LMFDB - Embedded newform 825.2.n.j.676.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [825,2,Mod(301,825)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("825.301"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(825, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.n (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,-2,-2,2,0,-2,5,1,-2,0,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	$\Q(\zeta_{15})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			676.1
Root			$-0.104528 + 0.994522i$ of defining polynomial
Character	$\chi$	$=$	825.676
Dual form			825.2.n.j.526.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.564602 - 1.73767i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-1.08268 + 0.786610i) q^{4} +(-0.564602 + 1.73767i) q^{6} +(1.41355 - 1.02700i) q^{7} +(-0.978148 - 0.710666i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-0.384301 + 3.29428i) q^{11} +1.33826 q^{12} +(1.65563 + 5.09549i) q^{13} +(-2.58268 - 1.87642i) q^{14} +(-1.50973 + 4.64646i) q^{16} +(-2.26531 + 6.97191i) q^{17} +(1.47815 - 1.07394i) q^{18} +(-4.86606 - 3.53540i) q^{19} -1.74724 q^{21} +(5.94135 - 1.19217i) q^{22} -8.35772 q^{23} +(0.373619 + 1.14988i) q^{24} +(7.91949 - 5.75385i) q^{26} +(0.309017 - 0.951057i) q^{27} +(-0.722562 + 2.22382i) q^{28} +(-4.48048 + 3.25526i) q^{29} +(-0.00660190 - 0.0203186i) q^{31} +6.50828 q^{32} +(2.24724 - 2.43925i) q^{33} +13.3939 q^{34} +(-1.08268 - 0.786610i) q^{36} +(-0.907432 + 0.659288i) q^{37} +(-3.39596 + 10.4517i) q^{38} +(1.65563 - 5.09549i) q^{39} +(2.96086 + 2.15119i) q^{41} +(0.986494 + 3.03612i) q^{42} +1.96950 q^{43} +(-2.17524 - 3.86894i) q^{44} +(4.71878 + 14.5229i) q^{46} +(3.09007 + 2.24507i) q^{47} +(3.95252 - 2.87167i) q^{48} +(-1.21974 + 3.75397i) q^{49} +(5.93066 - 4.30888i) q^{51} +(-5.80067 - 4.21443i) q^{52} +(-0.516329 - 1.58910i) q^{53} -1.82709 q^{54} -2.11251 q^{56} +(1.85867 + 5.72040i) q^{57} +(8.18625 + 5.94766i) q^{58} +(-4.58172 + 3.32882i) q^{59} +(2.86761 - 8.82559i) q^{61} +(-0.0315794 + 0.0229438i) q^{62} +(1.41355 + 1.02700i) q^{63} +(-0.655137 - 2.01630i) q^{64} +(-5.50739 - 2.52775i) q^{66} -0.350489 q^{67} +(-3.03158 - 9.33024i) q^{68} +(6.76153 + 4.91254i) q^{69} +(1.40238 - 4.31607i) q^{71} +(0.373619 - 1.14988i) q^{72} +(8.20305 - 5.95986i) q^{73} +(1.65796 + 1.20458i) q^{74} +8.04935 q^{76} +(2.84001 + 5.05130i) q^{77} -9.78903 q^{78} +(0.792323 + 2.43852i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(2.06635 - 6.35956i) q^{82} +(4.96915 - 15.2935i) q^{83} +(1.89169 - 1.37440i) q^{84} +(-1.11198 - 3.42233i) q^{86} +5.53818 q^{87} +(2.71704 - 2.94919i) q^{88} -14.5062 q^{89} +(7.57337 + 5.50238i) q^{91} +(9.04870 - 6.57426i) q^{92} +(-0.00660190 + 0.0203186i) q^{93} +(2.15652 - 6.63708i) q^{94} +(-5.26531 - 3.82547i) q^{96} +(0.587045 + 1.80674i) q^{97} +7.21182 q^{98} +(-3.25181 + 0.652498i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} + 5 q^{7} + q^{8} - 2 q^{9} - q^{11} + 2 q^{12} + 16 q^{13} - 10 q^{14} + 12 q^{16} + 4 q^{17} + 3 q^{18} + 2 q^{19} + 9 q^{22} - 10 q^{23} - 4 q^{24} + 16 q^{26}+ \cdots - 11 q^{99}+O(q^{100}) $ 8 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^6 + 5 * q^7 + q^8 - 2 * q^9 - q^11 + 2 * q^12 + 16 * q^13 - 10 * q^14 + 12 * q^16 + 4 * q^17 + 3 * q^18 + 2 * q^19 + 9 * q^22 - 10 * q^23 - 4 * q^24 + 16 * q^26 - 2 * q^27 + 5 * q^28 - 16 * q^29 - 5 * q^31 + 4 * q^33 + 34 * q^34 + 2 * q^36 + 5 * q^37 - 28 * q^38 + 16 * q^39 + 5 * q^41 + 15 * q^42 + 8 * q^43 - 19 * q^44 + 10 * q^46 + q^47 - 3 * q^48 - 11 * q^49 + 4 * q^51 - 26 * q^52 + 15 * q^53 - 2 * q^54 + 20 * q^56 - 13 * q^57 + 24 * q^58 + 3 * q^59 - 11 * q^61 + 15 * q^62 + 5 * q^63 - 9 * q^64 - 31 * q^66 - 6 * q^67 - 9 * q^68 + 15 * q^69 + q^71 - 4 * q^72 + 35 * q^73 + 5 * q^74 + 58 * q^76 + 25 * q^77 - 24 * q^78 - 30 * q^79 - 2 * q^81 + 25 * q^82 - 31 * q^83 - 62 * q^86 + 34 * q^87 - 17 * q^88 - 48 * q^89 + 5 * q^91 + 20 * q^92 - 5 * q^93 - 19 * q^94 - 20 * q^96 - 11 * q^97 - 26 * q^98 - 11 * q^99

Character values

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

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$1$

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 $

$2$	−0.564602	−	1.73767i	−0.399234	−	1.22872i	−0.925615	−	0.378467i	$-0.876451\pi$
$2$	−0.564602	−	1.73767i	−0.399234	−	1.22872i	0.526381	−	0.850249i	$-0.323549\pi$
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$4$	−1.08268	+	0.786610i	−0.541338	+	0.393305i
$5$		0			0
$5$		0			0
$6$	−0.564602	+	1.73767i	−0.230498	+	0.709399i
$7$	1.41355	−	1.02700i	0.534270	−	0.388170i	−0.287683	−	0.957726i	$-0.592885\pi$
$7$	1.41355	−	1.02700i	0.534270	−	0.388170i	0.821953	+	0.569556i	$0.192885\pi$
$8$	−0.978148	−	0.710666i	−0.345827	−	0.251258i
$9$	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
$12$	1.33826			0.386323
$13$	1.65563	+	5.09549i	0.459188	+	1.41323i	0.866147	+	0.499789i	$0.166589\pi$
$13$	1.65563	+	5.09549i	0.459188	+	1.41323i	−0.406960	+	0.913446i	$0.633411\pi$
$14$	−2.58268	−	1.87642i	−0.690249	−	0.501495i
$15$		0			0
$16$	−1.50973	+	4.64646i	−0.377432	+	1.16162i
$17$	−2.26531	+	6.97191i	−0.549419	+	1.69094i	0.160826	+	0.986983i	$0.448584\pi$
$17$	−2.26531	+	6.97191i	−0.549419	+	1.69094i	−0.710245	+	0.703955i	$0.751416\pi$
$18$	1.47815	−	1.07394i	0.348403	−	0.253129i
$19$	−4.86606	−	3.53540i	−1.11635	−	0.811077i	−0.132699	−	0.991156i	$-0.542364\pi$
$19$	−4.86606	−	3.53540i	−1.11635	−	0.811077i	−0.983652	+	0.180080i	$0.942364\pi$
$20$		0			0
$21$	−1.74724			−0.381279
$22$	5.94135	−	1.19217i	1.26670	−	0.254172i
$23$	−8.35772			−1.74270			−0.871352	−	0.490658i	$-0.836756\pi$
$23$	−8.35772			−1.74270			−0.871352	+	0.490658i	$0.836756\pi$
$24$	0.373619	+	1.14988i	0.0762647	+	0.234719i
$25$		0			0
$26$	7.91949	−	5.75385i	1.55314	−	1.12842i
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$	−0.722562	+	2.22382i	−0.136551	+	0.420262i
$29$	−4.48048	+	3.25526i	−0.832005	+	0.604487i	−0.920126	−	0.391623i	$-0.871914\pi$
$29$	−4.48048	+	3.25526i	−0.832005	+	0.604487i	0.0881210	+	0.996110i	$0.471914\pi$
$30$		0			0
$31$	−0.00660190	−	0.0203186i	−0.00118574	−	0.00364932i	0.950462	−	0.310841i	$-0.100611\pi$
$31$	−0.00660190	−	0.0203186i	−0.00118574	−	0.00364932i	−0.951648	+	0.307192i	$0.900611\pi$
$32$	6.50828			1.15051
$33$	2.24724	−	2.43925i	0.391194	−	0.424618i
$34$	13.3939			2.29703
$35$		0			0
$36$	−1.08268	−	0.786610i	−0.180446	−	0.131102i
$37$	−0.907432	+	0.659288i	−0.149181	+	0.108386i	−0.659872	−	0.751378i	$-0.729390\pi$
$37$	−0.907432	+	0.659288i	−0.149181	+	0.108386i	0.510691	+	0.859764i	$0.329390\pi$
$38$	−3.39596	+	10.4517i	−0.550897	+	1.69549i
$39$	1.65563	−	5.09549i	0.265112	−	0.815931i
$40$		0			0
$41$	2.96086	+	2.15119i	0.462409	+	0.335960i	0.794476	−	0.607296i	$-0.207746\pi$
$41$	2.96086	+	2.15119i	0.462409	+	0.335960i	−0.332066	+	0.943256i	$0.607746\pi$
$42$	0.986494	+	3.03612i	0.152219	+	0.468483i
$43$	1.96950			0.300346			0.150173	−	0.988660i	$-0.452017\pi$
$43$	1.96950			0.300346			0.150173	+	0.988660i	$0.452017\pi$
$44$	−2.17524	−	3.86894i	−0.327930	−	0.583264i
$45$		0			0
$46$	4.71878	+	14.5229i	0.695747	+	2.14129i
$47$	3.09007	+	2.24507i	0.450733	+	0.327476i	0.789885	−	0.613255i	$-0.210140\pi$
$47$	3.09007	+	2.24507i	0.450733	+	0.327476i	−0.339152	+	0.940731i	$0.610140\pi$
$48$	3.95252	−	2.87167i	0.570497	−	0.414490i
$49$	−1.21974	+	3.75397i	−0.174248	+	0.536282i
$50$		0			0
$51$	5.93066	−	4.30888i	0.830459	−	0.603364i
$52$	−5.80067	−	4.21443i	−0.804408	−	0.584437i
$53$	−0.516329	−	1.58910i	−0.0709232	−	0.218279i	0.909312	−	0.416115i	$-0.136609\pi$
$53$	−0.516329	−	1.58910i	−0.0709232	−	0.218279i	−0.980235	+	0.197836i	$0.936609\pi$
$54$	−1.82709			−0.248636
$55$		0			0
$56$	−2.11251			−0.282296
$57$	1.85867	+	5.72040i	0.246187	+	0.757685i
$58$	8.18625	+	5.94766i	1.07491	+	0.780966i
$59$	−4.58172	+	3.32882i	−0.596489	+	0.433375i	−0.844631	−	0.535349i	$-0.820180\pi$
$59$	−4.58172	+	3.32882i	−0.596489	+	0.433375i	0.248142	+	0.968724i	$0.420180\pi$
$60$		0			0
$61$	2.86761	−	8.82559i	0.367160	−	1.13000i	−0.581458	−	0.813576i	$-0.697518\pi$
$61$	2.86761	−	8.82559i	0.367160	−	1.13000i	0.948618	−	0.316425i	$-0.102482\pi$
$62$	−0.0315794	+	0.0229438i	−0.00401059	+	0.00291387i
$63$	1.41355	+	1.02700i	0.178090	+	0.129390i
$64$	−0.655137	−	2.01630i	−0.0818921	−	0.252038i
$65$		0			0
$66$	−5.50739	−	2.52775i	−0.677913	−	0.311144i
$67$	−0.350489			−0.0428190			−0.0214095	−	0.999771i	$-0.506815\pi$
$67$	−0.350489			−0.0428190			−0.0214095	+	0.999771i	$0.506815\pi$
$68$	−3.03158	−	9.33024i	−0.367633	−	1.13146i
$69$	6.76153	+	4.91254i	0.813993	+	0.591401i
$70$		0			0
$71$	1.40238	−	4.31607i	0.166431	−	0.512223i	−0.832708	−	0.553713i	$-0.813210\pi$
$71$	1.40238	−	4.31607i	0.166431	−	0.512223i	0.999139	+	0.0414901i	$0.0132105\pi$
$72$	0.373619	−	1.14988i	0.0440314	−	0.135515i
$73$	8.20305	−	5.95986i	0.960094	−	0.697549i	0.00692130	−	0.999976i	$-0.497797\pi$
$73$	8.20305	−	5.95986i	0.960094	−	0.697549i	0.953173	+	0.302427i	$0.0977969\pi$
$74$	1.65796	+	1.20458i	0.192734	+	0.140029i
$75$		0			0
$76$	8.04935			0.923324
$77$	2.84001	+	5.05130i	0.323649	+	0.575649i
$78$	−9.78903			−1.10839
$79$	0.792323	+	2.43852i	0.0891433	+	0.274355i	0.985683	−	0.168608i	$-0.0539273\pi$
$79$	0.792323	+	2.43852i	0.0891433	+	0.274355i	−0.896540	+	0.442963i	$0.853927\pi$
$80$		0			0
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	2.06635	−	6.35956i	0.228190	−	0.702296i
$83$	4.96915	−	15.2935i	0.545435	−	1.67868i	−0.174519	−	0.984654i	$-0.555837\pi$
$83$	4.96915	−	15.2935i	0.545435	−	1.67868i	0.719954	−	0.694022i	$-0.244163\pi$
$84$	1.89169	−	1.37440i	0.206401	−	0.149959i
$85$		0			0
$86$	−1.11198	−	3.42233i	−0.119908	−	0.369040i
$87$	5.53818			0.593755
$88$	2.71704	−	2.94919i	0.289637	−	0.314384i
$89$	−14.5062			−1.53765			−0.768825	−	0.639459i	$-0.779159\pi$
$89$	−14.5062			−1.53765			−0.768825	+	0.639459i	$0.779159\pi$
$90$		0			0
$91$	7.57337	+	5.50238i	0.793905	+	0.576806i
$92$	9.04870	−	6.57426i	0.943392	−	0.685414i
$93$	−0.00660190	+	0.0203186i	−0.000684585	+	0.00210694i
$94$	2.15652	−	6.63708i	0.222428	−	0.684562i
$95$		0			0
$96$	−5.26531	−	3.82547i	−0.537389	−	0.390436i
$97$	0.587045	+	1.80674i	0.0596054	+	0.183446i	0.976426	−	0.215853i	$-0.0692533\pi$
$97$	0.587045	+	1.80674i	0.0596054	+	0.183446i	−0.916820	+	0.399300i	$0.869253\pi$
$98$	7.21182			0.728504
$99$	−3.25181	+	0.652498i	−0.326819	+	0.0655785i
$100$		0			0
$101$	2.07354	+	6.38170i	0.206325	+	0.635003i	0.999656	+	0.0262128i	$0.00834474\pi$
$101$	2.07354	+	6.38170i	0.206325	+	0.635003i	−0.793332	+	0.608790i	$0.791655\pi$
$102$	−10.8359	−	7.87272i	−1.07291	−	0.779515i
$103$	−3.43572	+	2.49620i	−0.338532	+	0.245958i	−0.744042	−	0.668133i	$-0.767094\pi$
$103$	−3.43572	+	2.49620i	−0.338532	+	0.245958i	0.405510	+	0.914090i	$0.367094\pi$
$104$	2.00174	−	6.16074i	0.196287	−	0.604110i
$105$		0			0
$106$	−2.46980	+	1.79442i	−0.239888	+	0.174289i
$107$	−12.7202	−	9.24174i	−1.22970	−	0.893433i	−0.232837	−	0.972516i	$-0.574801\pi$
$107$	−12.7202	−	9.24174i	−1.22970	−	0.893433i	−0.996868	+	0.0790831i	$0.974801\pi$
$108$	0.413545	+	1.27276i	0.0397934	+	0.122472i
$109$	4.23895			0.406018			0.203009	−	0.979177i	$-0.434928\pi$
$109$	4.23895			0.406018			0.203009	+	0.979177i	$0.434928\pi$
$110$		0			0
$111$	1.12165			0.106462
$112$	2.63785	+	8.11848i	0.249254	+	0.767124i
$113$	−5.82203	−	4.22996i	−0.547691	−	0.397921i	0.279242	−	0.960221i	$-0.409917\pi$
$113$	−5.82203	−	4.22996i	−0.547691	−	0.397921i	−0.826933	+	0.562300i	$0.809917\pi$
$114$	8.89074	−	6.45950i	0.832694	−	0.604988i
$115$		0			0
$116$	2.29029	−	7.04879i	0.212648	−	0.654463i
$117$	−4.33448	+	3.14919i	−0.400723	+	0.291142i
$118$	8.37122	+	6.08205i	0.770633	+	0.559898i
$119$	3.95804	+	12.1816i	0.362833	+	1.11668i
$120$		0			0
$121$	−10.7046	−	2.53200i	−0.973148	−	0.230181i
$122$	−16.9550			−1.53503
$123$	−1.13095	−	3.48070i	−0.101974	−	0.313845i
$124$	0.0231305	+	0.0168053i	0.00207718	+	0.00150916i
$125$		0			0
$126$	0.986494	−	3.03612i	0.0878839	−	0.270479i
$127$	−3.92051	+	12.0661i	−0.347889	+	1.07069i	0.612130	+	0.790757i	$0.290313\pi$
$127$	−3.92051	+	12.0661i	−0.347889	+	1.07069i	−0.960019	+	0.279935i	$0.909687\pi$
$128$	7.39685	−	5.37413i	0.653796	−	0.475010i
$129$	−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	$0.513494\pi$
$132$	−0.514295	+	4.40861i	−0.0447637	+	0.383721i
$133$	−10.5093			−0.911268
$134$	0.197887	+	0.609032i	0.0170948	+	0.0526124i
$135$		0			0
$136$	7.17051	−	5.20968i	0.614866	−	0.446726i
$137$	−1.30416	+	4.01379i	−0.111422	+	0.342921i	−0.991184	−	0.132493i	$-0.957702\pi$
$137$	−1.30416	+	4.01379i	−0.111422	+	0.342921i	0.879762	+	0.475414i	$0.157702\pi$
$138$	4.71878	−	14.5229i	0.401690	−	1.23627i
$139$	−7.15855	+	5.20099i	−0.607180	+	0.441142i	−0.848420	−	0.529323i	$-0.822446\pi$
$139$	−7.15855	+	5.20099i	−0.607180	+	0.441142i	0.241240	+	0.970465i	$0.422446\pi$
$140$		0			0
$141$	−1.18030	−	3.63259i	−0.0993993	−	0.305919i
$142$	−8.29167			−0.695821
$143$	−17.4223	+	3.49590i	−1.45692	+	0.292342i
$144$	−4.88558			−0.407132
$145$		0			0
$146$	−14.9877	−	10.8892i	−1.24039	−	0.901197i
$147$	3.19332	−	2.32008i	0.263380	−	0.191357i
$148$	0.463852	−	1.42759i	0.0381284	−	0.117347i
$149$	2.95222	−	9.08598i	0.241855	−	0.744353i	−0.754283	−	0.656549i	$-0.772015\pi$
$149$	2.95222	−	9.08598i	0.241855	−	0.744353i	0.996138	−	0.0878033i	$-0.0279847\pi$
$150$		0			0
$151$	5.46214	+	3.96848i	0.444503	+	0.322950i	0.787422	−	0.616415i	$-0.211416\pi$
$151$	5.46214	+	3.96848i	0.444503	+	0.322950i	−0.342919	+	0.939365i	$0.611416\pi$
$152$	2.24724	+	6.91629i	0.182275	+	0.560985i
$153$	−7.33070			−0.592652
$154$	7.17400	−	7.78696i	0.578097	−	0.627491i
$155$		0			0
$156$	2.21566	+	6.81910i	0.177395	+	0.545965i
$157$	−10.2425	−	7.44162i	−0.817441	−	0.593906i	0.0985374	−	0.995133i	$-0.468584\pi$
$157$	−10.2425	−	7.44162i	−0.817441	−	0.593906i	−0.915978	+	0.401228i	$0.868584\pi$
$158$	3.78999	−	2.75359i	0.301515	−	0.219064i
$159$	−0.516329	+	1.58910i	−0.0409475	+	0.126024i
$160$		0			0
$161$	−11.8140	+	8.58338i	−0.931074	+	0.676465i
$162$	1.47815	+	1.07394i	0.116134	+	0.0843765i
$163$	7.23278	+	22.2602i	0.566515	+	1.74355i	0.663407	+	0.748259i	$0.269110\pi$
$163$	7.23278	+	22.2602i	0.566515	+	1.74355i	−0.0968923	+	0.995295i	$0.530890\pi$
$164$	−4.89781			−0.382454
$165$		0			0
$166$	−29.3805			−2.28037
$167$	−0.943091	−	2.90254i	−0.0729786	−	0.224605i	0.907913	−	0.419158i	$-0.137675\pi$
$167$	−0.943091	−	2.90254i	−0.0729786	−	0.224605i	−0.980892	+	0.194553i	$0.937675\pi$
$168$	1.70906	+	1.24170i	0.131857	+	0.0957994i
$169$	−12.7057	+	9.23123i	−0.977362	+	0.710095i
$170$		0			0
$171$	1.85867	−	5.72040i	0.142136	−	0.437450i
$172$	−2.13233	+	1.54923i	−0.162589	+	0.118128i
$173$	12.9503	+	9.40893i	0.984592	+	0.715348i	0.958730	−	0.284318i	$-0.0917670\pi$
$173$	12.9503	+	9.40893i	0.984592	+	0.715348i	0.0258617	+	0.999666i	$0.491767\pi$
$174$	−3.12687	−	9.62351i	−0.237047	−	0.729557i
$175$		0			0
$176$	−14.7266	−	6.75911i	−1.11006	−	0.509487i
$177$	5.66332			0.425681
$178$	8.19021	+	25.2069i	0.613883	+	1.88934i
$179$	15.6133	+	11.3437i	1.16699	+	0.847870i	0.990646	−	0.136458i	$-0.0435719\pi$
$179$	15.6133	+	11.3437i	1.16699	+	0.847870i	0.176347	+	0.984328i	$0.443572\pi$
$180$		0			0
$181$	−3.76724	+	11.5944i	−0.280017	+	0.861804i	0.707831	+	0.706382i	$0.249674\pi$
$181$	−3.76724	+	11.5944i	−0.280017	+	0.861804i	−0.987848	+	0.155422i	$0.950326\pi$
$182$	5.28536	−	16.2667i	0.391777	−	1.20576i
$183$	−7.50749	+	5.45451i	−0.554970	+	0.403209i
$184$	8.17508	+	5.93954i	0.602675	+	0.437869i
$185$		0			0
$186$	0.0390343			0.00286214
$187$	−22.0969	−	10.1419i	−1.61589	−	0.741649i
$188$	−5.11153			−0.372797
$189$	−0.539926	−	1.66172i	−0.0392739	−	0.120873i
$190$		0			0
$191$	10.8605	−	7.89064i	0.785841	−	0.570947i	−0.120885	−	0.992666i	$-0.538573\pi$
$191$	10.8605	−	7.89064i	0.785841	−	0.570947i	0.906726	+	0.421720i	$0.138573\pi$
$192$	−0.655137	+	2.01630i	−0.0472804	+	0.145514i
$193$	−2.34167	+	7.20693i	−0.168557	+	0.518766i	−0.999281	−	0.0379190i	$-0.987927\pi$
$193$	−2.34167	+	7.20693i	−0.168557	+	0.518766i	0.830723	+	0.556685i	$0.187927\pi$
$194$	2.80806	−	2.04018i	0.201607	−	0.146476i
$195$		0			0
$196$	−1.63233	−	5.02379i	−0.116595	−	0.358842i
$197$	6.89118			0.490976			0.245488	−	0.969400i	$-0.421052\pi$
$197$	6.89118			0.490976			0.245488	+	0.969400i	$0.421052\pi$
$198$	2.96980	+	5.28215i	0.211055	+	0.375386i
$199$	0.639398			0.0453257			0.0226629	−	0.999743i	$-0.492786\pi$
$199$	0.639398			0.0453257			0.0226629	+	0.999743i	$0.492786\pi$
$200$		0			0
$201$	0.283551	+	0.206012i	0.0200002	+	0.0145310i
$202$	9.91854	−	7.20624i	0.697866	−	0.507029i
$203$	−2.99021	+	9.20292i	−0.209872	+	0.645918i
$204$	−3.03158	+	9.33024i	−0.212253	+	0.653248i
$205$		0			0
$206$	6.27737	+	4.56078i	0.437365	+	0.317765i
$207$	−2.58268	−	7.94866i	−0.179508	−	0.552470i
$208$	−26.1755			−1.81495
$209$	13.5167	−	14.6715i	0.934966	−	1.01485i
$210$		0			0
$211$	−1.18090	−	3.63445i	−0.0812968	−	0.250206i	0.902144	−	0.431435i	$-0.141992\pi$
$211$	−1.18090	−	3.63445i	−0.0812968	−	0.250206i	−0.983441	+	0.181229i	$0.941992\pi$
$212$	1.80902	+	1.31433i	0.124244	+	0.0902684i
$213$	−3.67147	+	2.66748i	−0.251565	+	0.182772i
$214$	−8.87723	+	27.3213i	−0.606835	+	1.86765i
$215$		0			0
$216$	−0.978148	+	0.710666i	−0.0665545	+	0.0483547i
$217$	−0.0301993	−	0.0219411i	−0.00205006	−	0.00148946i
$218$	−2.39332	−	7.36589i	−0.162096	−	0.498881i
$219$	−10.1395			−0.685165
$220$		0			0
$221$	−39.2758			−2.64198
$222$	−0.633284	−	1.94905i	−0.0425033	−	0.130812i
$223$	−21.6171	−	15.7057i	−1.44758	−	1.05173i	−0.986388	−	0.164434i	$-0.947420\pi$
$223$	−21.6171	−	15.7057i	−1.44758	−	1.05173i	−0.461197	−	0.887298i	$-0.652580\pi$
$224$	9.19975	−	6.68401i	0.614684	−	0.446594i
$225$		0			0
$226$	−4.06312	+	12.5050i	−0.270275	+	0.831820i
$227$	9.90020	−	7.19291i	0.657099	−	0.477411i	−0.208583	−	0.978005i	$-0.566885\pi$
$227$	9.90020	−	7.19291i	0.657099	−	0.477411i	0.865682	+	0.500594i	$0.166885\pi$
$228$	−6.51206	−	4.73129i	−0.431272	−	0.313337i
$229$	−2.06628	−	6.35937i	−0.136544	−	0.420239i	0.859283	−	0.511500i	$-0.170910\pi$
$229$	−2.06628	−	6.35937i	−0.136544	−	0.420239i	−0.995827	+	0.0912615i	$0.970910\pi$
$230$		0			0
$231$	0.671466	−	5.75590i	0.0441792	−	0.378710i
$232$	6.69598			0.439612
$233$	2.01399	+	6.19844i	0.131941	+	0.406073i	0.995102	−	0.0988565i	$-0.0315185\pi$
$233$	2.01399	+	6.19844i	0.131941	+	0.406073i	−0.863161	+	0.504930i	$0.831518\pi$
$234$	7.91949	+	5.75385i	0.517714	+	0.376141i
$235$		0			0
$236$	2.34204	−	7.20806i	0.152454	−	0.469205i
$237$	0.792323	−	2.43852i	0.0514669	−	0.158399i
$238$	18.9328	−	13.7555i	1.22723	−	0.891637i
$239$	8.77126	+	6.37269i	0.567366	+	0.412215i	0.834147	−	0.551542i	$-0.185960\pi$
$239$	8.77126	+	6.37269i	0.567366	+	0.412215i	−0.266782	+	0.963757i	$0.585960\pi$
$240$		0			0
$241$	27.1803			1.75084			0.875420	−	0.483363i	$-0.160585\pi$
$241$	27.1803			1.75084			0.875420	+	0.483363i	$0.160585\pi$
$242$	1.64409	+	20.0306i	0.105686	+	1.28762i
$243$	1.00000			0.0641500
$244$	3.83761	+	11.8109i	0.245678	+	0.756118i
$245$		0			0
$246$	−5.40977	+	3.93043i	−0.344914	+	0.250595i
$247$	9.95823	−	30.6483i	0.633627	−	1.95010i
$248$	−0.00798208	+	0.0245663i	−0.000506862	+	0.00155996i
$249$	−13.0094	+	9.45188i	−0.824437	+	0.598989i
$250$		0			0
$251$	1.71332	+	5.27307i	0.108144	+	0.332833i	0.990455	−	0.137833i	$-0.0440137\pi$
$251$	1.71332	+	5.27307i	0.108144	+	0.332833i	−0.882311	+	0.470666i	$0.844014\pi$
$252$	−2.33826			−0.147297
$253$	3.21188	−	27.5327i	0.201929	−	1.73097i
$254$	23.1804			1.45447
$255$		0			0
$256$	−16.9451	−	12.3113i	−1.05907	−	0.769457i
$257$	−15.3260	+	11.1350i	−0.956008	+	0.694580i	−0.952220	−	0.305413i	$-0.901206\pi$
$257$	−15.3260	+	11.1350i	−0.956008	+	0.694580i	−0.00378765	+	0.999993i	$0.501206\pi$
$258$	−1.11198	+	3.42233i	−0.0692291	+	0.213065i
$259$	−0.605607	+	1.86387i	−0.0376306	+	0.115815i
$260$		0			0
$261$	−4.48048	−	3.25526i	−0.277335	−	0.201496i
$262$	0.547722	+	1.68571i	0.0338384	+	0.104144i
$263$	−3.20873			−0.197859			−0.0989293	−	0.995094i	$-0.531542\pi$
$263$	−3.20873			−0.197859			−0.0989293	+	0.995094i	$0.531542\pi$
$264$	−3.93162	+	0.788907i	−0.241974	+	0.0485539i
$265$		0			0
$266$	5.93355	+	18.2616i	0.363809	+	1.11969i
$267$	11.7357	+	8.52651i	0.718215	+	0.521814i
$268$	0.379466	−	0.275698i	0.0231796	−	0.0168409i
$269$	−1.00252	+	3.08544i	−0.0611248	+	0.188123i	−0.976956	−	0.213441i	$-0.931533\pi$
$269$	−1.00252	+	3.08544i	−0.0611248	+	0.188123i	0.915831	+	0.401563i	$0.131533\pi$
$270$		0			0
$271$	1.64212	−	1.19307i	0.0997517	−	0.0724738i	−0.536791	−	0.843715i	$-0.680364\pi$
$271$	1.64212	−	1.19307i	0.0997517	−	0.0724738i	0.636543	+	0.771241i	$0.280364\pi$
$272$	−28.9747	−	21.0514i	−1.75685	−	1.27643i
$273$	−2.89277	−	8.90304i	−0.175078	−	0.538836i
$274$	7.71096			0.465836
$275$		0			0
$276$	−11.1848			−0.673246
$277$	−3.49701	−	10.7627i	−0.210115	−	0.646668i	−0.999464	−	0.0327234i	$-0.989582\pi$
$277$	−3.49701	−	10.7627i	−0.210115	−	0.646668i	0.789349	−	0.613944i	$-0.210418\pi$
$278$	13.0793	+	9.50268i	0.784446	+	0.569933i
$279$	0.0172840	−	0.0125576i	0.00103477	−	0.000751802i
$280$		0			0
$281$	−3.18835	+	9.81272i	−0.190201	+	0.585378i	−0.999999	−	0.00133051i	$-0.999576\pi$
$281$	−3.18835	+	9.81272i	−0.190201	+	0.585378i	0.809798	+	0.586708i	$0.199576\pi$
$282$	−5.64583	+	4.10194i	−0.336205	+	0.244267i
$283$	−1.70370	−	1.23781i	−0.101274	−	0.0735801i	0.535996	−	0.844221i	$-0.319936\pi$
$283$	−1.70370	−	1.23781i	−0.101274	−	0.0735801i	−0.637270	+	0.770641i	$0.719936\pi$
$284$	1.87674	+	5.77602i	0.111364	+	0.342744i
$285$		0			0
$286$	15.9113	+	28.3003i	0.940858	+	1.67343i
$287$	6.39459			0.377461
$288$	2.01117	+	6.18975i	0.118509	+	0.364734i
$289$	−29.7227	−	21.5948i	−1.74839	−	1.27028i
$290$		0			0
$291$	0.587045	−	1.80674i	0.0344132	−	0.105913i
$292$	−4.19315	+	12.9052i	−0.245386	+	0.755220i
$293$	−18.9111	+	13.7398i	−1.10480	+	0.802685i	−0.981837	−	0.189726i	$-0.939240\pi$
$293$	−18.9111	+	13.7398i	−1.10480	+	0.802685i	−0.122964	+	0.992411i	$0.539240\pi$
$294$	−5.83448	−	4.23900i	−0.340274	−	0.247223i
$295$		0			0
$296$	1.35614			0.0788238
$297$	3.01430	+	1.38348i	0.174907	+	0.0802778i
$298$	−17.4552			−1.01115
$299$	−13.8372	−	42.5867i	−0.800228	−	2.46285i
$300$		0			0
$301$	2.78398	−	2.02268i	0.160466	−	0.116585i
$302$	3.81196	−	11.7320i	0.219353	−	0.675100i
$303$	2.07354	−	6.38170i	0.119122	−	0.366619i
$304$	23.7735	−	17.2725i	1.36351	−	0.990645i
$305$		0			0
$306$	4.13893	+	12.7383i	0.236607	+	0.728201i
$307$	32.0518			1.82929			0.914646	−	0.404256i	$-0.132469\pi$
$307$	32.0518			1.82929			0.914646	+	0.404256i	$0.132469\pi$
$308$	−7.04821	−	3.23494i	−0.401609	−	0.184328i
$309$	4.24678			0.241591
$310$		0			0
$311$	−1.32220	−	0.960634i	−0.0749751	−	0.0544726i	0.549666	−	0.835384i	$-0.314755\pi$
$311$	−1.32220	−	0.960634i	−0.0749751	−	0.0544726i	−0.624641	+	0.780912i	$0.714755\pi$
$312$	−5.24064	+	3.80755i	−0.296693	+	0.215560i
$313$	−9.39813	+	28.9245i	−0.531214	+	1.63491i	0.220477	+	0.975392i	$0.429239\pi$
$313$	−9.39813	+	28.9245i	−0.531214	+	1.63491i	−0.751691	+	0.659516i	$0.770761\pi$
$314$	−7.14811	+	21.9996i	−0.403391	+	1.24151i
$315$		0			0
$316$	−2.77599	−	2.01688i	−0.156162	−	0.113458i
$317$	9.09561	+	27.9934i	0.510861	+	1.57227i	0.790690	+	0.612217i	$0.209722\pi$
$317$	9.09561	+	27.9934i	0.510861	+	1.57227i	−0.279829	+	0.960050i	$0.590278\pi$
$318$	3.05284			0.171195
$319$	−9.00190	−	16.0110i	−0.504010	−	0.896443i
$320$		0			0
$321$	4.85867	+	14.9534i	0.271185	+	0.834620i
$322$	21.5853	+	15.6826i	1.20290	+	0.873958i
$323$	35.6717	−	25.9170i	1.98482	−	1.44206i
$324$	0.413545	−	1.27276i	0.0229747	−	0.0707090i
$325$		0			0
$326$	34.5972	−	25.1363i	1.91616	−	1.39217i
$327$	−3.42939	−	2.49159i	−0.189645	−	0.137786i
$328$	−1.36738	−	4.20837i	−0.0755010	−	0.232368i
$329$	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	$0.715444\pi$
$332$	6.65002	+	20.4666i	0.364967	+	1.12325i
$333$	−0.907432	−	0.659288i	−0.0497270	−	0.0361287i
$334$	−4.51117	+	3.27756i	−0.246840	+	0.179340i
$335$		0			0
$336$	2.63785	−	8.11848i	0.143907	−	0.442899i
$337$	−11.7227	+	8.51705i	−0.638577	+	0.463954i	−0.859361	−	0.511369i	$-0.829138\pi$
$337$	−11.7227	+	8.51705i	−0.638577	+	0.463954i	0.220784	+	0.975323i	$0.429138\pi$
$338$	23.2145	+	16.8663i	1.26270	+	0.917406i
$339$	2.22382	+	6.84421i	0.120781	+	0.371727i
$340$		0			0
$341$	0.0694723	−	0.0139401i	0.00376213	−	0.000754899i
$342$	−10.9896			−0.594247
$343$	5.91066	+	18.1911i	0.319146	+	0.982229i
$344$	−1.92646	−	1.39966i	−0.103868	−	0.0754644i
$345$		0			0
$346$	9.03783	−	27.8156i	0.485877	−	1.49537i
$347$	−1.35574	+	4.17255i	−0.0727802	+	0.223994i	−0.980829	−	0.194870i	$-0.937572\pi$
$347$	−1.35574	+	4.17255i	−0.0727802	+	0.223994i	0.908049	+	0.418864i	$0.137572\pi$
$348$	−5.99606	+	4.35639i	−0.321422	+	0.233527i
$349$	−11.6548	−	8.46769i	−0.623866	−	0.453265i	0.230404	−	0.973095i	$-0.425995\pi$
$349$	−11.6548	−	8.46769i	−0.623866	−	0.453265i	−0.854270	+	0.519830i	$0.825995\pi$
$350$		0			0
$351$	5.35772			0.285974
$352$	−2.50114	+	21.4401i	−0.133311	+	1.14276i
$353$	6.01065			0.319914			0.159957	−	0.987124i	$-0.448864\pi$
$353$	6.01065			0.319914			0.159957	+	0.987124i	$0.448864\pi$
$354$	−3.19752	−	9.84096i	−0.169946	−	0.523041i
$355$		0			0
$356$	15.7055	−	11.4107i	0.832389	−	0.604766i
$357$	3.95804	−	12.1816i	0.209482	−	0.644718i
$358$	10.8963	−	33.5354i	0.575888	−	1.77240i
$359$	1.98787	−	1.44428i	0.104916	−	0.0762259i	−0.534090	−	0.845427i	$-0.679346\pi$
$359$	1.98787	−	1.44428i	0.104916	−	0.0762259i	0.639006	+	0.769201i	$0.279346\pi$
$360$		0			0
$361$	5.30818	+	16.3369i	0.279378	+	0.859836i
$362$	22.2742			1.17070
$363$	7.17195	+	8.34045i	0.376430	+	0.437760i
$364$	−12.5277			−0.656632
$365$		0			0
$366$	13.7169	+	9.96589i	0.716992	+	0.520926i
$367$	1.19726	−	0.869862i	0.0624966	−	0.0454064i	−0.556098	−	0.831116i	$-0.687702\pi$
$367$	1.19726	−	0.869862i	0.0624966	−	0.0454064i	0.618595	+	0.785710i	$0.287702\pi$
$368$	12.6179	−	38.8338i	0.657752	−	2.02435i
$369$	−1.13095	+	3.48070i	−0.0588749	+	0.181198i
$370$		0			0
$371$	−2.36186	−	1.71599i	−0.122622	−	0.0890898i
$372$	−0.00883507	−	0.0271915i	−0.000458077	−	0.00140982i
$373$	24.3331			1.25992			0.629961	−	0.776627i	$-0.283071\pi$
$373$	24.3331			1.25992			0.629961	+	0.776627i	$0.283071\pi$
$374$	−5.14728	+	44.1232i	−0.266159	+	2.28156i
$375$		0			0
$376$	−1.42705	−	4.39201i	−0.0735945	−	0.226501i
$377$	−24.0052	−	17.4408i	−1.23633	−	0.898245i
$378$	−2.58268	+	1.87642i	−0.132839	+	0.0965128i
$379$	4.92299	−	15.1514i	0.252877	−	0.778276i	−0.741363	−	0.671104i	$-0.765820\pi$
$379$	4.92299	−	15.1514i	0.252877	−	0.778276i	0.994241	−	0.107172i	$-0.0341795\pi$
$380$		0			0
$381$	10.2640	−	7.45726i	0.525842	−	0.382047i
$382$	−19.8432	−	14.4169i	−1.01527	−	0.737634i
$383$	1.21133	+	3.72809i	0.0618960	+	0.190496i	0.977223	−	0.212215i	$-0.0680678\pi$
$383$	1.21133	+	3.72809i	0.0618960	+	0.190496i	−0.915327	+	0.402712i	$0.868068\pi$
$384$	−9.14301			−0.466577
$385$		0			0
$386$	13.8454			0.704710
$387$	0.608609	+	1.87310i	0.0309373	+	0.0952153i
$388$	−2.05678	−	1.49434i	−0.104417	−	0.0758635i
$389$	28.5510	−	20.7435i	1.44759	−	1.05174i	0.461209	−	0.887292i	$-0.347416\pi$
$389$	28.5510	−	20.7435i	1.44759	−	1.05174i	0.986386	−	0.164447i	$-0.0525840\pi$
$390$		0			0
$391$	18.9328	−	58.2693i	0.957475	−	2.94680i
$392$	3.86090	−	2.80511i	0.195005	−	0.141679i
$393$	0.784829	+	0.570212i	0.0395894	+	0.0287634i
$394$	−3.89078	−	11.9746i	−0.196015	−	0.603271i
$395$		0			0
$396$	3.00739	−	3.26435i	0.151127	−	0.164040i
$397$	−23.2231			−1.16553			−0.582767	−	0.812639i	$-0.698030\pi$
$397$	−23.2231			−1.16553			−0.582767	+	0.812639i	$0.698030\pi$
$398$	−0.361006	−	1.11106i	−0.0180956	−	0.0556925i
$399$	8.50217	+	6.17719i	0.425641	+	0.309246i
$400$		0			0
$401$	1.75973	−	5.41589i	0.0878766	−	0.270457i	−0.897455	−	0.441106i	$-0.854586\pi$
$401$	1.75973	−	5.41589i	0.0878766	−	0.270457i	0.985332	+	0.170649i	$0.0545864\pi$
$402$	0.197887	−	0.609032i	0.00986969	−	0.0303758i
$403$	0.0926028	−	0.0672799i	0.00461287	−	0.00335145i
$404$	−7.26488	−	5.27824i	−0.361441	−	0.262602i
$405$		0			0
$406$	17.6799			0.877438
$407$	−1.82315	−	3.24270i	−0.0903704	−	0.160735i
$408$	−8.86324			−0.438796
$409$	7.86540	+	24.2072i	0.388919	+	1.19697i	0.933597	+	0.358324i	$0.116652\pi$
$409$	7.86540	+	24.2072i	0.388919	+	1.19697i	−0.544679	+	0.838645i	$0.683348\pi$
$410$		0			0
$411$	3.41434	−	2.48066i	0.168417	−	0.122362i
$412$	1.75624	−	5.40515i	0.0865237	−	0.266292i
$413$	−3.05777	+	9.41086i	−0.150463	+	0.463078i
$414$	−12.3539	+	8.97566i	−0.607163	+	0.441130i
$415$		0			0
$416$	10.7753	+	33.1629i	0.528301	+	1.62594i
$417$	8.84846			0.433311
$418$	−33.1258	−	15.2039i	−1.62023	−	0.743645i
$419$	−13.4850			−0.658786			−0.329393	−	0.944193i	$-0.606844\pi$
$419$	−13.4850			−0.658786			−0.329393	+	0.944193i	$0.606844\pi$
$420$		0			0
$421$	−2.38633	−	1.73377i	−0.116303	−	0.0844990i	0.528113	−	0.849174i	$-0.322900\pi$
$421$	−2.38633	−	1.73377i	−0.116303	−	0.0844990i	−0.644416	+	0.764675i	$0.722900\pi$
$422$	−5.64872	+	4.10404i	−0.274975	+	0.199781i
$423$	−1.18030	+	3.63259i	−0.0573882	+	0.176623i
$424$	−0.624271	+	1.92131i	−0.0303173	+	0.0933070i
$425$		0			0
$426$	6.70810	+	4.87372i	0.325009	+	0.236133i
$427$	−5.01039	−	15.4204i	−0.242470	−	0.746246i
$428$	21.0415			1.01708
$429$	16.1497	+	7.41230i	0.779717	+	0.357869i
$430$		0			0
$431$	3.56072	+	10.9588i	0.171514	+	0.527866i	0.999457	−	0.0329464i	$-0.0104891\pi$
$431$	3.56072	+	10.9588i	0.171514	+	0.527866i	−0.827943	+	0.560812i	$0.810489\pi$
$432$	3.95252	+	2.87167i	0.190166	+	0.138163i
$433$	9.03174	−	6.56194i	0.434038	−	0.315347i	−0.349224	−	0.937039i	$-0.613555\pi$
$433$	9.03174	−	6.56194i	0.434038	−	0.315347i	0.783261	+	0.621693i	$0.213555\pi$
$434$	−0.0210757	+	0.0648642i	−0.00101166	+	0.00311358i
$435$		0			0
$436$	−4.58941	+	3.33440i	−0.219793	+	0.159689i
$437$	40.6692	+	29.5479i	1.94547	+	1.41347i
$438$	5.72480	+	17.6191i	0.273541	+	0.841874i
$439$	0.993624			0.0474231			0.0237115	−	0.999719i	$-0.492452\pi$
$439$	0.993624			0.0474231			0.0237115	+	0.999719i	$0.492452\pi$
$440$		0			0
$441$	−3.94716			−0.187960
$442$	22.1752	+	68.2483i	1.05477	+	3.24624i
$443$	−8.88506	−	6.45537i	−0.422142	−	0.306704i	0.356357	−	0.934350i	$-0.384019\pi$
$443$	−8.88506	−	6.45537i	−0.422142	−	0.306704i	−0.778499	+	0.627646i	$0.784019\pi$
$444$	−1.21438	+	0.882299i	−0.0576320	+	0.0418721i
$445$		0			0
$446$	−15.0863	+	46.4307i	−0.714355	+	2.19856i
$447$	−7.72900	+	5.61545i	−0.365569	+	0.265602i
$448$	−2.99681	−	2.17731i	−0.141586	−	0.102868i
$449$	8.96777	+	27.5999i	0.423215	+	1.30252i	0.904693	+	0.426064i	$0.140100\pi$
$449$	8.96777	+	27.5999i	0.423215	+	1.30252i	−0.481478	+	0.876458i	$0.659900\pi$
$450$		0			0
$451$	−8.22451	+	8.92722i	−0.387277	+	0.420366i
$452$	9.63070			0.452990
$453$	−2.08635	−	6.42113i	−0.0980254	−	0.301691i
$454$	−18.0886	−	13.1421i	−0.848938	−	0.616790i
$455$		0			0
$456$	2.24724	−	6.91629i	0.105237	−	0.323885i
$457$	1.09908	−	3.38262i	0.0514129	−	0.158232i	−0.922054	−	0.387062i	$-0.873490\pi$
$457$	1.09908	−	3.38262i	0.0514129	−	0.158232i	0.973466	+	0.228830i	$0.0734899\pi$
$458$	−9.88383	+	7.18103i	−0.461841	+	0.335547i
$459$	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	$0.300528\pi$
$462$	−10.3809	+	2.08301i	−0.482965	+	0.0969104i
$463$	17.8743			0.830690			0.415345	−	0.909664i	$-0.363661\pi$
$463$	17.8743			0.830690			0.415345	+	0.909664i	$0.363661\pi$
$464$	−8.36114	−	25.7329i	−0.388156	−	1.19462i
$465$		0			0
$466$	9.63371	−	6.99930i	0.446273	−	0.324236i
$467$	7.79502	−	23.9906i	0.360711	−	1.11015i	−0.591913	−	0.806002i	$-0.701627\pi$
$467$	7.79502	−	23.9906i	0.360711	−	1.11015i	0.952624	−	0.304151i	$-0.0983729\pi$
$468$	2.21566	−	6.81910i	0.102419	−	0.315213i
$469$	−0.495432	+	0.359952i	−0.0228769	+	0.0166210i
$470$		0			0
$471$	3.91229	+	12.0408i	0.180269	+	0.554810i
$472$	6.84727			0.315171
$473$	−0.756881	+	6.48809i	−0.0348014	+	0.298323i
$474$	−4.68468			−0.215175
$475$		0			0
$476$	−13.8674	−	10.0753i	−0.635613	−	0.461800i
$477$	1.35177	−	0.982116i	0.0618931	−	0.0449680i
$478$	6.12135	−	18.8396i	0.279984	−	0.861702i
$479$	−1.61793	+	4.97948i	−0.0739252	+	0.227518i	−0.981191	−	0.193039i	$-0.938166\pi$
$479$	−1.61793	+	4.97948i	−0.0739252	+	0.227518i	0.907266	+	0.420558i	$0.138166\pi$
$480$		0			0
$481$	−4.86176	−	3.53228i	−0.221677	−	0.161058i
$482$	−15.3461	−	47.2304i	−0.698995	−	2.15128i
$483$	14.6029			0.664456
$484$	13.5813	−	5.67904i	0.617333	−	0.258138i
$485$		0			0
$486$	−0.564602	−	1.73767i	−0.0256109	−	0.0788222i
$487$	7.31762	+	5.31656i	0.331593	+	0.240917i	0.741106	−	0.671388i	$-0.234301\pi$
$487$	7.31762	+	5.31656i	0.331593	+	0.240917i	−0.409513	+	0.912304i	$0.634301\pi$
$488$	−9.07699	+	6.59482i	−0.410896	+	0.298533i
$489$	7.23278	−	22.2602i	0.327078	−	1.00664i
$490$		0			0
$491$	28.1629	−	20.4615i	1.27097	−	0.923416i	0.271733	−	0.962373i	$-0.412403\pi$
$491$	28.1629	−	20.4615i	1.27097	−	0.923416i	0.999241	+	0.0389565i	$0.0124034\pi$
$492$	3.96241	+	2.87886i	0.178639	+	0.129789i
$493$	−12.5457	−	38.6117i	−0.565030	−	1.73898i
$494$	−58.8789			−2.64909
$495$		0			0
$496$	0.104377			0.00468664
$497$	−2.45028	−	7.54120i	−0.109910	−	0.338269i
$498$	23.7694	+	17.2694i	1.06513	+	0.773862i
$499$	−15.8561	+	11.5201i	−0.709815	+	0.515711i	−0.883114	−	0.469158i	$-0.844557\pi$
$499$	−15.8561	+	11.5201i	−0.709815	+	0.515711i	0.173299	+	0.984869i	$0.444557\pi$
$500$		0			0
$501$	−0.943091	+	2.90254i	−0.0421342	+	0.129676i
$502$	8.19549	−	5.95437i	0.365783	−	0.265757i
$503$	14.8989	+	10.8247i	0.664307	+	0.482647i	0.868115	−	0.496364i	$-0.165332\pi$
$503$	14.8989	+	10.8247i	0.664307	+	0.482647i	−0.203808	+	0.979011i	$0.565332\pi$
$504$	−0.652802	−	2.00912i	−0.0290781	−	0.0894932i
$505$		0			0
$506$	−49.6561	+	9.96384i	−2.20748	+	0.442947i
$507$	15.7051			0.697489
$508$	−5.24667	−	16.1476i	−0.232783	−	0.716433i
$509$	−1.00187	−	0.727900i	−0.0444070	−	0.0322636i	0.565360	−	0.824844i	$-0.308737\pi$
$509$	−1.00187	−	0.727900i	−0.0444070	−	0.0322636i	−0.609767	+	0.792580i	$0.708737\pi$
$510$		0			0
$511$	5.47459	−	16.8491i	0.242182	−	0.745359i
$512$	−6.17504	+	19.0048i	−0.272901	+	0.839902i
$513$	−4.86606	+	3.53540i	−0.214842	+	0.156092i
$514$	28.0019	+	20.3446i	1.23511	+	0.897362i
$515$		0			0
$516$	2.63570			0.116030
$517$	−8.58340	+	9.31678i	−0.377498	+	0.409752i
$518$	3.58071			0.157327
$519$	−4.94657	−	15.2240i	−0.217130	−	0.668258i
$520$		0			0
$521$	−26.8472	+	19.5057i	−1.17620	+	0.854558i	−0.991738	−	0.128282i	$-0.959054\pi$
$521$	−26.8472	+	19.5057i	−1.17620	+	0.854558i	−0.184461	+	0.982840i	$0.559054\pi$
$522$	−3.12687	+	9.62351i	−0.136859	+	0.421210i
$523$	−4.06383	+	12.5072i	−0.177699	+	0.546901i	−0.999746	−	0.0225177i	$-0.992832\pi$
$523$	−4.06383	+	12.5072i	−0.177699	+	0.546901i	0.822047	+	0.569419i	$0.192832\pi$
$524$	1.05031	−	0.763092i	0.0458829	−	0.0333359i
$525$		0			0
$526$	1.81165	+	5.57570i	0.0789919	+	0.243112i
$527$	0.156615			0.00682224
$528$	7.94115	+	14.1243i	0.345594	+	0.614681i
$529$	46.8514			2.03702
$530$		0			0
$531$	−4.58172	−	3.32882i	−0.198830	−	0.144458i
$532$	11.3781	−	8.26669i	0.493304	−	0.358407i
$533$	−6.05930	+	18.6486i	−0.262458	+	0.807761i
$534$	8.19021	−	25.2069i	0.354425	−	1.09081i
$535$		0			0
$536$	0.342830	+	0.249080i	0.0148080	+	0.0107586i
$537$	−5.96375	−	18.3545i	−0.257355	−	0.792057i
$538$	5.92750			0.255553
$539$	−11.8979	−	5.46082i	−0.512479	−	0.235214i
$540$		0			0
$541$	10.0900	+	31.0538i	0.433802	+	1.33511i	0.894309	+	0.447450i	$0.147668\pi$
$541$	10.0900	+	31.0538i	0.433802	+	1.33511i	−0.460507	+	0.887656i	$0.652332\pi$
$542$	−3.00030	−	2.17985i	−0.128874	−	0.0936324i
$543$	9.86277	−	7.16572i	0.423252	−	0.307511i
$544$	−14.7433	+	45.3752i	−0.632114	+	1.94545i
$545$		0			0
$546$	−13.8372	+	10.0533i	−0.592179	+	0.430243i
$547$	22.4136	+	16.2845i	0.958338	+	0.696273i	0.952764	−	0.303711i	$-0.0982258\pi$
$547$	22.4136	+	16.2845i	0.958338	+	0.696273i	0.00557389	+	0.999984i	$0.498226\pi$
$548$	−1.74531	−	5.37150i	−0.0745558	−	0.229459i
$549$	9.27977			0.396051
$550$		0			0
$551$	33.3110			1.41909
$552$	−3.12260	−	9.61038i	−0.132907	−	0.409045i
$553$	3.62435	+	2.63324i	0.154123	+	0.111977i
$554$	−16.7276	+	12.1533i	−0.710686	+	0.516343i
$555$		0			0
$556$	3.65924	−	11.2620i	0.155186	−	0.477614i
$557$	−18.9514	+	13.7690i	−0.802996	+	0.583411i	−0.911792	−	0.410653i	$-0.865301\pi$
$557$	−18.9514	+	13.7690i	−0.802996	+	0.583411i	0.108795	+	0.994064i	$0.465301\pi$
$558$	−0.0315794	−	0.0229438i	−0.00133686	−	0.000971289i
$559$	3.26075	+	10.0356i	0.137915	+	0.424459i
$560$		0			0
$561$	11.9155	+	21.1932i	0.503073	+	0.894778i
$562$	18.8514			0.795198
$563$	−6.82482	−	21.0046i	−0.287632	−	0.885240i	−0.985597	−	0.169108i	$-0.945911\pi$
$563$	−6.82482	−	21.0046i	−0.287632	−	0.885240i	0.697966	−	0.716131i	$-0.254089\pi$
$564$	4.13532	+	3.00448i	0.174128	+	0.126512i
$565$		0			0
$566$	−1.18899	+	3.65933i	−0.0499769	+	0.153813i
$567$	−0.539926	+	1.66172i	−0.0226748	+	0.0697858i
$568$	−4.43901	+	3.22513i	−0.186257	+	0.135323i
$569$	11.1119	+	8.07328i	0.465836	+	0.338449i	0.795816	−	0.605538i	$-0.207042\pi$
$569$	11.1119	+	8.07328i	0.465836	+	0.338449i	−0.329980	+	0.943988i	$0.607042\pi$
$570$		0			0
$571$	−26.5201			−1.10983			−0.554915	−	0.831907i	$-0.687249\pi$
$571$	−26.5201			−1.10983			−0.554915	+	0.831907i	$0.687249\pi$
$572$	16.1127	−	17.4894i	0.673708	−	0.731271i
$573$	−13.4244			−0.560811
$574$	−3.61040	−	11.1117i	−0.150695	−	0.463792i
$575$		0			0
$576$	1.71517	−	1.24614i	0.0714654	−	0.0519227i
$577$	−1.75758	+	5.40927i	−0.0731690	+	0.225191i	−0.980952	−	0.194248i	$-0.937773\pi$
$577$	−1.75758	+	5.40927i	−0.0731690	+	0.225191i	0.907783	+	0.419439i	$0.137773\pi$
$578$	−20.7430	+	63.8405i	−0.862797	+	2.65542i
$579$	6.13058	−	4.45413i	0.254778	−	0.185107i
$580$		0			0
$581$	−8.68228	−	26.7213i	−0.360202	−	1.10859i
$582$	−3.47096			−0.143876
$583$	5.43336	−	1.09024i	0.225027	−	0.0451532i
$584$	−12.2593			−0.507292
$585$		0			0
$586$	34.5524	+	25.1038i	1.42735	+	1.03703i
$587$	10.9590	−	7.96215i	0.452324	−	0.328633i	−0.338188	−	0.941078i	$-0.609814\pi$
$587$	10.9590	−	7.96215i	0.452324	−	0.328633i	0.790513	+	0.612446i	$0.209814\pi$
$588$	−1.63233	+	5.02379i	−0.0673161	+	0.207178i
$589$	−0.0397090	+	0.122212i	−0.00163618	+	0.00503565i
$590$		0			0
$591$	−5.57508	−	4.05054i	−0.229328	−	0.166617i
$592$	−1.69338	−	5.21169i	−0.0695975	−	0.214199i
$593$	−21.1786			−0.869702			−0.434851	−	0.900502i	$-0.643199\pi$
$593$	−21.1786			−0.869702			−0.434851	+	0.900502i	$0.643199\pi$
$594$	0.702153	−	6.01896i	0.0288097	−	0.246961i
$595$		0			0
$596$	3.95083	+	12.1594i	0.161833	+	0.498069i
$597$	−0.517284	−	0.375829i	−0.0211710	−	0.0153816i
$598$	−66.1889	+	48.0890i	−2.70666	+	1.96651i
$599$	−10.4573	+	32.1842i	−0.427273	+	1.31501i	0.473529	+	0.880778i	$0.342980\pi$
$599$	−10.4573	+	32.1842i	−0.427273	+	1.31501i	−0.900801	+	0.434231i	$0.857020\pi$
$600$		0			0
$601$	−23.7186	+	17.2325i	−0.967500	+	0.702930i	−0.954880	−	0.296990i	$-0.904017\pi$
$601$	−23.7186	+	17.2325i	−0.967500	+	0.702930i	−0.0126196	+	0.999920i	$0.504017\pi$
$602$	−5.08658	−	3.69562i	−0.207313	−	0.150622i
$603$	−0.108307	−	0.333334i	−0.00441060	−	0.0135744i
$604$	−9.03538			−0.367644
$605$		0			0
$606$	−12.2600			−0.498028
$607$	−2.21715	−	6.82370i	−0.0899915	−	0.276965i	0.895925	−	0.444206i	$-0.146514\pi$
$607$	−2.21715	−	6.82370i	−0.0899915	−	0.276965i	−0.985916	+	0.167241i	$0.946514\pi$
$608$	−31.6697	−	23.0094i	−1.28438	−	0.933154i
$609$	7.82847	−	5.68772i	0.317226	−	0.230478i
$610$		0			0
$611$	−6.32372	+	19.4624i	−0.255830	+	0.787364i
$612$	7.93678	−	5.76641i	0.320825	−	0.233093i
$613$	−22.2515	−	16.1667i	−0.898731	−	0.652967i	0.0394084	−	0.999223i	$-0.487453\pi$
$613$	−22.2515	−	16.1667i	−0.898731	−	0.652967i	−0.938140	+	0.346257i	$0.887453\pi$
$614$	−18.0965	−	55.6953i	−0.730315	−	2.24768i
$615$		0			0
$616$	0.811840	−	6.95921i	0.0327100	−	0.280395i
$617$	−24.0712			−0.969068			−0.484534	−	0.874772i	$-0.661011\pi$
$617$	−24.0712			−0.969068			−0.484534	+	0.874772i	$0.661011\pi$
$618$	−2.39774	−	7.37950i	−0.0964514	−	0.296847i
$619$	−21.8216	−	15.8543i	−0.877083	−	0.637238i	0.0553955	−	0.998464i	$-0.482358\pi$
$619$	−21.8216	−	15.8543i	−0.877083	−	0.637238i	−0.932478	+	0.361227i	$0.882358\pi$
$620$		0			0
$621$	−2.58268	+	7.94866i	−0.103639	+	0.318969i
$622$	−0.922745	+	2.83992i	−0.0369987	+	0.113870i
$623$	−20.5051	+	14.8978i	−0.821521	+	0.596870i
$624$	21.1765	+	15.3856i	0.847737	+	0.615917i
$625$		0			0
$626$	55.5673			2.22092
$627$	−19.5589	+	3.92463i	−0.781108	+	0.156735i
$628$	16.9430			0.676098
$629$	−2.54088	−	7.82003i	−0.101312	−	0.311805i
$630$		0			0
$631$	−7.87681	+	5.72284i	−0.313571	+	0.227823i	−0.733427	−	0.679768i	$-0.762080\pi$
$631$	−7.87681	+	5.72284i	−0.313571	+	0.227823i	0.419856	+	0.907591i	$0.362080\pi$
$632$	0.957964	−	2.94831i	0.0381058	−	0.117277i
$633$	−1.18090	+	3.63445i	−0.0469367	+	0.144456i
$634$	43.5078	−	31.6103i	1.72792	−	1.25540i
$635$		0			0
$636$	−0.690983	−	2.12663i	−0.0273993	−	0.0843262i
$637$	−21.1478			−0.837904
$638$	−22.7393	+	24.6821i	−0.900256	+	0.977175i
$639$	4.53818			0.179528
$640$		0			0
$641$	−20.3196	−	14.7631i	−0.802577	−	0.583107i	0.109092	−	0.994032i	$-0.465206\pi$
$641$	−20.3196	−	14.7631i	−0.802577	−	0.583107i	−0.911669	+	0.410925i	$0.865206\pi$
$642$	23.2409	−	16.8855i	0.917245	−	0.666418i
$643$	8.32051	−	25.6079i	0.328129	−	1.00988i	−0.641880	−	0.766806i	$-0.721845\pi$
$643$	8.32051	−	25.6079i	0.328129	−	1.00988i	0.970008	−	0.243071i	$-0.0781549\pi$
$644$	6.03897	−	18.5860i	0.237969	−	0.732393i
$645$		0			0
$646$	−65.1754	−	47.3527i	−2.56429	−	1.86307i
$647$	8.28198	+	25.4893i	0.325598	+	1.00209i	0.971170	+	0.238389i	$0.0766192\pi$
$647$	8.28198	+	25.4893i	0.325598	+	1.00209i	−0.645572	+	0.763700i	$0.723381\pi$
$648$	1.20906			0.0474962
$649$	−9.20530	−	16.3728i	−0.361340	−	0.642687i
$650$		0			0
$651$	0.0115351	+	0.0355014i	0.000452096	+	0.00139141i
$652$	−25.3409	−	18.4112i	−0.992425	−	0.721039i
$653$	23.2700	−	16.9066i	0.910625	−	0.661608i	−0.0305480	−	0.999533i	$-0.509725\pi$
$653$	23.2700	−	16.9066i	0.910625	−	0.661608i	0.941173	+	0.337926i	$0.109725\pi$
$654$	−2.39332	+	7.36589i	−0.0935863	+	0.288029i
$655$		0			0
$656$	−14.4655	+	10.5098i	−0.564784	+	0.410340i
$657$	8.20305	+	5.95986i	0.320031	+	0.232516i
$658$	−3.76795	−	11.5966i	−0.146890	−	0.452081i
$659$	36.5327			1.42311			0.711556	−	0.702629i	$-0.247991\pi$
$659$	36.5327			1.42311			0.711556	+	0.702629i	$0.247991\pi$
$660$		0			0
$661$	−35.7750			−1.39149			−0.695743	−	0.718291i	$-0.744925\pi$
$661$	−35.7750			−1.39149			−0.695743	+	0.718291i	$0.744925\pi$
$662$	12.8674	+	39.6018i	0.500106	+	1.53917i
$663$	31.7748	+	23.0858i	1.23403	+	0.896576i
$664$	−15.7291	+	11.4279i	−0.610408	+	0.443487i
$665$		0			0
$666$	−0.633284	+	1.94905i	−0.0245393	+	0.0755241i
$667$	37.4466	−	27.2065i	1.44994	−	1.05344i
$668$	3.30423	+	2.40066i	0.127844	+	0.0928844i
$669$	8.25698	+	25.4124i	0.319233	+	0.982499i
$670$		0			0
$671$	27.9720	+	12.8384i	1.07985	+	0.495621i
$672$	−11.3715			−0.438666
$673$	3.48925	+	10.7388i	0.134501	+	0.413951i	0.995512	−	0.0946349i	$-0.0301684\pi$
$673$	3.48925	+	10.7388i	0.134501	+	0.413951i	−0.861011	+	0.508586i	$0.830168\pi$
$674$	21.4185	+	15.5614i	0.825009	+	0.599404i
$675$		0			0
$676$	6.49478	−	19.9889i	0.249799	−	0.768803i
$677$	13.5527	−	41.7108i	0.520872	−	1.60308i	−0.251466	−	0.967866i	$-0.580913\pi$
$677$	13.5527	−	41.7108i	0.520872	−	1.60308i	0.772338	−	0.635212i	$-0.219087\pi$
$678$	10.6374	−	7.72851i	0.408526	−	0.296812i
$679$	2.68534	+	1.95101i	0.103054	+	0.0748729i
$680$		0			0
$681$	−12.2373			−0.468935
$682$	−0.0634474	−	0.112849i	−0.00242953	−	0.00432121i
$683$	18.5355			0.709241			0.354620	−	0.935010i	$-0.384610\pi$
$683$	18.5355			0.709241			0.354620	+	0.935010i	$0.384610\pi$
$684$	2.48739	+	7.65539i	0.0951076	+	0.292711i
$685$		0			0
$686$	28.2730	−	20.5415i	1.07947	−	0.784279i
$687$	−2.06628	+	6.35937i	−0.0788337	+	0.242625i
$688$	−2.97341	+	9.15120i	−0.113360	+	0.348886i
$689$	7.24238	−	5.26190i	0.275913	−	0.200462i
$690$		0			0
$691$	−8.71597	−	26.8250i	−0.331571	−	1.02047i	−0.968386	−	0.249455i	$-0.919749\pi$
$691$	−8.71597	−	26.8250i	−0.331571	−	1.02047i	0.636815	−	0.771017i	$-0.280251\pi$
$692$	−21.4221			−0.814347
$693$	−3.92646	+	4.26194i	−0.149154	+	0.161898i
$694$	8.01596			0.304282
$695$		0			0
$696$	−5.41716	−	3.93580i	−0.205337	−	0.149186i
$697$	−21.7052	+	15.7698i	−0.822144	+	0.597322i
$698$	−8.13371	+	25.0330i	−0.307865	+	0.947512i
$699$	2.01399	−	6.19844i	0.0761762	−	0.234446i
$700$		0			0
$701$	−0.255153	−	0.185379i	−0.00963699	−	0.00700168i	0.582956	−	0.812503i	$-0.301896\pi$
$701$	−0.255153	−	0.185379i	−0.00963699	−	0.00700168i	−0.592593	+	0.805502i	$0.701896\pi$
$702$	−3.02498	−	9.30992i	−0.114170	−	0.351380i
$703$	6.74647			0.254448
$704$	6.89405	−	1.38334i	0.259829	−	0.0521366i
$705$		0			0
$706$	−3.39362	−	10.4445i	−0.127721	−	0.393084i
$707$	9.48505	+	6.89129i	0.356722	+	0.259174i
$708$	−6.13154	+	4.45482i	−0.230437	+	0.167423i
$709$	12.0593	−	37.1146i	0.452895	−	1.39387i	−0.420693	−	0.907203i	$-0.638213\pi$
$709$	12.0593	−	37.1146i	0.452895	−	1.39387i	0.873589	−	0.486665i	$-0.161787\pi$
$710$		0			0
$711$	−2.07433	+	1.50709i	−0.0777934	+	0.0565202i
$712$	14.1892	+	10.3090i	0.531762	+	0.386348i
$713$	0.0551768	+	0.169817i	0.00206639	+	0.00635969i
$714$	−23.4023			−0.875808
$715$		0			0
$716$	−25.8272			−0.965209
$717$	−3.35032	−	10.3112i	−0.125120	−	0.385080i
$718$	−3.63203	−	2.63882i	−0.135546	−	0.0984800i
$719$	−23.0320	+	16.7337i	−0.858948	+	0.624062i	−0.927598	−	0.373579i	$-0.878131\pi$
$719$	−23.0320	+	16.7337i	−0.858948	+	0.624062i	0.0686507	+	0.997641i	$0.478131\pi$
$720$		0			0
$721$	−2.29295	+	7.05698i	−0.0853939	+	0.262816i
$722$	25.3911	−	18.4477i	0.944957	−	0.686552i
$723$	−21.9894	−	15.9762i	−0.817793	−	0.594161i
$724$	−5.04156	−	15.5163i	−0.187368	−	0.576659i
$725$		0			0
$726$	10.4436	−	17.1715i	0.387599	−	0.637294i
$727$	−45.8400			−1.70011			−0.850057	−	0.526691i	$-0.823432\pi$
$727$	−45.8400			−1.70011			−0.850057	+	0.526691i	$0.823432\pi$
$728$	−3.49753	−	10.7643i	−0.129627	−	0.398951i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$		0			0
$731$	−4.46153	+	13.7312i	−0.165016	+	0.507866i
$732$	3.83761	−	11.8109i	0.141842	−	0.436545i
$733$	30.7169	−	22.3171i	1.13455	−	0.824301i	0.148202	−	0.988957i	$-0.452651\pi$
$733$	30.7169	−	22.3171i	1.13455	−	0.824301i	0.986351	+	0.164656i	$0.0526513\pi$
$734$	−2.18751	−	1.58932i	−0.0807423	−	0.0586627i
$735$		0			0
$736$	−54.3944			−2.00500
$737$	0.134693	−	1.15461i	0.00496149	−	0.0425306i
$738$	6.68684			0.246146
$739$	6.52725	+	20.0888i	0.240109	+	0.738979i	0.996403	+	0.0847466i	$0.0270081\pi$
$739$	6.52725	+	20.0888i	0.240109	+	0.738979i	−0.756294	+	0.654232i	$0.772992\pi$
$740$		0			0
$741$	−26.0710	+	18.9417i	−0.957741	+	0.695840i
$742$	−1.64831	+	5.07298i	−0.0605113	+	0.186235i
$743$	−2.46606	+	7.58976i	−0.0904711	+	0.278441i	−0.986047	−	0.166467i	$-0.946764\pi$
$743$	−2.46606	+	7.58976i	−0.0904711	+	0.278441i	0.895576	+	0.444909i	$0.146764\pi$
$744$	0.0208973	−	0.0151828i	0.000766134	−	0.000556629i
$745$		0			0
$746$	−13.7385	−	42.2829i	−0.503004	−	1.54809i
$747$	16.0805			0.588355
$748$	31.9015	−	6.40126i	1.16643	−	0.234053i
$749$	−27.4718			−1.00380
$750$		0			0
$751$	7.78664	+	5.65733i	0.284139	+	0.206439i	0.720721	−	0.693226i	$-0.243811\pi$
$751$	7.78664	+	5.65733i	0.284139	+	0.206439i	−0.436582	+	0.899664i	$0.643811\pi$
$752$	−15.0968	+	10.9684i	−0.550523	+	0.399978i
$753$	1.71332	−	5.27307i	0.0624370	−	0.192161i
$754$	−16.7529	+	51.5600i	−0.610104	+	1.87771i
$755$		0			0
$756$	1.89169	+	1.37440i	0.0688002	+	0.0499863i
$757$	14.4049	+	44.3338i	0.523555	+	1.61134i	0.767155	+	0.641462i	$0.221672\pi$
$757$	14.4049	+	44.3338i	0.523555	+	1.61134i	−0.243600	+	0.969876i	$0.578328\pi$
$758$	−29.1076			−1.05724
$759$	−18.7818	+	20.3865i	−0.681735	+	0.739984i
$760$		0			0
$761$	−6.79661	−	20.9178i	−0.246377	−	0.758270i	−0.995407	−	0.0957342i	$-0.969480\pi$
$761$	−6.79661	−	20.9178i	−0.246377	−	0.758270i	0.749030	−	0.662536i	$-0.230520\pi$
$762$	−18.7533	−	13.6251i	−0.679361	−	0.493585i
$763$	5.99195	−	4.35341i	0.216923	−	0.157604i
$764$	−5.55158	+	17.0860i	−0.200849	+	0.618151i
$765$		0			0
$766$	5.79425	−	4.20977i	0.209355	−	0.152105i
$767$	−24.5476	−	17.8348i	−0.886361	−	0.643979i
$768$	6.47244	+	19.9201i	0.233554	+	0.718805i
$769$	48.0330			1.73211			0.866057	−	0.499946i	$-0.166647\pi$
$769$	48.0330			1.73211			0.866057	+	0.499946i	$0.166647\pi$
$770$		0			0
$771$	18.9439			0.682249
$772$	−3.13377	−	9.64476i	−0.112787	−	0.347123i
$773$	−13.8222	−	10.0424i	−0.497148	−	0.361199i	0.310778	−	0.950482i	$-0.399410\pi$
$773$	−13.8222	−	10.0424i	−0.497148	−	0.361199i	−0.807927	+	0.589283i	$0.799410\pi$
$774$	2.91121	−	2.11512i	0.104641	−	0.0760263i
$775$		0			0
$776$	0.709771	−	2.18445i	0.0254793	−	0.0784172i
$777$	1.58550	−	1.15193i	0.0568795	−	0.0413254i
$778$	−52.1653	−	37.9003i	−1.87022	−	1.35879i
$779$	−6.80242	−	20.9357i	−0.243722	−	0.750099i
$780$		0			0
$781$	13.6794	+	6.27849i	0.489488	+	0.224662i
$782$	−111.942			−4.00304
$783$	1.71139	+	5.26712i	0.0611602	+	0.188232i
$784$	−15.6012	−	11.3349i	−0.557186	−	0.404819i
$785$		0			0
$786$	0.547722	−	1.68571i	0.0195366	−	0.0601275i
$787$	6.95034	−	21.3910i	0.247753	−	0.762505i	−0.747418	−	0.664354i	$-0.768707\pi$
$787$	6.95034	−	21.3910i	0.247753	−	0.762505i	0.995171	−	0.0981518i	$-0.0312931\pi$
$788$	−7.46092	+	5.42068i	−0.265784	+	0.193104i
$789$	2.59591	+	1.88604i	0.0924170	+	0.0671449i
$790$		0			0
$791$	−12.5739			−0.447076
$792$	3.64445	+	1.67271i	0.129500	+	0.0594371i
$793$	49.7184			1.76555
$794$	13.1118	+	40.3540i	0.465321	+	1.43211i
$795$		0			0
$796$	−0.692261	+	0.502957i	−0.0245365	+	0.0178268i
$797$	1.05615	−	3.25051i	0.0374109	−	0.115139i	−0.930607	−	0.366020i	$-0.880720\pi$
$797$	1.05615	−	3.25051i	0.0374109	−	0.115139i	0.968018	+	0.250881i	$0.0807203\pi$
$798$	5.93355	−	18.2616i	0.210045	−	0.646453i
$799$	−22.6524	+	16.4579i	−0.801383	+	0.582239i
$800$		0			0
$801$	−4.48265	−	13.7962i	−0.158387	−	0.487464i
$802$	−10.4046			−0.367398
$803$	16.4810	+	29.3135i	0.581603	+	1.03445i
$804$	−0.469045			−0.0165420
$805$		0			0
$806$	−0.169194	−	0.122926i	−0.00595959	−	0.00432990i
$807$	2.62464	−	1.90691i	0.0923916	−	0.0671264i
$808$	2.50703	−	7.71584i	0.0881969	−	0.271442i
$809$	−3.12679	+	9.62328i	−0.109932	+	0.338336i	−0.990856	−	0.134921i	$-0.956922\pi$
$809$	−3.12679	+	9.62328i	−0.109932	+	0.338336i	0.880924	+	0.473257i	$0.156922\pi$
$810$		0			0
$811$	−20.5287	−	14.9150i	−0.720862	−	0.523737i	0.165798	−	0.986160i	$-0.446980\pi$
$811$	−20.5287	−	14.9150i	−0.720862	−	0.523737i	−0.886659	+	0.462423i	$0.846980\pi$
$812$	−4.00168	−	12.3159i	−0.140432	−	0.432204i
$813$	−2.02977			−0.0711872
$814$	−4.60538	+	4.99887i	−0.161419	+	0.175210i
$815$		0			0
$816$	11.0674	+	34.0618i	0.387435	+	1.19240i
$817$	−9.58370	−	6.96297i	−0.335291	−	0.243603i
$818$	37.6232	−	27.3349i	1.31547	−	0.955741i
$819$	−2.89277	+	8.90304i	−0.101082	+	0.311097i
$820$		0			0
$821$	−1.21284	+	0.881177i	−0.0423282	+	0.0307533i	−0.608748	−	0.793363i	$-0.708328\pi$
$821$	−1.21284	+	0.881177i	−0.0423282	+	0.0307533i	0.566420	+	0.824117i	$0.308328\pi$
$822$	−6.23830	−	4.53239i	−0.217586	−	0.158085i
$823$	5.90982	+	18.1885i	0.206003	+	0.634013i	0.999671	+	0.0256610i	$0.00816904\pi$
$823$	5.90982	+	18.1885i	0.206003	+	0.634013i	−0.793667	+	0.608352i	$0.791831\pi$
$824$	5.13460			0.178872
$825$		0			0
$826$	18.0794			0.629062
$827$	5.13910	+	15.8165i	0.178704	+	0.549994i	0.999783	−	0.0208200i	$-0.00662770\pi$
$827$	5.13910	+	15.8165i	0.178704	+	0.549994i	−0.821079	+	0.570814i	$0.806628\pi$
$828$	9.04870	+	6.57426i	0.314464	+	0.228471i
$829$	−20.7881	+	15.1034i	−0.722001	+	0.524564i	−0.887023	−	0.461725i	$-0.847231\pi$
$829$	−20.7881	+	15.1034i	−0.722001	+	0.524564i	0.165022	+	0.986290i	$0.447231\pi$
$830$		0			0
$831$	−3.49701	+	10.7627i	−0.121310	+	0.373354i
$832$	9.18940	−	6.67649i	0.318585	−	0.231466i
$833$	−23.4093	−	17.0078i	−0.811083	−	0.589286i
$834$	−4.99586	−	15.3757i	−0.172992	−	0.532416i
$835$		0			0
$836$	−3.09338	+	26.5169i	−0.106987	+	0.917105i
$837$	−0.0213642			−0.000738455
$838$	7.61367	+	23.4325i	0.263010	+	0.809461i
$839$	22.9737	+	16.6914i	0.793141	+	0.576250i	0.908894	−	0.417028i	$-0.136928\pi$
$839$	22.9737	+	16.6914i	0.793141	+	0.576250i	−0.115753	+	0.993278i	$0.536928\pi$
$840$		0			0
$841$	0.516507	−	1.58965i	0.0178106	−	0.0548154i
$842$	−1.66539	+	5.12555i	−0.0573932	+	0.176638i
$843$	8.34720	−	6.06459i	0.287493	−	0.208876i
$844$	4.13743	+	3.00602i	0.142416	+	0.103471i
$845$		0			0
$846$	6.97864			0.239930
$847$	−17.7318	+	7.41457i	−0.609273	+	0.254768i
$848$	8.16320			0.280325
$849$	0.650755	+	2.00282i	0.0223339	+	0.0687365i
$850$		0			0
$851$	7.58406	−	5.51014i	0.259978	−	0.188885i
$852$	1.87674	−	5.77602i	0.0642962	−	0.197883i
$853$	−4.66838	+	14.3678i	−0.159842	+	0.491943i	−0.998619	−	0.0525314i	$-0.983271\pi$
$853$	−4.66838	+	14.3678i	−0.159842	+	0.491943i	0.838777	+	0.544475i	$0.183271\pi$
$854$	−23.9666	+	17.4128i	−0.820122	+	0.595853i
$855$		0			0
$856$	5.87441	+	18.0796i	0.200783	+	0.617947i
$857$	−2.37040			−0.0809713			−0.0404856	−	0.999180i	$-0.512891\pi$
$857$	−2.37040			−0.0809713			−0.0404856	+	0.999180i	$0.512891\pi$
$858$	3.76194	−	32.2479i	0.128430	−	1.10092i
$859$	45.0423			1.53682			0.768411	−	0.639956i	$-0.221048\pi$
$859$	45.0423			1.53682			0.768411	+	0.639956i	$0.221048\pi$
$860$		0			0
$861$	−5.17333	−	3.75865i	−0.176307	−	0.128094i
$862$	17.0323	−	12.3747i	0.580123	−	0.421484i
$863$	7.73191	−	23.7964i	0.263197	−	0.810038i	−0.728906	−	0.684614i	$-0.759971\pi$
$863$	7.73191	−	23.7964i	0.263197	−	0.810038i	0.992103	−	0.125424i	$-0.0400292\pi$
$864$	2.01117	−	6.18975i	0.0684214	−	0.210579i
$865$		0			0
$866$	−16.5018	−	11.9893i	−0.560754	−	0.407412i
$867$	11.3530	+	34.9411i	0.385570	+	1.18666i
$868$	0.0499551			0.00169559
$869$	−8.33767	+	1.67301i	−0.282836	+	0.0567530i
$870$		0			0
$871$	−0.580278	−	1.78591i	−0.0196620	−	0.0605133i
$872$	−4.14632	−	3.01248i	−0.140412	−	0.102015i
$873$	−1.53690	+	1.11663i	−0.0520163	+	0.0377920i
$874$	28.3825	−	87.3522i	0.960051	−	2.95473i
$875$		0			0
$876$	10.9778	−	7.97585i	0.370906	−	0.269479i
$877$	−39.5411	−	28.7283i	−1.33521	−	0.970085i	−0.999606	−	0.0280807i	$-0.991060\pi$
$877$	−39.5411	−	28.7283i	−1.33521	−	0.970085i	−0.335601	−	0.942004i	$-0.608940\pi$
$878$	−0.561002	−	1.72659i	−0.0189329	−	0.0582695i
$879$	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	$0.229805\pi$
$882$	2.22857	+	6.85885i	0.0750400	+	0.230949i
$883$	−35.6410	−	25.8947i	−1.19941	−	0.871426i	−0.205187	−	0.978723i	$-0.565780\pi$
$883$	−35.6410	−	25.8947i	−1.19941	−	0.871426i	−0.994227	+	0.107297i	$0.965780\pi$
$884$	42.5230	−	30.8948i	1.43020	−	1.03910i
$885$		0			0
$886$	−6.20076	+	19.0840i	−0.208319	+	0.641139i
$887$	−9.81279	+	7.12941i	−0.329481	+	0.239382i	−0.740210	−	0.672375i	$-0.765274\pi$
$887$	−9.81279	+	7.12941i	−0.329481	+	0.239382i	0.410729	+	0.911757i	$0.365274\pi$
$888$	−1.09714	−	0.797116i	−0.0368175	−	0.0267495i
$889$	6.85007	+	21.0823i	0.229744	+	0.707079i
$890$		0			0
$891$	−1.62543	−	2.89102i	−0.0544538	−	0.0968528i
$892$	35.7585			1.19728
$893$	−7.09925	−	21.8493i	−0.237567	−	0.731158i
$894$	14.1216	+	10.2599i	0.472296	+	0.343143i
$895$		0			0
$896$	4.93655	−	15.1931i	0.164919	−	0.507567i
$897$	−13.8372	+	42.5867i	−0.462012	+	1.42193i
$898$	42.8963	−	31.1660i	1.43147	−	1.04002i
$899$	0.0957219	+	0.0695461i	0.00319251	+	0.00231949i
$900$		0			0
$901$	12.2487			0.408063
$902$	20.1561	+	9.25112i	0.671125	+	0.308029i
$903$	−3.44118			−0.114515
$904$	2.68872	+	8.27504i	0.0894256	+	0.275224i
$905$		0			0
$906$	−9.97983	+	7.25077i	−0.331558	+	0.240891i
$907$	−10.1565	+	31.2586i	−0.337242	+	1.03793i	0.628365	+	0.777919i	$0.283725\pi$
$907$	−10.1565	+	31.2586i	−0.337242	+	1.03793i	−0.965607	+	0.260006i	$0.916275\pi$
$908$	−5.06069	+	15.5752i	−0.167945	+	0.516881i
$909$	−5.42860	+	3.94411i	−0.180055	+	0.130818i
$910$		0			0
$911$	−14.4328	−	44.4195i	−0.478179	−	1.47168i	−0.841622	−	0.540067i	$-0.818399\pi$
$911$	−14.4328	−	44.4195i	−0.478179	−	1.47168i	0.363443	−	0.931617i	$-0.381601\pi$
$912$	−29.3857			−0.973058
$913$	48.4714	+	22.2471i	1.60417	+	0.736271i
$914$	−6.49842			−0.214949
$915$		0			0
$916$	7.23946	+	5.25978i	0.239199	+	0.173788i
$917$	−1.37128	+	0.996296i	−0.0452838	+	0.0329006i
$918$	4.13893	−	12.7383i	0.136605	−	0.420427i
$919$	2.26765	−	6.97910i	0.0748028	−	0.230219i	−0.906663	−	0.421855i	$-0.861379\pi$
$919$	2.26765	−	6.97910i	0.0748028	−	0.230219i	0.981466	+	0.191636i	$0.0613792\pi$
$920$		0			0
$921$	−25.9304	−	18.8396i	−0.854437	−	0.620785i
$922$	−14.2183	−	43.7594i	−0.468255	−	1.44114i
$923$	24.3143			0.800314
$924$	3.80067	+	6.75996i	0.125033	+	0.222386i
$925$		0			0
$926$	−10.0919	−	31.0596i	−0.331640	−	1.02068i
$927$	−3.43572	−	2.49620i	−0.112844	−	0.0819859i
$928$	−29.1603	+	21.1862i	−0.957232	+	0.695470i
$929$	3.93333	−	12.1055i	0.129048	−	0.397170i	−0.865569	−	0.500790i	$-0.833043\pi$
$929$	3.93333	−	12.1055i	0.129048	−	0.397170i	0.994617	+	0.103621i	$0.0330428\pi$
$930$		0			0
$931$	19.2071	−	13.9548i	0.629488	−	0.457350i
$932$	−7.05626	−	5.12667i	−0.231135	−	0.167930i
$933$	0.505035	+	1.55434i	0.0165341	+	0.0508868i
$934$	−46.0888			−1.50807
$935$		0			0
$936$	6.47778			0.211733
$937$	−5.94961	−	18.3110i	−0.194365	−	0.598195i	−0.999983	−	0.00575961i	$-0.998167\pi$
$937$	−5.94961	−	18.3110i	−0.194365	−	0.598195i	0.805618	−	0.592435i	$-0.201833\pi$
$938$	0.905199	+	0.657665i	0.0295558	+	0.0214735i
$939$	24.6046	−	17.8763i	0.802942	−	0.583371i
$940$		0			0
$941$	−12.7530	+	39.2496i	−0.415735	+	1.27950i	0.495857	+	0.868404i	$0.334854\pi$
$941$	−12.7530	+	39.2496i	−0.415735	+	1.27950i	−0.911592	+	0.411096i	$0.865146\pi$
$942$	18.7140	−	13.5965i	0.609735	−	0.442998i
$943$	−24.7461	−	17.9791i	−0.805842	−	0.585479i
$944$	−8.55007	−	26.3144i	−0.278281	−	0.856461i
$945$		0			0
$946$	11.7015	−	2.34798i	0.380448	−	0.0763395i
$947$	50.3012			1.63457			0.817285	−	0.576233i	$-0.195478\pi$
$947$	50.3012			1.63457			0.817285	+	0.576233i	$0.195478\pi$
$948$	1.06034	+	3.26338i	0.0344381	+	0.105990i
$949$	43.9496	+	31.9312i	1.42666	+	1.03653i
$950$		0			0
$951$	9.09561	−	27.9934i	0.294945	−	0.907749i
$952$	4.78550	−	14.7282i	0.155099	−	0.477345i
$953$	−7.30203	+	5.30523i	−0.236536	+	0.171853i	−0.699739	−	0.714399i	$-0.746700\pi$
$953$	−7.30203	+	5.30523i	−0.236536	+	0.171853i	0.463203	+	0.886252i	$0.346700\pi$
$954$	−2.46980	−	1.79442i	−0.0799628	−	0.0580963i
$955$		0			0
$956$	−14.5093			−0.469263
$957$	−2.12833	+	18.2443i	−0.0687991	+	0.589756i
$958$	9.56617			0.309069
$959$	2.27868	+	7.01305i	0.0735824	+	0.226463i
$960$		0			0
$961$	25.0792	−	18.2211i	0.809005	−	0.587777i
$962$	−3.39296	+	10.4425i	−0.109393	+	0.336678i
$963$	4.85867	−	14.9534i	0.156568	−	0.481868i
$964$	−29.4275	+	21.3803i	−0.947796	+	0.688614i
$965$		0			0
$966$	−8.24484	−	25.3750i	−0.265273	−	0.816428i
$967$	30.2503			0.972785			0.486392	−	0.873740i	$-0.338313\pi$
$967$	30.2503			0.972785			0.486392	+	0.873740i	$0.338313\pi$
$968$	8.67130	+	10.0841i	0.278706	+	0.324114i
$969$	−44.0926			−1.41646
$970$		0			0
$971$	−10.3785	−	7.54040i	−0.333061	−	0.241983i	0.408667	−	0.912683i	$-0.365994\pi$
$971$	−10.3785	−	7.54040i	−0.333061	−	0.241983i	−0.741728	+	0.670700i	$0.765994\pi$
$972$	−1.08268	+	0.786610i	−0.0347269	+	0.0252305i
$973$	−4.77751	+	14.7037i	−0.153160	+	0.471378i
$974$	5.10687	−	15.7173i	0.163635	−	0.503616i
$975$		0			0
$976$	36.6785	+	26.6485i	1.17405	+	0.852996i
$977$	4.06641	+	12.5151i	0.130096	+	0.400394i	0.994795	−	0.101896i	$-0.0324909\pi$
$977$	4.06641	+	12.5151i	0.130096	+	0.400394i	−0.864699	+	0.502290i	$0.832491\pi$
$978$	−42.7645			−1.36746
$979$	5.57474	−	47.7875i	0.178169	−	1.52729i
$980$		0			0
$981$	1.30991	+	4.03149i	0.0418222	+	0.128715i
$982$	−51.4562	−	37.3851i	−1.64203	−	1.19301i
$983$	18.1519	−	13.1881i	0.578954	−	0.420635i	−0.259393	−	0.965772i	$-0.583522\pi$
$983$	18.1519	−	13.1881i	0.578954	−	0.420635i	0.838347	+	0.545137i	$0.183522\pi$
$984$	−1.36738	+	4.20837i	−0.0435905	+	0.134158i
$985$		0			0
$986$	−60.0110	+	43.6005i	−1.91114	+	1.38852i
$987$	−5.39908	−	3.92266i	−0.171855	−	0.124860i
$988$	13.3267	+	41.0154i	0.423979	+	1.30487i
$989$	−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	$0.381427\pi$
$992$	−0.0429671	−	0.132239i	−0.00136421	−	0.00419859i
$993$	18.4377	+	13.3958i	0.585102	+	0.425101i
$994$	−11.7207	+	8.51555i	−0.371757	+	0.270097i
$995$		0			0
$996$	6.65002	−	20.4666i	0.210714	−	0.648511i
$997$	−13.6234	+	9.89794i	−0.431456	+	0.313471i	−0.782231	−	0.622989i	$-0.785918\pi$
$997$	−13.6234	+	9.89794i	−0.431456	+	0.313471i	0.350775	+	0.936460i	$0.385918\pi$
$998$	28.9705	+	21.0483i	0.917045	+	0.666272i
$999$	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.n.j.676.1		8
5.2	odd	4		825.2.bx.e.49.4		16
5.3	odd	4		825.2.bx.e.49.1		16
5.4	even	2		165.2.m.c.16.2	✓	8
11.3	even	5		9075.2.a.co.1.1		4
11.8	odd	10		9075.2.a.df.1.4		4
11.9	even	5	inner	825.2.n.j.526.1		8
15.14	odd	2		495.2.n.c.181.1		8
55.9	even	10		165.2.m.c.31.2	yes	8
55.14	even	10		1815.2.a.u.1.4		4
55.19	odd	10		1815.2.a.q.1.1		4
55.42	odd	20		825.2.bx.e.724.1		16
55.53	odd	20		825.2.bx.e.724.4		16
165.14	odd	10		5445.2.a.bj.1.1		4
165.74	even	10		5445.2.a.bq.1.4		4
165.119	odd	10		495.2.n.c.361.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.m.c.16.2	✓	8	5.4	even	2
165.2.m.c.31.2	yes	8	55.9	even	10
495.2.n.c.181.1		8	15.14	odd	2
495.2.n.c.361.1		8	165.119	odd	10
825.2.n.j.526.1		8	11.9	even	5	inner
825.2.n.j.676.1		8	1.1	even	1	trivial
825.2.bx.e.49.1		16	5.3	odd	4
825.2.bx.e.49.4		16	5.2	odd	4
825.2.bx.e.724.1		16	55.42	odd	20
825.2.bx.e.724.4		16	55.53	odd	20
1815.2.a.q.1.1		4	55.19	odd	10
1815.2.a.u.1.4		4	55.14	even	10
5445.2.a.bj.1.1		4	165.14	odd	10
5445.2.a.bq.1.4		4	165.74	even	10
9075.2.a.co.1.1		4	11.3	even	5
9075.2.a.df.1.4		4	11.8	odd	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.564602 - 1.73767i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-1.08268 + 0.786610i) q^{4} +(-0.564602 + 1.73767i) q^{6} +(1.41355 - 1.02700i) q^{7} +(-0.978148 - 0.710666i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-0.384301 + 3.29428i) q^{11} +1.33826 q^{12} +(1.65563 + 5.09549i) q^{13} +(-2.58268 - 1.87642i) q^{14} +(-1.50973 + 4.64646i) q^{16} +(-2.26531 + 6.97191i) q^{17} +(1.47815 - 1.07394i) q^{18} +(-4.86606 - 3.53540i) q^{19} -1.74724 q^{21} +(5.94135 - 1.19217i) q^{22} -8.35772 q^{23} +(0.373619 + 1.14988i) q^{24} +(7.91949 - 5.75385i) q^{26} +(0.309017 - 0.951057i) q^{27} +(-0.722562 + 2.22382i) q^{28} +(-4.48048 + 3.25526i) q^{29} +(-0.00660190 - 0.0203186i) q^{31} +6.50828 q^{32} +(2.24724 - 2.43925i) q^{33} +13.3939 q^{34} +(-1.08268 - 0.786610i) q^{36} +(-0.907432 + 0.659288i) q^{37} +(-3.39596 + 10.4517i) q^{38} +(1.65563 - 5.09549i) q^{39} +(2.96086 + 2.15119i) q^{41} +(0.986494 + 3.03612i) q^{42} +1.96950 q^{43} +(-2.17524 - 3.86894i) q^{44} +(4.71878 + 14.5229i) q^{46} +(3.09007 + 2.24507i) q^{47} +(3.95252 - 2.87167i) q^{48} +(-1.21974 + 3.75397i) q^{49} +(5.93066 - 4.30888i) q^{51} +(-5.80067 - 4.21443i) q^{52} +(-0.516329 - 1.58910i) q^{53} -1.82709 q^{54} -2.11251 q^{56} +(1.85867 + 5.72040i) q^{57} +(8.18625 + 5.94766i) q^{58} +(-4.58172 + 3.32882i) q^{59} +(2.86761 - 8.82559i) q^{61} +(-0.0315794 + 0.0229438i) q^{62} +(1.41355 + 1.02700i) q^{63} +(-0.655137 - 2.01630i) q^{64} +(-5.50739 - 2.52775i) q^{66} -0.350489 q^{67} +(-3.03158 - 9.33024i) q^{68} +(6.76153 + 4.91254i) q^{69} +(1.40238 - 4.31607i) q^{71} +(0.373619 - 1.14988i) q^{72} +(8.20305 - 5.95986i) q^{73} +(1.65796 + 1.20458i) q^{74} +8.04935 q^{76} +(2.84001 + 5.05130i) q^{77} -9.78903 q^{78} +(0.792323 + 2.43852i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(2.06635 - 6.35956i) q^{82} +(4.96915 - 15.2935i) q^{83} +(1.89169 - 1.37440i) q^{84} +(-1.11198 - 3.42233i) q^{86} +5.53818 q^{87} +(2.71704 - 2.94919i) q^{88} -14.5062 q^{89} +(7.57337 + 5.50238i) q^{91} +(9.04870 - 6.57426i) q^{92} +(-0.00660190 + 0.0203186i) q^{93} +(2.15652 - 6.63708i) q^{94} +(-5.26531 - 3.82547i) q^{96} +(0.587045 + 1.80674i) q^{97} +7.21182 q^{98} +(-3.25181 + 0.652498i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} + 5 q^{7} + q^{8} - 2 q^{9} - q^{11} + 2 q^{12} + 16 q^{13} - 10 q^{14} + 12 q^{16} + 4 q^{17} + 3 q^{18} + 2 q^{19} + 9 q^{22} - 10 q^{23} - 4 q^{24} + 16 q^{26}+ \cdots - 11 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^6 + 5 * q^7 + q^8 - 2 * q^9 - q^11 + 2 * q^12 + 16 * q^13 - 10 * q^14 + 12 * q^16 + 4 * q^17 + 3 * q^18 + 2 * q^19 + 9 * q^22 - 10 * q^23 - 4 * q^24 + 16 * q^26 - 2 * q^27 + 5 * q^28 - 16 * q^29 - 5 * q^31 + 4 * q^33 + 34 * q^34 + 2 * q^36 + 5 * q^37 - 28 * q^38 + 16 * q^39 + 5 * q^41 + 15 * q^42 + 8 * q^43 - 19 * q^44 + 10 * q^46 + q^47 - 3 * q^48 - 11 * q^49 + 4 * q^51 - 26 * q^52 + 15 * q^53 - 2 * q^54 + 20 * q^56 - 13 * q^57 + 24 * q^58 + 3 * q^59 - 11 * q^61 + 15 * q^62 + 5 * q^63 - 9 * q^64 - 31 * q^66 - 6 * q^67 - 9 * q^68 + 15 * q^69 + q^71 - 4 * q^72 + 35 * q^73 + 5 * q^74 + 58 * q^76 + 25 * q^77 - 24 * q^78 - 30 * q^79 - 2 * q^81 + 25 * q^82 - 31 * q^83 - 62 * q^86 + 34 * q^87 - 17 * q^88 - 48 * q^89 + 5 * q^91 + 20 * q^92 - 5 * q^93 - 19 * q^94 - 20 * q^96 - 11 * q^97 - 26 * q^98 - 11 * q^99

Introduction

L-functions

Modular forms

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