LMFDB - Embedded newform 950.2.bb.b.243.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(143,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([27, 34]))

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

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

chi := DirichletCharacter("950.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.bb (of order $36$, degree $12$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			243.2
Character	$\chi$	$=$	950.243
Dual form			950.2.bb.b.907.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.422618 - 0.906308i) q^{2} +(-0.284489 - 0.199201i) q^{3} +(-0.642788 + 0.766044i) q^{4} +(-0.0603074 + 0.342020i) q^{6} +(0.814083 + 3.03820i) q^{7} +(0.965926 + 0.258819i) q^{8} +(-0.984808 - 2.70574i) q^{9} +O(q^{10})$	\(q+(-0.422618 - 0.906308i) q^{2} +(-0.284489 - 0.199201i) q^{3} +(-0.642788 + 0.766044i) q^{4} +(-0.0603074 + 0.342020i) q^{6} +(0.814083 + 3.03820i) q^{7} +(0.965926 + 0.258819i) q^{8} +(-0.984808 - 2.70574i) q^{9} +(1.15790 + 2.00553i) q^{11} +(0.335463 - 0.0898869i) q^{12} +(-3.68660 - 5.26500i) q^{13} +(2.40950 - 2.02181i) q^{14} +(-0.173648 - 0.984808i) q^{16} +(-0.217593 + 0.101465i) q^{17} +(-2.03603 + 2.03603i) q^{18} +(4.33561 + 0.449974i) q^{19} +(0.373615 - 1.02650i) q^{21} +(1.32828 - 1.89699i) q^{22} +(0.265102 + 3.03012i) q^{23} +(-0.223238 - 0.266044i) q^{24} +(-3.21369 + 5.56628i) q^{26} +(-0.528480 + 1.97231i) q^{27} +(-2.85068 - 1.32929i) q^{28} +(9.33726 - 3.39848i) q^{29} +(7.73608 + 4.46643i) q^{31} +(-0.819152 + 0.573576i) q^{32} +(0.0700964 - 0.801206i) q^{33} +(0.183917 + 0.154325i) q^{34} +(2.70574 + 0.984808i) q^{36} +(2.25550 + 2.25550i) q^{37} +(-1.42449 - 4.11957i) q^{38} +2.23221i q^{39} +(11.4442 - 2.01793i) q^{41} +(-1.08822 + 0.0952069i) q^{42} +(0.196313 + 0.0171752i) q^{43} +(-2.28061 - 0.402133i) q^{44} +(2.63419 - 1.52085i) q^{46} +(1.58051 - 3.38941i) q^{47} +(-0.146774 + 0.314757i) q^{48} +(-2.50574 + 1.44669i) q^{49} +(0.0821147 + 0.0144790i) q^{51} +(6.40293 + 0.560183i) q^{52} +(-0.625382 + 0.0547139i) q^{53} +(2.01087 - 0.354570i) q^{54} +3.14537i q^{56} +(-1.14380 - 0.991671i) q^{57} +(-7.02617 - 7.02617i) q^{58} +(-9.92731 - 3.61324i) q^{59} +(-7.07266 - 5.93466i) q^{61} +(0.778550 - 8.89887i) q^{62} +(7.41885 - 5.19473i) q^{63} +(0.866025 + 0.500000i) q^{64} +(-0.755763 + 0.275075i) q^{66} +(10.5110 + 4.90137i) q^{67} +(0.0621391 - 0.231906i) q^{68} +(0.528185 - 0.914844i) q^{69} +(1.44488 + 1.72195i) q^{71} +(-0.250955 - 2.86843i) q^{72} +(8.79082 - 12.5546i) q^{73} +(1.09096 - 2.99739i) q^{74} +(-3.13158 + 3.03203i) q^{76} +(-5.15059 + 5.15059i) q^{77} +(2.02307 - 0.943371i) q^{78} +(-1.43404 - 8.13284i) q^{79} +(-6.07398 + 5.09667i) q^{81} +(-6.66541 - 9.51919i) q^{82} +(-2.76153 + 0.739950i) q^{83} +(0.546188 + 0.946026i) q^{84} +(-0.0673995 - 0.185179i) q^{86} +(-3.33332 - 0.893162i) q^{87} +(0.599371 + 2.23688i) q^{88} +(-2.79147 + 15.8312i) q^{89} +(12.9949 - 15.4868i) q^{91} +(-2.49161 - 1.74465i) q^{92} +(-1.31111 - 2.81168i) q^{93} -3.73981 q^{94} +0.347296 q^{96} +(-0.158681 - 0.340293i) q^{97} +(2.37011 + 1.65957i) q^{98} +(4.28614 - 5.10803i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{6}+O(q^{10}) $ 48 * q - 48 * q^6	$ 48 q - 48 q^{6} - 12 q^{11} + 36 q^{21} - 72 q^{31} + 48 q^{36} + 96 q^{41} + 72 q^{46} - 48 q^{51} - 108 q^{61} + 24 q^{66} - 60 q^{71} - 48 q^{76} - 168 q^{81} - 48 q^{86} + 252 q^{91}+O(q^{100}) $ 48 * q - 48 * q^6 - 12 * q^11 + 36 * q^21 - 72 * q^31 + 48 * q^36 + 96 * q^41 + 72 * q^46 - 48 * q^51 - 108 * q^61 + 24 * q^66 - 60 * q^71 - 48 * q^76 - 168 * q^81 - 48 * q^86 + 252 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{11}{18}\right)$

Coefficient data

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

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

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

$2$	−0.422618	−	0.906308i	−0.298836	−	0.640856i
$2$	−0.422618	−	0.906308i	−0.298836	−	0.640856i
$3$	−0.284489	−	0.199201i	−0.164250	−	0.115009i	0.488562	−	0.872529i	$-0.337522\pi$
$3$	−0.284489	−	0.199201i	−0.164250	−	0.115009i	−0.652811	+	0.757521i	$0.726411\pi$
$4$	−0.642788	+	0.766044i	−0.321394	+	0.383022i
$5$		0			0
$5$		0			0
$6$	−0.0603074	+	0.342020i	−0.0246204	+	0.139629i
$7$	0.814083	+	3.03820i	0.307694	+	1.14833i	0.930601	+	0.366035i	$0.119285\pi$
$7$	0.814083	+	3.03820i	0.307694	+	1.14833i	−0.622907	+	0.782296i	$0.714048\pi$
$8$	0.965926	+	0.258819i	0.341506	+	0.0915064i
$9$	−0.984808	−	2.70574i	−0.328269	−	0.901912i
$10$		0			0
$11$	1.15790	+	2.00553i	0.349119	+	0.604691i	0.986093	−	0.166194i	$-0.0531477\pi$
$11$	1.15790	+	2.00553i	0.349119	+	0.604691i	−0.636974	+	0.770885i	$0.719814\pi$
$12$	0.335463	−	0.0898869i	0.0968397	−	0.0259481i
$13$	−3.68660	−	5.26500i	−1.02248	−	1.46025i	−0.882625	−	0.470077i	$-0.844226\pi$
$13$	−3.68660	−	5.26500i	−1.02248	−	1.46025i	−0.139852	−	0.990172i	$-0.544663\pi$
$14$	2.40950	−	2.02181i	0.643965	−	0.540351i
$15$		0			0
$16$	−0.173648	−	0.984808i	−0.0434120	−	0.246202i
$17$	−0.217593	+	0.101465i	−0.0527740	+	0.0246089i	−0.448826	−	0.893619i	$-0.648158\pi$
$17$	−0.217593	+	0.101465i	−0.0527740	+	0.0246089i	0.396052	+	0.918228i	$0.370380\pi$
$18$	−2.03603	+	2.03603i	−0.479898	+	0.479898i
$19$	4.33561	+	0.449974i	0.994657	+	0.103231i
$19$	4.33561	+	0.449974i	0.994657	+	0.103231i
$20$		0			0
$21$	0.373615	−	1.02650i	0.0815295	−	0.224000i
$22$	1.32828	−	1.89699i	0.283191	−	0.404439i
$23$	0.265102	+	3.03012i	0.0552775	+	0.631825i	0.972416	+	0.233255i	$0.0749377\pi$
$23$	0.265102	+	3.03012i	0.0552775	+	0.631825i	−0.917138	+	0.398570i	$0.869507\pi$
$24$	−0.223238	−	0.266044i	−0.0455682	−	0.0543061i
$25$		0			0
$26$	−3.21369	+	5.56628i	−0.630257	+	1.09164i
$27$	−0.528480	+	1.97231i	−0.101706	+	0.379572i
$28$	−2.85068	−	1.32929i	−0.538727	−	0.251213i
$29$	9.33726	−	3.39848i	1.73389	−	0.631083i	0.734990	−	0.678077i	$-0.237187\pi$
$29$	9.33726	−	3.39848i	1.73389	−	0.631083i	0.998895	+	0.0469948i	$0.0149644\pi$
$30$		0			0
$31$	7.73608	+	4.46643i	1.38944	+	0.802194i	0.993252	−	0.115974i	$-0.0369990\pi$
$31$	7.73608	+	4.46643i	1.38944	+	0.802194i	0.396189	+	0.918169i	$0.370332\pi$
$32$	−0.819152	+	0.573576i	−0.144807	+	0.101395i
$33$	0.0700964	−	0.801206i	0.0122022	−	0.139472i
$34$	0.183917	+	0.154325i	0.0315416	+	0.0264665i
$35$		0			0
$36$	2.70574	+	0.984808i	0.450956	+	0.164135i
$37$	2.25550	+	2.25550i	0.370802	+	0.370802i	0.867769	−	0.496967i	$-0.165553\pi$
$37$	2.25550	+	2.25550i	0.370802	+	0.370802i	−0.496967	+	0.867769i	$0.665553\pi$
$38$	−1.42449	−	4.11957i	−0.231083	−	0.668282i
$39$			2.23221i			0.357439i
$40$		0			0
$41$	11.4442	−	2.01793i	1.78729	−	0.315148i	0.820678	−	0.571391i	$-0.193596\pi$
$41$	11.4442	−	2.01793i	1.78729	−	0.315148i	0.966612	+	0.256243i	$0.0824847\pi$
$42$	−1.08822	+	0.0952069i	−0.167916	+	0.0146907i
$43$	0.196313	+	0.0171752i	0.0299375	+	0.00261919i	0.102115	−	0.994773i	$-0.467439\pi$
$43$	0.196313	+	0.0171752i	0.0299375	+	0.00261919i	−0.0721772	+	0.997392i	$0.522995\pi$
$44$	−2.28061	−	0.402133i	−0.343815	−	0.0606238i
$45$		0			0
$46$	2.63419	−	1.52085i	0.388390	−	0.224237i
$47$	1.58051	−	3.38941i	0.230541	−	0.494397i	−0.756674	−	0.653793i	$-0.773177\pi$
$47$	1.58051	−	3.38941i	0.230541	−	0.494397i	0.987215	+	0.159396i	$0.0509546\pi$
$48$	−0.146774	+	0.314757i	−0.0211850	+	0.0454313i
$49$	−2.50574	+	1.44669i	−0.357962	+	0.206670i
$50$		0			0
$51$	0.0821147	+	0.0144790i	0.0114984	+	0.00202747i
$52$	6.40293	+	0.560183i	0.887926	+	0.0776835i
$53$	−0.625382	+	0.0547139i	−0.0859029	+	0.00751553i	−0.130026	−	0.991511i	$-0.541506\pi$
$53$	−0.625382	+	0.0547139i	−0.0859029	+	0.00751553i	0.0441233	+	0.999026i	$0.485951\pi$
$54$	2.01087	−	0.354570i	0.273644	−	0.0482509i
$55$		0			0
$56$			3.14537i			0.420318i
$57$	−1.14380	−	0.991671i	−0.151500	−	0.131350i
$58$	−7.02617	−	7.02617i	−0.922581	−	0.922581i
$59$	−9.92731	−	3.61324i	−1.29243	−	0.470404i	−0.397903	−	0.917428i	$-0.630262\pi$
$59$	−9.92731	−	3.61324i	−1.29243	−	0.470404i	−0.894522	+	0.447023i	$0.852484\pi$
$60$		0			0
$61$	−7.07266	−	5.93466i	−0.905561	−	0.759856i	0.0657085	−	0.997839i	$-0.479069\pi$
$61$	−7.07266	−	5.93466i	−0.905561	−	0.759856i	−0.971269	+	0.237983i	$0.923514\pi$
$62$	0.778550	−	8.89887i	0.0988760	−	1.13016i
$63$	7.41885	−	5.19473i	0.934687	−	0.654475i
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$		0			0
$66$	−0.755763	+	0.275075i	−0.0930280	+	0.0338594i
$67$	10.5110	+	4.90137i	1.28413	+	0.598798i	0.940335	−	0.340249i	$-0.110511\pi$
$67$	10.5110	+	4.90137i	1.28413	+	0.598798i	0.343790	+	0.939046i	$0.388289\pi$
$68$	0.0621391	−	0.231906i	0.00753548	−	0.0281228i
$69$	0.528185	−	0.914844i	0.0635861	−	0.110134i
$70$		0			0
$71$	1.44488	+	1.72195i	0.171476	+	0.204357i	0.844937	−	0.534865i	$-0.179638\pi$
$71$	1.44488	+	1.72195i	0.171476	+	0.204357i	−0.673461	+	0.739223i	$0.735193\pi$
$72$	−0.250955	−	2.86843i	−0.0295753	−	0.338048i
$73$	8.79082	−	12.5546i	1.02889	−	1.46940i	0.152196	−	0.988350i	$-0.451366\pi$
$73$	8.79082	−	12.5546i	1.02889	−	1.46940i	0.876692	−	0.481053i	$-0.159746\pi$
$74$	1.09096	−	2.99739i	0.126822	−	0.348440i
$75$		0			0
$76$	−3.13158	+	3.03203i	−0.359217	+	0.347798i
$77$	−5.15059	+	5.15059i	−0.586964	+	0.586964i
$78$	2.02307	−	0.943371i	0.229067	−	0.106816i
$79$	−1.43404	−	8.13284i	−0.161342	−	0.915016i	−0.952756	−	0.303736i	$-0.901766\pi$
$79$	−1.43404	−	8.13284i	−0.161342	−	0.915016i	0.791414	−	0.611280i	$-0.209345\pi$
$80$		0			0
$81$	−6.07398	+	5.09667i	−0.674886	+	0.566297i
$82$	−6.66541	−	9.51919i	−0.736072	−	1.05122i
$83$	−2.76153	+	0.739950i	−0.303117	+	0.0812201i	−0.407172	−	0.913352i	$-0.633485\pi$
$83$	−2.76153	+	0.739950i	−0.303117	+	0.0812201i	0.104055	+	0.994572i	$0.466818\pi$
$84$	0.546188	+	0.946026i	0.0595940	+	0.103220i
$85$		0			0
$86$	−0.0673995	−	0.185179i	−0.00726788	−	0.0199683i
$87$	−3.33332	−	0.893162i	−0.357370	−	0.0957570i
$88$	0.599371	+	2.23688i	0.0638932	+	0.238453i
$89$	−2.79147	+	15.8312i	−0.295895	+	1.67810i	0.367647	+	0.929966i	$0.380164\pi$
$89$	−2.79147	+	15.8312i	−0.295895	+	1.67810i	−0.663542	+	0.748139i	$0.730948\pi$
$90$		0			0
$91$	12.9949	−	15.4868i	1.36224	−	1.62345i
$92$	−2.49161	−	1.74465i	−0.259769	−	0.181892i
$93$	−1.31111	−	2.81168i	−0.135956	−	0.291558i
$94$	−3.73981			−0.385731
$95$		0			0
$96$	0.347296			0.0354458
$97$	−0.158681	−	0.340293i	−0.0161116	−	0.0345515i	0.898087	−	0.439817i	$-0.144957\pi$
$97$	−0.158681	−	0.340293i	−0.0161116	−	0.0345515i	−0.914199	+	0.405266i	$0.867179\pi$
$98$	2.37011	+	1.65957i	0.239418	+	0.167642i
$99$	4.28614	−	5.10803i	0.430774	−	0.513376i
$100$		0			0
$101$	−0.584726	+	3.31615i	−0.0581824	+	0.329969i	−0.999981	−	0.00620961i	$-0.998023\pi$
$101$	−0.584726	+	3.31615i	−0.0581824	+	0.329969i	0.941798	+	0.336178i	$0.109135\pi$
$102$	−0.0215807	−	0.0805403i	−0.00213681	−	0.00797467i
$103$	9.65516	+	2.58709i	0.951351	+	0.254914i	0.700935	−	0.713225i	$-0.252766\pi$
$103$	9.65516	+	2.58709i	0.951351	+	0.254914i	0.250415	+	0.968138i	$0.419433\pi$
$104$	−2.19829	−	6.03977i	−0.215561	−	0.592248i
$105$		0			0
$106$	0.313886	+	0.543666i	0.0304873	+	0.0528055i
$107$	−10.6053	+	2.84169i	−1.02526	+	0.274716i	−0.731990	−	0.681315i	$-0.761408\pi$
$107$	−10.6053	+	2.84169i	−1.02526	+	0.274716i	−0.293265	+	0.956031i	$0.594742\pi$
$108$	−1.17118	−	1.67262i	−0.112697	−	0.160948i
$109$	1.11750	−	0.937690i	0.107037	−	0.0898144i	−0.587699	−	0.809080i	$-0.699966\pi$
$109$	1.11750	−	0.937690i	0.107037	−	0.0898144i	0.694735	+	0.719265i	$0.255522\pi$
$110$		0			0
$111$	−0.192366	−	1.09096i	−0.0182586	−	0.103550i
$112$	2.85068	−	1.32929i	0.269364	−	0.125606i
$113$	−6.92743	+	6.92743i	−0.651677	+	0.651677i	−0.953397	−	0.301719i	$-0.902439\pi$
$113$	−6.92743	+	6.92743i	−0.651677	+	0.651677i	0.301719	+	0.953397i	$0.402439\pi$
$114$	−0.415370	+	1.45573i	−0.0389029	+	0.136342i
$115$		0			0
$116$	−3.39848	+	9.33726i	−0.315541	+	0.866943i
$117$	−10.6151	+	15.1600i	−0.981369	+	1.40154i
$118$	0.920750	+	10.5242i	0.0847619	+	0.968833i
$119$	−0.485410	−	0.578489i	−0.0444975	−	0.0530300i
$120$		0			0
$121$	2.81855	−	4.88188i	0.256232	−	0.443807i
$122$	−2.38960	+	8.91810i	−0.216344	+	0.807407i
$123$	−3.65773	−	1.70563i	−0.329806	−	0.153791i
$124$	−8.39414	+	3.05522i	−0.753816	+	0.274367i
$125$		0			0
$126$	−7.84337	−	4.52837i	−0.698743	−	0.403419i
$127$	13.8823	−	9.72052i	1.23186	−	0.862557i	0.237790	−	0.971316i	$-0.423577\pi$
$127$	13.8823	−	9.72052i	1.23186	−	0.862557i	0.994068	+	0.108760i	$0.0346880\pi$
$128$	0.0871557	−	0.996195i	0.00770355	−	0.0880520i
$129$	−0.0524275	−	0.0439919i	−0.00461599	−	0.00387327i
$130$		0			0
$131$	3.22111	+	1.17239i	0.281430	+	0.102432i	0.478878	−	0.877881i	$-0.341043\pi$
$131$	3.22111	+	1.17239i	0.281430	+	0.102432i	−0.197449	+	0.980313i	$0.563266\pi$
$132$	0.568702	+	0.568702i	0.0494992	+	0.0494992i
$133$	2.16243	+	13.5388i	0.187507	+	1.17396i
$134$		−	11.5976i		−	1.00188i
$135$		0			0
$136$	−0.236440	+	0.0416907i	−0.0202745	+	0.00357495i
$137$	−3.18844	+	0.278953i	−0.272407	+	0.0238325i	−0.222541	−	0.974923i	$-0.571435\pi$
$137$	−3.18844	+	0.278953i	−0.272407	+	0.0238325i	−0.0498663	+	0.998756i	$0.515880\pi$
$138$	−1.05235	−	0.0920688i	−0.0895821	−	0.00783742i
$139$	2.84133	+	0.501004i	0.240999	+	0.0424946i	0.292843	−	0.956161i	$-0.405399\pi$
$139$	2.84133	+	0.501004i	0.240999	+	0.0424946i	−0.0518440	+	0.998655i	$0.516510\pi$
$140$		0			0
$141$	−1.12481	+	0.649410i	−0.0947262	+	0.0546902i
$142$	0.949979	−	2.03724i	0.0797205	−	0.170961i
$143$	6.29045	−	13.4899i	0.526034	−	1.12808i
$144$	−2.49362	+	1.43969i	−0.207802	+	0.119974i
$145$		0			0
$146$	−15.0935	−	2.66139i	−1.24915	−	0.220258i
$147$	1.00104	+	0.0875792i	0.0825640	+	0.00722341i
$148$	−3.17762	+	0.278006i	−0.261199	+	0.0228520i
$149$	4.83703	−	0.852900i	0.396265	−	0.0698723i	0.0280351	−	0.999607i	$-0.491075\pi$
$149$	4.83703	−	0.852900i	0.396265	−	0.0698723i	0.368230	+	0.929735i	$0.379964\pi$
$150$		0			0
$151$			2.35678i			0.191792i	0.995391	+	0.0958961i	$0.0305717\pi$
$151$			2.35678i			0.191792i	−0.995391	+	0.0958961i	$0.969428\pi$
$152$	4.07142	+	1.55678i	0.330236	+	0.126272i
$153$	0.488825	+	0.488825i	0.0395192	+	0.0395192i
$154$	6.84475	+	2.49129i	0.551566	+	0.200753i
$155$		0			0
$156$	−1.70997	−	1.43484i	−0.136907	−	0.114879i
$157$	1.28184	−	14.6515i	0.102302	−	1.16931i	−0.755435	−	0.655224i	$-0.772574\pi$
$157$	1.28184	−	14.6515i	0.102302	−	1.16931i	0.857736	−	0.514090i	$-0.171870\pi$
$158$	−6.76481	+	4.73677i	−0.538179	+	0.376837i
$159$	0.188813	+	0.109011i	0.0149739	+	0.00864516i
$160$		0			0
$161$	−8.99030	+	3.27220i	−0.708535	+	0.257886i
$162$	7.18613	+	3.35095i	0.564596	+	0.263275i
$163$	−3.63221	+	13.5556i	−0.284497	+	1.06176i	0.664710	+	0.747102i	$0.268555\pi$
$163$	−3.63221	+	13.5556i	−0.284497	+	1.06176i	−0.949206	+	0.314654i	$0.898111\pi$
$164$	−5.81039	+	10.0639i	−0.453716	+	0.785859i
$165$		0			0
$166$	1.83770	+	2.19008i	0.142633	+	0.169983i
$167$	0.509063	+	5.81861i	0.0393924	+	0.450258i	0.990119	+	0.140228i	$0.0447835\pi$
$167$	0.509063	+	5.81861i	0.0393924	+	0.450258i	−0.950727	+	0.310030i	$0.899661\pi$
$168$	0.626562	−	0.894823i	0.0483403	−	0.0690371i
$169$	−9.68302	+	26.6039i	−0.744848	+	2.04645i
$170$		0			0
$171$	−3.05223	−	12.1742i	−0.233410	−	0.930981i
$172$	−0.139345	+	0.139345i	−0.0106249	+	0.0106249i
$173$	1.79976	−	0.839242i	0.136833	−	0.0638064i	−0.352996	−	0.935625i	$-0.614837\pi$
$173$	1.79976	−	0.839242i	0.136833	−	0.0638064i	0.489829	+	0.871819i	$0.337059\pi$
$174$	0.599245	+	3.39848i	0.0454286	+	0.257638i
$175$		0			0
$176$	1.77400	−	1.48856i	0.133720	−	0.112205i
$177$	2.10444	+	3.00546i	0.158180	+	0.225904i
$178$	15.5277	−	4.16063i	1.16385	−	0.311852i
$179$	−5.73760	−	9.93781i	−0.428848	−	0.742787i	0.567923	−	0.823082i	$-0.307747\pi$
$179$	−5.73760	−	9.93781i	−0.428848	−	0.742787i	−0.996771	+	0.0802948i	$0.974414\pi$
$180$		0			0
$181$	−0.917789	−	2.52160i	−0.0682187	−	0.187429i	0.900899	−	0.434030i	$-0.142909\pi$
$181$	−0.917789	−	2.52160i	−0.0682187	−	0.187429i	−0.969117	+	0.246600i	$0.920686\pi$
$182$	−19.5277	−	5.23242i	−1.44749	−	0.387853i
$183$	0.829899	+	3.09722i	0.0613479	+	0.228953i
$184$	−0.528185	+	2.99549i	−0.0389384	+	0.220830i
$185$		0			0
$186$	−1.99415	+	2.37654i	−0.146218	+	0.174256i
$187$	−0.455442	−	0.318904i	−0.0333052	−	0.0233206i
$188$	1.58051	+	3.38941i	0.115271	+	0.247198i
$189$	−6.42250			−0.467168
$190$		0			0
$191$	−18.5305			−1.34082			−0.670410	−	0.741991i	$-0.733882\pi$
$191$	−18.5305			−1.34082			−0.670410	+	0.741991i	$0.733882\pi$
$192$	−0.146774	−	0.314757i	−0.0105925	−	0.0227157i
$193$	6.11972	+	4.28507i	0.440507	+	0.308446i	0.772707	−	0.634763i	$-0.218902\pi$
$193$	6.11972	+	4.28507i	0.440507	+	0.308446i	−0.332200	+	0.943209i	$0.607791\pi$
$194$	−0.241348	+	0.287628i	−0.0173278	+	0.0206505i
$195$		0			0
$196$	0.502429	−	2.84942i	0.0358878	−	0.203530i
$197$	1.37768	+	5.14156i	0.0981555	+	0.366321i	0.997479	−	0.0709627i	$-0.0226071\pi$
$197$	1.37768	+	5.14156i	0.0981555	+	0.366321i	−0.899323	+	0.437284i	$0.855940\pi$
$198$	−6.44085	−	1.72582i	−0.457731	−	0.122649i
$199$	−0.840882	−	2.31030i	−0.0596085	−	0.163773i	0.906314	−	0.422606i	$-0.138884\pi$
$199$	−0.840882	−	2.31030i	−0.0596085	−	0.163773i	−0.965922	+	0.258833i	$0.916662\pi$
$200$		0			0
$201$	−2.01391	−	3.48819i	−0.142050	−	0.246038i
$202$	3.25256	−	0.871522i	0.228850	−	0.0613201i
$203$	17.9266	+	25.6018i	1.25820	+	1.79689i
$204$	−0.0638739	+	0.0535965i	−0.00447207	+	0.00375251i
$205$		0			0
$206$	−1.73574	−	9.84389i	−0.120935	−	0.685857i
$207$	7.93765	−	3.70139i	0.551705	−	0.257264i
$208$	−4.54485	+	4.54485i	−0.315128	+	0.315128i
$209$	4.11775	+	9.21624i	0.284831	+	0.637501i
$210$		0			0
$211$	−1.52968	+	4.20275i	−0.105307	+	0.289329i	−0.981144	−	0.193278i	$-0.938088\pi$
$211$	−1.52968	+	4.20275i	−0.105307	+	0.289329i	0.875837	+	0.482607i	$0.160310\pi$
$212$	0.360075	−	0.514240i	0.0247300	−	0.0353182i
$213$	−0.0680396	−	0.777697i	−0.00466200	−	0.0532869i
$214$	7.05745	+	8.41074i	0.482437	+	0.574946i
$215$		0			0
$216$	−1.02094	+	1.76833i	−0.0694665	+	0.120319i
$217$	−7.27209	+	27.1398i	−0.493661	+	1.84237i
$218$	−1.32211	−	0.616510i	−0.0895446	−	0.0417553i
$219$	−5.00177	+	1.82050i	−0.337988	+	0.123018i
$220$		0			0
$221$	1.33639	+	0.771566i	0.0898955	+	0.0519012i
$222$	−0.907450	+	0.635404i	−0.0609041	+	0.0426455i
$223$	−0.171733	+	1.96292i	−0.0115001	+	0.131447i	−0.999774	−	0.0212424i	$-0.993238\pi$
$223$	−0.171733	+	1.96292i	−0.0115001	+	0.131447i	0.988274	+	0.152689i	$0.0487934\pi$
$224$	−2.40950	−	2.02181i	−0.160991	−	0.135088i
$225$		0			0
$226$	9.20604	+	3.35072i	0.612376	+	0.222887i
$227$	−18.6196	−	18.6196i	−1.23583	−	1.23583i	−0.961690	−	0.274138i	$-0.911607\pi$
$227$	−18.6196	−	18.6196i	−1.23583	−	1.23583i	−0.274138	−	0.961690i	$-0.588393\pi$
$228$	1.49488	−	0.238765i	0.0990010	−	0.0158126i
$229$			6.83578i			0.451721i	0.974160	+	0.225861i	$0.0725194\pi$
$229$			6.83578i			0.451721i	−0.974160	+	0.225861i	$0.927481\pi$
$230$		0			0
$231$	2.49129	−	0.439281i	0.163915	−	0.0289026i
$232$	9.89869	−	0.866023i	0.649881	−	0.0568572i
$233$	−19.8900	−	1.74015i	−1.30304	−	0.114001i	−0.585586	−	0.810610i	$-0.699135\pi$
$233$	−19.8900	−	1.74015i	−1.30304	−	0.114001i	−0.717450	+	0.696610i	$0.754691\pi$
$234$	18.2258	+	3.21369i	1.19145	+	0.210086i
$235$		0			0
$236$	9.14906	−	5.28221i	0.595553	−	0.343843i
$237$	−1.21210	+	2.59936i	−0.0787345	+	0.168847i
$238$	−0.319146	+	0.684411i	−0.0206872	+	0.0443638i
$239$	12.8106	−	7.39620i	0.828649	−	0.478421i	−0.0247411	−	0.999694i	$-0.507876\pi$
$239$	12.8106	−	7.39620i	0.828649	−	0.478421i	0.853390	+	0.521273i	$0.174543\pi$
$240$		0			0
$241$	12.7500	+	2.24817i	0.821299	+	0.144817i	0.568481	−	0.822697i	$-0.307531\pi$
$241$	12.7500	+	2.24817i	0.821299	+	0.144817i	0.252818	+	0.967514i	$0.418643\pi$
$242$	−5.61566	−	0.491306i	−0.360988	−	0.0315824i
$243$	8.84560	−	0.773889i	0.567445	−	0.0496450i
$244$	9.09243	−	1.60324i	0.582083	−	0.102637i
$245$		0			0
$246$			4.03586i			0.257317i
$247$	−13.6145	−	24.4859i	−0.866272	−	1.55800i
$248$	6.31649	+	6.31649i	0.401097	+	0.401097i
$249$	0.933023	+	0.339592i	0.0591279	+	0.0215208i
$250$		0			0
$251$	−16.3375	−	13.7088i	−1.03121	−	0.865292i	−0.0402197	−	0.999191i	$-0.512806\pi$
$251$	−16.3375	−	13.7088i	−1.03121	−	0.865292i	−0.990995	+	0.133899i	$0.957250\pi$
$252$	−0.789347	+	9.02228i	−0.0497242	+	0.568350i
$253$	−5.77006	+	4.04024i	−0.362760	+	0.254008i
$254$	−14.6767	−	8.47360i	−0.920899	−	0.531681i
$255$		0			0
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	5.28705	+	2.46539i	0.329797	+	0.153787i	0.580463	−	0.814287i	$-0.302872\pi$
$257$	5.28705	+	2.46539i	0.329797	+	0.153787i	−0.250666	+	0.968074i	$0.580649\pi$
$258$	−0.0177134	+	0.0661073i	−0.00110279	+	0.00411566i
$259$	−5.01650	+	8.68882i	−0.311710	+	0.539897i
$260$		0			0
$261$	−18.3908	−	21.9173i	−1.13836	−	1.35665i
$262$	−0.298755	−	3.41479i	−0.0184572	−	0.210966i
$263$	−11.9997	+	17.1373i	−0.739931	+	1.05673i	0.256006	+	0.966675i	$0.417593\pi$
$263$	−11.9997	+	17.1373i	−0.739931	+	1.05673i	−0.995937	+	0.0900555i	$0.971296\pi$
$264$	0.275075	−	0.755763i	0.0169297	−	0.0465140i
$265$		0			0
$266$	11.3564	−	7.68156i	0.696306	−	0.470987i
$267$	3.94773	−	3.94773i	0.241597	−	0.241597i
$268$	−10.5110	+	4.90137i	−0.642063	+	0.299399i
$269$	3.35017	+	18.9998i	0.204263	+	1.15844i	0.898595	+	0.438780i	$0.144589\pi$
$269$	3.35017	+	18.9998i	0.204263	+	1.15844i	−0.694331	+	0.719656i	$0.744300\pi$
$270$		0			0
$271$	−20.7561	+	17.4165i	−1.26085	+	1.05798i	−0.265254	+	0.964178i	$0.585456\pi$
$271$	−20.7561	+	17.4165i	−1.26085	+	1.05798i	−0.995591	+	0.0937968i	$0.970100\pi$
$272$	0.137708	+	0.196668i	0.00834980	+	0.0119247i
$273$	−6.78189	+	1.81720i	−0.410458	+	0.109982i
$274$	1.60031	+	2.77182i	0.0966784	+	0.167452i
$275$		0			0
$276$	0.361300	+	0.992664i	0.0217477	+	0.0597514i
$277$	17.9635	+	4.81331i	1.07932	+	0.289204i	0.754318	−	0.656509i	$-0.227968\pi$
$277$	17.9635	+	4.81331i	1.07932	+	0.289204i	0.325004	+	0.945713i	$0.394634\pi$
$278$	−0.746736	−	2.78686i	−0.0447862	−	0.167144i
$279$	4.46643	−	25.3304i	0.267398	−	1.51649i
$280$		0			0
$281$	−9.54554	+	11.3759i	−0.569439	+	0.678631i	−0.971516	−	0.236975i	$-0.923844\pi$
$281$	−9.54554	+	11.3759i	−0.569439	+	0.678631i	0.402077	+	0.915606i	$0.368289\pi$
$282$	1.06393	+	0.744973i	0.0633562	+	0.0443625i
$283$	6.59744	+	14.1483i	0.392177	+	0.841027i	0.998935	+	0.0461400i	$0.0146920\pi$
$283$	6.59744	+	14.1483i	0.392177	+	0.841027i	−0.606758	+	0.794887i	$0.707530\pi$
$284$	−2.24784			−0.133385
$285$		0			0
$286$	−14.8845			−0.880138
$287$	15.4474	+	33.1271i	0.911833	+	1.95543i
$288$	2.35865	+	1.65155i	0.138985	+	0.0973184i
$289$	−10.8903	+	12.9786i	−0.640608	+	0.763447i
$290$		0			0
$291$	−0.0226437	+	0.128419i	−0.00132740	+	0.00752805i
$292$	3.96674	+	14.8041i	0.232136	+	0.866344i
$293$	−18.2487	−	4.88974i	−1.06610	−	0.285661i	−0.317212	−	0.948355i	$-0.602747\pi$
$293$	−18.2487	−	4.88974i	−1.06610	−	0.285661i	−0.748891	+	0.662693i	$0.769413\pi$
$294$	−0.343682	−	0.944259i	−0.0200439	−	0.0550703i
$295$		0			0
$296$	1.59488	+	2.76241i	0.0927005	+	0.160562i
$297$	−4.56747	+	1.22385i	−0.265031	+	0.0710149i
$298$	−2.81721	−	4.02339i	−0.163196	−	0.233069i
$299$	14.9763	−	12.5666i	0.866102	−	0.726746i
$300$		0			0
$301$	0.107634	+	0.610420i	0.00620390	+	0.0351840i
$302$	2.13597	−	0.996019i	0.122911	−	0.0573145i
$303$	0.826927	−	0.826927i	0.0475057	−	0.0475057i
$304$	−0.309733	−	4.34788i	−0.0177644	−	0.249368i
$305$		0			0
$306$	0.236440	−	0.649613i	0.0135164	−	0.0371359i
$307$	12.3302	−	17.6093i	0.703721	−	1.00502i	−0.295051	−	0.955482i	$-0.595337\pi$
$307$	12.3302	−	17.6093i	0.703721	−	1.00502i	0.998772	−	0.0495368i	$-0.0157745\pi$
$308$	−0.634845	−	7.25631i	−0.0361737	−	0.413467i
$309$	−2.23143	−	2.65931i	−0.126942	−	0.151283i
$310$		0			0
$311$	−4.91604	+	8.51483i	−0.278763	+	0.482832i	−0.971078	−	0.238764i	$-0.923258\pi$
$311$	−4.91604	+	8.51483i	−0.278763	+	0.482832i	0.692315	+	0.721596i	$0.256591\pi$
$312$	−0.577738	+	2.15615i	−0.0327080	+	0.122068i
$313$	−12.2440	−	5.70946i	−0.692071	−	0.322718i	0.0445661	−	0.999006i	$-0.485809\pi$
$313$	−12.2440	−	5.70946i	−0.692071	−	0.322718i	−0.736637	+	0.676289i	$0.763587\pi$
$314$	−13.8205	+	5.03024i	−0.779934	+	0.283873i
$315$		0			0
$316$	7.15190	+	4.12915i	0.402326	+	0.232283i
$317$	29.0083	−	20.3118i	1.62927	−	1.14083i	0.754473	−	0.656331i	$-0.227892\pi$
$317$	29.0083	−	20.3118i	1.62927	−	1.14083i	0.874794	−	0.484495i	$-0.160997\pi$
$318$	0.0190019	−	0.217193i	0.00106558	−	0.0121796i
$319$	17.6274	+	14.7911i	0.986942	+	0.828143i
$320$		0			0
$321$	3.58316	+	1.30416i	0.199992	+	0.0727913i
$322$	6.76509	+	6.76509i	0.377004	+	0.377004i
$323$	−0.989055	+	0.342003i	−0.0550325	+	0.0190295i
$324$		−	7.92902i		−	0.440501i
$325$		0			0
$326$	13.8206	−	2.43694i	0.765451	−	0.134970i
$327$	−0.504703	+	0.0441558i	−0.0279102	+	0.00244182i
$328$	11.5766	+	1.01282i	0.639209	+	0.0559236i
$329$	11.5844	+	2.04264i	0.638667	+	0.112614i
$330$		0			0
$331$	7.75064	−	4.47483i	0.426014	−	0.245959i	−0.271633	−	0.962401i	$-0.587564\pi$
$331$	7.75064	−	4.47483i	0.426014	−	0.245959i	0.697647	+	0.716442i	$0.254230\pi$
$332$	1.20824	−	2.59109i	0.0663110	−	0.142204i
$333$	3.88156	−	8.32403i	0.212708	−	0.456154i
$334$	5.05831	−	2.92042i	0.276779	−	0.159798i
$335$		0			0
$336$	−1.07578	−	0.189689i	−0.0586887	−	0.0103484i
$337$	−25.9706	−	2.27213i	−1.41471	−	0.123771i	−0.645983	−	0.763352i	$-0.723552\pi$
$337$	−25.9706	−	2.27213i	−1.41471	−	0.123771i	−0.768723	+	0.639581i	$0.779108\pi$
$338$	28.2035	−	2.46749i	1.53407	−	0.134214i
$339$	3.35072	−	0.590823i	0.181986	−	0.0320891i
$340$		0			0
$341$			20.6866i			1.12024i
$342$	−9.74361	+	7.91128i	−0.526874	+	0.427793i
$343$	9.13360	+	9.13360i	0.493168	+	0.493168i
$344$	0.185179	+	0.0673995i	0.00998417	+	0.00363394i
$345$		0			0
$346$	−1.52122	−	1.27646i	−0.0817815	−	0.0686228i
$347$	−2.19008	+	25.0328i	−0.117570	+	1.34383i	0.676698	+	0.736261i	$0.263410\pi$
$347$	−2.19008	+	25.0328i	−0.117570	+	1.34383i	−0.794268	+	0.607568i	$0.792145\pi$
$348$	2.82682	−	1.97936i	0.151534	−	0.106105i
$349$	−0.243694	−	0.140697i	−0.0130446	−	0.00753131i	0.493464	−	0.869766i	$-0.335731\pi$
$349$	−0.243694	−	0.140697i	−0.0130446	−	0.00753131i	−0.506508	+	0.862235i	$0.669064\pi$
$350$		0			0
$351$	12.3325	−	4.48867i	0.658262	−	0.239588i
$352$	−2.09882	−	0.978696i	−0.111867	−	0.0521647i
$353$	1.97283	−	7.36269i	0.105003	−	0.391877i	−0.893343	−	0.449376i	$-0.851646\pi$
$353$	1.97283	−	7.36269i	0.105003	−	0.391877i	0.998346	+	0.0574999i	$0.0183129\pi$
$354$	1.83449	−	3.17743i	0.0975022	−	0.168879i
$355$		0			0
$356$	−10.3331	−	12.3145i	−0.547653	−	0.652667i
$357$	0.0228580	+	0.261268i	0.00120977	+	0.0138278i
$358$	−6.58190	+	9.39993i	−0.347864	+	0.496802i
$359$	−7.21429	+	19.8211i	−0.380756	+	1.04612i	0.590283	+	0.807196i	$0.299016\pi$
$359$	−7.21429	+	19.8211i	−0.380756	+	1.04612i	−0.971039	+	0.238921i	$0.923206\pi$
$360$		0			0
$361$	18.5950	+	3.90183i	0.978687	+	0.205359i
$362$	−1.89747	+	1.89747i	−0.0997291	+	0.0997291i
$363$	−1.77432	+	0.827380i	−0.0931277	+	0.0434262i
$364$	3.51056	+	19.9094i	0.184003	+	1.04354i
$365$		0			0
$366$	2.45631	−	2.06109i	0.128393	−	0.107735i
$367$	−8.44137	−	12.0555i	−0.440636	−	0.629294i	0.535994	−	0.844222i	$-0.319937\pi$
$367$	−8.44137	−	12.0555i	−0.440636	−	0.629294i	−0.976630	+	0.214928i	$0.931048\pi$
$368$	2.93806	−	0.787250i	0.153157	−	0.0410382i
$369$	−16.7304	−	28.9778i	−0.870948	−	1.50853i
$370$		0			0
$371$	−0.675345	−	1.85549i	−0.0350621	−	0.0963324i
$372$	2.99664	+	0.802947i	0.155369	+	0.0416309i
$373$	−4.73827	−	17.6835i	−0.245338	−	0.915615i	−0.973213	−	0.229905i	$-0.926158\pi$
$373$	−4.73827	−	17.6835i	−0.245338	−	0.915615i	0.727875	−	0.685710i	$-0.240508\pi$
$374$	−0.0965470	+	0.547545i	−0.00499233	+	0.0283129i
$375$		0			0
$376$	2.40390	−	2.86486i	0.123972	−	0.147744i
$377$	−52.3157	−	36.6319i	−2.69440	−	1.88664i
$378$	2.71427	+	5.82077i	0.139607	+	0.299388i
$379$	−25.8268			−1.32663			−0.663316	−	0.748339i	$-0.730851\pi$
$379$	−25.8268			−1.32663			−0.663316	+	0.748339i	$0.730851\pi$
$380$		0			0
$381$	−5.88570			−0.301534
$382$	7.83133	+	16.7943i	0.400686	+	0.859273i
$383$	3.33844	+	2.33760i	0.170586	+	0.119446i	0.655752	−	0.754977i	$-0.272352\pi$
$383$	3.33844	+	2.33760i	0.170586	+	0.119446i	−0.485166	+	0.874422i	$0.661241\pi$
$384$	−0.223238	+	0.266044i	−0.0113921	+	0.0135765i
$385$		0			0
$386$	1.29729	−	7.35729i	0.0660303	−	0.374476i
$387$	−0.146859	−	0.548086i	−0.00746527	−	0.0278608i
$388$	0.362678	+	0.0971792i	0.0184122	+	0.00493353i
$389$	−11.5651	−	31.7747i	−0.586372	−	1.61104i	−0.777083	−	0.629398i	$-0.783302\pi$
$389$	−11.5651	−	31.7747i	−0.586372	−	1.61104i	0.190712	−	0.981646i	$-0.438920\pi$
$390$		0			0
$391$	−0.365137	−	0.632435i	−0.0184657	−	0.0319836i
$392$	−2.79479	+	0.748861i	−0.141158	+	0.0378232i
$393$	−0.682828	−	0.975179i	−0.0344441	−	0.0491913i
$394$	4.07761	−	3.42152i	0.205427	−	0.172374i
$395$		0			0
$396$	1.15790	+	6.56675i	0.0581865	+	0.329992i
$397$	15.3722	−	7.16818i	0.771509	−	0.359761i	0.00332922	−	0.999994i	$-0.498940\pi$
$397$	15.3722	−	7.16818i	0.771509	−	0.359761i	0.768180	+	0.640234i	$0.221162\pi$
$398$	−1.73847	+	1.73847i	−0.0871418	+	0.0871418i
$399$	2.08175	−	4.28238i	0.104218	−	0.214387i
$400$		0			0
$401$	−9.26933	+	25.4673i	−0.462888	+	1.27177i	0.460415	+	0.887704i	$0.347700\pi$
$401$	−9.26933	+	25.4673i	−0.462888	+	1.27177i	−0.923304	+	0.384071i	$0.874522\pi$
$402$	−2.31026	+	3.29939i	−0.115225	+	0.164559i
$403$	−5.00404	−	57.1964i	−0.249269	−	2.84916i
$404$	−2.16446	−	2.57950i	−0.107686	−	0.128335i
$405$		0			0
$406$	15.6270	−	27.0668i	0.775555	−	1.34330i
$407$	−1.91185	+	7.13512i	−0.0947669	+	0.353675i
$408$	0.0755692	+	0.0352385i	0.00374123	+	0.00174457i
$409$	1.28702	−	0.468436i	0.0636389	−	0.0231627i	−0.310005	−	0.950735i	$-0.600331\pi$
$409$	1.28702	−	0.468436i	0.0636389	−	0.0231627i	0.373643	+	0.927572i	$0.378108\pi$
$410$		0			0
$411$	0.962643	+	0.555782i	0.0474837	+	0.0274147i
$412$	−8.18804	+	5.73333i	−0.403396	+	0.282461i
$413$	2.89610	−	33.1026i	0.142508	−	1.62887i
$414$	−6.70919	−	5.62968i	−0.329739	−	0.276684i
$415$		0			0
$416$	6.03977	+	2.19829i	0.296124	+	0.107780i
$417$	−0.708526	−	0.708526i	−0.0346967	−	0.0346967i
$418$	6.61252	−	7.62690i	0.323429	−	0.373044i
$419$		−	34.0731i		−	1.66458i	−0.554341	−	0.832290i	$-0.687029\pi$
$419$		−	34.0731i		−	1.66458i	0.554341	−	0.832290i	$-0.312971\pi$
$420$		0			0
$421$	−14.3620	+	2.53241i	−0.699960	+	0.123422i	−0.512293	−	0.858811i	$-0.671204\pi$
$421$	−14.3620	+	2.53241i	−0.699960	+	0.123422i	−0.187667	+	0.982233i	$0.560093\pi$
$422$	4.45545	−	0.389802i	0.216888	−	0.0189752i
$423$	−10.7274	−	0.938523i	−0.521582	−	0.0456325i
$424$	−0.618234	−	0.109011i	−0.0300241	−	0.00529406i
$425$		0			0
$426$	−0.676078	+	0.390334i	−0.0327561	+	0.0189117i
$427$	12.2730	−	26.3194i	0.593930	−	1.27369i
$428$	4.64011	−	9.95075i	0.224288	−	0.480988i
$429$	−4.47677	+	2.58466i	−0.216140	+	0.124789i
$430$		0			0
$431$	11.5828	+	2.04237i	0.557925	+	0.0983773i	0.445498	−	0.895283i	$-0.353026\pi$
$431$	11.5828	+	2.04237i	0.557925	+	0.0983773i	0.112427	+	0.993660i	$0.464138\pi$
$432$	2.03412	+	0.177962i	0.0978666	+	0.00856222i
$433$	−11.1184	+	0.972738i	−0.534319	+	0.0467468i	−0.351122	−	0.936330i	$-0.614200\pi$
$433$	−11.1184	+	0.972738i	−0.534319	+	0.0467468i	−0.183196	+	0.983076i	$0.558644\pi$
$434$	27.6703	−	4.87902i	1.32822	−	0.234201i
$435$		0			0
$436$			1.45879i			0.0698632i
$437$	−0.214101	+	13.2567i	−0.0102418	+	0.634155i
$438$	3.76377	+	3.76377i	0.179840	+	0.179840i
$439$	−26.3863	−	9.60383i	−1.25935	−	0.458366i	−0.375799	−	0.926701i	$-0.622632\pi$
$439$	−26.3863	−	9.60383i	−1.25935	−	0.458366i	−0.883551	+	0.468336i	$0.844854\pi$
$440$		0			0
$441$	6.38203	+	5.35516i	0.303906	+	0.255007i
$442$	0.134493	−	1.53726i	0.00639717	−	0.0731200i
$443$	−8.96910	+	6.28023i	−0.426135	+	0.298383i	−0.766901	−	0.641765i	$-0.778202\pi$
$443$	−8.96910	+	6.28023i	−0.426135	+	0.298383i	0.340766	+	0.940148i	$0.389314\pi$
$444$	0.959376	+	0.553896i	0.0455300	+	0.0262867i
$445$		0			0
$446$	1.85159	−	0.673923i	0.0876752	−	0.0319112i
$447$	−1.54598	−	0.720902i	−0.0731223	−	0.0340975i
$448$	−0.814083	+	3.03820i	−0.0384618	+	0.143541i
$449$	11.0357	−	19.1145i	0.520809	−	0.902068i	−0.478898	−	0.877871i	$-0.658964\pi$
$449$	11.0357	−	19.1145i	0.520809	−	0.902068i	0.999707	−	0.0241974i	$-0.00770302\pi$
$450$		0			0
$451$	17.2983	+	20.6153i	0.814544	+	0.970735i
$452$	−0.853853	−	9.75958i	−0.0401618	−	0.459052i
$453$	0.469473	−	0.670478i	0.0220578	−	0.0315018i
$454$	−9.00612	+	24.7441i	−0.422678	+	1.16130i
$455$		0			0
$456$	−0.848159	−	1.25392i	−0.0397187	−	0.0587200i
$457$	13.3270	−	13.3270i	0.623410	−	0.623410i	−0.322992	−	0.946402i	$-0.604689\pi$
$457$	13.3270	−	13.3270i	0.623410	−	0.623410i	0.946402	+	0.322992i	$0.104689\pi$
$458$	6.19532	−	2.88893i	0.289488	−	0.134991i
$459$	−0.0851278	−	0.482784i	−0.00397343	−	0.0225344i
$460$		0			0
$461$	16.3482	−	13.7178i	0.761411	−	0.638900i	−0.177083	−	0.984196i	$-0.556666\pi$
$461$	16.3482	−	13.7178i	0.761411	−	0.638900i	0.938494	+	0.345296i	$0.112222\pi$
$462$	−1.45099	−	2.07222i	−0.0675060	−	0.0964085i
$463$	30.6582	−	8.21485i	1.42481	−	0.381777i	0.537622	−	0.843186i	$-0.319323\pi$
$463$	30.6582	−	8.21485i	1.42481	−	0.381777i	0.887187	+	0.461409i	$0.152656\pi$
$464$	−4.96825	−	8.60526i	−0.230645	−	0.399489i
$465$		0			0
$466$	6.82876	+	18.7619i	0.316336	+	0.869127i
$467$	−6.75939	−	1.81117i	−0.312787	−	0.0838111i	0.0990103	−	0.995086i	$-0.468432\pi$
$467$	−6.75939	−	1.81117i	−0.312787	−	0.0838111i	−0.411798	+	0.911275i	$0.635099\pi$
$468$	−4.78994	−	17.8763i	−0.221415	−	0.826333i
$469$	−6.33449	+	35.9247i	−0.292500	+	1.65885i
$470$		0			0
$471$	−3.28325	+	3.91283i	−0.151284	+	0.180294i
$472$	−8.65387	−	6.05950i	−0.398326	−	0.278911i
$473$	0.192865	+	0.413600i	0.00886793	+	0.0190173i
$474$	2.86808			0.131735
$475$		0			0
$476$	0.755164			0.0346129
$477$	0.763923	+	1.63824i	0.0349776	+	0.0750098i
$478$	−12.1172	−	8.48457i	−0.554229	−	0.388075i
$479$	16.1947	−	19.3000i	0.739953	−	0.881841i	−0.256453	−	0.966557i	$-0.582554\pi$
$479$	16.1947	−	19.3000i	0.739953	−	0.881841i	0.996405	+	0.0847156i	$0.0269982\pi$
$480$		0			0
$481$	3.56010	−	20.1903i	0.162327	−	0.920601i
$482$	−3.35085	−	12.5055i	−0.152627	−	0.569611i
$483$	3.20946	+	0.859973i	0.146036	+	0.0391301i
$484$	1.92800	+	5.29715i	0.0876366	+	0.240780i
$485$		0			0
$486$	−4.43969	−	7.68977i	−0.201389	−	0.348815i
$487$	31.3050	−	8.38814i	1.41856	−	0.380103i	0.533590	−	0.845744i	$-0.320843\pi$
$487$	31.3050	−	8.38814i	1.41856	−	0.380103i	0.884974	+	0.465641i	$0.154176\pi$
$488$	−5.29566	−	7.56298i	−0.239723	−	0.342360i
$489$	3.73361	−	3.13287i	0.168840	−	0.141673i
$490$		0			0
$491$	0.870398	+	4.93627i	0.0392805	+	0.222771i	0.998129	−	0.0611484i	$-0.0194763\pi$
$491$	0.870398	+	4.93627i	0.0392805	+	0.222771i	−0.958848	+	0.283919i	$0.908365\pi$
$492$	3.65773	−	1.70563i	0.164903	−	0.0768956i
$493$	−1.68689	+	1.68689i	−0.0759739	+	0.0759739i
$494$	−16.4380	+	22.6871i	−0.739581	+	1.02074i
$495$		0			0
$496$	3.05522	−	8.39414i	0.137183	−	0.376908i
$497$	−4.05536	+	5.79165i	−0.181908	+	0.259791i
$498$	−0.0865371	−	0.989124i	−0.00387782	−	0.0443237i
$499$	−1.36639	−	1.62840i	−0.0611679	−	0.0728971i	0.734593	−	0.678508i	$-0.237373\pi$
$499$	−1.36639	−	1.62840i	−0.0611679	−	0.0728971i	−0.795761	+	0.605611i	$0.792929\pi$
$500$		0			0
$501$	1.01425	−	1.75673i	0.0453134	−	0.0784851i
$502$	−5.51986	+	20.6004i	−0.246364	+	0.919441i
$503$	16.5778	+	7.73034i	0.739166	+	0.344679i	0.755466	−	0.655188i	$-0.227411\pi$
$503$	16.5778	+	7.73034i	0.739166	+	0.344679i	−0.0162995	+	0.999867i	$0.505189\pi$
$504$	8.51055	−	3.09759i	0.379090	−	0.137978i
$505$		0			0
$506$	6.10023	+	3.52197i	0.271188	+	0.156571i
$507$	8.05423	−	5.63963i	0.357701	−	0.250465i
$508$	−1.47705	+	16.8827i	−0.0655333	+	0.749049i
$509$	18.5795	+	15.5901i	0.823523	+	0.691018i	0.953794	−	0.300461i	$-0.0971404\pi$
$509$	18.5795	+	15.5901i	0.823523	+	0.691018i	−0.130271	+	0.991478i	$0.541585\pi$
$510$		0			0
$511$	45.2998	+	16.4878i	2.00394	+	0.729376i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−3.17877	+	8.31338i	−0.140346	+	0.367045i
$514$		−	5.83362i		−	0.257310i
$515$		0			0
$516$	0.0673995	−	0.0118844i	0.00296710	−	0.000523180i
$517$	8.62765	−	0.754822i	0.379444	−	0.0331970i
$518$	9.99481	+	0.874433i	0.439147	+	0.0384204i
$519$	−0.679189	−	0.119759i	−0.0298131	−	0.00525685i
$520$		0			0
$521$	−7.61460	+	4.39629i	−0.333602	+	0.192605i	−0.657439	−	0.753508i	$-0.728360\pi$
$521$	−7.61460	+	4.39629i	−0.333602	+	0.192605i	0.323837	+	0.946113i	$0.395027\pi$
$522$	−12.0915	+	25.9304i	−0.529232	+	1.13494i
$523$	−17.0447	+	36.5525i	−0.745313	+	1.59833i	0.0548140	+	0.998497i	$0.482543\pi$
$523$	−17.0447	+	36.5525i	−0.745313	+	1.59833i	−0.800127	+	0.599831i	$0.795234\pi$
$524$	−2.96859	+	1.71392i	−0.129683	+	0.0748728i
$525$		0			0
$526$	20.6029	+	3.63285i	0.898331	+	0.158400i
$527$	−2.13650	−	0.186920i	−0.0930676	−	0.00814236i
$528$	−0.801206	+	0.0700964i	−0.0348680	+	0.00305055i
$529$	13.5392	−	2.38733i	0.588661	−	0.103797i
$530$		0			0
$531$			30.4190i			1.32007i
$532$	−11.7613	−	7.04603i	−0.509916	−	0.305484i
$533$	−52.8147	−	52.8147i	−2.28766	−	2.28766i
$534$	−5.24625	−	1.90948i	−0.227027	−	0.0826312i
$535$		0			0
$536$	8.88430	+	7.45481i	0.383743	+	0.321999i
$537$	−0.347341	+	3.97013i	−0.0149889	+	0.171324i
$538$	15.8038	−	11.0659i	0.681350	−	0.477086i
$539$	−5.80277	−	3.35023i	−0.249943	−	0.144305i
$540$		0			0
$541$	−18.8360	+	6.85575i	−0.809823	+	0.294752i	−0.713551	−	0.700603i	$-0.752914\pi$
$541$	−18.8360	+	6.85575i	−0.809823	+	0.294752i	−0.0962725	+	0.995355i	$0.530692\pi$
$542$	24.5566	+	11.4509i	1.05480	+	0.491860i
$543$	−0.241206	+	0.900192i	−0.0103511	+	0.0386309i
$544$	0.120044	−	0.207922i	0.00514683	−	0.00891457i
$545$		0			0
$546$	4.51309	+	5.37849i	0.193143	+	0.230178i
$547$	−2.36286	−	27.0076i	−0.101029	−	1.15476i	−0.862324	−	0.506357i	$-0.830992\pi$
$547$	−2.36286	−	27.0076i	−0.101029	−	1.15476i	0.761296	−	0.648405i	$-0.224564\pi$
$548$	1.83580	−	2.62180i	0.0784216	−	0.111998i
$549$	−9.09243	+	24.9813i	−0.388056	+	1.06617i
$550$		0			0
$551$	42.0120	−	10.5330i	1.78977	−	0.448720i
$552$	0.746967	−	0.746967i	0.0317930	−	0.0317930i
$553$	23.5418	−	10.9777i	1.00110	−	0.466819i
$554$	−3.22937	−	18.3147i	−0.137203	−	0.778115i
$555$		0			0
$556$	−2.21016	+	1.85455i	−0.0937319	+	0.0786504i
$557$	−13.2937	−	18.9853i	−0.563271	−	0.804435i	0.431969	−	0.901888i	$-0.357819\pi$
$557$	−13.2937	−	18.9853i	−0.563271	−	0.804435i	−0.995240	+	0.0974540i	$0.968930\pi$
$558$	−24.8447	+	6.65712i	−1.05176	+	0.281818i
$559$	−0.633300	−	1.09691i	−0.0267857	−	0.0463943i
$560$		0			0
$561$	0.0660420	+	0.181449i	0.00278830	+	0.00766078i
$562$	14.3442	+	3.84352i	0.605074	+	0.162129i
$563$	5.63068	+	21.0140i	0.237305	+	0.885634i	0.977096	+	0.212798i	$0.0682576\pi$
$563$	5.63068	+	21.0140i	0.237305	+	0.885634i	−0.739791	+	0.672836i	$0.765076\pi$
$564$	0.225538	−	1.27909i	0.00949686	−	0.0538594i
$565$		0			0
$566$	10.0345	−	11.9586i	0.421781	−	0.502659i
$567$	−20.4294	−	14.3048i	−0.857955	−	0.600747i
$568$	0.949979	+	2.03724i	0.0398602	+	0.0854805i
$569$	20.7487			0.869829			0.434914	−	0.900472i	$-0.356779\pi$
$569$	20.7487			0.869829			0.434914	+	0.900472i	$0.356779\pi$
$570$		0			0
$571$	−21.4374			−0.897128			−0.448564	−	0.893751i	$-0.648064\pi$
$571$	−21.4374			−0.897128			−0.448564	+	0.893751i	$0.648064\pi$
$572$	6.29045	+	13.4899i	0.263017	+	0.564042i
$573$	5.27172	+	3.69130i	0.220229	+	0.154206i
$574$	23.4950	−	28.0002i	0.980662	−	1.16871i
$575$		0			0
$576$	0.500000	−	2.83564i	0.0208333	−	0.118152i
$577$	6.98602	+	26.0722i	0.290832	+	1.08540i	0.944471	+	0.328594i	$0.106575\pi$
$577$	6.98602	+	26.0722i	0.290832	+	1.08540i	−0.653639	+	0.756806i	$0.726759\pi$
$578$	16.3651	+	4.38500i	0.680697	+	0.182392i
$579$	−0.887398	−	2.43811i	−0.0368790	−	0.101324i
$580$		0			0
$581$	−4.49623	−	7.78770i	−0.186535	−	0.323088i
$582$	0.125957	−	0.0337500i	0.00522107	−	0.00139898i
$583$	−0.833858	−	1.19087i	−0.0345349	−	0.0493209i
$584$	11.7406	−	9.85157i	0.485831	−	0.407661i
$585$		0			0
$586$	3.28065	+	18.6055i	0.135522	+	0.768585i
$587$	23.4647	−	10.9418i	0.968490	−	0.451614i	0.127009	−	0.991902i	$-0.459462\pi$
$587$	23.4647	−	10.9418i	0.968490	−	0.451614i	0.841481	+	0.540287i	$0.181684\pi$
$588$	−0.710543	+	0.710543i	−0.0293023	+	0.0293023i
$589$	31.5309	+	22.8457i	1.29921	+	0.941342i
$590$		0			0
$591$	0.632271	−	1.73715i	0.0260082	−	0.0714568i
$592$	1.82957	−	2.61290i	0.0751949	−	0.107389i
$593$	0.323878	+	3.70194i	0.0133001	+	0.152020i	0.999941	−	0.0108915i	$-0.00346693\pi$
$593$	0.323878	+	3.70194i	0.0133001	+	0.152020i	−0.986641	+	0.162912i	$0.947911\pi$
$594$	3.03948	+	3.62231i	0.124711	+	0.148625i
$595$		0			0
$596$	−2.45583	+	4.25362i	−0.100595	+	0.174235i
$597$	−0.220994	+	0.824759i	−0.00904467	+	0.0337552i
$598$	−17.7185	−	8.26226i	−0.724562	−	0.337869i
$599$	−44.0649	+	16.0383i	−1.80044	+	0.655308i	−0.802138	+	0.597139i	$0.796304\pi$
$599$	−44.0649	+	16.0383i	−1.80044	+	0.655308i	−0.998307	+	0.0581691i	$0.981474\pi$
$600$		0			0
$601$	−0.732618	−	0.422977i	−0.0298841	−	0.0172536i	0.484984	−	0.874523i	$-0.338826\pi$
$601$	−0.732618	−	0.422977i	−0.0298841	−	0.0172536i	−0.514868	+	0.857270i	$0.672159\pi$
$602$	0.507741	−	0.355524i	0.0206940	−	0.0144901i
$603$	2.91048	−	33.2670i	0.118524	−	1.35474i
$604$	−1.80540	−	1.51491i	−0.0734607	−	0.0616408i
$605$		0			0
$606$	−1.09893	−	0.399976i	−0.0446408	−	0.0162479i
$607$	7.01280	+	7.01280i	0.284641	+	0.284641i	0.834957	−	0.550316i	$-0.185493\pi$
$607$	7.01280	+	7.01280i	0.284641	+	0.284641i	−0.550316	+	0.834957i	$0.685493\pi$
$608$	−3.80962	+	2.11821i	−0.154500	+	0.0859046i
$609$		−	10.8544i		−	0.439843i
$610$		0			0
$611$	−23.6720	+	4.17401i	−0.957666	+	0.168862i
$612$	−0.688673	+	0.0602511i	−0.0278380	+	0.00243551i
$613$	28.4242	+	2.48680i	1.14804	+	0.100441i	0.645254	−	0.763968i	$-0.276751\pi$
$613$	28.4242	+	2.48680i	1.14804	+	0.100441i	0.502790	+	0.864409i	$0.332307\pi$
$614$	−21.1705	−	3.73292i	−0.854370	−	0.150648i
$615$		0			0
$616$	−6.30816	+	3.64202i	−0.254163	+	0.146741i
$617$	−12.8561	+	27.5701i	−0.517569	+	1.10993i	0.457741	+	0.889086i	$0.348659\pi$
$617$	−12.8561	+	27.5701i	−0.517569	+	1.10993i	−0.975309	+	0.220844i	$0.929119\pi$
$618$	−1.46711	+	3.14624i	−0.0590160	+	0.126560i
$619$	33.6327	−	19.4178i	1.35181	−	0.780468i	0.363308	−	0.931669i	$-0.381647\pi$
$619$	33.6327	−	19.4178i	1.35181	−	0.780468i	0.988503	+	0.151201i	$0.0483140\pi$
$620$		0			0
$621$	−6.11646	−	1.07850i	−0.245445	−	0.0432786i
$622$	9.79466	+	0.856922i	0.392730	+	0.0343594i
$623$	−50.3708	+	4.40688i	−2.01806	+	0.176558i
$624$	2.19829	−	0.387619i	0.0880022	−	0.0155172i
$625$		0			0
$626$			13.5097i			0.539958i
$627$	0.664433	−	3.44217i	0.0265349	−	0.137467i
$628$	10.3997	+	10.3997i	0.414994	+	0.414994i
$629$	−0.719636	−	0.261926i	−0.0286938	−	0.0104437i
$630$		0			0
$631$	−15.6484	−	13.1306i	−0.622954	−	0.522720i	0.275777	−	0.961222i	$-0.411065\pi$
$631$	−15.6484	−	13.1306i	−0.622954	−	0.522720i	−0.898731	+	0.438501i	$0.855509\pi$
$632$	0.719759	−	8.22688i	0.0286305	−	0.327248i
$633$	1.27237	−	0.890921i	0.0505720	−	0.0354109i
$634$	−30.6682	−	17.7063i	−1.21799	−	0.703207i
$635$		0			0
$636$	−0.204874	+	0.0745682i	−0.00812379	+	0.00295682i
$637$	16.8545	+	7.85936i	0.667798	+	0.311399i
$638$	5.95565	−	22.2268i	0.235787	−	0.879967i
$639$	3.23620	−	5.60526i	0.128022	−	0.221741i
$640$		0			0
$641$	−10.0680	−	11.9986i	−0.397662	−	0.473916i	0.529643	−	0.848220i	$-0.322326\pi$
$641$	−10.0680	−	11.9986i	−0.397662	−	0.473916i	−0.927306	+	0.374305i	$0.877881\pi$
$642$	−0.332335	−	3.79861i	−0.0131162	−	0.149919i
$643$	20.8071	−	29.7156i	0.820550	−	1.17187i	−0.162169	−	0.986763i	$-0.551849\pi$
$643$	20.8071	−	29.7156i	0.820550	−	1.17187i	0.982719	−	0.185104i	$-0.0592622\pi$
$644$	3.27220	−	8.99030i	0.128943	−	0.354268i
$645$		0			0
$646$	0.727952	+	0.751852i	0.0286409	+	0.0295812i
$647$	−16.9030	+	16.9030i	−0.664527	+	0.664527i	−0.956444	−	0.291917i	$-0.905707\pi$
$647$	−16.9030	+	16.9030i	−0.664527	+	0.664527i	0.291917	+	0.956444i	$0.405707\pi$
$648$	−7.18613	+	3.35095i	−0.282298	+	0.131638i
$649$	−4.24830	−	24.0933i	−0.166760	−	0.945745i
$650$		0			0
$651$	7.47510	−	6.27235i	0.292972	−	0.245833i
$652$	−8.04945	−	11.4958i	−0.315241	−	0.450210i
$653$	−26.6186	+	7.13244i	−1.04167	+	0.279114i	−0.738805	−	0.673920i	$-0.764609\pi$
$653$	−26.6186	+	7.13244i	−1.04167	+	0.279114i	−0.302864	+	0.953034i	$0.597943\pi$
$654$	0.253316	+	0.438756i	0.00990542	+	0.0171567i
$655$		0			0
$656$	−3.97454	−	10.9200i	−0.155180	−	0.426353i
$657$	−42.6267	−	11.4218i	−1.66303	−	0.445606i
$658$	−3.04451	−	11.3623i	−0.118687	−	0.442947i
$659$	−1.46619	+	8.31520i	−0.0571148	+	0.323914i	−0.999957	−	0.00932686i	$-0.997031\pi$
$659$	−1.46619	+	8.31520i	−0.0571148	+	0.323914i	0.942842	+	0.333241i	$0.108142\pi$
$660$		0			0
$661$	8.84987	−	10.5469i	0.344220	−	0.410226i	−0.565964	−	0.824430i	$-0.691496\pi$
$661$	8.84987	−	10.5469i	0.344220	−	0.410226i	0.910184	+	0.414205i	$0.135940\pi$
$662$	−7.33114	−	5.13332i	−0.284933	−	0.199512i
$663$	−0.226491	−	0.485712i	−0.00879620	−	0.0188635i
$664$	−2.85895			−0.110949
$665$		0			0
$666$	−9.18455			−0.355894
$667$	12.7732	+	27.3921i	0.494578	+	1.06063i
$668$	−4.78453	−	3.35017i	−0.185119	−	0.129622i
$669$	0.439872	−	0.524219i	0.0170064	−	0.0202675i
$670$		0			0
$671$	3.71277	−	21.0562i	0.143330	−	0.812865i
$672$	0.282728	+	1.05516i	0.0109065	+	0.0407035i
$673$	−3.09625	−	0.829638i	−0.119352	−	0.0319802i	0.198649	−	0.980071i	$-0.436345\pi$
$673$	−3.09625	−	0.829638i	−0.119352	−	0.0319802i	−0.318000	+	0.948091i	$0.603011\pi$
$674$	8.91638	+	24.4976i	0.343446	+	0.943611i
$675$		0			0
$676$	−14.1556	−	24.5183i	−0.544447	−	0.943011i
$677$	28.7670	−	7.70810i	1.10561	−	0.296246i	0.340561	−	0.940222i	$-0.389383\pi$
$677$	28.7670	−	7.70810i	1.10561	−	0.296246i	0.765046	+	0.643976i	$0.222716\pi$
$678$	−1.95154	−	2.78709i	−0.0749486	−	0.107038i
$679$	0.904697	−	0.759131i	0.0347191	−	0.0291328i
$680$		0			0
$681$	1.58802	+	9.00612i	0.0608532	+	0.345115i
$682$	18.7485	−	8.74255i	0.717916	−	0.334770i
$683$	−15.0221	+	15.0221i	−0.574805	+	0.574805i	−0.933467	−	0.358662i	$-0.883233\pi$
$683$	−15.0221	+	15.0221i	−0.574805	+	0.574805i	0.358662	+	0.933467i	$0.383233\pi$
$684$	11.2879	+	5.48726i	0.431603	+	0.209810i
$685$		0			0
$686$	4.41783	−	12.1379i	0.168673	−	0.463427i
$687$	1.36169	−	1.94470i	0.0519519	−	0.0741950i
$688$	−0.0171752	−	0.196313i	−0.000654798	−	0.00748437i
$689$	2.59360	+	3.09093i	0.0988083	+	0.117755i
$690$		0			0
$691$	0.777870	−	1.34731i	0.0295916	−	0.0512541i	−0.850850	−	0.525408i	$-0.823913\pi$
$691$	0.777870	−	1.34731i	0.0295916	−	0.0512541i	0.880442	+	0.474154i	$0.157246\pi$
$692$	−0.513967	+	1.91815i	−0.0195381	+	0.0729171i
$693$	19.0085	+	8.86380i	0.722072	+	0.336708i
$694$	23.6130	−	8.59441i	0.896335	−	0.326239i
$695$		0			0
$696$	−2.98858	−	1.72546i	−0.113282	−	0.0654032i
$697$	−2.28544	+	1.60028i	−0.0865671	+	0.0606149i
$698$	−0.0245250	+	0.280322i	−0.000928286	+	0.0106104i
$699$	5.31183	+	4.45716i	0.200912	+	0.168585i
$700$		0			0
$701$	7.20316	+	2.62174i	0.272060	+	0.0990216i	0.474447	−	0.880284i	$-0.342648\pi$
$701$	7.20316	+	2.62174i	0.272060	+	0.0990216i	−0.202388	+	0.979305i	$0.564870\pi$
$702$	−9.28007	−	9.28007i	−0.350254	−	0.350254i
$703$	8.76406	+	10.7939i	0.330543	+	0.407099i
$704$			2.31579i			0.0872797i
$705$		0			0
$706$	−7.50662	+	1.32362i	−0.282515	+	0.0498151i
$707$	−10.5511	+	0.923104i	−0.396816	+	0.0347169i
$708$	−3.65502	−	0.319773i	−0.137364	−	0.0120178i
$709$	−17.2075	−	3.03414i	−0.646240	−	0.113950i	−0.159085	−	0.987265i	$-0.550854\pi$
$709$	−17.2075	−	3.03414i	−0.646240	−	0.113950i	−0.487155	+	0.873315i	$0.661965\pi$
$710$		0			0
$711$	−20.5931	+	11.8894i	−0.772301	+	0.445888i
$712$	−6.79377	+	14.5693i	−0.254607	+	0.546007i
$713$	−11.4830	+	24.6254i	−0.430041	+	0.922227i
$714$	0.227129	−	0.131133i	0.00850008	−	0.00490752i
$715$		0			0
$716$	11.3009	+	1.99265i	0.422333	+	0.0744687i
$717$	−5.11780	−	0.447749i	−0.191128	−	0.0167215i
$718$	21.0129	−	1.83839i	0.784194	−	0.0686081i
$719$	−11.7702	+	2.07540i	−0.438954	+	0.0773995i	−0.388758	−	0.921340i	$-0.627096\pi$
$719$	−11.7702	+	2.07540i	−0.438954	+	0.0773995i	−0.0501963	+	0.998739i	$0.515985\pi$
$720$		0			0
$721$			31.4404i			1.17090i
$722$	−4.32235	−	18.5018i	−0.160861	−	0.688566i
$723$	−3.17939	−	3.17939i	−0.118243	−	0.118243i
$724$	2.52160	+	0.917789i	0.0937147	+	0.0341093i
$725$		0			0
$726$	1.49972	+	1.25842i	0.0556599	+	0.0467042i
$727$	4.42516	−	50.5798i	0.164120	−	1.87590i	−0.253580	−	0.967315i	$-0.581608\pi$
$727$	4.42516	−	50.5798i	0.164120	−	1.87590i	0.417700	−	0.908585i	$-0.362836\pi$
$728$	16.5604	−	11.5957i	0.613770	−	0.429766i
$729$	17.9296	+	10.3516i	0.664058	+	0.383394i
$730$		0			0
$731$	−0.0444590	+	0.0161818i	−0.00164438	+	0.000598504i
$732$	−2.90606	−	1.35512i	−0.107411	−	0.0500866i
$733$	−2.20803	+	8.24048i	−0.0815555	+	0.304369i	−0.994640	−	0.103402i	$-0.967027\pi$
$733$	−2.20803	+	8.24048i	−0.0815555	+	0.304369i	0.913084	+	0.407771i	$0.133694\pi$
$734$	−7.35854	+	12.7454i	−0.271609	+	0.470440i
$735$		0			0
$736$	−1.95517	−	2.33008i	−0.0720684	−	0.0858878i
$737$	2.34080	+	26.7555i	0.0862246	+	0.985551i
$738$	−19.1923	+	27.4094i	−0.706478	+	1.00895i
$739$	−9.89227	+	27.1788i	−0.363893	+	0.999788i	0.613747	+	0.789503i	$0.289661\pi$
$739$	−9.89227	+	27.1788i	−0.363893	+	0.999788i	−0.977640	+	0.210285i	$0.932561\pi$
$740$		0			0
$741$	−1.00444	+	9.67798i	−0.0368989	+	0.355530i
$742$	−1.39624	+	1.39624i	−0.0512574	+	0.0512574i
$743$	−0.475867	+	0.221900i	−0.0174578	+	0.00814073i	−0.431328	−	0.902195i	$-0.641955\pi$
$743$	−0.475867	+	0.221900i	−0.0174578	+	0.00814073i	0.413870	+	0.910336i	$0.364177\pi$
$744$	−0.538717	−	3.05522i	−0.0197503	−	0.112010i
$745$		0			0
$746$	−14.0242	+	11.7677i	−0.513462	+	0.430846i
$747$	4.72169	+	6.74327i	0.172757	+	0.246723i
$748$	0.537047	−	0.143901i	0.0196364	−	0.00526155i
$749$	−17.2672	−	29.9077i	−0.630930	−	1.09280i
$750$		0			0
$751$	5.47554	+	15.0439i	0.199805	+	0.548960i	0.998614	−	0.0526243i	$-0.0167586\pi$
$751$	5.47554	+	15.0439i	0.199805	+	0.548960i	−0.798809	+	0.601584i	$0.794536\pi$
$752$	−3.61237	−	0.967933i	−0.131730	−	0.0352969i
$753$	1.91703	+	7.15445i	0.0698604	+	0.260723i
$754$	−11.0902	+	62.8955i	−0.403880	+	2.29052i
$755$		0			0
$756$	4.12831	−	4.91992i	0.150145	−	0.178936i
$757$	−32.2179	−	22.5592i	−1.17098	−	0.819929i	−0.184343	−	0.982862i	$-0.559016\pi$
$757$	−32.2179	−	22.5592i	−1.17098	−	0.819929i	−0.986637	+	0.162933i	$0.947905\pi$
$758$	10.9149	+	23.4070i	0.396446	+	0.850181i
$759$	2.44634			0.0887963
$760$		0			0
$761$	−2.85819			−0.103609			−0.0518046	−	0.998657i	$-0.516497\pi$
$761$	−2.85819			−0.103609			−0.0518046	+	0.998657i	$0.516497\pi$
$762$	2.48741	+	5.33426i	0.0901092	+	0.193240i
$763$	3.75862	+	2.63181i	0.136071	+	0.0952781i
$764$	11.9112	−	14.1952i	0.430931	−	0.513564i
$765$		0			0
$766$	0.707700	−	4.01357i	0.0255702	−	0.145016i
$767$	17.5742	+	65.5879i	0.634568	+	2.36824i
$768$	0.335463	+	0.0898869i	0.0121050	+	0.00324351i
$769$	2.06314	+	5.66844i	0.0743989	+	0.204409i	0.971317	−	0.237787i	$-0.0764219\pi$
$769$	2.06314	+	5.66844i	0.0743989	+	0.204409i	−0.896919	+	0.442196i	$0.854200\pi$
$770$		0			0
$771$	−1.01300	−	1.75456i	−0.0364822	−	0.0631890i
$772$	−7.21623	+	1.93358i	−0.259718	+	0.0695912i
$773$	−5.17160	−	7.38581i	−0.186010	−	0.265649i	0.715307	−	0.698811i	$-0.246287\pi$
$773$	−5.17160	−	7.38581i	−0.186010	−	0.265649i	−0.901316	+	0.433161i	$0.857398\pi$
$774$	−0.434669	+	0.364731i	−0.0156239	+	0.0131100i
$775$		0			0
$776$	−0.0652000	−	0.369767i	−0.00234054	−	0.0132739i
$777$	3.15796	−	1.47258i	0.113291	−	0.0528285i
$778$	−23.9101	+	23.9101i	−0.857218	+	0.857218i
$779$	50.5258	−	3.59934i	1.81027	−	0.128960i
$780$		0			0
$781$	−1.78040	+	4.89160i	−0.0637076	+	0.175035i
$782$	−0.418867	+	0.598205i	−0.0149787	+	0.0213918i
$783$	1.76832	+	20.2120i	0.0631947	+	0.722319i
$784$	1.85983	+	2.21645i	0.0664224	+	0.0791591i
$785$		0			0
$786$	−0.595237	+	1.03098i	−0.0212314	+	0.0367738i
$787$	−12.2347	+	45.6603i	−0.436118	+	1.62762i	0.302258	+	0.953226i	$0.402260\pi$
$787$	−12.2347	+	45.6603i	−0.436118	+	1.62762i	−0.738376	+	0.674389i	$0.764407\pi$
$788$	−4.82422	−	2.24957i	−0.171856	−	0.0801377i
$789$	6.82753	−	2.48502i	0.243067	−	0.0884690i
$790$		0			0
$791$	−26.6864	−	15.4074i	−0.948859	−	0.547824i
$792$	5.46215	−	3.82464i	0.194089	−	0.135903i
$793$	−5.17200	+	59.1163i	−0.183663	+	2.09928i
$794$	−12.9932	−	10.9026i	−0.461110	−	0.386917i
$795$		0			0
$796$	2.31030	+	0.840882i	0.0818865	+	0.0298043i
$797$	32.6039	+	32.6039i	1.15489	+	1.15489i	0.985559	+	0.169331i	$0.0541608\pi$
$797$	32.6039	+	32.6039i	1.15489	+	1.15489i	0.169331	+	0.985559i	$0.445839\pi$
$798$	−4.76094	−	0.0768908i	−0.168535	−	0.00272190i
$799$			0.897879i			0.0317647i
$800$		0			0
$801$	45.5841	−	8.03772i	1.61064	−	0.283999i
$802$	26.9986	−	2.36207i	0.953353	−	0.0834075i
$803$	35.3575	+	3.09338i	1.24774	+	0.109163i
$804$	3.96662	+	0.699423i	0.139892	+	0.0246667i
$805$		0			0
$806$	−49.7228	+	28.7075i	−1.75141	+	1.01118i
$807$	2.83169	−	6.07257i	0.0996801	−	0.213765i
$808$	−1.42308	+	3.05181i	−0.0500639	+	0.107362i
$809$	−30.7724	+	17.7665i	−1.08190	+	0.624636i	−0.931409	−	0.363975i	$-0.881419\pi$
$809$	−30.7724	+	17.7665i	−1.08190	+	0.624636i	−0.150492	+	0.988611i	$0.548086\pi$
$810$		0			0
$811$	−7.53281	−	1.32824i	−0.264513	−	0.0466407i	0.0398188	−	0.999207i	$-0.487322\pi$
$811$	−7.53281	−	1.32824i	−0.264513	−	0.0466407i	−0.304331	+	0.952566i	$0.598433\pi$
$812$	−31.1351	−	2.72397i	−1.09263	−	0.0955925i
$813$	9.37426	−	0.820142i	0.328770	−	0.0287636i
$814$	7.27460	−	1.28271i	0.254975	−	0.0449589i
$815$		0			0
$816$		−	0.0833814i		−	0.00291893i
$817$	0.843409	+	0.162801i	0.0295072	+	0.00569568i
$818$	−0.968464	−	0.968464i	−0.0338616	−	0.0338616i
$819$	−54.7006	−	19.9094i	−1.91139	−	0.695690i
$820$		0			0
$821$	−29.6346	−	24.8664i	−1.03425	−	0.867842i	−0.0429033	−	0.999079i	$-0.513661\pi$
$821$	−29.6346	−	24.8664i	−1.03425	−	0.867842i	−0.991351	+	0.131237i	$0.958105\pi$
$822$	0.0968792	−	1.10733i	0.00337905	−	0.0386227i
$823$	−5.00017	+	3.50116i	−0.174295	+	0.122043i	−0.657469	−	0.753482i	$-0.728373\pi$
$823$	−5.00017	+	3.50116i	−0.174295	+	0.122043i	0.483174	+	0.875524i	$0.339484\pi$
$824$	8.65658	+	4.99788i	0.301566	+	0.174109i
$825$		0			0
$826$	−31.2251	+	11.3650i	−1.08646	+	0.395439i
$827$	2.62171	+	1.22252i	0.0911657	+	0.0425113i	0.467666	−	0.883905i	$-0.345095\pi$
$827$	2.62171	+	1.22252i	0.0911657	+	0.0425113i	−0.376501	+	0.926416i	$0.622873\pi$
$828$	−2.26679	+	8.45979i	−0.0787766	+	0.293998i
$829$	2.38184	−	4.12547i	0.0827248	−	0.143284i	−0.821695	−	0.569928i	$-0.806971\pi$
$829$	2.38184	−	4.12547i	0.0827248	−	0.143284i	0.904419	+	0.426644i	$0.140304\pi$
$830$		0			0
$831$	−4.15160	−	4.94768i	−0.144017	−	0.171633i
$832$	−0.560183	−	6.40293i	−0.0194209	−	0.221982i
$833$	0.398442	−	0.569034i	0.0138052	−	0.0197159i
$834$	−0.342707	+	0.941579i	−0.0118670	+	0.0326042i
$835$		0			0
$836$	−9.70689	−	2.76971i	−0.335720	−	0.0957923i
$837$	−12.8976	+	12.8976i	−0.445805	+	0.445805i
$838$	−30.8807	+	14.3999i	−1.06676	+	0.497437i
$839$	5.03033	+	28.5284i	0.173666	+	0.984910i	0.939672	+	0.342077i	$0.111130\pi$
$839$	5.03033	+	28.5284i	0.173666	+	0.984910i	−0.766006	+	0.642834i	$0.777759\pi$
$840$		0			0
$841$	53.4194	−	44.8242i	1.84205	−	1.54566i
$842$	8.36478	+	11.9461i	0.288269	+	0.411691i
$843$	4.98169	−	1.33484i	0.171579	−	0.0459744i
$844$	−2.23624	−	3.87327i	−0.0769744	−	0.133324i
$845$		0			0
$846$	3.68299	+	10.1189i	0.126624	+	0.347896i
$847$	17.1267	+	4.58907i	0.588479	+	0.157682i
$848$	0.162479	+	0.606381i	0.00557956	+	0.0208232i
$849$	0.941451	−	5.33924i	0.0323105	−	0.183242i
$850$		0			0
$851$	−6.23651	+	7.43239i	−0.213785	+	0.254779i
$852$	0.639485	+	0.447772i	0.0219084	+	0.0153404i
$853$	−7.15576	−	15.3456i	−0.245009	−	0.525423i	0.744892	−	0.667185i	$-0.232501\pi$
$853$	−7.15576	−	15.3456i	−0.245009	−	0.525423i	−0.989901	+	0.141762i	$0.954723\pi$
$854$	−29.0403			−0.993738
$855$		0			0
$856$	−10.9794			−0.375269
$857$	−7.40335	−	15.8765i	−0.252893	−	0.542332i	0.738344	−	0.674424i	$-0.235608\pi$
$857$	−7.40335	−	15.8765i	−0.252893	−	0.542332i	−0.991237	+	0.132093i	$0.957830\pi$
$858$	4.23446	+	2.96500i	0.144562	+	0.101224i
$859$	−8.09561	+	9.64797i	−0.276218	+	0.329184i	−0.886263	−	0.463183i	$-0.846707\pi$
$859$	−8.09561	+	9.64797i	−0.276218	+	0.329184i	0.610044	+	0.792367i	$0.291152\pi$
$860$		0			0
$861$	2.20434	−	12.5014i	0.0751237	−	0.426047i
$862$	−3.04410	−	11.3607i	−0.103683	−	0.386949i
$863$	23.9057	+	6.40552i	0.813760	+	0.218046i	0.641617	−	0.767025i	$-0.278264\pi$
$863$	23.9057	+	6.40552i	0.813760	+	0.218046i	0.172144	+	0.985072i	$0.444931\pi$
$864$	−0.698367	−	1.91875i	−0.0237589	−	0.0652771i
$865$		0			0
$866$	5.58046	+	9.66564i	0.189632	+	0.328452i
$867$	5.68353	−	1.52290i	0.193023	−	0.0517203i
$868$	−16.1159	−	23.0159i	−0.547009	−	0.781209i
$869$	14.6502	−	12.2930i	0.496975	−	0.417011i
$870$		0			0
$871$	−12.9442	−	73.4099i	−0.438596	−	2.48740i
$872$	1.32211	−	0.616510i	0.0447723	−	0.0208777i
$873$	−0.764472	+	0.764472i	−0.0258735	+	0.0258735i
$874$	12.1052	−	5.40849i	0.409463	−	0.182945i
$875$		0			0
$876$	1.82050	−	5.00177i	0.0615089	−	0.168994i
$877$	20.4275	−	29.1735i	0.689788	−	0.985119i	−0.309625	−	0.950859i	$-0.600204\pi$
$877$	20.4275	−	29.1735i	0.689788	−	0.985119i	0.999413	−	0.0342603i	$-0.0109075\pi$
$878$	2.44731	+	27.9729i	0.0825927	+	0.944038i
$879$	4.21752	+	5.02624i	0.142253	+	0.169531i
$880$		0			0
$881$	−20.4541	+	35.4276i	−0.689116	+	1.19358i	0.283008	+	0.959118i	$0.408668\pi$
$881$	−20.4541	+	35.4276i	−0.689116	+	1.19358i	−0.972124	+	0.234467i	$0.924666\pi$
$882$	2.15626	−	8.04727i	0.0726050	−	0.270966i
$883$	−2.27260	−	1.05973i	−0.0764792	−	0.0356628i	0.384002	−	0.923332i	$-0.374545\pi$
$883$	−2.27260	−	1.05973i	−0.0764792	−	0.0356628i	−0.460481	+	0.887669i	$0.652323\pi$
$884$	−1.45007	+	0.527782i	−0.0487711	+	0.0177512i
$885$		0			0
$886$	9.48233	+	5.47463i	0.318565	+	0.183924i
$887$	21.4825	−	15.0422i	0.721311	−	0.505068i	−0.154336	−	0.988018i	$-0.549324\pi$
$887$	21.4825	−	15.0422i	0.721311	−	0.505068i	0.875648	+	0.482951i	$0.160435\pi$
$888$	0.0965505	−	1.10358i	0.00324002	−	0.0370336i
$889$	40.8342	+	34.2640i	1.36954	+	1.14918i
$890$		0			0
$891$	−17.2546	−	6.28016i	−0.578050	−	0.210393i
$892$	−1.39330	−	1.39330i	−0.0466510	−	0.0466510i
$893$	8.37763	−	13.9840i	0.280347	−	0.467957i
$894$			1.70580i			0.0570505i
$895$		0			0
$896$	3.09759	−	0.546188i	0.103483	−	0.0182469i
$897$	−6.76386	+	0.591762i	−0.225839	+	0.0197583i
$898$	−21.9875	−	1.92366i	−0.733733	−	0.0641933i
$899$	87.4129	+	15.4133i	2.91538	+	0.514061i
$900$		0			0
$901$	0.130527	−	0.0753599i	0.00434849	−	0.00251060i
$902$	11.3732	−	24.3899i	0.378687	−	0.812096i
$903$	0.0909758	−	0.195098i	0.00302749	−	0.00649246i
$904$	−8.48433	+	4.89843i	−0.282185	+	0.162919i
$905$		0			0
$906$	−0.806067	−	0.142131i	−0.0267798	−	0.00472200i
$907$	−19.9724	−	1.74736i	−0.663172	−	0.0580200i	−0.249400	−	0.968401i	$-0.580233\pi$
$907$	−19.9724	−	1.74736i	−0.663172	−	0.0580200i	−0.413772	+	0.910381i	$0.635789\pi$
$908$	26.2319	−	2.29500i	0.870538	−	0.0761622i
$909$	9.54846	−	1.68365i	0.316702	−	0.0558432i
$910$		0			0
$911$		−	19.0863i		−	0.632357i	−0.948700	−	0.316179i	$-0.897600\pi$
$911$		−	19.0863i		−	0.632357i	0.948700	−	0.316179i	$-0.102400\pi$
$912$	−0.777987	+	1.29862i	−0.0257617	+	0.0430016i
$913$	−4.68156	−	4.68156i	−0.154937	−	0.154937i
$914$	−17.7106	−	6.44612i	−0.585814	−	0.213219i
$915$		0			0
$916$	−5.23651	−	4.39396i	−0.173019	−	0.145180i
$917$	−0.939697	+	10.7408i	−0.0310315	+	0.354692i
$918$	−0.401574	+	0.281185i	−0.0132539	+	0.00928049i
$919$	−11.8248	−	6.82706i	−0.390065	−	0.225204i	0.292123	−	0.956381i	$-0.405638\pi$
$919$	−11.8248	−	6.82706i	−0.390065	−	0.225204i	−0.682188	+	0.731177i	$0.738972\pi$
$920$		0			0
$921$	−7.01560	+	2.55347i	−0.231172	+	0.0841397i
$922$	−19.3415	−	9.01911i	−0.636980	−	0.297029i
$923$	3.73935	−	13.9554i	0.123082	−	0.459349i
$924$	−1.26486	+	2.19080i	−0.0416108	+	0.0720720i
$925$		0			0
$926$	−20.4019	−	24.3141i	−0.670449	−	0.799010i
$927$	−2.50848	−	28.6721i	−0.0823894	−	0.941715i
$928$	−5.69934	+	8.13951i	−0.187090	+	0.267192i
$929$	−8.45330	+	23.2252i	−0.277344	+	0.761996i	0.720318	+	0.693644i	$0.243996\pi$
$929$	−8.45330	+	23.2252i	−0.277344	+	0.761996i	−0.997661	+	0.0683513i	$0.978226\pi$
$930$		0			0
$931$	−11.5149	+	5.14476i	−0.377385	+	0.168613i
$932$	14.1181	−	14.1181i	0.462453	−	0.462453i
$933$	3.09472	−	1.44309i	0.101317	−	0.0472447i
$934$	1.21516	+	6.89153i	0.0397613	+	0.225498i
$935$		0			0
$936$	−14.1771	+	11.8960i	−0.463394	+	0.388833i
$937$	−17.7200	−	25.3067i	−0.578886	−	0.826734i	0.417761	−	0.908557i	$-0.362815\pi$
$937$	−17.7200	−	25.3067i	−0.578886	−	0.826734i	−0.996647	+	0.0818225i	$0.973926\pi$
$938$	35.2359	−	9.44143i	1.15049	−	0.308274i
$939$	2.34594	+	4.06329i	0.0765569	+	0.132600i
$940$		0			0
$941$	−8.96941	−	24.6432i	−0.292394	−	0.803347i	−0.995715	−	0.0924742i	$-0.970522\pi$
$941$	−8.96941	−	24.6432i	−0.292394	−	0.803347i	0.703321	−	0.710873i	$-0.251700\pi$
$942$	4.93379	+	1.32201i	0.160752	+	0.0430733i
$943$	9.14846	+	34.1425i	0.297915	+	1.11183i
$944$	−1.83449	+	10.4039i	−0.0597076	+	0.338619i
$945$		0			0
$946$	0.293341	−	0.349590i	0.00953733	−	0.0113661i
$947$	−19.4122	−	13.5926i	−0.630812	−	0.441699i	0.213948	−	0.976845i	$-0.431368\pi$
$947$	−19.4122	−	13.5926i	−0.630812	−	0.441699i	−0.844760	+	0.535146i	$0.820257\pi$
$948$	−1.21210	−	2.59936i	−0.0393673	−	0.0844234i
$949$	−98.5081			−3.19771
$950$		0			0
$951$	−12.2987			−0.398811
$952$	−0.319146	−	0.684411i	−0.0103436	−	0.0221819i
$953$	40.5851	+	28.4180i	1.31468	+	0.920549i	0.999593	−	0.0285137i	$-0.00907744\pi$
$953$	40.5851	+	28.4180i	1.31468	+	0.920549i	0.315087	+	0.949063i	$0.397966\pi$
$954$	1.16190	−	1.38470i	0.0376179	−	0.0448313i
$955$		0			0
$956$	−2.56867	+	14.5677i	−0.0830769	+	0.471152i
$957$	−2.06838	−	7.71929i	−0.0668611	−	0.249529i
$958$	−24.3359	−	6.52079i	−0.786258	−	0.210677i
$959$	−3.44317	−	9.46003i	−0.111186	−	0.305480i
$960$		0			0
$961$	24.3980	+	42.2586i	0.787032	+	1.36318i
$962$	−19.8032	+	5.30626i	−0.638482	+	0.171081i
$963$	18.1331	+	25.8967i	0.584330	+	0.834509i
$964$	−9.91773	+	8.32196i	−0.319428	+	0.268032i
$965$		0			0
$966$	−0.576978	−	3.27220i	−0.0185639	−	0.105281i
$967$	−39.3598	+	18.3538i	−1.26573	+	0.590217i	−0.935380	−	0.353643i	$-0.884943\pi$
$967$	−39.3598	+	18.3538i	−1.26573	+	0.590217i	−0.330345	+	0.943860i	$0.607165\pi$
$968$	3.98604	−	3.98604i	0.128116	−	0.128116i
$969$	0.349502	+	0.0997249i	0.0112276	+	0.00320363i
$970$		0			0
$971$	13.0901	−	35.9649i	0.420083	−	1.15417i	−0.531576	−	0.847010i	$-0.678400\pi$
$971$	13.0901	−	35.9649i	0.420083	−	1.15417i	0.951659	−	0.307157i	$-0.0993776\pi$
$972$	−5.09301	+	7.27357i	−0.163358	+	0.233300i
$973$	0.790932	+	9.04039i	0.0253561	+	0.289822i
$974$	−20.8323	−	24.8270i	−0.667510	−	0.795507i
$975$		0			0
$976$	−4.61635	+	7.99575i	−0.147766	+	0.255938i
$977$	−9.13960	+	34.1094i	−0.292402	+	1.09126i	0.650857	+	0.759200i	$0.274410\pi$
$977$	−9.13960	+	34.1094i	−0.292402	+	1.09126i	−0.943259	+	0.332058i	$0.892257\pi$
$978$	−4.41724	−	2.05979i	−0.141248	−	0.0658649i
$979$	−34.9823	+	12.7325i	−1.11804	+	0.406933i
$980$		0			0
$981$	−3.63766	−	2.10020i	−0.116142	−	0.0670544i
$982$	4.10594	−	2.87501i	0.131026	−	0.0917452i
$983$	1.63863	−	18.7296i	0.0522640	−	0.597381i	−0.924230	−	0.381836i	$-0.875292\pi$
$983$	1.63863	−	18.7296i	0.0522640	−	0.597381i	0.976494	−	0.215544i	$-0.0691526\pi$
$984$	−3.09165	−	2.59420i	−0.0985581	−	0.0827001i
$985$		0			0
$986$	2.24176	+	0.815933i	0.0713921	+	0.0259846i
$987$	−2.88873	−	2.88873i	−0.0919492	−	0.0919492i
$988$	27.5085	+	5.30989i	0.875163	+	0.168930i
$989$			0.599407i			0.0190600i
$990$		0			0
$991$	4.15500	−	0.732639i	0.131988	−	0.0232730i	−0.107264	−	0.994231i	$-0.534209\pi$
$991$	4.15500	−	0.732639i	0.131988	−	0.0232730i	0.239252	+	0.970958i	$0.423098\pi$
$992$	−8.89887	+	0.778550i	−0.282539	+	0.0247190i
$993$	−3.09636	−	0.270896i	−0.0982600	−	0.00859664i
$994$	6.96289	+	1.22775i	0.220849	+	0.0389417i
$995$		0			0
$996$	−0.859878	+	0.496451i	−0.0272463	+	0.0157306i
$997$	−18.7675	+	40.2471i	−0.594373	+	1.27464i	0.347188	+	0.937796i	$0.387137\pi$
$997$	−18.7675	+	40.2471i	−0.594373	+	1.27464i	−0.941561	+	0.336842i	$0.890641\pi$
$998$	−0.898369	+	1.92656i	−0.0284374	+	0.0609841i
$999$	−5.64054	+	3.25657i	−0.178459	+	0.103033i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.bb.b.243.2	✓	48
5.2	odd	4	inner	950.2.bb.b.357.3	yes	48
5.3	odd	4	inner	950.2.bb.b.357.2	yes	48
5.4	even	2	inner	950.2.bb.b.243.3	yes	48
19.14	odd	18	inner	950.2.bb.b.793.3	yes	48
95.14	odd	18	inner	950.2.bb.b.793.2	yes	48
95.33	even	36	inner	950.2.bb.b.907.3	yes	48
95.52	even	36	inner	950.2.bb.b.907.2	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.bb.b.243.2	✓	48	1.1	even	1	trivial
950.2.bb.b.243.3	yes	48	5.4	even	2	inner
950.2.bb.b.357.2	yes	48	5.3	odd	4	inner
950.2.bb.b.357.3	yes	48	5.2	odd	4	inner
950.2.bb.b.793.2	yes	48	95.14	odd	18	inner
950.2.bb.b.793.3	yes	48	19.14	odd	18	inner
950.2.bb.b.907.2	yes	48	95.52	even	36	inner
950.2.bb.b.907.3	yes	48	95.33	even	36	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.bb (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.422618 - 0.906308i) q^{2} +(-0.284489 - 0.199201i) q^{3} +(-0.642788 + 0.766044i) q^{4} +(-0.0603074 + 0.342020i) q^{6} +(0.814083 + 3.03820i) q^{7} +(0.965926 + 0.258819i) q^{8} +(-0.984808 - 2.70574i) q^{9} +O(q^{10})\)	\(q+(-0.422618 - 0.906308i) q^{2} +(-0.284489 - 0.199201i) q^{3} +(-0.642788 + 0.766044i) q^{4} +(-0.0603074 + 0.342020i) q^{6} +(0.814083 + 3.03820i) q^{7} +(0.965926 + 0.258819i) q^{8} +(-0.984808 - 2.70574i) q^{9} +(1.15790 + 2.00553i) q^{11} +(0.335463 - 0.0898869i) q^{12} +(-3.68660 - 5.26500i) q^{13} +(2.40950 - 2.02181i) q^{14} +(-0.173648 - 0.984808i) q^{16} +(-0.217593 + 0.101465i) q^{17} +(-2.03603 + 2.03603i) q^{18} +(4.33561 + 0.449974i) q^{19} +(0.373615 - 1.02650i) q^{21} +(1.32828 - 1.89699i) q^{22} +(0.265102 + 3.03012i) q^{23} +(-0.223238 - 0.266044i) q^{24} +(-3.21369 + 5.56628i) q^{26} +(-0.528480 + 1.97231i) q^{27} +(-2.85068 - 1.32929i) q^{28} +(9.33726 - 3.39848i) q^{29} +(7.73608 + 4.46643i) q^{31} +(-0.819152 + 0.573576i) q^{32} +(0.0700964 - 0.801206i) q^{33} +(0.183917 + 0.154325i) q^{34} +(2.70574 + 0.984808i) q^{36} +(2.25550 + 2.25550i) q^{37} +(-1.42449 - 4.11957i) q^{38} +2.23221i q^{39} +(11.4442 - 2.01793i) q^{41} +(-1.08822 + 0.0952069i) q^{42} +(0.196313 + 0.0171752i) q^{43} +(-2.28061 - 0.402133i) q^{44} +(2.63419 - 1.52085i) q^{46} +(1.58051 - 3.38941i) q^{47} +(-0.146774 + 0.314757i) q^{48} +(-2.50574 + 1.44669i) q^{49} +(0.0821147 + 0.0144790i) q^{51} +(6.40293 + 0.560183i) q^{52} +(-0.625382 + 0.0547139i) q^{53} +(2.01087 - 0.354570i) q^{54} +3.14537i q^{56} +(-1.14380 - 0.991671i) q^{57} +(-7.02617 - 7.02617i) q^{58} +(-9.92731 - 3.61324i) q^{59} +(-7.07266 - 5.93466i) q^{61} +(0.778550 - 8.89887i) q^{62} +(7.41885 - 5.19473i) q^{63} +(0.866025 + 0.500000i) q^{64} +(-0.755763 + 0.275075i) q^{66} +(10.5110 + 4.90137i) q^{67} +(0.0621391 - 0.231906i) q^{68} +(0.528185 - 0.914844i) q^{69} +(1.44488 + 1.72195i) q^{71} +(-0.250955 - 2.86843i) q^{72} +(8.79082 - 12.5546i) q^{73} +(1.09096 - 2.99739i) q^{74} +(-3.13158 + 3.03203i) q^{76} +(-5.15059 + 5.15059i) q^{77} +(2.02307 - 0.943371i) q^{78} +(-1.43404 - 8.13284i) q^{79} +(-6.07398 + 5.09667i) q^{81} +(-6.66541 - 9.51919i) q^{82} +(-2.76153 + 0.739950i) q^{83} +(0.546188 + 0.946026i) q^{84} +(-0.0673995 - 0.185179i) q^{86} +(-3.33332 - 0.893162i) q^{87} +(0.599371 + 2.23688i) q^{88} +(-2.79147 + 15.8312i) q^{89} +(12.9949 - 15.4868i) q^{91} +(-2.49161 - 1.74465i) q^{92} +(-1.31111 - 2.81168i) q^{93} -3.73981 q^{94} +0.347296 q^{96} +(-0.158681 - 0.340293i) q^{97} +(2.37011 + 1.65957i) q^{98} +(4.28614 - 5.10803i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{6}+O(q^{10}) \) 48 * q - 48 * q^6	\( 48 q - 48 q^{6} - 12 q^{11} + 36 q^{21} - 72 q^{31} + 48 q^{36} + 96 q^{41} + 72 q^{46} - 48 q^{51} - 108 q^{61} + 24 q^{66} - 60 q^{71} - 48 q^{76} - 168 q^{81} - 48 q^{86} + 252 q^{91}+O(q^{100}) \) 48 * q - 48 * q^6 - 12 * q^11 + 36 * q^21 - 72 * q^31 + 48 * q^36 + 96 * q^41 + 72 * q^46 - 48 * q^51 - 108 * q^61 + 24 * q^66 - 60 * q^71 - 48 * q^76 - 168 * q^81 - 48 * q^86 + 252 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more