LMFDB - Embedded newform 460.2.o.a.99.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(19,460)]

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([11, 11, 15]))

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

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

chi := DirichletCharacter("460.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.o (of order $22$, 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:	$40$
Relative dimension:	$4$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{22}]$

Embedding invariants

Embedding label			99.2
Character	$\chi$	$=$	460.99
Dual form			460.2.o.a.79.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.926113 + 1.06879i) q^{2} +(1.23141 - 0.791378i) q^{3} +(-0.284630 - 1.97964i) q^{4} +(2.03400 - 0.928896i) q^{5} +(-0.294605 + 2.04902i) q^{6} +(1.19158 + 4.05815i) q^{7} +(2.37942 + 1.52916i) q^{8} +(-0.356159 + 0.779879i) q^{9} +O(q^{10})$	\(q+(-0.926113 + 1.06879i) q^{2} +(1.23141 - 0.791378i) q^{3} +(-0.284630 - 1.97964i) q^{4} +(2.03400 - 0.928896i) q^{5} +(-0.294605 + 2.04902i) q^{6} +(1.19158 + 4.05815i) q^{7} +(2.37942 + 1.52916i) q^{8} +(-0.356159 + 0.779879i) q^{9} +(-0.890917 + 3.03418i) q^{10} +(-1.91714 - 2.21250i) q^{12} +(-5.44085 - 2.48475i) q^{14} +(1.76957 - 2.75351i) q^{15} +(-3.83797 + 1.12693i) q^{16} +(-0.503685 - 1.10292i) q^{18} +(-2.41782 - 3.76220i) q^{20} +(4.67885 + 4.05425i) q^{21} +(3.12178 + 3.64067i) q^{23} +4.14019 q^{24} +(3.27430 - 3.77875i) q^{25} +(0.803554 + 5.58884i) q^{27} +(7.69453 - 3.51397i) q^{28} +(1.51259 - 10.5203i) q^{29} +(1.30410 + 4.44137i) q^{30} +(2.34994 - 5.14566i) q^{32} +(6.19327 + 7.14742i) q^{35} +(1.64526 + 0.483091i) q^{36} +(6.26018 + 0.900078i) q^{40} +(4.25965 + 9.32734i) q^{41} +(-8.66629 + 1.24602i) q^{42} +(-7.05450 - 10.9770i) q^{43} +1.91711i q^{45} +(-6.78224 - 0.0351445i) q^{46} -4.51713 q^{47} +(-3.83428 + 4.42500i) q^{48} +(-9.15994 + 5.88674i) q^{49} +(1.00632 + 6.99909i) q^{50} +(-6.71748 - 4.31706i) q^{54} +(-3.37030 + 11.4782i) q^{56} +(9.84318 + 11.3596i) q^{58} +(-5.95464 - 2.71939i) q^{60} +(5.31338 - 8.26778i) q^{61} +(-3.58926 - 0.516057i) q^{63} +(3.32332 + 7.27706i) q^{64} +(-8.31902 - 7.20847i) q^{67} +(6.72533 + 2.01265i) q^{69} -13.3748 q^{70} +(-2.04002 + 1.31104i) q^{72} +(1.04159 - 7.24439i) q^{75} +(-6.75963 + 5.85725i) q^{80} +(3.72804 + 4.30238i) q^{81} +(-13.9139 - 4.08549i) q^{82} +(0.390747 + 0.178448i) q^{83} +(6.69422 - 10.4164i) q^{84} +(18.2654 + 2.62617i) q^{86} +(-6.46292 - 14.1518i) q^{87} +(8.78487 + 13.6695i) q^{89} +(-2.04899 - 1.77546i) q^{90} +(6.31868 - 7.21625i) q^{92} +(4.18337 - 4.82787i) q^{94} +(-1.17842 - 8.19609i) q^{96} +(2.19145 - 15.2418i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 8 q^{4} - 8 q^{6} + 4 q^{9}+O(q^{10}) $ 40 * q - 8 * q^4 - 8 * q^6 + 4 * q^9	$ 40 q - 8 q^{4} - 8 q^{6} + 4 q^{9} - 16 q^{16} - 16 q^{24} + 20 q^{25} + 24 q^{29} + 8 q^{36} + 48 q^{41} - 4 q^{46} + 100 q^{49} - 276 q^{54} - 264 q^{56} - 32 q^{64} - 4 q^{69} - 40 q^{70} + 20 q^{81} + 352 q^{84} + 396 q^{86} - 56 q^{94} - 32 q^{96}+O(q^{100}) $ 40 * q - 8 * q^4 - 8 * q^6 + 4 * q^9 - 16 * q^16 - 16 * q^24 + 20 * q^25 + 24 * q^29 + 8 * q^36 + 48 * q^41 - 4 * q^46 + 100 * q^49 - 276 * q^54 - 264 * q^56 - 32 * q^64 - 4 * q^69 - 40 * q^70 + 20 * q^81 + 352 * q^84 + 396 * q^86 - 56 * q^94 - 32 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{19}{22}\right)$

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 $

$2$	−0.926113	+	1.06879i	−0.654861	+	0.755750i
$2$	−0.926113	+	1.06879i	−0.654861	+	0.755750i
$3$	1.23141	−	0.791378i	0.710954	−	0.456902i	−0.134526	−	0.990910i	$-0.542951\pi$
$3$	1.23141	−	0.791378i	0.710954	−	0.456902i	0.845479	+	0.534008i	$0.179315\pi$
$4$	−0.284630	−	1.97964i	−0.142315	−	0.989821i
$5$	2.03400	−	0.928896i	0.909632	−	0.415415i
$5$	2.03400	−	0.928896i	0.909632	−	0.415415i
$6$	−0.294605	+	2.04902i	−0.120272	+	0.836510i
$7$	1.19158	+	4.05815i	0.450375	+	1.53384i	0.801784	+	0.597614i	$0.203885\pi$
$7$	1.19158	+	4.05815i	0.450375	+	1.53384i	−0.351409	+	0.936222i	$0.614297\pi$
$8$	2.37942	+	1.52916i	0.841254	+	0.540641i
$9$	−0.356159	+	0.779879i	−0.118720	+	0.259960i
$10$	−0.890917	+	3.03418i	−0.281733	+	0.959493i
$11$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$11$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$12$	−1.91714	−	2.21250i	−0.553431	−	0.638693i
$13$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$13$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$14$	−5.44085	−	2.48475i	−1.45413	−	0.664079i
$15$	1.76957	−	2.75351i	0.456902	−	0.710954i
$16$	−3.83797	+	1.12693i	−0.959493	+	0.281733i
$17$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$17$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$18$	−0.503685	−	1.10292i	−0.118720	−	0.259960i
$19$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$19$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$20$	−2.41782	−	3.76220i	−0.540641	−	0.841254i
$21$	4.67885	+	4.05425i	1.02101	+	0.884709i
$22$		0			0
$23$	3.12178	+	3.64067i	0.650936	+	0.759133i
$23$	3.12178	+	3.64067i	0.650936	+	0.759133i
$24$	4.14019			0.845112
$25$	3.27430	−	3.77875i	0.654861	−	0.755750i
$26$		0			0
$27$	0.803554	+	5.58884i	0.154644	+	1.07557i
$28$	7.69453	−	3.51397i	1.45413	−	0.664079i
$29$	1.51259	−	10.5203i	0.280881	−	1.95357i	−0.0196728	−	0.999806i	$-0.506262\pi$
$29$	1.51259	−	10.5203i	0.280881	−	1.95357i	0.300554	−	0.953765i	$-0.402828\pi$
$30$	1.30410	+	4.44137i	0.238096	+	0.810879i
$31$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$31$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$32$	2.34994	−	5.14566i	0.415415	−	0.909632i
$33$		0			0
$34$		0			0
$35$	6.19327	+	7.14742i	1.04685	+	1.20813i
$36$	1.64526	+	0.483091i	0.274209	+	0.0805151i
$37$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$37$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$38$		0			0
$39$		0			0
$40$	6.26018	+	0.900078i	0.989821	+	0.142315i
$41$	4.25965	+	9.32734i	0.665246	+	1.45669i	0.877552	+	0.479482i	$0.159176\pi$
$41$	4.25965	+	9.32734i	0.665246	+	1.45669i	−0.212306	+	0.977203i	$0.568097\pi$
$42$	−8.66629	+	1.24602i	−1.33724	+	0.192266i
$43$	−7.05450	−	10.9770i	−1.07580	−	1.67398i	−0.622490	−	0.782628i	$-0.713879\pi$
$43$	−7.05450	−	10.9770i	−1.07580	−	1.67398i	−0.453312	−	0.891352i	$-0.649758\pi$
$44$		0			0
$45$			1.91711i			0.285786i
$46$	−6.78224	−	0.0351445i	−0.999987	−	0.00518177i
$47$	−4.51713			−0.658891			−0.329445	−	0.944175i	$-0.606862\pi$
$47$	−4.51713			−0.658891			−0.329445	+	0.944175i	$0.606862\pi$
$48$	−3.83428	+	4.42500i	−0.553431	+	0.638693i
$49$	−9.15994	+	5.88674i	−1.30856	+	0.840962i
$50$	1.00632	+	6.99909i	0.142315	+	0.989821i
$51$		0			0
$52$		0			0
$53$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$53$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$54$	−6.71748	−	4.31706i	−0.914134	−	0.587478i
$55$		0			0
$56$	−3.37030	+	11.4782i	−0.450375	+	1.53384i
$57$		0			0
$58$	9.84318	+	11.3596i	1.29247	+	1.49159i
$59$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$59$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$60$	−5.95464	−	2.71939i	−0.768741	−	0.351072i
$61$	5.31338	−	8.26778i	0.680308	−	1.05858i	−0.313726	−	0.949514i	$-0.601577\pi$
$61$	5.31338	−	8.26778i	0.680308	−	1.05858i	0.994034	−	0.109067i	$-0.0347863\pi$
$62$		0			0
$63$	−3.58926	−	0.516057i	−0.452204	−	0.0650171i
$64$	3.32332	+	7.27706i	0.415415	+	0.909632i
$65$		0			0
$66$		0			0
$67$	−8.31902	−	7.20847i	−1.01633	−	0.880655i	−0.0234443	−	0.999725i	$-0.507463\pi$
$67$	−8.31902	−	7.20847i	−1.01633	−	0.880655i	−0.992886	+	0.119070i	$0.962009\pi$
$68$		0			0
$69$	6.72533	+	2.01265i	0.809634	+	0.242294i
$70$	−13.3748			−1.59859
$71$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$71$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$72$	−2.04002	+	1.31104i	−0.240418	+	0.154507i
$73$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$73$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$74$		0			0
$75$	1.04159	−	7.24439i	0.120272	−	0.836510i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$79$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$80$	−6.75963	+	5.85725i	−0.755750	+	0.654861i
$81$	3.72804	+	4.30238i	0.414226	+	0.478043i
$82$	−13.9139	−	4.08549i	−1.53653	−	0.451167i
$83$	0.390747	+	0.178448i	0.0428900	+	0.0195872i	0.436745	−	0.899586i	$-0.356131\pi$
$83$	0.390747	+	0.178448i	0.0428900	+	0.0195872i	−0.393855	+	0.919173i	$0.628859\pi$
$84$	6.69422	−	10.4164i	0.730399	−	1.13652i
$85$		0			0
$86$	18.2654	+	2.62617i	1.96961	+	0.283187i
$87$	−6.46292	−	14.1518i	−0.692897	−	1.51723i
$88$		0			0
$89$	8.78487	+	13.6695i	0.931195	+	1.44897i	0.893185	+	0.449690i	$0.148466\pi$
$89$	8.78487	+	13.6695i	0.931195	+	1.44897i	0.0380101	+	0.999277i	$0.487898\pi$
$90$	−2.04899	−	1.77546i	−0.215982	−	0.187150i
$91$		0			0
$92$	6.31868	−	7.21625i	0.658768	−	0.752346i
$93$		0			0
$94$	4.18337	−	4.82787i	0.431482	−	0.497956i
$95$		0			0
$96$	−1.17842	−	8.19609i	−0.120272	−	0.836510i
$97$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$97$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$98$	2.19145	−	15.2418i	0.221370	−	1.53966i
$99$		0			0
$100$	−8.41254	−	5.40641i	−0.841254	−	0.540641i
$101$	4.28165	−	9.37551i	0.426040	−	0.932898i	−0.567912	−	0.823089i	$-0.692249\pi$
$101$	4.28165	−	9.37551i	0.426040	−	0.932898i	0.993953	−	0.109809i	$-0.0350239\pi$
$102$		0			0
$103$	−13.7138	+	11.8831i	−1.35126	+	1.17088i	−0.382198	+	0.924081i	$0.624833\pi$
$103$	−13.7138	+	11.8831i	−1.35126	+	1.17088i	−0.969067	+	0.246797i	$0.920622\pi$
$104$		0			0
$105$	13.2828	+	3.90017i	1.29626	+	0.380617i
$106$		0			0
$107$	6.91069	−	10.7532i	0.668082	−	1.03956i	−0.327426	−	0.944877i	$-0.606181\pi$
$107$	6.91069	−	10.7532i	0.668082	−	1.03956i	0.995508	−	0.0946787i	$-0.0301824\pi$
$108$	10.8352	−	3.18150i	1.04262	−	0.306140i
$109$	−20.6654	−	2.97123i	−1.97938	−	0.284592i	−0.991997	−	0.126258i	$-0.959703\pi$
$109$	−20.6654	−	2.97123i	−1.97938	−	0.284592i	−0.987386	−	0.158334i	$-0.949388\pi$
$110$		0			0
$111$		0			0
$112$	−9.14650	−	14.2322i	−0.864263	−	1.34482i
$113$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$113$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$114$		0			0
$115$	9.73150	+	4.50532i	0.907467	+	0.420123i
$116$	−21.2570			−1.97366
$117$		0			0
$118$		0			0
$119$		0			0
$120$	8.42114	−	3.84580i	0.768741	−	0.351072i
$121$	1.56546	−	10.8880i	0.142315	−	0.989821i
$122$	3.91574	+	13.3358i	0.354514	+	1.20737i
$123$	12.6268	+	8.11476i	1.13852	+	0.731683i
$124$		0			0
$125$	3.14987	−	10.7275i	0.281733	−	0.959493i
$126$	3.87562	−	3.35824i	0.345267	−	0.299176i
$127$	−10.1744	−	11.7419i	−0.902832	−	1.04192i	−0.998916	−	0.0465500i	$-0.985177\pi$
$127$	−10.1744	−	11.7419i	−0.902832	−	1.04192i	0.0960844	−	0.995373i	$-0.469368\pi$
$128$	−10.8554	−	3.18744i	−0.959493	−	0.281733i
$129$	−17.3739	−	7.93441i	−1.52969	−	0.698586i
$130$		0			0
$131$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$131$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$132$		0			0
$133$		0			0
$134$	15.4087	−	2.21544i	1.33111	−	0.191385i
$135$	6.82588	+	10.6213i	0.587478	+	0.914134i
$136$		0			0
$137$		0			0			−	1.00000i	$-0.5\pi$
$137$		0			0				1.00000i	$0.5\pi$
$138$	−8.37951	+	5.32403i	−0.713312	+	0.453212i
$139$		0			0		1.00000			$0$
$139$		0			0		−1.00000			$\pi$
$140$	12.3865	−	14.2948i	1.04685	−	1.20813i
$141$	−5.56243	+	3.57475i	−0.468441	+	0.301049i
$142$		0			0
$143$		0			0
$144$	0.488058	−	3.39452i	0.0406715	−	0.282877i
$145$	−6.69566	−	22.8033i	−0.556044	−	1.89371i
$146$		0			0
$147$	−6.62099	+	14.4979i	−0.546090	+	1.19577i
$148$		0			0
$149$	−15.0949	+	13.0798i	−1.23662	+	1.07154i	−0.241754	+	0.970338i	$0.577723\pi$
$149$	−15.0949	+	13.0798i	−1.23662	+	1.07154i	−0.994866	+	0.101200i	$0.967732\pi$
$150$	6.77811	+	7.82236i	0.553431	+	0.638693i
$151$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$151$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$157$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$158$		0			0
$159$		0			0
$160$		−	12.6491i		−	1.00000i
$161$	−11.0545	+	17.0068i	−0.871220	+	1.34032i
$162$	−8.05093			−0.632541
$163$	−15.5346	+	17.9279i	−1.21676	+	1.40422i	−0.328743	+	0.944419i	$0.606625\pi$
$163$	−15.5346	+	17.9279i	−1.21676	+	1.40422i	−0.888022	+	0.459802i	$0.847921\pi$
$164$	17.2524	−	11.0874i	1.34718	−	0.865783i
$165$		0			0
$166$	−0.552599	+	0.252364i	−0.0428900	+	0.0195872i
$167$	1.82330	−	12.6813i	0.141091	−	0.981312i	−0.789107	−	0.614255i	$-0.789456\pi$
$167$	1.82330	−	12.6813i	0.141091	−	0.981312i	0.930199	−	0.367057i	$-0.119634\pi$
$168$	4.93336	+	16.8015i	0.380617	+	1.29626i
$169$	10.9363	+	7.02833i	0.841254	+	0.540641i
$170$		0			0
$171$		0			0
$172$	−19.7227	+	17.0898i	−1.50384	+	1.30308i
$173$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$173$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$174$	21.1107	+	6.19867i	1.60040	+	0.469920i
$175$	19.2363	+	8.78493i	1.45413	+	0.664079i
$176$		0			0
$177$		0			0
$178$	−22.7457	−	3.27033i	−1.70486	−	0.245122i
$179$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$179$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$180$	3.79519	−	0.545666i	0.282877	−	0.0406715i
$181$	−12.7886	−	19.8994i	−0.950568	−	1.47911i	−0.876238	−	0.481878i	$-0.839955\pi$
$181$	−12.7886	−	19.8994i	−0.950568	−	1.47911i	−0.0743294	−	0.997234i	$-0.523682\pi$
$182$		0			0
$183$		−	14.3859i		−	1.06344i
$184$	1.86085	+	13.4364i	0.137184	+	0.990546i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	1.28571	+	8.94230i	0.0937699	+	0.652184i
$189$	−21.7228	+	9.92049i	−1.58010	+	0.721610i
$190$		0			0
$191$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$191$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$192$	9.85126	+	6.33102i	0.710954	+	0.456902i
$193$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$193$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$194$		0			0
$195$		0			0
$196$	14.2608	+	16.4579i	1.01863	+	1.17556i
$197$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$197$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$198$		0			0
$199$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$199$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$200$	13.5693	−	3.98430i	0.959493	−	0.281733i
$201$	−15.9487	−	2.29308i	−1.12494	−	0.161741i
$202$	6.05517	+	13.2590i	0.426040	+	0.932898i
$203$	44.4953	−	6.39746i	3.12296	−	0.449014i
$204$		0			0
$205$	17.3283	+	15.0150i	1.21026	+	1.04869i
$206$		−	25.6623i		−	1.78798i
$207$	−3.95113	+	1.13795i	−0.274623	+	0.0790931i
$208$		0			0
$209$		0			0
$210$	−16.4698	+	10.5845i	−1.13652	+	0.730399i
$211$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$211$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$212$		0			0
$213$		0			0
$214$	5.09289	+	17.3448i	0.348143	+	1.18567i
$215$	−24.5454	−	15.7743i	−1.67398	−	1.07580i
$216$	−6.63425	+	14.5270i	−0.451404	+	0.988436i
$217$		0			0
$218$	22.3141	−	19.3353i	1.51130	−	1.30955i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	7.05863	−	2.07260i	0.472681	−	0.138792i	−0.0367117	−	0.999326i	$-0.511688\pi$
$223$	7.05863	−	2.07260i	0.472681	−	0.138792i	0.509393	+	0.860534i	$0.329870\pi$
$224$	23.6820	+	3.40496i	1.58232	+	0.227503i
$225$	1.78079	+	3.89940i	0.118720	+	0.259960i
$226$		0			0
$227$	11.2604	+	17.5215i	0.747377	+	1.16294i	0.981635	+	0.190767i	$0.0610974\pi$
$227$	11.2604	+	17.5215i	0.747377	+	1.16294i	−0.234259	+	0.972174i	$0.575266\pi$
$228$		0			0
$229$			6.99126i			0.461996i	0.972954	+	0.230998i	$0.0741990\pi$
$229$			6.99126i			0.461996i	−0.972954	+	0.230998i	$0.925801\pi$
$230$	−13.8277	+	6.22851i	−0.911772	+	0.410696i
$231$		0			0
$232$	19.6864	−	22.7193i	1.29247	−	1.49159i
$233$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$233$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$234$		0			0
$235$	−9.18783	+	4.19594i	−0.599348	+	0.273713i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$239$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$240$	−3.68856	+	12.5621i	−0.238096	+	0.810879i
$241$	−3.76699	+	3.26411i	−0.242653	+	0.210260i	−0.767693	−	0.640817i	$-0.778596\pi$
$241$	−3.76699	+	3.26411i	−0.242653	+	0.210260i	0.525041	+	0.851077i	$0.324050\pi$
$242$	10.1872	+	11.7567i	0.654861	+	0.755750i
$243$	−8.25724	−	2.42455i	−0.529702	−	0.155535i
$244$	−17.8796	−	8.16534i	−1.14462	−	0.522732i
$245$	−13.1631	+	20.4823i	−0.840962	+	1.30856i
$246$	−20.3668	+	5.98025i	−1.29854	+	0.381287i
$247$		0			0
$248$		0			0
$249$	0.622388	−	0.0894859i	0.0394422	−	0.00567094i
$250$	8.54828	+	13.3014i	0.540641	+	0.841254i
$251$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$251$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$252$			7.25233i			0.456854i
$253$		0			0
$254$	21.9723			1.37866
$255$		0			0
$256$	13.4601	−	8.65025i	0.841254	−	0.540641i
$257$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$257$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$258$	24.5705	−	11.2210i	1.52969	−	0.698586i
$259$		0			0
$260$		0			0
$261$	7.66584	+	4.92654i	0.474504	+	0.304945i
$262$		0			0
$263$	3.19700	−	10.8880i	0.197136	−	0.671383i	−0.800286	−	0.599619i	$-0.795319\pi$
$263$	3.19700	−	10.8880i	0.197136	−	0.671383i	0.997422	−	0.0717640i	$-0.0228629\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	21.6355	+	9.88061i	1.32407	+	0.604684i
$268$	−11.9024	+	18.5204i	−0.727052	+	1.13132i
$269$	−30.9716	+	9.09410i	−1.88837	+	0.554477i	−0.894067	+	0.447934i	$0.852160\pi$
$269$	−30.9716	+	9.09410i	−1.88837	+	0.554477i	−0.994308	+	0.106543i	$0.966022\pi$
$270$	−17.6735	−	2.54106i	−1.07557	−	0.154644i
$271$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$271$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	2.07009	−	13.8866i	0.124605	−	0.835876i
$277$		0			0		1.00000			$0$
$277$		0			0		−1.00000			$\pi$
$278$		0			0
$279$		0			0
$280$	3.80686	+	26.4773i	0.227503	+	1.58232i
$281$	6.75192	−	3.08350i	0.402786	−	0.183946i	−0.203713	−	0.979031i	$-0.565301\pi$
$281$	6.75192	−	3.08350i	0.402786	−	0.183946i	0.606499	+	0.795085i	$0.292574\pi$
$282$	1.33077	−	9.25570i	0.0792461	−	0.551169i
$283$	9.24051	+	31.4703i	0.549291	+	1.87071i	0.488500	+	0.872564i	$0.337544\pi$
$283$	9.24051	+	31.4703i	0.549291	+	1.87071i	0.0607917	+	0.998150i	$0.480637\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−32.7760	+	28.4006i	−1.93471	+	1.67643i
$288$	3.17604	+	3.66534i	0.187150	+	0.215982i
$289$	16.3114	+	4.78945i	0.959493	+	0.281733i
$290$	30.5729	+	13.9622i	1.79530	+	0.819888i
$291$		0			0
$292$		0			0
$293$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$293$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$294$	−9.36349	−	20.5032i	−0.546090	−	1.19577i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		−	28.2466i		−	1.63628i
$299$		0			0
$300$	−14.6378			−0.845112
$301$	36.1404	−	41.7082i	2.08310	−	2.40402i
$302$		0			0
$303$	−2.14711	−	14.9335i	−0.123348	−	0.857906i
$304$		0			0
$305$	3.12750	−	21.7522i	0.179080	−	1.24553i
$306$		0			0
$307$	11.6689	+	7.49916i	0.665980	+	0.427999i	0.829474	−	0.558545i	$-0.188640\pi$
$307$	11.6689	+	7.49916i	0.665980	+	0.427999i	−0.163494	+	0.986544i	$0.552276\pi$
$308$		0			0
$309$	−7.48330	+	25.4858i	−0.425710	+	1.44984i
$310$		0			0
$311$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$311$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$312$		0			0
$313$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$313$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$314$		0			0
$315$	−7.77991	+	2.28439i	−0.438348	+	0.128711i
$316$		0			0
$317$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$317$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$318$		0			0
$319$		0			0
$320$	13.5193	+	11.7145i	0.755750	+	0.654861i
$321$		−	18.7106i		−	1.04432i
$322$	−7.93896	−	27.5652i	−0.442421	−	1.53615i
$323$		0			0
$324$	7.45607	−	8.60477i	0.414226	−	0.478043i
$325$		0			0
$326$	−4.77438	−	33.2065i	−0.264428	−	1.83914i
$327$	−27.7989	+	12.6953i	−1.53728	+	0.702052i
$328$	−4.12750	+	28.7074i	−0.227903	+	1.58510i
$329$	−5.38252	−	18.3312i	−0.296748	−	1.01063i
$330$		0			0
$331$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$331$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$332$	0.242045	−	0.824330i	0.0132840	−	0.0452410i
$333$		0			0
$334$	11.8651	+	13.6931i	0.649231	+	0.749252i
$335$	−23.6168	−	6.93452i	−1.29032	−	0.378873i
$336$	−22.5261	−	10.2873i	−1.22890	−	0.561221i
$337$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$337$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$338$	−17.6401	+	5.17959i	−0.959493	+	0.281733i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−12.4291	−	10.7699i	−0.671109	−	0.581519i
$344$		−	36.9065i		−	1.98986i
$345$	15.5489	−	2.15341i	0.837122	−	0.115936i
$346$		0			0
$347$	23.3209	−	26.9138i	1.25193	−	1.44481i	0.403950	−	0.914781i	$-0.367637\pi$
$347$	23.3209	−	26.9138i	1.25193	−	1.44481i	0.847982	−	0.530026i	$-0.177818\pi$
$348$	−26.1760	+	16.8223i	−1.40318	+	0.901770i
$349$	−2.47445	−	17.2102i	−0.132454	−	0.921239i	−0.942341	−	0.334653i	$-0.891381\pi$
$349$	−2.47445	−	17.2102i	−0.132454	−	0.921239i	0.809887	−	0.586586i	$-0.199528\pi$
$350$	−27.2043	+	12.4238i	−1.45413	+	0.664079i
$351$		0			0
$352$		0			0
$353$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$353$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$354$		0			0
$355$		0			0
$356$	24.5604	−	21.2817i	1.30170	−	1.12793i
$357$		0			0
$358$		0			0
$359$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$359$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$360$	−2.93157	+	4.56161i	−0.154507	+	0.240418i
$361$	18.2304	−	5.35292i	0.959493	−	0.281733i
$362$	33.1120	+	4.76079i	1.74033	+	0.250221i
$363$	−6.68882	−	14.6465i	−0.351072	−	0.768741i
$364$		0			0
$365$		0			0
$366$	15.3755	+	13.3230i	0.803691	+	0.696402i
$367$		−	23.3040i		−	1.21646i	−0.793762	−	0.608229i	$-0.791880\pi$
$367$		−	23.3040i		−	1.21646i	0.793762	−	0.608229i	$-0.208120\pi$
$368$	−16.0841	−	10.4548i	−0.838441	−	0.544993i
$369$	−8.79131			−0.457657
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$373$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$374$		0			0
$375$	−4.61070	−	15.7026i	−0.238096	−	0.810879i
$376$	−10.7482	−	6.90743i	−0.554294	−	0.356223i
$377$		0			0
$378$	9.51487	−	32.4047i	0.489392	−	1.66672i
$379$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$379$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$380$		0			0
$381$	−21.8211	−	6.40725i	−1.11793	−	0.328253i
$382$		0			0
$383$	10.6709	−	16.6042i	0.545257	−	0.848436i	−0.453833	−	0.891087i	$-0.649944\pi$
$383$	10.6709	−	16.6042i	0.545257	−	0.848436i	0.999090	+	0.0426504i	$0.0135802\pi$
$384$	−15.8899	+	4.66570i	−0.810879	+	0.238096i
$385$		0			0
$386$		0			0
$387$	11.0733	−	1.59210i	0.562886	−	0.0809308i
$388$		0			0
$389$	1.78538	+	1.54704i	0.0905223	+	0.0784380i	0.698946	−	0.715174i	$-0.253653\pi$
$389$	1.78538	+	1.54704i	0.0905223	+	0.0784380i	−0.608424	+	0.793612i	$0.708198\pi$
$390$		0			0
$391$		0			0
$392$	−30.7972			−1.55549
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$397$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$398$		0			0
$399$		0			0
$400$	−8.30830	+	18.1926i	−0.415415	+	0.909632i
$401$	−11.2212	+	38.2158i	−0.560358	+	1.90840i	−0.179558	+	0.983747i	$0.557467\pi$
$401$	−11.2212	+	38.2158i	−0.560358	+	1.90840i	−0.380800	+	0.924657i	$0.624351\pi$
$402$	17.2211	−	14.9222i	0.858913	−	0.744252i
$403$		0			0
$404$	−19.7788	−	5.80759i	−0.984034	−	0.288939i
$405$	11.5793	+	5.28808i	0.575380	+	0.262767i
$406$	−34.3702	+	53.4810i	−1.70576	+	2.65422i
$407$		0			0
$408$		0			0
$409$	−15.8994	−	34.8149i	−0.786177	−	1.72149i	−0.687283	−	0.726389i	$-0.741197\pi$
$409$	−15.8994	−	34.8149i	−0.786177	−	1.72149i	−0.0988936	−	0.995098i	$-0.531530\pi$
$410$	−32.0958	+	4.61469i	−1.58510	+	0.227903i
$411$		0			0
$412$	27.4277	+	23.7662i	1.35126	+	1.17088i
$413$		0			0
$414$	2.44296	−	5.27681i	0.120065	−	0.259341i
$415$	0.960538			0.0471509
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$419$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$420$	3.94027	−	27.4052i	0.192266	−	1.33724i
$421$	11.5152	+	39.2171i	0.561215	+	1.91132i	0.366267	+	0.930510i	$0.380636\pi$
$421$	11.5152	+	39.2171i	0.561215	+	1.91132i	0.194948	+	0.980814i	$0.437546\pi$
$422$		0			0
$423$	1.60882	−	3.52281i	0.0782233	−	0.171285i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	39.8832	+	11.7108i	1.93008	+	0.566724i
$428$	−23.2546	−	10.6200i	−1.12405	−	0.513337i
$429$		0			0
$430$	39.5913	−	11.6250i	1.90926	−	0.560609i
$431$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$431$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$432$	−9.38225	−	20.5443i	−0.451404	−	0.988436i
$433$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$433$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$434$		0			0
$435$	−26.2911	−	22.7814i	−1.26056	−	1.09228i
$436$			41.7557i			1.99974i
$437$		0			0
$438$		0			0
$439$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$439$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$440$		0			0
$441$	−1.32855	−	9.24026i	−0.0632642	−	0.440012i
$442$		0			0
$443$	0.505734	−	3.51746i	0.0240281	−	0.167119i	−0.974274	−	0.225367i	$-0.927642\pi$
$443$	0.505734	−	3.51746i	0.0240281	−	0.167119i	0.998302	+	0.0582471i	$0.0185511\pi$
$444$		0			0
$445$	30.5660	+	19.6436i	1.44897	+	0.931195i
$446$	−4.32191	+	9.46367i	−0.204648	+	0.448118i
$447$	−8.23689	+	28.0523i	−0.389592	+	1.32683i
$448$	−25.5714	+	22.1577i	−1.20813	+	1.04685i
$449$	26.5049	+	30.5883i	1.25084	+	1.44355i	0.849473	+	0.527633i	$0.176920\pi$
$449$	26.5049	+	30.5883i	1.25084	+	1.44355i	0.401370	+	0.915916i	$0.368534\pi$
$450$	−5.81686	−	1.70798i	−0.274209	−	0.0805151i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	−29.1552	−	4.19188i	−1.36832	−	0.196735i
$455$		0			0
$456$		0			0
$457$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$457$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$458$	−7.47220	−	6.47470i	−0.349153	−	0.302543i
$459$		0			0
$460$	6.14904	−	20.5472i	0.286701	−	0.958020i
$461$	34.2638			1.59582			0.797912	−	0.602774i	$-0.205938\pi$
$461$	34.2638			1.59582			0.797912	+	0.602774i	$0.205938\pi$
$462$		0			0
$463$	0.530357	−	0.340840i	0.0246478	−	0.0158402i	−0.528259	−	0.849083i	$-0.677155\pi$
$463$	0.530357	−	0.340840i	0.0246478	−	0.0158402i	0.552907	+	0.833243i	$0.313519\pi$
$464$	6.05037	+	42.0812i	0.280881	+	1.95357i
$465$		0			0
$466$		0			0
$467$	8.01825	+	27.3076i	0.371040	+	1.26365i	0.907618	+	0.419797i	$0.137899\pi$
$467$	8.01825	+	27.3076i	0.371040	+	1.26365i	−0.536578	+	0.843851i	$0.680283\pi$
$468$		0			0
$469$	19.3403	−	42.3493i	0.893051	−	1.95551i
$470$	4.02438	−	13.7058i	0.185631	−	0.632201i
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$479$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$480$	−10.0102	−	15.5762i	−0.456902	−	0.710954i
$481$		0			0
$482$		−	7.04906i		−	0.321076i
$483$	−0.153852	+	29.6906i	−0.00700051	+	1.35097i
$484$	−22.0000			−1.00000
$485$		0			0
$486$	10.2385	−	6.57987i	0.464427	−	0.298469i
$487$	−6.10153	−	42.4371i	−0.276487	−	1.92301i	−0.373311	−	0.927706i	$-0.621778\pi$
$487$	−6.10153	−	42.4371i	−0.276487	−	1.92301i	0.0968243	−	0.995301i	$-0.469132\pi$
$488$	25.2856	−	11.5475i	1.14462	−	0.522732i
$489$	−4.94170	+	34.3703i	−0.223471	+	1.55428i
$490$	−9.70069	−	33.0375i	−0.438233	−	1.49248i
$491$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$491$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$492$	12.4704	−	27.3063i	0.562207	−	1.23106i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−0.480760	+	0.748077i	−0.0215434	+	0.0335221i
$499$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$499$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$500$	−22.1331	−	3.18226i	−0.989821	−	0.142315i
$501$	−7.79051	−	17.0588i	−0.348054	−	0.762132i
$502$		0			0
$503$	21.2716	+	33.0992i	0.948452	+	1.47582i	0.878202	+	0.478291i	$0.158743\pi$
$503$	21.2716	+	33.0992i	0.948452	+	1.47582i	0.0702503	+	0.997529i	$0.477620\pi$
$504$	−7.75123	−	6.71648i	−0.345267	−	0.299176i
$505$		−	23.0470i		−	1.02558i
$506$		0			0
$507$	19.0291			0.845112
$508$	−20.3488	+	23.4838i	−0.902832	+	1.04192i
$509$	37.9574	−	24.3937i	1.68243	−	1.08123i	0.836117	−	0.548551i	$-0.184820\pi$
$509$	37.9574	−	24.3937i	1.68243	−	1.08123i	0.846315	−	0.532682i	$-0.178816\pi$
$510$		0			0
$511$		0			0
$512$	−3.22022	+	22.3971i	−0.142315	+	0.989821i
$513$		0			0
$514$		0			0
$515$	−16.8558	+	36.9090i	−0.742754	+	1.62640i
$516$	−10.7622	+	36.6526i	−0.473778	+	1.61354i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−24.6725	+	38.3912i	−1.08092	+	1.68195i	−0.518801	+	0.854895i	$0.673621\pi$
$521$	−24.6725	+	38.3912i	−1.08092	+	1.68195i	−0.562123	+	0.827054i	$0.690015\pi$
$522$	−12.3649	+	3.63066i	−0.541196	+	0.158909i
$523$	−44.8580	−	6.44960i	−1.96150	−	0.282021i	−0.999973	−	0.00731877i	$-0.997670\pi$
$523$	−44.8580	−	6.44960i	−1.96150	−	0.282021i	−0.961529	−	0.274703i	$-0.911421\pi$
$524$		0			0
$525$	30.6400	−	4.40536i	1.33724	−	0.192266i
$526$	8.67621	+	13.5004i	0.378301	+	0.588647i
$527$		0			0
$528$		0			0
$529$	−3.50900	+	22.7307i	−0.152565	+	0.988293i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	−30.5972	+	13.9733i	−1.32407	+	0.604684i
$535$	4.06769	−	28.2914i	0.175862	−	1.22314i
$536$	−8.77155	−	29.8732i	−0.378873	−	1.29032i
$537$		0			0
$538$	18.9636	−	41.5244i	0.817577	−	1.79024i
$539$		0			0
$540$	19.0835	−	16.5359i	0.821222	−	0.711593i
$541$	30.4344	+	35.1231i	1.30848	+	1.51006i	0.687199	+	0.726470i	$0.258840\pi$
$541$	30.4344	+	35.1231i	1.30848	+	1.51006i	0.621277	+	0.783591i	$0.286614\pi$
$542$		0			0
$543$	−31.4959	−	14.3837i	−1.35162	−	0.617264i
$544$		0			0
$545$	−44.7933	+	13.1525i	−1.91873	+	0.563391i
$546$		0			0
$547$	6.85872	+	15.0185i	0.293257	+	0.642144i	0.997712	−	0.0676046i	$-0.0215356\pi$
$547$	6.85872	+	15.0185i	0.293257	+	0.642144i	−0.704455	+	0.709749i	$0.748808\pi$
$548$		0			0
$549$	4.55546	+	7.08843i	0.194422	+	0.302527i
$550$		0			0
$551$		0			0
$552$	12.9247	+	15.0731i	0.550114	+	0.641552i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$557$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$558$		0			0
$559$		0			0
$560$	−31.8242	−	20.4522i	−1.34482	−	0.864263i
$561$		0			0
$562$	−2.95743	+	10.0721i	−0.124751	+	0.424864i
$563$	34.0951	−	29.5436i	1.43694	−	1.24511i	0.515330	−	0.856992i	$-0.327669\pi$
$563$	34.0951	−	29.5436i	1.43694	−	1.24511i	0.921608	−	0.388123i	$-0.126876\pi$
$564$	8.65997	+	9.99414i	0.364650	+	0.420829i
$565$		0			0
$566$	−42.1929	−	19.2689i	−1.77350	−	0.809931i
$567$	−13.0175	+	20.2556i	−0.546682	+	0.850654i
$568$		0			0
$569$	−6.80238	−	0.978035i	−0.285171	−	0.0410014i	−0.00175481	−	0.999998i	$-0.500559\pi$
$569$	−6.80238	−	0.978035i	−0.285171	−	0.0410014i	−0.283416	+	0.958997i	$0.591468\pi$
$570$		0			0
$571$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$571$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$572$		0			0
$573$		0			0
$574$		−	61.3329i		−	2.55998i
$575$	23.9788	+	0.124255i	0.999987	+	0.00518177i
$576$	−6.85885			−0.285786
$577$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$577$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$578$	−20.2251	+	12.9979i	−0.841254	+	0.540641i
$579$		0			0
$580$	−43.2367	+	19.7455i	−1.79530	+	0.819888i
$581$	−0.258563	+	1.79834i	−0.0107270	+	0.0746079i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−29.8240	−	34.4187i	−1.23097	−	1.42061i	−0.873597	−	0.486651i	$-0.838218\pi$
$587$	−29.8240	−	34.4187i	−1.23097	−	1.42061i	−0.357372	−	0.933962i	$-0.616327\pi$
$588$	30.5853	+	8.98065i	1.26132	+	0.370356i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$593$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$594$		0			0
$595$		0			0
$596$	30.1897	+	26.1596i	1.23662	+	1.07154i
$597$		0			0
$598$		0			0
$599$		0			0		1.00000			$0$
$599$		0			0		−1.00000			$\pi$
$600$	13.5562	−	15.6447i	0.553431	−	0.638693i
$601$	41.0148	−	26.3586i	1.67303	−	1.07519i	0.779214	−	0.626758i	$-0.215619\pi$
$601$	41.0148	−	26.3586i	1.67303	−	1.07519i	0.893816	−	0.448433i	$-0.148018\pi$
$602$	11.1073	+	77.2531i	0.452700	+	3.14860i
$603$	8.58463	−	3.92047i	0.349593	−	0.159654i
$604$		0			0
$605$	−6.92970	−	23.6004i	−0.281733	−	0.959493i
$606$	17.9492	+	11.5353i	0.729138	+	0.468588i
$607$	3.74237	−	8.19465i	0.151898	−	0.332611i	−0.818351	−	0.574719i	$-0.805112\pi$
$607$	3.74237	−	8.19465i	0.151898	−	0.332611i	0.970249	+	0.242108i	$0.0778388\pi$
$608$		0			0
$609$	49.7291	−	43.0905i	2.01512	−	1.74612i
$610$	20.3522	+	23.4877i	0.824035	+	0.950988i
$611$		0			0
$612$		0			0
$613$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$613$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$614$	−18.8218	+	5.52657i	−0.759585	+	0.223034i
$615$	33.2207	+	4.77642i	1.33959	+	0.192604i
$616$		0			0
$617$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$617$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$618$	−20.3086	−	31.6008i	−0.816932	−	1.27117i
$619$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$619$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$620$		0			0
$621$	−17.8386	+	20.3726i	−0.715839	+	0.817524i
$622$		0			0
$623$	−45.0051	+	51.9387i	−1.80309	+	2.08088i
$624$		0			0
$625$	−3.55787	−	24.7455i	−0.142315	−	0.989821i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	4.76354	−	10.4307i	0.189784	−	0.415569i
$631$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$631$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−31.6017	−	14.4320i	−1.25408	−	0.572717i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	−25.0407	+	3.60031i	−0.989821	+	0.142315i
$641$	−16.9498	−	26.3744i	−0.669477	−	1.04173i	−0.995351	−	0.0963128i	$-0.969295\pi$
$641$	−16.9498	−	26.3744i	−0.669477	−	1.04173i	0.325875	−	0.945413i	$-0.394341\pi$
$642$	19.9977	+	17.3281i	0.789247	+	0.683887i
$643$			23.5457i			0.928551i	0.885691	+	0.464276i	$0.153685\pi$
$643$			23.5457i			0.928551i	−0.885691	+	0.464276i	$0.846315\pi$
$644$	36.8138	+	17.0434i	1.45067	+	0.671605i
$645$	−42.7088			−1.68166
$646$		0			0
$647$	34.5849	−	22.2263i	1.35967	−	0.873808i	0.361390	−	0.932415i	$-0.382302\pi$
$647$	34.5849	−	22.2263i	1.35967	−	0.873808i	0.998281	+	0.0586071i	$0.0186659\pi$
$648$	2.29153	+	15.9380i	0.0900200	+	0.626103i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	39.9124	+	25.6502i	1.56309	+	1.00454i
$653$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$653$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$654$	12.1762	−	41.4685i	0.476129	−	1.62155i
$655$		0			0
$656$	−26.8597	−	30.9977i	−1.04869	−	1.21026i
$657$		0			0
$658$	24.5770	+	11.2240i	0.958112	+	0.437555i
$659$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$659$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$660$		0			0
$661$	12.2620	+	1.76301i	0.476936	+	0.0685731i	0.376591	−	0.926380i	$-0.377096\pi$
$661$	12.2620	+	1.76301i	0.476936	+	0.0685731i	0.100345	+	0.994953i	$0.468005\pi$
$662$		0			0
$663$		0			0
$664$	0.656876	+	1.02212i	0.0254917	+	0.0396659i
$665$		0			0
$666$		0			0
$667$	43.0230	−	27.3352i	1.66586	−	1.05842i
$668$	−25.6235			−0.991403
$669$	7.05184	−	8.13826i	0.272640	−	0.314643i
$670$	29.2834	−	18.8193i	1.13132	−	0.727052i
$671$		0			0
$672$	31.8568	−	14.5485i	1.22890	−	0.561221i
$673$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$673$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$674$		0			0
$675$	23.7499	+	15.2631i	0.914134	+	0.587478i
$676$	10.8008	−	23.6504i	0.415415	−	0.909632i
$677$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$677$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	27.7322	+	12.6649i	1.06270	+	0.485319i
$682$		0			0
$683$	−32.6674	+	9.59201i	−1.24998	+	0.367028i	−0.838757	−	0.544505i	$-0.816717\pi$
$683$	−32.6674	+	9.59201i	−1.24998	+	0.367028i	−0.411226	+	0.911534i	$0.634899\pi$
$684$		0			0
$685$		0			0
$686$	23.0215	−	3.30999i	0.878966	−	0.126376i
$687$	5.53273	+	8.60910i	0.211087	+	0.328457i
$688$	39.4453	+	34.1796i	1.50384	+	1.30308i
$689$		0			0
$690$	−12.0984	+	18.6128i	−0.460580	+	0.708576i
$691$		0			0		1.00000			$0$
$691$		0			0		−1.00000			$\pi$
$692$		0			0
$693$		0			0
$694$	7.16740	+	49.8504i	0.272071	+	1.89229i
$695$		0			0
$696$	6.26241	−	43.5560i	0.237376	−	1.65099i
$697$		0			0
$698$	20.6857	+	13.2939i	0.782965	+	0.503181i
$699$		0			0
$700$	11.9158	−	40.5815i	0.450375	−	1.53384i
$701$	−33.5018	+	29.0294i	−1.26534	+	1.09643i	−0.274475	+	0.961594i	$0.588504\pi$
$701$	−33.5018	+	29.0294i	−1.26534	+	1.09643i	−0.990868	+	0.134832i	$0.956950\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	−7.99339	+	12.4380i	−0.301049	+	0.468441i
$706$		0			0
$707$	43.1492	+	6.20391i	1.62279	+	0.233322i
$708$		0			0
$709$	−26.5597	+	3.81871i	−0.997470	+	0.143415i	−0.621664	−	0.783284i	$-0.713543\pi$
$709$	−26.5597	+	3.81871i	−0.997470	+	0.143415i	−0.375806	+	0.926698i	$0.622634\pi$
$710$		0			0
$711$		0			0
$712$			45.9591i			1.72239i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$719$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$720$	−2.16045	−	7.35781i	−0.0805151	−	0.274209i
$721$	−64.5646	−	41.4931i	−2.40451	−	1.54529i
$722$	−11.1622	+	24.4419i	−0.415415	+	0.909632i
$723$	−2.05555	+	7.00056i	−0.0764467	+	0.260354i
$724$	−35.7537	+	30.9808i	−1.32878	+	1.15139i
$725$	−34.8009	−	40.1624i	−1.29247	−	1.49159i
$726$	21.8486	+	6.41534i	0.810879	+	0.238096i
$727$	−23.8246	−	10.8803i	−0.883604	−	0.403528i	−0.0786754	−	0.996900i	$-0.525069\pi$
$727$	−23.8246	−	10.8803i	−0.883604	−	0.403528i	−0.804928	+	0.593372i	$0.797796\pi$
$728$		0			0
$729$	−28.4736	+	8.36059i	−1.05458	+	0.309652i
$730$		0			0
$731$		0			0
$732$	−28.4789	+	4.09465i	−1.05261	+	0.151343i
$733$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$733$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$734$	24.9071	+	21.5821i	0.919337	+	0.796610i
$735$			35.6390i			1.31457i
$736$	26.0696	−	7.50823i	0.960940	−	0.276757i
$737$		0			0
$738$	8.14175	−	9.39608i	0.299702	−	0.345874i
$739$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$739$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−1.33457	−	4.54512i	−0.0489605	−	0.166744i	0.931384	−	0.364039i	$-0.118603\pi$
$743$	−1.33457	−	4.54512i	−0.0489605	−	0.166744i	−0.980344	+	0.197295i	$0.936784\pi$
$744$		0			0
$745$	−18.5532	+	40.6258i	−0.679736	+	1.48842i
$746$		0			0
$747$	−0.278336	+	0.241179i	−0.0101838	+	0.00882429i
$748$		0			0
$749$	51.8729	+	15.2313i	1.89540	+	0.556538i
$750$	21.0528	+	9.61451i	0.768741	+	0.351072i
$751$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$751$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$752$	17.3366	−	5.09049i	0.632201	−	0.185631i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	25.8220	+	40.1798i	0.939137	+	1.46133i
$757$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$757$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	32.9908	−	38.0734i	1.19591	−	1.38016i	0.289820	−	0.957081i	$-0.406404\pi$
$761$	32.9908	−	38.0734i	1.19591	−	1.38016i	0.906094	−	0.423077i	$-0.139050\pi$
$762$	27.0568	−	17.3884i	0.980165	−	0.629914i
$763$	−12.5667	−	87.4036i	−0.454947	−	3.16422i
$764$		0			0
$765$		0			0
$766$	7.86400	+	26.7823i	0.284138	+	0.967685i
$767$		0			0
$768$	9.72920	−	21.3040i	0.351072	−	0.768741i
$769$	1.75240	−	5.96813i	0.0631932	−	0.215216i	−0.921843	−	0.387563i	$-0.873317\pi$
$769$	1.75240	−	5.96813i	0.0631932	−	0.215216i	0.985036	+	0.172347i	$0.0551351\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$773$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$774$	−8.55348	+	13.3095i	−0.307449	+	0.478399i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−3.30692	+	0.475464i	−0.118559	+	0.0170462i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	60.0117			2.14464
$784$	28.5217	−	32.9157i	1.01863	−	1.17556i
$785$		0			0
$786$		0			0
$787$	−50.7378	+	23.1712i	−1.80861	+	0.825964i	−0.859410	+	0.511286i	$0.829169\pi$
$787$	−50.7378	+	23.1712i	−1.80861	+	0.825964i	−0.949199	+	0.314678i	$0.898104\pi$
$788$		0			0
$789$	−4.67970	−	15.9376i	−0.166602	−	0.567394i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$797$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$798$		0			0
$799$		0			0
$800$	−11.7497	−	25.7283i	−0.415415	−	0.909632i
$801$	−13.7894	+	1.98262i	−0.487224	+	0.0700523i
$802$	−30.4526	−	47.3852i	−1.07532	−	1.67323i
$803$		0			0
$804$			32.2255i			1.13650i
$805$	−6.68738	+	44.8603i	−0.235699	+	1.58112i
$806$		0			0
$807$	−30.9419	+	35.7088i	−1.08921	+	1.25701i
$808$	24.5245	−	15.7610i	0.862771	−	0.554469i
$809$	3.10861	+	21.6209i	0.109293	+	0.760150i	0.968588	+	0.248670i	$0.0799935\pi$
$809$	3.10861	+	21.6209i	0.109293	+	0.760150i	−0.859295	+	0.511480i	$0.829097\pi$
$810$	−16.3756	+	7.47848i	−0.575380	+	0.262767i
$811$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$811$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$812$	−25.3294	−	86.2640i	−0.888887	−	3.02727i
$813$		0			0
$814$		0			0
$815$	−14.9442	+	50.8954i	−0.523473	+	1.78279i
$816$		0			0
$817$		0			0
$818$	51.9346	+	15.2494i	1.81585	+	0.533182i
$819$		0			0
$820$	24.7922	−	38.5775i	0.865783	−	1.34718i
$821$	−8.19029	+	2.40489i	−0.285843	+	0.0839311i	−0.421511	−	0.906823i	$-0.638500\pi$
$821$	−8.19029	+	2.40489i	−0.285843	+	0.0839311i	0.135668	+	0.990754i	$0.456682\pi$
$822$		0			0
$823$	23.8343	+	52.1899i	0.830813	+	1.81923i	0.421238	+	0.906950i	$0.361596\pi$
$823$	23.8343	+	52.1899i	0.830813	+	1.81923i	0.409575	+	0.912277i	$0.365677\pi$
$824$	−50.8023	+	7.30426i	−1.76978	+	0.254456i
$825$		0			0
$826$		0			0
$827$			47.4342i			1.64945i	0.565536	+	0.824724i	$0.308669\pi$
$827$			47.4342i			1.64945i	−0.565536	+	0.824724i	$0.691331\pi$
$828$	3.37735	+	7.49794i	0.117371	+	0.260571i
$829$	−57.5114			−1.99746			−0.998728	−	0.0504313i	$-0.983940\pi$
$829$	−57.5114			−1.99746			−0.998728	+	0.0504313i	$0.983940\pi$
$830$	−0.889567	+	1.02661i	−0.0308773	+	0.0356343i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−8.07106	−	27.4875i	−0.279311	−	0.951244i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$839$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$840$	25.6413	+	29.5916i	0.884709	+	1.02101i
$841$	−80.5636	−	23.6556i	−2.77805	−	0.815710i
$842$	−52.5792	−	24.0121i	−1.81200	−	0.827512i
$843$	5.87416	−	9.14037i	0.202317	−	0.314811i
$844$		0			0
$845$	28.7730	+	4.13693i	0.989821	+	0.142315i
$846$	2.27521	+	4.98201i	0.0782233	+	0.171285i
$847$	46.0507	−	6.62108i	1.58232	−	0.227503i
$848$		0			0
$849$	36.2837	+	31.4400i	1.24525	+	1.07902i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$853$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$854$	−49.4527	+	31.7813i	−1.69224	+	1.08753i
$855$		0			0
$856$	32.8869	−	15.0190i	1.12405	−	0.513337i
$857$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$857$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$858$		0			0
$859$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$859$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$860$	−24.2412	+	53.0809i	−0.826619	+	1.81004i
$861$	−17.8851	+	60.9109i	−0.609521	+	2.07584i
$862$		0			0
$863$	−34.6823	−	40.0255i	−1.18060	−	1.36248i	−0.917511	−	0.397711i	$-0.869805\pi$
$863$	−34.6823	−	40.0255i	−1.18060	−	1.36248i	−0.263088	−	0.964772i	$-0.584741\pi$
$864$	30.6465	+	8.99864i	1.04262	+	0.306140i
$865$		0			0
$866$		0			0
$867$	23.8762	−	7.01069i	0.810879	−	0.238096i
$868$		0			0
$869$		0			0
$870$	48.6971	−	7.00159i	1.65099	−	0.237376i
$871$		0			0
$872$	−44.6282	−	38.6705i	−1.51130	−	1.30955i
$873$		0			0
$874$		0			0
$875$	47.2869			1.59859
$876$		0			0
$877$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$877$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	15.6069	+	53.1524i	0.525811	+	1.79075i	0.607771	+	0.794113i	$0.292064\pi$
$881$	15.6069	+	53.1524i	0.525811	+	1.79075i	−0.0819595	+	0.996636i	$0.526118\pi$
$882$	11.1063	+	7.13758i	0.373968	+	0.240335i
$883$	−21.9537	+	48.0719i	−0.738801	+	1.61775i	0.0467162	+	0.998908i	$0.485124\pi$
$883$	−21.9537	+	48.0719i	−0.738801	+	1.61775i	−0.785517	+	0.618840i	$0.787603\pi$
$884$		0			0
$885$		0			0
$886$	3.29106	+	3.79809i	0.110565	+	0.127599i
$887$	−53.5159	−	15.7137i	−1.79689	−	0.527614i	−0.799555	−	0.600593i	$-0.794931\pi$
$887$	−53.5159	−	15.7137i	−1.79689	−	0.527614i	−0.997333	+	0.0729794i	$0.976749\pi$
$888$		0			0
$889$	35.5267	−	55.2806i	1.19153	−	1.85405i
$890$	−49.3024	+	14.4765i	−1.65262	+	0.485254i
$891$		0			0
$892$	−6.11211	−	13.3836i	−0.204648	−	0.448118i
$893$		0			0
$894$	−22.3537	−	34.7831i	−0.747621	−	1.16332i
$895$		0			0
$896$		−	47.8510i		−	1.59859i
$897$		0			0
$898$	−57.2390			−1.91009
$899$		0			0
$900$	7.21254	−	4.63522i	0.240418	−	0.154507i
$901$		0			0
$902$		0			0
$903$	11.4966	−	79.9605i	0.382582	−	2.66092i
$904$		0			0
$905$	−44.4964	−	28.5961i	−1.47911	−	0.950568i
$906$		0			0
$907$	−10.1818	+	34.6759i	−0.338080	+	1.15139i	0.598554	+	0.801083i	$0.295742\pi$
$907$	−10.1818	+	34.6759i	−0.338080	+	1.15139i	−0.936633	+	0.350311i	$0.886076\pi$
$908$	31.4812	−	27.2786i	1.04474	−	0.905273i
$909$	5.78682	+	6.67834i	0.191937	+	0.221507i
$910$		0			0
$911$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$911$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	−13.3630	−	29.2609i	−0.441767	−	0.967335i
$916$	13.8402	−	1.98992i	0.457293	−	0.0657488i
$917$		0			0
$918$		0			0
$919$		0			0			−	1.00000i	$-0.5\pi$
$919$		0			0				1.00000i	$0.5\pi$
$920$	16.2660	+	25.6011i	0.536274	+	0.844044i
$921$	20.3039			0.669035
$922$	−31.7321	+	36.6208i	−1.04504	+	1.20604i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	−0.126884	+	0.882497i	−0.00416966	+	0.0290006i
$927$	−4.38308	−	14.9274i	−0.143959	−	0.490281i
$928$	−50.5794	−	32.5054i	−1.66035	−	1.06704i
$929$	12.3765	−	27.1007i	0.406059	−	0.889145i	−0.590561	−	0.806993i	$-0.701093\pi$
$929$	12.3765	−	27.1007i	0.406059	−	0.889145i	0.996620	−	0.0821520i	$-0.0261793\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	−36.6120	−	16.7201i	−1.19798	−	0.547099i
$935$		0			0
$936$		0			0
$937$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$937$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$938$	27.3513	+	59.8910i	0.893051	+	1.95551i
$939$		0			0
$940$	10.9216	+	16.9943i	0.356223	+	0.554294i
$941$	−36.2284	−	31.3921i	−1.18101	−	1.02335i	−0.999199	−	0.0400189i	$-0.987258\pi$
$941$	−36.2284	−	31.3921i	−1.18101	−	1.02335i	−0.181812	−	0.983333i	$-0.558196\pi$
$942$		0			0
$943$	−20.6601	+	44.6259i	−0.672785	+	1.45322i
$944$		0			0
$945$	−34.9691	+	40.3565i	−1.13755	+	1.31280i
$946$		0			0
$947$	−6.68773	−	46.5142i	−0.217322	−	1.51151i	−0.747865	−	0.663851i	$-0.768921\pi$
$947$	−6.68773	−	46.5142i	−0.217322	−	1.51151i	0.530543	−	0.847658i	$-0.321988\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$953$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	25.9183	+	3.72649i	0.836510	+	0.120272i
$961$	12.8779	+	28.1986i	0.415415	+	0.909632i
$962$		0			0
$963$	5.92493	+	9.21937i	0.190928	+	0.297090i
$964$	7.53397	+	6.52822i	0.242653	+	0.210260i
$965$		0			0
$966$	−31.5906	−	27.6613i	−1.01641	−	0.889988i
$967$	61.6303			1.98190			0.990948	−	0.134244i	$-0.0428605\pi$
$967$	61.6303			1.98190			0.990948	+	0.134244i	$0.0428605\pi$
$968$	20.3745	−	23.5134i	0.654861	−	0.755750i
$969$		0			0
$970$		0			0
$971$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$971$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$972$	−2.44948	+	17.0365i	−0.0785670	+	0.546446i
$973$		0			0
$974$	51.0071	+	32.7803i	1.63437	+	1.05035i
$975$		0			0
$976$	−11.0754	+	37.7193i	−0.354514	+	1.20737i
$977$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$977$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$978$	−32.1581	−	37.1124i	−1.02830	−	1.18672i
$979$		0			0
$980$	44.2942	+	20.2285i	1.41493	+	0.646175i
$981$	9.67735	−	15.0583i	0.308974	−	0.480773i
$982$		0			0
$983$	0.0671341	+	0.00965242i	0.00214124	+	0.000307864i	0.143385	−	0.989667i	$-0.454201\pi$
$983$	0.0671341	+	0.00965242i	0.00214124	+	0.000307864i	−0.141244	+	0.989975i	$0.545110\pi$
$984$	17.6358	+	38.6169i	0.562207	+	1.23106i
$985$		0			0
$986$		0			0
$987$	−21.1350	−	18.3136i	−0.672733	−	0.582927i
$988$		0			0
$989$	17.9411	−	59.9510i	0.570495	−	1.90633i
$990$		0			0
$991$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$991$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	−0.354300	−	1.20664i	−0.0112264	−	0.0382337i
$997$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$997$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.o.a.99.2	yes	40
4.3	odd	2	inner	460.2.o.a.99.3	yes	40
5.4	even	2	inner	460.2.o.a.99.3	yes	40
20.19	odd	2	CM	460.2.o.a.99.2	yes	40
23.10	odd	22	inner	460.2.o.a.79.2	✓	40
92.79	even	22	inner	460.2.o.a.79.3	yes	40
115.79	odd	22	inner	460.2.o.a.79.3	yes	40
460.79	even	22	inner	460.2.o.a.79.2	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.o.a.79.2	✓	40	23.10	odd	22	inner
460.2.o.a.79.2	✓	40	460.79	even	22	inner
460.2.o.a.79.3	yes	40	92.79	even	22	inner
460.2.o.a.79.3	yes	40	115.79	odd	22	inner
460.2.o.a.99.2	yes	40	1.1	even	1	trivial
460.2.o.a.99.2	yes	40	20.19	odd	2	CM
460.2.o.a.99.3	yes	40	4.3	odd	2	inner
460.2.o.a.99.3	yes	40	5.4	even	2	inner

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.o (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.926113 + 1.06879i) q^{2} +(1.23141 - 0.791378i) q^{3} +(-0.284630 - 1.97964i) q^{4} +(2.03400 - 0.928896i) q^{5} +(-0.294605 + 2.04902i) q^{6} +(1.19158 + 4.05815i) q^{7} +(2.37942 + 1.52916i) q^{8} +(-0.356159 + 0.779879i) q^{9} +O(q^{10})\)	\(q+(-0.926113 + 1.06879i) q^{2} +(1.23141 - 0.791378i) q^{3} +(-0.284630 - 1.97964i) q^{4} +(2.03400 - 0.928896i) q^{5} +(-0.294605 + 2.04902i) q^{6} +(1.19158 + 4.05815i) q^{7} +(2.37942 + 1.52916i) q^{8} +(-0.356159 + 0.779879i) q^{9} +(-0.890917 + 3.03418i) q^{10} +(-1.91714 - 2.21250i) q^{12} +(-5.44085 - 2.48475i) q^{14} +(1.76957 - 2.75351i) q^{15} +(-3.83797 + 1.12693i) q^{16} +(-0.503685 - 1.10292i) q^{18} +(-2.41782 - 3.76220i) q^{20} +(4.67885 + 4.05425i) q^{21} +(3.12178 + 3.64067i) q^{23} +4.14019 q^{24} +(3.27430 - 3.77875i) q^{25} +(0.803554 + 5.58884i) q^{27} +(7.69453 - 3.51397i) q^{28} +(1.51259 - 10.5203i) q^{29} +(1.30410 + 4.44137i) q^{30} +(2.34994 - 5.14566i) q^{32} +(6.19327 + 7.14742i) q^{35} +(1.64526 + 0.483091i) q^{36} +(6.26018 + 0.900078i) q^{40} +(4.25965 + 9.32734i) q^{41} +(-8.66629 + 1.24602i) q^{42} +(-7.05450 - 10.9770i) q^{43} +1.91711i q^{45} +(-6.78224 - 0.0351445i) q^{46} -4.51713 q^{47} +(-3.83428 + 4.42500i) q^{48} +(-9.15994 + 5.88674i) q^{49} +(1.00632 + 6.99909i) q^{50} +(-6.71748 - 4.31706i) q^{54} +(-3.37030 + 11.4782i) q^{56} +(9.84318 + 11.3596i) q^{58} +(-5.95464 - 2.71939i) q^{60} +(5.31338 - 8.26778i) q^{61} +(-3.58926 - 0.516057i) q^{63} +(3.32332 + 7.27706i) q^{64} +(-8.31902 - 7.20847i) q^{67} +(6.72533 + 2.01265i) q^{69} -13.3748 q^{70} +(-2.04002 + 1.31104i) q^{72} +(1.04159 - 7.24439i) q^{75} +(-6.75963 + 5.85725i) q^{80} +(3.72804 + 4.30238i) q^{81} +(-13.9139 - 4.08549i) q^{82} +(0.390747 + 0.178448i) q^{83} +(6.69422 - 10.4164i) q^{84} +(18.2654 + 2.62617i) q^{86} +(-6.46292 - 14.1518i) q^{87} +(8.78487 + 13.6695i) q^{89} +(-2.04899 - 1.77546i) q^{90} +(6.31868 - 7.21625i) q^{92} +(4.18337 - 4.82787i) q^{94} +(-1.17842 - 8.19609i) q^{96} +(2.19145 - 15.2418i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{4} - 8 q^{6} + 4 q^{9}+O(q^{10}) \) 40 * q - 8 * q^4 - 8 * q^6 + 4 * q^9	\( 40 q - 8 q^{4} - 8 q^{6} + 4 q^{9} - 16 q^{16} - 16 q^{24} + 20 q^{25} + 24 q^{29} + 8 q^{36} + 48 q^{41} - 4 q^{46} + 100 q^{49} - 276 q^{54} - 264 q^{56} - 32 q^{64} - 4 q^{69} - 40 q^{70} + 20 q^{81} + 352 q^{84} + 396 q^{86} - 56 q^{94} - 32 q^{96}+O(q^{100}) \) 40 * q - 8 * q^4 - 8 * q^6 + 4 * q^9 - 16 * q^16 - 16 * q^24 + 20 * q^25 + 24 * q^29 + 8 * q^36 + 48 * q^41 - 4 * q^46 + 100 * q^49 - 276 * q^54 - 264 * q^56 - 32 * q^64 - 4 * q^69 - 40 * q^70 + 20 * q^81 + 352 * q^84 + 396 * q^86 - 56 * q^94 - 32 * q^96

Introduction

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