LMFDB - Embedded newform 825.2.bx.e.724.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(49,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 4]))

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

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

chi := DirichletCharacter("825.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.bx (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{60})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + x^{14} - x^{10} - x^{8} - x^{6} + x^{2} + 1 $ x^16 + x^14 - x^10 - x^8 - x^6 + x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			724.1
Root			$-0.406737 + 0.913545i$ of defining polynomial
Character	$\chi$	$=$	825.724
Dual form			825.2.bx.e.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.73767 - 0.564602i) q^{2} +(0.587785 + 0.809017i) q^{3} +(1.08268 + 0.786610i) q^{4} +(-0.564602 - 1.73767i) q^{6} +(-1.02700 + 1.41355i) q^{7} +(0.710666 + 0.978148i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-1.73767 - 0.564602i) q^{2} +(0.587785 + 0.809017i) q^{3} +(1.08268 + 0.786610i) q^{4} +(-0.564602 - 1.73767i) q^{6} +(-1.02700 + 1.41355i) q^{7} +(0.710666 + 0.978148i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(-0.384301 - 3.29428i) q^{11} +1.33826i q^{12} +(-5.09549 - 1.65563i) q^{13} +(2.58268 - 1.87642i) q^{14} +(-1.50973 - 4.64646i) q^{16} +(6.97191 - 2.26531i) q^{17} +(1.07394 - 1.47815i) q^{18} +(4.86606 - 3.53540i) q^{19} -1.74724 q^{21} +(-1.19217 + 5.94135i) q^{22} +8.35772i q^{23} +(-0.373619 + 1.14988i) q^{24} +(7.91949 + 5.75385i) q^{26} +(-0.951057 + 0.309017i) q^{27} +(-2.22382 + 0.722562i) q^{28} +(4.48048 + 3.25526i) q^{29} +(-0.00660190 + 0.0203186i) q^{31} +6.50828i q^{32} +(2.43925 - 2.24724i) q^{33} -13.3939 q^{34} +(-1.08268 + 0.786610i) q^{36} +(0.659288 - 0.907432i) q^{37} +(-10.4517 + 3.39596i) q^{38} +(-1.65563 - 5.09549i) q^{39} +(2.96086 - 2.15119i) q^{41} +(3.03612 + 0.986494i) q^{42} -1.96950i q^{43} +(2.17524 - 3.86894i) q^{44} +(4.71878 - 14.5229i) q^{46} +(2.24507 + 3.09007i) q^{47} +(2.87167 - 3.95252i) q^{48} +(1.21974 + 3.75397i) q^{49} +(5.93066 + 4.30888i) q^{51} +(-4.21443 - 5.80067i) q^{52} +(1.58910 + 0.516329i) q^{53} +1.82709 q^{54} -2.11251 q^{56} +(5.72040 + 1.85867i) q^{57} +(-5.94766 - 8.18625i) q^{58} +(4.58172 + 3.32882i) q^{59} +(2.86761 + 8.82559i) q^{61} +(0.0229438 - 0.0315794i) q^{62} +(-1.02700 - 1.41355i) q^{63} +(0.655137 - 2.01630i) q^{64} +(-5.50739 + 2.52775i) q^{66} -0.350489i q^{67} +(9.33024 + 3.03158i) q^{68} +(-6.76153 + 4.91254i) q^{69} +(1.40238 + 4.31607i) q^{71} +(-1.14988 + 0.373619i) q^{72} +(5.95986 - 8.20305i) q^{73} +(-1.65796 + 1.20458i) q^{74} +8.04935 q^{76} +(5.05130 + 2.84001i) q^{77} +9.78903i q^{78} +(-0.792323 + 2.43852i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-6.35956 + 2.06635i) q^{82} +(15.2935 - 4.96915i) q^{83} +(-1.89169 - 1.37440i) q^{84} +(-1.11198 + 3.42233i) q^{86} +5.53818i q^{87} +(2.94919 - 2.71704i) q^{88} +14.5062 q^{89} +(7.57337 - 5.50238i) q^{91} +(-6.57426 + 9.04870i) q^{92} +(-0.0203186 + 0.00660190i) q^{93} +(-2.15652 - 6.63708i) q^{94} +(-5.26531 + 3.82547i) q^{96} +(1.80674 + 0.587045i) q^{97} -7.21182i q^{98} +(3.25181 + 0.652498i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{4} - 4 q^{6} + 4 q^{9}+O(q^{10}) $ 16 * q - 4 * q^4 - 4 * q^6 + 4 * q^9	$ 16 q - 4 q^{4} - 4 q^{6} + 4 q^{9} - 2 q^{11} + 20 q^{14} + 24 q^{16} - 4 q^{19} + 8 q^{24} + 32 q^{26} + 32 q^{29} - 10 q^{31} - 68 q^{34} + 4 q^{36} - 32 q^{39} + 10 q^{41} + 38 q^{44} + 20 q^{46} + 22 q^{49} + 8 q^{51} + 4 q^{54} + 40 q^{56} - 6 q^{59} - 22 q^{61} + 18 q^{64} - 62 q^{66} - 30 q^{69} + 2 q^{71} - 10 q^{74} + 116 q^{76} + 60 q^{79} - 4 q^{81} - 124 q^{86} + 96 q^{89} + 10 q^{91} + 38 q^{94} - 40 q^{96} + 22 q^{99}+O(q^{100}) $ 16 * q - 4 * q^4 - 4 * q^6 + 4 * q^9 - 2 * q^11 + 20 * q^14 + 24 * q^16 - 4 * q^19 + 8 * q^24 + 32 * q^26 + 32 * q^29 - 10 * q^31 - 68 * q^34 + 4 * q^36 - 32 * q^39 + 10 * q^41 + 38 * q^44 + 20 * q^46 + 22 * q^49 + 8 * q^51 + 4 * q^54 + 40 * q^56 - 6 * q^59 - 22 * q^61 + 18 * q^64 - 62 * q^66 - 30 * q^69 + 2 * q^71 - 10 * q^74 + 116 * q^76 + 60 * q^79 - 4 * q^81 - 124 * q^86 + 96 * q^89 + 10 * q^91 + 38 * q^94 - 40 * q^96 + 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.73767	−	0.564602i	−1.22872	−	0.399234i	−0.378467	−	0.925615i	$-0.623549\pi$
$2$	−1.73767	−	0.564602i	−1.22872	−	0.399234i	−0.850249	+	0.526381i	$0.823549\pi$
$3$	0.587785	+	0.809017i	0.339358	+	0.467086i
$3$	0.587785	+	0.809017i	0.339358	+	0.467086i
$4$	1.08268	+	0.786610i	0.541338	+	0.393305i
$5$		0			0
$5$		0			0
$6$	−0.564602	−	1.73767i	−0.230498	−	0.709399i
$7$	−1.02700	+	1.41355i	−0.388170	+	0.534270i	−0.957726	−	0.287683i	$-0.907115\pi$
$7$	−1.02700	+	1.41355i	−0.388170	+	0.534270i	0.569556	+	0.821953i	$0.307115\pi$
$8$	0.710666	+	0.978148i	0.251258	+	0.345827i
$9$	−0.309017	+	0.951057i	−0.103006	+	0.317019i
$10$		0			0
$11$	−0.384301	−	3.29428i	−0.115871	−	0.993264i
$11$	−0.384301	−	3.29428i	−0.115871	−	0.993264i
$12$			1.33826i			0.386323i
$13$	−5.09549	−	1.65563i	−1.41323	−	0.459188i	−0.499789	−	0.866147i	$-0.666589\pi$
$13$	−5.09549	−	1.65563i	−1.41323	−	0.459188i	−0.913446	+	0.406960i	$0.866589\pi$
$14$	2.58268	−	1.87642i	0.690249	−	0.501495i
$15$		0			0
$16$	−1.50973	−	4.64646i	−0.377432	−	1.16162i
$17$	6.97191	−	2.26531i	1.69094	−	0.549419i	0.703955	−	0.710245i	$-0.251416\pi$
$17$	6.97191	−	2.26531i	1.69094	−	0.549419i	0.986983	+	0.160826i	$0.0514158\pi$
$18$	1.07394	−	1.47815i	0.253129	−	0.348403i
$19$	4.86606	−	3.53540i	1.11635	−	0.811077i	0.132699	−	0.991156i	$-0.457636\pi$
$19$	4.86606	−	3.53540i	1.11635	−	0.811077i	0.983652	+	0.180080i	$0.0576356\pi$
$20$		0			0
$21$	−1.74724			−0.381279
$22$	−1.19217	+	5.94135i	−0.254172	+	1.26670i
$23$			8.35772i			1.74270i	0.490658	+	0.871352i	$0.336756\pi$
$23$			8.35772i			1.74270i	−0.490658	+	0.871352i	$0.663244\pi$
$24$	−0.373619	+	1.14988i	−0.0762647	+	0.234719i
$25$		0			0
$26$	7.91949	+	5.75385i	1.55314	+	1.12842i
$27$	−0.951057	+	0.309017i	−0.183031	+	0.0594703i
$28$	−2.22382	+	0.722562i	−0.420262	+	0.136551i
$29$	4.48048	+	3.25526i	0.832005	+	0.604487i	0.920126	−	0.391623i	$-0.128086\pi$
$29$	4.48048	+	3.25526i	0.832005	+	0.604487i	−0.0881210	+	0.996110i	$0.528086\pi$
$30$		0			0
$31$	−0.00660190	+	0.0203186i	−0.00118574	+	0.00364932i	−0.951648	−	0.307192i	$-0.900611\pi$
$31$	−0.00660190	+	0.0203186i	−0.00118574	+	0.00364932i	0.950462	+	0.310841i	$0.100611\pi$
$32$			6.50828i			1.15051i
$33$	2.43925	−	2.24724i	0.424618	−	0.391194i
$34$	−13.3939			−2.29703
$35$		0			0
$36$	−1.08268	+	0.786610i	−0.180446	+	0.131102i
$37$	0.659288	−	0.907432i	0.108386	−	0.149181i	−0.751378	−	0.659872i	$-0.770610\pi$
$37$	0.659288	−	0.907432i	0.108386	−	0.149181i	0.859764	+	0.510691i	$0.170610\pi$
$38$	−10.4517	+	3.39596i	−1.69549	+	0.550897i
$39$	−1.65563	−	5.09549i	−0.265112	−	0.815931i
$40$		0			0
$41$	2.96086	−	2.15119i	0.462409	−	0.335960i	−0.332066	−	0.943256i	$-0.607746\pi$
$41$	2.96086	−	2.15119i	0.462409	−	0.335960i	0.794476	+	0.607296i	$0.207746\pi$
$42$	3.03612	+	0.986494i	0.468483	+	0.152219i
$43$		−	1.96950i		−	0.300346i	−0.988660	−	0.150173i	$-0.952017\pi$
$43$		−	1.96950i		−	0.300346i	0.988660	−	0.150173i	$-0.0479830\pi$
$44$	2.17524	−	3.86894i	0.327930	−	0.583264i
$45$		0			0
$46$	4.71878	−	14.5229i	0.695747	−	2.14129i
$47$	2.24507	+	3.09007i	0.327476	+	0.450733i	0.940731	−	0.339152i	$-0.110140\pi$
$47$	2.24507	+	3.09007i	0.327476	+	0.450733i	−0.613255	+	0.789885i	$0.710140\pi$
$48$	2.87167	−	3.95252i	0.414490	−	0.570497i
$49$	1.21974	+	3.75397i	0.174248	+	0.536282i
$50$		0			0
$51$	5.93066	+	4.30888i	0.830459	+	0.603364i
$52$	−4.21443	−	5.80067i	−0.584437	−	0.804408i
$53$	1.58910	+	0.516329i	0.218279	+	0.0709232i	0.416115	−	0.909312i	$-0.363391\pi$
$53$	1.58910	+	0.516329i	0.218279	+	0.0709232i	−0.197836	+	0.980235i	$0.563391\pi$
$54$	1.82709			0.248636
$55$		0			0
$56$	−2.11251			−0.282296
$57$	5.72040	+	1.85867i	0.757685	+	0.246187i
$58$	−5.94766	−	8.18625i	−0.780966	−	1.07491i
$59$	4.58172	+	3.32882i	0.596489	+	0.433375i	0.844631	−	0.535349i	$-0.179820\pi$
$59$	4.58172	+	3.32882i	0.596489	+	0.433375i	−0.248142	+	0.968724i	$0.579820\pi$
$60$		0			0
$61$	2.86761	+	8.82559i	0.367160	+	1.13000i	0.948618	+	0.316425i	$0.102482\pi$
$61$	2.86761	+	8.82559i	0.367160	+	1.13000i	−0.581458	+	0.813576i	$0.697518\pi$
$62$	0.0229438	−	0.0315794i	0.00291387	−	0.00401059i
$63$	−1.02700	−	1.41355i	−0.129390	−	0.178090i
$64$	0.655137	−	2.01630i	0.0818921	−	0.252038i
$65$		0			0
$66$	−5.50739	+	2.52775i	−0.677913	+	0.311144i
$67$		−	0.350489i		−	0.0428190i	−0.999771	−	0.0214095i	$-0.993185\pi$
$67$		−	0.350489i		−	0.0428190i	0.999771	−	0.0214095i	$-0.00681538\pi$
$68$	9.33024	+	3.03158i	1.13146	+	0.367633i
$69$	−6.76153	+	4.91254i	−0.813993	+	0.591401i
$70$		0			0
$71$	1.40238	+	4.31607i	0.166431	+	0.512223i	0.999139	−	0.0414901i	$-0.0132105\pi$
$71$	1.40238	+	4.31607i	0.166431	+	0.512223i	−0.832708	+	0.553713i	$0.813210\pi$
$72$	−1.14988	+	0.373619i	−0.135515	+	0.0440314i
$73$	5.95986	−	8.20305i	0.697549	−	0.960094i	−0.302427	−	0.953173i	$-0.597797\pi$
$73$	5.95986	−	8.20305i	0.697549	−	0.960094i	0.999976	−	0.00692130i	$-0.00220313\pi$
$74$	−1.65796	+	1.20458i	−0.192734	+	0.140029i
$75$		0			0
$76$	8.04935			0.923324
$77$	5.05130	+	2.84001i	0.575649	+	0.323649i
$78$			9.78903i			1.10839i
$79$	−0.792323	+	2.43852i	−0.0891433	+	0.274355i	−0.985683	−	0.168608i	$-0.946073\pi$
$79$	−0.792323	+	2.43852i	−0.0891433	+	0.274355i	0.896540	+	0.442963i	$0.146073\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−6.35956	+	2.06635i	−0.702296	+	0.228190i
$83$	15.2935	−	4.96915i	1.67868	−	0.545435i	0.694022	−	0.719954i	$-0.255837\pi$
$83$	15.2935	−	4.96915i	1.67868	−	0.545435i	0.984654	+	0.174519i	$0.0558371\pi$
$84$	−1.89169	−	1.37440i	−0.206401	−	0.149959i
$85$		0			0
$86$	−1.11198	+	3.42233i	−0.119908	+	0.369040i
$87$			5.53818i			0.593755i
$88$	2.94919	−	2.71704i	0.314384	−	0.289637i
$89$	14.5062			1.53765			0.768825	−	0.639459i	$-0.220841\pi$
$89$	14.5062			1.53765			0.768825	+	0.639459i	$0.220841\pi$
$90$		0			0
$91$	7.57337	−	5.50238i	0.793905	−	0.576806i
$92$	−6.57426	+	9.04870i	−0.685414	+	0.943392i
$93$	−0.0203186	+	0.00660190i	−0.00210694	+	0.000684585i
$94$	−2.15652	−	6.63708i	−0.222428	−	0.684562i
$95$		0			0
$96$	−5.26531	+	3.82547i	−0.537389	+	0.390436i
$97$	1.80674	+	0.587045i	0.183446	+	0.0596054i	0.399300	−	0.916820i	$-0.369253\pi$
$97$	1.80674	+	0.587045i	0.183446	+	0.0596054i	−0.215853	+	0.976426i	$0.569253\pi$
$98$		−	7.21182i		−	0.728504i
$99$	3.25181	+	0.652498i	0.326819	+	0.0655785i
$100$		0			0
$101$	2.07354	−	6.38170i	0.206325	−	0.635003i	−0.793332	−	0.608790i	$-0.791655\pi$
$101$	2.07354	−	6.38170i	0.206325	−	0.635003i	0.999656	−	0.0262128i	$-0.00834474\pi$
$102$	−7.87272	−	10.8359i	−0.779515	−	1.07291i
$103$	−2.49620	+	3.43572i	−0.245958	+	0.338532i	−0.914090	−	0.405510i	$-0.867094\pi$
$103$	−2.49620	+	3.43572i	−0.245958	+	0.338532i	0.668133	+	0.744042i	$0.267094\pi$
$104$	−2.00174	−	6.16074i	−0.196287	−	0.604110i
$105$		0			0
$106$	−2.46980	−	1.79442i	−0.239888	−	0.174289i
$107$	−9.24174	−	12.7202i	−0.893433	−	1.22970i	−0.972516	−	0.232837i	$-0.925199\pi$
$107$	−9.24174	−	12.7202i	−0.893433	−	1.22970i	0.0790831	−	0.996868i	$-0.474801\pi$
$108$	−1.27276	−	0.413545i	−0.122472	−	0.0397934i
$109$	−4.23895			−0.406018			−0.203009	−	0.979177i	$-0.565072\pi$
$109$	−4.23895			−0.406018			−0.203009	+	0.979177i	$0.565072\pi$
$110$		0			0
$111$	1.12165			0.106462
$112$	8.11848	+	2.63785i	0.767124	+	0.249254i
$113$	4.22996	+	5.82203i	0.397921	+	0.547691i	0.960221	−	0.279242i	$-0.0900833\pi$
$113$	4.22996	+	5.82203i	0.397921	+	0.547691i	−0.562300	+	0.826933i	$0.690083\pi$
$114$	−8.89074	−	6.45950i	−0.832694	−	0.604988i
$115$		0			0
$116$	2.29029	+	7.04879i	0.212648	+	0.654463i
$117$	3.14919	−	4.33448i	0.291142	−	0.400723i
$118$	−6.08205	−	8.37122i	−0.559898	−	0.770633i
$119$	−3.95804	+	12.1816i	−0.362833	+	1.11668i
$120$		0			0
$121$	−10.7046	+	2.53200i	−0.973148	+	0.230181i
$122$		−	16.9550i		−	1.53503i
$123$	3.48070	+	1.13095i	0.313845	+	0.101974i
$124$	−0.0231305	+	0.0168053i	−0.00207718	+	0.00150916i
$125$		0			0
$126$	0.986494	+	3.03612i	0.0878839	+	0.270479i
$127$	12.0661	−	3.92051i	1.07069	−	0.347889i	0.279935	−	0.960019i	$-0.409687\pi$
$127$	12.0661	−	3.92051i	1.07069	−	0.347889i	0.790757	+	0.612130i	$0.209687\pi$
$128$	5.37413	−	7.39685i	0.475010	−	0.653796i
$129$	1.59336	−	1.15764i	0.140287	−	0.101925i
$130$		0			0
$131$	−0.970102			−0.0847582			−0.0423791	−	0.999102i	$-0.513494\pi$
$131$	−0.970102			−0.0847582			−0.0423791	+	0.999102i	$0.513494\pi$
$132$	4.40861	−	0.514295i	0.383721	−	0.0447637i
$133$			10.5093i			0.911268i
$134$	−0.197887	+	0.609032i	−0.0170948	+	0.0526124i
$135$		0			0
$136$	7.17051	+	5.20968i	0.614866	+	0.446726i
$137$	4.01379	−	1.30416i	0.342921	−	0.111422i	−0.132493	−	0.991184i	$-0.542298\pi$
$137$	4.01379	−	1.30416i	0.342921	−	0.111422i	0.475414	+	0.879762i	$0.342298\pi$
$138$	14.5229	−	4.71878i	1.23627	−	0.401690i
$139$	7.15855	+	5.20099i	0.607180	+	0.441142i	0.848420	−	0.529323i	$-0.177554\pi$
$139$	7.15855	+	5.20099i	0.607180	+	0.441142i	−0.241240	+	0.970465i	$0.577554\pi$
$140$		0			0
$141$	−1.18030	+	3.63259i	−0.0993993	+	0.305919i
$142$		−	8.29167i		−	0.695821i
$143$	−3.49590	+	17.4223i	−0.292342	+	1.45692i
$144$	4.88558			0.407132
$145$		0			0
$146$	−14.9877	+	10.8892i	−1.24039	+	0.901197i
$147$	−2.32008	+	3.19332i	−0.191357	+	0.263380i
$148$	1.42759	−	0.463852i	0.117347	−	0.0381284i
$149$	−2.95222	−	9.08598i	−0.241855	−	0.744353i	−0.996138	−	0.0878033i	$-0.972015\pi$
$149$	−2.95222	−	9.08598i	−0.241855	−	0.744353i	0.754283	−	0.656549i	$-0.227985\pi$
$150$		0			0
$151$	5.46214	−	3.96848i	0.444503	−	0.322950i	−0.342919	−	0.939365i	$-0.611416\pi$
$151$	5.46214	−	3.96848i	0.444503	−	0.322950i	0.787422	+	0.616415i	$0.211416\pi$
$152$	6.91629	+	2.24724i	0.560985	+	0.182275i
$153$			7.33070i			0.592652i
$154$	−7.17400	−	7.78696i	−0.578097	−	0.627491i
$155$		0			0
$156$	2.21566	−	6.81910i	0.177395	−	0.545965i
$157$	−7.44162	−	10.2425i	−0.593906	−	0.817441i	0.401228	−	0.915978i	$-0.368584\pi$
$157$	−7.44162	−	10.2425i	−0.593906	−	0.817441i	−0.995133	+	0.0985374i	$0.968584\pi$
$158$	2.75359	−	3.78999i	0.219064	−	0.301515i
$159$	0.516329	+	1.58910i	0.0409475	+	0.126024i
$160$		0			0
$161$	−11.8140	−	8.58338i	−0.931074	−	0.676465i
$162$	1.07394	+	1.47815i	0.0843765	+	0.116134i
$163$	−22.2602	−	7.23278i	−1.74355	−	0.566515i	−0.748259	−	0.663407i	$-0.769110\pi$
$163$	−22.2602	−	7.23278i	−1.74355	−	0.566515i	−0.995295	+	0.0968923i	$0.969110\pi$
$164$	4.89781			0.382454
$165$		0			0
$166$	−29.3805			−2.28037
$167$	−2.90254	−	0.943091i	−0.224605	−	0.0729786i	0.194553	−	0.980892i	$-0.437675\pi$
$167$	−2.90254	−	0.943091i	−0.224605	−	0.0729786i	−0.419158	+	0.907913i	$0.637675\pi$
$168$	−1.24170	−	1.70906i	−0.0957994	−	0.131857i
$169$	12.7057	+	9.23123i	0.977362	+	0.710095i
$170$		0			0
$171$	1.85867	+	5.72040i	0.142136	+	0.437450i
$172$	1.54923	−	2.13233i	0.118128	−	0.162589i
$173$	−9.40893	−	12.9503i	−0.715348	−	0.984592i	−0.999666	−	0.0258617i	$-0.991767\pi$
$173$	−9.40893	−	12.9503i	−0.715348	−	0.984592i	0.284318	−	0.958730i	$-0.408233\pi$
$174$	3.12687	−	9.62351i	0.237047	−	0.729557i
$175$		0			0
$176$	−14.7266	+	6.75911i	−1.11006	+	0.509487i
$177$			5.66332i			0.425681i
$178$	−25.2069	−	8.19021i	−1.88934	−	0.613883i
$179$	−15.6133	+	11.3437i	−1.16699	+	0.847870i	−0.990646	−	0.136458i	$-0.956428\pi$
$179$	−15.6133	+	11.3437i	−1.16699	+	0.847870i	−0.176347	+	0.984328i	$0.556428\pi$
$180$		0			0
$181$	−3.76724	−	11.5944i	−0.280017	−	0.861804i	−0.987848	−	0.155422i	$-0.950326\pi$
$181$	−3.76724	−	11.5944i	−0.280017	−	0.861804i	0.707831	−	0.706382i	$-0.249674\pi$
$182$	−16.2667	+	5.28536i	−1.20576	+	0.391777i
$183$	−5.45451	+	7.50749i	−0.403209	+	0.554970i
$184$	−8.17508	+	5.93954i	−0.602675	+	0.437869i
$185$		0			0
$186$	0.0390343			0.00286214
$187$	−10.1419	−	22.0969i	−0.741649	−	1.61589i
$188$			5.11153i			0.372797i
$189$	0.539926	−	1.66172i	0.0392739	−	0.120873i
$190$		0			0
$191$	10.8605	+	7.89064i	0.785841	+	0.570947i	0.906726	−	0.421720i	$-0.138573\pi$
$191$	10.8605	+	7.89064i	0.785841	+	0.570947i	−0.120885	+	0.992666i	$0.538573\pi$
$192$	2.01630	−	0.655137i	0.145514	−	0.0472804i
$193$	−7.20693	+	2.34167i	−0.518766	+	0.168557i	−0.556685	−	0.830723i	$-0.687927\pi$
$193$	−7.20693	+	2.34167i	−0.518766	+	0.168557i	0.0379190	+	0.999281i	$0.487927\pi$
$194$	−2.80806	−	2.04018i	−0.201607	−	0.146476i
$195$		0			0
$196$	−1.63233	+	5.02379i	−0.116595	+	0.358842i
$197$			6.89118i			0.490976i	0.969400	+	0.245488i	$0.0789483\pi$
$197$			6.89118i			0.490976i	−0.969400	+	0.245488i	$0.921052\pi$
$198$	−5.28215	−	2.96980i	−0.375386	−	0.211055i
$199$	−0.639398			−0.0453257			−0.0226629	−	0.999743i	$-0.507214\pi$
$199$	−0.639398			−0.0453257			−0.0226629	+	0.999743i	$0.507214\pi$
$200$		0			0
$201$	0.283551	−	0.206012i	0.0200002	−	0.0145310i
$202$	−7.20624	+	9.91854i	−0.507029	+	0.697866i
$203$	−9.20292	+	2.99021i	−0.645918	+	0.209872i
$204$	3.03158	+	9.33024i	0.212253	+	0.653248i
$205$		0			0
$206$	6.27737	−	4.56078i	0.437365	−	0.317765i
$207$	−7.94866	−	2.58268i	−0.552470	−	0.179508i
$208$			26.1755i			1.81495i
$209$	−13.5167	−	14.6715i	−0.934966	−	1.01485i
$210$		0			0
$211$	−1.18090	+	3.63445i	−0.0812968	+	0.250206i	−0.983441	−	0.181229i	$-0.941992\pi$
$211$	−1.18090	+	3.63445i	−0.0812968	+	0.250206i	0.902144	+	0.431435i	$0.141992\pi$
$212$	1.31433	+	1.80902i	0.0902684	+	0.124244i
$213$	−2.66748	+	3.67147i	−0.182772	+	0.251565i
$214$	8.87723	+	27.3213i	0.606835	+	1.86765i
$215$		0			0
$216$	−0.978148	−	0.710666i	−0.0665545	−	0.0483547i
$217$	−0.0219411	−	0.0301993i	−0.00148946	−	0.00205006i
$218$	7.36589	+	2.39332i	0.498881	+	0.162096i
$219$	10.1395			0.685165
$220$		0			0
$221$	−39.2758			−2.64198
$222$	−1.94905	−	0.633284i	−0.130812	−	0.0425033i
$223$	15.7057	+	21.6171i	1.05173	+	1.44758i	0.887298	+	0.461197i	$0.152580\pi$
$223$	15.7057	+	21.6171i	1.05173	+	1.44758i	0.164434	+	0.986388i	$0.447420\pi$
$224$	−9.19975	−	6.68401i	−0.614684	−	0.446594i
$225$		0			0
$226$	−4.06312	−	12.5050i	−0.270275	−	0.831820i
$227$	−7.19291	+	9.90020i	−0.477411	+	0.657099i	−0.978005	−	0.208583i	$-0.933115\pi$
$227$	−7.19291	+	9.90020i	−0.477411	+	0.657099i	0.500594	+	0.865682i	$0.333115\pi$
$228$	4.73129	+	6.51206i	0.313337	+	0.431272i
$229$	2.06628	−	6.35937i	0.136544	−	0.420239i	−0.859283	−	0.511500i	$-0.829090\pi$
$229$	2.06628	−	6.35937i	0.136544	−	0.420239i	0.995827	+	0.0912615i	$0.0290899\pi$
$230$		0			0
$231$	0.671466	+	5.75590i	0.0441792	+	0.378710i
$232$			6.69598i			0.439612i
$233$	−6.19844	−	2.01399i	−0.406073	−	0.131941i	0.0988565	−	0.995102i	$-0.468482\pi$
$233$	−6.19844	−	2.01399i	−0.406073	−	0.131941i	−0.504930	+	0.863161i	$0.668482\pi$
$234$	−7.91949	+	5.75385i	−0.517714	+	0.376141i
$235$		0			0
$236$	2.34204	+	7.20806i	0.152454	+	0.469205i
$237$	−2.43852	+	0.792323i	−0.158399	+	0.0514669i
$238$	13.7555	−	18.9328i	0.891637	−	1.22723i
$239$	−8.77126	+	6.37269i	−0.567366	+	0.412215i	−0.834147	−	0.551542i	$-0.814040\pi$
$239$	−8.77126	+	6.37269i	−0.567366	+	0.412215i	0.266782	+	0.963757i	$0.414040\pi$
$240$		0			0
$241$	27.1803			1.75084			0.875420	−	0.483363i	$-0.160585\pi$
$241$	27.1803			1.75084			0.875420	+	0.483363i	$0.160585\pi$
$242$	20.0306	+	1.64409i	1.28762	+	0.105686i
$243$		−	1.00000i		−	0.0641500i
$244$	−3.83761	+	11.8109i	−0.245678	+	0.756118i
$245$		0			0
$246$	−5.40977	−	3.93043i	−0.344914	−	0.250595i
$247$	−30.6483	+	9.95823i	−1.95010	+	0.633627i
$248$	−0.0245663	+	0.00798208i	−0.00155996	+	0.000506862i
$249$	13.0094	+	9.45188i	0.824437	+	0.598989i
$250$		0			0
$251$	1.71332	−	5.27307i	0.108144	−	0.332833i	−0.882311	−	0.470666i	$-0.844014\pi$
$251$	1.71332	−	5.27307i	0.108144	−	0.332833i	0.990455	+	0.137833i	$0.0440137\pi$
$252$		−	2.33826i		−	0.147297i
$253$	27.5327	−	3.21188i	1.73097	−	0.201929i
$254$	−23.1804			−1.45447
$255$		0			0
$256$	−16.9451	+	12.3113i	−1.05907	+	0.769457i
$257$	11.1350	−	15.3260i	0.694580	−	0.956008i	−0.305413	−	0.952220i	$-0.598794\pi$
$257$	11.1350	−	15.3260i	0.694580	−	0.956008i	0.999993	−	0.00378765i	$-0.00120565\pi$
$258$	−3.42233	+	1.11198i	−0.213065	+	0.0692291i
$259$	0.605607	+	1.86387i	0.0376306	+	0.115815i
$260$		0			0
$261$	−4.48048	+	3.25526i	−0.277335	+	0.201496i
$262$	1.68571	+	0.547722i	0.104144	+	0.0338384i
$263$			3.20873i			0.197859i	0.995094	+	0.0989293i	$0.0315418\pi$
$263$			3.20873i			0.197859i	−0.995094	+	0.0989293i	$0.968458\pi$
$264$	3.93162	+	0.788907i	0.241974	+	0.0485539i
$265$		0			0
$266$	5.93355	−	18.2616i	0.363809	−	1.11969i
$267$	8.52651	+	11.7357i	0.521814	+	0.718215i
$268$	0.275698	−	0.379466i	0.0168409	−	0.0231796i
$269$	1.00252	+	3.08544i	0.0611248	+	0.188123i	0.976956	−	0.213441i	$-0.0684669\pi$
$269$	1.00252	+	3.08544i	0.0611248	+	0.188123i	−0.915831	+	0.401563i	$0.868467\pi$
$270$		0			0
$271$	1.64212	+	1.19307i	0.0997517	+	0.0724738i	0.636543	−	0.771241i	$-0.280364\pi$
$271$	1.64212	+	1.19307i	0.0997517	+	0.0724738i	−0.536791	+	0.843715i	$0.680364\pi$
$272$	−21.0514	−	28.9747i	−1.27643	−	1.75685i
$273$	8.90304	+	2.89277i	0.538836	+	0.175078i
$274$	−7.71096			−0.465836
$275$		0			0
$276$	−11.1848			−0.673246
$277$	−10.7627	−	3.49701i	−0.646668	−	0.210115i	−0.0327234	−	0.999464i	$-0.510418\pi$
$277$	−10.7627	−	3.49701i	−0.646668	−	0.210115i	−0.613944	+	0.789349i	$0.710418\pi$
$278$	−9.50268	−	13.0793i	−0.569933	−	0.784446i
$279$	−0.0172840	−	0.0125576i	−0.00103477	−	0.000751802i
$280$		0			0
$281$	−3.18835	−	9.81272i	−0.190201	−	0.585378i	0.809798	−	0.586708i	$-0.199576\pi$
$281$	−3.18835	−	9.81272i	−0.190201	−	0.585378i	−0.999999	+	0.00133051i	$0.999576\pi$
$282$	4.10194	−	5.64583i	0.244267	−	0.336205i
$283$	1.23781	+	1.70370i	0.0735801	+	0.101274i	0.844221	−	0.535996i	$-0.180064\pi$
$283$	1.23781	+	1.70370i	0.0735801	+	0.101274i	−0.770641	+	0.637270i	$0.780064\pi$
$284$	−1.87674	+	5.77602i	−0.111364	+	0.342744i
$285$		0			0
$286$	15.9113	−	28.3003i	0.940858	−	1.67343i
$287$			6.39459i			0.377461i
$288$	−6.18975	−	2.01117i	−0.364734	−	0.118509i
$289$	29.7227	−	21.5948i	1.74839	−	1.27028i
$290$		0			0
$291$	0.587045	+	1.80674i	0.0344132	+	0.105913i
$292$	12.9052	−	4.19315i	0.755220	−	0.245386i
$293$	−13.7398	+	18.9111i	−0.802685	+	1.10480i	0.189726	+	0.981837i	$0.439240\pi$
$293$	−13.7398	+	18.9111i	−0.802685	+	1.10480i	−0.992411	+	0.122964i	$0.960760\pi$
$294$	5.83448	−	4.23900i	0.340274	−	0.247223i
$295$		0			0
$296$	1.35614			0.0788238
$297$	1.38348	+	3.01430i	0.0802778	+	0.174907i
$298$			17.4552i			1.01115i
$299$	13.8372	−	42.5867i	0.800228	−	2.46285i
$300$		0			0
$301$	2.78398	+	2.02268i	0.160466	+	0.116585i
$302$	−11.7320	+	3.81196i	−0.675100	+	0.219353i
$303$	6.38170	−	2.07354i	0.366619	−	0.119122i
$304$	−23.7735	−	17.2725i	−1.36351	−	0.990645i
$305$		0			0
$306$	4.13893	−	12.7383i	0.236607	−	0.728201i
$307$			32.0518i			1.82929i	0.404256	+	0.914646i	$0.367531\pi$
$307$			32.0518i			1.82929i	−0.404256	+	0.914646i	$0.632469\pi$
$308$	3.23494	+	7.04821i	0.184328	+	0.401609i
$309$	−4.24678			−0.241591
$310$		0			0
$311$	−1.32220	+	0.960634i	−0.0749751	+	0.0544726i	−0.624641	−	0.780912i	$-0.714755\pi$
$311$	−1.32220	+	0.960634i	−0.0749751	+	0.0544726i	0.549666	+	0.835384i	$0.314755\pi$
$312$	3.80755	−	5.24064i	0.215560	−	0.296693i
$313$	−28.9245	+	9.39813i	−1.63491	+	0.531214i	−0.975392	−	0.220477i	$-0.929239\pi$
$313$	−28.9245	+	9.39813i	−1.63491	+	0.531214i	−0.659516	+	0.751691i	$0.729239\pi$
$314$	7.14811	+	21.9996i	0.403391	+	1.24151i
$315$		0			0
$316$	−2.77599	+	2.01688i	−0.156162	+	0.113458i
$317$	27.9934	+	9.09561i	1.57227	+	0.510861i	0.960050	−	0.279829i	$-0.0902778\pi$
$317$	27.9934	+	9.09561i	1.57227	+	0.510861i	0.612217	+	0.790690i	$0.290278\pi$
$318$		−	3.05284i		−	0.171195i
$319$	9.00190	−	16.0110i	0.504010	−	0.896443i
$320$		0			0
$321$	4.85867	−	14.9534i	0.271185	−	0.834620i
$322$	15.6826	+	21.5853i	0.873958	+	1.20290i
$323$	25.9170	−	35.6717i	1.44206	−	1.98482i
$324$	−0.413545	−	1.27276i	−0.0229747	−	0.0707090i
$325$		0			0
$326$	34.5972	+	25.1363i	1.91616	+	1.39217i
$327$	−2.49159	−	3.42939i	−0.137786	−	0.189645i
$328$	4.20837	+	1.36738i	0.232368	+	0.0755010i
$329$	−6.67364			−0.367929
$330$		0			0
$331$	−22.7902			−1.25266			−0.626332	−	0.779557i	$-0.715444\pi$
$331$	−22.7902			−1.25266			−0.626332	+	0.779557i	$0.715444\pi$
$332$	20.4666	+	6.65002i	1.12325	+	0.364967i
$333$	0.659288	+	0.907432i	0.0361287	+	0.0497270i
$334$	4.51117	+	3.27756i	0.246840	+	0.179340i
$335$		0			0
$336$	2.63785	+	8.11848i	0.143907	+	0.442899i
$337$	8.51705	−	11.7227i	0.463954	−	0.638577i	−0.511369	−	0.859361i	$-0.670862\pi$
$337$	8.51705	−	11.7227i	0.463954	−	0.638577i	0.975323	+	0.220784i	$0.0708615\pi$
$338$	−16.8663	−	23.2145i	−0.917406	−	1.26270i
$339$	−2.22382	+	6.84421i	−0.120781	+	0.371727i
$340$		0			0
$341$	0.0694723	+	0.0139401i	0.00376213	+	0.000754899i
$342$		−	10.9896i		−	0.594247i
$343$	−18.1911	−	5.91066i	−0.982229	−	0.319146i
$344$	1.92646	−	1.39966i	0.103868	−	0.0754644i
$345$		0			0
$346$	9.03783	+	27.8156i	0.485877	+	1.49537i
$347$	4.17255	−	1.35574i	0.223994	−	0.0727802i	−0.194870	−	0.980829i	$-0.562428\pi$
$347$	4.17255	−	1.35574i	0.223994	−	0.0727802i	0.418864	+	0.908049i	$0.362428\pi$
$348$	−4.35639	+	5.99606i	−0.233527	+	0.321422i
$349$	11.6548	−	8.46769i	0.623866	−	0.453265i	−0.230404	−	0.973095i	$-0.574005\pi$
$349$	11.6548	−	8.46769i	0.623866	−	0.453265i	0.854270	+	0.519830i	$0.174005\pi$
$350$		0			0
$351$	5.35772			0.285974
$352$	21.4401	−	2.50114i	1.14276	−	0.133311i
$353$		−	6.01065i		−	0.319914i	−0.987124	−	0.159957i	$-0.948864\pi$
$353$		−	6.01065i		−	0.319914i	0.987124	−	0.159957i	$-0.0511356\pi$
$354$	3.19752	−	9.84096i	0.169946	−	0.523041i
$355$		0			0
$356$	15.7055	+	11.4107i	0.832389	+	0.604766i
$357$	−12.1816	+	3.95804i	−0.644718	+	0.209482i
$358$	33.5354	−	10.8963i	1.77240	−	0.575888i
$359$	−1.98787	−	1.44428i	−0.104916	−	0.0762259i	0.534090	−	0.845427i	$-0.320654\pi$
$359$	−1.98787	−	1.44428i	−0.104916	−	0.0762259i	−0.639006	+	0.769201i	$0.720654\pi$
$360$		0			0
$361$	5.30818	−	16.3369i	0.279378	−	0.859836i
$362$			22.2742i			1.17070i
$363$	−8.34045	−	7.17195i	−0.437760	−	0.376430i
$364$	12.5277			0.656632
$365$		0			0
$366$	13.7169	−	9.96589i	0.716992	−	0.520926i
$367$	−0.869862	+	1.19726i	−0.0454064	+	0.0624966i	−0.831116	−	0.556098i	$-0.812298\pi$
$367$	−0.869862	+	1.19726i	−0.0454064	+	0.0624966i	0.785710	+	0.618595i	$0.212298\pi$
$368$	38.8338	−	12.6179i	2.02435	−	0.657752i
$369$	1.13095	+	3.48070i	0.0588749	+	0.181198i
$370$		0			0
$371$	−2.36186	+	1.71599i	−0.122622	+	0.0890898i
$372$	−0.0271915	−	0.00883507i	−0.00140982	−	0.000458077i
$373$		−	24.3331i		−	1.25992i	−0.776627	−	0.629961i	$-0.783071\pi$
$373$		−	24.3331i		−	1.25992i	0.776627	−	0.629961i	$-0.216929\pi$
$374$	5.14728	+	44.1232i	0.266159	+	2.28156i
$375$		0			0
$376$	−1.42705	+	4.39201i	−0.0735945	+	0.226501i
$377$	−17.4408	−	24.0052i	−0.898245	−	1.23633i
$378$	−1.87642	+	2.58268i	−0.0965128	+	0.132839i
$379$	−4.92299	−	15.1514i	−0.252877	−	0.778276i	−0.994241	−	0.107172i	$-0.965820\pi$
$379$	−4.92299	−	15.1514i	−0.252877	−	0.778276i	0.741363	−	0.671104i	$-0.234180\pi$
$380$		0			0
$381$	10.2640	+	7.45726i	0.525842	+	0.382047i
$382$	−14.4169	−	19.8432i	−0.737634	−	1.01527i
$383$	−3.72809	−	1.21133i	−0.190496	−	0.0618960i	0.212215	−	0.977223i	$-0.431932\pi$
$383$	−3.72809	−	1.21133i	−0.190496	−	0.0618960i	−0.402712	+	0.915327i	$0.631932\pi$
$384$	9.14301			0.466577
$385$		0			0
$386$	13.8454			0.704710
$387$	1.87310	+	0.608609i	0.0952153	+	0.0309373i
$388$	1.49434	+	2.05678i	0.0758635	+	0.104417i
$389$	−28.5510	−	20.7435i	−1.44759	−	1.05174i	−0.986386	−	0.164447i	$-0.947416\pi$
$389$	−28.5510	−	20.7435i	−1.44759	−	1.05174i	−0.461209	−	0.887292i	$-0.652584\pi$
$390$		0			0
$391$	18.9328	+	58.2693i	0.957475	+	2.94680i
$392$	−2.80511	+	3.86090i	−0.141679	+	0.195005i
$393$	−0.570212	−	0.784829i	−0.0287634	−	0.0395894i
$394$	3.89078	−	11.9746i	0.196015	−	0.603271i
$395$		0			0
$396$	3.00739	+	3.26435i	0.151127	+	0.164040i
$397$		−	23.2231i		−	1.16553i	−0.812639	−	0.582767i	$-0.801970\pi$
$397$		−	23.2231i		−	1.16553i	0.812639	−	0.582767i	$-0.198030\pi$
$398$	1.11106	+	0.361006i	0.0556925	+	0.0180956i
$399$	−8.50217	+	6.17719i	−0.425641	+	0.309246i
$400$		0			0
$401$	1.75973	+	5.41589i	0.0878766	+	0.270457i	0.985332	−	0.170649i	$-0.0545864\pi$
$401$	1.75973	+	5.41589i	0.0878766	+	0.270457i	−0.897455	+	0.441106i	$0.854586\pi$
$402$	−0.609032	+	0.197887i	−0.0303758	+	0.00986969i
$403$	0.0672799	−	0.0926028i	0.00335145	−	0.00461287i
$404$	7.26488	−	5.27824i	0.361441	−	0.262602i
$405$		0			0
$406$	17.6799			0.877438
$407$	−3.24270	−	1.82315i	−0.160735	−	0.0903704i
$408$			8.86324i			0.438796i
$409$	−7.86540	+	24.2072i	−0.388919	+	1.19697i	0.544679	+	0.838645i	$0.316652\pi$
$409$	−7.86540	+	24.2072i	−0.388919	+	1.19697i	−0.933597	+	0.358324i	$0.883348\pi$
$410$		0			0
$411$	3.41434	+	2.48066i	0.168417	+	0.122362i
$412$	−5.40515	+	1.75624i	−0.266292	+	0.0865237i
$413$	−9.41086	+	3.05777i	−0.463078	+	0.150463i
$414$	12.3539	+	8.97566i	0.607163	+	0.441130i
$415$		0			0
$416$	10.7753	−	33.1629i	0.528301	−	1.62594i
$417$			8.84846i			0.433311i
$418$	15.2039	+	33.1258i	0.743645	+	1.62023i
$419$	13.4850			0.658786			0.329393	−	0.944193i	$-0.393156\pi$
$419$	13.4850			0.658786			0.329393	+	0.944193i	$0.393156\pi$
$420$		0			0
$421$	−2.38633	+	1.73377i	−0.116303	+	0.0844990i	−0.644416	−	0.764675i	$-0.722900\pi$
$421$	−2.38633	+	1.73377i	−0.116303	+	0.0844990i	0.528113	+	0.849174i	$0.322900\pi$
$422$	4.10404	−	5.64872i	0.199781	−	0.274975i
$423$	−3.63259	+	1.18030i	−0.176623	+	0.0573882i
$424$	0.624271	+	1.92131i	0.0303173	+	0.0933070i
$425$		0			0
$426$	6.70810	−	4.87372i	0.325009	−	0.236133i
$427$	−15.4204	−	5.01039i	−0.746246	−	0.242470i
$428$		−	21.0415i		−	1.01708i
$429$	−16.1497	+	7.41230i	−0.779717	+	0.357869i
$430$		0			0
$431$	3.56072	−	10.9588i	0.171514	−	0.527866i	−0.827943	−	0.560812i	$-0.810489\pi$
$431$	3.56072	−	10.9588i	0.171514	−	0.527866i	0.999457	+	0.0329464i	$0.0104891\pi$
$432$	2.87167	+	3.95252i	0.138163	+	0.190166i
$433$	6.56194	−	9.03174i	0.315347	−	0.434038i	−0.621693	−	0.783261i	$-0.713555\pi$
$433$	6.56194	−	9.03174i	0.315347	−	0.434038i	0.937039	+	0.349224i	$0.113555\pi$
$434$	0.0210757	+	0.0648642i	0.00101166	+	0.00311358i
$435$		0			0
$436$	−4.58941	−	3.33440i	−0.219793	−	0.159689i
$437$	29.5479	+	40.6692i	1.41347	+	1.94547i
$438$	−17.6191	−	5.72480i	−0.841874	−	0.273541i
$439$	−0.993624			−0.0474231			−0.0237115	−	0.999719i	$-0.507548\pi$
$439$	−0.993624			−0.0474231			−0.0237115	+	0.999719i	$0.507548\pi$
$440$		0			0
$441$	−3.94716			−0.187960
$442$	68.2483	+	22.1752i	3.24624	+	1.05477i
$443$	6.45537	+	8.88506i	0.306704	+	0.422142i	0.934350	−	0.356357i	$-0.115981\pi$
$443$	6.45537	+	8.88506i	0.306704	+	0.422142i	−0.627646	+	0.778499i	$0.715981\pi$
$444$	1.21438	+	0.882299i	0.0576320	+	0.0418721i
$445$		0			0
$446$	−15.0863	−	46.4307i	−0.714355	−	2.19856i
$447$	5.61545	−	7.72900i	0.265602	−	0.365569i
$448$	2.17731	+	2.99681i	0.102868	+	0.141586i
$449$	−8.96777	+	27.5999i	−0.423215	+	1.30252i	0.481478	+	0.876458i	$0.340100\pi$
$449$	−8.96777	+	27.5999i	−0.423215	+	1.30252i	−0.904693	+	0.426064i	$0.859900\pi$
$450$		0			0
$451$	−8.22451	−	8.92722i	−0.387277	−	0.420366i
$452$			9.63070i			0.452990i
$453$	6.42113	+	2.08635i	0.301691	+	0.0980254i
$454$	18.0886	−	13.1421i	0.848938	−	0.616790i
$455$		0			0
$456$	2.24724	+	6.91629i	0.105237	+	0.323885i
$457$	−3.38262	+	1.09908i	−0.158232	+	0.0514129i	−0.387062	−	0.922054i	$-0.626510\pi$
$457$	−3.38262	+	1.09908i	−0.158232	+	0.0514129i	0.228830	+	0.973466i	$0.426510\pi$
$458$	−7.18103	+	9.88383i	−0.335547	+	0.461841i
$459$	−5.93066	+	4.30888i	−0.276820	+	0.201121i
$460$		0			0
$461$	25.1829			1.17288			0.586441	−	0.809992i	$-0.300528\pi$
$461$	25.1829			1.17288			0.586441	+	0.809992i	$0.300528\pi$
$462$	2.08301	−	10.3809i	0.0969104	−	0.482965i
$463$		−	17.8743i		−	0.830690i	−0.909664	−	0.415345i	$-0.863661\pi$
$463$		−	17.8743i		−	0.830690i	0.909664	−	0.415345i	$-0.136339\pi$
$464$	8.36114	−	25.7329i	0.388156	−	1.19462i
$465$		0			0
$466$	9.63371	+	6.99930i	0.446273	+	0.324236i
$467$	−23.9906	+	7.79502i	−1.11015	+	0.360711i	−0.806002	−	0.591913i	$-0.798373\pi$
$467$	−23.9906	+	7.79502i	−1.11015	+	0.360711i	−0.304151	+	0.952624i	$0.598373\pi$
$468$	6.81910	−	2.21566i	0.315213	−	0.102419i
$469$	0.495432	+	0.359952i	0.0228769	+	0.0166210i
$470$		0			0
$471$	3.91229	−	12.0408i	0.180269	−	0.554810i
$472$			6.84727i			0.315171i
$473$	−6.48809	+	0.756881i	−0.298323	+	0.0348014i
$474$	4.68468			0.215175
$475$		0			0
$476$	−13.8674	+	10.0753i	−0.635613	+	0.461800i
$477$	−0.982116	+	1.35177i	−0.0449680	+	0.0618931i
$478$	18.8396	−	6.12135i	0.861702	−	0.279984i
$479$	1.61793	+	4.97948i	0.0739252	+	0.227518i	0.981191	−	0.193039i	$-0.0618345\pi$
$479$	1.61793	+	4.97948i	0.0739252	+	0.227518i	−0.907266	+	0.420558i	$0.861834\pi$
$480$		0			0
$481$	−4.86176	+	3.53228i	−0.221677	+	0.161058i
$482$	−47.2304	−	15.3461i	−2.15128	−	0.698995i
$483$		−	14.6029i		−	0.664456i
$484$	−13.5813	−	5.67904i	−0.617333	−	0.258138i
$485$		0			0
$486$	−0.564602	+	1.73767i	−0.0256109	+	0.0788222i
$487$	5.31656	+	7.31762i	0.240917	+	0.331593i	0.912304	−	0.409513i	$-0.134301\pi$
$487$	5.31656	+	7.31762i	0.240917	+	0.331593i	−0.671388	+	0.741106i	$0.734301\pi$
$488$	−6.59482	+	9.07699i	−0.298533	+	0.410896i
$489$	−7.23278	−	22.2602i	−0.327078	−	1.00664i
$490$		0			0
$491$	28.1629	+	20.4615i	1.27097	+	0.923416i	0.999241	−	0.0389565i	$-0.0124034\pi$
$491$	28.1629	+	20.4615i	1.27097	+	0.923416i	0.271733	+	0.962373i	$0.412403\pi$
$492$	2.87886	+	3.96241i	0.129789	+	0.178639i
$493$	38.6117	+	12.5457i	1.73898	+	0.565030i
$494$	58.8789			2.64909
$495$		0			0
$496$	0.104377			0.00468664
$497$	−7.54120	−	2.45028i	−0.338269	−	0.109910i
$498$	−17.2694	−	23.7694i	−0.773862	−	1.06513i
$499$	15.8561	+	11.5201i	0.709815	+	0.515711i	0.883114	−	0.469158i	$-0.155443\pi$
$499$	15.8561	+	11.5201i	0.709815	+	0.515711i	−0.173299	+	0.984869i	$0.555443\pi$
$500$		0			0
$501$	−0.943091	−	2.90254i	−0.0421342	−	0.129676i
$502$	−5.95437	+	8.19549i	−0.265757	+	0.365783i
$503$	−10.8247	−	14.8989i	−0.482647	−	0.664307i	0.496364	−	0.868115i	$-0.334668\pi$
$503$	−10.8247	−	14.8989i	−0.482647	−	0.664307i	−0.979011	+	0.203808i	$0.934668\pi$
$504$	0.652802	−	2.00912i	0.0290781	−	0.0894932i
$505$		0			0
$506$	−49.6561	−	9.96384i	−2.20748	−	0.442947i
$507$			15.7051i			0.697489i
$508$	16.1476	+	5.24667i	0.716433	+	0.232783i
$509$	1.00187	−	0.727900i	0.0444070	−	0.0322636i	−0.565360	−	0.824844i	$-0.691263\pi$
$509$	1.00187	−	0.727900i	0.0444070	−	0.0322636i	0.609767	+	0.792580i	$0.291263\pi$
$510$		0			0
$511$	5.47459	+	16.8491i	0.242182	+	0.745359i
$512$	19.0048	−	6.17504i	0.839902	−	0.272901i
$513$	−3.53540	+	4.86606i	−0.156092	+	0.214842i
$514$	−28.0019	+	20.3446i	−1.23511	+	0.897362i
$515$		0			0
$516$	2.63570			0.116030
$517$	9.31678	−	8.58340i	0.409752	−	0.377498i
$518$		−	3.58071i		−	0.157327i
$519$	4.94657	−	15.2240i	0.217130	−	0.668258i
$520$		0			0
$521$	−26.8472	−	19.5057i	−1.17620	−	0.854558i	−0.184461	−	0.982840i	$-0.559054\pi$
$521$	−26.8472	−	19.5057i	−1.17620	−	0.854558i	−0.991738	+	0.128282i	$0.959054\pi$
$522$	9.62351	−	3.12687i	0.421210	−	0.136859i
$523$	−12.5072	+	4.06383i	−0.546901	+	0.177699i	−0.569419	−	0.822047i	$-0.692832\pi$
$523$	−12.5072	+	4.06383i	−0.546901	+	0.177699i	0.0225177	+	0.999746i	$0.492832\pi$
$524$	−1.05031	−	0.763092i	−0.0458829	−	0.0333359i
$525$		0			0
$526$	1.81165	−	5.57570i	0.0789919	−	0.243112i
$527$			0.156615i			0.00682224i
$528$	−14.1243	−	7.94115i	−0.614681	−	0.345594i
$529$	−46.8514			−2.03702
$530$		0			0
$531$	−4.58172	+	3.32882i	−0.198830	+	0.144458i
$532$	−8.26669	+	11.3781i	−0.358407	+	0.493304i
$533$	−18.6486	+	6.05930i	−0.807761	+	0.262458i
$534$	−8.19021	−	25.2069i	−0.354425	−	1.09081i
$535$		0			0
$536$	0.342830	−	0.249080i	0.0148080	−	0.0107586i
$537$	−18.3545	−	5.96375i	−0.792057	−	0.257355i
$538$		−	5.92750i		−	0.255553i
$539$	11.8979	−	5.46082i	0.512479	−	0.235214i
$540$		0			0
$541$	10.0900	−	31.0538i	0.433802	−	1.33511i	−0.460507	−	0.887656i	$-0.652332\pi$
$541$	10.0900	−	31.0538i	0.433802	−	1.33511i	0.894309	−	0.447450i	$-0.147668\pi$
$542$	−2.17985	−	3.00030i	−0.0936324	−	0.128874i
$543$	7.16572	−	9.86277i	0.307511	−	0.423252i
$544$	14.7433	+	45.3752i	0.632114	+	1.94545i
$545$		0			0
$546$	−13.8372	−	10.0533i	−0.592179	−	0.430243i
$547$	16.2845	+	22.4136i	0.696273	+	0.958338i	0.999984	+	0.00557389i	$0.00177423\pi$
$547$	16.2845	+	22.4136i	0.696273	+	0.958338i	−0.303711	+	0.952764i	$0.598226\pi$
$548$	5.37150	+	1.74531i	0.229459	+	0.0745558i
$549$	−9.27977			−0.396051
$550$		0			0
$551$	33.3110			1.41909
$552$	−9.61038	−	3.12260i	−0.409045	−	0.132907i
$553$	−2.63324	−	3.62435i	−0.111977	−	0.154123i
$554$	16.7276	+	12.1533i	0.710686	+	0.516343i
$555$		0			0
$556$	3.65924	+	11.2620i	0.155186	+	0.477614i
$557$	13.7690	−	18.9514i	0.583411	−	0.802996i	−0.410653	−	0.911792i	$-0.634699\pi$
$557$	13.7690	−	18.9514i	0.583411	−	0.802996i	0.994064	+	0.108795i	$0.0346993\pi$
$558$	0.0229438	+	0.0315794i	0.000971289	+	0.00133686i
$559$	−3.26075	+	10.0356i	−0.137915	+	0.424459i
$560$		0			0
$561$	11.9155	−	21.1932i	0.503073	−	0.894778i
$562$			18.8514i			0.795198i
$563$	21.0046	+	6.82482i	0.885240	+	0.287632i	0.716131	−	0.697966i	$-0.245911\pi$
$563$	21.0046	+	6.82482i	0.885240	+	0.287632i	0.169108	+	0.985597i	$0.445911\pi$
$564$	−4.13532	+	3.00448i	−0.174128	+	0.126512i
$565$		0			0
$566$	−1.18899	−	3.65933i	−0.0499769	−	0.153813i
$567$	1.66172	−	0.539926i	0.0697858	−	0.0226748i
$568$	−3.22513	+	4.43901i	−0.135323	+	0.186257i
$569$	−11.1119	+	8.07328i	−0.465836	+	0.338449i	−0.795816	−	0.605538i	$-0.792958\pi$
$569$	−11.1119	+	8.07328i	−0.465836	+	0.338449i	0.329980	+	0.943988i	$0.392958\pi$
$570$		0			0
$571$	−26.5201			−1.10983			−0.554915	−	0.831907i	$-0.687249\pi$
$571$	−26.5201			−1.10983			−0.554915	+	0.831907i	$0.687249\pi$
$572$	−17.4894	+	16.1127i	−0.731271	+	0.673708i
$573$			13.4244i			0.560811i
$574$	3.61040	−	11.1117i	0.150695	−	0.463792i
$575$		0			0
$576$	1.71517	+	1.24614i	0.0714654	+	0.0519227i
$577$	5.40927	−	1.75758i	0.225191	−	0.0731690i	−0.194248	−	0.980952i	$-0.562227\pi$
$577$	5.40927	−	1.75758i	0.225191	−	0.0731690i	0.419439	+	0.907783i	$0.362227\pi$
$578$	−63.8405	+	20.7430i	−2.65542	+	0.862797i
$579$	−6.13058	−	4.45413i	−0.254778	−	0.185107i
$580$		0			0
$581$	−8.68228	+	26.7213i	−0.360202	+	1.10859i
$582$		−	3.47096i		−	0.143876i
$583$	1.09024	−	5.43336i	0.0451532	−	0.225027i
$584$	12.2593			0.507292
$585$		0			0
$586$	34.5524	−	25.1038i	1.42735	−	1.03703i
$587$	−7.96215	+	10.9590i	−0.328633	+	0.452324i	−0.941078	−	0.338188i	$-0.890186\pi$
$587$	−7.96215	+	10.9590i	−0.328633	+	0.452324i	0.612446	+	0.790513i	$0.290186\pi$
$588$	−5.02379	+	1.63233i	−0.207178	+	0.0673161i
$589$	0.0397090	+	0.122212i	0.00163618	+	0.00503565i
$590$		0			0
$591$	−5.57508	+	4.05054i	−0.229328	+	0.166617i
$592$	−5.21169	−	1.69338i	−0.214199	−	0.0695975i
$593$			21.1786i			0.869702i	0.900502	+	0.434851i	$0.143199\pi$
$593$			21.1786i			0.869702i	−0.900502	+	0.434851i	$0.856801\pi$
$594$	−0.702153	−	6.01896i	−0.0288097	−	0.246961i
$595$		0			0
$596$	3.95083	−	12.1594i	0.161833	−	0.498069i
$597$	−0.375829	−	0.517284i	−0.0153816	−	0.0211710i
$598$	−48.0890	+	66.1889i	−1.96651	+	2.70666i
$599$	10.4573	+	32.1842i	0.427273	+	1.31501i	0.900801	+	0.434231i	$0.142980\pi$
$599$	10.4573	+	32.1842i	0.427273	+	1.31501i	−0.473529	+	0.880778i	$0.657020\pi$
$600$		0			0
$601$	−23.7186	−	17.2325i	−0.967500	−	0.702930i	−0.0126196	−	0.999920i	$-0.504017\pi$
$601$	−23.7186	−	17.2325i	−0.967500	−	0.702930i	−0.954880	+	0.296990i	$0.904017\pi$
$602$	−3.69562	−	5.08658i	−0.150622	−	0.207313i
$603$	0.333334	+	0.108307i	0.0135744	+	0.00441060i
$604$	9.03538			0.367644
$605$		0			0
$606$	−12.2600			−0.498028
$607$	−6.82370	−	2.21715i	−0.276965	−	0.0899915i	0.167241	−	0.985916i	$-0.446514\pi$
$607$	−6.82370	−	2.21715i	−0.276965	−	0.0899915i	−0.444206	+	0.895925i	$0.646514\pi$
$608$	23.0094	+	31.6697i	0.933154	+	1.28438i
$609$	−7.82847	−	5.68772i	−0.317226	−	0.230478i
$610$		0			0
$611$	−6.32372	−	19.4624i	−0.255830	−	0.787364i
$612$	−5.76641	+	7.93678i	−0.233093	+	0.320825i
$613$	16.1667	+	22.2515i	0.652967	+	0.898731i	0.999223	−	0.0394084i	$-0.0125473\pi$
$613$	16.1667	+	22.2515i	0.652967	+	0.898731i	−0.346257	+	0.938140i	$0.612547\pi$
$614$	18.0965	−	55.6953i	0.730315	−	2.24768i
$615$		0			0
$616$	0.811840	+	6.95921i	0.0327100	+	0.280395i
$617$		−	24.0712i		−	0.969068i	−0.874772	−	0.484534i	$-0.838989\pi$
$617$		−	24.0712i		−	0.969068i	0.874772	−	0.484534i	$-0.161011\pi$
$618$	7.37950	+	2.39774i	0.296847	+	0.0964514i
$619$	21.8216	−	15.8543i	0.877083	−	0.637238i	−0.0553955	−	0.998464i	$-0.517642\pi$
$619$	21.8216	−	15.8543i	0.877083	−	0.637238i	0.932478	+	0.361227i	$0.117642\pi$
$620$		0			0
$621$	−2.58268	−	7.94866i	−0.103639	−	0.318969i
$622$	2.83992	−	0.922745i	0.113870	−	0.0369987i
$623$	−14.8978	+	20.5051i	−0.596870	+	0.821521i
$624$	−21.1765	+	15.3856i	−0.847737	+	0.615917i
$625$		0			0
$626$	55.5673			2.22092
$627$	3.92463	−	19.5589i	0.156735	−	0.781108i
$628$		−	16.9430i		−	0.676098i
$629$	2.54088	−	7.82003i	0.101312	−	0.311805i
$630$		0			0
$631$	−7.87681	−	5.72284i	−0.313571	−	0.227823i	0.419856	−	0.907591i	$-0.362080\pi$
$631$	−7.87681	−	5.72284i	−0.313571	−	0.227823i	−0.733427	+	0.679768i	$0.762080\pi$
$632$	−2.94831	+	0.957964i	−0.117277	+	0.0381058i
$633$	−3.63445	+	1.18090i	−0.144456	+	0.0469367i
$634$	−43.5078	−	31.6103i	−1.72792	−	1.25540i
$635$		0			0
$636$	−0.690983	+	2.12663i	−0.0273993	+	0.0843262i
$637$		−	21.1478i		−	0.837904i
$638$	−24.6821	+	22.7393i	−0.977175	+	0.900256i
$639$	−4.53818			−0.179528
$640$		0			0
$641$	−20.3196	+	14.7631i	−0.802577	+	0.583107i	−0.911669	−	0.410925i	$-0.865206\pi$
$641$	−20.3196	+	14.7631i	−0.802577	+	0.583107i	0.109092	+	0.994032i	$0.465206\pi$
$642$	−16.8855	+	23.2409i	−0.666418	+	0.917245i
$643$	25.6079	−	8.32051i	1.00988	−	0.328129i	0.243071	−	0.970008i	$-0.421845\pi$
$643$	25.6079	−	8.32051i	1.00988	−	0.328129i	0.766806	+	0.641880i	$0.221845\pi$
$644$	−6.03897	−	18.5860i	−0.237969	−	0.732393i
$645$		0			0
$646$	−65.1754	+	47.3527i	−2.56429	+	1.86307i
$647$	25.4893	+	8.28198i	1.00209	+	0.325598i	0.763700	−	0.645572i	$-0.223381\pi$
$647$	25.4893	+	8.28198i	1.00209	+	0.325598i	0.238389	+	0.971170i	$0.423381\pi$
$648$		−	1.20906i		−	0.0474962i
$649$	9.20530	−	16.3728i	0.361340	−	0.642687i
$650$		0			0
$651$	0.0115351	−	0.0355014i	0.000452096	−	0.00139141i
$652$	−18.4112	−	25.3409i	−0.721039	−	0.992425i
$653$	16.9066	−	23.2700i	0.661608	−	0.910625i	−0.337926	−	0.941173i	$-0.609725\pi$
$653$	16.9066	−	23.2700i	0.661608	−	0.910625i	0.999533	+	0.0305480i	$0.00972525\pi$
$654$	2.39332	+	7.36589i	0.0935863	+	0.288029i
$655$		0			0
$656$	−14.4655	−	10.5098i	−0.564784	−	0.410340i
$657$	5.95986	+	8.20305i	0.232516	+	0.320031i
$658$	11.5966	+	3.76795i	0.452081	+	0.146890i
$659$	−36.5327			−1.42311			−0.711556	−	0.702629i	$-0.752009\pi$
$659$	−36.5327			−1.42311			−0.711556	+	0.702629i	$0.752009\pi$
$660$		0			0
$661$	−35.7750			−1.39149			−0.695743	−	0.718291i	$-0.744925\pi$
$661$	−35.7750			−1.39149			−0.695743	+	0.718291i	$0.744925\pi$
$662$	39.6018	+	12.8674i	1.53917	+	0.500106i
$663$	−23.0858	−	31.7748i	−0.896576	−	1.23403i
$664$	15.7291	+	11.4279i	0.610408	+	0.443487i
$665$		0			0
$666$	−0.633284	−	1.94905i	−0.0245393	−	0.0755241i
$667$	−27.2065	+	37.4466i	−1.05344	+	1.44994i
$668$	−2.40066	−	3.30423i	−0.0928844	−	0.127844i
$669$	−8.25698	+	25.4124i	−0.319233	+	0.982499i
$670$		0			0
$671$	27.9720	−	12.8384i	1.07985	−	0.495621i
$672$		−	11.3715i		−	0.438666i
$673$	−10.7388	−	3.48925i	−0.413951	−	0.134501i	0.0946349	−	0.995512i	$-0.469832\pi$
$673$	−10.7388	−	3.48925i	−0.413951	−	0.134501i	−0.508586	+	0.861011i	$0.669832\pi$
$674$	−21.4185	+	15.5614i	−0.825009	+	0.599404i
$675$		0			0
$676$	6.49478	+	19.9889i	0.249799	+	0.768803i
$677$	−41.7108	+	13.5527i	−1.60308	+	0.520872i	−0.967866	−	0.251466i	$-0.919087\pi$
$677$	−41.7108	+	13.5527i	−1.60308	+	0.520872i	−0.635212	+	0.772338i	$0.719087\pi$
$678$	7.72851	−	10.6374i	0.296812	−	0.408526i
$679$	−2.68534	+	1.95101i	−0.103054	+	0.0748729i
$680$		0			0
$681$	−12.2373			−0.468935
$682$	−0.112849	−	0.0634474i	−0.00432121	−	0.00242953i
$683$		−	18.5355i		−	0.709241i	−0.935010	−	0.354620i	$-0.884610\pi$
$683$		−	18.5355i		−	0.709241i	0.935010	−	0.354620i	$-0.115390\pi$
$684$	−2.48739	+	7.65539i	−0.0951076	+	0.292711i
$685$		0			0
$686$	28.2730	+	20.5415i	1.07947	+	0.784279i
$687$	6.35937	−	2.06628i	0.242625	−	0.0788337i
$688$	−9.15120	+	2.97341i	−0.348886	+	0.113360i
$689$	−7.24238	−	5.26190i	−0.275913	−	0.200462i
$690$		0			0
$691$	−8.71597	+	26.8250i	−0.331571	+	1.02047i	0.636815	+	0.771017i	$0.280251\pi$
$691$	−8.71597	+	26.8250i	−0.331571	+	1.02047i	−0.968386	+	0.249455i	$0.919749\pi$
$692$		−	21.4221i		−	0.814347i
$693$	−4.26194	+	3.92646i	−0.161898	+	0.149154i
$694$	−8.01596			−0.304282
$695$		0			0
$696$	−5.41716	+	3.93580i	−0.205337	+	0.149186i
$697$	15.7698	−	21.7052i	0.597322	−	0.822144i
$698$	−25.0330	+	8.13371i	−0.947512	+	0.307865i
$699$	−2.01399	−	6.19844i	−0.0761762	−	0.234446i
$700$		0			0
$701$	−0.255153	+	0.185379i	−0.00963699	+	0.00700168i	−0.592593	−	0.805502i	$-0.701896\pi$
$701$	−0.255153	+	0.185379i	−0.00963699	+	0.00700168i	0.582956	+	0.812503i	$0.301896\pi$
$702$	−9.30992	−	3.02498i	−0.351380	−	0.114170i
$703$		−	6.74647i		−	0.254448i
$704$	−6.89405	−	1.38334i	−0.259829	−	0.0521366i
$705$		0			0
$706$	−3.39362	+	10.4445i	−0.127721	+	0.393084i
$707$	6.89129	+	9.48505i	0.259174	+	0.356722i
$708$	−4.45482	+	6.13154i	−0.167423	+	0.230437i
$709$	−12.0593	−	37.1146i	−0.452895	−	1.39387i	−0.873589	−	0.486665i	$-0.838213\pi$
$709$	−12.0593	−	37.1146i	−0.452895	−	1.39387i	0.420693	−	0.907203i	$-0.361787\pi$
$710$		0			0
$711$	−2.07433	−	1.50709i	−0.0777934	−	0.0565202i
$712$	10.3090	+	14.1892i	0.386348	+	0.531762i
$713$	−0.169817	−	0.0551768i	−0.00635969	−	0.00206639i
$714$	23.4023			0.875808
$715$		0			0
$716$	−25.8272			−0.965209
$717$	−10.3112	−	3.35032i	−0.385080	−	0.125120i
$718$	2.63882	+	3.63203i	0.0984800	+	0.135546i
$719$	23.0320	+	16.7337i	0.858948	+	0.624062i	0.927598	−	0.373579i	$-0.121869\pi$
$719$	23.0320	+	16.7337i	0.858948	+	0.624062i	−0.0686507	+	0.997641i	$0.521869\pi$
$720$		0			0
$721$	−2.29295	−	7.05698i	−0.0853939	−	0.262816i
$722$	−18.4477	+	25.3911i	−0.686552	+	0.944957i
$723$	15.9762	+	21.9894i	0.594161	+	0.817793i
$724$	5.04156	−	15.5163i	0.187368	−	0.576659i
$725$		0			0
$726$	10.4436	+	17.1715i	0.387599	+	0.637294i
$727$		−	45.8400i		−	1.70011i	−0.526691	−	0.850057i	$-0.676568\pi$
$727$		−	45.8400i		−	1.70011i	0.526691	−	0.850057i	$-0.323432\pi$
$728$	10.7643	+	3.49753i	0.398951	+	0.129627i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$		0			0
$731$	−4.46153	−	13.7312i	−0.165016	−	0.507866i
$732$	−11.8109	+	3.83761i	−0.436545	+	0.141842i
$733$	22.3171	−	30.7169i	0.824301	−	1.13455i	−0.164656	−	0.986351i	$-0.552651\pi$
$733$	22.3171	−	30.7169i	0.824301	−	1.13455i	0.988957	−	0.148202i	$-0.0473487\pi$
$734$	2.18751	−	1.58932i	0.0807423	−	0.0586627i
$735$		0			0
$736$	−54.3944			−2.00500
$737$	−1.15461	+	0.134693i	−0.0425306	+	0.00496149i
$738$		−	6.68684i		−	0.246146i
$739$	−6.52725	+	20.0888i	−0.240109	+	0.738979i	0.756294	+	0.654232i	$0.227008\pi$
$739$	−6.52725	+	20.0888i	−0.240109	+	0.738979i	−0.996403	+	0.0847466i	$0.972992\pi$
$740$		0			0
$741$	−26.0710	−	18.9417i	−0.957741	−	0.695840i
$742$	5.07298	−	1.64831i	0.186235	−	0.0605113i
$743$	−7.58976	+	2.46606i	−0.278441	+	0.0904711i	−0.444909	−	0.895576i	$-0.646764\pi$
$743$	−7.58976	+	2.46606i	−0.278441	+	0.0904711i	0.166467	+	0.986047i	$0.446764\pi$
$744$	−0.0208973	−	0.0151828i	−0.000766134	−	0.000556629i
$745$		0			0
$746$	−13.7385	+	42.2829i	−0.503004	+	1.54809i
$747$			16.0805i			0.588355i
$748$	6.40126	−	31.9015i	0.234053	−	1.16643i
$749$	27.4718			1.00380
$750$		0			0
$751$	7.78664	−	5.65733i	0.284139	−	0.206439i	−0.436582	−	0.899664i	$-0.643811\pi$
$751$	7.78664	−	5.65733i	0.284139	−	0.206439i	0.720721	+	0.693226i	$0.243811\pi$
$752$	10.9684	−	15.0968i	0.399978	−	0.550523i
$753$	5.27307	−	1.71332i	0.192161	−	0.0624370i
$754$	16.7529	+	51.5600i	0.610104	+	1.87771i
$755$		0			0
$756$	1.89169	−	1.37440i	0.0688002	−	0.0499863i
$757$	44.3338	+	14.4049i	1.61134	+	0.523555i	0.969876	−	0.243600i	$-0.0783283\pi$
$757$	44.3338	+	14.4049i	1.61134	+	0.523555i	0.641462	+	0.767155i	$0.278328\pi$
$758$			29.1076i			1.05724i
$759$	18.7818	+	20.3865i	0.681735	+	0.739984i
$760$		0			0
$761$	−6.79661	+	20.9178i	−0.246377	+	0.758270i	0.749030	+	0.662536i	$0.230520\pi$
$761$	−6.79661	+	20.9178i	−0.246377	+	0.758270i	−0.995407	+	0.0957342i	$0.969480\pi$
$762$	−13.6251	−	18.7533i	−0.493585	−	0.679361i
$763$	4.35341	−	5.99195i	0.157604	−	0.216923i
$764$	5.55158	+	17.0860i	0.200849	+	0.618151i
$765$		0			0
$766$	5.79425	+	4.20977i	0.209355	+	0.152105i
$767$	−17.8348	−	24.5476i	−0.643979	−	0.886361i
$768$	−19.9201	−	6.47244i	−0.718805	−	0.233554i
$769$	−48.0330			−1.73211			−0.866057	−	0.499946i	$-0.833353\pi$
$769$	−48.0330			−1.73211			−0.866057	+	0.499946i	$0.833353\pi$
$770$		0			0
$771$	18.9439			0.682249
$772$	−9.64476	−	3.13377i	−0.347123	−	0.112787i
$773$	10.0424	+	13.8222i	0.361199	+	0.497148i	0.950482	−	0.310778i	$-0.100590\pi$
$773$	10.0424	+	13.8222i	0.361199	+	0.497148i	−0.589283	+	0.807927i	$0.700590\pi$
$774$	−2.91121	−	2.11512i	−0.104641	−	0.0760263i
$775$		0			0
$776$	0.709771	+	2.18445i	0.0254793	+	0.0784172i
$777$	−1.15193	+	1.58550i	−0.0413254	+	0.0568795i
$778$	37.9003	+	52.1653i	1.35879	+	1.87022i
$779$	6.80242	−	20.9357i	0.243722	−	0.750099i
$780$		0			0
$781$	13.6794	−	6.27849i	0.489488	−	0.224662i
$782$		−	111.942i		−	4.00304i
$783$	−5.26712	−	1.71139i	−0.188232	−	0.0611602i
$784$	15.6012	−	11.3349i	0.557186	−	0.404819i
$785$		0			0
$786$	0.547722	+	1.68571i	0.0195366	+	0.0601275i
$787$	−21.3910	+	6.95034i	−0.762505	+	0.247753i	−0.664354	−	0.747418i	$-0.731293\pi$
$787$	−21.3910	+	6.95034i	−0.762505	+	0.247753i	−0.0981518	+	0.995171i	$0.531293\pi$
$788$	−5.42068	+	7.46092i	−0.193104	+	0.265784i
$789$	−2.59591	+	1.88604i	−0.0924170	+	0.0671449i
$790$		0			0
$791$	−12.5739			−0.447076
$792$	1.67271	+	3.64445i	0.0594371	+	0.129500i
$793$		−	49.7184i		−	1.76555i
$794$	−13.1118	+	40.3540i	−0.465321	+	1.43211i
$795$		0			0
$796$	−0.692261	−	0.502957i	−0.0245365	−	0.0178268i
$797$	−3.25051	+	1.05615i	−0.115139	+	0.0374109i	−0.366020	−	0.930607i	$-0.619280\pi$
$797$	−3.25051	+	1.05615i	−0.115139	+	0.0374109i	0.250881	+	0.968018i	$0.419280\pi$
$798$	18.2616	−	5.93355i	0.646453	−	0.210045i
$799$	22.6524	+	16.4579i	0.801383	+	0.582239i
$800$		0			0
$801$	−4.48265	+	13.7962i	−0.158387	+	0.487464i
$802$		−	10.4046i		−	0.367398i
$803$	−29.3135	−	16.4810i	−1.03445	−	0.581603i
$804$	0.469045			0.0165420
$805$		0			0
$806$	−0.169194	+	0.122926i	−0.00595959	+	0.00432990i
$807$	−1.90691	+	2.62464i	−0.0671264	+	0.0923916i
$808$	7.71584	−	2.50703i	0.271442	−	0.0881969i
$809$	3.12679	+	9.62328i	0.109932	+	0.338336i	0.990856	−	0.134921i	$-0.0430781\pi$
$809$	3.12679	+	9.62328i	0.109932	+	0.338336i	−0.880924	+	0.473257i	$0.843078\pi$
$810$		0			0
$811$	−20.5287	+	14.9150i	−0.720862	+	0.523737i	−0.886659	−	0.462423i	$-0.846980\pi$
$811$	−20.5287	+	14.9150i	−0.720862	+	0.523737i	0.165798	+	0.986160i	$0.446980\pi$
$812$	−12.3159	−	4.00168i	−0.432204	−	0.140432i
$813$			2.02977i			0.0711872i
$814$	4.60538	+	4.99887i	0.161419	+	0.175210i
$815$		0			0
$816$	11.0674	−	34.0618i	0.387435	−	1.19240i
$817$	−6.96297	−	9.58370i	−0.243603	−	0.335291i
$818$	27.3349	−	37.6232i	0.955741	−	1.31547i
$819$	2.89277	+	8.90304i	0.101082	+	0.311097i
$820$		0			0
$821$	−1.21284	−	0.881177i	−0.0423282	−	0.0307533i	0.566420	−	0.824117i	$-0.308328\pi$
$821$	−1.21284	−	0.881177i	−0.0423282	−	0.0307533i	−0.608748	+	0.793363i	$0.708328\pi$
$822$	−4.53239	−	6.23830i	−0.158085	−	0.217586i
$823$	−18.1885	−	5.90982i	−0.634013	−	0.206003i	−0.0256610	−	0.999671i	$-0.508169\pi$
$823$	−18.1885	−	5.90982i	−0.634013	−	0.206003i	−0.608352	+	0.793667i	$0.708169\pi$
$824$	−5.13460			−0.178872
$825$		0			0
$826$	18.0794			0.629062
$827$	15.8165	+	5.13910i	0.549994	+	0.178704i	0.570814	−	0.821079i	$-0.306628\pi$
$827$	15.8165	+	5.13910i	0.549994	+	0.178704i	−0.0208200	+	0.999783i	$0.506628\pi$
$828$	−6.57426	−	9.04870i	−0.228471	−	0.314464i
$829$	20.7881	+	15.1034i	0.722001	+	0.524564i	0.887023	−	0.461725i	$-0.152769\pi$
$829$	20.7881	+	15.1034i	0.722001	+	0.524564i	−0.165022	+	0.986290i	$0.552769\pi$
$830$		0			0
$831$	−3.49701	−	10.7627i	−0.121310	−	0.373354i
$832$	−6.67649	+	9.18940i	−0.231466	+	0.318585i
$833$	17.0078	+	23.4093i	0.589286	+	0.811083i
$834$	4.99586	−	15.3757i	0.172992	−	0.532416i
$835$		0			0
$836$	−3.09338	−	26.5169i	−0.106987	−	0.917105i
$837$		−	0.0213642i		−	0.000738455i
$838$	−23.4325	−	7.61367i	−0.809461	−	0.263010i
$839$	−22.9737	+	16.6914i	−0.793141	+	0.576250i	−0.908894	−	0.417028i	$-0.863072\pi$
$839$	−22.9737	+	16.6914i	−0.793141	+	0.576250i	0.115753	+	0.993278i	$0.463072\pi$
$840$		0			0
$841$	0.516507	+	1.58965i	0.0178106	+	0.0548154i
$842$	5.12555	−	1.66539i	0.176638	−	0.0573932i
$843$	6.06459	−	8.34720i	0.208876	−	0.287493i
$844$	−4.13743	+	3.00602i	−0.142416	+	0.103471i
$845$		0			0
$846$	6.97864			0.239930
$847$	7.41457	−	17.7318i	0.254768	−	0.609273i
$848$		−	8.16320i		−	0.280325i
$849$	−0.650755	+	2.00282i	−0.0223339	+	0.0687365i
$850$		0			0
$851$	7.58406	+	5.51014i	0.259978	+	0.188885i
$852$	−5.77602	+	1.87674i	−0.197883	+	0.0642962i
$853$	−14.3678	+	4.66838i	−0.491943	+	0.159842i	−0.544475	−	0.838777i	$-0.683271\pi$
$853$	−14.3678	+	4.66838i	−0.491943	+	0.159842i	0.0525314	+	0.998619i	$0.483271\pi$
$854$	23.9666	+	17.4128i	0.820122	+	0.595853i
$855$		0			0
$856$	5.87441	−	18.0796i	0.200783	−	0.617947i
$857$		−	2.37040i		−	0.0809713i	−0.999180	−	0.0404856i	$-0.987109\pi$
$857$		−	2.37040i		−	0.0809713i	0.999180	−	0.0404856i	$-0.0128905\pi$
$858$	32.2479	−	3.76194i	1.10092	−	0.128430i
$859$	−45.0423			−1.53682			−0.768411	−	0.639956i	$-0.778952\pi$
$859$	−45.0423			−1.53682			−0.768411	+	0.639956i	$0.778952\pi$
$860$		0			0
$861$	−5.17333	+	3.75865i	−0.176307	+	0.128094i
$862$	−12.3747	+	17.0323i	−0.421484	+	0.580123i
$863$	23.7964	−	7.73191i	0.810038	−	0.263197i	0.125424	−	0.992103i	$-0.459971\pi$
$863$	23.7964	−	7.73191i	0.810038	−	0.263197i	0.684614	+	0.728906i	$0.259971\pi$
$864$	−2.01117	−	6.18975i	−0.0684214	−	0.210579i
$865$		0			0
$866$	−16.5018	+	11.9893i	−0.560754	+	0.407412i
$867$	34.9411	+	11.3530i	1.18666	+	0.385570i
$868$		−	0.0499551i		−	0.00169559i
$869$	8.33767	+	1.67301i	0.282836	+	0.0567530i
$870$		0			0
$871$	−0.580278	+	1.78591i	−0.0196620	+	0.0605133i
$872$	−3.01248	−	4.14632i	−0.102015	−	0.140412i
$873$	−1.11663	+	1.53690i	−0.0377920	+	0.0520163i
$874$	−28.3825	−	87.3522i	−0.960051	−	2.95473i
$875$		0			0
$876$	10.9778	+	7.97585i	0.370906	+	0.269479i
$877$	−28.7283	−	39.5411i	−0.970085	−	1.33521i	−0.942004	−	0.335601i	$-0.891060\pi$
$877$	−28.7283	−	39.5411i	−0.970085	−	1.33521i	−0.0280807	−	0.999606i	$-0.508940\pi$
$878$	1.72659	+	0.561002i	0.0582695	+	0.0189329i
$879$	−23.3755			−0.788435
$880$		0			0
$881$	44.5530			1.50103			0.750515	−	0.660853i	$-0.229805\pi$
$881$	44.5530			1.50103			0.750515	+	0.660853i	$0.229805\pi$
$882$	6.85885	+	2.22857i	0.230949	+	0.0750400i
$883$	25.8947	+	35.6410i	0.871426	+	1.19941i	0.978723	+	0.205187i	$0.0657804\pi$
$883$	25.8947	+	35.6410i	0.871426	+	1.19941i	−0.107297	+	0.994227i	$0.534220\pi$
$884$	−42.5230	−	30.8948i	−1.43020	−	1.03910i
$885$		0			0
$886$	−6.20076	−	19.0840i	−0.208319	−	0.641139i
$887$	7.12941	−	9.81279i	0.239382	−	0.329481i	−0.672375	−	0.740210i	$-0.734726\pi$
$887$	7.12941	−	9.81279i	0.239382	−	0.329481i	0.911757	+	0.410729i	$0.134726\pi$
$888$	0.797116	+	1.09714i	0.0267495	+	0.0368175i
$889$	−6.85007	+	21.0823i	−0.229744	+	0.707079i
$890$		0			0
$891$	−1.62543	+	2.89102i	−0.0544538	+	0.0968528i
$892$			35.7585i			1.19728i
$893$	21.8493	+	7.09925i	0.731158	+	0.237567i
$894$	−14.1216	+	10.2599i	−0.472296	+	0.343143i
$895$		0			0
$896$	4.93655	+	15.1931i	0.164919	+	0.507567i
$897$	42.5867	−	13.8372i	1.42193	−	0.462012i
$898$	31.1660	−	42.8963i	1.04002	−	1.43147i
$899$	−0.0957219	+	0.0695461i	−0.00319251	+	0.00231949i
$900$		0			0
$901$	12.2487			0.408063
$902$	9.25112	+	20.1561i	0.308029	+	0.671125i
$903$			3.44118i			0.114515i
$904$	−2.68872	+	8.27504i	−0.0894256	+	0.275224i
$905$		0			0
$906$	−9.97983	−	7.25077i	−0.331558	−	0.240891i
$907$	31.2586	−	10.1565i	1.03793	−	0.337242i	0.260006	−	0.965607i	$-0.416275\pi$
$907$	31.2586	−	10.1565i	1.03793	−	0.337242i	0.777919	+	0.628365i	$0.216275\pi$
$908$	−15.5752	+	5.06069i	−0.516881	+	0.167945i
$909$	5.42860	+	3.94411i	0.180055	+	0.130818i
$910$		0			0
$911$	−14.4328	+	44.4195i	−0.478179	+	1.47168i	0.363443	+	0.931617i	$0.381601\pi$
$911$	−14.4328	+	44.4195i	−0.478179	+	1.47168i	−0.841622	+	0.540067i	$0.818399\pi$
$912$		−	29.3857i		−	0.973058i
$913$	−22.2471	−	48.4714i	−0.736271	−	1.60417i
$914$	6.49842			0.214949
$915$		0			0
$916$	7.23946	−	5.25978i	0.239199	−	0.173788i
$917$	0.996296	−	1.37128i	0.0329006	−	0.0452838i
$918$	12.7383	−	4.13893i	0.420427	−	0.136605i
$919$	−2.26765	−	6.97910i	−0.0748028	−	0.230219i	0.906663	−	0.421855i	$-0.138621\pi$
$919$	−2.26765	−	6.97910i	−0.0748028	−	0.230219i	−0.981466	+	0.191636i	$0.938621\pi$
$920$		0			0
$921$	−25.9304	+	18.8396i	−0.854437	+	0.620785i
$922$	−43.7594	−	14.2183i	−1.44114	−	0.468255i
$923$		−	24.3143i		−	0.800314i
$924$	−3.80067	+	6.75996i	−0.125033	+	0.222386i
$925$		0			0
$926$	−10.0919	+	31.0596i	−0.331640	+	1.02068i
$927$	−2.49620	−	3.43572i	−0.0819859	−	0.112844i
$928$	−21.1862	+	29.1603i	−0.695470	+	0.957232i
$929$	−3.93333	−	12.1055i	−0.129048	−	0.397170i	0.865569	−	0.500790i	$-0.166957\pi$
$929$	−3.93333	−	12.1055i	−0.129048	−	0.397170i	−0.994617	+	0.103621i	$0.966957\pi$
$930$		0			0
$931$	19.2071	+	13.9548i	0.629488	+	0.457350i
$932$	−5.12667	−	7.05626i	−0.167930	−	0.231135i
$933$	−1.55434	−	0.505035i	−0.0508868	−	0.0165341i
$934$	46.0888			1.50807
$935$		0			0
$936$	6.47778			0.211733
$937$	−18.3110	−	5.94961i	−0.598195	−	0.194365i	−0.00575961	−	0.999983i	$-0.501833\pi$
$937$	−18.3110	−	5.94961i	−0.598195	−	0.194365i	−0.592435	+	0.805618i	$0.701833\pi$
$938$	−0.657665	−	0.905199i	−0.0214735	−	0.0295558i
$939$	−24.6046	−	17.8763i	−0.802942	−	0.583371i
$940$		0			0
$941$	−12.7530	−	39.2496i	−0.415735	−	1.27950i	−0.911592	−	0.411096i	$-0.865146\pi$
$941$	−12.7530	−	39.2496i	−0.415735	−	1.27950i	0.495857	−	0.868404i	$-0.334854\pi$
$942$	−13.5965	+	18.7140i	−0.442998	+	0.609735i
$943$	17.9791	+	24.7461i	0.585479	+	0.805842i
$944$	8.55007	−	26.3144i	0.278281	−	0.856461i
$945$		0			0
$946$	11.7015	+	2.34798i	0.380448	+	0.0763395i
$947$			50.3012i			1.63457i	0.576233	+	0.817285i	$0.304522\pi$
$947$			50.3012i			1.63457i	−0.576233	+	0.817285i	$0.695478\pi$
$948$	−3.26338	−	1.06034i	−0.105990	−	0.0344381i
$949$	−43.9496	+	31.9312i	−1.42666	+	1.03653i
$950$		0			0
$951$	9.09561	+	27.9934i	0.294945	+	0.907749i
$952$	−14.7282	+	4.78550i	−0.477345	+	0.155099i
$953$	−5.30523	+	7.30203i	−0.171853	+	0.236536i	−0.886252	−	0.463203i	$-0.846700\pi$
$953$	−5.30523	+	7.30203i	−0.171853	+	0.236536i	0.714399	+	0.699739i	$0.246700\pi$
$954$	2.46980	−	1.79442i	0.0799628	−	0.0580963i
$955$		0			0
$956$	−14.5093			−0.469263
$957$	18.2443	−	2.12833i	0.589756	−	0.0687991i
$958$		−	9.56617i		−	0.309069i
$959$	−2.27868	+	7.01305i	−0.0735824	+	0.226463i
$960$		0			0
$961$	25.0792	+	18.2211i	0.809005	+	0.587777i
$962$	10.4425	−	3.39296i	0.336678	−	0.109393i
$963$	14.9534	−	4.85867i	0.481868	−	0.156568i
$964$	29.4275	+	21.3803i	0.947796	+	0.688614i
$965$		0			0
$966$	−8.24484	+	25.3750i	−0.265273	+	0.816428i
$967$			30.2503i			0.972785i	0.873740	+	0.486392i	$0.161687\pi$
$967$			30.2503i			0.972785i	−0.873740	+	0.486392i	$0.838313\pi$
$968$	−10.0841	−	8.67130i	−0.324114	−	0.278706i
$969$	44.0926			1.41646
$970$		0			0
$971$	−10.3785	+	7.54040i	−0.333061	+	0.241983i	−0.741728	−	0.670700i	$-0.765994\pi$
$971$	−10.3785	+	7.54040i	−0.333061	+	0.241983i	0.408667	+	0.912683i	$0.365994\pi$
$972$	0.786610	−	1.08268i	0.0252305	−	0.0347269i
$973$	−14.7037	+	4.77751i	−0.471378	+	0.153160i
$974$	−5.10687	−	15.7173i	−0.163635	−	0.503616i
$975$		0			0
$976$	36.6785	−	26.6485i	1.17405	−	0.852996i
$977$	12.5151	+	4.06641i	0.400394	+	0.130096i	0.502290	−	0.864699i	$-0.332491\pi$
$977$	12.5151	+	4.06641i	0.400394	+	0.130096i	−0.101896	+	0.994795i	$0.532491\pi$
$978$			42.7645i			1.36746i
$979$	−5.57474	−	47.7875i	−0.178169	−	1.52729i
$980$		0			0
$981$	1.30991	−	4.03149i	0.0418222	−	0.128715i
$982$	−37.3851	−	51.4562i	−1.19301	−	1.64203i
$983$	13.1881	−	18.1519i	0.420635	−	0.578954i	−0.545137	−	0.838347i	$-0.683522\pi$
$983$	13.1881	−	18.1519i	0.420635	−	0.578954i	0.965772	+	0.259393i	$0.0835224\pi$
$984$	1.36738	+	4.20837i	0.0435905	+	0.134158i
$985$		0			0
$986$	−60.0110	−	43.6005i	−1.91114	−	1.38852i
$987$	−3.92266	−	5.39908i	−0.124860	−	0.171855i
$988$	−41.0154	−	13.3267i	−1.30487	−	0.423979i
$989$	16.4605			0.523414
$990$		0			0
$991$	22.9146			0.727907			0.363953	−	0.931417i	$-0.381427\pi$
$991$	22.9146			0.727907			0.363953	+	0.931417i	$0.381427\pi$
$992$	−0.132239	−	0.0429671i	−0.00419859	−	0.00136421i
$993$	−13.3958	−	18.4377i	−0.425101	−	0.585102i
$994$	11.7207	+	8.51555i	0.371757	+	0.270097i
$995$		0			0
$996$	6.65002	+	20.4666i	0.210714	+	0.648511i
$997$	9.89794	−	13.6234i	0.313471	−	0.431456i	−0.622989	−	0.782231i	$-0.714082\pi$
$997$	9.89794	−	13.6234i	0.313471	−	0.431456i	0.936460	+	0.350775i	$0.114082\pi$
$998$	−21.0483	−	28.9705i	−0.666272	−	0.917045i
$999$	−0.346608	+	1.06675i	−0.0109662	+	0.0337505i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.bx.e.724.1		16
5.2	odd	4		165.2.m.c.31.2	yes	8
5.3	odd	4		825.2.n.j.526.1		8
5.4	even	2	inner	825.2.bx.e.724.4		16
11.5	even	5	inner	825.2.bx.e.49.4		16
15.2	even	4		495.2.n.c.361.1		8
55.7	even	20		1815.2.a.q.1.1		4
55.18	even	20		9075.2.a.df.1.4		4
55.27	odd	20		165.2.m.c.16.2	✓	8
55.37	odd	20		1815.2.a.u.1.4		4
55.38	odd	20		825.2.n.j.676.1		8
55.48	odd	20		9075.2.a.co.1.1		4
55.49	even	10	inner	825.2.bx.e.49.1		16
165.62	odd	20		5445.2.a.bq.1.4		4
165.92	even	20		5445.2.a.bj.1.1		4
165.137	even	20		495.2.n.c.181.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.m.c.16.2	✓	8	55.27	odd	20
165.2.m.c.31.2	yes	8	5.2	odd	4
495.2.n.c.181.1		8	165.137	even	20
495.2.n.c.361.1		8	15.2	even	4
825.2.n.j.526.1		8	5.3	odd	4
825.2.n.j.676.1		8	55.38	odd	20
825.2.bx.e.49.1		16	55.49	even	10	inner
825.2.bx.e.49.4		16	11.5	even	5	inner
825.2.bx.e.724.1		16	1.1	even	1	trivial
825.2.bx.e.724.4		16	5.4	even	2	inner
1815.2.a.q.1.1		4	55.7	even	20
1815.2.a.u.1.4		4	55.37	odd	20
5445.2.a.bj.1.1		4	165.92	even	20
5445.2.a.bq.1.4		4	165.62	odd	20
9075.2.a.co.1.1		4	55.48	odd	20
9075.2.a.df.1.4		4	55.18	even	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.bx (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.73767 - 0.564602i) q^{2} +(0.587785 + 0.809017i) q^{3} +(1.08268 + 0.786610i) q^{4} +(-0.564602 - 1.73767i) q^{6} +(-1.02700 + 1.41355i) q^{7} +(0.710666 + 0.978148i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-1.73767 - 0.564602i) q^{2} +(0.587785 + 0.809017i) q^{3} +(1.08268 + 0.786610i) q^{4} +(-0.564602 - 1.73767i) q^{6} +(-1.02700 + 1.41355i) q^{7} +(0.710666 + 0.978148i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(-0.384301 - 3.29428i) q^{11} +1.33826i q^{12} +(-5.09549 - 1.65563i) q^{13} +(2.58268 - 1.87642i) q^{14} +(-1.50973 - 4.64646i) q^{16} +(6.97191 - 2.26531i) q^{17} +(1.07394 - 1.47815i) q^{18} +(4.86606 - 3.53540i) q^{19} -1.74724 q^{21} +(-1.19217 + 5.94135i) q^{22} +8.35772i q^{23} +(-0.373619 + 1.14988i) q^{24} +(7.91949 + 5.75385i) q^{26} +(-0.951057 + 0.309017i) q^{27} +(-2.22382 + 0.722562i) q^{28} +(4.48048 + 3.25526i) q^{29} +(-0.00660190 + 0.0203186i) q^{31} +6.50828i q^{32} +(2.43925 - 2.24724i) q^{33} -13.3939 q^{34} +(-1.08268 + 0.786610i) q^{36} +(0.659288 - 0.907432i) q^{37} +(-10.4517 + 3.39596i) q^{38} +(-1.65563 - 5.09549i) q^{39} +(2.96086 - 2.15119i) q^{41} +(3.03612 + 0.986494i) q^{42} -1.96950i q^{43} +(2.17524 - 3.86894i) q^{44} +(4.71878 - 14.5229i) q^{46} +(2.24507 + 3.09007i) q^{47} +(2.87167 - 3.95252i) q^{48} +(1.21974 + 3.75397i) q^{49} +(5.93066 + 4.30888i) q^{51} +(-4.21443 - 5.80067i) q^{52} +(1.58910 + 0.516329i) q^{53} +1.82709 q^{54} -2.11251 q^{56} +(5.72040 + 1.85867i) q^{57} +(-5.94766 - 8.18625i) q^{58} +(4.58172 + 3.32882i) q^{59} +(2.86761 + 8.82559i) q^{61} +(0.0229438 - 0.0315794i) q^{62} +(-1.02700 - 1.41355i) q^{63} +(0.655137 - 2.01630i) q^{64} +(-5.50739 + 2.52775i) q^{66} -0.350489i q^{67} +(9.33024 + 3.03158i) q^{68} +(-6.76153 + 4.91254i) q^{69} +(1.40238 + 4.31607i) q^{71} +(-1.14988 + 0.373619i) q^{72} +(5.95986 - 8.20305i) q^{73} +(-1.65796 + 1.20458i) q^{74} +8.04935 q^{76} +(5.05130 + 2.84001i) q^{77} +9.78903i q^{78} +(-0.792323 + 2.43852i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-6.35956 + 2.06635i) q^{82} +(15.2935 - 4.96915i) q^{83} +(-1.89169 - 1.37440i) q^{84} +(-1.11198 + 3.42233i) q^{86} +5.53818i q^{87} +(2.94919 - 2.71704i) q^{88} +14.5062 q^{89} +(7.57337 - 5.50238i) q^{91} +(-6.57426 + 9.04870i) q^{92} +(-0.0203186 + 0.00660190i) q^{93} +(-2.15652 - 6.63708i) q^{94} +(-5.26531 + 3.82547i) q^{96} +(1.80674 + 0.587045i) q^{97} -7.21182i q^{98} +(3.25181 + 0.652498i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{4} - 4 q^{6} + 4 q^{9}+O(q^{10}) \) 16 * q - 4 * q^4 - 4 * q^6 + 4 * q^9	\( 16 q - 4 q^{4} - 4 q^{6} + 4 q^{9} - 2 q^{11} + 20 q^{14} + 24 q^{16} - 4 q^{19} + 8 q^{24} + 32 q^{26} + 32 q^{29} - 10 q^{31} - 68 q^{34} + 4 q^{36} - 32 q^{39} + 10 q^{41} + 38 q^{44} + 20 q^{46} + 22 q^{49} + 8 q^{51} + 4 q^{54} + 40 q^{56} - 6 q^{59} - 22 q^{61} + 18 q^{64} - 62 q^{66} - 30 q^{69} + 2 q^{71} - 10 q^{74} + 116 q^{76} + 60 q^{79} - 4 q^{81} - 124 q^{86} + 96 q^{89} + 10 q^{91} + 38 q^{94} - 40 q^{96} + 22 q^{99}+O(q^{100}) \) 16 * q - 4 * q^4 - 4 * q^6 + 4 * q^9 - 2 * q^11 + 20 * q^14 + 24 * q^16 - 4 * q^19 + 8 * q^24 + 32 * q^26 + 32 * q^29 - 10 * q^31 - 68 * q^34 + 4 * q^36 - 32 * q^39 + 10 * q^41 + 38 * q^44 + 20 * q^46 + 22 * q^49 + 8 * q^51 + 4 * q^54 + 40 * q^56 - 6 * q^59 - 22 * q^61 + 18 * q^64 - 62 * q^66 - 30 * q^69 + 2 * q^71 - 10 * q^74 + 116 * q^76 + 60 * q^79 - 4 * q^81 - 124 * q^86 + 96 * q^89 + 10 * q^91 + 38 * q^94 - 40 * q^96 + 22 * q^99

Introduction

L-functions

Modular forms

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Representations

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Database

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