LMFDB - Embedded newform 460.2.m.a.261.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(41,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("460.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.m (of order $11$, degree $10$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			261.2
Character	$\chi$	$=$	460.261
Dual form			460.2.m.a.141.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.256560 + 0.561788i) q^{3} +(-0.654861 - 0.755750i) q^{5} +(-1.01950 - 0.655191i) q^{7} +(1.71480 - 1.97898i) q^{9} +O(q^{10})$	\(q+(0.256560 + 0.561788i) q^{3} +(-0.654861 - 0.755750i) q^{5} +(-1.01950 - 0.655191i) q^{7} +(1.71480 - 1.97898i) q^{9} +(-0.435403 - 3.02830i) q^{11} +(0.710838 - 0.456828i) q^{13} +(0.256560 - 0.561788i) q^{15} +(6.78397 - 1.99195i) q^{17} +(-2.86659 - 0.841706i) q^{19} +(0.106516 - 0.740837i) q^{21} +(4.79574 + 0.0297844i) q^{23} +(-0.142315 + 0.989821i) q^{25} +(3.32946 + 0.977619i) q^{27} +(-6.26337 + 1.83909i) q^{29} +(1.97917 - 4.33378i) q^{31} +(1.58955 - 1.02154i) q^{33} +(0.172468 + 1.19954i) q^{35} +(1.74486 - 2.01368i) q^{37} +(0.439013 + 0.282136i) q^{39} +(5.64911 + 6.51942i) q^{41} +(-0.718936 - 1.57425i) q^{43} -2.61857 q^{45} -11.7247 q^{47} +(-2.29781 - 5.03149i) q^{49} +(2.85955 + 3.30010i) q^{51} +(6.76575 + 4.34808i) q^{53} +(-2.00351 + 2.31217i) q^{55} +(-0.262591 - 1.82636i) q^{57} +(-5.99582 + 3.85328i) q^{59} +(4.71748 - 10.3298i) q^{61} +(-3.04485 + 0.894047i) q^{63} +(-0.810747 - 0.238057i) q^{65} +(-0.189773 + 1.31990i) q^{67} +(1.21366 + 2.70183i) q^{69} +(-1.49710 + 10.4126i) q^{71} +(4.29580 + 1.26136i) q^{73} +(-0.592582 + 0.173998i) q^{75} +(-1.54022 + 3.37261i) q^{77} +(-8.88784 + 5.71187i) q^{79} +(-0.812992 - 5.65448i) q^{81} +(6.38586 - 7.36968i) q^{83} +(-5.94797 - 3.82253i) q^{85} +(-2.64011 - 3.04685i) q^{87} +(-2.31000 - 5.05820i) q^{89} -1.02401 q^{91} +2.94244 q^{93} +(1.24110 + 2.71762i) q^{95} +(0.650000 + 0.750140i) q^{97} +(-6.73958 - 4.33126i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{5} + q^{7} + 21 q^{9}+O(q^{10}) $ 30 * q - 3 * q^5 + q^7 + 21 * q^9	$ 30 q - 3 q^{5} + q^{7} + 21 q^{9} + 2 q^{13} + 10 q^{17} + 3 q^{19} + 39 q^{21} + 10 q^{23} - 3 q^{25} + 21 q^{27} + 14 q^{29} - 2 q^{31} - 50 q^{33} - 10 q^{35} + 9 q^{37} + 38 q^{39} - 3 q^{41} - 50 q^{43} + 10 q^{45} - 6 q^{47} - 36 q^{49} - 36 q^{51} - 5 q^{53} - 11 q^{55} + 23 q^{57} + 14 q^{59} - 16 q^{61} - 52 q^{63} + 2 q^{65} + 27 q^{67} + 42 q^{69} + 19 q^{71} + 24 q^{73} - 10 q^{77} - 22 q^{79} + 35 q^{81} + 36 q^{83} + 10 q^{85} - 3 q^{87} - 28 q^{89} - 98 q^{91} - 60 q^{93} - 19 q^{95} - 2 q^{97} - 14 q^{99}+O(q^{100}) $ 30 * q - 3 * q^5 + q^7 + 21 * q^9 + 2 * q^13 + 10 * q^17 + 3 * q^19 + 39 * q^21 + 10 * q^23 - 3 * q^25 + 21 * q^27 + 14 * q^29 - 2 * q^31 - 50 * q^33 - 10 * q^35 + 9 * q^37 + 38 * q^39 - 3 * q^41 - 50 * q^43 + 10 * q^45 - 6 * q^47 - 36 * q^49 - 36 * q^51 - 5 * q^53 - 11 * q^55 + 23 * q^57 + 14 * q^59 - 16 * q^61 - 52 * q^63 + 2 * q^65 + 27 * q^67 + 42 * q^69 + 19 * q^71 + 24 * q^73 - 10 * q^77 - 22 * q^79 + 35 * q^81 + 36 * q^83 + 10 * q^85 - 3 * q^87 - 28 * q^89 - 98 * q^91 - 60 * q^93 - 19 * q^95 - 2 * q^97 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{11}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.256560	+	0.561788i	0.148125	+	0.324348i	0.969121	−	0.246585i	$-0.0793086\pi$
$3$	0.256560	+	0.561788i	0.148125	+	0.324348i	−0.820996	+	0.570934i	$0.806581\pi$
$4$		0			0
$5$	−0.654861	−	0.755750i	−0.292863	−	0.337981i
$5$	−0.654861	−	0.755750i	−0.292863	−	0.337981i
$6$		0			0
$7$	−1.01950	−	0.655191i	−0.385334	−	0.247639i	0.333604	−	0.942713i	$-0.391735\pi$
$7$	−1.01950	−	0.655191i	−0.385334	−	0.247639i	−0.718938	+	0.695074i	$0.755371\pi$
$8$		0			0
$9$	1.71480	−	1.97898i	0.571600	−	0.659661i
$10$		0			0
$11$	−0.435403	−	3.02830i	−0.131279	−	0.913066i	−0.943890	−	0.330259i	$-0.892864\pi$
$11$	−0.435403	−	3.02830i	−0.131279	−	0.913066i	0.812611	−	0.582806i	$-0.198045\pi$
$12$		0			0
$13$	0.710838	−	0.456828i	0.197151	−	0.126701i	−0.438341	−	0.898809i	$-0.644434\pi$
$13$	0.710838	−	0.456828i	0.197151	−	0.126701i	0.635492	+	0.772108i	$0.280797\pi$
$14$		0			0
$15$	0.256560	−	0.561788i	0.0662435	−	0.145053i
$16$		0			0
$17$	6.78397	−	1.99195i	1.64535	−	0.483119i	0.677686	−	0.735351i	$-0.262983\pi$
$17$	6.78397	−	1.99195i	1.64535	−	0.483119i	0.967667	+	0.252232i	$0.0811645\pi$
$18$		0			0
$19$	−2.86659	−	0.841706i	−0.657641	−	0.193101i	−0.0641483	−	0.997940i	$-0.520433\pi$
$19$	−2.86659	−	0.841706i	−0.657641	−	0.193101i	−0.593492	+	0.804840i	$0.702251\pi$
$20$		0			0
$21$	0.106516	−	0.740837i	0.0232438	−	0.161664i
$22$		0			0
$23$	4.79574	+	0.0297844i	0.999981	+	0.00621048i
$23$	4.79574	+	0.0297844i	0.999981	+	0.00621048i
$24$		0			0
$25$	−0.142315	+	0.989821i	−0.0284630	+	0.197964i
$26$		0			0
$27$	3.32946	+	0.977619i	0.640756	+	0.188143i
$28$		0			0
$29$	−6.26337	+	1.83909i	−1.16308	+	0.341511i	−0.805628	−	0.592421i	$-0.798172\pi$
$29$	−6.26337	+	1.83909i	−1.16308	+	0.341511i	−0.357450	+	0.933932i	$0.616354\pi$
$30$		0			0
$31$	1.97917	−	4.33378i	0.355470	−	0.778370i	−0.644436	−	0.764658i	$-0.722908\pi$
$31$	1.97917	−	4.33378i	0.355470	−	0.778370i	0.999906	−	0.0137123i	$-0.00436490\pi$
$32$		0			0
$33$	1.58955	−	1.02154i	0.276706	−	0.177828i
$34$		0			0
$35$	0.172468	+	1.19954i	0.0291525	+	0.202760i
$36$		0			0
$37$	1.74486	−	2.01368i	0.286853	−	0.331046i	−0.593974	−	0.804484i	$-0.702442\pi$
$37$	1.74486	−	2.01368i	0.286853	−	0.331046i	0.880827	+	0.473438i	$0.156987\pi$
$38$		0			0
$39$	0.439013	+	0.282136i	0.0702983	+	0.0451780i
$40$		0			0
$41$	5.64911	+	6.51942i	0.882243	+	1.01816i	0.999685	+	0.0250825i	$0.00798485\pi$
$41$	5.64911	+	6.51942i	0.882243	+	1.01816i	−0.117443	+	0.993080i	$0.537470\pi$
$42$		0			0
$43$	−0.718936	−	1.57425i	−0.109637	−	0.240071i	0.846859	−	0.531818i	$-0.178491\pi$
$43$	−0.718936	−	1.57425i	−0.109637	−	0.240071i	−0.956496	+	0.291747i	$0.905764\pi$
$44$		0			0
$45$	−2.61857			−0.390354
$46$		0			0
$47$	−11.7247			−1.71022			−0.855110	−	0.518446i	$-0.826511\pi$
$47$	−11.7247			−1.71022			−0.855110	+	0.518446i	$0.826511\pi$
$48$		0			0
$49$	−2.29781	−	5.03149i	−0.328258	−	0.718785i
$50$		0			0
$51$	2.85955	+	3.30010i	0.400417	+	0.462106i
$52$		0			0
$53$	6.76575	+	4.34808i	0.929347	+	0.597255i	0.915355	−	0.402647i	$-0.131910\pi$
$53$	6.76575	+	4.34808i	0.929347	+	0.597255i	0.0139920	+	0.999902i	$0.495546\pi$
$54$		0			0
$55$	−2.00351	+	2.31217i	−0.270153	+	0.311773i
$56$		0			0
$57$	−0.262591	−	1.82636i	−0.0347811	−	0.241908i
$58$		0			0
$59$	−5.99582	+	3.85328i	−0.780589	+	0.501654i	−0.869229	−	0.494409i	$-0.835384\pi$
$59$	−5.99582	+	3.85328i	−0.780589	+	0.501654i	0.0886399	+	0.996064i	$0.471748\pi$
$60$		0			0
$61$	4.71748	−	10.3298i	0.604011	−	1.32260i	−0.322585	−	0.946541i	$-0.604552\pi$
$61$	4.71748	−	10.3298i	0.604011	−	1.32260i	0.926596	−	0.376059i	$-0.122721\pi$
$62$		0			0
$63$	−3.04485	+	0.894047i	−0.383615	+	0.112639i
$64$		0			0
$65$	−0.810747	−	0.238057i	−0.100561	−	0.0295273i
$66$		0			0
$67$	−0.189773	+	1.31990i	−0.0231844	+	0.161251i	−0.998125	−	0.0612163i	$-0.980502\pi$
$67$	−0.189773	+	1.31990i	−0.0231844	+	0.161251i	0.974940	+	0.222468i	$0.0714111\pi$
$68$		0			0
$69$	1.21366	+	2.70183i	0.146108	+	0.325262i
$70$		0			0
$71$	−1.49710	+	10.4126i	−0.177673	+	1.23574i	0.684456	+	0.729054i	$0.260040\pi$
$71$	−1.49710	+	10.4126i	−0.177673	+	1.23574i	−0.862129	+	0.506689i	$0.830869\pi$
$72$		0			0
$73$	4.29580	+	1.26136i	0.502785	+	0.147631i	0.523283	−	0.852159i	$-0.324707\pi$
$73$	4.29580	+	1.26136i	0.502785	+	0.147631i	−0.0204980	+	0.999790i	$0.506525\pi$
$74$		0			0
$75$	−0.592582	+	0.173998i	−0.0684255	+	0.0200915i
$76$		0			0
$77$	−1.54022	+	3.37261i	−0.175524	+	0.384345i
$78$		0			0
$79$	−8.88784	+	5.71187i	−0.999961	+	0.642636i	−0.934776	−	0.355238i	$-0.884400\pi$
$79$	−8.88784	+	5.71187i	−0.999961	+	0.642636i	−0.0651846	+	0.997873i	$0.520764\pi$
$80$		0			0
$81$	−0.812992	−	5.65448i	−0.0903324	−	0.628276i
$82$		0			0
$83$	6.38586	−	7.36968i	0.700940	−	0.808927i	−0.287940	−	0.957649i	$-0.592970\pi$
$83$	6.38586	−	7.36968i	0.700940	−	0.808927i	0.988879	+	0.148721i	$0.0475157\pi$
$84$		0			0
$85$	−5.94797	−	3.82253i	−0.645148	−	0.414611i
$86$		0			0
$87$	−2.64011	−	3.04685i	−0.283049	−	0.326657i
$88$		0			0
$89$	−2.31000	−	5.05820i	−0.244860	−	0.536168i	0.746801	−	0.665048i	$-0.231589\pi$
$89$	−2.31000	−	5.05820i	−0.244860	−	0.536168i	−0.991660	+	0.128880i	$0.958862\pi$
$90$		0			0
$91$	−1.02401			−0.107345
$92$		0			0
$93$	2.94244			0.305117
$94$		0			0
$95$	1.24110	+	2.71762i	0.127334	+	0.278822i
$96$		0			0
$97$	0.650000	+	0.750140i	0.0659975	+	0.0761652i	0.787788	−	0.615946i	$-0.211226\pi$
$97$	0.650000	+	0.750140i	0.0659975	+	0.0761652i	−0.721791	+	0.692111i	$0.756681\pi$
$98$		0			0
$99$	−6.73958	−	4.33126i	−0.677353	−	0.435309i
$100$		0			0
$101$	−11.5677	+	13.3498i	−1.15103	+	1.32835i	−0.214921	+	0.976631i	$0.568950\pi$
$101$	−11.5677	+	13.3498i	−1.15103	+	1.32835i	−0.936104	+	0.351723i	$0.885596\pi$
$102$		0			0
$103$	1.78680	+	12.4274i	0.176058	+	1.22451i	0.865775	+	0.500433i	$0.166826\pi$
$103$	1.78680	+	12.4274i	0.176058	+	1.22451i	−0.689717	+	0.724079i	$0.742265\pi$
$104$		0			0
$105$	−0.629641	+	0.404646i	−0.0614466	+	0.0394894i
$106$		0			0
$107$	−4.54160	+	9.94472i	−0.439053	+	0.961392i	0.552718	+	0.833368i	$0.313591\pi$
$107$	−4.54160	+	9.94472i	−0.439053	+	0.961392i	−0.991771	+	0.128024i	$0.959137\pi$
$108$		0			0
$109$	−4.64702	+	1.36449i	−0.445104	+	0.130694i	−0.496601	−	0.867979i	$-0.665419\pi$
$109$	−4.64702	+	1.36449i	−0.445104	+	0.130694i	0.0514974	+	0.998673i	$0.483601\pi$
$110$		0			0
$111$	1.57892	+	0.463613i	0.149864	+	0.0440042i
$112$		0			0
$113$	−0.452318	+	3.14594i	−0.0425505	+	0.295945i	0.957423	+	0.288688i	$0.0932191\pi$
$113$	−0.452318	+	3.14594i	−0.0425505	+	0.295945i	−0.999974	+	0.00725693i	$0.997690\pi$
$114$		0			0
$115$	−3.11803	−	3.64388i	−0.290758	−	0.339794i
$116$		0			0
$117$	0.314890	−	2.19010i	0.0291115	−	0.202475i
$118$		0			0
$119$	−8.22134	−	2.41400i	−0.753649	−	0.221291i
$120$		0			0
$121$	1.57342	−	0.461997i	0.143038	−	0.0419998i
$122$		0			0
$123$	−2.21320	+	4.84622i	−0.199557	+	0.436969i
$124$		0			0
$125$	0.841254	−	0.540641i	0.0752440	−	0.0483564i
$126$		0			0
$127$	1.93979	+	13.4915i	0.172129	+	1.19718i	0.874376	+	0.485248i	$0.161271\pi$
$127$	1.93979	+	13.4915i	0.172129	+	1.19718i	−0.702248	+	0.711933i	$0.747820\pi$
$128$		0			0
$129$	0.699945	−	0.807779i	0.0616267	−	0.0711210i
$130$		0			0
$131$	8.23692	+	5.29355i	0.719663	+	0.462499i	0.848520	−	0.529164i	$-0.177494\pi$
$131$	8.23692	+	5.29355i	0.719663	+	0.462499i	−0.128857	+	0.991663i	$0.541131\pi$
$132$		0			0
$133$	2.37100	+	2.73628i	0.205592	+	0.237266i
$134$		0			0
$135$	−1.44150	−	3.15645i	−0.124065	−	0.271664i
$136$		0			0
$137$	21.6030			1.84567			0.922835	−	0.385195i	$-0.125866\pi$
$137$	21.6030			1.84567			0.922835	+	0.385195i	$0.125866\pi$
$138$		0			0
$139$	−14.3516			−1.21729			−0.608644	−	0.793444i	$-0.708286\pi$
$139$	−14.3516			−1.21729			−0.608644	+	0.793444i	$0.708286\pi$
$140$		0			0
$141$	−3.00808	−	6.58679i	−0.253326	−	0.554708i
$142$		0			0
$143$	−1.69291	−	1.95372i	−0.141568	−	0.163379i
$144$		0			0
$145$	5.49153	+	3.52919i	0.456047	+	0.293083i
$146$		0			0
$147$	2.23711	−	2.58176i	0.184514	−	0.212940i
$148$		0			0
$149$	0.857215	+	5.96206i	0.0702258	+	0.488431i	0.994334	+	0.106300i	$0.0339005\pi$
$149$	0.857215	+	5.96206i	0.0702258	+	0.488431i	−0.924108	+	0.382131i	$0.875190\pi$
$150$		0			0
$151$	4.65000	−	2.98838i	0.378412	−	0.243191i	−0.337583	−	0.941296i	$-0.609610\pi$
$151$	4.65000	−	2.98838i	0.378412	−	0.243191i	0.715995	+	0.698105i	$0.245973\pi$
$152$		0			0
$153$	7.69110	−	16.8412i	0.621789	−	1.36153i
$154$		0			0
$155$	−4.57134	+	1.34227i	−0.367179	+	0.107813i
$156$		0			0
$157$	6.32614	+	1.85752i	0.504881	+	0.148246i	0.524247	−	0.851566i	$-0.324347\pi$
$157$	6.32614	+	1.85752i	0.504881	+	0.148246i	−0.0193665	+	0.999812i	$0.506165\pi$
$158$		0			0
$159$	−0.706881	+	4.91646i	−0.0560593	+	0.389901i
$160$		0			0
$161$	−4.86973	−	3.17249i	−0.383788	−	0.250027i
$162$		0			0
$163$	1.31273	−	9.13023i	0.102821	−	0.715135i	−0.871569	−	0.490272i	$-0.836897\pi$
$163$	1.31273	−	9.13023i	0.102821	−	0.715135i	0.974390	−	0.224863i	$-0.0721935\pi$
$164$		0			0
$165$	−1.81297	−	0.532335i	−0.141139	−	0.0414423i
$166$		0			0
$167$	−6.23111	+	1.82962i	−0.482178	+	0.141580i	−0.513783	−	0.857920i	$-0.671756\pi$
$167$	−6.23111	+	1.82962i	−0.482178	+	0.141580i	0.0316050	+	0.999500i	$0.489938\pi$
$168$		0			0
$169$	−5.10380	+	11.1758i	−0.392600	+	0.859673i
$170$		0			0
$171$	−6.58135	+	4.22958i	−0.503288	+	0.323444i
$172$		0			0
$173$	2.03959	+	14.1856i	0.155067	+	1.07851i	0.907562	+	0.419917i	$0.137941\pi$
$173$	2.03959	+	14.1856i	0.155067	+	1.07851i	−0.752495	+	0.658597i	$0.771150\pi$
$174$		0			0
$175$	0.793612	−	0.915877i	0.0599914	−	0.0692338i
$176$		0			0
$177$	−3.70301	−	2.37978i	−0.278336	−	0.178875i
$178$		0			0
$179$	4.27083	+	4.92880i	0.319217	+	0.368396i	0.892567	−	0.450915i	$-0.148902\pi$
$179$	4.27083	+	4.92880i	0.319217	+	0.368396i	−0.573350	+	0.819310i	$0.694357\pi$
$180$		0			0
$181$	−5.83875	−	12.7851i	−0.433991	−	0.950307i	−0.992662	−	0.120918i	$-0.961416\pi$
$181$	−5.83875	−	12.7851i	−0.433991	−	0.950307i	0.558672	−	0.829389i	$-0.311311\pi$
$182$		0			0
$183$	7.01349			0.518452
$184$		0			0
$185$	−2.66448			−0.195896
$186$		0			0
$187$	−8.98598	−	19.6766i	−0.657120	−	1.43889i
$188$		0			0
$189$	−2.75385	−	3.17812i	−0.200313	−	0.231174i
$190$		0			0
$191$	17.1253	+	11.0058i	1.23914	+	0.796350i	0.985290	−	0.170892i	$-0.0546650\pi$
$191$	17.1253	+	11.0058i	1.23914	+	0.796350i	0.253855	+	0.967242i	$0.418301\pi$
$192$		0			0
$193$	13.3701	−	15.4299i	0.962403	−	1.11067i	−0.0313994	−	0.999507i	$-0.509996\pi$
$193$	13.3701	−	15.4299i	0.962403	−	1.11067i	0.993802	−	0.111165i	$-0.0354581\pi$
$194$		0			0
$195$	−0.0742678	−	0.516544i	−0.00531843	−	0.0369905i
$196$		0			0
$197$	−6.32606	+	4.06551i	−0.450713	+	0.289656i	−0.746238	−	0.665679i	$-0.768142\pi$
$197$	−6.32606	+	4.06551i	−0.450713	+	0.289656i	0.295525	+	0.955335i	$0.404505\pi$
$198$		0			0
$199$	10.8960	−	23.8588i	0.772393	−	1.69131i	0.0510824	−	0.998694i	$-0.483733\pi$
$199$	10.8960	−	23.8588i	0.772393	−	1.69131i	0.721311	−	0.692611i	$-0.243540\pi$
$200$		0			0
$201$	−0.790191	+	0.232021i	−0.0557358	+	0.0163655i
$202$		0			0
$203$	7.59044	+	2.22876i	0.532745	+	0.156428i
$204$		0			0
$205$	1.22767	−	8.53862i	0.0857441	−	0.596363i
$206$		0			0
$207$	8.28267	−	9.43962i	0.575686	−	0.656099i
$208$		0			0
$209$	−1.30081	+	9.04736i	−0.0899792	+	0.625819i
$210$		0			0
$211$	14.9359	+	4.38558i	1.02823	+	0.301916i	0.751991	−	0.659173i	$-0.229094\pi$
$211$	14.9359	+	4.38558i	1.02823	+	0.301916i	0.276239	+	0.961089i	$0.410912\pi$
$212$		0			0
$213$	−6.23374	+	1.83039i	−0.427129	+	0.125416i
$214$		0			0
$215$	−0.718936	+	1.57425i	−0.0490310	+	0.107363i
$216$		0			0
$217$	−4.85722	+	3.12154i	−0.329729	+	0.211904i
$218$		0			0
$219$	0.393513	+	2.73694i	0.0265911	+	0.184945i
$220$		0			0
$221$	3.91232	−	4.51506i	0.263171	−	0.303716i
$222$		0			0
$223$	−7.66069	−	4.92323i	−0.512998	−	0.329684i	0.258399	−	0.966038i	$-0.416805\pi$
$223$	−7.66069	−	4.92323i	−0.512998	−	0.329684i	−0.771397	+	0.636355i	$0.780442\pi$
$224$		0			0
$225$	1.71480	+	1.97898i	0.114320	+	0.131932i
$226$		0			0
$227$	−4.81936	−	10.5529i	−0.319872	−	0.700423i	0.679577	−	0.733604i	$-0.262163\pi$
$227$	−4.81936	−	10.5529i	−0.319872	−	0.700423i	−0.999449	+	0.0331813i	$0.989436\pi$
$228$		0			0
$229$	−5.98122			−0.395250			−0.197625	−	0.980278i	$-0.563323\pi$
$229$	−5.98122			−0.395250			−0.197625	+	0.980278i	$0.563323\pi$
$230$		0			0
$231$	−2.28985			−0.150661
$232$		0			0
$233$	−1.26385	−	2.76745i	−0.0827977	−	0.181302i	0.863705	−	0.503998i	$-0.168138\pi$
$233$	−1.26385	−	2.76745i	−0.0827977	−	0.181302i	−0.946503	+	0.322696i	$0.895411\pi$
$234$		0			0
$235$	7.67803	+	8.86092i	0.500860	+	0.578023i
$236$		0			0
$237$	−5.48913	−	3.52765i	−0.356557	−	0.229145i
$238$		0			0
$239$	11.5911	−	13.3768i	0.749766	−	0.865276i	−0.244780	−	0.969579i	$-0.578716\pi$
$239$	11.5911	−	13.3768i	0.749766	−	0.865276i	0.994546	+	0.104303i	$0.0332612\pi$
$240$		0			0
$241$	−1.32793	−	9.23598i	−0.0855397	−	0.594941i	−0.986834	−	0.161735i	$-0.948291\pi$
$241$	−1.32793	−	9.23598i	−0.0855397	−	0.594941i	0.901295	−	0.433207i	$-0.142618\pi$
$242$		0			0
$243$	11.7256	−	7.53556i	0.752195	−	0.483406i
$244$		0			0
$245$	−2.29781	+	5.03149i	−0.146801	+	0.321450i
$246$		0			0
$247$	−2.42219	+	0.711221i	−0.154121	+	0.0452539i
$248$		0			0
$249$	5.77855	+	1.69674i	0.366201	+	0.107526i
$250$		0			0
$251$	1.93709	−	13.4728i	0.122268	−	0.850394i	−0.832708	−	0.553712i	$-0.813211\pi$
$251$	1.93709	−	13.4728i	0.122268	−	0.850394i	0.954976	−	0.296682i	$-0.0958801\pi$
$252$		0			0
$253$	−1.99788	−	14.5359i	−0.125606	−	0.913863i
$254$		0			0
$255$	0.621439	−	4.32221i	0.0389160	−	0.270667i
$256$		0			0
$257$	25.1716	+	7.39105i	1.57016	+	0.461041i	0.947049	−	0.321090i	$-0.104049\pi$
$257$	25.1716	+	7.39105i	1.57016	+	0.461041i	0.623114	+	0.782131i	$0.285867\pi$
$258$		0			0
$259$	−3.09822	+	0.909720i	−0.192514	+	0.0565273i
$260$		0			0
$261$	−7.10089	+	15.5488i	−0.439534	+	0.962445i
$262$		0			0
$263$	−2.86298	+	1.83993i	−0.176539	+	0.113455i	−0.625926	−	0.779883i	$-0.715279\pi$
$263$	−2.86298	+	1.83993i	−0.176539	+	0.113455i	0.449387	+	0.893337i	$0.351642\pi$
$264$		0			0
$265$	−1.14456	−	7.96060i	−0.0703099	−	0.489016i
$266$		0			0
$267$	2.24898	−	2.59546i	0.137635	−	0.158840i
$268$		0			0
$269$	−3.36186	−	2.16054i	−0.204976	−	0.131730i	0.434126	−	0.900852i	$-0.357057\pi$
$269$	−3.36186	−	2.16054i	−0.204976	−	0.131730i	−0.639102	+	0.769122i	$0.720694\pi$
$270$		0			0
$271$	4.25340	+	4.90869i	0.258376	+	0.298182i	0.870086	−	0.492901i	$-0.164063\pi$
$271$	4.25340	+	4.90869i	0.258376	+	0.298182i	−0.611710	+	0.791082i	$0.709518\pi$
$272$		0			0
$273$	−0.262719	−	0.575275i	−0.0159005	−	0.0348172i
$274$		0			0
$275$	3.05944			0.184491
$276$		0			0
$277$	2.08678			0.125382			0.0626912	−	0.998033i	$-0.480032\pi$
$277$	2.08678			0.125382			0.0626912	+	0.998033i	$0.480032\pi$
$278$		0			0
$279$	−5.18260	−	11.3483i	−0.310274	−	0.679406i
$280$		0			0
$281$	6.36169	+	7.34179i	0.379507	+	0.437974i	0.913081	−	0.407779i	$-0.133697\pi$
$281$	6.36169	+	7.34179i	0.379507	+	0.437974i	−0.533574	+	0.845754i	$0.679151\pi$
$282$		0			0
$283$	14.7561	+	9.48320i	0.877162	+	0.563718i	0.899936	−	0.436023i	$-0.143613\pi$
$283$	14.7561	+	9.48320i	0.877162	+	0.563718i	−0.0227736	+	0.999741i	$0.507250\pi$
$284$		0			0
$285$	−1.20831	+	1.39447i	−0.0715743	+	0.0826011i
$286$		0			0
$287$	−1.48779	−	10.3478i	−0.0878212	−	0.610810i
$288$		0			0
$289$	27.7530	−	17.8358i	1.63253	−	1.04916i
$290$		0			0
$291$	−0.254656	+	0.557618i	−0.0149282	+	0.0326882i
$292$		0			0
$293$	−14.9950	+	4.40293i	−0.876017	+	0.257222i	−0.688673	−	0.725072i	$-0.741806\pi$
$293$	−14.9950	+	4.40293i	−0.876017	+	0.257222i	−0.187345	+	0.982294i	$0.559988\pi$
$294$		0			0
$295$	6.83854	+	2.00798i	0.398155	+	0.116909i
$296$		0			0
$297$	1.51086	−	10.5083i	0.0876690	−	0.609751i
$298$		0			0
$299$	3.42260	−	2.16965i	0.197934	−	0.125474i
$300$		0			0
$301$	−0.298482	+	2.07598i	−0.0172042	+	0.119658i
$302$		0			0
$303$	−10.4676	−	3.07355i	−0.601345	−	0.176571i
$304$		0			0
$305$	−10.8961	+	3.19937i	−0.623906	+	0.183195i
$306$		0			0
$307$	−8.54994	+	18.7218i	−0.487971	+	1.06851i	0.492223	+	0.870469i	$0.336184\pi$
$307$	−8.54994	+	18.7218i	−0.487971	+	1.06851i	−0.980194	+	0.198039i	$0.936543\pi$
$308$		0			0
$309$	−6.52317	+	4.19219i	−0.371090	+	0.238485i
$310$		0			0
$311$	−1.89207	−	13.1596i	−0.107289	−	0.746213i	−0.970453	−	0.241289i	$-0.922430\pi$
$311$	−1.89207	−	13.1596i	−0.107289	−	0.746213i	0.863164	−	0.504924i	$-0.168479\pi$
$312$		0			0
$313$	−15.6037	+	18.0076i	−0.881973	+	1.01785i	0.117719	+	0.993047i	$0.462442\pi$
$313$	−15.6037	+	18.0076i	−0.881973	+	1.01785i	−0.999692	+	0.0248045i	$0.992104\pi$
$314$		0			0
$315$	2.66963	+	1.71566i	0.150416	+	0.0966667i
$316$		0			0
$317$	17.8093	+	20.5531i	1.00027	+	1.15438i	0.988001	+	0.154450i	$0.0493607\pi$
$317$	17.8093	+	20.5531i	1.00027	+	1.15438i	0.0122713	+	0.999925i	$0.496094\pi$
$318$		0			0
$319$	8.29641	+	18.1666i	0.464510	+	1.01713i
$320$		0			0
$321$	−6.75202			−0.376861
$322$		0			0
$323$	−21.1235			−1.17534
$324$		0			0
$325$	0.351015	+	0.768616i	0.0194708	+	0.0426351i
$326$		0			0
$327$	−1.95879	−	2.26057i	−0.108321	−	0.125010i
$328$		0			0
$329$	11.9533	+	7.68191i	0.659006	+	0.423517i
$330$		0			0
$331$	−0.933211	+	1.07698i	−0.0512939	+	0.0591964i	−0.780817	−	0.624760i	$-0.785197\pi$
$331$	−0.933211	+	1.07698i	−0.0512939	+	0.0591964i	0.729523	+	0.683957i	$0.239742\pi$
$332$		0			0
$333$	−0.992947	−	6.90610i	−0.0544132	−	0.378452i
$334$		0			0
$335$	1.12179	−	0.720929i	0.0612898	−	0.0393885i
$336$		0			0
$337$	−3.08125	+	6.74699i	−0.167846	+	0.367532i	−0.974799	−	0.223084i	$-0.928388\pi$
$337$	−3.08125	+	6.74699i	−0.167846	+	0.367532i	0.806953	+	0.590616i	$0.201115\pi$
$338$		0			0
$339$	−1.88340	+	0.553015i	−0.102292	+	0.0300357i
$340$		0			0
$341$	−13.9857	−	4.10658i	−0.757369	−	0.222384i
$342$		0			0
$343$	−2.16126	+	15.0319i	−0.116697	+	0.811646i
$344$		0			0
$345$	1.24713	−	2.68655i	0.0671431	−	0.144639i
$346$		0			0
$347$	−0.0296491	+	0.206214i	−0.00159165	+	0.0110701i	−0.990602	−	0.136778i	$-0.956325\pi$
$347$	−0.0296491	+	0.206214i	−0.00159165	+	0.0110701i	0.989010	+	0.147848i	$0.0472345\pi$
$348$		0			0
$349$	−10.0837	−	2.96083i	−0.539766	−	0.158490i	0.000474818	−	1.00000i	$-0.499849\pi$
$349$	−10.0837	−	2.96083i	−0.539766	−	0.158490i	−0.540241	+	0.841510i	$0.681667\pi$
$350$		0			0
$351$	2.81331	−	0.826063i	0.150164	−	0.0440920i
$352$		0			0
$353$	−5.32325	+	11.6563i	−0.283328	+	0.620402i	−0.996770	−	0.0803129i	$-0.974408\pi$
$353$	−5.32325	+	11.6563i	−0.283328	+	0.620402i	0.713442	+	0.700715i	$0.247135\pi$
$354$		0			0
$355$	8.84967	−	5.68734i	0.469692	−	0.301853i
$356$		0			0
$357$	−0.753109	−	5.23799i	−0.0398588	−	0.277224i
$358$		0			0
$359$	7.82562	−	9.03125i	0.413021	−	0.476651i	−0.510678	−	0.859772i	$-0.670605\pi$
$359$	7.82562	−	9.03125i	0.413021	−	0.476651i	0.923698	+	0.383121i	$0.125151\pi$
$360$		0			0
$361$	−8.47495	−	5.44652i	−0.446050	−	0.286659i
$362$		0			0
$363$	0.663221	+	0.765398i	0.0348101	+	0.0401730i
$364$		0			0
$365$	−1.85988	−	4.07256i	−0.0973504	−	0.213168i
$366$		0			0
$367$	−7.38220			−0.385348			−0.192674	−	0.981263i	$-0.561716\pi$
$367$	−7.38220			−0.385348			−0.192674	+	0.981263i	$0.561716\pi$
$368$		0			0
$369$	22.5889			1.17593
$370$		0			0
$371$	−4.04884	−	8.86572i	−0.210205	−	0.460285i
$372$		0			0
$373$	4.75481	+	5.48734i	0.246195	+	0.284124i	0.865375	−	0.501125i	$-0.167080\pi$
$373$	4.75481	+	5.48734i	0.246195	+	0.284124i	−0.619180	+	0.785249i	$0.712535\pi$
$374$		0			0
$375$	0.519558	+	0.333899i	0.0268298	+	0.0172425i
$376$		0			0
$377$	−3.61209	+	4.16858i	−0.186032	+	0.214693i
$378$		0			0
$379$	−2.49135	−	17.3277i	−0.127972	−	0.890065i	−0.948120	−	0.317913i	$-0.897018\pi$
$379$	−2.49135	−	17.3277i	−0.127972	−	0.890065i	0.820148	−	0.572152i	$-0.193891\pi$
$380$		0			0
$381$	−7.08172	+	4.55114i	−0.362807	+	0.233162i
$382$		0			0
$383$	5.61067	−	12.2856i	0.286692	−	0.627767i	−0.710415	−	0.703783i	$-0.751493\pi$
$383$	5.61067	−	12.2856i	0.286692	−	0.627767i	0.997107	+	0.0760159i	$0.0242200\pi$
$384$		0			0
$385$	3.55748	−	1.04457i	0.181306	−	0.0532362i
$386$		0			0
$387$	−4.34825	−	1.27676i	−0.221034	−	0.0649014i
$388$		0			0
$389$	−0.507979	+	3.53307i	−0.0257555	+	0.179134i	−0.998639	−	0.0521642i	$-0.983388\pi$
$389$	−0.507979	+	3.53307i	−0.0257555	+	0.179134i	0.972883	+	0.231298i	$0.0742972\pi$
$390$		0			0
$391$	32.5935	−	9.35083i	1.64832	−	0.472892i
$392$		0			0
$393$	−0.860587	+	5.98551i	−0.0434109	+	0.301929i
$394$		0			0
$395$	10.1370	+	2.97650i	0.510050	+	0.149764i
$396$		0			0
$397$	−26.0140	+	7.63841i	−1.30561	+	0.383361i	−0.859279	−	0.511508i	$-0.829087\pi$
$397$	−26.0140	+	7.63841i	−1.30561	+	0.383361i	−0.446329	+	0.894869i	$0.647269\pi$
$398$		0			0
$399$	−0.928906	+	2.03402i	−0.0465035	+	0.101828i
$400$		0			0
$401$	−29.8215	+	19.1651i	−1.48922	+	0.957061i	−0.493010	+	0.870023i	$0.664104\pi$
$401$	−29.8215	+	19.1651i	−1.48922	+	0.957061i	−0.996205	+	0.0870374i	$0.972260\pi$
$402$		0			0
$403$	−0.572922	−	3.98476i	−0.0285393	−	0.198495i
$404$		0			0
$405$	−3.74098	+	4.31732i	−0.185891	+	0.214529i
$406$		0			0
$407$	−6.85773	−	4.40719i	−0.339925	−	0.218456i
$408$		0			0
$409$	16.2509	+	18.7546i	0.803557	+	0.927354i	0.998571	−	0.0534466i	$-0.0170207\pi$
$409$	16.2509	+	18.7546i	0.803557	+	0.927354i	−0.195014	+	0.980800i	$0.562475\pi$
$410$		0			0
$411$	5.54247	+	12.1363i	0.273390	+	0.598640i
$412$		0			0
$413$	8.63736			0.425016
$414$		0			0
$415$	−9.75148			−0.478681
$416$		0			0
$417$	−3.68205	−	8.06256i	−0.180311	−	0.394825i
$418$		0			0
$419$	14.8931	+	17.1876i	0.727577	+	0.839668i	0.992196	−	0.124685i	$-0.0397919\pi$
$419$	14.8931	+	17.1876i	0.727577	+	0.839668i	−0.264620	+	0.964353i	$0.585246\pi$
$420$		0			0
$421$	−18.3187	−	11.7727i	−0.892798	−	0.573766i	0.0118482	−	0.999930i	$-0.496229\pi$
$421$	−18.3187	−	11.7727i	−0.892798	−	0.573766i	−0.904646	+	0.426163i	$0.859865\pi$
$422$		0			0
$423$	−20.1055	+	23.2030i	−0.977562	+	1.12817i
$424$		0			0
$425$	1.00622	+	6.99840i	0.0488087	+	0.339472i
$426$		0			0
$427$	−11.5775	+	7.44039i	−0.560273	+	0.360066i
$428$		0			0
$429$	0.663245	−	1.45230i	0.0320218	−	0.0701179i
$430$		0			0
$431$	−8.55900	+	2.51315i	−0.412272	+	0.121054i	−0.481290	−	0.876561i	$-0.659832\pi$
$431$	−8.55900	+	2.51315i	−0.412272	+	0.121054i	0.0690177	+	0.997615i	$0.478013\pi$
$432$		0			0
$433$	−23.1810	−	6.80656i	−1.11401	−	0.327102i	−0.327604	−	0.944815i	$-0.606241\pi$
$433$	−23.1810	−	6.80656i	−1.11401	−	0.327102i	−0.786404	+	0.617713i	$0.788059\pi$
$434$		0			0
$435$	−0.573751	+	3.99052i	−0.0275092	+	0.191331i
$436$		0			0
$437$	−13.7223	−	4.12198i	−0.656429	−	0.197181i
$438$		0			0
$439$	−3.84804	+	26.7637i	−0.183657	+	1.27736i	0.664368	+	0.747406i	$0.268701\pi$
$439$	−3.84804	+	26.7637i	−0.183657	+	1.27736i	−0.848025	+	0.529957i	$0.822208\pi$
$440$		0			0
$441$	−13.8975	−	4.08068i	−0.661787	−	0.194318i
$442$		0			0
$443$	−14.3425	+	4.21135i	−0.681434	+	0.200087i	−0.604089	−	0.796917i	$-0.706463\pi$
$443$	−14.3425	+	4.21135i	−0.681434	+	0.200087i	−0.0773456	+	0.997004i	$0.524644\pi$
$444$		0			0
$445$	−2.31000	+	5.05820i	−0.109505	+	0.239781i
$446$		0			0
$447$	−3.12949	+	2.01120i	−0.148020	+	0.0951265i
$448$		0			0
$449$	4.37240	+	30.4107i	0.206347	+	1.43517i	0.784948	+	0.619561i	$0.212690\pi$
$449$	4.37240	+	30.4107i	0.206347	+	1.43517i	−0.578602	+	0.815610i	$0.696401\pi$
$450$		0			0
$451$	17.2831	−	19.9458i	0.813829	−	0.939209i
$452$		0			0
$453$	2.87184	+	1.84562i	0.134931	+	0.0867147i
$454$		0			0
$455$	0.670582	+	0.773893i	0.0314374	+	0.0362806i
$456$		0			0
$457$	−6.76998	−	14.8242i	−0.316686	−	0.693446i	0.682617	−	0.730776i	$-0.260842\pi$
$457$	−6.76998	−	14.8242i	−0.316686	−	0.693446i	−0.999303	+	0.0373306i	$0.988115\pi$
$458$		0			0
$459$	24.5343			1.14517
$460$		0			0
$461$	−24.1616			−1.12532			−0.562660	−	0.826688i	$-0.690222\pi$
$461$	−24.1616			−1.12532			−0.562660	+	0.826688i	$0.690222\pi$
$462$		0			0
$463$	−14.9258	−	32.6829i	−0.693659	−	1.51890i	−0.847494	−	0.530805i	$-0.821890\pi$
$463$	−14.9258	−	32.6829i	−0.693659	−	1.51890i	0.153834	−	0.988097i	$-0.450838\pi$
$464$		0			0
$465$	−1.92689	−	2.22375i	−0.0893574	−	0.103124i
$466$		0			0
$467$	34.4808	+	22.1594i	1.59558	+	1.02542i	0.969320	+	0.245802i	$0.0790512\pi$
$467$	34.4808	+	22.1594i	1.59558	+	1.02542i	0.626259	+	0.779615i	$0.284585\pi$
$468$		0			0
$469$	1.05826	−	1.22129i	0.0488658	−	0.0563942i
$470$		0			0
$471$	0.579500	+	4.03051i	0.0267020	+	0.185716i
$472$		0			0
$473$	−4.45427	+	2.86259i	−0.204808	+	0.131622i
$474$		0			0
$475$	1.24110	−	2.71762i	0.0569454	−	0.124693i
$476$		0			0
$477$	20.2067	−	5.93322i	0.925201	−	0.271664i
$478$		0			0
$479$	1.02681	+	0.301499i	0.0469162	+	0.0137759i	0.305106	−	0.952318i	$-0.401308\pi$
$479$	1.02681	+	0.301499i	0.0469162	+	0.0137759i	−0.258190	+	0.966094i	$0.583126\pi$
$480$		0			0
$481$	0.320410	−	2.22850i	0.0146094	−	0.101611i
$482$		0			0
$483$	0.532890	−	3.54969i	0.0242473	−	0.161516i
$484$		0			0
$485$	0.141258	−	0.982474i	0.00641422	−	0.0446119i
$486$		0			0
$487$	19.6254	+	5.76253i	0.889311	+	0.261125i	0.694309	−	0.719677i	$-0.255710\pi$
$487$	19.6254	+	5.76253i	0.889311	+	0.261125i	0.195003	+	0.980803i	$0.437528\pi$
$488$		0			0
$489$	5.46605	−	1.60498i	0.247183	−	0.0725796i
$490$		0			0
$491$	−8.62589	+	18.8881i	−0.389281	+	0.852407i	0.608965	+	0.793197i	$0.291585\pi$
$491$	−8.62589	+	18.8881i	−0.389281	+	0.852407i	−0.998246	+	0.0592092i	$0.981142\pi$
$492$		0			0
$493$	−38.8271	+	24.9527i	−1.74868	+	1.12381i
$494$		0			0
$495$	1.14013	+	7.92981i	0.0512452	+	0.356418i
$496$		0			0
$497$	8.34850	−	9.63468i	0.374481	−	0.432175i
$498$		0			0
$499$	−11.8239	−	7.59878i	−0.529312	−	0.340168i	0.248534	−	0.968623i	$-0.420051\pi$
$499$	−11.8239	−	7.59878i	−0.529312	−	0.340168i	−0.777846	+	0.628455i	$0.783688\pi$
$500$		0			0
$501$	−2.62651	−	3.03116i	−0.117344	−	0.135422i
$502$		0			0
$503$	−0.0298848	−	0.0654387i	−0.00133250	−	0.00291777i	0.908965	−	0.416873i	$-0.136874\pi$
$503$	−0.0298848	−	0.0654387i	−0.00133250	−	0.00291777i	−0.910297	+	0.413956i	$0.864147\pi$
$504$		0			0
$505$	17.6643			0.786052
$506$		0			0
$507$	−7.58784			−0.336988
$508$		0			0
$509$	−15.8881	−	34.7900i	−0.704226	−	1.54204i	−0.834771	−	0.550597i	$-0.814400\pi$
$509$	−15.8881	−	34.7900i	−0.704226	−	1.54204i	0.130545	−	0.991442i	$-0.458327\pi$
$510$		0			0
$511$	−3.55312	−	4.10052i	−0.157181	−	0.181396i
$512$		0			0
$513$	−8.72134	−	5.60486i	−0.385057	−	0.247461i
$514$		0			0
$515$	8.22193	−	9.48861i	0.362302	−	0.418118i
$516$		0			0
$517$	5.10497	+	35.5058i	0.224516	+	1.56154i
$518$		0			0
$519$	−7.44605	+	4.78528i	−0.326845	+	0.210051i
$520$		0			0
$521$	0.0529606	−	0.115967i	0.00232024	−	0.00508063i	−0.908468	−	0.417954i	$-0.862747\pi$
$521$	0.0529606	−	0.115967i	0.00232024	−	0.00508063i	0.910789	+	0.412873i	$0.135475\pi$
$522$		0			0
$523$	−37.3965	+	10.9806i	−1.63524	+	0.480148i	−0.965054	−	0.262049i	$-0.915602\pi$
$523$	−37.3965	+	10.9806i	−1.63524	+	0.480148i	−0.670181	+	0.742198i	$0.733784\pi$
$524$		0			0
$525$	0.718138	+	0.210864i	0.0313421	+	0.00920287i
$526$		0			0
$527$	4.79395	−	33.3427i	0.208828	−	1.45243i
$528$		0			0
$529$	22.9982	+	0.285677i	0.999923	+	0.0124207i
$530$		0			0
$531$	−2.65605	+	18.4732i	−0.115263	+	0.801670i
$532$		0			0
$533$	6.99385	+	2.05358i	0.302937	+	0.0889504i
$534$		0			0
$535$	10.4898	−	3.08009i	0.453515	−	0.133164i
$536$		0			0
$537$	−1.67322	+	3.66383i	−0.0722046	+	0.158106i
$538$		0			0
$539$	−14.2364	+	9.14917i	−0.613204	+	0.394082i
$540$		0			0
$541$	4.01017	+	27.8914i	0.172411	+	1.19914i	0.873771	+	0.486337i	$0.161667\pi$
$541$	4.01017	+	27.8914i	0.172411	+	1.19914i	−0.701360	+	0.712807i	$0.747424\pi$
$542$		0			0
$543$	5.68451	−	6.56028i	0.243946	−	0.281528i
$544$		0			0
$545$	4.07436	+	2.61843i	0.174526	+	0.112161i
$546$		0			0
$547$	−18.9151	−	21.8292i	−0.808753	−	0.933351i	0.190074	−	0.981770i	$-0.439127\pi$
$547$	−18.9151	−	21.8292i	−0.808753	−	0.933351i	−0.998827	+	0.0484186i	$0.984582\pi$
$548$		0			0
$549$	−12.3530	−	27.0494i	−0.527215	−	1.15444i
$550$		0			0
$551$	19.5025			0.830834
$552$		0			0
$553$	12.8035			0.544460
$554$		0			0
$555$	−0.683598	−	1.49687i	−0.0290171	−	0.0635386i
$556$		0			0
$557$	15.0480	+	17.3664i	0.637606	+	0.735837i	0.978950	−	0.204102i	$-0.0654273\pi$
$557$	15.0480	+	17.3664i	0.637606	+	0.735837i	−0.341343	+	0.939939i	$0.610882\pi$
$558$		0			0
$559$	−1.23021	−	0.790607i	−0.0520323	−	0.0334391i
$560$		0			0
$561$	8.74861	−	10.0964i	0.369367	−	0.426272i
$562$		0			0
$563$	−0.943746	−	6.56390i	−0.0397742	−	0.276635i	0.960222	−	0.279236i	$-0.0900812\pi$
$563$	−0.943746	−	6.56390i	−0.0397742	−	0.276635i	−0.999997	+	0.00260076i	$0.999172\pi$
$564$		0			0
$565$	2.67375	−	1.71831i	0.112485	−	0.0722900i
$566$		0			0
$567$	−2.87592	+	6.29739i	−0.120777	+	0.264466i
$568$		0			0
$569$	28.3182	−	8.31496i	1.18716	−	0.348581i	0.372229	−	0.928141i	$-0.378593\pi$
$569$	28.3182	−	8.31496i	1.18716	−	0.348581i	0.814930	+	0.579559i	$0.196775\pi$
$570$		0			0
$571$	23.8603	+	7.00602i	0.998523	+	0.293193i	0.739850	−	0.672772i	$-0.234897\pi$
$571$	23.8603	+	7.00602i	0.998523	+	0.293193i	0.258673	+	0.965965i	$0.416715\pi$
$572$		0			0
$573$	−1.78924	+	12.4444i	−0.0747466	+	0.519874i
$574$		0			0
$575$	−0.711986	+	4.74269i	−0.0296919	+	0.197784i
$576$		0			0
$577$	0.315548	−	2.19469i	0.0131365	−	0.0913660i	−0.982198	−	0.187846i	$-0.939849\pi$
$577$	0.315548	−	2.19469i	0.0131365	−	0.0913660i	0.995335	+	0.0964802i	$0.0307584\pi$
$578$		0			0
$579$	12.0986	+	3.55247i	0.502801	+	0.147636i
$580$		0			0
$581$	−11.3389	+	3.32941i	−0.470418	+	0.138127i
$582$		0			0
$583$	10.2215	−	22.3819i	0.423330	−	0.926962i
$584$		0			0
$585$	−1.86138	+	1.19624i	−0.0769586	+	0.0494583i
$586$		0			0
$587$	−5.51521	−	38.3591i	−0.227637	−	1.58325i	−0.708020	−	0.706192i	$-0.750412\pi$
$587$	−5.51521	−	38.3591i	−0.227637	−	1.58325i	0.480383	−	0.877059i	$-0.340498\pi$
$588$		0			0
$589$	−9.32125	+	10.7573i	−0.384075	+	0.443247i
$590$		0			0
$591$	−3.90697	−	2.51086i	−0.160711	−	0.103283i
$592$		0			0
$593$	−8.63091	−	9.96061i	−0.354429	−	0.409033i	0.550336	−	0.834943i	$-0.314499\pi$
$593$	−8.63091	−	9.96061i	−0.354429	−	0.409033i	−0.904766	+	0.425910i	$0.859954\pi$
$594$		0			0
$595$	3.55945	+	7.79411i	0.145923	+	0.319527i
$596$		0			0
$597$	16.1991			0.662983
$598$		0			0
$599$	34.4026			1.40565			0.702826	−	0.711362i	$-0.251921\pi$
$599$	34.4026			1.40565			0.702826	+	0.711362i	$0.251921\pi$
$600$		0			0
$601$	−15.9961	−	35.0267i	−0.652496	−	1.42877i	−0.889352	−	0.457222i	$-0.848844\pi$
$601$	−15.9961	−	35.0267i	−0.652496	−	1.42877i	0.236857	−	0.971545i	$-0.423883\pi$
$602$		0			0
$603$	2.28663	+	2.63892i	0.0931190	+	0.107465i
$604$		0			0
$605$	−1.37952	−	0.886567i	−0.0560857	−	0.0360441i
$606$		0			0
$607$	−24.7233	+	28.5322i	−1.00349	+	1.15809i	−0.0160827	+	0.999871i	$0.505120\pi$
$607$	−24.7233	+	28.5322i	−1.00349	+	1.15809i	−0.987405	+	0.158215i	$0.949426\pi$
$608$		0			0
$609$	0.695316	+	4.83603i	0.0281756	+	0.195966i
$610$		0			0
$611$	−8.33435	+	5.35616i	−0.337172	+	0.216687i
$612$		0			0
$613$	4.86944	−	10.6626i	0.196675	−	0.430658i	−0.785441	−	0.618937i	$-0.787564\pi$
$613$	4.86944	−	10.6626i	0.196675	−	0.430658i	0.982116	+	0.188279i	$0.0602909\pi$
$614$		0			0
$615$	5.11187	−	1.50098i	0.206130	−	0.0605253i
$616$		0			0
$617$	−38.8107	−	11.3958i	−1.56246	−	0.458779i	−0.617664	−	0.786442i	$-0.711921\pi$
$617$	−38.8107	−	11.3958i	−1.56246	−	0.458779i	−0.944795	+	0.327663i	$0.893739\pi$
$618$		0			0
$619$	2.30203	−	16.0110i	0.0925265	−	0.643536i	−0.889799	−	0.456353i	$-0.849155\pi$
$619$	2.30203	−	16.0110i	0.0925265	−	0.643536i	0.982325	−	0.187183i	$-0.0599356\pi$
$620$		0			0
$621$	15.9381	+	4.78757i	0.639575	+	0.192119i
$622$		0			0
$623$	−0.959046	+	6.67031i	−0.0384234	+	0.267240i
$624$		0			0
$625$	−0.959493	−	0.281733i	−0.0383797	−	0.0112693i
$626$		0			0
$627$	−5.41644	+	1.59041i	−0.216312	+	0.0635148i
$628$		0			0
$629$	7.82593	−	17.1364i	0.312040	−	0.683272i
$630$		0			0
$631$	13.2210	−	8.49661i	0.526319	−	0.338245i	−0.250348	−	0.968156i	$-0.580545\pi$
$631$	13.2210	−	8.49661i	0.526319	−	0.338245i	0.776667	+	0.629911i	$0.216909\pi$
$632$		0			0
$633$	1.36819	+	9.51598i	0.0543807	+	0.378226i
$634$		0			0
$635$	8.92594	−	10.3011i	0.354215	−	0.408786i
$636$		0			0
$637$	−3.93189	−	2.52687i	−0.155787	−	0.100118i
$638$		0			0
$639$	18.0391	+	20.8182i	0.713614	+	0.823554i
$640$		0			0
$641$	9.02209	+	19.7556i	0.356351	+	0.780300i	0.999889	+	0.0148862i	$0.00473861\pi$
$641$	9.02209	+	19.7556i	0.356351	+	0.780300i	−0.643538	+	0.765414i	$0.722534\pi$
$642$		0			0
$643$	22.7632			0.897693			0.448847	−	0.893609i	$-0.351835\pi$
$643$	22.7632			0.897693			0.448847	+	0.893609i	$0.351835\pi$
$644$		0			0
$645$	−1.06885			−0.0420857
$646$		0			0
$647$	−5.26761	−	11.5345i	−0.207091	−	0.453467i	0.777376	−	0.629037i	$-0.216550\pi$
$647$	−5.26761	−	11.5345i	−0.207091	−	0.453467i	−0.984467	+	0.175570i	$0.943823\pi$
$648$		0			0
$649$	14.2795	+	16.4794i	0.560518	+	0.646873i
$650$		0			0
$651$	−2.99981	−	1.92786i	−0.117572	−	0.0755589i
$652$		0			0
$653$	−2.38191	+	2.74887i	−0.0932114	+	0.107572i	−0.800439	−	0.599414i	$-0.795400\pi$
$653$	−2.38191	+	2.74887i	−0.0932114	+	0.107572i	0.707227	+	0.706986i	$0.249946\pi$
$654$		0			0
$655$	−1.39344	−	9.69158i	−0.0544462	−	0.378681i
$656$		0			0
$657$	9.86264	−	6.33834i	0.384778	−	0.247282i
$658$		0			0
$659$	20.1162	−	44.0483i	0.783615	−	1.71588i	0.0895296	−	0.995984i	$-0.471464\pi$
$659$	20.1162	−	44.0483i	0.783615	−	1.71588i	0.694085	−	0.719893i	$-0.255809\pi$
$660$		0			0
$661$	−9.04884	+	2.65698i	−0.351959	+	0.103345i	−0.452933	−	0.891545i	$-0.649622\pi$
$661$	−9.04884	+	2.65698i	−0.351959	+	0.103345i	0.100974	+	0.994889i	$0.467804\pi$
$662$		0			0
$663$	3.54025	+	1.03951i	0.137492	+	0.0403713i
$664$		0			0
$665$	0.515268	−	3.58377i	0.0199812	−	0.138972i
$666$		0			0
$667$	−30.0923	+	8.63325i	−1.16518	+	0.334281i
$668$		0			0
$669$	0.800383	−	5.56679i	0.0309446	−	0.215224i
$670$		0			0
$671$	−33.3358	−	9.78827i	−1.28691	−	0.377872i
$672$		0			0
$673$	10.7577	−	3.15875i	0.414679	−	0.121761i	−0.0677365	−	0.997703i	$-0.521578\pi$
$673$	10.7577	−	3.15875i	0.414679	−	0.121761i	0.482416	+	0.875942i	$0.339760\pi$
$674$		0			0
$675$	−1.44150	+	3.15645i	−0.0554834	+	0.121492i
$676$		0			0
$677$	−3.32467	+	2.13664i	−0.127777	+	0.0821176i	−0.602968	−	0.797765i	$-0.706015\pi$
$677$	−3.32467	+	2.13664i	−0.127777	+	0.0821176i	0.475191	+	0.879883i	$0.342379\pi$
$678$		0			0
$679$	−0.171188	−	1.19064i	−0.00656960	−	0.0456926i
$680$		0			0
$681$	4.69206	−	5.41492i	0.179800	−	0.207500i
$682$		0			0
$683$	−8.00154	−	5.14228i	−0.306171	−	0.196764i	0.378529	−	0.925590i	$-0.376430\pi$
$683$	−8.00154	−	5.14228i	−0.306171	−	0.196764i	−0.684699	+	0.728826i	$0.740066\pi$
$684$		0			0
$685$	−14.1470	−	16.3265i	−0.540528	−	0.623802i
$686$		0			0
$687$	−1.53454	−	3.36018i	−0.0585464	−	0.128199i
$688$		0			0
$689$	6.79568			0.258895
$690$		0			0
$691$	−1.41432			−0.0538034			−0.0269017	−	0.999638i	$-0.508564\pi$
$691$	−1.41432			−0.0538034			−0.0269017	+	0.999638i	$0.508564\pi$
$692$		0			0
$693$	4.03318	+	8.83143i	0.153208	+	0.335478i
$694$		0			0
$695$	9.39831	+	10.8462i	0.356498	+	0.411421i
$696$		0			0
$697$	51.3097	+	32.9748i	1.94349	+	1.24901i
$698$		0			0
$699$	1.23047	−	1.42003i	0.0465405	−	0.0537106i
$700$		0			0
$701$	−1.80525	−	12.5558i	−0.0681832	−	0.474225i	−0.995093	−	0.0989411i	$-0.968454\pi$
$701$	−1.80525	−	12.5558i	−0.0681832	−	0.474225i	0.926910	−	0.375283i	$-0.122455\pi$
$702$		0			0
$703$	−6.69672	+	4.30372i	−0.252572	+	0.162318i
$704$		0			0
$705$	−3.00808	+	6.58679i	−0.113291	+	0.248073i
$706$		0			0
$707$	20.5399	−	6.03105i	0.772481	−	0.226821i
$708$		0			0
$709$	18.5550	+	5.44825i	0.696849	+	0.204613i	0.610925	−	0.791688i	$-0.290798\pi$
$709$	18.5550	+	5.44825i	0.696849	+	0.204613i	0.0859238	+	0.996302i	$0.472616\pi$
$710$		0			0
$711$	−3.93717	+	27.3836i	−0.147655	+	1.02697i
$712$		0			0
$713$	9.62067	−	20.7247i	0.360297	−	0.776148i
$714$		0			0
$715$	−0.367905	+	2.55883i	−0.0137589	+	0.0956950i
$716$		0			0
$717$	10.4888	+	3.07978i	0.391710	+	0.115016i
$718$		0			0
$719$	−3.44447	+	1.01139i	−0.128457	+	0.0377184i	−0.345329	−	0.938482i	$-0.612233\pi$
$719$	−3.44447	+	1.01139i	−0.128457	+	0.0377184i	0.216872	+	0.976200i	$0.430415\pi$
$720$		0			0
$721$	6.32071	−	13.8404i	0.235396	−	0.515445i
$722$		0			0
$723$	4.84797	−	3.11560i	0.180298	−	0.115870i
$724$		0			0
$725$	−0.929002	−	6.46135i	−0.0345023	−	0.239968i
$726$		0			0
$727$	3.72872	−	4.30317i	0.138290	−	0.159596i	−0.682380	−	0.730998i	$-0.739055\pi$
$727$	3.72872	−	4.30317i	0.138290	−	0.159596i	0.820670	+	0.571402i	$0.193600\pi$
$728$		0			0
$729$	−7.17561	−	4.61149i	−0.265763	−	0.170796i
$730$		0			0
$731$	−8.01307	−	9.24758i	−0.296374	−	0.342034i
$732$		0			0
$733$	−11.0146	−	24.1186i	−0.406833	−	0.890840i	−0.996531	−	0.0832166i	$-0.973481\pi$
$733$	−11.0146	−	24.1186i	−0.406833	−	0.890840i	0.589698	−	0.807624i	$-0.299247\pi$
$734$		0			0
$735$	−3.41616			−0.126007
$736$		0			0
$737$	4.07967			0.150277
$738$		0			0
$739$	21.5298	+	47.1436i	0.791985	+	1.73420i	0.670881	+	0.741565i	$0.265916\pi$
$739$	21.5298	+	47.1436i	0.791985	+	1.73420i	0.121104	+	0.992640i	$0.461357\pi$
$740$		0			0
$741$	−1.02099	−	1.17829i	−0.0375071	−	0.0432855i
$742$		0			0
$743$	−4.86465	−	3.12632i	−0.178467	−	0.114694i	0.448357	−	0.893854i	$-0.352009\pi$
$743$	−4.86465	−	3.12632i	−0.178467	−	0.114694i	−0.626824	+	0.779161i	$0.715646\pi$
$744$		0			0
$745$	3.94447	−	4.55216i	0.144514	−	0.166778i
$746$		0			0
$747$	−3.63400	−	25.2750i	−0.132961	−	0.924765i
$748$		0			0
$749$	11.1458	−	7.16300i	0.407260	−	0.261730i
$750$		0			0
$751$	5.96974	−	13.0719i	0.217839	−	0.477001i	−0.768889	−	0.639382i	$-0.779190\pi$
$751$	5.96974	−	13.0719i	0.217839	−	0.477001i	0.986728	+	0.162381i	$0.0519174\pi$
$752$		0			0
$753$	8.06582	−	2.36834i	0.293935	−	0.0863071i
$754$		0			0
$755$	−5.30357	−	1.55727i	−0.193017	−	0.0566748i
$756$		0			0
$757$	2.65688	−	18.4790i	0.0965658	−	0.671630i	−0.882832	−	0.469689i	$-0.844366\pi$
$757$	2.65688	−	18.4790i	0.0965658	−	0.671630i	0.979398	−	0.201941i	$-0.0647248\pi$
$758$		0			0
$759$	7.65351	−	4.85172i	0.277805	−	0.176106i
$760$		0			0
$761$	4.20274	−	29.2307i	0.152349	−	1.05961i	−0.759919	−	0.650018i	$-0.774761\pi$
$761$	4.20274	−	29.2307i	0.152349	−	1.05961i	0.912268	−	0.409594i	$-0.134329\pi$
$762$		0			0
$763$	5.63162	+	1.65359i	0.203878	+	0.0598641i
$764$		0			0
$765$	−17.7643	+	5.21607i	−0.642270	+	0.188587i
$766$		0			0
$767$	−2.50177	+	5.47811i	−0.0903337	+	0.197803i
$768$		0			0
$769$	21.1442	−	13.5886i	0.762480	−	0.490016i	−0.100697	−	0.994917i	$-0.532107\pi$
$769$	21.1442	−	13.5886i	0.762480	−	0.490016i	0.863177	+	0.504901i	$0.168471\pi$
$770$		0			0
$771$	2.30582	+	16.0374i	0.0830422	+	0.577572i
$772$		0			0
$773$	25.2081	−	29.0917i	0.906672	−	1.04636i	−0.0920471	−	0.995755i	$-0.529341\pi$
$773$	25.2081	−	29.0917i	0.906672	−	1.04636i	0.998719	−	0.0506005i	$-0.0161135\pi$
$774$		0			0
$775$	4.00801	+	2.57579i	0.143972	+	0.0925251i
$776$		0			0
$777$	−1.30595	−	1.50715i	−0.0468507	−	0.0540686i
$778$		0			0
$779$	−10.7062	−	23.4434i	−0.383591	−	0.839946i
$780$		0			0
$781$	32.1841			1.15164
$782$		0			0
$783$	−22.6516			−0.809502
$784$		0			0
$785$	−2.73892	−	5.99739i	−0.0977562	−	0.214056i
$786$		0			0
$787$	29.6775	+	34.2496i	1.05789	+	1.22087i	0.974509	+	0.224349i	$0.0720257\pi$
$787$	29.6775	+	34.2496i	1.05789	+	1.22087i	0.0833788	+	0.996518i	$0.473429\pi$
$788$		0			0
$789$	−1.76817	−	1.13634i	−0.0629487	−	0.0404546i
$790$		0			0
$791$	2.52233	−	2.91092i	0.0896837	−	0.103500i
$792$		0			0
$793$	−1.36559	−	9.49791i	−0.0484936	−	0.337281i
$794$		0			0
$795$	4.17852	−	2.68537i	0.148197	−	0.0952404i
$796$		0			0
$797$	−3.83228	+	8.39152i	−0.135746	+	0.297243i	−0.965282	−	0.261211i	$-0.915878\pi$
$797$	−3.83228	+	8.39152i	−0.135746	+	0.297243i	0.829535	+	0.558454i	$0.188605\pi$
$798$		0			0
$799$	−79.5399	+	23.3550i	−2.81392	+	0.826241i
$800$		0			0
$801$	−13.9713	−	4.10234i	−0.493651	−	0.144949i
$802$		0			0
$803$	1.94937	−	13.5582i	0.0687917	−	0.478457i
$804$		0			0
$805$	0.791385	+	5.75783i	0.0278927	+	0.202937i
$806$		0			0
$807$	0.351245	−	2.44296i	0.0123644	−	0.0859963i
$808$		0			0
$809$	−32.9035	−	9.66135i	−1.15683	−	0.339675i	−0.353628	−	0.935386i	$-0.615052\pi$
$809$	−32.9035	−	9.66135i	−1.15683	−	0.339675i	−0.803199	+	0.595711i	$0.796870\pi$
$810$		0			0
$811$	−34.5972	+	10.1586i	−1.21487	+	0.356718i	−0.825521	−	0.564371i	$-0.809119\pi$
$811$	−34.5972	+	10.1586i	−1.21487	+	0.356718i	−0.389350	+	0.921090i	$0.627300\pi$
$812$		0			0
$813$	−1.66639	+	3.64889i	−0.0584429	+	0.127972i
$814$		0			0
$815$	−7.75982	+	4.98694i	−0.271815	+	0.174685i
$816$		0			0
$817$	0.735838	+	5.11786i	0.0257437	+	0.179051i
$818$		0			0
$819$	−1.75597	+	2.02649i	−0.0613584	+	0.0708114i
$820$		0			0
$821$	−6.50926	−	4.18325i	−0.227175	−	0.145996i	0.422103	−	0.906548i	$-0.361292\pi$
$821$	−6.50926	−	4.18325i	−0.227175	−	0.145996i	−0.649277	+	0.760552i	$0.724929\pi$
$822$		0			0
$823$	34.7573	+	40.1120i	1.21156	+	1.39822i	0.892843	+	0.450369i	$0.148708\pi$
$823$	34.7573	+	40.1120i	1.21156	+	1.39822i	0.318720	+	0.947849i	$0.396747\pi$
$824$		0			0
$825$	0.784929	+	1.71876i	0.0273277	+	0.0598394i
$826$		0			0
$827$	−27.6661			−0.962046			−0.481023	−	0.876708i	$-0.659735\pi$
$827$	−27.6661			−0.962046			−0.481023	+	0.876708i	$0.659735\pi$
$828$		0			0
$829$	−32.4476			−1.12695			−0.563476	−	0.826132i	$-0.690536\pi$
$829$	−32.4476			−1.12695			−0.563476	+	0.826132i	$0.690536\pi$
$830$		0			0
$831$	0.535384	+	1.17233i	0.0185723	+	0.0406676i
$832$		0			0
$833$	−25.6107	−	29.5564i	−0.887359	−	1.02407i
$834$		0			0
$835$	5.46325	+	3.51101i	0.189063	+	0.121504i
$836$		0			0
$837$	10.8264	−	12.4943i	0.374214	−	0.431866i
$838$		0			0
$839$	−3.90065	−	27.1296i	−0.134666	−	0.936619i	−0.939361	−	0.342931i	$-0.888580\pi$
$839$	−3.90065	−	27.1296i	−0.134666	−	0.936619i	0.804695	−	0.593688i	$-0.202329\pi$
$840$		0			0
$841$	11.4512	−	7.35923i	0.394869	−	0.253767i
$842$		0			0
$843$	−2.49237	+	5.45753i	−0.0858418	+	0.187967i
$844$		0			0
$845$	11.7883	−	3.46137i	0.405531	−	0.119075i
$846$		0			0
$847$	−1.90679	−	0.559885i	−0.0655182	−	0.0192379i
$848$		0			0
$849$	−1.54171	+	10.7228i	−0.0529114	+	0.368007i
$850$		0			0
$851$	8.42787	−	9.60509i	0.288904	−	0.329258i
$852$		0			0
$853$	−3.68924	+	25.6592i	−0.126317	+	0.878556i	0.823848	+	0.566810i	$0.191823\pi$
$853$	−3.68924	+	25.6592i	−0.126317	+	0.878556i	−0.950166	+	0.311746i	$0.899086\pi$
$854$		0			0
$855$	7.50637	+	2.20407i	0.256712	+	0.0753775i
$856$		0			0
$857$	−33.4915	+	9.83398i	−1.14405	+	0.335922i	−0.798214	−	0.602374i	$-0.794222\pi$
$857$	−33.4915	+	9.83398i	−1.14405	+	0.335922i	−0.345833	+	0.938296i	$0.612403\pi$
$858$		0			0
$859$	−3.70550	+	8.11392i	−0.126430	+	0.276843i	−0.962253	−	0.272155i	$-0.912264\pi$
$859$	−3.70550	+	8.11392i	−0.126430	+	0.276843i	0.835823	+	0.548999i	$0.184991\pi$
$860$		0			0
$861$	5.43155	−	3.49065i	0.185107	−	0.118961i
$862$		0			0
$863$	−2.48441	−	17.2795i	−0.0845704	−	0.588200i	−0.987405	−	0.158212i	$-0.949427\pi$
$863$	−2.48441	−	17.2795i	−0.0845704	−	0.588200i	0.902835	−	0.429988i	$-0.141482\pi$
$864$		0			0
$865$	9.38515	−	10.8310i	0.319105	−	0.368266i
$866$		0			0
$867$	17.1402	+	11.0154i	0.582113	+	0.374101i
$868$		0			0
$869$	21.1670	+	24.4281i	0.718043	+	0.828665i
$870$		0			0
$871$	0.468068	+	1.02493i	0.0158599	+	0.0347283i
$872$		0			0
$873$	2.59913			0.0879674
$874$		0			0
$875$	−1.21188			−0.0409690
$876$		0			0
$877$	−1.01935	−	2.23206i	−0.0344209	−	0.0753713i	0.891641	−	0.452744i	$-0.149555\pi$
$877$	−1.01935	−	2.23206i	−0.0344209	−	0.0753713i	−0.926061	+	0.377373i	$0.876828\pi$
$878$		0			0
$879$	−6.32063	−	7.29440i	−0.213190	−	0.246034i
$880$		0			0
$881$	0.0556755	+	0.0357805i	0.00187575	+	0.00120547i	0.541578	−	0.840650i	$-0.317827\pi$
$881$	0.0556755	+	0.0357805i	0.00187575	+	0.00120547i	−0.539703	+	0.841856i	$0.681463\pi$
$882$		0			0
$883$	7.99672	−	9.22870i	0.269111	−	0.310571i	−0.605069	−	0.796173i	$-0.706854\pi$
$883$	7.99672	−	9.22870i	0.269111	−	0.310571i	0.874180	+	0.485603i	$0.161400\pi$
$884$		0			0
$885$	0.626439	+	4.35698i	0.0210575	+	0.146458i
$886$		0			0
$887$	41.0148	−	26.3586i	1.37714	−	0.885036i	0.377974	−	0.925816i	$-0.376621\pi$
$887$	41.0148	−	26.3586i	1.37714	−	0.885036i	0.999168	+	0.0407802i	$0.0129844\pi$
$888$		0			0
$889$	6.86193	−	15.0255i	0.230142	−	0.503940i
$890$		0			0
$891$	−16.7695	+	4.92396i	−0.561798	+	0.164959i
$892$		0			0
$893$	33.6098	+	9.86874i	1.12471	+	0.330245i
$894$		0			0
$895$	0.928139	−	6.45535i	0.0310243	−	0.215779i
$896$		0			0
$897$	2.09699	+	1.36613i	0.0700164	+	0.0456137i
$898$		0			0
$899$	−4.42607	+	30.7840i	−0.147618	+	1.02670i
$900$		0			0
$901$	54.5598	+	16.0202i	1.81765	+	0.533710i
$902$		0			0
$903$	−1.24284	+	0.364931i	−0.0413592	+	0.0121442i
$904$		0			0
$905$	−5.83875	+	12.7851i	−0.194087	+	0.424990i
$906$		0			0
$907$	−30.3329	+	19.4937i	−1.00719	+	0.647279i	−0.936663	−	0.350231i	$-0.886103\pi$
$907$	−30.3329	+	19.4937i	−1.00719	+	0.647279i	−0.0705229	+	0.997510i	$0.522467\pi$
$908$		0			0
$909$	6.58281	+	45.7844i	0.218338	+	1.51857i
$910$		0			0
$911$	−13.4546	+	15.5275i	−0.445771	+	0.514448i	−0.933515	−	0.358540i	$-0.883275\pi$
$911$	−13.4546	+	15.5275i	−0.445771	+	0.514448i	0.487743	+	0.872987i	$0.337820\pi$
$912$		0			0
$913$	−25.0980	−	16.1295i	−0.830623	−	0.533809i
$914$		0			0
$915$	−4.59286	−	5.30044i	−0.151835	−	0.175227i
$916$		0			0
$917$	−4.92923	−	10.7935i	−0.162778	−	0.356433i
$918$		0			0
$919$	−19.8318			−0.654190			−0.327095	−	0.944991i	$-0.606070\pi$
$919$	−19.8318			−0.654190			−0.327095	+	0.944991i	$0.606070\pi$
$920$		0			0
$921$	−12.7112			−0.418850
$922$		0			0
$923$	3.69255	+	8.08555i	0.121542	+	0.266139i
$924$		0			0
$925$	1.74486	+	2.01368i	0.0573706	+	0.0662093i
$926$		0			0
$927$	27.6577	+	17.7745i	0.908398	+	0.583792i
$928$		0			0
$929$	−3.20472	+	3.69844i	−0.105143	+	0.121342i	−0.805882	−	0.592076i	$-0.798308\pi$
$929$	−3.20472	+	3.69844i	−0.105143	+	0.121342i	0.700739	+	0.713418i	$0.252854\pi$
$930$		0			0
$931$	2.35182	+	16.3573i	0.0770779	+	0.536089i
$932$		0			0
$933$	6.90748	−	4.43917i	0.226141	−	0.145332i
$934$		0			0
$935$	−8.98598	+	19.6766i	−0.293873	+	0.643492i
$936$		0			0
$937$	−15.2862	+	4.48844i	−0.499379	+	0.146631i	−0.521715	−	0.853120i	$-0.674708\pi$
$937$	−15.2862	+	4.48844i	−0.499379	+	0.146631i	0.0223362	+	0.999751i	$0.492890\pi$
$938$		0			0
$939$	−14.1198	−	4.14593i	−0.460781	−	0.135297i
$940$		0			0
$941$	−6.36954	+	44.3011i	−0.207641	+	1.44418i	0.573184	+	0.819427i	$0.305708\pi$
$941$	−6.36954	+	44.3011i	−0.207641	+	1.44418i	−0.780825	+	0.624749i	$0.785201\pi$
$942$		0			0
$943$	26.8975	+	31.4337i	0.875902	+	1.02362i
$944$		0			0
$945$	−0.598469	+	4.16245i	−0.0194682	+	0.135404i
$946$		0			0
$947$	−3.63833	−	1.06831i	−0.118230	−	0.0347154i	0.222082	−	0.975028i	$-0.428715\pi$
$947$	−3.63833	−	1.06831i	−0.118230	−	0.0347154i	−0.340312	+	0.940312i	$0.610533\pi$
$948$		0			0
$949$	3.62984	−	1.06582i	0.117830	−	0.0345979i
$950$		0			0
$951$	−6.97730	+	15.2782i	−0.226255	+	0.495428i
$952$		0			0
$953$	−34.5173	+	22.1829i	−1.11812	+	0.718575i	−0.963048	−	0.269328i	$-0.913198\pi$
$953$	−34.5173	+	22.1829i	−1.11812	+	0.718575i	−0.155075	+	0.987903i	$0.549562\pi$
$954$		0			0
$955$	−2.89709	−	20.1497i	−0.0937476	−	0.652029i
$956$		0			0
$957$	−8.07725	+	9.32164i	−0.261100	+	0.301326i
$958$		0			0
$959$	−22.0242	−	14.1541i	−0.711199	−	0.457060i
$960$		0			0
$961$	5.43613	+	6.27363i	0.175359	+	0.202375i
$962$		0			0
$963$	11.8925	+	26.0410i	0.383231	+	0.839158i
$964$		0			0
$965$	−20.4167			−0.657238
$966$		0			0
$967$	−37.8952			−1.21863			−0.609313	−	0.792930i	$-0.708555\pi$
$967$	−37.8952			−1.21863			−0.609313	+	0.792930i	$0.708555\pi$
$968$		0			0
$969$	−5.41944	−	11.8669i	−0.174098	−	0.381220i
$970$		0			0
$971$	2.86477	+	3.30612i	0.0919348	+	0.106098i	0.799853	−	0.600196i	$-0.204911\pi$
$971$	2.86477	+	3.30612i	0.0919348	+	0.106098i	−0.707918	+	0.706295i	$0.750365\pi$
$972$		0			0
$973$	14.6314	+	9.40305i	0.469062	+	0.301448i
$974$		0			0
$975$	−0.341743	+	0.394392i	−0.0109445	+	0.0126307i
$976$		0			0
$977$	2.16356	+	15.0479i	0.0692185	+	0.481425i	0.994715	+	0.102670i	$0.0327386\pi$
$977$	2.16356	+	15.0479i	0.0692185	+	0.481425i	−0.925497	+	0.378755i	$0.876352\pi$
$978$		0			0
$979$	−14.3119	+	9.19772i	−0.457411	+	0.293960i
$980$		0			0
$981$	−5.26841	+	11.5362i	−0.168207	+	0.368322i
$982$		0			0
$983$	−2.97438	+	0.873356i	−0.0948680	+	0.0278557i	−0.328822	−	0.944392i	$-0.606652\pi$
$983$	−2.97438	+	0.873356i	−0.0948680	+	0.0278557i	0.233954	+	0.972248i	$0.424833\pi$
$984$		0			0
$985$	7.21519	+	2.11857i	0.229895	+	0.0675033i
$986$		0			0
$987$	−1.24887	+	8.68608i	−0.0397520	+	0.276481i
$988$		0			0
$989$	−3.40094	−	7.57111i	−0.108144	−	0.240747i
$990$		0			0
$991$	5.65092	−	39.3030i	0.179507	−	1.24850i	−0.678398	−	0.734694i	$-0.737326\pi$
$991$	5.65092	−	39.3030i	0.179507	−	1.24850i	0.857906	−	0.513807i	$-0.171765\pi$
$992$		0			0
$993$	−0.844461	−	0.247956i	−0.0267982	−	0.00786865i
$994$		0			0
$995$	−25.1666	+	7.38958i	−0.797835	+	0.234266i
$996$		0			0
$997$	1.24048	−	2.71628i	0.0392864	−	0.0860253i	−0.888971	−	0.457963i	$-0.848579\pi$
$997$	1.24048	−	2.71628i	0.0392864	−	0.0860253i	0.928258	+	0.371938i	$0.121306\pi$
$998$		0			0
$999$	7.77806	−	4.99865i	0.246087	−	0.158150i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.m.a.261.2	yes	30
23.3	even	11	inner	460.2.m.a.141.2	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.m.a.141.2	✓	30	23.3	even	11	inner
460.2.m.a.261.2	yes	30	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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.256560 + 0.561788i) q^{3} +(-0.654861 - 0.755750i) q^{5} +(-1.01950 - 0.655191i) q^{7} +(1.71480 - 1.97898i) q^{9} +O(q^{10})\)	\(q+(0.256560 + 0.561788i) q^{3} +(-0.654861 - 0.755750i) q^{5} +(-1.01950 - 0.655191i) q^{7} +(1.71480 - 1.97898i) q^{9} +(-0.435403 - 3.02830i) q^{11} +(0.710838 - 0.456828i) q^{13} +(0.256560 - 0.561788i) q^{15} +(6.78397 - 1.99195i) q^{17} +(-2.86659 - 0.841706i) q^{19} +(0.106516 - 0.740837i) q^{21} +(4.79574 + 0.0297844i) q^{23} +(-0.142315 + 0.989821i) q^{25} +(3.32946 + 0.977619i) q^{27} +(-6.26337 + 1.83909i) q^{29} +(1.97917 - 4.33378i) q^{31} +(1.58955 - 1.02154i) q^{33} +(0.172468 + 1.19954i) q^{35} +(1.74486 - 2.01368i) q^{37} +(0.439013 + 0.282136i) q^{39} +(5.64911 + 6.51942i) q^{41} +(-0.718936 - 1.57425i) q^{43} -2.61857 q^{45} -11.7247 q^{47} +(-2.29781 - 5.03149i) q^{49} +(2.85955 + 3.30010i) q^{51} +(6.76575 + 4.34808i) q^{53} +(-2.00351 + 2.31217i) q^{55} +(-0.262591 - 1.82636i) q^{57} +(-5.99582 + 3.85328i) q^{59} +(4.71748 - 10.3298i) q^{61} +(-3.04485 + 0.894047i) q^{63} +(-0.810747 - 0.238057i) q^{65} +(-0.189773 + 1.31990i) q^{67} +(1.21366 + 2.70183i) q^{69} +(-1.49710 + 10.4126i) q^{71} +(4.29580 + 1.26136i) q^{73} +(-0.592582 + 0.173998i) q^{75} +(-1.54022 + 3.37261i) q^{77} +(-8.88784 + 5.71187i) q^{79} +(-0.812992 - 5.65448i) q^{81} +(6.38586 - 7.36968i) q^{83} +(-5.94797 - 3.82253i) q^{85} +(-2.64011 - 3.04685i) q^{87} +(-2.31000 - 5.05820i) q^{89} -1.02401 q^{91} +2.94244 q^{93} +(1.24110 + 2.71762i) q^{95} +(0.650000 + 0.750140i) q^{97} +(-6.73958 - 4.33126i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{5} + q^{7} + 21 q^{9}+O(q^{10}) \) 30 * q - 3 * q^5 + q^7 + 21 * q^9	\( 30 q - 3 q^{5} + q^{7} + 21 q^{9} + 2 q^{13} + 10 q^{17} + 3 q^{19} + 39 q^{21} + 10 q^{23} - 3 q^{25} + 21 q^{27} + 14 q^{29} - 2 q^{31} - 50 q^{33} - 10 q^{35} + 9 q^{37} + 38 q^{39} - 3 q^{41} - 50 q^{43} + 10 q^{45} - 6 q^{47} - 36 q^{49} - 36 q^{51} - 5 q^{53} - 11 q^{55} + 23 q^{57} + 14 q^{59} - 16 q^{61} - 52 q^{63} + 2 q^{65} + 27 q^{67} + 42 q^{69} + 19 q^{71} + 24 q^{73} - 10 q^{77} - 22 q^{79} + 35 q^{81} + 36 q^{83} + 10 q^{85} - 3 q^{87} - 28 q^{89} - 98 q^{91} - 60 q^{93} - 19 q^{95} - 2 q^{97} - 14 q^{99}+O(q^{100}) \) 30 * q - 3 * q^5 + q^7 + 21 * q^9 + 2 * q^13 + 10 * q^17 + 3 * q^19 + 39 * q^21 + 10 * q^23 - 3 * q^25 + 21 * q^27 + 14 * q^29 - 2 * q^31 - 50 * q^33 - 10 * q^35 + 9 * q^37 + 38 * q^39 - 3 * q^41 - 50 * q^43 + 10 * q^45 - 6 * q^47 - 36 * q^49 - 36 * q^51 - 5 * q^53 - 11 * q^55 + 23 * q^57 + 14 * q^59 - 16 * q^61 - 52 * q^63 + 2 * q^65 + 27 * q^67 + 42 * q^69 + 19 * q^71 + 24 * q^73 - 10 * q^77 - 22 * q^79 + 35 * q^81 + 36 * q^83 + 10 * q^85 - 3 * q^87 - 28 * q^89 - 98 * q^91 - 60 * q^93 - 19 * q^95 - 2 * q^97 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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