LMFDB - Embedded newform 784.2.x.p.557.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(165,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("784.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.x (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			557.1
Character	$\chi$	$=$	784.557
Dual form			784.2.x.p.373.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.38899 - 0.265911i) q^{2} +(-0.331669 + 0.0888704i) q^{3} +(1.85858 + 0.738696i) q^{4} +(2.28822 + 0.613128i) q^{5} +(0.484316 - 0.0352455i) q^{6} +(-2.38512 - 1.52026i) q^{8} +(-2.49597 + 1.44105i) q^{9} +(-3.01528 - 1.46009i) q^{10} +(0.684421 + 2.55430i) q^{11} +(-0.682082 - 0.0798296i) q^{12} +(-2.24784 - 2.24784i) q^{13} -0.813421 q^{15} +(2.90866 + 2.74586i) q^{16} +(-2.63388 + 4.56202i) q^{17} +(3.85007 - 1.33789i) q^{18} +(-1.90217 + 7.09898i) q^{19} +(3.79994 + 2.82985i) q^{20} +(-0.271438 - 3.72988i) q^{22} +(-0.0792419 + 0.0457503i) q^{23} +(0.926177 + 0.292256i) q^{24} +(0.529913 + 0.305946i) q^{25} +(2.52450 + 3.71995i) q^{26} +(1.42816 - 1.42816i) q^{27} +(-6.55020 - 6.55020i) q^{29} +(1.12983 + 0.216298i) q^{30} +(-0.331648 + 0.574432i) q^{31} +(-3.30994 - 4.58741i) q^{32} +(-0.454002 - 0.786355i) q^{33} +(4.87153 - 5.63622i) q^{34} +(-5.70346 + 0.834544i) q^{36} +(-1.00881 - 0.270309i) q^{37} +(4.52979 - 9.35460i) q^{38} +(0.945305 + 0.545772i) q^{39} +(-4.52558 - 4.94108i) q^{40} +2.43655i q^{41} +(5.68128 - 5.68128i) q^{43} +(-0.614795 + 5.25295i) q^{44} +(-6.59488 + 1.76709i) q^{45} +(0.122232 - 0.0424754i) q^{46} +(2.65163 + 4.59276i) q^{47} +(-1.20874 - 0.652221i) q^{48} +(-0.654689 - 0.565865i) q^{50} +(0.468149 - 1.74715i) q^{51} +(-2.51732 - 5.83827i) q^{52} +(0.233471 + 0.871326i) q^{53} +(-2.36347 + 1.60394i) q^{54} +6.26444i q^{55} -2.52356i q^{57} +(7.35639 + 10.8399i) q^{58} +(2.48528 + 9.27519i) q^{59} +(-1.51181 - 0.600871i) q^{60} +(-0.560807 + 2.09296i) q^{61} +(0.613404 - 0.709691i) q^{62} +(3.37762 + 7.25201i) q^{64} +(-3.76535 - 6.52177i) q^{65} +(0.421504 + 1.21296i) q^{66} +(-9.03564 + 2.42109i) q^{67} +(-8.26524 + 6.53325i) q^{68} +(0.0222162 - 0.0222162i) q^{69} +15.1936i q^{71} +(8.14396 + 0.357444i) q^{72} +(-4.17280 - 2.40917i) q^{73} +(1.32934 + 0.643709i) q^{74} +(-0.202945 - 0.0543790i) q^{75} +(-8.77932 + 11.7889i) q^{76} +(-1.16789 - 1.00944i) q^{78} +(-5.53028 - 9.57872i) q^{79} +(4.97209 + 8.06651i) q^{80} +(3.97639 - 6.88731i) q^{81} +(0.647906 - 3.38434i) q^{82} +(10.9512 + 10.9512i) q^{83} +(-8.82402 + 8.82402i) q^{85} +(-9.40196 + 6.38052i) q^{86} +(2.75462 + 1.59038i) q^{87} +(2.25076 - 7.13281i) q^{88} +(-1.96668 + 1.13547i) q^{89} +(9.63011 - 0.700819i) q^{90} +(-0.181073 + 0.0264950i) q^{92} +(0.0589474 - 0.219995i) q^{93} +(-2.46182 - 7.08439i) q^{94} +(-8.70516 + 15.0778i) q^{95} +(1.50549 + 1.22734i) q^{96} -17.4958 q^{97} +(-5.38916 - 5.38916i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 4 q^{4} + 8 q^{11} + 64 q^{15} - 36 q^{16} - 20 q^{18} - 56 q^{22} - 32 q^{29} - 96 q^{30} - 40 q^{32} + 80 q^{36} + 16 q^{37} + 16 q^{43} - 4 q^{44} - 64 q^{46} - 56 q^{50} - 16 q^{53} + 20 q^{58}+ \cdots - 80 q^{99}+O(q^{100}) $ 96 * q + 4 * q^4 + 8 * q^11 + 64 * q^15 - 36 * q^16 - 20 * q^18 - 56 * q^22 - 32 * q^29 - 96 * q^30 - 40 * q^32 + 80 * q^36 + 16 * q^37 + 16 * q^43 - 4 * q^44 - 64 * q^46 - 56 * q^50 - 16 * q^53 + 20 * q^58 - 8 * q^60 + 88 * q^64 - 40 * q^67 + 196 * q^72 + 28 * q^74 + 112 * q^78 - 80 * q^79 + 48 * q^81 + 108 * q^86 + 100 * q^88 + 128 * q^95 - 80 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.38899	−	0.265911i	−0.982164	−	0.188028i
$2$	−1.38899	−	0.265911i	−0.982164	−	0.188028i
$3$	−0.331669	+	0.0888704i	−0.191489	+	0.0513093i	−0.353289	−	0.935514i	$-0.614937\pi$
$3$	−0.331669	+	0.0888704i	−0.191489	+	0.0513093i	0.161800	+	0.986824i	$0.448270\pi$
$4$	1.85858	+	0.738696i	0.929291	+	0.369348i
$5$	2.28822	+	0.613128i	1.02332	+	0.274199i	0.731187	−	0.682177i	$-0.238967\pi$
$5$	2.28822	+	0.613128i	1.02332	+	0.274199i	0.292138	+	0.956376i	$0.405633\pi$
$6$	0.484316	−	0.0352455i	0.197721	−	0.0143889i
$7$		0			0
$7$		0			0
$8$	−2.38512	−	1.52026i	−0.843268	−	0.537493i
$9$	−2.49597	+	1.44105i	−0.831990	+	0.480350i
$10$	−3.01528	−	1.46009i	−0.953515	−	0.461722i
$11$	0.684421	+	2.55430i	0.206361	+	0.770149i	0.989030	+	0.147712i	$0.0471908\pi$
$11$	0.684421	+	2.55430i	0.206361	+	0.770149i	−0.782670	+	0.622437i	$0.786143\pi$
$12$	−0.682082	−	0.0798296i	−0.196900	−	0.0230448i
$13$	−2.24784	−	2.24784i	−0.623439	−	0.623439i	0.322970	−	0.946409i	$-0.395319\pi$
$13$	−2.24784	−	2.24784i	−0.623439	−	0.623439i	−0.946409	+	0.322970i	$0.895319\pi$
$14$		0			0
$15$	−0.813421			−0.210024
$16$	2.90866	+	2.74586i	0.727164	+	0.686464i
$17$	−2.63388	+	4.56202i	−0.638811	+	1.10645i	0.346883	+	0.937908i	$0.387240\pi$
$17$	−2.63388	+	4.56202i	−0.638811	+	1.10645i	−0.985694	+	0.168544i	$0.946093\pi$
$18$	3.85007	−	1.33789i	0.907469	−	0.315345i
$19$	−1.90217	+	7.09898i	−0.436387	+	1.62862i	0.301339	+	0.953517i	$0.402567\pi$
$19$	−1.90217	+	7.09898i	−0.436387	+	1.62862i	−0.737726	+	0.675101i	$0.764100\pi$
$20$	3.79994	+	2.82985i	0.849691	+	0.632774i
$21$		0			0
$22$	−0.271438	−	3.72988i	−0.0578707	−	0.795214i
$23$	−0.0792419	+	0.0457503i	−0.0165231	+	0.00953960i	−0.508239	−	0.861216i	$-0.669703\pi$
$23$	−0.0792419	+	0.0457503i	−0.0165231	+	0.00953960i	0.491716	+	0.870756i	$0.336370\pi$
$24$	0.926177	+	0.292256i	0.189055	+	0.0596565i
$25$	0.529913	+	0.305946i	0.105983	+	0.0611891i
$26$	2.52450	+	3.71995i	0.495095	+	0.729543i
$27$	1.42816	−	1.42816i	0.274850	−	0.274850i
$28$		0			0
$29$	−6.55020	−	6.55020i	−1.21634	−	1.21634i	−0.968903	−	0.247439i	$-0.920411\pi$
$29$	−6.55020	−	6.55020i	−1.21634	−	1.21634i	−0.247439	−	0.968903i	$-0.579589\pi$
$30$	1.12983	+	0.216298i	0.206278	+	0.0394904i
$31$	−0.331648	+	0.574432i	−0.0595658	+	0.103171i	−0.894271	−	0.447527i	$-0.852305\pi$
$31$	−0.331648	+	0.574432i	−0.0595658	+	0.103171i	0.834705	+	0.550698i	$0.185638\pi$
$32$	−3.30994	−	4.58741i	−0.585120	−	0.810947i
$33$	−0.454002	−	0.786355i	−0.0790317	−	0.136887i
$34$	4.87153	−	5.63622i	0.835461	−	0.966603i
$35$		0			0
$36$	−5.70346	+	0.834544i	−0.950577	+	0.139091i
$37$	−1.00881	−	0.270309i	−0.165847	−	0.0444385i	0.174940	−	0.984579i	$-0.444027\pi$
$37$	−1.00881	−	0.270309i	−0.165847	−	0.0444385i	−0.340787	+	0.940141i	$0.610693\pi$
$38$	4.52979	−	9.35460i	0.734829	−	1.51752i
$39$	0.945305	+	0.545772i	0.151370	+	0.0873935i
$40$	−4.52558	−	4.94108i	−0.715557	−	0.781253i
$41$			2.43655i			0.380525i	0.981733	+	0.190262i	$0.0609339\pi$
$41$			2.43655i			0.380525i	−0.981733	+	0.190262i	$0.939066\pi$
$42$		0			0
$43$	5.68128	−	5.68128i	0.866388	−	0.866388i	−0.125683	−	0.992070i	$-0.540112\pi$
$43$	5.68128	−	5.68128i	0.866388	−	0.866388i	0.992070	+	0.125683i	$0.0401122\pi$
$44$	−0.614795	+	5.25295i	−0.0926839	+	0.791912i
$45$	−6.59488	+	1.76709i	−0.983107	+	0.263423i
$46$	0.122232	−	0.0424754i	0.0180221	−	0.00626265i
$47$	2.65163	+	4.59276i	0.386780	+	0.669923i	0.992014	−	0.126125i	$-0.0402539\pi$
$47$	2.65163	+	4.59276i	0.386780	+	0.669923i	−0.605234	+	0.796047i	$0.706921\pi$
$48$	−1.20874	−	0.652221i	−0.174466	−	0.0941400i
$49$		0			0
$50$	−0.654689	−	0.565865i	−0.0925870	−	0.0800254i
$51$	0.468149	−	1.74715i	0.0655539	−	0.244651i
$52$	−2.51732	−	5.83827i	−0.349090	−	0.809622i
$53$	0.233471	+	0.871326i	0.0320697	+	0.119686i	0.980105	−	0.198479i	$-0.0636001\pi$
$53$	0.233471	+	0.871326i	0.0320697	+	0.119686i	−0.948035	+	0.318165i	$0.896933\pi$
$54$	−2.36347	+	1.60394i	−0.321627	+	0.218268i
$55$			6.26444i			0.844696i
$56$		0			0
$57$		−	2.52356i		−	0.334253i
$58$	7.35639	+	10.8399i	0.965941	+	1.42335i
$59$	2.48528	+	9.27519i	0.323556	+	1.20753i	0.915756	+	0.401736i	$0.131593\pi$
$59$	2.48528	+	9.27519i	0.323556	+	1.20753i	−0.592200	+	0.805791i	$0.701740\pi$
$60$	−1.51181	−	0.600871i	−0.195174	−	0.0775721i
$61$	−0.560807	+	2.09296i	−0.0718040	+	0.267976i	−0.992490	−	0.122329i	$-0.960964\pi$
$61$	−0.560807	+	2.09296i	−0.0718040	+	0.267976i	0.920686	+	0.390305i	$0.127630\pi$
$62$	0.613404	−	0.709691i	0.0779024	−	0.0901308i
$63$		0			0
$64$	3.37762	+	7.25201i	0.422203	+	0.906501i
$65$	−3.76535	−	6.52177i	−0.467034	−	0.808927i
$66$	0.421504	+	1.21296i	0.0518835	+	0.149305i
$67$	−9.03564	+	2.42109i	−1.10388	+	0.295783i	−0.764343	−	0.644810i	$-0.776937\pi$
$67$	−9.03564	+	2.42109i	−1.10388	+	0.295783i	−0.339536	+	0.940593i	$0.610270\pi$
$68$	−8.26524	+	6.53325i	−1.00231	+	0.792273i
$69$	0.0222162	−	0.0222162i	0.00267452	−	0.00267452i
$70$		0			0
$71$			15.1936i			1.80315i	0.432621	+	0.901576i	$0.357589\pi$
$71$			15.1936i			1.80315i	−0.432621	+	0.901576i	$0.642411\pi$
$72$	8.14396	+	0.357444i	0.959775	+	0.0421251i
$73$	−4.17280	−	2.40917i	−0.488390	−	0.281972i	0.235517	−	0.971870i	$-0.424322\pi$
$73$	−4.17280	−	2.40917i	−0.488390	−	0.281972i	−0.723906	+	0.689899i	$0.757655\pi$
$74$	1.32934	+	0.643709i	0.154533	+	0.0748296i
$75$	−0.202945	−	0.0543790i	−0.0234341	−	0.00627914i
$76$	−8.77932	+	11.7889i	−1.00706	+	1.35228i
$77$		0			0
$78$	−1.16789	−	1.00944i	−0.132238	−	0.114296i
$79$	−5.53028	−	9.57872i	−0.622205	−	1.07769i	−0.989074	−	0.147418i	$-0.952904\pi$
$79$	−5.53028	−	9.57872i	−0.622205	−	1.07769i	0.366869	−	0.930272i	$-0.380430\pi$
$80$	4.97209	+	8.06651i	0.555897	+	0.901863i
$81$	3.97639	−	6.88731i	0.441821	−	0.765257i
$82$	0.647906	−	3.38434i	0.0715493	−	0.373738i
$83$	10.9512	+	10.9512i	1.20205	+	1.20205i	0.973541	+	0.228512i	$0.0733861\pi$
$83$	10.9512	+	10.9512i	1.20205	+	1.20205i	0.228512	+	0.973541i	$0.426614\pi$
$84$		0			0
$85$	−8.82402	+	8.82402i	−0.957099	+	0.957099i
$86$	−9.40196	+	6.38052i	−1.01384	+	0.688029i
$87$	2.75462	+	1.59038i	0.295326	+	0.170507i
$88$	2.25076	−	7.13281i	0.239932	−	0.760360i
$89$	−1.96668	+	1.13547i	−0.208468	+	0.120359i	−0.600599	−	0.799550i	$-0.705071\pi$
$89$	−1.96668	+	1.13547i	−0.208468	+	0.120359i	0.392131	+	0.919909i	$0.371738\pi$
$90$	9.63011	−	0.700819i	1.01510	−	0.0738728i
$91$		0			0
$92$	−0.181073	+	0.0264950i	−0.0188782	+	0.00276230i
$93$	0.0589474	−	0.219995i	0.00611256	−	0.0228124i
$94$	−2.46182	−	7.08439i	−0.253917	−	0.730699i
$95$	−8.70516	+	15.0778i	−0.893131	+	1.54695i
$96$	1.50549	+	1.22734i	0.153653	+	0.125265i
$97$	−17.4958			−1.77643			−0.888215	−	0.459427i	$-0.848055\pi$
$97$	−17.4958			−1.77643			−0.888215	+	0.459427i	$0.848055\pi$
$98$		0			0
$99$	−5.38916	−	5.38916i	−0.541631	−	0.541631i
$100$	0.758886	+	0.960070i	0.0758886	+	0.0960070i
$101$	4.15082	+	15.4911i	0.413022	+	1.54142i	0.788766	+	0.614694i	$0.210721\pi$
$101$	4.15082	+	15.4911i	0.413022	+	1.54142i	−0.375744	+	0.926724i	$0.622613\pi$
$102$	−1.11484	+	2.30229i	−0.110386	+	0.227961i
$103$	10.5828	−	6.10999i	1.04276	−	0.602035i	0.122143	−	0.992513i	$-0.461023\pi$
$103$	10.5828	−	6.10999i	1.04276	−	0.602035i	0.920613	+	0.390477i	$0.127690\pi$
$104$	1.94407	+	8.77868i	0.190632	+	0.860820i
$105$		0			0
$106$	−0.0925932	−	1.27234i	−0.00899345	−	0.123581i
$107$	−7.29501	−	1.95469i	−0.705236	−	0.188967i	−0.111661	−	0.993746i	$-0.535617\pi$
$107$	−7.29501	−	1.95469i	−0.705236	−	0.188967i	−0.593575	+	0.804779i	$0.702284\pi$
$108$	3.70934	−	1.59938i	0.356931	−	0.153900i
$109$	4.23590	−	1.13501i	0.405726	−	0.108714i	−0.0501838	−	0.998740i	$-0.515981\pi$
$109$	4.23590	−	1.13501i	0.405726	−	0.108714i	0.455910	+	0.890026i	$0.349314\pi$
$110$	1.66579	−	8.70124i	0.158826	−	0.829630i
$111$	0.358612			0.0340379
$112$		0			0
$113$	12.7100			1.19565			0.597826	−	0.801626i	$-0.296031\pi$
$113$	12.7100			1.19565			0.597826	+	0.801626i	$0.296031\pi$
$114$	−0.671043	+	3.50519i	−0.0628489	+	0.328291i
$115$	−0.209374	+	0.0561016i	−0.0195242	+	0.00523150i
$116$	−7.33548	−	17.0127i	−0.681082	−	1.57959i
$117$	8.84979	+	2.37129i	0.818164	+	0.219226i
$118$	−0.985647	−	13.5440i	−0.0907362	−	1.24683i
$119$		0			0
$120$	1.94011	+	1.23661i	0.177107	+	0.112887i
$121$	3.47029	−	2.00357i	0.315480	−	0.182143i
$122$	1.33550	−	2.75798i	0.120910	−	0.249695i
$123$	−0.216537	−	0.808127i	−0.0195245	−	0.0728664i
$124$	−1.04073	+	0.822641i	−0.0934600	+	0.0738754i
$125$	−7.35050	−	7.35050i	−0.657449	−	0.657449i
$126$		0			0
$127$	18.3252			1.62610			0.813051	−	0.582193i	$-0.197805\pi$
$127$	18.3252			1.62610			0.813051	+	0.582193i	$0.197805\pi$
$128$	−2.76309	−	10.9711i	−0.244225	−	0.969719i
$129$	−1.37941	+	2.38920i	−0.121450	+	0.210358i
$130$	3.49581	+	10.0599i	0.306603	+	0.882314i
$131$	−2.55502	+	9.53546i	−0.223233	+	0.833117i	0.759872	+	0.650073i	$0.225262\pi$
$131$	−2.55502	+	9.53546i	−0.223233	+	0.833117i	−0.983105	+	0.183044i	$0.941405\pi$
$132$	−0.262923	−	1.79688i	−0.0228845	−	0.156398i
$133$		0			0
$134$	13.1942	−	0.960191i	1.13981	−	0.0829479i
$135$	4.14360	−	2.39231i	0.356625	−	0.205897i
$136$	13.2176	−	6.87679i	1.13340	−	0.589680i
$137$	14.6054	+	8.43243i	1.24782	+	0.720431i	0.970675	−	0.240396i	$-0.0772775\pi$
$137$	14.6054	+	8.43243i	1.24782	+	0.720431i	0.277148	+	0.960827i	$0.410611\pi$
$138$	−0.0367656	+	0.0249505i	−0.00312970	+	0.00212393i
$139$	−6.01333	+	6.01333i	−0.510044	+	0.510044i	−0.914540	−	0.404496i	$-0.867447\pi$
$139$	−6.01333	+	6.01333i	−0.510044	+	0.510044i	0.404496	+	0.914540i	$0.367447\pi$
$140$		0			0
$141$	−1.28762	−	1.28762i	−0.108437	−	0.108437i
$142$	4.04016	−	21.1038i	0.339043	−	1.77099i
$143$	4.20318	−	7.28012i	0.351488	−	0.608794i
$144$	−11.2168	−	2.66206i	−0.934736	−	0.221838i
$145$	−10.9722	−	19.0044i	−0.911193	−	1.57823i
$146$	5.15535	+	4.45590i	0.426660	+	0.368773i
$147$		0			0
$148$	−1.67527	−	1.24759i	−0.137707	−	0.102551i
$149$	2.88609	+	0.773325i	0.236438	+	0.0633533i	0.375092	−	0.926988i	$-0.377611\pi$
$149$	2.88609	+	0.773325i	0.236438	+	0.0633533i	−0.138655	+	0.990341i	$0.544278\pi$
$150$	0.267429	+	0.129497i	0.0218355	+	0.0105734i
$151$	−18.9197	−	10.9233i	−1.53966	−	0.888925i	−0.998858	−	0.0477779i	$-0.984786\pi$
$151$	−18.9197	−	10.9233i	−1.53966	−	0.888925i	−0.540806	−	0.841147i	$-0.681881\pi$
$152$	15.3292	−	14.0402i	1.24336	−	1.13881i
$153$		−	15.1822i		−	1.22741i
$154$		0			0
$155$	−1.11109	+	1.11109i	−0.0892445	+	0.0892445i
$156$	1.35377	+	1.71266i	0.108388	+	0.137122i
$157$	2.83703	−	0.760181i	0.226420	−	0.0606690i	−0.143825	−	0.989603i	$-0.545940\pi$
$157$	2.83703	−	0.760181i	0.226420	−	0.0606690i	0.370245	+	0.928934i	$0.379274\pi$
$158$	5.13440	+	14.7753i	0.408471	+	1.17546i
$159$	−0.154870	−	0.268243i	−0.0122820	−	0.0212730i
$160$	−4.76121	−	12.5264i	−0.376406	−	0.990301i
$161$		0			0
$162$	−7.35458	+	8.50903i	−0.577830	+	0.668533i
$163$	−2.56552	+	9.57465i	−0.200947	+	0.749944i	0.789700	+	0.613493i	$0.210236\pi$
$163$	−2.56552	+	9.57465i	−0.200947	+	0.749944i	−0.990647	+	0.136451i	$0.956430\pi$
$164$	−1.79987	+	4.52852i	−0.140546	+	0.353618i
$165$	−0.556723	−	2.07772i	−0.0433408	−	0.161750i
$166$	−12.2991	−	18.1232i	−0.954594	−	1.40663i
$167$		−	17.0258i		−	1.31750i	−0.752363	−	0.658749i	$-0.771086\pi$
$167$		−	17.0258i		−	1.31750i	0.752363	−	0.658749i	$-0.228914\pi$
$168$		0			0
$169$		−	2.89442i		−	0.222648i
$170$	14.6029	−	9.91006i	1.11999	−	0.760067i
$171$	−5.48223	−	20.4600i	−0.419237	−	1.56461i
$172$	14.7559	−	6.36239i	1.12512	−	0.485128i
$173$	−0.0633750	+	0.236519i	−0.00481831	+	0.0179822i	−0.968293	−	0.249817i	$-0.919630\pi$
$173$	−0.0633750	+	0.236519i	−0.00481831	+	0.0179822i	0.963475	+	0.267799i	$0.0862963\pi$
$174$	−3.40323	−	2.94150i	−0.257998	−	0.222995i
$175$		0			0
$176$	−5.02298	+	9.30889i	−0.378621	+	0.701684i
$177$	−1.64858	−	2.85542i	−0.123915	−	0.214627i
$178$	3.03364	−	1.05419i	0.227381	−	0.0790145i
$179$	−0.261058	+	0.0699503i	−0.0195124	+	0.00522833i	−0.268562	−	0.963262i	$-0.586548\pi$
$179$	−0.261058	+	0.0699503i	−0.0195124	+	0.00522833i	0.249050	+	0.968491i	$0.419882\pi$
$180$	−13.5625	−	1.58733i	−1.01089	−	0.118312i
$181$	0.745744	−	0.745744i	0.0554307	−	0.0554307i	−0.678848	−	0.734279i	$-0.737521\pi$
$181$	0.745744	−	0.745744i	0.0554307	−	0.0554307i	0.734279	+	0.678848i	$0.237521\pi$
$182$		0			0
$183$		−	0.744009i		−	0.0549987i
$184$	0.258554	+	0.0113481i	0.0190608	+	0.000836593i
$185$	−2.14264	−	1.23705i	−0.157530	−	0.0909500i
$186$	−0.140377	+	0.289896i	−0.0102929	+	0.0212562i
$187$	−13.4554	−	3.60537i	−0.983959	−	0.263651i
$188$	1.53562	+	10.4948i	0.111997	+	0.765410i
$189$		0			0
$190$	16.1007	−	18.6281i	1.16807	−	1.35142i
$191$	1.97887	+	3.42751i	0.143186	+	0.248006i	0.928695	−	0.370845i	$-0.120932\pi$
$191$	1.97887	+	3.42751i	0.143186	+	0.248006i	−0.785509	+	0.618851i	$0.787599\pi$
$192$	−1.76474	−	2.10510i	−0.127359	−	0.151922i
$193$	−0.444328	+	0.769598i	−0.0319834	+	0.0553969i	−0.881574	−	0.472046i	$-0.843516\pi$
$193$	−0.444328	+	0.769598i	−0.0319834	+	0.0553969i	0.849591	+	0.527443i	$0.176849\pi$
$194$	24.3015	+	4.65234i	1.74475	+	0.334018i
$195$	1.82844	+	1.82844i	0.130937	+	0.130937i
$196$		0			0
$197$	−4.83936	+	4.83936i	−0.344790	+	0.344790i	−0.858165	−	0.513374i	$-0.828395\pi$
$197$	−4.83936	+	4.83936i	−0.344790	+	0.344790i	0.513374	+	0.858165i	$0.328395\pi$
$198$	6.05245	+	8.91853i	0.430129	+	0.633812i
$199$	7.57734	+	4.37478i	0.537144	+	0.310120i	0.743920	−	0.668268i	$-0.232964\pi$
$199$	7.57734	+	4.37478i	0.537144	+	0.310120i	−0.206777	+	0.978388i	$0.566297\pi$
$200$	−0.798791	−	1.53532i	−0.0564831	−	0.108564i
$201$	2.78168	−	1.60600i	0.196204	−	0.113279i
$202$	−1.64619	−	22.6207i	−0.115825	−	1.59158i
$203$		0			0
$204$	2.16071	−	2.90141i	0.151280	−	0.203139i
$205$	−1.49391	+	5.57537i	−0.104340	+	0.389400i
$206$	−16.3241	+	5.67262i	−1.13736	+	0.395230i
$207$	0.131857	−	0.228383i	0.00916469	−	0.0158737i
$208$	−0.365948	−	12.7104i	−0.0253739	−	0.881310i
$209$	−19.4348			−1.34433
$210$		0			0
$211$	8.52893	+	8.52893i	0.587156	+	0.587156i	0.936860	−	0.349704i	$-0.113718\pi$
$211$	8.52893	+	8.52893i	0.587156	+	0.587156i	−0.349704	+	0.936860i	$0.613718\pi$
$212$	−0.209720	+	1.79189i	−0.0144036	+	0.123068i
$213$	−1.35026	−	5.03925i	−0.0925185	−	0.345284i
$214$	9.61292	+	4.65488i	0.657126	+	0.318201i
$215$	16.4834	−	9.51669i	1.12416	−	0.649033i
$216$	−5.57753	+	1.23517i	−0.379503	+	0.0840424i
$217$		0			0
$218$	−6.18543	+	0.450137i	−0.418930	+	0.0304871i
$219$	1.59809	+	0.428207i	0.107989	+	0.0289356i
$220$	−4.62752	+	11.6430i	−0.311987	+	0.784969i
$221$	16.1752	−	4.33414i	1.08806	−	0.291546i
$222$	−0.498108	−	0.0953590i	−0.0334308	−	0.00640008i
$223$	25.3314			1.69631			0.848156	−	0.529746i	$-0.177713\pi$
$223$	25.3314			1.69631			0.848156	+	0.529746i	$0.177713\pi$
$224$		0			0
$225$	−1.76353			−0.117569
$226$	−17.6540	−	3.37972i	−1.17433	−	0.224816i
$227$	−0.717124	+	0.192153i	−0.0475972	+	0.0127536i	−0.282539	−	0.959256i	$-0.591177\pi$
$227$	−0.717124	+	0.192153i	−0.0475972	+	0.0127536i	0.234942	+	0.972009i	$0.424510\pi$
$228$	1.86414	−	4.69024i	0.123456	−	0.310619i
$229$	15.5299	+	4.16121i	1.02624	+	0.274981i	0.732401	−	0.680873i	$-0.238400\pi$
$229$	15.5299	+	4.16121i	1.02624	+	0.274981i	0.293841	+	0.955854i	$0.405066\pi$
$230$	0.305736	−	0.0222495i	0.0201596	−	0.00146709i
$231$		0			0
$232$	5.66503	+	25.5811i	0.371927	+	1.67948i
$233$	−9.31438	+	5.37766i	−0.610206	+	0.352302i	−0.773046	−	0.634350i	$-0.781268\pi$
$233$	−9.31438	+	5.37766i	−0.610206	+	0.352302i	0.162840	+	0.986652i	$0.447934\pi$
$234$	−11.6617	−	5.64696i	−0.762350	−	0.369154i
$235$	3.25158	+	12.1350i	0.212109	+	0.791603i
$236$	−2.23245	+	19.0746i	−0.145320	+	1.24165i
$237$	2.68549	+	2.68549i	0.174441	+	0.174441i
$238$		0			0
$239$	3.00042			0.194081			0.0970405	−	0.995280i	$-0.469062\pi$
$239$	3.00042			0.194081			0.0970405	+	0.995280i	$0.469062\pi$
$240$	−2.36596	−	2.23354i	−0.152722	−	0.144174i
$241$	11.2985	−	19.5696i	0.727802	−	1.26059i	−0.230009	−	0.973189i	$-0.573875\pi$
$241$	11.2985	−	19.5696i	0.727802	−	1.26059i	0.957810	−	0.287401i	$-0.0927913\pi$
$242$	−5.35296	+	1.86015i	−0.344101	+	0.119575i
$243$	−2.27500	+	8.49041i	−0.145941	+	0.544660i
$244$	−2.58837	+	3.47567i	−0.165703	+	0.222507i
$245$		0			0
$246$	0.0858773	+	1.18006i	0.00547534	+	0.0752378i
$247$	20.2331	−	11.6816i	1.28740	−	0.743283i
$248$	1.66431	−	0.865899i	0.105684	−	0.0549846i
$249$	−4.60542	−	2.65894i	−0.291857	−	0.168503i
$250$	8.25519	+	12.1644i	0.522104	+	0.769341i
$251$	2.43982	−	2.43982i	0.154000	−	0.154000i	−0.625902	−	0.779902i	$-0.715269\pi$
$251$	2.43982	−	2.43982i	0.154000	−	0.154000i	0.779902	+	0.625902i	$0.215269\pi$
$252$		0			0
$253$	−0.171095	−	0.171095i	−0.0107566	−	0.0107566i
$254$	−25.4536	−	4.87289i	−1.59710	−	0.305752i
$255$	2.14246	−	3.71084i	0.134166	−	0.232382i
$256$	0.920552	+	15.9735i	0.0575345	+	0.998344i
$257$	−9.23633	−	15.9978i	−0.576147	−	0.997915i	−0.995916	−	0.0902843i	$-0.971222\pi$
$257$	−9.23633	−	15.9978i	−0.576147	−	0.997915i	0.419770	−	0.907631i	$-0.362111\pi$
$258$	2.55130	−	2.95178i	0.158837	−	0.183770i
$259$		0			0
$260$	−2.18060	−	14.9027i	−0.135235	−	0.924226i
$261$	25.7883	+	6.90995i	1.59625	+	0.427715i
$262$	6.08448	−	12.5652i	0.375900	−	0.776283i
$263$	8.37247	+	4.83385i	0.516269	+	0.298068i	0.735407	−	0.677626i	$-0.236991\pi$
$263$	8.37247	+	4.83385i	0.516269	+	0.298068i	−0.219138	+	0.975694i	$0.570324\pi$
$264$	−0.112613	+	2.56576i	−0.00693083	+	0.157911i
$265$			2.13694i			0.131271i
$266$		0			0
$267$	0.551378	−	0.551378i	0.0337438	−	0.0337438i
$268$	−18.5819	−	2.17479i	−1.13507	−	0.132847i
$269$	−23.3504	+	6.25673i	−1.42370	+	0.381480i	−0.886796	−	0.462162i	$-0.847074\pi$
$269$	−23.3504	+	6.25673i	−1.42370	+	0.381480i	−0.536906	+	0.843642i	$0.680407\pi$
$270$	−6.39156	+	2.22106i	−0.388978	+	0.135170i
$271$	−14.3220	−	24.8064i	−0.869999	−	1.50688i	−0.861996	−	0.506915i	$-0.830786\pi$
$271$	−14.3220	−	24.8064i	−0.869999	−	1.50688i	−0.00800296	−	0.999968i	$-0.502547\pi$
$272$	−20.1877	+	6.03708i	−1.22406	+	0.366052i
$273$		0			0
$274$	−18.0445	−	15.5963i	−1.09011	−	0.942206i
$275$	−0.418791	+	1.56295i	−0.0252541	+	0.0942495i
$276$	0.0577017	−	0.0248796i	0.00347323	−	0.00149758i
$277$	−4.26488	−	15.9168i	−0.256252	−	0.956345i	−0.967390	−	0.253293i	$-0.918486\pi$
$277$	−4.26488	−	15.9168i	−0.256252	−	0.956345i	0.711138	−	0.703053i	$-0.248180\pi$
$278$	9.95147	−	6.75344i	0.596850	−	0.405045i
$279$		−	1.91169i		−	0.114450i
$280$		0			0
$281$		−	19.5811i		−	1.16811i	−0.811715	−	0.584054i	$-0.801466\pi$
$281$		−	19.5811i		−	1.16811i	0.811715	−	0.584054i	$-0.198534\pi$
$282$	1.44610	+	2.13089i	0.0861141	+	0.126893i
$283$	0.131830	+	0.491997i	0.00783649	+	0.0292462i	0.969733	−	0.244166i	$-0.0785143\pi$
$283$	0.131830	+	0.491997i	0.00783649	+	0.0292462i	−0.961897	+	0.273412i	$0.911848\pi$
$284$	−11.2235	+	28.2386i	−0.665991	+	1.67565i
$285$	1.54726	−	5.77446i	0.0916519	−	0.342050i
$286$	−7.77404	+	8.99434i	−0.459689	+	0.531846i
$287$		0			0
$288$	14.8722	+	6.68025i	0.876352	+	0.393638i
$289$	−5.37469	−	9.30923i	−0.316158	−	0.547602i
$290$	10.1868	+	29.3146i	0.598189	+	1.72141i
$291$	5.80282	−	1.55486i	0.340167	−	0.0911475i
$292$	−5.97585	−	7.56007i	−0.349710	−	0.442420i
$293$	13.4219	−	13.4219i	0.784117	−	0.784117i	−0.196406	−	0.980523i	$-0.562927\pi$
$293$	13.4219	−	13.4219i	0.784117	−	0.784117i	0.980523	+	0.196406i	$0.0629270\pi$
$294$		0			0
$295$			22.7475i			1.32441i
$296$	1.99519	+	2.17837i	0.115968	+	0.126615i
$297$	4.62542	+	2.67049i	0.268394	+	0.154957i
$298$	−3.80311	−	1.84158i	−0.220308	−	0.106680i
$299$	0.280962	+	0.0752837i	0.0162485	+	0.00435377i
$300$	−0.337021	−	0.250983i	−0.0194579	−	0.0144905i
$301$		0			0
$302$	23.3746	+	20.2033i	1.34506	+	1.16257i
$303$	−2.75339	−	4.76901i	−0.158178	−	0.273973i
$304$	−25.0255	+	15.4254i	−1.43531	+	0.884708i
$305$	−2.56650	+	4.44532i	−0.146958	+	0.254538i
$306$	−4.03713	+	21.0879i	−0.230787	+	1.20552i
$307$	18.1617	+	18.1617i	1.03654	+	1.03654i	0.999307	+	0.0372355i	$0.0118552\pi$
$307$	18.1617	+	18.1617i	1.03654	+	1.03654i	0.0372355	+	0.999307i	$0.488145\pi$
$308$		0			0
$309$	−2.96699	+	2.96699i	−0.168786	+	0.168786i
$310$	1.83874	−	1.24784i	0.104433	−	0.0708723i
$311$	27.1628	+	15.6825i	1.54026	+	0.889271i	0.998822	+	0.0485315i	$0.0154541\pi$
$311$	27.1628	+	15.6825i	1.54026	+	0.889271i	0.541440	+	0.840739i	$0.317879\pi$
$312$	−1.42495	−	2.73884i	−0.0806721	−	0.155056i
$313$	−11.6376	+	6.71895i	−0.657794	+	0.379777i	−0.791436	−	0.611252i	$-0.790666\pi$
$313$	−11.6376	+	6.71895i	−0.657794	+	0.379777i	0.133642	+	0.991030i	$0.457333\pi$
$314$	−4.14275	+	0.301483i	−0.233789	+	0.0170137i
$315$		0			0
$316$	−3.20271	−	21.8880i	−0.180166	−	1.23130i
$317$	−6.10150	+	22.7711i	−0.342695	+	1.27895i	0.552588	+	0.833455i	$0.313640\pi$
$317$	−6.10150	+	22.7711i	−0.342695	+	1.27895i	−0.895282	+	0.445499i	$0.853026\pi$
$318$	0.143784	+	0.413768i	0.00806301	+	0.0232030i
$319$	12.2481	−	21.2143i	0.685760	−	1.18777i
$320$	3.28234	+	18.6651i	0.183489	+	1.04341i
$321$	2.59324			0.144741
$322$		0			0
$323$	−27.3756	−	27.3756i	−1.52322	−	1.52322i
$324$	12.4781	−	9.86329i	0.693227	−	0.547960i
$325$	−0.503444	−	1.87888i	−0.0279260	−	0.104221i
$326$	6.10949	−	12.6169i	0.338373	−	0.698784i
$327$	−1.30405	+	0.752892i	−0.0721140	+	0.0416350i
$328$	3.70419	−	5.81147i	0.204529	−	0.320885i
$329$		0			0
$330$	0.220793	+	3.03397i	0.0121543	+	0.167014i
$331$	−8.11450	−	2.17427i	−0.446013	−	0.119509i	0.0288201	−	0.999585i	$-0.490825\pi$
$331$	−8.11450	−	2.17427i	−0.446013	−	0.119509i	−0.474833	+	0.880076i	$0.657492\pi$
$332$	12.2641	+	28.4434i	0.673081	+	1.56103i
$333$	2.90748	−	0.779056i	0.159329	−	0.0426920i
$334$	−4.52736	+	23.6487i	−0.247726	+	1.29400i
$335$	−22.1600			−1.21073
$336$		0			0
$337$	−5.77753			−0.314722			−0.157361	−	0.987541i	$-0.550299\pi$
$337$	−5.77753			−0.314722			−0.157361	+	0.987541i	$0.550299\pi$
$338$	−0.769661	+	4.02032i	−0.0418640	+	0.218677i
$339$	−4.21549	+	1.12954i	−0.228954	+	0.0613481i
$340$	−22.9184	+	9.88189i	−1.24293	+	0.535921i
$341$	−1.69426	−	0.453975i	−0.0917491	−	0.0245841i
$342$	2.17422	+	29.8764i	0.117568	+	1.61553i
$343$		0			0
$344$	−22.1876	+	4.91353i	−1.19627	+	0.264920i
$345$	0.0644570	−	0.0372143i	0.00347025	−	0.00200355i
$346$	0.150920	−	0.311670i	0.00811352	−	0.0167555i
$347$	−3.13552	−	11.7019i	−0.168324	−	0.628193i	−0.997593	−	0.0693432i	$-0.977910\pi$
$347$	−3.13552	−	11.7019i	−0.168324	−	0.628193i	0.829269	−	0.558849i	$-0.188757\pi$
$348$	3.94488	+	4.99068i	0.211468	+	0.267528i
$349$	18.6177	+	18.6177i	0.996582	+	0.996582i	0.999994	−	0.00341200i	$-0.00108607\pi$
$349$	18.6177	+	18.6177i	0.996582	+	0.996582i	−0.00341200	+	0.999994i	$0.501086\pi$
$350$		0			0
$351$	−6.42057			−0.342705
$352$	9.45221	−	11.5943i	0.503804	−	0.617977i
$353$	11.3938	−	19.7346i	0.606430	−	1.05037i	−0.385394	−	0.922752i	$-0.625934\pi$
$353$	11.3938	−	19.7346i	0.606430	−	1.05037i	0.991824	−	0.127615i	$-0.0407323\pi$
$354$	1.53057	+	4.40453i	0.0813488	+	0.234098i
$355$	−9.31563	+	34.7664i	−0.494422	+	1.84521i
$356$	−4.49401	+	0.657574i	−0.238182	+	0.0348513i
$357$		0			0
$358$	0.381207	−	0.0277419i	0.0201474	−	0.00146620i
$359$	1.93301	−	1.11602i	0.102020	−	0.0589014i	−0.448122	−	0.893973i	$-0.647907\pi$
$359$	1.93301	−	1.11602i	0.102020	−	0.0589014i	0.550142	+	0.835071i	$0.314574\pi$
$360$	18.4160	+	5.81120i	0.970611	+	0.306277i
$361$	−30.3228	−	17.5069i	−1.59594	−	0.921415i
$362$	−1.23413	+	0.837529i	−0.0648646	+	0.0440195i
$363$	−0.972927	+	0.972927i	−0.0510654	+	0.0510654i
$364$		0			0
$365$	−8.07117	−	8.07117i	−0.422465	−	0.422465i
$366$	−0.197841	+	1.03342i	−0.0103413	+	0.0540178i
$367$	10.3207	−	17.8759i	0.538735	−	0.933117i	−0.460237	−	0.887796i	$-0.652236\pi$
$367$	10.3207	−	17.8759i	0.538735	−	0.933117i	0.998972	−	0.0453208i	$-0.0144310\pi$
$368$	−0.356111	−	0.0845148i	−0.0185636	−	0.00440564i
$369$	−3.51119	−	6.08155i	−0.182785	−	0.316593i
$370$	2.64716	+	2.28801i	0.137619	+	0.118948i
$371$		0			0
$372$	0.272068	−	0.365334i	0.0141061	−	0.0189417i
$373$	22.6365	+	6.06542i	1.17207	+	0.314056i	0.791777	−	0.610810i	$-0.209156\pi$
$373$	22.6365	+	6.06542i	1.17207	+	0.314056i	0.380295	+	0.924865i	$0.375823\pi$
$374$	17.7307	+	8.58578i	0.916835	+	0.443960i
$375$	3.09117	+	1.78469i	0.159628	+	0.0921610i
$376$	0.657721	−	14.9855i	0.0339194	−	0.772816i
$377$			29.4476i			1.51663i
$378$		0			0
$379$	5.39695	−	5.39695i	0.277223	−	0.277223i	−0.554777	−	0.831999i	$-0.687196\pi$
$379$	5.39695	−	5.39695i	0.277223	−	0.277223i	0.831999	+	0.554777i	$0.187196\pi$
$380$	−27.3172	+	21.5928i	−1.40134	+	1.10769i
$381$	−6.07791	+	1.62857i	−0.311381	+	0.0834342i
$382$	−1.83722	−	5.28698i	−0.0940003	−	0.270505i
$383$	9.29971	+	16.1076i	0.475193	+	0.823058i	0.999596	−	0.0284116i	$-0.00904490\pi$
$383$	9.29971	+	16.1076i	0.475193	+	0.823058i	−0.524403	+	0.851470i	$0.675712\pi$
$384$	1.89144	+	3.39322i	0.0965220	+	0.173160i
$385$		0			0
$386$	0.821811	−	0.950811i	0.0418291	−	0.0483950i
$387$	−5.99331	+	22.3673i	−0.304657	+	1.13699i
$388$	−32.5174	−	12.9241i	−1.65082	−	0.656121i
$389$	−1.00941	−	3.76716i	−0.0511790	−	0.191003i	0.935604	−	0.353052i	$-0.114856\pi$
$389$	−1.00941	−	3.76716i	−0.0511790	−	0.191003i	−0.986783	+	0.162050i	$0.948190\pi$
$390$	−2.05348	−	3.02589i	−0.103982	−	0.153222i
$391$		−	0.482004i		−	0.0243760i
$392$		0			0
$393$		−	3.38968i		−	0.170987i
$394$	8.00867	−	5.43498i	0.403471	−	0.273810i
$395$	−6.78153	−	25.3090i	−0.341216	−	1.27344i
$396$	−6.03524	−	13.9972i	−0.303282	−	0.703383i
$397$	−3.59757	+	13.4263i	−0.180557	+	0.673848i	0.814981	+	0.579488i	$0.196747\pi$
$397$	−3.59757	+	13.4263i	−0.180557	+	0.673848i	−0.995538	+	0.0943605i	$0.969919\pi$
$398$	−9.36154	−	8.09143i	−0.469252	−	0.405587i
$399$		0			0
$400$	0.701253	+	2.34496i	0.0350626	+	0.117248i
$401$	5.37440	+	9.30874i	0.268385	+	0.464856i	0.968445	−	0.249228i	$-0.0801768\pi$
$401$	5.37440	+	9.30874i	0.268385	+	0.464856i	−0.700060	+	0.714084i	$0.746843\pi$
$402$	−4.29077	+	1.49104i	−0.214004	+	0.0743663i
$403$	2.03672	−	0.545739i	0.101456	−	0.0271852i
$404$	−3.72855	+	31.8576i	−0.185503	+	1.58497i
$405$	13.3217	−	13.3217i	0.661959	−	0.661959i
$406$		0			0
$407$		−	2.76179i		−	0.136897i
$408$	−3.77272	+	3.45547i	−0.186777	+	0.171071i
$409$	−7.51025	−	4.33605i	−0.371358	−	0.214404i	0.302694	−	0.953088i	$-0.402114\pi$
$409$	−7.51025	−	4.33605i	−0.371358	−	0.214404i	−0.674052	+	0.738684i	$0.735447\pi$
$410$	3.55759	−	7.34687i	0.175697	−	0.362836i
$411$	−5.59354	−	1.49879i	−0.275909	−	0.0739297i
$412$	24.1825	−	3.53843i	1.19138	−	0.174326i
$413$		0			0
$414$	−0.243877	+	0.282159i	−0.0119859	+	0.0138674i
$415$	18.3444	+	31.7734i	0.900489	+	1.55969i
$416$	−2.87155	+	17.7520i	−0.140790	+	0.870362i
$417$	1.46003	−	2.52884i	0.0714979	−	0.123838i
$418$	26.9947	+	5.16793i	1.32035	+	0.252772i
$419$	3.96286	+	3.96286i	0.193598	+	0.193598i	0.797249	−	0.603651i	$-0.206288\pi$
$419$	3.96286	+	3.96286i	0.193598	+	0.193598i	−0.603651	+	0.797249i	$0.706288\pi$
$420$		0			0
$421$	−16.2008	+	16.2008i	−0.789580	+	0.789580i	−0.981425	−	0.191845i	$-0.938553\pi$
$421$	−16.2008	+	16.2008i	−0.789580	+	0.789580i	0.191845	+	0.981425i	$0.438553\pi$
$422$	−9.57865	−	14.1145i	−0.466282	−	0.687085i
$423$	−13.2368	−	7.64226i	−0.643594	−	0.371579i
$424$	0.767784	−	2.43316i	0.0372869	−	0.118164i
$425$	−2.79146	+	1.61165i	−0.135406	+	0.0781765i
$426$	0.535506	+	7.35852i	0.0259454	+	0.356521i
$427$		0			0
$428$	−12.1145	−	9.02176i	−0.585574	−	0.436083i
$429$	−0.747076	+	2.78813i	−0.0360692	+	0.134612i
$430$	−25.4259	+	8.83546i	−1.22614	+	0.426084i
$431$	0.282550	−	0.489392i	0.0136100	−	0.0235732i	−0.859140	−	0.511740i	$-0.829001\pi$
$431$	0.282550	−	0.489392i	0.0136100	−	0.0235732i	0.872750	+	0.488167i	$0.162334\pi$
$432$	8.07557	−	0.232504i	0.388536	−	0.0111864i
$433$	14.8949			0.715801			0.357900	−	0.933760i	$-0.383493\pi$
$433$	14.8949			0.715801			0.357900	+	0.933760i	$0.383493\pi$
$434$		0			0
$435$	5.32807	+	5.32807i	0.255462	+	0.255462i
$436$	8.71119	+	1.01954i	0.417191	+	0.0488272i
$437$	−0.174049	−	0.649561i	−0.00832591	−	0.0310727i
$438$	−2.10587	−	1.01973i	−0.100622	−	0.0487244i
$439$	−22.8504	+	13.1927i	−1.09059	+	0.629652i	−0.933733	−	0.357970i	$-0.883469\pi$
$439$	−22.8504	+	13.1927i	−1.09059	+	0.629652i	−0.156855	+	0.987622i	$0.550136\pi$
$440$	9.52357	−	14.9415i	0.454018	−	0.712306i
$441$		0			0
$442$	−23.6197	+	1.71890i	−1.12348	+	0.0817595i
$443$	10.6551	+	2.85503i	0.506241	+	0.135647i	0.502895	−	0.864348i	$-0.332268\pi$
$443$	10.6551	+	2.85503i	0.506241	+	0.135647i	0.00334579	+	0.999994i	$0.498935\pi$
$444$	0.666509	+	0.264905i	0.0316311	+	0.0125718i
$445$	−5.19640	+	1.39237i	−0.246333	+	0.0660047i
$446$	−35.1850	−	6.73590i	−1.66606	−	0.318954i
$447$	−1.02595			−0.0485258
$448$		0			0
$449$	31.5853			1.49060			0.745302	−	0.666728i	$-0.232306\pi$
$449$	31.5853			1.49060			0.745302	+	0.666728i	$0.232306\pi$
$450$	2.44952	+	0.468943i	0.115472	+	0.0221062i
$451$	−6.22366	+	1.66763i	−0.293061	+	0.0785254i
$452$	23.6225	+	9.38880i	1.11111	+	0.441612i
$453$	7.24583	+	1.94152i	0.340439	+	0.0912203i
$454$	1.04717	−	0.0762066i	0.0491462	−	0.00357655i
$455$		0			0
$456$	−3.83646	+	6.01899i	−0.179659	+	0.281865i
$457$	6.68269	−	3.85825i	0.312603	−	0.180482i	−0.335488	−	0.942045i	$-0.608901\pi$
$457$	6.68269	−	3.85825i	0.312603	−	0.180482i	0.648091	+	0.761563i	$0.275568\pi$
$458$	−20.4643	−	9.90945i	−0.956234	−	0.463038i
$459$	2.75370	+	10.2769i	0.128531	+	0.479686i
$460$	−0.430580	−	0.0503944i	−0.0200759	−	0.00234965i
$461$	−3.17728	−	3.17728i	−0.147980	−	0.147980i	0.629235	−	0.777215i	$-0.283368\pi$
$461$	−3.17728	−	3.17728i	−0.147980	−	0.147980i	−0.777215	+	0.629235i	$0.783368\pi$
$462$		0			0
$463$	−7.90920			−0.367571			−0.183786	−	0.982966i	$-0.558835\pi$
$463$	−7.90920			−0.367571			−0.183786	+	0.982966i	$0.558835\pi$
$464$	−1.06637	−	37.0382i	−0.0495050	−	1.71946i
$465$	0.269770	−	0.467255i	0.0125103	−	0.0216684i
$466$	14.3676	−	4.99271i	0.665564	−	0.231283i
$467$	6.10734	−	22.7929i	0.282614	−	1.05473i	−0.667952	−	0.744205i	$-0.732829\pi$
$467$	6.10734	−	22.7929i	0.282614	−	1.05473i	0.950565	−	0.310524i	$-0.100505\pi$
$468$	14.6964	+	10.9446i	0.679341	+	0.505912i
$469$		0			0
$470$	−1.28956	−	17.7201i	−0.0594828	−	0.817366i
$471$	−0.873398	+	0.504256i	−0.0402440	+	0.0232349i
$472$	8.17300	−	25.9007i	0.376193	−	1.19218i
$473$	18.4001	+	10.6233i	0.846036	+	0.488459i
$474$	−3.01601	−	4.44421i	−0.138530	−	0.204129i
$475$	−3.17988	+	3.17988i	−0.145903	+	0.145903i
$476$		0			0
$477$	−1.83836	−	1.83836i	−0.0841727	−	0.0841727i
$478$	−4.16755	−	0.797846i	−0.190619	−	0.0364926i
$479$	−16.9156	+	29.2986i	−0.772892	+	1.33869i	0.163080	+	0.986613i	$0.447857\pi$
$479$	−16.9156	+	29.2986i	−0.772892	+	1.33869i	−0.935972	+	0.352075i	$0.885476\pi$
$480$	2.69237	+	3.73150i	0.122889	+	0.170319i
$481$	1.66002	+	2.87525i	0.0756906	+	0.131100i
$482$	−20.8973	+	24.1776i	−0.951846	+	1.10126i
$483$		0			0
$484$	7.92984	−	1.16031i	0.360447	−	0.0527415i
$485$	−40.0343	−	10.7272i	−1.81787	−	0.487096i
$486$	5.41765	−	11.1881i	0.245750	−	0.507505i
$487$	−9.02294	−	5.20940i	−0.408868	−	0.236060i	0.281435	−	0.959580i	$-0.409190\pi$
$487$	−9.02294	−	5.20940i	−0.408868	−	0.236060i	−0.690303	+	0.723520i	$0.742523\pi$
$488$	4.51944	−	4.13940i	0.204585	−	0.187382i
$489$		−	3.40361i		−	0.153917i
$490$		0			0
$491$	−8.28383	+	8.28383i	−0.373844	+	0.373844i	−0.868875	−	0.495031i	$-0.835157\pi$
$491$	−8.28383	+	8.28383i	−0.373844	+	0.373844i	0.495031	+	0.868875i	$0.335157\pi$
$492$	0.194509	−	1.66193i	0.00876913	−	0.0749254i
$493$	47.1346	−	12.6297i	2.12284	−	0.568813i
$494$	−31.2099	+	10.8454i	−1.40420	+	0.487958i
$495$	−9.02736	−	15.6358i	−0.405750	−	0.702779i
$496$	−2.54196	+	0.760166i	−0.114137	+	0.0341324i
$497$		0			0
$498$	5.68984	+	4.91787i	0.254968	+	0.220375i
$499$	−3.13364	+	11.6949i	−0.140281	+	0.523536i	0.859639	+	0.510902i	$0.170688\pi$
$499$	−3.13364	+	11.6949i	−0.140281	+	0.523536i	−0.999920	+	0.0126342i	$0.995978\pi$
$500$	−8.23172	−	19.0913i	−0.368134	−	0.853789i
$501$	1.51309	+	5.64694i	0.0676000	+	0.252287i
$502$	−4.03765	+	2.74010i	−0.180209	+	0.122297i
$503$		−	26.5226i		−	1.18258i	−0.806458	−	0.591292i	$-0.798618\pi$
$503$		−	26.5226i		−	1.18258i	0.806458	−	0.591292i	$-0.201382\pi$
$504$		0			0
$505$			37.9920i			1.69062i
$506$	0.192153	+	0.283145i	0.00854222	+	0.0125873i
$507$	0.257229	+	0.959990i	0.0114239	+	0.0426347i
$508$	34.0590	+	13.5368i	1.51112	+	0.600598i
$509$	−8.63990	+	32.2445i	−0.382957	+	1.42921i	0.458406	+	0.888743i	$0.348421\pi$
$509$	−8.63990	+	32.2445i	−0.382957	+	1.42921i	−0.841363	+	0.540471i	$0.818246\pi$
$510$	−3.96261	+	4.58462i	−0.175467	+	0.203010i
$511$		0			0
$512$	2.96890	−	22.4318i	0.131208	−	0.991355i
$513$	7.42190	+	12.8551i	0.327685	+	0.567567i
$514$	8.57517	+	24.6768i	0.378234	+	1.08845i
$515$	27.9620	−	7.49241i	1.23215	−	0.330155i
$516$	−4.32863	+	3.42157i	−0.190558	+	0.150626i
$517$	−9.91643	+	9.91643i	−0.436124	+	0.436124i
$518$		0			0
$519$		−	0.0840780i		−	0.00369062i
$520$	−0.933973	+	21.2795i	−0.0409574	+	0.933170i
$521$	0.420026	+	0.242502i	0.0184017	+	0.0106242i	0.509173	−	0.860664i	$-0.329951\pi$
$521$	0.420026	+	0.242502i	0.0184017	+	0.0106242i	−0.490771	+	0.871289i	$0.663285\pi$
$522$	−33.9822	−	16.4552i	−1.48736	−	0.720226i
$523$	−19.8439	−	5.31716i	−0.867714	−	0.232503i	−0.202615	−	0.979259i	$-0.564944\pi$
$523$	−19.8439	−	5.31716i	−0.867714	−	0.232503i	−0.665099	+	0.746755i	$0.731611\pi$
$524$	−11.7925	+	15.8350i	−0.515159	+	0.691757i
$525$		0			0
$526$	−10.3439	−	8.94050i	−0.451015	−	0.389824i
$527$	−1.74705	−	3.02597i	−0.0761026	−	0.131813i
$528$	0.838682	−	3.53386i	0.0364989	−	0.153792i
$529$	−11.4958	+	19.9113i	−0.499818	+	0.865710i
$530$	0.568236	−	2.96818i	0.0246826	−	0.128930i
$531$	−19.5692	−	19.5692i	−0.849230	−	0.849230i
$532$		0			0
$533$	5.47697	−	5.47697i	0.237234	−	0.237234i
$534$	−0.912476	+	0.619241i	−0.0394867	+	0.0267972i
$535$	−15.4941	−	8.94555i	−0.669870	−	0.386750i
$536$	25.2318	+	7.96192i	1.08985	+	0.343902i
$537$	0.0803683	−	0.0464007i	0.00346815	−	0.00200234i
$538$	34.0973	−	2.48138i	1.47004	−	0.106980i
$539$		0			0
$540$	9.46842	−	1.38544i	0.407456	−	0.0596199i
$541$	3.27745	−	12.2316i	0.140909	−	0.525878i	−0.858995	−	0.511984i	$-0.828911\pi$
$541$	3.27745	−	12.2316i	0.140909	−	0.525878i	0.999903	−	0.0138940i	$-0.00442275\pi$
$542$	13.2968	+	38.2642i	0.571146	+	1.64359i
$543$	−0.181066	+	0.313615i	−0.00777027	+	0.0134585i
$544$	29.6458	−	3.01730i	1.27106	−	0.129365i
$545$	10.3886			0.444998
$546$		0			0
$547$	−26.3448	−	26.3448i	−1.12642	−	1.12642i	−0.990754	−	0.135668i	$-0.956682\pi$
$547$	−26.3448	−	26.3448i	−1.12642	−	1.12642i	−0.135668	−	0.990754i	$-0.543318\pi$
$548$	20.9163	+	26.4613i	0.893501	+	1.13037i
$549$	−1.61630	−	6.03212i	−0.0689821	−	0.257445i
$550$	0.997303	−	2.05956i	0.0425252	−	0.0878199i
$551$	58.9594	−	34.0402i	2.51175	−	1.45016i
$552$	−0.0867628	+	0.0192140i	−0.00369287	+	0.000817801i
$553$		0			0
$554$	1.69143	+	23.2423i	0.0718618	+	0.987470i
$555$	0.820584	+	0.219875i	0.0348318	+	0.00933316i
$556$	−15.6183	+	6.73425i	−0.662364	+	0.285596i
$557$	−16.8579	+	4.51707i	−0.714293	+	0.191394i	−0.597624	−	0.801776i	$-0.703888\pi$
$557$	−16.8579	+	4.51707i	−0.714293	+	0.191394i	−0.116669	+	0.993171i	$0.537222\pi$
$558$	−0.508339	+	2.65531i	−0.0215197	+	0.112408i
$559$	−25.5412			−1.08028
$560$		0			0
$561$	4.78316			0.201945
$562$	−5.20683	+	27.1979i	−0.219637	+	1.14727i
$563$	−13.2928	+	3.56178i	−0.560223	+	0.150111i	−0.527809	−	0.849363i	$-0.676986\pi$
$563$	−13.2928	+	3.56178i	−0.560223	+	0.150111i	−0.0324143	+	0.999475i	$0.510320\pi$
$564$	−1.44199	−	3.34432i	−0.0607188	−	0.140821i
$565$	29.0832	+	7.79282i	1.22354	+	0.327846i
$566$	−0.0522831	−	0.718434i	−0.00219762	−	0.0301980i
$567$		0			0
$568$	23.0983	−	36.2387i	0.969181	−	1.52054i
$569$	−6.20226	+	3.58088i	−0.260012	+	0.150118i	−0.624340	−	0.781153i	$-0.714632\pi$
$569$	−6.20226	+	3.58088i	−0.260012	+	0.150118i	0.364328	+	0.931271i	$0.381299\pi$
$570$	−3.68463	+	7.60923i	−0.154332	+	0.318716i
$571$	−8.75442	−	32.6720i	−0.366361	−	1.36728i	−0.865566	−	0.500795i	$-0.833041\pi$
$571$	−8.75442	−	32.6720i	−0.366361	−	1.36728i	0.499205	−	0.866484i	$-0.333625\pi$
$572$	13.1898	−	10.4258i	0.551491	−	0.435926i
$573$	−0.960934	−	0.960934i	−0.0401436	−	0.0401436i
$574$		0			0
$575$	−0.0559884			−0.00233488
$576$	−18.8809	−	13.2335i	−0.786706	−	0.551395i
$577$	−12.0285	+	20.8339i	−0.500752	+	0.867328i	0.499247	+	0.866460i	$0.333610\pi$
$577$	−12.0285	+	20.8339i	−0.500752	+	0.867328i	−1.00000		0.000868882i	$0.999723\pi$
$578$	4.98995	+	14.3596i	0.207555	+	0.597281i
$579$	0.0789751	−	0.294739i	0.00328209	−	0.0122489i
$580$	−6.35426	−	43.4265i	−0.263846	−	1.80319i
$581$		0			0
$582$	−8.47350	+	0.616648i	−0.351238	+	0.0255609i
$583$	−2.06583	+	1.19271i	−0.0855580	+	0.0493969i
$584$	6.29008	+	12.0899i	0.260286	+	0.500284i
$585$	18.7964	+	10.8521i	0.777135	+	0.448679i
$586$	−22.2119	+	15.0739i	−0.917567	+	0.622695i
$587$	−1.63189	+	1.63189i	−0.0673551	+	0.0673551i	−0.739982	−	0.672627i	$-0.765166\pi$
$587$	−1.63189	+	1.63189i	−0.0673551	+	0.0673551i	0.672627	+	0.739982i	$0.265166\pi$
$588$		0			0
$589$	−3.44703	−	3.44703i	−0.142032	−	0.142032i
$590$	6.04882	−	31.5960i	0.249026	−	1.30079i
$591$	1.17499	−	2.03514i	0.0483326	−	0.0837145i
$592$	−2.19204	−	3.55627i	−0.0900923	−	0.146162i
$593$	−4.25167	−	7.36410i	−0.174595	−	0.302408i	0.765426	−	0.643524i	$-0.222528\pi$
$593$	−4.25167	−	7.36410i	−0.174595	−	0.302408i	−0.940021	+	0.341116i	$0.889195\pi$
$594$	−5.71454	−	4.93923i	−0.234471	−	0.202659i
$595$		0			0
$596$	4.79278	+	3.56923i	0.196320	+	0.146201i
$597$	−2.90196	−	0.777577i	−0.118769	−	0.0318241i
$598$	−0.370235	−	0.179279i	−0.0151400	−	0.00733128i
$599$	10.0144	+	5.78179i	0.409176	+	0.236238i	0.690435	−	0.723394i	$-0.257419\pi$
$599$	10.0144	+	5.78179i	0.409176	+	0.236238i	−0.281260	+	0.959632i	$0.590752\pi$
$600$	0.401379	+	0.438230i	0.0163862	+	0.0178907i
$601$		−	4.27752i		−	0.174484i	−0.996187	−	0.0872418i	$-0.972195\pi$
$601$		−	4.27752i		−	0.174484i	0.996187	−	0.0872418i	$-0.0278053\pi$
$602$		0			0
$603$	19.0638	−	19.0638i	0.776337	−	0.776337i
$604$	−27.0948	−	34.2778i	−1.10247	−	1.39474i
$605$	9.16923	−	2.45689i	0.372782	−	0.0998867i
$606$	2.55630	+	7.35627i	0.103842	+	0.298828i
$607$	−0.381118	−	0.660116i	−0.0154691	−	0.0267933i	0.858187	−	0.513337i	$-0.171591\pi$
$607$	−0.381118	−	0.660116i	−0.0154691	−	0.0267933i	−0.873656	+	0.486544i	$0.838257\pi$
$608$	38.8620	−	14.7712i	1.57606	−	0.599050i
$609$		0			0
$610$	4.74691	−	5.49203i	0.192197	−	0.222366i
$611$	4.36335	−	16.2842i	0.176522	−	0.658790i
$612$	11.2151	−	28.2174i	0.453342	−	1.14062i
$613$	6.60873	+	24.6641i	0.266924	+	0.996174i	0.961062	+	0.276332i	$0.0891191\pi$
$613$	6.60873	+	24.6641i	0.266924	+	0.996174i	−0.694138	+	0.719842i	$0.744214\pi$
$614$	−20.3970	−	30.0558i	−0.823155	−	1.21295i
$615$		−	1.98194i		−	0.0799195i
$616$		0			0
$617$		−	34.9141i		−	1.40559i	−0.711392	−	0.702795i	$-0.751935\pi$
$617$		−	34.9141i		−	1.40559i	0.711392	−	0.702795i	$-0.248065\pi$
$618$	4.91008	−	3.33216i	0.197512	−	0.134039i
$619$	7.70066	+	28.7392i	0.309516	+	1.15513i	0.928988	+	0.370109i	$0.120680\pi$
$619$	7.70066	+	28.7392i	0.309516	+	1.15513i	−0.619473	+	0.785018i	$0.712654\pi$
$620$	−2.88580	+	1.24429i	−0.115896	+	0.0499718i
$621$	−0.0478314	+	0.178509i	−0.00191941	+	0.00716333i
$622$	−33.5587	−	29.0057i	−1.34558	−	1.16302i
$623$		0			0
$624$	1.25096	+	4.18313i	0.0500783	+	0.167459i
$625$	−13.8425	−	23.9760i	−0.553701	−	0.959038i
$626$	17.9511	−	6.23799i	0.717470	−	0.249320i
$627$	6.44591	−	1.72718i	0.257425	−	0.0689768i
$628$	5.83440	+	0.682848i	0.232818	+	0.0272486i
$629$	3.89023	−	3.89023i	0.155114	−	0.155114i
$630$		0			0
$631$		−	4.08175i		−	0.162492i	−0.996694	−	0.0812460i	$-0.974110\pi$
$631$		−	4.08175i		−	0.162492i	0.996694	−	0.0812460i	$-0.0258900\pi$
$632$	−1.37175	+	31.2539i	−0.0545654	+	1.24321i
$633$	−3.58675	−	2.07081i	−0.142561	−	0.0823074i
$634$	14.5300	−	30.0064i	0.577061	−	1.19171i
$635$	41.9322	+	11.2357i	1.66403	+	0.445875i
$636$	−0.0896888	−	0.612953i	−0.00355639	−	0.0243052i
$637$		0			0
$638$	−22.6535	+	26.2095i	−0.896862	+	1.03764i
$639$	−21.8948	−	37.9228i	−0.866143	−	1.50020i
$640$	0.404134	−	26.7985i	0.0159748	−	1.05930i
$641$	−1.79183	+	3.10354i	−0.0707730	+	0.122582i	−0.899240	−	0.437455i	$-0.855880\pi$
$641$	−1.79183	+	3.10354i	−0.0707730	+	0.122582i	0.828467	+	0.560037i	$0.189213\pi$
$642$	−3.60199	−	0.689573i	−0.142159	−	0.0272153i
$643$	−15.8733	−	15.8733i	−0.625982	−	0.625982i	0.321072	−	0.947055i	$-0.395957\pi$
$643$	−15.8733	−	15.8733i	−0.625982	−	0.625982i	−0.947055	+	0.321072i	$0.895957\pi$
$644$		0			0
$645$	−4.62128	+	4.62128i	−0.181963	+	0.181963i
$646$	30.7449	+	45.3039i	1.20964	+	1.78246i
$647$	−22.2411	−	12.8409i	−0.874388	−	0.504828i	−0.00558405	−	0.999984i	$-0.501777\pi$
$647$	−22.2411	−	12.8409i	−0.874388	−	0.504828i	−0.868804	+	0.495156i	$0.835111\pi$
$648$	−19.9547	+	10.3819i	−0.783894	+	0.407841i
$649$	−21.9906	+	12.6963i	−0.863206	+	0.498372i
$650$	0.199663	+	2.74361i	0.00783142	+	0.107613i
$651$		0			0
$652$	−11.8410	+	15.9001i	−0.463729	+	0.622697i
$653$	7.91347	−	29.5335i	0.309678	−	1.15573i	−0.619165	−	0.785261i	$-0.712529\pi$
$653$	7.91347	−	29.5335i	0.309678	−	1.15573i	0.928843	−	0.370473i	$-0.120805\pi$
$654$	2.01151	−	0.698998i	0.0786563	−	0.0273330i
$655$	−11.6929	+	20.2527i	−0.456880	+	0.791339i
$656$	−6.69041	+	7.08708i	−0.261217	+	0.276704i
$657$	13.8869			0.541780
$658$		0			0
$659$	3.02967	+	3.02967i	0.118019	+	0.118019i	0.763650	−	0.645631i	$-0.223405\pi$
$659$	3.02967	+	3.02967i	0.118019	+	0.118019i	−0.645631	+	0.763650i	$0.723405\pi$
$660$	0.500088	−	4.27286i	0.0194659	−	0.166321i
$661$	9.98584	+	37.2677i	0.388404	+	1.44954i	0.832730	+	0.553679i	$0.186777\pi$
$661$	9.98584	+	37.2677i	0.388404	+	1.44954i	−0.444326	+	0.895865i	$0.646557\pi$
$662$	10.6928	+	5.17778i	0.415587	+	0.201240i
$663$	−4.97965	+	2.87500i	−0.193393	+	0.111656i
$664$	−9.47131	−	42.7687i	−0.367558	−	1.65975i
$665$		0			0
$666$	−4.24561	+	0.308969i	−0.164514	+	0.0119723i
$667$	0.818724	+	0.219376i	0.0317011	+	0.00849429i
$668$	12.5769	−	31.6439i	0.486616	−	1.22434i
$669$	−8.40162	+	2.25121i	−0.324825	+	0.0870367i
$670$	30.7800	+	5.89260i	1.18914	+	0.227651i
$671$	−5.72987			−0.221199
$672$		0			0
$673$	19.2447			0.741828			0.370914	−	0.928667i	$-0.379044\pi$
$673$	19.2447			0.741828			0.370914	+	0.928667i	$0.379044\pi$
$674$	8.02492	+	1.53631i	0.309108	+	0.0591765i
$675$	1.19374	−	0.319863i	0.0459472	−	0.0123115i
$676$	2.13810	−	5.37952i	0.0822346	−	0.206905i
$677$	−26.7807	−	7.17588i	−1.02927	−	0.275791i	−0.295608	−	0.955309i	$-0.595522\pi$
$677$	−26.7807	−	7.17588i	−1.02927	−	0.275791i	−0.733659	+	0.679518i	$0.762189\pi$
$678$	6.15563	−	0.447968i	0.236406	−	0.0172041i
$679$		0			0
$680$	34.4612	−	7.63157i	1.32152	−	0.292657i
$681$	0.220771	−	0.127462i	0.00845996	−	0.00488436i
$682$	2.23259	+	1.08109i	0.0854902	+	0.0413970i
$683$	−0.564208	−	2.10565i	−0.0215888	−	0.0805705i	0.954291	−	0.298879i	$-0.0966127\pi$
$683$	−0.564208	−	2.10565i	−0.0215888	−	0.0805705i	−0.975880	+	0.218309i	$0.929946\pi$
$684$	4.92452	−	42.0762i	0.188294	−	1.60882i
$685$	28.2502	+	28.2502i	1.07939	+	1.07939i
$686$		0			0
$687$	−5.52058			−0.210623
$688$	32.1249	−	0.924911i	1.22475	−	0.0352619i
$689$	1.43380	−	2.48341i	0.0546233	−	0.0946103i
$690$	−0.0994258	+	0.0345504i	−0.00378507	+	0.00131531i
$691$	7.61200	−	28.4084i	0.289574	−	1.08071i	−0.655858	−	0.754885i	$-0.727693\pi$
$691$	7.61200	−	28.4084i	0.289574	−	1.08071i	0.945432	−	0.325820i	$-0.105641\pi$
$692$	−0.292503	+	0.392775i	−0.0111193	+	0.0149310i
$693$		0			0
$694$	1.24353	+	17.0876i	0.0472037	+	0.648637i
$695$	−17.4468	+	10.0729i	−0.661795	+	0.382087i
$696$	−4.15231	−	7.98098i	−0.157393	−	0.302518i
$697$	−11.1156	−	6.41759i	−0.421033	−	0.243083i
$698$	−20.9091	−	30.8104i	−0.791422	−	1.16619i
$699$	2.61138	−	2.61138i	0.0987713	−	0.0987713i
$700$		0			0
$701$	28.3466	+	28.3466i	1.07064	+	1.07064i	0.997308	+	0.0733289i	$0.0233623\pi$
$701$	28.3466	+	28.3466i	1.07064	+	1.07064i	0.0733289	+	0.997308i	$0.476638\pi$
$702$	8.91810	+	1.70730i	0.336592	+	0.0644380i
$703$	3.83783	−	6.64732i	0.144747	−	0.250708i
$704$	−16.2121	+	13.5909i	−0.611015	+	0.512225i
$705$	−2.15689	−	3.73585i	−0.0812333	−	0.140700i
$706$	−21.0735	+	24.3814i	−0.793112	+	0.917607i
$707$		0			0
$708$	−0.954729	−	6.52484i	−0.0358809	−	0.245218i
$709$	29.2811	+	7.84584i	1.09967	+	0.294657i	0.762632	−	0.646833i	$-0.223907\pi$
$709$	29.2811	+	7.84584i	1.09967	+	0.294657i	0.337042	+	0.941490i	$0.390574\pi$
$710$	22.1841	−	45.8130i	0.832554	−	1.71933i
$711$	27.6068	+	15.9388i	1.03534	+	0.597752i
$712$	6.41698	+	0.281646i	0.240487	+	0.0105551i
$713$		−	0.0606921i		−	0.00227294i
$714$		0			0
$715$	14.0815	−	14.0815i	0.526617	−	0.526617i
$716$	−0.536870	−	0.0628343i	−0.0200638	−	0.00234823i
$717$	−0.995146	+	0.266649i	−0.0371644	+	0.00995817i
$718$	−2.98169	+	1.03613i	−0.111276	+	0.0386682i
$719$	−0.695395	−	1.20446i	−0.0259338	−	0.0449187i	0.852767	−	0.522291i	$-0.174923\pi$
$719$	−0.695395	−	1.20446i	−0.0259338	−	0.0449187i	−0.878701	+	0.477372i	$0.841589\pi$
$720$	−24.0344	−	12.9687i	−0.895710	−	0.483316i
$721$		0			0
$722$	37.4628	+	32.3801i	1.39422	+	1.20506i
$723$	−2.00821	+	7.49473i	−0.0746861	+	0.278732i
$724$	1.93691	−	0.835148i	0.0719845	−	0.0310380i
$725$	−1.46703	−	5.47505i	−0.0544843	−	0.203338i
$726$	1.61010	−	1.09267i	0.0597563	−	0.0405529i
$727$			19.9346i			0.739332i	0.929165	+	0.369666i	$0.120528\pi$
$727$			19.9346i			0.739332i	−0.929165	+	0.369666i	$0.879472\pi$
$728$		0			0
$729$			20.8402i			0.771858i
$730$	9.06456	+	13.3570i	0.335494	+	0.494364i
$731$	10.9543	+	40.8820i	0.405159	+	1.51207i
$732$	0.549597	−	1.38280i	0.0203137	−	0.0511098i
$733$	3.59639	−	13.4219i	0.132836	−	0.495750i	−0.867162	−	0.498027i	$-0.834058\pi$
$733$	3.59639	−	13.4219i	0.132836	−	0.495750i	0.999997	+	0.00227682i	$0.000724735\pi$
$734$	−19.0887	+	22.0851i	−0.704578	+	0.815176i
$735$		0			0
$736$	0.472161	+	0.212084i	0.0174041	+	0.00781753i
$737$	−12.3684	−	21.4226i	−0.455595	−	0.789113i
$738$	3.25984	+	9.38087i	0.119997	+	0.345315i
$739$	−21.6421	+	5.79897i	−0.796116	+	0.213319i	−0.633878	−	0.773433i	$-0.718538\pi$
$739$	−21.6421	+	5.79897i	−0.796116	+	0.213319i	−0.162238	+	0.986752i	$0.551871\pi$
$740$	−3.06846	−	3.88192i	−0.112799	−	0.142702i
$741$	−5.67255	+	5.67255i	−0.208386	+	0.208386i
$742$		0			0
$743$			40.2309i			1.47593i	0.674839	+	0.737965i	$0.264213\pi$
$743$			40.2309i			1.47593i	−0.674839	+	0.737965i	$0.735787\pi$
$744$	−0.475046	+	0.435099i	−0.0174160	+	0.0159515i
$745$	6.12987	+	3.53908i	0.224581	+	0.129662i
$746$	−29.8289	−	14.4441i	−1.09212	−	0.528836i
$747$	−43.1152	−	11.5527i	−1.57750	−	0.422690i
$748$	−22.3448	−	16.6404i	−0.817005	−	0.608432i
$749$		0			0
$750$	−3.81904	−	3.30089i	−0.139452	−	0.120532i
$751$	−4.02133	−	6.96514i	−0.146740	−	0.254162i	0.783281	−	0.621668i	$-0.213545\pi$
$751$	−4.02133	−	6.96514i	−0.146740	−	0.254162i	−0.930021	+	0.367507i	$0.880212\pi$
$752$	−4.89837	+	20.6397i	−0.178625	+	0.752654i
$753$	−0.592384	+	1.02604i	−0.0215877	+	0.0373909i
$754$	7.83046	−	40.9024i	0.285169	−	1.48958i
$755$	−36.5951	−	36.5951i	−1.33183	−	1.33183i
$756$		0			0
$757$	12.7497	−	12.7497i	0.463394	−	0.463394i	−0.436372	−	0.899766i	$-0.643737\pi$
$757$	12.7497	−	12.7497i	0.463394	−	0.463394i	0.899766	+	0.436372i	$0.143737\pi$
$758$	−8.93141	+	6.06119i	−0.324404	+	0.220152i
$759$	0.0719520	+	0.0415415i	0.00261169	+	0.00150786i
$760$	43.6850	−	22.7283i	1.58462	−	0.824441i
$761$	17.9392	−	10.3572i	0.650297	−	0.375449i	−0.138273	−	0.990394i	$-0.544155\pi$
$761$	17.9392	−	10.3572i	0.650297	−	0.375449i	0.788570	+	0.614945i	$0.210822\pi$
$762$	8.87520	−	0.645881i	0.321515	−	0.0233978i
$763$		0			0
$764$	1.14601	+	7.83209i	0.0414612	+	0.283355i
$765$	9.30864	−	34.7403i	0.336555	−	1.25604i
$766$	−8.63401	−	24.8461i	−0.311959	−	0.897728i
$767$	15.2626	−	26.4357i	0.551102	−	0.954536i
$768$	−1.72489	−	5.21610i	−0.0622416	−	0.188220i
$769$	24.5641			0.885805			0.442902	−	0.896570i	$-0.353949\pi$
$769$	24.5641			0.885805			0.442902	+	0.896570i	$0.353949\pi$
$770$		0			0
$771$	4.48513	+	4.48513i	0.161528	+	0.161528i
$772$	−1.39432	+	1.10214i	−0.0501826	+	0.0396668i
$773$	−9.24937	−	34.5191i	−0.332677	−	1.24157i	−0.906366	−	0.422494i	$-0.861155\pi$
$773$	−9.24937	−	34.5191i	−0.332677	−	1.24157i	0.573689	−	0.819073i	$-0.305512\pi$
$774$	14.2724	−	29.4743i	0.513010	−	1.05943i
$775$	−0.351490	+	0.202933i	−0.0126259	+	0.00728956i
$776$	41.7297	+	26.5982i	1.49801	+	0.954819i
$777$		0			0
$778$	0.400325	+	5.50096i	0.0143524	+	0.197219i
$779$	−17.2970	−	4.63472i	−0.619730	−	0.166056i
$780$	2.04765	+	4.74897i	0.0733175	+	0.170040i
$781$	−38.8090	+	10.3988i	−1.38870	+	0.372100i
$782$	−0.128170	+	0.669498i	−0.00458336	+	0.0239412i
$783$	−18.7095			−0.668624
$784$		0			0
$785$	6.95785			0.248336
$786$	−0.901355	+	4.70823i	−0.0321503	+	0.167937i
$787$	−18.3945	+	4.92879i	−0.655693	+	0.175693i	−0.571302	−	0.820740i	$-0.693561\pi$
$787$	−18.3945	+	4.92879i	−0.655693	+	0.175693i	−0.0843917	+	0.996433i	$0.526895\pi$
$788$	−12.5692	+	5.41953i	−0.447758	+	0.193063i
$789$	−3.20647	−	0.859172i	−0.114153	−	0.0305873i
$790$	2.68952	+	36.9572i	0.0956887	+	1.31488i
$791$		0			0
$792$	4.66089	+	21.0467i	0.165617	+	0.747863i
$793$	5.96525	−	3.44404i	0.211832	−	0.122301i
$794$	8.56721	−	17.6924i	0.304039	−	0.627880i
$795$	−0.189910	−	0.708755i	−0.00673542	−	0.0251369i
$796$	10.8515	+	13.7282i	0.384620	+	0.486585i
$797$	3.26569	+	3.26569i	0.115677	+	0.115677i	0.762576	−	0.646899i	$-0.223934\pi$
$797$	3.26569	+	3.26569i	0.115677	+	0.115677i	−0.646899	+	0.762576i	$0.723934\pi$
$798$		0			0
$799$	−27.9364			−0.988317
$800$	−0.350482	−	3.44359i	−0.0123914	−	0.121749i
$801$	3.27252	−	5.66818i	0.115629	−	0.200275i
$802$	−4.98969	−	14.3589i	−0.176192	−	0.507029i
$803$	3.29777	−	12.3075i	0.116376	−	0.434321i
$804$	6.35632	−	0.930072i	0.224170	−	0.0328011i
$805$		0			0
$806$	−2.97411	+	0.216437i	−0.104758	+	0.00762366i
$807$	7.18858	−	4.15033i	0.253050	−	0.146098i
$808$	13.6502	−	43.2584i	0.480213	−	1.52182i
$809$	−25.2648	−	14.5866i	−0.888263	−	0.512839i	−0.0148891	−	0.999889i	$-0.504740\pi$
$809$	−25.2648	−	14.5866i	−0.888263	−	0.512839i	−0.873374	+	0.487050i	$0.838073\pi$
$810$	−22.0460	+	14.9613i	−0.774619	+	0.525686i
$811$	−32.8375	+	32.8375i	−1.15308	+	1.15308i	−0.167148	+	0.985932i	$0.553456\pi$
$811$	−32.8375	+	32.8375i	−1.15308	+	1.15308i	−0.985932	+	0.167148i	$0.946544\pi$
$812$		0			0
$813$	6.95471	+	6.95471i	0.243912	+	0.243912i
$814$	−0.734392	+	3.83610i	−0.0257404	+	0.134455i
$815$	−11.7410	+	20.3359i	−0.411268	+	0.712337i
$816$	6.15912	−	3.79640i	0.215612	−	0.132901i
$817$	29.5246	+	51.1381i	1.03293	+	1.78909i
$818$	9.27865	+	8.01978i	0.324421	+	0.280405i
$819$		0			0
$820$	−6.89507	+	9.25873i	−0.240786	+	0.323329i
$821$	−29.8798	−	8.00627i	−1.04281	−	0.279421i	−0.303534	−	0.952821i	$-0.598167\pi$
$821$	−29.8798	−	8.00627i	−1.04281	−	0.279421i	−0.739279	+	0.673400i	$0.764833\pi$
$822$	7.37083	+	3.56919i	0.257087	+	0.124490i
$823$	24.4402	+	14.1106i	0.851932	+	0.491863i	0.861302	−	0.508093i	$-0.169649\pi$
$823$	24.4402	+	14.1106i	0.851932	+	0.491863i	−0.00937002	+	0.999956i	$0.502983\pi$
$824$	−34.5301	−	1.51555i	−1.20291	−	0.0527966i
$825$		−	0.555600i		−	0.0193435i
$826$		0			0
$827$	−21.9283	+	21.9283i	−0.762522	+	0.762522i	−0.976778	−	0.214256i	$-0.931267\pi$
$827$	−21.9283	+	21.9283i	−0.762522	+	0.762522i	0.214256	+	0.976778i	$0.431267\pi$
$828$	0.413772	−	0.327066i	0.0143796	−	0.0113663i
$829$	1.36524	−	0.365814i	0.0474166	−	0.0127052i	−0.235033	−	0.971987i	$-0.575520\pi$
$829$	1.36524	−	0.365814i	0.0474166	−	0.0127052i	0.282449	+	0.959282i	$0.408853\pi$
$830$	−17.0312	−	49.0108i	−0.591162	−	1.70119i
$831$	2.82906	+	4.90007i	0.0981389	+	0.169982i
$832$	8.70901	−	23.8937i	0.301931	−	0.828366i
$833$		0			0
$834$	−2.70041	+	3.12430i	−0.0935076	+	0.108186i
$835$	10.4390	−	38.9589i	0.361257	−	1.34823i
$836$	−36.1211	−	14.3564i	−1.24928	−	0.496527i
$837$	0.346735	+	1.29403i	0.0119849	+	0.0447283i
$838$	−4.45060	−	6.55814i	−0.153743	−	0.226547i
$839$			4.25867i			0.147026i	0.997294	+	0.0735128i	$0.0234210\pi$
$839$			4.25867i			0.147026i	−0.997294	+	0.0735128i	$0.976579\pi$
$840$		0			0
$841$			56.8104i			1.95898i
$842$	26.8108	−	18.1948i	0.923960	−	0.627034i
$843$	1.74018	+	6.49443i	0.0599349	+	0.223680i
$844$	9.55143	+	22.1520i	0.328774	+	0.762504i
$845$	1.77465	−	6.62309i	0.0610499	−	0.227841i
$846$	16.3536	+	14.1348i	0.562248	+	0.485965i
$847$		0			0
$848$	−1.71345	+	3.17546i	−0.0588400	+	0.109046i
$849$	−0.0874479	−	0.151464i	−0.00300121	−	0.00519824i
$850$	4.30586	−	1.49628i	0.147690	−	0.0513221i
$851$	0.0923063	−	0.0247334i	0.00316422	−	0.000847850i
$852$	1.21290	−	10.3633i	0.0415533	−	0.355041i
$853$	−16.5250	+	16.5250i	−0.565806	+	0.565806i	−0.930951	−	0.365144i	$-0.881020\pi$
$853$	−16.5250	+	16.5250i	−0.565806	+	0.565806i	0.365144	+	0.930951i	$0.381020\pi$
$854$		0			0
$855$		−	50.1783i		−	1.71606i
$856$	14.4279	+	15.7525i	0.493134	+	0.538409i
$857$	22.7948	+	13.1606i	0.778655	+	0.449556i	0.835953	−	0.548801i	$-0.184915\pi$
$857$	22.7948	+	13.1606i	0.778655	+	0.449556i	−0.0572986	+	0.998357i	$0.518249\pi$
$858$	1.77908	−	3.67402i	0.0607367	−	0.125429i
$859$	46.9949	+	12.5923i	1.60345	+	0.429642i	0.946081	−	0.323930i	$-0.105004\pi$
$859$	46.9949	+	12.5923i	1.60345	+	0.429642i	0.657365	+	0.753572i	$0.271671\pi$
$860$	37.6657	−	5.51133i	1.28439	−	0.187935i
$861$		0			0
$862$	−0.522594	+	0.604627i	−0.0177996	+	0.0205937i
$863$	4.94765	+	8.56957i	0.168420	+	0.291712i	0.937864	−	0.347002i	$-0.112800\pi$
$863$	4.94765	+	8.56957i	0.168420	+	0.291712i	−0.769445	+	0.638714i	$0.779467\pi$
$864$	−11.2787	−	1.82444i	−0.383709	−	0.0620687i
$865$	−0.290032	+	0.502351i	−0.00986139	+	0.0170804i
$866$	−20.6888	−	3.96071i	−0.703034	−	0.134590i
$867$	2.60993	+	2.60993i	0.0886379	+	0.0886379i
$868$		0			0
$869$	20.6819	−	20.6819i	0.701584	−	0.701584i
$870$	−5.98384	−	8.81743i	−0.202871	−	0.298939i
$871$	25.7529	+	14.8684i	0.872604	+	0.503798i
$872$	−11.8286	−	3.73254i	−0.400569	−	0.126400i
$873$	43.6690	−	25.2123i	1.47797	−	0.853308i
$874$	0.0690270	+	0.948515i	0.00233487	+	0.0320840i
$875$		0			0
$876$	2.65387	+	1.97636i	0.0896659	+	0.0667751i
$877$	−8.79678	+	32.8300i	−0.297046	+	1.10859i	0.642533	+	0.766258i	$0.277884\pi$
$877$	−8.79678	+	32.8300i	−0.297046	+	1.10859i	−0.939579	+	0.342333i	$0.888783\pi$
$878$	35.2470	−	12.2483i	1.18953	−	0.413360i
$879$	−3.25882	+	5.64444i	−0.109917	+	0.190382i
$880$	−17.2012	+	18.2211i	−0.579854	+	0.614233i
$881$	−25.5121			−0.859526			−0.429763	−	0.902942i	$-0.641403\pi$
$881$	−25.5121			−0.859526			−0.429763	+	0.902942i	$0.641403\pi$
$882$		0			0
$883$	22.6764	+	22.6764i	0.763120	+	0.763120i	0.976885	−	0.213765i	$-0.0685727\pi$
$883$	22.6764	+	22.6764i	0.763120	+	0.763120i	−0.213765	+	0.976885i	$0.568573\pi$
$884$	33.2646	+	3.89323i	1.11881	+	0.130944i
$885$	−2.02158	−	7.54463i	−0.0679546	−	0.253610i
$886$	−14.0407	−	6.79893i	−0.471706	−	0.228415i
$887$	−46.9094	+	27.0831i	−1.57506	+	0.909362i	−0.579529	+	0.814952i	$0.696763\pi$
$887$	−46.9094	+	27.0831i	−1.57506	+	0.909362i	−0.995533	+	0.0944105i	$0.969903\pi$
$888$	−0.855333	−	0.545183i	−0.0287031	−	0.0182951i
$889$		0			0
$890$	7.58799	−	0.552206i	0.254350	−	0.0185100i
$891$	20.3138	+	5.44305i	0.680536	+	0.182349i
$892$	47.0804	+	18.7122i	1.57637	+	0.626530i
$893$	−37.6478	+	10.0877i	−1.25983	+	0.337572i
$894$	1.42504	+	0.272812i	0.0476603	+	0.00912420i
$895$	−0.640248			−0.0214011
$896$		0			0
$897$	−0.0998770			−0.00333479
$898$	−43.8717	−	8.39890i	−1.46402	−	0.280275i
$899$	5.93501	−	1.59028i	0.197944	−	0.0530389i
$900$	−3.27767	−	1.30271i	−0.109256	−	0.0434238i
$901$	−4.58994	−	1.22987i	−0.152913	−	0.0409729i
$902$	9.08804	−	0.661371i	0.302599	−	0.0220212i
$903$		0			0
$904$	−30.3148	−	19.3224i	−1.00826	−	0.642654i
$905$	2.16367	−	1.24919i	0.0719227	−	0.0415246i
$906$	−9.54811	−	4.62349i	−0.317215	−	0.153605i
$907$	3.40663	+	12.7137i	0.113115	+	0.422152i	0.999139	−	0.0414881i	$-0.0132099\pi$
$907$	3.40663	+	12.7137i	0.113115	+	0.422152i	−0.886024	+	0.463640i	$0.846543\pi$
$908$	−1.47478	−	0.172605i	−0.0489421	−	0.00572810i
$909$	−32.6837	−	32.6837i	−1.08405	−	1.08405i
$910$		0			0
$911$	24.5412			0.813085			0.406543	−	0.913632i	$-0.366734\pi$
$911$	24.5412			0.813085			0.406543	+	0.913632i	$0.366734\pi$
$912$	6.92932	−	7.34016i	0.229453	−	0.243057i
$913$	−20.4774	+	35.4679i	−0.677704	+	1.17382i
$914$	−10.3081	+	3.58207i	−0.340963	+	0.118484i
$915$	0.456172	−	1.70246i	0.0150806	−	0.0562815i
$916$	25.7897	+	19.2058i	0.852114	+	0.634578i
$917$		0			0
$918$	−1.09210	−	15.0068i	−0.0360446	−	0.495298i
$919$	−23.1901	+	13.3888i	−0.764972	+	0.441657i	−0.831078	−	0.556156i	$-0.812276\pi$
$919$	−23.1901	+	13.3888i	−0.764972	+	0.441657i	0.0661060	+	0.997813i	$0.478942\pi$
$920$	0.584671	+	0.184494i	0.0192760	+	0.00608257i
$921$	−7.63770	−	4.40963i	−0.251671	−	0.145302i
$922$	3.56833	+	5.25808i	0.117517	+	0.173166i
$923$	34.1528	−	34.1528i	1.12415	−	1.12415i
$924$		0			0
$925$	−0.451880	−	0.451880i	−0.0148577	−	0.0148577i
$926$	10.9858	+	2.10315i	0.361015	+	0.0691137i
$927$	−17.6096	+	30.5007i	−0.578375	+	1.00177i
$928$	−8.36771	+	51.7292i	−0.274683	+	1.69810i
$929$	12.9337	+	22.4019i	0.424342	+	0.734982i	0.996359	−	0.0852601i	$-0.0271721\pi$
$929$	12.9337	+	22.4019i	0.424342	+	0.734982i	−0.572017	+	0.820242i	$0.693839\pi$
$930$	−0.498956	+	0.577277i	−0.0163614	+	0.0189297i
$931$		0			0
$932$	−21.2840	+	3.11432i	−0.697181	+	0.102013i
$933$	−10.4028	−	2.78741i	−0.340571	−	0.0912558i
$934$	−14.5439	+	30.0351i	−0.475891	+	0.982777i
$935$	−28.5785	−	16.4998i	−0.934617	−	0.539601i
$936$	−17.5029	−	19.1098i	−0.572099	−	0.624624i
$937$			19.6850i			0.643080i	0.946896	+	0.321540i	$0.104200\pi$
$937$			19.6850i			0.643080i	−0.946896	+	0.321540i	$0.895800\pi$
$938$		0			0
$939$	3.26270	−	3.26270i	0.106474	−	0.106474i
$940$	−2.92079	+	24.9559i	−0.0952658	+	0.813972i
$941$	0.909688	−	0.243750i	0.0296550	−	0.00794603i	−0.243961	−	0.969785i	$-0.578447\pi$
$941$	0.909688	−	0.243750i	0.0296550	−	0.00794603i	0.273616	+	0.961839i	$0.411780\pi$
$942$	1.34723	−	0.468160i	0.0438950	−	0.0152535i
$943$	−0.111473	−	0.193077i	−0.00363005	−	0.00628744i
$944$	−18.2395	+	33.8025i	−0.593645	+	1.10018i
$945$		0			0
$946$	−22.7326	−	19.6484i	−0.739102	−	0.638825i
$947$	4.69782	−	17.5325i	0.152659	−	0.569730i	−0.846636	−	0.532173i	$-0.821376\pi$
$947$	4.69782	−	17.5325i	0.152659	−	0.569730i	0.999294	−	0.0375571i	$-0.0119576\pi$
$948$	3.00744	+	6.97495i	0.0976770	+	0.226536i
$949$	3.96437	+	14.7952i	0.128689	+	0.480273i
$950$	5.26239	−	3.57126i	0.170735	−	0.115867i
$951$		−	8.09471i		−	0.262489i
$952$		0			0
$953$		−	36.9302i		−	1.19629i	−0.801390	−	0.598143i	$-0.795906\pi$
$953$		−	36.9302i		−	1.19629i	0.801390	−	0.598143i	$-0.204094\pi$
$954$	2.06462	+	3.04230i	0.0668446	+	0.0984982i
$955$	2.42660	+	9.05621i	0.0785230	+	0.293052i
$956$	5.57653	+	2.21640i	0.180358	+	0.0716835i
$957$	−2.17698	+	8.12460i	−0.0703717	+	0.262631i
$958$	31.2864	−	36.1974i	1.01082	−	1.16949i
$959$		0			0
$960$	−2.74743	−	5.89894i	−0.0886729	−	0.190387i
$961$	15.2800	+	26.4658i	0.492904	+	0.853734i
$962$	−1.54119	−	4.43510i	−0.0496901	−	0.142993i
$963$	21.0249	−	5.63362i	0.677519	−	0.181541i
$964$	35.4552	−	28.0256i	1.14194	−	0.902642i
$965$	−1.48858	+	1.48858i	−0.0479192	+	0.0479192i
$966$		0			0
$967$		−	15.9039i		−	0.511436i	−0.966751	−	0.255718i	$-0.917688\pi$
$967$		−	15.9039i		−	0.511436i	0.966751	−	0.255718i	$-0.0823119\pi$
$968$	−11.3230	−	0.496974i	−0.363935	−	0.0159733i
$969$	11.5125	+	6.64675i	0.369835	+	0.213525i
$970$	52.7548	+	25.5455i	1.69385	+	0.820217i
$971$	−12.1746	−	3.26217i	−0.390701	−	0.104688i	0.0581203	−	0.998310i	$-0.481489\pi$
$971$	−12.1746	−	3.26217i	−0.390701	−	0.104688i	−0.448821	+	0.893622i	$0.648156\pi$
$972$	−10.5001	+	14.0996i	−0.336791	+	0.452245i
$973$		0			0
$974$	11.1475	+	9.63510i	0.357190	+	0.308728i
$975$	0.333953	+	0.578424i	0.0106951	+	0.0185244i
$976$	−7.37816	+	4.54781i	−0.236169	+	0.145572i
$977$	−20.7008	+	35.8548i	−0.662276	+	1.14710i	0.317740	+	0.948178i	$0.397076\pi$
$977$	−20.7008	+	35.8548i	−0.662276	+	1.14710i	−0.980016	+	0.198918i	$0.936257\pi$
$978$	−0.905059	+	4.72758i	−0.0289406	+	0.151171i
$979$	−4.24636	−	4.24636i	−0.135714	−	0.135714i
$980$		0			0
$981$	−8.93708	+	8.93708i	−0.285339	+	0.285339i
$982$	13.7089	−	9.30338i	0.437469	−	0.296883i
$983$	−1.97172	−	1.13838i	−0.0628882	−	0.0363085i	0.468226	−	0.883609i	$-0.344893\pi$
$983$	−1.97172	−	1.13838i	−0.0628882	−	0.0363085i	−0.531114	+	0.847300i	$0.678227\pi$
$984$	−0.712096	+	2.25667i	−0.0227008	+	0.0719401i
$985$	−14.0407	+	8.10640i	−0.447374	+	0.258291i
$986$	−68.8279	+	5.00886i	−2.19193	+	0.159515i
$987$		0			0
$988$	46.2341	−	6.76508i	1.47090	−	0.215226i
$989$	−0.190275	+	0.710116i	−0.00605039	+	0.0225804i
$990$	8.38115	+	24.1185i	0.266371	+	0.766536i
$991$	19.0720	−	33.0337i	0.605843	−	1.04935i	−0.386075	−	0.922468i	$-0.626169\pi$
$991$	19.0720	−	33.0337i	0.605843	−	1.04935i	0.991918	−	0.126883i	$-0.0404973\pi$
$992$	3.73289	−	0.379926i	0.118519	−	0.0120627i
$993$	2.88456			0.0915386
$994$		0			0
$995$	14.6564	+	14.6564i	0.464638	+	0.464638i
$996$	−6.59540	−	8.34387i	−0.208983	−	0.264385i
$997$	9.28031	+	34.6346i	0.293911	+	1.09689i	0.942079	+	0.335392i	$0.108869\pi$
$997$	9.28031	+	34.6346i	0.293911	+	1.09689i	−0.648168	+	0.761497i	$0.724465\pi$
$998$	7.46240	−	15.4108i	0.236218	−	0.487821i
$999$	−1.82678	+	1.05469i	−0.0577969	+	0.0333691i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.x.p.557.1		96
7.2	even	3	inner	784.2.x.p.765.14		96
7.3	odd	6		784.2.m.l.589.19	yes	48
7.4	even	3		784.2.m.l.589.20	yes	48
7.5	odd	6	inner	784.2.x.p.765.13		96
7.6	odd	2	inner	784.2.x.p.557.2		96
16.5	even	4	inner	784.2.x.p.165.14		96
112.5	odd	12	inner	784.2.x.p.373.2		96
112.37	even	12	inner	784.2.x.p.373.1		96
112.53	even	12		784.2.m.l.197.20	yes	48
112.69	odd	4	inner	784.2.x.p.165.13		96
112.101	odd	12		784.2.m.l.197.19	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
784.2.m.l.197.19	✓	48	112.101	odd	12
784.2.m.l.197.20	yes	48	112.53	even	12
784.2.m.l.589.19	yes	48	7.3	odd	6
784.2.m.l.589.20	yes	48	7.4	even	3
784.2.x.p.165.13		96	112.69	odd	4	inner
784.2.x.p.165.14		96	16.5	even	4	inner
784.2.x.p.373.1		96	112.37	even	12	inner
784.2.x.p.373.2		96	112.5	odd	12	inner
784.2.x.p.557.1		96	1.1	even	1	trivial
784.2.x.p.557.2		96	7.6	odd	2	inner
784.2.x.p.765.13		96	7.5	odd	6	inner
784.2.x.p.765.14		96	7.2	even	3	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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.38899 - 0.265911i) q^{2} +(-0.331669 + 0.0888704i) q^{3} +(1.85858 + 0.738696i) q^{4} +(2.28822 + 0.613128i) q^{5} +(0.484316 - 0.0352455i) q^{6} +(-2.38512 - 1.52026i) q^{8} +(-2.49597 + 1.44105i) q^{9} +(-3.01528 - 1.46009i) q^{10} +(0.684421 + 2.55430i) q^{11} +(-0.682082 - 0.0798296i) q^{12} +(-2.24784 - 2.24784i) q^{13} -0.813421 q^{15} +(2.90866 + 2.74586i) q^{16} +(-2.63388 + 4.56202i) q^{17} +(3.85007 - 1.33789i) q^{18} +(-1.90217 + 7.09898i) q^{19} +(3.79994 + 2.82985i) q^{20} +(-0.271438 - 3.72988i) q^{22} +(-0.0792419 + 0.0457503i) q^{23} +(0.926177 + 0.292256i) q^{24} +(0.529913 + 0.305946i) q^{25} +(2.52450 + 3.71995i) q^{26} +(1.42816 - 1.42816i) q^{27} +(-6.55020 - 6.55020i) q^{29} +(1.12983 + 0.216298i) q^{30} +(-0.331648 + 0.574432i) q^{31} +(-3.30994 - 4.58741i) q^{32} +(-0.454002 - 0.786355i) q^{33} +(4.87153 - 5.63622i) q^{34} +(-5.70346 + 0.834544i) q^{36} +(-1.00881 - 0.270309i) q^{37} +(4.52979 - 9.35460i) q^{38} +(0.945305 + 0.545772i) q^{39} +(-4.52558 - 4.94108i) q^{40} +2.43655i q^{41} +(5.68128 - 5.68128i) q^{43} +(-0.614795 + 5.25295i) q^{44} +(-6.59488 + 1.76709i) q^{45} +(0.122232 - 0.0424754i) q^{46} +(2.65163 + 4.59276i) q^{47} +(-1.20874 - 0.652221i) q^{48} +(-0.654689 - 0.565865i) q^{50} +(0.468149 - 1.74715i) q^{51} +(-2.51732 - 5.83827i) q^{52} +(0.233471 + 0.871326i) q^{53} +(-2.36347 + 1.60394i) q^{54} +6.26444i q^{55} -2.52356i q^{57} +(7.35639 + 10.8399i) q^{58} +(2.48528 + 9.27519i) q^{59} +(-1.51181 - 0.600871i) q^{60} +(-0.560807 + 2.09296i) q^{61} +(0.613404 - 0.709691i) q^{62} +(3.37762 + 7.25201i) q^{64} +(-3.76535 - 6.52177i) q^{65} +(0.421504 + 1.21296i) q^{66} +(-9.03564 + 2.42109i) q^{67} +(-8.26524 + 6.53325i) q^{68} +(0.0222162 - 0.0222162i) q^{69} +15.1936i q^{71} +(8.14396 + 0.357444i) q^{72} +(-4.17280 - 2.40917i) q^{73} +(1.32934 + 0.643709i) q^{74} +(-0.202945 - 0.0543790i) q^{75} +(-8.77932 + 11.7889i) q^{76} +(-1.16789 - 1.00944i) q^{78} +(-5.53028 - 9.57872i) q^{79} +(4.97209 + 8.06651i) q^{80} +(3.97639 - 6.88731i) q^{81} +(0.647906 - 3.38434i) q^{82} +(10.9512 + 10.9512i) q^{83} +(-8.82402 + 8.82402i) q^{85} +(-9.40196 + 6.38052i) q^{86} +(2.75462 + 1.59038i) q^{87} +(2.25076 - 7.13281i) q^{88} +(-1.96668 + 1.13547i) q^{89} +(9.63011 - 0.700819i) q^{90} +(-0.181073 + 0.0264950i) q^{92} +(0.0589474 - 0.219995i) q^{93} +(-2.46182 - 7.08439i) q^{94} +(-8.70516 + 15.0778i) q^{95} +(1.50549 + 1.22734i) q^{96} -17.4958 q^{97} +(-5.38916 - 5.38916i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 4 q^{4} + 8 q^{11} + 64 q^{15} - 36 q^{16} - 20 q^{18} - 56 q^{22} - 32 q^{29} - 96 q^{30} - 40 q^{32} + 80 q^{36} + 16 q^{37} + 16 q^{43} - 4 q^{44} - 64 q^{46} - 56 q^{50} - 16 q^{53} + 20 q^{58}+ \cdots - 80 q^{99}+O(q^{100}) \) 96 * q + 4 * q^4 + 8 * q^11 + 64 * q^15 - 36 * q^16 - 20 * q^18 - 56 * q^22 - 32 * q^29 - 96 * q^30 - 40 * q^32 + 80 * q^36 + 16 * q^37 + 16 * q^43 - 4 * q^44 - 64 * q^46 - 56 * q^50 - 16 * q^53 + 20 * q^58 - 8 * q^60 + 88 * q^64 - 40 * q^67 + 196 * q^72 + 28 * q^74 + 112 * q^78 - 80 * q^79 + 48 * q^81 + 108 * q^86 + 100 * q^88 + 128 * q^95 - 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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