LMFDB - Embedded newform 400.2.y.c.209.2

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			209.2
Root			$-0.357358 + 1.86824i$ of defining polynomial
Character	$\chi$	$=$	400.209
Dual form			400.2.y.c.289.2

$q$-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 $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{7}{10}\right)$	$1$

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	0.510665	−	0.859780i	$-0.329399\pi$
$3$	2.47539	−	0.804303i	1.42917	−	0.464365i	0.918503	+	0.395415i	$0.129399\pi$
$4$		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	$-0.975483\pi$
$7$		−	0.407162i		−	0.153893i	0.997035	−	0.0769463i	$-0.0245170\pi$
$8$		0			0
$9$	3.05361	−	2.21858i	1.01787	−	0.739525i
$10$		0			0
$11$	1.61803	+	1.17557i	0.487856	+	0.354448i	0.804359	−	0.594144i	$-0.202509\pi$
$11$	1.61803	+	1.17557i	0.487856	+	0.354448i	−0.316503	+	0.948591i	$0.602509\pi$
$12$		0			0
$13$	−0.411842	−	0.566852i	−0.114224	−	0.157216i	0.748077	−	0.663612i	$-0.230977\pi$
$13$	−0.411842	−	0.566852i	−0.114224	−	0.157216i	−0.862301	+	0.506396i	$0.830977\pi$
$14$		0			0
$15$	−4.24459	−	3.98193i	−1.09595	−	1.02813i
$16$		0			0
$17$	1.50527	+	0.489091i	0.365081	+	0.118622i	0.485812	−	0.874063i	$-0.338524\pi$
$17$	1.50527	+	0.489091i	0.365081	+	0.118622i	−0.120731	+	0.992685i	$0.538524\pi$
$18$		0			0
$19$	1.52988	−	4.70847i	0.350978	−	1.08020i	−0.607328	−	0.794452i	$-0.707758\pi$
$19$	1.52988	−	4.70847i	0.350978	−	1.08020i	0.958305	−	0.285747i	$-0.0922416\pi$
$20$		0			0
$21$	−0.327481	−	1.00788i	−0.0714623	−	0.219938i
$22$		0			0
$23$	0.706192	−	0.971990i	0.147251	−	0.202674i	−0.729020	−	0.684493i	$-0.760024\pi$
$23$	0.706192	−	0.971990i	0.147251	−	0.202674i	0.876271	+	0.481819i	$0.160024\pi$
$24$		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	−0.975288	−	0.220937i	$-0.929089\pi$
$29$	−1.70239	−	5.23943i	−0.316127	−	0.972938i	0.659161	−	0.752001i	$-0.270911\pi$
$30$		0			0
$31$	−2.53514	+	7.80237i	−0.455325	+	1.40135i	0.415428	+	0.909626i	$0.363632\pi$
$31$	−2.53514	+	7.80237i	−0.455325	+	1.40135i	−0.870753	+	0.491721i	$0.836368\pi$
$32$		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	0.981522	−	0.191348i	$-0.0612859\pi$
$37$	3.01846	+	4.15456i	0.496232	+	0.683005i	−0.485290	+	0.874353i	$0.661286\pi$
$38$		0			0
$39$	−1.47539	−	1.07193i	−0.236252	−	0.171647i
$40$		0			0
$41$	−5.83802	+	4.24157i	−0.911745	+	0.662422i	−0.941456	−	0.337137i	$-0.890541\pi$
$41$	−5.83802	+	4.24157i	−0.911745	+	0.662422i	0.0297106	+	0.999559i	$0.490541\pi$
$42$		0			0
$43$			9.16531i			1.39770i	0.715270	+	0.698848i	$0.246304\pi$
$43$			9.16531i			1.39770i	−0.715270	+	0.698848i	$0.753696\pi$
$44$		0			0
$45$	−7.63851	−	3.58973i	−1.13868	−	0.535126i
$46$		0			0
$47$	−1.21092	+	0.393451i	−0.176631	+	0.0573907i	−0.395997	−	0.918252i	$-0.629601\pi$
$47$	−1.21092	+	0.393451i	−0.176631	+	0.0573907i	0.219367	+	0.975643i	$0.429601\pi$
$48$		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	−0.621416	−	0.783481i	$-0.713442\pi$
$53$	−4.83133	+	1.56979i	−0.663634	+	0.215628i	−0.0422180	+	0.999108i	$0.513442\pi$
$54$		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	−0.190292	−	0.981728i	$-0.560943\pi$
$59$	5.25838	−	3.82044i	0.684583	−	0.497379i	0.874875	+	0.484349i	$0.160943\pi$
$60$		0			0
$61$	7.62101	+	5.53699i	0.975770	+	0.708938i	0.956759	−	0.290881i	$-0.0939483\pi$
$61$	7.62101	+	5.53699i	0.975770	+	0.708938i	0.0190107	+	0.999819i	$0.493948\pi$
$62$		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	0.482526	−	0.875882i	$-0.339720\pi$
$67$	2.93090	+	0.952307i	0.358066	+	0.116343i	−0.124459	+	0.992225i	$0.539720\pi$
$68$		0			0
$69$	0.966327	−	2.97405i	0.116332	−	0.358033i
$70$		0			0
$71$	−2.12183	−	6.53032i	−0.251815	−	0.775007i	−0.994440	−	0.105300i	$-0.966420\pi$
$71$	−2.12183	−	6.53032i	−0.251815	−	0.775007i	0.742625	−	0.669707i	$-0.233580\pi$
$72$		0			0
$73$	−0.320429	+	0.441032i	−0.0375033	+	0.0516189i	−0.827357	−	0.561677i	$-0.810157\pi$
$73$	−0.320429	+	0.441032i	−0.0375033	+	0.0516189i	0.789854	+	0.613296i	$0.210157\pi$
$74$		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	1.00000		0.000687140i	$-0.000218723\pi$
$79$	1.69390	+	5.21330i	0.190579	+	0.586542i	−0.809421	+	0.587229i	$0.800219\pi$
$80$		0			0
$81$	−1.87783	+	5.77938i	−0.208648	+	0.642153i
$82$		0			0
$83$	0.926457	+	0.301024i	0.101692	+	0.0330417i	0.359421	−	0.933176i	$-0.382974\pi$
$83$	0.926457	+	0.301024i	0.101692	+	0.0330417i	−0.257729	+	0.966217i	$0.582974\pi$
$84$		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	0.486347	−	0.873766i	$-0.338329\pi$
$89$	−1.83363	−	1.33221i	−0.194364	−	0.141214i	−0.680711	+	0.732552i	$0.738329\pi$
$90$		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	−0.930979	−	0.365073i	$-0.881044\pi$
$97$	−14.4736	+	4.70276i	−1.46957	+	0.477493i	−0.538593	+	0.842566i	$0.681044\pi$
$98$		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	−0.807351	−	0.590071i	$-0.799100\pi$
$103$	−11.3026	+	3.67243i	−1.11368	+	0.361856i	−0.306326	+	0.951927i	$0.599100\pi$
$104$		0			0
$105$	−1.62129	+	1.72823i	−0.158222	+	0.168658i
$106$		0			0
$107$		−	0.754919i		−	0.0729808i	−0.999334	−	0.0364904i	$-0.988382\pi$
$107$		−	0.754919i		−	0.0729808i	0.999334	−	0.0364904i	$-0.0116178\pi$
$108$		0			0
$109$	−7.40859	+	5.38265i	−0.709614	+	0.515565i	−0.883049	−	0.469281i	$-0.844513\pi$
$109$	−7.40859	+	5.38265i	−0.709614	+	0.515565i	0.173435	+	0.984845i	$0.444513\pi$
$110$		0			0
$111$	10.8134	+	7.85640i	1.02636	+	0.745697i
$112$		0			0
$113$	−7.54710	−	10.3877i	−0.709971	−	0.977191i	−0.999798	−	0.0201123i	$-0.993598\pi$
$113$	−7.54710	−	10.3877i	−0.709971	−	0.977191i	0.289827	−	0.957079i	$-0.406402\pi$
$114$		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	−0.953061	−	0.302780i	$-0.902085\pi$
$127$	−4.17632	+	5.74821i	−0.370588	+	0.510071i	0.582472	+	0.812850i	$0.302085\pi$
$128$		0			0
$129$	7.37169	+	22.6877i	0.649041	+	1.99754i
$130$		0			0
$131$	−0.739865	+	2.27707i	−0.0646423	+	0.198949i	−0.978161	−	0.207848i	$-0.933354\pi$
$131$	−0.739865	+	2.27707i	−0.0646423	+	0.198949i	0.913519	+	0.406796i	$0.133354\pi$
$132$		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	−0.949219	−	0.314615i	$-0.898125\pi$
$137$	−11.1793	−	15.3870i	−0.955111	−	1.31460i	−0.00589176	−	0.999983i	$-0.501875\pi$
$138$		0			0
$139$	5.44849	+	3.95856i	0.462135	+	0.335761i	0.794368	−	0.607437i	$-0.207802\pi$
$139$	5.44849	+	3.95856i	0.462135	+	0.335761i	−0.332233	+	0.943197i	$0.607802\pi$
$140$		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	$-0.964562\pi$
$157$		−	2.78418i		−	0.222202i	0.993809	−	0.111101i	$-0.0354376\pi$
$158$		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	−0.814645	−	0.579960i	$-0.803068\pi$
$163$	−14.2287	−	19.5842i	−1.11448	−	1.53395i	−0.299835	−	0.953991i	$-0.596932\pi$
$164$		0			0
$165$	−2.18685	−	11.4327i	−0.170246	−	0.890036i
$166$		0			0
$167$	−18.1140	−	5.88559i	−1.40170	−	0.455441i	−0.491961	−	0.870617i	$-0.663720\pi$
$167$	−18.1140	−	5.88559i	−1.40170	−	0.455441i	−0.909741	+	0.415176i	$0.863720\pi$
$168$		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	−0.994946	−	0.100415i	$-0.967983\pi$
$173$	−7.78642	+	10.7171i	−0.591991	+	0.814805i	0.402955	+	0.915220i	$0.367983\pi$
$174$		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	−0.987177	−	0.159627i	$-0.948971\pi$
$179$	−3.77772	−	11.6266i	−0.282360	−	0.869016i	0.704817	−	0.709389i	$-0.251029\pi$
$180$		0			0
$181$	3.37348	−	10.3825i	0.250748	−	0.771724i	−0.743889	−	0.668303i	$-0.767021\pi$
$181$	3.37348	−	10.3825i	0.250748	−	0.771724i	0.994638	−	0.103421i	$-0.0329790\pi$
$182$		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	−0.540956	−	0.841051i	$-0.681937\pi$
$191$	1.26824	−	0.921429i	0.0917665	−	0.0666723i	0.632722	+	0.774379i	$0.281937\pi$
$192$		0			0
$193$			1.65786i			0.119335i	0.998218	+	0.0596675i	$0.0190040\pi$
$193$			1.65786i			0.119335i	−0.998218	+	0.0596675i	$0.980996\pi$
$194$		0			0
$195$	−0.509065	+	4.04598i	−0.0364549	+	0.289739i
$196$		0			0
$197$	12.6330	−	4.10470i	0.900061	−	0.292448i	0.177799	−	0.984067i	$-0.443102\pi$
$197$	12.6330	−	4.10470i	0.900061	−	0.292448i	0.722262	+	0.691619i	$0.243102\pi$
$198$		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	0.385342	−	0.922774i	$-0.374083\pi$
$211$	−5.42091	−	3.93852i	−0.373191	−	0.271139i	−0.758533	+	0.651635i	$0.774083\pi$
$212$		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	−0.547985	−	0.836488i	$-0.684605\pi$
$223$	6.22564	−	8.56885i	0.416900	−	0.573813i	0.964884	+	0.262675i	$0.0846048\pi$
$224$		0			0
$225$	1.20390	+	18.8339i	0.0802598	+	1.25559i
$226$		0			0
$227$	11.5272	−	15.8658i	0.765087	−	1.05305i	−0.231687	−	0.972790i	$-0.574425\pi$
$227$	11.5272	−	15.8658i	0.765087	−	1.05305i	0.996774	−	0.0802612i	$-0.0255755\pi$
$228$		0			0
$229$	−2.73139	−	8.40637i	−0.180496	−	0.555508i	0.819346	−	0.573299i	$-0.194337\pi$
$229$	−2.73139	−	8.40637i	−0.180496	−	0.555508i	−0.999842	+	0.0177908i	$0.994337\pi$
$230$		0			0
$231$	0.654963	−	2.01577i	0.0430934	−	0.132628i
$232$		0			0
$233$	10.5210	+	3.41848i	0.689253	+	0.223952i	0.632642	−	0.774445i	$-0.281971\pi$
$233$	10.5210	+	3.41848i	0.689253	+	0.223952i	0.0566109	+	0.998396i	$0.481971\pi$
$234$		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	0.0803411	−	0.996767i	$-0.474399\pi$
$239$	−13.0296	−	9.46655i	−0.842814	−	0.612340i	−0.923155	+	0.384427i	$0.874399\pi$
$240$		0			0
$241$	−4.84498	+	3.52009i	−0.312093	+	0.226749i	−0.732794	−	0.680451i	$-0.761784\pi$
$241$	−4.84498	+	3.52009i	−0.312093	+	0.226749i	0.420701	+	0.907199i	$0.361784\pi$
$242$		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	$0.263223\pi$
$257$			23.5935i			1.47172i	−0.677132	+	0.735862i	$0.736777\pi$
$258$		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	0.671522	−	0.740985i	$-0.265641\pi$
$263$	−3.90363	−	5.37289i	−0.240708	−	0.331307i	−0.912230	+	0.409678i	$0.865641\pi$
$264$		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	−0.749749	−	0.661722i	$-0.769826\pi$
$269$	4.03078	−	12.4055i	0.245761	−	0.756375i	0.995510	−	0.0946532i	$-0.0301742\pi$
$270$		0			0
$271$	3.66147	+	11.2689i	0.222419	+	0.684534i	0.998543	+	0.0539549i	$0.0171827\pi$
$271$	3.66147	+	11.2689i	0.222419	+	0.684534i	−0.776125	+	0.630579i	$0.782817\pi$
$272$		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	−0.995600	−	0.0937053i	$-0.970129\pi$
$277$	−9.96641	+	13.7176i	−0.598824	+	0.824210i	0.396776	+	0.917915i	$0.370129\pi$
$278$		0			0
$279$	9.56882	+	29.4498i	0.572870	+	1.76311i
$280$		0			0
$281$	−1.56826	+	4.82659i	−0.0935543	+	0.287930i	−0.986874	−	0.161491i	$-0.948370\pi$
$281$	−1.56826	+	4.82659i	−0.0935543	+	0.287930i	0.893320	+	0.449421i	$0.148370\pi$
$282$		0			0
$283$	−11.2461	−	3.65408i	−0.668511	−	0.217212i	−0.0449525	−	0.998989i	$-0.514314\pi$
$283$	−11.2461	−	3.65408i	−0.668511	−	0.217212i	−0.623558	+	0.781777i	$0.714314\pi$
$284$		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	$-0.807834\pi$
$293$		−	19.4348i		−	1.13540i	0.823237	−	0.567698i	$-0.192166\pi$
$294$		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	$0.258303\pi$
$307$			25.4169i			1.45062i	−0.688423	+	0.725310i	$0.741697\pi$
$308$		0			0
$309$	−25.0246	+	18.1814i	−1.42360	+	1.03431i
$310$		0			0
$311$	12.8292	+	9.32097i	0.727478	+	0.528544i	0.888765	−	0.458364i	$-0.151564\pi$
$311$	12.8292	+	9.32097i	0.727478	+	0.528544i	−0.161287	+	0.986908i	$0.551564\pi$
$312$		0			0
$313$	−4.12416	−	5.67642i	−0.233111	−	0.320850i	0.676396	−	0.736538i	$-0.263541\pi$
$313$	−4.12416	−	5.67642i	−0.233111	−	0.320850i	−0.909507	+	0.415688i	$0.863541\pi$
$314$		0			0
$315$	−1.46160	+	3.11011i	−0.0823519	+	0.175235i
$316$		0			0
$317$	−12.3958	−	4.02763i	−0.696215	−	0.226214i	−0.0605344	−	0.998166i	$-0.519280\pi$
$317$	−12.3958	−	4.02763i	−0.696215	−	0.226214i	−0.635681	+	0.771952i	$0.719280\pi$
$318$		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	−0.681925	−	0.731422i	$-0.738857\pi$
$331$	5.45225	−	16.7803i	0.299683	−	0.922329i	0.981608	−	0.190907i	$-0.0611430\pi$
$332$		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	0.993382	+	0.114860i	$0.0366421\pi$
$337$	14.6062	+	20.1037i	0.795649	+	1.09512i	−0.197733	+	0.980256i	$0.563358\pi$
$338$		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	−0.627670	−	0.778479i	$-0.715991\pi$
$347$	−12.6276	+	4.10297i	−0.677887	+	0.220259i	−0.0502171	+	0.998738i	$0.515991\pi$
$348$		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	0.175522	−	0.984476i	$-0.443839\pi$
$353$	16.8377	−	5.47091i	0.896182	−	0.291187i	0.720660	+	0.693288i	$0.243839\pi$
$354$		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	−0.393677	+	0.919249i	$0.628797\pi$
$359$	−26.3289	+	19.1291i	−1.38959	+	1.00959i	−0.995910	+	0.0903458i	$0.971203\pi$
$360$		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	0.975572	−	0.219680i	$-0.0705014\pi$
$367$	31.3355	+	10.1815i	1.63570	+	0.531472i	0.660129	+	0.751152i	$0.270501\pi$
$368$		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	−0.753003	−	0.658018i	$-0.771395\pi$
$373$	2.03754	−	2.80444i	0.105500	−	0.145208i	0.858503	+	0.512809i	$0.171395\pi$
$374$		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	0.934582	−	0.355747i	$-0.115773\pi$
$379$	−0.595979	−	1.83424i	−0.0306134	−	0.0942183i	−0.965196	+	0.261528i	$0.915773\pi$
$380$		0			0
$381$	−5.71472	+	17.5881i	−0.292774	+	0.901065i
$382$		0			0
$383$	4.68874	+	1.52346i	0.239583	+	0.0778454i	0.426348	−	0.904559i	$-0.359800\pi$
$383$	4.68874	+	1.52346i	0.239583	+	0.0778454i	−0.186764	+	0.982405i	$0.559800\pi$
$384$		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	0.827445	−	0.561547i	$-0.189793\pi$
$389$	10.8295	+	7.86809i	0.549077	+	0.398928i	−0.278368	+	0.960475i	$0.589793\pi$
$390$		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	−0.257525	−	0.966272i	$-0.582907\pi$
$397$	2.03418	−	0.660946i	0.102093	−	0.0331719i	0.359618	+	0.933100i	$0.382907\pi$
$398$		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	−0.271474	−	0.962446i	$-0.587511\pi$
$409$	11.3248	−	8.22796i	0.559976	−	0.406847i	0.831450	+	0.555599i	$0.187511\pi$
$410$		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	−0.390560	−	0.920577i	$-0.627719\pi$
$419$	9.54925	−	29.3896i	0.466511	−	1.43577i	0.857072	−	0.515197i	$-0.172281\pi$
$420$		0			0
$421$	−2.54622	−	7.83646i	−0.124095	−	0.381926i	0.869640	−	0.493687i	$-0.164351\pi$
$421$	−2.54622	−	7.83646i	−0.124095	−	0.381926i	−0.993735	+	0.111761i	$0.964351\pi$
$422$		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	0.517552	+	0.855652i	$0.326843\pi$
$431$	−8.38925	+	25.8194i	−0.404096	+	1.24368i	−0.921648	+	0.388027i	$0.873157\pi$
$432$		0			0
$433$	−20.4387	−	6.64093i	−0.982220	−	0.319143i	−0.226481	−	0.974016i	$-0.572722\pi$
$433$	−20.4387	−	6.64093i	−0.982220	−	0.319143i	−0.755739	+	0.654873i	$0.772722\pi$
$434$		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	0.961233	−	0.275739i	$-0.0889224\pi$
$439$	20.8691	+	15.1623i	0.996027	+	0.723656i	0.0347942	+	0.999394i	$0.488922\pi$
$440$		0			0
$441$	20.8690	−	15.1622i	0.993763	−	0.722011i
$442$		0			0
$443$			3.18479i			0.151314i	0.997134	+	0.0756570i	$0.0241054\pi$
$443$			3.18479i			0.151314i	−0.997134	+	0.0756570i	$0.975895\pi$
$444$		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	$0.203638\pi$
$457$			25.5245i			1.19399i	−0.802246	+	0.596994i	$0.796362\pi$
$458$		0			0
$459$	2.58111	−	1.87528i	0.120476	−	0.0875307i
$460$		0			0
$461$	13.4614	+	9.78026i	0.626959	+	0.455512i	0.855345	−	0.518058i	$-0.173345\pi$
$461$	13.4614	+	9.78026i	0.626959	+	0.455512i	−0.228387	+	0.973571i	$0.573345\pi$
$462$		0			0
$463$	−10.4730	−	14.4149i	−0.486723	−	0.669916i	0.493057	−	0.869997i	$-0.335880\pi$
$463$	−10.4730	−	14.4149i	−0.486723	−	0.669916i	−0.979779	+	0.200081i	$0.935880\pi$
$464$		0			0
$465$	41.8292	−	23.0231i	1.93978	−	1.06767i
$466$		0			0
$467$	13.5507	+	4.40289i	0.627051	+	0.203741i	0.605269	−	0.796021i	$-0.293066\pi$
$467$	13.5507	+	4.40289i	0.627051	+	0.203741i	0.0217829	+	0.999763i	$0.493066\pi$
$468$		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	0.969489	−	0.245137i	$-0.0788328\pi$
$479$	0.898820	+	2.76628i	0.0410681	+	0.126395i	−0.928420	+	0.371531i	$0.878833\pi$
$480$		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	0.518831	−	0.854877i	$-0.326368\pi$
$487$	−10.0307	−	13.8060i	−0.454533	−	0.625612i	−0.973364	+	0.229266i	$0.926368\pi$
$488$		0			0
$489$	−50.9733	−	37.0343i	−2.30509	−	1.67475i
$490$		0			0
$491$	24.8990	−	18.0902i	1.12368	−	0.816398i	0.138913	−	0.990305i	$-0.455639\pi$
$491$	24.8990	−	18.0902i	1.12368	−	0.816398i	0.984762	+	0.173906i	$0.0556390\pi$
$492$		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	−0.245188	−	0.969475i	$-0.578850\pi$
$503$	2.83247	−	0.920324i	0.126293	−	0.0410352i	0.371482	+	0.928440i	$0.378850\pi$
$504$		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	−0.316629	+	0.948549i	$0.602551\pi$
$509$	−29.7038	+	21.5811i	−1.31660	+	0.956564i	−0.999968	+	0.00801464i	$0.997449\pi$
$510$		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	0.966554	−	0.256462i	$-0.0825568\pi$
$521$	0.772662	+	2.37801i	0.0338509	+	0.104182i	−0.932703	+	0.360644i	$0.882557\pi$
$522$		0			0
$523$	−24.7609	+	34.0805i	−1.08272	+	1.49024i	−0.226229	+	0.974074i	$0.572640\pi$
$523$	−24.7609	+	34.0805i	−1.08272	+	1.49024i	−0.856491	+	0.516162i	$0.827360\pi$
$524$		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	0.000161922	−	1.00000i	$-0.499948\pi$
$541$	22.1259	−	16.0754i	0.951268	−	0.691137i	0.951107	+	0.308863i	$0.0999485\pi$
$542$		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	−0.691814	−	0.722076i	$-0.743188\pi$
$547$	−19.3437	+	6.28515i	−0.827077	+	0.268734i	−0.135263	+	0.990810i	$0.543188\pi$
$548$		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	$-0.795677\pi$
$557$		−	28.2605i		−	1.19744i	0.800960	−	0.598718i	$-0.204323\pi$
$558$		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	0.938526	−	0.345210i	$-0.112192\pi$
$563$	7.59738	+	10.4569i	0.320192	+	0.440706i	−0.618334	+	0.785915i	$0.712192\pi$
$564$		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	−0.929088	−	0.369859i	$-0.879406\pi$
$569$	0.953142	−	2.93347i	0.0399578	−	0.122977i	0.969046	+	0.246882i	$0.0794059\pi$
$570$		0			0
$571$	1.27552	+	3.92564i	0.0533788	+	0.164283i	0.974192	−	0.225721i	$-0.0724737\pi$
$571$	1.27552	+	3.92564i	0.0533788	+	0.164283i	−0.920813	+	0.390004i	$0.872474\pi$
$572$		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	−0.879667	−	0.475589i	$-0.842235\pi$
$577$	−3.73579	+	5.14187i	−0.155523	+	0.214059i	0.724145	+	0.689648i	$0.242235\pi$
$578$		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	0.984254	−	0.176761i	$-0.0565621\pi$
$587$	12.4046	+	17.0735i	0.511992	+	0.704697i	−0.472261	+	0.881459i	$0.656562\pi$
$588$		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	$0.146650\pi$
$593$			21.6529i			0.889177i	−0.895735	+	0.444589i	$0.853350\pi$
$594$		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	$-0.896979\pi$
$607$		−	15.6708i		−	0.636059i	0.948081	−	0.318029i	$-0.103021\pi$
$608$		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	−0.968216	−	0.250117i	$-0.919531\pi$
$613$	−22.4537	−	30.9048i	−0.906896	−	1.24823i	0.0613201	−	0.998118i	$-0.480469\pi$
$614$		0			0
$615$	41.6696	+	5.24287i	1.68028	+	0.211413i
$616$		0			0
$617$	12.5842	+	4.08884i	0.506619	+	0.164611i	0.551164	−	0.834397i	$-0.314184\pi$
$617$	12.5842	+	4.08884i	0.506619	+	0.164611i	−0.0445449	+	0.999007i	$0.514184\pi$
$618$		0			0
$619$	1.86789	−	5.74878i	0.0750770	−	0.231063i	−0.906475	−	0.422260i	$-0.861237\pi$
$619$	1.86789	−	5.74878i	0.0750770	−	0.231063i	0.981552	+	0.191197i	$0.0612369\pi$
$620$		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	−0.394371	−	0.918952i	$-0.629037\pi$
$631$	11.6763	−	35.9361i	0.464828	−	1.43059i	0.859199	−	0.511642i	$-0.170963\pi$
$632$		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	−0.202372	−	0.979309i	$-0.564865\pi$
$641$	16.8737	−	12.2594i	0.666470	−	0.484219i	0.868842	+	0.495090i	$0.164865\pi$
$642$		0			0
$643$		−	37.5552i		−	1.48103i	−0.672039	−	0.740516i	$-0.734581\pi$
$643$		−	37.5552i		−	1.48103i	0.672039	−	0.740516i	$-0.265419\pi$
$644$		0			0
$645$	36.4956	−	38.9030i	1.43701	−	1.53180i
$646$		0			0
$647$	−26.0592	+	8.46714i	−1.02449	+	0.332878i	−0.772611	−	0.634880i	$-0.781049\pi$
$647$	−26.0592	+	8.46714i	−1.02449	+	0.332878i	−0.251882	+	0.967758i	$0.581049\pi$
$648$		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	0.153046	−	0.988219i	$-0.451092\pi$
$653$	21.9182	−	7.12164i	0.857724	−	0.278691i	0.704678	+	0.709528i	$0.251092\pi$
$654$		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	−0.861749	−	0.507335i	$-0.830631\pi$
$659$	−16.5717	+	12.0400i	−0.645540	+	0.469012i	0.216209	+	0.976347i	$0.430631\pi$
$660$		0			0
$661$	−11.3181	−	8.22311i	−0.440224	−	0.319842i	0.345500	−	0.938419i	$-0.387709\pi$
$661$	−11.3181	−	8.22311i	−0.440224	−	0.319842i	−0.785724	+	0.618577i	$0.787709\pi$
$662$		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	−0.888596	−	0.458691i	$-0.848319\pi$
$673$	−4.61160	+	6.34732i	−0.177764	+	0.244671i	0.710832	+	0.703362i	$0.248319\pi$
$674$		0			0
$675$	3.71967	+	9.36734i	0.143170	+	0.360549i
$676$		0			0
$677$	8.46310	−	11.6485i	0.325263	−	0.447687i	−0.614802	−	0.788682i	$-0.710764\pi$
$677$	8.46310	−	11.6485i	0.325263	−	0.447687i	0.940065	+	0.340995i	$0.110764\pi$
$678$		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	0.0691847	−	0.997604i	$-0.477960\pi$
$683$	−12.0537	−	3.91647i	−0.461221	−	0.149860i	−0.530405	+	0.847744i	$0.677960\pi$
$684$		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	−0.495855	−	0.868405i	$-0.665145\pi$
$691$	4.64805	−	3.37700i	0.176820	−	0.128467i	0.672675	+	0.739938i	$0.265145\pi$
$692$		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	−0.917417	−	0.397927i	$-0.869730\pi$
$709$	−21.8998	+	15.9111i	−0.822464	+	0.597555i	0.0949536	+	0.995482i	$0.469730\pi$
$710$		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	0.807463	+	0.589918i	$0.200840\pi$
$719$	−5.16263	+	15.8889i	−0.192534	+	0.592557i	−0.999997	+	0.00263916i	$0.999160\pi$
$720$		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	−0.917279	−	0.398246i	$-0.869619\pi$
$727$	−6.87743	+	9.46598i	−0.255070	+	0.351074i	0.662209	+	0.749319i	$0.269619\pi$
$728$		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	−0.359065	−	0.933312i	$-0.616904\pi$
$733$	−32.4385	−	10.5399i	−1.19814	−	0.389300i	−0.839077	+	0.544012i	$0.816904\pi$
$734$		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	0.499006	−	0.866599i	$-0.333699\pi$
$739$	−4.64794	−	3.37693i	−0.170977	−	0.124222i	−0.669983	+	0.742376i	$0.733699\pi$
$740$		0			0
$741$	−7.30434	+	5.30692i	−0.268332	+	0.194954i
$742$		0			0
$743$			36.4348i			1.33666i	0.743863	+	0.668332i	$0.232991\pi$
$743$			36.4348i			1.33666i	−0.743863	+	0.668332i	$0.767009\pi$
$744$		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	$-0.967939\pi$
$757$		−	5.53316i		−	0.201106i	0.994932	−	0.100553i	$-0.0320612\pi$
$758$		0			0
$759$	5.05975	−	3.67613i	0.183657	−	0.133435i
$760$		0			0
$761$	15.1041	+	10.9738i	0.547523	+	0.397799i	0.826871	−	0.562391i	$-0.190118\pi$
$761$	15.1041	+	10.9738i	0.547523	+	0.397799i	−0.279348	+	0.960190i	$0.590118\pi$
$762$		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	−0.850734	−	0.525596i	$-0.823842\pi$
$769$	4.06150	−	12.5000i	0.146462	−	0.450763i	0.997196	+	0.0748333i	$0.0238425\pi$
$770$		0			0
$771$	18.9764	+	58.4032i	0.683417	+	2.10334i
$772$		0			0
$773$	−16.4425	+	22.6311i	−0.591394	+	0.813984i	−0.994887	−	0.100999i	$-0.967796\pi$
$773$	−16.4425	+	22.6311i	−0.591394	+	0.813984i	0.403493	+	0.914983i	$0.367796\pi$
$774$		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	0.999963	+	0.00857605i	$0.00272988\pi$
$787$	19.6126	+	26.9944i	0.699114	+	0.962248i	−0.300849	+	0.953672i	$0.597270\pi$
$788$		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	−0.861455	−	0.507833i	$-0.830447\pi$
$797$	−35.5682	+	11.5568i	−1.25989	+	0.409363i	−0.398435	+	0.917197i	$0.630447\pi$
$798$		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	0.00359108	−	0.999994i	$-0.498857\pi$
$809$	27.1844	−	19.7506i	0.955751	−	0.694394i	0.952160	+	0.305600i	$0.0988569\pi$
$810$		0			0
$811$	−30.7471	−	22.3391i	−1.07968	−	0.784432i	−0.102051	−	0.994779i	$-0.532541\pi$
$811$	−30.7471	−	22.3391i	−1.07968	−	0.784432i	−0.977627	+	0.210347i	$0.932541\pi$
$812$		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	0.990769	+	0.135558i	$0.0432827\pi$
$821$	7.70479	+	23.7129i	0.268899	+	0.827587i	−0.721870	+	0.692028i	$0.756717\pi$
$822$		0			0
$823$	−14.9653	+	20.5980i	−0.521659	+	0.718002i	−0.985831	−	0.167743i	$-0.946352\pi$
$823$	−14.9653	+	20.5980i	−0.521659	+	0.718002i	0.464172	+	0.885745i	$0.346352\pi$
$824$		0			0
$825$	−20.0381	+	16.6109i	−0.697638	+	0.578316i
$826$		0			0
$827$	19.0082	−	26.1626i	0.660980	−	0.909761i	−0.338533	−	0.940954i	$-0.609931\pi$
$827$	19.0082	−	26.1626i	0.660980	−	0.909761i	0.999513	+	0.0311933i	$0.00993074\pi$
$828$		0			0
$829$	−7.71962	−	23.7585i	−0.268113	−	0.825168i	−0.990960	−	0.134159i	$-0.957167\pi$
$829$	−7.71962	−	23.7585i	−0.268113	−	0.825168i	0.722846	−	0.691009i	$-0.242833\pi$
$830$		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	0.283755	−	0.958897i	$-0.408420\pi$
$839$	−15.6566	−	11.3752i	−0.540524	−	0.392714i	−0.824280	+	0.566183i	$0.808420\pi$
$840$		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	−0.710756	−	0.703438i	$-0.751647\pi$
$853$	−25.4765	+	8.27783i	−0.872300	+	0.283427i	−0.161543	+	0.986866i	$0.551647\pi$
$854$		0			0
$855$	−28.5881	+	30.4739i	−0.977694	+	1.04218i
$856$		0			0
$857$			47.5186i			1.62320i	0.584210	+	0.811602i	$0.301404\pi$
$857$			47.5186i			1.62320i	−0.584210	+	0.811602i	$0.698596\pi$
$858$		0			0
$859$	−9.32717	+	6.77658i	−0.318239	+	0.231214i	−0.735424	−	0.677608i	$-0.763017\pi$
$859$	−9.32717	+	6.77658i	−0.318239	+	0.231214i	0.417185	+	0.908822i	$0.363017\pi$
$860$		0			0
$861$	6.18685	+	4.49501i	0.210847	+	0.153190i
$862$		0			0
$863$	10.5835	+	14.5669i	0.360266	+	0.495864i	0.950223	−	0.311571i	$-0.100855\pi$
$863$	10.5835	+	14.5669i	0.360266	+	0.495864i	−0.589957	+	0.807435i	$0.700855\pi$
$864$		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	−0.604902	−	0.796300i	$-0.706788\pi$
$877$	10.0495	−	13.8320i	0.339349	−	0.467074i	0.944251	+	0.329226i	$0.106788\pi$
$878$		0			0
$879$	−15.6315	−	48.1088i	−0.527238	−	1.62267i
$880$		0			0
$881$	−11.7516	+	36.1678i	−0.395923	+	1.21853i	0.532318	+	0.846545i	$0.321321\pi$
$881$	−11.7516	+	36.1678i	−0.395923	+	1.21853i	−0.928240	+	0.371981i	$0.878679\pi$
$882$		0			0
$883$	35.0458	+	11.3871i	1.17939	+	0.383206i	0.832138	−	0.554568i	$-0.187116\pi$
$883$	35.0458	+	11.3871i	1.17939	+	0.383206i	0.347247	+	0.937774i	$0.387116\pi$
$884$		0			0
$885$	−37.5324	−	4.72232i	−1.26164	−	0.158739i
$886$		0			0
$887$	−17.5594	−	24.1684i	−0.589586	−	0.811495i	0.405120	−	0.914264i	$-0.367230\pi$
$887$	−17.5594	−	24.1684i	−0.589586	−	0.811495i	−0.994705	+	0.102769i	$0.967230\pi$
$888$		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	$0.256789\pi$
$907$			43.4897i			1.44405i	−0.691866	+	0.722026i	$0.743211\pi$
$908$		0			0
$909$	56.1758	−	40.8141i	1.86323	−	1.35372i
$910$		0			0
$911$	−19.7150	−	14.3238i	−0.653186	−	0.474568i	0.211169	−	0.977450i	$-0.432273\pi$
$911$	−19.7150	−	14.3238i	−0.653186	−	0.474568i	−0.864355	+	0.502882i	$0.832273\pi$
$912$		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	−0.396344	−	0.918102i	$-0.629721\pi$
$919$	14.0647	−	43.2867i	0.463952	−	1.42790i	0.860296	−	0.509795i	$-0.170279\pi$
$920$		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	0.894730	−	0.446608i	$-0.147368\pi$
$929$	−2.79288	−	8.59560i	−0.0916314	−	0.282012i	−0.986361	+	0.164596i	$0.947368\pi$
$930$		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	0.358661	−	0.933468i	$-0.383234\pi$
$937$	−19.5892	−	26.9623i	−0.639953	−	0.880819i	−0.998613	+	0.0526490i	$0.983234\pi$
$938$		0			0
$939$	−14.7745	−	10.7343i	−0.482147	−	0.350300i
$940$		0			0
$941$	23.7050	−	17.2227i	0.772762	−	0.561444i	−0.130036	−	0.991509i	$-0.541509\pi$
$941$	23.7050	−	17.2227i	0.772762	−	0.561444i	0.902798	+	0.430065i	$0.141509\pi$
$942$		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	0.759961	−	0.649969i	$-0.225218\pi$
$947$	54.0634	−	17.5663i	1.75682	−	0.570827i	0.996863	+	0.0791426i	$0.0252182\pi$
$948$		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	−0.000720915	−	1.00000i	$-0.500229\pi$
$953$	18.1051	−	5.88270i	0.586481	−	0.190559i	0.587202	+	0.809441i	$0.300229\pi$
$954$		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	0.525201	−	0.850978i	$-0.323990\pi$
$967$	13.9905	+	4.54580i	0.449906	+	0.146183i	−0.0752956	+	0.997161i	$0.523990\pi$
$968$		0			0
$969$	6.30233	−	19.3966i	0.202460	−	0.623108i
$970$		0			0
$971$	12.0039	+	36.9441i	0.385223	+	1.18559i	0.936319	+	0.351151i	$0.114210\pi$
$971$	12.0039	+	36.9441i	0.385223	+	1.18559i	−0.551096	+	0.834442i	$0.685790\pi$
$972$		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	0.262827	−	0.964843i	$-0.415345\pi$
$977$	34.3586	−	47.2906i	1.09923	−	1.51296i	0.836402	−	0.548116i	$-0.184655\pi$
$978$		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	−0.150989	−	0.988535i	$-0.548246\pi$
$983$	−26.7812	−	8.70175i	−0.854189	−	0.277543i	−0.703199	+	0.710993i	$0.748246\pi$
$984$		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	0.0466640	−	0.998911i	$-0.485141\pi$
$991$	31.8297	−	23.1256i	1.01110	−	0.734610i	0.964440	+	0.264300i	$0.0851410\pi$
$992$		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	0.423583	−	0.905857i	$-0.360772\pi$
$997$	41.0074	−	13.3241i	1.29872	−	0.421979i	0.875136	+	0.483878i	$0.160772\pi$
$998$		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.209.2		8
4.3	odd	2		25.2.e.a.9.2	✓	8
12.11	even	2		225.2.m.a.109.1		8
20.3	even	4		125.2.d.b.76.2		16
20.7	even	4		125.2.d.b.76.3		16
20.19	odd	2		125.2.e.b.49.1		8
25.8	odd	20		10000.2.a.bj.1.8		8
25.14	even	10	inner	400.2.y.c.289.2		8
25.17	odd	20		10000.2.a.bj.1.1		8
100.3	even	20		625.2.d.o.126.3		16
100.11	odd	10		125.2.e.b.74.1		8
100.19	odd	10		625.2.b.c.624.3		8
100.23	even	20		125.2.d.b.51.2		16
100.27	even	20		125.2.d.b.51.3		16
100.31	odd	10		625.2.b.c.624.6		8
100.39	odd	10		25.2.e.a.14.2	yes	8
100.47	even	20		625.2.d.o.126.2		16
100.59	odd	10		625.2.e.a.124.1		8
100.63	even	20		625.2.d.o.501.3		16
100.67	even	20		625.2.a.f.1.3		8
100.71	odd	10		625.2.e.a.499.1		8
100.79	odd	10		625.2.e.i.499.2		8
100.83	even	20		625.2.a.f.1.6		8
100.87	even	20		625.2.d.o.501.2		16
100.91	odd	10		625.2.e.i.124.2		8
300.83	odd	20		5625.2.a.x.1.3		8
300.167	odd	20		5625.2.a.x.1.6		8
300.239	even	10		225.2.m.a.64.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.2.e.a.9.2	✓	8	4.3	odd	2
25.2.e.a.14.2	yes	8	100.39	odd	10
125.2.d.b.51.2		16	100.23	even	20
125.2.d.b.51.3		16	100.27	even	20
125.2.d.b.76.2		16	20.3	even	4
125.2.d.b.76.3		16	20.7	even	4
125.2.e.b.49.1		8	20.19	odd	2
125.2.e.b.74.1		8	100.11	odd	10
225.2.m.a.64.1		8	300.239	even	10
225.2.m.a.109.1		8	12.11	even	2
400.2.y.c.209.2		8	1.1	even	1	trivial
400.2.y.c.289.2		8	25.14	even	10	inner
625.2.a.f.1.3		8	100.67	even	20
625.2.a.f.1.6		8	100.83	even	20
625.2.b.c.624.3		8	100.19	odd	10
625.2.b.c.624.6		8	100.31	odd	10
625.2.d.o.126.2		16	100.47	even	20
625.2.d.o.126.3		16	100.3	even	20
625.2.d.o.501.2		16	100.87	even	20
625.2.d.o.501.3		16	100.63	even	20
625.2.e.a.124.1		8	100.59	odd	10
625.2.e.a.499.1		8	100.71	odd	10
625.2.e.i.124.2		8	100.91	odd	10
625.2.e.i.499.2		8	100.79	odd	10
5625.2.a.x.1.3		8	300.83	odd	20
5625.2.a.x.1.6		8	300.167	odd	20
10000.2.a.bj.1.1		8	25.17	odd	20
10000.2.a.bj.1.8		8	25.8	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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