LMFDB - Embedded newform 560.3.v.b.447.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [560,3,Mod(223,560)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("560.223"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(560, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 0, 3, 2])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	560.v (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [64] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$15.2588948042$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			447.17
Character	$\chi$	$=$	560.447
Dual form			560.3.v.b.223.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.491144 - 0.491144i) q^{3} +(-4.95801 + 0.646617i) q^{5} +(-3.29426 + 6.17640i) q^{7} +8.51755i q^{9} -15.9605i q^{11} +(-9.60885 - 9.60885i) q^{13} +(-2.11752 + 2.75268i) q^{15} +(21.9577 - 21.9577i) q^{17} -2.96061i q^{19} +(1.41554 + 4.65146i) q^{21} +(22.9485 + 22.9485i) q^{23} +(24.1638 - 6.41187i) q^{25} +(8.60365 + 8.60365i) q^{27} -2.31686i q^{29} +49.4445 q^{31} +(-7.83892 - 7.83892i) q^{33} +(12.3392 - 32.7528i) q^{35} +(-9.99566 - 9.99566i) q^{37} -9.43866 q^{39} -58.8211i q^{41} +(29.2176 + 29.2176i) q^{43} +(-5.50760 - 42.2301i) q^{45} +(-19.1831 - 19.1831i) q^{47} +(-27.2957 - 40.6933i) q^{49} -21.5688i q^{51} +(22.0868 - 22.0868i) q^{53} +(10.3203 + 79.1324i) q^{55} +(-1.45409 - 1.45409i) q^{57} -19.1059i q^{59} -88.8424i q^{61} +(-52.6078 - 28.0590i) q^{63} +(53.8540 + 41.4275i) q^{65} +(-20.9339 + 20.9339i) q^{67} +22.5420 q^{69} +80.0716i q^{71} +(-28.2084 - 28.2084i) q^{73} +(8.71874 - 15.0171i) q^{75} +(98.5784 + 52.5781i) q^{77} -57.9404 q^{79} -68.2067 q^{81} +(70.9391 - 70.9391i) q^{83} +(-94.6683 + 123.065i) q^{85} +(-1.13791 - 1.13791i) q^{87} +44.5086 q^{89} +(91.0021 - 27.6940i) q^{91} +(24.2844 - 24.2844i) q^{93} +(1.91438 + 14.6788i) q^{95} +(-72.3085 + 72.3085i) q^{97} +135.945 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 16 q^{21} - 72 q^{25} + 72 q^{37} + 272 q^{53} - 376 q^{57} - 88 q^{65} + 24 q^{77} - 432 q^{81} + 384 q^{85} + 840 q^{93}+O(q^{100}) $ 64 * q + 16 * q^21 - 72 * q^25 + 72 * q^37 + 272 * q^53 - 376 * q^57 - 88 * q^65 + 24 * q^77 - 432 * q^81 + 384 * q^85 + 840 * q^93

Character values

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

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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
$3$	0.491144	−	0.491144i	0.163715	−	0.163715i	−0.620495	−	0.784210i	$-0.713068\pi$
$3$	0.491144	−	0.491144i	0.163715	−	0.163715i	0.784210	+	0.620495i	$0.213068\pi$
$4$		0			0
$5$	−4.95801	+	0.646617i	−0.991602	+	0.129323i
$5$	−4.95801	+	0.646617i	−0.991602	+	0.129323i
$6$		0			0
$7$	−3.29426	+	6.17640i	−0.470608	+	0.882342i
$7$	−3.29426	+	6.17640i	−0.470608	+	0.882342i
$8$		0			0
$9$			8.51755i			0.946395i
$10$		0			0
$11$		−	15.9605i		−	1.45096i	−0.688246	−	0.725478i	$-0.741619\pi$
$11$		−	15.9605i		−	1.45096i	0.688246	−	0.725478i	$-0.258381\pi$
$12$		0			0
$13$	−9.60885	−	9.60885i	−0.739142	−	0.739142i	0.233270	−	0.972412i	$-0.425057\pi$
$13$	−9.60885	−	9.60885i	−0.739142	−	0.739142i	−0.972412	+	0.233270i	$0.925057\pi$
$14$		0			0
$15$	−2.11752	+	2.75268i	−0.141168	+	0.183512i
$16$		0			0
$17$	21.9577	−	21.9577i	1.29163	−	1.29163i	0.357849	−	0.933779i	$-0.383510\pi$
$17$	21.9577	−	21.9577i	1.29163	−	1.29163i	0.933779	−	0.357849i	$-0.116490\pi$
$18$		0			0
$19$		−	2.96061i		−	0.155822i	−0.996960	−	0.0779109i	$-0.975175\pi$
$19$		−	2.96061i		−	0.155822i	0.996960	−	0.0779109i	$-0.0248250\pi$
$20$		0			0
$21$	1.41554	+	4.65146i	0.0674069	+	0.221498i
$22$		0			0
$23$	22.9485	+	22.9485i	0.997761	+	0.997761i	0.999997	−	0.00223684i	$-0.000712008\pi$
$23$	22.9485	+	22.9485i	0.997761	+	0.997761i	−0.00223684	+	0.999997i	$0.500712\pi$
$24$		0			0
$25$	24.1638	−	6.41187i	0.966551	−	0.256475i
$26$		0			0
$27$	8.60365	+	8.60365i	0.318654	+	0.318654i
$28$		0			0
$29$		−	2.31686i		−	0.0798919i	−0.999202	−	0.0399459i	$-0.987281\pi$
$29$		−	2.31686i		−	0.0798919i	0.999202	−	0.0399459i	$-0.0127186\pi$
$30$		0			0
$31$	49.4445			1.59498			0.797492	−	0.603330i	$-0.206160\pi$
$31$	49.4445			1.59498			0.797492	+	0.603330i	$0.206160\pi$
$32$		0			0
$33$	−7.83892	−	7.83892i	−0.237543	−	0.237543i
$34$		0			0
$35$	12.3392	−	32.7528i	0.352549	−	0.935793i
$36$		0			0
$37$	−9.99566	−	9.99566i	−0.270153	−	0.270153i	0.559009	−	0.829162i	$-0.311182\pi$
$37$	−9.99566	−	9.99566i	−0.270153	−	0.270153i	−0.829162	+	0.559009i	$0.811182\pi$
$38$		0			0
$39$	−9.43866			−0.242017
$40$		0			0
$41$		−	58.8211i		−	1.43466i	−0.696733	−	0.717331i	$-0.745364\pi$
$41$		−	58.8211i		−	1.43466i	0.696733	−	0.717331i	$-0.254636\pi$
$42$		0			0
$43$	29.2176	+	29.2176i	0.679478	+	0.679478i	0.959882	−	0.280404i	$-0.0904684\pi$
$43$	29.2176	+	29.2176i	0.679478	+	0.679478i	−0.280404	+	0.959882i	$0.590468\pi$
$44$		0			0
$45$	−5.50760	−	42.2301i	−0.122391	−	0.938448i
$46$		0			0
$47$	−19.1831	−	19.1831i	−0.408150	−	0.408150i	0.472943	−	0.881093i	$-0.343192\pi$
$47$	−19.1831	−	19.1831i	−0.408150	−	0.408150i	−0.881093	+	0.472943i	$0.843192\pi$
$48$		0			0
$49$	−27.2957	−	40.6933i	−0.557055	−	0.830475i
$50$		0			0
$51$		−	21.5688i		−	0.422917i
$52$		0			0
$53$	22.0868	−	22.0868i	0.416732	−	0.416732i	−0.467344	−	0.884076i	$-0.654789\pi$
$53$	22.0868	−	22.0868i	0.416732	−	0.416732i	0.884076	+	0.467344i	$0.154789\pi$
$54$		0			0
$55$	10.3203	+	79.1324i	0.187643	+	1.43877i
$56$		0			0
$57$	−1.45409	−	1.45409i	−0.0255103	−	0.0255103i
$58$		0			0
$59$		−	19.1059i		−	0.323829i	−0.986805	−	0.161914i	$-0.948233\pi$
$59$		−	19.1059i		−	0.323829i	0.986805	−	0.161914i	$-0.0517669\pi$
$60$		0			0
$61$		−	88.8424i		−	1.45643i	−0.685347	−	0.728217i	$-0.740349\pi$
$61$		−	88.8424i		−	1.45643i	0.685347	−	0.728217i	$-0.259651\pi$
$62$		0			0
$63$	−52.6078	−	28.0590i	−0.835044	−	0.445381i
$64$		0			0
$65$	53.8540	+	41.4275i	0.828524	+	0.637347i
$66$		0			0
$67$	−20.9339	+	20.9339i	−0.312447	+	0.312447i	−0.845857	−	0.533410i	$-0.820910\pi$
$67$	−20.9339	+	20.9339i	−0.312447	+	0.312447i	0.533410	+	0.845857i	$0.320910\pi$
$68$		0			0
$69$	22.5420			0.326696
$70$		0			0
$71$			80.0716i			1.12777i	0.825854	+	0.563885i	$0.190694\pi$
$71$			80.0716i			1.12777i	−0.825854	+	0.563885i	$0.809306\pi$
$72$		0			0
$73$	−28.2084	−	28.2084i	−0.386416	−	0.386416i	0.486991	−	0.873407i	$-0.338095\pi$
$73$	−28.2084	−	28.2084i	−0.386416	−	0.386416i	−0.873407	+	0.486991i	$0.838095\pi$
$74$		0			0
$75$	8.71874	−	15.0171i	0.116250	−	0.200227i
$76$		0			0
$77$	98.5784	+	52.5781i	1.28024	+	0.682832i
$78$		0			0
$79$	−57.9404			−0.733423			−0.366711	−	0.930335i	$-0.619516\pi$
$79$	−57.9404			−0.733423			−0.366711	+	0.930335i	$0.619516\pi$
$80$		0			0
$81$	−68.2067			−0.842058
$82$		0			0
$83$	70.9391	−	70.9391i	0.854688	−	0.854688i	−0.136018	−	0.990706i	$-0.543430\pi$
$83$	70.9391	−	70.9391i	0.854688	−	0.854688i	0.990706	+	0.136018i	$0.0434305\pi$
$84$		0			0
$85$	−94.6683	+	123.065i	−1.11374	+	1.44782i
$86$		0			0
$87$	−1.13791	−	1.13791i	−0.0130795	−	0.0130795i
$88$		0			0
$89$	44.5086			0.500097			0.250049	−	0.968233i	$-0.419553\pi$
$89$	44.5086			0.500097			0.250049	+	0.968233i	$0.419553\pi$
$90$		0			0
$91$	91.0021	−	27.6940i	1.00002	−	0.304330i
$92$		0			0
$93$	24.2844	−	24.2844i	0.261122	−	0.261122i
$94$		0			0
$95$	1.91438	+	14.6788i	0.0201514	+	0.154513i
$96$		0			0
$97$	−72.3085	+	72.3085i	−0.745448	+	0.745448i	−0.973621	−	0.228172i	$-0.926725\pi$
$97$	−72.3085	+	72.3085i	−0.745448	+	0.745448i	0.228172	+	0.973621i	$0.426725\pi$
$98$		0			0
$99$	135.945			1.37318
$100$		0			0
$101$			90.8683i			0.899686i	0.893108	+	0.449843i	$0.148520\pi$
$101$			90.8683i			0.899686i	−0.893108	+	0.449843i	$0.851480\pi$
$102$		0			0
$103$	37.6299	−	37.6299i	0.365339	−	0.365339i	−0.500435	−	0.865774i	$-0.666827\pi$
$103$	37.6299	−	37.6299i	0.365339	−	0.365339i	0.865774	+	0.500435i	$0.166827\pi$
$104$		0			0
$105$	−10.0260	−	22.1467i	−0.0954857	−	0.210921i
$106$		0			0
$107$	−21.6954	+	21.6954i	−0.202760	+	0.202760i	−0.801182	−	0.598421i	$-0.795795\pi$
$107$	−21.6954	+	21.6954i	−0.202760	+	0.202760i	0.598421	+	0.801182i	$0.295795\pi$
$108$		0			0
$109$		−	151.360i		−	1.38862i	−0.719676	−	0.694310i	$-0.755709\pi$
$109$		−	151.360i		−	1.38862i	0.719676	−	0.694310i	$-0.244291\pi$
$110$		0			0
$111$	−9.81862			−0.0884561
$112$		0			0
$113$	101.308	−	101.308i	0.896530	−	0.896530i	−0.0985979	−	0.995127i	$-0.531436\pi$
$113$	101.308	−	101.308i	0.896530	−	0.896530i	0.995127	+	0.0985979i	$0.0314357\pi$
$114$		0			0
$115$	−128.618	−	98.9400i	−1.11842	−	0.860348i
$116$		0			0
$117$	81.8439	−	81.8439i	0.699520	−	0.699520i
$118$		0			0
$119$	63.2850	+	207.954i	0.531807	+	1.74751i
$120$		0			0
$121$	−133.738			−1.10527
$122$		0			0
$123$	−28.8897	−	28.8897i	−0.234875	−	0.234875i
$124$		0			0
$125$	−115.658	+	47.4149i	−0.925266	+	0.379319i
$126$		0			0
$127$	77.4910	−	77.4910i	0.610165	−	0.610165i	−0.332824	−	0.942989i	$-0.608001\pi$
$127$	77.4910	−	77.4910i	0.610165	−	0.610165i	0.942989	+	0.332824i	$0.108001\pi$
$128$		0			0
$129$	28.7001			0.222481
$130$		0			0
$131$	−195.400			−1.49160			−0.745802	−	0.666168i	$-0.767933\pi$
$131$	−195.400			−1.49160			−0.745802	+	0.666168i	$0.767933\pi$
$132$		0			0
$133$	18.2859	+	9.75302i	0.137488	+	0.0733310i
$134$		0			0
$135$	−48.2203	−	37.0937i	−0.357187	−	0.274768i
$136$		0			0
$137$	110.223	+	110.223i	0.804546	+	0.804546i	0.983802	−	0.179256i	$-0.0573691\pi$
$137$	110.223	+	110.223i	0.804546	+	0.804546i	−0.179256	+	0.983802i	$0.557369\pi$
$138$		0			0
$139$		−	75.6153i		−	0.543995i	−0.962298	−	0.271997i	$-0.912316\pi$
$139$		−	75.6153i		−	0.543995i	0.962298	−	0.271997i	$-0.0876842\pi$
$140$		0			0
$141$	−18.8433			−0.133640
$142$		0			0
$143$	−153.362	+	153.362i	−1.07246	+	1.07246i
$144$		0			0
$145$	1.49812	+	11.4870i	0.0103319	+	0.0792210i
$146$		0			0
$147$	−33.3924	−	6.58015i	−0.227159	−	0.0447629i
$148$		0			0
$149$		−	33.0747i		−	0.221978i	−0.993822	−	0.110989i	$-0.964598\pi$
$149$		−	33.0747i		−	0.221978i	0.993822	−	0.110989i	$-0.0354018\pi$
$150$		0			0
$151$		−	229.412i		−	1.51928i	−0.650342	−	0.759641i	$-0.725374\pi$
$151$		−	229.412i		−	1.51928i	0.650342	−	0.759641i	$-0.274626\pi$
$152$		0			0
$153$	187.026	+	187.026i	1.22239	+	1.22239i
$154$		0			0
$155$	−245.146	+	31.9717i	−1.58159	+	0.206269i
$156$		0			0
$157$	−131.004	+	131.004i	−0.834423	+	0.834423i	−0.988118	−	0.153695i	$-0.950883\pi$
$157$	−131.004	+	131.004i	−0.834423	+	0.834423i	0.153695	+	0.988118i	$0.450883\pi$
$158$		0			0
$159$		−	21.6956i		−	0.136450i
$160$		0			0
$161$	−217.337	+	66.1407i	−1.34992	+	0.410812i
$162$		0			0
$163$	169.398	+	169.398i	1.03925	+	1.03925i	0.999197	+	0.0400566i	$0.0127538\pi$
$163$	169.398	+	169.398i	1.03925	+	1.03925i	0.0400566	+	0.999197i	$0.487246\pi$
$164$		0			0
$165$	43.9342	+	33.7967i	0.266268	+	0.204828i
$166$		0			0
$167$	210.450	+	210.450i	1.26018	+	1.26018i	0.951005	+	0.309176i	$0.100053\pi$
$167$	210.450	+	210.450i	1.26018	+	1.26018i	0.309176	+	0.951005i	$0.399947\pi$
$168$		0			0
$169$			15.6600i			0.0926625i
$170$		0			0
$171$	25.2172			0.147469
$172$		0			0
$173$	133.546	+	133.546i	0.771943	+	0.771943i	0.978446	−	0.206503i	$-0.0662083\pi$
$173$	133.546	+	133.546i	0.771943	+	0.771943i	−0.206503	+	0.978446i	$0.566208\pi$
$174$		0			0
$175$	−39.9995	+	170.367i	−0.228568	+	0.973528i
$176$		0			0
$177$	−9.38376	−	9.38376i	−0.0530156	−	0.0530156i
$178$		0			0
$179$	212.267			1.18585			0.592925	−	0.805258i	$-0.297973\pi$
$179$	212.267			1.18585			0.592925	+	0.805258i	$0.297973\pi$
$180$		0			0
$181$			160.360i			0.885969i	0.896529	+	0.442985i	$0.146080\pi$
$181$			160.360i			0.885969i	−0.896529	+	0.442985i	$0.853920\pi$
$182$		0			0
$183$	−43.6345	−	43.6345i	−0.238440	−	0.238440i
$184$		0			0
$185$	56.0220	+	43.0952i	0.302822	+	0.232947i
$186$		0			0
$187$	−350.456	−	350.456i	−1.87410	−	1.87410i
$188$		0			0
$189$	−81.4822	+	24.7969i	−0.431123	+	0.131200i
$190$		0			0
$191$		−	156.241i		−	0.818017i	−0.912531	−	0.409008i	$-0.865875\pi$
$191$		−	156.241i		−	0.818017i	0.912531	−	0.409008i	$-0.134125\pi$
$192$		0			0
$193$	−4.24330	+	4.24330i	−0.0219860	+	0.0219860i	−0.718014	−	0.696028i	$-0.754949\pi$
$193$	−4.24330	+	4.24330i	−0.0219860	+	0.0219860i	0.696028	+	0.718014i	$0.254949\pi$
$194$		0			0
$195$	46.7970	−	6.10320i	0.239985	−	0.0312985i
$196$		0			0
$197$	−150.320	−	150.320i	−0.763046	−	0.763046i	0.213826	−	0.976872i	$-0.431407\pi$
$197$	−150.320	−	150.320i	−0.763046	−	0.763046i	−0.976872	+	0.213826i	$0.931407\pi$
$198$		0			0
$199$		−	56.1024i		−	0.281922i	−0.990015	−	0.140961i	$-0.954981\pi$
$199$		−	56.1024i		−	0.281922i	0.990015	−	0.140961i	$-0.0450191\pi$
$200$		0			0
$201$			20.5632i			0.102304i
$202$		0			0
$203$	14.3099	+	7.63235i	0.0704920	+	0.0375978i
$204$		0			0
$205$	38.0348	+	291.636i	0.185535	+	1.42261i
$206$		0			0
$207$	−195.465	+	195.465i	−0.944276	+	0.944276i
$208$		0			0
$209$	−47.2529			−0.226090
$210$		0			0
$211$		−	235.285i		−	1.11509i	−0.830146	−	0.557546i	$-0.811743\pi$
$211$		−	235.285i		−	1.11509i	0.830146	−	0.557546i	$-0.188257\pi$
$212$		0			0
$213$	39.3267	+	39.3267i	0.184632	+	0.184632i
$214$		0			0
$215$	−163.754	−	125.968i	−0.761645	−	0.585900i
$216$		0			0
$217$	−162.883	+	305.389i	−0.750613	+	1.40732i
$218$		0			0
$219$	−27.7088			−0.126524
$220$		0			0
$221$	−421.976			−1.90939
$222$		0			0
$223$	−177.683	+	177.683i	−0.796786	+	0.796786i	−0.982587	−	0.185801i	$-0.940512\pi$
$223$	−177.683	+	177.683i	−0.796786	+	0.796786i	0.185801	+	0.982587i	$0.440512\pi$
$224$		0			0
$225$	54.6135	+	205.816i	0.242727	+	0.914739i
$226$		0			0
$227$	−83.7643	−	83.7643i	−0.369006	−	0.369006i	0.498109	−	0.867114i	$-0.334028\pi$
$227$	−83.7643	−	83.7643i	−0.369006	−	0.369006i	−0.867114	+	0.498109i	$0.834028\pi$
$228$		0			0
$229$	13.9777			0.0610378			0.0305189	−	0.999534i	$-0.490284\pi$
$229$	13.9777			0.0610378			0.0305189	+	0.999534i	$0.490284\pi$
$230$		0			0
$231$	74.2397	−	22.5928i	0.321384	−	0.0978044i
$232$		0			0
$233$	−4.40471	+	4.40471i	−0.0189043	+	0.0189043i	−0.716496	−	0.697591i	$-0.754255\pi$
$233$	−4.40471	+	4.40471i	−0.0189043	+	0.0189043i	0.697591	+	0.716496i	$0.254255\pi$
$234$		0			0
$235$	107.514	+	82.7057i	0.457506	+	0.351939i
$236$		0			0
$237$	−28.4571	+	28.4571i	−0.120072	+	0.120072i
$238$		0			0
$239$	−261.035			−1.09220			−0.546099	−	0.837721i	$-0.683888\pi$
$239$	−261.035			−1.09220			−0.546099	+	0.837721i	$0.683888\pi$
$240$		0			0
$241$		−	309.944i		−	1.28607i	−0.765835	−	0.643037i	$-0.777674\pi$
$241$		−	309.944i		−	1.28607i	0.765835	−	0.643037i	$-0.222326\pi$
$242$		0			0
$243$	−110.932	+	110.932i	−0.456511	+	0.456511i
$244$		0			0
$245$	161.645	+	184.108i	0.659777	+	0.751461i
$246$		0			0
$247$	−28.4481	+	28.4481i	−0.115174	+	0.115174i
$248$		0			0
$249$		−	69.6827i		−	0.279850i
$250$		0			0
$251$	278.611			1.11000			0.555002	−	0.831849i	$-0.312718\pi$
$251$	278.611			1.11000			0.555002	+	0.831849i	$0.312718\pi$
$252$		0			0
$253$	366.270	−	366.270i	1.44771	−	1.44771i
$254$		0			0
$255$	13.9468	+	106.938i	0.0546932	+	0.419366i
$256$		0			0
$257$	93.5178	−	93.5178i	0.363882	−	0.363882i	−0.501358	−	0.865240i	$-0.667166\pi$
$257$	93.5178	−	93.5178i	0.363882	−	0.363882i	0.865240	+	0.501358i	$0.167166\pi$
$258$		0			0
$259$	94.6655	−	28.8089i	0.365504	−	0.111231i
$260$		0			0
$261$	19.7340			0.0756093
$262$		0			0
$263$	270.976	+	270.976i	1.03033	+	1.03033i	0.999525	+	0.0308028i	$0.00980638\pi$
$263$	270.976	+	270.976i	1.03033	+	1.03033i	0.0308028	+	0.999525i	$0.490194\pi$
$264$		0			0
$265$	−95.2248	+	123.788i	−0.359339	+	0.467125i
$266$		0			0
$267$	21.8602	−	21.8602i	0.0818733	−	0.0818733i
$268$		0			0
$269$	520.489			1.93490			0.967451	−	0.253057i	$-0.0814360\pi$
$269$	520.489			1.93490			0.967451	+	0.253057i	$0.0814360\pi$
$270$		0			0
$271$	−333.962			−1.23233			−0.616165	−	0.787617i	$-0.711315\pi$
$271$	−333.962			−1.23233			−0.616165	+	0.787617i	$0.711315\pi$
$272$		0			0
$273$	31.0934	−	58.2969i	0.113895	−	0.213542i
$274$		0			0
$275$	−102.337	−	385.666i	−0.372134	−	1.40242i
$276$		0			0
$277$	−28.0153	−	28.0153i	−0.101138	−	0.101138i	0.654727	−	0.755865i	$-0.272784\pi$
$277$	−28.0153	−	28.0153i	−0.101138	−	0.101138i	−0.755865	+	0.654727i	$0.772784\pi$
$278$		0			0
$279$			421.146i			1.50948i
$280$		0			0
$281$	−251.416			−0.894720			−0.447360	−	0.894354i	$-0.647636\pi$
$281$	−251.416			−0.894720			−0.447360	+	0.894354i	$0.647636\pi$
$282$		0			0
$283$	216.495	−	216.495i	0.765001	−	0.765001i	−0.212221	−	0.977222i	$-0.568070\pi$
$283$	216.495	−	216.495i	0.765001	−	0.765001i	0.977222	+	0.212221i	$0.0680696\pi$
$284$		0			0
$285$	8.14962	+	6.26915i	0.0285952	+	0.0219970i
$286$		0			0
$287$	363.302	+	193.772i	1.26586	+	0.675164i
$288$		0			0
$289$		−	675.280i		−	2.33661i
$290$		0			0
$291$			71.0278i			0.244082i
$292$		0			0
$293$	−243.677	−	243.677i	−0.831664	−	0.831664i	0.156081	−	0.987744i	$-0.450114\pi$
$293$	−243.677	−	243.677i	−0.831664	−	0.831664i	−0.987744	+	0.156081i	$0.950114\pi$
$294$		0			0
$295$	12.3542	+	94.7273i	0.0418787	+	0.321110i
$296$		0			0
$297$	137.319	−	137.319i	0.462352	−	0.462352i
$298$		0			0
$299$		−	441.017i		−	1.47497i
$300$		0			0
$301$	−276.709	+	84.2090i	−0.919300	+	0.279764i
$302$		0			0
$303$	44.6295	+	44.6295i	0.147292	+	0.147292i
$304$		0			0
$305$	57.4471	+	440.482i	0.188351	+	1.44420i
$306$		0			0
$307$	117.282	+	117.282i	0.382025	+	0.382025i	0.871831	−	0.489806i	$-0.162932\pi$
$307$	117.282	+	117.282i	0.382025	+	0.382025i	−0.489806	+	0.871831i	$0.662932\pi$
$308$		0			0
$309$		−	36.9634i		−	0.119623i
$310$		0			0
$311$	−54.6370			−0.175682			−0.0878408	−	0.996135i	$-0.527997\pi$
$311$	−54.6370			−0.175682			−0.0878408	+	0.996135i	$0.527997\pi$
$312$		0			0
$313$	−196.335	−	196.335i	−0.627268	−	0.627268i	0.320112	−	0.947380i	$-0.396279\pi$
$313$	−196.335	−	196.335i	−0.627268	−	0.627268i	−0.947380	+	0.320112i	$0.896279\pi$
$314$		0			0
$315$	278.973	+	105.100i	0.885630	+	0.333651i
$316$		0			0
$317$	269.963	+	269.963i	0.851620	+	0.851620i	0.990333	−	0.138713i	$-0.0442966\pi$
$317$	269.963	+	269.963i	0.851620	+	0.851620i	−0.138713	+	0.990333i	$0.544297\pi$
$318$		0			0
$319$	−36.9783			−0.115920
$320$		0			0
$321$			21.3111i			0.0663897i
$322$		0			0
$323$	−65.0082	−	65.0082i	−0.201264	−	0.201264i
$324$		0			0
$325$	−293.797	−	170.575i	−0.903990	−	0.524847i
$326$		0			0
$327$	−74.3395	−	74.3395i	−0.227338	−	0.227338i
$328$		0			0
$329$	181.676	−	55.2882i	0.552207	−	0.168049i
$330$		0			0
$331$			39.6844i			0.119892i	0.998202	+	0.0599462i	$0.0190929\pi$
$331$			39.6844i			0.119892i	−0.998202	+	0.0599462i	$0.980907\pi$
$332$		0			0
$333$	85.1386	−	85.1386i	0.255671	−	0.255671i
$334$		0			0
$335$	90.2544	−	117.327i	0.269416	−	0.350230i
$336$		0			0
$337$	225.495	+	225.495i	0.669125	+	0.669125i	0.957513	−	0.288389i	$-0.0931195\pi$
$337$	225.495	+	225.495i	0.669125	+	0.669125i	−0.288389	+	0.957513i	$0.593120\pi$
$338$		0			0
$339$		−	99.5135i		−	0.293550i
$340$		0			0
$341$		−	789.159i		−	2.31425i
$342$		0			0
$343$	341.257	−	34.5349i	0.994918	−	0.100685i
$344$		0			0
$345$	−111.764	+	14.5761i	−0.323953	+	0.0422495i
$346$		0			0
$347$	−117.686	+	117.686i	−0.339152	+	0.339152i	−0.856048	−	0.516896i	$-0.827087\pi$
$347$	−117.686	+	117.686i	−0.339152	+	0.339152i	0.516896	+	0.856048i	$0.327087\pi$
$348$		0			0
$349$	−510.239			−1.46200			−0.731001	−	0.682376i	$-0.760947\pi$
$349$	−510.239			−1.46200			−0.731001	+	0.682376i	$0.760947\pi$
$350$		0			0
$351$		−	165.342i		−	0.471061i
$352$		0			0
$353$	99.7353	+	99.7353i	0.282536	+	0.282536i	0.834120	−	0.551583i	$-0.185976\pi$
$353$	99.7353	+	99.7353i	0.282536	+	0.282536i	−0.551583	+	0.834120i	$0.685976\pi$
$354$		0			0
$355$	−51.7757	−	396.996i	−0.145847	−	1.11830i
$356$		0			0
$357$	133.217	+	71.0532i	0.373158	+	0.199028i
$358$		0			0
$359$	63.6900			0.177409			0.0887047	−	0.996058i	$-0.471727\pi$
$359$	63.6900			0.177409			0.0887047	+	0.996058i	$0.471727\pi$
$360$		0			0
$361$	352.235			0.975720
$362$		0			0
$363$	−65.6846	+	65.6846i	−0.180949	+	0.180949i
$364$		0			0
$365$	158.098	+	121.618i	0.433144	+	0.333199i
$366$		0			0
$367$	−108.480	−	108.480i	−0.295585	−	0.295585i	0.543697	−	0.839282i	$-0.317024\pi$
$367$	−108.480	−	108.480i	−0.295585	−	0.295585i	−0.839282	+	0.543697i	$0.817024\pi$
$368$		0			0
$369$	501.012			1.35776
$370$		0			0
$371$	63.6571	+	209.176i	0.171582	+	0.563817i
$372$		0			0
$373$	62.1492	−	62.1492i	0.166620	−	0.166620i	−0.618872	−	0.785492i	$-0.712410\pi$
$373$	62.1492	−	62.1492i	0.166620	−	0.166620i	0.785492	+	0.618872i	$0.212410\pi$
$374$		0			0
$375$	−33.5173	+	80.0924i	−0.0893796	+	0.213580i
$376$		0			0
$377$	−22.2624	+	22.2624i	−0.0590515	+	0.0590515i
$378$		0			0
$379$	465.783			1.22898			0.614490	−	0.788925i	$-0.289362\pi$
$379$	465.783			1.22898			0.614490	+	0.788925i	$0.289362\pi$
$380$		0			0
$381$		−	76.1185i		−	0.199786i
$382$		0			0
$383$	−237.812	+	237.812i	−0.620920	+	0.620920i	−0.945767	−	0.324847i	$-0.894687\pi$
$383$	−237.812	+	237.812i	−0.620920	+	0.620920i	0.324847	+	0.945767i	$0.394687\pi$
$384$		0			0
$385$	−522.751	−	196.940i	−1.35779	−	0.511533i
$386$		0			0
$387$	−248.862	+	248.862i	−0.643055	+	0.643055i
$388$		0			0
$389$			12.4104i			0.0319033i	0.999873	+	0.0159517i	$0.00507779\pi$
$389$			12.4104i			0.0319033i	−0.999873	+	0.0159517i	$0.994922\pi$
$390$		0			0
$391$	1007.79			2.57747
$392$		0			0
$393$	−95.9696	+	95.9696i	−0.244197	+	0.244197i
$394$		0			0
$395$	287.269	−	37.4653i	0.727264	−	0.0948488i
$396$		0			0
$397$	249.742	−	249.742i	0.629073	−	0.629073i	−0.318762	−	0.947835i	$-0.603267\pi$
$397$	249.742	−	249.742i	0.629073	−	0.629073i	0.947835	+	0.318762i	$0.103267\pi$
$398$		0			0
$399$	13.7712	−	4.19088i	0.0345142	−	0.0105035i
$400$		0			0
$401$	−236.331			−0.589353			−0.294677	−	0.955597i	$-0.595212\pi$
$401$	−236.331			−0.589353			−0.294677	+	0.955597i	$0.595212\pi$
$402$		0			0
$403$	−475.104	−	475.104i	−1.17892	−	1.17892i
$404$		0			0
$405$	338.170	−	44.1037i	0.834987	−	0.108898i
$406$		0			0
$407$	−159.536	+	159.536i	−0.391980	+	0.391980i
$408$		0			0
$409$	−814.143			−1.99057			−0.995285	−	0.0969984i	$-0.969076\pi$
$409$	−814.143			−1.99057			−0.995285	+	0.0969984i	$0.969076\pi$
$410$		0			0
$411$	108.271			0.263432
$412$		0			0
$413$	118.006	+	62.9398i	0.285728	+	0.152397i
$414$		0			0
$415$	−305.847	+	397.588i	−0.736980	+	0.958042i
$416$		0			0
$417$	−37.1380	−	37.1380i	−0.0890600	−	0.0890600i
$418$		0			0
$419$			604.798i			1.44343i	0.692190	+	0.721716i	$0.256646\pi$
$419$			604.798i			1.44343i	−0.692190	+	0.721716i	$0.743354\pi$
$420$		0			0
$421$	−111.199			−0.264131			−0.132066	−	0.991241i	$-0.542161\pi$
$421$	−111.199			−0.264131			−0.132066	+	0.991241i	$0.542161\pi$
$422$		0			0
$423$	163.393	−	163.393i	0.386271	−	0.386271i
$424$		0			0
$425$	389.791	−	671.370i	0.917154	−	1.57970i
$426$		0			0
$427$	548.726	+	292.670i	1.28507	+	0.685410i
$428$		0			0
$429$			150.646i			0.351156i
$430$		0			0
$431$		−	719.477i		−	1.66932i	−0.550766	−	0.834660i	$-0.685664\pi$
$431$		−	719.477i		−	1.66932i	0.550766	−	0.834660i	$-0.314336\pi$
$432$		0			0
$433$	42.0857	+	42.0857i	0.0971956	+	0.0971956i	0.754033	−	0.656837i	$-0.228106\pi$
$433$	42.0857	+	42.0857i	0.0971956	+	0.0971956i	−0.656837	+	0.754033i	$0.728106\pi$
$434$		0			0
$435$	6.37759	+	4.90600i	0.0146611	+	0.0112782i
$436$		0			0
$437$	67.9416	−	67.9416i	0.155473	−	0.155473i
$438$		0			0
$439$		−	383.392i		−	0.873331i	−0.899624	−	0.436666i	$-0.856159\pi$
$439$		−	383.392i		−	0.873331i	0.899624	−	0.436666i	$-0.143841\pi$
$440$		0			0
$441$	346.607	−	232.493i	0.785958	−	0.527194i
$442$		0			0
$443$	270.350	+	270.350i	0.610270	+	0.610270i	0.943016	−	0.332746i	$-0.107975\pi$
$443$	270.350	+	270.350i	0.610270	+	0.610270i	−0.332746	+	0.943016i	$0.607975\pi$
$444$		0			0
$445$	−220.674	+	28.7801i	−0.495898	+	0.0646743i
$446$		0			0
$447$	−16.2445	−	16.2445i	−0.0363411	−	0.0363411i
$448$		0			0
$449$		−	169.459i		−	0.377413i	−0.982033	−	0.188707i	$-0.939570\pi$
$449$		−	169.459i		−	0.377413i	0.982033	−	0.188707i	$-0.0604296\pi$
$450$		0			0
$451$	−938.815			−2.08163
$452$		0			0
$453$	−112.674	−	112.674i	−0.248729	−	0.248729i
$454$		0			0
$455$	−433.282	+	196.151i	−0.952268	+	0.431101i
$456$		0			0
$457$	−13.5160	−	13.5160i	−0.0295755	−	0.0295755i	0.692164	−	0.721740i	$-0.256657\pi$
$457$	−13.5160	−	13.5160i	−0.0295755	−	0.0295755i	−0.721740	+	0.692164i	$0.756657\pi$
$458$		0			0
$459$	377.832			0.823164
$460$		0			0
$461$		−	201.869i		−	0.437894i	−0.975737	−	0.218947i	$-0.929738\pi$
$461$		−	201.869i		−	0.437894i	0.975737	−	0.218947i	$-0.0702622\pi$
$462$		0			0
$463$	186.508	+	186.508i	0.402824	+	0.402824i	0.879227	−	0.476403i	$-0.158060\pi$
$463$	186.508	+	186.508i	0.402824	+	0.402824i	−0.476403	+	0.879227i	$0.658060\pi$
$464$		0			0
$465$	−104.700	+	136.105i	−0.225160	+	0.292699i
$466$		0			0
$467$	−199.008	−	199.008i	−0.426142	−	0.426142i	0.461170	−	0.887312i	$-0.347430\pi$
$467$	−199.008	−	199.008i	−0.426142	−	0.426142i	−0.887312	+	0.461170i	$0.847430\pi$
$468$		0			0
$469$	−60.3344	−	198.258i	−0.128645	−	0.422725i
$470$		0			0
$471$			128.684i			0.273215i
$472$		0			0
$473$	466.327	−	466.327i	0.985893	−	0.985893i
$474$		0			0
$475$	−18.9831	−	71.5396i	−0.0399644	−	0.150610i
$476$		0			0
$477$	188.125	+	188.125i	0.394393	+	0.394393i
$478$		0			0
$479$			72.0428i			0.150403i	0.997168	+	0.0752013i	$0.0239599\pi$
$479$			72.0428i			0.150403i	−0.997168	+	0.0752013i	$0.976040\pi$
$480$		0			0
$481$			192.094i			0.399363i
$482$		0			0
$483$	−74.2593	+	139.229i	−0.153746	+	0.288258i
$484$		0			0
$485$	311.750	−	405.262i	0.642784	−	0.835592i
$486$		0			0
$487$	−158.323	+	158.323i	−0.325099	+	0.325099i	−0.850719	−	0.525620i	$-0.823833\pi$
$487$	−158.323	+	158.323i	−0.325099	+	0.325099i	0.525620	+	0.850719i	$0.323833\pi$
$488$		0			0
$489$	166.398			0.340282
$490$		0			0
$491$			224.397i			0.457019i	0.973542	+	0.228510i	$0.0733853\pi$
$491$			224.397i			0.457019i	−0.973542	+	0.228510i	$0.926615\pi$
$492$		0			0
$493$	−50.8730	−	50.8730i	−0.103191	−	0.103191i
$494$		0			0
$495$	−674.015	+	87.9041i	−1.36165	+	0.177584i
$496$		0			0
$497$	−494.554	−	263.777i	−0.995078	−	0.530738i
$498$		0			0
$499$	248.404			0.497804			0.248902	−	0.968529i	$-0.419930\pi$
$499$	248.404			0.497804			0.248902	+	0.968529i	$0.419930\pi$
$500$		0			0
$501$	206.723			0.412620
$502$		0			0
$503$	329.152	−	329.152i	0.654377	−	0.654377i	−0.299667	−	0.954044i	$-0.596876\pi$
$503$	329.152	−	329.152i	0.654377	−	0.654377i	0.954044	+	0.299667i	$0.0968755\pi$
$504$		0			0
$505$	−58.7570	−	450.526i	−0.116351	−	0.892131i
$506$		0			0
$507$	7.69130	+	7.69130i	0.0151702	+	0.0151702i
$508$		0			0
$509$	27.0955			0.0532328			0.0266164	−	0.999646i	$-0.491527\pi$
$509$	27.0955			0.0532328			0.0266164	+	0.999646i	$0.491527\pi$
$510$		0			0
$511$	267.152	−	81.3004i	0.522802	−	0.159101i
$512$		0			0
$513$	25.4721	−	25.4721i	0.0496531	−	0.0496531i
$514$		0			0
$515$	−162.237	+	210.902i	−0.315024	+	0.409518i
$516$		0			0
$517$	−306.171	+	306.171i	−0.592208	+	0.592208i
$518$		0			0
$519$	131.181			0.252757
$520$		0			0
$521$		−	191.193i		−	0.366972i	−0.983022	−	0.183486i	$-0.941262\pi$
$521$		−	191.193i		−	0.366972i	0.983022	−	0.183486i	$-0.0587383\pi$
$522$		0			0
$523$	343.867	−	343.867i	0.657490	−	0.657490i	−0.297295	−	0.954786i	$-0.596085\pi$
$523$	343.867	−	343.867i	0.657490	−	0.657490i	0.954786	+	0.297295i	$0.0960846\pi$
$524$		0			0
$525$	64.0295	+	103.320i	0.121961	+	0.196801i
$526$		0			0
$527$	1085.69	−	1085.69i	2.06013	−	2.06013i
$528$		0			0
$529$			524.267i			0.991053i
$530$		0			0
$531$	162.736			0.306470
$532$		0			0
$533$	−565.203	+	565.203i	−1.06042	+	1.06042i
$534$		0			0
$535$	93.5372	−	121.594i	0.174836	−	0.227279i
$536$		0			0
$537$	104.254	−	104.254i	0.194141	−	0.194141i
$538$		0			0
$539$	−649.486	+	435.654i	−1.20498	+	0.808263i
$540$		0			0
$541$	−606.156			−1.12044			−0.560218	−	0.828345i	$-0.689283\pi$
$541$	−606.156			−1.12044			−0.560218	+	0.828345i	$0.689283\pi$
$542$		0			0
$543$	78.7601	+	78.7601i	0.145046	+	0.145046i
$544$		0			0
$545$	97.8718	+	750.443i	0.179581	+	1.37696i
$546$		0			0
$547$	−570.421	+	570.421i	−1.04282	+	1.04282i	−0.0437767	+	0.999041i	$0.513939\pi$
$547$	−570.421	+	570.421i	−1.04282	+	1.04282i	−0.999041	+	0.0437767i	$0.986061\pi$
$548$		0			0
$549$	756.720			1.37836
$550$		0			0
$551$	−6.85934			−0.0124489
$552$		0			0
$553$	190.871	−	357.863i	0.345155	−	0.647130i
$554$		0			0
$555$	48.6809	−	6.34889i	0.0877133	−	0.0114394i
$556$		0			0
$557$	−310.163	−	310.163i	−0.556845	−	0.556845i	0.371563	−	0.928408i	$-0.378822\pi$
$557$	−310.163	−	310.163i	−0.556845	−	0.556845i	−0.928408	+	0.371563i	$0.878822\pi$
$558$		0			0
$559$		−	561.494i		−	1.00446i
$560$		0			0
$561$	−344.249			−0.613634
$562$		0			0
$563$	−190.159	+	190.159i	−0.337759	+	0.337759i	−0.855523	−	0.517764i	$-0.826765\pi$
$563$	−190.159	+	190.159i	−0.337759	+	0.337759i	0.517764	+	0.855523i	$0.326765\pi$
$564$		0			0
$565$	−436.778	+	567.793i	−0.773059	+	1.00494i
$566$		0			0
$567$	224.691	−	421.272i	0.396280	−	0.742984i
$568$		0			0
$569$			1011.32i			1.77737i	0.458523	+	0.888683i	$0.348379\pi$
$569$			1011.32i			1.77737i	−0.458523	+	0.888683i	$0.651621\pi$
$570$		0			0
$571$			518.496i			0.908049i	0.890989	+	0.454025i	$0.150012\pi$
$571$			518.496i			0.908049i	−0.890989	+	0.454025i	$0.849988\pi$
$572$		0			0
$573$	−76.7370	−	76.7370i	−0.133921	−	0.133921i
$574$		0			0
$575$	701.665	+	407.379i	1.22029	+	0.708486i
$576$		0			0
$577$	68.4024	−	68.4024i	0.118548	−	0.118548i	−0.645344	−	0.763892i	$-0.723286\pi$
$577$	68.4024	−	68.4024i	0.118548	−	0.118548i	0.763892	+	0.645344i	$0.223286\pi$
$578$		0			0
$579$			4.16814i			0.00719887i
$580$		0			0
$581$	204.456	+	671.840i	0.351904	+	1.15635i
$582$		0			0
$583$	−352.516	−	352.516i	−0.604659	−	0.604659i
$584$		0			0
$585$	−352.861	+	458.705i	−0.603182	+	0.784111i
$586$		0			0
$587$	344.226	+	344.226i	0.586416	+	0.586416i	0.936659	−	0.350243i	$-0.113901\pi$
$587$	344.226	+	344.226i	0.586416	+	0.586416i	−0.350243	+	0.936659i	$0.613901\pi$
$588$		0			0
$589$		−	146.386i		−	0.248533i
$590$		0			0
$591$	−147.658			−0.249844
$592$		0			0
$593$	367.831	+	367.831i	0.620289	+	0.620289i	0.945605	−	0.325317i	$-0.105471\pi$
$593$	367.831	+	367.831i	0.620289	+	0.620289i	−0.325317	+	0.945605i	$0.605471\pi$
$594$		0			0
$595$	−448.234	−	990.116i	−0.753335	−	1.66406i
$596$		0			0
$597$	−27.5544	−	27.5544i	−0.0461547	−	0.0461547i
$598$		0			0
$599$	−794.866			−1.32699			−0.663494	−	0.748181i	$-0.730927\pi$
$599$	−794.866			−1.32699			−0.663494	+	0.748181i	$0.730927\pi$
$600$		0			0
$601$			543.276i			0.903954i	0.892030	+	0.451977i	$0.149281\pi$
$601$			543.276i			0.903954i	−0.892030	+	0.451977i	$0.850719\pi$
$602$		0			0
$603$	−178.306	−	178.306i	−0.295698	−	0.295698i
$604$		0			0
$605$	663.074	−	86.4773i	1.09599	−	0.142938i
$606$		0			0
$607$	−653.078	−	653.078i	−1.07591	−	1.07591i	−0.996872	−	0.0790389i	$-0.974815\pi$
$607$	−653.078	−	653.078i	−1.07591	−	1.07591i	−0.0790389	−	0.996872i	$-0.525185\pi$
$608$		0			0
$609$	10.7768	−	3.27962i	0.0176959	−	0.00538526i
$610$		0			0
$611$			368.654i			0.603362i
$612$		0			0
$613$	−65.3839	+	65.3839i	−0.106662	+	0.106662i	−0.758424	−	0.651762i	$-0.774030\pi$
$613$	−65.3839	+	65.3839i	−0.106662	+	0.106662i	0.651762	+	0.758424i	$0.274030\pi$
$614$		0			0
$615$	161.916	+	124.555i	0.263278	+	0.202528i
$616$		0			0
$617$	256.584	+	256.584i	0.415857	+	0.415857i	0.883773	−	0.467916i	$-0.154995\pi$
$617$	256.584	+	256.584i	0.415857	+	0.415857i	−0.467916	+	0.883773i	$0.654995\pi$
$618$		0			0
$619$			779.719i			1.25964i	0.776740	+	0.629822i	$0.216872\pi$
$619$			779.719i			1.25964i	−0.776740	+	0.629822i	$0.783128\pi$
$620$		0			0
$621$			394.882i			0.635880i
$622$		0			0
$623$	−146.623	+	274.903i	−0.235350	+	0.441257i
$624$		0			0
$625$	542.776	−	309.870i	0.868441	−	0.495792i
$626$		0			0
$627$	−23.2080	+	23.2080i	−0.0370143	+	0.0370143i
$628$		0			0
$629$	−438.963			−0.697875
$630$		0			0
$631$		−	328.081i		−	0.519938i	−0.965617	−	0.259969i	$-0.916288\pi$
$631$		−	328.081i		−	0.519938i	0.965617	−	0.259969i	$-0.0837123\pi$
$632$		0			0
$633$	−115.559	−	115.559i	−0.182557	−	0.182557i
$634$		0			0
$635$	−334.094	+	434.308i	−0.526133	+	0.683950i
$636$		0			0
$637$	−128.735	+	653.296i	−0.202096	+	1.02558i
$638$		0			0
$639$	−682.014			−1.06731
$640$		0			0
$641$	539.896			0.842272			0.421136	−	0.906998i	$-0.361632\pi$
$641$	539.896			0.842272			0.421136	+	0.906998i	$0.361632\pi$
$642$		0			0
$643$	−303.322	+	303.322i	−0.471730	+	0.471730i	−0.902474	−	0.430744i	$-0.858251\pi$
$643$	−303.322	+	303.322i	−0.471730	+	0.471730i	0.430744	+	0.902474i	$0.358251\pi$
$644$		0			0
$645$	−142.295	+	18.5580i	−0.220613	+	0.0287720i
$646$		0			0
$647$	−251.201	−	251.201i	−0.388255	−	0.388255i	0.485810	−	0.874065i	$-0.338525\pi$
$647$	−251.201	−	251.201i	−0.388255	−	0.388255i	−0.874065	+	0.485810i	$0.838525\pi$
$648$		0			0
$649$	−304.940			−0.469861
$650$		0			0
$651$	69.9909	+	229.989i	0.107513	+	0.353286i
$652$		0			0
$653$	10.6691	−	10.6691i	0.0163386	−	0.0163386i	−0.698890	−	0.715229i	$-0.746322\pi$
$653$	10.6691	−	10.6691i	0.0163386	−	0.0163386i	0.715229	+	0.698890i	$0.246322\pi$
$654$		0			0
$655$	968.796	−	126.349i	1.47908	−	0.192899i
$656$		0			0
$657$	240.267	−	240.267i	0.365703	−	0.365703i
$658$		0			0
$659$	80.4525			0.122083			0.0610413	−	0.998135i	$-0.480558\pi$
$659$	80.4525			0.122083			0.0610413	+	0.998135i	$0.480558\pi$
$660$		0			0
$661$			636.247i			0.962552i	0.876569	+	0.481276i	$0.159827\pi$
$661$			636.247i			0.962552i	−0.876569	+	0.481276i	$0.840173\pi$
$662$		0			0
$663$	−207.251	+	207.251i	−0.312596	+	0.312596i
$664$		0			0
$665$	−96.9682	−	36.5316i	−0.145817	−	0.0549348i
$666$		0			0
$667$	53.1685	−	53.1685i	0.0797130	−	0.0797130i
$668$		0			0
$669$			174.536i			0.260891i
$670$		0			0
$671$	−1417.97			−2.11322
$672$		0			0
$673$	−603.639	+	603.639i	−0.896938	+	0.896938i	−0.995164	−	0.0982261i	$-0.968683\pi$
$673$	−603.639	+	603.639i	−0.896938	+	0.896938i	0.0982261	+	0.995164i	$0.468683\pi$
$674$		0			0
$675$	263.062	+	152.731i	0.389722	+	0.226268i
$676$		0			0
$677$	−225.360	+	225.360i	−0.332881	+	0.332881i	−0.853679	−	0.520799i	$-0.825634\pi$
$677$	−225.360	+	225.360i	−0.332881	+	0.332881i	0.520799	+	0.853679i	$0.325634\pi$
$678$		0			0
$679$	−208.403	−	684.809i	−0.306926	−	1.00855i
$680$		0			0
$681$	−82.2807			−0.120823
$682$		0			0
$683$	−820.220	−	820.220i	−1.20091	−	1.20091i	−0.973891	−	0.227016i	$-0.927103\pi$
$683$	−820.220	−	820.220i	−1.20091	−	1.20091i	−0.227016	−	0.973891i	$-0.572897\pi$
$684$		0			0
$685$	−617.758	−	475.214i	−0.901837	−	0.693743i
$686$		0			0
$687$	6.86505	−	6.86505i	0.00999279	−	0.00999279i
$688$		0			0
$689$	−424.457			−0.616048
$690$		0			0
$691$	−767.462			−1.11065			−0.555327	−	0.831632i	$-0.687407\pi$
$691$	−767.462			−1.11065			−0.555327	+	0.831632i	$0.687407\pi$
$692$		0			0
$693$	−447.837	+	839.647i	−0.646229	+	1.21161i
$694$		0			0
$695$	48.8942	+	374.902i	0.0703513	+	0.539427i
$696$		0			0
$697$	−1291.58	−	1291.58i	−1.85305	−	1.85305i
$698$		0			0
$699$			4.32669i			0.00618983i
$700$		0			0
$701$	557.104			0.794727			0.397364	−	0.917661i	$-0.369925\pi$
$701$	557.104			0.794727			0.397364	+	0.917661i	$0.369925\pi$
$702$		0			0
$703$	−29.5933	+	29.5933i	−0.0420957	+	0.0420957i
$704$		0			0
$705$	93.4253	−	12.1844i	0.132518	−	0.0172828i
$706$		0			0
$707$	−561.239	−	299.344i	−0.793831	−	0.423400i
$708$		0			0
$709$		−	467.586i		−	0.659501i	−0.944068	−	0.329751i	$-0.893035\pi$
$709$		−	467.586i		−	0.659501i	0.944068	−	0.329751i	$-0.106965\pi$
$710$		0			0
$711$		−	493.510i		−	0.694107i
$712$		0			0
$713$	1134.68	+	1134.68i	1.59141	+	1.59141i
$714$		0			0
$715$	661.205	−	859.538i	0.924762	−	1.20215i
$716$		0			0
$717$	−128.206	+	128.206i	−0.178809	+	0.178809i
$718$		0			0
$719$		−	711.632i		−	0.989752i	−0.868963	−	0.494876i	$-0.835213\pi$
$719$		−	711.632i		−	0.989752i	0.868963	−	0.494876i	$-0.164787\pi$
$720$		0			0
$721$	108.454	+	356.380i	0.150422	+	0.494285i
$722$		0			0
$723$	−152.227	−	152.227i	−0.210549	−	0.210549i
$724$		0			0
$725$	−14.8554	−	55.9842i	−0.0204903	−	0.0772196i
$726$		0			0
$727$	197.113	+	197.113i	0.271132	+	0.271132i	0.829556	−	0.558424i	$-0.188594\pi$
$727$	197.113	+	197.113i	0.271132	+	0.271132i	−0.558424	+	0.829556i	$0.688594\pi$
$728$		0			0
$729$		−	504.893i		−	0.692583i
$730$		0			0
$731$	1283.10			1.75527
$732$		0			0
$733$	77.4789	+	77.4789i	0.105701	+	0.105701i	0.757979	−	0.652278i	$-0.226187\pi$
$733$	77.4789	+	77.4789i	0.105701	+	0.105701i	−0.652278	+	0.757979i	$0.726187\pi$
$734$		0			0
$735$	169.815	+	11.0323i	0.231041	+	0.0150100i
$736$		0			0
$737$	334.116	+	334.116i	0.453346	+	0.453346i
$738$		0			0
$739$	1005.55			1.36070			0.680348	−	0.732889i	$-0.261829\pi$
$739$	1005.55			1.36070			0.680348	+	0.732889i	$0.261829\pi$
$740$		0			0
$741$			27.9442i			0.0377115i
$742$		0			0
$743$	335.017	+	335.017i	0.450898	+	0.450898i	0.895653	−	0.444754i	$-0.146709\pi$
$743$	335.017	+	335.017i	0.450898	+	0.450898i	−0.444754	+	0.895653i	$0.646709\pi$
$744$		0			0
$745$	21.3867	+	163.985i	0.0287070	+	0.220114i
$746$		0			0
$747$	604.228	+	604.228i	0.808873	+	0.808873i
$748$		0			0
$749$	−62.5290	−	205.469i	−0.0834833	−	0.274325i
$750$		0			0
$751$			872.535i			1.16183i	0.813964	+	0.580916i	$0.197305\pi$
$751$			872.535i			1.16183i	−0.813964	+	0.580916i	$0.802695\pi$
$752$		0			0
$753$	136.838	−	136.838i	0.181724	−	0.181724i
$754$		0			0
$755$	148.342	+	1137.43i	0.196479	+	1.50652i
$756$		0			0
$757$	−307.075	−	307.075i	−0.405647	−	0.405647i	0.474570	−	0.880218i	$-0.342603\pi$
$757$	−307.075	−	307.075i	−0.405647	−	0.405647i	−0.880218	+	0.474570i	$0.842603\pi$
$758$		0			0
$759$		−	359.783i		−	0.474022i
$760$		0			0
$761$			590.401i			0.775823i	0.921697	+	0.387911i	$0.126803\pi$
$761$			590.401i			0.775823i	−0.921697	+	0.387911i	$0.873197\pi$
$762$		0			0
$763$	934.857	+	498.618i	1.22524	+	0.653497i
$764$		0			0
$765$	−1048.21	−	806.342i	−1.37021	−	1.05404i
$766$		0			0
$767$	−183.586	+	183.586i	−0.239356	+	0.239356i
$768$		0			0
$769$	250.547			0.325808			0.162904	−	0.986642i	$-0.447914\pi$
$769$	250.547			0.325808			0.162904	+	0.986642i	$0.447914\pi$
$770$		0			0
$771$		−	91.8615i		−	0.119146i
$772$		0			0
$773$	245.390	+	245.390i	0.317451	+	0.317451i	0.847787	−	0.530336i	$-0.177934\pi$
$773$	245.390	+	245.390i	0.317451	+	0.317451i	−0.530336	+	0.847787i	$0.677934\pi$
$774$		0			0
$775$	1194.76	−	317.032i	1.54163	−	0.409073i
$776$		0			0
$777$	32.3451	−	60.6437i	0.0416282	−	0.0780485i
$778$		0			0
$779$	−174.146			−0.223551
$780$		0			0
$781$	1277.98			1.63634
$782$		0			0
$783$	19.9335	−	19.9335i	0.0254578	−	0.0254578i
$784$		0			0
$785$	564.812	−	734.232i	0.719506	−	0.935327i
$786$		0			0
$787$	−506.460	−	506.460i	−0.643532	−	0.643532i	0.307890	−	0.951422i	$-0.400377\pi$
$787$	−506.460	−	506.460i	−0.643532	−	0.643532i	−0.951422	+	0.307890i	$0.900377\pi$
$788$		0			0
$789$	266.177			0.337360
$790$		0			0
$791$	291.983	+	959.451i	0.369131	+	1.21296i
$792$		0			0
$793$	−853.674	+	853.674i	−1.07651	+	1.07651i
$794$		0			0
$795$	14.0287	+	107.567i	0.0176462	+	0.135304i
$796$		0			0
$797$	538.516	−	538.516i	0.675679	−	0.675679i	−0.283340	−	0.959019i	$-0.591443\pi$
$797$	538.516	−	538.516i	0.675679	−	0.675679i	0.959019	+	0.283340i	$0.0914425\pi$
$798$		0			0
$799$	−842.431			−1.05436
$800$		0			0
$801$			379.105i			0.473289i
$802$		0			0
$803$	−450.221	+	450.221i	−0.560673	+	0.560673i
$804$		0			0
$805$	1034.79	−	468.460i	1.28546	−	0.581938i
$806$		0			0
$807$	255.635	−	255.635i	0.316772	−	0.316772i
$808$		0			0
$809$			827.755i			1.02318i	0.859229	+	0.511591i	$0.170944\pi$
$809$			827.755i			1.02318i	−0.859229	+	0.511591i	$0.829056\pi$
$810$		0			0
$811$	−691.728			−0.852933			−0.426466	−	0.904503i	$-0.640242\pi$
$811$	−691.728			−0.852933			−0.426466	+	0.904503i	$0.640242\pi$
$812$		0			0
$813$	−164.023	+	164.023i	−0.201751	+	0.201751i
$814$		0			0
$815$	−949.415	−	730.343i	−1.16493	−	0.896127i
$816$		0			0
$817$	86.5019	−	86.5019i	0.105877	−	0.105877i
$818$		0			0
$819$	235.885	+	775.115i	0.288016	+	0.946417i
$820$		0			0
$821$	616.342			0.750721			0.375361	−	0.926879i	$-0.377519\pi$
$821$	616.342			0.750721			0.375361	+	0.926879i	$0.377519\pi$
$822$		0			0
$823$	89.0330	+	89.0330i	0.108181	+	0.108181i	0.759125	−	0.650944i	$-0.225627\pi$
$823$	89.0330	+	89.0330i	0.108181	+	0.108181i	−0.650944	+	0.759125i	$0.725627\pi$
$824$		0			0
$825$	−239.680	−	139.156i	−0.290521	−	0.168673i
$826$		0			0
$827$	−278.878	+	278.878i	−0.337217	+	0.337217i	−0.855319	−	0.518102i	$-0.826639\pi$
$827$	−278.878	+	278.878i	−0.337217	+	0.337217i	0.518102	+	0.855319i	$0.326639\pi$
$828$		0			0
$829$	246.319			0.297128			0.148564	−	0.988903i	$-0.452535\pi$
$829$	246.319			0.297128			0.148564	+	0.988903i	$0.452535\pi$
$830$		0			0
$831$	−27.5191			−0.0331156
$832$		0			0
$833$	−1492.88	−	294.180i	−1.79217	−	0.353157i
$834$		0			0
$835$	−1179.50	−	907.334i	−1.41257	−	1.08663i
$836$		0			0
$837$	425.403	+	425.403i	0.508247	+	0.508247i
$838$		0			0
$839$		−	1027.98i		−	1.22524i	−0.790377	−	0.612621i	$-0.790115\pi$
$839$		−	1027.98i		−	1.22524i	0.790377	−	0.612621i	$-0.209885\pi$
$840$		0			0
$841$	835.632			0.993617
$842$		0			0
$843$	−123.482	+	123.482i	−0.146479	+	0.146479i
$844$		0			0
$845$	−10.1260	−	77.6423i	−0.0119834	−	0.0918843i
$846$		0			0
$847$	440.568	−	826.019i	0.520151	−	0.975228i
$848$		0			0
$849$		−	212.661i		−	0.250484i
$850$		0			0
$851$		−	458.771i		−	0.539096i
$852$		0			0
$853$	−931.832	−	931.832i	−1.09242	−	1.09242i	−0.995270	−	0.0971475i	$-0.969028\pi$
$853$	−931.832	−	931.832i	−1.09242	−	1.09242i	−0.0971475	−	0.995270i	$-0.530972\pi$
$854$		0			0
$855$	−125.027	+	16.3059i	−0.146230	+	0.0190712i
$856$		0			0
$857$	−283.056	+	283.056i	−0.330287	+	0.330287i	−0.852695	−	0.522408i	$-0.825034\pi$
$857$	−283.056	+	283.056i	−0.330287	+	0.330287i	0.522408	+	0.852695i	$0.325034\pi$
$858$		0			0
$859$			1638.61i			1.90758i	0.300474	+	0.953790i	$0.402855\pi$
$859$			1638.61i			1.90758i	−0.300474	+	0.953790i	$0.597145\pi$
$860$		0			0
$861$	273.604	−	83.2639i	0.317775	−	0.0967060i
$862$		0			0
$863$	−1.73448	−	1.73448i	−0.00200982	−	0.00200982i	0.706101	−	0.708111i	$-0.250452\pi$
$863$	−1.73448	−	1.73448i	−0.00200982	−	0.00200982i	−0.708111	+	0.706101i	$0.750452\pi$
$864$		0			0
$865$	−748.477	−	575.770i	−0.865291	−	0.665630i
$866$		0			0
$867$	−331.660	−	331.660i	−0.382537	−	0.382537i
$868$		0			0
$869$			924.758i			1.06416i
$870$		0			0
$871$	402.302			0.461885
$872$		0			0
$873$	−615.891	−	615.891i	−0.705489	−	0.705489i
$874$		0			0
$875$	88.1553	−	870.548i	0.100749	−	0.994912i
$876$		0			0
$877$	189.068	+	189.068i	0.215585	+	0.215585i	0.806635	−	0.591050i	$-0.201287\pi$
$877$	189.068	+	189.068i	0.215585	+	0.215585i	−0.591050	+	0.806635i	$0.701287\pi$
$878$		0			0
$879$	−239.362			−0.272311
$880$		0			0
$881$		−	457.338i		−	0.519113i	−0.965728	−	0.259556i	$-0.916424\pi$
$881$		−	457.338i		−	0.519113i	0.965728	−	0.259556i	$-0.0835763\pi$
$882$		0			0
$883$	−882.255	−	882.255i	−0.999157	−	0.999157i	0.000843057	−	1.00000i	$-0.499732\pi$
$883$	−882.255	−	882.255i	−0.999157	−	0.999157i	−1.00000		0.000843057i	$0.999732\pi$
$884$		0			0
$885$	52.5925	+	40.4571i	0.0594265	+	0.0457142i
$886$		0			0
$887$	1029.89	+	1029.89i	1.16110	+	1.16110i	0.984236	+	0.176860i	$0.0565941\pi$
$887$	1029.89	+	1029.89i	1.16110	+	1.16110i	0.176860	+	0.984236i	$0.443406\pi$
$888$		0			0
$889$	223.340	+	733.890i	0.251226	+	0.825523i
$890$		0			0
$891$			1088.61i			1.22179i
$892$		0			0
$893$	−56.7936	+	56.7936i	−0.0635987	+	0.0635987i
$894$		0			0
$895$	−1052.42	+	137.256i	−1.17589	+	0.153358i
$896$		0			0
$897$	−216.603	−	216.603i	−0.241475	−	0.241475i
$898$		0			0
$899$		−	114.556i		−	0.127426i
$900$		0			0
$901$		−	969.949i		−	1.07652i
$902$		0			0
$903$	−94.5455	+	177.263i	−0.104702	+	0.196305i
$904$		0			0
$905$	−103.692	−	795.069i	−0.114577	−	0.878529i
$906$		0			0
$907$	−1049.05	+	1049.05i	−1.15661	+	1.15661i	−0.171412	+	0.985199i	$0.554833\pi$
$907$	−1049.05	+	1049.05i	−1.15661	+	1.15661i	−0.985199	+	0.171412i	$0.945167\pi$
$908$		0			0
$909$	−773.976			−0.851459
$910$		0			0
$911$		−	822.503i		−	0.902857i	−0.892307	−	0.451428i	$-0.850915\pi$
$911$		−	822.503i		−	0.902857i	0.892307	−	0.451428i	$-0.149085\pi$
$912$		0			0
$913$	−1132.23	−	1132.23i	−1.24012	−	1.24012i
$914$		0			0
$915$	244.555	+	188.125i	0.267273	+	0.205602i
$916$		0			0
$917$	643.698	−	1206.87i	0.701961	−	1.31610i
$918$		0			0
$919$	408.042			0.444006			0.222003	−	0.975046i	$-0.428740\pi$
$919$	408.042			0.444006			0.222003	+	0.975046i	$0.428740\pi$
$920$		0			0
$921$	115.205			0.125086
$922$		0			0
$923$	769.396	−	769.396i	0.833582	−	0.833582i
$924$		0			0
$925$	−305.624	−	177.442i	−0.330404	−	0.191829i
$926$		0			0
$927$	320.515	+	320.515i	0.345755	+	0.345755i
$928$		0			0
$929$	−584.172			−0.628818			−0.314409	−	0.949288i	$-0.601806\pi$
$929$	−584.172			−0.628818			−0.314409	+	0.949288i	$0.601806\pi$
$930$		0			0
$931$	−120.477	+	80.8120i	−0.129406	+	0.0868013i
$932$		0			0
$933$	−26.8346	+	26.8346i	−0.0287617	+	0.0287617i
$934$		0			0
$935$	1964.18	+	1510.95i	2.10072	+	1.61599i
$936$		0			0
$937$	−119.120	+	119.120i	−0.127129	+	0.127129i	−0.767808	−	0.640680i	$-0.778653\pi$
$937$	−119.120	+	119.120i	−0.127129	+	0.127129i	0.640680	+	0.767808i	$0.278653\pi$
$938$		0			0
$939$	−192.857			−0.205386
$940$		0			0
$941$			764.546i			0.812483i	0.913766	+	0.406241i	$0.133161\pi$
$941$			764.546i			0.812483i	−0.913766	+	0.406241i	$0.866839\pi$
$942$		0			0
$943$	1349.86	−	1349.86i	1.43145	−	1.43145i
$944$		0			0
$945$	387.956	−	175.631i	0.410535	−	0.185853i
$946$		0			0
$947$	553.104	−	553.104i	0.584059	−	0.584059i	−0.351957	−	0.936016i	$-0.614484\pi$
$947$	553.104	−	553.104i	0.584059	−	0.584059i	0.936016	+	0.351957i	$0.114484\pi$
$948$		0			0
$949$			542.101i			0.571233i
$950$		0			0
$951$	265.182			0.278845
$952$		0			0
$953$	778.903	−	778.903i	0.817317	−	0.817317i	−0.168402	−	0.985718i	$-0.553861\pi$
$953$	778.903	−	778.903i	0.817317	−	0.817317i	0.985718	+	0.168402i	$0.0538606\pi$
$954$		0			0
$955$	101.028	+	774.646i	0.105789	+	0.811148i
$956$		0			0
$957$	−18.1617	+	18.1617i	−0.0189777	+	0.0189777i
$958$		0			0
$959$	−1043.88	+	317.677i	−1.08851	+	0.331259i
$960$		0			0
$961$	1483.76			1.54397
$962$		0			0
$963$	−184.791	−	184.791i	−0.191891	−	0.191891i
$964$		0			0
$965$	18.2945	−	23.7821i	0.0189581	−	0.0246447i
$966$		0			0
$967$	303.813	−	303.813i	0.314181	−	0.314181i	−0.532346	−	0.846527i	$-0.678690\pi$
$967$	303.813	−	303.813i	0.314181	−	0.314181i	0.846527	+	0.532346i	$0.178690\pi$
$968$		0			0
$969$	−63.8568			−0.0658997
$970$		0			0
$971$	871.227			0.897247			0.448624	−	0.893721i	$-0.351914\pi$
$971$	871.227			0.897247			0.448624	+	0.893721i	$0.351914\pi$
$972$		0			0
$973$	467.030	+	249.096i	0.479990	+	0.256009i
$974$		0			0
$975$	−228.074	+	60.5195i	−0.233922	+	0.0620713i
$976$		0			0
$977$	−849.373	−	849.373i	−0.869369	−	0.869369i	0.123034	−	0.992402i	$-0.460738\pi$
$977$	−849.373	−	849.373i	−0.869369	−	0.869369i	−0.992402	+	0.123034i	$0.960738\pi$
$978$		0			0
$979$		−	710.381i		−	0.725619i
$980$		0			0
$981$	1289.21			1.31418
$982$		0			0
$983$	524.628	−	524.628i	0.533700	−	0.533700i	−0.387971	−	0.921672i	$-0.626824\pi$
$983$	524.628	−	524.628i	0.533700	−	0.533700i	0.921672	+	0.387971i	$0.126824\pi$
$984$		0			0
$985$	842.488	+	648.089i	0.855318	+	0.657958i
$986$		0			0
$987$	62.0747	−	116.384i	0.0628923	−	0.117917i
$988$		0			0
$989$			1341.00i			1.35591i
$990$		0			0
$991$			417.414i			0.421205i	0.977572	+	0.210603i	$0.0675426\pi$
$991$			417.414i			0.421205i	−0.977572	+	0.210603i	$0.932457\pi$
$992$		0			0
$993$	19.4908	+	19.4908i	0.0196282	+	0.0196282i
$994$		0			0
$995$	36.2768	+	278.156i	0.0364591	+	0.279554i
$996$		0			0
$997$	19.9946	−	19.9946i	0.0200547	−	0.0200547i	−0.697008	−	0.717063i	$-0.745486\pi$
$997$	19.9946	−	19.9946i	0.0200547	−	0.0200547i	0.717063	+	0.697008i	$0.245486\pi$
$998$		0			0
$999$		−	171.998i		−	0.172170i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.3.v.b.447.17	yes	64
4.3	odd	2	inner	560.3.v.b.447.16	yes	64
5.3	odd	4	inner	560.3.v.b.223.18	yes	64
7.6	odd	2	inner	560.3.v.b.447.15	yes	64
20.3	even	4	inner	560.3.v.b.223.15	✓	64
28.27	even	2	inner	560.3.v.b.447.18	yes	64
35.13	even	4	inner	560.3.v.b.223.16	yes	64
140.83	odd	4	inner	560.3.v.b.223.17	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.3.v.b.223.15	✓	64	20.3	even	4	inner
560.3.v.b.223.16	yes	64	35.13	even	4	inner
560.3.v.b.223.17	yes	64	140.83	odd	4	inner
560.3.v.b.223.18	yes	64	5.3	odd	4	inner
560.3.v.b.447.15	yes	64	7.6	odd	2	inner
560.3.v.b.447.16	yes	64	4.3	odd	2	inner
560.3.v.b.447.17	yes	64	1.1	even	1	trivial
560.3.v.b.447.18	yes	64	28.27	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	560.v (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.491144 - 0.491144i) q^{3} +(-4.95801 + 0.646617i) q^{5} +(-3.29426 + 6.17640i) q^{7} +8.51755i q^{9} -15.9605i q^{11} +(-9.60885 - 9.60885i) q^{13} +(-2.11752 + 2.75268i) q^{15} +(21.9577 - 21.9577i) q^{17} -2.96061i q^{19} +(1.41554 + 4.65146i) q^{21} +(22.9485 + 22.9485i) q^{23} +(24.1638 - 6.41187i) q^{25} +(8.60365 + 8.60365i) q^{27} -2.31686i q^{29} +49.4445 q^{31} +(-7.83892 - 7.83892i) q^{33} +(12.3392 - 32.7528i) q^{35} +(-9.99566 - 9.99566i) q^{37} -9.43866 q^{39} -58.8211i q^{41} +(29.2176 + 29.2176i) q^{43} +(-5.50760 - 42.2301i) q^{45} +(-19.1831 - 19.1831i) q^{47} +(-27.2957 - 40.6933i) q^{49} -21.5688i q^{51} +(22.0868 - 22.0868i) q^{53} +(10.3203 + 79.1324i) q^{55} +(-1.45409 - 1.45409i) q^{57} -19.1059i q^{59} -88.8424i q^{61} +(-52.6078 - 28.0590i) q^{63} +(53.8540 + 41.4275i) q^{65} +(-20.9339 + 20.9339i) q^{67} +22.5420 q^{69} +80.0716i q^{71} +(-28.2084 - 28.2084i) q^{73} +(8.71874 - 15.0171i) q^{75} +(98.5784 + 52.5781i) q^{77} -57.9404 q^{79} -68.2067 q^{81} +(70.9391 - 70.9391i) q^{83} +(-94.6683 + 123.065i) q^{85} +(-1.13791 - 1.13791i) q^{87} +44.5086 q^{89} +(91.0021 - 27.6940i) q^{91} +(24.2844 - 24.2844i) q^{93} +(1.91438 + 14.6788i) q^{95} +(-72.3085 + 72.3085i) q^{97} +135.945 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 16 q^{21} - 72 q^{25} + 72 q^{37} + 272 q^{53} - 376 q^{57} - 88 q^{65} + 24 q^{77} - 432 q^{81} + 384 q^{85} + 840 q^{93}+O(q^{100}) \) 64 * q + 16 * q^21 - 72 * q^25 + 72 * q^37 + 272 * q^53 - 376 * q^57 - 88 * q^65 + 24 * q^77 - 432 * q^81 + 384 * q^85 + 840 * q^93

Introduction

L-functions

Modular forms

Varieties

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Database

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