LMFDB - Embedded newform 560.3.v.b.223.20

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			223.20
Character	$\chi$	$=$	560.223
Dual form			560.3.v.b.447.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.904360 + 0.904360i) q^{3} +(-2.12642 + 4.52530i) q^{5} +(-5.39452 + 4.46084i) q^{7} -7.36427i q^{9} -1.26996i q^{11} +(-5.68460 + 5.68460i) q^{13} +(-6.01555 + 2.16945i) q^{15} +(-3.36775 - 3.36775i) q^{17} -10.5554i q^{19} +(-8.91279 - 0.844384i) q^{21} +(-17.3860 + 17.3860i) q^{23} +(-15.9567 - 19.2454i) q^{25} +(14.7992 - 14.7992i) q^{27} -33.6429i q^{29} -19.7373 q^{31} +(1.14850 - 1.14850i) q^{33} +(-8.71560 - 33.8975i) q^{35} +(23.2693 - 23.2693i) q^{37} -10.2819 q^{39} -44.1112i q^{41} +(-34.3775 + 34.3775i) q^{43} +(33.3255 + 15.6595i) q^{45} +(-15.2233 + 15.2233i) q^{47} +(9.20178 - 48.1282i) q^{49} -6.09132i q^{51} +(-44.2336 - 44.2336i) q^{53} +(5.74694 + 2.70047i) q^{55} +(9.54592 - 9.54592i) q^{57} +46.7572i q^{59} +12.0294i q^{61} +(32.8508 + 39.7267i) q^{63} +(-13.6367 - 37.8124i) q^{65} +(-49.0186 - 49.0186i) q^{67} -31.4464 q^{69} +98.6344i q^{71} +(-48.8054 + 48.8054i) q^{73} +(2.97421 - 31.8353i) q^{75} +(5.66508 + 6.85082i) q^{77} -13.3286 q^{79} -39.5108 q^{81} +(41.6147 + 41.6147i) q^{83} +(22.4014 - 8.07882i) q^{85} +(30.4253 - 30.4253i) q^{87} -110.162 q^{89} +(5.30761 - 56.0238i) q^{91} +(-17.8496 - 17.8496i) q^{93} +(47.7666 + 22.4453i) q^{95} +(54.3644 + 54.3644i) q^{97} -9.35231 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.904360	+	0.904360i	0.301453	+	0.301453i	0.841582	−	0.540129i	$-0.181625\pi$
$3$	0.904360	+	0.904360i	0.301453	+	0.301453i	−0.540129	+	0.841582i	$0.681625\pi$
$4$		0			0
$5$	−2.12642	+	4.52530i	−0.425285	+	0.905060i
$5$	−2.12642	+	4.52530i	−0.425285	+	0.905060i
$6$		0			0
$7$	−5.39452	+	4.46084i	−0.770646	+	0.637263i
$7$	−5.39452	+	4.46084i	−0.770646	+	0.637263i
$8$		0			0
$9$		−	7.36427i		−	0.818252i
$10$		0			0
$11$		−	1.26996i		−	0.115451i	−0.998333	−	0.0577254i	$-0.981615\pi$
$11$		−	1.26996i		−	0.115451i	0.998333	−	0.0577254i	$-0.0183848\pi$
$12$		0			0
$13$	−5.68460	+	5.68460i	−0.437277	+	0.437277i	−0.891095	−	0.453817i	$-0.850062\pi$
$13$	−5.68460	+	5.68460i	−0.437277	+	0.437277i	0.453817	+	0.891095i	$0.350062\pi$
$14$		0			0
$15$	−6.01555	+	2.16945i	−0.401037	+	0.144630i
$16$		0			0
$17$	−3.36775	−	3.36775i	−0.198103	−	0.198103i	0.601083	−	0.799186i	$-0.294736\pi$
$17$	−3.36775	−	3.36775i	−0.198103	−	0.198103i	−0.799186	+	0.601083i	$0.794736\pi$
$18$		0			0
$19$		−	10.5554i		−	0.555550i	−0.960646	−	0.277775i	$-0.910403\pi$
$19$		−	10.5554i		−	0.555550i	0.960646	−	0.277775i	$-0.0895970\pi$
$20$		0			0
$21$	−8.91279	−	0.844384i	−0.424419	−	0.0402088i
$22$		0			0
$23$	−17.3860	+	17.3860i	−0.755913	+	0.755913i	−0.975576	−	0.219663i	$-0.929504\pi$
$23$	−17.3860	+	17.3860i	−0.755913	+	0.755913i	0.219663	+	0.975576i	$0.429504\pi$
$24$		0			0
$25$	−15.9567	−	19.2454i	−0.638266	−	0.769816i
$26$		0			0
$27$	14.7992	−	14.7992i	0.548118	−	0.548118i
$28$		0			0
$29$		−	33.6429i		−	1.16010i	−0.814581	−	0.580050i	$-0.803033\pi$
$29$		−	33.6429i		−	1.16010i	0.814581	−	0.580050i	$-0.196967\pi$
$30$		0			0
$31$	−19.7373			−0.636687			−0.318343	−	0.947975i	$-0.603126\pi$
$31$	−19.7373			−0.636687			−0.318343	+	0.947975i	$0.603126\pi$
$32$		0			0
$33$	1.14850	−	1.14850i	0.0348030	−	0.0348030i
$34$		0			0
$35$	−8.71560	−	33.8975i	−0.249017	−	0.968499i
$36$		0			0
$37$	23.2693	−	23.2693i	0.628900	−	0.628900i	−0.318891	−	0.947791i	$-0.603310\pi$
$37$	23.2693	−	23.2693i	0.628900	−	0.628900i	0.947791	+	0.318891i	$0.103310\pi$
$38$		0			0
$39$	−10.2819			−0.263637
$40$		0			0
$41$		−	44.1112i		−	1.07588i	−0.842982	−	0.537941i	$-0.819202\pi$
$41$		−	44.1112i		−	1.07588i	0.842982	−	0.537941i	$-0.180798\pi$
$42$		0			0
$43$	−34.3775	+	34.3775i	−0.799476	+	0.799476i	−0.983013	−	0.183537i	$-0.941245\pi$
$43$	−34.3775	+	34.3775i	−0.799476	+	0.799476i	0.183537	+	0.983013i	$0.441245\pi$
$44$		0			0
$45$	33.3255	+	15.6595i	0.740567	+	0.347990i
$46$		0			0
$47$	−15.2233	+	15.2233i	−0.323900	+	0.323900i	−0.850261	−	0.526361i	$-0.823556\pi$
$47$	−15.2233	+	15.2233i	−0.323900	+	0.323900i	0.526361	+	0.850261i	$0.323556\pi$
$48$		0			0
$49$	9.20178	−	48.1282i	0.187791	−	0.982209i
$50$		0			0
$51$		−	6.09132i		−	0.119438i
$52$		0			0
$53$	−44.2336	−	44.2336i	−0.834597	−	0.834597i	0.153545	−	0.988142i	$-0.450931\pi$
$53$	−44.2336	−	44.2336i	−0.834597	−	0.834597i	−0.988142	+	0.153545i	$0.950931\pi$
$54$		0			0
$55$	5.74694	+	2.70047i	0.104490	+	0.0490994i
$56$		0			0
$57$	9.54592	−	9.54592i	0.167472	−	0.167472i
$58$		0			0
$59$			46.7572i			0.792495i	0.918144	+	0.396247i	$0.129688\pi$
$59$			46.7572i			0.792495i	−0.918144	+	0.396247i	$0.870312\pi$
$60$		0			0
$61$			12.0294i			0.197204i	0.995127	+	0.0986020i	$0.0314371\pi$
$61$			12.0294i			0.197204i	−0.995127	+	0.0986020i	$0.968563\pi$
$62$		0			0
$63$	32.8508	+	39.7267i	0.521442	+	0.630583i
$64$		0			0
$65$	−13.6367	−	37.8124i	−0.209795	−	0.581729i
$66$		0			0
$67$	−49.0186	−	49.0186i	−0.731620	−	0.731620i	0.239320	−	0.970941i	$-0.423075\pi$
$67$	−49.0186	−	49.0186i	−0.731620	−	0.731620i	−0.970941	+	0.239320i	$0.923075\pi$
$68$		0			0
$69$	−31.4464			−0.455745
$70$		0			0
$71$			98.6344i			1.38922i	0.719388	+	0.694608i	$0.244422\pi$
$71$			98.6344i			1.38922i	−0.719388	+	0.694608i	$0.755578\pi$
$72$		0			0
$73$	−48.8054	+	48.8054i	−0.668568	+	0.668568i	−0.957384	−	0.288817i	$-0.906738\pi$
$73$	−48.8054	+	48.8054i	−0.668568	+	0.668568i	0.288817	+	0.957384i	$0.406738\pi$
$74$		0			0
$75$	2.97421	−	31.8353i	0.0396561	−	0.424471i
$76$		0			0
$77$	5.66508	+	6.85082i	0.0735725	+	0.0889717i
$78$		0			0
$79$	−13.3286			−0.168716			−0.0843580	−	0.996436i	$-0.526884\pi$
$79$	−13.3286			−0.168716			−0.0843580	+	0.996436i	$0.526884\pi$
$80$		0			0
$81$	−39.5108			−0.487788
$82$		0			0
$83$	41.6147	+	41.6147i	0.501382	+	0.501382i	0.911867	−	0.410485i	$-0.134641\pi$
$83$	41.6147	+	41.6147i	0.501382	+	0.501382i	−0.410485	+	0.911867i	$0.634641\pi$
$84$		0			0
$85$	22.4014	−	8.07882i	0.263545	−	0.0950449i
$86$		0			0
$87$	30.4253	−	30.4253i	0.349716	−	0.349716i
$88$		0			0
$89$	−110.162			−1.23777			−0.618887	−	0.785480i	$-0.712416\pi$
$89$	−110.162			−1.23777			−0.618887	+	0.785480i	$0.712416\pi$
$90$		0			0
$91$	5.30761	−	56.0238i	0.0583254	−	0.615647i
$92$		0			0
$93$	−17.8496	−	17.8496i	−0.191931	−	0.191931i
$94$		0			0
$95$	47.7666	+	22.4453i	0.502806	+	0.236267i
$96$		0			0
$97$	54.3644	+	54.3644i	0.560458	+	0.560458i	0.929437	−	0.368980i	$-0.120293\pi$
$97$	54.3644	+	54.3644i	0.560458	+	0.560458i	−0.368980	+	0.929437i	$0.620293\pi$
$98$		0			0
$99$	−9.35231			−0.0944678
$100$		0			0
$101$		−	105.100i		−	1.04060i	−0.853985	−	0.520298i	$-0.825821\pi$
$101$		−	105.100i		−	1.04060i	0.853985	−	0.520298i	$-0.174179\pi$
$102$		0			0
$103$	−63.6401	−	63.6401i	−0.617865	−	0.617865i	0.327118	−	0.944983i	$-0.393922\pi$
$103$	−63.6401	−	63.6401i	−0.617865	−	0.617865i	−0.944983	+	0.327118i	$0.893922\pi$
$104$		0			0
$105$	22.7735	−	38.5375i	0.216890	−	0.367024i
$106$		0			0
$107$	−67.9200	−	67.9200i	−0.634767	−	0.634767i	0.314493	−	0.949260i	$-0.398165\pi$
$107$	−67.9200	−	67.9200i	−0.634767	−	0.634767i	−0.949260	+	0.314493i	$0.898165\pi$
$108$		0			0
$109$			10.1797i			0.0933919i	0.998909	+	0.0466960i	$0.0148692\pi$
$109$			10.1797i			0.0933919i	−0.998909	+	0.0466960i	$0.985131\pi$
$110$		0			0
$111$	42.0876			0.379168
$112$		0			0
$113$	47.2055	+	47.2055i	0.417748	+	0.417748i	0.884427	−	0.466679i	$-0.154550\pi$
$113$	47.2055	+	47.2055i	0.417748	+	0.417748i	−0.466679	+	0.884427i	$0.654550\pi$
$114$		0			0
$115$	−41.7069	−	115.647i	−0.362668	−	1.00562i
$116$		0			0
$117$	41.8629	+	41.8629i	0.357803	+	0.357803i
$118$		0			0
$119$	33.1904	+	3.14441i	0.278911	+	0.0264236i
$120$		0			0
$121$	119.387			0.986671
$122$		0			0
$123$	39.8924	−	39.8924i	0.324328	−	0.324328i
$124$		0			0
$125$	121.022	−	31.2848i	0.968174	−	0.250278i
$126$		0			0
$127$	47.8009	+	47.8009i	0.376385	+	0.376385i	0.869796	−	0.493411i	$-0.164250\pi$
$127$	47.8009	+	47.8009i	0.376385	+	0.376385i	−0.493411	+	0.869796i	$0.664250\pi$
$128$		0			0
$129$	−62.1792			−0.482009
$130$		0			0
$131$	−242.199			−1.84885			−0.924424	−	0.381366i	$-0.875454\pi$
$131$	−242.199			−1.84885			−0.924424	+	0.381366i	$0.875454\pi$
$132$		0			0
$133$	47.0862	+	56.9416i	0.354032	+	0.428133i
$134$		0			0
$135$	35.5014	+	98.4400i	0.262973	+	0.729185i
$136$		0			0
$137$	−129.504	+	129.504i	−0.945287	+	0.945287i	−0.998579	−	0.0532920i	$-0.983029\pi$
$137$	−129.504	+	129.504i	−0.945287	+	0.945287i	0.0532920	+	0.998579i	$0.483029\pi$
$138$		0			0
$139$			177.868i			1.27962i	0.768532	+	0.639812i	$0.220988\pi$
$139$			177.868i			1.27962i	−0.768532	+	0.639812i	$0.779012\pi$
$140$		0			0
$141$	−27.5346			−0.195281
$142$		0			0
$143$	7.21921	+	7.21921i	0.0504840	+	0.0504840i
$144$		0			0
$145$	152.244	+	71.5391i	1.04996	+	0.493373i
$146$		0			0
$147$	51.8470	−	35.2035i	0.352700	−	0.239480i
$148$		0			0
$149$			188.233i			1.26331i	0.775250	+	0.631655i	$0.217624\pi$
$149$			188.233i			1.26331i	−0.775250	+	0.631655i	$0.782376\pi$
$150$		0			0
$151$			104.514i			0.692146i	0.938208	+	0.346073i	$0.112485\pi$
$151$			104.514i			0.692146i	−0.938208	+	0.346073i	$0.887515\pi$
$152$		0			0
$153$	−24.8010	+	24.8010i	−0.162098	+	0.162098i
$154$		0			0
$155$	41.9698	−	89.3171i	0.270773	−	0.576239i
$156$		0			0
$157$	40.8950	+	40.8950i	0.260478	+	0.260478i	0.825248	−	0.564770i	$-0.191035\pi$
$157$	40.8950	+	40.8950i	0.260478	+	0.260478i	−0.564770	+	0.825248i	$0.691035\pi$
$158$		0			0
$159$		−	80.0062i		−	0.503184i
$160$		0			0
$161$	16.2330	−	171.345i	0.100826	−	1.06426i
$162$		0			0
$163$	208.247	−	208.247i	1.27759	−	1.27759i	0.335578	−	0.942012i	$-0.391068\pi$
$163$	208.247	−	208.247i	1.27759	−	1.27759i	0.942012	−	0.335578i	$-0.108932\pi$
$164$		0			0
$165$	2.75511	+	7.63949i	0.0166976	+	0.0463000i
$166$		0			0
$167$	13.7013	−	13.7013i	0.0820435	−	0.0820435i	−0.664894	−	0.746938i	$-0.731523\pi$
$167$	13.7013	−	13.7013i	0.0820435	−	0.0820435i	0.746938	+	0.664894i	$0.231523\pi$
$168$		0			0
$169$			104.371i			0.617577i
$170$		0			0
$171$	−77.7332			−0.454580
$172$		0			0
$173$	−211.305	+	211.305i	−1.22142	+	1.22142i	−0.254286	+	0.967129i	$0.581841\pi$
$173$	−211.305	+	211.305i	−1.22142	+	1.22142i	−0.967129	+	0.254286i	$0.918159\pi$
$174$		0			0
$175$	171.929	+	32.6396i	0.982453	+	0.186512i
$176$		0			0
$177$	−42.2853	+	42.2853i	−0.238900	+	0.238900i
$178$		0			0
$179$	94.8760			0.530034			0.265017	−	0.964244i	$-0.414622\pi$
$179$	94.8760			0.530034			0.265017	+	0.964244i	$0.414622\pi$
$180$		0			0
$181$		−	264.208i		−	1.45971i	−0.683602	−	0.729855i	$-0.739588\pi$
$181$		−	264.208i		−	1.45971i	0.683602	−	0.729855i	$-0.260412\pi$
$182$		0			0
$183$	−10.8789	+	10.8789i	−0.0594478	+	0.0594478i
$184$		0			0
$185$	55.8202	+	154.781i	0.301731	+	0.836653i
$186$		0			0
$187$	−4.27690	+	4.27690i	−0.0228711	+	0.0228711i
$188$		0			0
$189$	−13.8177	+	145.851i	−0.0731097	+	0.771700i
$190$		0			0
$191$			113.662i			0.595090i	0.954708	+	0.297545i	$0.0961678\pi$
$191$			113.662i			0.595090i	−0.954708	+	0.297545i	$0.903832\pi$
$192$		0			0
$193$	191.262	+	191.262i	0.990995	+	0.990995i	0.999960	−	0.00896468i	$-0.00285358\pi$
$193$	191.262	+	191.262i	0.990995	+	0.990995i	−0.00896468	+	0.999960i	$0.502854\pi$
$194$		0			0
$195$	21.8636	−	46.5284i	0.112121	−	0.238607i
$196$		0			0
$197$	−61.9383	+	61.9383i	−0.314407	+	0.314407i	−0.846614	−	0.532207i	$-0.821363\pi$
$197$	−61.9383	+	61.9383i	−0.314407	+	0.314407i	0.532207	+	0.846614i	$0.321363\pi$
$198$		0			0
$199$		−	20.4522i		−	0.102775i	−0.998679	−	0.0513875i	$-0.983636\pi$
$199$		−	20.4522i		−	0.102775i	0.998679	−	0.0513875i	$-0.0163644\pi$
$200$		0			0
$201$		−	88.6608i		−	0.441099i
$202$		0			0
$203$	150.076	+	181.487i	0.739289	+	0.894027i
$204$		0			0
$205$	199.616	+	93.7990i	0.973737	+	0.457556i
$206$		0			0
$207$	128.035	+	128.035i	0.618527	+	0.618527i
$208$		0			0
$209$	−13.4050			−0.0641386
$210$		0			0
$211$		−	368.795i		−	1.74784i	−0.486067	−	0.873922i	$-0.661569\pi$
$211$		−	368.795i		−	1.74784i	0.486067	−	0.873922i	$-0.338431\pi$
$212$		0			0
$213$	−89.2009	+	89.2009i	−0.418784	+	0.418784i
$214$		0			0
$215$	−82.4673	−	228.669i	−0.383569	−	1.06358i
$216$		0			0
$217$	106.473	−	88.0449i	0.490660	−	0.405737i
$218$		0			0
$219$	−88.2753			−0.403084
$220$		0			0
$221$	38.2887			0.173252
$222$		0			0
$223$	274.050	+	274.050i	1.22892	+	1.22892i	0.964372	+	0.264551i	$0.0852238\pi$
$223$	274.050	+	274.050i	1.22892	+	1.22892i	0.264551	+	0.964372i	$0.414776\pi$
$224$		0			0
$225$	−141.728	+	117.509i	−0.629903	+	0.522262i
$226$		0			0
$227$	11.3851	−	11.3851i	0.0501547	−	0.0501547i	−0.681585	−	0.731739i	$-0.738709\pi$
$227$	11.3851	−	11.3851i	0.0501547	−	0.0501547i	0.731739	+	0.681585i	$0.238709\pi$
$228$		0			0
$229$	−249.659			−1.09022			−0.545108	−	0.838366i	$-0.683511\pi$
$229$	−249.659			−1.09022			−0.545108	+	0.838366i	$0.683511\pi$
$230$		0			0
$231$	−1.07233	+	11.3189i	−0.00464213	+	0.0489995i
$232$		0			0
$233$	−21.4722	−	21.4722i	−0.0921554	−	0.0921554i	0.659526	−	0.751682i	$-0.270757\pi$
$233$	−21.4722	−	21.4722i	−0.0921554	−	0.0921554i	−0.751682	+	0.659526i	$0.770757\pi$
$234$		0			0
$235$	−36.5188	−	101.261i	−0.155399	−	0.430898i
$236$		0			0
$237$	−12.0538	−	12.0538i	−0.0508600	−	0.0508600i
$238$		0			0
$239$	349.200			1.46109			0.730544	−	0.682865i	$-0.239266\pi$
$239$	349.200			1.46109			0.730544	+	0.682865i	$0.239266\pi$
$240$		0			0
$241$		−	219.615i		−	0.911267i	−0.890167	−	0.455634i	$-0.849413\pi$
$241$		−	219.615i		−	0.911267i	0.890167	−	0.455634i	$-0.150587\pi$
$242$		0			0
$243$	−168.925	−	168.925i	−0.695163	−	0.695163i
$244$		0			0
$245$	198.228	+	143.982i	0.809093	+	0.587681i
$246$		0			0
$247$	60.0035	+	60.0035i	0.242929	+	0.242929i
$248$		0			0
$249$			75.2694i			0.302287i
$250$		0			0
$251$	166.747			0.664330			0.332165	−	0.943221i	$-0.392221\pi$
$251$	166.747			0.664330			0.332165	+	0.943221i	$0.392221\pi$
$252$		0			0
$253$	22.0795	+	22.0795i	0.0872707	+	0.0872707i
$254$		0			0
$255$	27.5650	+	12.9527i	0.108098	+	0.0507950i
$256$		0			0
$257$	172.983	+	172.983i	0.673085	+	0.673085i	0.958426	−	0.285341i	$-0.0921069\pi$
$257$	172.983	+	172.983i	0.673085	+	0.673085i	−0.285341	+	0.958426i	$0.592107\pi$
$258$		0			0
$259$	−21.7261	+	229.327i	−0.0838847	+	0.885434i
$260$		0			0
$261$	−247.755			−0.949254
$262$		0			0
$263$	−232.175	+	232.175i	−0.882795	+	0.882795i	−0.993818	−	0.111023i	$-0.964587\pi$
$263$	−232.175	+	232.175i	−0.882795	+	0.882795i	0.111023	+	0.993818i	$0.464587\pi$
$264$		0			0
$265$	294.230	−	106.111i	1.11030	−	0.400419i
$266$		0			0
$267$	−99.6260	−	99.6260i	−0.373131	−	0.373131i
$268$		0			0
$269$	37.2174			0.138355			0.0691774	−	0.997604i	$-0.477963\pi$
$269$	37.2174			0.138355			0.0691774	+	0.997604i	$0.477963\pi$
$270$		0			0
$271$	−539.312			−1.99008			−0.995040	−	0.0994763i	$-0.968283\pi$
$271$	−539.312			−1.99008			−0.995040	+	0.0994763i	$0.968283\pi$
$272$		0			0
$273$	55.4657	−	45.8657i	0.203171	−	0.168006i
$274$		0			0
$275$	−24.4408	+	20.2643i	−0.0888758	+	0.0736883i
$276$		0			0
$277$	223.341	−	223.341i	0.806287	−	0.806287i	−0.177783	−	0.984070i	$-0.556892\pi$
$277$	223.341	−	223.341i	0.806287	−	0.806287i	0.984070	+	0.177783i	$0.0568925\pi$
$278$		0			0
$279$			145.351i			0.520970i
$280$		0			0
$281$	−218.422			−0.777304			−0.388652	−	0.921385i	$-0.627059\pi$
$281$	−218.422			−0.777304			−0.388652	+	0.921385i	$0.627059\pi$
$282$		0			0
$283$	−71.5781	−	71.5781i	−0.252926	−	0.252926i	0.569243	−	0.822169i	$-0.307236\pi$
$283$	−71.5781	−	71.5781i	−0.252926	−	0.252926i	−0.822169	+	0.569243i	$0.807236\pi$
$284$		0			0
$285$	22.8995	+	63.4968i	0.0803491	+	0.222796i
$286$		0			0
$287$	196.773	+	237.959i	0.685620	+	0.829124i
$288$		0			0
$289$		−	266.316i		−	0.921510i
$290$		0			0
$291$			98.3299i			0.337904i
$292$		0			0
$293$	70.6039	−	70.6039i	0.240969	−	0.240969i	−0.576282	−	0.817251i	$-0.695497\pi$
$293$	70.6039	−	70.6039i	0.240969	−	0.240969i	0.817251	+	0.576282i	$0.195497\pi$
$294$		0			0
$295$	−211.590	−	99.4256i	−0.717255	−	0.337036i
$296$		0			0
$297$	−18.7943	−	18.7943i	−0.0632806	−	0.0632806i
$298$		0			0
$299$		−	197.665i		−	0.661087i
$300$		0			0
$301$	32.0976	−	338.803i	0.106637	−	1.12559i
$302$		0			0
$303$	95.0484	−	95.0484i	0.313691	−	0.313691i
$304$		0			0
$305$	−54.4368	−	25.5797i	−0.178481	−	0.0838678i
$306$		0			0
$307$	306.962	−	306.962i	0.999877	−	0.999877i	−0.000122802	−	1.00000i	$-0.500039\pi$
$307$	306.962	−	306.962i	0.999877	−	0.999877i	1.00000		0.000122802i	$3.90891e-5\pi$
$308$		0			0
$309$		−	115.107i		−	0.372515i
$310$		0			0
$311$	−416.307			−1.33861			−0.669304	−	0.742989i	$-0.733408\pi$
$311$	−416.307			−1.33861			−0.669304	+	0.742989i	$0.733408\pi$
$312$		0			0
$313$	−355.123	+	355.123i	−1.13458	+	1.13458i	−0.145172	+	0.989406i	$0.546374\pi$
$313$	−355.123	+	355.123i	−1.13458	+	1.13458i	−0.989406	+	0.145172i	$0.953626\pi$
$314$		0			0
$315$	−249.630	+	64.1840i	−0.792476	+	0.203759i
$316$		0			0
$317$	−89.1819	+	89.1819i	−0.281331	+	0.281331i	−0.833640	−	0.552309i	$-0.813747\pi$
$317$	−89.1819	+	89.1819i	−0.281331	+	0.281331i	0.552309	+	0.833640i	$0.313747\pi$
$318$		0			0
$319$	−42.7251			−0.133934
$320$		0			0
$321$		−	122.848i		−	0.382705i
$322$		0			0
$323$	−35.5481	+	35.5481i	−0.110056	+	0.110056i
$324$		0			0
$325$	200.110	+	18.6952i	0.615722	+	0.0575237i
$326$		0			0
$327$	−9.20613	+	9.20613i	−0.0281533	+	0.0281533i
$328$		0			0
$329$	14.2137	−	150.031i	0.0432027	−	0.456021i
$330$		0			0
$331$		−	286.057i		−	0.864220i	−0.901821	−	0.432110i	$-0.857769\pi$
$331$		−	286.057i		−	0.864220i	0.901821	−	0.432110i	$-0.142231\pi$
$332$		0			0
$333$	−171.361	−	171.361i	−0.514599	−	0.514599i
$334$		0			0
$335$	326.058	−	117.589i	0.973307	−	0.351013i
$336$		0			0
$337$	315.339	−	315.339i	0.935723	−	0.935723i	−0.0623320	−	0.998055i	$-0.519854\pi$
$337$	315.339	−	315.339i	0.935723	−	0.935723i	0.998055	+	0.0623320i	$0.0198538\pi$
$338$		0			0
$339$			85.3815i			0.251863i
$340$		0			0
$341$			25.0655i			0.0735059i
$342$		0			0
$343$	165.053	+	300.677i	0.481205	+	0.876608i
$344$		0			0
$345$	66.8683	−	142.304i	0.193821	−	0.412476i
$346$		0			0
$347$	−256.959	−	256.959i	−0.740515	−	0.740515i	0.232162	−	0.972677i	$-0.425420\pi$
$347$	−256.959	−	256.959i	−0.740515	−	0.740515i	−0.972677	+	0.232162i	$0.925420\pi$
$348$		0			0
$349$	−551.816			−1.58113			−0.790567	−	0.612375i	$-0.790214\pi$
$349$	−551.816			−1.58113			−0.790567	+	0.612375i	$0.790214\pi$
$350$		0			0
$351$			168.255i			0.479359i
$352$		0			0
$353$	−289.440	+	289.440i	−0.819944	+	0.819944i	−0.986100	−	0.166156i	$-0.946865\pi$
$353$	−289.440	+	289.440i	−0.819944	+	0.819944i	0.166156	+	0.986100i	$0.446865\pi$
$354$		0			0
$355$	−446.350	−	209.738i	−1.25732	−	0.590812i
$356$		0			0
$357$	27.1724	+	32.8598i	0.0761132	+	0.0920442i
$358$		0			0
$359$	−489.143			−1.36251			−0.681257	−	0.732044i	$-0.738567\pi$
$359$	−489.143			−1.36251			−0.681257	+	0.732044i	$0.738567\pi$
$360$		0			0
$361$	249.582			0.691364
$362$		0			0
$363$	107.969	+	107.969i	0.297435	+	0.297435i
$364$		0			0
$365$	−117.078	−	324.640i	−0.320762	−	0.889425i
$366$		0			0
$367$	−49.8445	+	49.8445i	−0.135816	+	0.135816i	−0.771746	−	0.635930i	$-0.780617\pi$
$367$	−49.8445	+	49.8445i	−0.135816	+	0.135816i	0.635930	+	0.771746i	$0.280617\pi$
$368$		0			0
$369$	−324.846			−0.880343
$370$		0			0
$371$	435.938	+	41.3001i	1.17504	+	0.111321i
$372$		0			0
$373$	−124.957	−	124.957i	−0.335006	−	0.335006i	0.519478	−	0.854484i	$-0.326127\pi$
$373$	−124.957	−	124.957i	−0.335006	−	0.335006i	−0.854484	+	0.519478i	$0.826127\pi$
$374$		0			0
$375$	137.740	+	81.1545i	0.367306	+	0.216412i
$376$		0			0
$377$	191.247	+	191.247i	0.507285	+	0.507285i
$378$		0			0
$379$	−341.107			−0.900019			−0.450009	−	0.893024i	$-0.648579\pi$
$379$	−341.107			−0.900019			−0.450009	+	0.893024i	$0.648579\pi$
$380$		0			0
$381$			86.4583i			0.226925i
$382$		0			0
$383$	−229.435	−	229.435i	−0.599048	−	0.599048i	0.341011	−	0.940059i	$-0.389231\pi$
$383$	−229.435	−	229.435i	−0.599048	−	0.599048i	−0.940059	+	0.341011i	$0.889231\pi$
$384$		0			0
$385$	−43.0484	+	11.0684i	−0.111814	+	0.0287492i
$386$		0			0
$387$	253.165	+	253.165i	0.654173	+	0.654173i
$388$		0			0
$389$		−	338.375i		−	0.869859i	−0.900464	−	0.434930i	$-0.856773\pi$
$389$		−	338.375i		−	0.869859i	0.900464	−	0.434930i	$-0.143227\pi$
$390$		0			0
$391$	117.103			0.299497
$392$		0			0
$393$	−219.035	−	219.035i	−0.557341	−	0.557341i
$394$		0			0
$395$	28.3422	−	60.3157i	0.0717523	−	0.152698i
$396$		0			0
$397$	54.8168	+	54.8168i	0.138077	+	0.138077i	0.772767	−	0.634690i	$-0.218872\pi$
$397$	54.8168	+	54.8168i	0.138077	+	0.138077i	−0.634690	+	0.772767i	$0.718872\pi$
$398$		0			0
$399$	−8.91286	+	94.0786i	−0.0223380	+	0.235786i
$400$		0			0
$401$	−414.174			−1.03285			−0.516427	−	0.856332i	$-0.672738\pi$
$401$	−414.174			−1.03285			−0.516427	+	0.856332i	$0.672738\pi$
$402$		0			0
$403$	112.199	−	112.199i	0.278409	−	0.278409i
$404$		0			0
$405$	84.0168	−	178.798i	0.207449	−	0.441477i
$406$		0			0
$407$	−29.5510	−	29.5510i	−0.0726070	−	0.0726070i
$408$		0			0
$409$	−279.231			−0.682715			−0.341358	−	0.939933i	$-0.610887\pi$
$409$	−279.231			−0.682715			−0.341358	+	0.939933i	$0.610887\pi$
$410$		0			0
$411$	−234.237			−0.569920
$412$		0			0
$413$	−208.577	−	252.233i	−0.505028	−	0.610733i
$414$		0			0
$415$	−276.810	+	99.8286i	−0.667011	+	0.240551i
$416$		0			0
$417$	−160.856	+	160.856i	−0.385746	+	0.385746i
$418$		0			0
$419$			800.277i			1.90997i	0.296657	+	0.954984i	$0.404128\pi$
$419$			800.277i			1.90997i	−0.296657	+	0.954984i	$0.595872\pi$
$420$		0			0
$421$	455.032			1.08084			0.540418	−	0.841397i	$-0.318266\pi$
$421$	455.032			1.08084			0.540418	+	0.841397i	$0.318266\pi$
$422$		0			0
$423$	112.108	+	112.108i	0.265031	+	0.265031i
$424$		0			0
$425$	−11.0757	+	118.552i	−0.0260604	+	0.278945i
$426$		0			0
$427$	−53.6615	−	64.8931i	−0.125671	−	0.151975i
$428$		0			0
$429$			13.0575i			0.0304371i
$430$		0			0
$431$		−	27.6204i		−	0.0640845i	−0.999487	−	0.0320423i	$-0.989799\pi$
$431$		−	27.6204i		−	0.0640845i	0.999487	−	0.0320423i	$-0.0102011\pi$
$432$		0			0
$433$	356.596	−	356.596i	0.823548	−	0.823548i	−0.163067	−	0.986615i	$-0.552139\pi$
$433$	356.596	−	356.596i	0.823548	−	0.823548i	0.986615	+	0.163067i	$0.0521386\pi$
$434$		0			0
$435$	72.9865	+	202.381i	0.167785	+	0.465243i
$436$		0			0
$437$	183.517	+	183.517i	0.419947	+	0.419947i
$438$		0			0
$439$		−	114.996i		−	0.261949i	−0.991386	−	0.130975i	$-0.958189\pi$
$439$		−	114.996i		−	0.261949i	0.991386	−	0.130975i	$-0.0418106\pi$
$440$		0			0
$441$	−354.429	−	67.7643i	−0.803694	−	0.153661i
$442$		0			0
$443$	−247.575	+	247.575i	−0.558861	+	0.558861i	−0.928983	−	0.370122i	$-0.879316\pi$
$443$	−247.575	+	247.575i	−0.558861	+	0.558861i	0.370122	+	0.928983i	$0.379316\pi$
$444$		0			0
$445$	234.251	−	498.515i	0.526406	−	1.12026i
$446$		0			0
$447$	−170.230	+	170.230i	−0.380829	+	0.380829i
$448$		0			0
$449$		−	147.163i		−	0.327756i	−0.986481	−	0.163878i	$-0.947600\pi$
$449$		−	147.163i		−	0.327756i	0.986481	−	0.163878i	$-0.0524004\pi$
$450$		0			0
$451$	−56.0193			−0.124211
$452$		0			0
$453$	−94.5182	+	94.5182i	−0.208649	+	0.208649i
$454$		0			0
$455$	242.238	+	143.149i	0.532392	+	0.314613i
$456$		0			0
$457$	426.763	−	426.763i	0.933836	−	0.933836i	−0.0641070	−	0.997943i	$-0.520420\pi$
$457$	426.763	−	426.763i	0.933836	−	0.933836i	0.997943	+	0.0641070i	$0.0204199\pi$
$458$		0			0
$459$	−99.6800			−0.217168
$460$		0			0
$461$		−	324.715i		−	0.704370i	−0.935930	−	0.352185i	$-0.885439\pi$
$461$		−	324.715i		−	0.704370i	0.935930	−	0.352185i	$-0.114561\pi$
$462$		0			0
$463$	125.828	−	125.828i	0.271766	−	0.271766i	−0.558045	−	0.829811i	$-0.688448\pi$
$463$	125.828	−	125.828i	0.271766	−	0.271766i	0.829811	+	0.558045i	$0.188448\pi$
$464$		0			0
$465$	118.731	−	42.8190i	0.255335	−	0.0920838i
$466$		0			0
$467$	101.704	−	101.704i	0.217782	−	0.217782i	−0.589781	−	0.807563i	$-0.700786\pi$
$467$	101.704	−	101.704i	0.217782	−	0.217782i	0.807563	+	0.589781i	$0.200786\pi$
$468$		0			0
$469$	483.096	+	45.7677i	1.03006	+	0.0975858i
$470$		0			0
$471$			73.9676i			0.157044i
$472$		0			0
$473$	43.6579	+	43.6579i	0.0923001	+	0.0923001i
$474$		0			0
$475$	−203.144	+	168.430i	−0.427671	+	0.354589i
$476$		0			0
$477$	−325.748	+	325.748i	−0.682910	+	0.682910i
$478$		0			0
$479$		−	745.527i		−	1.55642i	−0.628002	−	0.778212i	$-0.716127\pi$
$479$		−	745.527i		−	1.55642i	0.628002	−	0.778212i	$-0.283873\pi$
$480$		0			0
$481$			264.553i			0.550007i
$482$		0			0
$483$	169.638	−	140.277i	0.351218	−	0.290429i
$484$		0			0
$485$	−361.617	+	130.413i	−0.745602	+	0.268894i
$486$		0			0
$487$	−665.491	−	665.491i	−1.36651	−	1.36651i	−0.865358	−	0.501154i	$-0.832909\pi$
$487$	−665.491	−	665.491i	−1.36651	−	1.36651i	−0.501154	−	0.865358i	$-0.667091\pi$
$488$		0			0
$489$	376.661			0.770268
$490$		0			0
$491$			652.956i			1.32985i	0.746910	+	0.664925i	$0.231536\pi$
$491$			652.956i			1.32985i	−0.746910	+	0.664925i	$0.768464\pi$
$492$		0			0
$493$	−113.301	+	113.301i	−0.229819	+	0.229819i
$494$		0			0
$495$	19.8870	−	42.3220i	0.0401757	−	0.0854990i
$496$		0			0
$497$	−439.992	−	532.085i	−0.885296	−	1.07059i
$498$		0			0
$499$	521.128			1.04434			0.522172	−	0.852840i	$-0.325122\pi$
$499$	521.128			1.04434			0.522172	+	0.852840i	$0.325122\pi$
$500$		0			0
$501$	24.7817			0.0494646
$502$		0			0
$503$	339.032	+	339.032i	0.674020	+	0.674020i	0.958640	−	0.284621i	$-0.0918676\pi$
$503$	339.032	+	339.032i	0.674020	+	0.674020i	−0.284621	+	0.958640i	$0.591868\pi$
$504$		0			0
$505$	475.610	+	223.487i	0.941801	+	0.442549i
$506$		0			0
$507$	−94.3885	+	94.3885i	−0.186171	+	0.186171i
$508$		0			0
$509$	254.066			0.499147			0.249573	−	0.968356i	$-0.419710\pi$
$509$	254.066			0.499147			0.249573	+	0.968356i	$0.419710\pi$
$510$		0			0
$511$	45.5688	−	480.995i	0.0891756	−	0.941283i
$512$		0			0
$513$	−156.212	−	156.212i	−0.304507	−	0.304507i
$514$		0			0
$515$	423.316	−	152.665i	0.821973	−	0.296436i
$516$		0			0
$517$	19.3329	+	19.3329i	0.0373944	+	0.0373944i
$518$		0			0
$519$	−382.191			−0.736399
$520$		0			0
$521$		−	550.319i		−	1.05627i	−0.849159	−	0.528137i	$-0.822891\pi$
$521$		−	550.319i		−	1.05627i	0.849159	−	0.528137i	$-0.177109\pi$
$522$		0			0
$523$	−557.209	−	557.209i	−1.06541	−	1.06541i	−0.997706	−	0.0677028i	$-0.978433\pi$
$523$	−557.209	−	557.209i	−1.06541	−	1.06541i	−0.0677028	−	0.997706i	$-0.521567\pi$
$524$		0			0
$525$	125.968	+	185.004i	0.239939	+	0.352388i
$526$		0			0
$527$	66.4703	+	66.4703i	0.126130	+	0.126130i
$528$		0			0
$529$		−	75.5461i		−	0.142809i
$530$		0			0
$531$	344.333			0.648461
$532$		0			0
$533$	250.754	+	250.754i	0.470459	+	0.470459i
$534$		0			0
$535$	451.785	−	162.932i	0.844458	−	0.304545i
$536$		0			0
$537$	85.8020	+	85.8020i	0.159780	+	0.159780i
$538$		0			0
$539$	−61.1208	−	11.6859i	−0.113397	−	0.0216807i
$540$		0			0
$541$	533.895			0.986866			0.493433	−	0.869784i	$-0.335742\pi$
$541$	533.895			0.986866			0.493433	+	0.869784i	$0.335742\pi$
$542$		0			0
$543$	238.939	−	238.939i	0.440034	−	0.440034i
$544$		0			0
$545$	−46.0663	−	21.6464i	−0.0845253	−	0.0397181i
$546$		0			0
$547$	71.9174	+	71.9174i	0.131476	+	0.131476i	0.769782	−	0.638306i	$-0.220365\pi$
$547$	71.9174	+	71.9174i	0.131476	+	0.131476i	−0.638306	+	0.769782i	$0.720365\pi$
$548$		0			0
$549$	88.5881			0.161363
$550$		0			0
$551$	−355.116			−0.644494
$552$		0			0
$553$	71.9013	−	59.4566i	0.130020	−	0.107516i
$554$		0			0
$555$	−89.4961	+	190.459i	−0.161254	+	0.343170i
$556$		0			0
$557$	−355.063	+	355.063i	−0.637456	+	0.637456i	−0.949927	−	0.312471i	$-0.898843\pi$
$557$	−355.063	+	355.063i	−0.637456	+	0.637456i	0.312471	+	0.949927i	$0.398843\pi$
$558$		0			0
$559$		−	390.845i		−	0.699185i
$560$		0			0
$561$	−7.73572			−0.0137892
$562$		0			0
$563$	58.3961	+	58.3961i	0.103723	+	0.103723i	0.757064	−	0.653341i	$-0.226633\pi$
$563$	58.3961	+	58.3961i	0.103723	+	0.103723i	−0.653341	+	0.757064i	$0.726633\pi$
$564$		0			0
$565$	−313.998	+	113.240i	−0.555748	+	0.200425i
$566$		0			0
$567$	213.142	−	176.252i	0.375912	−	0.310849i
$568$		0			0
$569$			721.380i			1.26780i	0.773413	+	0.633902i	$0.218548\pi$
$569$			721.380i			1.26780i	−0.773413	+	0.633902i	$0.781452\pi$
$570$		0			0
$571$			432.701i			0.757795i	0.925439	+	0.378897i	$0.123697\pi$
$571$			432.701i			0.757795i	−0.925439	+	0.378897i	$0.876303\pi$
$572$		0			0
$573$	−102.791	+	102.791i	−0.179392	+	0.179392i
$574$		0			0
$575$	612.023	+	57.1781i	1.06439	+	0.0994402i
$576$		0			0
$577$	−426.273	−	426.273i	−0.738775	−	0.738775i	0.233566	−	0.972341i	$-0.424961\pi$
$577$	−426.273	−	426.273i	−0.738775	−	0.738775i	−0.972341	+	0.233566i	$0.924961\pi$
$578$		0			0
$579$			345.939i			0.597477i
$580$		0			0
$581$	−410.128	−	38.8549i	−0.705901	−	0.0668759i
$582$		0			0
$583$	−56.1748	+	56.1748i	−0.0963548	+	0.0963548i
$584$		0			0
$585$	−278.461	+	100.424i	−0.476001	+	0.171665i
$586$		0			0
$587$	169.531	−	169.531i	0.288809	−	0.288809i	−0.547800	−	0.836609i	$-0.684534\pi$
$587$	169.531	−	169.531i	0.288809	−	0.288809i	0.836609	+	0.547800i	$0.184534\pi$
$588$		0			0
$589$			208.336i			0.353711i
$590$		0			0
$591$	−112.029			−0.189558
$592$		0			0
$593$	−114.854	+	114.854i	−0.193683	+	0.193683i	−0.797285	−	0.603603i	$-0.793731\pi$
$593$	−114.854	+	114.854i	−0.193683	+	0.193683i	0.603603	+	0.797285i	$0.293731\pi$
$594$		0			0
$595$	−84.8063	+	143.510i	−0.142532	+	0.241194i
$596$		0			0
$597$	18.4962	−	18.4962i	0.0309819	−	0.0309819i
$598$		0			0
$599$	386.473			0.645198			0.322599	−	0.946536i	$-0.395444\pi$
$599$	386.473			0.645198			0.322599	+	0.946536i	$0.395444\pi$
$600$		0			0
$601$			726.731i			1.20920i	0.796528	+	0.604601i	$0.206668\pi$
$601$			726.731i			1.20920i	−0.796528	+	0.604601i	$0.793332\pi$
$602$		0			0
$603$	−360.986	+	360.986i	−0.598650	+	0.598650i
$604$		0			0
$605$	−253.868	+	540.263i	−0.419616	+	0.892996i
$606$		0			0
$607$	−270.361	+	270.361i	−0.445405	+	0.445405i	−0.893824	−	0.448419i	$-0.851987\pi$
$607$	−270.361	+	270.361i	−0.445405	+	0.445405i	0.448419	+	0.893824i	$0.351987\pi$
$608$		0			0
$609$	−28.4075	+	299.852i	−0.0466462	+	0.492368i
$610$		0			0
$611$		−	173.077i		−	0.283268i
$612$		0			0
$613$	464.995	+	464.995i	0.758556	+	0.758556i	0.976059	−	0.217504i	$-0.0697915\pi$
$613$	464.995	+	464.995i	0.758556	+	0.758556i	−0.217504	+	0.976059i	$0.569791\pi$
$614$		0			0
$615$	95.6968	+	265.353i	0.155605	+	0.431468i
$616$		0			0
$617$	−268.886	+	268.886i	−0.435796	+	0.435796i	−0.890594	−	0.454798i	$-0.849711\pi$
$617$	−268.886	+	268.886i	−0.435796	+	0.435796i	0.454798	+	0.890594i	$0.349711\pi$
$618$		0			0
$619$		−	20.3355i		−	0.0328522i	−0.999865	−	0.0164261i	$-0.994771\pi$
$619$		−	20.3355i		−	0.0328522i	0.999865	−	0.0164261i	$-0.00522882\pi$
$620$		0			0
$621$			514.597i			0.828659i
$622$		0			0
$623$	594.271	−	491.415i	0.953886	−	0.788788i
$624$		0			0
$625$	−115.771	+	614.184i	−0.185233	+	0.982695i
$626$		0			0
$627$	−12.1229	−	12.1229i	−0.0193348	−	0.0193348i
$628$		0			0
$629$	−156.730			−0.249174
$630$		0			0
$631$		−	144.263i		−	0.228625i	−0.993445	−	0.114313i	$-0.963533\pi$
$631$		−	144.263i		−	0.228625i	0.993445	−	0.114313i	$-0.0364666\pi$
$632$		0			0
$633$	333.523	−	333.523i	0.526893	−	0.526893i
$634$		0			0
$635$	−317.958	+	114.668i	−0.500721	+	0.180580i
$636$		0			0
$637$	221.281	+	325.898i	0.347381	+	0.511614i
$638$		0			0
$639$	726.370			1.13673
$640$		0			0
$641$	292.930			0.456989			0.228494	−	0.973545i	$-0.426620\pi$
$641$	292.930			0.456989			0.228494	+	0.973545i	$0.426620\pi$
$642$		0			0
$643$	−134.832	−	134.832i	−0.209692	−	0.209692i	0.594445	−	0.804137i	$-0.297372\pi$
$643$	−134.832	−	134.832i	−0.209692	−	0.209692i	−0.804137	+	0.594445i	$0.797372\pi$
$644$		0			0
$645$	132.219	−	281.379i	0.204991	−	0.436247i
$646$		0			0
$647$	−553.531	+	553.531i	−0.855535	+	0.855535i	−0.990808	−	0.135273i	$-0.956809\pi$
$647$	−553.531	+	553.531i	−0.855535	+	0.855535i	0.135273	+	0.990808i	$0.456809\pi$
$648$		0			0
$649$	59.3797			0.0914941
$650$		0			0
$651$	175.914	+	16.6659i	0.270222	+	0.0256004i
$652$		0			0
$653$	493.172	+	493.172i	0.755240	+	0.755240i	0.975452	−	0.220212i	$-0.0706750\pi$
$653$	493.172	+	493.172i	0.755240	+	0.755240i	−0.220212	+	0.975452i	$0.570675\pi$
$654$		0			0
$655$	515.018	−	1096.02i	0.786287	−	1.67332i
$656$		0			0
$657$	359.416	+	359.416i	0.547057	+	0.547057i
$658$		0			0
$659$	669.889			1.01652			0.508262	−	0.861203i	$-0.330288\pi$
$659$	669.889			1.01652			0.508262	+	0.861203i	$0.330288\pi$
$660$		0			0
$661$			696.612i			1.05388i	0.849904	+	0.526938i	$0.176660\pi$
$661$			696.612i			1.05388i	−0.849904	+	0.526938i	$0.823340\pi$
$662$		0			0
$663$	34.6267	+	34.6267i	0.0522273	+	0.0522273i
$664$		0			0
$665$	−357.803	+	91.9971i	−0.538050	+	0.138342i
$666$		0			0
$667$	584.916	+	584.916i	0.876935	+	0.876935i
$668$		0			0
$669$			495.679i			0.740925i
$670$		0			0
$671$	15.2769			0.0227673
$672$		0			0
$673$	596.598	+	596.598i	0.886476	+	0.886476i	0.994183	−	0.107707i	$-0.0343508\pi$
$673$	596.598	+	596.598i	0.886476	+	0.886476i	−0.107707	+	0.994183i	$0.534351\pi$
$674$		0			0
$675$	−520.962	−	48.6707i	−0.771795	−	0.0721048i
$676$		0			0
$677$	−640.789	−	640.789i	−0.946513	−	0.946513i	0.0521272	−	0.998640i	$-0.483400\pi$
$677$	−640.789	−	640.789i	−0.946513	−	0.946513i	−0.998640	+	0.0521272i	$0.983400\pi$
$678$		0			0
$679$	−535.781	−	50.7591i	−0.789074	−	0.0747556i
$680$		0			0
$681$	20.5925			0.0302386
$682$		0			0
$683$	−807.544	+	807.544i	−1.18235	+	1.18235i	−0.203215	+	0.979134i	$0.565139\pi$
$683$	−807.544	+	807.544i	−1.18235	+	1.18235i	−0.979134	+	0.203215i	$0.934861\pi$
$684$		0			0
$685$	−310.665	−	861.427i	−0.453525	−	1.25756i
$686$		0			0
$687$	−225.782	−	225.782i	−0.328649	−	0.328649i
$688$		0			0
$689$	502.901			0.729900
$690$		0			0
$691$	828.536			1.19904			0.599520	−	0.800360i	$-0.295358\pi$
$691$	828.536			1.19904			0.599520	+	0.800360i	$0.295358\pi$
$692$		0			0
$693$	50.4513	−	41.7192i	0.0728012	−	0.0602008i
$694$		0			0
$695$	−804.904	−	378.222i	−1.15814	−	0.544204i
$696$		0			0
$697$	−148.555	+	148.555i	−0.213136	+	0.213136i
$698$		0			0
$699$		−	38.8372i		−	0.0555611i
$700$		0			0
$701$	250.093			0.356766			0.178383	−	0.983961i	$-0.442913\pi$
$701$	250.093			0.356766			0.178383	+	0.983961i	$0.442913\pi$
$702$		0			0
$703$	−245.618	−	245.618i	−0.349385	−	0.349385i
$704$		0			0
$705$	58.5503	−	124.602i	0.0830500	−	0.176741i
$706$		0			0
$707$	468.835	+	566.965i	0.663133	+	0.801931i
$708$		0			0
$709$		−	235.177i		−	0.331703i	−0.986151	−	0.165851i	$-0.946963\pi$
$709$		−	235.177i		−	0.331703i	0.986151	−	0.165851i	$-0.0530372\pi$
$710$		0			0
$711$			98.1551i			0.138052i
$712$		0			0
$713$	343.152	−	343.152i	0.481280	−	0.481280i
$714$		0			0
$715$	−48.0202	+	17.3180i	−0.0671611	+	0.0242210i
$716$		0			0
$717$	315.803	+	315.803i	0.440450	+	0.440450i
$718$		0			0
$719$		−	1023.00i		−	1.42281i	−0.702783	−	0.711405i	$-0.748059\pi$
$719$		−	1023.00i		−	1.42281i	0.702783	−	0.711405i	$-0.251941\pi$
$720$		0			0
$721$	627.197	+	59.4196i	0.869898	+	0.0824128i
$722$		0			0
$723$	198.611	−	198.611i	0.274704	−	0.274704i
$724$		0			0
$725$	−647.471	+	536.828i	−0.893064	+	0.740453i
$726$		0			0
$727$	−148.496	+	148.496i	−0.204259	+	0.204259i	−0.801822	−	0.597563i	$-0.796136\pi$
$727$	−148.496	+	148.496i	−0.204259	+	0.204259i	0.597563	+	0.801822i	$0.296136\pi$
$728$		0			0
$729$			50.0603i			0.0686698i
$730$		0			0
$731$	231.550			0.316757
$732$		0			0
$733$	912.975	−	912.975i	1.24553	−	1.24553i	0.287859	−	0.957673i	$-0.407057\pi$
$733$	912.975	−	912.975i	1.24553	−	1.24553i	0.957673	−	0.287859i	$-0.0929433\pi$
$734$		0			0
$735$	49.0579	+	309.480i	0.0667454	+	0.421062i
$736$		0			0
$737$	−62.2515	+	62.2515i	−0.0844661	+	0.0844661i
$738$		0			0
$739$	1331.79			1.80215			0.901075	−	0.433663i	$-0.142779\pi$
$739$	1331.79			1.80215			0.901075	+	0.433663i	$0.142779\pi$
$740$		0			0
$741$			108.530i			0.146464i
$742$		0			0
$743$	204.549	−	204.549i	0.275301	−	0.275301i	−0.555929	−	0.831230i	$-0.687637\pi$
$743$	204.549	−	204.549i	0.275301	−	0.275301i	0.831230	+	0.555929i	$0.187637\pi$
$744$		0			0
$745$	−851.811	−	400.263i	−1.14337	−	0.537266i
$746$		0			0
$747$	306.462	−	306.462i	0.410257	−	0.410257i
$748$		0			0
$749$	669.377	+	63.4157i	0.893694	+	0.0846672i
$750$		0			0
$751$		−	1160.74i		−	1.54559i	−0.634657	−	0.772794i	$-0.718859\pi$
$751$		−	1160.74i		−	1.54559i	0.634657	−	0.772794i	$-0.281141\pi$
$752$		0			0
$753$	150.799	+	150.799i	0.200265	+	0.200265i
$754$		0			0
$755$	−472.957	−	222.241i	−0.626433	−	0.294359i
$756$		0			0
$757$	−236.165	+	236.165i	−0.311975	+	0.311975i	−0.845674	−	0.533699i	$-0.820801\pi$
$757$	−236.165	+	236.165i	−0.311975	+	0.311975i	0.533699	+	0.845674i	$0.320801\pi$
$758$		0			0
$759$			39.9356i			0.0526161i
$760$		0			0
$761$			326.095i			0.428508i	0.976778	+	0.214254i	$0.0687321\pi$
$761$			326.095i			0.428508i	−0.976778	+	0.214254i	$0.931268\pi$
$762$		0			0
$763$	−45.4101	−	54.9147i	−0.0595152	−	0.0719721i
$764$		0			0
$765$	−59.4946	−	164.970i	−0.0777707	−	0.215646i
$766$		0			0
$767$	−265.796	−	265.796i	−0.346540	−	0.346540i
$768$		0			0
$769$	194.577			0.253026			0.126513	−	0.991965i	$-0.459621\pi$
$769$	194.577			0.253026			0.126513	+	0.991965i	$0.459621\pi$
$770$		0			0
$771$			312.877i			0.405807i
$772$		0			0
$773$	480.514	−	480.514i	0.621623	−	0.621623i	−0.324324	−	0.945946i	$-0.605137\pi$
$773$	480.514	−	480.514i	0.621623	−	0.621623i	0.945946	+	0.324324i	$0.105137\pi$
$774$		0			0
$775$	314.941	+	379.852i	0.406375	+	0.490131i
$776$		0			0
$777$	−227.043	+	187.746i	−0.292204	+	0.241630i
$778$		0			0
$779$	−465.613			−0.597706
$780$		0			0
$781$	125.262			0.160386
$782$		0			0
$783$	−497.888	−	497.888i	−0.635872	−	0.635872i
$784$		0			0
$785$	−272.022	+	98.1021i	−0.346525	+	0.124971i
$786$		0			0
$787$	747.490	−	747.490i	0.949797	−	0.949797i	−0.0490018	−	0.998799i	$-0.515604\pi$
$787$	747.490	−	747.490i	0.949797	−	0.949797i	0.998799	+	0.0490018i	$0.0156040\pi$
$788$		0			0
$789$	−419.939			−0.532243
$790$		0			0
$791$	−465.227	−	44.0749i	−0.588151	−	0.0557205i
$792$		0			0
$793$	−68.3826	−	68.3826i	−0.0862328	−	0.0862328i
$794$		0			0
$795$	362.052	+	170.127i	0.455411	+	0.213996i
$796$		0			0
$797$	−864.487	−	864.487i	−1.08468	−	1.08468i	−0.996066	−	0.0886105i	$-0.971757\pi$
$797$	−864.487	−	864.487i	−1.08468	−	1.08468i	−0.0886105	−	0.996066i	$-0.528243\pi$
$798$		0			0
$799$	102.536			0.128331
$800$		0			0
$801$			811.262i			1.01281i
$802$		0			0
$803$	61.9808	+	61.9808i	0.0771866	+	0.0771866i
$804$		0			0
$805$	740.871	+	437.812i	0.920336	+	0.543866i
$806$		0			0
$807$	33.6579	+	33.6579i	0.0417075	+	0.0417075i
$808$		0			0
$809$		−	648.082i		−	0.801090i	−0.916277	−	0.400545i	$-0.868821\pi$
$809$		−	648.082i		−	0.801090i	0.916277	−	0.400545i	$-0.131179\pi$
$810$		0			0
$811$	1023.59			1.26213			0.631066	−	0.775729i	$-0.282618\pi$
$811$	1023.59			1.26213			0.631066	+	0.775729i	$0.282618\pi$
$812$		0			0
$813$	−487.732	−	487.732i	−0.599916	−	0.599916i
$814$		0			0
$815$	499.559	+	1385.20i	0.612956	+	1.69964i
$816$		0			0
$817$	362.870	+	362.870i	0.444149	+	0.444149i
$818$		0			0
$819$	−412.575	−	39.0867i	−0.503754	−	0.0477249i
$820$		0			0
$821$	−678.092			−0.825934			−0.412967	−	0.910746i	$-0.635508\pi$
$821$	−678.092			−0.825934			−0.412967	+	0.910746i	$0.635508\pi$
$822$		0			0
$823$	−1003.44	+	1003.44i	−1.21925	+	1.21925i	−0.251350	+	0.967896i	$0.580875\pi$
$823$	−1003.44	+	1003.44i	−1.21925	+	1.21925i	−0.967896	+	0.251350i	$0.919125\pi$
$824$		0			0
$825$	−40.4295	−	3.77712i	−0.0490055	−	0.00457833i
$826$		0			0
$827$	−173.348	−	173.348i	−0.209611	−	0.209611i	0.594491	−	0.804102i	$-0.297353\pi$
$827$	−173.348	−	173.348i	−0.209611	−	0.209611i	−0.804102	+	0.594491i	$0.797353\pi$
$828$		0			0
$829$	1000.54			1.20693			0.603463	−	0.797391i	$-0.293787\pi$
$829$	1000.54			1.20693			0.603463	+	0.797391i	$0.293787\pi$
$830$		0			0
$831$	403.962			0.486115
$832$		0			0
$833$	−193.073	+	131.095i	−0.231781	+	0.157377i
$834$		0			0
$835$	32.8676	+	91.1370i	0.0393624	+	0.109146i
$836$		0			0
$837$	−292.096	+	292.096i	−0.348979	+	0.348979i
$838$		0			0
$839$		−	709.026i		−	0.845085i	−0.906343	−	0.422542i	$-0.861138\pi$
$839$		−	709.026i		−	0.845085i	0.906343	−	0.422542i	$-0.138862\pi$
$840$		0			0
$841$	−290.845			−0.345833
$842$		0			0
$843$	−197.532	−	197.532i	−0.234321	−	0.234321i
$844$		0			0
$845$	−472.308	−	221.936i	−0.558944	−	0.262646i
$846$		0			0
$847$	−644.037	+	532.567i	−0.760374	+	0.628769i
$848$		0			0
$849$		−	129.465i		−	0.152491i
$850$		0			0
$851$			809.120i			0.950787i
$852$		0			0
$853$	−69.5704	+	69.5704i	−0.0815596	+	0.0815596i	−0.746710	−	0.665150i	$-0.768368\pi$
$853$	−69.5704	+	69.5704i	−0.0815596	+	0.0815596i	0.665150	+	0.746710i	$0.268368\pi$
$854$		0			0
$855$	165.294	−	351.766i	0.193326	−	0.411422i
$856$		0			0
$857$	−696.784	−	696.784i	−0.813050	−	0.813050i	0.172040	−	0.985090i	$-0.444964\pi$
$857$	−696.784	−	696.784i	−0.813050	−	0.813050i	−0.985090	+	0.172040i	$0.944964\pi$
$858$		0			0
$859$			1271.54i			1.48026i	0.672466	+	0.740128i	$0.265235\pi$
$859$			1271.54i			1.48026i	−0.672466	+	0.740128i	$0.734765\pi$
$860$		0			0
$861$	−37.2468	+	393.154i	−0.0432599	+	0.456625i
$862$		0			0
$863$	292.312	−	292.312i	0.338717	−	0.338717i	−0.517168	−	0.855884i	$-0.673014\pi$
$863$	292.312	−	292.312i	0.338717	−	0.338717i	0.855884	+	0.517168i	$0.173014\pi$
$864$		0			0
$865$	−506.894	−	1405.54i	−0.586005	−	1.62490i
$866$		0			0
$867$	240.846	−	240.846i	0.277792	−	0.277792i
$868$		0			0
$869$			16.9267i			0.0194784i
$870$		0			0
$871$	557.302			0.639842
$872$		0			0
$873$	400.354	−	400.354i	0.458596	−	0.458596i
$874$		0			0
$875$	−513.298	+	708.625i	−0.586627	+	0.809857i
$876$		0			0
$877$	647.803	−	647.803i	0.738658	−	0.738658i	−0.233660	−	0.972318i	$-0.575070\pi$
$877$	647.803	−	647.803i	0.738658	−	0.738658i	0.972318	+	0.233660i	$0.0750702\pi$
$878$		0			0
$879$	127.703			0.145282
$880$		0			0
$881$			1482.05i			1.68224i	0.540852	+	0.841118i	$0.318102\pi$
$881$			1482.05i			1.68224i	−0.540852	+	0.841118i	$0.681898\pi$
$882$		0			0
$883$	450.273	−	450.273i	0.509935	−	0.509935i	−0.404571	−	0.914506i	$-0.632579\pi$
$883$	450.273	−	450.273i	0.509935	−	0.509935i	0.914506	+	0.404571i	$0.132579\pi$
$884$		0			0
$885$	−101.437	−	281.270i	−0.114618	−	0.317819i
$886$		0			0
$887$	−565.300	+	565.300i	−0.637317	+	0.637317i	−0.949893	−	0.312576i	$-0.898808\pi$
$887$	−565.300	+	565.300i	−0.637317	+	0.637317i	0.312576	+	0.949893i	$0.398808\pi$
$888$		0			0
$889$	−471.095	−	44.6308i	−0.529916	−	0.0502034i
$890$		0			0
$891$			50.1771i			0.0563155i
$892$		0			0
$893$	160.689	+	160.689i	0.179942	+	0.179942i
$894$		0			0
$895$	−201.747	+	429.342i	−0.225415	+	0.479712i
$896$		0			0
$897$	178.760	−	178.760i	0.199287	−	0.199287i
$898$		0			0
$899$			664.020i			0.738620i
$900$		0			0
$901$			297.936i			0.330672i
$902$		0			0
$903$	335.427	−	277.372i	0.371459	−	0.307167i
$904$		0			0
$905$	1195.62	+	561.817i	1.32112	+	0.620792i
$906$		0			0
$907$	−431.192	−	431.192i	−0.475405	−	0.475405i	0.428254	−	0.903659i	$-0.359129\pi$
$907$	−431.192	−	431.192i	−0.475405	−	0.475405i	−0.903659	+	0.428254i	$0.859129\pi$
$908$		0			0
$909$	−773.986			−0.851470
$910$		0			0
$911$		−	737.904i		−	0.809993i	−0.914318	−	0.404997i	$-0.867273\pi$
$911$		−	737.904i		−	0.809993i	0.914318	−	0.404997i	$-0.132727\pi$
$912$		0			0
$913$	52.8490	−	52.8490i	0.0578850	−	0.0578850i
$914$		0			0
$915$	−26.0972	−	72.3637i	−0.0285216	−	0.0790860i
$916$		0			0
$917$	1306.55	−	1080.41i	1.42481	−	1.17820i
$918$		0			0
$919$	−1502.99			−1.63546			−0.817729	−	0.575603i	$-0.804767\pi$
$919$	−1502.99			−1.63546			−0.817729	+	0.575603i	$0.804767\pi$
$920$		0			0
$921$	555.209			0.602832
$922$		0			0
$923$	−560.697	−	560.697i	−0.607473	−	0.607473i
$924$		0			0
$925$	−819.127	−	76.5268i	−0.885543	−	0.0827316i
$926$		0			0
$927$	−468.663	+	468.663i	−0.505569	+	0.505569i
$928$		0			0
$929$	1160.37			1.24905			0.624525	−	0.781004i	$-0.285292\pi$
$929$	1160.37			1.24905			0.624525	+	0.781004i	$0.285292\pi$
$930$		0			0
$931$	−508.015	−	97.1289i	−0.545666	−	0.104327i
$932$		0			0
$933$	−376.491	−	376.491i	−0.403528	−	0.403528i
$934$		0			0
$935$	−10.2598	−	28.4488i	−0.0109730	−	0.0304265i
$936$		0			0
$937$	514.044	+	514.044i	0.548606	+	0.548606i	0.926038	−	0.377431i	$-0.123193\pi$
$937$	514.044	+	514.044i	0.548606	+	0.548606i	−0.377431	+	0.926038i	$0.623193\pi$
$938$		0			0
$939$	−642.318			−0.684045
$940$		0			0
$941$			497.636i			0.528838i	0.964408	+	0.264419i	$0.0851801\pi$
$941$			497.636i			0.528838i	−0.964408	+	0.264419i	$0.914820\pi$
$942$		0			0
$943$	766.917	+	766.917i	0.813273	+	0.813273i
$944$		0			0
$945$	−630.639	−	372.671i	−0.667342	−	0.394361i
$946$		0			0
$947$	604.530	+	604.530i	0.638363	+	0.638363i	0.950152	−	0.311789i	$-0.100928\pi$
$947$	604.530	+	604.530i	0.638363	+	0.638363i	−0.311789	+	0.950152i	$0.600928\pi$
$948$		0			0
$949$		−	554.879i		−	0.584699i
$950$		0			0
$951$	−161.305			−0.169616
$952$		0			0
$953$	−1107.39	−	1107.39i	−1.16200	−	1.16200i	−0.984037	−	0.177965i	$-0.943049\pi$
$953$	−1107.39	−	1107.39i	−1.16200	−	1.16200i	−0.177965	−	0.984037i	$-0.556951\pi$
$954$		0			0
$955$	−514.355	−	241.694i	−0.538592	−	0.253083i
$956$		0			0
$957$	−38.6388	−	38.6388i	−0.0403750	−	0.0403750i
$958$		0			0
$959$	120.916	−	1276.31i	0.126085	−	1.33088i
$960$		0			0
$961$	−571.440			−0.594630
$962$		0			0
$963$	−500.181	+	500.181i	−0.519399	+	0.519399i
$964$		0			0
$965$	−1272.22	+	458.814i	−1.31836	+	0.475455i
$966$		0			0
$967$	−710.155	−	710.155i	−0.734390	−	0.734390i	0.237097	−	0.971486i	$-0.423804\pi$
$967$	−710.155	−	710.155i	−0.734390	−	0.734390i	−0.971486	+	0.237097i	$0.923804\pi$
$968$		0			0
$969$	−64.2966			−0.0663536
$970$		0			0
$971$	1519.61			1.56500			0.782500	−	0.622651i	$-0.213944\pi$
$971$	1519.61			1.56500			0.782500	+	0.622651i	$0.213944\pi$
$972$		0			0
$973$	−793.439	−	959.511i	−0.815457	−	0.986137i
$974$		0			0
$975$	164.064	+	197.878i	0.168271	+	0.202952i
$976$		0			0
$977$	−361.913	+	361.913i	−0.370433	+	0.370433i	−0.867635	−	0.497202i	$-0.834361\pi$
$977$	−361.913	+	361.913i	−0.370433	+	0.370433i	0.497202	+	0.867635i	$0.334361\pi$
$978$		0			0
$979$			139.901i			0.142902i
$980$		0			0
$981$	74.9662			0.0764181
$982$		0			0
$983$	−83.5940	−	83.5940i	−0.0850397	−	0.0850397i	0.663307	−	0.748347i	$-0.269152\pi$
$983$	−83.5940	−	83.5940i	−0.0850397	−	0.0850397i	−0.748347	+	0.663307i	$0.769152\pi$
$984$		0			0
$985$	−148.582	−	411.996i	−0.150845	−	0.418270i
$986$		0			0
$987$	148.536	−	122.828i	0.150493	−	0.124445i
$988$		0			0
$989$		−	1195.37i		−	1.20867i
$990$		0			0
$991$			1610.97i			1.62560i	0.582543	+	0.812800i	$0.302058\pi$
$991$			1610.97i			1.62560i	−0.582543	+	0.812800i	$0.697942\pi$
$992$		0			0
$993$	258.698	−	258.698i	0.260522	−	0.260522i
$994$		0			0
$995$	92.5525	+	43.4901i	0.0930176	+	0.0437086i
$996$		0			0
$997$	−524.198	−	524.198i	−0.525775	−	0.525775i	0.393535	−	0.919310i	$-0.371252\pi$
$997$	−524.198	−	524.198i	−0.525775	−	0.525775i	−0.919310	+	0.393535i	$0.871252\pi$
$998$		0			0
$999$		−	688.733i		−	0.689423i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.3.v.b.223.20	yes	64
4.3	odd	2	inner	560.3.v.b.223.13	✓	64
5.2	odd	4	inner	560.3.v.b.447.19	yes	64
7.6	odd	2	inner	560.3.v.b.223.14	yes	64
20.7	even	4	inner	560.3.v.b.447.14	yes	64
28.27	even	2	inner	560.3.v.b.223.19	yes	64
35.27	even	4	inner	560.3.v.b.447.13	yes	64
140.27	odd	4	inner	560.3.v.b.447.20	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.3.v.b.223.13	✓	64	4.3	odd	2	inner
560.3.v.b.223.14	yes	64	7.6	odd	2	inner
560.3.v.b.223.19	yes	64	28.27	even	2	inner
560.3.v.b.223.20	yes	64	1.1	even	1	trivial
560.3.v.b.447.13	yes	64	35.27	even	4	inner
560.3.v.b.447.14	yes	64	20.7	even	4	inner
560.3.v.b.447.19	yes	64	5.2	odd	4	inner
560.3.v.b.447.20	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)

\(f(q)\)	\(=\)	\(q+(0.904360 + 0.904360i) q^{3} +(-2.12642 + 4.52530i) q^{5} +(-5.39452 + 4.46084i) q^{7} -7.36427i q^{9} -1.26996i q^{11} +(-5.68460 + 5.68460i) q^{13} +(-6.01555 + 2.16945i) q^{15} +(-3.36775 - 3.36775i) q^{17} -10.5554i q^{19} +(-8.91279 - 0.844384i) q^{21} +(-17.3860 + 17.3860i) q^{23} +(-15.9567 - 19.2454i) q^{25} +(14.7992 - 14.7992i) q^{27} -33.6429i q^{29} -19.7373 q^{31} +(1.14850 - 1.14850i) q^{33} +(-8.71560 - 33.8975i) q^{35} +(23.2693 - 23.2693i) q^{37} -10.2819 q^{39} -44.1112i q^{41} +(-34.3775 + 34.3775i) q^{43} +(33.3255 + 15.6595i) q^{45} +(-15.2233 + 15.2233i) q^{47} +(9.20178 - 48.1282i) q^{49} -6.09132i q^{51} +(-44.2336 - 44.2336i) q^{53} +(5.74694 + 2.70047i) q^{55} +(9.54592 - 9.54592i) q^{57} +46.7572i q^{59} +12.0294i q^{61} +(32.8508 + 39.7267i) q^{63} +(-13.6367 - 37.8124i) q^{65} +(-49.0186 - 49.0186i) q^{67} -31.4464 q^{69} +98.6344i q^{71} +(-48.8054 + 48.8054i) q^{73} +(2.97421 - 31.8353i) q^{75} +(5.66508 + 6.85082i) q^{77} -13.3286 q^{79} -39.5108 q^{81} +(41.6147 + 41.6147i) q^{83} +(22.4014 - 8.07882i) q^{85} +(30.4253 - 30.4253i) q^{87} -110.162 q^{89} +(5.30761 - 56.0238i) q^{91} +(-17.8496 - 17.8496i) q^{93} +(47.7666 + 22.4453i) q^{95} +(54.3644 + 54.3644i) q^{97} -9.35231 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 16 q^{21} - 72 q^{25} + 72 q^{37} + 272 q^{53} - 376 q^{57} - 88 q^{65} + 24 q^{77} - 432 q^{81} + 384 q^{85} + 840 q^{93}+O(q^{100}) \) 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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