LMFDB - Embedded newform 189.4.o.a.125.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,4,Mod(62,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("189.62");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	189.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.1513609911$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			125.21
Character	$\chi$	$=$	189.125
Dual form			189.4.o.a.62.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.67796 - 2.70082i) q^{2} +(10.5889 - 18.3405i) q^{4} +(-3.43953 + 5.95744i) q^{5} +(14.2961 - 11.7738i) q^{7} -71.1815i q^{8} +O(q^{10})$	\(q+(4.67796 - 2.70082i) q^{2} +(10.5889 - 18.3405i) q^{4} +(-3.43953 + 5.95744i) q^{5} +(14.2961 - 11.7738i) q^{7} -71.1815i q^{8} +37.1582i q^{10} +(10.9244 - 6.30723i) q^{11} +(22.5632 + 13.0269i) q^{13} +(35.0774 - 93.6886i) q^{14} +(-107.537 - 186.260i) q^{16} -124.623 q^{17} -41.3246i q^{19} +(72.8415 + 126.165i) q^{20} +(34.0694 - 59.0099i) q^{22} +(97.6910 + 56.4019i) q^{23} +(38.8392 + 67.2715i) q^{25} +140.733 q^{26} +(-64.5583 - 386.868i) q^{28} +(-114.888 + 66.3304i) q^{29} +(155.062 + 89.5251i) q^{31} +(-512.952 - 296.153i) q^{32} +(-582.982 + 336.585i) q^{34} +(20.9702 + 125.664i) q^{35} +148.290 q^{37} +(-111.610 - 193.315i) q^{38} +(424.060 + 244.831i) q^{40} +(-93.6165 + 162.149i) q^{41} +(99.1611 + 171.752i) q^{43} -267.146i q^{44} +609.326 q^{46} +(92.1405 + 159.592i) q^{47} +(65.7542 - 336.638i) q^{49} +(363.377 + 209.796i) q^{50} +(477.838 - 275.880i) q^{52} +359.147i q^{53} +86.7756i q^{55} +(-838.078 - 1017.61i) q^{56} +(-358.293 + 620.582i) q^{58} +(182.287 - 315.730i) q^{59} +(-300.892 + 173.720i) q^{61} +967.165 q^{62} -1478.83 q^{64} +(-155.214 + 89.6127i) q^{65} +(-182.332 + 315.809i) q^{67} +(-1319.62 + 2285.65i) q^{68} +(437.494 + 531.216i) q^{70} +565.793i q^{71} -737.140i q^{73} +(693.694 - 400.504i) q^{74} +(-757.912 - 437.580i) q^{76} +(81.9162 - 218.791i) q^{77} +(-451.543 - 782.096i) q^{79} +1479.51 q^{80} +1011.37i q^{82} +(-382.494 - 662.499i) q^{83} +(428.645 - 742.436i) q^{85} +(927.743 + 535.633i) q^{86} +(-448.958 - 777.618i) q^{88} -395.916 q^{89} +(475.941 - 79.4223i) q^{91} +(2068.87 - 1194.47i) q^{92} +(862.059 + 497.710i) q^{94} +(246.189 + 142.137i) q^{95} +(-243.773 + 140.742i) q^{97} +(-601.604 - 1752.37i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 6 q^{2} + 78 q^{4} + 5 q^{7}+O(q^{10}) $ 44 * q + 6 * q^2 + 78 * q^4 + 5 * q^7	$ 44 q + 6 q^{2} + 78 q^{4} + 5 q^{7} + 18 q^{11} - 204 q^{14} - 242 q^{16} - 34 q^{22} + 102 q^{23} - 352 q^{25} + 300 q^{28} - 246 q^{29} - 1068 q^{32} + 328 q^{37} - 170 q^{43} + 968 q^{46} - 79 q^{49} - 288 q^{50} - 1212 q^{56} - 538 q^{58} - 808 q^{64} - 4350 q^{65} - 590 q^{67} + 384 q^{70} + 5304 q^{74} + 2787 q^{77} - 302 q^{79} - 612 q^{85} + 13692 q^{86} + 1294 q^{88} + 210 q^{91} + 10194 q^{92} - 6336 q^{95}+O(q^{100}) $ 44 * q + 6 * q^2 + 78 * q^4 + 5 * q^7 + 18 * q^11 - 204 * q^14 - 242 * q^16 - 34 * q^22 + 102 * q^23 - 352 * q^25 + 300 * q^28 - 246 * q^29 - 1068 * q^32 + 328 * q^37 - 170 * q^43 + 968 * q^46 - 79 * q^49 - 288 * q^50 - 1212 * q^56 - 538 * q^58 - 808 * q^64 - 4350 * q^65 - 590 * q^67 + 384 * q^70 + 5304 * q^74 + 2787 * q^77 - 302 * q^79 - 612 * q^85 + 13692 * q^86 + 1294 * q^88 + 210 * q^91 + 10194 * q^92 - 6336 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	4.67796	−	2.70082i	1.65391	−	0.954885i	0.678466	−	0.734632i	$-0.262645\pi$
$2$	4.67796	−	2.70082i	1.65391	−	0.954885i	0.975443	−	0.220252i	$-0.0706881\pi$
$3$		0			0
$3$		0			0
$4$	10.5889	−	18.3405i	1.32361	−	2.29256i
$5$	−3.43953	+	5.95744i	−0.307641	+	0.532850i	−0.977846	−	0.209326i	$-0.932873\pi$
$5$	−3.43953	+	5.95744i	−0.307641	+	0.532850i	0.670205	+	0.742176i	$0.266206\pi$
$6$		0			0
$7$	14.2961	−	11.7738i	0.771914	−	0.635727i
$7$	14.2961	−	11.7738i	0.771914	−	0.635727i
$8$		−	71.1815i		−	3.14581i
$9$		0			0
$10$			37.1582i			1.17505i
$11$	10.9244	−	6.30723i	0.299440	−	0.172882i	−0.342751	−	0.939426i	$-0.611359\pi$
$11$	10.9244	−	6.30723i	0.299440	−	0.172882i	0.642191	+	0.766544i	$0.278025\pi$
$12$		0			0
$13$	22.5632	+	13.0269i	0.481377	+	0.277923i	0.720990	−	0.692945i	$-0.243687\pi$
$13$	22.5632	+	13.0269i	0.481377	+	0.277923i	−0.239613	+	0.970869i	$0.577021\pi$
$14$	35.0774	−	93.6886i	0.669630	−	1.78852i
$15$		0			0
$16$	−107.537	−	186.260i	−1.68027	−	2.91032i
$17$	−124.623			−1.77797			−0.888987	−	0.457932i	$-0.848590\pi$
$17$	−124.623			−1.77797			−0.888987	+	0.457932i	$0.848590\pi$
$18$		0			0
$19$		−	41.3246i		−	0.498974i	−0.968378	−	0.249487i	$-0.919738\pi$
$19$		−	41.3246i		−	0.498974i	0.968378	−	0.249487i	$-0.0802620\pi$
$20$	72.8415	+	126.165i	0.814393	+	1.41057i
$21$		0			0
$22$	34.0694	−	59.0099i	0.330164	−	0.571862i
$23$	97.6910	+	56.4019i	0.885651	+	0.511331i	0.872517	−	0.488583i	$-0.162486\pi$
$23$	97.6910	+	56.4019i	0.885651	+	0.511331i	0.0131335	+	0.999914i	$0.495819\pi$
$24$		0			0
$25$	38.8392	+	67.2715i	0.310714	+	0.538172i
$26$	140.733			1.06154
$27$		0			0
$28$	−64.5583	−	386.868i	−0.435727	−	2.61111i
$29$	−114.888	+	66.3304i	−0.735658	+	0.424732i	−0.820489	−	0.571663i	$-0.806298\pi$
$29$	−114.888	+	66.3304i	−0.735658	+	0.424732i	0.0848304	+	0.996395i	$0.472965\pi$
$30$		0			0
$31$	155.062	+	89.5251i	0.898386	+	0.518683i	0.876676	−	0.481081i	$-0.159756\pi$
$31$	155.062	+	89.5251i	0.898386	+	0.518683i	0.0217097	+	0.999764i	$0.493089\pi$
$32$	−512.952	−	296.153i	−2.83369	−	1.63603i
$33$		0			0
$34$	−582.982	+	336.585i	−2.94061	+	1.69776i
$35$	20.9702	+	125.664i	0.101274	+	0.606890i
$36$		0			0
$37$	148.290			0.658884			0.329442	−	0.944176i	$-0.393139\pi$
$37$	148.290			0.658884			0.329442	+	0.944176i	$0.393139\pi$
$38$	−111.610	−	193.315i	−0.476462	−	0.825257i
$39$		0			0
$40$	424.060	+	244.831i	1.67624	+	0.967779i
$41$	−93.6165	+	162.149i	−0.356596	+	0.617643i	−0.987390	−	0.158308i	$-0.949396\pi$
$41$	−93.6165	+	162.149i	−0.356596	+	0.617643i	0.630794	+	0.775951i	$0.282729\pi$
$42$		0			0
$43$	99.1611	+	171.752i	0.351673	+	0.609115i	0.986543	−	0.163504i	$-0.0522796\pi$
$43$	99.1611	+	171.752i	0.351673	+	0.609115i	−0.634870	+	0.772619i	$0.718946\pi$
$44$		−	267.146i		−	0.915312i
$45$		0			0
$46$	609.326			1.95305
$47$	92.1405	+	159.592i	0.285959	+	0.495295i	0.972841	−	0.231473i	$-0.0743546\pi$
$47$	92.1405	+	159.592i	0.285959	+	0.495295i	−0.686882	+	0.726769i	$0.741021\pi$
$48$		0			0
$49$	65.7542	−	336.638i	0.191703	−	0.981453i
$50$	363.377	+	209.796i	1.02779	+	0.593392i
$51$		0			0
$52$	477.838	−	275.880i	1.27431	−	0.735724i
$53$			359.147i			0.930804i	0.885099	+	0.465402i	$0.154090\pi$
$53$			359.147i			0.930804i	−0.885099	+	0.465402i	$0.845910\pi$
$54$		0			0
$55$			86.7756i			0.212742i
$56$	−838.078	−	1017.61i	−1.99987	−	2.42829i
$57$		0			0
$58$	−358.293	+	620.582i	−0.811141	+	1.40494i
$59$	182.287	−	315.730i	0.402232	−	0.696687i	−0.591763	−	0.806112i	$-0.701568\pi$
$59$	182.287	−	315.730i	0.402232	−	0.696687i	0.993995	+	0.109425i	$0.0349011\pi$
$60$		0			0
$61$	−300.892	+	173.720i	−0.631561	+	0.364632i	−0.781356	−	0.624085i	$-0.785472\pi$
$61$	−300.892	+	173.720i	−0.631561	+	0.364632i	0.149795	+	0.988717i	$0.452139\pi$
$62$	967.165			1.98113
$63$		0			0
$64$	−1478.83			−2.88833
$65$	−155.214	+	89.6127i	−0.296183	+	0.171001i
$66$		0			0
$67$	−182.332	+	315.809i	−0.332469	+	0.575854i	−0.982995	−	0.183630i	$-0.941215\pi$
$67$	−182.332	+	315.809i	−0.332469	+	0.575854i	0.650526	+	0.759484i	$0.274548\pi$
$68$	−1319.62	+	2285.65i	−2.35334	+	4.07611i
$69$		0			0
$70$	437.494	+	531.216i	0.747008	+	0.907035i
$71$			565.793i			0.945736i	0.881133	+	0.472868i	$0.156781\pi$
$71$			565.793i			0.945736i	−0.881133	+	0.472868i	$0.843219\pi$
$72$		0			0
$73$		−	737.140i		−	1.18186i	−0.806723	−	0.590929i	$-0.798761\pi$
$73$		−	737.140i		−	1.18186i	0.806723	−	0.590929i	$-0.201239\pi$
$74$	693.694	−	400.504i	1.08973	−	0.629158i
$75$		0			0
$76$	−757.912	−	437.580i	−1.14393	−	0.660446i
$77$	81.9162	−	218.791i	0.121237	−	0.323812i
$78$		0			0
$79$	−451.543	−	782.096i	−0.643070	−	1.11383i	−0.984744	−	0.174012i	$-0.944327\pi$
$79$	−451.543	−	782.096i	−0.643070	−	1.11383i	0.341673	−	0.939819i	$-0.389006\pi$
$80$	1479.51			2.06768
$81$		0			0
$82$			1011.37i			1.36203i
$83$	−382.494	−	662.499i	−0.505833	−	0.876129i	−0.999977	−	0.00674855i	$-0.997852\pi$
$83$	−382.494	−	662.499i	−0.505833	−	0.876129i	0.494144	−	0.869380i	$-0.335481\pi$
$84$		0			0
$85$	428.645	−	742.436i	0.546978	−	0.947393i
$86$	927.743	+	535.633i	1.16327	+	0.671614i
$87$		0			0
$88$	−448.958	−	777.618i	−0.543853	−	0.941981i
$89$	−395.916			−0.471539			−0.235770	−	0.971809i	$-0.575761\pi$
$89$	−395.916			−0.471539			−0.235770	+	0.971809i	$0.575761\pi$
$90$		0			0
$91$	475.941	−	79.4223i	0.548265	−	0.0914914i
$92$	2068.87	−	1194.47i	2.34451	−	1.35360i
$93$		0			0
$94$	862.059	+	497.710i	0.945900	+	0.546115i
$95$	246.189	+	142.137i	0.265878	+	0.153505i
$96$		0			0
$97$	−243.773	+	140.742i	−0.255169	+	0.147322i	−0.622129	−	0.782915i	$-0.713732\pi$
$97$	−243.773	+	140.742i	−0.255169	+	0.147322i	0.366960	+	0.930237i	$0.380399\pi$
$98$	−601.604	−	1752.37i	−0.620114	−	1.80629i
$99$		0			0
$100$	1645.06			1.64506
$101$	552.396	+	956.777i	0.544212	+	0.942603i	0.998656	+	0.0518275i	$0.0165046\pi$
$101$	552.396	+	956.777i	0.544212	+	0.942603i	−0.454444	+	0.890775i	$0.650162\pi$
$102$		0			0
$103$	1350.73	+	779.844i	1.29215	+	0.746023i	0.979035	−	0.203693i	$-0.0652944\pi$
$103$	1350.73	+	779.844i	1.29215	+	0.746023i	0.313114	+	0.949715i	$0.398628\pi$
$104$	927.272	−	1606.08i	0.874293	−	1.51432i
$105$		0			0
$106$	969.991	+	1680.07i	0.888810	+	1.53946i
$107$		−	741.988i		−	0.670380i	−0.942151	−	0.335190i	$-0.891200\pi$
$107$		−	741.988i		−	0.670380i	0.942151	−	0.335190i	$-0.108800\pi$
$108$		0			0
$109$	−694.460			−0.610249			−0.305125	−	0.952312i	$-0.598698\pi$
$109$	−694.460			−0.610249			−0.305125	+	0.952312i	$0.598698\pi$
$110$	234.365	+	405.933i	0.203144	+	0.351856i
$111$		0			0
$112$	−3730.36	−	1396.66i	−3.14719	−	1.17832i
$113$	−1407.16	−	812.424i	−1.17145	−	0.676340i	−0.217432	−	0.976075i	$-0.569768\pi$
$113$	−1407.16	−	812.424i	−1.17145	−	0.676340i	−0.954022	+	0.299736i	$0.903101\pi$
$114$		0			0
$115$	−672.022	+	387.992i	−0.544925	+	0.314613i
$116$			2809.46i			2.24872i
$117$		0			0
$118$		−	1969.30i		−	1.53634i
$119$	−1781.62	+	1467.29i	−1.37244	+	1.13031i
$120$		0			0
$121$	−585.938	+	1014.87i	−0.440224	+	0.762490i
$122$	−938.373	+	1625.31i	−0.696363	+	1.20614i
$123$		0			0
$124$	3283.86	−	1895.94i	2.37822	−	1.37307i
$125$	−1394.24			−0.997636
$126$		0			0
$127$	−1099.84			−0.768466			−0.384233	−	0.923236i	$-0.625534\pi$
$127$	−1099.84			−0.768466			−0.384233	+	0.923236i	$0.625534\pi$
$128$	−2814.28	+	1624.82i	−1.94335	+	1.12200i
$129$		0			0
$130$	−484.056	+	838.409i	−0.326573	+	0.565641i
$131$	597.844	−	1035.50i	0.398732	−	0.690624i	−0.594838	−	0.803846i	$-0.702784\pi$
$131$	597.844	−	1035.50i	0.398732	−	0.690624i	0.993570	+	0.113222i	$0.0361172\pi$
$132$		0			0
$133$	−486.548	−	590.778i	−0.317211	−	0.385165i
$134$			1969.79i			1.26988i
$135$		0			0
$136$			8870.86i			5.59316i
$137$	1175.08	−	678.431i	0.732800	−	0.423082i	−0.0866457	−	0.996239i	$-0.527615\pi$
$137$	1175.08	−	678.431i	0.732800	−	0.423082i	0.819446	+	0.573157i	$0.194281\pi$
$138$		0			0
$139$	−828.064	−	478.083i	−0.505291	−	0.291730i	0.225605	−	0.974219i	$-0.427564\pi$
$139$	−828.064	−	478.083i	−0.505291	−	0.291730i	−0.730896	+	0.682489i	$0.760898\pi$
$140$	2526.79	+	946.041i	1.52538	+	0.571108i
$141$		0			0
$142$	1528.10	+	2646.76i	0.903068	+	1.56416i
$143$	328.654			0.192192
$144$		0			0
$145$		−	912.582i		−	0.522660i
$146$	−1990.88	−	3448.31i	−1.12854	−	1.95469i
$147$		0			0
$148$	1570.22	−	2719.70i	0.872105	−	1.51053i
$149$	166.537	+	96.1501i	0.0915653	+	0.0528653i	0.545083	−	0.838382i	$-0.316498\pi$
$149$	166.537	+	96.1501i	0.0915653	+	0.0528653i	−0.453518	+	0.891247i	$0.649831\pi$
$150$		0			0
$151$	−307.926	−	533.343i	−0.165951	−	0.287436i	0.771041	−	0.636785i	$-0.219736\pi$
$151$	−307.926	−	533.343i	−0.165951	−	0.287436i	−0.936993	+	0.349349i	$0.886403\pi$
$152$	−2941.54			−1.56968
$153$		0			0
$154$	−207.714	−	1244.74i	−0.108689	−	0.651322i
$155$	−1066.68	+	615.849i	−0.552761	+	0.319137i
$156$		0			0
$157$	722.630	+	417.211i	0.367339	+	0.212083i	0.672295	−	0.740283i	$-0.265309\pi$
$157$	722.630	+	417.211i	0.367339	+	0.212083i	−0.304956	+	0.952366i	$0.598642\pi$
$158$	−4224.60	−	2439.07i	−2.12716	−	1.22812i
$159$		0			0
$160$	3528.63	−	2037.26i	1.74352	−	1.00662i
$161$	2060.66	−	343.871i	1.00871	−	0.168328i
$162$		0			0
$163$	−3304.12			−1.58772			−0.793860	−	0.608100i	$-0.791932\pi$
$163$	−3304.12			−1.58772			−0.793860	+	0.608100i	$0.791932\pi$
$164$	1982.59	+	3433.94i	0.943988	+	1.63504i
$165$		0			0
$166$	−3578.58	−	2066.09i	−1.67320	−	0.966024i
$167$	956.456	−	1656.63i	0.443190	−	0.767628i	−0.554734	−	0.832028i	$-0.687180\pi$
$167$	956.456	−	1656.63i	0.443190	−	0.767628i	0.997924	+	0.0643998i	$0.0205133\pi$
$168$		0			0
$169$	−759.101	−	1314.80i	−0.345517	−	0.598453i
$170$		−	4630.78i		−	2.08920i
$171$		0			0
$172$	4200.02			1.86191
$173$	313.536	+	543.061i	0.137790	+	0.238660i	0.926660	−	0.375901i	$-0.122667\pi$
$173$	313.536	+	543.061i	0.137790	+	0.238660i	−0.788870	+	0.614561i	$0.789333\pi$
$174$		0			0
$175$	1347.29	+	504.431i	0.581975	+	0.217894i
$176$	−2349.57	−	1356.53i	−1.00628	−	0.580977i
$177$		0			0
$178$	−1852.08	+	1069.30i	−0.779883	+	0.450266i
$179$		−	1174.10i		−	0.490259i	−0.969490	−	0.245130i	$-0.921169\pi$
$179$		−	1174.10i		−	0.490259i	0.969490	−	0.245130i	$-0.0788305\pi$
$180$		0			0
$181$		−	1625.05i		−	0.667344i	−0.942689	−	0.333672i	$-0.891712\pi$
$181$		−	1625.05i		−	0.667344i	0.942689	−	0.333672i	$-0.108288\pi$
$182$	2011.93	−	1656.97i	0.819417	−	0.674849i
$183$		0			0
$184$	4014.77	−	6953.79i	1.60855	−	2.78609i
$185$	−510.048	+	883.428i	−0.202700	+	0.351086i
$186$		0			0
$187$	−1361.44	+	786.027i	−0.532397	+	0.307380i
$188$	3902.65			1.51399
$189$		0			0
$190$	1535.55			0.586318
$191$	−113.173	+	65.3404i	−0.0428739	+	0.0247532i	−0.521284	−	0.853383i	$-0.674547\pi$
$191$	−113.173	+	65.3404i	−0.0428739	+	0.0247532i	0.478410	+	0.878137i	$0.341213\pi$
$192$		0			0
$193$	−570.103	+	987.447i	−0.212626	+	0.368280i	−0.952536	−	0.304427i	$-0.901535\pi$
$193$	−570.103	+	987.447i	−0.212626	+	0.368280i	0.739909	+	0.672707i	$0.234868\pi$
$194$	−760.240	+	1316.77i	−0.281351	+	0.487314i
$195$		0			0
$196$	−5477.84	−	4770.58i	−1.99630	−	1.73855i
$197$		−	3462.71i		−	1.25232i	−0.779693	−	0.626162i	$-0.784625\pi$
$197$		−	3462.71i		−	1.25232i	0.779693	−	0.626162i	$-0.215375\pi$
$198$		0			0
$199$		−	2522.77i		−	0.898667i	−0.893364	−	0.449333i	$-0.851662\pi$
$199$		−	2522.77i		−	0.898667i	0.893364	−	0.449333i	$-0.148338\pi$
$200$	4788.49	−	2764.63i	1.69299	−	0.977446i
$201$		0			0
$202$	5168.17	+	2983.84i	1.80015	+	1.03932i
$203$	−861.477	+	2300.93i	−0.297851	+	0.795534i
$204$		0			0
$205$	−643.994	−	1115.43i	−0.219407	−	0.380025i
$206$	8424.88			2.84946
$207$		0			0
$208$		−	5603.51i		−	1.86795i
$209$	−260.643	−	451.447i	−0.0862635	−	0.149413i
$210$		0			0
$211$	−1033.33	+	1789.77i	−0.337143	+	0.583948i	−0.983894	−	0.178753i	$-0.942794\pi$
$211$	−1033.33	+	1789.77i	−0.337143	+	0.583948i	0.646751	+	0.762701i	$0.276127\pi$
$212$	6586.92	+	3802.96i	2.13392	+	1.23202i
$213$		0			0
$214$	−2003.98	−	3470.99i	−0.640135	−	1.10875i
$215$	−1364.27			−0.432756
$216$		0			0
$217$	3270.83	−	545.817i	1.02322	−	0.170749i
$218$	−3248.65	+	1875.61i	−1.00930	+	0.582718i
$219$		0			0
$220$	1591.51	+	918.856i	0.487724	+	0.281588i
$221$	−2811.90	−	1623.45i	−0.855877	−	0.494141i
$222$		0			0
$223$	−5321.42	+	3072.32i	−1.59797	+	0.922591i	−0.606097	+	0.795390i	$0.707266\pi$
$223$	−5321.42	+	3072.32i	−1.59797	+	0.922591i	−0.991877	+	0.127201i	$0.959401\pi$
$224$	−10820.0	+	1805.59i	−3.22743	+	0.538575i
$225$		0			0
$226$	−8776.84			−2.58331
$227$	−455.878	−	789.603i	−0.133294	−	0.230871i	0.791651	−	0.610974i	$-0.209222\pi$
$227$	−455.878	−	789.603i	−0.133294	−	0.230871i	−0.924944	+	0.380103i	$0.875889\pi$
$228$		0			0
$229$	2305.74	+	1331.22i	0.665360	+	0.384146i	0.794316	−	0.607504i	$-0.207829\pi$
$229$	2305.74	+	1331.22i	0.665360	+	0.384146i	−0.128956	+	0.991650i	$0.541163\pi$
$230$	−2095.80	+	3630.02i	−0.600838	+	1.04068i
$231$		0			0
$232$	4721.49	+	8177.87i	1.33613	+	2.31424i
$233$			1984.29i			0.557918i	0.960303	+	0.278959i	$0.0899894\pi$
$233$			1984.29i			0.557918i	−0.960303	+	0.278959i	$0.910011\pi$
$234$		0			0
$235$	−1267.68			−0.351891
$236$	−3860.42	−	6686.45i	−1.06480	−	1.84428i
$237$		0			0
$238$	−4371.45	+	11675.8i	−1.19059	+	3.17995i
$239$	1544.98	+	891.996i	0.418145	+	0.241416i	0.694283	−	0.719702i	$-0.255722\pi$
$239$	1544.98	+	891.996i	0.418145	+	0.241416i	−0.276138	+	0.961118i	$0.589055\pi$
$240$		0			0
$241$	5182.09	−	2991.88i	1.38510	−	0.799685i	0.392338	−	0.919821i	$-0.371666\pi$
$241$	5182.09	−	2991.88i	1.38510	−	0.799685i	0.992757	+	0.120136i	$0.0383331\pi$
$242$			6330.05i			1.68145i
$243$		0			0
$244$			7357.99i			1.93052i
$245$	1779.34	+	1549.61i	0.463991	+	0.404084i
$246$		0			0
$247$	538.330	−	932.414i	0.138677	−	0.240195i
$248$	6372.53	−	11037.5i	1.63168	−	2.82615i
$249$		0			0
$250$	−6522.19	+	3765.59i	−1.65000	+	0.952627i
$251$	−6093.37			−1.53231			−0.766155	−	0.642656i	$-0.777833\pi$
$251$	−6093.37			−1.53231			−0.766155	+	0.642656i	$0.777833\pi$
$252$		0			0
$253$	1422.96			0.353599
$254$	−5145.02	+	2970.48i	−1.27097	+	0.733797i
$255$		0			0
$256$	−2861.40	+	4956.10i	−0.698585	+	1.20998i
$257$	2276.03	−	3942.19i	0.552431	−	0.956838i	−0.445668	−	0.895198i	$-0.647034\pi$
$257$	2276.03	−	3942.19i	0.552431	−	0.956838i	0.998098	−	0.0616394i	$-0.0196329\pi$
$258$		0			0
$259$	2119.96	−	1745.94i	0.508602	−	0.418870i
$260$			3795.59i			0.905355i
$261$		0			0
$262$		−	6458.68i		−	1.52297i
$263$	773.268	−	446.447i	0.181300	−	0.104673i	−0.406604	−	0.913605i	$-0.633287\pi$
$263$	773.268	−	446.447i	0.181300	−	0.104673i	0.587903	+	0.808931i	$0.299954\pi$
$264$		0			0
$265$	−2139.60	−	1235.30i	−0.495979	−	0.286353i
$266$	−3871.64	−	1449.56i	−0.892426	−	0.334128i
$267$		0			0
$268$	3861.39	+	6688.12i	0.880119	+	1.52441i
$269$	−1159.42			−0.262792			−0.131396	−	0.991330i	$-0.541946\pi$
$269$	−1159.42			−0.262792			−0.131396	+	0.991330i	$0.541946\pi$
$270$		0			0
$271$		−	2122.71i		−	0.475813i	−0.971288	−	0.237907i	$-0.923539\pi$
$271$		−	2122.71i		−	0.475813i	0.971288	−	0.237907i	$-0.0764612\pi$
$272$	13401.7	+	23212.4i	2.98748	+	5.17447i
$273$		0			0
$274$	3664.64	−	6347.35i	0.807989	−	1.39948i
$275$	848.594	+	489.936i	0.186080	+	0.107434i
$276$		0			0
$277$	1721.64	+	2981.97i	0.373442	+	0.646821i	0.990093	−	0.140416i	$-0.0448440\pi$
$277$	1721.64	+	2981.97i	0.373442	+	0.646821i	−0.616650	+	0.787237i	$0.711511\pi$
$278$	−5164.87			−1.11427
$279$		0			0
$280$	8944.97	−	1492.69i	1.90916	−	0.318590i
$281$	3015.50	−	1741.00i	0.640178	−	0.369607i	−0.144505	−	0.989504i	$-0.546159\pi$
$281$	3015.50	−	1741.00i	0.640178	−	0.369607i	0.784683	+	0.619897i	$0.212826\pi$
$282$		0			0
$283$	3071.99	+	1773.61i	0.645268	+	0.372546i	0.786641	−	0.617411i	$-0.211818\pi$
$283$	3071.99	+	1773.61i	0.645268	+	0.372546i	−0.141373	+	0.989956i	$0.545152\pi$
$284$	10376.9	+	5991.11i	2.16815	+	1.25178i
$285$		0			0
$286$	1537.43	−	887.635i	0.317867	−	0.183521i
$287$	570.762	+	3420.31i	0.117390	+	0.703465i
$288$		0			0
$289$	10617.9			2.16119
$290$	−2464.72	−	4269.02i	−0.499080	−	0.864433i
$291$		0			0
$292$	−13519.5	−	7805.48i	−2.70948	−	1.56432i
$293$	−1203.25	+	2084.09i	−0.239914	+	0.415542i	−0.960689	−	0.277626i	$-0.910452\pi$
$293$	−1203.25	+	2084.09i	−0.239914	+	0.415542i	0.720776	+	0.693168i	$0.243786\pi$
$294$		0			0
$295$	1253.96	+	2171.93i	0.247486	+	0.428659i
$296$		−	10555.5i		−	2.07272i
$297$		0			0
$298$	1038.74			0.201921
$299$	1469.48	+	2545.22i	0.284222	+	0.492286i
$300$		0			0
$301$	3439.79	+	1287.87i	0.658692	+	0.246617i
$302$	−2880.93	−	1663.30i	−0.548936	−	0.316929i
$303$		0			0
$304$	−7697.13	+	4443.94i	−1.45217	+	0.838412i
$305$		−	2390.06i		−	0.448703i
$306$		0			0
$307$			7862.81i			1.46174i	0.682517	+	0.730870i	$0.260886\pi$
$307$			7862.81i			1.46174i	−0.682517	+	0.730870i	$0.739114\pi$
$308$	−3145.33	−	3819.13i	−0.581888	−	0.706542i
$309$		0			0
$310$	−3326.60	+	5761.83i	−0.609477	+	1.05565i
$311$	1367.04	−	2367.77i	0.249252	−	0.431718i	−0.714066	−	0.700078i	$-0.753148\pi$
$311$	1367.04	−	2367.77i	0.249252	−	0.431718i	0.963319	+	0.268360i	$0.0864818\pi$
$312$		0			0
$313$	−3509.53	+	2026.23i	−0.633771	+	0.365908i	−0.782211	−	0.623014i	$-0.785908\pi$
$313$	−3509.53	+	2026.23i	−0.633771	+	0.365908i	0.148440	+	0.988921i	$0.452575\pi$
$314$	4507.25			0.810060
$315$		0			0
$316$	−19125.3			−3.40470
$317$	968.686	−	559.271i	0.171630	−	0.0990909i	−0.411724	−	0.911309i	$-0.635073\pi$
$317$	968.686	−	559.271i	0.171630	−	0.0990909i	0.583354	+	0.812218i	$0.301740\pi$
$318$		0			0
$319$	−836.721	+	1449.24i	−0.146857	+	0.254364i
$320$	5086.47	−	8810.03i	0.888570	−	1.53905i
$321$		0			0
$322$	8710.95	−	7174.09i	1.50759	−	1.24160i
$323$			5150.00i			0.887163i
$324$		0			0
$325$			2023.82i			0.345419i
$326$	−15456.5	+	8923.83i	−2.62594	+	1.51609i
$327$		0			0
$328$	11542.0	+	6663.76i	1.94298	+	1.12178i
$329$	3196.25	+	1196.69i	0.535608	+	0.200534i
$330$		0			0
$331$	3521.44	+	6099.32i	0.584761	+	1.01284i	0.994905	+	0.100815i	$0.0321452\pi$
$331$	3521.44	+	6099.32i	0.584761	+	1.01284i	−0.410144	+	0.912021i	$0.634521\pi$
$332$	−16200.7			−2.67810
$333$		0			0
$334$		−	10332.9i		−	1.69278i
$335$	−1254.28	−	2172.47i	−0.204562	−	0.354313i
$336$		0			0
$337$	1296.20	−	2245.08i	0.209520	−	0.362900i	−0.742043	−	0.670352i	$-0.766143\pi$
$337$	1296.20	−	2245.08i	0.209520	−	0.362900i	0.951564	+	0.307452i	$0.0994764\pi$
$338$	−7102.09	−	4100.39i	−1.14291	−	0.659858i
$339$		0			0
$340$	−9077.74	−	15723.1i	−1.44797	−	2.50796i
$341$	2258.62			0.358684
$342$		0			0
$343$	−3023.49	−	5586.78i	−0.475957	−	0.879468i
$344$	12225.6	−	7058.43i	1.91616	−	1.10629i
$345$		0			0
$346$	2933.42	+	1693.61i	0.455785	+	0.263148i
$347$	7226.45	+	4172.19i	1.11797	+	0.645462i	0.940882	−	0.338733i	$-0.109998\pi$
$347$	7226.45	+	4172.19i	1.11797	+	0.645462i	0.177090	+	0.984195i	$0.443332\pi$
$348$		0			0
$349$	−9981.26	+	5762.68i	−1.53090	+	0.883866i	−0.531581	+	0.847008i	$0.678402\pi$
$349$	−9981.26	+	5762.68i	−1.53090	+	0.883866i	−0.999320	+	0.0368588i	$0.988265\pi$
$350$	7664.95	−	1279.08i	1.17060	−	0.195343i
$351$		0			0
$352$	−7471.62			−1.13136
$353$	5107.82	+	8847.00i	0.770146	+	1.33393i	0.937482	+	0.348033i	$0.113150\pi$
$353$	5107.82	+	8847.00i	0.770146	+	1.33393i	−0.167336	+	0.985900i	$0.553516\pi$
$354$		0			0
$355$	−3370.68	−	1946.06i	−0.503935	−	0.290947i
$356$	−4192.30	+	7261.28i	−0.624134	+	1.08103i
$357$		0			0
$358$	−3171.04	−	5492.40i	−0.468141	−	0.810844i
$359$			6593.91i			0.969396i	0.874682	+	0.484698i	$0.161070\pi$
$359$			6593.91i			0.969396i	−0.874682	+	0.484698i	$0.838930\pi$
$360$		0			0
$361$	5151.28			0.751025
$362$	−4388.98	−	7601.93i	−0.637236	−	1.10373i
$363$		0			0
$364$	3583.03	−	9569.97i	0.515940	−	1.37803i
$365$	4391.47	+	2535.41i	0.629753	+	0.363588i
$366$		0			0
$367$	4531.96	−	2616.53i	0.644595	−	0.372157i	−0.141787	−	0.989897i	$-0.545285\pi$
$367$	4531.96	−	2616.53i	0.644595	−	0.372157i	0.786382	+	0.617740i	$0.211952\pi$
$368$		−	24261.3i		−	3.43670i
$369$		0			0
$370$			5510.19i			0.774219i
$371$	4228.53	+	5134.38i	0.591737	+	0.718501i
$372$		0			0
$373$	4889.02	−	8468.04i	0.678670	−	1.17549i	−0.296711	−	0.954967i	$-0.595890\pi$
$373$	4889.02	−	8468.04i	0.678670	−	1.17549i	0.975381	−	0.220524i	$-0.0707768\pi$
$374$	−4245.84	+	7354.00i	−0.587024	+	1.01676i
$375$		0			0
$376$	11360.0	−	6558.69i	1.55810	−	0.899571i
$377$	−3456.31			−0.472172
$378$		0			0
$379$	−3637.54			−0.493002			−0.246501	−	0.969143i	$-0.579281\pi$
$379$	−3637.54			−0.493002			−0.246501	+	0.969143i	$0.579281\pi$
$380$	5213.72	−	3010.14i	0.703837	−	0.406361i
$381$		0			0
$382$	−352.946	+	611.320i	−0.0472730	+	0.0818792i
$383$	4495.26	−	7786.02i	0.599731	−	1.03876i	−0.393129	−	0.919483i	$-0.628608\pi$
$383$	4495.26	−	7786.02i	0.599731	−	1.03876i	0.992860	−	0.119281i	$-0.0380591\pi$
$384$		0			0
$385$	1021.68	+	1240.55i	0.135246	+	0.164219i
$386$			6158.98i			0.812134i
$387$		0			0
$388$			5961.21i			0.779987i
$389$	4843.12	−	2796.17i	0.631249	−	0.364452i	−0.149987	−	0.988688i	$-0.547923\pi$
$389$	4843.12	−	2796.17i	0.631249	−	0.364452i	0.781236	+	0.624236i	$0.214590\pi$
$390$		0			0
$391$	−12174.6	−	7028.99i	−1.57466	−	0.909133i
$392$	−23962.4	−	4680.48i	−3.08746	−	0.603062i
$393$		0			0
$394$	−9352.16	−	16198.4i	−1.19583	−	2.07123i
$395$	6212.39			0.791339
$396$		0			0
$397$			11561.7i			1.46163i	0.682575	+	0.730815i	$0.260860\pi$
$397$			11561.7i			1.46163i	−0.682575	+	0.730815i	$0.739140\pi$
$398$	−6813.56	−	11801.4i	−0.858123	−	1.48631i
$399$		0			0
$400$	8353.35	−	14468.4i	1.04417	−	1.80855i
$401$	−3685.19	−	2127.65i	−0.458927	−	0.264962i	0.252666	−	0.967554i	$-0.418693\pi$
$401$	−3685.19	−	2127.65i	−0.458927	−	0.264962i	−0.711593	+	0.702592i	$0.752026\pi$
$402$		0			0
$403$	2332.46	+	4039.95i	0.288308	+	0.499365i
$404$	23397.0			2.88130
$405$		0			0
$406$	2184.44	+	13090.3i	0.267025	+	1.60015i
$407$	1619.98	−	935.298i	0.197296	−	0.113909i
$408$		0			0
$409$	−4853.21	−	2802.00i	−0.586738	−	0.338753i	0.177068	−	0.984199i	$-0.443339\pi$
$409$	−4853.21	−	2802.00i	−0.586738	−	0.338753i	−0.763807	+	0.645445i	$0.776672\pi$
$410$	−6025.16	−	3478.63i	−0.725759	−	0.419017i
$411$		0			0
$412$	28605.4	−	16515.3i	3.42060	−	1.97488i
$413$	−1111.37	−	6659.90i	−0.132413	−	0.793492i
$414$		0			0
$415$	5262.40			0.622460
$416$	−7715.90	−	13364.3i	−0.909382	−	1.57510i
$417$		0			0
$418$	−2438.56	−	1407.90i	−0.285344	−	0.164743i
$419$	−2039.72	+	3532.89i	−0.237820	+	0.411917i	−0.960089	−	0.279696i	$-0.909766\pi$
$419$	−2039.72	+	3532.89i	−0.237820	+	0.411917i	0.722268	+	0.691613i	$0.243100\pi$
$420$		0			0
$421$	8228.54	+	14252.3i	0.952576	+	1.64991i	0.739820	+	0.672805i	$0.234911\pi$
$421$	8228.54	+	14252.3i	0.952576	+	1.64991i	0.212756	+	0.977105i	$0.431756\pi$
$422$			11163.3i			1.28773i
$423$		0			0
$424$	25564.6			2.92813
$425$	−4840.27	−	8383.60i	−0.552441	−	0.956857i
$426$		0			0
$427$	−2256.22	+	6026.15i	−0.255705	+	0.682965i
$428$	−13608.4	−	7856.81i	−1.53688	−	0.887321i
$429$		0			0
$430$	−6382.01	+	3684.65i	−0.715739	+	0.413232i
$431$			354.675i			0.0396382i	0.999804	+	0.0198191i	$0.00630903\pi$
$431$			354.675i			0.0396382i	−0.999804	+	0.0198191i	$0.993691\pi$
$432$		0			0
$433$		−	3100.88i		−	0.344155i	−0.985083	−	0.172077i	$-0.944952\pi$
$433$		−	3100.88i		−	0.344155i	0.985083	−	0.172077i	$-0.0550479\pi$
$434$	13826.6	−	11387.2i	1.52926	−	1.25946i
$435$		0			0
$436$	−7353.55	+	12736.7i	−0.807732	+	1.39903i
$437$	2330.78	−	4037.04i	0.255141	−	0.441917i
$438$		0			0
$439$	13194.9	−	7618.07i	1.43453	−	0.828224i	0.437065	−	0.899430i	$-0.356018\pi$
$439$	13194.9	−	7618.07i	1.43453	−	0.828224i	0.997462	+	0.0712055i	$0.0226846\pi$
$440$	6176.82			0.669246
$441$		0			0
$442$	−17538.6			−1.88739
$443$	−9086.84	+	5246.29i	−0.974557	+	0.562661i	−0.900623	−	0.434602i	$-0.856889\pi$
$443$	−9086.84	+	5246.29i	−0.974557	+	0.562661i	−0.0739349	+	0.997263i	$0.523556\pi$
$444$		0			0
$445$	1361.77	−	2358.65i	0.145065	−	0.251260i
$446$	−16595.6	+	28744.4i	−1.76194	+	3.05176i
$447$		0			0
$448$	−21141.4	+	17411.4i	−2.22955	+	1.83619i
$449$		−	13387.2i		−	1.40708i	−0.710656	−	0.703540i	$-0.751602\pi$
$449$		−	13387.2i		−	1.40708i	0.710656	−	0.703540i	$-0.248398\pi$
$450$		0			0
$451$			2361.84i			0.246596i
$452$	−29800.5	+	17205.3i	−3.10110	+	1.79042i
$453$		0			0
$454$	−4265.16	−	2462.49i	−0.440911	−	0.254560i
$455$	−1163.86	+	3108.57i	−0.119918	+	0.320290i
$456$		0			0
$457$	−8043.99	−	13932.6i	−0.823374	−	1.42613i	−0.903156	−	0.429313i	$-0.858756\pi$
$457$	−8043.99	−	13932.6i	−0.823374	−	1.42613i	0.0797820	−	0.996812i	$-0.474578\pi$
$458$	14381.5			1.46726
$459$		0			0
$460$			16433.6i			1.66570i
$461$	−9398.54	−	16278.7i	−0.949530	−	1.64463i	−0.746416	−	0.665480i	$-0.768227\pi$
$461$	−9398.54	−	16278.7i	−0.949530	−	1.64463i	−0.203115	−	0.979155i	$-0.565106\pi$
$462$		0			0
$463$	−108.245	+	187.487i	−0.0108652	+	0.0188191i	−0.871407	−	0.490561i	$-0.836792\pi$
$463$	−108.245	+	187.487i	−0.0108652	+	0.0188191i	0.860542	+	0.509380i	$0.170125\pi$
$464$	24709.4	+	14266.0i	2.47221	+	1.42733i
$465$		0			0
$466$	5359.20	+	9282.42i	0.532748	+	0.922746i
$467$	−15356.4			−1.52165			−0.760826	−	0.648956i	$-0.775206\pi$
$467$	−15356.4			−1.52165			−0.760826	+	0.648956i	$0.775206\pi$
$468$		0			0
$469$	1111.65	+	6661.57i	0.109448	+	0.655869i
$470$	−5930.16	+	3423.78i	−0.581995	+	0.336015i
$471$		0			0
$472$	−22474.1	−	12975.4i	−2.19164	−	1.26535i
$473$	2166.56	+	1250.86i	0.210610	+	0.121596i
$474$		0			0
$475$	2779.97	−	1605.01i	0.268534	−	0.155038i
$476$	8045.46	+	48212.7i	0.774712	+	4.64249i
$477$		0			0
$478$	9636.49			0.922098
$479$	8696.60	+	15063.0i	0.829557	+	1.43683i	0.898386	+	0.439206i	$0.144740\pi$
$479$	8696.60	+	15063.0i	0.829557	+	1.43683i	−0.0688295	+	0.997628i	$0.521926\pi$
$480$		0			0
$481$	3345.89	+	1931.75i	0.317172	+	0.183119i
$482$	16161.1	−	27991.8i	1.52721	−	2.64521i
$483$		0			0
$484$	12408.8	+	21492.7i	1.16537	+	2.01848i
$485$		−	1936.35i		−	0.181289i
$486$		0			0
$487$	−14133.8			−1.31512			−0.657560	−	0.753402i	$-0.728412\pi$
$487$	−14133.8			−1.31512			−0.657560	+	0.753402i	$0.728412\pi$
$488$	12365.6	+	21417.9i	1.14706	+	1.98677i
$489$		0			0
$490$	12508.9	+	2443.31i	1.15325	+	0.225260i
$491$	7929.45	+	4578.07i	0.728821	+	0.420785i	0.817991	−	0.575232i	$-0.195088\pi$
$491$	7929.45	+	4578.07i	0.728821	+	0.420785i	−0.0891699	+	0.996016i	$0.528421\pi$
$492$		0			0
$493$	14317.7	−	8266.30i	1.30798	−	0.755163i
$494$		−	5815.73i		−	0.529680i
$495$		0			0
$496$		−	38509.2i		−	3.48612i
$497$	6661.54	+	8088.60i	0.601229	+	0.730027i
$498$		0			0
$499$	−7528.00	+	13038.9i	−0.675349	+	1.16974i	0.301017	+	0.953619i	$0.402674\pi$
$499$	−7528.00	+	13038.9i	−0.675349	+	1.16974i	−0.976367	+	0.216121i	$0.930659\pi$
$500$	−14763.4	+	25571.0i	−1.32048	+	2.28714i
$501$		0			0
$502$	−28504.5	+	16457.1i	−2.53430	+	1.46318i
$503$	−13644.2			−1.20948			−0.604739	−	0.796424i	$-0.706722\pi$
$503$	−13644.2			−1.20948			−0.604739	+	0.796424i	$0.706722\pi$
$504$		0			0
$505$	−7599.93			−0.669688
$506$	6656.54	−	3843.16i	0.584821	−	0.337647i
$507$		0			0
$508$	−11646.1	+	20171.6i	−1.01715	+	1.76175i
$509$	442.839	−	767.020i	0.0385629	−	0.0667929i	−0.846100	−	0.533025i	$-0.821055\pi$
$509$	442.839	−	767.020i	0.0385629	−	0.0667929i	0.884663	+	0.466232i	$0.154389\pi$
$510$		0			0
$511$	−8678.95	−	10538.2i	−0.751339	−	0.912293i
$512$			4915.40i			0.424281i
$513$		0			0
$514$		−	24588.6i		−	2.11003i
$515$	−9291.75	+	5364.60i	−0.795036	+	0.459014i
$516$		0			0
$517$	2013.17	+	1162.30i	0.171255	+	0.0988742i
$518$	5201.62	−	13893.1i	0.441208	−	1.17843i
$519$		0			0
$520$	6378.76	+	11048.3i	0.537937	+	0.931734i
$521$	8268.31			0.695281			0.347641	−	0.937628i	$-0.386983\pi$
$521$	8268.31			0.695281			0.347641	+	0.937628i	$0.386983\pi$
$522$		0			0
$523$		−	1489.91i		−	0.124568i	−0.998058	−	0.0622841i	$-0.980162\pi$
$523$		−	1489.91i		−	0.124568i	0.998058	−	0.0622841i	$-0.0198385\pi$
$524$	−12661.0	−	21929.5i	−1.05553	−	1.82823i
$525$		0			0
$526$	2411.55	−	4176.92i	0.199902	−	0.346240i
$527$	−19324.3	−	11156.9i	−1.59731	−	0.922206i
$528$		0			0
$529$	278.849	+	482.981i	0.0229185	+	0.0396960i
$530$	−13345.3			−1.09374
$531$		0			0
$532$	−15987.1	+	2667.84i	−1.30288	+	0.217417i
$533$	−4224.58	+	2439.06i	−0.343315	+	0.198213i
$534$		0			0
$535$	4420.35	+	2552.09i	0.357212	+	0.206236i
$536$	22479.7	+	12978.7i	1.81152	+	1.04588i
$537$		0			0
$538$	−5423.72	+	3131.39i	−0.434634	+	0.250936i
$539$	−1404.93	−	4092.31i	−0.112272	−	0.327028i
$540$		0			0
$541$	668.496			0.0531255			0.0265628	−	0.999647i	$-0.491544\pi$
$541$	668.496			0.0531255			0.0265628	+	0.999647i	$0.491544\pi$
$542$	−5733.06	−	9929.95i	−0.454347	−	0.786952i
$543$		0			0
$544$	63925.7	+	36907.5i	5.03822	+	2.90882i
$545$	2388.62	−	4137.20i	0.187738	−	0.325171i
$546$		0			0
$547$	−10234.9	−	17727.3i	−0.800022	−	1.38568i	−0.919601	−	0.392855i	$-0.871488\pi$
$547$	−10234.9	−	17727.3i	−0.800022	−	1.38568i	0.119578	−	0.992825i	$-0.461846\pi$
$548$		−	28735.3i		−	2.23998i
$549$		0			0
$550$	5292.92			0.410347
$551$	2741.07	+	4747.68i	0.211930	+	0.367074i
$552$		0			0
$553$	−15663.5	−	5864.49i	−1.20449	−	0.450965i
$554$	16107.6	+	9299.70i	1.23528	+	0.713189i
$555$		0			0
$556$	−17536.5	+	10124.7i	−1.33762	+	0.772273i
$557$		−	18144.3i		−	1.38025i	−0.723692	−	0.690123i	$-0.757556\pi$
$557$		−	18144.3i		−	1.38025i	0.723692	−	0.690123i	$-0.242444\pi$
$558$		0			0
$559$			5167.04i			0.390952i
$560$	21151.2	−	17419.5i	1.59607	−	1.31448i
$561$		0			0
$562$	9404.27	−	16288.7i	0.705864	−	1.22259i
$563$	2055.50	−	3560.22i	0.153870	−	0.266511i	−0.778777	−	0.627301i	$-0.784160\pi$
$563$	2055.50	−	3560.22i	0.153870	−	0.266511i	0.932647	+	0.360790i	$0.117493\pi$
$564$		0			0
$565$	9679.93	−	5588.71i	0.720775	−	0.416140i
$566$	19160.9			1.42295
$567$		0			0
$568$	40274.0			2.97510
$569$	16501.7	−	9527.28i	1.21580	−	0.701941i	0.251781	−	0.967784i	$-0.418984\pi$
$569$	16501.7	−	9527.28i	1.21580	−	0.701941i	0.964016	+	0.265843i	$0.0856504\pi$
$570$		0			0
$571$	4482.05	−	7763.14i	0.328491	−	0.568962i	−0.653722	−	0.756735i	$-0.726793\pi$
$571$	4482.05	−	7763.14i	0.328491	−	0.568962i	0.982213	+	0.187772i	$0.0601268\pi$
$572$	3480.07	−	6027.66i	0.254387	−	0.440611i
$573$		0			0
$574$	11907.6	+	14458.5i	0.865881	+	1.05137i
$575$			8762.43i			0.635511i
$576$		0			0
$577$			13608.3i			0.981840i	0.871205	+	0.490920i	$0.163339\pi$
$577$			13608.3i			0.981840i	−0.871205	+	0.490920i	$0.836661\pi$
$578$	49670.3	−	28677.2i	3.57442	−	2.06369i
$579$		0			0
$580$	−16737.2	−	9663.21i	−1.19823	−	0.691798i
$581$	−13268.3	−	4967.70i	−0.947438	−	0.354725i
$582$		0			0
$583$	2265.22	+	3923.48i	0.160919	+	0.278720i
$584$	−52470.7			−3.71790
$585$		0			0
$586$			12999.1i			0.916359i
$587$	4471.37	+	7744.64i	0.314401	+	0.544558i	0.979310	−	0.202366i	$-0.0648631\pi$
$587$	4471.37	+	7744.64i	0.314401	+	0.544558i	−0.664909	+	0.746924i	$0.731530\pi$
$588$		0			0
$589$	3699.59	−	6407.87i	0.258809	−	0.448271i
$590$	11732.0	+	6773.45i	0.818640	+	0.472642i
$591$		0			0
$592$	−15946.7	−	27620.5i	−1.10710	−	1.91756i
$593$	19338.8			1.33921			0.669604	−	0.742719i	$-0.266464\pi$
$593$	19338.8			1.33921			0.669604	+	0.742719i	$0.266464\pi$
$594$		0			0
$595$	−2613.37	−	15660.7i	−0.180063	−	1.07903i
$596$	3526.88	−	2036.24i	0.242393	−	0.139946i
$597$		0			0
$598$	13748.3	+	7937.61i	0.940153	+	0.542798i
$599$	−7181.37	−	4146.16i	−0.489854	−	0.282817i	0.234660	−	0.972078i	$-0.424602\pi$
$599$	−7181.37	−	4146.16i	−0.489854	−	0.282817i	−0.724514	+	0.689260i	$0.757936\pi$
$600$		0			0
$601$	−16063.4	+	9274.20i	−1.09025	+	0.629455i	−0.933643	−	0.358206i	$-0.883389\pi$
$601$	−16063.4	+	9274.20i	−1.09025	+	0.629455i	−0.156606	+	0.987661i	$0.550055\pi$
$602$	19569.5	−	3265.65i	1.32491	−	0.221093i
$603$		0			0
$604$	−13042.3			−0.878618
$605$	−4030.70	−	6981.38i	−0.270862	−	0.469146i
$606$		0			0
$607$	4155.60	+	2399.24i	0.277876	+	0.160432i	0.632461	−	0.774592i	$-0.282045\pi$
$607$	4155.60	+	2399.24i	0.277876	+	0.160432i	−0.354586	+	0.935024i	$0.615378\pi$
$608$	−12238.4	+	21197.5i	−0.816336	+	1.41394i
$609$		0			0
$610$	−6455.12	−	11180.6i	−0.428460	−	0.742114i
$611$			4801.21i			0.317899i
$612$		0			0
$613$	−19326.3			−1.27338			−0.636690	−	0.771120i	$-0.719697\pi$
$613$	−19326.3			−1.27338			−0.636690	+	0.771120i	$0.719697\pi$
$614$	21236.0	+	36781.9i	1.39579	+	2.41758i
$615$		0			0
$616$	−15573.9	−	5830.91i	−1.01865	−	0.381387i
$617$	−18359.9	−	10600.1i	−1.19796	−	0.691642i	−0.237859	−	0.971300i	$-0.576446\pi$
$617$	−18359.9	−	10600.1i	−1.19796	−	0.691642i	−0.960100	+	0.279658i	$0.909779\pi$
$618$		0			0
$619$	3393.65	−	1959.33i	0.220359	−	0.127224i	−0.385757	−	0.922600i	$-0.626060\pi$
$619$	3393.65	−	1959.33i	0.220359	−	0.127224i	0.606117	+	0.795376i	$0.292726\pi$
$620$			26084.6i			1.68965i
$621$		0			0
$622$		−	14768.5i		−	0.952029i
$623$	−5660.04	+	4661.44i	−0.363988	+	0.299770i
$624$		0			0
$625$	−59.3801	+	102.849i	−0.00380033	+	0.00658236i
$626$	−10945.0	+	18957.2i	−0.698799	+	1.21036i
$627$		0			0
$628$	15303.7	−	8835.58i	0.972426	−	0.561430i
$629$	−18480.4			−1.17148
$630$		0			0
$631$	−5823.13			−0.367378			−0.183689	−	0.982984i	$-0.558804\pi$
$631$	−5823.13			−0.367378			−0.183689	+	0.982984i	$0.558804\pi$
$632$	−55670.7	+	32141.5i	−3.50390	+	2.02297i
$633$		0			0
$634$	3020.98	−	5232.50i	0.189241	−	0.327774i
$635$	3782.94	−	6552.25i	0.236412	−	0.409477i
$636$		0			0
$637$	5868.97	−	6739.07i	0.365050	−	0.419170i
$638$			9039.34i			0.560926i
$639$		0			0
$640$		−	22354.5i		−	1.38069i
$641$	−18914.5	+	10920.3i	−1.16549	+	0.672894i	−0.952613	−	0.304186i	$-0.901616\pi$
$641$	−18914.5	+	10920.3i	−1.16549	+	0.672894i	−0.212874	+	0.977080i	$0.568282\pi$
$642$		0			0
$643$	−21222.1	−	12252.6i	−1.30158	−	0.751470i	−0.320909	−	0.947110i	$-0.603988\pi$
$643$	−21222.1	−	12252.6i	−1.30158	−	0.751470i	−0.980676	+	0.195640i	$0.937322\pi$
$644$	15513.3	−	41434.7i	0.949240	−	2.53533i
$645$		0			0
$646$	13909.2	+	24091.5i	0.847138	+	1.46729i
$647$	−1181.15			−0.0717709			−0.0358855	−	0.999356i	$-0.511425\pi$
$647$	−1181.15			−0.0717709			−0.0358855	+	0.999356i	$0.511425\pi$
$648$		0			0
$649$		−	4598.89i		−	0.278155i
$650$	5465.96	+	9467.33i	0.329835	+	0.571291i
$651$		0			0
$652$	−34986.9	+	60599.0i	−2.10152	+	3.63994i
$653$	19828.3	+	11447.9i	1.18827	+	0.686050i	0.957914	−	0.287056i	$-0.0926764\pi$
$653$	19828.3	+	11447.9i	1.18827	+	0.686050i	0.230360	+	0.973106i	$0.426010\pi$
$654$		0			0
$655$	4112.60	+	7123.24i	0.245332	+	0.424928i
$656$	40269.1			2.39672
$657$		0			0
$658$	18184.0	−	3034.44i	1.07733	−	0.179779i
$659$	27.2112	−	15.7104i	0.00160849	−	0.000928663i	−0.499196	−	0.866489i	$-0.666371\pi$
$659$	27.2112	−	15.7104i	0.00160849	−	0.000928663i	0.500804	+	0.865561i	$0.333038\pi$
$660$		0			0
$661$	9789.93	+	5652.22i	0.576073	+	0.332596i	0.759571	−	0.650424i	$-0.225409\pi$
$661$	9789.93	+	5652.22i	0.576073	+	0.332596i	−0.183498	+	0.983020i	$0.558742\pi$
$662$	32946.3	+	19021.6i	1.93428	+	1.11676i
$663$		0			0
$664$	−47157.6	+	27226.5i	−2.75613	+	1.59125i
$665$	5193.02	−	866.582i	0.302822	−	0.0505333i
$666$		0			0
$667$	−14964.6			−0.868715
$668$	−20255.6	−	35083.7i	−1.17322	−	2.03208i
$669$		0			0
$670$	−11734.9	−	6775.15i	−0.676655	−	0.390667i
$671$	−2191.38	+	3795.58i	−0.126076	+	0.218371i
$672$		0			0
$673$	4328.66	+	7497.46i	0.247931	+	0.429429i	0.962952	−	0.269674i	$-0.0869161\pi$
$673$	4328.66	+	7497.46i	0.247931	+	0.429429i	−0.715021	+	0.699103i	$0.753583\pi$
$674$		−	14003.2i		−	0.800271i
$675$		0			0
$676$	−32152.1			−1.82932
$677$	−10348.5	−	17924.2i	−0.587483	−	1.01755i	−0.994561	−	0.104156i	$-0.966786\pi$
$677$	−10348.5	−	17924.2i	−0.587483	−	1.01755i	0.407078	−	0.913393i	$-0.366548\pi$
$678$		0			0
$679$	−1827.92	+	4882.20i	−0.103312	+	0.275938i
$680$	−52847.7	−	30511.6i	−2.98032	−	1.72069i
$681$		0			0
$682$	10565.7	−	6100.13i	0.593230	−	0.342502i
$683$			20058.0i			1.12372i	0.827233	+	0.561859i	$0.189914\pi$
$683$			20058.0i			1.12372i	−0.827233	+	0.561859i	$0.810086\pi$
$684$		0			0
$685$			9333.94i			0.520630i
$686$	−29232.7	−	17968.8i	−1.62698	−	1.00008i
$687$		0			0
$688$	21327.1	−	36939.6i	1.18181	−	2.04696i
$689$	−4678.56	+	8103.50i	−0.258692	+	0.448068i
$690$		0			0
$691$	−4672.42	+	2697.62i	−0.257232	+	0.148513i	−0.623071	−	0.782165i	$-0.714115\pi$
$691$	−4672.42	+	2697.62i	−0.257232	+	0.148513i	0.365839	+	0.930678i	$0.380782\pi$
$692$	13280.0			0.729522
$693$		0			0
$694$	45073.4			2.46537
$695$	5696.30	−	3288.76i	0.310897	−	0.179496i
$696$		0			0
$697$	11666.8	−	20207.5i	0.634019	−	1.09815i
$698$	−31128.0	+	53915.2i	−1.68798	+	2.92367i
$699$		0			0
$700$	23517.8	−	19368.6i	1.26984	−	1.04581i
$701$			18702.4i			1.00767i	0.863799	+	0.503837i	$0.168079\pi$
$701$			18702.4i			1.00767i	−0.863799	+	0.503837i	$0.831921\pi$
$702$		0			0
$703$		−	6128.01i		−	0.328766i
$704$	−16155.4	+	9327.30i	−0.864883	+	0.499340i
$705$		0			0
$706$	47788.3	+	27590.6i	2.54750	+	1.47080i
$707$	19162.0	+	7174.33i	1.01932	+	0.381639i
$708$		0			0
$709$	−9346.71	−	16189.0i	−0.495096	−	0.857531i	0.504888	−	0.863185i	$-0.331534\pi$
$709$	−9346.71	−	16189.0i	−0.495096	−	0.857531i	−0.999984	+	0.00565368i	$0.998200\pi$
$710$	−21023.9			−1.11128
$711$		0			0
$712$			28181.9i			1.48337i
$713$	10098.8	+	17491.6i	0.530438	+	0.918745i
$714$		0			0
$715$	−1130.41	+	1957.94i	−0.0591260	+	0.102409i
$716$	−21533.6	−	12432.4i	−1.12395	−	0.648912i
$717$		0			0
$718$	17809.0	+	30846.0i	0.925661	+	1.60329i
$719$	18386.7			0.953697			0.476848	−	0.878986i	$-0.341779\pi$
$719$	18386.7			0.953697			0.476848	+	0.878986i	$0.341779\pi$
$720$		0			0
$721$	28491.8	−	4754.56i	1.47169	−	0.245588i
$722$	24097.5	−	13912.7i	1.24213	−	0.717142i
$723$		0			0
$724$	−29804.2	−	17207.5i	−1.52992	−	0.883302i
$725$	−8924.29	−	5152.44i	−0.457159	−	0.263941i
$726$		0			0
$727$	−1268.25	+	732.227i	−0.0647000	+	0.0373546i	−0.532001	−	0.846744i	$-0.678560\pi$
$727$	−1268.25	+	732.227i	−0.0647000	+	0.0373546i	0.467301	+	0.884098i	$0.345226\pi$
$728$	−5653.40	−	33878.2i	−0.287814	−	1.72474i
$729$		0			0
$730$	27390.8			1.38874
$731$	−12357.8	−	21404.3i	−0.625265	−	1.08299i
$732$		0			0
$733$	5272.89	+	3044.31i	0.265701	+	0.153402i	0.626932	−	0.779074i	$-0.284310\pi$
$733$	5272.89	+	3044.31i	0.265701	+	0.153402i	−0.361231	+	0.932476i	$0.617644\pi$
$734$	14133.5	−	24480.0i	0.710734	−	1.23103i
$735$		0			0
$736$	−33407.2	−	57863.0i	−1.67311	−	2.89790i
$737$			4600.05i			0.229912i
$738$		0			0
$739$	239.229			0.0119082			0.00595412	−	0.999982i	$-0.498105\pi$
$739$	239.229			0.0119082			0.00595412	+	0.999982i	$0.498105\pi$
$740$	10801.7	+	18709.0i	0.536590	+	0.929402i
$741$		0			0
$742$	33647.9	+	12597.9i	1.66476	+	0.623294i
$743$	−5720.45	−	3302.70i	−0.282454	−	0.163075i	0.352080	−	0.935970i	$-0.385474\pi$
$743$	−5720.45	−	3302.70i	−0.282454	−	0.163075i	−0.634534	+	0.772895i	$0.718808\pi$
$744$		0			0
$745$	−1145.62	+	661.423i	−0.0563385	+	0.0325271i
$746$		−	52817.5i		−	2.59221i
$747$		0			0
$748$			33292.5i			1.62740i
$749$	−8736.03	−	10607.5i	−0.426178	−	0.517476i
$750$		0			0
$751$	−16064.2	+	27824.1i	−0.780549	+	1.35195i	0.151073	+	0.988523i	$0.451727\pi$
$751$	−16064.2	+	27824.1i	−0.780549	+	1.35195i	−0.931622	+	0.363428i	$0.881606\pi$
$752$	19817.1	−	34324.2i	0.960978	−	1.66446i
$753$		0			0
$754$	−16168.5	+	9334.87i	−0.780930	+	0.450870i
$755$	4236.48			0.204214
$756$		0			0
$757$	37994.5			1.82422			0.912109	−	0.409948i	$-0.134453\pi$
$757$	37994.5			1.82422			0.912109	+	0.409948i	$0.134453\pi$
$758$	−17016.3	+	9824.34i	−0.815380	+	0.470760i
$759$		0			0
$760$	10117.5	−	17524.1i	0.482896	−	0.836401i
$761$	−2352.30	+	4074.31i	−0.112051	+	0.194078i	−0.916597	−	0.399812i	$-0.869075\pi$
$761$	−2352.30	+	4074.31i	−0.112051	+	0.194078i	0.804546	+	0.593890i	$0.202409\pi$
$762$		0			0
$763$	−9928.03	+	8176.45i	−0.471060	+	0.387952i
$764$			2767.53i			0.131054i
$765$		0			0
$766$		−	48563.6i		−	2.29070i
$767$	8225.95	−	4749.25i	0.387251	−	0.223580i
$768$		0			0
$769$	−9940.18	−	5738.97i	−0.466128	−	0.269119i	0.248490	−	0.968635i	$-0.420066\pi$
$769$	−9940.18	−	5738.97i	−0.466128	−	0.269119i	−0.714617	+	0.699516i	$0.753399\pi$
$770$	8129.88	+	3043.86i	0.380494	+	0.142459i
$771$		0			0
$772$	12073.5	+	20911.9i	0.562868	+	0.974916i
$773$	22568.8			1.05012			0.525059	−	0.851066i	$-0.324043\pi$
$773$	22568.8			1.05012			0.525059	+	0.851066i	$0.324043\pi$
$774$		0			0
$775$			13908.4i			0.644649i
$776$	10018.3	+	17352.1i	0.463446	+	0.802713i
$777$		0			0
$778$	15103.9	−	26160.8i	0.696018	−	1.20554i
$779$	6700.72	+	3868.66i	0.308188	+	0.177932i
$780$		0			0
$781$	3568.58	+	6180.97i	0.163501	+	0.283191i
$782$	−75936.1			−3.47247
$783$		0			0
$784$	−69773.4	+	23953.8i	−3.17845	+	1.09119i
$785$	−4971.02	+	2870.02i	−0.226017	+	0.130491i
$786$		0			0
$787$	−1440.47	−	831.659i	−0.0652445	−	0.0376689i	0.467023	−	0.884245i	$-0.345327\pi$
$787$	−1440.47	−	831.659i	−0.0652445	−	0.0376689i	−0.532267	+	0.846576i	$0.678660\pi$
$788$	−63507.7	−	36666.2i	−2.87103	−	1.65759i
$789$		0			0
$790$	29061.3	−	16778.5i	1.30880	−	0.755638i
$791$	−29682.1	+	4953.19i	−1.33423	+	0.222649i
$792$		0			0
$793$	−9052.11			−0.405359
$794$	31226.2	+	54085.4i	1.39569	+	2.41740i
$795$		0			0
$796$	−46268.8	−	26713.3i	−2.06025	−	1.18948i
$797$	−5493.37	+	9514.80i	−0.244147	+	0.422875i	−0.961891	−	0.273432i	$-0.911841\pi$
$797$	−5493.37	+	9514.80i	−0.244147	+	0.422875i	0.717744	+	0.696307i	$0.245175\pi$
$798$		0			0
$799$	−11482.8	−	19888.9i	−0.508428	−	0.880622i
$800$		−	46009.4i		−	2.03335i
$801$		0			0
$802$	−22985.6			−1.01203
$803$	−4649.31	−	8052.84i	−0.204322	−	0.353896i
$804$		0			0
$805$	−5039.11	+	13459.0i	−0.220628	+	0.589278i
$806$	21822.3	+	12599.1i	0.953672	+	0.550603i
$807$		0			0
$808$	68104.8	−	39320.3i	2.96525	−	1.71199i
$809$			29805.7i			1.29532i	0.761930	+	0.647659i	$0.224252\pi$
$809$			29805.7i			1.29532i	−0.761930	+	0.647659i	$0.775748\pi$
$810$		0			0
$811$			12409.9i			0.537323i	0.963235	+	0.268662i	$0.0865813\pi$
$811$			12409.9i			0.537323i	−0.963235	+	0.268662i	$0.913419\pi$
$812$	33078.0	+	40164.1i	1.42957	+	1.73582i
$813$		0			0
$814$	5052.14	−	8750.57i	0.217540	−	0.376790i
$815$	11364.6	−	19684.1i	0.488448	−	0.846017i
$816$		0			0
$817$	7097.58	−	4097.79i	0.303932	−	0.175476i
$818$	−30270.8			−1.29388
$819$		0			0
$820$	−27276.7			−1.16164
$821$	3158.37	−	1823.49i	0.134261	−	0.0775154i	−0.431365	−	0.902177i	$-0.641968\pi$
$821$	3158.37	−	1823.49i	0.134261	−	0.0775154i	0.565626	+	0.824662i	$0.308635\pi$
$822$		0			0
$823$	20305.8	−	35170.6i	0.860042	−	1.48964i	−0.0118459	−	0.999930i	$-0.503771\pi$
$823$	20305.8	−	35170.6i	0.860042	−	1.48964i	0.871888	−	0.489706i	$-0.162896\pi$
$824$	55510.5	−	96146.9i	2.34684	−	4.06485i
$825$		0			0
$826$	−23186.1	−	28153.2i	−0.976693	−	1.18592i
$827$			15836.6i			0.665891i	0.942946	+	0.332945i	$0.108042\pi$
$827$			15836.6i			0.665891i	−0.942946	+	0.332945i	$0.891958\pi$
$828$		0			0
$829$		−	8427.35i		−	0.353069i	−0.984294	−	0.176534i	$-0.943511\pi$
$829$		−	8427.35i		−	0.353069i	0.984294	−	0.176534i	$-0.0564886\pi$
$830$	24617.3	−	14212.8i	1.02949	−	0.594377i
$831$		0			0
$832$	−33367.1	−	19264.5i	−1.39038	−	0.802735i
$833$	−8194.50	+	41952.9i	−0.340844	+	1.74500i
$834$		0			0
$835$	6579.52	+	11396.1i	0.272687	+	0.472308i
$836$	−11039.7			−0.456717
$837$		0			0
$838$			22035.6i			0.908363i
$839$	1249.78	+	2164.69i	0.0514270	+	0.0890742i	0.890593	−	0.454801i	$-0.150290\pi$
$839$	1249.78	+	2164.69i	0.0514270	+	0.0890742i	−0.839166	+	0.543875i	$0.816956\pi$
$840$		0			0
$841$	−3395.06	+	5880.42i	−0.139205	+	0.241110i
$842$	76985.6	+	44447.6i	3.15095	+	1.81920i
$843$		0			0
$844$	21883.5	+	37903.4i	0.892491	+	1.54584i
$845$	10443.8			0.425181
$846$		0			0
$847$	3572.35	+	21407.4i	0.144920	+	0.868439i
$848$	66894.8	−	38621.7i	2.70894	−	1.56400i
$849$		0			0
$850$	−45285.2	−	26145.4i	−1.82738	−	1.05504i
$851$	14486.6	+	8363.83i	0.583541	+	0.336908i
$852$		0			0
$853$	14523.6	−	8385.18i	0.582974	−	0.336580i	−0.179340	−	0.983787i	$-0.557396\pi$
$853$	14523.6	−	8385.18i	0.582974	−	0.336580i	0.762314	+	0.647207i	$0.224063\pi$
$854$	5721.07	+	34283.7i	0.229240	+	1.37373i
$855$		0			0
$856$	−52815.8			−2.10889
$857$	5953.98	+	10312.6i	0.237321	+	0.411052i	0.959945	−	0.280190i	$-0.0903974\pi$
$857$	5953.98	+	10312.6i	0.237321	+	0.411052i	−0.722624	+	0.691242i	$0.757064\pi$
$858$		0			0
$859$	40304.1	+	23269.6i	1.60088	+	0.924270i	0.991311	+	0.131538i	$0.0419915\pi$
$859$	40304.1	+	23269.6i	1.60088	+	0.924270i	0.609571	+	0.792732i	$0.291342\pi$
$860$	−14446.1	+	25021.4i	−0.572800	+	0.992118i
$861$		0			0
$862$	957.913	+	1659.15i	0.0378499	+	0.0655580i
$863$		−	33359.8i		−	1.31585i	−0.753083	−	0.657926i	$-0.771434\pi$
$863$		−	33359.8i		−	1.31585i	0.753083	−	0.657926i	$-0.228566\pi$
$864$		0			0
$865$	−4313.67			−0.169560
$866$	−8374.93	−	14505.8i	−0.328628	−	0.569200i
$867$		0			0
$868$	24623.8	−	65768.1i	0.962889	−	2.57179i
$869$	−9865.71	−	5695.97i	−0.385122	−	0.222350i
$870$		0			0
$871$	−8228.01	+	4750.44i	−0.320087	+	0.184802i
$872$			49432.7i			1.91973i
$873$		0			0
$874$		−	25180.1i		−	0.974520i
$875$	−19932.1	+	16415.5i	−0.770089	+	0.634223i
$876$		0			0
$877$	−2221.72	+	3848.13i	−0.0855441	+	0.148167i	−0.905623	−	0.424084i	$-0.860596\pi$
$877$	−2221.72	+	3848.13i	−0.0855441	+	0.148167i	0.820079	+	0.572251i	$0.193930\pi$
$878$	41150.1	−	71274.0i	1.58172	−	2.73961i
$879$		0			0
$880$	16162.9	−	9331.63i	0.619147	−	0.357465i
$881$	31877.6			1.21905			0.609525	−	0.792767i	$-0.291360\pi$
$881$	31877.6			1.21905			0.609525	+	0.792767i	$0.291360\pi$
$882$		0			0
$883$	7852.54			0.299274			0.149637	−	0.988741i	$-0.452190\pi$
$883$	7852.54			0.299274			0.149637	+	0.988741i	$0.452190\pi$
$884$	−59549.7	+	34381.0i	−2.26569	+	1.30810i
$885$		0			0
$886$	−28338.6	+	49083.9i	−1.07455	+	1.86118i
$887$	6816.09	−	11805.8i	0.258018	−	0.446900i	−0.707693	−	0.706520i	$-0.750264\pi$
$887$	6816.09	−	11805.8i	0.258018	−	0.446900i	0.965711	+	0.259620i	$0.0835973\pi$
$888$		0			0
$889$	−15723.4	+	12949.3i	−0.593190	+	0.488535i
$890$		−	14711.5i		−	0.554081i
$891$		0			0
$892$			130130.i			4.88460i
$893$	6595.07	−	3807.66i	0.247139	−	0.142686i
$894$		0			0
$895$	6994.64	+	4038.36i	0.261235	+	0.150824i
$896$	−21102.7	+	56363.3i	−0.786819	+	2.10152i
$897$		0			0
$898$	−36156.3	−	62624.6i	−1.34360	−	2.32718i
$899$	−23752.9			−0.881207
$900$		0			0
$901$		−	44758.0i		−	1.65495i
$902$	6378.91	+	11048.6i	0.235471	+	0.407847i
$903$		0			0
$904$	−57829.5	+	100164.i	−2.12763	+	3.68517i
$905$	9681.16	+	5589.42i	0.355594	+	0.205302i
$906$		0			0
$907$	12109.3	+	20974.0i	0.443312	+	0.767840i	0.997933	−	0.0642638i	$-0.0204699\pi$
$907$	12109.3	+	20974.0i	0.443312	+	0.767840i	−0.554621	+	0.832103i	$0.687137\pi$
$908$	−19308.9			−0.705715
$909$		0			0
$910$	2951.19	+	17685.1i	0.107507	+	0.644238i
$911$	−23767.6	+	13722.2i	−0.864385	+	0.499053i	−0.865478	−	0.500946i	$-0.832985\pi$
$911$	−23767.6	+	13722.2i	−0.864385	+	0.499053i	0.00109314	+	0.999999i	$0.499652\pi$
$912$		0			0
$913$	−8357.06	−	4824.95i	−0.302933	−	0.174899i
$914$	−75258.9	−	43450.7i	−2.72357	−	1.57245i
$915$		0			0
$916$	48830.3	−	28192.2i	1.76135	−	1.01692i
$917$	−3644.94	−	21842.4i	−0.131261	−	0.786586i
$918$		0			0
$919$	34400.6			1.23479			0.617395	−	0.786653i	$-0.288188\pi$
$919$	34400.6			1.23479			0.617395	+	0.786653i	$0.288188\pi$
$920$	27617.9	+	47835.5i	0.989711	+	1.71423i
$921$		0			0
$922$	−87932.0	−	50767.5i	−3.14087	−	1.81338i
$923$	−7370.51	+	12766.1i	−0.262842	+	0.455256i
$924$		0			0
$925$	5759.47	+	9975.69i	0.204724	+	0.354593i
$926$			1169.41i			0.0415001i
$927$		0			0
$928$	78575.8			2.77950
$929$	−9180.18	−	15900.5i	−0.324211	−	0.561550i	0.657141	−	0.753767i	$-0.271765\pi$
$929$	−9180.18	−	15900.5i	−0.324211	−	0.561550i	−0.981352	+	0.192217i	$0.938432\pi$
$930$		0			0
$931$	−13911.4	−	2717.26i	−0.489719	−	0.0956550i
$932$	36392.7	+	21011.4i	1.27906	+	0.738466i
$933$		0			0
$934$	−71836.8	+	41475.0i	−2.51667	+	1.45300i
$935$		−	10814.3i		−	0.378250i
$936$		0			0
$937$		−	55153.5i		−	1.92293i	−0.274924	−	0.961466i	$-0.588653\pi$
$937$		−	55153.5i		−	1.92293i	0.274924	−	0.961466i	$-0.411347\pi$
$938$	23191.9	+	28160.2i	0.807296	+	0.980238i
$939$		0			0
$940$	−13423.3	+	23249.8i	−0.465766	+	0.806730i
$941$	−20322.4	+	35199.5i	−0.704029	+	1.21941i	0.263011	+	0.964793i	$0.415284\pi$
$941$	−20322.4	+	35199.5i	−0.704029	+	1.21941i	−0.967041	+	0.254622i	$0.918049\pi$
$942$		0			0
$943$	−18291.0	+	10560.3i	−0.631640	+	0.364677i
$944$	−78410.6			−2.70344
$945$		0			0
$946$	13513.4			0.464439
$947$	30834.2	−	17802.2i	1.05806	−	0.610868i	0.133162	−	0.991094i	$-0.457487\pi$
$947$	30834.2	−	17802.2i	1.05806	−	0.610868i	0.924894	+	0.380226i	$0.124154\pi$
$948$		0			0
$949$	9602.62	−	16632.2i	0.328466	−	0.568920i
$950$	8669.72	−	15016.4i	0.296087	−	0.512838i
$951$		0			0
$952$	104444.	+	126818.i	3.55572	+	4.31744i
$953$		−	28893.7i		−	0.982118i	−0.871126	−	0.491059i	$-0.836610\pi$
$953$		−	28893.7i		−	0.982118i	0.871126	−	0.491059i	$-0.163390\pi$
$954$		0			0
$955$		−	898.962i		−	0.0304604i
$956$	32719.2	−	18890.5i	1.10692	−	0.639081i
$957$		0			0
$958$	81364.7	+	46975.9i	2.74402	+	1.58426i
$959$	8811.24	−	23534.0i	0.296694	−	0.792444i
$960$		0			0
$961$	1133.99	+	1964.13i	0.0380648	+	0.0659302i
$962$	20869.3			0.699431
$963$		0			0
$964$		−	126723.i		−	4.23388i
$965$	−3921.77	−	6792.71i	−0.130825	−	0.226596i
$966$		0			0
$967$	24894.3	−	43118.2i	0.827867	−	1.43391i	−0.0718412	−	0.997416i	$-0.522887\pi$
$967$	24894.3	−	43118.2i	0.827867	−	1.43391i	0.899708	−	0.436492i	$-0.143779\pi$
$968$	72240.2	+	41707.9i	2.39865	+	1.38486i
$969$		0			0
$970$	−5229.74	−	9058.18i	−0.173110	−	0.299836i
$971$	23098.3			0.763397			0.381698	−	0.924287i	$-0.375339\pi$
$971$	23098.3			0.763397			0.381698	+	0.924287i	$0.375339\pi$
$972$		0			0
$973$	−17466.9	+	2914.78i	−0.575502	+	0.0960365i
$974$	−66117.4	+	38172.9i	−2.17509	+	1.25579i
$975$		0			0
$976$	64714.2	+	37362.8i	2.12239	+	1.22536i
$977$	−3023.09	−	1745.38i	−0.0989940	−	0.0571542i	0.449686	−	0.893187i	$-0.351536\pi$
$977$	−3023.09	−	1745.38i	−0.0989940	−	0.0571542i	−0.548680	+	0.836033i	$0.684869\pi$
$978$		0			0
$979$	−4325.16	+	2497.13i	−0.141198	+	0.0815206i
$980$	47261.7	−	16225.4i	1.54053	−	0.528877i
$981$		0			0
$982$	49458.2			1.60720
$983$	−7109.05	−	12313.2i	−0.230665	−	0.399523i	0.727339	−	0.686278i	$-0.240757\pi$
$983$	−7109.05	−	12313.2i	−0.230665	−	0.399523i	−0.958004	+	0.286755i	$0.907423\pi$
$984$		0			0
$985$	20628.9	+	11910.1i	0.667301	+	0.385266i
$986$	44651.6	−	77338.9i	1.44219	−	2.49794i
$987$		0			0
$988$	−11400.6	−	19746.4i	−0.367107	−	0.635848i
$989$			22371.5i			0.719285i
$990$		0			0
$991$	−263.472			−0.00844549			−0.00422274	−	0.999991i	$-0.501344\pi$
$991$	−263.472			−0.00844549			−0.00422274	+	0.999991i	$0.501344\pi$
$992$	−53026.3	−	91844.2i	−1.69716	−	2.93957i
$993$		0			0
$994$	53008.3	+	19846.5i	1.69147	+	0.633293i
$995$	15029.3	+	8677.16i	0.478854	+	0.276467i
$996$		0			0
$997$	−41959.3	+	24225.2i	−1.33286	+	0.769528i	−0.985737	−	0.168290i	$-0.946175\pi$
$997$	−41959.3	+	24225.2i	−1.33286	+	0.769528i	−0.347125	+	0.937819i	$0.612842\pi$
$998$			81327.1i			2.57952i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.4.o.a.125.21		44
3.2	odd	2		63.4.o.a.41.1	yes	44
7.6	odd	2	inner	189.4.o.a.125.22		44
9.2	odd	6	inner	189.4.o.a.62.22		44
9.4	even	3		567.4.c.c.566.14		44
9.5	odd	6		567.4.c.c.566.31		44
9.7	even	3		63.4.o.a.20.2	yes	44
21.20	even	2		63.4.o.a.41.2	yes	44
63.13	odd	6		567.4.c.c.566.32		44
63.20	even	6	inner	189.4.o.a.62.21		44
63.34	odd	6		63.4.o.a.20.1	✓	44
63.41	even	6		567.4.c.c.566.13		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.o.a.20.1	✓	44	63.34	odd	6
63.4.o.a.20.2	yes	44	9.7	even	3
63.4.o.a.41.1	yes	44	3.2	odd	2
63.4.o.a.41.2	yes	44	21.20	even	2
189.4.o.a.62.21		44	63.20	even	6	inner
189.4.o.a.62.22		44	9.2	odd	6	inner
189.4.o.a.125.21		44	1.1	even	1	trivial
189.4.o.a.125.22		44	7.6	odd	2	inner
567.4.c.c.566.13		44	63.41	even	6
567.4.c.c.566.14		44	9.4	even	3
567.4.c.c.566.31		44	9.5	odd	6
567.4.c.c.566.32		44	63.13	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	189.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(4.67796 - 2.70082i) q^{2} +(10.5889 - 18.3405i) q^{4} +(-3.43953 + 5.95744i) q^{5} +(14.2961 - 11.7738i) q^{7} -71.1815i q^{8} +O(q^{10})\)	\(q+(4.67796 - 2.70082i) q^{2} +(10.5889 - 18.3405i) q^{4} +(-3.43953 + 5.95744i) q^{5} +(14.2961 - 11.7738i) q^{7} -71.1815i q^{8} +37.1582i q^{10} +(10.9244 - 6.30723i) q^{11} +(22.5632 + 13.0269i) q^{13} +(35.0774 - 93.6886i) q^{14} +(-107.537 - 186.260i) q^{16} -124.623 q^{17} -41.3246i q^{19} +(72.8415 + 126.165i) q^{20} +(34.0694 - 59.0099i) q^{22} +(97.6910 + 56.4019i) q^{23} +(38.8392 + 67.2715i) q^{25} +140.733 q^{26} +(-64.5583 - 386.868i) q^{28} +(-114.888 + 66.3304i) q^{29} +(155.062 + 89.5251i) q^{31} +(-512.952 - 296.153i) q^{32} +(-582.982 + 336.585i) q^{34} +(20.9702 + 125.664i) q^{35} +148.290 q^{37} +(-111.610 - 193.315i) q^{38} +(424.060 + 244.831i) q^{40} +(-93.6165 + 162.149i) q^{41} +(99.1611 + 171.752i) q^{43} -267.146i q^{44} +609.326 q^{46} +(92.1405 + 159.592i) q^{47} +(65.7542 - 336.638i) q^{49} +(363.377 + 209.796i) q^{50} +(477.838 - 275.880i) q^{52} +359.147i q^{53} +86.7756i q^{55} +(-838.078 - 1017.61i) q^{56} +(-358.293 + 620.582i) q^{58} +(182.287 - 315.730i) q^{59} +(-300.892 + 173.720i) q^{61} +967.165 q^{62} -1478.83 q^{64} +(-155.214 + 89.6127i) q^{65} +(-182.332 + 315.809i) q^{67} +(-1319.62 + 2285.65i) q^{68} +(437.494 + 531.216i) q^{70} +565.793i q^{71} -737.140i q^{73} +(693.694 - 400.504i) q^{74} +(-757.912 - 437.580i) q^{76} +(81.9162 - 218.791i) q^{77} +(-451.543 - 782.096i) q^{79} +1479.51 q^{80} +1011.37i q^{82} +(-382.494 - 662.499i) q^{83} +(428.645 - 742.436i) q^{85} +(927.743 + 535.633i) q^{86} +(-448.958 - 777.618i) q^{88} -395.916 q^{89} +(475.941 - 79.4223i) q^{91} +(2068.87 - 1194.47i) q^{92} +(862.059 + 497.710i) q^{94} +(246.189 + 142.137i) q^{95} +(-243.773 + 140.742i) q^{97} +(-601.604 - 1752.37i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 6 q^{2} + 78 q^{4} + 5 q^{7}+O(q^{10}) \) 44 * q + 6 * q^2 + 78 * q^4 + 5 * q^7	\( 44 q + 6 q^{2} + 78 q^{4} + 5 q^{7} + 18 q^{11} - 204 q^{14} - 242 q^{16} - 34 q^{22} + 102 q^{23} - 352 q^{25} + 300 q^{28} - 246 q^{29} - 1068 q^{32} + 328 q^{37} - 170 q^{43} + 968 q^{46} - 79 q^{49} - 288 q^{50} - 1212 q^{56} - 538 q^{58} - 808 q^{64} - 4350 q^{65} - 590 q^{67} + 384 q^{70} + 5304 q^{74} + 2787 q^{77} - 302 q^{79} - 612 q^{85} + 13692 q^{86} + 1294 q^{88} + 210 q^{91} + 10194 q^{92} - 6336 q^{95}+O(q^{100}) \) 44 * q + 6 * q^2 + 78 * q^4 + 5 * q^7 + 18 * q^11 - 204 * q^14 - 242 * q^16 - 34 * q^22 + 102 * q^23 - 352 * q^25 + 300 * q^28 - 246 * q^29 - 1068 * q^32 + 328 * q^37 - 170 * q^43 + 968 * q^46 - 79 * q^49 - 288 * q^50 - 1212 * q^56 - 538 * q^58 - 808 * q^64 - 4350 * q^65 - 590 * q^67 + 384 * q^70 + 5304 * q^74 + 2787 * q^77 - 302 * q^79 - 612 * q^85 + 13692 * q^86 + 1294 * q^88 + 210 * q^91 + 10194 * q^92 - 6336 * q^95

Introduction

L-functions

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