LMFDB - Embedded newform 1350.3.k.b.449.6

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			449.6
Character	$\chi$	$=$	1350.449
Dual form			1350.3.k.b.899.6

$q$-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 $\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times$.

$n$	$1001$	$1027$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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	−0.437264	−	0.899333i	$-0.644053\pi$
$7$	0.860641	−	0.496891i	0.122949	−	0.0709844i	0.560213	+	0.828349i	$0.310719\pi$
$8$	2.82843			0.353553
$9$		0			0
$10$		0			0
$11$	−4.31820	+	2.49311i	−0.392564	+	0.226647i	−0.683270	−	0.730166i	$-0.739443\pi$
$11$	−4.31820	+	2.49311i	−0.392564	+	0.226647i	0.290707	+	0.956812i	$0.406110\pi$
$12$		0			0
$13$	1.22998	+	0.710132i	0.0946142	+	0.0546255i	0.546561	−	0.837420i	$-0.315937\pi$
$13$	1.22998	+	0.710132i	0.0946142	+	0.0546255i	−0.451946	+	0.892045i	$0.649270\pi$
$14$	−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	−0.792883	−	0.609374i	$-0.791421\pi$
$23$	3.01971	−	5.23030i	0.131292	−	0.227404i	0.924175	+	0.381970i	$0.124754\pi$
$24$		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	−0.185885	−	0.982572i	$-0.559515\pi$
$29$	16.5910	−	9.57883i	0.572104	−	0.330305i	0.757989	+	0.652267i	$0.226182\pi$
$30$		0			0
$31$	−13.6022	+	23.5597i	−0.438780	+	0.759990i	−0.997596	−	0.0693023i	$-0.977923\pi$
$31$	−13.6022	+	23.5597i	−0.438780	+	0.759990i	0.558815	+	0.829292i	$0.311256\pi$
$32$	−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	$-0.674698\pi$
$37$		−	63.1320i		−	1.70627i	0.521689	−	0.853136i	$-0.325302\pi$
$38$	−19.4951	−	33.7664i	−0.513028	−	0.888591i
$39$		0			0
$40$		0			0
$41$	−58.1104	−	33.5501i	−1.41733	−	0.818294i	−0.421264	−	0.906938i	$-0.638413\pi$
$41$	−58.1104	−	33.5501i	−1.41733	−	0.818294i	−0.996063	+	0.0886435i	$0.971747\pi$
$42$		0			0
$43$	23.9528	−	13.8292i	0.557042	−	0.321609i	−0.194915	−	0.980820i	$-0.562443\pi$
$43$	23.9528	−	13.8292i	0.557042	−	0.321609i	0.751958	+	0.659212i	$0.229110\pi$
$44$		−	9.97245i		−	0.226647i
$45$		0			0
$46$	−8.54104			−0.185675
$47$	3.37944	+	5.85337i	0.0719031	+	0.124540i	0.899735	−	0.436436i	$-0.143759\pi$
$47$	3.37944	+	5.85337i	0.0719031	+	0.124540i	−0.827832	+	0.560976i	$0.810426\pi$
$48$		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	0.999876	+	0.0157198i	$0.00500398\pi$
$59$	89.2923	+	51.5529i	1.51343	+	0.873778i	0.513552	+	0.858058i	$0.328329\pi$
$60$		0			0
$61$	36.0064	+	62.3649i	0.590269	+	1.02238i	0.994196	+	0.107585i	$0.0343117\pi$
$61$	36.0064	+	62.3649i	0.590269	+	1.02238i	−0.403927	+	0.914791i	$0.632355\pi$
$62$	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	0.365366	−	0.930864i	$-0.380944\pi$
$67$	−17.2928	−	9.98403i	−0.258102	−	0.149015i	−0.623469	+	0.781848i	$0.714277\pi$
$68$	24.1344	−	41.8020i	0.354918	−	0.614735i
$69$		0			0
$70$		0			0
$71$		−	55.1081i		−	0.776170i	−0.921624	−	0.388085i	$-0.873137\pi$
$71$		−	55.1081i		−	0.776170i	0.921624	−	0.388085i	$-0.126863\pi$
$72$		0			0
$73$		−	132.751i		−	1.81851i	−0.416241	−	0.909254i	$-0.636653\pi$
$73$		−	132.751i		−	1.81851i	0.416241	−	0.909254i	$-0.363347\pi$
$74$	−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	0.713116	−	0.701046i	$-0.247283\pi$
$79$	−19.7946	−	34.2853i	−0.250565	−	0.433992i	−0.963682	+	0.267054i	$0.913950\pi$
$80$		0			0
$81$		0			0
$82$			94.8939i			1.15724i
$83$	−60.5938	−	104.952i	−0.730046	−	1.26448i	−0.956863	−	0.290540i	$-0.906165\pi$
$83$	−60.5938	−	104.952i	−0.730046	−	1.26448i	0.226817	−	0.973937i	$-0.427168\pi$
$84$		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	$-0.863425\pi$
$89$		−	74.0513i		−	0.832037i	0.909356	−	0.416018i	$-0.136575\pi$
$90$		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	−0.489753	−	0.871861i	$-0.662913\pi$
$97$	1.98117	−	1.14383i	0.0204245	−	0.0117921i	0.510177	+	0.860069i	$0.329580\pi$
$98$	67.8998			0.692855
$99$		0			0
$100$		0			0
$101$	98.4221	−	56.8240i	0.974476	−	0.562614i	0.0738781	−	0.997267i	$-0.476462\pi$
$101$	98.4221	−	56.8240i	0.974476	−	0.562614i	0.900598	+	0.434653i	$0.143129\pi$
$102$		0			0
$103$	−49.1412	−	28.3717i	−0.477099	−	0.275453i	0.242108	−	0.970249i	$-0.422161\pi$
$103$	−49.1412	−	28.3717i	−0.477099	−	0.275453i	−0.719207	+	0.694796i	$0.755495\pi$
$104$	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	−0.352947	−	0.935643i	$-0.614820\pi$
$113$	71.6214	−	124.052i	0.633817	−	1.09780i	0.986764	−	0.162161i	$-0.0518463\pi$
$114$		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	$-0.774848\pi$
$127$		−	165.052i		−	1.29962i	0.760096	−	0.649811i	$-0.225152\pi$
$128$	−5.65685	−	9.79796i	−0.0441942	−	0.0765466i
$129$		0			0
$130$		0			0
$131$	−45.4381	−	26.2337i	−0.346856	−	0.200257i	0.316444	−	0.948611i	$-0.397511\pi$
$131$	−45.4381	−	26.2337i	−0.346856	−	0.200257i	−0.663300	+	0.748354i	$0.730844\pi$
$132$		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	0.558319	−	0.829626i	$-0.311447\pi$
$137$	−60.1866	−	104.246i	−0.439318	−	0.760921i	−0.997637	+	0.0687051i	$0.978113\pi$
$138$		0			0
$139$	−33.1992	+	57.5027i	−0.238843	+	0.413689i	−0.960383	−	0.278685i	$-0.910102\pi$
$139$	−33.1992	+	57.5027i	−0.238843	+	0.413689i	0.721539	+	0.692373i	$0.243435\pi$
$140$		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	0.751444	−	0.659796i	$-0.229357\pi$
$149$	82.8092	+	47.8099i	0.555766	+	0.320872i	−0.195678	+	0.980668i	$0.562691\pi$
$150$		0			0
$151$	−135.262	−	234.281i	−0.895776	−	1.55153i	−0.832841	−	0.553512i	$-0.813287\pi$
$151$	−135.262	−	234.281i	−0.895776	−	1.55153i	−0.0629346	−	0.998018i	$-0.520046\pi$
$152$	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	0.396398	−	0.918079i	$-0.370260\pi$
$157$	−31.4759	−	18.1726i	−0.200483	−	0.115749i	−0.596881	+	0.802330i	$0.703594\pi$
$158$	−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	$-0.907583\pi$
$163$		−	93.3260i		−	0.572552i	0.958147	−	0.286276i	$-0.0924175\pi$
$164$	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	−0.768132	−	0.640291i	$-0.778814\pi$
$167$	28.4639	−	49.3009i	0.170443	−	0.295215i	0.938575	+	0.345076i	$0.112147\pi$
$168$		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	0.987749	+	0.156049i	$0.0498758\pi$
$173$	108.820	+	188.482i	0.629017	+	1.08949i	−0.358732	+	0.933441i	$0.616791\pi$
$174$		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	$-0.949766\pi$
$179$		−	56.2638i		−	0.314323i	0.987573	−	0.157161i	$-0.0502343\pi$
$180$		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	−0.420935	−	0.907091i	$-0.638298\pi$
$191$	29.4446	−	16.9999i	0.154160	−	0.0890045i	0.575096	+	0.818086i	$0.304965\pi$
$192$		0			0
$193$	−158.577	−	91.5542i	−0.821640	−	0.474374i	0.0293415	−	0.999569i	$-0.490659\pi$
$193$	−158.577	−	91.5542i	−0.821640	−	0.474374i	−0.850982	+	0.525195i	$0.823992\pi$
$194$	−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	−0.610226	−	0.792227i	$-0.708921\pi$
$211$	80.3859	−	139.232i	0.380976	−	0.659869i	0.991202	+	0.132358i	$0.0422548\pi$
$212$	−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	−0.520294	+	0.853987i	$0.674178\pi$
$223$	−338.964	+	195.701i	−1.52002	+	0.877582i	−0.999722	+	0.0235946i	$0.992489\pi$
$224$			5.62168i			0.0250968i
$225$		0			0
$226$	−202.576			−0.896353
$227$	−170.350	−	295.054i	−0.750439	−	1.29980i	−0.947610	−	0.319429i	$-0.896509\pi$
$227$	−170.350	−	295.054i	−0.750439	−	1.29980i	0.197172	−	0.980369i	$-0.436824\pi$
$228$		0			0
$229$	−47.2232	+	81.7931i	−0.206215	+	0.357175i	−0.950519	−	0.310666i	$-0.899448\pi$
$229$	−47.2232	+	81.7931i	−0.206215	+	0.357175i	0.744304	+	0.667841i	$0.232781\pi$
$230$		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	−0.351059	−	0.936353i	$-0.614178\pi$
$239$	−319.661	−	184.556i	−1.33749	−	0.772203i	−0.986435	+	0.164151i	$0.947512\pi$
$240$		0			0
$241$	187.815	+	325.306i	0.779316	+	1.34982i	0.932336	+	0.361592i	$0.117767\pi$
$241$	187.815	+	325.306i	0.779316	+	1.34982i	−0.153020	+	0.988223i	$0.548900\pi$
$242$	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	$-0.840869\pi$
$251$		−	240.639i		−	0.958722i	0.877618	−	0.479361i	$-0.159131\pi$
$252$		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	−0.961742	−	0.273958i	$-0.911667\pi$
$257$	−62.6094	+	108.443i	−0.243616	+	0.421956i	0.718125	+	0.695914i	$0.245000\pi$
$258$		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	0.763675	−	0.645600i	$-0.223393\pi$
$263$	−46.6216	−	80.7510i	−0.177269	−	0.307038i	−0.940944	+	0.338562i	$0.890059\pi$
$264$		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	$0.0453178\pi$
$269$			76.3366i			0.283779i	−0.989882	+	0.141890i	$0.954682\pi$
$270$		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	−0.626898	−	0.779101i	$-0.715676\pi$
$277$	−73.5785	+	42.4806i	−0.265626	+	0.153359i	0.361272	+	0.932460i	$0.382343\pi$
$278$	93.9016			0.337775
$279$		0			0
$280$		0			0
$281$	185.539	−	107.121i	0.660282	−	0.381214i	−0.132102	−	0.991236i	$-0.542173\pi$
$281$	185.539	−	107.121i	0.660282	−	0.381214i	0.792384	+	0.610022i	$0.208839\pi$
$282$		0			0
$283$	327.494	+	189.079i	1.15722	+	0.668123i	0.950637	−	0.310305i	$-0.100431\pi$
$283$	327.494	+	189.079i	1.15722	+	0.668123i	0.206586	+	0.978428i	$0.433765\pi$
$284$	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	−0.820205	−	0.572070i	$-0.806141\pi$
$293$	25.0000	−	43.3012i	0.0853242	−	0.147786i	0.905529	+	0.424284i	$0.139474\pi$
$294$		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	$0.0759320\pi$
$307$			145.083i			0.472583i	−0.971682	+	0.236292i	$0.924068\pi$
$308$	−4.95522	−	8.58270i	−0.0160884	−	0.0278659i
$309$		0			0
$310$		0			0
$311$	−90.5772	−	52.2947i	−0.291245	−	0.168150i	0.347258	−	0.937770i	$-0.387113\pi$
$311$	−90.5772	−	52.2947i	−0.291245	−	0.168150i	−0.638503	+	0.769619i	$0.720446\pi$
$312$		0			0
$313$	−50.0335	+	28.8869i	−0.159852	+	0.0922903i	−0.577792	−	0.816184i	$-0.696085\pi$
$313$	−50.0335	+	28.8869i	−0.159852	+	0.0922903i	0.417940	+	0.908474i	$0.362752\pi$
$314$			51.3999i			0.163694i
$315$		0			0
$316$	79.1786			0.250565
$317$	−49.1500	−	85.1303i	−0.155047	−	0.268550i	0.778029	−	0.628228i	$-0.216220\pi$
$317$	−49.1500	−	85.1303i	−0.155047	−	0.268550i	−0.933076	+	0.359679i	$0.882886\pi$
$318$		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	0.980873	−	0.194649i	$-0.0623569\pi$
$331$	106.537	+	184.528i	0.321865	+	0.557487i	−0.659008	+	0.752136i	$0.729024\pi$
$332$	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	0.272731	−	0.962090i	$-0.412073\pi$
$337$	−142.921	−	82.5154i	−0.424097	−	0.244853i	−0.696829	+	0.717237i	$0.745406\pi$
$338$	−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	−0.923753	−	0.382989i	$-0.874895\pi$
$347$	−45.1789	+	78.2522i	−0.130199	+	0.225511i	0.793554	+	0.608499i	$0.208228\pi$
$348$		0			0
$349$	−177.488	−	307.418i	−0.508561	−	0.880853i	−0.999951	−	0.00991327i	$-0.996844\pi$
$349$	−177.488	−	307.418i	−0.508561	−	0.880853i	0.491390	−	0.870939i	$-0.336489\pi$
$350$		0			0
$351$		0			0
$352$		−	28.2064i		−	0.0801317i
$353$	180.548	+	312.718i	0.511467	+	0.885887i	0.999912	+	0.0132919i	$0.00423108\pi$
$353$	180.548	+	312.718i	0.511467	+	0.885887i	−0.488445	+	0.872595i	$0.662436\pi$
$354$		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	$-0.896527\pi$
$359$		−	229.312i		−	0.638753i	0.947628	−	0.319377i	$-0.103473\pi$
$360$		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	0.0716052	−	0.997433i	$-0.477188\pi$
$367$	356.434	−	205.787i	0.971210	−	0.560728i	0.899605	+	0.436705i	$0.143854\pi$
$368$	−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	0.992407	+	0.122999i	$0.0392511\pi$
$373$	594.984	+	343.514i	1.59513	+	0.920949i	0.602723	+	0.797950i	$0.294082\pi$
$374$	−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	−0.952638	−	0.304108i	$-0.901642\pi$
$383$	−81.5612	+	141.268i	−0.212954	+	0.368846i	0.739684	+	0.672954i	$0.234975\pi$
$384$		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	−0.113075	−	0.993586i	$-0.536070\pi$
$389$	268.744	−	155.159i	0.690858	−	0.398867i	0.803933	+	0.594719i	$0.202737\pi$
$390$		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	$-0.889532\pi$
$397$		−	270.057i		−	0.680244i	0.940381	−	0.340122i	$-0.110468\pi$
$398$	−235.376	−	407.684i	−0.591398	−	1.02433i
$399$		0			0
$400$		0			0
$401$	525.394	+	303.336i	1.31021	+	0.756449i	0.982130	−	0.188201i	$-0.0602658\pi$
$401$	525.394	+	303.336i	1.31021	+	0.756449i	0.328078	+	0.944651i	$0.393599\pi$
$402$		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	0.0959493	+	0.995386i	$0.469411\pi$
$409$	−332.949	+	576.684i	−0.814055	+	1.40998i	−0.910004	+	0.414599i	$0.863922\pi$
$410$		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	0.706514	−	0.707699i	$-0.250267\pi$
$419$	187.245	+	108.106i	0.446886	+	0.258010i	−0.259628	+	0.965709i	$0.583600\pi$
$420$		0			0
$421$	−157.752	−	273.234i	−0.374708	−	0.649013i	0.615576	−	0.788078i	$-0.288924\pi$
$421$	−157.752	−	273.234i	−0.374708	−	0.649013i	−0.990283	+	0.139065i	$0.955590\pi$
$422$	−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	$0.304919\pi$
$431$			705.119i			1.63601i	−0.575213	+	0.818003i	$0.695081\pi$
$432$		0			0
$433$		−	152.735i		−	0.352737i	−0.984324	−	0.176369i	$-0.943565\pi$
$433$		−	152.735i		−	0.352737i	0.984324	−	0.176369i	$-0.0564351\pi$
$434$	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	0.943502	−	0.331368i	$-0.107510\pi$
$439$	81.1173	+	140.499i	0.184778	+	0.320044i	−0.758724	+	0.651412i	$0.774177\pi$
$440$		0			0
$441$		0			0
$442$			48.4753i			0.109673i
$443$	193.783	+	335.641i	0.437433	+	0.757655i	0.997491	−	0.0707979i	$-0.0225545\pi$
$443$	193.783	+	335.641i	0.437433	+	0.757655i	−0.560058	+	0.828453i	$0.689221\pi$
$444$		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	$-0.960545\pi$
$449$		−	111.025i		−	0.247272i	0.992328	−	0.123636i	$-0.0394554\pi$
$450$		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	−0.755643	−	0.654984i	$-0.772675\pi$
$457$	−258.768	+	149.400i	−0.566232	+	0.326914i	0.189411	+	0.981898i	$0.439342\pi$
$458$	133.567			0.291632
$459$		0			0
$460$		0			0
$461$	180.036	−	103.944i	0.390534	−	0.225475i	−0.291857	−	0.956462i	$-0.594273\pi$
$461$	180.036	−	103.944i	0.390534	−	0.225475i	0.682392	+	0.730987i	$0.260940\pi$
$462$		0			0
$463$	749.220	+	432.563i	1.61819	+	0.934261i	0.987389	+	0.158313i	$0.0506056\pi$
$463$	749.220	+	432.563i	1.61819	+	0.934261i	0.630798	+	0.775947i	$0.282728\pi$
$464$	−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	−0.199194	−	0.979960i	$-0.563832\pi$
$479$	263.392	−	152.069i	0.549879	−	0.317473i	0.749073	+	0.662487i	$0.230499\pi$
$480$		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	$0.381587\pi$
$487$			907.378i			1.86320i	−0.363486	+	0.931600i	$0.618413\pi$
$488$	101.842	+	176.395i	0.208692	+	0.361465i
$489$		0			0
$490$		0			0
$491$	−56.6785	−	32.7234i	−0.115435	−	0.0666464i	0.441171	−	0.897423i	$-0.354563\pi$
$491$	−56.6785	−	32.7234i	−0.115435	−	0.0666464i	−0.556606	+	0.830777i	$0.687897\pi$
$492$		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	−0.242785	−	0.970080i	$-0.578061\pi$
$499$	358.642	−	621.186i	0.718721	−	1.24486i	0.961507	−	0.274782i	$-0.0886057\pi$
$500$		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	0.944916	−	0.327313i	$-0.106143\pi$
$509$	577.161	+	333.224i	1.13391	+	0.654664i	0.188996	+	0.981978i	$0.439477\pi$
$510$		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	$0.329790\pi$
$521$			896.544i			1.72081i	−0.509608	+	0.860407i	$0.670210\pi$
$522$		0			0
$523$		−	354.070i		−	0.676999i	−0.940967	−	0.338499i	$-0.890081\pi$
$523$		−	354.070i		−	0.676999i	0.940967	−	0.338499i	$-0.109919\pi$
$524$	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	−0.269837	−	0.962906i	$-0.586970\pi$
$547$	234.742	−	135.528i	0.429145	−	0.247767i	0.698982	+	0.715139i	$0.253637\pi$
$548$	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	−0.888564	−	0.458752i	$-0.848297\pi$
$563$	−26.4560	+	45.8232i	−0.0469911	+	0.0813911i	0.841573	+	0.540143i	$0.181630\pi$
$564$		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	−0.938773	−	0.344536i	$-0.888036\pi$
$569$	−631.466	+	364.577i	−1.10978	+	0.640733i	−0.171009	+	0.985269i	$0.554703\pi$
$570$		0			0
$571$	198.741	−	344.229i	0.348057	−	0.602853i	−0.637847	−	0.770163i	$-0.720175\pi$
$571$	198.741	−	344.229i	0.348057	−	0.602853i	0.985904	+	0.167310i	$0.0535081\pi$
$572$	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	$-0.977304\pi$
$577$		−	82.2138i		−	0.142485i	0.997459	−	0.0712425i	$-0.0226964\pi$
$578$	−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	0.955290	+	0.295671i	$0.0955431\pi$
$587$	430.684	+	745.966i	0.733703	+	1.27081i	−0.221587	+	0.975141i	$0.571124\pi$
$588$		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	0.258934	−	0.965895i	$-0.416629\pi$
$599$	−268.405	−	154.964i	−0.448089	−	0.258704i	−0.707023	+	0.707191i	$0.749962\pi$
$600$		0			0
$601$	−208.891	−	361.810i	−0.347573	−	0.602014i	0.638245	−	0.769833i	$-0.279661\pi$
$601$	−208.891	−	361.810i	−0.347573	−	0.602014i	−0.985818	+	0.167820i	$0.946327\pi$
$602$	−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	−0.256277	−	0.966603i	$-0.582496\pi$
$607$	−741.461	−	428.083i	−1.22152	−	0.705244i	−0.965241	+	0.261360i	$0.915829\pi$
$608$	−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	$0.314158\pi$
$613$			1022.92i			1.66870i	−0.551231	+	0.834352i	$0.685842\pi$
$614$	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	−0.999585	−	0.0287987i	$-0.990832\pi$
$617$	−292.984	+	507.463i	−0.474852	+	0.822468i	0.524733	+	0.851267i	$0.324165\pi$
$618$		0			0
$619$	−455.788	−	789.447i	−0.736329	−	1.27536i	−0.954138	−	0.299367i	$-0.903224\pi$
$619$	−455.788	−	789.447i	−0.736329	−	1.27536i	0.217809	−	0.975991i	$-0.430109\pi$
$620$		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	−0.0438265	−	0.999039i	$-0.513955\pi$
$641$	512.450	−	295.863i	0.799454	−	0.461565i	0.843280	+	0.537474i	$0.180622\pi$
$642$		0			0
$643$	−647.010	−	373.551i	−1.00624	−	0.580950i	−0.0961484	−	0.995367i	$-0.530652\pi$
$643$	−647.010	−	373.551i	−1.00624	−	0.580950i	−0.910087	+	0.414417i	$0.863986\pi$
$644$	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	−0.792845	−	0.609423i	$-0.791401\pi$
$653$	85.7737	−	148.564i	0.131353	−	0.227511i	0.924198	+	0.381913i	$0.124734\pi$
$654$		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	−0.436803	−	0.899557i	$-0.643889\pi$
$659$	81.6071	−	47.1159i	0.123835	−	0.0714960i	0.560638	+	0.828061i	$0.310556\pi$
$660$		0			0
$661$	−422.390	+	731.602i	−0.639017	+	1.10681i	0.346631	+	0.938001i	$0.387325\pi$
$661$	−422.390	+	731.602i	−0.639017	+	1.10681i	−0.985649	+	0.168809i	$0.946008\pi$
$662$	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	0.0270541	−	0.999634i	$-0.491387\pi$
$673$	609.933	−	352.145i	0.906290	−	0.523247i	0.879235	+	0.476387i	$0.158054\pi$
$674$			233.389i			0.346274i
$675$		0			0
$676$	333.966			0.494032
$677$	639.435	+	1107.53i	0.944513	+	1.63594i	0.756724	+	0.653734i	$0.226799\pi$
$677$	639.435	+	1107.53i	0.944513	+	1.63594i	0.187788	+	0.982210i	$0.439868\pi$
$678$		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	0.549589	−	0.835435i	$-0.314784\pi$
$691$	−310.061	−	537.041i	−0.448713	−	0.777194i	−0.998303	+	0.0582407i	$0.981451\pi$
$692$	−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	$-0.984873\pi$
$701$		−	66.6004i		−	0.0950077i	0.998871	−	0.0475038i	$-0.0151266\pi$
$702$		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	0.782173	−	0.623062i	$-0.214111\pi$
$709$	−105.287	−	182.363i	−0.148501	−	0.257211i	−0.930674	+	0.365851i	$0.880778\pi$
$710$		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	$-0.784698\pi$
$719$		−	900.163i		−	1.25197i	0.779837	−	0.625983i	$-0.215302\pi$
$720$		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	−0.877082	−	0.480341i	$-0.840513\pi$
$727$	−654.034	+	377.607i	−0.899635	+	0.519404i	−0.0225530	+	0.999746i	$0.507179\pi$
$728$	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	0.423641	−	0.905830i	$-0.360752\pi$
$733$	−109.224	−	63.0608i	−0.149010	−	0.0860311i	−0.572651	+	0.819799i	$0.694085\pi$
$734$	−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	−0.506926	−	0.861989i	$-0.669218\pi$
$743$	366.330	−	634.502i	0.493042	−	0.853973i	0.999968	+	0.00801616i	$0.00255165\pi$
$744$		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	−0.824742	−	0.565509i	$-0.808680\pi$
$751$	58.1082	−	100.646i	0.0773744	−	0.134016i	0.902116	+	0.431493i	$0.142013\pi$
$752$	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	$-0.859998\pi$
$757$		−	644.638i		−	0.851570i	0.904824	−	0.425785i	$-0.140002\pi$
$758$	−109.413	−	189.509i	−0.144344	−	0.250012i
$759$		0			0
$760$		0			0
$761$	−917.597	−	529.775i	−1.20578	−	0.696156i	−0.243943	−	0.969789i	$-0.578441\pi$
$761$	−917.597	−	529.775i	−1.20578	−	0.696156i	−0.961834	+	0.273634i	$0.911774\pi$
$762$		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	−0.998524	−	0.0543206i	$-0.982701\pi$
$769$	−347.756	+	602.331i	−0.452219	+	0.783266i	0.546305	+	0.837586i	$0.316034\pi$
$770$		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	0.717385	−	0.696677i	$-0.245339\pi$
$787$	372.045	+	214.800i	0.472738	+	0.272936i	−0.244647	+	0.969612i	$0.578672\pi$
$788$	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	−0.608536	−	0.793526i	$-0.708243\pi$
$797$	305.208	−	528.635i	0.382945	−	0.663281i	0.991482	+	0.130245i	$0.0415764\pi$
$798$		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	$0.0602286\pi$
$809$			304.324i			0.376173i	−0.982152	+	0.188087i	$0.939771\pi$
$810$		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	−0.994851	−	0.101349i	$-0.967684\pi$
$821$	−1153.10	+	665.742i	−1.40451	+	0.810892i	−0.409655	+	0.912241i	$0.634351\pi$
$822$		0			0
$823$	−771.647	−	445.511i	−0.937603	−	0.541325i	−0.0483950	−	0.998828i	$-0.515411\pi$
$823$	−771.647	−	445.511i	−0.937603	−	0.541325i	−0.889208	+	0.457503i	$0.848744\pi$
$824$	−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	−0.215511	−	0.976502i	$-0.569142\pi$
$839$	438.301	−	253.053i	0.522409	−	0.301613i	0.737920	+	0.674888i	$0.235808\pi$
$840$		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	−0.511130	−	0.859503i	$-0.670773\pi$
$853$	−19.0595	+	11.0040i	−0.0223441	+	0.0129004i	0.488786	+	0.872404i	$0.337440\pi$
$854$		−	101.208i		−	0.118511i
$855$		0			0
$856$	263.570			0.307909
$857$	−61.2491	−	106.086i	−0.0714691	−	0.123788i	0.828076	−	0.560615i	$-0.189435\pi$
$857$	−61.2491	−	106.086i	−0.0714691	−	0.123788i	−0.899545	+	0.436827i	$0.856102\pi$
$858$		0			0
$859$	705.014	−	1221.12i	0.820738	−	1.42156i	−0.0843962	−	0.996432i	$-0.526896\pi$
$859$	705.014	−	1221.12i	0.820738	−	1.42156i	0.905134	−	0.425127i	$-0.139771\pi$
$860$		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	−0.364805	−	0.931084i	$-0.618864\pi$
$877$	−1187.06	−	685.352i	−1.35355	−	0.781473i	−0.988745	+	0.149611i	$0.952198\pi$
$878$	114.717	−	198.696i	0.130657	−	0.226305i
$879$		0			0
$880$		0			0
$881$		−	629.262i		−	0.714259i	−0.934055	−	0.357130i	$-0.883755\pi$
$881$		−	629.262i		−	0.714259i	0.934055	−	0.357130i	$-0.116245\pi$
$882$		0			0
$883$			537.868i			0.609137i	0.952490	+	0.304569i	$0.0985123\pi$
$883$			537.868i			0.609137i	−0.952490	+	0.304569i	$0.901488\pi$
$884$	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	−0.673982	−	0.738748i	$-0.735417\pi$
$887$	268.569	−	465.175i	0.302784	−	0.524437i	0.976765	+	0.214311i	$0.0687507\pi$
$888$		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	−0.242546	−	0.970140i	$-0.577982\pi$
$907$	432.047	−	249.443i	0.476347	−	0.275019i	0.718893	+	0.695121i	$0.244649\pi$
$908$	681.398			0.750439
$909$		0			0
$910$		0			0
$911$	−980.687	+	566.200i	−1.07650	+	0.621515i	−0.929949	−	0.367689i	$-0.880149\pi$
$911$	−980.687	+	566.200i	−1.07650	+	0.621515i	−0.146547	+	0.989204i	$0.546816\pi$
$912$		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	−0.633594	−	0.773666i	$-0.718421\pi$
$929$	−260.470	+	150.382i	−0.280377	+	0.161876i	0.353217	+	0.935541i	$0.385088\pi$
$930$		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	$0.0530545\pi$
$937$			310.906i			0.331810i	−0.986142	+	0.165905i	$0.946945\pi$
$938$	14.0318	+	24.3037i	0.0149592	+	0.0259102i
$939$		0			0
$940$		0			0
$941$	−1259.21	−	727.005i	−1.33816	−	0.772588i	−0.351627	−	0.936140i	$-0.614371\pi$
$941$	−1259.21	−	727.005i	−1.33816	−	0.772588i	−0.986535	+	0.163553i	$0.947705\pi$
$942$		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	0.811232	−	0.584724i	$-0.198797\pi$
$947$	−95.4294	−	165.289i	−0.100770	−	0.174539i	−0.912002	+	0.410185i	$0.865464\pi$
$948$		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	0.296171	−	0.955135i	$-0.404290\pi$
$967$	−370.279	−	213.781i	−0.382915	−	0.221076i	−0.679086	+	0.734059i	$0.737624\pi$
$968$	−135.959	+	235.488i	−0.140454	+	0.243273i
$969$		0			0
$970$		0			0
$971$			932.208i			0.960050i	0.877255	+	0.480025i	$0.159372\pi$
$971$			932.208i			0.960050i	−0.877255	+	0.480025i	$0.840628\pi$
$972$		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	−0.913372	−	0.407126i	$-0.866531\pi$
$977$	−101.710	+	176.167i	−0.104105	+	0.180315i	0.809267	+	0.587440i	$0.199864\pi$
$978$		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	0.957132	+	0.289653i	$0.0935398\pi$
$983$	717.012	+	1241.90i	0.729412	+	1.26338i	−0.227719	+	0.973727i	$0.573127\pi$
$984$		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	−0.864334	−	0.502917i	$-0.832260\pi$
$997$	−858.379	+	495.586i	−0.860962	+	0.497077i	0.00337211	+	0.999994i	$0.498927\pi$
$998$	−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.449.6		32
3.2	odd	2		450.3.k.c.149.11		32
5.2	odd	4		1350.3.i.g.1151.7		16
5.3	odd	4		270.3.h.a.71.1		16
5.4	even	2	inner	1350.3.k.b.449.11		32
9.2	odd	6	inner	1350.3.k.b.899.11		32
9.7	even	3		450.3.k.c.299.6		32
15.2	even	4		450.3.i.g.401.2		16
15.8	even	4		90.3.h.a.41.7	yes	16
15.14	odd	2		450.3.k.c.149.6		32
20.3	even	4		2160.3.bs.d.881.3		16
45.2	even	12		1350.3.i.g.251.7		16
45.7	odd	12		450.3.i.g.101.2		16
45.13	odd	12		810.3.d.c.161.7		16
45.23	even	12		810.3.d.c.161.11		16
45.29	odd	6	inner	1350.3.k.b.899.6		32
45.34	even	6		450.3.k.c.299.11		32
45.38	even	12		270.3.h.a.251.1		16
45.43	odd	12		90.3.h.a.11.7	✓	16
60.23	odd	4		720.3.bs.d.401.2		16
180.43	even	12		720.3.bs.d.641.2		16
180.83	odd	12		2160.3.bs.d.1601.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.3.h.a.11.7	✓	16	45.43	odd	12
90.3.h.a.41.7	yes	16	15.8	even	4
270.3.h.a.71.1		16	5.3	odd	4
270.3.h.a.251.1		16	45.38	even	12
450.3.i.g.101.2		16	45.7	odd	12
450.3.i.g.401.2		16	15.2	even	4
450.3.k.c.149.6		32	15.14	odd	2
450.3.k.c.149.11		32	3.2	odd	2
450.3.k.c.299.6		32	9.7	even	3
450.3.k.c.299.11		32	45.34	even	6
720.3.bs.d.401.2		16	60.23	odd	4
720.3.bs.d.641.2		16	180.43	even	12
810.3.d.c.161.7		16	45.13	odd	12
810.3.d.c.161.11		16	45.23	even	12
1350.3.i.g.251.7		16	45.2	even	12
1350.3.i.g.1151.7		16	5.2	odd	4
1350.3.k.b.449.6		32	1.1	even	1	trivial
1350.3.k.b.449.11		32	5.4	even	2	inner
1350.3.k.b.899.6		32	45.29	odd	6	inner
1350.3.k.b.899.11		32	9.2	odd	6	inner
2160.3.bs.d.881.3		16	20.3	even	4
2160.3.bs.d.1601.3		16	180.83	odd	12

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

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