LMFDB - Embedded newform 560.4.q.n.81.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,4,Mod(81,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

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

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

chi := DirichletCharacter("560.81");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	560.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$33.0410696032$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 38 x^{8} - 5 x^{7} + 1102 x^{6} - 137 x^{5} + 11161 x^{4} + 10784 x^{3} + 81600 x^{2} + \cdots + 4096 $ x^10 - x^9 + 38x^8 - 5x^7 + 1102x^6 - 137x^5 + 11161x^4 + 10784x^3 + 81600x^2 + 18432x + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			81.1
Root			$1.92311 - 3.33093i$ of defining polynomial
Character	$\chi$	$=$	560.81
Dual form			560.4.q.n.401.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.48397 + 7.76647i) q^{3} +(2.50000 + 4.33013i) q^{5} +(-12.3509 - 13.8005i) q^{7} +(-26.7120 - 46.2666i) q^{9} +(11.5560 - 20.0155i) q^{11} +61.0473 q^{13} -44.8397 q^{15} +(-0.344154 + 0.596093i) q^{17} +(31.6124 + 54.7542i) q^{19} +(162.563 - 34.0419i) q^{21} +(62.2508 + 107.822i) q^{23} +(-12.5000 + 21.6506i) q^{25} +236.970 q^{27} +104.167 q^{29} +(140.011 - 242.506i) q^{31} +(103.633 + 179.498i) q^{33} +(28.8807 - 87.9824i) q^{35} +(131.936 + 228.519i) q^{37} +(-273.735 + 474.122i) q^{39} -243.366 q^{41} -172.541 q^{43} +(133.560 - 231.333i) q^{45} +(-53.6907 - 92.9951i) q^{47} +(-37.9094 + 340.899i) q^{49} +(-3.08636 - 5.34573i) q^{51} +(-22.4043 + 38.8054i) q^{53} +115.560 q^{55} -566.996 q^{57} +(228.623 - 395.986i) q^{59} +(-236.901 - 410.324i) q^{61} +(-308.586 + 940.076i) q^{63} +(152.618 + 264.343i) q^{65} +(-114.727 + 198.713i) q^{67} -1116.52 q^{69} -407.688 q^{71} +(174.238 - 301.789i) q^{73} +(-112.099 - 194.162i) q^{75} +(-418.952 + 87.7317i) q^{77} +(420.068 + 727.579i) q^{79} +(-341.342 + 591.221i) q^{81} +885.652 q^{83} -3.44154 q^{85} +(-467.082 + 809.010i) q^{87} +(428.048 + 741.401i) q^{89} +(-753.991 - 842.486i) q^{91} +(1255.61 + 2174.78i) q^{93} +(-158.062 + 273.771i) q^{95} +189.436 q^{97} -1234.74 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 8 q^{3} + 25 q^{5} + 62 q^{7} - 81 q^{9} + 47 q^{11} + 2 q^{13} - 80 q^{15} + 2 q^{17} - 21 q^{19} + 178 q^{21} + 201 q^{23} - 125 q^{25} + 1036 q^{27} + 380 q^{29} + 388 q^{31} + 262 q^{33} + 95 q^{35}+ \cdots - 70 q^{99}+O(q^{100}) $ 10 * q - 8 * q^3 + 25 * q^5 + 62 * q^7 - 81 * q^9 + 47 * q^11 + 2 * q^13 - 80 * q^15 + 2 * q^17 - 21 * q^19 + 178 * q^21 + 201 * q^23 - 125 * q^25 + 1036 * q^27 + 380 * q^29 + 388 * q^31 + 262 * q^33 + 95 * q^35 + 145 * q^37 + 14 * q^39 - 562 * q^41 - 1136 * q^43 + 405 * q^45 - 473 * q^47 + 998 * q^49 + 732 * q^51 - 351 * q^53 + 470 * q^55 + 1908 * q^57 + 708 * q^59 - 1944 * q^61 - 1955 * q^63 + 5 * q^65 + 1118 * q^67 + 748 * q^69 - 1728 * q^71 + 1652 * q^73 - 200 * q^75 + 787 * q^77 + 218 * q^79 + 455 * q^81 + 3004 * q^83 + 20 * q^85 + 390 * q^87 - 2322 * q^89 - 524 * q^91 + 2288 * q^93 + 105 * q^95 + 1196 * q^97 - 70 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

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
$3$	−4.48397	+	7.76647i	−0.862941	+	1.49466i	0.00613580	+	0.999981i	$0.498047\pi$
$3$	−4.48397	+	7.76647i	−0.862941	+	1.49466i	−0.869077	+	0.494677i	$0.835286\pi$
$4$		0			0
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$6$		0			0
$7$	−12.3509	−	13.8005i	−0.666887	−	0.745159i
$7$	−12.3509	−	13.8005i	−0.666887	−	0.745159i
$8$		0			0
$9$	−26.7120	−	46.2666i	−0.989335	−	1.71358i
$10$		0			0
$11$	11.5560	−	20.0155i	0.316751	−	0.548628i	−0.663057	−	0.748569i	$-0.730741\pi$
$11$	11.5560	−	20.0155i	0.316751	−	0.548628i	0.979808	+	0.199940i	$0.0640748\pi$
$12$		0			0
$13$	61.0473			1.30242			0.651211	−	0.758897i	$-0.274261\pi$
$13$	61.0473			1.30242			0.651211	+	0.758897i	$0.274261\pi$
$14$		0			0
$15$	−44.8397			−0.771838
$16$		0			0
$17$	−0.344154	+	0.596093i	−0.00490998	+	0.00850434i	−0.868470	−	0.495742i	$-0.834896\pi$
$17$	−0.344154	+	0.596093i	−0.00490998	+	0.00850434i	0.863560	+	0.504246i	$0.168230\pi$
$18$		0			0
$19$	31.6124	+	54.7542i	0.381704	+	0.661130i	0.991306	−	0.131577i	$-0.0420041\pi$
$19$	31.6124	+	54.7542i	0.381704	+	0.661130i	−0.609602	+	0.792707i	$0.708671\pi$
$20$		0			0
$21$	162.563	−	34.0419i	1.68924	−	0.353740i
$22$		0			0
$23$	62.2508	+	107.822i	0.564356	+	0.977493i	0.997109	+	0.0759809i	$0.0242088\pi$
$23$	62.2508	+	107.822i	0.564356	+	0.977493i	−0.432753	+	0.901512i	$0.642458\pi$
$24$		0			0
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$		0			0
$27$	236.970			1.68907
$28$		0			0
$29$	104.167			0.667011			0.333506	−	0.942748i	$-0.391768\pi$
$29$	104.167			0.667011			0.333506	+	0.942748i	$0.391768\pi$
$30$		0			0
$31$	140.011	−	242.506i	0.811185	−	1.40501i	−0.100850	−	0.994902i	$-0.532156\pi$
$31$	140.011	−	242.506i	0.811185	−	1.40501i	0.912035	−	0.410112i	$-0.134510\pi$
$32$		0			0
$33$	103.633	+	179.498i	0.546674	+	0.946868i
$34$		0			0
$35$	28.8807	−	87.9824i	0.139478	−	0.424907i
$36$		0			0
$37$	131.936	+	228.519i	0.586219	+	1.01536i	0.994722	+	0.102604i	$0.0327174\pi$
$37$	131.936	+	228.519i	0.586219	+	1.01536i	−0.408504	+	0.912757i	$0.633949\pi$
$38$		0			0
$39$	−273.735	+	474.122i	−1.12391	+	1.94668i
$40$		0			0
$41$	−243.366			−0.927009			−0.463505	−	0.886095i	$-0.653408\pi$
$41$	−243.366			−0.927009			−0.463505	+	0.886095i	$0.653408\pi$
$42$		0			0
$43$	−172.541			−0.611913			−0.305956	−	0.952046i	$-0.598976\pi$
$43$	−172.541			−0.611913			−0.305956	+	0.952046i	$0.598976\pi$
$44$		0			0
$45$	133.560	−	231.333i	0.442444	−	0.766336i
$46$		0			0
$47$	−53.6907	−	92.9951i	−0.166630	−	0.288611i	0.770603	−	0.637315i	$-0.219955\pi$
$47$	−53.6907	−	92.9951i	−0.166630	−	0.288611i	−0.937233	+	0.348704i	$0.886622\pi$
$48$		0			0
$49$	−37.9094	+	340.899i	−0.110523	+	0.993874i
$50$		0			0
$51$	−3.08636	−	5.34573i	−0.00847405	−	0.0146775i
$52$		0			0
$53$	−22.4043	+	38.8054i	−0.0580654	+	0.100572i	−0.893597	−	0.448870i	$-0.851827\pi$
$53$	−22.4043	+	38.8054i	−0.0580654	+	0.100572i	0.835532	+	0.549443i	$0.185160\pi$
$54$		0			0
$55$	115.560			0.283310
$56$		0			0
$57$	−566.996			−1.31755
$58$		0			0
$59$	228.623	−	395.986i	0.504477	−	0.873780i	−0.495509	−	0.868603i	$-0.665019\pi$
$59$	228.623	−	395.986i	0.504477	−	0.873780i	0.999987	−	0.00517746i	$-0.00164804\pi$
$60$		0			0
$61$	−236.901	−	410.324i	−0.497247	−	0.861256i	0.502748	−	0.864433i	$-0.332322\pi$
$61$	−236.901	−	410.324i	−0.497247	−	0.861256i	−0.999995	+	0.00317642i	$0.998989\pi$
$62$		0			0
$63$	−308.586	+	940.076i	−0.617113	+	1.87998i
$64$		0			0
$65$	152.618	+	264.343i	0.291230	+	0.504426i
$66$		0			0
$67$	−114.727	+	198.713i	−0.209196	+	0.362338i	−0.951461	−	0.307768i	$-0.900418\pi$
$67$	−114.727	+	198.713i	−0.209196	+	0.362338i	0.742266	+	0.670106i	$0.233751\pi$
$68$		0			0
$69$	−1116.52			−1.94802
$70$		0			0
$71$	−407.688			−0.681460			−0.340730	−	0.940161i	$-0.610674\pi$
$71$	−407.688			−0.681460			−0.340730	+	0.940161i	$0.610674\pi$
$72$		0			0
$73$	174.238	−	301.789i	0.279356	−	0.483859i	−0.691869	−	0.722023i	$-0.743212\pi$
$73$	174.238	−	301.789i	0.279356	−	0.483859i	0.971225	+	0.238165i	$0.0765457\pi$
$74$		0			0
$75$	−112.099	−	194.162i	−0.172588	−	0.298932i
$76$		0			0
$77$	−418.952	+	87.7317i	−0.620052	+	0.129844i
$78$		0			0
$79$	420.068	+	727.579i	0.598244	+	1.03619i	0.993080	+	0.117438i	$0.0374682\pi$
$79$	420.068	+	727.579i	0.598244	+	1.03619i	−0.394836	+	0.918752i	$0.629199\pi$
$80$		0			0
$81$	−341.342	+	591.221i	−0.468233	+	0.811003i
$82$		0			0
$83$	885.652			1.17124			0.585620	−	0.810586i	$-0.300851\pi$
$83$	885.652			1.17124			0.585620	+	0.810586i	$0.300851\pi$
$84$		0			0
$85$	−3.44154			−0.00439162
$86$		0			0
$87$	−467.082	+	809.010i	−0.575592	+	0.996954i
$88$		0			0
$89$	428.048	+	741.401i	0.509809	+	0.883015i	0.999935	+	0.0113636i	$0.00361722\pi$
$89$	428.048	+	741.401i	0.509809	+	0.883015i	−0.490127	+	0.871651i	$0.663049\pi$
$90$		0			0
$91$	−753.991	−	842.486i	−0.868569	−	0.970511i
$92$		0			0
$93$	1255.61	+	2174.78i	1.40001	+	2.42489i
$94$		0			0
$95$	−158.062	+	273.771i	−0.170703	+	0.295666i
$96$		0			0
$97$	189.436			0.198292			0.0991459	−	0.995073i	$-0.468389\pi$
$97$	189.436			0.198292			0.0991459	+	0.995073i	$0.468389\pi$
$98$		0			0
$99$	−1234.74			−1.25349
$100$		0			0
$101$	−397.902	+	689.186i	−0.392007	+	0.678976i	−0.992714	−	0.120493i	$-0.961552\pi$
$101$	−397.902	+	689.186i	−0.392007	+	0.678976i	0.600707	+	0.799469i	$0.294886\pi$
$102$		0			0
$103$	970.353	+	1680.70i	0.928269	+	1.60781i	0.786218	+	0.617950i	$0.212037\pi$
$103$	970.353	+	1680.70i	0.928269	+	1.60781i	0.142052	+	0.989859i	$0.454630\pi$
$104$		0			0
$105$	553.812	+	618.812i	0.514729	+	0.575142i
$106$		0			0
$107$	244.344	+	423.217i	0.220763	+	0.382373i	0.955040	−	0.296477i	$-0.0958119\pi$
$107$	244.344	+	423.217i	0.220763	+	0.382373i	−0.734277	+	0.678850i	$0.762479\pi$
$108$		0			0
$109$	−815.027	+	1411.67i	−0.716197	+	1.24049i	0.246300	+	0.969194i	$0.420785\pi$
$109$	−815.027	+	1411.67i	−0.716197	+	1.24049i	−0.962496	+	0.271295i	$0.912548\pi$
$110$		0			0
$111$	−2366.38			−2.02349
$112$		0			0
$113$	345.925			0.287981			0.143991	−	0.989579i	$-0.454007\pi$
$113$	345.925			0.287981			0.143991	+	0.989579i	$0.454007\pi$
$114$		0			0
$115$	−311.254	+	539.108i	−0.252388	+	0.437148i
$116$		0			0
$117$	−1630.70	−	2824.45i	−1.28853	−	2.23180i
$118$		0			0
$119$	12.4770	−	2.61278i	0.00961149	−	0.00201272i
$120$		0			0
$121$	398.419	+	690.082i	0.299338	+	0.518469i
$122$		0			0
$123$	1091.25	−	1890.09i	0.799954	−	1.38556i
$124$		0			0
$125$	−125.000			−0.0894427
$126$		0			0
$127$	1665.24			1.16351			0.581757	−	0.813362i	$-0.302365\pi$
$127$	1665.24			1.16351			0.581757	+	0.813362i	$0.302365\pi$
$128$		0			0
$129$	773.669	−	1340.03i	0.528045	−	0.914601i
$130$		0			0
$131$	338.374	+	586.080i	0.225678	+	0.390886i	0.956523	−	0.291658i	$-0.0942069\pi$
$131$	338.374	+	586.080i	0.225678	+	0.390886i	−0.730844	+	0.682544i	$0.760874\pi$
$132$		0			0
$133$	365.195	−	1112.53i	0.238094	−	0.725329i
$134$		0			0
$135$	592.425	+	1026.11i	0.377687	+	0.654174i
$136$		0			0
$137$	517.117	−	895.673i	0.322484	−	0.558558i	−0.658516	−	0.752567i	$-0.728816\pi$
$137$	517.117	−	895.673i	0.322484	−	0.558558i	0.981000	+	0.194008i	$0.0621489\pi$
$138$		0			0
$139$	−435.826			−0.265944			−0.132972	−	0.991120i	$-0.542452\pi$
$139$	−435.826			−0.265944			−0.132972	+	0.991120i	$0.542452\pi$
$140$		0			0
$141$	962.992			0.575167
$142$		0			0
$143$	705.462	−	1221.90i	0.412543	−	0.714546i
$144$		0			0
$145$	260.418	+	451.056i	0.149148	+	0.258332i
$146$		0			0
$147$	−2477.59	−	1823.00i	−1.39013	−	1.02285i
$148$		0			0
$149$	−1059.97	−	1835.93i	−0.582795	−	1.00943i	−0.995146	−	0.0984057i	$-0.968626\pi$
$149$	−1059.97	−	1835.93i	−0.582795	−	1.00943i	0.412351	−	0.911025i	$-0.364708\pi$
$150$		0			0
$151$	−1200.20	+	2078.81i	−0.646827	+	1.12034i	0.337050	+	0.941487i	$0.390571\pi$
$151$	−1200.20	+	2078.81i	−0.646827	+	1.12034i	−0.983876	+	0.178850i	$0.942762\pi$
$152$		0			0
$153$	36.7723			0.0194305
$154$		0			0
$155$	1400.11			0.725546
$156$		0			0
$157$	253.094	−	438.372i	0.128657	−	0.222840i	−0.794500	−	0.607265i	$-0.792267\pi$
$157$	253.094	−	438.372i	0.128657	−	0.222840i	0.923156	+	0.384425i	$0.125600\pi$
$158$		0			0
$159$	−200.921	−	348.005i	−0.100214	−	0.173576i
$160$		0			0
$161$	719.140	−	2190.79i	0.352026	−	1.07241i
$162$		0			0
$163$	1300.47	+	2252.49i	0.624913	+	1.08238i	0.988558	+	0.150844i	$0.0481991\pi$
$163$	1300.47	+	2252.49i	0.624913	+	1.08238i	−0.363644	+	0.931538i	$0.618468\pi$
$164$		0			0
$165$	−518.167	+	897.491i	−0.244480	+	0.423452i
$166$		0			0
$167$	−546.077			−0.253034			−0.126517	−	0.991964i	$-0.540380\pi$
$167$	−546.077			−0.253034			−0.126517	+	0.991964i	$0.540380\pi$
$168$		0			0
$169$	1529.78			0.696303
$170$		0			0
$171$	1688.86	−	2925.19i	0.755266	−	1.30816i
$172$		0			0
$173$	1510.16	+	2615.67i	0.663673	+	1.14951i	0.979643	+	0.200746i	$0.0643365\pi$
$173$	1510.16	+	2615.67i	0.663673	+	1.14951i	−0.315971	+	0.948769i	$0.602330\pi$
$174$		0			0
$175$	453.177	−	94.8987i	0.195754	−	0.0409924i
$176$		0			0
$177$	2050.28	+	3551.18i	0.870668	+	1.50804i
$178$		0			0
$179$	999.583	−	1731.33i	0.417387	−	0.722936i	−0.578288	−	0.815832i	$-0.696279\pi$
$179$	999.583	−	1731.33i	0.417387	−	0.722936i	0.995676	+	0.0928961i	$0.0296125\pi$
$180$		0			0
$181$	−681.145			−0.279719			−0.139859	−	0.990171i	$-0.544665\pi$
$181$	−681.145			−0.279719			−0.139859	+	0.990171i	$0.544665\pi$
$182$		0			0
$183$	4249.03			1.71638
$184$		0			0
$185$	−659.678	+	1142.60i	−0.262165	+	0.454083i
$186$		0			0
$187$	7.95408	+	13.7769i	0.00311048	+	0.00538751i
$188$		0			0
$189$	−2926.80	−	3270.31i	−1.12642	−	1.25862i
$190$		0			0
$191$	−806.381	−	1396.69i	−0.305485	−	0.529116i	0.671884	−	0.740656i	$-0.265485\pi$
$191$	−806.381	−	1396.69i	−0.305485	−	0.529116i	−0.977369	+	0.211541i	$0.932152\pi$
$192$		0			0
$193$	−404.461	+	700.547i	−0.150848	+	0.261277i	−0.931540	−	0.363640i	$-0.881534\pi$
$193$	−404.461	+	700.547i	−0.150848	+	0.261277i	0.780691	+	0.624917i	$0.214867\pi$
$194$		0			0
$195$	−2737.35			−1.00526
$196$		0			0
$197$	3704.23			1.33967			0.669836	−	0.742509i	$-0.266364\pi$
$197$	3704.23			1.33967			0.669836	+	0.742509i	$0.266364\pi$
$198$		0			0
$199$	−183.964	+	318.635i	−0.0655319	+	0.113505i	−0.896930	−	0.442173i	$-0.854208\pi$
$199$	−183.964	+	318.635i	−0.0655319	+	0.113505i	0.831398	+	0.555678i	$0.187541\pi$
$200$		0			0
$201$	−1028.87	−	1782.05i	−0.361047	−	0.625353i
$202$		0			0
$203$	−1286.56	−	1437.56i	−0.444821	−	0.497029i
$204$		0			0
$205$	−608.415	−	1053.81i	−0.207286	−	0.359029i
$206$		0			0
$207$	3325.69	−	5760.27i	1.11667	−	1.93414i
$208$		0			0
$209$	1461.25			0.483620
$210$		0			0
$211$	1073.36			0.350205			0.175102	−	0.984550i	$-0.443974\pi$
$211$	1073.36			0.350205			0.175102	+	0.984550i	$0.443974\pi$
$212$		0			0
$213$	1828.06	−	3166.30i	0.588060	−	1.01855i
$214$		0			0
$215$	−431.352	−	747.124i	−0.136828	−	0.236993i
$216$		0			0
$217$	−5075.98	+	1062.95i	−1.58793	+	0.332524i
$218$		0			0
$219$	1562.55	+	2706.42i	0.482135	+	0.835083i
$220$		0			0
$221$	−21.0097	+	36.3899i	−0.00639487	+	0.0110762i
$222$		0			0
$223$	1725.16			0.518050			0.259025	−	0.965871i	$-0.416599\pi$
$223$	1725.16			0.518050			0.259025	+	0.965871i	$0.416599\pi$
$224$		0			0
$225$	1335.60			0.395734
$226$		0			0
$227$	−1808.49	+	3132.40i	−0.528784	+	0.915880i	0.470653	+	0.882318i	$0.344018\pi$
$227$	−1808.49	+	3132.40i	−0.528784	+	0.915880i	−0.999437	+	0.0335619i	$0.989315\pi$
$228$		0			0
$229$	−730.893	−	1265.94i	−0.210912	−	0.365309i	0.741089	−	0.671407i	$-0.234310\pi$
$229$	−730.893	−	1265.94i	−0.210912	−	0.365309i	−0.952000	+	0.306098i	$0.900977\pi$
$230$		0			0
$231$	1197.20	−	3647.17i	0.340997	−	1.03881i
$232$		0			0
$233$	−1067.66	−	1849.24i	−0.300192	−	0.519947i	0.675988	−	0.736913i	$-0.263717\pi$
$233$	−1067.66	−	1849.24i	−0.300192	−	0.519947i	−0.976179	+	0.216966i	$0.930384\pi$
$234$		0			0
$235$	268.454	−	464.976i	0.0745191	−	0.129071i
$236$		0			0
$237$	−7534.29			−2.06500
$238$		0			0
$239$	−5952.35			−1.61099			−0.805493	−	0.592605i	$-0.798100\pi$
$239$	−5952.35			−1.61099			−0.805493	+	0.592605i	$0.798100\pi$
$240$		0			0
$241$	1923.78	−	3332.08i	0.514197	−	0.890615i	−0.485668	−	0.874144i	$-0.661423\pi$
$241$	1923.78	−	3332.08i	0.514197	−	0.890615i	0.999864	−	0.0164713i	$-0.00524321\pi$
$242$		0			0
$243$	137.960	+	238.954i	0.0364203	+	0.0630819i
$244$		0			0
$245$	−1570.91	+	688.094i	−0.409639	+	0.179432i
$246$		0			0
$247$	1929.85	+	3342.60i	0.497139	+	0.861071i
$248$		0			0
$249$	−3971.24	+	6878.39i	−1.01071	+	1.75060i
$250$		0			0
$251$	1731.69			0.435470			0.217735	−	0.976008i	$-0.430133\pi$
$251$	1731.69			0.435470			0.217735	+	0.976008i	$0.430133\pi$
$252$		0			0
$253$	2877.47			0.715041
$254$		0			0
$255$	15.4318	−	26.7287i	0.00378971	−	0.00656397i
$256$		0			0
$257$	2027.21	+	3511.24i	0.492039	+	0.852237i	0.999958	−	0.00916808i	$-0.00291833\pi$
$257$	2027.21	+	3511.24i	0.492039	+	0.852237i	−0.507919	+	0.861405i	$0.669585\pi$
$258$		0			0
$259$	1524.16	−	4643.21i	0.365663	−	1.11396i
$260$		0			0
$261$	−2782.51	−	4819.46i	−0.659898	−	1.14298i
$262$		0			0
$263$	−3167.91	+	5486.98i	−0.742744	+	1.28647i	0.208498	+	0.978023i	$0.433143\pi$
$263$	−3167.91	+	5486.98i	−0.742744	+	1.28647i	−0.951242	+	0.308447i	$0.900191\pi$
$264$		0			0
$265$	−224.043			−0.0519353
$266$		0			0
$267$	−7677.42			−1.75974
$268$		0			0
$269$	660.817	−	1144.57i	0.149780	−	0.259426i	−0.781366	−	0.624073i	$-0.785477\pi$
$269$	660.817	−	1144.57i	0.149780	−	0.259426i	0.931146	+	0.364647i	$0.118810\pi$
$270$		0			0
$271$	−1168.00	−	2023.04i	−0.261812	−	0.453471i	0.704912	−	0.709295i	$-0.250987\pi$
$271$	−1168.00	−	2023.04i	−0.261812	−	0.453471i	−0.966723	+	0.255824i	$0.917653\pi$
$272$		0			0
$273$	9924.02	−	2078.16i	2.20011	−	0.460719i
$274$		0			0
$275$	288.899	+	500.388i	0.0633501	+	0.109726i
$276$		0			0
$277$	3542.61	−	6135.99i	0.768430	−	1.33096i	−0.169984	−	0.985447i	$-0.554372\pi$
$277$	3542.61	−	6135.99i	0.768430	−	1.33096i	0.938414	−	0.345513i	$-0.112295\pi$
$278$		0			0
$279$	−14959.9			−3.21013
$280$		0			0
$281$	2123.17			0.450738			0.225369	−	0.974273i	$-0.427641\pi$
$281$	2123.17			0.450738			0.225369	+	0.974273i	$0.427641\pi$
$282$		0			0
$283$	2945.82	−	5102.30i	0.618765	−	1.07173i	−0.370946	−	0.928654i	$-0.620967\pi$
$283$	2945.82	−	5102.30i	0.618765	−	1.07173i	0.989711	−	0.143078i	$-0.0457001\pi$
$284$		0			0
$285$	−1417.49	−	2455.16i	−0.294613	−	0.510286i
$286$		0			0
$287$	3005.79	+	3358.58i	0.618210	+	0.690769i
$288$		0			0
$289$	2456.26	+	4254.37i	0.499952	+	0.865942i
$290$		0			0
$291$	−849.426	+	1471.25i	−0.171114	+	0.296378i
$292$		0			0
$293$	−8137.75			−1.62257			−0.811284	−	0.584652i	$-0.801231\pi$
$293$	−8137.75			−1.62257			−0.811284	+	0.584652i	$0.801231\pi$
$294$		0			0
$295$	2286.23			0.451218
$296$		0			0
$297$	2738.42	−	4743.08i	0.535014	−	0.926671i
$298$		0			0
$299$	3800.25	+	6582.22i	0.735030	+	1.27311i
$300$		0			0
$301$	2131.04	+	2381.16i	0.408077	+	0.455972i
$302$		0			0
$303$	−3568.36	−	6180.58i	−0.676558	−	1.17183i
$304$		0			0
$305$	1184.50	−	2051.62i	0.222375	−	0.385166i
$306$		0			0
$307$	4797.24			0.891833			0.445917	−	0.895075i	$-0.352878\pi$
$307$	4797.24			0.891833			0.445917	+	0.895075i	$0.352878\pi$
$308$		0			0
$309$	−17404.1			−3.20417
$310$		0			0
$311$	2594.76	−	4494.26i	0.473105	−	0.819442i	−0.526421	−	0.850224i	$-0.676467\pi$
$311$	2594.76	−	4494.26i	0.473105	−	0.819442i	0.999526	+	0.0307823i	$0.00979987\pi$
$312$		0			0
$313$	1122.62	+	1944.44i	0.202729	+	0.351138i	0.949407	−	0.314049i	$-0.101686\pi$
$313$	1122.62	+	1944.44i	0.202729	+	0.351138i	−0.746678	+	0.665186i	$0.768352\pi$
$314$		0			0
$315$	−4842.11	+	1013.98i	−0.866102	+	0.181368i
$316$		0			0
$317$	4871.13	+	8437.05i	0.863060	+	1.49486i	0.868961	+	0.494881i	$0.164788\pi$
$317$	4871.13	+	8437.05i	0.863060	+	1.49486i	−0.00590040	+	0.999983i	$0.501878\pi$
$318$		0			0
$319$	1203.75	−	2084.96i	0.211276	−	0.365941i
$320$		0			0
$321$	−4382.53			−0.762022
$322$		0			0
$323$	−43.5181			−0.00749663
$324$		0			0
$325$	−763.092	+	1321.71i	−0.130242	+	0.225586i
$326$		0			0
$327$	−7309.12	−	12659.8i	−1.23607	−	2.14094i
$328$		0			0
$329$	−620.252	+	1889.54i	−0.103938	+	0.316637i
$330$		0			0
$331$	5665.38	+	9812.73i	0.940778	+	1.62948i	0.763992	+	0.645226i	$0.223237\pi$
$331$	5665.38	+	9812.73i	0.940778	+	1.62948i	0.176786	+	0.984249i	$0.443430\pi$
$332$		0			0
$333$	7048.54	−	12208.4i	1.15993	−	2.00906i
$334$		0			0
$335$	−1147.27			−0.187110
$336$		0			0
$337$	3637.35			0.587950			0.293975	−	0.955813i	$-0.405022\pi$
$337$	3637.35			0.587950			0.293975	+	0.955813i	$0.405022\pi$
$338$		0			0
$339$	−1551.12	+	2686.61i	−0.248511	+	0.430433i
$340$		0			0
$341$	−3235.93	−	5604.79i	−0.513887	−	0.890078i
$342$		0			0
$343$	5172.80	−	3687.24i	0.814300	−	0.580444i
$344$		0			0
$345$	−2791.31	−	4834.69i	−0.435591	−	0.754467i
$346$		0			0
$347$	−2015.06	+	3490.19i	−0.311741	+	0.539951i	−0.978739	−	0.205108i	$-0.934245\pi$
$347$	−2015.06	+	3490.19i	−0.311741	+	0.539951i	0.666998	+	0.745059i	$0.267579\pi$
$348$		0			0
$349$	2887.69			0.442906			0.221453	−	0.975171i	$-0.428920\pi$
$349$	2887.69			0.442906			0.221453	+	0.975171i	$0.428920\pi$
$350$		0			0
$351$	14466.4			2.19988
$352$		0			0
$353$	262.459	−	454.592i	0.0395731	−	0.0685425i	−0.845561	−	0.533880i	$-0.820734\pi$
$353$	262.459	−	454.592i	0.0395731	−	0.0685425i	0.885134	+	0.465337i	$0.154067\pi$
$354$		0			0
$355$	−1019.22	−	1765.34i	−0.152379	−	0.263928i
$356$		0			0
$357$	−35.6545	+	108.618i	−0.00528582	+	0.0161027i
$358$		0			0
$359$	−1642.66	−	2845.17i	−0.241493	−	0.418279i	0.719646	−	0.694341i	$-0.244304\pi$
$359$	−1642.66	−	2845.17i	−0.241493	−	0.418279i	−0.961140	+	0.276062i	$0.910971\pi$
$360$		0			0
$361$	1430.82	−	2478.25i	0.208605	−	0.361314i
$362$		0			0
$363$	−7146.00			−1.03324
$364$		0			0
$365$	1742.38			0.249864
$366$		0			0
$367$	4526.98	−	7840.95i	0.643886	−	1.11524i	−0.340671	−	0.940182i	$-0.610654\pi$
$367$	4526.98	−	7840.95i	0.643886	−	1.11524i	0.984558	−	0.175061i	$-0.0560123\pi$
$368$		0			0
$369$	6500.80	+	11259.7i	0.917122	+	1.58850i
$370$		0			0
$371$	812.249	−	170.091i	0.113665	−	0.0238024i
$372$		0			0
$373$	2604.55	+	4511.22i	0.361551	+	0.626225i	0.988216	−	0.153064i	$-0.0489139\pi$
$373$	2604.55	+	4511.22i	0.361551	+	0.626225i	−0.626665	+	0.779289i	$0.715581\pi$
$374$		0			0
$375$	560.497	−	970.809i	0.0771838	−	0.133686i
$376$		0			0
$377$	6359.12			0.868730
$378$		0			0
$379$	−3200.68			−0.433794			−0.216897	−	0.976194i	$-0.569594\pi$
$379$	−3200.68			−0.433794			−0.216897	+	0.976194i	$0.569594\pi$
$380$		0			0
$381$	−7466.90	+	12933.1i	−1.00404	+	1.73906i
$382$		0			0
$383$	−1101.40	−	1907.69i	−0.146943	−	0.254513i	0.783153	−	0.621829i	$-0.213610\pi$
$383$	−1101.40	−	1907.69i	−0.146943	−	0.254513i	−0.930096	+	0.367316i	$0.880277\pi$
$384$		0			0
$385$	−1427.27	−	1594.79i	−0.188936	−	0.211111i
$386$		0			0
$387$	4608.92	+	7982.89i	0.605387	+	1.04856i
$388$		0			0
$389$	3120.79	−	5405.38i	0.406762	−	0.704533i	−0.587762	−	0.809034i	$-0.699991\pi$
$389$	3120.79	−	5405.38i	0.406762	−	0.704533i	0.994525	+	0.104500i	$0.0333244\pi$
$390$		0			0
$391$	−85.6955			−0.0110839
$392$		0			0
$393$	−6069.04			−0.778988
$394$		0			0
$395$	−2100.34	+	3637.89i	−0.267543	+	0.463398i
$396$		0			0
$397$	−5203.58	−	9012.87i	−0.657834	−	1.13940i	−0.981175	−	0.193120i	$-0.938139\pi$
$397$	−5203.58	−	9012.87i	−0.657834	−	1.13940i	0.323341	−	0.946283i	$-0.395194\pi$
$398$		0			0
$399$	7002.92	+	7824.84i	0.878658	+	0.981785i
$400$		0			0
$401$	7486.63	+	12967.2i	0.932330	+	1.61484i	0.779327	+	0.626618i	$0.215561\pi$
$401$	7486.63	+	12967.2i	0.932330	+	1.61484i	0.153003	+	0.988226i	$0.451105\pi$
$402$		0			0
$403$	8547.30	−	14804.4i	1.05651	−	1.82992i
$404$		0			0
$405$	−3413.42			−0.418800
$406$		0			0
$407$	6098.58			0.742741
$408$		0			0
$409$	3529.55	−	6113.36i	0.426711	−	0.739086i	−0.569867	−	0.821737i	$-0.693005\pi$
$409$	3529.55	−	6113.36i	0.426711	−	0.739086i	0.996579	+	0.0826512i	$0.0263387\pi$
$410$		0			0
$411$	4637.48	+	8032.35i	0.556569	+	0.964006i
$412$		0			0
$413$	−8288.52	+	1735.68i	−0.987534	+	0.206797i
$414$		0			0
$415$	2214.13	+	3834.99i	0.261897	+	0.453619i
$416$		0			0
$417$	1954.23	−	3384.83i	0.229494	−	0.397496i
$418$		0			0
$419$	−928.543			−0.108263			−0.0541316	−	0.998534i	$-0.517239\pi$
$419$	−928.543			−0.108263			−0.0541316	+	0.998534i	$0.517239\pi$
$420$		0			0
$421$	7105.06			0.822517			0.411258	−	0.911519i	$-0.365089\pi$
$421$	7105.06			0.822517			0.411258	+	0.911519i	$0.365089\pi$
$422$		0			0
$423$	−2868.38	+	4968.18i	−0.329705	+	0.571066i
$424$		0			0
$425$	−8.60386	−	14.9023i	−0.000981996	−	0.00170087i
$426$		0			0
$427$	−2736.75	+	8337.24i	−0.310165	+	0.944888i
$428$		0			0
$429$	6326.54	+	10957.9i	0.712001	+	1.23322i
$430$		0			0
$431$	−2159.64	+	3740.60i	−0.241360	+	0.418047i	−0.961102	−	0.276194i	$-0.910927\pi$
$431$	−2159.64	+	3740.60i	−0.241360	+	0.418047i	0.719742	+	0.694241i	$0.244260\pi$
$432$		0			0
$433$	4600.60			0.510602			0.255301	−	0.966862i	$-0.417825\pi$
$433$	4600.60			0.510602			0.255301	+	0.966862i	$0.417825\pi$
$434$		0			0
$435$	−4670.82			−0.514825
$436$		0			0
$437$	−3935.79	+	6816.99i	−0.430834	+	0.746226i
$438$		0			0
$439$	961.868	+	1666.00i	0.104573	+	0.181125i	0.913564	−	0.406696i	$-0.133319\pi$
$439$	961.868	+	1666.00i	0.104573	+	0.181125i	−0.808991	+	0.587821i	$0.799986\pi$
$440$		0			0
$441$	16784.9	−	7352.16i	1.81242	−	0.793884i
$442$		0			0
$443$	−2267.44	−	3927.32i	−0.243181	−	0.421202i	0.718438	−	0.695591i	$-0.244858\pi$
$443$	−2267.44	−	3927.32i	−0.243181	−	0.421202i	−0.961619	+	0.274390i	$0.911524\pi$
$444$		0			0
$445$	−2140.24	+	3707.00i	−0.227993	+	0.394896i
$446$		0			0
$447$	19011.6			2.01167
$448$		0			0
$449$	−17431.9			−1.83221			−0.916105	−	0.400937i	$-0.868684\pi$
$449$	−17431.9			−1.83221			−0.916105	+	0.400937i	$0.868684\pi$
$450$		0			0
$451$	−2812.33	+	4871.10i	−0.293631	+	0.508583i
$452$		0			0
$453$	−10763.3	−	18642.6i	−1.11635	−	1.93357i
$454$		0			0
$455$	1763.09	−	5371.09i	0.181660	−	0.553408i
$456$		0			0
$457$	981.162	+	1699.42i	0.100431	+	0.173951i	0.911862	−	0.410496i	$-0.134645\pi$
$457$	981.162	+	1699.42i	0.100431	+	0.173951i	−0.811431	+	0.584448i	$0.801311\pi$
$458$		0			0
$459$	−81.5542	+	141.256i	−0.00829330	+	0.0143644i
$460$		0			0
$461$	14344.4			1.44920			0.724602	−	0.689167i	$-0.242024\pi$
$461$	14344.4			1.44920			0.724602	+	0.689167i	$0.242024\pi$
$462$		0			0
$463$	−11657.8			−1.17016			−0.585081	−	0.810975i	$-0.698937\pi$
$463$	−11657.8			−1.17016			−0.585081	+	0.810975i	$0.698937\pi$
$464$		0			0
$465$	−6278.06	+	10873.9i	−0.626103	+	1.08444i
$466$		0			0
$467$	−8256.88	−	14301.3i	−0.818164	−	1.41710i	−0.907033	−	0.421059i	$-0.861659\pi$
$467$	−8256.88	−	14301.3i	−0.818164	−	1.41710i	0.0888691	−	0.996043i	$-0.471675\pi$
$468$		0			0
$469$	4159.33	−	870.995i	0.409509	−	0.0857544i
$470$		0			0
$471$	2269.73	+	3931.30i	0.222046	+	0.384596i
$472$		0			0
$473$	−1993.88	+	3453.50i	−0.193824	+	0.335713i
$474$		0			0
$475$	−1580.62			−0.152681
$476$		0			0
$477$	2393.86			0.229785
$478$		0			0
$479$	−7810.03	+	13527.4i	−0.744988	+	1.29036i	0.205212	+	0.978718i	$0.434212\pi$
$479$	−7810.03	+	13527.4i	−0.744988	+	1.29036i	−0.950200	+	0.311640i	$0.899122\pi$
$480$		0			0
$481$	8054.32	+	13950.5i	0.763504	+	1.32243i
$482$		0			0
$483$	13790.1	+	15408.6i	1.29911	+	1.45159i
$484$		0			0
$485$	473.590	+	820.282i	0.0443394	+	0.0767981i
$486$		0			0
$487$	950.691	−	1646.65i	0.0884598	−	0.153217i	−0.818400	−	0.574648i	$-0.805139\pi$
$487$	950.691	−	1646.65i	0.0884598	−	0.153217i	0.906860	+	0.421431i	$0.138472\pi$
$488$		0			0
$489$	−23325.1			−2.15705
$490$		0			0
$491$	15964.1			1.46731			0.733654	−	0.679524i	$-0.237814\pi$
$491$	15964.1			1.46731			0.733654	+	0.679524i	$0.237814\pi$
$492$		0			0
$493$	−35.8495	+	62.0932i	−0.00327501	+	0.00567249i
$494$		0			0
$495$	−3086.84	−	5346.56i	−0.280289	−	0.485475i
$496$		0			0
$497$	5035.33	+	5626.31i	0.454457	+	0.507796i
$498$		0			0
$499$	−3424.59	−	5931.56i	−0.307226	−	0.532130i	0.670529	−	0.741884i	$-0.266067\pi$
$499$	−3424.59	−	5931.56i	−0.307226	−	0.532130i	−0.977754	+	0.209753i	$0.932734\pi$
$500$		0			0
$501$	2448.59	−	4241.09i	0.218354	−	0.378199i
$502$		0			0
$503$	766.190			0.0679179			0.0339590	−	0.999423i	$-0.489188\pi$
$503$	766.190			0.0679179			0.0339590	+	0.999423i	$0.489188\pi$
$504$		0			0
$505$	−3979.02			−0.350621
$506$		0			0
$507$	−6859.49	+	11881.0i	−0.600869	+	1.04074i
$508$		0			0
$509$	−6802.36	−	11782.0i	−0.592356	−	1.02599i	−0.993914	−	0.110157i	$-0.964865\pi$
$509$	−6802.36	−	11782.0i	−0.592356	−	1.02599i	0.401558	−	0.915834i	$-0.368469\pi$
$510$		0			0
$511$	−6316.84	+	1322.79i	−0.546850	+	0.114515i
$512$		0			0
$513$	7491.18	+	12975.1i	0.644724	+	1.11669i
$514$		0			0
$515$	−4851.76	+	8403.50i	−0.415135	+	0.719034i
$516$		0			0
$517$	−2481.80			−0.211120
$518$		0			0
$519$	−27086.1			−2.29084
$520$		0			0
$521$	−9214.16	+	15959.4i	−0.774817	+	1.34202i	0.160080	+	0.987104i	$0.448825\pi$
$521$	−9214.16	+	15959.4i	−0.774817	+	1.34202i	−0.934897	+	0.354919i	$0.884509\pi$
$522$		0			0
$523$	2170.06	+	3758.66i	0.181435	+	0.314254i	0.942369	−	0.334575i	$-0.108593\pi$
$523$	2170.06	+	3758.66i	0.181435	+	0.314254i	−0.760935	+	0.648828i	$0.775259\pi$
$524$		0			0
$525$	−1295.01	+	3945.11i	−0.107655	+	0.327959i
$526$		0			0
$527$	96.3708	+	166.919i	0.00796581	+	0.0137972i
$528$		0			0
$529$	−1666.82	+	2887.03i	−0.136996	+	0.237283i
$530$		0			0
$531$	−24427.9			−1.99639
$532$		0			0
$533$	−14856.8			−1.20736
$534$		0			0
$535$	−1221.72	+	2116.08i	−0.0987282	+	0.171002i
$536$		0			0
$537$	8964.21	+	15526.5i	0.720362	+	1.24770i
$538$		0			0
$539$	6385.19	+	4698.19i	0.510259	+	0.375446i
$540$		0			0
$541$	−6308.12	−	10926.0i	−0.501308	−	0.868290i	−0.999999	−	0.00151060i	$-0.999519\pi$
$541$	−6308.12	−	10926.0i	−0.501308	−	0.868290i	0.498691	−	0.866780i	$-0.333814\pi$
$542$		0			0
$543$	3054.24	−	5290.09i	0.241381	−	0.418084i
$544$		0			0
$545$	−8150.27			−0.640586
$546$		0			0
$547$	−20677.8			−1.61630			−0.808151	−	0.588975i	$-0.799532\pi$
$547$	−20677.8			−1.61630			−0.808151	+	0.588975i	$0.799532\pi$
$548$		0			0
$549$	−12656.2	+	21921.2i	−0.983887	+	1.70414i
$550$		0			0
$551$	3292.96	+	5703.58i	0.254601	+	0.440981i
$552$		0			0
$553$	4852.75	−	14783.4i	0.373164	−	1.13681i
$554$		0			0
$555$	−5915.96	−	10246.7i	−0.452466	−	0.783694i
$556$		0			0
$557$	507.586	−	879.164i	0.0386124	−	0.0668786i	−0.846073	−	0.533066i	$-0.821040\pi$
$557$	507.586	−	879.164i	0.0386124	−	0.0668786i	0.884686	+	0.466188i	$0.154373\pi$
$558$		0			0
$559$	−10533.2			−0.796969
$560$		0			0
$561$	−142.664			−0.0107366
$562$		0			0
$563$	2648.32	−	4587.03i	0.198248	−	0.343375i	−0.749713	−	0.661763i	$-0.769808\pi$
$563$	2648.32	−	4587.03i	0.198248	−	0.343375i	0.947960	+	0.318388i	$0.103142\pi$
$564$		0			0
$565$	864.812	+	1497.90i	0.0643945	+	0.111535i
$566$		0			0
$567$	12375.0	−	2591.43i	0.916584	−	0.191940i
$568$		0			0
$569$	−7370.61	−	12766.3i	−0.543044	−	0.940580i	−0.998727	−	0.0504381i	$-0.983938\pi$
$569$	−7370.61	−	12766.3i	−0.543044	−	0.940580i	0.455683	−	0.890142i	$-0.349395\pi$
$570$		0			0
$571$	6830.70	−	11831.1i	0.500624	−	0.867105i	−0.499376	−	0.866385i	$-0.666437\pi$
$571$	6830.70	−	11831.1i	0.500624	−	0.867105i	1.00000		0.000720144i	$-0.000229229\pi$
$572$		0			0
$573$	14463.2			1.05446
$574$		0			0
$575$	−3112.54			−0.225742
$576$		0			0
$577$	−539.307	+	934.107i	−0.0389110	+	0.0673958i	−0.884825	−	0.465923i	$-0.845722\pi$
$577$	−539.307	+	934.107i	−0.0389110	+	0.0673958i	0.845914	+	0.533319i	$0.179056\pi$
$578$		0			0
$579$	−3627.18	−	6282.46i	−0.260346	−	0.450933i
$580$		0			0
$581$	−10938.6	−	12222.5i	−0.781085	−	0.872760i
$582$		0			0
$583$	517.807	+	896.868i	0.0367845	+	0.0637126i
$584$		0			0
$585$	8153.50	−	14122.3i	0.576249	−	0.998092i
$586$		0			0
$587$	−3863.36			−0.271649			−0.135824	−	0.990733i	$-0.543368\pi$
$587$	−3863.36			−0.271649			−0.135824	+	0.990733i	$0.543368\pi$
$588$		0			0
$589$	17704.3			1.23853
$590$		0			0
$591$	−16609.7	+	28768.8i	−1.15606	+	2.00235i
$592$		0			0
$593$	4720.41	+	8175.98i	0.326887	+	0.566185i	0.981892	−	0.189439i	$-0.0606671\pi$
$593$	4720.41	+	8175.98i	0.326887	+	0.566185i	−0.655006	+	0.755624i	$0.727334\pi$
$594$		0			0
$595$	42.5062	+	47.4951i	0.00292872	+	0.00327246i
$596$		0			0
$597$	−1649.78	−	2857.50i	−0.113100	−	0.195896i
$598$		0			0
$599$	−10684.5	+	18506.0i	−0.728807	+	1.26233i	0.228581	+	0.973525i	$0.426592\pi$
$599$	−10684.5	+	18506.0i	−0.728807	+	1.26233i	−0.957388	+	0.288806i	$0.906742\pi$
$600$		0			0
$601$	5801.37			0.393748			0.196874	−	0.980429i	$-0.436921\pi$
$601$	5801.37			0.393748			0.196874	+	0.980429i	$0.436921\pi$
$602$		0			0
$603$	12258.4			0.827859
$604$		0			0
$605$	−1992.09	+	3450.41i	−0.133868	+	0.231866i
$606$		0			0
$607$	13370.0	+	23157.5i	0.894023	+	1.54849i	0.835009	+	0.550236i	$0.185462\pi$
$607$	13370.0	+	23157.5i	0.894023	+	1.54849i	0.0590141	+	0.998257i	$0.481204\pi$
$608$		0			0
$609$	16933.7	−	3546.04i	1.12674	−	0.235949i
$610$		0			0
$611$	−3277.68	−	5677.10i	−0.217022	−	0.375894i
$612$		0			0
$613$	4169.87	−	7222.43i	0.274746	−	0.475875i	−0.695325	−	0.718696i	$-0.744739\pi$
$613$	4169.87	−	7222.43i	0.274746	−	0.475875i	0.970071	+	0.242821i	$0.0780728\pi$
$614$		0			0
$615$	10912.5			0.715501
$616$		0			0
$617$	−26639.2			−1.73818			−0.869088	−	0.494658i	$-0.835293\pi$
$617$	−26639.2			−1.73818			−0.869088	+	0.494658i	$0.835293\pi$
$618$		0			0
$619$	13930.2	−	24127.7i	0.904523	−	1.56668i	0.0829678	−	0.996552i	$-0.473560\pi$
$619$	13930.2	−	24127.7i	0.904523	−	1.56668i	0.821556	−	0.570128i	$-0.193107\pi$
$620$		0			0
$621$	14751.6	+	25550.5i	0.953237	+	1.65105i
$622$		0			0
$623$	4944.94	−	15064.3i	0.318001	−	0.968760i
$624$		0			0
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	−6552.19	+	11348.7i	−0.417335	+	0.722846i
$628$		0			0
$629$	−181.625			−0.0115133
$630$		0			0
$631$	10886.7			0.686833			0.343417	−	0.939183i	$-0.388416\pi$
$631$	10886.7			0.686833			0.343417	+	0.939183i	$0.388416\pi$
$632$		0			0
$633$	−4812.92	+	8336.23i	−0.302206	+	0.523437i
$634$		0			0
$635$	4163.11	+	7210.71i	0.260170	+	0.450627i
$636$		0			0
$637$	−2314.27	+	20811.0i	−0.143948	+	1.29444i
$638$		0			0
$639$	10890.2	+	18862.4i	0.674193	+	1.16774i
$640$		0			0
$641$	8425.73	−	14593.8i	0.519183	−	0.899251i	−0.480568	−	0.876957i	$-0.659570\pi$
$641$	8425.73	−	14593.8i	0.519183	−	0.899251i	0.999751	−	0.0222942i	$-0.00709704\pi$
$642$		0			0
$643$	−4793.72			−0.294006			−0.147003	−	0.989136i	$-0.546963\pi$
$643$	−4793.72			−0.294006			−0.147003	+	0.989136i	$0.546963\pi$
$644$		0			0
$645$	7736.69			0.472298
$646$		0			0
$647$	−13342.3	+	23109.5i	−0.810725	+	1.40422i	0.101633	+	0.994822i	$0.467593\pi$
$647$	−13342.3	+	23109.5i	−0.810725	+	1.40422i	−0.912358	+	0.409394i	$0.865740\pi$
$648$		0			0
$649$	−5283.92	−	9152.01i	−0.319587	−	0.553541i
$650$		0			0
$651$	14505.2	−	44188.7i	0.873278	−	2.66036i
$652$		0			0
$653$	−8770.94	−	15191.7i	−0.525625	−	0.910409i	−0.999554	−	0.0298466i	$-0.990498\pi$
$653$	−8770.94	−	15191.7i	−0.525625	−	0.910409i	0.473929	−	0.880563i	$-0.342835\pi$
$654$		0			0
$655$	−1691.87	+	2930.40i	−0.100926	+	0.174810i
$656$		0			0
$657$	−18617.0			−1.10551
$658$		0			0
$659$	26285.3			1.55377			0.776883	−	0.629645i	$-0.216800\pi$
$659$	26285.3			1.55377			0.776883	+	0.629645i	$0.216800\pi$
$660$		0			0
$661$	−12522.1	+	21689.0i	−0.736845	+	1.27625i	0.217064	+	0.976157i	$0.430352\pi$
$661$	−12522.1	+	21689.0i	−0.736845	+	1.27625i	−0.953909	+	0.300096i	$0.902981\pi$
$662$		0			0
$663$	−188.414	−	326.343i	−0.0110368	−	0.0191163i
$664$		0			0
$665$	5730.39	−	1199.99i	0.334158	−	0.0699753i
$666$		0			0
$667$	6484.48	+	11231.4i	0.376432	+	0.651999i
$668$		0			0
$669$	−7735.57	+	13398.4i	−0.447047	+	0.774308i
$670$		0			0
$671$	−10950.5			−0.630013
$672$		0			0
$673$	20799.4			1.19132			0.595658	−	0.803238i	$-0.296891\pi$
$673$	20799.4			1.19132			0.595658	+	0.803238i	$0.296891\pi$
$674$		0			0
$675$	−2962.12	+	5130.55i	−0.168907	+	0.292555i
$676$		0			0
$677$	−14886.3	−	25783.8i	−0.845089	−	1.46374i	−0.885543	−	0.464556i	$-0.846214\pi$
$677$	−14886.3	−	25783.8i	−0.845089	−	1.46374i	0.0404540	−	0.999181i	$-0.487120\pi$
$678$		0			0
$679$	−2339.71	−	2614.32i	−0.132238	−	0.147759i
$680$		0			0
$681$	−16218.5	−	28091.2i	−0.912619	−	1.58070i
$682$		0			0
$683$	11945.2	−	20689.6i	0.669208	−	1.15910i	−0.308918	−	0.951089i	$-0.599967\pi$
$683$	11945.2	−	20689.6i	0.669208	−	1.15910i	0.978126	−	0.208014i	$-0.0666999\pi$
$684$		0			0
$685$	5171.17			0.288438
$686$		0			0
$687$	13109.2			0.728017
$688$		0			0
$689$	−1367.72	+	2368.97i	−0.0756257	+	0.130987i
$690$		0			0
$691$	−12648.8	−	21908.3i	−0.696356	−	1.20612i	−0.969721	−	0.244214i	$-0.921470\pi$
$691$	−12648.8	−	21908.3i	−0.696356	−	1.20612i	0.273365	−	0.961910i	$-0.411863\pi$
$692$		0			0
$693$	15250.1	+	17040.0i	0.835937	+	0.934049i
$694$		0			0
$695$	−1089.56	−	1887.18i	−0.0594670	−	0.103000i
$696$		0			0
$697$	83.7554	−	145.069i	0.00455160	−	0.00788360i
$698$		0			0
$699$	19149.4			1.03619
$700$		0			0
$701$	18659.1			1.00534			0.502670	−	0.864478i	$-0.332351\pi$
$701$	18659.1			1.00534			0.502670	+	0.864478i	$0.332351\pi$
$702$		0			0
$703$	−8341.59	+	14448.1i	−0.447524	+	0.775134i
$704$		0			0
$705$	2407.48	+	4169.88i	0.128611	+	0.222761i
$706$		0			0
$707$	14425.6	−	3020.83i	0.767369	−	0.160693i
$708$		0			0
$709$	12847.4	+	22252.3i	0.680528	+	1.17871i	0.974820	+	0.222993i	$0.0715828\pi$
$709$	12847.4	+	22252.3i	0.680528	+	1.17871i	−0.294292	+	0.955715i	$0.595084\pi$
$710$		0			0
$711$	22441.7	−	38870.2i	1.18373	−	2.05028i
$712$		0			0
$713$	34863.2			1.83119
$714$		0			0
$715$	7054.62			0.368990
$716$		0			0
$717$	26690.2	−	46228.8i	1.39019	−	2.40787i
$718$		0			0
$719$	−13627.3	−	23603.2i	−0.706834	−	1.22427i	−0.966025	−	0.258447i	$-0.916789\pi$
$719$	−13627.3	−	23603.2i	−0.706834	−	1.22427i	0.259191	−	0.965826i	$-0.416544\pi$
$720$		0			0
$721$	11209.8	−	34149.6i	0.579022	−	1.76394i
$722$		0			0
$723$	17252.3	+	29881.9i	0.887443	+	1.53710i
$724$		0			0
$725$	−1302.09	+	2255.28i	−0.0667011	+	0.115530i
$726$		0			0
$727$	13194.3			0.673110			0.336555	−	0.941664i	$-0.390738\pi$
$727$	13194.3			0.673110			0.336555	+	0.941664i	$0.390738\pi$
$728$		0			0
$729$	−20906.9			−1.06218
$730$		0			0
$731$	59.3807	−	102.850i	0.00300448	−	0.00520391i
$732$		0			0
$733$	−2904.47	−	5030.70i	−0.146356	−	0.253497i	0.783522	−	0.621364i	$-0.213421\pi$
$733$	−2904.47	−	5030.70i	−0.146356	−	0.253497i	−0.929878	+	0.367868i	$0.880088\pi$
$734$		0			0
$735$	1699.85	−	15285.8i	0.0853059	−	0.767109i
$736$		0			0
$737$	2651.56	+	4592.64i	0.132526	+	0.229542i
$738$		0			0
$739$	6968.34	−	12069.5i	0.346867	−	0.600791i	−0.638824	−	0.769353i	$-0.720579\pi$
$739$	6968.34	−	12069.5i	0.346867	−	0.600791i	0.985691	+	0.168562i	$0.0539122\pi$
$740$		0			0
$741$	−34613.6			−1.71601
$742$		0			0
$743$	−32424.2			−1.60098			−0.800489	−	0.599347i	$-0.795427\pi$
$743$	−32424.2			−1.60098			−0.800489	+	0.599347i	$0.795427\pi$
$744$		0			0
$745$	5299.87	−	9179.65i	0.260634	−	0.451431i
$746$		0			0
$747$	−23657.6	−	40976.1i	−1.15875	−	2.00701i
$748$		0			0
$749$	2822.74	−	8599.19i	0.137704	−	0.419503i
$750$		0			0
$751$	−17644.2	−	30560.6i	−0.857316	−	1.48491i	−0.874480	−	0.485062i	$-0.838797\pi$
$751$	−17644.2	−	30560.6i	−0.857316	−	1.48491i	0.0171639	−	0.999853i	$-0.494536\pi$
$752$		0			0
$753$	−7764.83	+	13449.1i	−0.375785	+	0.650879i
$754$		0			0
$755$	−12002.0			−0.578539
$756$		0			0
$757$	2079.86			0.0998595			0.0499298	−	0.998753i	$-0.484100\pi$
$757$	2079.86			0.0998595			0.0499298	+	0.998753i	$0.484100\pi$
$758$		0			0
$759$	−12902.5	+	22347.8i	−0.617038	+	1.06874i
$760$		0			0
$761$	−6125.72	−	10610.1i	−0.291797	−	0.505407i	0.682438	−	0.730944i	$-0.260920\pi$
$761$	−6125.72	−	10610.1i	−0.291797	−	0.505407i	−0.974235	+	0.225537i	$0.927586\pi$
$762$		0			0
$763$	29548.1	−	6187.60i	1.40198	−	0.293586i
$764$		0			0
$765$	91.9307	+	159.229i	0.00434479	+	0.00752539i
$766$		0			0
$767$	13956.8	−	24173.9i	0.657042	−	1.13803i
$768$		0			0
$769$	4335.87			0.203323			0.101661	−	0.994819i	$-0.467584\pi$
$769$	4335.87			0.203323			0.101661	+	0.994819i	$0.467584\pi$
$770$		0			0
$771$	−36359.9			−1.69840
$772$		0			0
$773$	−15199.7	+	26326.7i	−0.707240	+	1.22498i	0.258637	+	0.965975i	$0.416727\pi$
$773$	−15199.7	+	26326.7i	−0.707240	+	1.22498i	−0.965877	+	0.259001i	$0.916607\pi$
$774$		0			0
$775$	3500.28	+	6062.66i	0.162237	+	0.281003i
$776$		0			0
$777$	29227.0	+	32657.4i	1.34944	+	1.50782i
$778$		0			0
$779$	−7693.37	−	13325.3i	−0.353843	−	0.612874i
$780$		0			0
$781$	−4711.23	+	8160.10i	−0.215853	+	0.373868i
$782$		0			0
$783$	24684.4			1.12663
$784$		0			0
$785$	2530.94			0.115074
$786$		0			0
$787$	17637.1	−	30548.4i	0.798850	−	1.38365i	−0.121515	−	0.992590i	$-0.538775\pi$
$787$	17637.1	−	30548.4i	0.798850	−	1.38365i	0.920365	−	0.391059i	$-0.127891\pi$
$788$		0			0
$789$	−28409.6	−	49206.9i	−1.28189	−	2.22030i
$790$		0			0
$791$	−4272.49	−	4773.94i	−0.192051	−	0.214592i
$792$		0			0
$793$	−14462.2	−	25049.2i	−0.647625	−	1.12172i
$794$		0			0
$795$	1004.60	−	1740.02i	0.0448171	−	0.0776255i
$796$		0			0
$797$	−27524.0			−1.22328			−0.611638	−	0.791138i	$-0.709489\pi$
$797$	−27524.0			−1.22328			−0.611638	+	0.791138i	$0.709489\pi$
$798$		0			0
$799$	73.9116			0.00327260
$800$		0			0
$801$	22868.1	−	39608.7i	1.00874	−	1.74720i
$802$		0			0
$803$	−4026.97	−	6974.92i	−0.176972	−	0.306525i
$804$		0			0
$805$	11284.2	−	2363.01i	0.494059	−	0.103460i
$806$		0			0
$807$	5926.17	+	10264.4i	0.258502	+	0.447739i
$808$		0			0
$809$	3533.68	−	6120.51i	0.153569	−	0.265990i	−0.778968	−	0.627064i	$-0.784257\pi$
$809$	3533.68	−	6120.51i	0.153569	−	0.265990i	0.932537	+	0.361074i	$0.117590\pi$
$810$		0			0
$811$	37757.5			1.63483			0.817413	−	0.576052i	$-0.195407\pi$
$811$	37757.5			1.63483			0.817413	+	0.576052i	$0.195407\pi$
$812$		0			0
$813$	20949.1			0.903713
$814$		0			0
$815$	−6502.36	+	11262.4i	−0.279470	+	0.484056i
$816$		0			0
$817$	−5454.43	−	9447.34i	−0.233569	−	0.404554i
$818$		0			0
$819$	−18838.3	+	57389.1i	−0.803742	+	2.44852i
$820$		0			0
$821$	12653.7	+	21916.9i	0.537902	+	0.931673i	0.999017	+	0.0443325i	$0.0141161\pi$
$821$	12653.7	+	21916.9i	0.537902	+	0.931673i	−0.461115	+	0.887340i	$0.652551\pi$
$822$		0			0
$823$	−12742.4	+	22070.5i	−0.539699	+	0.934786i	0.459221	+	0.888322i	$0.348129\pi$
$823$	−12742.4	+	22070.5i	−0.539699	+	0.934786i	−0.998920	+	0.0464643i	$0.985205\pi$
$824$		0			0
$825$	−5181.67			−0.218670
$826$		0			0
$827$	−34985.7			−1.47107			−0.735534	−	0.677488i	$-0.763069\pi$
$827$	−34985.7			−1.47107			−0.735534	+	0.677488i	$0.763069\pi$
$828$		0			0
$829$	−1949.04	+	3375.84i	−0.0816564	+	0.141433i	−0.903962	−	0.427614i	$-0.859354\pi$
$829$	−1949.04	+	3375.84i	−0.0816564	+	0.141433i	0.822305	+	0.569047i	$0.192688\pi$
$830$		0			0
$831$	31770.0	+	55027.2i	1.32622	+	2.29708i
$832$		0			0
$833$	−190.161	−	139.919i	−0.00790957	−	0.00581983i
$834$		0			0
$835$	−1365.19	−	2364.58i	−0.0565802	−	0.0979997i
$836$		0			0
$837$	33178.4	−	57466.7i	1.37015	−	2.37317i
$838$		0			0
$839$	−22118.8			−0.910161			−0.455081	−	0.890450i	$-0.650390\pi$
$839$	−22118.8			−0.910161			−0.455081	+	0.890450i	$0.650390\pi$
$840$		0			0
$841$	−13538.2			−0.555096
$842$		0			0
$843$	−9520.22	+	16489.5i	−0.388961	+	0.673699i
$844$		0			0
$845$	3824.45	+	6624.13i	0.155698	+	0.269677i
$846$		0			0
$847$	4602.65	−	14021.5i	0.186717	−	0.568814i
$848$		0			0
$849$	26417.9	+	45757.2i	1.06792	+	1.84968i
$850$		0			0
$851$	−16426.2	+	28451.0i	−0.661672	+	1.14605i
$852$		0			0
$853$	33152.4			1.33074			0.665368	−	0.746516i	$-0.268275\pi$
$853$	33152.4			1.33074			0.665368	+	0.746516i	$0.268275\pi$
$854$		0			0
$855$	16888.6			0.675530
$856$		0			0
$857$	5173.12	−	8960.11i	0.206197	−	0.357143i	−0.744317	−	0.667827i	$-0.767225\pi$
$857$	5173.12	−	8960.11i	0.206197	−	0.357143i	0.950513	+	0.310684i	$0.100558\pi$
$858$		0			0
$859$	−5952.82	−	10310.6i	−0.236447	−	0.409538i	0.723245	−	0.690591i	$-0.242650\pi$
$859$	−5952.82	−	10310.6i	−0.236447	−	0.409538i	−0.959692	+	0.281053i	$0.909316\pi$
$860$		0			0
$861$	−39562.2	+	8284.63i	−1.56594	+	0.327920i
$862$		0			0
$863$	15401.2	+	26675.6i	0.607487	+	1.05220i	0.991653	+	0.128935i	$0.0411558\pi$
$863$	15401.2	+	26675.6i	0.607487	+	1.05220i	−0.384166	+	0.923264i	$0.625511\pi$
$864$		0			0
$865$	−7550.80	+	13078.4i	−0.296803	+	0.514079i
$866$		0			0
$867$	−44055.3			−1.72572
$868$		0			0
$869$	19417.2			0.757977
$870$		0			0
$871$	−7003.77	+	12130.9i	−0.272461	+	0.471917i
$872$		0			0
$873$	−5060.22	−	8764.56i	−0.196177	−	0.339789i
$874$		0			0
$875$	1543.87	+	1725.07i	0.0596482	+	0.0666490i
$876$		0			0
$877$	10846.6	+	18786.9i	0.417634	+	0.723363i	0.995701	−	0.0926262i	$-0.0295262\pi$
$877$	10846.6	+	18786.9i	0.417634	+	0.723363i	−0.578067	+	0.815989i	$0.696193\pi$
$878$		0			0
$879$	36489.5	−	63201.6i	1.40018	−	2.42518i
$880$		0			0
$881$	−29963.1			−1.14584			−0.572918	−	0.819612i	$-0.694189\pi$
$881$	−29963.1			−1.14584			−0.572918	+	0.819612i	$0.694189\pi$
$882$		0			0
$883$	4090.61			0.155900			0.0779501	−	0.996957i	$-0.475163\pi$
$883$	4090.61			0.155900			0.0779501	+	0.996957i	$0.475163\pi$
$884$		0			0
$885$	−10251.4	+	17755.9i	−0.389375	+	0.674417i
$886$		0			0
$887$	−14409.7	−	24958.3i	−0.545468	−	0.944778i	−0.998577	−	0.0533229i	$-0.983019\pi$
$887$	−14409.7	−	24958.3i	−0.545468	−	0.944778i	0.453110	−	0.891455i	$-0.350315\pi$
$888$		0			0
$889$	−20567.3	−	22981.2i	−0.775933	−	0.867003i
$890$		0			0
$891$	7889.07	+	13664.3i	0.296626	+	0.513771i
$892$		0			0
$893$	3394.58	−	5879.59i	0.127206	−	0.220328i
$894$		0			0
$895$	9995.83			0.373323
$896$		0			0
$897$	−68160.8			−2.53715
$898$		0			0
$899$	14584.5	−	25261.2i	0.541070	−	0.937160i
$900$		0			0
$901$	−15.4211	−	26.7101i	−0.000570200	−	0.000987616i
$902$		0			0
$903$	−28048.7	+	5873.62i	−1.03367	+	0.216458i
$904$		0			0
$905$	−1702.86	−	2949.44i	−0.0625470	−	0.108335i
$906$		0			0
$907$	−10319.4	+	17873.7i	−0.377784	+	0.654340i	−0.990739	−	0.135777i	$-0.956647\pi$
$907$	−10319.4	+	17873.7i	−0.377784	+	0.654340i	0.612956	+	0.790117i	$0.289980\pi$
$908$		0			0
$909$	42515.1			1.55130
$910$		0			0
$911$	15080.1			0.548435			0.274218	−	0.961668i	$-0.411581\pi$
$911$	15080.1			0.548435			0.274218	+	0.961668i	$0.411581\pi$
$912$		0			0
$913$	10234.6	−	17726.8i	0.370991	−	0.642576i
$914$		0			0
$915$	10622.6	+	18398.8i	0.383794	+	0.664750i
$916$		0			0
$917$	3908.99	−	11908.4i	0.140770	−	0.428843i
$918$		0			0
$919$	−1082.14	−	1874.33i	−0.0388429	−	0.0672778i	0.845950	−	0.533262i	$-0.179034\pi$
$919$	−1082.14	−	1874.33i	−0.0388429	−	0.0672778i	−0.884793	+	0.465984i	$0.845701\pi$
$920$		0			0
$921$	−21510.7	+	37257.6i	−0.769600	+	1.33299i
$922$		0			0
$923$	−24888.3			−0.887549
$924$		0			0
$925$	−6596.78			−0.234487
$926$		0			0
$927$	51840.2	−	89789.9i	1.83674	−	3.18132i
$928$		0			0
$929$	−6819.56	−	11811.8i	−0.240842	−	0.417151i	0.720112	−	0.693858i	$-0.244090\pi$
$929$	−6819.56	−	11811.8i	−0.240842	−	0.417151i	−0.960954	+	0.276707i	$0.910757\pi$
$930$		0			0
$931$	−19864.0	+	8700.91i	−0.699267	+	0.306295i
$932$		0			0
$933$	23269.7	+	40304.3i	0.816523	+	1.41426i
$934$		0			0
$935$	−39.7704	+	68.8843i	−0.00139105	+	0.00240937i
$936$		0			0
$937$	6568.49			0.229011			0.114505	−	0.993423i	$-0.463472\pi$
$937$	6568.49			0.229011			0.114505	+	0.993423i	$0.463472\pi$
$938$		0			0
$939$	−20135.2			−0.699774
$940$		0			0
$941$	−4727.25	+	8187.84i	−0.163766	+	0.283652i	−0.936216	−	0.351424i	$-0.885698\pi$
$941$	−4727.25	+	8187.84i	−0.163766	+	0.283652i	0.772450	+	0.635075i	$0.219031\pi$
$942$		0			0
$943$	−15149.7	−	26240.1i	−0.523163	−	0.906145i
$944$		0			0
$945$	6843.87	−	20849.2i	0.235588	−	0.717697i
$946$		0			0
$947$	17038.4	+	29511.3i	0.584660	+	1.01266i	0.994918	+	0.100691i	$0.0321053\pi$
$947$	17038.4	+	29511.3i	0.584660	+	1.01266i	−0.410258	+	0.911969i	$0.634561\pi$
$948$		0			0
$949$	10636.7	−	18423.4i	0.363839	−	0.630188i
$950$		0			0
$951$	−87368.1			−2.97908
$952$		0			0
$953$	−32862.3			−1.11702			−0.558508	−	0.829499i	$-0.688626\pi$
$953$	−32862.3			−1.11702			−0.558508	+	0.829499i	$0.688626\pi$
$954$		0			0
$955$	4031.90	−	6983.46i	0.136617	−	0.236628i
$956$		0			0
$957$	10795.2	+	18697.8i	0.364638	+	0.631572i
$958$		0			0
$959$	−18747.6	+	3925.90i	−0.631275	+	0.132194i
$960$		0			0
$961$	−24310.7	−	42107.4i	−0.816042	−	1.41343i
$962$		0			0
$963$	13053.9	−	22610.0i	0.436817	−	0.756590i
$964$		0			0
$965$	−4044.61			−0.134923
$966$		0			0
$967$	−57597.8			−1.91543			−0.957715	−	0.287720i	$-0.907103\pi$
$967$	−57597.8			−1.91543			−0.957715	+	0.287720i	$0.907103\pi$
$968$		0			0
$969$	195.134	−	337.982i	0.00646915	−	0.0112049i
$970$		0			0
$971$	−14092.8	−	24409.5i	−0.465768	−	0.806734i	0.533468	−	0.845820i	$-0.320889\pi$
$971$	−14092.8	−	24409.5i	−0.465768	−	0.806734i	−0.999236	+	0.0390865i	$0.987555\pi$
$972$		0			0
$973$	5382.85	+	6014.63i	0.177355	+	0.198171i
$974$		0			0
$975$	−6843.37	−	11853.1i	−0.224783	−	0.389335i
$976$		0			0
$977$	−22131.8	+	38333.4i	−0.724727	+	1.25526i	0.234359	+	0.972150i	$0.424701\pi$
$977$	−22131.8	+	38333.4i	−0.724727	+	1.25526i	−0.959086	+	0.283114i	$0.908633\pi$
$978$		0			0
$979$	19786.0			0.645929
$980$		0			0
$981$	87084.1			2.83423
$982$		0			0
$983$	73.6999	−	127.652i	0.00239131	−	0.00414187i	−0.864827	−	0.502070i	$-0.832572\pi$
$983$	73.6999	−	127.652i	0.00239131	−	0.00414187i	0.867219	+	0.497928i	$0.165905\pi$
$984$		0			0
$985$	9260.57	+	16039.8i	0.299560	+	0.518853i
$986$		0			0
$987$	−11893.8	−	13289.8i	−0.383571	−	0.428591i
$988$		0			0
$989$	−10740.8	−	18603.6i	−0.345337	−	0.598141i
$990$		0			0
$991$	6243.42	−	10813.9i	0.200130	−	0.346635i	−0.748440	−	0.663202i	$-0.769197\pi$
$991$	6243.42	−	10813.9i	0.200130	−	0.346635i	0.948570	+	0.316567i	$0.102530\pi$
$992$		0			0
$993$	−101614.			−3.24734
$994$		0			0
$995$	−1839.64			−0.0586135
$996$		0			0
$997$	3310.57	−	5734.08i	0.105162	−	0.182147i	−0.808642	−	0.588301i	$-0.799797\pi$
$997$	3310.57	−	5734.08i	0.105162	−	0.182147i	0.913805	+	0.406154i	$0.133130\pi$
$998$		0			0
$999$	31264.8	+	54152.2i	0.990164	+	1.71501i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.4.q.n.81.1		10
4.3	odd	2		35.4.e.c.11.2	✓	10
7.2	even	3	inner	560.4.q.n.401.1		10
12.11	even	2		315.4.j.g.46.4		10
20.3	even	4		175.4.k.d.74.3		20
20.7	even	4		175.4.k.d.74.8		20
20.19	odd	2		175.4.e.d.151.4		10
28.3	even	6		245.4.a.n.1.4		5
28.11	odd	6		245.4.a.m.1.4		5
28.19	even	6		245.4.e.o.226.2		10
28.23	odd	6		35.4.e.c.16.2	yes	10
28.27	even	2		245.4.e.o.116.2		10
84.11	even	6		2205.4.a.bu.1.2		5
84.23	even	6		315.4.j.g.226.4		10
84.59	odd	6		2205.4.a.bt.1.2		5
140.23	even	12		175.4.k.d.149.8		20
140.39	odd	6		1225.4.a.bg.1.2		5
140.59	even	6		1225.4.a.bf.1.2		5
140.79	odd	6		175.4.e.d.51.4		10
140.107	even	12		175.4.k.d.149.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.e.c.11.2	✓	10	4.3	odd	2
35.4.e.c.16.2	yes	10	28.23	odd	6
175.4.e.d.51.4		10	140.79	odd	6
175.4.e.d.151.4		10	20.19	odd	2
175.4.k.d.74.3		20	20.3	even	4
175.4.k.d.74.8		20	20.7	even	4
175.4.k.d.149.3		20	140.107	even	12
175.4.k.d.149.8		20	140.23	even	12
245.4.a.m.1.4		5	28.11	odd	6
245.4.a.n.1.4		5	28.3	even	6
245.4.e.o.116.2		10	28.27	even	2
245.4.e.o.226.2		10	28.19	even	6
315.4.j.g.46.4		10	12.11	even	2
315.4.j.g.226.4		10	84.23	even	6
560.4.q.n.81.1		10	1.1	even	1	trivial
560.4.q.n.401.1		10	7.2	even	3	inner
1225.4.a.bf.1.2		5	140.59	even	6
1225.4.a.bg.1.2		5	140.39	odd	6
2205.4.a.bt.1.2		5	84.59	odd	6
2205.4.a.bu.1.2		5	84.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	560.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.48397 + 7.76647i) q^{3} +(2.50000 + 4.33013i) q^{5} +(-12.3509 - 13.8005i) q^{7} +(-26.7120 - 46.2666i) q^{9} +(11.5560 - 20.0155i) q^{11} +61.0473 q^{13} -44.8397 q^{15} +(-0.344154 + 0.596093i) q^{17} +(31.6124 + 54.7542i) q^{19} +(162.563 - 34.0419i) q^{21} +(62.2508 + 107.822i) q^{23} +(-12.5000 + 21.6506i) q^{25} +236.970 q^{27} +104.167 q^{29} +(140.011 - 242.506i) q^{31} +(103.633 + 179.498i) q^{33} +(28.8807 - 87.9824i) q^{35} +(131.936 + 228.519i) q^{37} +(-273.735 + 474.122i) q^{39} -243.366 q^{41} -172.541 q^{43} +(133.560 - 231.333i) q^{45} +(-53.6907 - 92.9951i) q^{47} +(-37.9094 + 340.899i) q^{49} +(-3.08636 - 5.34573i) q^{51} +(-22.4043 + 38.8054i) q^{53} +115.560 q^{55} -566.996 q^{57} +(228.623 - 395.986i) q^{59} +(-236.901 - 410.324i) q^{61} +(-308.586 + 940.076i) q^{63} +(152.618 + 264.343i) q^{65} +(-114.727 + 198.713i) q^{67} -1116.52 q^{69} -407.688 q^{71} +(174.238 - 301.789i) q^{73} +(-112.099 - 194.162i) q^{75} +(-418.952 + 87.7317i) q^{77} +(420.068 + 727.579i) q^{79} +(-341.342 + 591.221i) q^{81} +885.652 q^{83} -3.44154 q^{85} +(-467.082 + 809.010i) q^{87} +(428.048 + 741.401i) q^{89} +(-753.991 - 842.486i) q^{91} +(1255.61 + 2174.78i) q^{93} +(-158.062 + 273.771i) q^{95} +189.436 q^{97} -1234.74 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 8 q^{3} + 25 q^{5} + 62 q^{7} - 81 q^{9} + 47 q^{11} + 2 q^{13} - 80 q^{15} + 2 q^{17} - 21 q^{19} + 178 q^{21} + 201 q^{23} - 125 q^{25} + 1036 q^{27} + 380 q^{29} + 388 q^{31} + 262 q^{33} + 95 q^{35}+ \cdots - 70 q^{99}+O(q^{100}) \) 10 * q - 8 * q^3 + 25 * q^5 + 62 * q^7 - 81 * q^9 + 47 * q^11 + 2 * q^13 - 80 * q^15 + 2 * q^17 - 21 * q^19 + 178 * q^21 + 201 * q^23 - 125 * q^25 + 1036 * q^27 + 380 * q^29 + 388 * q^31 + 262 * q^33 + 95 * q^35 + 145 * q^37 + 14 * q^39 - 562 * q^41 - 1136 * q^43 + 405 * q^45 - 473 * q^47 + 998 * q^49 + 732 * q^51 - 351 * q^53 + 470 * q^55 + 1908 * q^57 + 708 * q^59 - 1944 * q^61 - 1955 * q^63 + 5 * q^65 + 1118 * q^67 + 748 * q^69 - 1728 * q^71 + 1652 * q^73 - 200 * q^75 + 787 * q^77 + 218 * q^79 + 455 * q^81 + 3004 * q^83 + 20 * q^85 + 390 * q^87 - 2322 * q^89 - 524 * q^91 + 2288 * q^93 + 105 * q^95 + 1196 * q^97 - 70 * q^99

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