LMFDB - Embedded newform 400.3.bg.e.97.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [400,3,Mod(17,400)] 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("400.17"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(400, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([0, 0, 13])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	400.bg (of order $20$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [56] 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:	$10.8992105744$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			97.4
Character	$\chi$	$=$	400.97
Dual form			400.3.bg.e.33.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.304092 - 0.0481634i) q^{3} +(-1.19185 + 4.85587i) q^{5} +(5.20977 + 5.20977i) q^{7} +(-8.46936 + 2.75186i) q^{9} +(-0.00492385 + 0.0151541i) q^{11} +(-7.35975 - 3.74998i) q^{13} +(-0.128557 + 1.53404i) q^{15} +(-16.3649 - 2.59194i) q^{17} +(1.93234 + 2.65964i) q^{19} +(1.83517 + 1.33333i) q^{21} +(-5.56670 - 10.9253i) q^{23} +(-22.1590 - 11.5750i) q^{25} +(-4.91185 + 2.50271i) q^{27} +(-22.5752 + 31.0721i) q^{29} +(19.1612 - 13.9214i) q^{31} +(-0.000767432 + 0.00484538i) q^{33} +(-31.5073 + 19.0887i) q^{35} +(-7.24555 + 14.2202i) q^{37} +(-2.41865 - 0.785868i) q^{39} +(12.8290 + 39.4837i) q^{41} +(-46.2243 + 46.2243i) q^{43} +(-3.26846 - 44.4059i) q^{45} +(4.56574 + 28.8270i) q^{47} +5.28342i q^{49} -5.10126 q^{51} +(38.5577 - 6.10694i) q^{53} +(-0.0677177 - 0.0419710i) q^{55} +(0.715706 + 0.715706i) q^{57} +(-44.3689 + 14.4163i) q^{59} +(-5.55183 + 17.0868i) q^{61} +(-58.4600 - 29.7868i) q^{63} +(26.9812 - 31.2686i) q^{65} +(82.3392 + 13.0412i) q^{67} +(-2.21899 - 3.05417i) q^{69} +(-87.7801 - 63.7759i) q^{71} +(56.9118 + 111.696i) q^{73} +(-7.29586 - 2.45260i) q^{75} +(-0.104601 + 0.0532970i) q^{77} +(78.7669 - 108.413i) q^{79} +(63.4671 - 46.1115i) q^{81} +(-20.4786 + 129.296i) q^{83} +(32.0906 - 76.3765i) q^{85} +(-5.36840 + 10.5361i) q^{87} +(-65.2768 - 21.2097i) q^{89} +(-18.8061 - 57.8792i) q^{91} +(5.15625 - 5.15625i) q^{93} +(-15.2179 + 6.21329i) q^{95} +(-10.8430 - 68.4600i) q^{97} -0.141895i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 10 q^{5} + 4 q^{7} + 40 q^{9} + 16 q^{11} + 14 q^{13} + 10 q^{15} + 22 q^{17} - 50 q^{19} + 100 q^{21} + 48 q^{23} + 150 q^{25} + 210 q^{27} + 108 q^{31} - 140 q^{33} - 70 q^{35} + 236 q^{37} - 80 q^{39}+ \cdots + 386 q^{97}+O(q^{100}) $ 56 * q - 10 * q^5 + 4 * q^7 + 40 * q^9 + 16 * q^11 + 14 * q^13 + 10 * q^15 + 22 * q^17 - 50 * q^19 + 100 * q^21 + 48 * q^23 + 150 * q^25 + 210 * q^27 + 108 * q^31 - 140 * q^33 - 70 * q^35 + 236 * q^37 - 80 * q^39 + 104 * q^41 - 96 * q^43 + 20 * q^45 - 104 * q^47 + 200 * q^51 + 88 * q^53 + 140 * q^55 - 280 * q^57 - 200 * q^59 + 108 * q^61 + 654 * q^63 - 510 * q^65 + 282 * q^67 + 40 * q^69 - 470 * q^71 + 62 * q^73 - 350 * q^75 - 396 * q^77 + 560 * q^79 - 586 * q^81 + 468 * q^83 + 50 * q^85 + 280 * q^87 + 230 * q^89 + 62 * q^91 - 300 * q^93 + 360 * q^95 + 386 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{17}{20}\right)$	$1$

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
$3$	0.304092	−	0.0481634i	0.101364	−	0.0160545i	−0.105546	−	0.994414i	$-0.533659\pi$
$3$	0.304092	−	0.0481634i	0.101364	−	0.0160545i	0.206910	+	0.978360i	$0.433659\pi$
$4$		0			0
$5$	−1.19185	+	4.85587i	−0.238371	+	0.971174i
$5$	−1.19185	+	4.85587i	−0.238371	+	0.971174i
$6$		0			0
$7$	5.20977	+	5.20977i	0.744253	+	0.744253i	0.973393	−	0.229140i	$-0.0735915\pi$
$7$	5.20977	+	5.20977i	0.744253	+	0.744253i	−0.229140	+	0.973393i	$0.573592\pi$
$8$		0			0
$9$	−8.46936	+	2.75186i	−0.941040	+	0.305762i
$10$		0			0
$11$	−0.00492385	+	0.0151541i	−0.000447623	+	0.00137764i	−0.951280	−	0.308328i	$-0.900231\pi$
$11$	−0.00492385	+	0.0151541i	−0.000447623	+	0.00137764i	0.950832	+	0.309706i	$0.100231\pi$
$12$		0			0
$13$	−7.35975	−	3.74998i	−0.566135	−	0.288460i	0.147403	−	0.989076i	$-0.452908\pi$
$13$	−7.35975	−	3.74998i	−0.566135	−	0.288460i	−0.713538	+	0.700616i	$0.752908\pi$
$14$		0			0
$15$	−0.128557	+	1.53404i	−0.00857049	+	0.102269i
$16$		0			0
$17$	−16.3649	−	2.59194i	−0.962639	−	0.152467i	−0.344717	−	0.938707i	$-0.612025\pi$
$17$	−16.3649	−	2.59194i	−0.962639	−	0.152467i	−0.617922	+	0.786240i	$0.712025\pi$
$18$		0			0
$19$	1.93234	+	2.65964i	0.101702	+	0.139981i	0.856835	−	0.515591i	$-0.172428\pi$
$19$	1.93234	+	2.65964i	0.101702	+	0.139981i	−0.755133	+	0.655572i	$0.772428\pi$
$20$		0			0
$21$	1.83517	+	1.33333i	0.0873890	+	0.0634919i
$22$		0			0
$23$	−5.56670	−	10.9253i	−0.242030	−	0.475011i	0.737754	−	0.675070i	$-0.235887\pi$
$23$	−5.56670	−	10.9253i	−0.242030	−	0.475011i	−0.979784	+	0.200059i	$0.935887\pi$
$24$		0			0
$25$	−22.1590	−	11.5750i	−0.886359	−	0.462999i
$26$		0			0
$27$	−4.91185	+	2.50271i	−0.181920	+	0.0926931i
$28$		0			0
$29$	−22.5752	+	31.0721i	−0.778455	+	1.07145i	0.216996	+	0.976173i	$0.430374\pi$
$29$	−22.5752	+	31.0721i	−0.778455	+	1.07145i	−0.995451	+	0.0952788i	$0.969626\pi$
$30$		0			0
$31$	19.1612	−	13.9214i	0.618102	−	0.449077i	−0.234156	−	0.972199i	$-0.575233\pi$
$31$	19.1612	−	13.9214i	0.618102	−	0.449077i	0.852258	+	0.523122i	$0.175233\pi$
$32$		0			0
$33$	−0.000767432		0.00484538i	−2.32555e−5		0.000146830i
$34$		0			0
$35$	−31.5073	+	19.0887i	−0.900207	+	0.545391i
$36$		0			0
$37$	−7.24555	+	14.2202i	−0.195826	+	0.384330i	−0.967950	−	0.251141i	$-0.919194\pi$
$37$	−7.24555	+	14.2202i	−0.195826	+	0.384330i	0.772125	+	0.635471i	$0.219194\pi$
$38$		0			0
$39$	−2.41865	−	0.785868i	−0.0620168	−	0.0201505i
$40$		0			0
$41$	12.8290	+	39.4837i	0.312903	+	0.963016i	0.976609	+	0.215023i	$0.0689825\pi$
$41$	12.8290	+	39.4837i	0.312903	+	0.963016i	−0.663706	+	0.747993i	$0.731017\pi$
$42$		0			0
$43$	−46.2243	+	46.2243i	−1.07498	+	1.07498i	−0.0780332	+	0.996951i	$0.524864\pi$
$43$	−46.2243	+	46.2243i	−1.07498	+	1.07498i	−0.996951	+	0.0780332i	$0.975136\pi$
$44$		0			0
$45$	−3.26846	−	44.4059i	−0.0726324	−	0.986798i
$46$		0			0
$47$	4.56574	+	28.8270i	0.0971435	+	0.613340i	0.987444	+	0.157967i	$0.0504940\pi$
$47$	4.56574	+	28.8270i	0.0971435	+	0.613340i	−0.890301	+	0.455373i	$0.849506\pi$
$48$		0			0
$49$			5.28342i			0.107825i
$50$		0			0
$51$	−5.10126			−0.100025
$52$		0			0
$53$	38.5577	−	6.10694i	0.727504	−	0.115225i	0.218313	−	0.975879i	$-0.429945\pi$
$53$	38.5577	−	6.10694i	0.727504	−	0.115225i	0.509191	+	0.860653i	$0.329945\pi$
$54$		0			0
$55$	−0.0677177	−	0.0419710i	−0.00123123	−	0.000763109i
$56$		0			0
$57$	0.715706	+	0.715706i	0.0125562	+	0.0125562i
$58$		0			0
$59$	−44.3689	+	14.4163i	−0.752015	+	0.244344i	−0.659848	−	0.751399i	$-0.729379\pi$
$59$	−44.3689	+	14.4163i	−0.752015	+	0.244344i	−0.0921669	+	0.995744i	$0.529379\pi$
$60$		0			0
$61$	−5.55183	+	17.0868i	−0.0910136	+	0.280111i	−0.986194	−	0.165592i	$-0.947046\pi$
$61$	−5.55183	+	17.0868i	−0.0910136	+	0.280111i	0.895181	+	0.445703i	$0.147046\pi$
$62$		0			0
$63$	−58.4600	−	29.7868i	−0.927936	−	0.472807i
$64$		0			0
$65$	26.9812	−	31.2686i	0.415095	−	0.481055i
$66$		0			0
$67$	82.3392	+	13.0412i	1.22894	+	0.194645i	0.736946	−	0.675952i	$-0.236267\pi$
$67$	82.3392	+	13.0412i	1.22894	+	0.194645i	0.491997	+	0.870597i	$0.336267\pi$
$68$		0			0
$69$	−2.21899	−	3.05417i	−0.0321592	−	0.0442634i
$70$		0			0
$71$	−87.7801	−	63.7759i	−1.23634	−	0.898253i	−0.238990	−	0.971022i	$-0.576816\pi$
$71$	−87.7801	−	63.7759i	−1.23634	−	0.898253i	−0.997349	+	0.0727693i	$0.976816\pi$
$72$		0			0
$73$	56.9118	+	111.696i	0.779614	+	1.53008i	0.846542	+	0.532321i	$0.178680\pi$
$73$	56.9118	+	111.696i	0.779614	+	1.53008i	−0.0669283	+	0.997758i	$0.521320\pi$
$74$		0			0
$75$	−7.29586	−	2.45260i	−0.0972781	−	0.0327014i
$76$		0			0
$77$	−0.104601	+	0.0532970i	−0.00135846	+	0.000692169i
$78$		0			0
$79$	78.7669	−	108.413i	0.997049	−	1.37232i	0.0699304	−	0.997552i	$-0.477722\pi$
$79$	78.7669	−	108.413i	0.997049	−	1.37232i	0.927119	−	0.374768i	$-0.122278\pi$
$80$		0			0
$81$	63.4671	−	46.1115i	0.783544	−	0.569278i
$82$		0			0
$83$	−20.4786	+	129.296i	−0.246730	+	1.55779i	0.483967	+	0.875086i	$0.339196\pi$
$83$	−20.4786	+	129.296i	−0.246730	+	1.55779i	−0.730696	+	0.682703i	$0.760804\pi$
$84$		0			0
$85$	32.0906	−	76.3765i	0.377537	−	0.898547i
$86$		0			0
$87$	−5.36840	+	10.5361i	−0.0617057	+	0.121104i
$88$		0			0
$89$	−65.2768	−	21.2097i	−0.733447	−	0.238311i	−0.0816033	−	0.996665i	$-0.526004\pi$
$89$	−65.2768	−	21.2097i	−0.733447	−	0.238311i	−0.651843	+	0.758354i	$0.726004\pi$
$90$		0			0
$91$	−18.8061	−	57.8792i	−0.206660	−	0.636035i
$92$		0			0
$93$	5.15625	−	5.15625i	0.0554436	−	0.0554436i
$94$		0			0
$95$	−15.2179	+	6.21329i	−0.160189	+	0.0654031i
$96$		0			0
$97$	−10.8430	−	68.4600i	−0.111784	−	0.705774i	−0.978388	−	0.206778i	$-0.933702\pi$
$97$	−10.8430	−	68.4600i	−0.111784	−	0.705774i	0.866604	−	0.498996i	$-0.166298\pi$
$98$		0			0
$99$		−	0.141895i		−	0.00143328i
$100$		0			0
$101$	16.3060			0.161446			0.0807228	−	0.996737i	$-0.474277\pi$
$101$	16.3060			0.161446			0.0807228	+	0.996737i	$0.474277\pi$
$102$		0			0
$103$	10.9428	−	1.73317i	0.106241	−	0.0168269i	−0.103088	−	0.994672i	$-0.532872\pi$
$103$	10.9428	−	1.73317i	0.106241	−	0.0168269i	0.209328	+	0.977845i	$0.432872\pi$
$104$		0			0
$105$	−8.66173	+	7.32222i	−0.0824926	+	0.0697354i
$106$		0			0
$107$	111.065	+	111.065i	1.03799	+	1.03799i	0.999249	+	0.0387372i	$0.0123335\pi$
$107$	111.065	+	111.065i	1.03799	+	1.03799i	0.0387372	+	0.999249i	$0.487666\pi$
$108$		0			0
$109$	−154.778	+	50.2905i	−1.41998	+	0.461381i	−0.915597	−	0.402097i	$-0.868281\pi$
$109$	−154.778	+	50.2905i	−1.41998	+	0.461381i	−0.504387	+	0.863478i	$0.668281\pi$
$110$		0			0
$111$	−1.51842	+	4.67322i	−0.0136795	+	0.0421011i
$112$		0			0
$113$	−50.6257	−	25.7951i	−0.448015	−	0.228275i	0.215401	−	0.976526i	$-0.430894\pi$
$113$	−50.6257	−	25.7951i	−0.448015	−	0.228275i	−0.663416	+	0.748250i	$0.730894\pi$
$114$		0			0
$115$	59.6863	−	14.0099i	0.519012	−	0.121825i
$116$		0			0
$117$	72.6518	+	11.5069i	0.620955	+	0.0983497i
$118$		0			0
$119$	−71.7538	−	98.7606i	−0.602973	−	0.829921i
$120$		0			0
$121$	97.8909	+	71.1219i	0.809015	+	0.587784i
$122$		0			0
$123$	5.80287	+	11.3888i	0.0471778	+	0.0925916i
$124$		0			0
$125$	82.6168	−	93.8055i	0.660934	−	0.750444i
$126$		0			0
$127$	151.665	−	77.2771i	1.19421	−	0.608481i	0.260141	−	0.965571i	$-0.416231\pi$
$127$	151.665	−	77.2771i	1.19421	−	0.608481i	0.934070	+	0.357090i	$0.116231\pi$
$128$		0			0
$129$	−11.8301	+	16.2828i	−0.0917064	+	0.126223i
$130$		0			0
$131$	193.977	−	140.933i	1.48074	−	1.07582i	0.503428	−	0.864037i	$-0.332072\pi$
$131$	193.977	−	140.933i	1.48074	−	1.07582i	0.977316	−	0.211787i	$-0.0679282\pi$
$132$		0			0
$133$	−3.78905	+	23.9231i	−0.0284891	+	0.179873i
$134$		0			0
$135$	−6.29865	−	26.8342i	−0.0466567	−	0.198772i
$136$		0			0
$137$	−15.4651	+	30.3519i	−0.112884	+	0.221547i	−0.940536	−	0.339695i	$-0.889676\pi$
$137$	−15.4651	+	30.3519i	−0.112884	+	0.221547i	0.827652	+	0.561242i	$0.189676\pi$
$138$		0			0
$139$	54.7441	+	17.7874i	0.393843	+	0.127967i	0.499242	−	0.866463i	$-0.333612\pi$
$139$	54.7441	+	17.7874i	0.393843	+	0.127967i	−0.105399	+	0.994430i	$0.533612\pi$
$140$		0			0
$141$	2.77681	+	8.54615i	0.0196937	+	0.0606110i
$142$		0			0
$143$	0.0930658	−	0.0930658i	0.000650810	−	0.000650810i
$144$		0			0
$145$	−123.976	−	146.656i	−0.855005	−	1.01142i
$146$		0			0
$147$	0.254467	+	1.60664i	0.00173107	+	0.0109296i
$148$		0			0
$149$			73.2146i			0.491373i	0.969349	+	0.245687i	$0.0790134\pi$
$149$			73.2146i			0.491373i	−0.969349	+	0.245687i	$0.920987\pi$
$150$		0			0
$151$	239.940			1.58901			0.794505	−	0.607258i	$-0.207731\pi$
$151$	239.940			1.58901			0.794505	+	0.607258i	$0.207731\pi$
$152$		0			0
$153$	145.733	−	23.0818i	0.952500	−	0.150861i
$154$		0			0
$155$	44.7632	+	109.636i	0.288795	+	0.707331i
$156$		0			0
$157$	33.6220	+	33.6220i	0.214153	+	0.214153i	0.806029	−	0.591876i	$-0.201612\pi$
$157$	33.6220	+	33.6220i	0.214153	+	0.214153i	−0.591876	+	0.806029i	$0.701612\pi$
$158$		0			0
$159$	11.4310	−	3.71415i	0.0718929	−	0.0233594i
$160$		0			0
$161$	27.9169	−	85.9193i	0.173397	−	0.533660i
$162$		0			0
$163$	4.54279	+	2.31467i	0.0278699	+	0.0142004i	0.467870	−	0.883797i	$-0.345022\pi$
$163$	4.54279	+	2.31467i	0.0278699	+	0.0142004i	−0.440000	+	0.897998i	$0.645022\pi$
$164$		0			0
$165$	−0.0226139	−	0.00950153i	−0.000137054	−	5.75850e-5i
$166$		0			0
$167$	76.5318	+	12.1214i	0.458274	+	0.0725835i	0.381304	−	0.924450i	$-0.375475\pi$
$167$	76.5318	+	12.1214i	0.458274	+	0.0725835i	0.0769706	+	0.997033i	$0.475475\pi$
$168$		0			0
$169$	−59.2321	−	81.5260i	−0.350486	−	0.482402i
$170$		0			0
$171$	−23.6846	−	17.2079i	−0.138506	−	0.100631i
$172$		0			0
$173$	8.32806	+	16.3447i	0.0481391	+	0.0944783i	0.913823	−	0.406113i	$-0.133116\pi$
$173$	8.32806	+	16.3447i	0.0481391	+	0.0944783i	−0.865684	+	0.500591i	$0.833116\pi$
$174$		0			0
$175$	−55.1403	−	175.746i	−0.315087	−	1.00426i
$176$		0			0
$177$	−12.7979	+	6.52085i	−0.0723044	+	0.0368409i
$178$		0			0
$179$	−176.529	+	242.971i	−0.986193	+	1.35738i	−0.0527675	+	0.998607i	$0.516804\pi$
$179$	−176.529	+	242.971i	−0.986193	+	1.35738i	−0.933425	+	0.358771i	$0.883196\pi$
$180$		0			0
$181$	128.129	−	93.0908i	0.707892	−	0.514314i	−0.174601	−	0.984639i	$-0.555863\pi$
$181$	128.129	−	93.0908i	0.707892	−	0.514314i	0.882493	+	0.470325i	$0.155863\pi$
$182$		0			0
$183$	−0.865309	+	5.46335i	−0.00472847	+	0.0298544i
$184$		0			0
$185$	−60.4158	−	52.1318i	−0.326572	−	0.281794i
$186$		0			0
$187$	0.119857	−	0.235232i	0.000640944	−	0.00125792i
$188$		0			0
$189$	−38.6282	−	12.5511i	−0.204382	−	0.0664077i
$190$		0			0
$191$	−38.7640	−	119.303i	−0.202953	−	0.624625i	−0.999791	−	0.0204322i	$-0.993496\pi$
$191$	−38.7640	−	119.303i	−0.202953	−	0.624625i	0.796838	−	0.604193i	$-0.206504\pi$
$192$		0			0
$193$	−181.855	+	181.855i	−0.942256	+	0.942256i	−0.998421	−	0.0561658i	$-0.982112\pi$
$193$	−181.855	+	181.855i	−0.942256	+	0.942256i	0.0561658	+	0.998421i	$0.482112\pi$
$194$		0			0
$195$	6.69875	−	10.8080i	0.0343526	−	0.0554258i
$196$		0			0
$197$	20.8407	+	131.583i	0.105790	+	0.667934i	0.982408	+	0.186747i	$0.0597943\pi$
$197$	20.8407	+	131.583i	0.105790	+	0.667934i	−0.876618	+	0.481187i	$0.840206\pi$
$198$		0			0
$199$		−	88.0843i		−	0.442635i	−0.975202	−	0.221317i	$-0.928964\pi$
$199$		−	88.0843i		−	0.442635i	0.975202	−	0.221317i	$-0.0710356\pi$
$200$		0			0
$201$	25.6668			0.127695
$202$		0			0
$203$	−279.490	+	44.2669i	−1.37680	+	0.218063i
$204$		0			0
$205$	−207.018	+	15.2374i	−1.00984	+	0.0743286i
$206$		0			0
$207$	77.2111	+	77.2111i	0.373001	+	0.373001i
$208$		0			0
$209$	−0.0498188	+	0.0161871i	−0.000238368	+	7.74503e-5i
$210$		0			0
$211$	−68.7332	+	211.539i	−0.325750	+	1.00255i	0.645351	+	0.763886i	$0.276711\pi$
$211$	−68.7332	+	211.539i	−0.325750	+	1.00255i	−0.971101	+	0.238669i	$0.923289\pi$
$212$		0			0
$213$	−29.7649	−	15.1660i	−0.139741	−	0.0712017i
$214$		0			0
$215$	−169.367	−	279.552i	−0.787752	−	1.30024i
$216$		0			0
$217$	172.353	+	27.2980i	0.794251	+	0.125797i
$218$		0			0
$219$	22.6861	+	31.2247i	0.103589	+	0.142579i
$220$		0			0
$221$	110.722	+	80.4440i	0.501003	+	0.364000i
$222$		0			0
$223$	40.4867	+	79.4597i	0.181555	+	0.356321i	0.963790	−	0.266662i	$-0.0859206\pi$
$223$	40.4867	+	79.4597i	0.181555	+	0.356321i	−0.782235	+	0.622983i	$0.785921\pi$
$224$		0			0
$225$	219.525	+	37.0541i	0.975666	+	0.164685i
$226$		0			0
$227$	−334.709	+	170.543i	−1.47449	+	0.751289i	−0.992192	−	0.124719i	$-0.960197\pi$
$227$	−334.709	+	170.543i	−1.47449	+	0.751289i	−0.482296	+	0.876008i	$0.660197\pi$
$228$		0			0
$229$	60.1228	−	82.7519i	0.262545	−	0.361362i	−0.657310	−	0.753620i	$-0.728306\pi$
$229$	60.1228	−	82.7519i	0.262545	−	0.361362i	0.919855	+	0.392258i	$0.128306\pi$
$230$		0			0
$231$	−0.0292414	+	0.0212452i	−0.000126586	+	9.19704e-5i
$232$		0			0
$233$	−7.73105	+	48.8119i	−0.0331805	+	0.209493i	−0.998709	−	0.0508057i	$-0.983821\pi$
$233$	−7.73105	+	48.8119i	−0.0331805	+	0.209493i	0.965528	+	0.260299i	$0.0838211\pi$
$234$		0			0
$235$	−145.422	−	12.1868i	−0.618816	−	0.0518589i
$236$		0			0
$237$	18.7308	−	36.7613i	0.0790330	−	0.155111i
$238$		0			0
$239$	−333.655	−	108.411i	−1.39604	−	0.453602i	−0.488135	−	0.872768i	$-0.662323\pi$
$239$	−333.655	−	108.411i	−1.39604	−	0.453602i	−0.907910	+	0.419166i	$0.862323\pi$
$240$		0			0
$241$	−61.6285	−	189.673i	−0.255720	−	0.787025i	−0.993687	−	0.112188i	$-0.964214\pi$
$241$	−61.6285	−	189.673i	−0.255720	−	0.787025i	0.737967	−	0.674837i	$-0.235786\pi$
$242$		0			0
$243$	52.1615	−	52.1615i	0.214657	−	0.214657i
$244$		0			0
$245$	−25.6556	−	6.29705i	−0.104717	−	0.0257023i
$246$		0			0
$247$	−4.24795	−	26.8205i	−0.0171982	−	0.108585i
$248$		0			0
$249$			40.3043i			0.161865i
$250$		0			0
$251$	159.329			0.634776			0.317388	−	0.948296i	$-0.397194\pi$
$251$	159.329			0.634776			0.317388	+	0.948296i	$0.397194\pi$
$252$		0			0
$253$	0.192972	−	0.0305637i	0.000762734	−	0.000120805i
$254$		0			0
$255$	6.07995	−	24.7711i	0.0238429	−	0.0971414i
$256$		0			0
$257$	176.897	+	176.897i	0.688314	+	0.688314i	0.961859	−	0.273545i	$-0.0881964\pi$
$257$	176.897	+	176.897i	0.688314	+	0.688314i	−0.273545	+	0.961859i	$0.588196\pi$
$258$		0			0
$259$	−111.832	+	36.3363i	−0.431782	+	0.140295i
$260$		0			0
$261$	105.691	−	325.284i	0.404948	−	1.24630i
$262$		0			0
$263$	398.342	+	202.966i	1.51461	+	0.771732i	0.996501	−	0.0835821i	$-0.0266361\pi$
$263$	398.342	+	202.966i	1.51461	+	0.771732i	0.518109	+	0.855314i	$0.326636\pi$
$264$		0			0
$265$	−16.3006	+	194.510i	−0.0615117	+	0.734000i
$266$		0			0
$267$	−20.8717	−	3.30575i	−0.0781711	−	0.0123811i
$268$		0			0
$269$	23.4782	+	32.3149i	0.0872794	+	0.120130i	0.850424	−	0.526098i	$-0.176346\pi$
$269$	23.4782	+	32.3149i	0.0872794	+	0.120130i	−0.763144	+	0.646228i	$0.776346\pi$
$270$		0			0
$271$	−106.223	−	77.1756i	−0.391967	−	0.284781i	0.374294	−	0.927310i	$-0.377885\pi$
$271$	−106.223	−	77.1756i	−0.391967	−	0.284781i	−0.766261	+	0.642529i	$0.777885\pi$
$272$		0			0
$273$	−8.50644	−	16.6948i	−0.0311591	−	0.0611532i
$274$		0			0
$275$	0.284515	−	0.278805i	0.00103460	−	0.00101384i
$276$		0			0
$277$	−162.600	+	82.8488i	−0.587003	+	0.299093i	−0.722154	−	0.691732i	$-0.756848\pi$
$277$	−162.600	+	82.8488i	−0.587003	+	0.299093i	0.135151	+	0.990825i	$0.456848\pi$
$278$		0			0
$279$	−123.973	+	170.634i	−0.444347	+	0.611592i
$280$		0			0
$281$	−152.477	+	110.781i	−0.542621	+	0.394237i	−0.825058	−	0.565049i	$-0.808857\pi$
$281$	−152.477	+	110.781i	−0.542621	+	0.394237i	0.282436	+	0.959286i	$0.408857\pi$
$282$		0			0
$283$	−39.6693	+	250.462i	−0.140174	+	0.885024i	0.812926	+	0.582368i	$0.197874\pi$
$283$	−39.6693	+	250.462i	−0.140174	+	0.885024i	−0.953100	+	0.302657i	$0.902126\pi$
$284$		0			0
$285$	−4.32839	+	2.62236i	−0.0151873	+	0.00920126i
$286$		0			0
$287$	−138.865	+	272.537i	−0.483849	+	0.949606i
$288$		0			0
$289$	−13.7648	−	4.47244i	−0.0476289	−	0.0154756i
$290$		0			0
$291$	−6.59454	−	20.2959i	−0.0226617	−	0.0697454i
$292$		0			0
$293$	−371.385	+	371.385i	−1.26752	+	1.26752i	−0.320161	+	0.947363i	$0.603737\pi$
$293$	−371.385	+	371.385i	−1.26752	+	1.26752i	−0.947363	+	0.320161i	$0.896263\pi$
$294$		0			0
$295$	−17.1226	−	232.632i	−0.0580429	−	0.788582i
$296$		0			0
$297$	−0.0137410	−	0.0867575i	−4.62661e−5	−	0.000292113i
$298$		0			0
$299$			101.282i			0.338736i
$300$		0			0
$301$	−481.636			−1.60012
$302$		0			0
$303$	4.95853	−	0.785354i	0.0163648	−	0.00259193i
$304$		0			0
$305$	−76.3542	−	47.3239i	−0.250342	−	0.155160i
$306$		0			0
$307$	−192.147	−	192.147i	−0.625887	−	0.625887i	0.321143	−	0.947031i	$-0.395933\pi$
$307$	−192.147	−	192.147i	−0.625887	−	0.625887i	−0.947031	+	0.321143i	$0.895933\pi$
$308$		0			0
$309$	3.24414	−	1.05408i	0.0104988	−	0.00341127i
$310$		0			0
$311$	−167.394	+	515.187i	−0.538246	+	1.65655i	0.198284	+	0.980145i	$0.436463\pi$
$311$	−167.394	+	515.187i	−0.538246	+	1.65655i	−0.736530	+	0.676405i	$0.763537\pi$
$312$		0			0
$313$	−100.623	−	51.2702i	−0.321481	−	0.163803i	0.285801	−	0.958289i	$-0.407740\pi$
$313$	−100.623	−	51.2702i	−0.321481	−	0.163803i	−0.607282	+	0.794486i	$0.707740\pi$
$314$		0			0
$315$	214.317	−	248.373i	0.680371	−	0.788484i
$316$		0			0
$317$	371.223	+	58.7959i	1.17105	+	0.185476i	0.711507	−	0.702680i	$-0.248013\pi$
$317$	371.223	+	58.7959i	1.17105	+	0.185476i	0.459543	+	0.888156i	$0.348013\pi$
$318$		0			0
$319$	−0.359711	−	0.495100i	−0.00112762	−	0.00155204i
$320$		0			0
$321$	39.1231	+	28.4246i	0.121879	+	0.0885501i
$322$		0			0
$323$	−24.7288	−	48.5331i	−0.0765599	−	0.150257i
$324$		0			0
$325$	119.679	+	168.285i	0.368242	+	0.517799i
$326$		0			0
$327$	−44.6447	+	22.7476i	−0.136528	+	0.0695645i
$328$		0			0
$329$	−126.395	+	173.968i	−0.384181	+	0.528779i
$330$		0			0
$331$	245.947	−	178.691i	0.743044	−	0.539853i	−0.150619	−	0.988592i	$-0.548127\pi$
$331$	245.947	−	178.691i	0.743044	−	0.539853i	0.893663	+	0.448739i	$0.148127\pi$
$332$		0			0
$333$	22.2332	−	140.375i	0.0667662	−	0.421545i
$334$		0			0
$335$	−161.463	+	384.285i	−0.481978	+	1.14712i
$336$		0			0
$337$	−120.484	+	236.463i	−0.357519	+	0.701671i	−0.997788	−	0.0664804i	$-0.978823\pi$
$337$	−120.484	+	236.463i	−0.357519	+	0.701671i	0.640269	+	0.768151i	$0.278823\pi$
$338$		0			0
$339$	−16.6373	−	5.40577i	−0.0490775	−	0.0159462i
$340$		0			0
$341$	0.116619	+	0.358916i	0.000341991	+	0.00105254i
$342$		0			0
$343$	227.753	−	227.753i	0.664004	−	0.664004i
$344$		0			0
$345$	17.4754	−	7.13499i	0.0506533	−	0.0206811i
$346$		0			0
$347$	−74.7456	−	471.925i	−0.215405	−	1.36002i	−0.824025	−	0.566553i	$-0.808277\pi$
$347$	−74.7456	−	471.925i	−0.215405	−	1.36002i	0.608620	−	0.793462i	$-0.291723\pi$
$348$		0			0
$349$		−	668.360i		−	1.91507i	−0.288313	−	0.957536i	$-0.593094\pi$
$349$		−	668.360i		−	1.91507i	0.288313	−	0.957536i	$-0.406906\pi$
$350$		0			0
$351$	45.5351			0.129730
$352$		0			0
$353$	−407.821	+	64.5925i	−1.15530	+	0.182982i	−0.704540	−	0.709664i	$-0.748847\pi$
$353$	−407.821	+	64.5925i	−1.15530	+	0.182982i	−0.450759	+	0.892645i	$0.648847\pi$
$354$		0			0
$355$	414.309	−	350.237i	1.16707	−	0.986584i
$356$		0			0
$357$	−26.5764	−	26.5764i	−0.0744437	−	0.0744437i
$358$		0			0
$359$	−208.215	+	67.6531i	−0.579985	+	0.188449i	−0.584294	−	0.811542i	$-0.698628\pi$
$359$	−208.215	+	67.6531i	−0.579985	+	0.188449i	0.00430872	+	0.999991i	$0.498628\pi$
$360$		0			0
$361$	108.215	−	333.053i	0.299766	−	0.922584i
$362$		0			0
$363$	33.1933	+	16.9128i	0.0914416	+	0.0465918i
$364$		0			0
$365$	−610.211	+	143.232i	−1.67181	+	0.392415i
$366$		0			0
$367$	434.943	+	68.8883i	1.18513	+	0.187706i	0.717719	−	0.696333i	$-0.245186\pi$
$367$	434.943	+	68.8883i	1.18513	+	0.187706i	0.467413	+	0.884039i	$0.345186\pi$
$368$		0			0
$369$	−217.307	−	299.097i	−0.588908	−	0.810562i
$370$		0			0
$371$	232.693	+	169.061i	0.627204	+	0.455690i
$372$		0			0
$373$	202.184	+	396.808i	0.542047	+	1.06383i	0.985839	+	0.167697i	$0.0536331\pi$
$373$	202.184	+	396.808i	0.542047	+	1.06383i	−0.443791	+	0.896130i	$0.646367\pi$
$374$		0			0
$375$	20.6051	−	32.5046i	0.0549469	−	0.0866789i
$376$		0			0
$377$	282.668	−	144.026i	0.749781	−	0.382033i
$378$		0			0
$379$	−13.1824	+	18.1441i	−0.0347822	+	0.0478735i	−0.826054	−	0.563591i	$-0.809419\pi$
$379$	−13.1824	+	18.1441i	−0.0347822	+	0.0478735i	0.791272	+	0.611465i	$0.209419\pi$
$380$		0			0
$381$	42.3981	−	30.8040i	0.111281	−	0.0808505i
$382$		0			0
$383$	10.8701	−	68.6309i	0.0283814	−	0.179193i	−0.969425	−	0.245386i	$-0.921085\pi$
$383$	10.8701	−	68.6309i	0.0283814	−	0.179193i	0.997807	+	0.0661930i	$0.0210853\pi$
$384$		0			0
$385$	−0.134134	−	0.571453i	−0.000348400	−	0.00148429i
$386$		0			0
$387$	264.287	−	518.693i	0.682913	−	1.34029i
$388$		0			0
$389$	198.486	+	64.4919i	0.510246	+	0.165789i	0.552814	−	0.833305i	$-0.313554\pi$
$389$	198.486	+	64.4919i	0.510246	+	0.165789i	−0.0425683	+	0.999094i	$0.513554\pi$
$390$		0			0
$391$	62.7806	+	193.219i	0.160564	+	0.494166i
$392$		0			0
$393$	52.1992	−	52.1992i	0.132822	−	0.132822i
$394$		0			0
$395$	432.562	+	511.694i	1.09509	+	1.29543i
$396$		0			0
$397$	−63.3818	−	400.177i	−0.159652	−	1.00800i	−0.929244	−	0.369466i	$-0.879540\pi$
$397$	−63.3818	−	400.177i	−0.159652	−	1.00800i	0.769592	−	0.638536i	$-0.220460\pi$
$398$		0			0
$399$			7.45732i			0.0186900i
$400$		0			0
$401$	−769.970			−1.92012			−0.960062	−	0.279788i	$-0.909736\pi$
$401$	−769.970			−1.92012			−0.960062	+	0.279788i	$0.909736\pi$
$402$		0			0
$403$	−193.226	+	30.6040i	−0.479470	+	0.0759406i
$404$		0			0
$405$	148.268	+	363.146i	0.366094	+	0.896657i
$406$		0			0
$407$	−0.179818	−	0.179818i	−0.000441812	−	0.000441812i
$408$		0			0
$409$	527.294	−	171.328i	1.28923	−	0.418895i	0.417407	−	0.908720i	$-0.362939\pi$
$409$	527.294	−	171.328i	1.28923	−	0.418895i	0.871821	+	0.489824i	$0.162939\pi$
$410$		0			0
$411$	−3.24095	+	9.97463i	−0.00788553	+	0.0242692i
$412$		0			0
$413$	−306.257	−	156.046i	−0.741543	−	0.377835i
$414$		0			0
$415$	−603.440	−	253.544i	−1.45407	−	0.610948i
$416$		0			0
$417$	17.5040	+	2.77235i	0.0419759	+	0.00664833i
$418$		0			0
$419$	145.995	+	200.945i	0.348437	+	0.479583i	0.946882	−	0.321581i	$-0.104214\pi$
$419$	145.995	+	200.945i	0.348437	+	0.479583i	−0.598445	+	0.801164i	$0.704214\pi$
$420$		0			0
$421$	614.701	+	446.607i	1.46010	+	1.06082i	0.983337	+	0.181791i	$0.0581893\pi$
$421$	614.701	+	446.607i	1.46010	+	1.06082i	0.476761	+	0.879033i	$0.341811\pi$
$422$		0			0
$423$	−117.997	−	231.582i	−0.278952	−	0.547474i
$424$		0			0
$425$	332.627	+	246.857i	0.782652	+	0.580841i
$426$		0			0
$427$	−117.942	+	60.0944i	−0.276211	+	0.140736i
$428$		0			0
$429$	0.0238182	−	0.0327829i	5.55202e−5	−	7.64171e-5i
$430$		0			0
$431$	−103.495	+	75.1934i	−0.240127	+	0.174463i	−0.701340	−	0.712827i	$-0.747414\pi$
$431$	−103.495	+	75.1934i	−0.240127	+	0.174463i	0.461213	+	0.887290i	$0.347414\pi$
$432$		0			0
$433$	84.3368	−	532.482i	0.194773	−	1.22975i	−0.675567	−	0.737299i	$-0.736101\pi$
$433$	84.3368	−	532.482i	0.194773	−	1.22975i	0.870340	−	0.492451i	$-0.163899\pi$
$434$		0			0
$435$	−44.7635	−	38.6257i	−0.102905	−	0.0887947i
$436$		0			0
$437$	18.3005	−	35.9167i	0.0418775	−	0.0821892i
$438$		0			0
$439$	212.729	+	69.1197i	0.484576	+	0.157448i	0.541109	−	0.840953i	$-0.318005\pi$
$439$	212.729	+	69.1197i	0.484576	+	0.157448i	−0.0565333	+	0.998401i	$0.518005\pi$
$440$		0			0
$441$	−14.5392	−	44.7471i	−0.0329688	−	0.101467i
$442$		0			0
$443$	247.036	−	247.036i	0.557644	−	0.557644i	−0.370992	−	0.928636i	$-0.620982\pi$
$443$	247.036	−	247.036i	0.557644	−	0.557644i	0.928636	+	0.370992i	$0.120982\pi$
$444$		0			0
$445$	180.792	−	291.697i	0.406274	−	0.655498i
$446$		0			0
$447$	3.52627	+	22.2640i	0.00788874	+	0.0498076i
$448$		0			0
$449$			449.315i			1.00070i	0.865823	+	0.500350i	$0.166795\pi$
$449$			449.315i			1.00070i	−0.865823	+	0.500350i	$0.833205\pi$
$450$		0			0
$451$	−0.661506			−0.00146675
$452$		0			0
$453$	72.9640	−	11.5564i	0.161068	−	0.0255107i
$454$		0			0
$455$	303.468	−	22.3365i	0.666962	−	0.0490911i
$456$		0			0
$457$	387.513	+	387.513i	0.847951	+	0.847951i	0.989877	−	0.141927i	$-0.0453297\pi$
$457$	387.513	+	387.513i	0.847951	+	0.847951i	−0.141927	+	0.989877i	$0.545330\pi$
$458$		0			0
$459$	86.8687	−	28.2253i	0.189256	−	0.0614931i
$460$		0			0
$461$	99.5542	−	306.396i	0.215953	−	0.664634i	−0.783132	−	0.621856i	$-0.786379\pi$
$461$	99.5542	−	306.396i	0.215953	−	0.664634i	0.999085	−	0.0427785i	$-0.0136210\pi$
$462$		0			0
$463$	507.902	+	258.789i	1.09698	+	0.558939i	0.906267	−	0.422706i	$-0.138920\pi$
$463$	507.902	+	258.789i	1.09698	+	0.558939i	0.190714	+	0.981646i	$0.438920\pi$
$464$		0			0
$465$	18.8926	+	31.1836i	0.0406293	+	0.0670615i
$466$		0			0
$467$	−512.366	−	81.1507i	−1.09714	−	0.173770i	−0.418484	−	0.908224i	$-0.637438\pi$
$467$	−512.366	−	81.1507i	−1.09714	−	0.173770i	−0.678659	+	0.734454i	$0.737438\pi$
$468$		0			0
$469$	361.026	+	496.910i	0.769779	+	1.05951i
$470$		0			0
$471$	11.8435	+	8.60484i	0.0251455	+	0.0182693i
$472$		0			0
$473$	−0.472884	−	0.928088i	−0.000999755	−	0.00196213i
$474$		0			0
$475$	−12.0334	−	81.3015i	−0.0253336	−	0.171161i
$476$		0			0
$477$	−309.754	+	157.827i	−0.649379	+	0.330875i
$478$		0			0
$479$	385.360	−	530.403i	0.804510	−	1.10731i	−0.187638	−	0.982238i	$-0.560083\pi$
$479$	385.360	−	530.403i	0.804510	−	1.10731i	0.992147	−	0.125074i	$-0.0399170\pi$
$480$		0			0
$481$	106.651	−	77.4864i	0.221727	−	0.161094i
$482$		0			0
$483$	4.35113	−	27.4719i	0.00900855	−	0.0568777i
$484$		0			0
$485$	345.356	+	28.9420i	0.712075	+	0.0596743i
$486$		0			0
$487$	−337.237	+	661.865i	−0.692479	+	1.35907i	0.230065	+	0.973175i	$0.426106\pi$
$487$	−337.237	+	661.865i	−0.692479	+	1.35907i	−0.922544	+	0.385891i	$0.873894\pi$
$488$		0			0
$489$	1.49291	+	0.485075i	0.00305298	+	0.000991973i
$490$		0			0
$491$	−253.951	−	781.581i	−0.517212	−	1.59182i	−0.779221	−	0.626750i	$-0.784385\pi$
$491$	−253.951	−	781.581i	−0.517212	−	1.59182i	0.262009	−	0.965066i	$-0.415615\pi$
$492$		0			0
$493$	449.977	−	449.977i	0.912732	−	0.912732i
$494$		0			0
$495$	0.689023	+	0.169118i	0.00139197	+	0.000341652i
$496$		0			0
$497$	−125.056	−	789.572i	−0.251622	−	1.58868i
$498$		0			0
$499$			214.512i			0.429883i	0.976627	+	0.214941i	$0.0689561\pi$
$499$			214.512i			0.429883i	−0.976627	+	0.214941i	$0.931044\pi$
$500$		0			0
$501$	23.8565			0.0476178
$502$		0			0
$503$	267.349	−	42.3440i	0.531510	−	0.0841829i	0.115089	−	0.993355i	$-0.463285\pi$
$503$	267.349	−	42.3440i	0.531510	−	0.0841829i	0.416420	+	0.909172i	$0.363285\pi$
$504$		0			0
$505$	−19.4344	+	79.1799i	−0.0384839	+	0.156792i
$506$		0			0
$507$	−21.9386	−	21.9386i	−0.0432714	−	0.0432714i
$508$		0			0
$509$	−29.0432	+	9.43670i	−0.0570593	+	0.0185397i	−0.337408	−	0.941359i	$-0.609550\pi$
$509$	−29.0432	+	9.43670i	−0.0570593	+	0.0185397i	0.280348	+	0.959898i	$0.409550\pi$
$510$		0			0
$511$	−285.412	+	878.407i	−0.558536	+	1.71900i
$512$		0			0
$513$	−16.1477	−	8.22765i	−0.0314769	−	0.0160383i
$514$		0			0
$515$	−4.62615	+	55.2024i	−0.00898282	+	0.107189i
$516$		0			0
$517$	−0.459327	−	0.0727502i	−0.000888446	−	0.000140716i
$518$		0			0
$519$	3.31972	+	4.56920i	0.00639637	+	0.00880385i
$520$		0			0
$521$	666.465	+	484.215i	1.27920	+	0.929395i	0.999529	−	0.0306998i	$-0.00977359\pi$
$521$	666.465	+	484.215i	1.27920	+	0.929395i	0.279674	+	0.960095i	$0.409774\pi$
$522$		0			0
$523$	−389.695	−	764.820i	−0.745115	−	1.46237i	−0.881734	−	0.471746i	$-0.843624\pi$
$523$	−389.695	−	764.820i	−0.745115	−	1.46237i	0.136620	−	0.990624i	$-0.456376\pi$
$524$		0			0
$525$	−25.2322	−	50.7872i	−0.0480614	−	0.0967376i
$526$		0			0
$527$	−349.653	+	178.157i	−0.663478	+	0.338059i
$528$		0			0
$529$	222.565	−	306.335i	0.420728	−	0.579083i
$530$		0			0
$531$	336.104	−	244.194i	0.632964	−	0.459876i
$532$		0			0
$533$	53.6446	−	338.698i	0.100646	−	0.635457i
$534$		0			0
$535$	−671.688	+	406.943i	−1.25549	+	0.760641i
$536$		0			0
$537$	−41.9786	+	82.3877i	−0.0781725	+	0.153422i
$538$		0			0
$539$	−0.0800652	−	0.0260148i	−0.000148544	−	4.82649e-5i
$540$		0			0
$541$	−78.9271	−	242.913i	−0.145891	−	0.449007i	0.851233	−	0.524787i	$-0.175855\pi$
$541$	−78.9271	−	242.913i	−0.145891	−	0.449007i	−0.997125	+	0.0757807i	$0.975855\pi$
$542$		0			0
$543$	34.4793	−	34.4793i	0.0634978	−	0.0634978i
$544$		0			0
$545$	−59.7313	−	811.522i	−0.109599	−	1.48903i
$546$		0			0
$547$	−124.567	−	786.484i	−0.227727	−	1.43781i	−0.791139	−	0.611636i	$-0.790512\pi$
$547$	−124.567	−	786.484i	−0.227727	−	1.43781i	0.563412	−	0.826176i	$-0.309488\pi$
$548$		0			0
$549$		−	159.992i		−	0.291424i
$550$		0			0
$551$	−126.263			−0.229153
$552$		0			0
$553$	975.166	−	154.451i	1.76341	−	0.279297i
$554$		0			0
$555$	−20.8828	−	12.9430i	−0.0376267	−	0.0233208i
$556$		0			0
$557$	−305.214	−	305.214i	−0.547960	−	0.547960i	0.377890	−	0.925850i	$-0.376650\pi$
$557$	−305.214	−	305.214i	−0.547960	−	0.547960i	−0.925850	+	0.377890i	$0.876650\pi$
$558$		0			0
$559$	513.540	−	166.859i	0.918676	−	0.298496i
$560$		0			0
$561$	0.0251179	−	0.0773048i	4.47734e−5	−	0.000137798i
$562$		0			0
$563$	−23.8528	−	12.1536i	−0.0423674	−	0.0215873i	0.432678	−	0.901548i	$-0.357569\pi$
$563$	−23.8528	−	12.1536i	−0.0423674	−	0.0215873i	−0.475046	+	0.879961i	$0.657569\pi$
$564$		0			0
$565$	185.596	−	215.088i	0.328489	−	0.380687i
$566$		0			0
$567$	570.879	+	90.4184i	1.00684	+	0.159468i
$568$		0			0
$569$	356.899	+	491.229i	0.627239	+	0.863320i	0.997855	−	0.0654660i	$-0.0208534\pi$
$569$	356.899	+	491.229i	0.627239	+	0.863320i	−0.370616	+	0.928786i	$0.620853\pi$
$570$		0			0
$571$	−513.921	−	373.385i	−0.900036	−	0.653915i	0.0384389	−	0.999261i	$-0.487761\pi$
$571$	−513.921	−	373.385i	−0.900036	−	0.653915i	−0.938475	+	0.345346i	$0.887761\pi$
$572$		0			0
$573$	−17.5339	−	34.4122i	−0.0306001	−	0.0600562i
$574$		0			0
$575$	−3.10720	+	306.527i	−0.00540383	+	0.533090i
$576$		0			0
$577$	−859.619	+	437.998i	−1.48981	+	0.759095i	−0.994004	−	0.109340i	$-0.965126\pi$
$577$	−859.619	+	437.998i	−1.48981	+	0.759095i	−0.495803	+	0.868435i	$0.665126\pi$
$578$		0			0
$579$	−46.5420	+	64.0595i	−0.0803834	+	0.110638i
$580$		0			0
$581$	−780.294	+	566.916i	−1.34302	+	0.975760i
$582$		0			0
$583$	−0.0973076	+	0.614376i	−0.000166908	+	0.00105382i
$584$		0			0
$585$	−142.466	+	339.073i	−0.243532	+	0.579612i
$586$		0			0
$587$	−33.1929	+	65.1447i	−0.0565467	+	0.110979i	−0.917550	−	0.397620i	$-0.869836\pi$
$587$	−33.1929	+	65.1447i	−0.0565467	+	0.110979i	0.861004	+	0.508599i	$0.169836\pi$
$588$		0			0
$589$	74.0517	+	24.0608i	0.125724	+	0.0408503i
$590$		0			0
$591$	12.6750	+	39.0096i	0.0214467	+	0.0660060i
$592$		0			0
$593$	−11.1016	+	11.1016i	−0.0187211	+	0.0187211i	−0.716405	−	0.697684i	$-0.754214\pi$
$593$	−11.1016	+	11.1016i	−0.0187211	+	0.0187211i	0.697684	+	0.716405i	$0.254214\pi$
$594$		0			0
$595$	565.089	−	230.719i	0.949729	−	0.387763i
$596$		0			0
$597$	−4.24244	−	26.7857i	−0.00710627	−	0.0448672i
$598$		0			0
$599$		−	460.985i		−	0.769592i	−0.923002	−	0.384796i	$-0.874272\pi$
$599$		−	460.985i		−	0.769592i	0.923002	−	0.384796i	$-0.125728\pi$
$600$		0			0
$601$	−685.715			−1.14096			−0.570478	−	0.821313i	$-0.693242\pi$
$601$	−685.715			−1.14096			−0.570478	+	0.821313i	$0.693242\pi$
$602$		0			0
$603$	−733.247	+	116.135i	−1.21600	+	0.192595i
$604$		0			0
$605$	−462.030	+	390.579i	−0.763686	+	0.645584i
$606$		0			0
$607$	296.064	+	296.064i	0.487749	+	0.487749i	0.907595	−	0.419846i	$-0.137916\pi$
$607$	296.064	+	296.064i	0.487749	+	0.487749i	−0.419846	+	0.907595i	$0.637916\pi$
$608$		0			0
$609$	−82.8586	+	26.9224i	−0.136057	+	0.0442076i
$610$		0			0
$611$	74.4979	−	229.281i	0.121928	−	0.375255i
$612$		0			0
$613$	289.170	+	147.339i	0.471729	+	0.240358i	0.673659	−	0.739042i	$-0.264721\pi$
$613$	289.170	+	147.339i	0.471729	+	0.240358i	−0.201930	+	0.979400i	$0.564721\pi$
$614$		0			0
$615$	−62.2186	+	14.6042i	−0.101168	+	0.0237467i
$616$		0			0
$617$	−139.099	−	22.0311i	−0.225444	−	0.0357068i	0.0426905	−	0.999088i	$-0.486407\pi$
$617$	−139.099	−	22.0311i	−0.225444	−	0.0357068i	−0.268134	+	0.963382i	$0.586407\pi$
$618$		0			0
$619$	275.089	+	378.627i	0.444409	+	0.611676i	0.971185	−	0.238328i	$-0.0765993\pi$
$619$	275.089	+	378.627i	0.444409	+	0.611676i	−0.526776	+	0.850004i	$0.676599\pi$
$620$		0			0
$621$	54.6856	+	39.7314i	0.0880605	+	0.0639797i
$622$		0			0
$623$	−229.579	−	450.575i	−0.368506	−	0.723234i
$624$		0			0
$625$	357.040	+	512.979i	0.571264	+	0.820766i
$626$		0			0
$627$	−0.0143699	+	0.00732182i	−2.29185e−5	+	1.16775e-5i
$628$		0			0
$629$	155.430	−	213.931i	0.247107	−	0.340114i
$630$		0			0
$631$	−742.298	+	539.311i	−1.17638	+	0.854693i	−0.991759	−	0.128116i	$-0.959107\pi$
$631$	−742.298	+	539.311i	−1.17638	+	0.854693i	−0.184624	+	0.982809i	$0.559107\pi$
$632$		0			0
$633$	−10.7128	+	67.6378i	−0.0169238	+	0.106853i
$634$		0			0
$635$	194.485	+	828.568i	0.306276	+	1.30483i
$636$		0			0
$637$	19.8127	−	38.8846i	0.0311032	−	0.0610434i
$638$		0			0
$639$	918.943	+	298.583i	1.43810	+	0.467266i
$640$		0			0
$641$	223.674	+	688.399i	0.348946	+	1.07394i	0.959437	+	0.281922i	$0.0909720\pi$
$641$	223.674	+	688.399i	0.348946	+	1.07394i	−0.610491	+	0.792023i	$0.709028\pi$
$642$		0			0
$643$	−126.289	+	126.289i	−0.196405	+	0.196405i	−0.798457	−	0.602052i	$-0.794350\pi$
$643$	−126.289	+	126.289i	−0.196405	+	0.196405i	0.602052	+	0.798457i	$0.294350\pi$
$644$		0			0
$645$	−64.9672	−	76.8522i	−0.100724	−	0.119151i
$646$		0			0
$647$	−45.1994	−	285.378i	−0.0698600	−	0.441079i	−0.997682	−	0.0680545i	$-0.978321\pi$
$647$	−45.1994	−	285.378i	−0.0698600	−	0.441079i	0.927822	−	0.373024i	$-0.121679\pi$
$648$		0			0
$649$		−	0.743352i		−	0.00114538i
$650$		0			0
$651$	53.7258			0.0825281
$652$		0			0
$653$	−27.7696	+	4.39828i	−0.0425263	+	0.00673550i	−0.177661	−	0.984092i	$-0.556853\pi$
$653$	−27.7696	+	4.39828i	−0.0425263	+	0.00673550i	0.135135	+	0.990827i	$0.456853\pi$
$654$		0			0
$655$	453.159	+	1109.90i	0.691846	+	1.69451i
$656$		0			0
$657$	−789.378	−	789.378i	−1.20149	−	1.20149i
$658$		0			0
$659$	251.811	−	81.8182i	0.382110	−	0.124155i	−0.111662	−	0.993746i	$-0.535618\pi$
$659$	251.811	−	81.8182i	0.382110	−	0.124155i	0.493773	+	0.869591i	$0.335618\pi$
$660$		0			0
$661$	−189.648	+	583.677i	−0.286911	+	0.883021i	0.698908	+	0.715211i	$0.253670\pi$
$661$	−189.648	+	583.677i	−0.286911	+	0.883021i	−0.985819	+	0.167810i	$0.946330\pi$
$662$		0			0
$663$	37.5440	+	19.1296i	0.0566275	+	0.0288531i
$664$		0			0
$665$	−111.652	−	46.9120i	−0.167897	−	0.0705443i
$666$		0			0
$667$	465.140	+	73.6709i	0.697361	+	0.110451i
$668$		0			0
$669$	16.1387	+	22.2131i	0.0241237	+	0.0332034i
$670$		0			0
$671$	−0.231598	−	0.168266i	−0.000345153	−	0.000250768i
$672$		0			0
$673$	31.7428	+	62.2988i	0.0471662	+	0.0925689i	0.913387	−	0.407093i	$-0.133458\pi$
$673$	31.7428	+	62.2988i	0.0471662	+	0.0925689i	−0.866220	+	0.499662i	$0.833458\pi$
$674$		0			0
$675$	137.810	+	1.39696i	0.204164	+	0.00206956i
$676$		0			0
$677$	−480.023	+	244.584i	−0.709044	+	0.361276i	−0.771028	−	0.636801i	$-0.780257\pi$
$677$	−480.023	+	244.584i	−0.709044	+	0.361276i	0.0619841	+	0.998077i	$0.480257\pi$
$678$		0			0
$679$	300.172	−	413.151i	0.442079	−	0.608469i
$680$		0			0
$681$	−93.5683	+	67.9814i	−0.137398	+	0.0998258i
$682$		0			0
$683$	−139.326	+	879.672i	−0.203992	+	1.28795i	0.646885	+	0.762587i	$0.276071\pi$
$683$	−139.326	+	879.672i	−0.203992	+	1.28795i	−0.850877	+	0.525365i	$0.823929\pi$
$684$		0			0
$685$	−128.953	−	111.271i	−0.188252	−	0.162440i
$686$		0			0
$687$	14.2972	−	28.0599i	0.0208111	−	0.0408441i
$688$		0			0
$689$	−306.676	−	99.6451i	−0.445103	−	0.144623i
$690$		0			0
$691$	−304.837	−	938.192i	−0.441153	−	1.35773i	−0.886648	−	0.462446i	$-0.846972\pi$
$691$	−304.837	−	938.192i	−0.441153	−	1.35773i	0.445494	−	0.895285i	$-0.353028\pi$
$692$		0			0
$693$	0.739240	−	0.739240i	0.00106672	−	0.00106672i
$694$		0			0
$695$	−151.620	+	244.630i	−0.218159	+	0.351986i
$696$		0			0
$697$	−107.606	−	679.397i	−0.154384	−	0.974744i
$698$		0			0
$699$			15.2157i			0.0217678i
$700$		0			0
$701$	−817.348			−1.16597			−0.582987	−	0.812481i	$-0.698116\pi$
$701$	−817.348			−1.16597			−0.582987	+	0.812481i	$0.698116\pi$
$702$		0			0
$703$	−51.8214	+	8.20770i	−0.0737146	+	0.0116752i
$704$		0			0
$705$	−44.8086	+	3.29809i	−0.0635582	+	0.00467815i
$706$		0			0
$707$	84.9506	+	84.9506i	0.120156	+	0.120156i
$708$		0			0
$709$	−824.089	+	267.763i	−1.16233	+	0.377662i	−0.825773	−	0.564002i	$-0.809261\pi$
$709$	−824.089	+	267.763i	−1.16233	+	0.377662i	−0.336552	+	0.941665i	$0.609261\pi$
$710$		0			0
$711$	−368.766	+	1134.95i	−0.518659	+	1.59627i
$712$		0			0
$713$	−258.759	−	131.844i	−0.362916	−	0.184915i
$714$		0			0
$715$	0.340995	+	0.562836i	0.000476916	+	0.000787183i
$716$		0			0
$717$	−106.683	−	16.8969i	−0.148791	−	0.0235662i
$718$		0			0
$719$	−702.075	−	966.323i	−0.976460	−	1.34398i	−0.938715	−	0.344694i	$-0.887983\pi$
$719$	−702.075	−	966.323i	−0.976460	−	1.34398i	−0.0377446	−	0.999287i	$-0.512017\pi$
$720$		0			0
$721$	66.0388	+	47.9800i	0.0915933	+	0.0665464i
$722$		0			0
$723$	−27.8760	−	54.7098i	−0.0385561	−	0.0756706i
$724$		0			0
$725$	859.902	−	427.219i	1.18607	−	0.589267i
$726$		0			0
$727$	−353.144	+	179.936i	−0.485754	+	0.247504i	−0.679676	−	0.733513i	$-0.737879\pi$
$727$	−353.144	+	179.936i	−0.485754	+	0.247504i	0.193921	+	0.981017i	$0.437879\pi$
$728$		0			0
$729$	−401.654	+	552.829i	−0.550966	+	0.758339i
$730$		0			0
$731$	876.265	−	636.644i	1.19872	−	0.870922i
$732$		0			0
$733$	20.8879	−	131.881i	0.0284965	−	0.179920i	−0.969335	−	0.245744i	$-0.920968\pi$
$733$	20.8879	−	131.881i	0.0284965	−	0.179920i	0.997831	+	0.0658244i	$0.0209677\pi$
$734$		0			0
$735$	−8.10495	−	0.679222i	−0.0110271	−	0.000924112i
$736$		0			0
$737$	−0.603054	+	1.18356i	−0.000818255	+	0.00160592i
$738$		0			0
$739$	164.642	+	53.4955i	0.222791	+	0.0723891i	0.418285	−	0.908316i	$-0.362631\pi$
$739$	164.642	+	53.4955i	0.222791	+	0.0723891i	−0.195495	+	0.980705i	$0.562631\pi$
$740$		0			0
$741$	−2.58353	−	7.95130i	−0.00348655	−	0.0107305i
$742$		0			0
$743$	587.217	−	587.217i	0.790332	−	0.790332i	−0.191216	−	0.981548i	$-0.561243\pi$
$743$	587.217	−	587.217i	0.790332	−	0.790332i	0.981548	+	0.191216i	$0.0612430\pi$
$744$		0			0
$745$	−355.521	−	87.2610i	−0.477209	−	0.117129i
$746$		0			0
$747$	−182.366	−	1151.41i	−0.244131	−	1.54138i
$748$		0			0
$749$			1157.24i			1.54505i
$750$		0			0
$751$	−1229.55			−1.63721			−0.818607	−	0.574354i	$-0.805253\pi$
$751$	−1229.55			−1.63721			−0.818607	+	0.574354i	$0.805253\pi$
$752$		0			0
$753$	48.4506	−	7.67382i	0.0643434	−	0.0101910i
$754$		0			0
$755$	−285.974	+	1165.12i	−0.378773	+	1.54321i
$756$		0			0
$757$	178.090	+	178.090i	0.235258	+	0.235258i	0.814883	−	0.579625i	$-0.196801\pi$
$757$	178.090	+	178.090i	0.235258	+	0.235258i	−0.579625	+	0.814883i	$0.696801\pi$
$758$		0			0
$759$	0.0572091	−	0.0185884i	7.53743e−5	−	2.44906e-5i
$760$		0			0
$761$	−254.019	+	781.791i	−0.333797	+	1.02732i	0.633515	+	0.773731i	$0.281612\pi$
$761$	−254.019	+	781.791i	−0.333797	+	1.02732i	−0.967312	+	0.253591i	$0.918388\pi$
$762$		0			0
$763$	−1068.36	−	544.357i	−1.40021	−	0.713443i
$764$		0			0
$765$	−61.6096	+	735.168i	−0.0805354	+	0.961004i
$766$		0			0
$767$	380.605	+	60.2819i	0.496225	+	0.0785944i
$768$		0			0
$769$	−577.219	−	794.474i	−0.750610	−	1.03313i	−0.997937	−	0.0641945i	$-0.979552\pi$
$769$	−577.219	−	794.474i	−0.750610	−	1.03313i	0.247327	−	0.968932i	$-0.420448\pi$
$770$		0			0
$771$	62.3128	+	45.2729i	0.0808207	+	0.0587197i
$772$		0			0
$773$	−425.185	−	834.473i	−0.550046	−	1.07953i	−0.983930	−	0.178556i	$-0.942857\pi$
$773$	−425.185	−	834.473i	−0.550046	−	1.07953i	0.433884	−	0.900969i	$-0.357143\pi$
$774$		0			0
$775$	−585.731	+	86.6941i	−0.755782	+	0.111863i
$776$		0			0
$777$	−32.2570	+	16.4358i	−0.0415148	+	0.0211529i
$778$		0			0
$779$	−80.2221	+	110.416i	−0.102981	+	0.141741i
$780$		0			0
$781$	1.39868	−	1.01620i	0.00179088	−	0.00130115i
$782$		0			0
$783$	33.1215	−	209.121i	0.0423007	−	0.267076i
$784$		0			0
$785$	−203.337	+	123.192i	−0.259028	+	0.156932i
$786$		0			0
$787$	−142.203	+	279.088i	−0.180689	+	0.354623i	−0.963530	−	0.267599i	$-0.913770\pi$
$787$	−142.203	+	279.088i	−0.180689	+	0.354623i	0.782841	+	0.622222i	$0.213770\pi$
$788$		0			0
$789$	130.908	+	42.5347i	0.165917	+	0.0539096i
$790$		0			0
$791$	−129.362	−	398.135i	−0.163542	−	0.503331i
$792$		0			0
$793$	104.935	−	104.935i	0.132327	−	0.132327i
$794$		0			0
$795$	4.41139	+	59.9340i	0.00554891	+	0.0753887i
$796$		0			0
$797$	−177.193	−	1118.75i	−0.222325	−	1.40370i	−0.806096	−	0.591785i	$-0.798423\pi$
$797$	−177.193	−	1118.75i	−0.222325	−	1.40370i	0.583771	−	0.811918i	$-0.301577\pi$
$798$		0			0
$799$		−	483.584i		−	0.605236i
$800$		0			0
$801$	611.218			0.763069
$802$		0			0
$803$	−1.97287	+	0.312472i	−0.00245687	+	0.000389131i
$804$		0			0
$805$	383.940	+	237.964i	0.476944	+	0.295607i
$806$		0			0
$807$	8.69591	+	8.69591i	0.0107756	+	0.0107756i
$808$		0			0
$809$	599.534	−	194.800i	0.741080	−	0.240792i	0.0859416	−	0.996300i	$-0.472610\pi$
$809$	599.534	−	194.800i	0.741080	−	0.240792i	0.655139	+	0.755509i	$0.272610\pi$
$810$		0			0
$811$	−325.384	+	1001.43i	−0.401213	+	1.23481i	0.522803	+	0.852454i	$0.324886\pi$
$811$	−325.384	+	1001.43i	−0.401213	+	1.23481i	−0.924016	+	0.382354i	$0.875114\pi$
$812$		0			0
$813$	−36.0186	−	18.3524i	−0.0443033	−	0.0225737i
$814$		0			0
$815$	−16.6541	+	19.3005i	−0.0204344	+	0.0236815i
$816$		0			0
$817$	−212.261	−	33.6188i	−0.259805	−	0.0411491i
$818$		0			0
$819$	318.551	+	438.448i	0.388951	+	0.535345i
$820$		0			0
$821$	814.064	+	591.452i	0.991552	+	0.720405i	0.960260	−	0.279105i	$-0.0900379\pi$
$821$	814.064	+	591.452i	0.991552	+	0.720405i	0.0312917	+	0.999510i	$0.490038\pi$
$822$		0			0
$823$	162.195	+	318.326i	0.197078	+	0.386787i	0.968304	−	0.249774i	$-0.0803563\pi$
$823$	162.195	+	318.326i	0.197078	+	0.386787i	−0.771226	+	0.636561i	$0.780356\pi$
$824$		0			0
$825$	0.0730906	−	0.0984856i	8.85947e−5	−	0.000119376i
$826$		0			0
$827$	−687.457	+	350.277i	−0.831266	+	0.423551i	−0.817203	−	0.576350i	$-0.804476\pi$
$827$	−687.457	+	350.277i	−0.831266	+	0.423551i	−0.0140628	+	0.999901i	$0.504476\pi$
$828$		0			0
$829$	−80.1869	+	110.368i	−0.0967272	+	0.133134i	−0.854637	−	0.519225i	$-0.826221\pi$
$829$	−80.1869	+	110.368i	−0.0967272	+	0.133134i	0.757910	+	0.652359i	$0.226221\pi$
$830$		0			0
$831$	−45.4550	+	33.0250i	−0.0546992	+	0.0397413i
$832$		0			0
$833$	13.6943	−	86.4624i	0.0164397	−	0.103796i
$834$		0			0
$835$	−150.075	+	357.182i	−0.179730	+	0.427762i
$836$		0			0
$837$	−59.2755	+	116.335i	−0.0708190	+	0.138990i
$838$		0			0
$839$	−167.630	−	54.4663i	−0.199798	−	0.0649182i	0.207409	−	0.978254i	$-0.433497\pi$
$839$	−167.630	−	54.4663i	−0.199798	−	0.0649182i	−0.407206	+	0.913336i	$0.633497\pi$
$840$		0			0
$841$	−195.952	−	603.078i	−0.232999	−	0.717097i
$842$		0			0
$843$	−41.0313	+	41.0313i	−0.0486730	+	0.0486730i
$844$		0			0
$845$	466.476	−	190.457i	0.552042	−	0.225392i
$846$		0			0
$847$	139.460	+	880.517i	0.164652	+	1.03957i
$848$		0			0
$849$			78.0740i			0.0919600i
$850$		0			0
$851$	195.693			0.229957
$852$		0			0
$853$	1497.82	−	237.231i	1.75594	−	0.278113i	0.806310	−	0.591493i	$-0.201461\pi$
$853$	1497.82	−	237.231i	1.75594	−	0.278113i	0.949628	+	0.313379i	$0.101461\pi$
$854$		0			0
$855$	111.788	−	94.5002i	0.130746	−	0.110526i
$856$		0			0
$857$	−20.1336	−	20.1336i	−0.0234931	−	0.0234931i	0.695263	−	0.718756i	$-0.255288\pi$
$857$	−20.1336	−	20.1336i	−0.0234931	−	0.0234931i	−0.718756	+	0.695263i	$0.755288\pi$
$858$		0			0
$859$	561.717	−	182.513i	0.653920	−	0.212472i	0.0367783	−	0.999323i	$-0.488290\pi$
$859$	561.717	−	182.513i	0.653920	−	0.212472i	0.617142	+	0.786852i	$0.288290\pi$
$860$		0			0
$861$	−29.1013	+	89.5645i	−0.0337994	+	0.104024i
$862$		0			0
$863$	215.182	+	109.640i	0.249341	+	0.127046i	0.574195	−	0.818719i	$-0.305315\pi$
$863$	215.182	+	109.640i	0.249341	+	0.127046i	−0.324854	+	0.945764i	$0.605315\pi$
$864$		0			0
$865$	−89.2938	+	20.9595i	−0.103230	+	0.0242306i
$866$		0			0
$867$	−4.40116	−	0.697075i	−0.00507631	−	0.000804009i
$868$		0			0
$869$	1.25506	+	1.72745i	0.00144426	+	0.00198786i
$870$		0			0
$871$	−557.091	−	404.751i	−0.639600	−	0.464696i
$872$		0			0
$873$	280.226	+	549.974i	0.320992	+	0.629982i
$874$		0			0
$875$	919.119	−	58.2905i	1.05042	−	0.0666177i
$876$		0			0
$877$	−853.531	+	434.896i	−0.973239	+	0.495890i	−0.866923	−	0.498442i	$-0.833906\pi$
$877$	−853.531	+	434.896i	−0.973239	+	0.495890i	−0.106316	+	0.994332i	$0.533906\pi$
$878$		0			0
$879$	−95.0479	+	130.822i	−0.108132	+	0.148831i
$880$		0			0
$881$	730.560	−	530.783i	0.829239	−	0.602477i	−0.0901049	−	0.995932i	$-0.528720\pi$
$881$	730.560	−	530.783i	0.829239	−	0.602477i	0.919344	+	0.393455i	$0.128720\pi$
$882$		0			0
$883$	27.0756	−	170.949i	0.0306632	−	0.193600i	−0.967602	−	0.252481i	$-0.918753\pi$
$883$	27.0756	−	170.949i	0.0306632	−	0.193600i	0.998265	+	0.0588815i	$0.0187534\pi$
$884$		0			0
$885$	−16.4112	−	69.9167i	−0.0185437	−	0.0790020i
$886$		0			0
$887$	11.0071	−	21.6026i	0.0124093	−	0.0243546i	−0.884719	−	0.466125i	$-0.845650\pi$
$887$	11.0071	−	21.6026i	0.0124093	−	0.0243546i	0.897128	+	0.441771i	$0.145650\pi$
$888$		0			0
$889$	1192.73	+	387.543i	1.34166	+	0.435931i
$890$		0			0
$891$	0.386274	+	1.18883i	0.000433529	+	0.00133426i
$892$		0			0
$893$	−67.8467	+	67.8467i	−0.0759761	+	0.0759761i
$894$		0			0
$895$	−969.438	−	1146.79i	−1.08317	−	1.28132i
$896$		0			0
$897$	4.87810	+	30.7991i	0.00543824	+	0.0343357i
$898$		0			0
$899$			909.655i			1.01185i
$900$		0			0
$901$	−646.821			−0.717892
$902$		0			0
$903$	−146.462	+	23.1972i	−0.162195	+	0.0256891i
$904$		0			0
$905$	299.327	+	733.126i	0.330748	+	0.810084i
$906$		0			0
$907$	−438.721	−	438.721i	−0.483706	−	0.483706i	0.422607	−	0.906313i	$-0.361115\pi$
$907$	−438.721	−	438.721i	−0.483706	−	0.483706i	−0.906313	+	0.422607i	$0.861115\pi$
$908$		0			0
$909$	−138.101	+	44.8719i	−0.151927	+	0.0493640i
$910$		0			0
$911$	272.037	−	837.244i	0.298614	−	0.919038i	−0.683370	−	0.730072i	$-0.739486\pi$
$911$	272.037	−	837.244i	0.298614	−	0.919038i	0.981984	−	0.188966i	$-0.0605136\pi$
$912$		0			0
$913$	−1.85853	−	0.946970i	−0.00203563	−	0.00103721i
$914$		0			0
$915$	−25.4980	−	10.7133i	−0.0278667	−	0.0117086i
$916$		0			0
$917$	1744.81	+	276.350i	1.90273	+	0.301363i
$918$		0			0
$919$	−112.533	−	154.888i	−0.122451	−	0.168540i	0.743391	−	0.668858i	$-0.233216\pi$
$919$	−112.533	−	154.888i	−0.122451	−	0.168540i	−0.865842	+	0.500318i	$0.833216\pi$
$920$		0			0
$921$	−67.6850	−	49.1760i	−0.0734908	−	0.0533942i
$922$		0			0
$923$	406.881	+	798.549i	0.440824	+	0.865167i
$924$		0			0
$925$	325.152	−	231.238i	0.351516	−	0.249987i
$926$		0			0
$927$	−87.9089	+	44.7918i	−0.0948316	+	0.0483191i
$928$		0			0
$929$	684.405	−	942.002i	0.736711	−	1.01400i	−0.262090	−	0.965043i	$-0.584412\pi$
$929$	684.405	−	942.002i	0.736711	−	1.01400i	0.998801	−	0.0489527i	$-0.0155883\pi$
$930$		0			0
$931$	−14.0520	+	10.2093i	−0.0150934	+	0.0109660i
$932$		0			0
$933$	−26.0901	+	164.726i	−0.0279637	+	0.176556i
$934$		0			0
$935$	0.999404	+	0.862370i	0.00106888	+	0.000922321i
$936$		0			0
$937$	−357.510	+	701.653i	−0.381547	+	0.748829i	−0.999295	−	0.0375477i	$-0.988045\pi$
$937$	−357.510	+	701.653i	−0.381547	+	0.748829i	0.617747	+	0.786377i	$0.288045\pi$
$938$		0			0
$939$	−33.0681	−	10.7445i	−0.0352163	−	0.0114425i
$940$		0			0
$941$	−87.1483	−	268.215i	−0.0926124	−	0.285032i	0.894012	−	0.448044i	$-0.147879\pi$
$941$	−87.1483	−	268.215i	−0.0926124	−	0.285032i	−0.986624	+	0.163012i	$0.947879\pi$
$942$		0			0
$943$	359.954	−	359.954i	0.381711	−	0.381711i
$944$		0			0
$945$	106.985	−	172.614i	0.113212	−	0.182661i
$946$		0			0
$947$	−158.446	−	1000.39i	−0.167313	−	1.05638i	−0.918250	−	0.396001i	$-0.870398\pi$
$947$	−158.446	−	1000.39i	−0.167313	−	1.05638i	0.750937	−	0.660374i	$-0.229602\pi$
$948$		0			0
$949$		−	1035.47i		−	1.09112i
$950$		0			0
$951$	115.718			0.121680
$952$		0			0
$953$	455.212	−	72.0985i	0.477662	−	0.0756542i	0.0870388	−	0.996205i	$-0.472260\pi$
$953$	455.212	−	72.0985i	0.477662	−	0.0756542i	0.390623	+	0.920551i	$0.372260\pi$
$954$		0			0
$955$	625.523	−	46.0410i	0.654997	−	0.0482105i
$956$		0			0
$957$	−0.133231	−	0.133231i	−0.000139217	−	0.000139217i
$958$		0			0
$959$	−238.696	+	77.5570i	−0.248901	+	0.0808728i
$960$		0			0
$961$	−123.621	+	380.465i	−0.128638	+	0.395906i
$962$		0			0
$963$	−1246.28	−	635.011i	−1.29416	−	0.659409i
$964$		0			0
$965$	−666.321	−	1099.81i	−0.690488	−	1.13970i
$966$		0			0
$967$	989.452	+	156.714i	1.02322	+	0.162062i	0.645421	−	0.763827i	$-0.276682\pi$
$967$	989.452	+	156.714i	1.02322	+	0.162062i	0.377797	+	0.925889i	$0.376682\pi$
$968$		0			0
$969$	−9.85736	−	13.5675i	−0.0101727	−	0.0140015i
$970$		0			0
$971$	373.712	+	271.518i	0.384873	+	0.279627i	0.763351	−	0.645983i	$-0.223552\pi$
$971$	373.712	+	271.518i	0.384873	+	0.279627i	−0.378478	+	0.925610i	$0.623552\pi$
$972$		0			0
$973$	192.536	+	377.873i	0.197879	+	0.388358i
$974$		0			0
$975$	44.4985	+	45.4099i	0.0456395	+	0.0465742i
$976$		0			0
$977$	−22.3418	+	11.3837i	−0.0228677	+	0.0116517i	−0.465387	−	0.885107i	$-0.654085\pi$
$977$	−22.3418	+	11.3837i	−0.0228677	+	0.0116517i	0.442519	+	0.896759i	$0.354085\pi$
$978$		0			0
$979$	0.642826	−	0.884774i	0.000656615	−	0.000903753i
$980$		0			0
$981$	1172.48	−	851.856i	1.19519	−	0.868355i
$982$		0			0
$983$	188.847	−	1192.33i	0.192112	−	1.21295i	−0.683505	−	0.729946i	$-0.739545\pi$
$983$	188.847	−	1192.33i	0.192112	−	1.21295i	0.875618	−	0.483005i	$-0.160455\pi$
$984$		0			0
$985$	−663.789	−	55.6278i	−0.673897	−	0.0564749i
$986$		0			0
$987$	−30.0569	+	58.9900i	−0.0304528	+	0.0597670i
$988$		0			0
$989$	762.329	+	247.696i	0.770808	+	0.250451i
$990$		0			0
$991$	310.612	+	955.967i	0.313433	+	0.964648i	0.976395	+	0.215995i	$0.0692994\pi$
$991$	310.612	+	955.967i	0.313433	+	0.964648i	−0.662961	+	0.748654i	$0.730701\pi$
$992$		0			0
$993$	66.1843	−	66.1843i	0.0666508	−	0.0666508i
$994$		0			0
$995$	427.726	+	104.983i	0.429875	+	0.105511i
$996$		0			0
$997$	59.5222	+	375.808i	0.0597013	+	0.376939i	0.999390	+	0.0349096i	$0.0111143\pi$
$997$	59.5222	+	375.808i	0.0597013	+	0.376939i	−0.939689	+	0.342030i	$0.888886\pi$
$998$		0			0
$999$		−	87.9810i		−	0.0880691i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.3.bg.e.97.4		56
4.3	odd	2		200.3.u.a.97.4	yes	56
25.8	odd	20	inner	400.3.bg.e.33.4		56
100.83	even	20		200.3.u.a.33.4	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.3.u.a.33.4	✓	56	100.83	even	20
200.3.u.a.97.4	yes	56	4.3	odd	2
400.3.bg.e.33.4		56	25.8	odd	20	inner
400.3.bg.e.97.4		56	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	400.bg (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.304092 - 0.0481634i) q^{3} +(-1.19185 + 4.85587i) q^{5} +(5.20977 + 5.20977i) q^{7} +(-8.46936 + 2.75186i) q^{9} +(-0.00492385 + 0.0151541i) q^{11} +(-7.35975 - 3.74998i) q^{13} +(-0.128557 + 1.53404i) q^{15} +(-16.3649 - 2.59194i) q^{17} +(1.93234 + 2.65964i) q^{19} +(1.83517 + 1.33333i) q^{21} +(-5.56670 - 10.9253i) q^{23} +(-22.1590 - 11.5750i) q^{25} +(-4.91185 + 2.50271i) q^{27} +(-22.5752 + 31.0721i) q^{29} +(19.1612 - 13.9214i) q^{31} +(-0.000767432 + 0.00484538i) q^{33} +(-31.5073 + 19.0887i) q^{35} +(-7.24555 + 14.2202i) q^{37} +(-2.41865 - 0.785868i) q^{39} +(12.8290 + 39.4837i) q^{41} +(-46.2243 + 46.2243i) q^{43} +(-3.26846 - 44.4059i) q^{45} +(4.56574 + 28.8270i) q^{47} +5.28342i q^{49} -5.10126 q^{51} +(38.5577 - 6.10694i) q^{53} +(-0.0677177 - 0.0419710i) q^{55} +(0.715706 + 0.715706i) q^{57} +(-44.3689 + 14.4163i) q^{59} +(-5.55183 + 17.0868i) q^{61} +(-58.4600 - 29.7868i) q^{63} +(26.9812 - 31.2686i) q^{65} +(82.3392 + 13.0412i) q^{67} +(-2.21899 - 3.05417i) q^{69} +(-87.7801 - 63.7759i) q^{71} +(56.9118 + 111.696i) q^{73} +(-7.29586 - 2.45260i) q^{75} +(-0.104601 + 0.0532970i) q^{77} +(78.7669 - 108.413i) q^{79} +(63.4671 - 46.1115i) q^{81} +(-20.4786 + 129.296i) q^{83} +(32.0906 - 76.3765i) q^{85} +(-5.36840 + 10.5361i) q^{87} +(-65.2768 - 21.2097i) q^{89} +(-18.8061 - 57.8792i) q^{91} +(5.15625 - 5.15625i) q^{93} +(-15.2179 + 6.21329i) q^{95} +(-10.8430 - 68.4600i) q^{97} -0.141895i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 10 q^{5} + 4 q^{7} + 40 q^{9} + 16 q^{11} + 14 q^{13} + 10 q^{15} + 22 q^{17} - 50 q^{19} + 100 q^{21} + 48 q^{23} + 150 q^{25} + 210 q^{27} + 108 q^{31} - 140 q^{33} - 70 q^{35} + 236 q^{37} - 80 q^{39}+ \cdots + 386 q^{97}+O(q^{100}) \) 56 * q - 10 * q^5 + 4 * q^7 + 40 * q^9 + 16 * q^11 + 14 * q^13 + 10 * q^15 + 22 * q^17 - 50 * q^19 + 100 * q^21 + 48 * q^23 + 150 * q^25 + 210 * q^27 + 108 * q^31 - 140 * q^33 - 70 * q^35 + 236 * q^37 - 80 * q^39 + 104 * q^41 - 96 * q^43 + 20 * q^45 - 104 * q^47 + 200 * q^51 + 88 * q^53 + 140 * q^55 - 280 * q^57 - 200 * q^59 + 108 * q^61 + 654 * q^63 - 510 * q^65 + 282 * q^67 + 40 * q^69 - 470 * q^71 + 62 * q^73 - 350 * q^75 - 396 * q^77 + 560 * q^79 - 586 * q^81 + 468 * q^83 + 50 * q^85 + 280 * q^87 + 230 * q^89 + 62 * q^91 - 300 * q^93 + 360 * q^95 + 386 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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