LMFDB - Embedded newform 128.4.e.a.33.3

Newspace parameters

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	128.e (of order $4$, degree $2$, not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$7.55224448073$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
Defining polynomial:	$x^{10} - 2 x^{9} - x^{8} + 6 x^{7} + 14 x^{6} - 80 x^{5} + 56 x^{4} + 96 x^{3} - 64 x^{2} - 512 x + 1024$
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{20} $
Twist minimal:	no (minimal twist has level 16)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			33.3
Root			$-1.62580 + 1.16481i$ of defining polynomial
Character	$\chi$	$=$	128.33
Dual form			128.4.e.a.97.3

$q$-expansion

$f(q)$	$=$	$q+(0.756776 + 0.756776i) q^{3} +(-8.22587 + 8.22587i) q^{5} +2.67171i q^{7} -25.8546i q^{9} +O(q^{10})$	\(q+(0.756776 + 0.756776i) q^{3} +(-8.22587 + 8.22587i) q^{5} +2.67171i q^{7} -25.8546i q^{9} +(-45.2213 + 45.2213i) q^{11} +(-35.3968 - 35.3968i) q^{13} -12.4503 q^{15} -72.4991 q^{17} +(19.4427 + 19.4427i) q^{19} +(-2.02188 + 2.02188i) q^{21} +139.462i q^{23} -10.3299i q^{25} +(39.9991 - 39.9991i) q^{27} +(-66.0434 - 66.0434i) q^{29} -188.682 q^{31} -68.4447 q^{33} +(-21.9771 - 21.9771i) q^{35} +(84.0653 - 84.0653i) q^{37} -53.5748i q^{39} +104.629i q^{41} +(-31.4857 + 31.4857i) q^{43} +(212.676 + 212.676i) q^{45} +488.151 q^{47} +335.862 q^{49} +(-54.8656 - 54.8656i) q^{51} +(-149.560 + 149.560i) q^{53} -743.968i q^{55} +29.4275i q^{57} +(284.698 - 284.698i) q^{59} +(228.069 + 228.069i) q^{61} +69.0758 q^{63} +582.338 q^{65} +(139.151 + 139.151i) q^{67} +(-105.541 + 105.541i) q^{69} +453.655i q^{71} -259.747i q^{73} +(7.81740 - 7.81740i) q^{75} +(-120.818 - 120.818i) q^{77} -323.190 q^{79} -637.533 q^{81} +(-563.897 - 563.897i) q^{83} +(596.368 - 596.368i) q^{85} -99.9602i q^{87} +866.853i q^{89} +(94.5697 - 94.5697i) q^{91} +(-142.790 - 142.790i) q^{93} -319.866 q^{95} -936.077 q^{97} +(1169.18 + 1169.18i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10q - 2q^{3} + 2q^{5} + O(q^{10}) $	$ 10q - 2q^{3} + 2q^{5} + 18q^{11} + 2q^{13} + 124q^{15} - 4q^{17} - 26q^{19} - 52q^{21} + 184q^{27} + 202q^{29} - 368q^{31} - 4q^{33} + 476q^{35} + 10q^{37} - 838q^{43} - 194q^{45} + 944q^{47} + 94q^{49} - 1500q^{51} + 378q^{53} + 1706q^{59} - 910q^{61} - 2628q^{63} - 492q^{65} + 1942q^{67} - 580q^{69} - 2954q^{75} + 268q^{77} + 4416q^{79} + 482q^{81} - 2562q^{83} + 12q^{85} + 3332q^{91} + 2192q^{93} - 6900q^{95} - 4q^{97} + 4958q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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			0
$2$		0			0
$3$	0.756776	+	0.756776i	0.145642	+	0.145642i	0.776168	−	0.630526i	$-0.217161\pi$
$3$	0.756776	+	0.756776i	0.145642	+	0.145642i	−0.630526	+	0.776168i	$0.717161\pi$
$4$		0			0
$5$	−8.22587	+	8.22587i	−0.735744	+	0.735744i	−0.971751	−	0.236007i	$-0.924161\pi$
$5$	−8.22587	+	8.22587i	−0.735744	+	0.735744i	0.236007	+	0.971751i	$0.424161\pi$
$6$		0			0
$7$			2.67171i			0.144259i	0.997395	+	0.0721293i	$0.0229794\pi$
$7$			2.67171i			0.144259i	−0.997395	+	0.0721293i	$0.977021\pi$
$8$		0			0
$9$		−	25.8546i		−	0.957577i
$10$		0			0
$11$	−45.2213	+	45.2213i	−1.23952	+	1.23952i	−0.279323	+	0.960197i	$0.590110\pi$
$11$	−45.2213	+	45.2213i	−1.23952	+	1.23952i	−0.960197	+	0.279323i	$0.909890\pi$
$12$		0			0
$13$	−35.3968	−	35.3968i	−0.755176	−	0.755176i	0.220264	−	0.975440i	$-0.429308\pi$
$13$	−35.3968	−	35.3968i	−0.755176	−	0.755176i	−0.975440	+	0.220264i	$0.929308\pi$
$14$		0			0
$15$	−12.4503			−0.214310
$16$		0			0
$17$	−72.4991			−1.03433			−0.517165	−	0.855886i	$-0.673013\pi$
$17$	−72.4991			−1.03433			−0.517165	+	0.855886i	$0.673013\pi$
$18$		0			0
$19$	19.4427	+	19.4427i	0.234761	+	0.234761i	0.814676	−	0.579916i	$-0.196915\pi$
$19$	19.4427	+	19.4427i	0.234761	+	0.234761i	−0.579916	+	0.814676i	$0.696915\pi$
$20$		0			0
$21$	−2.02188	+	2.02188i	−0.0210100	+	0.0210100i
$22$		0			0
$23$			139.462i			1.26434i	0.774830	+	0.632170i	$0.217835\pi$
$23$			139.462i			1.26434i	−0.774830	+	0.632170i	$0.782165\pi$
$24$		0			0
$25$		−	10.3299i		−	0.0826390i
$26$		0			0
$27$	39.9991	−	39.9991i	0.285105	−	0.285105i
$28$		0			0
$29$	−66.0434	−	66.0434i	−0.422895	−	0.422895i	0.463304	−	0.886199i	$-0.346664\pi$
$29$	−66.0434	−	66.0434i	−0.422895	−	0.422895i	−0.886199	+	0.463304i	$0.846664\pi$
$30$		0			0
$31$	−188.682			−1.09317			−0.546584	−	0.837404i	$-0.684072\pi$
$31$	−188.682			−1.09317			−0.546584	+	0.837404i	$0.684072\pi$
$32$		0			0
$33$	−68.4447			−0.361051
$34$		0			0
$35$	−21.9771	−	21.9771i	−0.106137	−	0.106137i
$36$		0			0
$37$	84.0653	−	84.0653i	0.373520	−	0.373520i	−0.495237	−	0.868758i	$-0.664919\pi$
$37$	84.0653	−	84.0653i	0.373520	−	0.373520i	0.868758	+	0.495237i	$0.164919\pi$
$38$		0			0
$39$		−	53.5748i		−	0.219970i
$40$		0			0
$41$			104.629i			0.398545i	0.979944	+	0.199272i	$0.0638578\pi$
$41$			104.629i			0.398545i	−0.979944	+	0.199272i	$0.936142\pi$
$42$		0			0
$43$	−31.4857	+	31.4857i	−0.111663	+	0.111663i	−0.760731	−	0.649067i	$-0.775159\pi$
$43$	−31.4857	+	31.4857i	−0.111663	+	0.111663i	0.649067	+	0.760731i	$0.275159\pi$
$44$		0			0
$45$	212.676	+	212.676i	0.704532	+	0.704532i
$46$		0			0
$47$	488.151			1.51498			0.757491	−	0.652846i	$-0.226425\pi$
$47$	488.151			1.51498			0.757491	+	0.652846i	$0.226425\pi$
$48$		0			0
$49$	335.862			0.979189
$50$		0			0
$51$	−54.8656	−	54.8656i	−0.150641	−	0.150641i
$52$		0			0
$53$	−149.560	+	149.560i	−0.387617	+	0.387617i	−0.873837	−	0.486220i	$-0.838376\pi$
$53$	−149.560	+	149.560i	−0.387617	+	0.387617i	0.486220	+	0.873837i	$0.338376\pi$
$54$		0			0
$55$		−	743.968i		−	1.82394i
$56$		0			0
$57$			29.4275i			0.0683819i
$58$		0			0
$59$	284.698	−	284.698i	0.628212	−	0.628212i	−0.319406	−	0.947618i	$-0.603483\pi$
$59$	284.698	−	284.698i	0.628212	−	0.628212i	0.947618	+	0.319406i	$0.103483\pi$
$60$		0			0
$61$	228.069	+	228.069i	0.478709	+	0.478709i	0.904719	−	0.426010i	$-0.140081\pi$
$61$	228.069	+	228.069i	0.478709	+	0.478709i	−0.426010	+	0.904719i	$0.640081\pi$
$62$		0			0
$63$	69.0758			0.138139
$64$		0			0
$65$	582.338			1.11123
$66$		0			0
$67$	139.151	+	139.151i	0.253730	+	0.253730i	0.822498	−	0.568768i	$-0.192580\pi$
$67$	139.151	+	139.151i	0.253730	+	0.253730i	−0.568768	+	0.822498i	$0.692580\pi$
$68$		0			0
$69$	−105.541	+	105.541i	−0.184140	+	0.184140i
$70$		0			0
$71$			453.655i			0.758294i	0.925336	+	0.379147i	$0.123783\pi$
$71$			453.655i			0.758294i	−0.925336	+	0.379147i	$0.876217\pi$
$72$		0			0
$73$		−	259.747i		−	0.416454i	−0.978081	−	0.208227i	$-0.933231\pi$
$73$		−	259.747i		−	0.416454i	0.978081	−	0.208227i	$-0.0667692\pi$
$74$		0			0
$75$	7.81740	−	7.81740i	0.0120357	−	0.0120357i
$76$		0			0
$77$	−120.818	−	120.818i	−0.178811	−	0.178811i
$78$		0			0
$79$	−323.190			−0.460275			−0.230138	−	0.973158i	$-0.573918\pi$
$79$	−323.190			−0.460275			−0.230138	+	0.973158i	$0.573918\pi$
$80$		0			0
$81$	−637.533			−0.874531
$82$		0			0
$83$	−563.897	−	563.897i	−0.745732	−	0.745732i	0.227943	−	0.973674i	$-0.426800\pi$
$83$	−563.897	−	563.897i	−0.745732	−	0.745732i	−0.973674	+	0.227943i	$0.926800\pi$
$84$		0			0
$85$	596.368	−	596.368i	0.761002	−	0.761002i
$86$		0			0
$87$		−	99.9602i		−	0.123182i
$88$		0			0
$89$			866.853i			1.03243i	0.856459	+	0.516215i	$0.172659\pi$
$89$			866.853i			1.03243i	−0.856459	+	0.516215i	$0.827341\pi$
$90$		0			0
$91$	94.5697	−	94.5697i	0.108941	−	0.108941i
$92$		0			0
$93$	−142.790	−	142.790i	−0.159211	−	0.159211i
$94$		0			0
$95$	−319.866			−0.345448
$96$		0			0
$97$	−936.077			−0.979837			−0.489919	−	0.871768i	$-0.662974\pi$
$97$	−936.077			−0.979837			−0.489919	+	0.871768i	$0.662974\pi$
$98$		0			0
$99$	1169.18	+	1169.18i	1.18694	+	1.18694i
$100$		0			0
$101$	1.58844	−	1.58844i	0.00156491	−	0.00156491i	−0.706324	−	0.707889i	$-0.749648\pi$
$101$	1.58844	−	1.58844i	0.00156491	−	0.00156491i	0.707889	+	0.706324i	$0.249648\pi$
$102$		0			0
$103$			1388.28i			1.32807i	0.747700	+	0.664036i	$0.231158\pi$
$103$			1388.28i			1.32807i	−0.747700	+	0.664036i	$0.768842\pi$
$104$		0			0
$105$		−	33.2635i		−	0.0309160i
$106$		0			0
$107$	−821.526	+	821.526i	−0.742243	+	0.742243i	−0.973009	−	0.230767i	$-0.925877\pi$
$107$	−821.526	+	821.526i	−0.742243	+	0.742243i	0.230767	+	0.973009i	$0.425877\pi$
$108$		0			0
$109$	−532.797	−	532.797i	−0.468190	−	0.468190i	0.433138	−	0.901328i	$-0.357406\pi$
$109$	−532.797	−	532.797i	−0.468190	−	0.468190i	−0.901328	+	0.433138i	$0.857406\pi$
$110$		0			0
$111$	127.237			0.108800
$112$		0			0
$113$	−67.2680			−0.0560003			−0.0280002	−	0.999608i	$-0.508914\pi$
$113$	−67.2680			−0.0560003			−0.0280002	+	0.999608i	$0.508914\pi$
$114$		0			0
$115$	−1147.19	−	1147.19i	−0.930230	−	0.930230i
$116$		0			0
$117$	−915.168	+	915.168i	−0.723140	+	0.723140i
$118$		0			0
$119$		−	193.696i		−	0.149211i
$120$		0			0
$121$		−	2758.92i		−	2.07282i
$122$		0			0
$123$	−79.1808	+	79.1808i	−0.0580447	+	0.0580447i
$124$		0			0
$125$	−943.262	−	943.262i	−0.674943	−	0.674943i
$126$		0			0
$127$	−1903.59			−1.33005			−0.665026	−	0.746820i	$-0.731579\pi$
$127$	−1903.59			−1.33005			−0.665026	+	0.746820i	$0.731579\pi$
$128$		0			0
$129$	−47.6552			−0.0325257
$130$		0			0
$131$	918.430	+	918.430i	0.612546	+	0.612546i	0.943609	−	0.331062i	$-0.107407\pi$
$131$	918.430	+	918.430i	0.612546	+	0.612546i	−0.331062	+	0.943609i	$0.607407\pi$
$132$		0			0
$133$	−51.9451	+	51.9451i	−0.0338662	+	0.0338662i
$134$		0			0
$135$			658.054i			0.419528i
$136$		0			0
$137$			477.234i			0.297612i	0.988866	+	0.148806i	$0.0475430\pi$
$137$			477.234i			0.297612i	−0.988866	+	0.148806i	$0.952457\pi$
$138$		0			0
$139$	−1513.89	+	1513.89i	−0.923788	+	0.923788i	−0.997295	−	0.0735064i	$-0.976581\pi$
$139$	−1513.89	+	1513.89i	−0.923788	+	0.923788i	0.0735064	+	0.997295i	$0.476581\pi$
$140$		0			0
$141$	369.421	+	369.421i	0.220644	+	0.220644i
$142$		0			0
$143$	3201.37			1.87211
$144$		0			0
$145$	1086.53			0.622285
$146$		0			0
$147$	254.172	+	254.172i	0.142611	+	0.142611i
$148$		0			0
$149$	−375.353	+	375.353i	−0.206377	+	0.206377i	−0.802725	−	0.596349i	$-0.796618\pi$
$149$	−375.353	+	375.353i	−0.206377	+	0.206377i	0.596349	+	0.802725i	$0.296618\pi$
$150$		0			0
$151$		−	2997.52i		−	1.61546i	−0.589553	−	0.807730i	$-0.700696\pi$
$151$		−	2997.52i		−	1.61546i	0.589553	−	0.807730i	$-0.299304\pi$
$152$		0			0
$153$			1874.43i			0.990451i
$154$		0			0
$155$	1552.07	−	1552.07i	0.804293	−	0.804293i
$156$		0			0
$157$	1509.01	+	1509.01i	0.767082	+	0.767082i	0.977592	−	0.210510i	$-0.0675125\pi$
$157$	1509.01	+	1509.01i	0.767082	+	0.767082i	−0.210510	+	0.977592i	$0.567512\pi$
$158$		0			0
$159$	−226.368			−0.112906
$160$		0			0
$161$	−372.601			−0.182392
$162$		0			0
$163$	−1425.19	−	1425.19i	−0.684844	−	0.684844i	0.276244	−	0.961088i	$-0.410910\pi$
$163$	−1425.19	−	1425.19i	−0.684844	−	0.684844i	−0.961088	+	0.276244i	$0.910910\pi$
$164$		0			0
$165$	563.017	−	563.017i	0.265641	−	0.265641i
$166$		0			0
$167$			792.415i			0.367179i	0.983003	+	0.183590i	$0.0587717\pi$
$167$			792.415i			0.367179i	−0.983003	+	0.183590i	$0.941228\pi$
$168$		0			0
$169$			308.861i			0.140583i
$170$		0			0
$171$	502.682	−	502.682i	0.224802	−	0.224802i
$172$		0			0
$173$	773.594	+	773.594i	0.339972	+	0.339972i	0.856357	−	0.516384i	$-0.172722\pi$
$173$	773.594	+	773.594i	0.339972	+	0.339972i	−0.516384	+	0.856357i	$0.672722\pi$
$174$		0			0
$175$	27.5984			0.0119214
$176$		0			0
$177$	430.905			0.182988
$178$		0			0
$179$	426.050	+	426.050i	0.177902	+	0.177902i	0.790441	−	0.612539i	$-0.209852\pi$
$179$	426.050	+	426.050i	0.177902	+	0.177902i	−0.612539	+	0.790441i	$0.709852\pi$
$180$		0			0
$181$	2618.06	−	2618.06i	1.07513	−	1.07513i	0.0781951	−	0.996938i	$-0.475084\pi$
$181$	2618.06	−	2618.06i	1.07513	−	1.07513i	0.996938	−	0.0781951i	$-0.0249157\pi$
$182$		0			0
$183$			345.194i			0.139440i
$184$		0			0
$185$			1383.02i			0.549631i
$186$		0			0
$187$	3278.50	−	3278.50i	1.28207	−	1.28207i
$188$		0			0
$189$	106.866	+	106.866i	0.0411288	+	0.0411288i
$190$		0			0
$191$	−3216.39			−1.21848			−0.609240	−	0.792986i	$-0.708525\pi$
$191$	−3216.39			−1.21848			−0.609240	+	0.792986i	$0.708525\pi$
$192$		0			0
$193$	2852.57			1.06390			0.531950	−	0.846776i	$-0.321459\pi$
$193$	2852.57			1.06390			0.531950	+	0.846776i	$0.321459\pi$
$194$		0			0
$195$	440.700	+	440.700i	0.161842	+	0.161842i
$196$		0			0
$197$	−1609.02	+	1609.02i	−0.581918	+	0.581918i	−0.935430	−	0.353512i	$-0.884987\pi$
$197$	−1609.02	+	1609.02i	−0.581918	+	0.581918i	0.353512	+	0.935430i	$0.384987\pi$
$198$		0			0
$199$		−	747.136i		−	0.266146i	−0.991106	−	0.133073i	$-0.957516\pi$
$199$		−	747.136i		−	0.266146i	0.991106	−	0.133073i	$-0.0424845\pi$
$200$		0			0
$201$			210.612i			0.0739074i
$202$		0			0
$203$	176.449	−	176.449i	0.0610062	−	0.0610062i
$204$		0			0
$205$	−860.666	−	860.666i	−0.293227	−	0.293227i
$206$		0			0
$207$	3605.73			1.21070
$208$		0			0
$209$	−1758.44			−0.581981
$210$		0			0
$211$	−2227.13	−	2227.13i	−0.726645	−	0.726645i	0.243305	−	0.969950i	$-0.421769\pi$
$211$	−2227.13	−	2227.13i	−0.726645	−	0.726645i	−0.969950	+	0.243305i	$0.921769\pi$
$212$		0			0
$213$	−343.315	+	343.315i	−0.110439	+	0.110439i
$214$		0			0
$215$		−	517.995i		−	0.164311i
$216$		0			0
$217$		−	504.102i		−	0.157699i
$218$		0			0
$219$	196.570	−	196.570i	0.0606530	−	0.0606530i
$220$		0			0
$221$	2566.23	+	2566.23i	0.781102	+	0.781102i
$222$		0			0
$223$	358.053			0.107520			0.0537601	−	0.998554i	$-0.482879\pi$
$223$	358.053			0.107520			0.0537601	+	0.998554i	$0.482879\pi$
$224$		0			0
$225$	−267.075			−0.0791332
$226$		0			0
$227$	3455.40	+	3455.40i	1.01032	+	1.01032i	0.999946	+	0.0103741i	$0.00330223\pi$
$227$	3455.40	+	3455.40i	1.01032	+	1.01032i	0.0103741	+	0.999946i	$0.496698\pi$
$228$		0			0
$229$	1430.03	−	1430.03i	0.412659	−	0.412659i	−0.470005	−	0.882664i	$-0.655748\pi$
$229$	1430.03	−	1430.03i	0.412659	−	0.412659i	0.882664	+	0.470005i	$0.155748\pi$
$230$		0			0
$231$		−	182.864i		−	0.0520847i
$232$		0			0
$233$		−	926.479i		−	0.260496i	−0.991481	−	0.130248i	$-0.958423\pi$
$233$		−	926.479i		−	0.260496i	0.991481	−	0.130248i	$-0.0415774\pi$
$234$		0			0
$235$	−4015.47	+	4015.47i	−1.11464	+	1.11464i
$236$		0			0
$237$	−244.583	−	244.583i	−0.0670352	−	0.0670352i
$238$		0			0
$239$	792.472			0.214480			0.107240	−	0.994233i	$-0.465799\pi$
$239$	792.472			0.214480			0.107240	+	0.994233i	$0.465799\pi$
$240$		0			0
$241$	1449.01			0.387299			0.193650	−	0.981071i	$-0.437967\pi$
$241$	1449.01			0.387299			0.193650	+	0.981071i	$0.437967\pi$
$242$		0			0
$243$	−1562.44	−	1562.44i	−0.412473	−	0.412473i
$244$		0			0
$245$	−2762.76	+	2762.76i	−0.720433	+	0.720433i
$246$		0			0
$247$		−	1376.42i		−	0.354572i
$248$		0			0
$249$		−	853.487i		−	0.217219i
$250$		0			0
$251$	−3580.04	+	3580.04i	−0.900280	+	0.900280i	−0.995460	−	0.0951802i	$-0.969657\pi$
$251$	−3580.04	+	3580.04i	−0.900280	+	0.900280i	0.0951802	+	0.995460i	$0.469657\pi$
$252$		0			0
$253$	−6306.64	−	6306.64i	−1.56717	−	1.56717i
$254$		0			0
$255$	902.634			0.221667
$256$		0			0
$257$	−4708.87			−1.14292			−0.571461	−	0.820629i	$-0.693623\pi$
$257$	−4708.87			−1.14292			−0.571461	+	0.820629i	$0.693623\pi$
$258$		0			0
$259$	224.598	+	224.598i	0.0538835	+	0.0538835i
$260$		0			0
$261$	−1707.53	+	1707.53i	−0.404955	+	0.404955i
$262$		0			0
$263$			2967.82i			0.695830i	0.937526	+	0.347915i	$0.113110\pi$
$263$			2967.82i			0.695830i	−0.937526	+	0.347915i	$0.886890\pi$
$264$		0			0
$265$		−	2460.53i		−	0.570374i
$266$		0			0
$267$	−656.013	+	656.013i	−0.150365	+	0.150365i
$268$		0			0
$269$	663.633	+	663.633i	0.150418	+	0.150418i	0.778305	−	0.627887i	$-0.216080\pi$
$269$	663.633	+	663.633i	0.150418	+	0.150418i	−0.627887	+	0.778305i	$0.716080\pi$
$270$		0			0
$271$	−8058.74			−1.80640			−0.903199	−	0.429223i	$-0.858788\pi$
$271$	−8058.74			−1.80640			−0.903199	+	0.429223i	$0.858788\pi$
$272$		0			0
$273$	143.136			0.0317326
$274$		0			0
$275$	467.130	+	467.130i	0.102433	+	0.102433i
$276$		0			0
$277$	−482.477	+	482.477i	−0.104654	+	0.104654i	−0.757495	−	0.652841i	$-0.773577\pi$
$277$	−482.477	+	482.477i	−0.104654	+	0.104654i	0.652841	+	0.757495i	$0.273577\pi$
$278$		0			0
$279$			4878.29i			1.04679i
$280$		0			0
$281$		−	5899.10i		−	1.25235i	−0.779682	−	0.626175i	$-0.784619\pi$
$281$		−	5899.10i		−	1.25235i	0.779682	−	0.626175i	$-0.215381\pi$
$282$		0			0
$283$	−679.897	+	679.897i	−0.142812	+	0.142812i	−0.774898	−	0.632086i	$-0.782199\pi$
$283$	−679.897	+	679.897i	−0.142812	+	0.142812i	0.632086	+	0.774898i	$0.282199\pi$
$284$		0			0
$285$	−242.067	−	242.067i	−0.0503116	−	0.0503116i
$286$		0			0
$287$	−279.538			−0.0574935
$288$		0			0
$289$	343.118			0.0698388
$290$		0			0
$291$	−708.401	−	708.401i	−0.142705	−	0.142705i
$292$		0			0
$293$	3552.87	−	3552.87i	0.708398	−	0.708398i	−0.257800	−	0.966198i	$-0.582998\pi$
$293$	3552.87	−	3552.87i	0.708398	−	0.708398i	0.966198	+	0.257800i	$0.0829976\pi$
$294$		0			0
$295$			4683.78i			0.924407i
$296$		0			0
$297$			3617.62i			0.706786i
$298$		0			0
$299$	4936.50	−	4936.50i	0.954799	−	0.954799i
$300$		0			0
$301$	−84.1205	−	84.1205i	−0.0161084	−	0.0161084i
$302$		0			0
$303$	2.40419			0.000455831
$304$		0			0
$305$	−3752.13			−0.704415
$306$		0			0
$307$	2735.56	+	2735.56i	0.508556	+	0.508556i	0.914083	−	0.405527i	$-0.132912\pi$
$307$	2735.56	+	2735.56i	0.508556	+	0.508556i	−0.405527	+	0.914083i	$0.632912\pi$
$308$		0			0
$309$	−1050.62	+	1050.62i	−0.193423	+	0.193423i
$310$		0			0
$311$		−	5796.70i		−	1.05692i	−0.848960	−	0.528458i	$-0.822771\pi$
$311$		−	5796.70i		−	1.05692i	0.848960	−	0.528458i	$-0.177229\pi$
$312$		0			0
$313$			8362.62i			1.51017i	0.655627	+	0.755085i	$0.272404\pi$
$313$			8362.62i			1.51017i	−0.655627	+	0.755085i	$0.727596\pi$
$314$		0			0
$315$	−568.209	+	568.209i	−0.101635	+	0.101635i
$316$		0			0
$317$	344.406	+	344.406i	0.0610214	+	0.0610214i	0.736959	−	0.675938i	$-0.236261\pi$
$317$	344.406	+	344.406i	0.0610214	+	0.0610214i	−0.675938	+	0.736959i	$0.736261\pi$
$318$		0			0
$319$	5973.13			1.04837
$320$		0			0
$321$	−1243.42			−0.216203
$322$		0			0
$323$	−1409.58	−	1409.58i	−0.242820	−	0.242820i
$324$		0			0
$325$	−365.644	+	365.644i	−0.0624071	+	0.0624071i
$326$		0			0
$327$		−	806.416i		−	0.136376i
$328$		0			0
$329$			1304.20i			0.218549i
$330$		0			0
$331$	2687.86	−	2687.86i	0.446339	−	0.446339i	−0.447797	−	0.894135i	$-0.647791\pi$
$331$	2687.86	−	2687.86i	0.446339	−	0.446339i	0.894135	+	0.447797i	$0.147791\pi$
$332$		0			0
$333$	−2173.47	−	2173.47i	−0.357675	−	0.357675i
$334$		0			0
$335$	−2289.27			−0.373361
$336$		0			0
$337$	−1795.31			−0.290199			−0.145099	−	0.989417i	$-0.546350\pi$
$337$	−1795.31			−0.290199			−0.145099	+	0.989417i	$0.546350\pi$
$338$		0			0
$339$	−50.9068	−	50.9068i	−0.00815598	−	0.00815598i
$340$		0			0
$341$	8532.42	−	8532.42i	1.35500	−	1.35500i
$342$		0			0
$343$			1813.72i			0.285515i
$344$		0			0
$345$		−	1736.34i		−	0.270960i
$346$		0			0
$347$	−1967.33	+	1967.33i	−0.304357	+	0.304357i	−0.842716	−	0.538359i	$-0.819045\pi$
$347$	−1967.33	+	1967.33i	−0.304357	+	0.304357i	0.538359	+	0.842716i	$0.319045\pi$
$348$		0			0
$349$	7363.37	+	7363.37i	1.12938	+	1.12938i	0.990279	+	0.139097i	$0.0444200\pi$
$349$	7363.37	+	7363.37i	1.12938	+	1.12938i	0.139097	+	0.990279i	$0.455580\pi$
$350$		0			0
$351$	−2831.68			−0.430609
$352$		0			0
$353$	10644.3			1.60493			0.802466	−	0.596698i	$-0.203521\pi$
$353$	10644.3			1.60493			0.802466	+	0.596698i	$0.203521\pi$
$354$		0			0
$355$	−3731.70	−	3731.70i	−0.557911	−	0.557911i
$356$		0			0
$357$	146.585	−	146.585i	0.0217313	−	0.0217313i
$358$		0			0
$359$		−	7459.42i		−	1.09664i	−0.836269	−	0.548319i	$-0.815268\pi$
$359$		−	7459.42i		−	1.09664i	0.836269	−	0.548319i	$-0.184732\pi$
$360$		0			0
$361$		−	6102.96i		−	0.889775i
$362$		0			0
$363$	2087.89	−	2087.89i	0.301889	−	0.301889i
$364$		0			0
$365$	2136.65	+	2136.65i	0.306403	+	0.306403i
$366$		0			0
$367$	6251.35			0.889149			0.444574	−	0.895742i	$-0.353355\pi$
$367$	6251.35			0.889149			0.444574	+	0.895742i	$0.353355\pi$
$368$		0			0
$369$	2705.14			0.381637
$370$		0			0
$371$	−399.582	−	399.582i	−0.0559171	−	0.0559171i
$372$		0			0
$373$	−8911.86	+	8911.86i	−1.23710	+	1.23710i	−0.275921	+	0.961180i	$0.588983\pi$
$373$	−8911.86	+	8911.86i	−1.23710	+	1.23710i	−0.961180	+	0.275921i	$0.911017\pi$
$374$		0			0
$375$		−	1427.68i		−	0.196600i
$376$		0			0
$377$			4675.45i			0.638721i
$378$		0			0
$379$	1184.03	−	1184.03i	0.160473	−	0.160473i	−0.622303	−	0.782776i	$-0.713803\pi$
$379$	1184.03	−	1184.03i	0.160473	−	0.160473i	0.782776	+	0.622303i	$0.213803\pi$
$380$		0			0
$381$	−1440.59	−	1440.59i	−0.193711	−	0.193711i
$382$		0			0
$383$	2880.38			0.384283			0.192142	−	0.981367i	$-0.438457\pi$
$383$	2880.38			0.384283			0.192142	+	0.981367i	$0.438457\pi$
$384$		0			0
$385$	1987.66			0.263119
$386$		0			0
$387$	814.050	+	814.050i	0.106926	+	0.106926i
$388$		0			0
$389$	−9244.24	+	9244.24i	−1.20489	+	1.20489i	−0.232226	+	0.972662i	$0.574601\pi$
$389$	−9244.24	+	9244.24i	−1.20489	+	1.20489i	−0.972662	+	0.232226i	$0.925399\pi$
$390$		0			0
$391$		−	10110.9i		−	1.30774i
$392$		0			0
$393$			1390.09i			0.178424i
$394$		0			0
$395$	2658.52	−	2658.52i	0.338645	−	0.338645i
$396$		0			0
$397$	4257.80	+	4257.80i	0.538270	+	0.538270i	0.923020	−	0.384751i	$-0.125713\pi$
$397$	4257.80	+	4257.80i	0.538270	+	0.538270i	−0.384751	+	0.923020i	$0.625713\pi$
$398$		0			0
$399$	−78.6216			−0.00986467
$400$		0			0
$401$	12722.6			1.58437			0.792187	−	0.610278i	$-0.208942\pi$
$401$	12722.6			1.58437			0.792187	+	0.610278i	$0.208942\pi$
$402$		0			0
$403$	6678.72	+	6678.72i	0.825535	+	0.825535i
$404$		0			0
$405$	5244.26	−	5244.26i	0.643431	−	0.643431i
$406$		0			0
$407$			7603.08i			0.925972i
$408$		0			0
$409$			232.991i			0.0281678i	0.999901	+	0.0140839i	$0.00448320\pi$
$409$			232.991i			0.0281678i	−0.999901	+	0.0140839i	$0.995517\pi$
$410$		0			0
$411$	−361.159	+	361.159i	−0.0433447	+	0.0433447i
$412$		0			0
$413$	760.629	+	760.629i	0.0906250	+	0.0906250i
$414$		0			0
$415$	9277.08			1.09734
$416$		0			0
$417$	−2291.35			−0.269084
$418$		0			0
$419$	−6125.69	−	6125.69i	−0.714223	−	0.714223i	0.253193	−	0.967416i	$-0.418519\pi$
$419$	−6125.69	−	6125.69i	−0.714223	−	0.714223i	−0.967416	+	0.253193i	$0.918519\pi$
$420$		0			0
$421$	8308.44	−	8308.44i	0.961825	−	0.961825i	−0.0374725	−	0.999298i	$-0.511931\pi$
$421$	8308.44	−	8308.44i	0.961825	−	0.961825i	0.999298	+	0.0374725i	$0.0119307\pi$
$422$		0			0
$423$		−	12620.9i		−	1.45071i
$424$		0			0
$425$			748.907i			0.0854760i
$426$		0			0
$427$	−609.333	+	609.333i	−0.0690579	+	0.0690579i
$428$		0			0
$429$	2422.72	+	2422.72i	0.272657	+	0.272657i
$430$		0			0
$431$	−8737.57			−0.976506			−0.488253	−	0.872702i	$-0.662366\pi$
$431$	−8737.57			−0.976506			−0.488253	+	0.872702i	$0.662366\pi$
$432$		0			0
$433$	−11627.5			−1.29049			−0.645247	−	0.763974i	$-0.723245\pi$
$433$	−11627.5			−1.29049			−0.645247	+	0.763974i	$0.723245\pi$
$434$		0			0
$435$	822.260	+	822.260i	0.0906306	+	0.0906306i
$436$		0			0
$437$	−2711.51	+	2711.51i	−0.296817	+	0.296817i
$438$		0			0
$439$			17631.8i			1.91690i	0.285261	+	0.958450i	$0.407920\pi$
$439$			17631.8i			1.91690i	−0.285261	+	0.958450i	$0.592080\pi$
$440$		0			0
$441$		−	8683.57i		−	0.937649i
$442$		0			0
$443$	−4549.81	+	4549.81i	−0.487964	+	0.487964i	−0.907663	−	0.419699i	$-0.862136\pi$
$443$	−4549.81	+	4549.81i	−0.487964	+	0.487964i	0.419699	+	0.907663i	$0.362136\pi$
$444$		0			0
$445$	−7130.62	−	7130.62i	−0.759604	−	0.759604i
$446$		0			0
$447$	−568.116			−0.0601140
$448$		0			0
$449$	−12926.5			−1.35867			−0.679334	−	0.733830i	$-0.737731\pi$
$449$	−12926.5			−1.35867			−0.679334	+	0.733830i	$0.737731\pi$
$450$		0			0
$451$	−4731.46	−	4731.46i	−0.494004	−	0.494004i
$452$		0			0
$453$	2268.45	−	2268.45i	0.235278	−	0.235278i
$454$		0			0
$455$			1555.84i			0.160305i
$456$		0			0
$457$			9320.32i			0.954018i	0.878898	+	0.477009i	$0.158279\pi$
$457$			9320.32i			0.954018i	−0.878898	+	0.477009i	$0.841721\pi$
$458$		0			0
$459$	−2899.90	+	2899.90i	−0.294892	+	0.294892i
$460$		0			0
$461$	−12885.0	−	12885.0i	−1.30177	−	1.30177i	−0.927200	−	0.374566i	$-0.877792\pi$
$461$	−12885.0	−	12885.0i	−1.30177	−	1.30177i	−0.374566	−	0.927200i	$-0.622208\pi$
$462$		0			0
$463$	−7038.37			−0.706482			−0.353241	−	0.935532i	$-0.614920\pi$
$463$	−7038.37			−0.706482			−0.353241	+	0.935532i	$0.614920\pi$
$464$		0			0
$465$	2349.14			0.234277
$466$		0			0
$467$	6001.76	+	6001.76i	0.594707	+	0.594707i	0.938899	−	0.344192i	$-0.111847\pi$
$467$	6001.76	+	6001.76i	0.594707	+	0.594707i	−0.344192	+	0.938899i	$0.611847\pi$
$468$		0			0
$469$	−371.769	+	371.769i	−0.0366028	+	0.0366028i
$470$		0			0
$471$			2283.96i			0.223438i
$472$		0			0
$473$		−	2847.65i		−	0.276818i
$474$		0			0
$475$	200.840	−	200.840i	0.0194004	−	0.0194004i
$476$		0			0
$477$	3866.82	+	3866.82i	0.371173	+	0.371173i
$478$		0			0
$479$	587.317			0.0560234			0.0280117	−	0.999608i	$-0.491082\pi$
$479$	587.317			0.0560234			0.0280117	+	0.999608i	$0.491082\pi$
$480$		0			0
$481$	−5951.28			−0.564148
$482$		0			0
$483$	−281.975	−	281.975i	−0.0265638	−	0.0265638i
$484$		0			0
$485$	7700.05	−	7700.05i	0.720910	−	0.720910i
$486$		0			0
$487$			8366.45i			0.778481i	0.921136	+	0.389240i	$0.127262\pi$
$487$			8366.45i			0.778481i	−0.921136	+	0.389240i	$0.872738\pi$
$488$		0			0
$489$		−	2157.10i		−	0.199483i
$490$		0			0
$491$	1529.30	−	1529.30i	0.140563	−	0.140563i	−0.633324	−	0.773887i	$-0.718310\pi$
$491$	1529.30	−	1529.30i	0.140563	−	0.140563i	0.773887	+	0.633324i	$0.218310\pi$
$492$		0			0
$493$	4788.09	+	4788.09i	0.437413	+	0.437413i
$494$		0			0
$495$	−19235.0			−1.74656
$496$		0			0
$497$	−1212.03			−0.109390
$498$		0			0
$499$	11364.5	+	11364.5i	1.01952	+	1.01952i	0.999806	+	0.0197191i	$0.00627718\pi$
$499$	11364.5	+	11364.5i	1.01952	+	1.01952i	0.0197191	+	0.999806i	$0.493723\pi$
$500$		0			0
$501$	−599.681	+	599.681i	−0.0534766	+	0.0534766i
$502$		0			0
$503$			12570.2i			1.11427i	0.830421	+	0.557137i	$0.188100\pi$
$503$			12570.2i			1.11427i	−0.830421	+	0.557137i	$0.811900\pi$
$504$		0			0
$505$			26.1326i			0.00230274i
$506$		0			0
$507$	−233.738	+	233.738i	−0.0204747	+	0.0204747i
$508$		0			0
$509$	−11880.4	−	11880.4i	−1.03456	−	1.03456i	−0.999381	−	0.0351750i	$-0.988801\pi$
$509$	−11880.4	−	11880.4i	−1.03456	−	1.03456i	−0.0351750	−	0.999381i	$-0.511199\pi$
$510$		0			0
$511$	693.968			0.0600770
$512$		0			0
$513$	1555.38			0.133863
$514$		0			0
$515$	−11419.8	−	11419.8i	−0.977122	−	0.977122i
$516$		0			0
$517$	−22074.8	+	22074.8i	−1.87785	+	1.87785i
$518$		0			0
$519$			1170.87i			0.0990283i
$520$		0			0
$521$		−	6612.98i		−	0.556085i	−0.960569	−	0.278042i	$-0.910314\pi$
$521$		−	6612.98i		−	0.556085i	0.960569	−	0.278042i	$-0.0896856\pi$
$522$		0			0
$523$	5129.30	−	5129.30i	0.428850	−	0.428850i	−0.459387	−	0.888236i	$-0.651931\pi$
$523$	5129.30	−	5129.30i	0.428850	−	0.428850i	0.888236	+	0.459387i	$0.151931\pi$
$524$		0			0
$525$	20.8858	+	20.8858i	0.00173625	+	0.00173625i
$526$		0			0
$527$	13679.3			1.13070
$528$		0			0
$529$	−7282.60			−0.598553
$530$		0			0
$531$	−7360.75	−	7360.75i	−0.601562	−	0.601562i
$532$		0			0
$533$	3703.53	−	3703.53i	0.300972	−	0.300972i
$534$		0			0
$535$		−	13515.5i		−	1.09220i
$536$		0			0
$537$			644.849i			0.0518199i
$538$		0			0
$539$	−15188.1	+	15188.1i	−1.21372	+	1.21372i
$540$		0			0
$541$	10968.5	+	10968.5i	0.871672	+	0.871672i	0.992655	−	0.120983i	$-0.0386047\pi$
$541$	10968.5	+	10968.5i	0.871672	+	0.871672i	−0.120983	+	0.992655i	$0.538605\pi$
$542$		0			0
$543$	3962.57			0.313168
$544$		0			0
$545$	8765.44			0.688936
$546$		0			0
$547$	13088.8	+	13088.8i	1.02311	+	1.02311i	0.999727	+	0.0233784i	$0.00744226\pi$
$547$	13088.8	+	13088.8i	1.02311	+	1.02311i	0.0233784	+	0.999727i	$0.492558\pi$
$548$		0			0
$549$	5896.63	−	5896.63i	0.458401	−	0.458401i
$550$		0			0
$551$		−	2568.12i		−	0.198558i
$552$		0			0
$553$		−	863.469i		−	0.0663986i
$554$		0			0
$555$	−1046.64	+	1046.64i	−0.0800491	+	0.0800491i
$556$		0			0
$557$	−5049.87	−	5049.87i	−0.384147	−	0.384147i	0.488447	−	0.872594i	$-0.337564\pi$
$557$	−5049.87	−	5049.87i	−0.384147	−	0.384147i	−0.872594	+	0.488447i	$0.837564\pi$
$558$		0			0
$559$	2228.98			0.168651
$560$		0			0
$561$	4962.18			0.373446
$562$		0			0
$563$	−3249.06	−	3249.06i	−0.243217	−	0.243217i	0.574962	−	0.818180i	$-0.305017\pi$
$563$	−3249.06	−	3249.06i	−0.243217	−	0.243217i	−0.818180	+	0.574962i	$0.805017\pi$
$564$		0			0
$565$	553.338	−	553.338i	0.0412019	−	0.0412019i
$566$		0			0
$567$		−	1703.30i		−	0.126159i
$568$		0			0
$569$			2806.05i			0.206741i	0.994643	+	0.103371i	$0.0329628\pi$
$569$			2806.05i			0.206741i	−0.994643	+	0.103371i	$0.967037\pi$
$570$		0			0
$571$	−12038.8	+	12038.8i	−0.882324	+	0.882324i	−0.993770	−	0.111446i	$-0.964452\pi$
$571$	−12038.8	+	12038.8i	−0.882324	+	0.882324i	0.111446	+	0.993770i	$0.464452\pi$
$572$		0			0
$573$	−2434.08	−	2434.08i	−0.177461	−	0.177461i
$574$		0			0
$575$	1440.62			0.104484
$576$		0			0
$577$	7206.84			0.519973			0.259987	−	0.965612i	$-0.416282\pi$
$577$	7206.84			0.519973			0.259987	+	0.965612i	$0.416282\pi$
$578$		0			0
$579$	2158.76	+	2158.76i	0.154948	+	0.154948i
$580$		0			0
$581$	1506.57	−	1506.57i	0.107578	−	0.107578i
$582$		0			0
$583$		−	13526.6i		−	0.960918i
$584$		0			0
$585$		−	15056.1i		−	1.06409i
$586$		0			0
$587$	10377.0	−	10377.0i	0.729647	−	0.729647i	−0.240903	−	0.970549i	$-0.577443\pi$
$587$	10377.0	−	10377.0i	0.729647	−	0.729647i	0.970549	+	0.240903i	$0.0774435\pi$
$588$		0			0
$589$	−3668.48	−	3668.48i	−0.256633	−	0.256633i
$590$		0			0
$591$	−2435.33			−0.169503
$592$		0			0
$593$	−4758.60			−0.329531			−0.164766	−	0.986333i	$-0.552687\pi$
$593$	−4758.60			−0.329531			−0.164766	+	0.986333i	$0.552687\pi$
$594$		0			0
$595$	1593.32	+	1593.32i	0.109781	+	0.109781i
$596$		0			0
$597$	565.414	−	565.414i	0.0387619	−	0.0387619i
$598$		0			0
$599$		−	14256.4i		−	0.972455i	−0.873832	−	0.486227i	$-0.838373\pi$
$599$		−	14256.4i		−	0.972455i	0.873832	−	0.486227i	$-0.161627\pi$
$600$		0			0
$601$			10385.2i			0.704862i	0.935838	+	0.352431i	$0.114645\pi$
$601$			10385.2i			0.704862i	−0.935838	+	0.352431i	$0.885355\pi$
$602$		0			0
$603$	3597.68	−	3597.68i	0.242966	−	0.242966i
$604$		0			0
$605$	22694.5	+	22694.5i	1.52506	+	1.52506i
$606$		0			0
$607$	16243.6			1.08618			0.543088	−	0.839676i	$-0.317255\pi$
$607$	16243.6			1.08618			0.543088	+	0.839676i	$0.317255\pi$
$608$		0			0
$609$	267.064			0.0177701
$610$		0			0
$611$	−17279.0	−	17279.0i	−1.14408	−	1.14408i
$612$		0			0
$613$	500.502	−	500.502i	0.0329773	−	0.0329773i	−0.690426	−	0.723403i	$-0.742577\pi$
$613$	500.502	−	500.502i	0.0329773	−	0.0329773i	0.723403	+	0.690426i	$0.242577\pi$
$614$		0			0
$615$		−	1302.66i		−	0.0854121i
$616$		0			0
$617$			11575.9i			0.755316i	0.925945	+	0.377658i	$0.123271\pi$
$617$			11575.9i			0.755316i	−0.925945	+	0.377658i	$0.876729\pi$
$618$		0			0
$619$	18356.1	−	18356.1i	1.19191	−	1.19191i	0.215380	−	0.976530i	$-0.430901\pi$
$619$	18356.1	−	18356.1i	1.19191	−	1.19191i	0.976530	−	0.215380i	$-0.0690992\pi$
$620$		0			0
$621$	5578.34	+	5578.34i	0.360469	+	0.360469i
$622$		0			0
$623$	−2315.98			−0.148937
$624$		0			0
$625$	16809.5			1.07581
$626$		0			0
$627$	−1330.75	−	1330.75i	−0.0847607	−	0.0847607i
$628$		0			0
$629$	−6094.66	+	6094.66i	−0.386343	+	0.386343i
$630$		0			0
$631$			10224.8i			0.645079i	0.946556	+	0.322539i	$0.104537\pi$
$631$			10224.8i			0.645079i	−0.946556	+	0.322539i	$0.895463\pi$
$632$		0			0
$633$		−	3370.88i		−	0.211660i
$634$		0			0
$635$	15658.7	−	15658.7i	0.978578	−	0.978578i
$636$		0			0
$637$	−11888.4	−	11888.4i	−0.739461	−	0.739461i
$638$		0			0
$639$	11729.0			0.726125
$640$		0			0
$641$	19804.4			1.22032			0.610162	−	0.792277i	$-0.291104\pi$
$641$	19804.4			1.22032			0.610162	+	0.792277i	$0.291104\pi$
$642$		0			0
$643$	15680.7	+	15680.7i	0.961723	+	0.961723i	0.999294	−	0.0375712i	$-0.0119621\pi$
$643$	15680.7	+	15680.7i	0.961723	+	0.961723i	−0.0375712	+	0.999294i	$0.511962\pi$
$644$		0			0
$645$	392.006	−	392.006i	0.0239306	−	0.0239306i
$646$		0			0
$647$			9232.26i			0.560985i	0.959856	+	0.280493i	$0.0904978\pi$
$647$			9232.26i			0.560985i	−0.959856	+	0.280493i	$0.909502\pi$
$648$		0			0
$649$			25748.8i			1.55736i
$650$		0			0
$651$	381.492	−	381.492i	0.0229675	−	0.0229675i
$652$		0			0
$653$	19697.9	+	19697.9i	1.18046	+	1.18046i	0.979626	+	0.200833i	$0.0643648\pi$
$653$	19697.9	+	19697.9i	1.18046	+	1.18046i	0.200833	+	0.979626i	$0.435635\pi$
$654$		0			0
$655$	−15109.8			−0.901355
$656$		0			0
$657$	−6715.66			−0.398786
$658$		0			0
$659$	3888.06	+	3888.06i	0.229829	+	0.229829i	0.812621	−	0.582792i	$-0.198040\pi$
$659$	3888.06	+	3888.06i	0.229829	+	0.229829i	−0.582792	+	0.812621i	$0.698040\pi$
$660$		0			0
$661$	8110.20	−	8110.20i	0.477232	−	0.477232i	−0.427013	−	0.904245i	$-0.640434\pi$
$661$	8110.20	−	8110.20i	0.477232	−	0.477232i	0.904245	+	0.427013i	$0.140434\pi$
$662$		0			0
$663$			3884.13i			0.227522i
$664$		0			0
$665$		−	854.587i		−	0.0498338i
$666$		0			0
$667$	9210.54	−	9210.54i	0.534683	−	0.534683i
$668$		0			0
$669$	270.966	+	270.966i	0.0156594	+	0.0156594i
$670$		0			0
$671$	−20627.1			−1.18674
$672$		0			0
$673$	−28428.2			−1.62827			−0.814135	−	0.580676i	$-0.802788\pi$
$673$	−28428.2			−1.62827			−0.814135	+	0.580676i	$0.802788\pi$
$674$		0			0
$675$	−413.186	−	413.186i	−0.0235608	−	0.0235608i
$676$		0			0
$677$	16967.4	−	16967.4i	0.963235	−	0.963235i	−0.0361128	−	0.999348i	$-0.511498\pi$
$677$	16967.4	−	16967.4i	0.963235	−	0.963235i	0.999348	+	0.0361128i	$0.0114975\pi$
$678$		0			0
$679$		−	2500.92i		−	0.141350i
$680$		0			0
$681$			5229.92i			0.294289i
$682$		0			0
$683$	−9550.16	+	9550.16i	−0.535032	+	0.535032i	−0.922066	−	0.387034i	$-0.873500\pi$
$683$	−9550.16	+	9550.16i	−0.535032	+	0.535032i	0.387034	+	0.922066i	$0.373500\pi$
$684$		0			0
$685$	−3925.66	−	3925.66i	−0.218966	−	0.218966i
$686$		0			0
$687$	2164.42			0.120201
$688$		0			0
$689$	10587.9			0.585439
$690$		0			0
$691$	−20859.7	−	20859.7i	−1.14839	−	1.14839i	−0.986868	−	0.161527i	$-0.948358\pi$
$691$	−20859.7	−	20859.7i	−1.14839	−	1.14839i	−0.161527	−	0.986868i	$-0.551642\pi$
$692$		0			0
$693$	−3123.70	+	3123.70i	−0.171226	+	0.171226i
$694$		0			0
$695$		−	24906.1i		−	1.35934i
$696$		0			0
$697$		−	7585.52i		−	0.412227i
$698$		0			0
$699$	701.137	−	701.137i	0.0379391	−	0.0379391i
$700$		0			0
$701$	−23495.4	−	23495.4i	−1.26592	−	1.26592i	−0.948178	−	0.317740i	$-0.897076\pi$
$701$	−23495.4	−	23495.4i	−1.26592	−	1.26592i	−0.317740	−	0.948178i	$-0.602924\pi$
$702$		0			0
$703$	3268.91			0.175376
$704$		0			0
$705$	−6077.62			−0.324676
$706$		0			0
$707$	4.24384	+	4.24384i	0.000225751	+	0.000225751i
$708$		0			0
$709$	−4559.45	+	4559.45i	−0.241515	+	0.241515i	−0.817477	−	0.575962i	$-0.804628\pi$
$709$	−4559.45	+	4559.45i	−0.241515	+	0.241515i	0.575962	+	0.817477i	$0.304628\pi$
$710$		0			0
$711$			8355.95i			0.440749i
$712$		0			0
$713$		−	26313.9i		−	1.38214i
$714$		0			0
$715$	−26334.1	+	26334.1i	−1.37740	+	1.37740i
$716$		0			0
$717$	599.724	+	599.724i	0.0312372	+	0.0312372i
$718$		0			0
$719$	6494.67			0.336871			0.168436	−	0.985713i	$-0.446128\pi$
$719$	6494.67			0.336871			0.168436	+	0.985713i	$0.446128\pi$
$720$		0			0
$721$	−3709.08			−0.191586
$722$		0			0
$723$	1096.58	+	1096.58i	0.0564069	+	0.0564069i
$724$		0			0
$725$	−682.221	+	682.221i	−0.0349476	+	0.0349476i
$726$		0			0
$727$			24866.4i			1.26856i	0.773103	+	0.634280i	$0.218704\pi$
$727$			24866.4i			1.26856i	−0.773103	+	0.634280i	$0.781296\pi$
$728$		0			0
$729$			14848.5i			0.754384i
$730$		0			0
$731$	2282.68	−	2282.68i	0.115497	−	0.115497i
$732$		0			0
$733$	14914.3	+	14914.3i	0.751533	+	0.751533i	0.974765	−	0.223232i	$-0.0716607\pi$
$733$	14914.3	+	14914.3i	0.751533	+	0.751533i	−0.223232	+	0.974765i	$0.571661\pi$
$734$		0			0
$735$	−4181.58			−0.209850
$736$		0			0
$737$	−12585.1			−0.629008
$738$		0			0
$739$	8451.86	+	8451.86i	0.420713	+	0.420713i	0.885449	−	0.464737i	$-0.153851\pi$
$739$	8451.86	+	8451.86i	0.420713	+	0.420713i	−0.464737	+	0.885449i	$0.653851\pi$
$740$		0			0
$741$	1041.64	−	1041.64i	0.0516404	−	0.0516404i
$742$		0			0
$743$			5622.43i			0.277614i	0.990319	+	0.138807i	$0.0443267\pi$
$743$			5622.43i			0.277614i	−0.990319	+	0.138807i	$0.955673\pi$
$744$		0			0
$745$		−	6175.21i		−	0.303681i
$746$		0			0
$747$	−14579.3	+	14579.3i	−0.714095	+	0.714095i
$748$		0			0
$749$	−2194.88	−	2194.88i	−0.107075	−	0.107075i
$750$		0			0
$751$	32314.9			1.57016			0.785079	−	0.619396i	$-0.212622\pi$
$751$	32314.9			1.57016			0.785079	+	0.619396i	$0.212622\pi$
$752$		0			0
$753$	−5418.58			−0.262236
$754$		0			0
$755$	24657.2	+	24657.2i	1.18857	+	1.18857i
$756$		0			0
$757$	−12692.8	+	12692.8i	−0.609418	+	0.609418i	−0.942794	−	0.333376i	$-0.891812\pi$
$757$	−12692.8	+	12692.8i	−0.609418	+	0.609418i	0.333376	+	0.942794i	$0.391812\pi$
$758$		0			0
$759$		−	9545.42i		−	0.456491i
$760$		0			0
$761$		−	13108.2i		−	0.624404i	−0.950016	−	0.312202i	$-0.898933\pi$
$761$		−	13108.2i		−	0.624404i	0.950016	−	0.312202i	$-0.101067\pi$
$762$		0			0
$763$	1423.48	−	1423.48i	0.0675404	−	0.0675404i
$764$		0			0
$765$	−15418.8	−	15418.8i	−0.728718	−	0.728718i
$766$		0			0
$767$	−20154.8			−0.948822
$768$		0			0
$769$	23661.2			1.10955			0.554776	−	0.832000i	$-0.312804\pi$
$769$	23661.2			1.10955			0.554776	+	0.832000i	$0.312804\pi$
$770$		0			0
$771$	−3563.56	−	3563.56i	−0.166457	−	0.166457i
$772$		0			0
$773$	−21370.5	+	21370.5i	−0.994362	+	0.994362i	−0.999984	−	0.00562228i	$-0.998210\pi$
$773$	−21370.5	+	21370.5i	−0.994362	+	0.994362i	0.00562228	+	0.999984i	$0.498210\pi$
$774$		0			0
$775$			1949.06i			0.0903384i
$776$		0			0
$777$			339.940i			0.0156954i
$778$		0			0
$779$	−2034.27	+	2034.27i	−0.0935627	+	0.0935627i
$780$		0			0
$781$	−20514.8	−	20514.8i	−0.939921	−	0.939921i
$782$		0			0
$783$	−5283.35			−0.241139
$784$		0			0
$785$	−24825.8			−1.12875
$786$		0			0
$787$	−20890.9	−	20890.9i	−0.946226	−	0.946226i	0.0524002	−	0.998626i	$-0.483313\pi$
$787$	−20890.9	−	20890.9i	−0.946226	−	0.946226i	−0.998626	+	0.0524002i	$0.983313\pi$
$788$		0			0
$789$	−2245.97	+	2245.97i	−0.101342	+	0.101342i
$790$		0			0
$791$		−	179.720i		−	0.00807853i
$792$		0			0
$793$		−	16145.8i		−	0.723020i
$794$		0			0
$795$	1862.07	−	1862.07i	0.0830702	−	0.0830702i
$796$		0			0
$797$	6834.83	+	6834.83i	0.303767

Overview	Random
Universe	Knowledge

Degree 1	Degree 2
Degree 3	Degree 4
$\zeta$ zeros

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:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	128.e (of order \(4\), degree \(2\), not minimal)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

Related objects

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