LMFDB - Embedded newform 810.3.g.k.487.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,3,Mod(163,810)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(810, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("810.163");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	810.g (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$22.0709014132$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 54 x^{9} + 921 x^{8} - 1350 x^{7} + 1458 x^{6} - 18792 x^{5} + 231804 x^{4} - 552420 x^{3} + \cdots + 656100 $ x^12 - 54x^9 + 921x^8 - 1350x^7 + 1458x^6 - 18792x^5 + 231804x^4 - 552420x^3 + 583200x^2 + 874800*x + 656100
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			487.6
Root			$2.88670 + 2.88670i$ of defining polynomial
Character	$\chi$	$=$	810.487
Dual form			810.3.g.k.163.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 + 1.00000i) q^{2} +2.00000i q^{4} +(4.59534 - 1.97049i) q^{5} +(-4.92840 - 4.92840i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(6.56583 + 2.62486i) q^{10} -15.5486 q^{11} +(-0.530580 + 0.530580i) q^{13} -9.85679i q^{14} -4.00000 q^{16} +(-0.0724241 - 0.0724241i) q^{17} -31.0103i q^{19} +(3.94097 + 9.19069i) q^{20} +(-15.5486 - 15.5486i) q^{22} +(22.2272 - 22.2272i) q^{23} +(17.2344 - 18.1101i) q^{25} -1.06116 q^{26} +(9.85679 - 9.85679i) q^{28} -2.55355i q^{29} -13.7371 q^{31} +(-4.00000 - 4.00000i) q^{32} -0.144848i q^{34} +(-32.3590 - 12.9363i) q^{35} +(-5.59532 - 5.59532i) q^{37} +(31.0103 - 31.0103i) q^{38} +(-5.24972 + 13.1317i) q^{40} -28.4552 q^{41} +(-57.5825 + 57.5825i) q^{43} -31.0971i q^{44} +44.4545 q^{46} +(-51.7532 - 51.7532i) q^{47} -0.421810i q^{49} +(35.3445 - 0.875739i) q^{50} +(-1.06116 - 1.06116i) q^{52} +(45.9584 - 45.9584i) q^{53} +(-71.4510 + 30.6382i) q^{55} +19.7136 q^{56} +(2.55355 - 2.55355i) q^{58} -54.4786i q^{59} +13.3219 q^{61} +(-13.7371 - 13.7371i) q^{62} -8.00000i q^{64} +(-1.39270 + 3.48370i) q^{65} +(2.56026 + 2.56026i) q^{67} +(0.144848 - 0.144848i) q^{68} +(-19.4227 - 45.2954i) q^{70} +113.445 q^{71} +(-63.0708 + 63.0708i) q^{73} -11.1906i q^{74} +62.0206 q^{76} +(76.6295 + 76.6295i) q^{77} -44.4965i q^{79} +(-18.3814 + 7.88194i) q^{80} +(-28.4552 - 28.4552i) q^{82} +(81.0071 - 81.0071i) q^{83} +(-0.475525 - 0.190103i) q^{85} -115.165 q^{86} +(31.0971 - 31.0971i) q^{88} +31.4039i q^{89} +5.22982 q^{91} +(44.4545 + 44.4545i) q^{92} -103.506i q^{94} +(-61.1053 - 142.503i) q^{95} +(77.7325 + 77.7325i) q^{97} +(0.421810 - 0.421810i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} + 6 q^{7} - 24 q^{8} - 6 q^{10} + 12 q^{11} - 48 q^{16} - 18 q^{17} - 12 q^{20} + 12 q^{22} + 54 q^{23} - 54 q^{25} - 12 q^{28} + 72 q^{31} - 48 q^{32} - 168 q^{35} + 66 q^{37} + 36 q^{38}+ \cdots + 12 q^{98}+O(q^{100}) $ 12 * q + 12 * q^2 + 6 * q^7 - 24 * q^8 - 6 * q^10 + 12 * q^11 - 48 * q^16 - 18 * q^17 - 12 * q^20 + 12 * q^22 + 54 * q^23 - 54 * q^25 - 12 * q^28 + 72 * q^31 - 48 * q^32 - 168 * q^35 + 66 * q^37 + 36 * q^38 - 12 * q^40 - 24 * q^41 - 108 * q^43 + 108 * q^46 - 48 * q^47 - 54 * q^50 + 192 * q^53 - 276 * q^55 - 24 * q^56 - 60 * q^58 + 456 * q^61 + 72 * q^62 - 264 * q^65 - 12 * q^67 + 36 * q^68 - 174 * q^70 - 84 * q^71 - 216 * q^73 + 72 * q^76 + 48 * q^77 - 24 * q^82 + 246 * q^83 - 324 * q^85 - 216 * q^86 - 24 * q^88 + 612 * q^91 + 108 * q^92 - 432 * q^95 + 102 * q^97 + 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$			2.00000i			0.500000i
$5$	4.59534	−	1.97049i	0.919069	−	0.394097i
$5$	4.59534	−	1.97049i	0.919069	−	0.394097i
$6$		0			0
$7$	−4.92840	−	4.92840i	−0.704057	−	0.704057i	0.261222	−	0.965279i	$-0.415875\pi$
$7$	−4.92840	−	4.92840i	−0.704057	−	0.704057i	−0.965279	+	0.261222i	$0.915875\pi$
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$		0			0
$10$	6.56583	+	2.62486i	0.656583	+	0.262486i
$11$	−15.5486			−1.41351			−0.706753	−	0.707460i	$-0.749841\pi$
$11$	−15.5486			−1.41351			−0.706753	+	0.707460i	$0.749841\pi$
$12$		0			0
$13$	−0.530580	+	0.530580i	−0.0408139	+	0.0408139i	−0.727219	−	0.686405i	$-0.759188\pi$
$13$	−0.530580	+	0.530580i	−0.0408139	+	0.0408139i	0.686405	+	0.727219i	$0.259188\pi$
$14$		−	9.85679i		−	0.704057i
$15$		0			0
$16$	−4.00000			−0.250000
$17$	−0.0724241	−	0.0724241i	−0.00426024	−	0.00426024i	0.704973	−	0.709234i	$-0.250959\pi$
$17$	−0.0724241	−	0.0724241i	−0.00426024	−	0.00426024i	−0.709234	+	0.704973i	$0.750959\pi$
$18$		0			0
$19$		−	31.0103i		−	1.63212i	−0.577966	−	0.816061i	$-0.696153\pi$
$19$		−	31.0103i		−	1.63212i	0.577966	−	0.816061i	$-0.303847\pi$
$20$	3.94097	+	9.19069i	0.197049	+	0.459534i
$21$		0			0
$22$	−15.5486	−	15.5486i	−0.706753	−	0.706753i
$23$	22.2272	−	22.2272i	0.966402	−	0.966402i	−0.0330516	−	0.999454i	$-0.510523\pi$
$23$	22.2272	−	22.2272i	0.966402	−	0.966402i	0.999454	+	0.0330516i	$0.0105226\pi$
$24$		0			0
$25$	17.2344	−	18.1101i	0.689375	−	0.724405i
$26$	−1.06116			−0.0408139
$27$		0			0
$28$	9.85679	−	9.85679i	0.352028	−	0.352028i
$29$		−	2.55355i		−	0.0880533i	−0.999030	−	0.0440266i	$-0.985981\pi$
$29$		−	2.55355i		−	0.0880533i	0.999030	−	0.0440266i	$-0.0140186\pi$
$30$		0			0
$31$	−13.7371			−0.443133			−0.221567	−	0.975145i	$-0.571117\pi$
$31$	−13.7371			−0.443133			−0.221567	+	0.975145i	$0.571117\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$		0			0
$34$		−	0.144848i		−	0.00426024i
$35$	−32.3590	−	12.9363i	−0.924543	−	0.369610i
$36$		0			0
$37$	−5.59532	−	5.59532i	−0.151225	−	0.151225i	0.627440	−	0.778665i	$-0.284103\pi$
$37$	−5.59532	−	5.59532i	−0.151225	−	0.151225i	−0.778665	+	0.627440i	$0.784103\pi$
$38$	31.0103	−	31.0103i	0.816061	−	0.816061i
$39$		0			0
$40$	−5.24972	+	13.1317i	−0.131243	+	0.328291i
$41$	−28.4552			−0.694029			−0.347014	−	0.937860i	$-0.612805\pi$
$41$	−28.4552			−0.694029			−0.347014	+	0.937860i	$0.612805\pi$
$42$		0			0
$43$	−57.5825	+	57.5825i	−1.33913	+	1.33913i	−0.442221	+	0.896906i	$0.645809\pi$
$43$	−57.5825	+	57.5825i	−1.33913	+	1.33913i	−0.896906	+	0.442221i	$0.854191\pi$
$44$		−	31.0971i		−	0.706753i
$45$		0			0
$46$	44.4545			0.966402
$47$	−51.7532	−	51.7532i	−1.10113	−	1.10113i	−0.994274	−	0.106857i	$-0.965921\pi$
$47$	−51.7532	−	51.7532i	−1.10113	−	1.10113i	−0.106857	−	0.994274i	$-0.534079\pi$
$48$		0			0
$49$		−	0.421810i		−	0.00860837i
$50$	35.3445	−	0.875739i	0.706890	−	0.0175148i
$51$		0			0
$52$	−1.06116	−	1.06116i	−0.0204069	−	0.0204069i
$53$	45.9584	−	45.9584i	0.867139	−	0.867139i	−0.125015	−	0.992155i	$-0.539898\pi$
$53$	45.9584	−	45.9584i	0.867139	−	0.867139i	0.992155	+	0.125015i	$0.0398980\pi$
$54$		0			0
$55$	−71.4510	+	30.6382i	−1.29911	+	0.557059i
$56$	19.7136			0.352028
$57$		0			0
$58$	2.55355	−	2.55355i	0.0440266	−	0.0440266i
$59$		−	54.4786i		−	0.923366i	−0.887045	−	0.461683i	$-0.847246\pi$
$59$		−	54.4786i		−	0.923366i	0.887045	−	0.461683i	$-0.152754\pi$
$60$		0			0
$61$	13.3219			0.218392			0.109196	−	0.994020i	$-0.465172\pi$
$61$	13.3219			0.218392			0.109196	+	0.994020i	$0.465172\pi$
$62$	−13.7371	−	13.7371i	−0.221567	−	0.221567i
$63$		0			0
$64$		−	8.00000i		−	0.125000i
$65$	−1.39270	+	3.48370i	−0.0214261	+	0.0535954i
$66$		0			0
$67$	2.56026	+	2.56026i	0.0382129	+	0.0382129i	0.725955	−	0.687742i	$-0.241398\pi$
$67$	2.56026	+	2.56026i	0.0382129	+	0.0382129i	−0.687742	+	0.725955i	$0.741398\pi$
$68$	0.144848	−	0.144848i	0.00213012	−	0.00213012i
$69$		0			0
$70$	−19.4227	−	45.2954i	−0.277467	−	0.647077i
$71$	113.445			1.59781			0.798906	−	0.601456i	$-0.205413\pi$
$71$	113.445			1.59781			0.798906	+	0.601456i	$0.205413\pi$
$72$		0			0
$73$	−63.0708	+	63.0708i	−0.863984	+	0.863984i	−0.991798	−	0.127814i	$-0.959204\pi$
$73$	−63.0708	+	63.0708i	−0.863984	+	0.863984i	0.127814	+	0.991798i	$0.459204\pi$
$74$		−	11.1906i		−	0.151225i
$75$		0			0
$76$	62.0206			0.816061
$77$	76.6295	+	76.6295i	0.995189	+	0.995189i
$78$		0			0
$79$		−	44.4965i		−	0.563247i	−0.959525	−	0.281624i	$-0.909127\pi$
$79$		−	44.4965i		−	0.563247i	0.959525	−	0.281624i	$-0.0908729\pi$
$80$	−18.3814	+	7.88194i	−0.229767	+	0.0985243i
$81$		0			0
$82$	−28.4552	−	28.4552i	−0.347014	−	0.347014i
$83$	81.0071	−	81.0071i	0.975989	−	0.975989i	−0.0237297	−	0.999718i	$-0.507554\pi$
$83$	81.0071	−	81.0071i	0.975989	−	0.975989i	0.999718	+	0.0237297i	$0.00755411\pi$
$84$		0			0
$85$	−0.475525	−	0.190103i	−0.00559441	−	0.00223651i
$86$	−115.165			−1.33913
$87$		0			0
$88$	31.0971	−	31.0971i	0.353377	−	0.353377i
$89$			31.4039i			0.352853i	0.984314	+	0.176427i	$0.0564538\pi$
$89$			31.4039i			0.352853i	−0.984314	+	0.176427i	$0.943546\pi$
$90$		0			0
$91$	5.22982			0.0574705
$92$	44.4545	+	44.4545i	0.483201	+	0.483201i
$93$		0			0
$94$		−	103.506i		−	1.10113i
$95$	−61.1053	−	142.503i	−0.643214	−	1.50003i
$96$		0			0
$97$	77.7325	+	77.7325i	0.801366	+	0.801366i	0.983309	−	0.181943i	$-0.0582388\pi$
$97$	77.7325	+	77.7325i	0.801366	+	0.801366i	−0.181943	+	0.983309i	$0.558239\pi$
$98$	0.421810	−	0.421810i	0.00430419	−	0.00430419i
$99$		0			0
$100$	36.2202	+	34.4688i	0.362202	+	0.344688i
$101$	118.996			1.17818			0.589090	−	0.808067i	$-0.299486\pi$
$101$	118.996			1.17818			0.589090	+	0.808067i	$0.299486\pi$
$102$		0			0
$103$	−25.9628	+	25.9628i	−0.252066	+	0.252066i	−0.821817	−	0.569751i	$-0.807040\pi$
$103$	−25.9628	+	25.9628i	−0.252066	+	0.252066i	0.569751	+	0.821817i	$0.307040\pi$
$104$		−	2.12232i		−	0.0204069i
$105$		0			0
$106$	91.9168			0.867139
$107$	−96.2280	−	96.2280i	−0.899327	−	0.899327i	0.0960496	−	0.995377i	$-0.469379\pi$
$107$	−96.2280	−	96.2280i	−0.899327	−	0.899327i	−0.995377	+	0.0960496i	$0.969379\pi$
$108$		0			0
$109$			94.0446i			0.862794i	0.902162	+	0.431397i	$0.141979\pi$
$109$			94.0446i			0.862794i	−0.902162	+	0.431397i	$0.858021\pi$
$110$	−102.089	−	40.8128i	−0.928084	−	0.371025i
$111$		0			0
$112$	19.7136	+	19.7136i	0.176014	+	0.176014i
$113$	−60.2985	+	60.2985i	−0.533615	+	0.533615i	−0.921646	−	0.388031i	$-0.873155\pi$
$113$	−60.2985	+	60.2985i	−0.533615	+	0.533615i	0.388031	+	0.921646i	$0.373155\pi$
$114$		0			0
$115$	58.3434	−	145.940i	0.507334	−	1.26905i
$116$	5.10709			0.0440266
$117$		0			0
$118$	54.4786	−	54.4786i	0.461683	−	0.461683i
$119$			0.713870i			0.00599891i
$120$		0			0
$121$	120.758			0.998000
$122$	13.3219	+	13.3219i	0.109196	+	0.109196i
$123$		0			0
$124$		−	27.4743i		−	0.221567i
$125$	43.5122	−	117.182i	0.348097	−	0.937458i
$126$		0			0
$127$	−22.3186	−	22.3186i	−0.175737	−	0.175737i	0.613757	−	0.789495i	$-0.289657\pi$
$127$	−22.3186	−	22.3186i	−0.175737	−	0.175737i	−0.789495	+	0.613757i	$0.789657\pi$
$128$	8.00000	−	8.00000i	0.0625000	−	0.0625000i
$129$		0			0
$130$	−4.87640	+	2.09100i	−0.0375107	+	0.0160846i
$131$	26.1150			0.199351			0.0996757	−	0.995020i	$-0.468219\pi$
$131$	26.1150			0.199351			0.0996757	+	0.995020i	$0.468219\pi$
$132$		0			0
$133$	−152.831	+	152.831i	−1.14911	+	1.14911i
$134$			5.12053i			0.0382129i
$135$		0			0
$136$	0.289697			0.00213012
$137$	−68.6576	−	68.6576i	−0.501150	−	0.501150i	0.410645	−	0.911795i	$-0.365304\pi$
$137$	−68.6576	−	68.6576i	−0.501150	−	0.501150i	−0.911795	+	0.410645i	$0.865304\pi$
$138$		0			0
$139$			216.015i			1.55406i	0.629462	+	0.777032i	$0.283276\pi$
$139$			216.015i			1.55406i	−0.629462	+	0.777032i	$0.716724\pi$
$140$	25.8727	−	64.7180i	0.184805	−	0.462272i
$141$		0			0
$142$	113.445	+	113.445i	0.798906	+	0.798906i
$143$	8.24976	−	8.24976i	0.0576906	−	0.0576906i
$144$		0			0
$145$	−5.03172	−	11.7344i	−0.0347015	−	0.0809270i
$146$	−126.142			−0.863984
$147$		0			0
$148$	11.1906	−	11.1906i	0.0756125	−	0.0756125i
$149$		−	47.3544i		−	0.317815i	−0.987294	−	0.158907i	$-0.949203\pi$
$149$		−	47.3544i		−	0.317815i	0.987294	−	0.158907i	$-0.0507971\pi$
$150$		0			0
$151$	−171.921			−1.13855			−0.569275	−	0.822147i	$-0.692776\pi$
$151$	−171.921			−1.13855			−0.569275	+	0.822147i	$0.692776\pi$
$152$	62.0206	+	62.0206i	0.408030	+	0.408030i
$153$		0			0
$154$			153.259i			0.995189i
$155$	−63.1268	+	27.0688i	−0.407270	+	0.174637i
$156$		0			0
$157$	−156.134	−	156.134i	−0.994483	−	0.994483i	0.00550221	−	0.999985i	$-0.498249\pi$
$157$	−156.134	−	156.134i	−0.994483	−	0.994483i	−0.999985	+	0.00550221i	$0.998249\pi$
$158$	44.4965	−	44.4965i	0.281624	−	0.281624i
$159$		0			0
$160$	−26.2633	−	10.4994i	−0.164146	−	0.0656215i
$161$	−219.089			−1.36080
$162$		0			0
$163$	108.025	−	108.025i	0.662729	−	0.662729i	−0.293293	−	0.956023i	$-0.594751\pi$
$163$	108.025	−	108.025i	0.662729	−	0.662729i	0.956023	+	0.293293i	$0.0947512\pi$
$164$		−	56.9104i		−	0.347014i
$165$		0			0
$166$	162.014			0.975989
$167$	96.1424	+	96.1424i	0.575703	+	0.575703i	0.933716	−	0.358013i	$-0.116546\pi$
$167$	96.1424	+	96.1424i	0.575703	+	0.575703i	−0.358013	+	0.933716i	$0.616546\pi$
$168$		0			0
$169$			168.437i			0.996668i
$170$	−0.285421	−	0.665628i	−0.00167895	−	0.00391546i
$171$		0			0
$172$	−115.165	−	115.165i	−0.669563	−	0.669563i
$173$	−39.0596	+	39.0596i	−0.225778	+	0.225778i	−0.810926	−	0.585148i	$-0.801036\pi$
$173$	−39.0596	+	39.0596i	−0.225778	+	0.225778i	0.585148	+	0.810926i	$0.301036\pi$
$174$		0			0
$175$	−174.192	+	4.31599i	−0.995381	+	0.0246628i
$176$	62.1943			0.353377
$177$		0			0
$178$	−31.4039	+	31.4039i	−0.176427	+	0.176427i
$179$			259.402i			1.44917i	0.689184	+	0.724586i	$0.257969\pi$
$179$			259.402i			1.44917i	−0.689184	+	0.724586i	$0.742031\pi$
$180$		0			0
$181$	329.156			1.81854			0.909270	−	0.416208i	$-0.136641\pi$
$181$	329.156			1.81854			0.909270	+	0.416208i	$0.136641\pi$
$182$	5.22982	+	5.22982i	0.0287353	+	0.0287353i
$183$		0			0
$184$			88.9090i			0.483201i
$185$	−36.7379	−	14.6869i	−0.198583	−	0.0793888i
$186$		0			0
$187$	1.12609	+	1.12609i	0.00602188	+	0.00602188i
$188$	103.506	−	103.506i	0.550566	−	0.550566i
$189$		0			0
$190$	81.3977	−	203.608i	0.428409	−	1.07162i
$191$	45.0760			0.236000			0.118000	−	0.993014i	$-0.462352\pi$
$191$	45.0760			0.236000			0.118000	+	0.993014i	$0.462352\pi$
$192$		0			0
$193$	−62.6628	+	62.6628i	−0.324678	+	0.324678i	−0.850558	−	0.525881i	$-0.823736\pi$
$193$	−62.6628	+	62.6628i	−0.324678	+	0.324678i	0.525881	+	0.850558i	$0.323736\pi$
$194$			155.465i			0.801366i
$195$		0			0
$196$	0.843621			0.00430419
$197$	23.5158	+	23.5158i	0.119370	+	0.119370i	0.764268	−	0.644898i	$-0.223100\pi$
$197$	23.5158	+	23.5158i	0.119370	+	0.119370i	−0.644898	+	0.764268i	$0.723100\pi$
$198$		0			0
$199$			103.892i			0.522070i	0.965329	+	0.261035i	$0.0840639\pi$
$199$			103.892i			0.522070i	−0.965329	+	0.261035i	$0.915936\pi$
$200$	1.75148	+	70.6890i	0.00875739	+	0.353445i
$201$		0			0
$202$	118.996	+	118.996i	0.589090	+	0.589090i
$203$	−12.5849	+	12.5849i	−0.0619945	+	0.0619945i
$204$		0			0
$205$	−130.761	+	56.0705i	−0.637860	+	0.273515i
$206$	−51.9256			−0.252066
$207$		0			0
$208$	2.12232	−	2.12232i	0.0102035	−	0.0102035i
$209$			482.166i			2.30701i
$210$		0			0
$211$	−237.745			−1.12675			−0.563376	−	0.826201i	$-0.690498\pi$
$211$	−237.745			−1.12675			−0.563376	+	0.826201i	$0.690498\pi$
$212$	91.9168	+	91.9168i	0.433570	+	0.433570i
$213$		0			0
$214$		−	192.456i		−	0.899327i
$215$	−151.146	+	378.077i	−0.703004	+	1.75850i
$216$		0			0
$217$	67.7020	+	67.7020i	0.311991	+	0.311991i
$218$	−94.0446	+	94.0446i	−0.431397	+	0.431397i
$219$		0			0
$220$	−61.2764	−	142.902i	−0.278529	−	0.649555i
$221$	0.0768536			0.000347754
$222$		0			0
$223$	116.654	−	116.654i	0.523113	−	0.523113i	−0.395397	−	0.918510i	$-0.629393\pi$
$223$	116.654	−	116.654i	0.523113	−	0.523113i	0.918510	+	0.395397i	$0.129393\pi$
$224$			39.4272i			0.176014i
$225$		0			0
$226$	−120.597			−0.533615
$227$	126.238	+	126.238i	0.556113	+	0.556113i	0.928199	−	0.372085i	$-0.121357\pi$
$227$	126.238	+	126.238i	0.556113	+	0.556113i	−0.372085	+	0.928199i	$0.621357\pi$
$228$		0			0
$229$			135.461i			0.591534i	0.955260	+	0.295767i	$0.0955751\pi$
$229$			135.461i			0.591534i	−0.955260	+	0.295767i	$0.904425\pi$
$230$	204.284	−	87.5969i	0.888190	−	0.380856i
$231$		0			0
$232$	5.10709	+	5.10709i	0.0220133	+	0.0220133i
$233$	151.530	−	151.530i	0.650341	−	0.650341i	−0.302734	−	0.953075i	$-0.597899\pi$
$233$	151.530	−	151.530i	0.650341	−	0.650341i	0.953075	+	0.302734i	$0.0978993\pi$
$234$		0			0
$235$	−339.803	−	135.845i	−1.44597	−	0.578063i
$236$	108.957			0.461683
$237$		0			0
$238$	−0.713870	+	0.713870i	−0.00299945	+	0.00299945i
$239$		−	75.6077i		−	0.316350i	−0.987411	−	0.158175i	$-0.949439\pi$
$239$		−	75.6077i		−	0.316350i	0.987411	−	0.158175i	$-0.0505610\pi$
$240$		0			0
$241$	53.5278			0.222107			0.111053	−	0.993814i	$-0.464578\pi$
$241$	53.5278			0.222107			0.111053	+	0.993814i	$0.464578\pi$
$242$	120.758	+	120.758i	0.499000	+	0.499000i
$243$		0			0
$244$			26.6438i			0.109196i
$245$	−0.831171	−	1.93836i	−0.00339254	−	0.00791169i
$246$		0			0
$247$	16.4535	+	16.4535i	0.0666132	+	0.0666132i
$248$	27.4743	−	27.4743i	0.110783	−	0.110783i
$249$		0			0
$250$	160.694	−	73.6701i	0.642778	−	0.294680i
$251$	−124.172			−0.494708			−0.247354	−	0.968925i	$-0.579561\pi$
$251$	−124.172			−0.494708			−0.247354	+	0.968925i	$0.579561\pi$
$252$		0			0
$253$	−345.602	+	345.602i	−1.36602	+	1.36602i
$254$		−	44.6373i		−	0.175737i
$255$		0			0
$256$	16.0000			0.0625000
$257$	37.4229	+	37.4229i	0.145614	+	0.145614i	0.776156	−	0.630541i	$-0.217167\pi$
$257$	37.4229	+	37.4229i	0.145614	+	0.145614i	−0.630541	+	0.776156i	$0.717167\pi$
$258$		0			0
$259$			55.1519i			0.212942i
$260$	−6.96740	−	2.78540i	−0.0267977	−	0.0107131i
$261$		0			0
$262$	26.1150	+	26.1150i	0.0996757	+	0.0996757i
$263$	183.928	−	183.928i	0.699345	−	0.699345i	−0.264924	−	0.964269i	$-0.585347\pi$
$263$	183.928	−	183.928i	0.699345	−	0.699345i	0.964269	+	0.264924i	$0.0853470\pi$
$264$		0			0
$265$	120.634	−	301.755i	0.455224	−	1.13870i
$266$	−305.662			−1.14911
$267$		0			0
$268$	−5.12053	+	5.12053i	−0.0191065	+	0.0191065i
$269$		−	113.484i		−	0.421873i	−0.977500	−	0.210937i	$-0.932349\pi$
$269$		−	113.484i		−	0.421873i	0.977500	−	0.210937i	$-0.0676514\pi$
$270$		0			0
$271$	382.379			1.41099			0.705496	−	0.708714i	$-0.250724\pi$
$271$	382.379			1.41099			0.705496	+	0.708714i	$0.250724\pi$
$272$	0.289697	+	0.289697i	0.00106506	+	0.00106506i
$273$		0			0
$274$		−	137.315i		−	0.501150i
$275$	−267.970	+	281.586i	−0.974436	+	1.02395i
$276$		0			0
$277$	−200.706	−	200.706i	−0.724569	−	0.724569i	0.244964	−	0.969532i	$-0.421224\pi$
$277$	−200.706	−	200.706i	−0.724569	−	0.724569i	−0.969532	+	0.244964i	$0.921224\pi$
$278$	−216.015	+	216.015i	−0.777032	+	0.777032i
$279$		0			0
$280$	90.5907	−	38.8453i	0.323538	−	0.138733i
$281$	−341.173			−1.21414			−0.607069	−	0.794649i	$-0.707655\pi$
$281$	−341.173			−1.21414			−0.607069	+	0.794649i	$0.707655\pi$
$282$		0			0
$283$	−18.6586	+	18.6586i	−0.0659314	+	0.0659314i	−0.739304	−	0.673372i	$-0.764845\pi$
$283$	−18.6586	+	18.6586i	−0.0659314	+	0.0659314i	0.673372	+	0.739304i	$0.264845\pi$
$284$			226.889i			0.798906i
$285$		0			0
$286$	16.4995			0.0576906
$287$	140.238	+	140.238i	0.488636	+	0.488636i
$288$		0			0
$289$		−	288.990i		−	0.999964i
$290$	6.70270	−	16.7661i	0.0231127	−	0.0578143i
$291$		0			0
$292$	−126.142	−	126.142i	−0.431992	−	0.431992i
$293$	−73.9615	+	73.9615i	−0.252428	+	0.252428i	−0.821966	−	0.569537i	$-0.807122\pi$
$293$	−73.9615	+	73.9615i	−0.252428	+	0.252428i	0.569537	+	0.821966i	$0.307122\pi$
$294$		0			0
$295$	−107.349	−	250.348i	−0.363896	−	0.848637i
$296$	22.3813			0.0756125
$297$		0			0
$298$	47.3544	−	47.3544i	0.158907	−	0.158907i
$299$			23.5867i			0.0788852i
$300$		0			0
$301$	567.578			1.88564
$302$	−171.921	−	171.921i	−0.569275	−	0.569275i
$303$		0			0
$304$			124.041i			0.408030i
$305$	61.2187	−	26.2506i	0.200717	−	0.0860676i
$306$		0			0
$307$	−348.965	−	348.965i	−1.13670	−	1.13670i	−0.989039	−	0.147656i	$-0.952827\pi$
$307$	−348.965	−	348.965i	−1.13670	−	1.13670i	−0.147656	−	0.989039i	$-0.547173\pi$
$308$	−153.259	+	153.259i	−0.497594	+	0.497594i
$309$		0			0
$310$	−90.1956	−	36.0580i	−0.290954	−	0.116316i
$311$	94.7211			0.304570			0.152285	−	0.988337i	$-0.451337\pi$
$311$	94.7211			0.304570			0.152285	+	0.988337i	$0.451337\pi$
$312$		0			0
$313$	98.2701	−	98.2701i	0.313962	−	0.313962i	−0.532480	−	0.846442i	$-0.678740\pi$
$313$	98.2701	−	98.2701i	0.313962	−	0.313962i	0.846442	+	0.532480i	$0.178740\pi$
$314$		−	312.268i		−	0.994483i
$315$		0			0
$316$	88.9930			0.281624
$317$	−63.5961	−	63.5961i	−0.200619	−	0.200619i	0.599646	−	0.800265i	$-0.295308\pi$
$317$	−63.5961	−	63.5961i	−0.200619	−	0.200619i	−0.800265	+	0.599646i	$0.795308\pi$
$318$		0			0
$319$			39.7040i			0.124464i
$320$	−15.7639	−	36.7628i	−0.0492621	−	0.114884i
$321$		0			0
$322$	−219.089	−	219.089i	−0.680402	−	0.680402i
$323$	−2.24589	+	2.24589i	−0.00695323	+	0.00695323i
$324$		0			0
$325$	0.464650	+	18.7531i	0.00142969	+	0.0577018i
$326$	216.050			0.662729
$327$		0			0
$328$	56.9104	−	56.9104i	0.173507	−	0.173507i
$329$			510.120i			1.55052i
$330$		0			0
$331$	411.528			1.24329			0.621643	−	0.783300i	$-0.286465\pi$
$331$	411.528			1.24329			0.621643	+	0.783300i	$0.286465\pi$
$332$	162.014	+	162.014i	0.487994	+	0.487994i
$333$		0			0
$334$			192.285i			0.575703i
$335$	16.8103	+	6.72033i	0.0501799	+	0.0200607i
$336$		0			0
$337$	−269.145	−	269.145i	−0.798650	−	0.798650i	0.184232	−	0.982883i	$-0.441020\pi$
$337$	−269.145	−	269.145i	−0.798650	−	0.798650i	−0.982883	+	0.184232i	$0.941020\pi$
$338$	−168.437	+	168.437i	−0.498334	+	0.498334i
$339$		0			0
$340$	0.380206	−	0.951049i	0.00111825	−	0.00279720i
$341$	213.593			0.626371
$342$		0			0
$343$	−243.570	+	243.570i	−0.710117	+	0.710117i
$344$		−	230.330i		−	0.669563i
$345$		0			0
$346$	−78.1193			−0.225778
$347$	−51.5478	−	51.5478i	−0.148553	−	0.148553i	0.628918	−	0.777471i	$-0.283498\pi$
$347$	−51.5478	−	51.5478i	−0.148553	−	0.148553i	−0.777471	+	0.628918i	$0.783498\pi$
$348$		0			0
$349$			506.314i			1.45076i	0.688351	+	0.725378i	$0.258335\pi$
$349$			506.314i			1.45076i	−0.688351	+	0.725378i	$0.741665\pi$
$350$	−178.508	−	169.876i	−0.510022	−	0.485359i
$351$		0			0
$352$	62.1943	+	62.1943i	0.176688	+	0.176688i
$353$	178.011	−	178.011i	0.504280	−	0.504280i	−0.408485	−	0.912765i	$-0.633943\pi$
$353$	178.011	−	178.011i	0.504280	−	0.504280i	0.912765	+	0.408485i	$0.133943\pi$
$354$		0			0
$355$	521.317	−	223.541i	1.46850	−	0.629693i
$356$	−62.8079			−0.176427
$357$		0			0
$358$	−259.402	+	259.402i	−0.724586	+	0.724586i
$359$			136.845i			0.381183i	0.981669	+	0.190591i	$0.0610406\pi$
$359$			136.845i			0.381183i	−0.981669	+	0.190591i	$0.938959\pi$
$360$		0			0
$361$	−600.639			−1.66382
$362$	329.156	+	329.156i	0.909270	+	0.909270i
$363$		0			0
$364$			10.4596i			0.0287353i
$365$	−165.552	+	414.112i	−0.453567	+	1.13455i
$366$		0			0
$367$	−351.898	−	351.898i	−0.958849	−	0.958849i	0.0403371	−	0.999186i	$-0.487157\pi$
$367$	−351.898	−	351.898i	−0.958849	−	0.958849i	−0.999186	+	0.0403371i	$0.987157\pi$
$368$	−88.9090	+	88.9090i	−0.241601	+	0.241601i
$369$		0			0
$370$	−22.0510	−	51.4249i	−0.0595973	−	0.138986i
$371$	−453.002			−1.22103
$372$		0			0
$373$	−232.717	+	232.717i	−0.623906	+	0.623906i	−0.946528	−	0.322622i	$-0.895436\pi$
$373$	−232.717	+	232.717i	−0.623906	+	0.623906i	0.322622	+	0.946528i	$0.395436\pi$
$374$			2.25218i			0.00602188i
$375$		0			0
$376$	207.013			0.550566
$377$	1.35486	+	1.35486i	0.00359380	+	0.00359380i
$378$		0			0
$379$			7.37650i			0.0194631i	0.999953	+	0.00973154i	$0.00309769\pi$
$379$			7.37650i			0.0194631i	−0.999953	+	0.00973154i	$0.996902\pi$
$380$	285.006	−	122.211i	0.750016	−	0.321607i
$381$		0			0
$382$	45.0760	+	45.0760i	0.118000	+	0.118000i
$383$	105.288	−	105.288i	0.274904	−	0.274904i	−0.556167	−	0.831071i	$-0.687728\pi$
$383$	105.288	−	105.288i	0.274904	−	0.274904i	0.831071	+	0.556167i	$0.187728\pi$
$384$		0			0
$385$	503.136	+	201.142i	1.30685	+	0.522446i
$386$	−125.326			−0.324678
$387$		0			0
$388$	−155.465	+	155.465i	−0.400683	+	0.400683i
$389$			24.9160i			0.0640513i	0.999487	+	0.0320256i	$0.0101958\pi$
$389$			24.9160i			0.0640513i	−0.999487	+	0.0320256i	$0.989804\pi$
$390$		0			0
$391$	−3.21958			−0.00823422
$392$	0.843621	+	0.843621i	0.00215209	+	0.00215209i
$393$		0			0
$394$			47.0317i			0.119370i
$395$	−87.6797	−	204.477i	−0.221974	−	0.517663i
$396$		0			0
$397$	505.397	+	505.397i	1.27304	+	1.27304i	0.944484	+	0.328557i	$0.106562\pi$
$397$	505.397	+	505.397i	1.27304	+	1.27304i	0.328557	+	0.944484i	$0.393438\pi$
$398$	−103.892	+	103.892i	−0.261035	+	0.261035i
$399$		0			0
$400$	−68.9375	+	72.4405i	−0.172344	+	0.181101i
$401$	472.519			1.17835			0.589176	−	0.808005i	$-0.299452\pi$
$401$	472.519			1.17835			0.589176	+	0.808005i	$0.299452\pi$
$402$		0			0
$403$	7.28865	−	7.28865i	0.0180860	−	0.0180860i
$404$			237.993i			0.589090i
$405$		0			0
$406$	−25.1698			−0.0619945
$407$	86.9993	+	86.9993i	0.213757	+	0.213757i
$408$		0			0
$409$			399.811i			0.977532i	0.872415	+	0.488766i	$0.162553\pi$
$409$			399.811i			0.977532i	−0.872415	+	0.488766i	$0.837447\pi$
$410$	−186.832	−	74.6909i	−0.455688	−	0.182173i
$411$		0			0
$412$	−51.9256	−	51.9256i	−0.126033	−	0.126033i
$413$	−268.492	+	268.492i	−0.650102	+	0.650102i
$414$		0			0
$415$	212.632	−	531.879i	0.512367	−	1.28164i
$416$	4.24464			0.0102035
$417$		0			0
$418$	−482.166	+	482.166i	−1.15351	+	1.15351i
$419$		−	233.913i		−	0.558266i	−0.960252	−	0.279133i	$-0.909953\pi$
$419$		−	233.913i		−	0.558266i	0.960252	−	0.279133i	$-0.0900470\pi$
$420$		0			0
$421$	392.219			0.931637			0.465818	−	0.884880i	$-0.345760\pi$
$421$	392.219			0.931637			0.465818	+	0.884880i	$0.345760\pi$
$422$	−237.745	−	237.745i	−0.563376	−	0.563376i
$423$		0			0
$424$			183.834i			0.433570i
$425$	−2.55979	+	0.0634246i	−0.00602305	+	0.000149234i
$426$		0			0
$427$	−65.6556	−	65.6556i	−0.153760	−	0.153760i
$428$	192.456	−	192.456i	0.449663	−	0.449663i
$429$		0			0
$430$	−529.222	+	226.931i	−1.23075	+	0.527746i
$431$	631.965			1.46628			0.733138	−	0.680080i	$-0.238055\pi$
$431$	631.965			1.46628			0.733138	+	0.680080i	$0.238055\pi$
$432$		0			0
$433$	51.6054	−	51.6054i	0.119181	−	0.119181i	−0.645001	−	0.764182i	$-0.723143\pi$
$433$	51.6054	−	51.6054i	0.119181	−	0.119181i	0.764182	+	0.645001i	$0.223143\pi$
$434$			135.404i			0.311991i
$435$		0			0
$436$	−188.089			−0.431397
$437$	−689.274	−	689.274i	−1.57729	−	1.57729i
$438$		0			0
$439$			384.467i			0.875779i	0.899029	+	0.437890i	$0.144274\pi$
$439$			384.467i			0.875779i	−0.899029	+	0.437890i	$0.855726\pi$
$440$	81.6256	−	204.178i	0.185513	−	0.464042i
$441$		0			0
$442$	0.0768536	+	0.0768536i	0.000173877	+	0.000173877i
$443$	−400.458	+	400.458i	−0.903969	+	0.903969i	−0.995777	−	0.0918077i	$-0.970735\pi$
$443$	−400.458	+	400.458i	−0.903969	+	0.903969i	0.0918077	+	0.995777i	$0.470735\pi$
$444$		0			0
$445$	61.8810	+	144.312i	0.139058	+	0.324297i
$446$	233.309			0.523113
$447$		0			0
$448$	−39.4272	+	39.4272i	−0.0880071	+	0.0880071i
$449$		−	139.408i		−	0.310485i	−0.987876	−	0.155242i	$-0.950384\pi$
$449$		−	139.408i		−	0.310485i	0.987876	−	0.155242i	$-0.0496159\pi$
$450$		0			0
$451$	442.437			0.981014
$452$	−120.597	−	120.597i	−0.266807	−	0.266807i
$453$		0			0
$454$			252.475i			0.556113i
$455$	24.0328	−	10.3053i	0.0528194	−	0.0226490i
$456$		0			0
$457$	−89.9790	−	89.9790i	−0.196891	−	0.196891i	0.601775	−	0.798666i	$-0.294460\pi$
$457$	−89.9790	−	89.9790i	−0.196891	−	0.196891i	−0.798666	+	0.601775i	$0.794460\pi$
$458$	−135.461	+	135.461i	−0.295767	+	0.295767i
$459$		0			0
$460$	291.881	+	116.687i	0.634523	+	0.253667i
$461$	737.839			1.60052			0.800260	−	0.599654i	$-0.204695\pi$
$461$	737.839			1.60052			0.800260	+	0.599654i	$0.204695\pi$
$462$		0			0
$463$	163.525	−	163.525i	0.353185	−	0.353185i	−0.508108	−	0.861293i	$-0.669655\pi$
$463$	163.525	−	163.525i	0.353185	−	0.353185i	0.861293	+	0.508108i	$0.169655\pi$
$464$			10.2142i			0.0220133i
$465$		0			0
$466$	303.059			0.650341
$467$	−326.594	−	326.594i	−0.699345	−	0.699345i	0.264925	−	0.964269i	$-0.414653\pi$
$467$	−326.594	−	326.594i	−0.699345	−	0.699345i	−0.964269	+	0.264925i	$0.914653\pi$
$468$		0			0
$469$		−	25.2360i		−	0.0538081i
$470$	−203.958	−	475.647i	−0.433953	−	1.01202i
$471$		0			0
$472$	108.957	+	108.957i	0.230842	+	0.230842i
$473$	895.325	−	895.325i	1.89286	−	1.89286i
$474$		0			0
$475$	−561.600	−	534.443i	−1.18232	−	1.12514i
$476$	−1.42774			−0.00299945
$477$		0			0
$478$	75.6077	−	75.6077i	0.158175	−	0.158175i
$479$		−	380.472i		−	0.794305i	−0.917753	−	0.397153i	$-0.869998\pi$
$479$		−	380.472i		−	0.794305i	0.917753	−	0.397153i	$-0.130002\pi$
$480$		0			0
$481$	5.93754			0.0123441
$482$	53.5278	+	53.5278i	0.111053	+	0.111053i
$483$		0			0
$484$			241.516i			0.499000i
$485$	510.378	+	204.037i	1.05233	+	0.420694i
$486$		0			0
$487$	−65.5715	−	65.5715i	−0.134644	−	0.134644i	0.636573	−	0.771217i	$-0.280351\pi$
$487$	−65.5715	−	65.5715i	−0.134644	−	0.134644i	−0.771217	+	0.636573i	$0.780351\pi$
$488$	−26.6438	+	26.6438i	−0.0545980	+	0.0545980i
$489$		0			0
$490$	1.10719	−	2.76953i	0.00225958	−	0.00565211i
$491$	693.335			1.41209			0.706044	−	0.708168i	$-0.250478\pi$
$491$	693.335			1.41209			0.706044	+	0.708168i	$0.250478\pi$
$492$		0			0
$493$	−0.184938	+	0.184938i	−0.000375128	+	0.000375128i
$494$			32.9069i			0.0666132i
$495$		0			0
$496$	54.9485			0.110783
$497$	−559.100	−	559.100i	−1.12495	−	1.12495i
$498$		0			0
$499$		−	778.554i		−	1.56023i	−0.625638	−	0.780114i	$-0.715161\pi$
$499$		−	778.554i		−	1.56023i	0.625638	−	0.780114i	$-0.284839\pi$
$500$	234.365	+	87.0244i	0.468729	+	0.174049i
$501$		0			0
$502$	−124.172	−	124.172i	−0.247354	−	0.247354i
$503$	126.686	−	126.686i	0.251860	−	0.251860i	−0.569873	−	0.821733i	$-0.693007\pi$
$503$	126.686	−	126.686i	0.251860	−	0.251860i	0.821733	+	0.569873i	$0.193007\pi$
$504$		0			0
$505$	546.829	−	234.480i	1.08283	−	0.464318i
$506$	−691.204			−1.36602
$507$		0			0
$508$	44.6373	−	44.6373i	0.0878686	−	0.0878686i
$509$		−	783.712i		−	1.53971i	−0.638219	−	0.769855i	$-0.720329\pi$
$509$		−	783.712i		−	1.53971i	0.638219	−	0.769855i	$-0.279671\pi$
$510$		0			0
$511$	621.676			1.21659
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$		0			0
$514$			74.8458i			0.145614i
$515$	−68.1487	+	170.467i	−0.132328	+	0.331005i
$516$		0			0
$517$	804.688	+	804.688i	1.55646	+	1.55646i
$518$	−55.1519	+	55.1519i	−0.106471	+	0.106471i
$519$		0			0
$520$	−4.18200	−	9.75279i	−0.00804231	−	0.0187554i
$521$	−729.063			−1.39935			−0.699677	−	0.714459i	$-0.746673\pi$
$521$	−729.063			−1.39935			−0.699677	+	0.714459i	$0.746673\pi$
$522$		0			0
$523$	66.0843	−	66.0843i	0.126356	−	0.126356i	−0.641101	−	0.767457i	$-0.721522\pi$
$523$	66.0843	−	66.0843i	0.126356	−	0.126356i	0.767457	+	0.641101i	$0.221522\pi$
$524$			52.2301i			0.0996757i
$525$		0			0
$526$	367.855			0.699345
$527$	0.994900	+	0.994900i	0.00188785	+	0.00188785i
$528$		0			0
$529$		−	459.101i		−	0.867866i
$530$	422.389	−	181.121i	0.796961	−	0.341737i
$531$		0			0
$532$	−305.662	−	305.662i	−0.574553	−	0.574553i
$533$	15.0978	−	15.0978i	0.0283260	−	0.0283260i
$534$		0			0
$535$	−631.816	−	252.585i	−1.18097	−	0.472121i
$536$	−10.2411			−0.0191065
$537$		0			0
$538$	113.484	−	113.484i	0.210937	−	0.210937i
$539$			6.55855i			0.0121680i
$540$		0			0
$541$	696.867			1.28811			0.644054	−	0.764980i	$-0.277251\pi$
$541$	696.867			1.28811			0.644054	+	0.764980i	$0.277251\pi$
$542$	382.379	+	382.379i	0.705496	+	0.705496i
$543$		0			0
$544$			0.579393i			0.00106506i
$545$	185.313	+	432.167i	0.340025	+	0.792968i
$546$		0			0
$547$	106.839	+	106.839i	0.195319	+	0.195319i	0.797990	−	0.602671i	$-0.205897\pi$
$547$	106.839	+	106.839i	0.195319	+	0.195319i	−0.602671	+	0.797990i	$0.705897\pi$
$548$	137.315	−	137.315i	0.250575	−	0.250575i
$549$		0			0
$550$	−549.556	+	13.6165i	−0.999193	+	0.0247572i
$551$	−79.1862			−0.143714
$552$		0			0
$553$	−219.297	+	219.297i	−0.396558	+	0.396558i
$554$		−	401.411i		−	0.724569i
$555$		0			0
$556$	−432.030			−0.777032
$557$	−306.738	−	306.738i	−0.550697	−	0.550697i	0.375945	−	0.926642i	$-0.377318\pi$
$557$	−306.738	−	306.738i	−0.550697	−	0.550697i	−0.926642	+	0.375945i	$0.877318\pi$
$558$		0			0
$559$		−	61.1042i		−	0.109310i
$560$	129.436	+	51.7454i	0.231136	+	0.0924025i
$561$		0			0
$562$	−341.173	−	341.173i	−0.607069	−	0.607069i
$563$	−421.135	+	421.135i	−0.748019	+	0.748019i	−0.974107	−	0.226088i	$-0.927406\pi$
$563$	−421.135	+	421.135i	−0.748019	+	0.748019i	0.226088	+	0.974107i	$0.427406\pi$
$564$		0			0
$565$	−158.275	+	395.909i	−0.280133	+	0.700725i
$566$	−37.3171			−0.0659314
$567$		0			0
$568$	−226.889	+	226.889i	−0.399453	+	0.399453i
$569$		−	569.420i		−	1.00074i	−0.865812	−	0.500369i	$-0.833198\pi$
$569$		−	569.420i		−	1.00074i	0.865812	−	0.500369i	$-0.166802\pi$
$570$		0			0
$571$	61.4514			0.107621			0.0538104	−	0.998551i	$-0.482863\pi$
$571$	61.4514			0.107621			0.0538104	+	0.998551i	$0.482863\pi$
$572$	16.4995	+	16.4995i	0.0288453	+	0.0288453i
$573$		0			0
$574$			280.477i			0.488636i
$575$	−19.4653	−	785.611i	−0.0338526	−	1.36628i
$576$		0			0
$577$	149.331	+	149.331i	0.258806	+	0.258806i	0.824568	−	0.565762i	$-0.191418\pi$
$577$	149.331	+	149.331i	0.258806	+	0.258806i	−0.565762	+	0.824568i	$0.691418\pi$
$578$	288.990	−	288.990i	0.499982	−	0.499982i
$579$		0			0
$580$	23.4688	−	10.0634i	0.0404635	−	0.0173508i
$581$	−798.470			−1.37430
$582$		0			0
$583$	−714.587	+	714.587i	−1.22571	+	1.22571i
$584$		−	252.283i		−	0.431992i
$585$		0			0
$586$	−147.923			−0.252428
$587$	419.729	+	419.729i	0.715040	+	0.715040i	0.967585	−	0.252545i	$-0.0812676\pi$
$587$	419.729	+	419.729i	0.715040	+	0.715040i	−0.252545	+	0.967585i	$0.581268\pi$
$588$		0			0
$589$			425.993i			0.723247i
$590$	142.999	−	357.697i	0.242371	−	0.606266i
$591$		0			0
$592$	22.3813	+	22.3813i	0.0378062	+	0.0378062i
$593$	130.883	−	130.883i	0.220714	−	0.220714i	−0.588085	−	0.808799i	$-0.700118\pi$
$593$	130.883	−	130.883i	0.220714	−	0.220714i	0.808799	+	0.588085i	$0.200118\pi$
$594$		0			0
$595$	1.40667	+	3.28048i	0.00236415	+	0.00551341i
$596$	94.7088			0.158907
$597$		0			0
$598$	−23.5867	+	23.5867i	−0.0394426	+	0.0394426i
$599$			513.805i			0.857771i	0.903359	+	0.428886i	$0.141094\pi$
$599$			513.805i			0.857771i	−0.903359	+	0.428886i	$0.858906\pi$
$600$		0			0
$601$	1037.79			1.72678			0.863389	−	0.504539i	$-0.168337\pi$
$601$	1037.79			1.72678			0.863389	+	0.504539i	$0.168337\pi$
$602$	567.578	+	567.578i	0.942821	+	0.942821i
$603$		0			0
$604$		−	343.842i		−	0.569275i
$605$	554.925	−	237.952i	0.917231	−	0.393309i
$606$		0			0
$607$	−152.466	−	152.466i	−0.251180	−	0.251180i	0.570274	−	0.821454i	$-0.306837\pi$
$607$	−152.466	−	152.466i	−0.251180	−	0.251180i	−0.821454	+	0.570274i	$0.806837\pi$
$608$	−124.041	+	124.041i	−0.204015	+	0.204015i
$609$		0			0
$610$	87.4693	+	34.9681i	0.143392	+	0.0573248i
$611$	54.9184			0.0898828
$612$		0			0
$613$	444.947	−	444.947i	0.725852	−	0.725852i	−0.243938	−	0.969791i	$-0.578439\pi$
$613$	444.947	−	444.947i	0.725852	−	0.725852i	0.969791	+	0.243938i	$0.0784395\pi$
$614$		−	697.931i		−	1.13670i
$615$		0			0
$616$	−306.518			−0.497594
$617$	−140.737	−	140.737i	−0.228098	−	0.228098i	0.583800	−	0.811898i	$-0.301565\pi$
$617$	−140.737	−	140.737i	−0.228098	−	0.228098i	−0.811898	+	0.583800i	$0.801565\pi$
$618$		0			0
$619$		−	289.059i		−	0.466977i	−0.972360	−	0.233489i	$-0.924986\pi$
$619$		−	289.059i		−	0.466977i	0.972360	−	0.233489i	$-0.0750142\pi$
$620$	−54.1376	−	126.254i	−0.0873187	−	0.203635i
$621$		0			0
$622$	94.7211	+	94.7211i	0.152285	+	0.152285i
$623$	154.771	−	154.771i	0.248429	−	0.248429i
$624$		0			0
$625$	−30.9525	−	624.233i	−0.0495241	−	0.998773i
$626$	196.540			0.313962
$627$		0			0
$628$	312.268	−	312.268i	0.497241	−	0.497241i
$629$			0.810473i			0.00128851i
$630$		0			0
$631$	−1022.87			−1.62104			−0.810518	−	0.585714i	$-0.800814\pi$
$631$	−1022.87			−1.62104			−0.810518	+	0.585714i	$0.800814\pi$
$632$	88.9930	+	88.9930i	0.140812	+	0.140812i
$633$		0			0
$634$		−	127.192i		−	0.200619i
$635$	−146.540	−	58.5832i	−0.230772	−	0.0922571i
$636$		0			0
$637$	0.223804	+	0.223804i	0.000351341	+	0.000351341i
$638$	−39.7040	+	39.7040i	−0.0622319	+	0.0622319i
$639$		0			0
$640$	20.9989	−	52.5266i	0.0328107	−	0.0820729i
$641$	589.888			0.920262			0.460131	−	0.887851i	$-0.347802\pi$
$641$	589.888			0.920262			0.460131	+	0.887851i	$0.347802\pi$
$642$		0			0
$643$	90.2460	−	90.2460i	0.140351	−	0.140351i	−0.633440	−	0.773792i	$-0.718358\pi$
$643$	90.2460	−	90.2460i	0.140351	−	0.140351i	0.773792	+	0.633440i	$0.218358\pi$
$644$		−	438.179i		−	0.680402i
$645$		0			0
$646$	−4.49179			−0.00695323
$647$	−285.308	−	285.308i	−0.440970	−	0.440970i	0.451368	−	0.892338i	$-0.350936\pi$
$647$	−285.308	−	285.308i	−0.440970	−	0.440970i	−0.892338	+	0.451368i	$0.850936\pi$
$648$		0			0
$649$			847.064i			1.30518i
$650$	−18.2884	+	19.2177i	−0.0281361	+	0.0295658i
$651$		0			0
$652$	216.050	+	216.050i	0.331365	+	0.331365i
$653$	−278.897	+	278.897i	−0.427101	+	0.427101i	−0.887640	−	0.460539i	$-0.847656\pi$
$653$	−278.897	+	278.897i	−0.427101	+	0.427101i	0.460539	+	0.887640i	$0.347656\pi$
$654$		0			0
$655$	120.008	−	51.4593i	0.183218	−	0.0785638i
$656$	113.821			0.173507
$657$		0			0
$658$	−510.120	+	510.120i	−0.775259	+	0.775259i
$659$		−	921.517i		−	1.39836i	−0.714948	−	0.699178i	$-0.753549\pi$
$659$		−	921.517i		−	1.39836i	0.714948	−	0.699178i	$-0.246451\pi$
$660$		0			0
$661$	657.495			0.994697			0.497349	−	0.867551i	$-0.334307\pi$
$661$	657.495			0.994697			0.497349	+	0.867551i	$0.334307\pi$
$662$	411.528	+	411.528i	0.621643	+	0.621643i
$663$		0			0
$664$			324.028i			0.487994i
$665$	−401.160	+	1003.46i	−0.603248	+	1.50897i
$666$		0			0
$667$	−56.7583	−	56.7583i	−0.0850949	−	0.0850949i
$668$	−192.285	+	192.285i	−0.287851	+	0.287851i
$669$		0			0
$670$	10.0899	+	23.5306i	0.0150596	+	0.0351203i
$671$	−207.137			−0.308698
$672$		0			0
$673$	464.706	−	464.706i	0.690499	−	0.690499i	−0.271843	−	0.962342i	$-0.587633\pi$
$673$	464.706	−	464.706i	0.690499	−	0.690499i	0.962342	+	0.271843i	$0.0876332\pi$
$674$		−	538.290i		−	0.798650i
$675$		0			0
$676$	−336.874			−0.498334
$677$	−511.200	−	511.200i	−0.755096	−	0.755096i	0.220329	−	0.975426i	$-0.429287\pi$
$677$	−511.200	−	511.200i	−0.755096	−	0.755096i	−0.975426	+	0.220329i	$0.929287\pi$
$678$		0			0
$679$		−	766.193i		−	1.12841i
$680$	1.33126	−	0.570843i	0.00195773	−	0.000839475i
$681$		0			0
$682$	213.593	+	213.593i	0.313186	+	0.313186i
$683$	372.411	−	372.411i	0.545258	−	0.545258i	−0.379807	−	0.925066i	$-0.624010\pi$
$683$	372.411	−	372.411i	0.545258	−	0.545258i	0.925066	+	0.379807i	$0.124010\pi$
$684$		0			0
$685$	−450.794	−	180.216i	−0.658093	−	0.263090i
$686$	−487.141			−0.710117
$687$		0			0
$688$	230.330	−	230.330i	0.334782	−	0.334782i
$689$			48.7692i			0.0707826i
$690$		0			0
$691$	−777.220			−1.12478			−0.562388	−	0.826873i	$-0.690117\pi$
$691$	−777.220			−1.12478			−0.562388	+	0.826873i	$0.690117\pi$
$692$	−78.1193	−	78.1193i	−0.112889	−	0.112889i
$693$		0			0
$694$		−	103.096i		−	0.148553i
$695$	425.654	+	992.662i	0.612452	+	1.42829i
$696$		0			0
$697$	2.06084	+	2.06084i	0.00295673	+	0.00295673i
$698$	−506.314	+	506.314i	−0.725378	+	0.725378i
$699$		0			0
$700$	−8.63198	−	348.383i	−0.0123314	−	0.497691i
$701$	443.096			0.632091			0.316046	−	0.948744i	$-0.397645\pi$
$701$	443.096			0.632091			0.316046	+	0.948744i	$0.397645\pi$
$702$		0			0
$703$	−173.513	+	173.513i	−0.246817	+	0.246817i
$704$			124.389i			0.176688i
$705$		0			0
$706$	356.022			0.504280
$707$	−586.461	−	586.461i	−0.829506	−	0.829506i
$708$		0			0
$709$		−	693.069i		−	0.977530i	−0.872416	−	0.488765i	$-0.837448\pi$
$709$		−	693.069i		−	0.977530i	0.872416	−	0.488765i	$-0.162552\pi$
$710$	744.858	+	297.776i	1.04910	+	0.419403i
$711$		0			0
$712$	−62.8079	−	62.8079i	−0.0882133	−	0.0882133i
$713$	−305.339	+	305.339i	−0.428245	+	0.428245i
$714$		0			0
$715$	21.6545	−	54.1665i	0.0302860	−	0.0757574i
$716$	−518.804			−0.724586
$717$		0			0
$718$	−136.845	+	136.845i	−0.190591	+	0.190591i
$719$		−	628.389i		−	0.873976i	−0.899467	−	0.436988i	$-0.856045\pi$
$719$		−	628.389i		−	0.873976i	0.899467	−	0.436988i	$-0.143955\pi$
$720$		0			0
$721$	255.910			0.354938
$722$	−600.639	−	600.639i	−0.831910	−	0.831910i
$723$		0			0
$724$			658.311i			0.909270i
$725$	−46.2450	−	44.0088i	−0.0637862	−	0.0607017i
$726$		0			0
$727$	−647.362	−	647.362i	−0.890456	−	0.890456i	0.104110	−	0.994566i	$-0.466801\pi$
$727$	−647.362	−	647.362i	−0.890456	−	0.890456i	−0.994566	+	0.104110i	$0.966801\pi$
$728$	−10.4596	+	10.4596i	−0.0143676	+	0.0143676i
$729$		0			0
$730$	−579.664	+	248.560i	−0.794060	+	0.340493i
$731$	8.34072			0.0114100
$732$		0			0
$733$	253.494	−	253.494i	0.345831	−	0.345831i	−0.512723	−	0.858554i	$-0.671363\pi$
$733$	253.494	−	253.494i	0.345831	−	0.345831i	0.858554	+	0.512723i	$0.171363\pi$
$734$		−	703.795i		−	0.958849i
$735$		0			0
$736$	−177.818			−0.241601
$737$	−39.8084	−	39.8084i	−0.0540142	−	0.0540142i
$738$		0			0
$739$		−	49.2308i		−	0.0666181i	−0.999445	−	0.0333091i	$-0.989395\pi$
$739$		−	49.2308i		−	0.0666181i	0.999445	−	0.0333091i	$-0.0106046\pi$
$740$	29.3739	−	73.4759i	0.0396944	−	0.0992917i
$741$		0			0
$742$	−453.002	−	453.002i	−0.610515	−	0.610515i
$743$	207.254	−	207.254i	0.278941	−	0.278941i	−0.553745	−	0.832686i	$-0.686802\pi$
$743$	207.254	−	207.254i	0.278941	−	0.278941i	0.832686	+	0.553745i	$0.186802\pi$
$744$		0			0
$745$	−93.3111	−	217.610i	−0.125250	−	0.292094i
$746$	−465.434			−0.623906
$747$		0			0
$748$	−2.25218	+	2.25218i	−0.00301094	+	0.00301094i
$749$			948.499i			1.26635i
$750$		0			0
$751$	−850.897			−1.13302			−0.566509	−	0.824055i	$-0.691706\pi$
$751$	−850.897			−1.13302			−0.566509	+	0.824055i	$0.691706\pi$
$752$	207.013	+	207.013i	0.275283	+	0.275283i
$753$		0			0
$754$			2.70972i			0.00359380i
$755$	−790.037	+	338.768i	−1.04641	+	0.448699i
$756$		0			0
$757$	−145.058	−	145.058i	−0.191622	−	0.191622i	0.604775	−	0.796397i	$-0.293263\pi$
$757$	−145.058	−	145.058i	−0.191622	−	0.191622i	−0.796397	+	0.604775i	$0.793263\pi$
$758$	−7.37650	+	7.37650i	−0.00973154	+	0.00973154i
$759$		0			0
$760$	407.217	+	162.795i	0.535812	+	0.214204i
$761$	669.391			0.879620			0.439810	−	0.898091i	$-0.355046\pi$
$761$	669.391			0.879620			0.439810	+	0.898091i	$0.355046\pi$
$762$		0			0
$763$	463.489	−	463.489i	0.607456	−	0.607456i
$764$			90.1520i			0.118000i
$765$		0			0
$766$	210.577			0.274904
$767$	28.9053	+	28.9053i	0.0376861	+	0.0376861i
$768$		0			0
$769$			1261.02i			1.63981i	0.572498	+	0.819906i	$0.305975\pi$
$769$			1261.02i			1.63981i	−0.572498	+	0.819906i	$0.694025\pi$
$770$	301.995	+	704.278i	0.392201	+	0.914647i
$771$		0			0
$772$	−125.326	−	125.326i	−0.162339	−	0.162339i
$773$	−134.657	+	134.657i	−0.174201	+	0.174201i	−0.788822	−	0.614621i	$-0.789309\pi$
$773$	−134.657	+	134.657i	−0.174201	+	0.174201i	0.614621	+	0.788822i	$0.289309\pi$
$774$		0			0
$775$	−236.751	+	248.781i	−0.305485	+	0.321008i
$776$	−310.930			−0.400683
$777$		0			0
$778$	−24.9160	+	24.9160i	−0.0320256	+	0.0320256i
$779$			882.404i			1.13274i
$780$		0			0
$781$	−1763.90			−2.25852
$782$	−3.21958	−	3.21958i	−0.00411711	−	0.00411711i
$783$		0			0
$784$			1.68724i			0.00215209i
$785$	−1025.15	−	409.829i	−1.30592	−	0.522075i
$786$		0			0
$787$	−392.745	−	392.745i	−0.499041	−	0.499041i	0.412099	−	0.911139i	$-0.364796\pi$
$787$	−392.745	−	392.745i	−0.499041	−	0.499041i	−0.911139	+	0.412099i	$0.864796\pi$
$788$	−47.0317	+	47.0317i	−0.0596849	+	0.0596849i
$789$		0			0
$790$	116.797	−	292.157i	0.147844	−	0.369818i
$791$	594.349			0.751390
$792$		0			0
$793$	−7.06834	+	7.06834i	−0.00891342	+	0.00891342i
$794$			1010.79i			1.27304i
$795$		0			0
$796$	−207.784			−0.261035
$797$	−459.788	−	459.788i	−0.576898	−	0.576898i	0.357149	−	0.934047i	$-0.383749\pi$
$797$	−459.788	−	459.788i	−0.576898	−	0.576898i	−0.934047	+	0.357149i	$0.883749\pi$
$798$		0			0
$799$			7.49636i			0.00938218i
$800$	−141.378	+	3.50295i	−0.176722	+	0.00437869i
$801$		0			0
$802$	472.519	+	472.519i	0.589176	+	0.589176i
$803$	980.661	−	980.661i	1.22125	−	1.22125i
$804$		0			0
$805$	−1006.79	+	431.712i	−1.25067	+	0.536289i
$806$	14.5773			0.0180860
$807$		0			0
$808$	−237.993	+	237.993i	−0.294545	+	0.294545i
$809$		−	449.236i		−	0.555298i	−0.960683	−	0.277649i	$-0.910445\pi$
$809$		−	449.236i		−	0.555298i	0.960683	−	0.277649i	$-0.0895553\pi$
$810$		0			0
$811$	972.918			1.19965			0.599826	−	0.800130i	$-0.295236\pi$
$811$	972.918			1.19965			0.599826	+	0.800130i	$0.295236\pi$
$812$	−25.1698	−	25.1698i	−0.0309973	−	0.0309973i
$813$		0			0
$814$			173.999i			0.213757i
$815$	283.550	−	709.273i	0.347914	−	0.870274i
$816$		0			0
$817$	1785.65	+	1785.65i	2.18562	+	2.18562i
$818$	−399.811	+	399.811i	−0.488766	+	0.488766i
$819$		0			0
$820$	−112.141	−	261.523i	−0.136757	−	0.318930i
$821$	1588.20			1.93447			0.967236	−	0.253879i	$-0.0817064\pi$
$821$	1588.20			1.93447			0.967236	+	0.253879i	$0.0817064\pi$
$822$		0			0
$823$	683.088	−	683.088i	0.829998	−	0.829998i	−0.157518	−	0.987516i	$-0.550349\pi$
$823$	683.088	−	683.088i	0.829998	−	0.829998i	0.987516	+	0.157518i	$0.0503493\pi$
$824$		−	103.851i		−	0.126033i
$825$		0			0
$826$	−536.984			−0.650102
$827$	722.776	+	722.776i	0.873973	+	0.873973i	0.992903	−	0.118930i	$-0.0379463\pi$
$827$	722.776	+	722.776i	0.873973	+	0.873973i	−0.118930	+	0.992903i	$0.537946\pi$
$828$		0			0
$829$			107.427i			0.129587i	0.997899	+	0.0647934i	$0.0206388\pi$
$829$			107.427i			0.129587i	−0.997899	+	0.0647934i	$0.979361\pi$
$830$	744.511	−	319.246i	0.897001	−	0.384634i
$831$		0			0
$832$	4.24464	+	4.24464i	0.00510173	+	0.00510173i
$833$	−0.0305493	+	0.0305493i	−3.66738e−5	+	3.66738e-5i
$834$		0			0
$835$	631.255	+	252.360i	0.755993	+	0.302228i
$836$	−964.332			−1.15351
$837$		0			0
$838$	233.913	−	233.913i	0.279133	−	0.279133i
$839$			672.590i			0.801657i	0.916153	+	0.400828i	$0.131278\pi$
$839$			672.590i			0.801657i	−0.916153	+	0.400828i	$0.868722\pi$
$840$		0			0
$841$	834.479			0.992247
$842$	392.219	+	392.219i	0.465818	+	0.465818i
$843$		0			0
$844$		−	475.489i		−	0.563376i
$845$	331.903	+	774.026i	0.392784	+	0.916007i
$846$		0			0
$847$	−595.143	−	595.143i	−0.702648	−	0.702648i
$848$	−183.834	+	183.834i	−0.216785	+	0.216785i
$849$		0			0
$850$	−2.62322	−	2.49637i	−0.00308614	−	0.00293691i
$851$	−248.737			−0.292288
$852$		0			0
$853$	110.233	−	110.233i	0.129230	−	0.129230i	−0.639533	−	0.768763i	$-0.720872\pi$
$853$	110.233	−	110.233i	0.129230	−	0.129230i	0.768763	+	0.639533i	$0.220872\pi$
$854$		−	131.311i		−	0.153760i
$855$		0			0
$856$	384.912			0.449663
$857$	−128.202	−	128.202i	−0.149594	−	0.149594i	0.628343	−	0.777937i	$-0.283734\pi$
$857$	−128.202	−	128.202i	−0.149594	−	0.149594i	−0.777937	+	0.628343i	$0.783734\pi$
$858$		0			0
$859$		−	1562.66i		−	1.81916i	−0.415525	−	0.909582i	$-0.636402\pi$
$859$		−	1562.66i		−	1.81916i	0.415525	−	0.909582i	$-0.363598\pi$
$860$	−756.153	−	302.292i	−0.879248	−	0.351502i
$861$		0			0
$862$	631.965	+	631.965i	0.733138	+	0.733138i
$863$	−597.809	+	597.809i	−0.692711	+	0.692711i	−0.962828	−	0.270117i	$-0.912938\pi$
$863$	−597.809	+	597.809i	−0.692711	+	0.692711i	0.270117	+	0.962828i	$0.412938\pi$
$864$		0			0
$865$	−102.526	+	256.459i	−0.118527	+	0.296484i
$866$	103.211			0.119181
$867$		0			0
$868$	−135.404	+	135.404i	−0.155995	+	0.155995i
$869$			691.857i			0.796153i
$870$		0			0
$871$	−2.71685			−0.00311923
$872$	−188.089	−	188.089i	−0.215699	−	0.215699i
$873$		0			0
$874$		−	1378.55i		−	1.57729i
$875$	−791.966	+	363.076i	−0.905104	+	0.414944i
$876$		0			0
$877$	−293.667	−	293.667i	−0.334854	−	0.334854i	0.519572	−	0.854427i	$-0.326091\pi$
$877$	−293.667	−	293.667i	−0.334854	−	0.334854i	−0.854427	+	0.519572i	$0.826091\pi$
$878$	−384.467	+	384.467i	−0.437890	+	0.437890i
$879$		0			0
$880$	285.804	−	122.553i	0.324777	−	0.139265i
$881$	656.851			0.745575			0.372787	−	0.927917i	$-0.378402\pi$
$881$	656.851			0.745575			0.372787	+	0.927917i	$0.378402\pi$
$882$		0			0
$883$	304.550	−	304.550i	0.344904	−	0.344904i	−0.513303	−	0.858207i	$-0.671578\pi$
$883$	304.550	−	304.550i	0.344904	−	0.344904i	0.858207	+	0.513303i	$0.171578\pi$
$884$			0.153707i			0.000173877i
$885$		0			0
$886$	−800.917			−0.903969
$887$	896.785	+	896.785i	1.01103	+	1.01103i	0.999938	+	0.0110930i	$0.00353109\pi$
$887$	896.785	+	896.785i	1.01103	+	1.01103i	0.0110930	+	0.999938i	$0.496469\pi$
$888$		0			0
$889$			219.990i			0.247458i
$890$	−82.4309	+	206.193i	−0.0926190	+	0.231677i
$891$		0			0
$892$	233.309	+	233.309i	0.261557	+	0.261557i
$893$	−1604.88	+	1604.88i	−1.79718	+	1.79718i
$894$		0			0
$895$	511.147	+	1192.04i	0.571114	+	1.33189i
$896$	−78.8543			−0.0880071
$897$		0			0
$898$	139.408	−	139.408i	0.155242	−	0.155242i
$899$			35.0784i			0.0390193i
$900$		0			0
$901$	−6.65699			−0.00738845
$902$	442.437	+	442.437i	0.490507	+	0.490507i
$903$		0			0
$904$		−	241.194i		−	0.266807i
$905$	1512.58	−	648.596i	1.67136	−	0.716681i
$906$		0			0
$907$	151.614	+	151.614i	0.167160	+	0.167160i	0.785730	−	0.618570i	$-0.212288\pi$
$907$	151.614	+	151.614i	0.167160	+	0.167160i	−0.618570	+	0.785730i	$0.712288\pi$
$908$	−252.475	+	252.475i	−0.278057	+	0.278057i
$909$		0			0
$910$	34.3381	+	13.7275i	0.0377342	+	0.0150852i
$911$	−218.956			−0.240346			−0.120173	−	0.992753i	$-0.538345\pi$
$911$	−218.956			−0.240346			−0.120173	+	0.992753i	$0.538345\pi$
$912$		0			0
$913$	−1259.54	+	1259.54i	−1.37957	+	1.37957i
$914$		−	179.958i		−	0.196891i
$915$		0			0
$916$	−270.922			−0.295767
$917$	−128.705	−	128.705i	−0.140355	−	0.140355i
$918$		0			0
$919$		−	430.583i		−	0.468534i	−0.972172	−	0.234267i	$-0.924731\pi$
$919$		−	430.583i		−	0.468534i	0.972172	−	0.234267i	$-0.0752690\pi$
$920$	175.194	+	408.567i	0.190428	+	0.444095i
$921$		0			0
$922$	737.839	+	737.839i	0.800260	+	0.800260i
$923$	−60.1915	+	60.1915i	−0.0652129	+	0.0652129i
$924$		0			0
$925$	−197.764	+	4.90004i	−0.213799	+	0.00529734i
$926$	327.049			0.353185
$927$		0			0
$928$	−10.2142	+	10.2142i	−0.0110067	+	0.0110067i
$929$			404.256i			0.435151i	0.976043	+	0.217576i	$0.0698149\pi$
$929$			404.256i			0.435151i	−0.976043	+	0.217576i	$0.930185\pi$
$930$		0			0
$931$	−13.0805			−0.0140499
$932$	303.059	+	303.059i	0.325171	+	0.325171i
$933$		0			0
$934$		−	653.188i		−	0.699345i
$935$	7.39373	+	2.95583i	0.00790773	+	0.00316132i
$936$		0			0
$937$	−715.314	−	715.314i	−0.763409	−	0.763409i	0.213528	−	0.976937i	$-0.431504\pi$
$937$	−715.314	−	715.314i	−0.763409	−	0.763409i	−0.976937	+	0.213528i	$0.931504\pi$
$938$	25.2360	−	25.2360i	0.0269040	−	0.0269040i
$939$		0			0
$940$	271.690	−	679.605i	0.289031	−	0.722984i
$941$	204.048			0.216841			0.108421	−	0.994105i	$-0.465421\pi$
$941$	204.048			0.216841			0.108421	+	0.994105i	$0.465421\pi$
$942$		0			0
$943$	−632.480	+	632.480i	−0.670711	+	0.670711i
$944$			217.914i			0.230842i
$945$		0			0
$946$	1790.65			1.89286
$947$	−1054.86	−	1054.86i	−1.11390	−	1.11390i	−0.992619	−	0.121278i	$-0.961301\pi$
$947$	−1054.86	−	1054.86i	−1.11390	−	1.11390i	−0.121278	−	0.992619i	$-0.538699\pi$
$948$		0			0
$949$		−	66.9282i		−	0.0705250i
$950$	−27.1569	−	1096.04i	−0.0285862	−	1.15373i
$951$		0			0
$952$	−1.42774	−	1.42774i	−0.00149973	−	0.00149973i
$953$	57.1888	−	57.1888i	0.0600092	−	0.0600092i	−0.676465	−	0.736474i	$-0.736489\pi$
$953$	57.1888	−	57.1888i	0.0600092	−	0.0600092i	0.736474	+	0.676465i	$0.236489\pi$
$954$		0			0
$955$	207.140	−	88.8216i	0.216900	−	0.0930069i
$956$	151.215			0.158175
$957$		0			0
$958$	380.472	−	380.472i	0.397153	−	0.397153i
$959$			676.743i			0.705676i
$960$		0			0
$961$	−772.291			−0.803633
$962$	5.93754	+	5.93754i	0.00617207	+	0.00617207i
$963$		0			0
$964$			107.056i			0.111053i
$965$	−164.481	+	411.433i	−0.170447	+	0.426356i
$966$		0			0
$967$	58.4254	+	58.4254i	0.0604192	+	0.0604192i	0.736671	−	0.676252i	$-0.236397\pi$
$967$	58.4254	+	58.4254i	0.0604192	+	0.0604192i	−0.676252	+	0.736671i	$0.736397\pi$
$968$	−241.516	+	241.516i	−0.249500	+	0.249500i
$969$		0			0
$970$	306.341	+	714.415i	0.315816	+	0.736510i
$971$	540.835			0.556988			0.278494	−	0.960438i	$-0.410165\pi$
$971$	540.835			0.556988			0.278494	+	0.960438i	$0.410165\pi$
$972$		0			0
$973$	1064.61	−	1064.61i	1.09415	−	1.09415i
$974$		−	131.143i		−	0.134644i
$975$		0			0
$976$	−53.2876			−0.0545980
$977$	1145.43	+	1145.43i	1.17239	+	1.17239i	0.981637	+	0.190757i	$0.0610942\pi$
$977$	1145.43	+	1145.43i	1.17239	+	1.17239i	0.190757	+	0.981637i	$0.438906\pi$
$978$		0			0
$979$		−	488.286i		−	0.498760i
$980$	3.87673	−	1.66234i	0.00395584	−	0.00169627i
$981$		0			0
$982$	693.335	+	693.335i	0.706044	+	0.706044i
$983$	431.839	−	431.839i	0.439308	−	0.439308i	−0.452471	−	0.891779i	$-0.649457\pi$
$983$	431.839	−	431.839i	0.439308	−	0.439308i	0.891779	+	0.452471i	$0.149457\pi$
$984$		0			0
$985$	154.401	+	61.7258i	0.156752	+	0.0626658i
$986$	−0.369877			−0.000375128
$987$		0			0
$988$	−32.9069	+	32.9069i	−0.0333066	+	0.0333066i
$989$			2559.80i			2.58827i
$990$		0			0
$991$	−770.833			−0.777834			−0.388917	−	0.921273i	$-0.627151\pi$
$991$	−770.833			−0.777834			−0.388917	+	0.921273i	$0.627151\pi$
$992$	54.9485	+	54.9485i	0.0553916	+	0.0553916i
$993$		0			0
$994$		−	1118.20i		−	1.12495i
$995$	204.718	+	477.420i	0.205746	+	0.479819i
$996$		0			0
$997$	−568.812	−	568.812i	−0.570524	−	0.570524i	0.361751	−	0.932275i	$-0.382179\pi$
$997$	−568.812	−	568.812i	−0.570524	−	0.570524i	−0.932275	+	0.361751i	$0.882179\pi$
$998$	778.554	−	778.554i	0.780114	−	0.780114i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.3.g.k.487.6		12
3.2	odd	2		810.3.g.i.487.1		12
5.3	odd	4	inner	810.3.g.k.163.6		12
9.2	odd	6		270.3.l.b.37.4		24
9.4	even	3		90.3.k.a.7.1	✓	24
9.5	odd	6		270.3.l.b.127.5		24
9.7	even	3		90.3.k.a.67.3	yes	24
15.8	even	4		810.3.g.i.163.1		12
45.13	odd	12		90.3.k.a.43.3	yes	24
45.23	even	12		270.3.l.b.73.4		24
45.38	even	12		270.3.l.b.253.5		24
45.43	odd	12		90.3.k.a.13.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.3.k.a.7.1	✓	24	9.4	even	3
90.3.k.a.13.1	yes	24	45.43	odd	12
90.3.k.a.43.3	yes	24	45.13	odd	12
90.3.k.a.67.3	yes	24	9.7	even	3
270.3.l.b.37.4		24	9.2	odd	6
270.3.l.b.73.4		24	45.23	even	12
270.3.l.b.127.5		24	9.5	odd	6
270.3.l.b.253.5		24	45.38	even	12
810.3.g.i.163.1		12	15.8	even	4
810.3.g.i.487.1		12	3.2	odd	2
810.3.g.k.163.6		12	5.3	odd	4	inner
810.3.g.k.487.6		12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	810.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +2.00000i q^{4} +(4.59534 - 1.97049i) q^{5} +(-4.92840 - 4.92840i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(6.56583 + 2.62486i) q^{10} -15.5486 q^{11} +(-0.530580 + 0.530580i) q^{13} -9.85679i q^{14} -4.00000 q^{16} +(-0.0724241 - 0.0724241i) q^{17} -31.0103i q^{19} +(3.94097 + 9.19069i) q^{20} +(-15.5486 - 15.5486i) q^{22} +(22.2272 - 22.2272i) q^{23} +(17.2344 - 18.1101i) q^{25} -1.06116 q^{26} +(9.85679 - 9.85679i) q^{28} -2.55355i q^{29} -13.7371 q^{31} +(-4.00000 - 4.00000i) q^{32} -0.144848i q^{34} +(-32.3590 - 12.9363i) q^{35} +(-5.59532 - 5.59532i) q^{37} +(31.0103 - 31.0103i) q^{38} +(-5.24972 + 13.1317i) q^{40} -28.4552 q^{41} +(-57.5825 + 57.5825i) q^{43} -31.0971i q^{44} +44.4545 q^{46} +(-51.7532 - 51.7532i) q^{47} -0.421810i q^{49} +(35.3445 - 0.875739i) q^{50} +(-1.06116 - 1.06116i) q^{52} +(45.9584 - 45.9584i) q^{53} +(-71.4510 + 30.6382i) q^{55} +19.7136 q^{56} +(2.55355 - 2.55355i) q^{58} -54.4786i q^{59} +13.3219 q^{61} +(-13.7371 - 13.7371i) q^{62} -8.00000i q^{64} +(-1.39270 + 3.48370i) q^{65} +(2.56026 + 2.56026i) q^{67} +(0.144848 - 0.144848i) q^{68} +(-19.4227 - 45.2954i) q^{70} +113.445 q^{71} +(-63.0708 + 63.0708i) q^{73} -11.1906i q^{74} +62.0206 q^{76} +(76.6295 + 76.6295i) q^{77} -44.4965i q^{79} +(-18.3814 + 7.88194i) q^{80} +(-28.4552 - 28.4552i) q^{82} +(81.0071 - 81.0071i) q^{83} +(-0.475525 - 0.190103i) q^{85} -115.165 q^{86} +(31.0971 - 31.0971i) q^{88} +31.4039i q^{89} +5.22982 q^{91} +(44.4545 + 44.4545i) q^{92} -103.506i q^{94} +(-61.1053 - 142.503i) q^{95} +(77.7325 + 77.7325i) q^{97} +(0.421810 - 0.421810i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} + 6 q^{7} - 24 q^{8} - 6 q^{10} + 12 q^{11} - 48 q^{16} - 18 q^{17} - 12 q^{20} + 12 q^{22} + 54 q^{23} - 54 q^{25} - 12 q^{28} + 72 q^{31} - 48 q^{32} - 168 q^{35} + 66 q^{37} + 36 q^{38}+ \cdots + 12 q^{98}+O(q^{100}) \) 12 * q + 12 * q^2 + 6 * q^7 - 24 * q^8 - 6 * q^10 + 12 * q^11 - 48 * q^16 - 18 * q^17 - 12 * q^20 + 12 * q^22 + 54 * q^23 - 54 * q^25 - 12 * q^28 + 72 * q^31 - 48 * q^32 - 168 * q^35 + 66 * q^37 + 36 * q^38 - 12 * q^40 - 24 * q^41 - 108 * q^43 + 108 * q^46 - 48 * q^47 - 54 * q^50 + 192 * q^53 - 276 * q^55 - 24 * q^56 - 60 * q^58 + 456 * q^61 + 72 * q^62 - 264 * q^65 - 12 * q^67 + 36 * q^68 - 174 * q^70 - 84 * q^71 - 216 * q^73 + 72 * q^76 + 48 * q^77 - 24 * q^82 + 246 * q^83 - 324 * q^85 - 216 * q^86 - 24 * q^88 + 612 * q^91 + 108 * q^92 - 432 * q^95 + 102 * q^97 + 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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