.491387\pi$
$674$		−	233.389i		−	0.346274i
$675$		0			0
$676$	333.966			0.494032
$677$	639.435	−	1107.53i	0.944513	−	1.63594i	0.187788	−	0.982210i	$-0.439868\pi$
$677$	639.435	−	1107.53i	0.944513	−	1.63594i	0.756724	−	0.653734i	$-0.226799\pi$
$678$		0			0
$679$	1.13672	+	1.96886i	0.00167411	+	0.00289964i
$680$		0			0
$681$		0			0
$682$	−166.133	−	95.9170i	−0.243597	−	0.140641i
$683$	−571.914			−0.837356			−0.418678	−	0.908135i	$-0.637506\pi$
$683$	−571.914			−0.837356			−0.418678	+	0.908135i	$0.637506\pi$
$684$		0			0
$685$		0			0
$686$	118.077	+	68.1716i	0.172123	+	0.0993755i
$687$		0			0
$688$	−95.8113	+	55.3167i	−0.139261	+	0.0804022i
$689$	107.995	−	62.3508i	0.156741	−	0.0904947i
$690$		0			0
$691$	−310.061	+	537.041i	−0.448713	+	0.777194i	−0.998303	−	0.0582407i	$-0.981451\pi$
$691$	−310.061	+	537.041i	−0.448713	+	0.777194i	0.549589	+	0.835435i	$0.314784\pi$
$692$	−435.280			−0.629017
$693$		0			0
$694$	127.785			0.184129
$695$		0			0
$696$		0			0
$697$	1402.46	−	809.711i	2.01214	−	1.16171i
$698$	−251.005	−	434.754i	−0.359607	−	0.622857i
$699$		0			0
$700$		0			0
$701$			66.6004i			0.0950077i	0.998871	+	0.0475038i	$0.0151266\pi$
$701$			66.6004i			0.0950077i	−0.998871	+	0.0475038i	$0.984873\pi$
$702$		0			0
$703$			1740.56i			2.47591i
$704$	−34.5456	−	19.9449i	−0.0490704	−	0.0283308i
$705$		0			0
$706$	255.333	+	442.250i	0.361662	+	0.626417i
$707$	56.4707	+	97.8101i	0.0798737	+	0.138345i
$708$		0			0
$709$	−105.287	+	182.363i	−0.148501	+	0.257211i	−0.930674	−	0.365851i	$-0.880778\pi$
$709$	−105.287	+	182.363i	−0.148501	+	0.257211i	0.782173	+	0.623062i	$0.214111\pi$
$710$		0			0
$711$		0			0
$712$			209.449i			0.294169i
$713$	82.1495	−	142.287i	0.115217	−	0.199561i
$714$		0			0
$715$		0			0
$716$	97.4518	−	56.2638i	0.136106	−	0.0785807i
$717$		0			0
$718$	−280.849	−	162.148i	−0.391155	−	0.225833i
$719$			900.163i			1.25197i	0.779837	+	0.625983i	$0.215302\pi$
$719$			900.163i			1.25197i	−0.779837	+	0.625983i	$0.784698\pi$
$720$		0			0
$721$	−56.3906			−0.0782116
$722$	−282.217	+	488.814i	−0.390882	+	0.677028i
$723$		0			0
$724$	130.959	+	226.827i	0.180882	+	0.313297i
$725$		0			0
$726$		0			0
$727$	−654.034	−	377.607i	−0.899635	−	0.519404i	−0.0225530	−	0.999746i	$-0.507179\pi$
$727$	−654.034	−	377.607i	−0.899635	−	0.519404i	−0.877082	+	0.480341i	$0.840513\pi$
$728$	3.99213			0.00548370
$729$		0			0
$730$		0			0
$731$	−578.087	−	333.759i	−0.790817	−	0.456578i
$732$		0			0
$733$	−109.224	+	63.0608i	−0.149010	+	0.0860311i	−0.572651	−	0.819799i	$-0.694085\pi$
$733$	−109.224	+	63.0608i	−0.149010	+	0.0860311i	0.423641	+	0.905830i	$0.360752\pi$
$734$	−504.074	+	291.027i	−0.686749	+	0.396495i
$735$		0			0
$736$	17.0821	−	29.5870i	0.0232094	−	0.0401998i
$737$	99.5653			0.135095
$738$		0			0
$739$	−503.837			−0.681782			−0.340891	−	0.940103i	$-0.610729\pi$
$739$	−503.837			−0.681782			−0.340891	+	0.940103i	$0.610729\pi$
$740$		0			0
$741$		0			0
$742$	−106.866	+	61.6992i	−0.144024	+	0.0831526i
$743$	366.330	+	634.502i	0.493042	+	0.853973i	0.999968	−	0.00801616i	$-0.00255165\pi$
$743$	366.330	+	634.502i	0.493042	+	0.853973i	−0.506926	+	0.861989i	$0.669218\pi$
$744$		0			0
$745$		0			0
$746$			971.604i			1.30242i
$747$		0			0
$748$		−	240.679i		−	0.321764i
$749$	80.1999	+	46.3034i	0.107076	+	0.0618203i
$750$		0			0
$751$	58.1082	+	100.646i	0.0773744	+	0.134016i	0.902116	−	0.431493i	$-0.142013\pi$
$751$	58.1082	+	100.646i	0.0773744	+	0.134016i	−0.824742	+	0.565509i	$0.808680\pi$
$752$	13.5178	+	23.4135i	0.0179758	+	0.0311349i
$753$		0			0
$754$	−19.2396	+	33.3240i	−0.0255167	+	0.0441963i
$755$		0			0
$756$		0			0
$757$			644.638i			0.851570i	0.904824	+	0.425785i	$0.140002\pi$
$757$			644.638i			0.851570i	−0.904824	+	0.425785i	$0.859998\pi$
$758$	−109.413	+	189.509i	−0.144344	+	0.250012i
$759$		0			0
$760$		0			0
$761$	−917.597	+	529.775i	−1.20578	+	0.696156i	−0.961834	−	0.273634i	$-0.911774\pi$
$761$	−917.597	+	529.775i	−1.20578	+	0.696156i	−0.243943	+	0.969789i	$0.578441\pi$
$762$		0			0
$763$	18.7235	+	10.8100i	0.0245393	+	0.0141678i
$764$		−	67.9994i		−	0.0890045i
$765$		0			0
$766$	230.690			0.301162
$767$	73.2187	−	126.819i	0.0954612	−	0.165344i
$768$		0			0
$769$	−347.756	−	602.331i	−0.452219	−	0.783266i	0.546305	−	0.837586i	$-0.316034\pi$
$769$	−347.756	−	602.331i	−0.452219	−	0.783266i	−0.998524	+	0.0543206i	$0.982701\pi$
$770$		0			0
$771$		0			0
$772$	317.153	+	183.108i	0.410820	+	0.237187i
$773$	−931.046			−1.20446			−0.602229	−	0.798323i	$-0.705721\pi$
$773$	−931.046			−1.20446			−0.602229	+	0.798323i	$0.705721\pi$
$774$		0			0
$775$		0			0
$776$	5.60360	+	3.23524i	0.00722114	+	0.00416913i
$777$		0			0
$778$	−380.061	+	219.428i	−0.488510	+	0.282042i
$779$	−1602.12	+	924.982i	−2.05663	+	1.18740i
$780$		0			0
$781$	137.391	−	237.968i	0.175916	−	0.304696i
$782$	206.133			0.263597
$783$		0			0
$784$	192.050			0.244961
$785$		0			0
$786$		0			0
$787$	372.045	−	214.800i	0.472738	−	0.272936i	−0.244647	−	0.969612i	$-0.578672\pi$
$787$	372.045	−	214.800i	0.472738	−	0.272936i	0.717385	+	0.696677i	$0.245339\pi$
$788$	30.9351	+	53.5811i	0.0392577	+	0.0679964i
$789$		0			0
$790$		0			0
$791$			142.352i			0.179965i
$792$		0			0
$793$		−	102.277i		−	0.128975i
$794$	−330.751	−	190.959i	−0.416563	−	0.240503i
$795$		0			0
$796$	−332.873	−	576.552i	−0.418182	−	0.724312i
$797$	305.208	+	528.635i	0.382945	+	0.663281i	0.991482	−	0.130245i	$-0.0415764\pi$
$797$	305.208	+	528.635i	0.382945	+	0.663281i	−0.608536	+	0.793526i	$0.708243\pi$
$798$		0			0
$799$	−81.5608	+	141.268i	−0.102079	+	0.176805i
$800$		0			0
$801$		0			0
$802$			857.964i			1.06978i
$803$	330.964	−	573.246i	0.412159	−	0.713880i
$804$		0			0
$805$		0			0
$806$	47.3209	−	27.3208i	0.0587108	−	0.0338967i
$807$		0			0
$808$	278.380	+	160.723i	0.344529	+	0.198914i
$809$		−	304.324i		−	0.376173i	−0.982152	−	0.188087i	$-0.939771\pi$
$809$		−	304.324i		−	0.376173i	0.982152	−	0.188087i	$-0.0602286\pi$
$810$		0			0
$811$	−639.398			−0.788407			−0.394204	−	0.919023i	$-0.628980\pi$
$811$	−639.398			−0.788407			−0.394204	+	0.919023i	$0.628980\pi$
$812$	19.0385	−	32.9757i	0.0234465	−	0.0406105i
$813$		0			0
$814$	222.591	+	385.538i	0.273453	+	0.473634i
$815$		0			0
$816$		0			0
$817$	660.384	+	381.273i	0.808303	+	0.466674i
$818$	941.721			1.15125
$819$		0			0
$820$		0			0
$821$	−1153.10	−	665.742i	−1.40451	−	0.810892i	−0.409655	−	0.912241i	$-0.634351\pi$
$821$	−1153.10	−	665.742i	−1.40451	−	0.810892i	−0.994851	+	0.101349i	$0.967684\pi$
$822$		0			0
$823$	−771.647	+	445.511i	−0.937603	+	0.541325i	−0.889208	−	0.457503i	$-0.848744\pi$
$823$	−771.647	+	445.511i	−0.937603	+	0.541325i	−0.0483950	+	0.998828i	$0.515411\pi$
$824$	−138.992	+	80.2473i	−0.168680	+	0.0973875i
$825$		0			0
$826$	−72.4535	+	125.493i	−0.0877161	+	0.151929i
$827$	−494.513			−0.597960			−0.298980	−	0.954259i	$-0.596646\pi$
$827$	−494.513			−0.597960			−0.298980	+	0.954259i	$0.596646\pi$
$828$		0			0
$829$	752.153			0.907302			0.453651	−	0.891179i	$-0.350121\pi$
$829$	752.153			0.907302			0.453651	+	0.891179i	$0.350121\pi$
$830$		0			0
$831$		0			0
$832$	9.83988	−	5.68105i	0.0118268	−	0.00682819i
$833$	579.375	+	1003.51i	0.695528	+	1.20469i
$834$		0			0
$835$		0			0
$836$			274.942i			0.328878i
$837$		0			0
$838$			305.770i			0.364881i
$839$	438.301	+	253.053i	0.522409	+	0.301613i	0.737920	−	0.674888i	$-0.235808\pi$
$839$	438.301	+	253.053i	0.522409	+	0.301613i	−0.215511	+	0.976502i	$0.569142\pi$
$840$		0			0
$841$	−236.992	−	410.482i	−0.281798	−	0.488088i
$842$	−223.095	−	386.412i	−0.264958	−	0.458921i
$843$		0			0
$844$	160.772	−	278.465i	0.190488	−	0.329935i
$845$		0			0
$846$		0			0
$847$		−	95.5398i		−	0.112798i
$848$	−175.604	+	304.154i	−0.207080	+	0.358673i
$849$		0			0
$850$		0			0
$851$	−330.199	+	190.641i	−0.388013	+	0.224020i
$852$		0			0
$853$	−19.0595	−	11.0040i	−0.0223441	−	0.0129004i	0.488786	−	0.872404i	$-0.337440\pi$
$853$	−19.0595	−	11.0040i	−0.0223441	−	0.0129004i	−0.511130	+	0.859503i	$0.670773\pi$
$854$			101.208i			0.118511i
$855$		0			0
$856$	263.570			0.307909
$857$	−61.2491	+	106.086i	−0.0714691	+	0.123788i	−0.899545	−	0.436827i	$-0.856102\pi$
$857$	−61.2491	+	106.086i	−0.0714691	+	0.123788i	0.828076	+	0.560615i	$0.189435\pi$
$858$		0			0
$859$	705.014	+	1221.12i	0.820738	+	1.42156i	0.905134	+	0.425127i	$0.139771\pi$
$859$	705.014	+	1221.12i	0.820738	+	1.42156i	−0.0843962	+	0.996432i	$0.526896\pi$
$860$		0			0
$861$		0			0
$862$	863.591	+	498.594i	1.00185	+	0.578416i
$863$	674.484			0.781557			0.390778	−	0.920485i	$-0.372206\pi$
$863$	674.484			0.781557			0.390778	+	0.920485i	$0.372206\pi$
$864$		0			0
$865$		0			0
$866$	−187.062	−	108.000i	−0.216007	−	0.124711i
$867$		0			0
$868$	−46.8264	+	27.0352i	−0.0539475	+	0.0311466i
$869$	170.954	−	98.7006i	0.196725	−	0.113580i
$870$		0			0
$871$	−14.1800	+	24.5604i	−0.0162801	+	0.0281979i
$872$	61.5333			0.0705657
$873$		0			0
$874$	−235.478			−0.269426
$875$		0			0
$876$		0			0
$877$	−1187.06	+	685.352i	−1.35355	+	0.781473i	−0.988745	−	0.149611i	$-0.952198\pi$
$877$	−1187.06	+	685.352i	−1.35355	+	0.781473i	−0.364805	+	0.931084i	$0.618864\pi$
$878$	114.717	+	198.696i	0.130657	+	0.226305i
$879$		0			0
$880$		0			0
$881$			629.262i			0.714259i	0.934055	+	0.357130i	$0.116245\pi$
$881$			629.262i			0.714259i	−0.934055	+	0.357130i	$0.883755\pi$
$882$		0			0
$883$		−	537.868i		−	0.609137i	−0.952490	−	0.304569i	$-0.901488\pi$
$883$		−	537.868i		−	0.609137i	0.952490	−	0.304569i	$-0.0985123\pi$
$884$	59.3699	+	34.2772i	0.0671605	+	0.0387751i
$885$		0			0
$886$	274.050	+	474.669i	0.309312	+	0.535743i
$887$	268.569	+	465.175i	0.302784	+	0.524437i	0.976765	−	0.214311i	$-0.0687507\pi$
$887$	268.569	+	465.175i	0.302784	+	0.524437i	−0.673982	+	0.738748i	$0.735417\pi$
$888$		0			0
$889$	−82.0128	+	142.050i	−0.0922529	+	0.159787i
$890$		0			0
$891$		0			0
$892$			782.803i			0.877582i
$893$	93.1719	−	161.378i	0.104336	−	0.180715i
$894$		0			0
$895$		0			0
$896$	−9.73704	+	5.62168i	−0.0108672	+	0.00627420i
$897$		0			0
$898$	−135.977	−	78.5065i	−0.151422	−	0.0874237i
$899$		−	521.172i		−	0.579725i
$900$		0			0
$901$	−2119.04			−2.35188
$902$	−236.581	+	409.771i	−0.262285	+	0.454291i
$903$		0			0
$904$	202.576	+	350.872i	0.224088	+	0.388132i
$905$		0			0
$906$		0			0
$907$	432.047	+	249.443i	0.476347	+	0.275019i	0.718893	−	0.695121i	$-0.244649\pi$
$907$	432.047	+	249.443i	0.476347	+	0.275019i	−0.242546	+	0.970140i	$0.577982\pi$
$908$	681.398			0.750439
$909$		0			0
$910$		0			0
$911$	−980.687	−	566.200i	−1.07650	−	0.621515i	−0.146547	−	0.989204i	$-0.546816\pi$
$911$	−980.687	−	566.200i	−1.07650	−	0.621515i	−0.929949	+	0.367689i	$0.880149\pi$
$912$		0			0
$913$	523.312	−	302.135i	0.573179	−	0.330925i
$914$	365.953	−	211.283i	0.400386	−	0.231163i
$915$		0			0
$916$	−94.4465	+	163.586i	−0.103108	+	0.178587i
$917$	−52.1412			−0.0568606
$918$		0			0
$919$	20.1454			0.0219210			0.0109605	−	0.999940i	$-0.496511\pi$
$919$	20.1454			0.0219210			0.0109605	+	0.999940i	$0.496511\pi$
$920$		0			0
$921$		0			0
$922$	−254.610	+	146.999i	−0.276149	+	0.159435i
$923$	39.1340	+	67.7821i	0.0423987	+	0.0734367i
$924$		0			0
$925$		0			0
$926$			1223.47i			1.32124i
$927$		0			0
$928$		−	108.372i		−	0.116780i
$929$	−260.470	−	150.382i	−0.280377	−	0.161876i	0.353217	−	0.935541i	$-0.385088\pi$
$929$	−260.470	−	150.382i	−0.280377	−	0.161876i	−0.633594	+	0.773666i	$0.718421\pi$
$930$		0			0
$931$	−661.855	−	1146.37i	−0.710908	−	1.23133i
$932$	−117.982	−	204.352i	−0.126591	−	0.219261i
$933$		0			0
$934$	604.382	−	1046.82i	0.647090	−	1.12079i
$935$		0			0
$936$		0			0
$937$		−	310.906i		−	0.331810i	−0.986142	−	0.165905i	$-0.946945\pi$
$937$		−	310.906i		−	0.331810i	0.986142	−	0.165905i	$-0.0530545\pi$
$938$	14.0318	−	24.3037i	0.0149592	−	0.0259102i
$939$		0			0
$940$		0			0
$941$	−1259.21	+	727.005i	−1.33816	+	0.772588i	−0.986535	−	0.163553i	$-0.947705\pi$
$941$	−1259.21	+	727.005i	−1.33816	+	0.772588i	−0.351627	+	0.936140i	$0.614371\pi$
$942$		0			0
$943$	−350.954	−	202.623i	−0.372167	−	0.214871i
$944$			412.423i			0.436889i
$945$		0			0
$946$	195.035			0.206168
$947$	−95.4294	+	165.289i	−0.100770	+	0.174539i	−0.912002	−	0.410185i	$-0.865464\pi$
$947$	−95.4294	+	165.289i	−0.100770	+	0.174539i	0.811232	+	0.584724i	$0.198797\pi$
$948$		0			0
$949$	94.2708	+	163.282i	0.0993370	+	0.172057i
$950$		0			0
$951$		0			0
$952$	−58.7494	−	33.9190i	−0.0617115	−	0.0356292i
$953$	808.807			0.848695			0.424348	−	0.905499i	$-0.360503\pi$
$953$	808.807			0.848695			0.424348	+	0.905499i	$0.360503\pi$
$954$		0			0
$955$		0			0
$956$	639.322	+	369.113i	0.668747	+	0.386101i
$957$		0			0
$958$	−372.493	+	215.059i	−0.388823	+	0.224487i
$959$	−103.598	+	59.8124i	−0.108027	+	0.0623695i
$960$		0			0
$961$	110.461	−	191.324i	0.114944	−	0.199088i
$962$	−126.804			−0.131813
$963$		0			0
$964$	−751.261			−0.779316
$965$		0			0
$966$		0			0
$967$	−370.279	+	213.781i	−0.382915	+	0.221076i	−0.679086	−	0.734059i	$-0.737624\pi$
$967$	−370.279	+	213.781i	−0.382915	+	0.221076i	0.296171	+	0.955135i	$0.404290\pi$
$968$	−135.959	−	235.488i	−0.140454	−	0.243273i
$969$		0			0
$970$		0			0
$971$		−	932.208i		−	0.960050i	−0.877255	−	0.480025i	$-0.840628\pi$
$971$		−	932.208i		−	0.960050i	0.877255	−	0.480025i	$-0.159372\pi$
$972$		0			0
$973$		−	65.9856i		−	0.0678166i
$974$	1111.31	+	641.613i	1.14097	+	0.658741i
$975$		0			0
$976$	144.026	+	249.460i	0.147567	+	0.255594i
$977$	−101.710	−	176.167i	−0.104105	−	0.180315i	0.809267	−	0.587440i	$-0.199864\pi$
$977$	−101.710	−	176.167i	−0.104105	−	0.180315i	−0.913372	+	0.407126i	$0.866531\pi$
$978$		0			0
$979$	184.618	−	319.768i	0.188578	−	0.326627i
$980$		0			0
$981$		0			0
$982$		−	92.5557i		−	0.0942522i
$983$	717.012	−	1241.90i	0.729412	−	1.26338i	−0.227719	−	0.973727i	$-0.573127\pi$
$983$	717.012	−	1241.90i	0.729412	−	1.26338i	0.957132	−	0.289653i	$-0.0935398\pi$
$984$		0			0
$985$		0			0
$986$	566.271	−	326.937i	0.574312	−	0.331579i
$987$		0			0
$988$	−67.8218	−	39.1569i	−0.0686455	−	0.0396325i
$989$			167.041i			0.168898i
$990$		0			0
$991$	−983.596			−0.992528			−0.496264	−	0.868172i	$-0.665295\pi$
$991$	−983.596			−0.992528			−0.496264	+	0.868172i	$0.665295\pi$
$992$	−76.9456	+	133.274i	−0.0775661	+	0.134348i
$993$		0			0
$994$	−38.7250	−	67.0737i	−0.0389588	−	0.0674785i
$995$		0			0
$996$		0			0
$997$	−858.379	−	495.586i	−0.860962	−	0.497077i	0.00337211	−	0.999994i	$-0.498927\pi$
$997$	−858.379	−	495.586i	−0.860962	−	0.497077i	−0.864334	+	0.502917i	$0.832260\pi$
$998$	−1014.39			−1.01643
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1350.3.k.b.899.6		32
3.2	odd	2		450.3.k.c.299.11		32
5.2	odd	4		270.3.h.a.251.1		16
5.3	odd	4		1350.3.i.g.251.7		16
5.4	even	2	inner	1350.3.k.b.899.11		32
9.4	even	3		450.3.k.c.149.6		32
9.5	odd	6	inner	1350.3.k.b.449.11		32
15.2	even	4		90.3.h.a.11.7	✓	16
15.8	even	4		450.3.i.g.101.2		16
15.14	odd	2		450.3.k.c.299.6		32
20.7	even	4		2160.3.bs.d.1601.3		16
45.2	even	12		810.3.d.c.161.7		16
45.4	even	6		450.3.k.c.149.11		32
45.7	odd	12		810.3.d.c.161.11		16
45.13	odd	12		450.3.i.g.401.2		16
45.14	odd	6	inner	1350.3.k.b.449.6		32
45.22	odd	12		90.3.h.a.41.7	yes	16
45.23	even	12		1350.3.i.g.1151.7		16
45.32	even	12		270.3.h.a.71.1		16
60.47	odd	4		720.3.bs.d.641.2		16
180.67	even	12		720.3.bs.d.401.2		16
180.167	odd	12		2160.3.bs.d.881.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.3.h.a.11.7	✓	16	15.2	even	4
90.3.h.a.41.7	yes	16	45.22	odd	12
270.3.h.a.71.1		16	45.32	even	12
270.3.h.a.251.1		16	5.2	odd	4
450.3.i.g.101.2		16	15.8	even	4
450.3.i.g.401.2		16	45.13	odd	12
450.3.k.c.149.6		32	9.4	even	3
450.3.k.c.149.11		32	45.4	even	6
450.3.k.c.299.6		32	15.14	odd	2
450.3.k.c.299.11		32	3.2	odd	2
720.3.bs.d.401.2		16	180.67	even	12
720.3.bs.d.641.2		16	60.47	odd	4
810.3.d.c.161.7		16	45.2	even	12
810.3.d.c.161.11		16	45.7	odd	12
1350.3.i.g.251.7		16	5.3	odd	4
1350.3.i.g.1151.7		16	45.23	even	12
1350.3.k.b.449.6		32	45.14	odd	6	inner
1350.3.k.b.449.11		32	9.5	odd	6	inner
1350.3.k.b.899.6		32	1.1	even	1	trivial
1350.3.k.b.899.11		32	5.4	even	2	inner
2160.3.bs.d.881.3		16	180.167	odd	12
2160.3.bs.d.1601.3		16	20.7	even	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:	\( N \)	\(=\)	\( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1350.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(0.860641 + 0.496891i) q^{7} +2.82843 q^{8} +(-4.31820 - 2.49311i) q^{11} +(1.22998 - 0.710132i) q^{13} +(-1.21713 + 0.702710i) q^{14} +(-2.00000 + 3.46410i) q^{16} -24.1344 q^{17} +27.5702 q^{19} +(6.10686 - 3.52579i) q^{22} +(3.01971 + 5.23030i) q^{23} +2.00856i q^{26} -1.98756i q^{28} +(16.5910 + 9.57883i) q^{29} +(-13.6022 - 23.5597i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(17.0656 - 29.5585i) q^{34} +63.1320i q^{37} +(-19.4951 + 33.7664i) q^{38} +(-58.1104 + 33.5501i) q^{41} +(23.9528 + 13.8292i) q^{43} +9.97245i q^{44} -8.54104 q^{46} +(3.37944 - 5.85337i) q^{47} +(-24.0062 - 41.5800i) q^{49} +(-2.45997 - 1.42026i) q^{52} +87.8018 q^{53} +(2.43426 + 1.40542i) q^{56} +(-23.4633 + 13.5465i) q^{58} +(89.2923 - 51.5529i) q^{59} +(36.0064 - 62.3649i) q^{61} +38.4728 q^{62} +8.00000 q^{64} +(-17.2928 + 9.98403i) q^{67} +(24.1344 + 41.8020i) q^{68} +55.1081i q^{71} +132.751i q^{73} +(-77.3206 - 44.6411i) q^{74} +(-27.5702 - 47.7530i) q^{76} +(-2.47761 - 4.29135i) q^{77} +(-19.7946 + 34.2853i) q^{79} -94.8939i q^{82} +(-60.5938 + 104.952i) q^{83} +(-33.8744 + 19.5574i) q^{86} +(-12.2137 - 7.05159i) q^{88} +74.0513i q^{89} +1.41143 q^{91} +(6.03943 - 10.4606i) q^{92} +(4.77926 + 8.27791i) q^{94} +(1.98117 + 1.14383i) q^{97} +67.8998 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{4} - 72 q^{14} - 64 q^{16} - 160 q^{19} - 144 q^{29} - 32 q^{31} + 96 q^{34} - 216 q^{41} + 48 q^{46} + 168 q^{49} + 144 q^{56} + 288 q^{59} - 152 q^{61} + 256 q^{64} - 576 q^{74} + 160 q^{76}+ \cdots + 168 q^{94}+O(q^{100}) \) 32 * q - 32 * q^4 - 72 * q^14 - 64 * q^16 - 160 * q^19 - 144 * q^29 - 32 * q^31 + 96 * q^34 - 216 * q^41 + 48 * q^46 + 168 * q^49 + 144 * q^56 + 288 * q^59 - 152 * q^61 + 256 * q^64 - 576 * q^74 + 160 * q^76 - 160 * q^79 + 432 * q^86 - 1312 * q^91 + 168 * q^94

Introduction

L-functions

Modular forms

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Database

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