LMFDB - Embedded newform 560.3.v.b.223.30

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			223.30
Character	$\chi$	$=$	560.223
Dual form			560.3.v.b.447.30

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.85761 + 2.85761i) q^{3} +(2.38475 + 4.39465i) q^{5} +(-5.83264 + 3.87043i) q^{7} +7.33188i q^{9} -11.7125i q^{11} +(-14.4927 + 14.4927i) q^{13} +(-5.74353 + 19.3729i) q^{15} +(-5.99637 - 5.99637i) q^{17} +36.6798i q^{19} +(-27.7276 - 5.60723i) q^{21} +(23.3020 - 23.3020i) q^{23} +(-13.6260 + 20.9603i) q^{25} +(4.76683 - 4.76683i) q^{27} +20.4842i q^{29} -26.3284 q^{31} +(33.4698 - 33.4698i) q^{33} +(-30.9186 - 16.4024i) q^{35} +(-23.8254 + 23.8254i) q^{37} -82.8292 q^{39} -4.49681i q^{41} +(16.6452 - 16.6452i) q^{43} +(-32.2211 + 17.4847i) q^{45} +(36.6777 - 36.6777i) q^{47} +(19.0395 - 45.1497i) q^{49} -34.2706i q^{51} +(61.3395 + 61.3395i) q^{53} +(51.4724 - 27.9314i) q^{55} +(-104.817 + 104.817i) q^{57} -43.1156i q^{59} +87.5037i q^{61} +(-28.3776 - 42.7643i) q^{63} +(-98.2520 - 29.1290i) q^{65} +(18.1881 + 18.1881i) q^{67} +133.176 q^{69} -2.44203i q^{71} +(48.9892 - 48.9892i) q^{73} +(-98.8340 + 20.9586i) q^{75} +(45.3325 + 68.3149i) q^{77} -60.5548 q^{79} +93.2304 q^{81} +(-26.3121 - 26.3121i) q^{83} +(12.0521 - 40.6518i) q^{85} +(-58.5359 + 58.5359i) q^{87} -150.664 q^{89} +(28.4378 - 140.624i) q^{91} +(-75.2364 - 75.2364i) q^{93} +(-161.195 + 87.4720i) q^{95} +(-4.43919 - 4.43919i) q^{97} +85.8747 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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
$3$	2.85761	+	2.85761i	0.952537	+	0.952537i	0.998924	−	0.0463866i	$-0.0147706\pi$
$3$	2.85761	+	2.85761i	0.952537	+	0.952537i	−0.0463866	+	0.998924i	$0.514771\pi$
$4$		0			0
$5$	2.38475	+	4.39465i	0.476949	+	0.878931i
$5$	2.38475	+	4.39465i	0.476949	+	0.878931i
$6$		0			0
$7$	−5.83264	+	3.87043i	−0.833235	+	0.552919i
$7$	−5.83264	+	3.87043i	−0.833235	+	0.552919i
$8$		0			0
$9$			7.33188i			0.814654i
$10$		0			0
$11$		−	11.7125i		−	1.06477i	−0.846501	−	0.532387i	$-0.821295\pi$
$11$		−	11.7125i		−	1.06477i	0.846501	−	0.532387i	$-0.178705\pi$
$12$		0			0
$13$	−14.4927	+	14.4927i	−1.11483	+	1.11483i	−0.122337	+	0.992489i	$0.539039\pi$
$13$	−14.4927	+	14.4927i	−1.11483	+	1.11483i	−0.992489	+	0.122337i	$0.960961\pi$
$14$		0			0
$15$	−5.74353	+	19.3729i	−0.382902	+	1.29153i
$16$		0			0
$17$	−5.99637	−	5.99637i	−0.352728	−	0.352728i	0.508396	−	0.861124i	$-0.330239\pi$
$17$	−5.99637	−	5.99637i	−0.352728	−	0.352728i	−0.861124	+	0.508396i	$0.830239\pi$
$18$		0			0
$19$			36.6798i			1.93051i	0.261302	+	0.965257i	$0.415848\pi$
$19$			36.6798i			1.93051i	−0.261302	+	0.965257i	$0.584152\pi$
$20$		0			0
$21$	−27.7276	−	5.60723i	−1.32036	−	0.267011i
$22$		0			0
$23$	23.3020	−	23.3020i	1.01313	−	1.01313i	0.0132199	−	0.999913i	$-0.495792\pi$
$23$	23.3020	−	23.3020i	1.01313	−	1.01313i	0.999913	−	0.0132199i	$-0.00420816\pi$
$24$		0			0
$25$	−13.6260	+	20.9603i	−0.545038	+	0.838411i
$26$		0			0
$27$	4.76683	−	4.76683i	0.176549	−	0.176549i
$28$		0			0
$29$			20.4842i			0.706352i	0.935557	+	0.353176i	$0.114898\pi$
$29$			20.4842i			0.706352i	−0.935557	+	0.353176i	$0.885102\pi$
$30$		0			0
$31$	−26.3284			−0.849304			−0.424652	−	0.905357i	$-0.639604\pi$
$31$	−26.3284			−0.849304			−0.424652	+	0.905357i	$0.639604\pi$
$32$		0			0
$33$	33.4698	−	33.4698i	1.01424	−	1.01424i
$34$		0			0
$35$	−30.9186	−	16.4024i	−0.883389	−	0.468641i
$36$		0			0
$37$	−23.8254	+	23.8254i	−0.643931	+	0.643931i	−0.951519	−	0.307589i	$-0.900478\pi$
$37$	−23.8254	+	23.8254i	−0.643931	+	0.643931i	0.307589	+	0.951519i	$0.400478\pi$
$38$		0			0
$39$	−82.8292			−2.12382
$40$		0			0
$41$		−	4.49681i		−	0.109678i	−0.998495	−	0.0548392i	$-0.982535\pi$
$41$		−	4.49681i		−	0.109678i	0.998495	−	0.0548392i	$-0.0174646\pi$
$42$		0			0
$43$	16.6452	−	16.6452i	0.387097	−	0.387097i	−0.486553	−	0.873651i	$-0.661746\pi$
$43$	16.6452	−	16.6452i	0.387097	−	0.387097i	0.873651	+	0.486553i	$0.161746\pi$
$44$		0			0
$45$	−32.2211	+	17.4847i	−0.716024	+	0.388549i
$46$		0			0
$47$	36.6777	−	36.6777i	0.780378	−	0.780378i	−0.199517	−	0.979894i	$-0.563937\pi$
$47$	36.6777	−	36.6777i	0.780378	−	0.780378i	0.979894	+	0.199517i	$0.0639373\pi$
$48$		0			0
$49$	19.0395	−	45.1497i	0.388561	−	0.921423i
$50$		0			0
$51$		−	34.2706i		−	0.671973i
$52$		0			0
$53$	61.3395	+	61.3395i	1.15735	+	1.15735i	0.985043	+	0.172306i	$0.0551218\pi$
$53$	61.3395	+	61.3395i	1.15735	+	1.15735i	0.172306	+	0.985043i	$0.444878\pi$
$54$		0			0
$55$	51.4724	−	27.9314i	0.935862	−	0.507843i
$56$		0			0
$57$	−104.817	+	104.817i	−1.83889	+	1.83889i
$58$		0			0
$59$		−	43.1156i		−	0.730773i	−0.930856	−	0.365387i	$-0.880937\pi$
$59$		−	43.1156i		−	0.730773i	0.930856	−	0.365387i	$-0.119063\pi$
$60$		0			0
$61$			87.5037i			1.43449i	0.696823	+	0.717243i	$0.254596\pi$
$61$			87.5037i			1.43449i	−0.696823	+	0.717243i	$0.745404\pi$
$62$		0			0
$63$	−28.3776	−	42.7643i	−0.450438	−	0.678798i
$64$		0			0
$65$	−98.2520	−	29.1290i	−1.51157	−	0.448139i
$66$		0			0
$67$	18.1881	+	18.1881i	0.271465	+	0.271465i	0.829690	−	0.558225i	$-0.188517\pi$
$67$	18.1881	+	18.1881i	0.271465	+	0.271465i	−0.558225	+	0.829690i	$0.688517\pi$
$68$		0			0
$69$	133.176			1.93009
$70$		0			0
$71$		−	2.44203i		−	0.0343949i	−0.999852	−	0.0171974i	$-0.994526\pi$
$71$		−	2.44203i		−	0.0343949i	0.999852	−	0.0171974i	$-0.00547438\pi$
$72$		0			0
$73$	48.9892	−	48.9892i	0.671085	−	0.671085i	−0.286881	−	0.957966i	$-0.592619\pi$
$73$	48.9892	−	48.9892i	0.671085	−	0.671085i	0.957966	+	0.286881i	$0.0926185\pi$
$74$		0			0
$75$	−98.8340	+	20.9586i	−1.31779	+	0.279448i
$76$		0			0
$77$	45.3325	+	68.3149i	0.588733	+	0.887206i
$78$		0			0
$79$	−60.5548			−0.766516			−0.383258	−	0.923641i	$-0.625198\pi$
$79$	−60.5548			−0.766516			−0.383258	+	0.923641i	$0.625198\pi$
$80$		0			0
$81$	93.2304			1.15099
$82$		0			0
$83$	−26.3121	−	26.3121i	−0.317013	−	0.317013i	0.530606	−	0.847619i	$-0.321964\pi$
$83$	−26.3121	−	26.3121i	−0.317013	−	0.317013i	−0.847619	+	0.530606i	$0.821964\pi$
$84$		0			0
$85$	12.0521	−	40.6518i	0.141790	−	0.478257i
$86$		0			0
$87$	−58.5359	+	58.5359i	−0.672827	+	0.672827i
$88$		0			0
$89$	−150.664			−1.69285			−0.846424	−	0.532509i	$-0.821249\pi$
$89$	−150.664			−1.69285			−0.846424	+	0.532509i	$0.821249\pi$
$90$		0			0
$91$	28.4378	−	140.624i	0.312503	−	1.54532i
$92$		0			0
$93$	−75.2364	−	75.2364i	−0.808993	−	0.808993i
$94$		0			0
$95$	−161.195	+	87.4720i	−1.69679	+	0.920758i
$96$		0			0
$97$	−4.43919	−	4.43919i	−0.0457648	−	0.0457648i	0.683854	−	0.729619i	$-0.260303\pi$
$97$	−4.43919	−	4.43919i	−0.0457648	−	0.0457648i	−0.729619	+	0.683854i	$0.760303\pi$
$98$		0			0
$99$	85.8747			0.867421
$100$		0			0
$101$			93.1407i			0.922186i	0.887352	+	0.461093i	$0.152542\pi$
$101$			93.1407i			0.922186i	−0.887352	+	0.461093i	$0.847458\pi$
$102$		0			0
$103$	93.5378	+	93.5378i	0.908134	+	0.908134i	0.996122	−	0.0879879i	$-0.0280437\pi$
$103$	93.5378	+	93.5378i	0.908134	+	0.908134i	−0.0879879	+	0.996122i	$0.528044\pi$
$104$		0			0
$105$	−41.4815	−	135.225i	−0.395062	−	1.28786i
$106$		0			0
$107$	62.3576	+	62.3576i	0.582781	+	0.582781i	0.935667	−	0.352885i	$-0.114799\pi$
$107$	62.3576	+	62.3576i	0.582781	+	0.582781i	−0.352885	+	0.935667i	$0.614799\pi$
$108$		0			0
$109$			126.472i			1.16029i	0.814512	+	0.580147i	$0.197005\pi$
$109$			126.472i			1.16029i	−0.814512	+	0.580147i	$0.802995\pi$
$110$		0			0
$111$	−136.168			−1.22674
$112$		0			0
$113$	120.350	+	120.350i	1.06504	+	1.06504i	0.997732	+	0.0673089i	$0.0214413\pi$
$113$	120.350	+	120.350i	1.06504	+	1.06504i	0.0673089	+	0.997732i	$0.478559\pi$
$114$		0			0
$115$	157.974	+	46.8349i	1.37369	+	0.407260i
$116$		0			0
$117$	−106.259	−	106.259i	−0.908196	−	0.908196i
$118$		0			0
$119$	58.1833	+	11.7661i	0.488935	+	0.0988751i
$120$		0			0
$121$	−16.1827			−0.133742
$122$		0			0
$123$	12.8501	−	12.8501i	0.104473	−	0.104473i
$124$		0			0
$125$	−124.608	−	9.89640i	−0.996861	−	0.0791712i
$126$		0			0
$127$	111.195	+	111.195i	0.875554	+	0.875554i	0.993071	−	0.117516i	$-0.0374933\pi$
$127$	111.195	+	111.195i	0.875554	+	0.875554i	−0.117516	+	0.993071i	$0.537493\pi$
$128$		0			0
$129$	95.1310			0.737449
$130$		0			0
$131$	−29.2689			−0.223426			−0.111713	−	0.993740i	$-0.535634\pi$
$131$	−29.2689			−0.223426			−0.111713	+	0.993740i	$0.535634\pi$
$132$		0			0
$133$	−141.967	−	213.940i	−1.06742	−	1.60857i
$134$		0			0
$135$	32.3163	+	9.58089i	0.239380	+	0.0709695i
$136$		0			0
$137$	62.2531	−	62.2531i	0.454402	−	0.454402i	−0.442410	−	0.896813i	$-0.645876\pi$
$137$	62.2531	−	62.2531i	0.454402	−	0.454402i	0.896813	+	0.442410i	$0.145876\pi$
$138$		0			0
$139$			28.7928i			0.207143i	0.994622	+	0.103571i	$0.0330270\pi$
$139$			28.7928i			0.207143i	−0.994622	+	0.103571i	$0.966973\pi$
$140$		0			0
$141$	209.621			1.48668
$142$		0			0
$143$	169.746	+	169.746i	1.18704	+	1.18704i
$144$		0			0
$145$	−90.0211	+	48.8497i	−0.620835	+	0.336894i
$146$		0			0
$147$	183.428	−	74.6130i	1.24781	−	0.507571i
$148$		0			0
$149$		−	188.205i		−	1.26312i	−0.775328	−	0.631559i	$-0.782415\pi$
$149$		−	188.205i		−	1.26312i	0.775328	−	0.631559i	$-0.217585\pi$
$150$		0			0
$151$			55.8374i			0.369784i	0.982759	+	0.184892i	$0.0591936\pi$
$151$			55.8374i			0.369784i	−0.982759	+	0.184892i	$0.940806\pi$
$152$		0			0
$153$	43.9647	−	43.9647i	0.287351	−	0.287351i
$154$		0			0
$155$	−62.7866	−	115.704i	−0.405075	−	0.746479i
$156$		0			0
$157$	−80.6749	−	80.6749i	−0.513853	−	0.513853i	0.401852	−	0.915705i	$-0.368367\pi$
$157$	−80.6749	−	80.6749i	−0.513853	−	0.513853i	−0.915705	+	0.401852i	$0.868367\pi$
$158$		0			0
$159$			350.569i			2.20484i
$160$		0			0
$161$	−45.7235	+	226.102i	−0.283997	+	1.40436i
$162$		0			0
$163$	191.804	−	191.804i	1.17671	−	1.17671i	0.196132	−	0.980578i	$-0.437162\pi$
$163$	191.804	−	191.804i	1.17671	−	1.17671i	0.980578	−	0.196132i	$-0.0628380\pi$
$164$		0			0
$165$	226.905	+	67.2711i	1.37518	+	0.407704i
$166$		0			0
$167$	157.215	−	157.215i	0.941408	−	0.941408i	−0.0569677	−	0.998376i	$-0.518143\pi$
$167$	157.215	−	157.215i	0.941408	−	0.941408i	0.998376	+	0.0569677i	$0.0181432\pi$
$168$		0			0
$169$		−	251.078i		−	1.48567i
$170$		0			0
$171$	−268.932			−1.57270
$172$		0			0
$173$	73.1229	−	73.1229i	0.422676	−	0.422676i	−0.463448	−	0.886124i	$-0.653388\pi$
$173$	73.1229	−	73.1229i	0.422676	−	0.422676i	0.886124	+	0.463448i	$0.153388\pi$
$174$		0			0
$175$	−1.65002	−	174.992i	−0.00942867	−	0.999956i
$176$		0			0
$177$	123.208	−	123.208i	0.696088	−	0.696088i
$178$		0			0
$179$	−10.2298			−0.0571499			−0.0285749	−	0.999592i	$-0.509097\pi$
$179$	−10.2298			−0.0571499			−0.0285749	+	0.999592i	$0.509097\pi$
$180$		0			0
$181$		−	38.8562i		−	0.214675i	−0.994223	−	0.107338i	$-0.965767\pi$
$181$		−	38.8562i		−	0.214675i	0.994223	−	0.107338i	$-0.0342326\pi$
$182$		0			0
$183$	−250.051	+	250.051i	−1.36640	+	1.36640i
$184$		0			0
$185$	−161.522	−	47.8869i	−0.873093	−	0.258848i
$186$		0			0
$187$	−70.2325	+	70.2325i	−0.375575	+	0.375575i
$188$		0			0
$189$	−9.35353	+	46.2530i	−0.0494896	+	0.244725i
$190$		0			0
$191$			175.620i			0.919478i	0.888054	+	0.459739i	$0.152057\pi$
$191$			175.620i			0.919478i	−0.888054	+	0.459739i	$0.847943\pi$
$192$		0			0
$193$	−0.630383	−	0.630383i	−0.00326623	−	0.00326623i	0.705472	−	0.708738i	$-0.250735\pi$
$193$	−0.630383	−	0.630383i	−0.00326623	−	0.00326623i	−0.708738	+	0.705472i	$0.750735\pi$
$194$		0			0
$195$	−197.527	−	364.006i	−1.01296	−	1.86669i
$196$		0			0
$197$	68.0549	−	68.0549i	0.345456	−	0.345456i	−0.512958	−	0.858414i	$-0.671450\pi$
$197$	68.0549	−	68.0549i	0.345456	−	0.345456i	0.858414	+	0.512958i	$0.171450\pi$
$198$		0			0
$199$		−	212.860i		−	1.06965i	−0.844964	−	0.534824i	$-0.820378\pi$
$199$		−	212.860i		−	1.06965i	0.844964	−	0.534824i	$-0.179622\pi$
$200$		0			0
$201$			103.949i			0.517160i
$202$		0			0
$203$	−79.2828	−	119.477i	−0.390556	−	0.588557i
$204$		0			0
$205$	19.7619	−	10.7238i	0.0963996	−	0.0523110i
$206$		0			0
$207$	170.848	+	170.848i	0.825352	+	0.825352i
$208$		0			0
$209$	429.612			2.05556
$210$		0			0
$211$			33.9546i			0.160922i	0.996758	+	0.0804611i	$0.0256393\pi$
$211$			33.9546i			0.160922i	−0.996758	+	0.0804611i	$0.974361\pi$
$212$		0			0
$213$	6.97838	−	6.97838i	0.0327624	−	0.0327624i
$214$		0			0
$215$	112.844	+	33.4553i	0.524858	+	0.155606i
$216$		0			0
$217$	153.564	−	101.902i	0.707670	−	0.469597i
$218$		0			0
$219$	279.984			1.27847
$220$		0			0
$221$	173.808			0.786460
$222$		0			0
$223$	−103.146	−	103.146i	−0.462539	−	0.462539i	0.436948	−	0.899487i	$-0.356059\pi$
$223$	−103.146	−	103.146i	−0.462539	−	0.462539i	−0.899487	+	0.436948i	$0.856059\pi$
$224$		0			0
$225$	−153.678	−	99.9039i	−0.683015	−	0.444017i
$226$		0			0
$227$	−40.4365	+	40.4365i	−0.178134	+	0.178134i	−0.790542	−	0.612408i	$-0.790201\pi$
$227$	−40.4365	+	40.4365i	−0.178134	+	0.178134i	0.612408	+	0.790542i	$0.290201\pi$
$228$		0			0
$229$	240.198			1.04890			0.524450	−	0.851441i	$-0.324271\pi$
$229$	240.198			1.04890			0.524450	+	0.851441i	$0.324271\pi$
$230$		0			0
$231$	−65.6747	+	324.760i	−0.284306	+	1.40589i
$232$		0			0
$233$	193.833	+	193.833i	0.831901	+	0.831901i	0.987777	−	0.155876i	$-0.0498200\pi$
$233$	193.833	+	193.833i	0.831901	+	0.831901i	−0.155876	+	0.987777i	$0.549820\pi$
$234$		0			0
$235$	248.653	+	73.7188i	1.05810	+	0.313697i
$236$		0			0
$237$	−173.042	−	173.042i	−0.730135	−	0.730135i
$238$		0			0
$239$	−34.1812			−0.143018			−0.0715088	−	0.997440i	$-0.522781\pi$
$239$	−34.1812			−0.143018			−0.0715088	+	0.997440i	$0.522781\pi$
$240$		0			0
$241$			259.267i			1.07580i	0.843010	+	0.537898i	$0.180781\pi$
$241$			259.267i			1.07580i	−0.843010	+	0.537898i	$0.819219\pi$
$242$		0			0
$243$	223.515	+	223.515i	0.919814	+	0.919814i
$244$		0			0
$245$	243.822	−	23.9988i	0.995191	−	0.0979545i
$246$		0			0
$247$	−531.590	−	531.590i	−2.15219	−	2.15219i
$248$		0			0
$249$		−	150.379i		−	0.603933i
$250$		0			0
$251$	274.718			1.09450			0.547248	−	0.836971i	$-0.315676\pi$
$251$	274.718			1.09450			0.547248	+	0.836971i	$0.315676\pi$
$252$		0			0
$253$	−272.925	−	272.925i	−1.07876	−	1.07876i
$254$		0			0
$255$	150.607	−	81.7267i	0.590617	−	0.320497i
$256$		0			0
$257$	−120.905	−	120.905i	−0.470449	−	0.470449i	0.431611	−	0.902060i	$-0.357945\pi$
$257$	−120.905	−	120.905i	−0.470449	−	0.470449i	−0.902060	+	0.431611i	$0.857945\pi$
$258$		0			0
$259$	46.7505	−	231.180i	0.180504	−	0.892587i
$260$		0			0
$261$	−150.188			−0.575433
$262$		0			0
$263$	12.3440	−	12.3440i	0.0469355	−	0.0469355i	−0.683250	−	0.730185i	$-0.739434\pi$
$263$	12.3440	−	12.3440i	0.0469355	−	0.0469355i	0.730185	+	0.683250i	$0.239434\pi$
$264$		0			0
$265$	−123.287	+	415.845i	−0.465233	+	1.56923i
$266$		0			0
$267$	−430.538	−	430.538i	−1.61250	−	1.61250i
$268$		0			0
$269$	−229.919			−0.854718			−0.427359	−	0.904082i	$-0.640556\pi$
$269$	−229.919			−0.854718			−0.427359	+	0.904082i	$0.640556\pi$
$270$		0			0
$271$	−89.5182			−0.330325			−0.165163	−	0.986266i	$-0.552815\pi$
$271$	−89.5182			−0.330325			−0.165163	+	0.986266i	$0.552815\pi$
$272$		0			0
$273$	483.113	−	320.585i	1.76964	−	1.17430i
$274$		0			0
$275$	245.497	+	159.594i	0.892718	+	0.580342i
$276$		0			0
$277$	−84.1873	+	84.1873i	−0.303925	+	0.303925i	−0.842547	−	0.538622i	$-0.818945\pi$
$277$	−84.1873	+	84.1873i	−0.303925	+	0.303925i	0.538622	+	0.842547i	$0.318945\pi$
$278$		0			0
$279$		−	193.037i		−	0.691888i
$280$		0			0
$281$	157.171			0.559328			0.279664	−	0.960098i	$-0.409777\pi$
$281$	157.171			0.559328			0.279664	+	0.960098i	$0.409777\pi$
$282$		0			0
$283$	−8.32484	−	8.32484i	−0.0294164	−	0.0294164i	0.692246	−	0.721662i	$-0.256621\pi$
$283$	−8.32484	−	8.32484i	−0.0294164	−	0.0294164i	−0.721662	+	0.692246i	$0.756621\pi$
$284$		0			0
$285$	−710.593	−	210.671i	−2.49331	−	0.739198i
$286$		0			0
$287$	17.4046	+	26.2283i	0.0606432	+	0.0913878i
$288$		0			0
$289$		−	217.087i		−	0.751166i
$290$		0			0
$291$		−	25.3710i		−	0.0871854i
$292$		0			0
$293$	282.847	−	282.847i	0.965347	−	0.965347i	−0.0340727	−	0.999419i	$-0.510848\pi$
$293$	282.847	−	282.847i	0.965347	−	0.965347i	0.999419	+	0.0340727i	$0.0108478\pi$
$294$		0			0
$295$	189.478	−	102.820i	0.642299	−	0.348542i
$296$		0			0
$297$	−55.8316	−	55.8316i	−0.187985	−	0.187985i
$298$		0			0
$299$			675.421i			2.25893i
$300$		0			0
$301$	−32.6613	+	161.510i	−0.108509	+	0.536577i
$302$		0			0
$303$	−266.160	+	266.160i	−0.878416	+	0.878416i
$304$		0			0
$305$	−384.548	+	208.674i	−1.26081	+	0.684178i
$306$		0			0
$307$	255.354	−	255.354i	0.831773	−	0.831773i	−0.155986	−	0.987759i	$-0.549855\pi$
$307$	255.354	−	255.354i	0.831773	−	0.831773i	0.987759	+	0.155986i	$0.0498555\pi$
$308$		0			0
$309$			534.589i			1.73006i
$310$		0			0
$311$	−42.0102			−0.135081			−0.0675405	−	0.997717i	$-0.521515\pi$
$311$	−42.0102			−0.135081			−0.0675405	+	0.997717i	$0.521515\pi$
$312$		0			0
$313$	−425.054	+	425.054i	−1.35800	+	1.35800i	−0.481619	+	0.876381i	$0.659951\pi$
$313$	−425.054	+	425.054i	−1.35800	+	1.35800i	−0.876381	+	0.481619i	$0.840049\pi$
$314$		0			0
$315$	120.261	−	226.692i	0.381780	−	0.719656i
$316$		0			0
$317$	−122.941	+	122.941i	−0.387826	+	0.387826i	−0.873911	−	0.486085i	$-0.838424\pi$
$317$	−122.941	+	122.941i	−0.387826	+	0.387826i	0.486085	+	0.873911i	$0.338424\pi$
$318$		0			0
$319$	239.922			0.752105
$320$		0			0
$321$			356.387i			1.11024i
$322$		0			0
$323$	219.946	−	219.946i	0.680946	−	0.680946i
$324$		0			0
$325$	−106.294	−	501.249i	−0.327059	−	1.54230i
$326$		0			0
$327$	−361.408	+	361.408i	−1.10522	+	1.10522i
$328$		0			0
$329$	−71.9694	+	355.887i	−0.218752	+	1.08172i
$330$		0			0
$331$			341.959i			1.03311i	0.856255	+	0.516554i	$0.172785\pi$
$331$			341.959i			1.03311i	−0.856255	+	0.516554i	$0.827215\pi$
$332$		0			0
$333$	−174.685	−	174.685i	−0.524581	−	0.524581i
$334$		0			0
$335$	−36.5564	+	123.305i	−0.109124	+	0.368074i
$336$		0			0
$337$	65.4453	−	65.4453i	0.194200	−	0.194200i	−0.603308	−	0.797508i	$-0.706151\pi$
$337$	65.4453	−	65.4453i	0.194200	−	0.194200i	0.797508	+	0.603308i	$0.206151\pi$
$338$		0			0
$339$			687.825i			2.02898i
$340$		0			0
$341$			308.372i			0.904316i
$342$		0			0
$343$	63.6987	+	337.033i	0.185710	+	0.982605i
$344$		0			0
$345$	317.592	+	585.264i	0.920557	+	1.69642i
$346$		0			0
$347$	−167.988	−	167.988i	−0.484115	−	0.484115i	0.422328	−	0.906443i	$-0.361213\pi$
$347$	−167.988	−	167.988i	−0.484115	−	0.484115i	−0.906443	+	0.422328i	$0.861213\pi$
$348$		0			0
$349$	585.750			1.67837			0.839183	−	0.543849i	$-0.183034\pi$
$349$	585.750			1.67837			0.839183	+	0.543849i	$0.183034\pi$
$350$		0			0
$351$			138.169i			0.393644i
$352$		0			0
$353$	273.147	−	273.147i	0.773788	−	0.773788i	−0.204978	−	0.978766i	$-0.565712\pi$
$353$	273.147	−	273.147i	0.773788	−	0.773788i	0.978766	+	0.204978i	$0.0657124\pi$
$354$		0			0
$355$	10.7319	−	5.82364i	0.0302307	−	0.0164046i
$356$		0			0
$357$	132.642	+	199.888i	0.371547	+	0.559911i
$358$		0			0
$359$	−629.890			−1.75457			−0.877284	−	0.479972i	$-0.840647\pi$
$359$	−629.890			−1.75457			−0.877284	+	0.479972i	$0.840647\pi$
$360$		0			0
$361$	−984.405			−2.72688
$362$		0			0
$363$	−46.2439	−	46.2439i	−0.127394	−	0.127394i
$364$		0			0
$365$	332.117	+	98.4637i	0.909911	+	0.269764i
$366$		0			0
$367$	−319.121	+	319.121i	−0.869539	+	0.869539i	−0.992421	−	0.122882i	$-0.960786\pi$
$367$	−319.121	+	319.121i	−0.869539	+	0.869539i	0.122882	+	0.992421i	$0.460786\pi$
$368$		0			0
$369$	32.9701			0.0893498
$370$		0			0
$371$	−595.182	−	120.361i	−1.60426	−	0.324423i
$372$		0			0
$373$	−177.325	−	177.325i	−0.475403	−	0.475403i	0.428255	−	0.903658i	$-0.359129\pi$
$373$	−177.325	−	177.325i	−0.475403	−	0.475403i	−0.903658	+	0.428255i	$0.859129\pi$
$374$		0			0
$375$	−327.800	−	384.360i	−0.874134	−	1.02496i
$376$		0			0
$377$	−296.872	−	296.872i	−0.787460	−	0.787460i
$378$		0			0
$379$	−159.370			−0.420502			−0.210251	−	0.977647i	$-0.567428\pi$
$379$	−159.370			−0.420502			−0.210251	+	0.977647i	$0.567428\pi$
$380$		0			0
$381$			635.507i			1.66800i
$382$		0			0
$383$	176.444	+	176.444i	0.460690	+	0.460690i	0.898882	−	0.438192i	$-0.144381\pi$
$383$	176.444	+	176.444i	0.460690	+	0.460690i	−0.438192	+	0.898882i	$0.644381\pi$
$384$		0			0
$385$	−192.114	+	362.134i	−0.498996	+	0.940608i
$386$		0			0
$387$	122.041	+	122.041i	0.315350	+	0.315350i
$388$		0			0
$389$		−	215.017i		−	0.552743i	−0.961051	−	0.276372i	$-0.910868\pi$
$389$		−	215.017i		−	0.552743i	0.961051	−	0.276372i	$-0.0891320\pi$
$390$		0			0
$391$	−279.456			−0.714720
$392$		0			0
$393$	−83.6390	−	83.6390i	−0.212822	−	0.212822i
$394$		0			0
$395$	−144.408	−	266.117i	−0.365590	−	0.673715i
$396$		0			0
$397$	−228.720	−	228.720i	−0.576120	−	0.576120i	0.357712	−	0.933832i	$-0.383557\pi$
$397$	−228.720	−	228.720i	−0.576120	−	0.576120i	−0.933832	+	0.357712i	$0.883557\pi$
$398$		0			0
$399$	205.672	−	1017.04i	0.515468	−	2.54898i
$400$		0			0
$401$	91.4324			0.228011			0.114005	−	0.993480i	$-0.463632\pi$
$401$	91.4324			0.228011			0.114005	+	0.993480i	$0.463632\pi$
$402$		0			0
$403$	381.571	−	381.571i	0.946826	−	0.946826i
$404$		0			0
$405$	222.331	+	409.716i	0.548966	+	1.01164i
$406$		0			0
$407$	279.056	+	279.056i	0.685640	+	0.685640i
$408$		0			0
$409$	−449.942			−1.10010			−0.550051	−	0.835131i	$-0.685392\pi$
$409$	−449.942			−1.10010			−0.550051	+	0.835131i	$0.685392\pi$
$410$		0			0
$411$	355.790			0.865670
$412$		0			0
$413$	166.876	+	251.478i	0.404059	+	0.608906i
$414$		0			0
$415$	52.8847	−	178.380i	0.127433	−	0.429831i
$416$		0			0
$417$	−82.2787	+	82.2787i	−0.197311	+	0.197311i
$418$		0			0
$419$		−	90.3853i		−	0.215717i	−0.994166	−	0.107858i	$-0.965601\pi$
$419$		−	90.3853i		−	0.215717i	0.994166	−	0.107858i	$-0.0343993\pi$
$420$		0			0
$421$	−578.784			−1.37478			−0.687392	−	0.726287i	$-0.741244\pi$
$421$	−578.784			−1.37478			−0.687392	+	0.726287i	$0.741244\pi$
$422$		0			0
$423$	268.917	+	268.917i	0.635737	+	0.635737i
$424$		0			0
$425$	207.392	−	43.9793i	0.487981	−	0.103481i
$426$		0			0
$427$	−338.677	−	510.378i	−0.793155	−	1.19526i
$428$		0			0
$429$			970.137i			2.26139i
$430$		0			0
$431$		−	390.588i		−	0.906237i	−0.891450	−	0.453119i	$-0.850311\pi$
$431$		−	390.588i		−	0.906237i	0.891450	−	0.453119i	$-0.149689\pi$
$432$		0			0
$433$	19.2331	−	19.2331i	0.0444183	−	0.0444183i	−0.684549	−	0.728967i	$-0.740001\pi$
$433$	19.2331	−	19.2331i	0.0444183	−	0.0444183i	0.728967	+	0.684549i	$0.240001\pi$
$434$		0			0
$435$	−396.839	−	117.652i	−0.912273	−	0.270464i
$436$		0			0
$437$	854.714	+	854.714i	1.95587	+	1.95587i
$438$		0			0
$439$			383.748i			0.874141i	0.899427	+	0.437071i	$0.143984\pi$
$439$			383.748i			0.874141i	−0.899427	+	0.437071i	$0.856016\pi$
$440$		0			0
$441$	331.033	+	139.595i	0.750641	+	0.316542i
$442$		0			0
$443$	−568.705	+	568.705i	−1.28376	+	1.28376i	−0.345245	+	0.938513i	$0.612204\pi$
$443$	−568.705	+	568.705i	−1.28376	+	1.28376i	−0.938513	+	0.345245i	$0.887796\pi$
$444$		0			0
$445$	−359.295	−	662.114i	−0.807403	−	1.48790i
$446$		0			0
$447$	537.816	−	537.816i	1.20317	−	1.20317i
$448$		0			0
$449$		−	135.957i		−	0.302799i	−0.988473	−	0.151399i	$-0.951622\pi$
$449$		−	135.957i		−	0.302799i	0.988473	−	0.151399i	$-0.0483779\pi$
$450$		0			0
$451$	−52.6689			−0.116783
$452$		0			0
$453$	−159.562	+	159.562i	−0.352233	+	0.352233i
$454$		0			0
$455$	685.811	−	210.379i	1.50728	−	0.462371i
$456$		0			0
$457$	23.9199	−	23.9199i	0.0523411	−	0.0523411i	−0.680452	−	0.732793i	$-0.738216\pi$
$457$	23.9199	−	23.9199i	0.0523411	−	0.0523411i	0.732793	+	0.680452i	$0.238216\pi$
$458$		0			0
$459$	−57.1674			−0.124548
$460$		0			0
$461$		−	621.530i		−	1.34822i	−0.738630	−	0.674111i	$-0.764527\pi$
$461$		−	621.530i		−	1.34822i	0.738630	−	0.674111i	$-0.235473\pi$
$462$		0			0
$463$	252.742	−	252.742i	0.545878	−	0.545878i	−0.379368	−	0.925246i	$-0.623859\pi$
$463$	252.742	−	252.742i	0.545878	−	0.545878i	0.925246	+	0.379368i	$0.123859\pi$
$464$		0			0
$465$	151.218	−	510.058i	0.325200	−	1.09690i
$466$		0			0
$467$	−159.233	+	159.233i	−0.340971	+	0.340971i	−0.856732	−	0.515761i	$-0.827509\pi$
$467$	−159.233	+	159.233i	−0.340971	+	0.340971i	0.515761	+	0.856732i	$0.327509\pi$
$468$		0			0
$469$	−176.481	−	35.6889i	−0.376292	−	0.0760958i
$470$		0			0
$471$		−	461.075i		−	0.978928i
$472$		0			0
$473$	−194.957	−	194.957i	−0.412171	−	0.412171i
$474$		0			0
$475$	−768.818	−	499.797i	−1.61856	−	1.05220i
$476$		0			0
$477$	−449.734	+	449.734i	−0.942839	+	0.942839i
$478$		0			0
$479$		−	180.606i		−	0.377048i	−0.982069	−	0.188524i	$-0.939630\pi$
$479$		−	180.606i		−	0.377048i	0.982069	−	0.188524i	$-0.0603704\pi$
$480$		0			0
$481$		−	690.591i		−	1.43574i
$482$		0			0
$483$	−776.770	+	515.450i	−1.60822	+	1.06719i
$484$		0			0
$485$	8.92235	−	30.0950i	0.0183966	−	0.0620516i
$486$		0			0
$487$	−115.113	−	115.113i	−0.236371	−	0.236371i	0.578974	−	0.815346i	$-0.303453\pi$
$487$	−115.113	−	115.113i	−0.236371	−	0.236371i	−0.815346	+	0.578974i	$0.803453\pi$
$488$		0			0
$489$	1096.20			2.24172
$490$		0			0
$491$		−	281.934i		−	0.574204i	−0.957900	−	0.287102i	$-0.907308\pi$
$491$		−	281.934i		−	0.574204i	0.957900	−	0.287102i	$-0.0926919\pi$
$492$		0			0
$493$	122.831	−	122.831i	0.249150	−	0.249150i
$494$		0			0
$495$	204.789	+	377.389i	0.413716	+	0.762403i
$496$		0			0
$497$	9.45174	+	14.2435i	0.0190176	+	0.0286590i
$498$		0			0
$499$	791.794			1.58676			0.793381	−	0.608725i	$-0.208319\pi$
$499$	791.794			1.58676			0.793381	+	0.608725i	$0.208319\pi$
$500$		0			0
$501$	898.520			1.79345
$502$		0			0
$503$	−545.299	−	545.299i	−1.08409	−	1.08409i	−0.996123	−	0.0879699i	$-0.971962\pi$
$503$	−545.299	−	545.299i	−1.08409	−	1.08409i	−0.0879699	−	0.996123i	$-0.528038\pi$
$504$		0			0
$505$	−409.321	+	222.117i	−0.810537	+	0.439836i
$506$		0			0
$507$	717.485	−	717.485i	1.41516	−	1.41516i
$508$		0			0
$509$	52.8163			0.103765			0.0518824	−	0.998653i	$-0.483478\pi$
$509$	52.8163			0.103765			0.0518824	+	0.998653i	$0.483478\pi$
$510$		0			0
$511$	−96.1271	+	475.346i	−0.188116	+	0.930227i
$512$		0			0
$513$	174.846	+	174.846i	0.340831	+	0.340831i
$514$		0			0
$515$	−188.002	+	634.130i	−0.365053	+	1.23132i
$516$		0			0
$517$	−429.588	−	429.588i	−0.830925	−	0.830925i
$518$		0			0
$519$	417.914			0.805229
$520$		0			0
$521$		−	217.945i		−	0.418320i	−0.977881	−	0.209160i	$-0.932927\pi$
$521$		−	217.945i		−	0.418320i	0.977881	−	0.209160i	$-0.0670729\pi$
$522$		0			0
$523$	92.4479	+	92.4479i	0.176765	+	0.176765i	0.789944	−	0.613179i	$-0.210110\pi$
$523$	92.4479	+	92.4479i	0.176765	+	0.176765i	−0.613179	+	0.789944i	$0.710110\pi$
$524$		0			0
$525$	495.345	−	504.775i	0.943514	−	0.961476i
$526$		0			0
$527$	157.875	+	157.875i	0.299573	+	0.299573i
$528$		0			0
$529$		−	556.971i		−	1.05288i
$530$		0			0
$531$	316.119			0.595327
$532$		0			0
$533$	65.1711	+	65.1711i	0.122272	+	0.122272i
$534$		0			0
$535$	−125.333	+	422.747i	−0.234267	+	0.790181i
$536$		0			0
$537$	−29.2329	−	29.2329i	−0.0544374	−	0.0544374i
$538$		0			0
$539$	−528.816	−	223.000i	−0.981107	−	0.413729i
$540$		0			0
$541$	587.090			1.08519			0.542597	−	0.839993i	$-0.317441\pi$
$541$	587.090			1.08519			0.542597	+	0.839993i	$0.317441\pi$
$542$		0			0
$543$	111.036	−	111.036i	0.204486	−	0.204486i
$544$		0			0
$545$	−555.801	+	301.604i	−1.01982	+	0.553402i
$546$		0			0
$547$	569.353	+	569.353i	1.04086	+	1.04086i	0.999129	+	0.0417361i	$0.0132889\pi$
$547$	569.353	+	569.353i	1.04086	+	1.04086i	0.0417361	+	0.999129i	$0.486711\pi$
$548$		0			0
$549$	−641.567			−1.16861
$550$		0			0
$551$	−751.356			−1.36362
$552$		0			0
$553$	353.195	−	234.373i	0.638688	−	0.423822i
$554$		0			0
$555$	−324.726	−	598.410i	−0.585091	−	1.07822i
$556$		0			0
$557$	−672.490	+	672.490i	−1.20734	+	1.20734i	−0.235460	+	0.971884i	$0.575660\pi$
$557$	−672.490	+	672.490i	−1.20734	+	1.20734i	−0.971884	+	0.235460i	$0.924340\pi$
$558$		0			0
$559$			482.469i			0.863092i
$560$		0			0
$561$	−401.395			−0.715498
$562$		0			0
$563$	102.534	+	102.534i	0.182122	+	0.182122i	0.792280	−	0.610158i	$-0.208894\pi$
$563$	102.534	+	102.534i	0.182122	+	0.182122i	−0.610158	+	0.792280i	$0.708894\pi$
$564$		0			0
$565$	−241.891	+	815.898i	−0.428126	+	1.44407i
$566$		0			0
$567$	−543.780	+	360.842i	−0.959048	+	0.636406i
$568$		0			0
$569$			393.120i			0.690896i	0.938438	+	0.345448i	$0.112273\pi$
$569$			393.120i			0.690896i	−0.938438	+	0.345448i	$0.887727\pi$
$570$		0			0
$571$		−	732.228i		−	1.28236i	−0.767390	−	0.641181i	$-0.778445\pi$
$571$		−	732.228i		−	1.28236i	0.767390	−	0.641181i	$-0.221555\pi$
$572$		0			0
$573$	−501.855	+	501.855i	−0.875837	+	0.875837i
$574$		0			0
$575$	170.905	+	805.930i	0.297225	+	1.40162i
$576$		0			0
$577$	−218.570	−	218.570i	−0.378804	−	0.378804i	0.491867	−	0.870671i	$-0.336315\pi$
$577$	−218.570	−	218.570i	−0.378804	−	0.378804i	−0.870671	+	0.491867i	$0.836315\pi$
$578$		0			0
$579$		−	3.60278i		−	0.00622241i
$580$		0			0
$581$	255.308	+	51.6297i	0.439428	+	0.0888636i
$582$		0			0
$583$	718.439	−	718.439i	1.23231	−	1.23231i
$584$		0			0
$585$	213.571	−	720.372i	0.365078	−	1.23141i
$586$		0			0
$587$	−70.1851	+	70.1851i	−0.119566	+	0.119566i	−0.764358	−	0.644792i	$-0.776944\pi$
$587$	−70.1851	+	70.1851i	−0.119566	+	0.119566i	0.644792	+	0.764358i	$0.276944\pi$
$588$		0			0
$589$		−	965.720i		−	1.63959i
$590$		0			0
$591$	388.949			0.658120
$592$		0			0
$593$	−49.9921	+	49.9921i	−0.0843037	+	0.0843037i	−0.748001	−	0.663697i	$-0.768986\pi$
$593$	−49.9921	+	49.9921i	−0.0843037	+	0.0843037i	0.663697	+	0.748001i	$0.268986\pi$
$594$		0			0
$595$	87.0443	+	283.755i	0.146293	+	0.476899i
$596$		0			0
$597$	608.271	−	608.271i	1.01888	−	1.01888i
$598$		0			0
$599$	−600.100			−1.00184			−0.500918	−	0.865495i	$-0.667004\pi$
$599$	−600.100			−1.00184			−0.500918	+	0.865495i	$0.667004\pi$
$600$		0			0
$601$		−	92.4735i		−	0.153866i	−0.997036	−	0.0769330i	$-0.975487\pi$
$601$		−	92.4735i		−	0.153866i	0.997036	−	0.0769330i	$-0.0245128\pi$
$602$		0			0
$603$	−133.353	+	133.353i	−0.221150	+	0.221150i
$604$		0			0
$605$	−38.5917	−	71.1175i	−0.0637880	−	0.117550i
$606$		0			0
$607$	−73.6071	+	73.6071i	−0.121264	+	0.121264i	−0.765134	−	0.643871i	$-0.777327\pi$
$607$	−73.6071	+	73.6071i	−0.121264	+	0.121264i	0.643871	+	0.765134i	$0.277327\pi$
$608$		0			0
$609$	114.860	−	567.979i	0.188604	−	0.932642i
$610$		0			0
$611$			1063.12i			1.73997i
$612$		0			0
$613$	172.983	+	172.983i	0.282191	+	0.282191i	0.833982	−	0.551791i	$-0.186056\pi$
$613$	172.983	+	172.983i	0.282191	+	0.282191i	−0.551791	+	0.833982i	$0.686056\pi$
$614$		0			0
$615$	87.1162	+	25.8276i	0.141652	+	0.0419960i
$616$		0			0
$617$	609.132	−	609.132i	0.987247	−	0.987247i	−0.0126723	−	0.999920i	$-0.504034\pi$
$617$	609.132	−	609.132i	0.987247	−	0.987247i	0.999920	+	0.0126723i	$0.00403382\pi$
$618$		0			0
$619$			294.093i			0.475111i	0.971374	+	0.237555i	$0.0763461\pi$
$619$			294.093i			0.475111i	−0.971374	+	0.237555i	$0.923654\pi$
$620$		0			0
$621$		−	222.154i		−	0.357736i
$622$		0			0
$623$	878.767	−	583.133i	1.41054	−	0.936009i
$624$		0			0
$625$	−253.666	−	571.208i	−0.405866	−	0.913932i
$626$		0			0
$627$	1227.66	+	1227.66i	1.95800	+	1.95800i
$628$		0			0
$629$	285.733			0.454265
$630$		0			0
$631$		−	528.242i		−	0.837150i	−0.908182	−	0.418575i	$-0.862530\pi$
$631$		−	528.242i		−	0.837150i	0.908182	−	0.418575i	$-0.137470\pi$
$632$		0			0
$633$	−97.0290	+	97.0290i	−0.153284	+	0.153284i
$634$		0			0
$635$	−223.492	+	753.838i	−0.351956	+	1.18715i
$636$		0			0
$637$	378.409	+	930.277i	0.594049	+	1.46040i
$638$		0			0
$639$	17.9047			0.0280199
$640$		0			0
$641$	1022.97			1.59590			0.797952	−	0.602722i	$-0.205917\pi$
$641$	1022.97			1.59590			0.797952	+	0.602722i	$0.205917\pi$
$642$		0			0
$643$	−406.646	−	406.646i	−0.632421	−	0.632421i	0.316254	−	0.948675i	$-0.397575\pi$
$643$	−406.646	−	406.646i	−0.632421	−	0.632421i	−0.948675	+	0.316254i	$0.897575\pi$
$644$		0			0
$645$	226.863	+	418.068i	0.351726	+	0.648167i
$646$		0			0
$647$	−588.599	+	588.599i	−0.909736	+	0.909736i	−0.996251	−	0.0865148i	$-0.972427\pi$
$647$	−588.599	+	588.599i	−0.909736	+	0.909736i	0.0865148	+	0.996251i	$0.472427\pi$
$648$		0			0
$649$	−504.992			−0.778108
$650$		0			0
$651$	730.025	+	147.630i	1.12139	+	0.226773i
$652$		0			0
$653$	38.7491	+	38.7491i	0.0593401	+	0.0593401i	0.736154	−	0.676814i	$-0.236640\pi$
$653$	38.7491	+	38.7491i	0.0593401	+	0.0593401i	−0.676814	+	0.736154i	$0.736640\pi$
$654$		0			0
$655$	−69.7989	−	128.627i	−0.106563	−	0.196376i
$656$		0			0
$657$	359.183	+	359.183i	0.546702	+	0.546702i
$658$		0			0
$659$	−257.285			−0.390417			−0.195208	−	0.980762i	$-0.562538\pi$
$659$	−257.285			−0.390417			−0.195208	+	0.980762i	$0.562538\pi$
$660$		0			0
$661$			888.512i			1.34419i	0.740463	+	0.672097i	$0.234606\pi$
$661$			888.512i			1.34419i	−0.740463	+	0.672097i	$0.765394\pi$
$662$		0			0
$663$	496.675	+	496.675i	0.749132	+	0.749132i
$664$		0			0
$665$	601.638	−	1134.09i	0.904718	−	1.70539i
$666$		0			0
$667$	477.324	+	477.324i	0.715629	+	0.715629i
$668$		0			0
$669$		−	589.504i		−	0.881172i
$670$		0			0
$671$	1024.89			1.52740
$672$		0			0
$673$	692.344	+	692.344i	1.02874	+	1.02874i	0.999575	+	0.0291678i	$0.00928572\pi$
$673$	692.344	+	692.344i	1.02874	+	1.02874i	0.0291678	+	0.999575i	$0.490714\pi$
$674$		0			0
$675$	34.9615	+	164.867i	0.0517948	+	0.244247i
$676$		0			0
$677$	−809.012	−	809.012i	−1.19500	−	1.19500i	−0.975646	−	0.219349i	$-0.929607\pi$
$677$	−809.012	−	809.012i	−1.19500	−	1.19500i	−0.219349	−	0.975646i	$-0.570393\pi$
$678$		0			0
$679$	43.0738	+	8.71062i	0.0634371	+	0.0128286i
$680$		0			0
$681$	−231.103			−0.339359
$682$		0			0
$683$	422.972	−	422.972i	0.619286	−	0.619286i	−0.326062	−	0.945348i	$-0.605722\pi$
$683$	422.972	−	422.972i	0.619286	−	0.619286i	0.945348	+	0.326062i	$0.105722\pi$
$684$		0			0
$685$	422.039	+	125.123i	0.616115	+	0.182661i
$686$		0			0
$687$	686.393	+	686.393i	0.999117	+	0.999117i
$688$		0			0
$689$	−1777.95			−2.58049
$690$		0			0
$691$	646.537			0.935655			0.467827	−	0.883820i	$-0.345037\pi$
$691$	646.537			0.935655			0.467827	+	0.883820i	$0.345037\pi$
$692$		0			0
$693$	−500.876	+	332.372i	−0.722765	+	0.479614i
$694$		0			0
$695$	−126.535	+	68.6637i	−0.182064	+	0.0987966i
$696$		0			0
$697$	−26.9646	+	26.9646i	−0.0386866	+	0.0386866i
$698$		0			0
$699$			1107.80i			1.58483i
$700$		0			0
$701$	564.754			0.805640			0.402820	−	0.915279i	$-0.368030\pi$
$701$	564.754			0.805640			0.402820	+	0.915279i	$0.368030\pi$
$702$		0			0
$703$	−873.912	−	873.912i	−1.24312	−	1.24312i
$704$		0			0
$705$	499.894	+	921.214i	0.709070	+	1.30669i
$706$		0			0
$707$	−360.495	−	543.257i	−0.509894	−	0.768397i
$708$		0			0
$709$		−	642.159i		−	0.905725i	−0.891580	−	0.452862i	$-0.850403\pi$
$709$		−	642.159i		−	0.905725i	0.891580	−	0.452862i	$-0.149597\pi$
$710$		0			0
$711$		−	443.981i		−	0.624445i
$712$		0			0
$713$	−613.506	+	613.506i	−0.860457	+	0.860457i
$714$		0			0
$715$	−341.174	+	1150.78i	−0.477166	+	1.60948i
$716$		0			0
$717$	−97.6765	−	97.6765i	−0.136229	−	0.136229i
$718$		0			0
$719$		−	1332.43i		−	1.85318i	−0.376077	−	0.926588i	$-0.622727\pi$
$719$		−	1332.43i		−	1.85318i	0.376077	−	0.926588i	$-0.377273\pi$
$720$		0			0
$721$	−907.604	−	183.541i	−1.25881	−	0.254564i
$722$		0			0
$723$	−740.884	+	740.884i	−1.02474	+	1.02474i
$724$		0			0
$725$	−429.355	−	279.117i	−0.592214	−	0.384989i
$726$		0			0
$727$	130.596	−	130.596i	0.179637	−	0.179637i	−0.611560	−	0.791198i	$-0.709458\pi$
$727$	130.596	−	130.596i	0.179637	−	0.179637i	0.791198	+	0.611560i	$0.209458\pi$
$728$		0			0
$729$			438.363i			0.601321i
$730$		0			0
$731$	−199.622			−0.273080
$732$		0			0
$733$	430.727	−	430.727i	0.587622	−	0.587622i	−0.349364	−	0.936987i	$-0.613602\pi$
$733$	430.727	−	430.727i	0.587622	−	0.587622i	0.936987	+	0.349364i	$0.113602\pi$
$734$		0			0
$735$	765.327	+	628.168i	1.04126	+	0.854651i
$736$		0			0
$737$	213.029	−	213.029i	0.289048	−	0.289048i
$738$		0			0
$739$	−1201.95			−1.62646			−0.813230	−	0.581942i	$-0.802293\pi$
$739$	−1201.95			−1.62646			−0.813230	+	0.581942i	$0.802293\pi$
$740$		0			0
$741$		−	3038.15i		−	4.10007i
$742$		0			0
$743$	925.606	−	925.606i	1.24577	−	1.24577i	0.288197	−	0.957571i	$-0.406944\pi$
$743$	925.606	−	925.606i	1.24577	−	1.24577i	0.957571	−	0.288197i	$-0.0930557\pi$
$744$		0			0
$745$	827.094	−	448.821i	1.11019	−	0.602444i
$746$		0			0
$747$	192.917	−	192.917i	0.258255	−	0.258255i
$748$		0			0
$749$	−605.060	−	122.359i	−0.807824	−	0.163363i
$750$		0			0
$751$		−	334.942i		−	0.445995i	−0.974819	−	0.222998i	$-0.928416\pi$
$751$		−	334.942i		−	0.445995i	0.974819	−	0.222998i	$-0.0715842\pi$
$752$		0			0
$753$	785.038	+	785.038i	1.04255	+	1.04255i
$754$		0			0
$755$	−245.386	+	133.158i	−0.325015	+	0.176368i
$756$		0			0
$757$	921.038	−	921.038i	1.21669	−	1.21669i	0.247913	−	0.968782i	$-0.420255\pi$
$757$	921.038	−	921.038i	1.21669	−	1.21669i	0.968782	−	0.247913i	$-0.0797446\pi$
$758$		0			0
$759$		−	1559.83i		−	2.05511i
$760$		0			0
$761$			168.289i			0.221142i	0.993868	+	0.110571i	$0.0352679\pi$
$761$			168.289i			0.221142i	−0.993868	+	0.110571i	$0.964732\pi$
$762$		0			0
$763$	−489.502	−	737.667i	−0.641549	−	0.966798i
$764$		0			0
$765$	298.054	+	88.3649i	0.389614	+	0.115510i
$766$		0			0
$767$	624.863	+	624.863i	0.814684	+	0.814684i
$768$		0			0
$769$	100.837			0.131127			0.0655636	−	0.997848i	$-0.479115\pi$
$769$	100.837			0.131127			0.0655636	+	0.997848i	$0.479115\pi$
$770$		0			0
$771$		−	691.001i		−	0.896240i
$772$		0			0
$773$	349.162	−	349.162i	0.451697	−	0.451697i	−0.444221	−	0.895917i	$-0.646519\pi$
$773$	349.162	−	349.162i	0.451697	−	0.451697i	0.895917	+	0.444221i	$0.146519\pi$
$774$		0			0
$775$	358.750	−	551.851i	0.462903	−	0.712066i
$776$		0			0
$777$	794.218	−	527.028i	1.02216	−	0.678286i
$778$		0			0
$779$	164.942			0.211736
$780$		0			0
$781$	−28.6023			−0.0366227
$782$		0			0
$783$	97.6449	+	97.6449i	0.124706	+	0.124706i
$784$		0			0
$785$	162.149	−	546.927i	0.206559	−	0.696723i
$786$		0			0
$787$	−262.165	+	262.165i	−0.333119	+	0.333119i	−0.853770	−	0.520651i	$-0.825689\pi$
$787$	−262.165	+	262.165i	−0.333119	+	0.333119i	0.520651	+	0.853770i	$0.325689\pi$
$788$		0			0
$789$	70.5489			0.0894156
$790$		0			0
$791$	−1167.76	−	236.151i	−1.47631	−	0.298548i
$792$		0			0
$793$	−1268.17	−	1268.17i	−1.59920	−	1.59920i
$794$		0			0
$795$	−1540.63	+	836.019i	−1.93790	+	1.05160i
$796$		0			0
$797$	391.513	+	391.513i	0.491234	+	0.491234i	0.908695	−	0.417461i	$-0.137080\pi$
$797$	391.513	+	391.513i	0.491234	+	0.491234i	−0.417461	+	0.908695i	$0.637080\pi$
$798$		0			0
$799$	−439.867			−0.550522
$800$		0			0
$801$		−	1104.65i		−	1.37909i
$802$		0			0
$803$	−573.786	−	573.786i	−0.714553	−	0.714553i
$804$		0			0
$805$	−1102.68	+	338.256i	−1.36979	+	0.420194i
$806$		0			0
$807$	−657.019	−	657.019i	−0.814150	−	0.814150i
$808$		0			0
$809$			1187.70i			1.46811i	0.679090	+	0.734055i	$0.262374\pi$
$809$			1187.70i			1.46811i	−0.679090	+	0.734055i	$0.737626\pi$
$810$		0			0
$811$	594.162			0.732629			0.366315	−	0.930491i	$-0.380619\pi$
$811$	594.162			0.732629			0.366315	+	0.930491i	$0.380619\pi$
$812$		0			0
$813$	−255.808	−	255.808i	−0.314647	−	0.314647i
$814$		0			0
$815$	1300.31	+	385.507i	1.59548	+	0.473015i
$816$		0			0
$817$	610.542	+	610.542i	0.747297	+	0.747297i
$818$		0			0
$819$	1031.04	+	208.502i	1.25890	+	0.254582i
$820$		0			0
$821$	−1377.44			−1.67775			−0.838877	−	0.544321i	$-0.816787\pi$
$821$	−1377.44			−1.67775			−0.838877	+	0.544321i	$0.816787\pi$
$822$		0			0
$823$	−372.252	+	372.252i	−0.452310	+	0.452310i	−0.896121	−	0.443810i	$-0.853626\pi$
$823$	−372.252	+	372.252i	−0.452310	+	0.452310i	0.443810	+	0.896121i	$0.353626\pi$
$824$		0			0
$825$	245.478	+	1157.59i	0.297549	+	1.40314i
$826$		0			0
$827$	−720.119	−	720.119i	−0.870760	−	0.870760i	0.121795	−	0.992555i	$-0.461135\pi$
$827$	−720.119	−	720.119i	−0.870760	−	0.870760i	−0.992555	+	0.121795i	$0.961135\pi$
$828$		0			0
$829$	624.212			0.752969			0.376485	−	0.926423i	$-0.377133\pi$
$829$	624.212			0.752969			0.376485	+	0.926423i	$0.377133\pi$
$830$		0			0
$831$	−481.149			−0.579000
$832$		0			0
$833$	−384.902	+	156.567i	−0.462068	+	0.187955i
$834$		0			0
$835$	1065.82	+	315.988i	1.27644	+	0.378428i
$836$		0			0
$837$	−125.503	+	125.503i	−0.149944	+	0.149944i
$838$		0			0
$839$		−	748.029i		−	0.891572i	−0.895140	−	0.445786i	$-0.852924\pi$
$839$		−	748.029i		−	0.891572i	0.895140	−	0.445786i	$-0.147076\pi$
$840$		0			0
$841$	421.397			0.501066
$842$		0			0
$843$	449.134	+	449.134i	0.532781	+	0.532781i
$844$		0			0
$845$	1103.40	−	598.759i	1.30580	−	0.708590i
$846$		0			0
$847$	94.3881	−	62.6342i	0.111438	−	0.0739483i
$848$		0			0
$849$		−	47.5783i		−	0.0560404i
$850$		0			0
$851$			1110.36i			1.30477i
$852$		0			0
$853$	−629.600	+	629.600i	−0.738101	+	0.738101i	−0.972210	−	0.234110i	$-0.924783\pi$
$853$	−629.600	+	629.600i	−0.738101	+	0.738101i	0.234110	+	0.972210i	$0.424783\pi$
$854$		0			0
$855$	−641.334	−	1181.86i	−0.750098	−	1.38229i
$856$		0			0
$857$	997.028	+	997.028i	1.16339	+	1.16339i	0.983728	+	0.179665i	$0.0575014\pi$
$857$	997.028	+	997.028i	1.16339	+	1.16339i	0.179665	+	0.983728i	$0.442499\pi$
$858$		0			0
$859$			182.926i			0.212952i	0.994315	+	0.106476i	$0.0339567\pi$
$859$			182.926i			0.212952i	−0.994315	+	0.106476i	$0.966043\pi$
$860$		0			0
$861$	−25.2147	+	124.686i	−0.0292853	+	0.144815i
$862$		0			0
$863$	−310.483	+	310.483i	−0.359771	+	0.359771i	−0.863729	−	0.503957i	$-0.831877\pi$
$863$	−310.483	+	310.483i	−0.359771	+	0.359771i	0.503957	+	0.863729i	$0.331877\pi$
$864$		0			0
$865$	495.729	+	146.970i	0.573098	+	0.169908i
$866$		0			0
$867$	620.350	−	620.350i	0.715514	−	0.715514i
$868$		0			0
$869$			709.248i			0.816166i
$870$		0			0
$871$	−527.191			−0.605271
$872$		0			0
$873$	32.5476	−	32.5476i	0.0372825	−	0.0372825i
$874$		0			0
$875$	765.095	−	424.564i	0.874395	−	0.485215i
$876$		0			0
$877$	−393.583	+	393.583i	−0.448784	+	0.448784i	−0.894950	−	0.446166i	$-0.852789\pi$
$877$	−393.583	+	393.583i	−0.448784	+	0.448784i	0.446166	+	0.894950i	$0.352789\pi$
$878$		0			0
$879$	1616.53			1.83906
$880$		0			0
$881$			1426.89i			1.61963i	0.586685	+	0.809815i	$0.300433\pi$
$881$			1426.89i			1.61963i	−0.586685	+	0.809815i	$0.699567\pi$
$882$		0			0
$883$	15.5765	−	15.5765i	0.0176404	−	0.0176404i	−0.698232	−	0.715872i	$-0.746029\pi$
$883$	15.5765	−	15.5765i	0.0176404	−	0.0176404i	0.715872	+	0.698232i	$0.246029\pi$
$884$		0			0
$885$	835.274	+	247.636i	0.943813	+	0.279814i
$886$		0			0
$887$	437.315	−	437.315i	0.493027	−	0.493027i	−0.416232	−	0.909259i	$-0.636649\pi$
$887$	437.315	−	437.315i	0.493027	−	0.493027i	0.909259	+	0.416232i	$0.136649\pi$
$888$		0			0
$889$	−1078.94	−	218.189i	−1.21365	−	0.245432i
$890$		0			0
$891$		−	1091.96i		−	1.22555i
$892$		0			0
$893$	1345.33	+	1345.33i	1.50653	+	1.50653i
$894$		0			0
$895$	−24.3956	−	44.9566i	−0.0272576	−	0.0502308i
$896$		0			0
$897$	−1930.09	+	1930.09i	−2.15172	+	2.15172i
$898$		0			0
$899$		−	539.317i		−	0.599908i
$900$		0			0
$901$		−	735.629i		−	0.816459i
$902$		0			0
$903$	−554.865	+	368.198i	−0.614469	+	0.407750i
$904$		0			0
$905$	170.760	−	92.6623i	0.188685	−	0.102389i
$906$		0			0
$907$	−78.2530	−	78.2530i	−0.0862767	−	0.0862767i	0.662651	−	0.748928i	$-0.269431\pi$
$907$	−78.2530	−	78.2530i	−0.0862767	−	0.0862767i	−0.748928	+	0.662651i	$0.769431\pi$
$908$		0			0
$909$	−682.897			−0.751262
$910$		0			0
$911$			1258.62i			1.38158i	0.723055	+	0.690790i	$0.242737\pi$
$911$			1258.62i			1.38158i	−0.723055	+	0.690790i	$0.757263\pi$
$912$		0			0
$913$	−308.180	+	308.180i	−0.337547	+	0.337547i
$914$		0			0
$915$	−1695.20	−	502.580i	−1.85268	−	0.549268i
$916$		0			0
$917$	170.715	−	113.283i	0.186167	−	0.123537i
$918$		0			0
$919$	211.416			0.230050			0.115025	−	0.993363i	$-0.463305\pi$
$919$	211.416			0.230050			0.115025	+	0.993363i	$0.463305\pi$
$920$		0			0
$921$	1459.41			1.58459
$922$		0			0
$923$	35.3917	+	35.3917i	0.0383443	+	0.0383443i
$924$		0			0
$925$	−174.743	−	824.032i	−0.188912	−	0.890846i
$926$		0			0
$927$	−685.808	+	685.808i	−0.739814	+	0.739814i
$928$		0			0
$929$	−612.755			−0.659586			−0.329793	−	0.944053i	$-0.606979\pi$
$929$	−612.755			−0.659586			−0.329793	+	0.944053i	$0.606979\pi$
$930$		0			0
$931$	1656.08	+	698.363i	1.77882	+	0.750122i
$932$		0			0
$933$	−120.049	−	120.049i	−0.128670	−	0.128670i
$934$		0			0
$935$	−476.135	−	141.161i	−0.509235	−	0.150974i
$936$		0			0
$937$	−442.331	−	442.331i	−0.472072	−	0.472072i	0.430513	−	0.902585i	$-0.358333\pi$
$937$	−442.331	−	442.331i	−0.472072	−	0.472072i	−0.902585	+	0.430513i	$0.858333\pi$
$938$		0			0
$939$	−2429.28			−2.58709
$940$		0			0
$941$		−	320.999i		−	0.341126i	−0.985347	−	0.170563i	$-0.945441\pi$
$941$		−	320.999i		−	0.341126i	0.985347	−	0.170563i	$-0.0545586\pi$
$942$		0			0
$943$	−104.785	−	104.785i	−0.111119	−	0.111119i
$944$		0			0
$945$	−225.572	+	69.1961i	−0.238700	+	0.0732234i
$946$		0			0
$947$	−1056.12	−	1056.12i	−1.11522	−	1.11522i	−0.992432	−	0.122791i	$-0.960815\pi$
$947$	−1056.12	−	1056.12i	−1.11522	−	1.11522i	−0.122791	−	0.992432i	$-0.539185\pi$
$948$		0			0
$949$			1419.97i			1.49629i
$950$		0			0
$951$	−702.635			−0.738838
$952$		0			0
$953$	−387.860	−	387.860i	−0.406989	−	0.406989i	0.473698	−	0.880687i	$-0.342919\pi$
$953$	−387.860	−	387.860i	−0.406989	−	0.406989i	−0.880687	+	0.473698i	$0.842919\pi$
$954$		0			0
$955$	−771.790	+	418.810i	−0.808157	+	0.438545i
$956$		0			0
$957$	685.602	+	685.602i	0.716408	+	0.716408i
$958$		0			0
$959$	−122.154	+	604.047i	−0.127376	+	0.629872i
$960$		0			0
$961$	−267.814			−0.278683
$962$		0			0
$963$	−457.198	+	457.198i	−0.474765	+	0.474765i
$964$		0			0
$965$	1.26701	−	4.27362i	0.00131296	−	0.00442862i
$966$		0			0
$967$	−950.567	−	950.567i	−0.983006	−	0.983006i	0.0168518	−	0.999858i	$-0.494636\pi$
$967$	−950.567	−	950.567i	−0.983006	−	0.983006i	−0.999858	+	0.0168518i	$0.994636\pi$
$968$		0			0
$969$	1257.04			1.29725
$970$		0			0
$971$	1734.43			1.78623			0.893116	−	0.449827i	$-0.148514\pi$
$971$	1734.43			1.78623			0.893116	+	0.449827i	$0.148514\pi$
$972$		0			0
$973$	−111.441	−	167.938i	−0.114533	−	0.172599i
$974$		0			0
$975$	1128.63	−	1736.12i	1.15757	−	1.78064i
$976$		0			0
$977$	−653.112	+	653.112i	−0.668487	+	0.668487i	−0.957366	−	0.288879i	$-0.906718\pi$
$977$	−653.112	+	653.112i	−0.668487	+	0.668487i	0.288879	+	0.957366i	$0.406718\pi$
$978$		0			0
$979$			1764.65i			1.80250i
$980$		0			0
$981$	−927.278			−0.945238
$982$		0			0
$983$	777.104	+	777.104i	0.790543	+	0.790543i	0.981582	−	0.191039i	$-0.0611857\pi$
$983$	777.104	+	777.104i	0.790543	+	0.790543i	−0.191039	+	0.981582i	$0.561186\pi$
$984$		0			0
$985$	461.371	+	136.784i	0.468397	+	0.138867i
$986$		0			0
$987$	−1222.65	+	811.326i	−1.23875	+	0.822012i
$988$		0			0
$989$		−	775.734i		−	0.784362i
$990$		0			0
$991$		−	1560.44i		−	1.57461i	−0.616562	−	0.787306i	$-0.711475\pi$
$991$		−	1560.44i		−	1.57461i	0.616562	−	0.787306i	$-0.288525\pi$
$992$		0			0
$993$	−977.185	+	977.185i	−0.984074	+	0.984074i
$994$		0			0
$995$	935.445	−	507.617i	0.940146	−	0.510168i
$996$		0			0
$997$	14.9480	+	14.9480i	0.0149930	+	0.0149930i	0.714564	−	0.699571i	$-0.246625\pi$
$997$	14.9480	+	14.9480i	0.0149930	+	0.0149930i	−0.699571	+	0.714564i	$0.746625\pi$
$998$		0			0
$999$			227.144i			0.227371i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.3.v.b.223.30	yes	64
4.3	odd	2	inner	560.3.v.b.223.3	✓	64
5.2	odd	4	inner	560.3.v.b.447.29	yes	64
7.6	odd	2	inner	560.3.v.b.223.4	yes	64
20.7	even	4	inner	560.3.v.b.447.4	yes	64
28.27	even	2	inner	560.3.v.b.223.29	yes	64
35.27	even	4	inner	560.3.v.b.447.3	yes	64
140.27	odd	4	inner	560.3.v.b.447.30	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.3.v.b.223.3	✓	64	4.3	odd	2	inner
560.3.v.b.223.4	yes	64	7.6	odd	2	inner
560.3.v.b.223.29	yes	64	28.27	even	2	inner
560.3.v.b.223.30	yes	64	1.1	even	1	trivial
560.3.v.b.447.3	yes	64	35.27	even	4	inner
560.3.v.b.447.4	yes	64	20.7	even	4	inner
560.3.v.b.447.29	yes	64	5.2	odd	4	inner
560.3.v.b.447.30	yes	64	140.27	odd	4	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)

\(f(q)\)	\(=\)	\(q+(2.85761 + 2.85761i) q^{3} +(2.38475 + 4.39465i) q^{5} +(-5.83264 + 3.87043i) q^{7} +7.33188i q^{9} -11.7125i q^{11} +(-14.4927 + 14.4927i) q^{13} +(-5.74353 + 19.3729i) q^{15} +(-5.99637 - 5.99637i) q^{17} +36.6798i q^{19} +(-27.7276 - 5.60723i) q^{21} +(23.3020 - 23.3020i) q^{23} +(-13.6260 + 20.9603i) q^{25} +(4.76683 - 4.76683i) q^{27} +20.4842i q^{29} -26.3284 q^{31} +(33.4698 - 33.4698i) q^{33} +(-30.9186 - 16.4024i) q^{35} +(-23.8254 + 23.8254i) q^{37} -82.8292 q^{39} -4.49681i q^{41} +(16.6452 - 16.6452i) q^{43} +(-32.2211 + 17.4847i) q^{45} +(36.6777 - 36.6777i) q^{47} +(19.0395 - 45.1497i) q^{49} -34.2706i q^{51} +(61.3395 + 61.3395i) q^{53} +(51.4724 - 27.9314i) q^{55} +(-104.817 + 104.817i) q^{57} -43.1156i q^{59} +87.5037i q^{61} +(-28.3776 - 42.7643i) q^{63} +(-98.2520 - 29.1290i) q^{65} +(18.1881 + 18.1881i) q^{67} +133.176 q^{69} -2.44203i q^{71} +(48.9892 - 48.9892i) q^{73} +(-98.8340 + 20.9586i) q^{75} +(45.3325 + 68.3149i) q^{77} -60.5548 q^{79} +93.2304 q^{81} +(-26.3121 - 26.3121i) q^{83} +(12.0521 - 40.6518i) q^{85} +(-58.5359 + 58.5359i) q^{87} -150.664 q^{89} +(28.4378 - 140.624i) q^{91} +(-75.2364 - 75.2364i) q^{93} +(-161.195 + 87.4720i) q^{95} +(-4.43919 - 4.43919i) q^{97} +85.8747 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 16 q^{21} - 72 q^{25} + 72 q^{37} + 272 q^{53} - 376 q^{57} - 88 q^{65} + 24 q^{77} - 432 q^{81} + 384 q^{85} + 840 q^{93}+O(q^{100}) \) 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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Representations

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Database

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