LMFDB - Embedded newform 128.4.g.a.113.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,4,Mod(17,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("128.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	128.g (of order $8$, degree $4$, 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:	$7.55224448073$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$11$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			113.6
Character	$\chi$	$=$	128.113
Dual form			128.4.g.a.17.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.477813 + 1.15354i) q^{3} +(-16.3468 - 6.77105i) q^{5} +(18.0222 + 18.0222i) q^{7} +(17.9895 - 17.9895i) q^{9} +O(q^{10})$	\(q+(0.477813 + 1.15354i) q^{3} +(-16.3468 - 6.77105i) q^{5} +(18.0222 + 18.0222i) q^{7} +(17.9895 - 17.9895i) q^{9} +(20.1053 - 48.5384i) q^{11} +(37.8086 - 15.6609i) q^{13} -22.0920i q^{15} -53.0615i q^{17} +(32.4427 - 13.4382i) q^{19} +(-12.1781 + 29.4006i) q^{21} +(-32.1343 + 32.1343i) q^{23} +(132.981 + 132.981i) q^{25} +(60.4929 + 25.0570i) q^{27} +(-52.0634 - 125.692i) q^{29} +53.3354 q^{31} +65.5976 q^{33} +(-172.576 - 416.634i) q^{35} +(-57.3789 - 23.7671i) q^{37} +(36.1309 + 36.1309i) q^{39} +(240.383 - 240.383i) q^{41} +(-56.3244 + 135.979i) q^{43} +(-415.879 + 172.263i) q^{45} +314.904i q^{47} +306.601i q^{49} +(61.2086 - 25.3534i) q^{51} +(-177.524 + 428.580i) q^{53} +(-657.312 + 657.312i) q^{55} +(31.0031 + 31.0031i) q^{57} +(133.963 + 55.4894i) q^{59} +(-191.454 - 462.211i) q^{61} +648.422 q^{63} -724.089 q^{65} +(55.4766 + 133.932i) q^{67} +(-52.4224 - 21.7141i) q^{69} +(-191.132 - 191.132i) q^{71} +(-175.452 + 175.452i) q^{73} +(-89.8593 + 216.940i) q^{75} +(1237.11 - 512.428i) q^{77} -1222.08i q^{79} -605.154i q^{81} +(-896.581 + 371.376i) q^{83} +(-359.282 + 867.384i) q^{85} +(120.115 - 120.115i) q^{87} +(883.293 + 883.293i) q^{89} +(963.639 + 399.152i) q^{91} +(25.4843 + 61.5246i) q^{93} -621.324 q^{95} -682.976 q^{97} +(-511.499 - 1234.87i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 44 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	$ 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 4 q^{13} + 4 q^{19} - 4 q^{21} - 324 q^{23} - 4 q^{25} + 268 q^{27} - 4 q^{29} + 752 q^{31} - 8 q^{33} + 460 q^{35} - 4 q^{37} - 596 q^{39} - 4 q^{41} - 804 q^{43} + 104 q^{45} + 1384 q^{51} + 748 q^{53} + 292 q^{55} - 4 q^{57} - 1372 q^{59} - 1828 q^{61} - 2512 q^{63} - 8 q^{65} - 2036 q^{67} - 1060 q^{69} - 220 q^{71} - 4 q^{73} + 1712 q^{75} + 1900 q^{77} - 2436 q^{83} + 496 q^{85} + 1292 q^{87} - 4 q^{89} + 3604 q^{91} - 112 q^{93} + 6088 q^{95} - 8 q^{97} + 5424 q^{99}+O(q^{100}) $ 44 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9 + 4 * q^11 - 4 * q^13 + 4 * q^19 - 4 * q^21 - 324 * q^23 - 4 * q^25 + 268 * q^27 - 4 * q^29 + 752 * q^31 - 8 * q^33 + 460 * q^35 - 4 * q^37 - 596 * q^39 - 4 * q^41 - 804 * q^43 + 104 * q^45 + 1384 * q^51 + 748 * q^53 + 292 * q^55 - 4 * q^57 - 1372 * q^59 - 1828 * q^61 - 2512 * q^63 - 8 * q^65 - 2036 * q^67 - 1060 * q^69 - 220 * q^71 - 4 * q^73 + 1712 * q^75 + 1900 * q^77 - 2436 * q^83 + 496 * q^85 + 1292 * q^87 - 4 * q^89 + 3604 * q^91 - 112 * q^93 + 6088 * q^95 - 8 * q^97 + 5424 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$1$

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
$3$	0.477813	+	1.15354i	0.0919551	+	0.221999i	0.963165	−	0.268912i	$-0.0866640\pi$
$3$	0.477813	+	1.15354i	0.0919551	+	0.221999i	−0.871210	+	0.490911i	$0.836664\pi$
$4$		0			0
$5$	−16.3468	−	6.77105i	−1.46210	−	0.605621i	−0.497057	−	0.867718i	$-0.665586\pi$
$5$	−16.3468	−	6.77105i	−1.46210	−	0.605621i	−0.965042	+	0.262096i	$0.915586\pi$
$6$		0			0
$7$	18.0222	+	18.0222i	0.973108	+	0.973108i	0.999648	−	0.0265394i	$-0.00844875\pi$
$7$	18.0222	+	18.0222i	0.973108	+	0.973108i	−0.0265394	+	0.999648i	$0.508449\pi$
$8$		0			0
$9$	17.9895	−	17.9895i	0.666279	−	0.666279i
$10$		0			0
$11$	20.1053	−	48.5384i	0.551088	−	1.33044i	−0.365575	−	0.930782i	$-0.619128\pi$
$11$	20.1053	−	48.5384i	0.551088	−	1.33044i	0.916663	−	0.399662i	$-0.130872\pi$
$12$		0			0
$13$	37.8086	−	15.6609i	0.806633	−	0.334118i	0.0590233	−	0.998257i	$-0.481201\pi$
$13$	37.8086	−	15.6609i	0.806633	−	0.334118i	0.747610	+	0.664138i	$0.231201\pi$
$14$		0			0
$15$		−	22.0920i		−	0.380275i
$16$		0			0
$17$		−	53.0615i		−	0.757018i	−0.925598	−	0.378509i	$-0.876437\pi$
$17$		−	53.0615i		−	0.757018i	0.925598	−	0.378509i	$-0.123563\pi$
$18$		0			0
$19$	32.4427	−	13.4382i	0.391730	−	0.162260i	−0.178120	−	0.984009i	$-0.557001\pi$
$19$	32.4427	−	13.4382i	0.391730	−	0.162260i	0.569850	+	0.821749i	$0.307001\pi$
$20$		0			0
$21$	−12.1781	+	29.4006i	−0.126547	+	0.305512i
$22$		0			0
$23$	−32.1343	+	32.1343i	−0.291324	+	0.291324i	−0.837603	−	0.546279i	$-0.816044\pi$
$23$	−32.1343	+	32.1343i	−0.291324	+	0.291324i	0.546279	+	0.837603i	$0.316044\pi$
$24$		0			0
$25$	132.981	+	132.981i	1.06385	+	1.06385i
$26$		0			0
$27$	60.4929	+	25.0570i	0.431180	+	0.178601i
$28$		0			0
$29$	−52.0634	−	125.692i	−0.333377	−	0.804842i	−0.998320	−	0.0579483i	$-0.981544\pi$
$29$	−52.0634	−	125.692i	−0.333377	−	0.804842i	0.664943	−	0.746894i	$-0.268456\pi$
$30$		0			0
$31$	53.3354			0.309010			0.154505	−	0.987992i	$-0.450622\pi$
$31$	53.3354			0.309010			0.154505	+	0.987992i	$0.450622\pi$
$32$		0			0
$33$	65.5976			0.346033
$34$		0			0
$35$	−172.576	−	416.634i	−0.833446	−	2.01212i
$36$		0			0
$37$	−57.3789	−	23.7671i	−0.254947	−	0.105602i	0.251550	−	0.967844i	$-0.419060\pi$
$37$	−57.3789	−	23.7671i	−0.254947	−	0.105602i	−0.506497	+	0.862242i	$0.669060\pi$
$38$		0			0
$39$	36.1309	+	36.1309i	0.148348	+	0.148348i
$40$		0			0
$41$	240.383	−	240.383i	0.915647	−	0.915647i	−0.0810624	−	0.996709i	$-0.525831\pi$
$41$	240.383	−	240.383i	0.915647	−	0.915647i	0.996709	+	0.0810624i	$0.0258313\pi$
$42$		0			0
$43$	−56.3244	+	135.979i	−0.199753	+	0.482247i	−0.991736	−	0.128297i	$-0.959049\pi$
$43$	−56.3244	+	135.979i	−0.199753	+	0.482247i	0.791983	+	0.610544i	$0.209049\pi$
$44$		0			0
$45$	−415.879	+	172.263i	−1.37768	+	0.570653i
$46$		0			0
$47$			314.904i			0.977309i	0.872477	+	0.488655i	$0.162512\pi$
$47$			314.904i			0.977309i	−0.872477	+	0.488655i	$0.837488\pi$
$48$		0			0
$49$			306.601i			0.893880i
$50$		0			0
$51$	61.2086	−	25.3534i	0.168057	−	0.0696116i
$52$		0			0
$53$	−177.524	+	428.580i	−0.460089	+	1.11075i	0.508271	+	0.861197i	$0.330285\pi$
$53$	−177.524	+	428.580i	−0.460089	+	1.11075i	−0.968360	+	0.249557i	$0.919715\pi$
$54$		0			0
$55$	−657.312	+	657.312i	−1.61149	+	1.61149i
$56$		0			0
$57$	31.0031	+	31.0031i	0.0720431	+	0.0720431i
$58$		0			0
$59$	133.963	+	55.4894i	0.295602	+	0.122442i	0.525556	−	0.850759i	$-0.323857\pi$
$59$	133.963	+	55.4894i	0.295602	+	0.122442i	−0.229954	+	0.973202i	$0.573857\pi$
$60$		0			0
$61$	−191.454	−	462.211i	−0.401855	−	0.970164i	−0.987216	−	0.159391i	$-0.949047\pi$
$61$	−191.454	−	462.211i	−0.401855	−	0.970164i	0.585360	−	0.810773i	$-0.300953\pi$
$62$		0			0
$63$	648.422			1.29672
$64$		0			0
$65$	−724.089			−1.38173
$66$		0			0
$67$	55.4766	+	133.932i	0.101157	+	0.244216i	0.966353	−	0.257218i	$-0.0828060\pi$
$67$	55.4766	+	133.932i	0.101157	+	0.244216i	−0.865196	+	0.501434i	$0.832806\pi$
$68$		0			0
$69$	−52.4224	−	21.7141i	−0.0914625	−	0.0378850i
$70$		0			0
$71$	−191.132	−	191.132i	−0.319482	−	0.319482i	0.529086	−	0.848568i	$-0.322535\pi$
$71$	−191.132	−	191.132i	−0.319482	−	0.319482i	−0.848568	+	0.529086i	$0.822535\pi$
$72$		0			0
$73$	−175.452	+	175.452i	−0.281302	+	0.281302i	−0.833628	−	0.552326i	$-0.813740\pi$
$73$	−175.452	+	175.452i	−0.281302	+	0.281302i	0.552326	+	0.833628i	$0.313740\pi$
$74$		0			0
$75$	−89.8593	+	216.940i	−0.138347	+	0.334000i
$76$		0			0
$77$	1237.11	−	512.428i	1.83093	−	0.758398i
$78$		0			0
$79$		−	1222.08i		−	1.74043i	−0.492668	−	0.870217i	$-0.663978\pi$
$79$		−	1222.08i		−	1.74043i	0.492668	−	0.870217i	$-0.336022\pi$
$80$		0			0
$81$		−	605.154i		−	0.830116i
$82$		0			0
$83$	−896.581	+	371.376i	−1.18569	+	0.491131i	−0.886351	−	0.463015i	$-0.846768\pi$
$83$	−896.581	+	371.376i	−1.18569	+	0.491131i	−0.299344	+	0.954145i	$0.596768\pi$
$84$		0			0
$85$	−359.282	+	867.384i	−0.458466	+	1.10684i
$86$		0			0
$87$	120.115	−	120.115i	0.148019	−	0.148019i
$88$		0			0
$89$	883.293	+	883.293i	1.05201	+	1.05201i	0.998571	+	0.0534390i	$0.0170183\pi$
$89$	883.293	+	883.293i	1.05201	+	1.05201i	0.0534390	+	0.998571i	$0.482982\pi$
$90$		0			0
$91$	963.639	+	399.152i	1.11007	+	0.459808i
$92$		0			0
$93$	25.4843	+	61.5246i	0.0284151	+	0.0686001i
$94$		0			0
$95$	−621.324			−0.671016
$96$		0			0
$97$	−682.976			−0.714904			−0.357452	−	0.933932i	$-0.616354\pi$
$97$	−682.976			−0.714904			−0.357452	+	0.933932i	$0.616354\pi$
$98$		0			0
$99$	−511.499	−	1234.87i	−0.519268	−	1.25362i
$100$		0			0
$101$	919.967	+	381.063i	0.906338	+	0.375417i	0.786654	−	0.617395i	$-0.211812\pi$
$101$	919.967	+	381.063i	0.906338	+	0.375417i	0.119684	+	0.992812i	$0.461812\pi$
$102$		0			0
$103$	188.265	+	188.265i	0.180100	+	0.180100i	0.791400	−	0.611299i	$-0.209353\pi$
$103$	188.265	+	188.265i	0.180100	+	0.180100i	−0.611299	+	0.791400i	$0.709353\pi$
$104$		0			0
$105$	398.146	−	398.146i	0.370049	−	0.370049i
$106$		0			0
$107$	48.3932	−	116.832i	0.0437229	−	0.105556i	−0.900509	−	0.434837i	$-0.856806\pi$
$107$	48.3932	−	116.832i	0.0437229	−	0.105556i	0.944232	+	0.329280i	$0.106806\pi$
$108$		0			0
$109$	394.289	−	163.320i	0.346477	−	0.143516i	−0.202657	−	0.979250i	$-0.564958\pi$
$109$	394.289	−	163.320i	0.346477	−	0.143516i	0.549134	+	0.835734i	$0.314958\pi$
$110$		0			0
$111$		−	77.5452i		−	0.0663087i
$112$		0			0
$113$		−	914.060i		−	0.760952i	−0.924791	−	0.380476i	$-0.875760\pi$
$113$		−	914.060i		−	0.760952i	0.924791	−	0.380476i	$-0.124240\pi$
$114$		0			0
$115$	742.874	−	307.709i	0.602377	−	0.249513i
$116$		0			0
$117$	398.428	−	961.891i	0.314827	−	0.760059i
$118$		0			0
$119$	956.286	−	956.286i	0.736660	−	0.736660i
$120$		0			0
$121$	−1010.60	−	1010.60i	−0.759276	−	0.759276i
$122$		0			0
$123$	392.150	+	162.434i	0.287471	+	0.119074i
$124$		0			0
$125$	−427.009	−	1030.89i	−0.305543	−	0.737645i
$126$		0			0
$127$	2159.36			1.50876			0.754379	−	0.656439i	$-0.227938\pi$
$127$	2159.36			1.50876			0.754379	+	0.656439i	$0.227938\pi$
$128$		0			0
$129$	−183.770			−0.125427
$130$		0			0
$131$	896.246	+	2163.73i	0.597751	+	1.44310i	0.875867	+	0.482552i	$0.160290\pi$
$131$	896.246	+	2163.73i	0.597751	+	1.44310i	−0.278116	+	0.960547i	$0.589710\pi$
$132$		0			0
$133$	826.876	+	342.503i	0.539092	+	0.223299i
$134$		0			0
$135$	−819.201	−	819.201i	−0.522264	−	0.522264i
$136$		0			0
$137$	−118.307	+	118.307i	−0.0737786	+	0.0737786i	−0.743033	−	0.669255i	$-0.766614\pi$
$137$	−118.307	+	118.307i	−0.0737786	+	0.0737786i	0.669255	+	0.743033i	$0.266614\pi$
$138$		0			0
$139$	−924.203	+	2231.22i	−0.563956	+	1.36151i	0.342623	+	0.939473i	$0.388685\pi$
$139$	−924.203	+	2231.22i	−0.563956	+	1.36151i	−0.906579	+	0.422037i	$0.861315\pi$
$140$		0			0
$141$	−363.255	+	150.465i	−0.216962	+	0.0898686i
$142$		0			0
$143$		−	2150.04i		−	1.25731i
$144$		0			0
$145$			2407.18i			1.37866i
$146$		0			0
$147$	−353.677	+	146.498i	−0.198441	+	0.0821968i
$148$		0			0
$149$	366.708	−	885.311i	0.201623	−	0.486762i	−0.790434	−	0.612547i	$-0.790145\pi$
$149$	366.708	−	885.311i	0.201623	−	0.486762i	0.992058	+	0.125785i	$0.0401450\pi$
$150$		0			0
$151$	−1212.74	+	1212.74i	−0.653584	+	0.653584i	−0.953854	−	0.300270i	$-0.902923\pi$
$151$	−1212.74	+	1212.74i	−0.653584	+	0.653584i	0.300270	+	0.953854i	$0.402923\pi$
$152$		0			0
$153$	−954.551	−	954.551i	−0.504385	−	0.504385i
$154$		0			0
$155$	−871.861	−	361.137i	−0.451804	−	0.187143i
$156$		0			0
$157$	896.752	+	2164.95i	0.455851	+	1.10052i	0.970062	+	0.242858i	$0.0780848\pi$
$157$	896.752	+	2164.95i	0.455851	+	1.10052i	−0.514211	+	0.857664i	$0.671915\pi$
$158$		0			0
$159$	−579.208			−0.288894
$160$		0			0
$161$	−1158.26			−0.566980
$162$		0			0
$163$	−363.960	−	878.678i	−0.174893	−	0.422229i	0.811989	−	0.583673i	$-0.198385\pi$
$163$	−363.960	−	878.678i	−0.174893	−	0.422229i	−0.986882	+	0.161444i	$0.948385\pi$
$164$		0			0
$165$	−1072.31	−	444.165i	−0.505934	−	0.209565i
$166$		0			0
$167$	−800.950	−	800.950i	−0.371134	−	0.371134i	0.496756	−	0.867890i	$-0.334524\pi$
$167$	−800.950	−	800.950i	−0.371134	−	0.371134i	−0.867890	+	0.496756i	$0.834524\pi$
$168$		0			0
$169$	−369.282	+	369.282i	−0.168085	+	0.168085i
$170$		0			0
$171$	341.882	−	825.376i	0.152891	−	0.369112i
$172$		0			0
$173$	217.486	−	90.0857i	0.0955790	−	0.0395901i	−0.334382	−	0.942438i	$-0.608527\pi$
$173$	217.486	−	90.0857i	0.0955790	−	0.0395901i	0.429961	+	0.902848i	$0.358527\pi$
$174$		0			0
$175$			4793.23i			2.07048i
$176$		0			0
$177$			181.046i			0.0768826i
$178$		0			0
$179$	1959.23	−	811.539i	0.818099	−	0.338868i	0.0659185	−	0.997825i	$-0.479002\pi$
$179$	1959.23	−	811.539i	0.818099	−	0.338868i	0.752180	+	0.658957i	$0.229002\pi$
$180$		0			0
$181$	−468.260	+	1130.48i	−0.192295	+	0.464242i	−0.990392	−	0.138287i	$-0.955840\pi$
$181$	−468.260	+	1130.48i	−0.192295	+	0.464242i	0.798097	+	0.602529i	$0.205840\pi$
$182$		0			0
$183$	441.700	−	441.700i	0.178423	−	0.178423i
$184$		0			0
$185$	777.031	+	777.031i	0.308803	+	0.308803i
$186$		0			0
$187$	−2575.52	−	1066.82i	−1.00717	−	0.417183i
$188$		0			0
$189$	638.634	+	1541.80i	0.245787	+	0.593383i
$190$		0			0
$191$	−5115.66			−1.93799			−0.968996	−	0.247078i	$-0.920530\pi$
$191$	−5115.66			−1.93799			−0.968996	+	0.247078i	$0.920530\pi$
$192$		0			0
$193$	4101.82			1.52982			0.764910	−	0.644137i	$-0.222783\pi$
$193$	4101.82			1.52982			0.764910	+	0.644137i	$0.222783\pi$
$194$		0			0
$195$	−345.979	−	835.267i	−0.127057	−	0.306742i
$196$		0			0
$197$	−2365.10	−	979.657i	−0.855363	−	0.354303i	−0.0884706	−	0.996079i	$-0.528198\pi$
$197$	−2365.10	−	979.657i	−0.855363	−	0.354303i	−0.766892	+	0.641776i	$0.778198\pi$
$198$		0			0
$199$	3419.40	+	3419.40i	1.21807	+	1.21807i	0.968309	+	0.249757i	$0.0803506\pi$
$199$	3419.40	+	3419.40i	1.21807	+	1.21807i	0.249757	+	0.968309i	$0.419649\pi$
$200$		0			0
$201$	−127.989	+	127.989i	−0.0449138	+	0.0449138i
$202$		0			0
$203$	1326.95	−	3203.55i	0.458787	−	1.10761i
$204$		0			0
$205$	−5557.13	+	2301.84i	−1.89330	+	0.784231i
$206$		0			0
$207$			1156.16i			0.388206i
$208$		0			0
$209$		−	1844.90i		−	0.610594i
$210$		0			0
$211$	−4175.73	+	1729.64i	−1.36241	+	0.564330i	−0.939720	−	0.341944i	$-0.888915\pi$
$211$	−4175.73	+	1729.64i	−1.36241	+	0.564330i	−0.422692	+	0.906273i	$0.638915\pi$
$212$		0			0
$213$	129.154	−	311.805i	0.0415468	−	0.100303i
$214$		0			0
$215$	1841.44	−	1841.44i	0.584118	−	0.584118i
$216$		0			0
$217$	961.222	+	961.222i	0.300701	+	0.300701i
$218$		0			0
$219$	−286.224	−	118.558i	−0.0883160	−	0.0365817i
$220$		0			0
$221$	−830.988	−	2006.18i	−0.252934	−	0.610636i
$222$		0			0
$223$	−717.256			−0.215386			−0.107693	−	0.994184i	$-0.534346\pi$
$223$	−717.256			−0.215386			−0.107693	+	0.994184i	$0.534346\pi$
$224$		0			0
$225$	4784.54			1.41764
$226$		0			0
$227$	2316.16	+	5591.71i	0.677221	+	1.63496i	0.769056	+	0.639181i	$0.220727\pi$
$227$	2316.16	+	5591.71i	0.677221	+	1.63496i	−0.0918358	+	0.995774i	$0.529273\pi$
$228$		0			0
$229$	−197.065	−	81.6271i	−0.0568665	−	0.0235549i	0.354069	−	0.935219i	$-0.384798\pi$
$229$	−197.065	−	81.6271i	−0.0568665	−	0.0235549i	−0.410935	+	0.911664i	$0.634798\pi$
$230$		0			0
$231$	1182.21	+	1182.21i	0.336727	+	0.336727i
$232$		0			0
$233$	−4600.59	+	4600.59i	−1.29354	+	1.29354i	−0.360955	+	0.932583i	$0.617549\pi$
$233$	−4600.59	+	4600.59i	−1.29354	+	1.29354i	−0.932583	+	0.360955i	$0.882451\pi$
$234$		0			0
$235$	2132.23	−	5147.67i	0.591879	−	1.42892i
$236$		0			0
$237$	1409.72	−	583.924i	0.386375	−	0.160042i
$238$		0			0
$239$			1366.19i			0.369755i	0.982762	+	0.184878i	$0.0591889\pi$
$239$			1366.19i			0.369755i	−0.982762	+	0.184878i	$0.940811\pi$
$240$		0			0
$241$		−	1568.87i		−	0.419336i	−0.977773	−	0.209668i	$-0.932762\pi$
$241$		−	1568.87i		−	0.419336i	0.977773	−	0.209668i	$-0.0672382\pi$
$242$		0			0
$243$	2331.38	−	965.689i	0.615465	−	0.254934i
$244$		0			0
$245$	2076.01	−	5011.93i	0.541353	−	1.30694i
$246$		0			0
$247$	1016.16	−	1016.16i	0.261768	−	0.261768i
$248$		0			0
$249$	−856.796	−	856.796i	−0.218061	−	0.218061i
$250$		0			0
$251$	−1774.13	−	734.870i	−0.446144	−	0.184799i	0.148289	−	0.988944i	$-0.452623\pi$
$251$	−1774.13	−	734.870i	−0.446144	−	0.184799i	−0.594433	+	0.804145i	$0.702623\pi$
$252$		0			0
$253$	913.678	+	2205.81i	0.227045	+	0.548136i
$254$		0			0
$255$	−1172.23			−0.287875
$256$		0			0
$257$	805.660			0.195547			0.0977737	−	0.995209i	$-0.468828\pi$
$257$	805.660			0.195547			0.0977737	+	0.995209i	$0.468828\pi$
$258$		0			0
$259$	−605.759	−	1462.43i	−0.145328	−	0.350854i
$260$		0			0
$261$	−3197.74	−	1324.55i	−0.758371	−	0.314128i
$262$		0			0
$263$	−2159.44	−	2159.44i	−0.506300	−	0.506300i	0.407089	−	0.913389i	$-0.366544\pi$
$263$	−2159.44	−	2159.44i	−0.506300	−	0.506300i	−0.913389	+	0.407089i	$0.866544\pi$
$264$		0			0
$265$	5803.87	−	5803.87i	1.34539	−	1.34539i
$266$		0			0
$267$	−596.867	+	1440.96i	−0.136808	+	0.330283i
$268$		0			0
$269$	2403.35	−	995.499i	0.544738	−	0.225638i	−0.0933062	−	0.995637i	$-0.529744\pi$
$269$	2403.35	−	995.499i	0.544738	−	0.225638i	0.638045	+	0.769999i	$0.279744\pi$
$270$		0			0
$271$			363.916i			0.0815731i	0.999168	+	0.0407866i	$0.0129864\pi$
$271$			363.916i			0.0815731i	−0.999168	+	0.0407866i	$0.987014\pi$
$272$		0			0
$273$			1302.32i			0.288717i
$274$		0			0
$275$	9128.32	−	3781.08i	2.00167	−	0.829118i
$276$		0			0
$277$	236.874	−	571.865i	0.0513805	−	0.124043i	−0.896105	−	0.443842i	$-0.853615\pi$
$277$	236.874	−	571.865i	0.0513805	−	0.124043i	0.947486	+	0.319798i	$0.103615\pi$
$278$		0			0
$279$	959.479	−	959.479i	0.205887	−	0.205887i
$280$		0			0
$281$	−5905.54	−	5905.54i	−1.25372	−	1.25372i	−0.954040	−	0.299680i	$-0.903120\pi$
$281$	−5905.54	−	5905.54i	−1.25372	−	1.25372i	−0.299680	−	0.954040i	$-0.596880\pi$
$282$		0			0
$283$	2127.03	+	881.046i	0.446781	+	0.185063i	0.594719	−	0.803934i	$-0.297264\pi$
$283$	2127.03	+	881.046i	0.446781	+	0.185063i	−0.147938	+	0.988997i	$0.547264\pi$
$284$		0			0
$285$	−296.877	−	716.723i	−0.0617033	−	0.148965i
$286$		0			0
$287$	8664.47			1.78205
$288$		0			0
$289$	2097.48			0.426924
$290$		0			0
$291$	−326.334	−	787.841i	−0.0657391	−	0.158708i
$292$		0			0
$293$	1783.51	+	738.755i	0.355610	+	0.147299i	0.553335	−	0.832959i	$-0.313355\pi$
$293$	1783.51	+	738.755i	0.355610	+	0.147299i	−0.197724	+	0.980258i	$0.563355\pi$
$294$		0			0
$295$	−1814.14	−	1814.14i	−0.358046	−	0.358046i
$296$		0			0
$297$	2432.45	−	2432.45i	0.475237	−	0.475237i
$298$		0			0
$299$	−711.703	+	1718.20i	−0.137655	+	0.332329i
$300$		0			0
$301$	−3465.74	+	1435.56i	−0.663660	+	0.274897i
$302$		0			0
$303$			1243.30i			0.235728i
$304$		0			0
$305$			8852.00i			1.66185i
$306$		0			0
$307$	−6622.54	+	2743.14i	−1.23117	+	0.509966i	−0.900943	−	0.433937i	$-0.857124\pi$
$307$	−6622.54	+	2743.14i	−1.23117	+	0.509966i	−0.330223	+	0.943903i	$0.607124\pi$
$308$		0			0
$309$	−127.216	+	307.128i	−0.0234210	+	0.0565433i
$310$		0			0
$311$	−777.649	+	777.649i	−0.141789	+	0.141789i	−0.774438	−	0.632649i	$-0.781967\pi$
$311$	−777.649	+	777.649i	−0.141789	+	0.141789i	0.632649	+	0.774438i	$0.281967\pi$
$312$		0			0
$313$	3478.96	+	3478.96i	0.628251	+	0.628251i	0.947628	−	0.319377i	$-0.103474\pi$
$313$	3478.96	+	3478.96i	0.628251	+	0.628251i	−0.319377	+	0.947628i	$0.603474\pi$
$314$		0			0
$315$	−10599.6	−	4390.50i	−1.89594	−	0.785323i
$316$		0			0
$317$	2639.41	+	6372.11i	0.467648	+	1.12900i	0.965187	+	0.261560i	$0.0842369\pi$
$317$	2639.41	+	6372.11i	0.467648	+	1.12900i	−0.497540	+	0.867441i	$0.665763\pi$
$318$		0			0
$319$	−7147.64			−1.25452
$320$		0			0
$321$	157.893			0.0274540
$322$		0			0
$323$	−713.052	−	1721.46i	−0.122834	−	0.296547i
$324$		0			0
$325$	7110.44	+	2945.24i	1.21359	+	0.502685i
$326$		0			0
$327$	376.792	+	376.792i	0.0637207	+	0.0637207i
$328$		0			0
$329$	−5675.28	+	5675.28i	−0.951028	+	0.951028i
$330$		0			0
$331$	−1414.82	+	3415.68i	−0.234941	+	0.567198i	−0.996746	−	0.0806085i	$-0.974314\pi$
$331$	−1414.82	+	3415.68i	−0.234941	+	0.567198i	0.761805	+	0.647807i	$0.224314\pi$
$332$		0			0
$333$	−1459.78	+	604.660i	−0.240226	+	0.0995050i
$334$		0			0
$335$		−	2565.00i		−	0.418331i
$336$		0			0
$337$		−	5963.90i		−	0.964018i	−0.876166	−	0.482009i	$-0.839907\pi$
$337$		−	5963.90i		−	0.964018i	0.876166	−	0.482009i	$-0.160093\pi$
$338$		0			0
$339$	1054.41	−	436.750i	0.168931	−	0.0699734i
$340$		0			0
$341$	1072.32	−	2588.82i	0.170292	−	0.411121i
$342$		0			0
$343$	655.996	−	655.996i	0.103267	−	0.103267i
$344$		0			0
$345$	709.909	+	709.909i	0.110783	+	0.110783i
$346$		0			0
$347$	11609.9	+	4808.98i	1.79612	+	0.743975i	0.987901	+	0.155086i	$0.0495656\pi$
$347$	11609.9	+	4808.98i	1.79612	+	0.743975i	0.808214	+	0.588889i	$0.200434\pi$
$348$		0			0
$349$	−3007.79	−	7261.44i	−0.461327	−	1.11374i	−0.967853	−	0.251518i	$-0.919070\pi$
$349$	−3007.79	−	7261.44i	−0.461327	−	1.11374i	0.506525	−	0.862225i	$-0.330930\pi$
$350$		0			0
$351$	2679.57			0.407478
$352$		0			0
$353$	−4646.74			−0.700627			−0.350313	−	0.936633i	$-0.613925\pi$
$353$	−4646.74			−0.700627			−0.350313	+	0.936633i	$0.613925\pi$
$354$		0			0
$355$	1830.23	+	4418.57i	0.273630	+	0.660600i
$356$		0			0
$357$	1560.04	+	646.190i	0.231278	+	0.0957983i
$358$		0			0
$359$	−1380.53	−	1380.53i	−0.202957	−	0.202957i	0.598309	−	0.801266i	$-0.295840\pi$
$359$	−1380.53	−	1380.53i	−0.202957	−	0.202957i	−0.801266	+	0.598309i	$0.795840\pi$
$360$		0			0
$361$	−3978.10	+	3978.10i	−0.579983	+	0.579983i
$362$		0			0
$363$	682.890	−	1648.64i	0.0987394	−	0.238378i
$364$		0			0
$365$	4056.06	−	1680.07i	0.581654	−	0.240929i
$366$		0			0
$367$		−	8418.93i		−	1.19745i	−0.800954	−	0.598725i	$-0.795674\pi$
$367$		−	8418.93i		−	1.19745i	0.800954	−	0.598725i	$-0.204326\pi$
$368$		0			0
$369$		−	8648.75i		−	1.22015i
$370$		0			0
$371$	−10923.3	+	4524.59i	−1.52860	+	0.633167i
$372$		0			0
$373$	−2147.40	+	5184.27i	−0.298091	+	0.719655i	0.701882	+	0.712293i	$0.252343\pi$
$373$	−2147.40	+	5184.27i	−0.298091	+	0.719655i	−0.999973	+	0.00736187i	$0.997657\pi$
$374$		0			0
$375$	985.145	−	985.145i	0.135660	−	0.135660i
$376$		0			0
$377$	−3936.89	−	3936.89i	−0.537825	−	0.537825i
$378$		0			0
$379$	7606.92	+	3150.89i	1.03098	+	0.427046i	0.833066	−	0.553173i	$-0.186583\pi$
$379$	7606.92	+	3150.89i	1.03098	+	0.427046i	0.197914	+	0.980219i	$0.436583\pi$
$380$		0			0
$381$	1031.77	+	2490.91i	0.138738	+	0.334943i
$382$		0			0
$383$	−12379.9			−1.65166			−0.825828	−	0.563922i	$-0.809292\pi$
$383$	−12379.9			−1.65166			−0.825828	+	0.563922i	$0.809292\pi$
$384$		0			0
$385$	−23692.5			−3.13631
$386$		0			0
$387$	1432.95	+	3459.45i	0.188220	+	0.454402i
$388$		0			0
$389$	−2056.29	−	851.744i	−0.268016	−	0.111016i	0.244629	−	0.969617i	$-0.421334\pi$
$389$	−2056.29	−	851.744i	−0.268016	−	0.111016i	−0.512644	+	0.858601i	$0.671334\pi$
$390$		0			0
$391$	1705.09	+	1705.09i	0.220538	+	0.220538i
$392$		0			0
$393$	−2067.72	+	2067.72i	−0.265401	+	0.265401i
$394$		0			0
$395$	−8274.74	+	19977.0i	−1.05404	+	2.54469i
$396$		0			0
$397$	10550.8	−	4370.29i	1.33383	−	0.552490i	0.402083	−	0.915603i	$-0.368286\pi$
$397$	10550.8	−	4370.29i	1.33383	−	0.552490i	0.931745	+	0.363114i	$0.118286\pi$
$398$		0			0
$399$			1117.49i			0.140212i
$400$		0			0
$401$			3711.66i			0.462224i	0.972927	+	0.231112i	$0.0742363\pi$
$401$			3711.66i			0.462224i	−0.972927	+	0.231112i	$0.925764\pi$
$402$		0			0
$403$	2016.54	−	835.278i	0.249258	−	0.103246i
$404$		0			0
$405$	−4097.53	+	9892.32i	−0.502736	+	1.21371i
$406$		0			0
$407$	−2307.24	+	2307.24i	−0.280996	+	0.280996i
$408$		0			0
$409$	6598.84	+	6598.84i	0.797780	+	0.797780i	0.982745	−	0.184965i	$-0.0592173\pi$
$409$	6598.84	+	6598.84i	0.797780	+	0.797780i	−0.184965	+	0.982745i	$0.559217\pi$
$410$		0			0
$411$	−193.001	−	79.9436i	−0.0231631	−	0.00959447i
$412$		0			0
$413$	1414.27	+	3414.36i	0.168503	+	0.406803i
$414$		0			0
$415$	17170.8			2.03104
$416$		0			0
$417$	−3015.41			−0.354113
$418$		0			0
$419$	−866.138	−	2091.04i	−0.100987	−	0.243804i	0.865308	−	0.501240i	$-0.167123\pi$
$419$	−866.138	−	2091.04i	−0.100987	−	0.243804i	−0.966296	+	0.257435i	$0.917123\pi$
$420$		0			0
$421$	−5360.95	−	2220.58i	−0.620610	−	0.257065i	0.0501475	−	0.998742i	$-0.484031\pi$
$421$	−5360.95	−	2220.58i	−0.620610	−	0.257065i	−0.670757	+	0.741677i	$0.734031\pi$
$422$		0			0
$423$	5664.98	+	5664.98i	0.651161	+	0.651161i
$424$		0			0
$425$	7056.18	−	7056.18i	0.805353	−	0.805353i
$426$		0			0
$427$	4879.64	−	11780.5i	0.553026	−	1.33512i
$428$		0			0
$429$	2480.16	−	1027.31i	0.279122	−	0.115616i
$430$		0			0
$431$		−	3632.29i		−	0.405943i	−0.979185	−	0.202971i	$-0.934940\pi$
$431$		−	3632.29i		−	0.405943i	0.979185	−	0.202971i	$-0.0650599\pi$
$432$		0			0
$433$			4662.59i			0.517482i	0.965947	+	0.258741i	$0.0833076\pi$
$433$			4662.59i			0.517482i	−0.965947	+	0.258741i	$0.916692\pi$
$434$		0			0
$435$	−2776.79	+	1150.18i	−0.306061	+	0.126775i
$436$		0			0
$437$	−610.696	+	1474.35i	−0.0668502	+	0.161391i
$438$		0			0
$439$	−8537.50	+	8537.50i	−0.928184	+	0.928184i	−0.997589	−	0.0694048i	$-0.977890\pi$
$439$	−8537.50	+	8537.50i	−0.928184	+	0.928184i	0.0694048	+	0.997589i	$0.477890\pi$
$440$		0			0
$441$	5515.60	+	5515.60i	0.595573	+	0.595573i
$442$		0			0
$443$	−4536.01	−	1878.88i	−0.486484	−	0.201508i	0.125940	−	0.992038i	$-0.459805\pi$
$443$	−4536.01	−	1878.88i	−0.486484	−	0.201508i	−0.612424	+	0.790530i	$0.709805\pi$
$444$		0			0
$445$	−8458.16	−	20419.8i	−0.901023	−	2.17526i
$446$		0			0
$447$	1196.46			0.126601
$448$		0			0
$449$	17669.7			1.85720			0.928602	−	0.371077i	$-0.121011\pi$
$449$	17669.7			1.85720			0.928602	+	0.371077i	$0.121011\pi$
$450$		0			0
$451$	−6834.84	−	16500.8i	−0.713615	−	1.72282i
$452$		0			0
$453$	−1978.41	−	819.482i	−0.205196	−	0.0849948i
$454$		0			0
$455$	−13049.7	−	13049.7i	−1.34457	−	1.34457i
$456$		0			0
$457$	10783.5	−	10783.5i	1.10378	−	1.10378i	0.109833	−	0.993950i	$-0.464968\pi$
$457$	10783.5	−	10783.5i	1.10378	−	1.10378i	0.993950	−	0.109833i	$-0.0350317\pi$
$458$		0			0
$459$	1329.56	−	3209.84i	0.135204	−	0.326411i
$460$		0			0
$461$	−96.4913	+	39.9680i	−0.00974847	+	0.00403795i	−0.387552	−	0.921848i	$-0.626679\pi$
$461$	−96.4913	+	39.9680i	−0.00974847	+	0.00403795i	0.377804	+	0.925886i	$0.376679\pi$
$462$		0			0
$463$		−	16514.0i		−	1.65761i	−0.559539	−	0.828804i	$-0.689022\pi$
$463$		−	16514.0i		−	1.65761i	0.559539	−	0.828804i	$-0.310978\pi$
$464$		0			0
$465$		−	1178.28i		−	0.117509i
$466$		0			0
$467$	4949.67	−	2050.22i	0.490457	−	0.203154i	−0.123728	−	0.992316i	$-0.539485\pi$
$467$	4949.67	−	2050.22i	0.490457	−	0.203154i	0.614185	+	0.789162i	$0.289485\pi$
$468$		0			0
$469$	−1413.95	+	3413.57i	−0.139211	+	0.336086i
$470$		0			0
$471$	−2068.88	+	2068.88i	−0.202397	+	0.202397i
$472$		0			0
$473$	5467.80	+	5467.80i	0.531521	+	0.531521i
$474$		0			0
$475$	6101.30	+	2527.24i	0.589362	+	0.244122i
$476$		0			0
$477$	4516.38	+	10903.5i	0.433524	+	1.04662i
$478$		0			0
$479$	19166.1			1.82823			0.914114	−	0.405456i	$-0.132887\pi$
$479$	19166.1			1.82823			0.914114	+	0.405456i	$0.132887\pi$
$480$		0			0
$481$	−2541.63			−0.240932
$482$		0			0
$483$	−553.432	−	1336.10i	−0.0521367	−	0.125869i
$484$		0			0
$485$	11164.4	+	4624.46i	1.04526	+	0.432961i
$486$		0			0
$487$	3738.42	+	3738.42i	0.347852	+	0.347852i	0.859309	−	0.511457i	$-0.170894\pi$
$487$	3738.42	+	3738.42i	0.347852	+	0.347852i	−0.511457	+	0.859309i	$0.670894\pi$
$488$		0			0
$489$	839.687	−	839.687i	0.0776523	−	0.0776523i
$490$		0			0
$491$	1743.88	−	4210.09i	0.160285	−	0.386963i	−0.823250	−	0.567679i	$-0.807842\pi$
$491$	1743.88	−	4210.09i	0.160285	−	0.386963i	0.983535	+	0.180716i	$0.0578416\pi$
$492$		0			0
$493$	−6669.41	+	2762.56i	−0.609280	+	0.252372i
$494$		0			0
$495$			23649.5i			2.14740i
$496$		0			0
$497$		−	6889.26i		−	0.621782i
$498$		0			0
$499$	6509.03	−	2696.13i	0.583936	−	0.241874i	−0.0711034	−	0.997469i	$-0.522652\pi$
$499$	6509.03	−	2696.13i	0.583936	−	0.241874i	0.655039	+	0.755595i	$0.272652\pi$
$500$		0			0
$501$	541.225	−	1306.63i	0.0482638	−	0.116519i
$502$		0			0
$503$	−3534.14	+	3534.14i	−0.313280	+	0.313280i	−0.846179	−	0.532899i	$-0.821103\pi$
$503$	−3534.14	+	3534.14i	−0.313280	+	0.313280i	0.532899	+	0.846179i	$0.321103\pi$
$504$		0			0
$505$	−12458.3	−	12458.3i	−1.09780	−	1.09780i
$506$		0			0
$507$	−602.430	−	249.535i	−0.0527710	−	0.0218584i
$508$		0			0
$509$	−4345.28	−	10490.4i	−0.378391	−	0.913518i	−0.992268	−	0.124115i	$-0.960391\pi$
$509$	−4345.28	−	10490.4i	−0.378391	−	0.913518i	0.613876	−	0.789402i	$-0.289609\pi$
$510$		0			0
$511$	−6324.05			−0.547475
$512$		0			0
$513$	2299.28			0.197886
$514$		0			0
$515$	−1802.78	−	4352.28i	−0.154252	−	0.372397i
$516$		0			0
$517$	15285.0	+	6331.24i	1.30026	+	0.538583i
$518$		0			0
$519$	207.835	+	207.835i	0.0175779	+	0.0175779i
$520$		0			0
$521$	−8864.19	+	8864.19i	−0.745388	+	0.745388i	−0.973609	−	0.228221i	$-0.926709\pi$
$521$	−8864.19	+	8864.19i	−0.745388	+	0.745388i	0.228221	+	0.973609i	$0.426709\pi$
$522$		0			0
$523$	−1505.26	+	3634.02i	−0.125852	+	0.303833i	−0.974230	−	0.225558i	$-0.927579\pi$
$523$	−1505.26	+	3634.02i	−0.125852	+	0.303833i	0.848378	+	0.529391i	$0.177579\pi$
$524$		0			0
$525$	−5529.20	+	2290.27i	−0.459645	+	0.190391i
$526$		0			0
$527$		−	2830.06i		−	0.233926i
$528$		0			0
$529$			10101.8i			0.830260i
$530$		0			0
$531$	3408.16	−	1411.71i	0.278534	−	0.115373i
$532$		0			0
$533$	5323.95	−	12853.2i	0.432657	−	1.04453i
$534$		0			0
$535$	−1582.15	+	1582.15i	−0.127854	+	0.127854i
$536$		0			0
$537$	1872.29	+	1872.29i	0.150457	+	0.150457i
$538$		0			0
$539$	14881.9	+	6164.29i	1.18926	+	0.492606i
$540$		0			0
$541$	−4671.40	−	11277.8i	−0.371237	−	0.896245i	−0.993541	−	0.113470i	$-0.963804\pi$
$541$	−4671.40	−	11277.8i	−0.371237	−	0.896245i	0.622305	−	0.782775i	$-0.286196\pi$
$542$		0			0
$543$	−1527.80			−0.120744
$544$		0			0
$545$	−7551.19			−0.593500
$546$		0			0
$547$	−6749.10	−	16293.8i	−0.527552	−	1.27362i	−0.933122	−	0.359559i	$-0.882927\pi$
$547$	−6749.10	−	16293.8i	−0.527552	−	1.27362i	0.405571	−	0.914064i	$-0.367073\pi$
$548$		0			0
$549$	−11759.1	−	4870.79i	−0.914148	−	0.378652i
$550$		0			0
$551$	−3378.15	−	3378.15i	−0.261187	−	0.261187i
$552$		0			0
$553$	22024.5	−	22024.5i	1.69363	−	1.69363i
$554$		0			0
$555$	−525.063	+	1267.61i	−0.0401580	+	0.0969499i
$556$		0			0
$557$	−2590.39	+	1072.98i	−0.197053	+	0.0816220i	−0.479028	−	0.877800i	$-0.659011\pi$
$557$	−2590.39	+	1072.98i	−0.197053	+	0.0816220i	0.281975	+	0.959422i	$0.409011\pi$
$558$		0			0
$559$			6023.28i			0.455738i
$560$		0			0
$561$		−	3480.71i		−	0.261953i
$562$		0			0
$563$	7377.58	−	3055.89i	0.552270	−	0.228758i	−0.0890556	−	0.996027i	$-0.528385\pi$
$563$	7377.58	−	3055.89i	0.552270	−	0.228758i	0.641325	+	0.767269i	$0.278385\pi$
$564$		0			0
$565$	−6189.15	+	14941.9i	−0.460849	+	1.11259i
$566$		0			0
$567$	10906.2	−	10906.2i	0.807792	−	0.807792i
$568$		0			0
$569$	16799.5	+	16799.5i	1.23773	+	1.23773i	0.960925	+	0.276810i	$0.0892773\pi$
$569$	16799.5	+	16799.5i	1.23773	+	1.23773i	0.276810	+	0.960925i	$0.410723\pi$
$570$		0			0
$571$	−8801.25	−	3645.60i	−0.645045	−	0.267186i	0.0360851	−	0.999349i	$-0.488511\pi$
$571$	−8801.25	−	3645.60i	−0.645045	−	0.267186i	−0.681130	+	0.732162i	$0.738511\pi$
$572$		0			0
$573$	−2444.33	−	5901.13i	−0.178208	−	0.430232i
$574$		0			0
$575$	−8546.51			−0.619851
$576$		0			0
$577$	11551.9			0.833472			0.416736	−	0.909028i	$-0.363174\pi$
$577$	11551.9			0.833472			0.416736	+	0.909028i	$0.363174\pi$
$578$		0			0
$579$	1959.90	+	4731.62i	0.140675	+	0.339619i
$580$		0			0
$581$	−22851.4	−	9465.36i	−1.63173	−	0.675886i
$582$		0			0
$583$	17233.4	+	17233.4i	1.22425	+	1.22425i
$584$		0			0
$585$	−13026.0	+	13026.0i	−0.920615	+	0.920615i
$586$		0			0
$587$	−2507.65	+	6054.00i	−0.176323	+	0.425682i	−0.987190	−	0.159549i	$-0.948996\pi$
$587$	−2507.65	+	6054.00i	−0.176323	+	0.425682i	0.810867	+	0.585231i	$0.198996\pi$
$588$		0			0
$589$	1730.35	−	716.733i	0.121049	−	0.0501400i
$590$		0			0
$591$		−	3196.34i		−	0.222470i
$592$		0			0
$593$		−	7192.49i		−	0.498078i	−0.968493	−	0.249039i	$-0.919885\pi$
$593$		−	7192.49i		−	0.498078i	0.968493	−	0.249039i	$-0.0801147\pi$
$594$		0			0
$595$	−22107.2	+	9157.12i	−1.52321	+	0.630933i
$596$		0			0
$597$	−2310.59	+	5578.26i	−0.158402	+	0.382417i
$598$		0			0
$599$	−8885.88	+	8885.88i	−0.606122	+	0.606122i	−0.941930	−	0.335808i	$-0.890991\pi$
$599$	−8885.88	+	8885.88i	−0.606122	+	0.606122i	0.335808	+	0.941930i	$0.390991\pi$
$600$		0			0
$601$	1468.96	+	1468.96i	0.0997009	+	0.0997009i	0.755198	−	0.655497i	$-0.227541\pi$
$601$	1468.96	+	1468.96i	0.0997009	+	0.0997009i	−0.655497	+	0.755198i	$0.727541\pi$
$602$		0			0
$603$	3407.38	+	1411.38i	0.230115	+	0.0953167i
$604$		0			0
$605$	9677.19	+	23362.8i	0.650303	+	1.56997i
$606$		0			0
$607$	1305.90			0.0873225			0.0436613	−	0.999046i	$-0.486098\pi$
$607$	1305.90			0.0873225			0.0436613	+	0.999046i	$0.486098\pi$
$608$		0			0
$609$	4329.46			0.288076
$610$		0			0
$611$	4931.67	+	11906.1i	0.326537	+	0.788330i
$612$		0			0
$613$	−15396.4	−	6377.39i	−1.01444	−	0.420196i	−0.187370	−	0.982289i	$-0.559996\pi$
$613$	−15396.4	−	6377.39i	−1.01444	−	0.420196i	−0.827074	+	0.562093i	$0.809996\pi$
$614$		0			0
$615$	−5310.53	−	5310.53i	−0.348197	−	0.348197i
$616$		0			0
$617$	−14943.6	+	14943.6i	−0.975049	+	0.975049i	−0.999696	−	0.0246473i	$-0.992154\pi$
$617$	−14943.6	+	14943.6i	−0.975049	+	0.975049i	0.0246473	+	0.999696i	$0.492154\pi$
$618$		0			0
$619$	9902.61	−	23907.0i	0.643004	−	1.55235i	−0.179604	−	0.983739i	$-0.557482\pi$
$619$	9902.61	−	23907.0i	0.643004	−	1.55235i	0.822608	−	0.568609i	$-0.192518\pi$
$620$		0			0
$621$	−2749.08	+	1138.71i	−0.177644	+	0.0735826i
$622$		0			0
$623$			31837.8i			2.04744i
$624$		0			0
$625$		−	3764.96i		−	0.240957i
$626$		0			0
$627$	2128.17	−	881.515i	0.135551	−	0.0561472i
$628$		0			0
$629$	−1261.12	+	3044.61i	−0.0799429	+	0.192999i
$630$		0			0
$631$	−11209.4	+	11209.4i	−0.707191	+	0.707191i	−0.965944	−	0.258753i	$-0.916688\pi$
$631$	−11209.4	+	11209.4i	−0.707191	+	0.707191i	0.258753	+	0.965944i	$0.416688\pi$
$632$		0			0
$633$	−3990.43	−	3990.43i	−0.250561	−	0.250561i
$634$		0			0
$635$	−35298.5	−	14621.1i	−2.20595	−	0.913736i
$636$		0			0
$637$	4801.63	+	11592.2i	0.298662	+	0.721033i
$638$		0			0
$639$	−6876.77			−0.425729
$640$		0			0
$641$	−8922.84			−0.549814			−0.274907	−	0.961471i	$-0.588647\pi$
$641$	−8922.84			−0.549814			−0.274907	+	0.961471i	$0.588647\pi$
$642$		0			0
$643$	7149.00	+	17259.2i	0.438459	+	1.05853i	0.976481	+	0.215603i	$0.0691715\pi$
$643$	7149.00	+	17259.2i	0.438459	+	1.05853i	−0.538022	+	0.842930i	$0.680828\pi$
$644$		0			0
$645$	3004.05	+	1244.32i	0.183386	+	0.0759611i
$646$		0			0
$647$	15074.6	+	15074.6i	0.915985	+	0.915985i	0.996734	−	0.0807492i	$-0.0257313\pi$
$647$	15074.6	+	15074.6i	0.915985	+	0.915985i	−0.0807492	+	0.996734i	$0.525731\pi$
$648$		0			0
$649$	5386.73	−	5386.73i	0.325805	−	0.325805i
$650$		0			0
$651$	−649.526	+	1568.09i	−0.0391043	+	0.0944062i
$652$		0			0
$653$	717.534	−	297.212i	0.0430004	−	0.0178114i	−0.361080	−	0.932535i	$-0.617592\pi$
$653$	717.534	−	297.212i	0.0430004	−	0.0178114i	0.404080	+	0.914724i	$0.367592\pi$
$654$		0			0
$655$		−	41438.5i		−	2.47197i
$656$		0			0
$657$			6312.58i			0.374851i
$658$		0			0
$659$	−6945.56	+	2876.95i	−0.410562	+	0.170061i	−0.578398	−	0.815754i	$-0.696322\pi$
$659$	−6945.56	+	2876.95i	−0.410562	+	0.170061i	0.167836	+	0.985815i	$0.446322\pi$
$660$		0			0
$661$	−797.182	+	1924.57i	−0.0469089	+	0.113248i	−0.945597	−	0.325340i	$-0.894521\pi$
$661$	−797.182	+	1924.57i	−0.0469089	+	0.113248i	0.898688	+	0.438588i	$0.144521\pi$
$662$		0			0
$663$	1917.16	−	1917.16i	0.112302	−	0.112302i
$664$		0			0
$665$	−11197.6	−	11197.6i	−0.652971	−	0.652971i
$666$		0			0
$667$	5712.04	+	2366.01i	0.331591	+	0.137349i
$668$		0			0
$669$	−342.714	−	827.385i	−0.0198058	−	0.0478155i
$670$		0			0
$671$	−26284.2			−1.51221
$672$		0			0
$673$	6013.47			0.344431			0.172216	−	0.985059i	$-0.444907\pi$
$673$	6013.47			0.344431			0.172216	+	0.985059i	$0.444907\pi$
$674$		0			0
$675$	4712.31	+	11376.5i	0.268707	+	0.648716i
$676$		0			0
$677$	19577.8	+	8109.41i	1.11143	+	0.460369i	0.861430	−	0.507877i	$-0.169569\pi$
$677$	19577.8	+	8109.41i	1.11143	+	0.460369i	0.250000	+	0.968246i	$0.419569\pi$
$678$		0			0
$679$	−12308.7	−	12308.7i	−0.695679	−	0.695679i
$680$		0			0
$681$	−5343.58	+	5343.58i	−0.300685	+	0.300685i
$682$		0			0
$683$	5715.60	−	13798.7i	0.320207	−	0.773048i	−0.679035	−	0.734106i	$-0.737601\pi$
$683$	5715.60	−	13798.7i	0.320207	−	0.773048i	0.999241	−	0.0389416i	$-0.0123986\pi$
$684$		0			0
$685$	2735.00	−	1132.88i	0.152553	−	0.0631897i
$686$		0			0
$687$		−	266.325i		−	0.0147903i
$688$		0			0
$689$			18984.2i			1.04970i
$690$		0			0
$691$	8261.06	−	3421.84i	0.454798	−	0.188384i	−0.143511	−	0.989649i	$-0.545839\pi$
$691$	8261.06	−	3421.84i	0.454798	−	0.188384i	0.598310	+	0.801265i	$0.295839\pi$
$692$		0			0
$693$	13036.7	−	31473.4i	0.714608	−	1.72522i
$694$		0			0
$695$	30215.5	−	30215.5i	1.64912	−	1.64912i
$696$		0			0
$697$	−12755.1	−	12755.1i	−0.693161	−	0.693161i
$698$		0			0
$699$	−7505.19	−	3108.75i	−0.406112	−	0.168217i
$700$		0			0
$701$	8530.14	+	20593.6i	0.459599	+	1.10957i	0.968560	+	0.248780i	$0.0800298\pi$
$701$	8530.14	+	20593.6i	0.459599	+	1.10957i	−0.508961	+	0.860790i	$0.669970\pi$
$702$		0			0
$703$	−2180.92			−0.117005
$704$		0			0
$705$	6956.86			0.371646
$706$		0			0
$707$	9712.25	+	23447.4i	0.516643	+	1.24729i
$708$		0			0
$709$	11948.6	+	4949.27i	0.632919	+	0.262163i	0.675993	−	0.736908i	$-0.263715\pi$
$709$	11948.6	+	4949.27i	0.632919	+	0.262163i	−0.0430740	+	0.999072i	$0.513715\pi$
$710$		0			0
$711$	−21984.6	−	21984.6i	−1.15962	−	1.15962i
$712$		0			0
$713$	−1713.89	+	1713.89i	−0.0900222	+	0.0900222i
$714$		0			0
$715$	−14558.0	+	35146.2i	−0.761453	+	1.83831i
$716$		0			0
$717$	−1575.96	+	652.783i	−0.0820854	+	0.0340009i
$718$		0			0
$719$			3624.32i			0.187989i	0.995573	+	0.0939947i	$0.0299637\pi$
$719$			3624.32i			0.187989i	−0.995573	+	0.0939947i	$0.970036\pi$
$720$		0			0
$721$			6785.92i			0.350514i
$722$		0			0
$723$	1809.76	−	749.626i	0.0930921	−	0.0385600i
$724$		0			0
$725$	9791.24	−	23638.1i	0.501569	−	1.21089i
$726$		0			0
$727$	24377.4	−	24377.4i	1.24361	−	1.24361i	0.285123	−	0.958491i	$-0.407966\pi$
$727$	24377.4	−	24377.4i	1.24361	−	1.24361i	0.958491	−	0.285123i	$-0.0920345\pi$
$728$		0			0
$729$	−9325.61	−	9325.61i	−0.473790	−	0.473790i
$730$		0			0
$731$	7215.26	+	2988.66i	0.365070	+	0.151217i
$732$		0			0
$733$	−2874.93	−	6940.70i	−0.144868	−	0.349742i	0.834745	−	0.550637i	$-0.185615\pi$
$733$	−2874.93	−	6940.70i	−0.144868	−	0.349742i	−0.979613	+	0.200895i	$0.935615\pi$
$734$		0			0
$735$	6773.41			0.339920
$736$		0			0
$737$	7616.24			0.380662
$738$		0			0
$739$	−9423.24	−	22749.7i	−0.469066	−	1.13242i	−0.964572	−	0.263820i	$-0.915017\pi$
$739$	−9423.24	−	22749.7i	−0.469066	−	1.13242i	0.495506	−	0.868604i	$-0.334983\pi$
$740$		0			0
$741$	1657.72	+	686.650i	0.0821833	+	0.0340414i
$742$		0			0
$743$	4515.42	+	4515.42i	0.222954	+	0.222954i	0.809741	−	0.586787i	$-0.199607\pi$
$743$	4515.42	+	4515.42i	0.222954	+	0.222954i	−0.586787	+	0.809741i	$0.699607\pi$
$744$		0			0
$745$	−11989.0	+	11989.0i	−0.589587	+	0.589587i
$746$		0			0
$747$	−9448.20	+	22810.0i	−0.462773	+	1.11723i
$748$		0			0
$749$	2977.72	−	1233.41i	0.145265	−	0.0601707i
$750$		0			0
$751$			25582.2i			1.24302i	0.783406	+	0.621510i	$0.213481\pi$
$751$			25582.2i			1.24302i	−0.783406	+	0.621510i	$0.786519\pi$
$752$		0			0
$753$		−	2397.67i		−	0.116037i
$754$		0			0
$755$	28035.9	−	11612.8i	1.35143	−	0.559780i
$756$		0			0
$757$	7681.53	−	18544.9i	0.368811	−	0.890389i	−0.625135	−	0.780517i	$-0.714956\pi$
$757$	7681.53	−	18544.9i	0.368811	−	0.890389i	0.993946	−	0.109872i	$-0.0350440\pi$
$758$		0			0
$759$	−2107.93	+	2107.93i	−0.100808	+	0.100808i
$760$		0			0
$761$	−9053.82	−	9053.82i	−0.431276	−	0.431276i	0.457786	−	0.889062i	$-0.348642\pi$
$761$	−9053.82	−	9053.82i	−0.431276	−	0.431276i	−0.889062	+	0.457786i	$0.848642\pi$
$762$		0			0
$763$	10049.3	+	4162.58i	0.476816	+	0.197504i
$764$		0			0
$765$	9140.51	+	22067.1i	0.431995	+	1.04293i
$766$		0			0
$767$	5933.98			0.279353
$768$		0			0
$769$	−22171.5			−1.03969			−0.519847	−	0.854259i	$-0.674011\pi$
$769$	−22171.5			−1.03969			−0.519847	+	0.854259i	$0.674011\pi$
$770$		0			0
$771$	384.954	+	929.362i	0.0179816	+	0.0434113i
$772$		0			0
$773$	4511.27	+	1868.63i	0.209908	+	0.0869469i	0.485160	−	0.874425i	$-0.338761\pi$
$773$	4511.27	+	1868.63i	0.209908	+	0.0869469i	−0.275252	+	0.961372i	$0.588761\pi$
$774$		0			0
$775$	7092.61	+	7092.61i	0.328741	+	0.328741i
$776$		0			0
$777$	1397.54	−	1397.54i	0.0645255	−	0.0645255i
$778$		0			0
$779$	4568.36	−	11029.0i	0.210114	−	0.507259i
$780$		0			0
$781$	−13120.0	+	5434.50i	−0.601116	+	0.248991i
$782$		0			0
$783$		−	8908.03i		−	0.406574i
$784$		0			0
$785$		−	41461.9i		−	1.88514i
$786$		0			0
$787$	−23455.4	+	9715.54i	−1.06238	+	0.440053i	−0.844296	−	0.535877i	$-0.819981\pi$
$787$	−23455.4	+	9715.54i	−1.06238	+	0.440053i	−0.218086	+	0.975930i	$0.569981\pi$
$788$		0			0
$789$	1459.20	−	3522.81i	0.0658413	−	0.158955i
$790$		0			0
$791$	16473.4	−	16473.4i	0.740489	−	0.740489i
$792$		0			0
$793$	−14477.2	−	14477.2i	−0.648300	−	0.648300i
$794$		0			0
$795$	9468.17	+	3921.84i	0.422392	+	0.174960i
$796$		0			0
$797$	−11912.1	−	28758.4i	−0.529421	−	1.27814i	−0.931903	−	0.362708i	$-0.881852\pi$
$797$	−11912.1	−	28758.4i	−0.529421	−	1.27814i	0.402482	−	0.915428i	$-0.368148\pi$
$798$		0			0
$799$	16709.3			0.739841
$800$		0			0
$801$	31780.1			1.40186
$802$		0			0
$803$	4988.64	+	12043.6i	0.219234	+	0.529279i
$804$		0			0
$805$	18933.8	+	7842.65i	0.828981	+	0.343375i
$806$		0			0
$807$	2296.70	+	2296.70i	0.100183	+	0.100183i
$808$		0			0
$809$	2278.00	−	2278.00i	0.0989992	−	0.0989992i	−0.655873	−	0.754872i	$-0.727699\pi$
$809$	2278.00	−	2278.00i	0.0989992	−	0.0989992i	0.754872	+	0.655873i	$0.227699\pi$
$810$		0			0
$811$	11666.4	−	28165.2i	0.505134	−	1.21950i	−0.441521	−	0.897251i	$-0.645561\pi$
$811$	11666.4	−	28165.2i	0.505134	−	1.21950i	0.946655	−	0.322250i	$-0.104439\pi$
$812$		0			0
$813$	−419.792	+	173.884i	−0.0181092	+	0.00750106i
$814$		0			0
$815$			16827.9i			0.723260i
$816$		0			0
$817$			5168.43i			0.221323i
$818$		0			0
$819$	24516.0	−	10154.8i	1.04598	−	0.433259i
$820$		0			0
$821$	−12455.2	+	30069.5i	−0.529463	+	1.27824i	0.402413	+	0.915458i	$0.368172\pi$
$821$	−12455.2	+	30069.5i	−0.529463	+	1.27824i	−0.931876	+	0.362778i	$0.881828\pi$
$822$		0			0
$823$	−18709.3	+	18709.3i	−0.792424	+	0.792424i	−0.981888	−	0.189464i	$-0.939325\pi$
$823$	−18709.3	+	18709.3i	−0.792424	+	0.792424i	0.189464	+	0.981888i	$0.439325\pi$
$824$		0			0
$825$	8723.26	+	8723.26i	0.368127	+	0.368127i
$826$		0			0
$827$	−31391.1	−	13002.6i	−1.31992	−	0.546730i	−0.392160	−	0.919897i	$-0.628272\pi$
$827$	−31391.1	−	13002.6i	−1.31992	−	0.546730i	−0.927764	+	0.373167i	$0.878272\pi$
$828$		0			0
$829$	3317.38	+	8008.87i	0.138984	+	0.335536i	0.978011	−	0.208553i	$-0.0668753\pi$
$829$	3317.38	+	8008.87i	0.138984	+	0.335536i	−0.839027	+	0.544089i	$0.816875\pi$
$830$		0			0
$831$	772.852			0.0322622
$832$		0			0
$833$	16268.7			0.676683
$834$		0			0
$835$	7669.66	+	18516.2i	0.317868	+	0.767401i
$836$		0			0
$837$	3226.41	+	1336.42i	0.133239	+	0.0551895i
$838$		0			0
$839$	−13722.1	−	13722.1i	−0.564649	−	0.564649i	0.365976	−	0.930624i	$-0.380735\pi$
$839$	−13722.1	−	13722.1i	−0.564649	−	0.564649i	−0.930624	+	0.365976i	$0.880735\pi$
$840$		0			0
$841$	4157.72	−	4157.72i	0.170475	−	0.170475i
$842$		0			0
$843$	3990.55	−	9634.04i	0.163039	−	0.393611i
$844$		0			0
$845$	8537.00	−	3536.14i	0.347552	−	0.143961i
$846$		0			0
$847$		−	36426.4i		−	1.47772i
$848$		0			0
$849$			2874.60i			0.116202i
$850$		0			0
$851$	2607.57	−	1080.09i	0.105037	−	0.0435077i
$852$		0			0
$853$	8865.17	−	21402.4i	0.355847	−	0.859092i	−0.640027	−	0.768352i	$-0.721077\pi$
$853$	8865.17	−	21402.4i	0.355847	−	0.859092i	0.995875	−	0.0907394i	$-0.0289230\pi$
$854$		0			0
$855$	−11177.3	+	11177.3i	−0.447084	+	0.447084i
$856$		0			0
$857$	−7933.81	−	7933.81i	−0.316236	−	0.316236i	0.531084	−	0.847319i	$-0.321785\pi$
$857$	−7933.81	−	7933.81i	−0.316236	−	0.316236i	−0.847319	+	0.531084i	$0.821785\pi$
$858$		0			0
$859$	3978.15	+	1647.80i	0.158012	+	0.0654509i	0.460288	−	0.887770i	$-0.347746\pi$
$859$	3978.15	+	1647.80i	0.158012	+	0.0654509i	−0.302275	+	0.953221i	$0.597746\pi$
$860$		0			0
$861$	4139.99	+	9994.83i	0.163868	+	0.395613i
$862$		0			0
$863$	−11315.5			−0.446331			−0.223166	−	0.974781i	$-0.571639\pi$
$863$	−11315.5			−0.446331			−0.223166	+	0.974781i	$0.571639\pi$
$864$		0			0
$865$	−4165.17			−0.163723
$866$		0			0
$867$	1002.20	+	2419.53i	0.0392578	+	0.0947768i
$868$		0			0
$869$	−59317.7	−	24570.2i	−2.31555	−	0.959133i
$870$		0			0
$871$	4194.99	+	4194.99i	0.163194	+	0.163194i
$872$		0			0
$873$	−12286.4	+	12286.4i	−0.476325	+	0.476325i
$874$		0			0
$875$	10883.3	−	26274.6i	0.420483	−	1.01513i
$876$		0			0
$877$	7769.43	−	3218.20i	0.299151	−	0.123912i	−0.228060	−	0.973647i	$-0.573238\pi$
$877$	7769.43	−	3218.20i	0.299151	−	0.123912i	0.527210	+	0.849735i	$0.323238\pi$
$878$		0			0
$879$			2410.34i			0.0924901i
$880$		0			0
$881$			15431.2i			0.590115i	0.955479	+	0.295058i	$0.0953389\pi$
$881$			15431.2i			0.590115i	−0.955479	+	0.295058i	$0.904661\pi$
$882$		0			0
$883$	−39311.6	+	16283.4i	−1.49824	+	0.620589i	−0.973090	−	0.230424i	$-0.925989\pi$
$883$	−39311.6	+	16283.4i	−1.49824	+	0.620589i	−0.525145	+	0.851013i	$0.675989\pi$
$884$		0			0
$885$	1225.87	−	2959.51i	0.0465618	−	0.112410i
$886$		0			0
$887$	24315.7	−	24315.7i	0.920451	−	0.920451i	−0.0766105	−	0.997061i	$-0.524410\pi$
$887$	24315.7	−	24315.7i	0.920451	−	0.920451i	0.997061	+	0.0766105i	$0.0244098\pi$
$888$		0			0
$889$	38916.5	+	38916.5i	1.46818	+	1.46818i
$890$		0			0
$891$	−29373.2	−	12166.8i	−1.10442	−	0.457467i
$892$		0			0
$893$	4231.75	+	10216.4i	0.158578	+	0.382841i
$894$		0			0
$895$	−37522.0			−1.40137
$896$		0			0
$897$	−2322.08			−0.0864348
$898$		0			0
$899$	−2776.82	−	6703.84i	−0.103017	−	0.248705i
$900$		0			0
$901$	22741.1	+	9419.66i	0.840860	+	0.348296i
$902$		0			0
$903$	−3311.95	−	3311.95i	−0.122054	−	0.122054i
$904$		0			0
$905$	15309.1	−	15309.1i	0.562310	−	0.562310i
$906$		0			0
$907$	−10871.5	+	26246.1i	−0.397996	+	0.960848i	0.590145	+	0.807297i	$0.299071\pi$
$907$	−10871.5	+	26246.1i	−0.397996	+	0.960848i	−0.988141	+	0.153550i	$0.950929\pi$
$908$		0			0
$909$	23404.9	−	9694.63i	0.854007	−	0.353741i
$910$		0			0
$911$		−	2752.62i		−	0.100108i	−0.998747	−	0.0500540i	$-0.984061\pi$
$911$		−	2752.62i		−	0.100108i	0.998747	−	0.0500540i	$-0.0159394\pi$
$912$		0			0
$913$			50985.3i			1.84816i
$914$		0			0
$915$	−10211.1	+	4229.60i	−0.368929	+	0.152815i
$916$		0			0
$917$	−22842.9	+	55147.6i	−0.822615	+	1.98597i
$918$		0			0
$919$	−27290.8	+	27290.8i	−0.979586	+	0.979586i	−0.999796	−	0.0202098i	$-0.993567\pi$
$919$	−27290.8	+	27290.8i	−0.979586	+	0.979586i	0.0202098	+	0.999796i	$0.493567\pi$
$920$		0			0
$921$	−6328.66	−	6328.66i	−0.226424	−	0.226424i
$922$		0			0
$923$	−10219.8	−	4233.16i	−0.364450	−	0.150960i
$924$		0			0
$925$	−4469.74	−	10790.9i	−0.158880	−	0.383570i
$926$		0			0
$927$	6773.61			0.239994
$928$		0			0
$929$	−19815.1			−0.699798			−0.349899	−	0.936787i	$-0.613784\pi$
$929$	−19815.1			−0.699798			−0.349899	+	0.936787i	$0.613784\pi$
$930$		0			0
$931$	4120.17	+	9946.96i	0.145041	+	0.350159i
$932$		0			0
$933$	−1268.62	−	525.480i	−0.0445153	−	0.0184388i
$934$		0			0
$935$	34878.0	+	34878.0i	1.21993	+	1.21993i
$936$		0			0
$937$	−19332.2	+	19332.2i	−0.674018	+	0.674018i	−0.958640	−	0.284622i	$-0.908132\pi$
$937$	−19332.2	+	19332.2i	−0.674018	+	0.674018i	0.284622	+	0.958640i	$0.408132\pi$
$938$		0			0
$939$	−2350.83	+	5675.42i	−0.0817003	+	0.197242i
$940$		0			0
$941$	−4000.39	+	1657.02i	−0.138586	+	0.0574041i	−0.450898	−	0.892575i	$-0.648896\pi$
$941$	−4000.39	+	1657.02i	−0.138586	+	0.0574041i	0.312313	+	0.949979i	$0.398896\pi$
$942$		0			0
$943$			15449.1i			0.533500i
$944$		0			0
$945$		−	29527.7i		−	1.01644i
$946$		0			0
$947$	−35953.4	+	14892.4i	−1.23372	+	0.511022i	−0.901745	−	0.432268i	$-0.857713\pi$
$947$	−35953.4	+	14892.4i	−1.23372	+	0.511022i	−0.331970	+	0.943290i	$0.607713\pi$
$948$		0			0
$949$	−3885.86	+	9381.31i	−0.132919	+	0.320896i
$950$		0			0
$951$	−6089.35	+	6089.35i	−0.207635	+	0.207635i
$952$		0			0
$953$	1350.98	+	1350.98i	0.0459208	+	0.0459208i	0.729694	−	0.683773i	$-0.239662\pi$
$953$	1350.98	+	1350.98i	0.0459208	+	0.0459208i	−0.683773	+	0.729694i	$0.739662\pi$
$954$		0			0
$955$	83624.5	+	34638.4i	2.83354	+	1.17369i
$956$		0			0
$957$	−3415.23	−	8245.10i	−0.115359	−	0.278502i
$958$		0			0
$959$	−4264.31			−0.143589
$960$		0			0
$961$	−26946.3			−0.904513
$962$		0			0
$963$	−1231.17	−	2972.32i	−0.0411984	−	0.0994616i
$964$		0			0
$965$	−67051.5	−	27773.6i	−2.23675	−	0.926492i
$966$		0			0
$967$	2303.21	+	2303.21i	0.0765939	+	0.0765939i	0.744366	−	0.667772i	$-0.232752\pi$
$967$	2303.21	+	2303.21i	0.0765939	+	0.0765939i	−0.667772	+	0.744366i	$0.732752\pi$
$968$		0			0
$969$	1645.07	−	1645.07i	0.0545379	−	0.0545379i
$970$		0			0
$971$	−3262.48	+	7876.32i	−0.107825	+	0.260312i	−0.968578	−	0.248711i	$-0.919993\pi$
$971$	−3262.48	+	7876.32i	−0.107825	+	0.260312i	0.860753	+	0.509023i	$0.169993\pi$
$972$		0			0
$973$	−56867.8	+	23555.4i	−1.87369	+	0.776107i
$974$		0			0
$975$			9609.46i			0.315640i
$976$		0			0
$977$		−	43245.0i		−	1.41610i	−0.706162	−	0.708050i	$-0.749575\pi$
$977$		−	43245.0i		−	1.41610i	0.706162	−	0.708050i	$-0.250425\pi$
$978$		0			0
$979$	60632.5	−	25114.8i	1.97939	−	0.819890i
$980$		0			0
$981$	4155.03	−	10031.1i	0.135229	−	0.326472i
$982$		0			0
$983$	−14901.6	+	14901.6i	−0.483506	+	0.483506i	−0.906249	−	0.422743i	$-0.861067\pi$
$983$	−14901.6	+	14901.6i	−0.483506	+	0.483506i	0.422743	+	0.906249i	$0.361067\pi$
$984$		0			0
$985$	32028.4	+	32028.4i	1.03605	+	1.03605i
$986$		0			0
$987$	−9258.39	−	3834.95i	−0.298579	−	0.123676i
$988$		0			0
$989$	−2559.65	−	6179.54i	−0.0822973	−	0.198683i
$990$		0			0
$991$	18330.8			0.587586			0.293793	−	0.955869i	$-0.405082\pi$
$991$	18330.8			0.587586			0.293793	+	0.955869i	$0.405082\pi$
$992$		0			0
$993$	−4616.15			−0.147522
$994$		0			0
$995$	−32743.2	−	79049.1i	−1.04325	−	2.51862i
$996$		0			0
$997$	39601.9	+	16403.7i	1.25798	+	0.521072i	0.909289	−	0.416166i	$-0.136626\pi$
$997$	39601.9	+	16403.7i	1.25798	+	0.521072i	0.348690	+	0.937238i	$0.386626\pi$
$998$		0			0
$999$	−2875.49	−	2875.49i	−0.0910674	−	0.0910674i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.4.g.a.113.6		44
4.3	odd	2		32.4.g.a.5.1	✓	44
8.3	odd	2		256.4.g.b.225.6		44
8.5	even	2		256.4.g.a.225.6		44
32.3	odd	8		256.4.g.b.33.6		44
32.13	even	8	inner	128.4.g.a.17.6		44
32.19	odd	8		32.4.g.a.13.1	yes	44
32.29	even	8		256.4.g.a.33.6		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.4.g.a.5.1	✓	44	4.3	odd	2
32.4.g.a.13.1	yes	44	32.19	odd	8
128.4.g.a.17.6		44	32.13	even	8	inner
128.4.g.a.113.6		44	1.1	even	1	trivial
256.4.g.a.33.6		44	32.29	even	8
256.4.g.a.225.6		44	8.5	even	2
256.4.g.b.33.6		44	32.3	odd	8
256.4.g.b.225.6		44	8.3	odd	2

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:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	128.g (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.477813 + 1.15354i) q^{3} +(-16.3468 - 6.77105i) q^{5} +(18.0222 + 18.0222i) q^{7} +(17.9895 - 17.9895i) q^{9} +O(q^{10})\)	\(q+(0.477813 + 1.15354i) q^{3} +(-16.3468 - 6.77105i) q^{5} +(18.0222 + 18.0222i) q^{7} +(17.9895 - 17.9895i) q^{9} +(20.1053 - 48.5384i) q^{11} +(37.8086 - 15.6609i) q^{13} -22.0920i q^{15} -53.0615i q^{17} +(32.4427 - 13.4382i) q^{19} +(-12.1781 + 29.4006i) q^{21} +(-32.1343 + 32.1343i) q^{23} +(132.981 + 132.981i) q^{25} +(60.4929 + 25.0570i) q^{27} +(-52.0634 - 125.692i) q^{29} +53.3354 q^{31} +65.5976 q^{33} +(-172.576 - 416.634i) q^{35} +(-57.3789 - 23.7671i) q^{37} +(36.1309 + 36.1309i) q^{39} +(240.383 - 240.383i) q^{41} +(-56.3244 + 135.979i) q^{43} +(-415.879 + 172.263i) q^{45} +314.904i q^{47} +306.601i q^{49} +(61.2086 - 25.3534i) q^{51} +(-177.524 + 428.580i) q^{53} +(-657.312 + 657.312i) q^{55} +(31.0031 + 31.0031i) q^{57} +(133.963 + 55.4894i) q^{59} +(-191.454 - 462.211i) q^{61} +648.422 q^{63} -724.089 q^{65} +(55.4766 + 133.932i) q^{67} +(-52.4224 - 21.7141i) q^{69} +(-191.132 - 191.132i) q^{71} +(-175.452 + 175.452i) q^{73} +(-89.8593 + 216.940i) q^{75} +(1237.11 - 512.428i) q^{77} -1222.08i q^{79} -605.154i q^{81} +(-896.581 + 371.376i) q^{83} +(-359.282 + 867.384i) q^{85} +(120.115 - 120.115i) q^{87} +(883.293 + 883.293i) q^{89} +(963.639 + 399.152i) q^{91} +(25.4843 + 61.5246i) q^{93} -621.324 q^{95} -682.976 q^{97} +(-511.499 - 1234.87i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 44 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	\( 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 4 q^{13} + 4 q^{19} - 4 q^{21} - 324 q^{23} - 4 q^{25} + 268 q^{27} - 4 q^{29} + 752 q^{31} - 8 q^{33} + 460 q^{35} - 4 q^{37} - 596 q^{39} - 4 q^{41} - 804 q^{43} + 104 q^{45} + 1384 q^{51} + 748 q^{53} + 292 q^{55} - 4 q^{57} - 1372 q^{59} - 1828 q^{61} - 2512 q^{63} - 8 q^{65} - 2036 q^{67} - 1060 q^{69} - 220 q^{71} - 4 q^{73} + 1712 q^{75} + 1900 q^{77} - 2436 q^{83} + 496 q^{85} + 1292 q^{87} - 4 q^{89} + 3604 q^{91} - 112 q^{93} + 6088 q^{95} - 8 q^{97} + 5424 q^{99}+O(q^{100}) \) 44 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9 + 4 * q^11 - 4 * q^13 + 4 * q^19 - 4 * q^21 - 324 * q^23 - 4 * q^25 + 268 * q^27 - 4 * q^29 + 752 * q^31 - 8 * q^33 + 460 * q^35 - 4 * q^37 - 596 * q^39 - 4 * q^41 - 804 * q^43 + 104 * q^45 + 1384 * q^51 + 748 * q^53 + 292 * q^55 - 4 * q^57 - 1372 * q^59 - 1828 * q^61 - 2512 * q^63 - 8 * q^65 - 2036 * q^67 - 1060 * q^69 - 220 * q^71 - 4 * q^73 + 1712 * q^75 + 1900 * q^77 - 2436 * q^83 + 496 * q^85 + 1292 * q^87 - 4 * q^89 + 3604 * q^91 - 112 * q^93 + 6088 * q^95 - 8 * q^97 + 5424 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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