LMFDB - Embedded newform 400.2.y.c.289.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(129,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("400.129");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.y (of order $10$, degree $4$, not 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:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	8.0.58140625.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 $ x^8 - 3x^7 + 4x^6 - 7x^5 + 11x^4 + 5x^3 - 10x^2 - 25*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 25)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			289.2
Root			$-0.357358 - 1.86824i$ of defining polynomial
Character	$\chi$	$=$	400.289
Dual form			400.2.y.c.209.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.47539 + 0.804303i) q^{3} +(-1.07822 + 1.95894i) q^{5} +0.407162i q^{7} +(3.05361 + 2.21858i) q^{9} +O(q^{10})$	\(q+(2.47539 + 0.804303i) q^{3} +(-1.07822 + 1.95894i) q^{5} +0.407162i q^{7} +(3.05361 + 2.21858i) q^{9} +(1.61803 - 1.17557i) q^{11} +(-0.411842 + 0.566852i) q^{13} +(-4.24459 + 3.98193i) q^{15} +(1.50527 - 0.489091i) q^{17} +(1.52988 + 4.70847i) q^{19} +(-0.327481 + 1.00788i) q^{21} +(0.706192 + 0.971990i) q^{23} +(-2.67490 - 4.22433i) q^{25} +(1.18484 + 1.63079i) q^{27} +(-1.70239 + 5.23943i) q^{29} +(-2.53514 - 7.80237i) q^{31} +(4.95078 - 1.60861i) q^{33} +(-0.797605 - 0.439008i) q^{35} +(3.01846 - 4.15456i) q^{37} +(-1.47539 + 1.07193i) q^{39} +(-5.83802 - 4.24157i) q^{41} -9.16531i q^{43} +(-7.63851 + 3.58973i) q^{45} +(-1.21092 - 0.393451i) q^{47} +6.83422 q^{49} +4.11950 q^{51} +(-4.83133 - 1.56979i) q^{53} +(0.558282 + 4.43715i) q^{55} +12.8858i q^{57} +(5.25838 + 3.82044i) q^{59} +(7.62101 - 5.53699i) q^{61} +(-0.903319 + 1.24331i) q^{63} +(-0.666375 - 1.41796i) q^{65} +(2.93090 - 0.952307i) q^{67} +(0.966327 + 2.97405i) q^{69} +(-2.12183 + 6.53032i) q^{71} +(-0.320429 - 0.441032i) q^{73} +(-3.22378 - 12.6083i) q^{75} +(0.478647 + 0.658801i) q^{77} +(1.69390 - 5.21330i) q^{79} +(-1.87783 - 5.77938i) q^{81} +(0.926457 - 0.301024i) q^{83} +(-0.664904 + 3.47608i) q^{85} +(-8.42819 + 11.6004i) q^{87} +(-1.83363 + 1.33221i) q^{89} +(-0.230800 - 0.167686i) q^{91} -21.3529i q^{93} +(-10.8732 - 2.07982i) q^{95} +(-14.4736 - 4.70276i) q^{97} +7.54893 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 5 q^{3} + q^{9}+O(q^{10}) $ 8 * q + 5 * q^3 + q^9	$ 8 q + 5 q^{3} + q^{9} + 4 q^{11} - 5 q^{13} - 15 q^{15} - 10 q^{17} + 5 q^{19} - 4 q^{21} - 5 q^{23} - 10 q^{25} + 5 q^{27} - 5 q^{29} + 9 q^{31} + 10 q^{33} - 15 q^{35} + 30 q^{37} + 3 q^{39} - 4 q^{41} - 15 q^{45} + 14 q^{49} + 4 q^{51} - 10 q^{53} + 10 q^{55} - 9 q^{61} - 10 q^{63} + 5 q^{65} - 20 q^{67} + 17 q^{69} - 6 q^{71} + 15 q^{73} + 10 q^{75} + 10 q^{77} - 15 q^{79} + 28 q^{81} + 45 q^{83} - 15 q^{85} + 20 q^{87} - 25 q^{89} - 6 q^{91} - 15 q^{95} - 60 q^{97} + 8 q^{99}+O(q^{100}) $ 8 * q + 5 * q^3 + q^9 + 4 * q^11 - 5 * q^13 - 15 * q^15 - 10 * q^17 + 5 * q^19 - 4 * q^21 - 5 * q^23 - 10 * q^25 + 5 * q^27 - 5 * q^29 + 9 * q^31 + 10 * q^33 - 15 * q^35 + 30 * q^37 + 3 * q^39 - 4 * q^41 - 15 * q^45 + 14 * q^49 + 4 * q^51 - 10 * q^53 + 10 * q^55 - 9 * q^61 - 10 * q^63 + 5 * q^65 - 20 * q^67 + 17 * q^69 - 6 * q^71 + 15 * q^73 + 10 * q^75 + 10 * q^77 - 15 * q^79 + 28 * q^81 + 45 * q^83 - 15 * q^85 + 20 * q^87 - 25 * q^89 - 6 * q^91 - 15 * q^95 - 60 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{3}{10}\right)$	$1$

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
$3$	2.47539	+	0.804303i	1.42917	+	0.464365i	0.918503	−	0.395415i	$-0.129399\pi$
$3$	2.47539	+	0.804303i	1.42917	+	0.464365i	0.510665	+	0.859780i	$0.329399\pi$
$4$		0			0
$5$	−1.07822	+	1.95894i	−0.482193	+	0.876065i
$5$	−1.07822	+	1.95894i	−0.482193	+	0.876065i
$6$		0			0
$7$			0.407162i			0.153893i	0.997035	+	0.0769463i	$0.0245170\pi$
$7$			0.407162i			0.153893i	−0.997035	+	0.0769463i	$0.975483\pi$
$8$		0			0
$9$	3.05361	+	2.21858i	1.01787	+	0.739525i
$10$		0			0
$11$	1.61803	−	1.17557i	0.487856	−	0.354448i	−0.316503	−	0.948591i	$-0.602509\pi$
$11$	1.61803	−	1.17557i	0.487856	−	0.354448i	0.804359	+	0.594144i	$0.202509\pi$
$12$		0			0
$13$	−0.411842	+	0.566852i	−0.114224	+	0.157216i	−0.862301	−	0.506396i	$-0.830977\pi$
$13$	−0.411842	+	0.566852i	−0.114224	+	0.157216i	0.748077	+	0.663612i	$0.230977\pi$
$14$		0			0
$15$	−4.24459	+	3.98193i	−1.09595	+	1.02813i
$16$		0			0
$17$	1.50527	−	0.489091i	0.365081	−	0.118622i	−0.120731	−	0.992685i	$-0.538524\pi$
$17$	1.50527	−	0.489091i	0.365081	−	0.118622i	0.485812	+	0.874063i	$0.338524\pi$
$18$		0			0
$19$	1.52988	+	4.70847i	0.350978	+	1.08020i	0.958305	+	0.285747i	$0.0922416\pi$
$19$	1.52988	+	4.70847i	0.350978	+	1.08020i	−0.607328	+	0.794452i	$0.707758\pi$
$20$		0			0
$21$	−0.327481	+	1.00788i	−0.0714623	+	0.219938i
$22$		0			0
$23$	0.706192	+	0.971990i	0.147251	+	0.202674i	0.876271	−	0.481819i	$-0.160024\pi$
$23$	0.706192	+	0.971990i	0.147251	+	0.202674i	−0.729020	+	0.684493i	$0.760024\pi$
$24$		0			0
$25$	−2.67490	−	4.22433i	−0.534980	−	0.844865i
$26$		0			0
$27$	1.18484	+	1.63079i	0.228022	+	0.313846i
$28$		0			0
$29$	−1.70239	+	5.23943i	−0.316127	+	0.972938i	0.659161	+	0.752001i	$0.270911\pi$
$29$	−1.70239	+	5.23943i	−0.316127	+	0.972938i	−0.975288	+	0.220937i	$0.929089\pi$
$30$		0			0
$31$	−2.53514	−	7.80237i	−0.455325	−	1.40135i	−0.870753	−	0.491721i	$-0.836368\pi$
$31$	−2.53514	−	7.80237i	−0.455325	−	1.40135i	0.415428	−	0.909626i	$-0.363632\pi$
$32$		0			0
$33$	4.95078	−	1.60861i	0.861821	−	0.280023i
$34$		0			0
$35$	−0.797605	−	0.439008i	−0.134820	−	0.0742060i
$36$		0			0
$37$	3.01846	−	4.15456i	0.496232	−	0.683005i	−0.485290	−	0.874353i	$-0.661286\pi$
$37$	3.01846	−	4.15456i	0.496232	−	0.683005i	0.981522	+	0.191348i	$0.0612859\pi$
$38$		0			0
$39$	−1.47539	+	1.07193i	−0.236252	+	0.171647i
$40$		0			0
$41$	−5.83802	−	4.24157i	−0.911745	−	0.662422i	0.0297106	−	0.999559i	$-0.490541\pi$
$41$	−5.83802	−	4.24157i	−0.911745	−	0.662422i	−0.941456	+	0.337137i	$0.890541\pi$
$42$		0			0
$43$		−	9.16531i		−	1.39770i	−0.715270	−	0.698848i	$-0.753696\pi$
$43$		−	9.16531i		−	1.39770i	0.715270	−	0.698848i	$-0.246304\pi$
$44$		0			0
$45$	−7.63851	+	3.58973i	−1.13868	+	0.535126i
$46$		0			0
$47$	−1.21092	−	0.393451i	−0.176631	−	0.0573907i	0.219367	−	0.975643i	$-0.429601\pi$
$47$	−1.21092	−	0.393451i	−0.176631	−	0.0573907i	−0.395997	+	0.918252i	$0.629601\pi$
$48$		0			0
$49$	6.83422			0.976317
$50$		0			0
$51$	4.11950			0.576846
$52$		0			0
$53$	−4.83133	−	1.56979i	−0.663634	−	0.215628i	−0.0422180	−	0.999108i	$-0.513442\pi$
$53$	−4.83133	−	1.56979i	−0.663634	−	0.215628i	−0.621416	+	0.783481i	$0.713442\pi$
$54$		0			0
$55$	0.558282	+	4.43715i	0.0752787	+	0.598306i
$56$		0			0
$57$			12.8858i			1.70677i
$58$		0			0
$59$	5.25838	+	3.82044i	0.684583	+	0.497379i	0.874875	−	0.484349i	$-0.160943\pi$
$59$	5.25838	+	3.82044i	0.684583	+	0.497379i	−0.190292	+	0.981728i	$0.560943\pi$
$60$		0			0
$61$	7.62101	−	5.53699i	0.975770	−	0.708938i	0.0190107	−	0.999819i	$-0.493948\pi$
$61$	7.62101	−	5.53699i	0.975770	−	0.708938i	0.956759	+	0.290881i	$0.0939483\pi$
$62$		0			0
$63$	−0.903319	+	1.24331i	−0.113807	+	0.156643i
$64$		0			0
$65$	−0.666375	−	1.41796i	−0.0826536	−	0.175877i
$66$		0			0
$67$	2.93090	−	0.952307i	0.358066	−	0.116343i	−0.124459	−	0.992225i	$-0.539720\pi$
$67$	2.93090	−	0.952307i	0.358066	−	0.116343i	0.482526	+	0.875882i	$0.339720\pi$
$68$		0			0
$69$	0.966327	+	2.97405i	0.116332	+	0.358033i
$70$		0			0
$71$	−2.12183	+	6.53032i	−0.251815	+	0.775007i	0.742625	+	0.669707i	$0.233580\pi$
$71$	−2.12183	+	6.53032i	−0.251815	+	0.775007i	−0.994440	+	0.105300i	$0.966420\pi$
$72$		0			0
$73$	−0.320429	−	0.441032i	−0.0375033	−	0.0516189i	0.789854	−	0.613296i	$-0.210157\pi$
$73$	−0.320429	−	0.441032i	−0.0375033	−	0.0516189i	−0.827357	+	0.561677i	$0.810157\pi$
$74$		0			0
$75$	−3.22378	−	12.6083i	−0.372250	−	1.45588i
$76$		0			0
$77$	0.478647	+	0.658801i	0.0545469	+	0.0750774i
$78$		0			0
$79$	1.69390	−	5.21330i	0.190579	−	0.586542i	−0.809421	−	0.587229i	$-0.800219\pi$
$79$	1.69390	−	5.21330i	0.190579	−	0.586542i	1.00000		0.000687140i	$0.000218723\pi$
$80$		0			0
$81$	−1.87783	−	5.77938i	−0.208648	−	0.642153i
$82$		0			0
$83$	0.926457	−	0.301024i	0.101692	−	0.0330417i	−0.257729	−	0.966217i	$-0.582974\pi$
$83$	0.926457	−	0.301024i	0.101692	−	0.0330417i	0.359421	+	0.933176i	$0.382974\pi$
$84$		0			0
$85$	−0.664904	+	3.47608i	−0.0721190	+	0.377033i
$86$		0			0
$87$	−8.42819	+	11.6004i	−0.903596	+	1.24369i
$88$		0			0
$89$	−1.83363	+	1.33221i	−0.194364	+	0.141214i	−0.680711	−	0.732552i	$-0.738329\pi$
$89$	−1.83363	+	1.33221i	−0.194364	+	0.141214i	0.486347	+	0.873766i	$0.338329\pi$
$90$		0			0
$91$	−0.230800	−	0.167686i	−0.0241945	−	0.0175783i
$92$		0			0
$93$		−	21.3529i		−	2.21420i
$94$		0			0
$95$	−10.8732	−	2.07982i	−1.11556	−	0.213385i
$96$		0			0
$97$	−14.4736	−	4.70276i	−1.46957	−	0.477493i	−0.538593	−	0.842566i	$-0.681044\pi$
$97$	−14.4736	−	4.70276i	−1.46957	−	0.477493i	−0.930979	+	0.365073i	$0.881044\pi$
$98$		0			0
$99$	7.54893			0.758696
$100$		0			0
$101$	18.3965			1.83052			0.915261	−	0.402861i	$-0.131984\pi$
$101$	18.3965			1.83052			0.915261	+	0.402861i	$0.131984\pi$
$102$		0			0
$103$	−11.3026	−	3.67243i	−1.11368	−	0.361856i	−0.306326	−	0.951927i	$-0.599100\pi$
$103$	−11.3026	−	3.67243i	−1.11368	−	0.361856i	−0.807351	+	0.590071i	$0.799100\pi$
$104$		0			0
$105$	−1.62129	−	1.72823i	−0.158222	−	0.168658i
$106$		0			0
$107$			0.754919i			0.0729808i	0.999334	+	0.0364904i	$0.0116178\pi$
$107$			0.754919i			0.0729808i	−0.999334	+	0.0364904i	$0.988382\pi$
$108$		0			0
$109$	−7.40859	−	5.38265i	−0.709614	−	0.515565i	0.173435	−	0.984845i	$-0.444513\pi$
$109$	−7.40859	−	5.38265i	−0.709614	−	0.515565i	−0.883049	+	0.469281i	$0.844513\pi$
$110$		0			0
$111$	10.8134	−	7.85640i	1.02636	−	0.745697i
$112$		0			0
$113$	−7.54710	+	10.3877i	−0.709971	+	0.977191i	0.289827	+	0.957079i	$0.406402\pi$
$113$	−7.54710	+	10.3877i	−0.709971	+	0.977191i	−0.999798	+	0.0201123i	$0.993598\pi$
$114$		0			0
$115$	−2.66550	+	0.335373i	−0.248559	+	0.0312737i
$116$		0			0
$117$	−2.51521	+	0.817241i	−0.232531	+	0.0755539i
$118$		0			0
$119$	0.199139	+	0.612887i	0.0182551	+	0.0561833i
$120$		0			0
$121$	−2.16312	+	6.65740i	−0.196647	+	0.605218i
$122$		0			0
$123$	−11.0399	−	15.1951i	−0.995432	−	1.37009i
$124$		0			0
$125$	11.1593	−	0.685229i	0.998120	−	0.0612887i
$126$		0			0
$127$	−4.17632	−	5.74821i	−0.370588	−	0.510071i	0.582472	−	0.812850i	$-0.302085\pi$
$127$	−4.17632	−	5.74821i	−0.370588	−	0.510071i	−0.953061	+	0.302780i	$0.902085\pi$
$128$		0			0
$129$	7.37169	−	22.6877i	0.649041	−	1.99754i
$130$		0			0
$131$	−0.739865	−	2.27707i	−0.0646423	−	0.198949i	0.913519	−	0.406796i	$-0.133354\pi$
$131$	−0.739865	−	2.27707i	−0.0646423	−	0.198949i	−0.978161	+	0.207848i	$0.933354\pi$
$132$		0			0
$133$	−1.91711	+	0.622907i	−0.166234	+	0.0540129i
$134$		0			0
$135$	−4.47214	+	0.562683i	−0.384900	+	0.0484281i
$136$		0			0
$137$	−11.1793	+	15.3870i	−0.955111	+	1.31460i	−0.00589176	+	0.999983i	$0.501875\pi$
$137$	−11.1793	+	15.3870i	−0.955111	+	1.31460i	−0.949219	+	0.314615i	$0.898125\pi$
$138$		0			0
$139$	5.44849	−	3.95856i	0.462135	−	0.335761i	−0.332233	−	0.943197i	$-0.607802\pi$
$139$	5.44849	−	3.95856i	0.462135	−	0.335761i	0.794368	+	0.607437i	$0.207802\pi$
$140$		0			0
$141$	−2.68104	−	1.94789i	−0.225784	−	0.164042i
$142$		0			0
$143$			1.40134i			0.117186i
$144$		0			0
$145$	−8.42819	−	8.98413i	−0.699923	−	0.746092i
$146$		0			0
$147$	16.9174	+	5.49679i	1.39532	+	0.453367i
$148$		0			0
$149$	0.720492			0.0590250			0.0295125	−	0.999564i	$-0.490605\pi$
$149$	0.720492			0.0590250			0.0295125	+	0.999564i	$0.490605\pi$
$150$		0			0
$151$	15.5178			1.26282			0.631412	−	0.775447i	$-0.282476\pi$
$151$	15.5178			1.26282			0.631412	+	0.775447i	$0.282476\pi$
$152$		0			0
$153$	5.68158	+	1.84606i	0.459329	+	0.149245i
$154$		0			0
$155$	18.0178	+	3.44645i	1.44723	+	0.276825i
$156$		0			0
$157$			2.78418i			0.222202i	0.993809	+	0.111101i	$0.0354376\pi$
$157$			2.78418i			0.222202i	−0.993809	+	0.111101i	$0.964562\pi$
$158$		0			0
$159$	−10.6968	−	7.77171i	−0.848315	−	0.616337i
$160$		0			0
$161$	−0.395757	+	0.287534i	−0.0311900	+	0.0226609i
$162$		0			0
$163$	−14.2287	+	19.5842i	−1.11448	+	1.53395i	−0.299835	+	0.953991i	$0.596932\pi$
$163$	−14.2287	+	19.5842i	−1.11448	+	1.53395i	−0.814645	+	0.579960i	$0.803068\pi$
$164$		0			0
$165$	−2.18685	+	11.4327i	−0.170246	+	0.890036i
$166$		0			0
$167$	−18.1140	+	5.88559i	−1.40170	+	0.455441i	−0.909741	−	0.415176i	$-0.863720\pi$
$167$	−18.1140	+	5.88559i	−1.40170	+	0.455441i	−0.491961	+	0.870617i	$0.663720\pi$
$168$		0			0
$169$	3.86551	+	11.8968i	0.297347	+	0.915141i
$170$		0			0
$171$	−5.77447	+	17.7720i	−0.441585	+	1.35906i
$172$		0			0
$173$	−7.78642	−	10.7171i	−0.591991	−	0.814805i	0.402955	−	0.915220i	$-0.367983\pi$
$173$	−7.78642	−	10.7171i	−0.591991	−	0.814805i	−0.994946	+	0.100415i	$0.967983\pi$
$174$		0			0
$175$	1.71998	−	1.08912i	0.130018	−	0.0823294i
$176$		0			0
$177$	9.94376	+	13.6864i	0.747419	+	1.02873i
$178$		0			0
$179$	−3.77772	+	11.6266i	−0.282360	+	0.869016i	0.704817	+	0.709389i	$0.251029\pi$
$179$	−3.77772	+	11.6266i	−0.282360	+	0.869016i	−0.987177	+	0.159627i	$0.948971\pi$
$180$		0			0
$181$	3.37348	+	10.3825i	0.250748	+	0.771724i	0.994638	+	0.103421i	$0.0329790\pi$
$181$	3.37348	+	10.3825i	0.250748	+	0.771724i	−0.743889	+	0.668303i	$0.767021\pi$
$182$		0			0
$183$	23.3184	−	7.57661i	1.72375	−	0.560079i
$184$		0			0
$185$	4.88398	+	10.3925i	0.359077	+	0.764072i
$186$		0			0
$187$	1.86061	−	2.56091i	0.136062	−	0.187273i
$188$		0			0
$189$	−0.663995	+	0.482421i	−0.0482986	+	0.0350910i
$190$		0			0
$191$	1.26824	+	0.921429i	0.0917665	+	0.0666723i	0.632722	−	0.774379i	$-0.281937\pi$
$191$	1.26824	+	0.921429i	0.0917665	+	0.0666723i	−0.540956	+	0.841051i	$0.681937\pi$
$192$		0			0
$193$		−	1.65786i		−	0.119335i	−0.998218	−	0.0596675i	$-0.980996\pi$
$193$		−	1.65786i		−	0.119335i	0.998218	−	0.0596675i	$-0.0190040\pi$
$194$		0			0
$195$	−0.509065	−	4.04598i	−0.0364549	−	0.289739i
$196$		0			0
$197$	12.6330	+	4.10470i	0.900061	+	0.292448i	0.722262	−	0.691619i	$-0.243102\pi$
$197$	12.6330	+	4.10470i	0.900061	+	0.292448i	0.177799	+	0.984067i	$0.443102\pi$
$198$		0			0
$199$	12.1025			0.857921			0.428960	−	0.903323i	$-0.358880\pi$
$199$	12.1025			0.857921			0.428960	+	0.903323i	$0.358880\pi$
$200$		0			0
$201$	8.02107			0.565763
$202$		0			0
$203$	−2.13330	−	0.693150i	−0.149728	−	0.0486496i
$204$		0			0
$205$	14.6036	−	6.86300i	1.01996	−	0.479333i
$206$		0			0
$207$			4.53482i			0.315192i
$208$		0			0
$209$	8.01054	+	5.81999i	0.554100	+	0.402577i
$210$		0			0
$211$	−5.42091	+	3.93852i	−0.373191	+	0.271139i	−0.758533	−	0.651635i	$-0.774083\pi$
$211$	−5.42091	+	3.93852i	−0.373191	+	0.271139i	0.385342	+	0.922774i	$0.374083\pi$
$212$		0			0
$213$	−10.5047	+	14.4585i	−0.719772	+	0.990681i
$214$		0			0
$215$	17.9543	+	9.88219i	1.22447	+	0.673960i
$216$		0			0
$217$	3.17683	−	1.03221i	0.215657	−	0.0700712i
$218$		0			0
$219$	−0.438463	−	1.34945i	−0.0296286	−	0.0911873i
$220$		0			0
$221$	−0.342690	+	1.05469i	−0.0230518	+	0.0709463i
$222$		0			0
$223$	6.22564	+	8.56885i	0.416900	+	0.573813i	0.964884	−	0.262675i	$-0.0846048\pi$
$223$	6.22564	+	8.56885i	0.416900	+	0.573813i	−0.547985	+	0.836488i	$0.684605\pi$
$224$		0			0
$225$	1.20390	−	18.8339i	0.0802598	−	1.25559i
$226$		0			0
$227$	11.5272	+	15.8658i	0.765087	+	1.05305i	0.996774	+	0.0802612i	$0.0255755\pi$
$227$	11.5272	+	15.8658i	0.765087	+	1.05305i	−0.231687	+	0.972790i	$0.574425\pi$
$228$		0			0
$229$	−2.73139	+	8.40637i	−0.180496	+	0.555508i	−0.999842	−	0.0177908i	$-0.994337\pi$
$229$	−2.73139	+	8.40637i	−0.180496	+	0.555508i	0.819346	+	0.573299i	$0.194337\pi$
$230$		0			0
$231$	0.654963	+	2.01577i	0.0430934	+	0.132628i
$232$		0			0
$233$	10.5210	−	3.41848i	0.689253	−	0.223952i	0.0566109	−	0.998396i	$-0.481971\pi$
$233$	10.5210	−	3.41848i	0.689253	−	0.223952i	0.632642	+	0.774445i	$0.281971\pi$
$234$		0			0
$235$	2.07638	−	1.94789i	0.135448	−	0.127066i
$236$		0			0
$237$	8.38615	−	11.5425i	0.544739	−	0.749769i
$238$		0			0
$239$	−13.0296	+	9.46655i	−0.842814	+	0.612340i	−0.923155	−	0.384427i	$-0.874399\pi$
$239$	−13.0296	+	9.46655i	−0.842814	+	0.612340i	0.0803411	+	0.996767i	$0.474399\pi$
$240$		0			0
$241$	−4.84498	−	3.52009i	−0.312093	−	0.226749i	0.420701	−	0.907199i	$-0.361784\pi$
$241$	−4.84498	−	3.52009i	−0.312093	−	0.226749i	−0.732794	+	0.680451i	$0.761784\pi$
$242$		0			0
$243$		−	21.8639i		−	1.40257i
$244$		0			0
$245$	−7.36877	+	13.3878i	−0.470773	+	0.855317i
$246$		0			0
$247$	−3.29908	−	1.07193i	−0.209915	−	0.0682056i
$248$		0			0
$249$	2.53546			0.160678
$250$		0			0
$251$	−3.73176			−0.235547			−0.117773	−	0.993041i	$-0.537576\pi$
$251$	−3.73176			−0.235547			−0.117773	+	0.993041i	$0.537576\pi$
$252$		0			0
$253$	2.28528	+	0.742534i	0.143675	+	0.0466827i
$254$		0			0
$255$	−4.44172	+	8.06987i	−0.278151	+	0.505355i
$256$		0			0
$257$		−	23.5935i		−	1.47172i	−0.677132	−	0.735862i	$-0.736777\pi$
$257$		−	23.5935i		−	1.47172i	0.677132	−	0.735862i	$-0.263223\pi$
$258$		0			0
$259$	1.69158	+	1.22900i	0.105109	+	0.0763665i
$260$		0			0
$261$	−16.8225	+	12.2223i	−1.04129	+	0.756540i
$262$		0			0
$263$	−3.90363	+	5.37289i	−0.240708	+	0.331307i	−0.912230	−	0.409678i	$-0.865641\pi$
$263$	−3.90363	+	5.37289i	−0.240708	+	0.331307i	0.671522	+	0.740985i	$0.265641\pi$
$264$		0			0
$265$	8.28436	−	7.77171i	0.508904	−	0.477413i
$266$		0			0
$267$	−5.61044	+	1.82294i	−0.343353	+	0.111562i
$268$		0			0
$269$	4.03078	+	12.4055i	0.245761	+	0.756375i	0.995510	+	0.0946532i	$0.0301742\pi$
$269$	4.03078	+	12.4055i	0.245761	+	0.756375i	−0.749749	+	0.661722i	$0.769826\pi$
$270$		0			0
$271$	3.66147	−	11.2689i	0.222419	−	0.684534i	−0.776125	−	0.630579i	$-0.782817\pi$
$271$	3.66147	−	11.2689i	0.222419	−	0.684534i	0.998543	−	0.0539549i	$-0.0171827\pi$
$272$		0			0
$273$	−0.436451	−	0.600723i	−0.0264152	−	0.0363574i
$274$		0			0
$275$	−9.29407	−	3.69057i	−0.560453	−	0.222550i
$276$		0			0
$277$	−9.96641	−	13.7176i	−0.598824	−	0.824210i	0.396776	−	0.917915i	$-0.370129\pi$
$277$	−9.96641	−	13.7176i	−0.598824	−	0.824210i	−0.995600	+	0.0937053i	$0.970129\pi$
$278$		0			0
$279$	9.56882	−	29.4498i	0.572870	−	1.76311i
$280$		0			0
$281$	−1.56826	−	4.82659i	−0.0935543	−	0.287930i	0.893320	−	0.449421i	$-0.148370\pi$
$281$	−1.56826	−	4.82659i	−0.0935543	−	0.287930i	−0.986874	+	0.161491i	$0.948370\pi$
$282$		0			0
$283$	−11.2461	+	3.65408i	−0.668511	+	0.217212i	−0.623558	−	0.781777i	$-0.714314\pi$
$283$	−11.2461	+	3.65408i	−0.668511	+	0.217212i	−0.0449525	+	0.998989i	$0.514314\pi$
$284$		0			0
$285$	−25.2425	−	13.8937i	−1.49524	−	0.822991i
$286$		0			0
$287$	1.72700	−	2.37702i	0.101942	−	0.140311i
$288$		0			0
$289$	−11.7267	+	8.51992i	−0.689804	+	0.501172i
$290$		0			0
$291$	−32.0454	−	23.2823i	−1.87853	−	1.36484i
$292$		0			0
$293$			19.4348i			1.13540i	0.823237	+	0.567698i	$0.192166\pi$
$293$			19.4348i			1.13540i	−0.823237	+	0.567698i	$0.807834\pi$
$294$		0			0
$295$	−13.1537	+	6.18160i	−0.765837	+	0.359907i
$296$		0			0
$297$	3.83422	+	1.24581i	0.222484	+	0.0722894i
$298$		0			0
$299$	−0.841814			−0.0486834
$300$		0			0
$301$	3.73176			0.215095
$302$		0			0
$303$	45.5386	+	14.7964i	2.61612	+	0.850030i
$304$		0			0
$305$	2.62953	+	20.8992i	0.150566	+	1.19668i
$306$		0			0
$307$		−	25.4169i		−	1.45062i	−0.688423	−	0.725310i	$-0.741697\pi$
$307$		−	25.4169i		−	1.45062i	0.688423	−	0.725310i	$-0.258303\pi$
$308$		0			0
$309$	−25.0246	−	18.1814i	−1.42360	−	1.03431i
$310$		0			0
$311$	12.8292	−	9.32097i	0.727478	−	0.528544i	−0.161287	−	0.986908i	$-0.551564\pi$
$311$	12.8292	−	9.32097i	0.727478	−	0.528544i	0.888765	+	0.458364i	$0.151564\pi$
$312$		0			0
$313$	−4.12416	+	5.67642i	−0.233111	+	0.320850i	−0.909507	−	0.415688i	$-0.863541\pi$
$313$	−4.12416	+	5.67642i	−0.233111	+	0.320850i	0.676396	+	0.736538i	$0.263541\pi$
$314$		0			0
$315$	−1.46160	−	3.11011i	−0.0823519	−	0.175235i
$316$		0			0
$317$	−12.3958	+	4.02763i	−0.696215	+	0.226214i	−0.635681	−	0.771952i	$-0.719280\pi$
$317$	−12.3958	+	4.02763i	−0.696215	+	0.226214i	−0.0605344	+	0.998166i	$0.519280\pi$
$318$		0			0
$319$	3.40479	+	10.4789i	0.190632	+	0.586704i
$320$		0			0
$321$	−0.607184	+	1.86872i	−0.0338897	+	0.104302i
$322$		0			0
$323$	4.60575	+	6.33927i	0.256271	+	0.352726i
$324$		0			0
$325$	3.49620	+	0.223484i	0.193934	+	0.0123966i
$326$		0			0
$327$	−14.0099	−	19.2829i	−0.774747	−	1.06635i
$328$		0			0
$329$	0.160198	−	0.493039i	0.00883201	−	0.0271821i
$330$		0			0
$331$	5.45225	+	16.7803i	0.299683	+	0.922329i	0.981608	+	0.190907i	$0.0611430\pi$
$331$	5.45225	+	16.7803i	0.299683	+	0.922329i	−0.681925	+	0.731422i	$0.738857\pi$
$332$		0			0
$333$	18.4344	−	5.98970i	1.01020	−	0.328234i
$334$		0			0
$335$	−1.29463	+	6.76825i	−0.0707333	+	0.369789i
$336$		0			0
$337$	14.6062	−	20.1037i	0.795649	−	1.09512i	−0.197733	−	0.980256i	$-0.563358\pi$
$337$	14.6062	−	20.1037i	0.795649	−	1.09512i	0.993382	−	0.114860i	$-0.0366421\pi$
$338$		0			0
$339$	−27.0369	+	19.6434i	−1.46844	+	1.06689i
$340$		0			0
$341$	−13.2742	−	9.64426i	−0.718837	−	0.522266i
$342$		0			0
$343$			5.63276i			0.304141i
$344$		0			0
$345$	−6.86789	−	1.31369i	−0.369755	−	0.0707267i
$346$		0			0
$347$	−12.6276	−	4.10297i	−0.677887	−	0.220259i	−0.0502171	−	0.998738i	$-0.515991\pi$
$347$	−12.6276	−	4.10297i	−0.677887	−	0.220259i	−0.627670	+	0.778479i	$0.715991\pi$
$348$		0			0
$349$	18.1283			0.970385			0.485192	−	0.874407i	$-0.338750\pi$
$349$	18.1283			0.970385			0.485192	+	0.874407i	$0.338750\pi$
$350$		0			0
$351$	−1.41238			−0.0753875
$352$		0			0
$353$	16.8377	+	5.47091i	0.896182	+	0.291187i	0.720660	−	0.693288i	$-0.243839\pi$
$353$	16.8377	+	5.47091i	0.896182	+	0.291187i	0.175522	+	0.984476i	$0.443839\pi$
$354$		0			0
$355$	−10.5047	−	11.1976i	−0.557533	−	0.594309i
$356$		0			0
$357$			1.67730i			0.0887723i
$358$		0			0
$359$	−26.3289	−	19.1291i	−1.38959	−	1.00959i	−0.995910	−	0.0903458i	$-0.971203\pi$
$359$	−26.3289	−	19.1291i	−1.38959	−	1.00959i	−0.393677	−	0.919249i	$-0.628797\pi$
$360$		0			0
$361$	−4.45789	+	3.23885i	−0.234626	+	0.170466i
$362$		0			0
$363$	−10.7091	+	14.7399i	−0.562084	+	0.773642i
$364$		0			0
$365$	1.20945	−	0.152172i	0.0633054	−	0.00796507i
$366$		0			0
$367$	31.3355	−	10.1815i	1.63570	−	0.531472i	0.660129	−	0.751152i	$-0.270501\pi$
$367$	31.3355	−	10.1815i	1.63570	−	0.531472i	0.975572	+	0.219680i	$0.0705014\pi$
$368$		0			0
$369$	−8.41677	−	25.9042i	−0.438160	−	1.34852i
$370$		0			0
$371$	0.639160	−	1.96713i	0.0331835	−	0.102128i
$372$		0			0
$373$	2.03754	+	2.80444i	0.105500	+	0.145208i	0.858503	−	0.512809i	$-0.171395\pi$
$373$	2.03754	+	2.80444i	0.105500	+	0.145208i	−0.753003	+	0.658018i	$0.771395\pi$
$374$		0			0
$375$	28.1748	+	7.27927i	1.45494	+	0.375900i
$376$		0			0
$377$	−2.26886	−	3.12282i	−0.116852	−	0.160834i
$378$		0			0
$379$	−0.595979	+	1.83424i	−0.0306134	+	0.0942183i	−0.965196	−	0.261528i	$-0.915773\pi$
$379$	−0.595979	+	1.83424i	−0.0306134	+	0.0942183i	0.934582	+	0.355747i	$0.115773\pi$
$380$		0			0
$381$	−5.71472	−	17.5881i	−0.292774	−	0.901065i
$382$		0			0
$383$	4.68874	−	1.52346i	0.239583	−	0.0778454i	−0.186764	−	0.982405i	$-0.559800\pi$
$383$	4.68874	−	1.52346i	0.239583	−	0.0778454i	0.426348	+	0.904559i	$0.359800\pi$
$384$		0			0
$385$	−1.80664	+	0.227311i	−0.0920748	+	0.0115848i
$386$		0			0
$387$	20.3339	−	27.9873i	1.03363	−	1.42267i
$388$		0			0
$389$	10.8295	−	7.86809i	0.549077	−	0.398928i	−0.278368	−	0.960475i	$-0.589793\pi$
$389$	10.8295	−	7.86809i	0.549077	−	0.398928i	0.827445	+	0.561547i	$0.189793\pi$
$390$		0			0
$391$	1.53840	+	1.11771i	0.0778002	+	0.0565252i
$392$		0			0
$393$		−	6.23172i		−	0.314349i
$394$		0			0
$395$	8.38615	+	8.93932i	0.421953	+	0.449786i
$396$		0			0
$397$	2.03418	+	0.660946i	0.102093	+	0.0331719i	0.359618	−	0.933100i	$-0.382907\pi$
$397$	2.03418	+	0.660946i	0.102093	+	0.0331719i	−0.257525	+	0.966272i	$0.582907\pi$
$398$		0			0
$399$	−5.24660			−0.262659
$400$		0			0
$401$	−26.8213			−1.33939			−0.669696	−	0.742635i	$-0.733576\pi$
$401$	−26.8213			−1.33939			−0.669696	+	0.742635i	$0.733576\pi$
$402$		0			0
$403$	5.46687	+	1.77629i	0.272324	+	0.0884835i
$404$		0			0
$405$	13.3462	+	2.55286i	0.663177	+	0.126852i
$406$		0			0
$407$		−	10.2706i		−	0.509097i
$408$		0			0
$409$	11.3248	+	8.22796i	0.559976	+	0.406847i	0.831450	−	0.555599i	$-0.187511\pi$
$409$	11.3248	+	8.22796i	0.559976	+	0.406847i	−0.271474	+	0.962446i	$0.587511\pi$
$410$		0			0
$411$	−40.0489	+	29.0972i	−1.97547	+	1.43526i
$412$		0			0
$413$	−1.55554	+	2.14101i	−0.0765429	+	0.105352i
$414$		0			0
$415$	−0.409233	+	2.13944i	−0.0200885	+	0.105021i
$416$		0			0
$417$	16.6710	−	5.41674i	0.816384	−	0.265259i
$418$		0			0
$419$	9.54925	+	29.3896i	0.466511	+	1.43577i	0.857072	+	0.515197i	$0.172281\pi$
$419$	9.54925	+	29.3896i	0.466511	+	1.43577i	−0.390560	+	0.920577i	$0.627719\pi$
$420$		0			0
$421$	−2.54622	+	7.83646i	−0.124095	+	0.381926i	−0.993735	−	0.111761i	$-0.964351\pi$
$421$	−2.54622	+	7.83646i	−0.124095	+	0.381926i	0.869640	+	0.493687i	$0.164351\pi$
$422$		0			0
$423$	−2.82477	−	3.88796i	−0.137345	−	0.189039i
$424$		0			0
$425$	−6.09252	−	5.05047i	−0.295530	−	0.244984i
$426$		0			0
$427$	2.25445	+	3.10298i	0.109100	+	0.150164i
$428$		0			0
$429$	−1.12710	+	3.46885i	−0.0544168	+	0.167478i
$430$		0			0
$431$	−8.38925	−	25.8194i	−0.404096	−	1.24368i	−0.921648	−	0.388027i	$-0.873157\pi$
$431$	−8.38925	−	25.8194i	−0.404096	−	1.24368i	0.517552	−	0.855652i	$-0.326843\pi$
$432$		0			0
$433$	−20.4387	+	6.64093i	−0.982220	+	0.319143i	−0.755739	−	0.654873i	$-0.772722\pi$
$433$	−20.4387	+	6.64093i	−0.982220	+	0.319143i	−0.226481	+	0.974016i	$0.572722\pi$
$434$		0			0
$435$	−13.6371	−	29.0181i	−0.653849	−	1.39131i
$436$		0			0
$437$	−3.49620	+	4.81211i	−0.167246	+	0.230194i
$438$		0			0
$439$	20.8691	−	15.1623i	0.996027	−	0.723656i	0.0347942	−	0.999394i	$-0.488922\pi$
$439$	20.8691	−	15.1623i	0.996027	−	0.723656i	0.961233	+	0.275739i	$0.0889224\pi$
$440$		0			0
$441$	20.8690	+	15.1622i	0.993763	+	0.722011i
$442$		0			0
$443$		−	3.18479i		−	0.151314i	−0.997134	−	0.0756570i	$-0.975895\pi$
$443$		−	3.18479i		−	0.151314i	0.997134	−	0.0756570i	$-0.0241054\pi$
$444$		0			0
$445$	−0.632669	−	5.02837i	−0.0299914	−	0.238368i
$446$		0			0
$447$	1.78350	+	0.579494i	0.0843566	+	0.0274091i
$448$		0			0
$449$	−36.0785			−1.70265			−0.851325	−	0.524639i	$-0.824200\pi$
$449$	−36.0785			−1.70265			−0.851325	+	0.524639i	$0.824200\pi$
$450$		0			0
$451$	−14.4324			−0.679594
$452$		0			0
$453$	38.4127	+	12.4811i	1.80479	+	0.586411i
$454$		0			0
$455$	0.577340	−	0.271322i	0.0270661	−	0.0127198i
$456$		0			0
$457$		−	25.5245i		−	1.19399i	−0.802246	−	0.596994i	$-0.796362\pi$
$457$		−	25.5245i		−	1.19399i	0.802246	−	0.596994i	$-0.203638\pi$
$458$		0			0
$459$	2.58111	+	1.87528i	0.120476	+	0.0875307i
$460$		0			0
$461$	13.4614	−	9.78026i	0.626959	−	0.455512i	−0.228387	−	0.973571i	$-0.573345\pi$
$461$	13.4614	−	9.78026i	0.626959	−	0.455512i	0.855345	+	0.518058i	$0.173345\pi$
$462$		0			0
$463$	−10.4730	+	14.4149i	−0.486723	+	0.669916i	−0.979779	−	0.200081i	$-0.935880\pi$
$463$	−10.4730	+	14.4149i	−0.486723	+	0.669916i	0.493057	+	0.869997i	$0.335880\pi$
$464$		0			0
$465$	41.8292	+	23.0231i	1.93978	+	1.06767i
$466$		0			0
$467$	13.5507	−	4.40289i	0.627051	−	0.203741i	0.0217829	−	0.999763i	$-0.493066\pi$
$467$	13.5507	−	4.40289i	0.627051	−	0.203741i	0.605269	+	0.796021i	$0.293066\pi$
$468$		0			0
$469$	0.387743	+	1.19335i	0.0179043	+	0.0551038i
$470$		0			0
$471$	−2.23932	+	6.89193i	−0.103183	+	0.317563i
$472$		0			0
$473$	−10.7745	−	14.8298i	−0.495411	−	0.681874i
$474$		0			0
$475$	15.7979	−	19.0574i	0.724856	−	0.874413i
$476$		0			0
$477$	−11.2703	−	15.5122i	−0.516031	−	0.710255i
$478$		0			0
$479$	0.898820	−	2.76628i	0.0410681	−	0.126395i	−0.928420	−	0.371531i	$-0.878833\pi$
$479$	0.898820	−	2.76628i	0.0410681	−	0.126395i	0.969489	+	0.245137i	$0.0788328\pi$
$480$		0			0
$481$	1.11189	+	3.42205i	0.0506978	+	0.156032i
$482$		0			0
$483$	−1.21092	+	0.393451i	−0.0550987	+	0.0179026i
$484$		0			0
$485$	24.8181	−	23.2823i	1.12693	−	1.05720i
$486$		0			0
$487$	−10.0307	+	13.8060i	−0.454533	+	0.625612i	−0.973364	−	0.229266i	$-0.926368\pi$
$487$	−10.0307	+	13.8060i	−0.454533	+	0.625612i	0.518831	+	0.854877i	$0.326368\pi$
$488$		0			0
$489$	−50.9733	+	37.0343i	−2.30509	+	1.67475i
$490$		0			0
$491$	24.8990	+	18.0902i	1.12368	+	0.816398i	0.984762	−	0.173906i	$-0.0556390\pi$
$491$	24.8990	+	18.0902i	1.12368	+	0.816398i	0.138913	+	0.990305i	$0.455639\pi$
$492$		0			0
$493$			8.71937i			0.392701i
$494$		0			0
$495$	−8.13939	+	14.7879i	−0.365838	+	0.664667i
$496$		0			0
$497$	−2.65890	−	0.863928i	−0.119268	−	0.0387525i
$498$		0			0
$499$	−11.8824			−0.531927			−0.265964	−	0.963983i	$-0.585690\pi$
$499$	−11.8824			−0.531927			−0.265964	+	0.963983i	$0.585690\pi$
$500$		0			0
$501$	−49.5730			−2.21476
$502$		0			0
$503$	2.83247	+	0.920324i	0.126293	+	0.0410352i	0.371482	−	0.928440i	$-0.378850\pi$
$503$	2.83247	+	0.920324i	0.126293	+	0.0410352i	−0.245188	+	0.969475i	$0.578850\pi$
$504$		0			0
$505$	−19.8354	+	36.0377i	−0.882665	+	1.60366i
$506$		0			0
$507$			32.5584i			1.44597i
$508$		0			0
$509$	−29.7038	−	21.5811i	−1.31660	−	0.956564i	−0.999968	−	0.00801464i	$-0.997449\pi$
$509$	−29.7038	−	21.5811i	−1.31660	−	0.956564i	−0.316629	−	0.948549i	$-0.602551\pi$
$510$		0			0
$511$	0.179571	−	0.130466i	0.00794377	−	0.00577149i
$512$		0			0
$513$	−5.86588	+	8.07369i	−0.258985	+	0.356462i
$514$		0			0
$515$	19.3807	−	18.1814i	0.854017	−	0.801169i
$516$		0			0
$517$	−2.42184	+	0.786902i	−0.106512	+	0.0346079i
$518$		0			0
$519$	−10.6546	−	32.7916i	−0.467687	−	1.43939i
$520$		0			0
$521$	0.772662	−	2.37801i	0.0338509	−	0.104182i	−0.932703	−	0.360644i	$-0.882557\pi$
$521$	0.772662	−	2.37801i	0.0338509	−	0.104182i	0.966554	+	0.256462i	$0.0825568\pi$
$522$		0			0
$523$	−24.7609	−	34.0805i	−1.08272	−	1.49024i	−0.856491	−	0.516162i	$-0.827360\pi$
$523$	−24.7609	−	34.0805i	−1.08272	−	1.49024i	−0.226229	−	0.974074i	$-0.572640\pi$
$524$		0			0
$525$	5.13361	−	1.31260i	0.224049	−	0.0572865i
$526$		0			0
$527$	−7.63214	−	10.5047i	−0.332461	−	0.457594i
$528$		0			0
$529$	6.66133	−	20.5015i	0.289623	−	0.891369i
$530$		0			0
$531$	7.58111	+	23.3322i	0.328992	+	1.01253i
$532$		0			0
$533$	4.80868	−	1.56244i	0.208287	−	0.0676766i
$534$		0			0
$535$	−1.47884	−	0.813966i	−0.0639359	−	0.0351908i
$536$		0			0
$537$	−18.7027	+	25.7420i	−0.807080	+	1.11085i
$538$		0			0
$539$	11.0580	−	8.03411i	0.476302	−	0.346053i
$540$		0			0
$541$	22.1259	+	16.0754i	0.951268	+	0.691137i	0.951107	−	0.308863i	$-0.0999485\pi$
$541$	22.1259	+	16.0754i	0.951268	+	0.691137i	0.000161922		1.00000i	$0.499948\pi$
$542$		0			0
$543$			28.4140i			1.21936i
$544$		0			0
$545$	18.5324	−	8.70932i	0.793839	−	0.373066i
$546$		0			0
$547$	−19.3437	−	6.28515i	−0.827077	−	0.268734i	−0.135263	−	0.990810i	$-0.543188\pi$
$547$	−19.3437	−	6.28515i	−0.827077	−	0.268734i	−0.691814	+	0.722076i	$0.743188\pi$
$548$		0			0
$549$	35.5558			1.51748
$550$		0			0
$551$	−27.2742			−1.16192
$552$		0			0
$553$	2.12266	+	0.689692i	0.0902645	+	0.0293287i
$554$		0			0
$555$	3.73103	+	29.6537i	0.158373	+	1.25873i
$556$		0			0
$557$			28.2605i			1.19744i	0.800960	+	0.598718i	$0.204323\pi$
$557$			28.2605i			1.19744i	−0.800960	+	0.598718i	$0.795677\pi$
$558$		0			0
$559$	5.19537	+	3.77466i	0.219741	+	0.159651i
$560$		0			0
$561$	6.66550	−	4.84277i	0.281418	−	0.204462i
$562$		0			0
$563$	7.59738	−	10.4569i	0.320192	−	0.440706i	−0.618334	−	0.785915i	$-0.712192\pi$
$563$	7.59738	−	10.4569i	0.320192	−	0.440706i	0.938526	+	0.345210i	$0.112192\pi$
$564$		0			0
$565$	−12.2115	−	25.9845i	−0.513740	−	1.09318i
$566$		0			0
$567$	2.35314	−	0.764582i	0.0988226	−	0.0321094i
$568$		0			0
$569$	0.953142	+	2.93347i	0.0399578	+	0.122977i	0.969046	−	0.246882i	$-0.0794059\pi$
$569$	0.953142	+	2.93347i	0.0399578	+	0.122977i	−0.929088	+	0.369859i	$0.879406\pi$
$570$		0			0
$571$	1.27552	−	3.92564i	0.0533788	−	0.164283i	−0.920813	−	0.390004i	$-0.872474\pi$
$571$	1.27552	−	3.92564i	0.0533788	−	0.164283i	0.974192	+	0.225721i	$0.0724737\pi$
$572$		0			0
$573$	2.39828	+	3.30095i	0.100190	+	0.137899i
$574$		0			0
$575$	2.21701	−	5.58316i	0.0924557	−	0.232834i
$576$		0			0
$577$	−3.73579	−	5.14187i	−0.155523	−	0.214059i	0.724145	−	0.689648i	$-0.242235\pi$
$577$	−3.73579	−	5.14187i	−0.155523	−	0.214059i	−0.879667	+	0.475589i	$0.842235\pi$
$578$		0			0
$579$	1.33342	−	4.10384i	0.0554150	−	0.170550i
$580$		0			0
$581$	0.122565	+	0.377218i	0.00508487	+	0.0156496i
$582$		0			0
$583$	−9.66266	+	3.13959i	−0.400187	+	0.130028i
$584$		0			0
$585$	1.11101	−	5.80831i	0.0459348	−	0.240144i
$586$		0			0
$587$	12.4046	−	17.0735i	0.511992	−	0.704697i	−0.472261	−	0.881459i	$-0.656562\pi$
$587$	12.4046	−	17.0735i	0.511992	−	0.704697i	0.984254	+	0.176761i	$0.0565621\pi$
$588$		0			0
$589$	32.8588	−	23.8733i	1.35392	−	0.983683i
$590$		0			0
$591$	27.9701	+	20.3215i	1.15054	+	0.835913i
$592$		0			0
$593$		−	21.6529i		−	0.889177i	−0.895735	−	0.444589i	$-0.853350\pi$
$593$		−	21.6529i		−	0.889177i	0.895735	−	0.444589i	$-0.146650\pi$
$594$		0			0
$595$	−1.41532	−	0.270723i	−0.0580227	−	0.0110986i
$596$		0			0
$597$	29.9583	+	9.73405i	1.22611	+	0.398388i
$598$		0			0
$599$	−3.38501			−0.138308			−0.0691539	−	0.997606i	$-0.522030\pi$
$599$	−3.38501			−0.138308			−0.0691539	+	0.997606i	$0.522030\pi$
$600$		0			0
$601$	28.8265			1.17586			0.587928	−	0.808913i	$-0.299944\pi$
$601$	28.8265			1.17586			0.587928	+	0.808913i	$0.299944\pi$
$602$		0			0
$603$	11.0626	+	3.59445i	0.450503	+	0.146377i
$604$		0			0
$605$	−10.7091	−	11.4155i	−0.435388	−	0.464108i
$606$		0			0
$607$			15.6708i			0.636059i	0.948081	+	0.318029i	$0.103021\pi$
$607$			15.6708i			0.636059i	−0.948081	+	0.318029i	$0.896979\pi$
$608$		0			0
$609$	−4.72324	−	3.43163i	−0.191395	−	0.139057i
$610$		0			0
$611$	0.721736	−	0.524372i	0.0291983	−	0.0212138i
$612$		0			0
$613$	−22.4537	+	30.9048i	−0.906896	+	1.24823i	0.0613201	+	0.998118i	$0.480469\pi$
$613$	−22.4537	+	30.9048i	−0.906896	+	1.24823i	−0.968216	+	0.250117i	$0.919531\pi$
$614$		0			0
$615$	41.6696	−	5.24287i	1.68028	−	0.211413i
$616$		0			0
$617$	12.5842	−	4.08884i	0.506619	−	0.164611i	−0.0445449	−	0.999007i	$-0.514184\pi$
$617$	12.5842	−	4.08884i	0.506619	−	0.164611i	0.551164	+	0.834397i	$0.314184\pi$
$618$		0			0
$619$	1.86789	+	5.74878i	0.0750770	+	0.231063i	0.981552	−	0.191197i	$-0.0612369\pi$
$619$	1.86789	+	5.74878i	0.0750770	+	0.231063i	−0.906475	+	0.422260i	$0.861237\pi$
$620$		0			0
$621$	−0.748388	+	2.30330i	−0.0300318	+	0.0924284i
$622$		0			0
$623$	−0.542423	−	0.746582i	−0.0217317	−	0.0299112i
$624$		0			0
$625$	−10.6898	+	22.5993i	−0.427594	+	0.903971i
$626$		0			0
$627$	15.1482	+	20.8497i	0.604960	+	0.832655i
$628$		0			0
$629$	2.51164	−	7.73003i	0.100146	−	0.308216i
$630$		0			0
$631$	11.6763	+	35.9361i	0.464828	+	1.43059i	0.859199	+	0.511642i	$0.170963\pi$
$631$	11.6763	+	35.9361i	0.464828	+	1.43059i	−0.394371	+	0.918952i	$0.629037\pi$
$632$		0			0
$633$	−16.5866	+	5.38932i	−0.659259	+	0.214206i
$634$		0			0
$635$	15.7634	−	1.98334i	0.625550	−	0.0787066i
$636$		0			0
$637$	−2.81462	+	3.87399i	−0.111519	+	0.153493i
$638$		0			0
$639$	−20.9673	+	15.2336i	−0.829452	+	0.602632i
$640$		0			0
$641$	16.8737	+	12.2594i	0.666470	+	0.484219i	0.868842	−	0.495090i	$-0.164865\pi$
$641$	16.8737	+	12.2594i	0.666470	+	0.484219i	−0.202372	+	0.979309i	$0.564865\pi$
$642$		0			0
$643$			37.5552i			1.48103i	0.672039	+	0.740516i	$0.265419\pi$
$643$			37.5552i			1.48103i	−0.672039	+	0.740516i	$0.734581\pi$
$644$		0			0
$645$	36.4956	+	38.9030i	1.43701	+	1.53180i
$646$		0			0
$647$	−26.0592	−	8.46714i	−1.02449	−	0.332878i	−0.251882	−	0.967758i	$-0.581049\pi$
$647$	−26.0592	−	8.46714i	−1.02449	−	0.332878i	−0.772611	+	0.634880i	$0.781049\pi$
$648$		0			0
$649$	12.9994			0.510272
$650$		0			0
$651$	8.69410			0.340749
$652$		0			0
$653$	21.9182	+	7.12164i	0.857724	+	0.278691i	0.704678	−	0.709528i	$-0.251092\pi$
$653$	21.9182	+	7.12164i	0.857724	+	0.278691i	0.153046	+	0.988219i	$0.451092\pi$
$654$		0			0
$655$	5.25838	+	1.00582i	0.205462	+	0.0393008i
$656$		0			0
$657$		−	2.05763i		−	0.0802760i
$658$		0			0
$659$	−16.5717	−	12.0400i	−0.645540	−	0.469012i	0.216209	−	0.976347i	$-0.430631\pi$
$659$	−16.5717	−	12.0400i	−0.645540	−	0.469012i	−0.861749	+	0.507335i	$0.830631\pi$
$660$		0			0
$661$	−11.3181	+	8.22311i	−0.440224	+	0.319842i	−0.785724	−	0.618577i	$-0.787709\pi$
$661$	−11.3181	+	8.22311i	−0.440224	+	0.319842i	0.345500	+	0.938419i	$0.387709\pi$
$662$		0			0
$663$	−1.69659	+	2.33515i	−0.0658899	+	0.0906897i
$664$		0			0
$665$	0.846822	−	4.42713i	0.0328384	−	0.171677i
$666$		0			0
$667$	−6.29489	+	2.04533i	−0.243739	+	0.0791957i
$668$		0			0
$669$	8.51893	+	26.2186i	0.329361	+	1.01367i
$670$		0			0
$671$	5.82193	−	17.9181i	0.224753	−	0.691719i
$672$		0			0
$673$	−4.61160	−	6.34732i	−0.177764	−	0.244671i	0.710832	−	0.703362i	$-0.248319\pi$
$673$	−4.61160	−	6.34732i	−0.177764	−	0.244671i	−0.888596	+	0.458691i	$0.848319\pi$
$674$		0			0
$675$	3.71967	−	9.36734i	0.143170	−	0.360549i
$676$		0			0
$677$	8.46310	+	11.6485i	0.325263	+	0.447687i	0.940065	−	0.340995i	$-0.110764\pi$
$677$	8.46310	+	11.6485i	0.325263	+	0.447687i	−0.614802	+	0.788682i	$0.710764\pi$
$678$		0			0
$679$	1.91478	−	5.89310i	0.0734826	−	0.226156i
$680$		0			0
$681$	15.7734	+	48.5455i	0.604437	+	1.86027i
$682$		0			0
$683$	−12.0537	+	3.91647i	−0.461221	+	0.149860i	−0.530405	−	0.847744i	$-0.677960\pi$
$683$	−12.0537	+	3.91647i	−0.461221	+	0.149860i	0.0691847	+	0.997604i	$0.477960\pi$
$684$		0			0
$685$	−18.0885	−	38.4901i	−0.691125	−	1.47063i
$686$		0			0
$687$	−13.5225	+	18.6122i	−0.515917	+	0.710099i
$688$		0			0
$689$	2.87959	−	2.09214i	0.109704	−	0.0797043i
$690$		0			0
$691$	4.64805	+	3.37700i	0.176820	+	0.128467i	0.672675	−	0.739938i	$-0.265145\pi$
$691$	4.64805	+	3.37700i	0.176820	+	0.128467i	−0.495855	+	0.868405i	$0.665145\pi$
$692$		0			0
$693$			3.07364i			0.116758i
$694$		0			0
$695$	1.87993	+	14.9415i	0.0713098	+	0.566762i
$696$		0			0
$697$	−10.8623	−	3.52937i	−0.411439	−	0.133685i
$698$		0			0
$699$	28.7931			1.08905
$700$		0			0
$701$	−30.5834			−1.15512			−0.577560	−	0.816348i	$-0.695995\pi$
$701$	−30.5834			−1.15512			−0.577560	+	0.816348i	$0.695995\pi$
$702$		0			0
$703$	24.1795	+	7.85640i	0.911948	+	0.296310i
$704$		0			0
$705$	6.70655	−	3.15175i	0.252583	−	0.118702i
$706$		0			0
$707$			7.49036i			0.281704i
$708$		0			0
$709$	−21.8998	−	15.9111i	−0.822464	−	0.597555i	0.0949536	−	0.995482i	$-0.469730\pi$
$709$	−21.8998	−	15.9111i	−0.822464	−	0.597555i	−0.917417	+	0.397927i	$0.869730\pi$
$710$		0			0
$711$	16.7386	−	12.1613i	0.627747	−	0.456085i
$712$		0			0
$713$	5.79353	−	7.97410i	0.216969	−	0.298633i
$714$		0			0
$715$	−2.74513	−	1.51094i	−0.102662	−	0.0565061i
$716$		0			0
$717$	−39.8673	+	12.9537i	−1.48887	+	0.483764i
$718$		0			0
$719$	−5.16263	−	15.8889i	−0.192534	−	0.592557i	−0.999997	−	0.00263916i	$-0.999160\pi$
$719$	−5.16263	−	15.8889i	−0.192534	−	0.592557i	0.807463	−	0.589918i	$-0.200840\pi$
$720$		0			0
$721$	1.49527	−	4.60198i	0.0556869	−	0.171387i
$722$		0			0
$723$	−9.16202	−	12.6104i	−0.340739	−	0.468987i
$724$		0			0
$725$	26.6868	−	6.82348i	0.991123	−	0.253418i
$726$		0			0
$727$	−6.87743	−	9.46598i	−0.255070	−	0.351074i	0.662209	−	0.749319i	$-0.269619\pi$
$727$	−6.87743	−	9.46598i	−0.255070	−	0.351074i	−0.917279	+	0.398246i	$0.869619\pi$
$728$		0			0
$729$	11.9517	−	36.7835i	0.442655	−	1.36235i
$730$		0			0
$731$	−4.48267	−	13.7962i	−0.165798	−	0.510272i
$732$		0			0
$733$	−32.4385	+	10.5399i	−1.19814	+	0.389300i	−0.839077	−	0.544012i	$-0.816904\pi$
$733$	−32.4385	+	10.5399i	−1.19814	+	0.389300i	−0.359065	+	0.933312i	$0.616904\pi$
$734$		0			0
$735$	−29.0085	+	27.2134i	−1.06999	+	1.00378i
$736$		0			0
$737$	3.62279	−	4.98635i	0.133447	−	0.183674i
$738$		0			0
$739$	−4.64794	+	3.37693i	−0.170977	+	0.124222i	−0.669983	−	0.742376i	$-0.733699\pi$
$739$	−4.64794	+	3.37693i	−0.170977	+	0.124222i	0.499006	+	0.866599i	$0.333699\pi$
$740$		0			0
$741$	−7.30434	−	5.30692i	−0.268332	−	0.194954i
$742$		0			0
$743$		−	36.4348i		−	1.33666i	−0.743863	−	0.668332i	$-0.767009\pi$
$743$		−	36.4348i		−	1.33666i	0.743863	−	0.668332i	$-0.232991\pi$
$744$		0			0
$745$	−0.776846	+	1.41140i	−0.0284615	+	0.0517097i
$746$		0			0
$747$	3.49688	+	1.13621i	0.127944	+	0.0415716i
$748$		0			0
$749$	−0.307374			−0.0112312
$750$		0			0
$751$	−1.48912			−0.0543387			−0.0271693	−	0.999631i	$-0.508649\pi$
$751$	−1.48912			−0.0543387			−0.0271693	+	0.999631i	$0.508649\pi$
$752$		0			0
$753$	−9.23757	−	3.00147i	−0.336636	−	0.109380i
$754$		0			0
$755$	−16.7316	+	30.3985i	−0.608925	+	1.10632i
$756$		0			0
$757$			5.53316i			0.201106i	0.994932	+	0.100553i	$0.0320612\pi$
$757$			5.53316i			0.201106i	−0.994932	+	0.100553i	$0.967939\pi$
$758$		0			0
$759$	5.05975	+	3.67613i	0.183657	+	0.133435i
$760$		0			0
$761$	15.1041	−	10.9738i	0.547523	−	0.397799i	−0.279348	−	0.960190i	$-0.590118\pi$
$761$	15.1041	−	10.9738i	0.547523	−	0.397799i	0.826871	+	0.562391i	$0.190118\pi$
$762$		0			0
$763$	2.19161	−	3.01649i	0.0793416	−	0.109204i
$764$		0			0
$765$	−9.74230	+	9.13943i	−0.352233	+	0.330437i
$766$		0			0
$767$	−4.33125	+	1.40731i	−0.156392	+	0.0508149i
$768$		0			0
$769$	4.06150	+	12.5000i	0.146462	+	0.450763i	0.997196	−	0.0748333i	$-0.0238425\pi$
$769$	4.06150	+	12.5000i	0.146462	+	0.450763i	−0.850734	+	0.525596i	$0.823842\pi$
$770$		0			0
$771$	18.9764	−	58.4032i	0.683417	−	2.10334i
$772$		0			0
$773$	−16.4425	−	22.6311i	−0.591394	−	0.813984i	0.403493	−	0.914983i	$-0.367796\pi$
$773$	−16.4425	−	22.6311i	−0.591394	−	0.813984i	−0.994887	+	0.100999i	$0.967796\pi$
$774$		0			0
$775$	−26.1785	+	31.5798i	−0.940359	+	1.13438i
$776$		0			0
$777$	3.19882	+	4.40280i	0.114757	+	0.157950i
$778$		0			0
$779$	11.0399	−	33.9772i	0.395544	−	1.21736i
$780$		0			0
$781$	4.24366	+	13.0606i	0.151850	+	0.467347i
$782$		0			0
$783$	−10.5615	+	3.43163i	−0.377437	+	0.122637i
$784$		0			0
$785$	−5.45404	−	3.00195i	−0.194663	−	0.107144i
$786$		0			0
$787$	19.6126	−	26.9944i	0.699114	−	0.962248i	−0.300849	−	0.953672i	$-0.597270\pi$
$787$	19.6126	−	26.9944i	0.699114	−	0.962248i	0.999963	−	0.00857605i	$-0.00272988\pi$
$788$		0			0
$789$	−13.9845	+	10.1603i	−0.497860	+	0.361716i
$790$		0			0
$791$	−4.22947	−	3.07289i	−0.150383	−	0.109259i
$792$		0			0
$793$			6.60035i			0.234385i
$794$		0			0
$795$	26.7578	−	12.5749i	0.949003	−	0.445986i
$796$		0			0
$797$	−35.5682	−	11.5568i	−1.25989	−	0.409363i	−0.398435	−	0.917197i	$-0.630447\pi$
$797$	−35.5682	−	11.5568i	−1.25989	−	0.409363i	−0.861455	+	0.507833i	$0.830447\pi$
$798$		0			0
$799$	−2.01519			−0.0712923
$800$		0			0
$801$	−8.55478			−0.302268
$802$		0			0
$803$	−1.03693	−	0.336919i	−0.0365924	−	0.0118896i
$804$		0			0
$805$	−0.136551	−	1.08529i	−0.00481278	−	0.0382514i
$806$		0			0
$807$			33.9504i			1.19511i
$808$		0			0
$809$	27.1844	+	19.7506i	0.955751	+	0.694394i	0.952160	−	0.305600i	$-0.0988569\pi$
$809$	27.1844	+	19.7506i	0.955751	+	0.694394i	0.00359108	+	0.999994i	$0.498857\pi$
$810$		0			0
$811$	−30.7471	+	22.3391i	−1.07968	+	0.784432i	−0.977627	−	0.210347i	$-0.932541\pi$
$811$	−30.7471	+	22.3391i	−1.07968	+	0.784432i	−0.102051	+	0.994779i	$0.532541\pi$
$812$		0			0
$813$	18.1272	−	24.9499i	0.635747	−	0.875031i
$814$		0			0
$815$	−23.0226	−	48.9892i	−0.806446	−	1.71602i
$816$		0			0
$817$	43.1546	−	14.0218i	1.50979	−	0.490560i
$818$		0			0
$819$	−0.332749	−	1.02410i	−0.0116272	−	0.0357848i
$820$		0			0
$821$	7.70479	−	23.7129i	0.268899	−	0.827587i	−0.721870	−	0.692028i	$-0.756717\pi$
$821$	7.70479	−	23.7129i	0.268899	−	0.827587i	0.990769	−	0.135558i	$-0.0432827\pi$
$822$		0			0
$823$	−14.9653	−	20.5980i	−0.521659	−	0.718002i	0.464172	−	0.885745i	$-0.346352\pi$
$823$	−14.9653	−	20.5980i	−0.521659	−	0.718002i	−0.985831	+	0.167743i	$0.946352\pi$
$824$		0			0
$825$	−20.0381	−	16.6109i	−0.697638	−	0.578316i
$826$		0			0
$827$	19.0082	+	26.1626i	0.660980	+	0.909761i	0.999513	−	0.0311933i	$-0.00993074\pi$
$827$	19.0082	+	26.1626i	0.660980	+	0.909761i	−0.338533	+	0.940954i	$0.609931\pi$
$828$		0			0
$829$	−7.71962	+	23.7585i	−0.268113	+	0.825168i	0.722846	+	0.691009i	$0.242833\pi$
$829$	−7.71962	+	23.7585i	−0.268113	+	0.825168i	−0.990960	+	0.134159i	$0.957167\pi$
$830$		0			0
$831$	−13.6377	−	41.9724i	−0.473085	−	1.45601i
$832$		0			0
$833$	10.2873	−	3.34256i	0.356435	−	0.115813i
$834$		0			0
$835$	8.00128	−	41.8302i	0.276896	−	1.44759i
$836$		0			0
$837$	9.72030	−	13.3788i	0.335983	−	0.462440i
$838$		0			0
$839$	−15.6566	+	11.3752i	−0.540524	+	0.392714i	−0.824280	−	0.566183i	$-0.808420\pi$
$839$	−15.6566	+	11.3752i	−0.540524	+	0.392714i	0.283755	+	0.958897i	$0.408420\pi$
$840$		0			0
$841$	−1.09201	−	0.793390i	−0.0376554	−	0.0273583i
$842$		0			0
$843$		−	13.2091i		−	0.454944i
$844$		0			0
$845$	−27.4730	−	5.25505i	−0.945101	−	0.180779i
$846$		0			0
$847$	−2.71064	−	0.880739i	−0.0931385	−	0.0302625i
$848$		0			0
$849$	−30.7775			−1.05628
$850$		0			0
$851$	6.16980			0.211498
$852$		0			0
$853$	−25.4765	−	8.27783i	−0.872300	−	0.283427i	−0.161543	−	0.986866i	$-0.551647\pi$
$853$	−25.4765	−	8.27783i	−0.872300	−	0.283427i	−0.710756	+	0.703438i	$0.751647\pi$
$854$		0			0
$855$	−28.5881	−	30.4739i	−0.977694	−	1.04218i
$856$		0			0
$857$		−	47.5186i		−	1.62320i	−0.584210	−	0.811602i	$-0.698596\pi$
$857$		−	47.5186i		−	1.62320i	0.584210	−	0.811602i	$-0.301404\pi$
$858$		0			0
$859$	−9.32717	−	6.77658i	−0.318239	−	0.231214i	0.417185	−	0.908822i	$-0.363017\pi$
$859$	−9.32717	−	6.77658i	−0.318239	−	0.231214i	−0.735424	+	0.677608i	$0.763017\pi$
$860$		0			0
$861$	6.18685	−	4.49501i	0.210847	−	0.153190i
$862$		0			0
$863$	10.5835	−	14.5669i	0.360266	−	0.495864i	−0.589957	−	0.807435i	$-0.700855\pi$
$863$	10.5835	−	14.5669i	0.360266	−	0.495864i	0.950223	+	0.311571i	$0.100855\pi$
$864$		0			0
$865$	29.3896	−	3.69779i	0.999276	−	0.125729i
$866$		0			0
$867$	−35.8807	+	11.6583i	−1.21857	+	0.395938i
$868$		0			0
$869$	−3.38781	−	10.4266i	−0.114924	−	0.353698i
$870$		0			0
$871$	−0.667251	+	2.05359i	−0.0226089	+	0.0695831i
$872$		0			0
$873$	−33.7633	−	46.4712i	−1.14271	−	1.57281i
$874$		0			0
$875$	0.278999	+	4.54365i	0.00943188	+	0.153603i
$876$		0			0
$877$	10.0495	+	13.8320i	0.339349	+	0.467074i	0.944251	−	0.329226i	$-0.106788\pi$
$877$	10.0495	+	13.8320i	0.339349	+	0.467074i	−0.604902	+	0.796300i	$0.706788\pi$
$878$		0			0
$879$	−15.6315	+	48.1088i	−0.527238	+	1.62267i
$880$		0			0
$881$	−11.7516	−	36.1678i	−0.395923	−	1.21853i	−0.928240	−	0.371981i	$-0.878679\pi$
$881$	−11.7516	−	36.1678i	−0.395923	−	1.21853i	0.532318	−	0.846545i	$-0.321321\pi$
$882$		0			0
$883$	35.0458	−	11.3871i	1.17939	−	0.383206i	0.347247	−	0.937774i	$-0.387116\pi$
$883$	35.0458	−	11.3871i	1.17939	−	0.383206i	0.832138	+	0.554568i	$0.187116\pi$
$884$		0			0
$885$	−37.5324	+	4.72232i	−1.26164	+	0.158739i
$886$		0			0
$887$	−17.5594	+	24.1684i	−0.589586	+	0.811495i	−0.994705	−	0.102769i	$-0.967230\pi$
$887$	−17.5594	+	24.1684i	−0.589586	+	0.811495i	0.405120	+	0.914264i	$0.367230\pi$
$888$		0			0
$889$	2.34045	−	1.70044i	0.0784961	−	0.0570308i
$890$		0			0
$891$	−9.83247	−	7.14371i	−0.329400	−	0.239323i
$892$		0			0
$893$		−	6.30351i		−	0.210939i
$894$		0			0
$895$	−18.7027	−	19.9364i	−0.625162	−	0.666399i
$896$		0			0
$897$	−2.08382	−	0.677074i	−0.0695767	−	0.0226068i
$898$		0			0
$899$	45.1958			1.50736
$900$		0			0
$901$	−8.04022			−0.267859
$902$		0			0
$903$	9.23757	+	3.00147i	0.307407	+	0.0998826i
$904$		0			0
$905$	−23.9760	−	4.58613i	−0.796990	−	0.152448i
$906$		0			0
$907$		−	43.4897i		−	1.44405i	−0.691866	−	0.722026i	$-0.743211\pi$
$907$		−	43.4897i		−	1.44405i	0.691866	−	0.722026i	$-0.256789\pi$
$908$		0			0
$909$	56.1758	+	40.8141i	1.86323	+	1.35372i
$910$		0			0
$911$	−19.7150	+	14.3238i	−0.653186	+	0.474568i	−0.864355	−	0.502882i	$-0.832273\pi$
$911$	−19.7150	+	14.3238i	−0.653186	+	0.474568i	0.211169	+	0.977450i	$0.432273\pi$
$912$		0			0
$913$	1.14516	−	1.57618i	0.0378994	−	0.0521640i
$914$		0			0
$915$	−10.3002	+	53.8486i	−0.340513	+	1.78018i
$916$		0			0
$917$	0.927136	−	0.301245i	0.0306167	−	0.00994797i
$918$		0			0
$919$	14.0647	+	43.2867i	0.463952	+	1.42790i	0.860296	+	0.509795i	$0.170279\pi$
$919$	14.0647	+	43.2867i	0.463952	+	1.42790i	−0.396344	+	0.918102i	$0.629721\pi$
$920$		0			0
$921$	20.4429	−	62.9168i	0.673617	−	2.07318i
$922$		0			0
$923$	−2.82787	−	3.89223i	−0.0930804	−	0.128114i
$924$		0			0
$925$	−25.6243	−	1.63795i	−0.842522	−	0.0538555i
$926$		0			0
$927$	−26.3661	−	36.2898i	−0.865977	−	1.19191i
$928$		0			0
$929$	−2.79288	+	8.59560i	−0.0916314	+	0.282012i	−0.986361	−	0.164596i	$-0.947368\pi$
$929$	−2.79288	+	8.59560i	−0.0916314	+	0.282012i	0.894730	+	0.446608i	$0.147368\pi$
$930$		0			0
$931$	10.4555	+	32.1787i	0.342665	+	1.05462i
$932$		0			0
$933$	39.2542	−	12.7545i	1.28513	−	0.417562i
$934$		0			0
$935$	3.01054	+	6.40605i	0.0984550	+	0.209500i
$936$		0			0
$937$	−19.5892	+	26.9623i	−0.639953	+	0.880819i	−0.998613	−	0.0526490i	$-0.983234\pi$
$937$	−19.5892	+	26.9623i	−0.639953	+	0.880819i	0.358661	+	0.933468i	$0.383234\pi$
$938$		0			0
$939$	−14.7745	+	10.7343i	−0.482147	+	0.350300i
$940$		0			0
$941$	23.7050	+	17.2227i	0.772762	+	0.561444i	0.902798	−	0.430065i	$-0.141509\pi$
$941$	23.7050	+	17.2227i	0.772762	+	0.561444i	−0.130036	+	0.991509i	$0.541509\pi$
$942$		0			0
$943$		−	8.66985i		−	0.282329i
$944$		0			0
$945$	−0.229103	−	1.82088i	−0.00745272	−	0.0592333i
$946$		0			0
$947$	54.0634	+	17.5663i	1.75682	+	0.570827i	0.996863	−	0.0791426i	$-0.0252182\pi$
$947$	54.0634	+	17.5663i	1.75682	+	0.570827i	0.759961	+	0.649969i	$0.225218\pi$
$948$		0			0
$949$	0.381966			0.0123991
$950$		0			0
$951$	−33.9238			−1.10005
$952$		0			0
$953$	18.1051	+	5.88270i	0.586481	+	0.190559i	0.587202	−	0.809441i	$-0.300229\pi$
$953$	18.1051	+	5.88270i	0.586481	+	0.190559i	−0.000720915		1.00000i	$0.500229\pi$
$954$		0			0
$955$	−3.17246	+	1.49090i	−0.102658	+	0.0482445i
$956$		0			0
$957$			28.6778i			0.927021i
$958$		0			0
$959$	−6.26498	−	4.55178i	−0.202307	−	0.146985i
$960$		0			0
$961$	−29.3705	+	21.3389i	−0.947435	+	0.688352i
$962$		0			0
$963$	−1.67485	+	2.30523i	−0.0539711	+	0.0742849i
$964$		0			0
$965$	3.24764	+	1.78753i	0.104545	+	0.0575425i
$966$		0			0
$967$	13.9905	−	4.54580i	0.449906	−	0.146183i	−0.0752956	−	0.997161i	$-0.523990\pi$
$967$	13.9905	−	4.54580i	0.449906	−	0.146183i	0.525201	+	0.850978i	$0.323990\pi$
$968$		0			0
$969$	6.30233	+	19.3966i	0.202460	+	0.623108i
$970$		0			0
$971$	12.0039	−	36.9441i	0.385223	−	1.18559i	−0.551096	−	0.834442i	$-0.685790\pi$
$971$	12.0039	−	36.9441i	0.385223	−	1.18559i	0.936319	−	0.351151i	$-0.114210\pi$
$972$		0			0
$973$	1.61177	+	2.21842i	0.0516711	+	0.0711191i
$974$		0			0
$975$	8.47472	+	3.36522i	0.271408	+	0.107773i
$976$		0			0
$977$	34.3586	+	47.2906i	1.09923	+	1.51296i	0.836402	+	0.548116i	$0.184655\pi$
$977$	34.3586	+	47.2906i	1.09923	+	1.51296i	0.262827	+	0.964843i	$0.415345\pi$
$978$		0			0
$979$	−1.40077	+	4.31111i	−0.0447687	+	0.137784i
$980$		0			0
$981$	−10.6811	−	32.8730i	−0.341021	−	1.04955i
$982$		0			0
$983$	−26.7812	+	8.70175i	−0.854189	+	0.277543i	−0.703199	−	0.710993i	$-0.748246\pi$
$983$	−26.7812	+	8.70175i	−0.854189	+	0.277543i	−0.150989	+	0.988535i	$0.548246\pi$
$984$		0			0
$985$	−21.6619	+	20.3215i	−0.690206	+	0.647496i
$986$		0			0
$987$	0.793106	−	1.09162i	0.0252449	−	0.0347466i
$988$		0			0
$989$	8.90859	−	6.47247i	0.283277	−	0.205812i
$990$		0			0
$991$	31.8297	+	23.1256i	1.01110	+	0.734610i	0.964440	−	0.264300i	$-0.0851410\pi$
$991$	31.8297	+	23.1256i	1.01110	+	0.734610i	0.0466640	+	0.998911i	$0.485141\pi$
$992$		0			0
$993$			45.9231i			1.45733i
$994$		0			0
$995$	−13.0491	+	23.7080i	−0.413683	+	0.751594i
$996$		0			0
$997$	41.0074	+	13.3241i	1.29872	+	0.421979i	0.875136	−	0.483878i	$-0.160772\pi$
$997$	41.0074	+	13.3241i	1.29872	+	0.421979i	0.423583	+	0.905857i	$0.360772\pi$
$998$		0			0
$999$	10.3516			0.327511

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.y.c.289.2		8
4.3	odd	2		25.2.e.a.14.2	yes	8
12.11	even	2		225.2.m.a.64.1		8
20.3	even	4		125.2.d.b.51.3		16
20.7	even	4		125.2.d.b.51.2		16
20.19	odd	2		125.2.e.b.74.1		8
25.3	odd	20		10000.2.a.bj.1.1		8
25.9	even	10	inner	400.2.y.c.209.2		8
25.22	odd	20		10000.2.a.bj.1.8		8
100.3	even	20		625.2.a.f.1.3		8
100.11	odd	10		625.2.e.i.499.2		8
100.19	odd	10		625.2.e.i.124.2		8
100.23	even	20		625.2.d.o.126.2		16
100.27	even	20		625.2.d.o.126.3		16
100.31	odd	10		625.2.e.a.124.1		8
100.39	odd	10		625.2.e.a.499.1		8
100.47	even	20		625.2.a.f.1.6		8
100.59	odd	10		25.2.e.a.9.2	✓	8
100.63	even	20		125.2.d.b.76.3		16
100.67	even	20		625.2.d.o.501.3		16
100.71	odd	10		625.2.b.c.624.3		8
100.79	odd	10		625.2.b.c.624.6		8
100.83	even	20		625.2.d.o.501.2		16
100.87	even	20		125.2.d.b.76.2		16
100.91	odd	10		125.2.e.b.49.1		8
300.47	odd	20		5625.2.a.x.1.3		8
300.59	even	10		225.2.m.a.109.1		8
300.203	odd	20		5625.2.a.x.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.2.e.a.9.2	✓	8	100.59	odd	10
25.2.e.a.14.2	yes	8	4.3	odd	2
125.2.d.b.51.2		16	20.7	even	4
125.2.d.b.51.3		16	20.3	even	4
125.2.d.b.76.2		16	100.87	even	20
125.2.d.b.76.3		16	100.63	even	20
125.2.e.b.49.1		8	100.91	odd	10
125.2.e.b.74.1		8	20.19	odd	2
225.2.m.a.64.1		8	12.11	even	2
225.2.m.a.109.1		8	300.59	even	10
400.2.y.c.209.2		8	25.9	even	10	inner
400.2.y.c.289.2		8	1.1	even	1	trivial
625.2.a.f.1.3		8	100.3	even	20
625.2.a.f.1.6		8	100.47	even	20
625.2.b.c.624.3		8	100.71	odd	10
625.2.b.c.624.6		8	100.79	odd	10
625.2.d.o.126.2		16	100.23	even	20
625.2.d.o.126.3		16	100.27	even	20
625.2.d.o.501.2		16	100.83	even	20
625.2.d.o.501.3		16	100.67	even	20
625.2.e.a.124.1		8	100.31	odd	10
625.2.e.a.499.1		8	100.39	odd	10
625.2.e.i.124.2		8	100.19	odd	10
625.2.e.i.499.2		8	100.11	odd	10
5625.2.a.x.1.3		8	300.47	odd	20
5625.2.a.x.1.6		8	300.203	odd	20
10000.2.a.bj.1.1		8	25.3	odd	20
10000.2.a.bj.1.8		8	25.22	odd	20

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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.y (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.47539 + 0.804303i) q^{3} +(-1.07822 + 1.95894i) q^{5} +0.407162i q^{7} +(3.05361 + 2.21858i) q^{9} +O(q^{10})\)	\(q+(2.47539 + 0.804303i) q^{3} +(-1.07822 + 1.95894i) q^{5} +0.407162i q^{7} +(3.05361 + 2.21858i) q^{9} +(1.61803 - 1.17557i) q^{11} +(-0.411842 + 0.566852i) q^{13} +(-4.24459 + 3.98193i) q^{15} +(1.50527 - 0.489091i) q^{17} +(1.52988 + 4.70847i) q^{19} +(-0.327481 + 1.00788i) q^{21} +(0.706192 + 0.971990i) q^{23} +(-2.67490 - 4.22433i) q^{25} +(1.18484 + 1.63079i) q^{27} +(-1.70239 + 5.23943i) q^{29} +(-2.53514 - 7.80237i) q^{31} +(4.95078 - 1.60861i) q^{33} +(-0.797605 - 0.439008i) q^{35} +(3.01846 - 4.15456i) q^{37} +(-1.47539 + 1.07193i) q^{39} +(-5.83802 - 4.24157i) q^{41} -9.16531i q^{43} +(-7.63851 + 3.58973i) q^{45} +(-1.21092 - 0.393451i) q^{47} +6.83422 q^{49} +4.11950 q^{51} +(-4.83133 - 1.56979i) q^{53} +(0.558282 + 4.43715i) q^{55} +12.8858i q^{57} +(5.25838 + 3.82044i) q^{59} +(7.62101 - 5.53699i) q^{61} +(-0.903319 + 1.24331i) q^{63} +(-0.666375 - 1.41796i) q^{65} +(2.93090 - 0.952307i) q^{67} +(0.966327 + 2.97405i) q^{69} +(-2.12183 + 6.53032i) q^{71} +(-0.320429 - 0.441032i) q^{73} +(-3.22378 - 12.6083i) q^{75} +(0.478647 + 0.658801i) q^{77} +(1.69390 - 5.21330i) q^{79} +(-1.87783 - 5.77938i) q^{81} +(0.926457 - 0.301024i) q^{83} +(-0.664904 + 3.47608i) q^{85} +(-8.42819 + 11.6004i) q^{87} +(-1.83363 + 1.33221i) q^{89} +(-0.230800 - 0.167686i) q^{91} -21.3529i q^{93} +(-10.8732 - 2.07982i) q^{95} +(-14.4736 - 4.70276i) q^{97} +7.54893 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 5 q^{3} + q^{9}+O(q^{10}) \) 8 * q + 5 * q^3 + q^9	\( 8 q + 5 q^{3} + q^{9} + 4 q^{11} - 5 q^{13} - 15 q^{15} - 10 q^{17} + 5 q^{19} - 4 q^{21} - 5 q^{23} - 10 q^{25} + 5 q^{27} - 5 q^{29} + 9 q^{31} + 10 q^{33} - 15 q^{35} + 30 q^{37} + 3 q^{39} - 4 q^{41} - 15 q^{45} + 14 q^{49} + 4 q^{51} - 10 q^{53} + 10 q^{55} - 9 q^{61} - 10 q^{63} + 5 q^{65} - 20 q^{67} + 17 q^{69} - 6 q^{71} + 15 q^{73} + 10 q^{75} + 10 q^{77} - 15 q^{79} + 28 q^{81} + 45 q^{83} - 15 q^{85} + 20 q^{87} - 25 q^{89} - 6 q^{91} - 15 q^{95} - 60 q^{97} + 8 q^{99}+O(q^{100}) \) 8 * q + 5 * q^3 + q^9 + 4 * q^11 - 5 * q^13 - 15 * q^15 - 10 * q^17 + 5 * q^19 - 4 * q^21 - 5 * q^23 - 10 * q^25 + 5 * q^27 - 5 * q^29 + 9 * q^31 + 10 * q^33 - 15 * q^35 + 30 * q^37 + 3 * q^39 - 4 * q^41 - 15 * q^45 + 14 * q^49 + 4 * q^51 - 10 * q^53 + 10 * q^55 - 9 * q^61 - 10 * q^63 + 5 * q^65 - 20 * q^67 + 17 * q^69 - 6 * q^71 + 15 * q^73 + 10 * q^75 + 10 * q^77 - 15 * q^79 + 28 * q^81 + 45 * q^83 - 15 * q^85 + 20 * q^87 - 25 * q^89 - 6 * q^91 - 15 * q^95 - 60 * q^97 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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