LMFDB - Embedded newform 224.3.r.c.191.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,3,Mod(95,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 4]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("224.95");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	224.r (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.10355792167$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 28 x^{9} - 100 x^{8} + 140 x^{7} + 392 x^{6} + 1400 x^{5} + 8040 x^{4} + 11256 x^{3} + \cdots + 9604 $ x^12 - 28x^9 - 100x^8 + 140x^7 + 392x^6 + 1400x^5 + 8040x^4 + 11256x^3 + 9800x^2 + 13720*x + 9604
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			191.5
Root			$-0.924901 - 3.45178i$ of defining polynomial
Character	$\chi$	$=$	224.191
Dual form			224.3.r.c.95.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.51065 - 2.02688i) q^{3} +(1.21646 - 2.10698i) q^{5} +(-2.97300 - 6.33729i) q^{7} +(3.71646 - 6.43710i) q^{9} +O(q^{10})$	\(q+(3.51065 - 2.02688i) q^{3} +(1.21646 - 2.10698i) q^{5} +(-2.97300 - 6.33729i) q^{7} +(3.71646 - 6.43710i) q^{9} +(6.39055 - 3.68959i) q^{11} -8.56707 q^{13} -9.86249i q^{15} +(-7.45812 - 12.9178i) q^{17} +(22.9151 + 13.2300i) q^{19} +(-23.2821 - 16.2221i) q^{21} +(12.9208 + 7.45980i) q^{23} +(9.54044 + 16.5245i) q^{25} +6.35253i q^{27} -52.0780 q^{29} +(18.4688 - 10.6629i) q^{31} +(14.9567 - 25.9057i) q^{33} +(-16.9691 - 1.44504i) q^{35} +(10.9063 - 18.8902i) q^{37} +(-30.0760 + 17.3644i) q^{39} +58.5138 q^{41} -58.6983i q^{43} +(-9.04188 - 15.6610i) q^{45} +(57.4110 + 33.1463i) q^{47} +(-31.3225 + 37.6816i) q^{49} +(-52.3658 - 30.2334i) q^{51} +(36.0642 + 62.4650i) q^{53} -17.9530i q^{55} +107.263 q^{57} +(-15.3096 + 8.83897i) q^{59} +(-44.1746 + 76.5126i) q^{61} +(-51.8428 - 4.41480i) q^{63} +(-10.4215 + 18.0506i) q^{65} +(-80.0413 + 46.2119i) q^{67} +60.4804 q^{69} -11.8459i q^{71} +(-33.2555 - 57.6001i) q^{73} +(66.9863 + 38.6746i) q^{75} +(-42.3811 - 29.5296i) q^{77} +(15.9202 + 9.19151i) q^{79} +(46.3240 + 80.2355i) q^{81} +101.779i q^{83} -36.2901 q^{85} +(-182.828 + 105.556i) q^{87} +(-23.2850 + 40.3308i) q^{89} +(25.4699 + 54.2920i) q^{91} +(43.2250 - 74.8678i) q^{93} +(55.7507 - 32.1877i) q^{95} -135.924 q^{97} -54.8488i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{5} + 32 q^{9}+O(q^{10}) $ 12 * q + 2 * q^5 + 32 * q^9	$ 12 q + 2 q^{5} + 32 q^{9} - 128 q^{13} - 6 q^{17} - 62 q^{21} - 32 q^{25} + 128 q^{29} - 134 q^{33} - 66 q^{37} + 384 q^{41} - 192 q^{45} - 12 q^{49} - 2 q^{53} + 468 q^{57} - 434 q^{61} + 160 q^{65} + 124 q^{69} - 10 q^{73} - 370 q^{77} + 422 q^{81} + 1020 q^{85} - 522 q^{89} + 306 q^{93} - 768 q^{97}+O(q^{100}) $ 12 * q + 2 * q^5 + 32 * q^9 - 128 * q^13 - 6 * q^17 - 62 * q^21 - 32 * q^25 + 128 * q^29 - 134 * q^33 - 66 * q^37 + 384 * q^41 - 192 * q^45 - 12 * q^49 - 2 * q^53 + 468 * q^57 - 434 * q^61 + 160 * q^65 + 124 * q^69 - 10 * q^73 - 370 * q^77 + 422 * q^81 + 1020 * q^85 - 522 * q^89 + 306 * q^93 - 768 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	3.51065	−	2.02688i	1.17022	−	0.675626i	0.216487	−	0.976286i	$-0.430540\pi$
$3$	3.51065	−	2.02688i	1.17022	−	0.675626i	0.953731	+	0.300660i	$0.0972069\pi$
$4$		0			0
$5$	1.21646	−	2.10698i	0.243293	−	0.421395i	−0.718358	−	0.695674i	$-0.755106\pi$
$5$	1.21646	−	2.10698i	0.243293	−	0.421395i	0.961650	+	0.274279i	$0.0884391\pi$
$6$		0			0
$7$	−2.97300	−	6.33729i	−0.424714	−	0.905327i
$7$	−2.97300	−	6.33729i	−0.424714	−	0.905327i
$8$		0			0
$9$	3.71646	−	6.43710i	0.412940	−	0.715234i
$10$		0			0
$11$	6.39055	−	3.68959i	0.580959	−	0.335417i	−0.180555	−	0.983565i	$-0.557789\pi$
$11$	6.39055	−	3.68959i	0.580959	−	0.335417i	0.761514	+	0.648148i	$0.224456\pi$
$12$		0			0
$13$	−8.56707			−0.659006			−0.329503	−	0.944155i	$-0.606881\pi$
$13$	−8.56707			−0.659006			−0.329503	+	0.944155i	$0.606881\pi$
$14$		0			0
$15$		−	9.86249i		−	0.657499i
$16$		0			0
$17$	−7.45812	−	12.9178i	−0.438713	−	0.759873i	0.558878	−	0.829250i	$-0.311232\pi$
$17$	−7.45812	−	12.9178i	−0.438713	−	0.759873i	−0.997591	+	0.0693771i	$0.977899\pi$
$18$		0			0
$19$	22.9151	+	13.2300i	1.20606	+	0.696317i	0.961895	−	0.273418i	$-0.0881542\pi$
$19$	22.9151	+	13.2300i	1.20606	+	0.696317i	0.244161	+	0.969735i	$0.421488\pi$
$20$		0			0
$21$	−23.2821	−	16.2221i	−1.10867	−	0.772482i
$22$		0			0
$23$	12.9208	+	7.45980i	0.561772	+	0.324339i	0.753856	−	0.657039i	$-0.228191\pi$
$23$	12.9208	+	7.45980i	0.561772	+	0.324339i	−0.192084	+	0.981378i	$0.561525\pi$
$24$		0			0
$25$	9.54044	+	16.5245i	0.381617	+	0.660981i
$26$		0			0
$27$			6.35253i			0.235279i
$28$		0			0
$29$	−52.0780			−1.79579			−0.897896	−	0.440207i	$-0.854905\pi$
$29$	−52.0780			−1.79579			−0.897896	+	0.440207i	$0.854905\pi$
$30$		0			0
$31$	18.4688	−	10.6629i	0.595767	−	0.343966i	−0.171608	−	0.985165i	$-0.554896\pi$
$31$	18.4688	−	10.6629i	0.595767	−	0.343966i	0.767374	+	0.641199i	$0.221563\pi$
$32$		0			0
$33$	14.9567	−	25.9057i	0.453233	−	0.785022i
$34$		0			0
$35$	−16.9691	−	1.44504i	−0.484830	−	0.0412868i
$36$		0			0
$37$	10.9063	−	18.8902i	0.294765	−	0.510547i	−0.680166	−	0.733059i	$-0.738092\pi$
$37$	10.9063	−	18.8902i	0.294765	−	0.510547i	0.974930	+	0.222511i	$0.0714255\pi$
$38$		0			0
$39$	−30.0760	+	17.3644i	−0.771180	+	0.445241i
$40$		0			0
$41$	58.5138			1.42717			0.713583	−	0.700571i	$-0.247071\pi$
$41$	58.5138			1.42717			0.713583	+	0.700571i	$0.247071\pi$
$42$		0			0
$43$		−	58.6983i		−	1.36508i	−0.730849	−	0.682539i	$-0.760876\pi$
$43$		−	58.6983i		−	1.36508i	0.730849	−	0.682539i	$-0.239124\pi$
$44$		0			0
$45$	−9.04188	−	15.6610i	−0.200931	−	0.348022i
$46$		0			0
$47$	57.4110	+	33.1463i	1.22151	+	0.705240i	0.965240	−	0.261365i	$-0.0841728\pi$
$47$	57.4110	+	33.1463i	1.22151	+	0.705240i	0.256271	+	0.966605i	$0.417506\pi$
$48$		0			0
$49$	−31.3225	+	37.6816i	−0.639235	+	0.769011i
$50$		0			0
$51$	−52.3658	−	30.2334i	−1.02678	−	0.592812i
$52$		0			0
$53$	36.0642	+	62.4650i	0.680456	+	1.17858i	0.974842	+	0.222898i	$0.0715517\pi$
$53$	36.0642	+	62.4650i	0.680456	+	1.17858i	−0.294385	+	0.955687i	$0.595115\pi$
$54$		0			0
$55$		−	17.9530i		−	0.326418i
$56$		0			0
$57$	107.263			1.88180
$58$		0			0
$59$	−15.3096	+	8.83897i	−0.259484	+	0.149813i	−0.624099	−	0.781345i	$-0.714534\pi$
$59$	−15.3096	+	8.83897i	−0.259484	+	0.149813i	0.364615	+	0.931158i	$0.381201\pi$
$60$		0			0
$61$	−44.1746	+	76.5126i	−0.724173	+	1.25431i	0.235140	+	0.971962i	$0.424445\pi$
$61$	−44.1746	+	76.5126i	−0.724173	+	1.25431i	−0.959313	+	0.282344i	$0.908888\pi$
$62$		0			0
$63$	−51.8428	−	4.41480i	−0.822902	−	0.0700761i
$64$		0			0
$65$	−10.4215	+	18.0506i	−0.160331	+	0.277702i
$66$		0			0
$67$	−80.0413	+	46.2119i	−1.19465	+	0.689730i	−0.959357	−	0.282196i	$-0.908937\pi$
$67$	−80.0413	+	46.2119i	−1.19465	+	0.689730i	−0.235290	+	0.971925i	$0.575604\pi$
$68$		0			0
$69$	60.4804			0.876528
$70$		0			0
$71$		−	11.8459i		−	0.166844i	−0.996514	−	0.0834222i	$-0.973415\pi$
$71$		−	11.8459i		−	0.166844i	0.996514	−	0.0834222i	$-0.0265850\pi$
$72$		0			0
$73$	−33.2555	−	57.6001i	−0.455554	−	0.789043i	0.543166	−	0.839626i	$-0.317226\pi$
$73$	−33.2555	−	57.6001i	−0.455554	−	0.789043i	−0.998720	+	0.0505826i	$0.983892\pi$
$74$		0			0
$75$	66.9863	+	38.6746i	0.893151	+	0.515661i
$76$		0			0
$77$	−42.3811	−	29.5296i	−0.550404	−	0.383502i
$78$		0			0
$79$	15.9202	+	9.19151i	0.201521	+	0.116348i	0.597365	−	0.801970i	$-0.296214\pi$
$79$	15.9202	+	9.19151i	0.201521	+	0.116348i	−0.395844	+	0.918318i	$0.629548\pi$
$80$		0			0
$81$	46.3240	+	80.2355i	0.571901	+	0.990561i
$82$		0			0
$83$			101.779i			1.22626i	0.789984	+	0.613128i	$0.210089\pi$
$83$			101.779i			1.22626i	−0.789984	+	0.613128i	$0.789911\pi$
$84$		0			0
$85$	−36.2901			−0.426942
$86$		0			0
$87$	−182.828	+	105.556i	−2.10147	+	1.21328i
$88$		0			0
$89$	−23.2850	+	40.3308i	−0.261629	+	0.453155i	−0.966675	−	0.256007i	$-0.917593\pi$
$89$	−23.2850	+	40.3308i	−0.261629	+	0.453155i	0.705046	+	0.709162i	$0.250926\pi$
$90$		0			0
$91$	25.4699	+	54.2920i	0.279889	+	0.596616i
$92$		0			0
$93$	43.2250	−	74.8678i	0.464785	−	0.805031i
$94$		0			0
$95$	55.7507	−	32.1877i	0.586849	−	0.338818i
$96$		0			0
$97$	−135.924			−1.40128			−0.700639	−	0.713516i	$-0.747102\pi$
$97$	−135.924			−1.40128			−0.700639	+	0.713516i	$0.747102\pi$
$98$		0			0
$99$		−	54.8488i		−	0.554029i
$100$		0			0
$101$	44.7274	+	77.4701i	0.442845	+	0.767030i	0.997899	−	0.0647838i	$-0.0206358\pi$
$101$	44.7274	+	77.4701i	0.442845	+	0.767030i	−0.555054	+	0.831814i	$0.687302\pi$
$102$		0			0
$103$	4.54400	+	2.62348i	0.0441165	+	0.0254707i	0.521896	−	0.853009i	$-0.325225\pi$
$103$	4.54400	+	2.62348i	0.0441165	+	0.0254707i	−0.477780	+	0.878480i	$0.658558\pi$
$104$		0			0
$105$	−62.5014	+	29.3212i	−0.595252	+	0.279249i
$106$		0			0
$107$	−13.0278	−	7.52159i	−0.121755	−	0.0702952i	0.437886	−	0.899031i	$-0.355727\pi$
$107$	−13.0278	−	7.52159i	−0.121755	−	0.0702952i	−0.559641	+	0.828735i	$0.689061\pi$
$108$		0			0
$109$	3.67603	+	6.36707i	0.0337250	+	0.0584135i	0.882395	−	0.470509i	$-0.155930\pi$
$109$	3.67603	+	6.36707i	0.0337250	+	0.0584135i	−0.848670	+	0.528922i	$0.822596\pi$
$110$		0			0
$111$		−	88.4228i		−	0.796602i
$112$		0			0
$113$	170.683			1.51047			0.755236	−	0.655454i	$-0.227522\pi$
$113$	170.683			1.51047			0.755236	+	0.655454i	$0.227522\pi$
$114$		0			0
$115$	31.4353	−	18.1492i	0.273350	−	0.157819i
$116$		0			0
$117$	−31.8392	+	55.1471i	−0.272130	+	0.471343i
$118$		0			0
$119$	−59.6911	+	85.6690i	−0.501606	+	0.719908i
$120$		0			0
$121$	−33.2739	+	57.6321i	−0.274991	+	0.476298i
$122$		0			0
$123$	205.422	−	118.600i	1.67010	−	0.964230i
$124$		0			0
$125$	107.246			0.857964
$126$		0			0
$127$		−	194.746i		−	1.53343i	−0.641987	−	0.766716i	$-0.721890\pi$
$127$		−	194.746i		−	1.53343i	0.641987	−	0.766716i	$-0.278110\pi$
$128$		0			0
$129$	−118.974	−	206.070i	−0.922282	−	1.59744i
$130$		0			0
$131$	−25.9409	−	14.9770i	−0.198022	−	0.114328i	0.397711	−	0.917511i	$-0.369805\pi$
$131$	−25.9409	−	14.9770i	−0.198022	−	0.114328i	−0.595732	+	0.803183i	$0.703138\pi$
$132$		0			0
$133$	15.7160	−	184.552i	0.118165	−	1.38761i
$134$		0			0
$135$	13.3846	+	7.72762i	0.0991454	+	0.0572416i
$136$		0			0
$137$	−88.9157	−	154.007i	−0.649020	−	1.12414i	−0.983357	−	0.181682i	$-0.941846\pi$
$137$	−88.9157	−	154.007i	−0.649020	−	1.12414i	0.334337	−	0.942454i	$-0.391488\pi$
$138$		0			0
$139$		−	120.142i		−	0.864334i	−0.901793	−	0.432167i	$-0.857749\pi$
$139$		−	120.142i		−	0.864334i	0.901793	−	0.432167i	$-0.142251\pi$
$140$		0			0
$141$	268.734			1.90591
$142$		0			0
$143$	−54.7483	+	31.6090i	−0.382855	+	0.221042i
$144$		0			0
$145$	−63.3509	+	109.727i	−0.436903	+	0.756738i
$146$		0			0
$147$	−33.5867	+	195.774i	−0.228481	+	1.33179i
$148$		0			0
$149$	41.2640	−	71.4713i	0.276939	−	0.479673i	−0.693683	−	0.720280i	$-0.744013\pi$
$149$	41.2640	−	71.4713i	0.276939	−	0.479673i	0.970623	+	0.240607i	$0.0773466\pi$
$150$		0			0
$151$	246.068	−	142.067i	1.62959	−	0.940843i	0.645373	−	0.763868i	$-0.276702\pi$
$151$	246.068	−	142.067i	1.62959	−	0.940843i	0.984215	−	0.176975i	$-0.0566312\pi$
$152$		0			0
$153$	−110.871			−0.724649
$154$		0			0
$155$		−	51.8843i		−	0.334738i
$156$		0			0
$157$	−28.1271	−	48.7175i	−0.179153	−	0.310303i	0.762437	−	0.647062i	$-0.224003\pi$
$157$	−28.1271	−	48.7175i	−0.179153	−	0.310303i	−0.941591	+	0.336759i	$0.890669\pi$
$158$		0			0
$159$	253.218	+	146.195i	1.59256	+	0.919468i
$160$		0			0
$161$	8.86152	−	104.061i	0.0550405	−	0.646339i
$162$		0			0
$163$	−166.695	−	96.2414i	−1.02267	−	0.590438i	−0.107793	−	0.994173i	$-0.534378\pi$
$163$	−166.695	−	96.2414i	−1.02267	−	0.590438i	−0.914876	+	0.403735i	$0.867712\pi$
$164$		0			0
$165$	−36.3885	−	63.0267i	−0.220536	−	0.381980i
$166$		0			0
$167$		−	132.185i		−	0.791530i	−0.918352	−	0.395765i	$-0.870480\pi$
$167$		−	132.185i		−	0.791530i	0.918352	−	0.395765i	$-0.129520\pi$
$168$		0			0
$169$	−95.6052			−0.565712
$170$		0			0
$171$	170.326	−	98.3378i	0.996059	−	0.575075i
$172$		0			0
$173$	−102.145	+	176.920i	−0.590434	+	1.02266i	0.403740	+	0.914874i	$0.367710\pi$
$173$	−102.145	+	176.920i	−0.590434	+	1.02266i	−0.994174	+	0.107788i	$0.965623\pi$
$174$		0			0
$175$	76.3570	−	109.588i	0.436326	−	0.626217i
$176$		0			0
$177$	−35.8310	+	62.0612i	−0.202435	+	0.350628i
$178$		0			0
$179$	−106.903	+	61.7205i	−0.597224	+	0.344808i	−0.767949	−	0.640511i	$-0.778722\pi$
$179$	−106.903	+	61.7205i	−0.597224	+	0.344808i	0.170725	+	0.985319i	$0.445389\pi$
$180$		0			0
$181$	−131.612			−0.727136			−0.363568	−	0.931568i	$-0.618442\pi$
$181$	−131.612			−0.727136			−0.363568	+	0.931568i	$0.618442\pi$
$182$		0			0
$183$			358.146i			1.95708i
$184$		0			0
$185$	−26.5342	−	45.9586i	−0.143428	−	0.248425i
$186$		0			0
$187$	−95.3230	−	55.0347i	−0.509749	−	0.294303i
$188$		0			0
$189$	40.2579	−	18.8861i	0.213005	−	0.0999264i
$190$		0			0
$191$	149.814	+	86.4954i	0.784369	+	0.452856i	0.837976	−	0.545706i	$-0.183739\pi$
$191$	149.814	+	86.4954i	0.784369	+	0.452856i	−0.0536074	+	0.998562i	$0.517072\pi$
$192$		0			0
$193$	−99.7579	−	172.786i	−0.516880	−	0.895263i	−0.999808	−	0.0196024i	$-0.993760\pi$
$193$	−99.7579	−	172.786i	−0.516880	−	0.895263i	0.482928	−	0.875660i	$-0.339573\pi$
$194$		0			0
$195$			84.4926i			0.433296i
$196$		0			0
$197$	−9.40658			−0.0477492			−0.0238746	−	0.999715i	$-0.507600\pi$
$197$	−9.40658			−0.0477492			−0.0238746	+	0.999715i	$0.507600\pi$
$198$		0			0
$199$	−266.746	+	154.006i	−1.34043	+	0.773899i	−0.986871	−	0.161513i	$-0.948363\pi$
$199$	−266.746	+	154.006i	−1.34043	+	0.773899i	−0.353561	+	0.935411i	$0.615029\pi$
$200$		0			0
$201$	−187.332	+	324.468i	−0.931998	+	1.61427i
$202$		0			0
$203$	154.828	+	330.033i	0.762699	+	1.62578i
$204$		0			0
$205$	71.1799	−	123.287i	0.347219	−	0.601401i
$206$		0			0
$207$	96.0390	−	55.4482i	0.463957	−	0.267866i
$208$		0			0
$209$	195.253			0.934226
$210$		0			0
$211$		−	274.103i		−	1.29906i	−0.760334	−	0.649532i	$-0.774965\pi$
$211$		−	274.103i		−	1.29906i	0.760334	−	0.649532i	$-0.225035\pi$
$212$		0			0
$213$	−24.0103	−	41.5870i	−0.112724	−	0.195244i
$214$		0			0
$215$	−123.676	−	71.4044i	−0.575237	−	0.332113i
$216$		0			0
$217$	−122.482	−	85.3410i	−0.564433	−	0.393276i
$218$		0			0
$219$	−233.497	−	134.809i	−1.06620	−	0.615568i
$220$		0			0
$221$	63.8943	+	110.668i	0.289114	+	0.500761i
$222$		0			0
$223$		−	93.9923i		−	0.421490i	−0.977541	−	0.210745i	$-0.932411\pi$
$223$		−	93.9923i		−	0.421490i	0.977541	−	0.210745i	$-0.0675890\pi$
$224$		0			0
$225$	141.827			0.630341
$226$		0			0
$227$	−136.226	+	78.6500i	−0.600113	+	0.346476i	−0.769086	−	0.639145i	$-0.779288\pi$
$227$	−136.226	+	78.6500i	−0.600113	+	0.346476i	0.168973	+	0.985621i	$0.445955\pi$
$228$		0			0
$229$	−41.1365	+	71.2506i	−0.179636	+	0.311138i	−0.941756	−	0.336298i	$-0.890825\pi$
$229$	−41.1365	+	71.2506i	−0.179636	+	0.311138i	0.762120	+	0.647436i	$0.224159\pi$
$230$		0			0
$231$	−208.638	−	17.7671i	−0.903196	−	0.0769137i
$232$		0			0
$233$	166.177	−	287.828i	0.713207	−	1.23531i	−0.250440	−	0.968132i	$-0.580575\pi$
$233$	166.177	−	287.828i	0.713207	−	1.23531i	0.963647	−	0.267179i	$-0.0860915\pi$
$234$		0			0
$235$	139.677	−	80.6424i	0.594369	−	0.343159i
$236$		0			0
$237$	74.5202			0.314431
$238$		0			0
$239$			36.6386i			0.153300i	0.997058	+	0.0766499i	$0.0244224\pi$
$239$			36.6386i			0.153300i	−0.997058	+	0.0766499i	$0.975578\pi$
$240$		0			0
$241$	230.374	+	399.020i	0.955910	+	1.65568i	0.732273	+	0.681011i	$0.238460\pi$
$241$	230.374	+	399.020i	0.955910	+	1.65568i	0.223637	+	0.974673i	$0.428207\pi$
$242$		0			0
$243$	275.742	+	159.200i	1.13474	+	0.655142i
$244$		0			0
$245$	41.2914	+	111.834i	0.168536	+	0.456465i
$246$		0			0
$247$	−196.315	−	113.343i	−0.794798	−	0.458877i
$248$		0			0
$249$	206.294	+	357.312i	0.828490	+	1.43499i
$250$		0			0
$251$		−	23.1867i		−	0.0923775i	−0.998933	−	0.0461887i	$-0.985292\pi$
$251$		−	23.1867i		−	0.0923775i	0.998933	−	0.0461887i	$-0.0147076\pi$
$252$		0			0
$253$	110.094			0.435155
$254$		0			0
$255$	−127.402	+	73.5556i	−0.499616	+	0.288453i
$256$		0			0
$257$	101.126	−	175.155i	0.393486	−	0.681538i	−0.599420	−	0.800434i	$-0.704602\pi$
$257$	101.126	−	175.155i	0.393486	−	0.681538i	0.992907	+	0.118896i	$0.0379356\pi$
$258$		0			0
$259$	−152.137	−	12.9556i	−0.587403	−	0.0500216i
$260$		0			0
$261$	−193.546	+	335.231i	−0.741555	+	1.28441i
$262$		0			0
$263$	−27.1209	+	15.6583i	−0.103121	+	0.0595372i	−0.550674	−	0.834721i	$-0.685629\pi$
$263$	−27.1209	+	15.6583i	−0.103121	+	0.0595372i	0.447552	+	0.894258i	$0.352296\pi$
$264$		0			0
$265$	175.483			0.662200
$266$		0			0
$267$			188.783i			0.707053i
$268$		0			0
$269$	−44.6656	−	77.3631i	−0.166043	−	0.287595i	0.770982	−	0.636857i	$-0.219766\pi$
$269$	−44.6656	−	77.3631i	−0.166043	−	0.287595i	−0.937025	+	0.349262i	$0.886432\pi$
$270$		0			0
$271$	−46.3103	−	26.7372i	−0.170887	−	0.0986614i	0.412117	−	0.911131i	$-0.364789\pi$
$271$	−46.3103	−	26.7372i	−0.170887	−	0.0986614i	−0.583004	+	0.812469i	$0.698123\pi$
$272$		0			0
$273$	199.459	+	138.976i	0.730621	+	0.509070i
$274$		0			0
$275$	121.937	+	70.4005i	0.443408	+	0.256002i
$276$		0			0
$277$	−20.3184	−	35.1924i	−0.0733515	−	0.127048i	0.827017	−	0.562177i	$-0.190036\pi$
$277$	−20.3184	−	35.1924i	−0.0733515	−	0.127048i	−0.900368	+	0.435129i	$0.856703\pi$
$278$		0			0
$279$		−	158.514i		−	0.568150i
$280$		0			0
$281$	5.49585			0.0195582			0.00977910	−	0.999952i	$-0.496887\pi$
$281$	5.49585			0.0195582			0.00977910	+	0.999952i	$0.496887\pi$
$282$		0			0
$283$	255.061	−	147.260i	0.901276	−	0.520352i	0.0236618	−	0.999720i	$-0.492467\pi$
$283$	255.061	−	147.260i	0.901276	−	0.520352i	0.877614	+	0.479368i	$0.159134\pi$
$284$		0			0
$285$	130.481	−	226.000i	0.457828	−	0.792981i
$286$		0			0
$287$	−173.962	−	370.819i	−0.606138	−	1.29205i
$288$		0			0
$289$	33.2529	−	57.5957i	0.115062	−	0.199293i
$290$		0			0
$291$	−477.182	+	275.501i	−1.63980	+	0.946739i
$292$		0			0
$293$	−163.827			−0.559135			−0.279568	−	0.960126i	$-0.590191\pi$
$293$	−163.827			−0.559135			−0.279568	+	0.960126i	$0.590191\pi$
$294$		0			0
$295$			43.0091i			0.145794i
$296$		0			0
$297$	23.4382	+	40.5962i	0.0789165	+	0.136687i
$298$		0			0
$299$	−110.693	−	63.9087i	−0.370211	−	0.213741i
$300$		0			0
$301$	−371.988	+	174.510i	−1.23584	+	0.579768i
$302$		0			0
$303$	314.045	+	181.314i	1.03645	+	0.598395i
$304$		0			0
$305$	107.473	+	186.150i	0.352372	+	0.610326i
$306$		0			0
$307$			559.026i			1.82093i	0.413586	+	0.910465i	$0.364276\pi$
$307$			559.026i			1.82093i	−0.413586	+	0.910465i	$0.635724\pi$
$308$		0			0
$309$	21.2699			0.0688346
$310$		0			0
$311$	−280.938	+	162.199i	−0.903336	+	0.521541i	−0.878281	−	0.478145i	$-0.841309\pi$
$311$	−280.938	+	162.199i	−0.903336	+	0.521541i	−0.0250551	+	0.999686i	$0.507976\pi$
$312$		0			0
$313$	50.9596	−	88.2646i	0.162810	−	0.281995i	−0.773065	−	0.634326i	$-0.781278\pi$
$313$	50.9596	−	88.2646i	0.162810	−	0.281995i	0.935875	+	0.352331i	$0.114611\pi$
$314$		0			0
$315$	−72.3668	+	103.861i	−0.229736	+	0.329718i
$316$		0			0
$317$	−274.099	+	474.754i	−0.864667	+	1.49765i	0.00271028	+	0.999996i	$0.499137\pi$
$317$	−274.099	+	474.754i	−0.864667	+	1.49765i	−0.867377	+	0.497651i	$0.834196\pi$
$318$		0			0
$319$	−332.807	+	192.146i	−1.04328	+	0.602339i
$320$		0			0
$321$	−60.9813			−0.189973
$322$		0			0
$323$		−	394.684i		−	1.22193i
$324$		0			0
$325$	−81.7336	−	141.567i	−0.251488	−	0.435590i
$326$		0			0
$327$	25.8105	+	14.9017i	0.0789313	+	0.0455710i
$328$		0			0
$329$	39.3745	−	462.374i	0.119679	−	1.40539i
$330$		0			0
$331$	−140.905	−	81.3518i	−0.425696	−	0.245776i	0.271815	−	0.962349i	$-0.412376\pi$
$331$	−140.905	−	81.3518i	−0.425696	−	0.245776i	−0.697511	+	0.716574i	$0.745709\pi$
$332$		0			0
$333$	−81.0656	−	140.410i	−0.243440	−	0.421651i
$334$		0			0
$335$			224.860i			0.671225i
$336$		0			0
$337$	−598.848			−1.77700			−0.888499	−	0.458879i	$-0.848251\pi$
$337$	−598.848			−1.77700			−0.888499	+	0.458879i	$0.848251\pi$
$338$		0			0
$339$	599.210	−	345.954i	1.76758	−	1.02051i
$340$		0			0
$341$	78.6837	−	136.284i	0.230744	−	0.399660i
$342$		0			0
$343$	331.921	+	86.4727i	0.967699	+	0.252107i
$344$		0			0
$345$	73.5722	−	127.431i	0.213253	−	0.369365i
$346$		0			0
$347$	−94.3313	+	54.4622i	−0.271848	+	0.156952i	−0.629727	−	0.776816i	$-0.716833\pi$
$347$	−94.3313	+	54.4622i	−0.271848	+	0.156952i	0.357879	+	0.933768i	$0.383500\pi$
$348$		0			0
$349$	−277.893			−0.796255			−0.398128	−	0.917330i	$-0.630340\pi$
$349$	−277.893			−0.796255			−0.398128	+	0.917330i	$0.630340\pi$
$350$		0			0
$351$		−	54.4226i		−	0.155050i
$352$		0			0
$353$	52.0900	+	90.2225i	0.147564	+	0.255588i	0.930327	−	0.366732i	$-0.119524\pi$
$353$	52.0900	+	90.2225i	0.147564	+	0.255588i	−0.782763	+	0.622320i	$0.786190\pi$
$354$		0			0
$355$	−24.9591	−	14.4102i	−0.0703074	−	0.0405920i
$356$		0			0
$357$	−35.9143	+	421.741i	−0.100600	+	1.18135i
$358$		0			0
$359$	581.956	+	335.992i	1.62105	+	0.935911i	0.986641	+	0.162911i	$0.0520883\pi$
$359$	581.956	+	335.992i	1.62105	+	0.935911i	0.634405	+	0.773001i	$0.281245\pi$
$360$		0			0
$361$	169.567	+	293.699i	0.469714	+	0.813569i
$362$		0			0
$363$			269.769i			0.743164i
$364$		0			0
$365$	−161.816			−0.443332
$366$		0			0
$367$	86.1727	−	49.7518i	0.234803	−	0.135564i	−0.377983	−	0.925813i	$-0.623382\pi$
$367$	86.1727	−	49.7518i	0.234803	−	0.135564i	0.612786	+	0.790249i	$0.290049\pi$
$368$		0			0
$369$	217.464	−	376.659i	0.589334	−	1.02076i
$370$		0			0
$371$	288.640	−	414.258i	0.778006	−	1.11660i
$372$		0			0
$373$	308.281	−	533.959i	0.826491	−	1.43152i	−0.0742836	−	0.997237i	$-0.523667\pi$
$373$	308.281	−	533.959i	0.826491	−	1.43152i	0.900775	−	0.434287i	$-0.143000\pi$
$374$		0			0
$375$	376.502	−	217.373i	1.00401	−	0.579663i
$376$		0			0
$377$	446.156			1.18344
$378$		0			0
$379$		−	212.094i		−	0.559616i	−0.960056	−	0.279808i	$-0.909729\pi$
$379$		−	212.094i		−	0.559616i	0.960056	−	0.279808i	$-0.0902707\pi$
$380$		0			0
$381$	−394.726	−	683.685i	−1.03603	−	1.79445i
$382$		0			0
$383$	388.045	+	224.038i	1.01317	+	0.584955i	0.912119	−	0.409926i	$-0.134445\pi$
$383$	388.045	+	224.038i	1.01317	+	0.584955i	0.101053	+	0.994881i	$0.467779\pi$
$384$		0			0
$385$	−113.773	+	53.3742i	−0.295515	+	0.138634i
$386$		0			0
$387$	−377.847	−	218.150i	−0.976349	−	0.563696i
$388$		0			0
$389$	15.0297	+	26.0322i	0.0386368	+	0.0669208i	0.884697	−	0.466166i	$-0.154365\pi$
$389$	15.0297	+	26.0322i	0.0386368	+	0.0669208i	−0.846060	+	0.533087i	$0.821032\pi$
$390$		0			0
$391$		−	222.544i		−	0.569167i
$392$		0			0
$393$	−121.426			−0.308972
$394$		0			0
$395$	38.7326	−	22.3623i	0.0980571	−	0.0566133i
$396$		0			0
$397$	150.913	−	261.389i	0.380133	−	0.658410i	−0.610948	−	0.791671i	$-0.709211\pi$
$397$	150.913	−	261.389i	0.380133	−	0.658410i	0.991081	+	0.133261i	$0.0425448\pi$
$398$		0			0
$399$	−318.892	−	679.754i	−0.799227	−	1.70364i
$400$		0			0
$401$	−27.1956	+	47.1042i	−0.0678195	+	0.117467i	−0.897941	−	0.440115i	$-0.854938\pi$
$401$	−27.1956	+	47.1042i	−0.0678195	+	0.117467i	0.830122	+	0.557582i	$0.188271\pi$
$402$		0			0
$403$	−158.223	+	91.3503i	−0.392614	+	0.226676i
$404$		0			0
$405$	225.406			0.556557
$406$		0			0
$407$		−	160.959i		−	0.395476i
$408$		0			0
$409$	77.7710	+	134.703i	0.190149	+	0.329348i	0.945300	−	0.326204i	$-0.105769\pi$
$409$	77.7710	+	134.703i	0.190149	+	0.329348i	−0.755150	+	0.655552i	$0.772436\pi$
$410$		0			0
$411$	−624.305	−	360.443i	−1.51899	−	0.876989i
$412$		0			0
$413$	101.530	+	70.7428i	0.245837	+	0.171290i
$414$		0			0
$415$	214.446	+	123.811i	0.516738	+	0.298339i
$416$		0			0
$417$	−243.514	−	421.779i	−0.583967	−	1.01146i
$418$		0			0
$419$		−	384.000i		−	0.916468i	−0.888832	−	0.458234i	$-0.848482\pi$
$419$		−	384.000i		−	0.916468i	0.888832	−	0.458234i	$-0.151518\pi$
$420$		0			0
$421$	−295.132			−0.701026			−0.350513	−	0.936558i	$-0.613993\pi$
$421$	−295.132			−0.701026			−0.350513	+	0.936558i	$0.613993\pi$
$422$		0			0
$423$	426.732	−	246.374i	1.00882	−	0.582444i
$424$		0			0
$425$	142.307	−	246.484i	0.334841	−	0.579962i
$426$		0			0
$427$	616.214	+	52.4751i	1.44312	+	0.122892i
$428$		0			0
$429$	−128.135	+	221.936i	−0.298683	+	0.517334i
$430$		0			0
$431$	−417.311	+	240.935i	−0.968239	+	0.559013i	−0.898699	−	0.438566i	$-0.855486\pi$
$431$	−417.311	+	240.935i	−0.968239	+	0.559013i	−0.0695400	+	0.997579i	$0.522153\pi$
$432$		0			0
$433$	9.18001			0.0212009			0.0106005	−	0.999944i	$-0.496626\pi$
$433$	9.18001			0.0212009			0.0106005	+	0.999944i	$0.496626\pi$
$434$		0			0
$435$			513.618i			1.18073i
$436$		0			0
$437$	197.387	+	341.884i	0.451686	+	0.782343i
$438$		0			0
$439$	−169.939	−	98.1143i	−0.387105	−	0.223495i	0.293800	−	0.955867i	$-0.405080\pi$
$439$	−169.939	−	98.1143i	−0.387105	−	0.223495i	−0.680905	+	0.732372i	$0.738413\pi$
$440$		0			0
$441$	126.151	+	341.668i	0.286057	+	0.774758i
$442$		0			0
$443$	55.9819	+	32.3212i	0.126370	+	0.0729598i	0.561852	−	0.827237i	$-0.310089\pi$
$443$	55.9819	+	32.3212i	0.126370	+	0.0729598i	−0.435482	+	0.900197i	$0.643422\pi$
$444$		0			0
$445$	56.6506	+	98.1218i	0.127305	+	0.220498i
$446$		0			0
$447$		−	334.548i		−	0.748429i
$448$		0			0
$449$	−834.833			−1.85932			−0.929658	−	0.368424i	$-0.879898\pi$
$449$	−834.833			−1.85932			−0.929658	+	0.368424i	$0.879898\pi$
$450$		0			0
$451$	373.935	−	215.892i	0.829125	−	0.478696i
$452$		0			0
$453$	575.906	−	997.498i	1.27132	−	2.20198i
$454$		0			0
$455$	145.375	+	12.3798i	0.319506	+	0.0272083i
$456$		0			0
$457$	−25.0154	+	43.3280i	−0.0547383	+	0.0948095i	−0.892096	−	0.451846i	$-0.850766\pi$
$457$	−25.0154	+	43.3280i	−0.0547383	+	0.0948095i	0.837358	+	0.546655i	$0.184099\pi$
$458$		0			0
$459$	82.0610	−	47.3780i	0.178782	−	0.103220i
$460$		0			0
$461$	−439.355			−0.953048			−0.476524	−	0.879161i	$-0.658104\pi$
$461$	−439.355			−0.953048			−0.476524	+	0.879161i	$0.658104\pi$
$462$		0			0
$463$			244.469i			0.528010i	0.964521	+	0.264005i	$0.0850435\pi$
$463$			244.469i			0.528010i	−0.964521	+	0.264005i	$0.914956\pi$
$464$		0			0
$465$	−105.163	−	182.148i	−0.226157	−	0.391716i
$466$		0			0
$467$	385.416	+	222.520i	0.825301	+	0.476488i	0.852241	−	0.523149i	$-0.175243\pi$
$467$	385.416	+	222.520i	0.825301	+	0.476488i	−0.0269400	+	0.999637i	$0.508576\pi$
$468$		0			0
$469$	530.821	+	369.857i	1.13181	+	0.788608i
$470$		0			0
$471$	−197.489	−	114.020i	−0.419297	−	0.242081i
$472$		0			0
$473$	−216.573	−	375.115i	−0.457870	−	0.793054i
$474$		0			0
$475$			504.881i			1.06291i
$476$		0			0
$477$	536.125			1.12395
$478$		0			0
$479$	−230.123	+	132.862i	−0.480424	+	0.277373i	−0.720593	−	0.693358i	$-0.756131\pi$
$479$	−230.123	+	132.862i	−0.480424	+	0.277373i	0.240169	+	0.970731i	$0.422797\pi$
$480$		0			0
$481$	−93.4350	+	161.834i	−0.194251	+	0.336453i
$482$		0			0
$483$	−179.808	−	383.282i	−0.372274	−	0.793545i
$484$		0			0
$485$	−165.346	+	286.388i	−0.340920	+	0.590492i
$486$		0			0
$487$	−21.3034	+	12.2995i	−0.0437441	+	0.0252557i	−0.521713	−	0.853121i	$-0.674707\pi$
$487$	−21.3034	+	12.2995i	−0.0437441	+	0.0252557i	0.477968	+	0.878377i	$0.341373\pi$
$488$		0			0
$489$	−780.278			−1.59566
$490$		0			0
$491$			532.126i			1.08376i	0.840456	+	0.541880i	$0.182287\pi$
$491$			532.126i			1.08376i	−0.840456	+	0.541880i	$0.817713\pi$
$492$		0			0
$493$	388.404	+	672.735i	0.787837	+	1.36457i
$494$		0			0
$495$	−115.565	−	66.7216i	−0.233465	−	0.134791i
$496$		0			0
$497$	−75.0712	+	35.2180i	−0.151049	+	0.0708612i
$498$		0			0
$499$	628.228	+	362.708i	1.25897	+	0.726869i	0.972875	−	0.231330i	$-0.0743078\pi$
$499$	628.228	+	362.708i	1.25897	+	0.726869i	0.286100	+	0.958200i	$0.407641\pi$
$500$		0			0
$501$	−267.924	−	464.058i	−0.534778	−	0.926263i
$502$		0			0
$503$		−	46.8524i		−	0.0931459i	−0.998915	−	0.0465729i	$-0.985170\pi$
$503$		−	46.8524i		−	0.0931459i	0.998915	−	0.0465729i	$-0.0148300\pi$
$504$		0			0
$505$	217.637			0.430964
$506$		0			0
$507$	−335.637	+	193.780i	−0.662006	+	0.382209i
$508$		0			0
$509$	−431.957	+	748.172i	−0.848639	+	1.46989i	0.0337834	+	0.999429i	$0.489244\pi$
$509$	−431.957	+	748.172i	−0.848639	+	1.46989i	−0.882423	+	0.470457i	$0.844089\pi$
$510$		0			0
$511$	−266.160	+	381.995i	−0.520862	+	0.747544i
$512$		0			0
$513$	−84.0441	+	145.569i	−0.163829	+	0.283760i
$514$		0			0
$515$	11.0552	−	6.38273i	0.0214664	−	0.0123937i
$516$		0			0
$517$	489.184			0.946197
$518$		0			0
$519$			828.142i			1.59565i
$520$		0			0
$521$	169.288	+	293.215i	0.324928	+	0.562792i	0.981498	−	0.191473i	$-0.0613266\pi$
$521$	169.288	+	293.215i	0.324928	+	0.562792i	−0.656570	+	0.754265i	$0.727993\pi$
$522$		0			0
$523$	−323.498	−	186.772i	−0.618544	−	0.357116i	0.157758	−	0.987478i	$-0.449573\pi$
$523$	−323.498	−	186.772i	−0.618544	−	0.357116i	−0.776302	+	0.630361i	$0.782907\pi$
$524$		0			0
$525$	45.9416	−	539.492i	0.0875079	−	1.02760i
$526$		0			0
$527$	−275.485	−	159.051i	−0.522741	−	0.301805i
$528$		0			0
$529$	−153.203	−	265.355i	−0.289608	−	0.501616i
$530$		0			0
$531$			131.399i			0.247456i
$532$		0			0
$533$	−501.292			−0.940510
$534$		0			0
$535$	−31.6956	+	18.2995i	−0.0592441	+	0.0342046i
$536$		0			0
$537$	−250.200	+	433.359i	−0.465922	+	0.807000i
$538$		0			0
$539$	−61.1389	+	356.373i	−0.113430	+	0.661174i
$540$		0			0
$541$	294.267	−	509.685i	0.543931	−	0.942116i	−0.454743	−	0.890623i	$-0.650269\pi$
$541$	294.267	−	509.685i	0.543931	−	0.942116i	0.998673	−	0.0514928i	$-0.0163979\pi$
$542$		0			0
$543$	−462.043	+	266.761i	−0.850908	+	0.491272i
$544$		0			0
$545$	17.8870			0.0328202
$546$		0			0
$547$		−	206.784i		−	0.378032i	−0.981974	−	0.189016i	$-0.939470\pi$
$547$		−	206.784i		−	0.378032i	0.981974	−	0.189016i	$-0.0605298\pi$
$548$		0			0
$549$	328.346	+	568.713i	0.598081	+	1.03591i
$550$		0			0
$551$	−1193.37	−	688.993i	−2.16583	−	1.25044i
$552$		0			0
$553$	10.9186	−	128.217i	0.0197443	−	0.231857i
$554$		0			0
$555$	−186.305	−	107.563i	−0.335684	−	0.193807i
$556$		0			0
$557$	238.327	+	412.794i	0.427876	+	0.741103i	0.996684	−	0.0813674i	$-0.0259287\pi$
$557$	238.327	+	412.794i	0.427876	+	0.741103i	−0.568808	+	0.822470i	$0.692595\pi$
$558$		0			0
$559$			502.873i			0.899594i
$560$		0			0
$561$	−446.195			−0.795356
$562$		0			0
$563$	405.901	−	234.347i	0.720961	−	0.416247i	−0.0941451	−	0.995558i	$-0.530012\pi$
$563$	405.901	−	234.347i	0.720961	−	0.416247i	0.815106	+	0.579311i	$0.196678\pi$
$564$		0			0
$565$	207.630	−	359.625i	0.367486	−	0.636505i
$566$		0			0
$567$	370.754	−	532.109i	0.653888	−	0.938463i
$568$		0			0
$569$	−179.141	+	310.282i	−0.314835	+	0.545311i	−0.979402	−	0.201918i	$-0.935283\pi$
$569$	−179.141	+	310.282i	−0.314835	+	0.545311i	0.664567	+	0.747228i	$0.268616\pi$
$570$		0			0
$571$	−321.513	+	185.626i	−0.563070	+	0.325089i	−0.754377	−	0.656442i	$-0.772061\pi$
$571$	−321.513	+	185.626i	−0.563070	+	0.325089i	0.191307	+	0.981530i	$0.438727\pi$
$572$		0			0
$573$	701.262			1.22384
$574$		0			0
$575$			284.679i			0.495094i
$576$		0			0
$577$	535.691	+	927.844i	0.928408	+	1.60805i	0.785987	+	0.618243i	$0.212155\pi$
$577$	535.691	+	927.844i	0.928408	+	1.60805i	0.142421	+	0.989806i	$0.454511\pi$
$578$		0			0
$579$	−700.431	−	404.394i	−1.20972	−	0.698435i
$580$		0			0
$581$	645.004	−	302.590i	1.11016	−	0.520808i
$582$		0			0
$583$	460.940	+	266.124i	0.790635	+	0.456473i
$584$		0			0
$585$	77.4625	+	134.169i	0.132414	+	0.229349i
$586$		0			0
$587$		−	283.490i		−	0.482948i	−0.970407	−	0.241474i	$-0.922369\pi$
$587$		−	283.490i		−	0.482948i	0.970407	−	0.241474i	$-0.0776308\pi$
$588$		0			0
$589$	564.284			0.958037
$590$		0			0
$591$	−33.0233	+	19.0660i	−0.0558769	+	0.0322606i
$592$		0			0
$593$	310.680	−	538.113i	0.523912	−	0.907442i	−0.475700	−	0.879607i	$-0.657805\pi$
$593$	310.680	−	538.113i	0.523912	−	0.907442i	0.999613	−	0.0278350i	$-0.00886130\pi$
$594$		0			0
$595$	107.891	+	229.981i	0.181329	+	0.386523i
$596$		0			0
$597$	−624.302	+	1081.32i	−1.04573	+	1.81126i
$598$		0			0
$599$	910.469	−	525.659i	1.51998	−	0.877562i	0.520259	−	0.854009i	$-0.325836\pi$
$599$	910.469	−	525.659i	1.51998	−	0.877562i	0.999723	−	0.0235529i	$-0.00749780\pi$
$600$		0			0
$601$	−427.201			−0.710817			−0.355409	−	0.934711i	$-0.615658\pi$
$601$	−427.201			−0.710817			−0.355409	+	0.934711i	$0.615658\pi$
$602$		0			0
$603$			686.979i			1.13927i
$604$		0			0
$605$	80.9530	+	140.215i	0.133807	+	0.231760i
$606$		0			0
$607$	−621.252	−	358.680i	−1.02348	−	0.590906i	−0.108369	−	0.994111i	$-0.534563\pi$
$607$	−621.252	−	358.680i	−1.02348	−	0.590906i	−0.915110	+	0.403205i	$0.867896\pi$
$608$		0			0
$609$	1212.48	+	844.816i	1.99094	+	1.38722i
$610$		0			0
$611$	−491.844	−	283.966i	−0.804983	−	0.464757i
$612$		0			0
$613$	4.87305	+	8.44037i	0.00794951	+	0.0137690i	0.869973	−	0.493100i	$-0.164136\pi$
$613$	4.87305	+	8.44037i	0.00794951	+	0.0137690i	−0.862023	+	0.506869i	$0.830803\pi$
$614$		0			0
$615$		−	577.091i		−	0.938360i
$616$		0			0
$617$	505.878			0.819900			0.409950	−	0.912108i	$-0.365546\pi$
$617$	505.878			0.819900			0.409950	+	0.912108i	$0.365546\pi$
$618$		0			0
$619$	−272.815	+	157.510i	−0.440735	+	0.254458i	−0.703909	−	0.710290i	$-0.748564\pi$
$619$	−272.815	+	157.510i	−0.440735	+	0.254458i	0.263175	+	0.964748i	$0.415230\pi$
$620$		0			0
$621$	−47.3886	+	82.0795i	−0.0763102	+	0.132173i
$622$		0			0
$623$	324.814	+	27.6603i	0.521371	+	0.0443985i
$624$		0			0
$625$	−108.051	+	187.149i	−0.172881	+	0.299439i
$626$		0			0
$627$	685.466	−	395.754i	1.09325	−	0.631187i
$628$		0			0
$629$	−325.362			−0.517268
$630$		0			0
$631$			381.905i			0.605238i	0.953112	+	0.302619i	$0.0978609\pi$
$631$			381.905i			0.605238i	−0.953112	+	0.302619i	$0.902139\pi$
$632$		0			0
$633$	−555.573	−	962.280i	−0.877682	−	1.52019i
$634$		0			0
$635$	−410.325	−	236.901i	−0.646181	−	0.373073i
$636$		0			0
$637$	268.342	−	322.821i	0.421260	−	0.506783i
$638$		0			0
$639$	−76.2536	−	44.0250i	−0.119333	−	0.0688968i
$640$		0			0
$641$	−68.4839	−	118.618i	−0.106839	−	0.185051i	0.807649	−	0.589664i	$-0.200740\pi$
$641$	−68.4839	−	118.618i	−0.106839	−	0.185051i	−0.914488	+	0.404613i	$0.867406\pi$
$642$		0			0
$643$			260.130i			0.404556i	0.979328	+	0.202278i	$0.0648345\pi$
$643$			260.130i			0.404556i	−0.979328	+	0.202278i	$0.935166\pi$
$644$		0			0
$645$	−578.911			−0.897537
$646$		0			0
$647$	378.735	−	218.663i	0.585371	−	0.337964i	−0.177894	−	0.984050i	$-0.556929\pi$
$647$	378.735	−	218.663i	0.585371	−	0.337964i	0.763265	+	0.646086i	$0.223595\pi$
$648$		0			0
$649$	−65.2243	+	112.972i	−0.100500	+	0.174071i
$650$		0			0
$651$	−602.967	−	51.3470i	−0.926217	−	0.0788741i
$652$		0			0
$653$	590.447	−	1022.68i	0.904206	−	1.56613i	0.0822270	−	0.996614i	$-0.473797\pi$
$653$	590.447	−	1022.68i	0.904206	−	1.56613i	0.821979	−	0.569518i	$-0.192870\pi$
$654$		0			0
$655$	−63.1122	+	36.4379i	−0.0963545	+	0.0556303i
$656$		0			0
$657$	−494.371			−0.752467
$658$		0			0
$659$			129.818i			0.196992i	0.995137	+	0.0984960i	$0.0314032\pi$
$659$			129.818i			0.196992i	−0.995137	+	0.0984960i	$0.968597\pi$
$660$		0			0
$661$	316.779	+	548.677i	0.479241	+	0.830070i	0.999717	−	0.0238063i	$-0.00757850\pi$
$661$	316.779	+	548.677i	0.479241	+	0.830070i	−0.520475	+	0.853877i	$0.674245\pi$
$662$		0			0
$663$	448.621	+	259.012i	0.676654	+	0.390666i
$664$		0			0
$665$	−369.729	−	257.614i	−0.555984	−	0.387390i
$666$		0			0
$667$	−672.887	−	388.491i	−1.00883	−	0.582446i
$668$		0			0
$669$	−190.511	−	329.975i	−0.284770	−	0.493235i
$670$		0			0
$671$			651.944i			0.971600i
$672$		0			0
$673$	1074.74			1.59694			0.798471	−	0.602033i	$-0.205642\pi$
$673$	1074.74			1.59694			0.798471	+	0.602033i	$0.205642\pi$
$674$		0			0
$675$	−104.973	+	60.6059i	−0.155515	+	0.0897866i
$676$		0			0
$677$	−277.711	+	481.010i	−0.410208	+	0.710502i	−0.994912	−	0.100745i	$-0.967877\pi$
$677$	−277.711	+	481.010i	−0.410208	+	0.710502i	0.584704	+	0.811247i	$0.301211\pi$
$678$		0			0
$679$	404.102	+	861.390i	0.595143	+	1.26861i
$680$		0			0
$681$	−318.828	+	552.226i	−0.468176	+	0.810904i
$682$		0			0
$683$	128.117	−	73.9682i	0.187579	−	0.108299i	−0.403270	−	0.915081i	$-0.632126\pi$
$683$	128.117	−	73.9682i	0.187579	−	0.108299i	0.590849	+	0.806782i	$0.298793\pi$
$684$		0			0
$685$	−432.651			−0.631607
$686$		0			0
$687$			333.515i			0.485466i
$688$		0			0
$689$	−308.965	−	535.142i	−0.448425	−	0.776694i
$690$		0			0
$691$	506.502	+	292.429i	0.732999	+	0.423197i	0.819518	−	0.573053i	$-0.194241\pi$
$691$	506.502	+	292.429i	0.732999	+	0.423197i	−0.0865192	+	0.996250i	$0.527574\pi$
$692$		0			0
$693$	−347.593	+	163.066i	−0.501577	+	0.235304i
$694$		0			0
$695$	−253.137	−	146.149i	−0.364226	−	0.210286i
$696$		0			0
$697$	−436.403	−	755.872i	−0.626116	−	1.08446i
$698$		0			0
$699$		−	1347.28i		−	1.92745i
$700$		0			0
$701$	−1138.04			−1.62345			−0.811727	−	0.584037i	$-0.801472\pi$
$701$	−1138.04			−1.62345			−0.811727	+	0.584037i	$0.801472\pi$
$702$		0			0
$703$	499.837	−	288.581i	0.711005	−	0.410499i
$704$		0			0
$705$	326.905	−	566.215i	0.463694	−	0.803142i
$706$		0			0
$707$	357.976	−	513.769i	0.506331	−	0.726689i
$708$		0			0
$709$	421.341	−	729.785i	0.594276	−	1.02932i	−0.399373	−	0.916789i	$-0.630772\pi$
$709$	421.341	−	729.785i	0.594276	−	1.02932i	0.993649	−	0.112527i	$-0.0358945\pi$
$710$		0			0
$711$	118.333	−	68.3198i	0.166432	−	0.0960897i
$712$		0			0
$713$	318.174			0.446247
$714$		0			0
$715$			153.804i			0.215111i
$716$		0			0
$717$	74.2620	+	128.626i	0.103573	+	0.179394i
$718$		0			0
$719$	48.8258	+	28.1896i	0.0679079	+	0.0392066i	0.533570	−	0.845756i	$-0.320850\pi$
$719$	48.8258	+	28.1896i	0.0679079	+	0.0392066i	−0.465662	+	0.884963i	$0.654184\pi$
$720$		0			0
$721$	3.11644	−	36.5963i	0.00432238	−	0.0507576i
$722$		0			0
$723$	1617.53	+	933.880i	2.23725	+	1.29167i
$724$		0			0
$725$	−496.847	−	860.564i	−0.685306	−	1.18698i
$726$		0			0
$727$			929.204i			1.27813i	0.769151	+	0.639067i	$0.220680\pi$
$727$			929.204i			1.27813i	−0.769151	+	0.639067i	$0.779320\pi$
$728$		0			0
$729$	456.881			0.626723
$730$		0			0
$731$	−758.256	+	437.779i	−1.03729	+	0.598877i
$732$		0			0
$733$	−273.917	+	474.437i	−0.373692	+	0.647254i	−0.990130	−	0.140149i	$-0.955242\pi$
$733$	−273.917	+	474.437i	−0.373692	+	0.647254i	0.616438	+	0.787403i	$0.288575\pi$
$734$		0			0
$735$	371.634	+	308.918i	0.505624	+	0.420297i
$736$		0			0
$737$	−341.005	+	590.639i	−0.462694	+	0.801409i
$738$		0			0
$739$	−473.319	+	273.271i	−0.640485	+	0.369784i	−0.784801	−	0.619747i	$-0.787235\pi$
$739$	−473.319	+	273.271i	−0.640485	+	0.369784i	0.144316	+	0.989532i	$0.453902\pi$
$740$		0			0
$741$	−918.926			−1.24012
$742$		0			0
$743$		−	904.617i		−	1.21752i	−0.793354	−	0.608760i	$-0.791667\pi$
$743$		−	904.617i		−	1.21752i	0.793354	−	0.608760i	$-0.208333\pi$
$744$		0			0
$745$	−100.392	−	173.884i	−0.134755	−	0.233402i
$746$		0			0
$747$	655.163	+	378.259i	0.877059	+	0.506370i
$748$		0			0
$749$	−8.93491	+	104.922i	−0.0119291	+	0.140083i
$750$		0			0
$751$	−792.217	−	457.386i	−1.05488	−	0.609037i	−0.130870	−	0.991400i	$-0.541777\pi$
$751$	−792.217	−	457.386i	−1.05488	−	0.609037i	−0.924012	+	0.382363i	$0.875110\pi$
$752$		0			0
$753$	−46.9967	−	81.4006i	−0.0624126	−	0.108102i
$754$		0			0
$755$		−	691.278i		−	0.915601i
$756$		0			0
$757$	−780.766			−1.03140			−0.515698	−	0.856771i	$-0.672467\pi$
$757$	−780.766			−1.03140			−0.515698	+	0.856771i	$0.672467\pi$
$758$		0			0
$759$	386.503	−	223.148i	0.509227	−	0.294002i
$760$		0			0
$761$	−77.5839	+	134.379i	−0.101950	+	0.176583i	−0.912488	−	0.409104i	$-0.865841\pi$
$761$	−77.5839	+	134.379i	−0.101950	+	0.176583i	0.810538	+	0.585686i	$0.199175\pi$
$762$		0			0
$763$	29.4211	−	42.2254i	0.0385598	−	0.0553412i
$764$		0			0
$765$	−134.871	+	233.603i	−0.176302	+	0.305364i
$766$		0			0
$767$	131.158	−	75.7242i	0.171001	−	0.0987277i
$768$		0			0
$769$	354.951			0.461575			0.230788	−	0.973004i	$-0.425870\pi$
$769$	354.951			0.461575			0.230788	+	0.973004i	$0.425870\pi$
$770$		0			0
$771$		−	819.880i		−	1.06340i
$772$		0			0
$773$	−433.669	−	751.136i	−0.561020	−	0.971715i	−0.997408	−	0.0719566i	$-0.977076\pi$
$773$	−433.669	−	751.136i	−0.561020	−	0.971715i	0.436388	−	0.899759i	$-0.356258\pi$
$774$		0			0
$775$	352.400	+	203.458i	0.454710	+	0.262527i
$776$		0			0
$777$	−560.361	+	262.881i	−0.721186	+	0.338328i
$778$		0			0
$779$	1340.85	+	774.139i	1.72124	+	0.993760i
$780$		0			0
$781$	−43.7066	−	75.7021i	−0.0559624	−	0.0969297i
$782$		0			0
$783$		−	330.827i		−	0.422512i
$784$		0			0
$785$	−136.862			−0.174347
$786$		0			0
$787$	81.7643	−	47.2066i	0.103894	−	0.0599830i	−0.447153	−	0.894458i	$-0.647562\pi$
$787$	81.7643	−	47.2066i	0.103894	−	0.0599830i	0.551046	+	0.834475i	$0.314229\pi$
$788$		0			0
$789$	−63.4748	+	109.942i	−0.0804497	+	0.139343i
$790$		0			0
$791$	−507.441	−	1081.67i	−0.641519	−	1.36747i
$792$		0			0
$793$	378.447	−	655.489i	0.477234	−	0.826594i
$794$		0			0
$795$	616.060	−	355.682i	0.774918	−	0.447399i
$796$		0			0
$797$	1065.20			1.33651			0.668256	−	0.743931i	$-0.267041\pi$
$797$	1065.20			1.33651			0.668256	+	0.743931i	$0.267041\pi$
$798$		0			0
$799$		−	988.835i		−	1.23759i
$800$		0			0
$801$	173.076	+	299.776i	0.216074	+	0.374252i
$802$		0			0
$803$	−425.041	−	245.398i	−0.529317	−	0.305601i
$804$		0			0
$805$	−208.473	−	145.257i	−0.258973	−	0.180443i
$806$		0			0
$807$	−313.611	−	181.063i	−0.388613	−	0.224366i
$808$		0			0
$809$	254.373	+	440.587i	0.314429	+	0.544607i	0.979316	−	0.202337i	$-0.0648537\pi$
$809$	254.373	+	440.587i	0.314429	+	0.544607i	−0.664887	+	0.746944i	$0.731520\pi$
$810$		0			0
$811$			652.893i			0.805047i	0.915410	+	0.402524i	$0.131867\pi$
$811$			652.893i			0.805047i	−0.915410	+	0.402524i	$0.868133\pi$
$812$		0			0
$813$	−216.772			−0.266633
$814$		0			0
$815$	−405.557	+	234.148i	−0.497616	+	0.287298i
$816$		0			0
$817$	776.580	−	1345.08i	0.950527	−	1.64636i
$818$		0			0
$819$	444.141	+	37.8219i	0.542297	+	0.0461806i
$820$		0			0
$821$	87.7543	−	151.995i	0.106887	−	0.185134i	−0.807621	−	0.589702i	$-0.799245\pi$
$821$	87.7543	−	151.995i	0.106887	−	0.185134i	0.914508	+	0.404569i	$0.132578\pi$
$822$		0			0
$823$	−753.427	+	434.991i	−0.915464	+	0.528544i	−0.882185	−	0.470902i	$-0.843928\pi$
$823$	−753.427	+	434.991i	−0.915464	+	0.528544i	−0.0332791	+	0.999446i	$0.510595\pi$
$824$		0			0
$825$	570.773			0.691846
$826$		0			0
$827$			269.724i			0.326148i	0.986614	+	0.163074i	$0.0521409\pi$
$827$			269.724i			0.326148i	−0.986614	+	0.163074i	$0.947859\pi$
$828$		0			0
$829$	−72.2989	−	125.225i	−0.0872122	−	0.151056i	0.819120	−	0.573623i	$-0.194462\pi$
$829$	−72.2989	−	125.225i	−0.0872122	−	0.151056i	−0.906332	+	0.422567i	$0.861129\pi$
$830$		0			0
$831$	−142.661	−	82.3656i	−0.171674	−	0.0991163i
$832$		0			0
$833$	720.372	+	123.586i	0.864792	+	0.148362i
$834$		0			0
$835$	−278.512	−	160.799i	−0.333547	−	0.192573i
$836$		0			0
$837$	67.7367	+	117.323i	0.0809280	+	0.140171i
$838$		0			0
$839$		−	920.554i		−	1.09720i	−0.836084	−	0.548602i	$-0.815160\pi$
$839$		−	920.554i		−	1.09720i	0.836084	−	0.548602i	$-0.184840\pi$
$840$		0			0
$841$	1871.12			2.22487
$842$		0			0
$843$	19.2940	−	11.1394i	0.0228874	−	0.0132140i
$844$		0			0
$845$	−116.300	+	201.438i	−0.137633	+	0.238388i
$846$		0			0
$847$	464.155	+	39.5262i	0.547999	+	0.0466661i
$848$		0			0
$849$	596.954	−	1033.95i	0.703126	−	1.21785i
$850$		0			0
$851$	281.835	−	162.718i	0.331181	−	0.191207i
$852$		0			0
$853$	−206.715			−0.242338			−0.121169	−	0.992632i	$-0.538664\pi$
$853$	−206.715			−0.242338			−0.121169	+	0.992632i	$0.538664\pi$
$854$		0			0
$855$		−	478.497i		−	0.559646i
$856$		0			0
$857$	−560.474	−	970.769i	−0.653995	−	1.13275i	−0.982145	−	0.188127i	$-0.939758\pi$
$857$	−560.474	−	970.769i	−0.653995	−	1.13275i	0.328150	−	0.944626i	$-0.393575\pi$
$858$		0			0
$859$	23.2497	+	13.4232i	0.0270660	+	0.0156265i	0.513472	−	0.858106i	$-0.328359\pi$
$859$	23.2497	+	13.4232i	0.0270660	+	0.0156265i	−0.486406	+	0.873733i	$0.661692\pi$
$860$		0			0
$861$	−1362.32	−	949.219i	−1.58226	−	1.10246i
$862$		0			0
$863$	338.354	+	195.349i	0.392067	+	0.226360i	0.683055	−	0.730367i	$-0.260651\pi$
$863$	338.354	+	195.349i	0.392067	+	0.226360i	−0.290988	+	0.956727i	$0.593984\pi$
$864$		0			0
$865$	248.511	+	430.434i	0.287296	+	0.497612i
$866$		0			0
$867$		−	269.598i		−	0.310955i
$868$		0			0
$869$	135.651			0.156101
$870$		0			0
$871$	685.720	−	395.901i	0.787279	−	0.454536i
$872$		0			0
$873$	−505.156	+	874.956i	−0.578644	+	1.00224i
$874$		0			0
$875$	−318.841	−	679.646i	−0.364390	−	0.776738i
$876$		0			0
$877$	−72.5325	+	125.630i	−0.0827053	+	0.143250i	−0.904411	−	0.426662i	$-0.859689\pi$
$877$	−72.5325	+	125.630i	−0.0827053	+	0.143250i	0.821706	+	0.569912i	$0.193023\pi$
$878$		0			0
$879$	−575.139	+	332.057i	−0.654311	+	0.377766i
$880$		0			0
$881$	−360.233			−0.408891			−0.204445	−	0.978878i	$-0.565539\pi$
$881$	−360.233			−0.408891			−0.204445	+	0.978878i	$0.565539\pi$
$882$		0			0
$883$			145.555i			0.164841i	0.996598	+	0.0824205i	$0.0262650\pi$
$883$			145.555i			0.164841i	−0.996598	+	0.0824205i	$0.973735\pi$
$884$		0			0
$885$	87.1743	+	150.990i	0.0985020	+	0.170610i
$886$		0			0
$887$	1149.57	+	663.707i	1.29603	+	0.748261i	0.979715	−	0.200395i	$-0.0642226\pi$
$887$	1149.57	+	663.707i	1.29603	+	0.748261i	0.316310	+	0.948656i	$0.397556\pi$
$888$		0			0
$889$	−1234.16	+	578.980i	−1.38826	+	0.651271i
$890$		0			0
$891$	592.071	+	341.833i	0.664502	+	0.383650i
$892$		0			0
$893$	877.051	+	1519.10i	0.982140	+	1.70112i
$894$		0			0
$895$			300.323i			0.335556i
$896$		0			0
$897$	−518.140			−0.577637
$898$		0			0
$899$	−961.816	+	555.305i	−1.06987	+	0.617692i
$900$		0			0
$901$	537.942	−	931.743i	0.597050	−	1.03412i
$902$		0			0
$903$	−952.212	+	1366.62i	−1.05450	+	1.51342i
$904$		0			0
$905$	−160.101	+	277.303i	−0.176907	+	0.306412i
$906$		0			0
$907$	−392.834	+	226.803i	−0.433114	+	0.250058i	−0.700672	−	0.713483i	$-0.747116\pi$
$907$	−392.834	+	226.803i	−0.433114	+	0.250058i	0.267558	+	0.963542i	$0.413783\pi$
$908$		0			0
$909$	664.910			0.731475
$910$		0			0
$911$		−	891.300i		−	0.978376i	−0.872178	−	0.489188i	$-0.837293\pi$
$911$		−	891.300i		−	0.978376i	0.872178	−	0.489188i	$-0.162707\pi$
$912$		0			0
$913$	375.523	+	650.425i	0.411307	+	0.712404i
$914$		0			0
$915$	754.605	+	435.671i	0.824704	+	0.476143i
$916$		0			0
$917$	−17.7912	+	208.921i	−0.0194015	+	0.227831i
$918$		0			0
$919$	−1405.23	−	811.309i	−1.52909	−	0.882818i	−0.999400	−	0.0346230i	$-0.988977\pi$
$919$	−1405.23	−	811.309i	−1.52909	−	0.882818i	−0.529685	−	0.848195i	$-0.677690\pi$
$920$		0			0
$921$	1133.08	+	1962.55i	1.23027	+	2.13089i
$922$		0			0
$923$			101.485i			0.109951i
$924$		0			0
$925$	416.203			0.449949
$926$		0			0
$927$	33.7752	−	19.5001i	0.0364350	−	0.0210357i
$928$		0			0
$929$	−255.412	+	442.387i	−0.274932	+	0.476197i	−0.970118	−	0.242634i	$-0.921989\pi$
$929$	−255.412	+	442.387i	−0.274932	+	0.476197i	0.695186	+	0.718830i	$0.255322\pi$
$930$		0			0
$931$	−1216.29	+	449.078i	−1.30643	+	0.482361i
$932$		0			0
$933$	−657.516	+	1138.85i	−0.704734	+	1.22063i
$934$		0			0
$935$	−231.914	+	133.895i	−0.248036	+	0.143204i
$936$		0			0
$937$	898.415			0.958820			0.479410	−	0.877591i	$-0.340851\pi$
$937$	898.415			0.958820			0.479410	+	0.877591i	$0.340851\pi$
$938$		0			0
$939$		−	413.155i		−	0.439995i
$940$		0			0
$941$	−853.746	−	1478.73i	−0.907276	−	1.57145i	−0.817833	−	0.575456i	$-0.804825\pi$
$941$	−853.746	−	1478.73i	−0.907276	−	1.57145i	−0.0894429	−	0.995992i	$-0.528509\pi$
$942$		0			0
$943$	756.043	+	436.501i	0.801742	+	0.462886i
$944$		0			0
$945$	9.17966	−	107.797i	0.00971393	−	0.114070i
$946$		0			0
$947$	−1211.13	−	699.247i	−1.27891	−	0.738381i	−0.302265	−	0.953224i	$-0.597743\pi$
$947$	−1211.13	−	699.247i	−1.27891	−	0.738381i	−0.976649	+	0.214843i	$0.931076\pi$
$948$		0			0
$949$	284.902	+	493.465i	0.300213	+	0.519984i
$950$		0			0
$951$			2222.26i			2.33677i
$952$		0			0
$953$	−99.5631			−0.104473			−0.0522367	−	0.998635i	$-0.516635\pi$
$953$	−99.5631			−0.104473			−0.0522367	+	0.998635i	$0.516635\pi$
$954$		0			0
$955$	364.488	−	210.437i	0.381662	−	0.220353i
$956$		0			0
$957$	−778.913	+	1349.12i	−0.813912	+	1.40974i
$958$		0			0
$959$	−711.638	+	1021.35i	−0.742063	+	1.06501i
$960$		0			0
$961$	−253.103	+	438.387i	−0.263375	+	0.456178i
$962$		0			0
$963$	−96.8345	+	55.9074i	−0.100555	+	0.0580555i
$964$		0			0
$965$	−485.407			−0.503012
$966$		0			0
$967$		−	272.789i		−	0.282099i	−0.990003	−	0.141049i	$-0.954952\pi$
$967$		−	272.789i		−	0.282099i	0.990003	−	0.141049i	$-0.0450476\pi$
$968$		0			0
$969$	−799.977	−	1385.60i	−0.825569	−	1.42993i
$970$		0			0
$971$	1039.50	+	600.155i	1.07055	+	0.618080i	0.928330	−	0.371756i	$-0.121244\pi$
$971$	1039.50	+	600.155i	1.07055	+	0.618080i	0.142215	+	0.989836i	$0.454578\pi$
$972$		0			0
$973$	−761.378	+	357.184i	−0.782506	+	0.367095i
$974$		0			0
$975$	−573.877	−	331.328i	−0.588592	−	0.339824i
$976$		0			0
$977$	−269.972	−	467.606i	−0.276328	−	0.478614i	0.694141	−	0.719839i	$-0.255784\pi$
$977$	−269.972	−	467.606i	−0.276328	−	0.478614i	−0.970469	+	0.241225i	$0.922451\pi$
$978$		0			0
$979$			343.648i			0.351019i
$980$		0			0
$981$	54.6473			0.0557057
$982$		0			0
$983$	−487.338	+	281.365i	−0.495766	+	0.286231i	−0.726963	−	0.686676i	$-0.759069\pi$
$983$	−487.338	+	281.365i	−0.495766	+	0.286231i	0.231197	+	0.972907i	$0.425736\pi$
$984$		0			0
$985$	−11.4428	+	19.8194i	−0.0116170	+	0.0201213i
$986$		0			0
$987$	−798.945	−	1703.04i	−0.809468	−	1.72547i
$988$		0			0
$989$	437.878	−	758.427i	0.442748	−	0.766862i
$990$		0			0
$991$	424.335	−	244.990i	0.428189	−	0.247215i	−0.270386	−	0.962752i	$-0.587151\pi$
$991$	424.335	−	244.990i	0.428189	−	0.247215i	0.698575	+	0.715537i	$0.253818\pi$
$992$		0			0
$993$	−659.561			−0.664210
$994$		0			0
$995$			749.370i			0.753135i
$996$		0			0
$997$	832.723	+	1442.32i	0.835229	+	1.44666i	0.893844	+	0.448378i	$0.147998\pi$
$997$	832.723	+	1442.32i	0.835229	+	1.44666i	−0.0586148	+	0.998281i	$0.518668\pi$
$998$		0			0
$999$	120.001	+	69.2826i	0.120121	+	0.0693519i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.3.r.c.191.5	yes	12
4.3	odd	2	inner	224.3.r.c.191.2	yes	12
7.2	even	3		1568.3.d.j.1471.5		6
7.4	even	3	inner	224.3.r.c.95.2	✓	12
7.5	odd	6		1568.3.d.k.1471.2		6
8.3	odd	2		448.3.r.g.191.5		12
8.5	even	2		448.3.r.g.191.2		12
28.11	odd	6	inner	224.3.r.c.95.5	yes	12
28.19	even	6		1568.3.d.k.1471.5		6
28.23	odd	6		1568.3.d.j.1471.2		6
56.11	odd	6		448.3.r.g.319.2		12
56.53	even	6		448.3.r.g.319.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.3.r.c.95.2	✓	12	7.4	even	3	inner
224.3.r.c.95.5	yes	12	28.11	odd	6	inner
224.3.r.c.191.2	yes	12	4.3	odd	2	inner
224.3.r.c.191.5	yes	12	1.1	even	1	trivial
448.3.r.g.191.2		12	8.5	even	2
448.3.r.g.191.5		12	8.3	odd	2
448.3.r.g.319.2		12	56.11	odd	6
448.3.r.g.319.5		12	56.53	even	6
1568.3.d.j.1471.2		6	28.23	odd	6
1568.3.d.j.1471.5		6	7.2	even	3
1568.3.d.k.1471.2		6	7.5	odd	6
1568.3.d.k.1471.5		6	28.19	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	224.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.51065 - 2.02688i) q^{3} +(1.21646 - 2.10698i) q^{5} +(-2.97300 - 6.33729i) q^{7} +(3.71646 - 6.43710i) q^{9} +O(q^{10})\)	\(q+(3.51065 - 2.02688i) q^{3} +(1.21646 - 2.10698i) q^{5} +(-2.97300 - 6.33729i) q^{7} +(3.71646 - 6.43710i) q^{9} +(6.39055 - 3.68959i) q^{11} -8.56707 q^{13} -9.86249i q^{15} +(-7.45812 - 12.9178i) q^{17} +(22.9151 + 13.2300i) q^{19} +(-23.2821 - 16.2221i) q^{21} +(12.9208 + 7.45980i) q^{23} +(9.54044 + 16.5245i) q^{25} +6.35253i q^{27} -52.0780 q^{29} +(18.4688 - 10.6629i) q^{31} +(14.9567 - 25.9057i) q^{33} +(-16.9691 - 1.44504i) q^{35} +(10.9063 - 18.8902i) q^{37} +(-30.0760 + 17.3644i) q^{39} +58.5138 q^{41} -58.6983i q^{43} +(-9.04188 - 15.6610i) q^{45} +(57.4110 + 33.1463i) q^{47} +(-31.3225 + 37.6816i) q^{49} +(-52.3658 - 30.2334i) q^{51} +(36.0642 + 62.4650i) q^{53} -17.9530i q^{55} +107.263 q^{57} +(-15.3096 + 8.83897i) q^{59} +(-44.1746 + 76.5126i) q^{61} +(-51.8428 - 4.41480i) q^{63} +(-10.4215 + 18.0506i) q^{65} +(-80.0413 + 46.2119i) q^{67} +60.4804 q^{69} -11.8459i q^{71} +(-33.2555 - 57.6001i) q^{73} +(66.9863 + 38.6746i) q^{75} +(-42.3811 - 29.5296i) q^{77} +(15.9202 + 9.19151i) q^{79} +(46.3240 + 80.2355i) q^{81} +101.779i q^{83} -36.2901 q^{85} +(-182.828 + 105.556i) q^{87} +(-23.2850 + 40.3308i) q^{89} +(25.4699 + 54.2920i) q^{91} +(43.2250 - 74.8678i) q^{93} +(55.7507 - 32.1877i) q^{95} -135.924 q^{97} -54.8488i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{5} + 32 q^{9}+O(q^{10}) \) 12 * q + 2 * q^5 + 32 * q^9	\( 12 q + 2 q^{5} + 32 q^{9} - 128 q^{13} - 6 q^{17} - 62 q^{21} - 32 q^{25} + 128 q^{29} - 134 q^{33} - 66 q^{37} + 384 q^{41} - 192 q^{45} - 12 q^{49} - 2 q^{53} + 468 q^{57} - 434 q^{61} + 160 q^{65} + 124 q^{69} - 10 q^{73} - 370 q^{77} + 422 q^{81} + 1020 q^{85} - 522 q^{89} + 306 q^{93} - 768 q^{97}+O(q^{100}) \) 12 * q + 2 * q^5 + 32 * q^9 - 128 * q^13 - 6 * q^17 - 62 * q^21 - 32 * q^25 + 128 * q^29 - 134 * q^33 - 66 * q^37 + 384 * q^41 - 192 * q^45 - 12 * q^49 - 2 * q^53 + 468 * q^57 - 434 * q^61 + 160 * q^65 + 124 * q^69 - 10 * q^73 - 370 * q^77 + 422 * q^81 + 1020 * q^85 - 522 * q^89 + 306 * q^93 - 768 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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