LMFDB - Embedded newform 784.2.x.p.165.14

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			165.14
Character	$\chi$	$=$	784.165
Dual form			784.2.x.p.765.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.464209 - 1.33586i) q^{2} +(0.0888704 + 0.331669i) q^{3} +(-1.56902 - 1.24023i) q^{4} +(-0.613128 + 2.28822i) q^{5} +(0.484316 + 0.0352455i) q^{6} +(-2.38512 + 1.52026i) q^{8} +(2.49597 - 1.44105i) q^{9} +O(q^{10})$	\(q+(0.464209 - 1.33586i) q^{2} +(0.0888704 + 0.331669i) q^{3} +(-1.56902 - 1.24023i) q^{4} +(-0.613128 + 2.28822i) q^{5} +(0.484316 + 0.0352455i) q^{6} +(-2.38512 + 1.52026i) q^{8} +(2.49597 - 1.44105i) q^{9} +(2.77212 + 1.88126i) q^{10} +(-2.55430 + 0.684421i) q^{11} +(0.271906 - 0.630615i) q^{12} +(-2.24784 + 2.24784i) q^{13} -0.813421 q^{15} +(0.923653 + 3.89190i) q^{16} +(-2.63388 + 4.56202i) q^{17} +(-0.766383 - 4.00320i) q^{18} +(7.09898 + 1.90217i) q^{19} +(3.79994 - 2.82985i) q^{20} +(-0.271438 + 3.72988i) q^{22} +(0.0792419 - 0.0457503i) q^{23} +(-0.716189 - 0.655965i) q^{24} +(-0.529913 - 0.305946i) q^{25} +(1.95932 + 4.04626i) q^{26} +(1.42816 + 1.42816i) q^{27} +(-6.55020 + 6.55020i) q^{29} +(-0.377597 + 1.08661i) q^{30} +(-0.331648 + 0.574432i) q^{31} +(5.62778 + 0.572785i) q^{32} +(-0.454002 - 0.786355i) q^{33} +(4.87153 + 5.63622i) q^{34} +(-5.70346 - 0.834544i) q^{36} +(0.270309 - 1.00881i) q^{37} +(5.83643 - 8.60021i) q^{38} +(-0.945305 - 0.545772i) q^{39} +(-2.01631 - 6.38981i) q^{40} -2.43655i q^{41} +(5.68128 + 5.68128i) q^{43} +(4.85658 + 2.09405i) q^{44} +(1.76709 + 6.59488i) q^{45} +(-0.0243311 - 0.127093i) q^{46} +(2.65163 + 4.59276i) q^{47} +(-1.20874 + 0.652221i) q^{48} +(-0.654689 + 0.565865i) q^{50} +(-1.74715 - 0.468149i) q^{51} +(6.31475 - 0.739067i) q^{52} +(-0.871326 + 0.233471i) q^{53} +(2.57079 - 1.24486i) q^{54} -6.26444i q^{55} +2.52356i q^{57} +(5.70947 + 11.7908i) q^{58} +(-9.27519 + 2.48528i) q^{59} +(1.27627 + 1.00883i) q^{60} +(2.09296 + 0.560807i) q^{61} +(0.613404 + 0.709691i) q^{62} +(3.37762 - 7.25201i) q^{64} +(-3.76535 - 6.52177i) q^{65} +(-1.26121 + 0.241449i) q^{66} +(2.42109 + 9.03564i) q^{67} +(9.79058 - 3.89128i) q^{68} +(0.0222162 + 0.0222162i) q^{69} -15.1936i q^{71} +(-3.76243 + 7.23160i) q^{72} +(4.17280 + 2.40917i) q^{73} +(-1.22214 - 0.829390i) q^{74} +(0.0543790 - 0.202945i) q^{75} +(-8.77932 - 11.7889i) q^{76} +(-1.16789 + 1.00944i) q^{78} +(-5.53028 - 9.57872i) q^{79} +(-9.47185 - 0.272705i) q^{80} +(3.97639 - 6.88731i) q^{81} +(-3.25488 - 1.13107i) q^{82} +(10.9512 - 10.9512i) q^{83} +(-8.82402 - 8.82402i) q^{85} +(10.2267 - 4.95207i) q^{86} +(-2.75462 - 1.59038i) q^{87} +(5.05181 - 5.51562i) q^{88} +(1.96668 - 1.13547i) q^{89} +(9.63011 + 0.700819i) q^{90} +(-0.181073 - 0.0264950i) q^{92} +(-0.219995 - 0.0589474i) q^{93} +(7.36617 - 1.41020i) q^{94} +(-8.70516 + 15.0778i) q^{95} +(0.310168 + 1.91746i) q^{96} -17.4958 q^{97} +(-5.38916 + 5.38916i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 4 q^{4}+O(q^{10}) $ 96 * q + 4 * q^4	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.464209	−	1.33586i	0.328245	−	0.944593i
$2$	0.464209	−	1.33586i	0.328245	−	0.944593i
$3$	0.0888704	+	0.331669i	0.0513093	+	0.191489i	0.986824	−	0.161800i	$-0.0517299\pi$
$3$	0.0888704	+	0.331669i	0.0513093	+	0.191489i	−0.935514	+	0.353289i	$0.885063\pi$
$4$	−1.56902	−	1.24023i	−0.784510	−	0.620116i
$5$	−0.613128	+	2.28822i	−0.274199	+	1.02332i	0.682177	+	0.731187i	$0.261033\pi$
$5$	−0.613128	+	2.28822i	−0.274199	+	1.02332i	−0.956376	+	0.292138i	$0.905633\pi$
$6$	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
$10$	2.77212	+	1.88126i	0.876620	+	0.594907i
$11$	−2.55430	+	0.684421i	−0.770149	+	0.206361i	−0.622437	−	0.782670i	$-0.713857\pi$
$11$	−2.55430	+	0.684421i	−0.770149	+	0.206361i	−0.147712	+	0.989030i	$0.547191\pi$
$12$	0.271906	−	0.630615i	0.0784926	−	0.182043i
$13$	−2.24784	+	2.24784i	−0.623439	+	0.623439i	−0.946409	−	0.322970i	$-0.895319\pi$
$13$	−2.24784	+	2.24784i	−0.623439	+	0.623439i	0.322970	+	0.946409i	$0.395319\pi$
$14$		0			0
$15$	−0.813421			−0.210024
$16$	0.923653	+	3.89190i	0.230913	+	0.972974i
$17$	−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	$0.946093\pi$
$18$	−0.766383	−	4.00320i	−0.180638	−	0.943564i
$19$	7.09898	+	1.90217i	1.62862	+	0.436387i	0.953517	−	0.301339i	$-0.0974335\pi$
$19$	7.09898	+	1.90217i	1.62862	+	0.436387i	0.675101	+	0.737726i	$0.264100\pi$
$20$	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	−0.491716	−	0.870756i	$-0.663630\pi$
$23$	0.0792419	−	0.0457503i	0.0165231	−	0.00953960i	0.508239	+	0.861216i	$0.330297\pi$
$24$	−0.716189	−	0.655965i	−0.146192	−	0.133898i
$25$	−0.529913	−	0.305946i	−0.105983	−	0.0611891i
$26$	1.95932	+	4.04626i	0.384255	+	0.793536i
$27$	1.42816	+	1.42816i	0.274850	+	0.274850i
$28$		0			0
$29$	−6.55020	+	6.55020i	−1.21634	+	1.21634i	−0.247439	+	0.968903i	$0.579589\pi$
$29$	−6.55020	+	6.55020i	−1.21634	+	1.21634i	−0.968903	+	0.247439i	$0.920411\pi$
$30$	−0.377597	+	1.08661i	−0.0689395	+	0.198388i
$31$	−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	$0.185638\pi$
$32$	5.62778	+	0.572785i	0.994861	+	0.101255i
$33$	−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
$37$	0.270309	−	1.00881i	0.0444385	−	0.165847i	−0.940141	−	0.340787i	$-0.889307\pi$
$37$	0.270309	−	1.00881i	0.0444385	−	0.165847i	0.984579	+	0.174940i	$0.0559732\pi$
$38$	5.83643	−	8.60021i	0.946793	−	1.39514i
$39$	−0.945305	−	0.545772i	−0.151370	−	0.0873935i
$40$	−2.01631	−	6.38981i	−0.318806	−	1.01032i
$41$		−	2.43655i		−	0.380525i	−0.981733	−	0.190262i	$-0.939066\pi$
$41$		−	2.43655i		−	0.380525i	0.981733	−	0.190262i	$-0.0609339\pi$
$42$		0			0
$43$	5.68128	+	5.68128i	0.866388	+	0.866388i	0.992070	−	0.125683i	$-0.0401122\pi$
$43$	5.68128	+	5.68128i	0.866388	+	0.866388i	−0.125683	+	0.992070i	$0.540112\pi$
$44$	4.85658	+	2.09405i	0.732158	+	0.315689i
$45$	1.76709	+	6.59488i	0.263423	+	0.983107i
$46$	−0.0243311	−	0.127093i	−0.00358742	−	0.0187389i
$47$	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
$51$	−1.74715	−	0.468149i	−0.244651	−	0.0655539i
$52$	6.31475	−	0.739067i	0.875698	−	0.102490i
$53$	−0.871326	+	0.233471i	−0.119686	+	0.0320697i	−0.318165	−	0.948035i	$-0.603067\pi$
$53$	−0.871326	+	0.233471i	−0.119686	+	0.0320697i	0.198479	+	0.980105i	$0.436400\pi$
$54$	2.57079	−	1.24486i	0.349840	−	0.169403i
$55$		−	6.26444i		−	0.844696i
$56$		0			0
$57$			2.52356i			0.334253i
$58$	5.70947	+	11.7908i	0.749690	+	1.54821i
$59$	−9.27519	+	2.48528i	−1.20753	+	0.323556i	−0.805791	−	0.592200i	$-0.798260\pi$
$59$	−9.27519	+	2.48528i	−1.20753	+	0.323556i	−0.401736	+	0.915756i	$0.631593\pi$
$60$	1.27627	+	1.00883i	0.164766	+	0.130239i
$61$	2.09296	+	0.560807i	0.267976	+	0.0718040i	0.390305	−	0.920686i	$-0.372370\pi$
$61$	2.09296	+	0.560807i	0.267976	+	0.0718040i	−0.122329	+	0.992490i	$0.539036\pi$
$62$	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
$66$	−1.26121	+	0.241449i	−0.155244	+	0.0297203i
$67$	2.42109	+	9.03564i	0.295783	+	1.10388i	0.940593	+	0.339536i	$0.110270\pi$
$67$	2.42109	+	9.03564i	0.295783	+	1.10388i	−0.644810	+	0.764343i	$0.723063\pi$
$68$	9.79058	−	3.89128i	1.18728	−	0.471887i
$69$	0.0222162	+	0.0222162i	0.00267452	+	0.00267452i
$70$		0			0
$71$		−	15.1936i		−	1.80315i	−0.432621	−	0.901576i	$-0.642411\pi$
$71$		−	15.1936i		−	1.80315i	0.432621	−	0.901576i	$-0.357589\pi$
$72$	−3.76243	+	7.23160i	−0.443406	+	0.852252i
$73$	4.17280	+	2.40917i	0.488390	+	0.281972i	0.723906	−	0.689899i	$-0.242345\pi$
$73$	4.17280	+	2.40917i	0.488390	+	0.281972i	−0.235517	+	0.971870i	$0.575678\pi$
$74$	−1.22214	−	0.829390i	−0.142071	−	0.0964146i
$75$	0.0543790	−	0.202945i	0.00627914	−	0.0234341i
$76$	−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	$-0.380430\pi$
$80$	−9.47185	−	0.272705i	−1.05898	−	0.0304893i
$81$	3.97639	−	6.88731i	0.441821	−	0.765257i
$82$	−3.25488	−	1.13107i	−0.359441	−	0.124905i
$83$	10.9512	−	10.9512i	1.20205	−	1.20205i	0.228512	−	0.973541i	$-0.426614\pi$
$83$	10.9512	−	10.9512i	1.20205	−	1.20205i	0.973541	−	0.228512i	$-0.0733861\pi$
$84$		0			0
$85$	−8.82402	−	8.82402i	−0.957099	−	0.957099i
$86$	10.2267	−	4.95207i	1.10277	−	0.533996i
$87$	−2.75462	−	1.59038i	−0.295326	−	0.170507i
$88$	5.05181	−	5.51562i	0.538525	−	0.587967i
$89$	1.96668	−	1.13547i	0.208468	−	0.120359i	−0.392131	−	0.919909i	$-0.628262\pi$
$89$	1.96668	−	1.13547i	0.208468	−	0.120359i	0.600599	+	0.799550i	$0.294929\pi$
$90$	9.63011	+	0.700819i	1.01510	+	0.0738728i
$91$		0			0
$92$	−0.181073	−	0.0264950i	−0.0188782	−	0.00276230i
$93$	−0.219995	−	0.0589474i	−0.0228124	−	0.00611256i
$94$	7.36617	−	1.41020i	0.759763	−	0.145451i
$95$	−8.70516	+	15.0778i	−0.893131	+	1.54695i
$96$	0.310168	+	1.91746i	0.0316564	+	0.195700i
$97$	−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
$100$	0.452002	+	1.13725i	0.0452002	+	0.113725i
$101$	−15.4911	+	4.15082i	−1.54142	+	0.413022i	−0.926724	−	0.375744i	$-0.877387\pi$
$101$	−15.4911	+	4.15082i	−1.54142	+	0.413022i	−0.614694	+	0.788766i	$0.710721\pi$
$102$	−1.43642	+	2.11663i	−0.142227	+	0.209577i
$103$	−10.5828	+	6.10999i	−1.04276	+	0.602035i	−0.920613	−	0.390477i	$-0.872310\pi$
$103$	−10.5828	+	6.10999i	−1.04276	+	0.602035i	−0.122143	+	0.992513i	$0.538977\pi$
$104$	1.94407	−	8.77868i	0.190632	−	0.860820i
$105$		0			0
$106$	−0.0925932	+	1.27234i	−0.00899345	+	0.123581i
$107$	1.95469	−	7.29501i	0.188967	−	0.705236i	−0.804779	−	0.593575i	$-0.797716\pi$
$107$	1.95469	−	7.29501i	0.188967	−	0.705236i	0.993746	−	0.111661i	$-0.0356171\pi$
$108$	−0.469566	−	4.01207i	−0.0451840	−	0.386062i
$109$	−1.13501	−	4.23590i	−0.108714	−	0.405726i	0.890026	−	0.455910i	$-0.150686\pi$
$109$	−1.13501	−	4.23590i	−0.108714	−	0.405726i	−0.998740	+	0.0501838i	$0.984019\pi$
$110$	−8.36838	−	2.90800i	−0.797894	−	0.277267i
$111$	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	$0.296031\pi$
$114$	3.37111	+	1.17146i	0.315733	+	0.109717i
$115$	0.0561016	+	0.209374i	0.00523150	+	0.0195242i
$116$	18.4012	−	2.15364i	1.70851	−	0.199960i
$117$	−2.37129	+	8.84979i	−0.219226	+	0.818164i
$118$	−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
$122$	1.72073	−	2.53556i	0.155787	−	0.229559i
$123$	0.808127	−	0.216537i	0.0728664	−	0.0195245i
$124$	1.23279	−	0.489975i	0.110708	−	0.0440010i
$125$	−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	$0.197805\pi$
$128$	−8.11972	−	7.87846i	−0.717689	−	0.696364i
$129$	−1.37941	+	2.38920i	−0.121450	+	0.210358i
$130$	−10.4601	+	2.00250i	−0.917408	+	0.175631i
$131$	9.53546	+	2.55502i	0.833117	+	0.223233i	0.650073	−	0.759872i	$-0.274738\pi$
$131$	9.53546	+	2.55502i	0.833117	+	0.223233i	0.183044	+	0.983105i	$0.441405\pi$
$132$	−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
$136$	−0.653319	−	14.8852i	−0.0560217	−	1.27639i
$137$	−14.6054	−	8.43243i	−1.24782	−	0.720431i	−0.277148	−	0.960827i	$-0.589389\pi$
$137$	−14.6054	−	8.43243i	−1.24782	−	0.720431i	−0.970675	+	0.240396i	$0.922723\pi$
$138$	0.0399906	−	0.0193647i	0.00340423	−	0.00164843i
$139$	−6.01333	−	6.01333i	−0.510044	−	0.510044i	0.404496	−	0.914540i	$-0.367447\pi$
$139$	−6.01333	−	6.01333i	−0.510044	−	0.510044i	−0.914540	+	0.404496i	$0.867447\pi$
$140$		0			0
$141$	−1.28762	+	1.28762i	−0.108437	+	0.108437i
$142$	−20.2965	−	7.05301i	−1.70324	−	0.591875i
$143$	4.20318	−	7.28012i	0.351488	−	0.608794i
$144$	7.91383	+	8.38303i	0.659485	+	0.698586i
$145$	−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
$149$	−0.773325	+	2.88609i	−0.0633533	+	0.236438i	−0.990341	−	0.138655i	$-0.955722\pi$
$149$	−0.773325	+	2.88609i	−0.0633533	+	0.236438i	0.926988	+	0.375092i	$0.122389\pi$
$150$	−0.245862	−	0.166851i	−0.0200746	−	0.0136234i
$151$	18.9197	+	10.9233i	1.53966	+	0.888925i	0.998858	+	0.0477779i	$0.0152140\pi$
$151$	18.9197	+	10.9233i	1.53966	+	0.888925i	0.540806	+	0.841147i	$0.318119\pi$
$152$	−19.8237	+	6.25539i	−1.60792	+	0.507379i
$153$			15.1822i			1.22741i
$154$		0			0
$155$	−1.11109	−	1.11109i	−0.0892445	−	0.0892445i
$156$	0.806320	+	2.02872i	0.0645572	+	0.162428i
$157$	−0.760181	−	2.83703i	−0.0606690	−	0.226420i	0.928934	−	0.370245i	$-0.120726\pi$
$157$	−0.760181	−	2.83703i	−0.0606690	−	0.226420i	−0.989603	+	0.143825i	$0.954060\pi$
$158$	−15.3630	+	2.94113i	−1.22221	+	0.233984i
$159$	−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
$163$	9.57465	+	2.56552i	0.749944	+	0.200947i	0.613493	−	0.789700i	$-0.289764\pi$
$163$	9.57465	+	2.56552i	0.749944	+	0.200947i	0.136451	+	0.990647i	$0.456430\pi$
$164$	−3.02188	+	3.82299i	−0.235969	+	0.298526i
$165$	2.07772	−	0.556723i	0.161750	−	0.0433408i
$166$	−9.54561	−	19.7129i	−0.740883	−	1.53002i
$167$			17.0258i			1.31750i	0.752363	+	0.658749i	$0.228914\pi$
$167$			17.0258i			1.31750i	−0.752363	+	0.658749i	$0.771086\pi$
$168$		0			0
$169$			2.89442i			0.222648i
$170$	−15.8838	+	7.69143i	−1.21823	+	0.589906i
$171$	20.4600	−	5.48223i	1.56461	−	0.419237i
$172$	−1.86795	−	15.9602i	−0.142430	−	1.21695i
$173$	0.236519	+	0.0633750i	0.0179822	+	0.00481831i	0.267799	−	0.963475i	$-0.413704\pi$
$173$	0.236519	+	0.0633750i	0.0179822	+	0.00481831i	−0.249817	+	0.968293i	$0.580370\pi$
$174$	−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
$178$	−0.603867	−	3.15430i	−0.0452617	−	0.236425i
$179$	0.0699503	+	0.261058i	0.00522833	+	0.0195124i	0.968491	−	0.249050i	$-0.0801182\pi$
$179$	0.0699503	+	0.261058i	0.00522833	+	0.0195124i	−0.963262	+	0.268562i	$0.913452\pi$
$180$	5.40657	−	12.5391i	0.402982	−	0.934610i
$181$	0.745744	+	0.745744i	0.0554307	+	0.0554307i	0.734279	−	0.678848i	$-0.237521\pi$
$181$	0.745744	+	0.745744i	0.0554307	+	0.0554307i	−0.678848	+	0.734279i	$0.737521\pi$
$182$		0			0
$183$			0.744009i			0.0549987i
$184$	−0.119449	+	0.229588i	−0.00880591	+	0.0169255i
$185$	2.14264	+	1.23705i	0.157530	+	0.0909500i
$186$	−0.180869	+	0.266517i	−0.0132619	+	0.0195420i
$187$	3.60537	−	13.4554i	0.263651	−	0.983959i
$188$	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	$0.787599\pi$
$192$	2.70544	+	0.475762i	0.195248	+	0.0343352i
$193$	−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	$0.176849\pi$
$194$	−8.12171	+	23.3719i	−0.583105	+	1.67800i
$195$	1.82844	−	1.82844i	0.130937	−	0.130937i
$196$		0			0
$197$	−4.83936	−	4.83936i	−0.344790	−	0.344790i	0.513374	−	0.858165i	$-0.328395\pi$
$197$	−4.83936	−	4.83936i	−0.344790	−	0.344790i	−0.858165	+	0.513374i	$0.828395\pi$
$198$	4.69745	+	9.70084i	0.333833	+	0.689408i
$199$	−7.57734	−	4.37478i	−0.537144	−	0.310120i	0.206777	−	0.978388i	$-0.433703\pi$
$199$	−7.57734	−	4.37478i	−0.537144	−	0.310120i	−0.743920	+	0.668268i	$0.767036\pi$
$200$	1.72902	−	0.0758880i	0.122260	−	0.00536609i
$201$	−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
$205$	5.57537	+	1.49391i	0.389400	+	0.104340i
$206$	3.24943	+	16.9734i	0.226399	+	1.18259i
$207$	0.131857	−	0.228383i	0.00916469	−	0.0158737i
$208$	−10.8246	−	6.67214i	−0.750550	−	0.462630i
$209$	−19.4348			−1.34433
$210$		0			0
$211$	8.52893	−	8.52893i	0.587156	−	0.587156i	−0.349704	−	0.936860i	$-0.613718\pi$
$211$	8.52893	−	8.52893i	0.587156	−	0.587156i	0.936860	+	0.349704i	$0.113718\pi$
$212$	1.65669	+	0.714324i	0.113782	+	0.0490600i
$213$	5.03925	−	1.35026i	0.345284	−	0.0925185i
$214$	−8.83770	−	5.99760i	−0.604133	−	0.409987i
$215$	−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
$219$	−0.428207	+	1.59809i	−0.0289356	+	0.107989i
$220$	−7.76935	+	9.82903i	−0.523809	+	0.662673i
$221$	−4.33414	−	16.1752i	−0.291546	−	1.08806i
$222$	0.166471	−	0.479054i	0.0111728	−	0.0321520i
$223$	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
$226$	5.90007	−	16.9787i	0.392467	−	1.12940i
$227$	0.192153	+	0.717124i	0.0127536	+	0.0475972i	0.972009	−	0.234942i	$-0.0754900\pi$
$227$	0.192153	+	0.717124i	0.0127536	+	0.0475972i	−0.959256	+	0.282539i	$0.908823\pi$
$228$	3.12979	−	3.95951i	0.207276	−	0.262225i
$229$	−4.16121	+	15.5299i	−0.274981	+	1.02624i	0.680873	+	0.732401i	$0.261600\pi$
$229$	−4.16121	+	15.5299i	−0.274981	+	1.02624i	−0.955854	+	0.293841i	$0.905066\pi$
$230$	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	−0.162840	−	0.986652i	$-0.552066\pi$
$233$	9.31438	−	5.37766i	0.610206	−	0.352302i	0.773046	+	0.634350i	$0.218732\pi$
$234$	10.7213	+	7.27586i	0.700871	+	0.475638i
$235$	−12.1350	+	3.25158i	−0.791603	+	0.212109i
$236$	17.6353	+	7.60392i	1.14796	+	0.494973i
$237$	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	$0.469062\pi$
$240$	−0.751319	−	3.16575i	−0.0484974	−	0.204348i
$241$	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	$-0.0927913\pi$
$242$	1.06554	+	5.56587i	0.0684958	+	0.357788i
$243$	8.49041	+	2.27500i	0.544660	+	0.145941i
$244$	−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
$248$	−0.0822634	−	1.87428i	−0.00522373	−	0.119017i
$249$	4.60542	+	2.65894i	0.291857	+	0.168503i
$250$	6.40704	+	13.2314i	0.405217	+	0.836826i
$251$	2.43982	+	2.43982i	0.154000	+	0.154000i	0.779902	−	0.625902i	$-0.215269\pi$
$251$	2.43982	+	2.43982i	0.154000	+	0.154000i	−0.625902	+	0.779902i	$0.715269\pi$
$252$		0			0
$253$	−0.171095	+	0.171095i	−0.0107566	+	0.0107566i
$254$	8.50673	−	24.4799i	0.533760	−	1.53600i
$255$	2.14246	−	3.71084i	0.134166	−	0.232382i
$256$	−14.2937	+	7.18953i	−0.893358	+	0.449345i
$257$	−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
$261$	−6.90995	+	25.7883i	−0.427715	+	1.59625i
$262$	7.83958	−	11.5519i	0.484331	−	0.713681i
$263$	−8.37247	−	4.83385i	−0.516269	−	0.298068i	0.219138	−	0.975694i	$-0.429676\pi$
$263$	−8.37247	−	4.83385i	−0.516269	−	0.298068i	−0.735407	+	0.677626i	$0.763009\pi$
$264$	2.27832	+	1.18535i	0.140221	+	0.0729534i
$265$		−	2.13694i		−	0.131271i
$266$		0			0
$267$	0.551378	+	0.551378i	0.0337438	+	0.0337438i
$268$	7.40754	−	17.1798i	0.452487	−	1.04942i
$269$	6.25673	+	23.3504i	0.381480	+	1.42370i	0.843642	+	0.536906i	$0.180407\pi$
$269$	6.25673	+	23.3504i	0.381480	+	1.42370i	−0.462162	+	0.886796i	$0.652926\pi$
$270$	1.27229	+	6.64579i	0.0774289	+	0.404450i
$271$	−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
$275$	1.56295	+	0.418791i	0.0942495	+	0.0252541i
$276$	−0.00730446	−	0.0624109i	−0.000439677	−	0.00375670i
$277$	15.9168	−	4.26488i	0.956345	−	0.256252i	0.253293	−	0.967390i	$-0.418486\pi$
$277$	15.9168	−	4.26488i	0.956345	−	0.256252i	0.703053	+	0.711138i	$0.251820\pi$
$278$	−10.8244	+	5.24151i	−0.649204	+	0.314365i
$279$			1.91169i			0.114450i
$280$		0			0
$281$			19.5811i			1.16811i	0.811715	+	0.584054i	$0.198534\pi$
$281$			19.5811i			1.16811i	−0.811715	+	0.584054i	$0.801466\pi$
$282$	1.12235	+	2.31780i	0.0668352	+	0.138023i
$283$	−0.491997	+	0.131830i	−0.0292462	+	0.00783649i	−0.273412	−	0.961897i	$-0.588152\pi$
$283$	−0.491997	+	0.131830i	−0.0292462	+	0.00783649i	0.244166	+	0.969733i	$0.421486\pi$
$284$	−18.8436	+	23.8391i	−1.11816	+	1.41459i
$285$	−5.77446	−	1.54726i	−0.342050	−	0.0916519i
$286$	−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
$290$	−30.4806	+	5.83528i	−1.78988	+	0.342659i
$291$	−1.55486	−	5.80282i	−0.0911475	−	0.340167i
$292$	−3.55929	−	8.95527i	−0.208292	−	0.524068i
$293$	13.4219	+	13.4219i	0.784117	+	0.784117i	0.980523	−	0.196406i	$-0.0629270\pi$
$293$	13.4219	+	13.4219i	0.784117	+	0.784117i	−0.196406	+	0.980523i	$0.562927\pi$
$294$		0			0
$295$		−	22.7475i		−	1.32441i
$296$	0.888927	+	2.81706i	0.0516678	+	0.163739i
$297$	−4.62542	−	2.67049i	−0.268394	−	0.154957i
$298$	3.49641	+	2.37280i	0.202542	+	0.137452i
$299$	−0.0752837	+	0.280962i	−0.00435377	+	0.0162485i
$300$	−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
$304$	−0.846039	+	29.3854i	−0.0485237	+	1.68537i
$305$	−2.56650	+	4.44532i	−0.146958	+	0.254538i
$306$	20.2813	+	7.04772i	1.15940	+	0.402891i
$307$	18.1617	−	18.1617i	1.03654	−	1.03654i	0.0372355	−	0.999307i	$-0.488145\pi$
$307$	18.1617	−	18.1617i	1.03654	−	1.03654i	0.999307	−	0.0372355i	$-0.0118552\pi$
$308$		0			0
$309$	−2.96699	−	2.96699i	−0.168786	−	0.168786i
$310$	−2.00003	+	0.968475i	−0.113594	+	0.0550057i
$311$	−27.1628	−	15.6825i	−1.54026	−	0.889271i	−0.998822	−	0.0485315i	$-0.984546\pi$
$311$	−27.1628	−	15.6825i	−1.54026	−	0.889271i	−0.541440	−	0.840739i	$-0.682121\pi$
$312$	3.08438	−	0.135376i	0.174619	−	0.00766413i
$313$	11.6376	−	6.71895i	0.657794	−	0.379777i	−0.133642	−	0.991030i	$-0.542667\pi$
$313$	11.6376	−	6.71895i	0.657794	−	0.379777i	0.791436	+	0.611252i	$0.209334\pi$
$314$	−4.14275	−	0.301483i	−0.233789	−	0.0170137i
$315$		0			0
$316$	−3.20271	+	21.8880i	−0.180166	+	1.23130i
$317$	22.7711	+	6.10150i	1.27895	+	0.342695i	0.833455	−	0.552588i	$-0.186360\pi$
$317$	22.7711	+	6.10150i	1.27895	+	0.342695i	0.445499	+	0.895282i	$0.353026\pi$
$318$	−0.430226	+	0.0823635i	−0.0241259	+	0.00461871i
$319$	12.2481	−	21.2143i	0.685760	−	1.18777i
$320$	14.5233	+	12.1752i	0.811878	+	0.680612i
$321$	2.59324			0.144741
$322$		0			0
$323$	−27.3756	+	27.3756i	−1.52322	+	1.52322i
$324$	−14.7809	+	5.87469i	−0.821161	+	0.326372i
$325$	1.87888	−	0.503444i	0.104221	−	0.0279260i
$326$	7.87180	−	11.5994i	0.435978	−	0.642432i
$327$	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
$331$	2.17427	−	8.11450i	0.119509	−	0.446013i	−0.880076	−	0.474833i	$-0.842508\pi$
$331$	2.17427	−	8.11450i	0.119509	−	0.446013i	0.999585	+	0.0288201i	$0.00917498\pi$
$332$	−30.7648	+	3.60065i	−1.68844	+	0.197611i
$333$	−0.779056	−	2.90748i	−0.0426920	−	0.159329i
$334$	22.7441	+	7.90354i	1.24450	+	0.432462i
$335$	−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	$0.550299\pi$
$338$	3.86653	+	1.34362i	0.210312	+	0.0730831i
$339$	1.12954	+	4.21549i	0.0613481	+	0.228954i
$340$	2.90125	+	24.7889i	0.157342	+	1.34437i
$341$	0.453975	−	1.69426i	0.0245841	−	0.0917491i
$342$	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
$346$	0.194454	−	0.286536i	0.0104539	−	0.0154043i
$347$	11.7019	−	3.13552i	0.628193	−	0.168324i	0.0693432	−	0.997593i	$-0.477910\pi$
$347$	11.7019	−	3.13552i	0.628193	−	0.168324i	0.558849	+	0.829269i	$0.311243\pi$
$348$	2.34961	+	5.91170i	0.125953	+	0.316900i
$349$	18.6177	−	18.6177i	0.996582	−	0.996582i	−0.00341200	−	0.999994i	$-0.501086\pi$
$349$	18.6177	−	18.6177i	0.996582	−	0.996582i	0.999994	+	0.00341200i	$0.00108607\pi$
$350$		0			0
$351$	−6.42057			−0.342705
$352$	−14.7670	+	2.38871i	−0.787086	+	0.127319i
$353$	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	$-0.0407323\pi$
$354$	−4.57972	+	0.876752i	−0.243409	+	0.0465988i
$355$	34.7664	+	9.31563i	1.84521	+	0.494422i
$356$	−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	−0.550142	−	0.835071i	$-0.685426\pi$
$359$	−1.93301	+	1.11602i	−0.102020	+	0.0589014i	0.448122	+	0.893973i	$0.352093\pi$
$360$	−14.2407	−	13.0432i	−0.750549	−	0.687435i
$361$	30.3228	+	17.5069i	1.59594	+	0.921415i
$362$	1.34239	−	0.650026i	0.0705543	−	0.0341646i
$363$	−0.972927	−	0.972927i	−0.0510654	−	0.0510654i
$364$		0			0
$365$	−8.07117	+	8.07117i	−0.422465	+	0.422465i
$366$	0.993889	+	0.345375i	0.0519514	+	0.0180531i
$367$	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	$-0.0144310\pi$
$368$	0.251247	+	0.266144i	0.0130972	+	0.0138737i
$369$	−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
$373$	−6.06542	+	22.6365i	−0.314056	+	1.17207i	0.610810	+	0.791777i	$0.290844\pi$
$373$	−6.06542	+	22.6365i	−0.314056	+	1.17207i	−0.924865	+	0.380295i	$0.875823\pi$
$374$	−16.3009	−	11.0624i	−0.842898	−	0.572022i
$375$	−3.09117	−	1.78469i	−0.159628	−	0.0921610i
$376$	−13.3067	−	6.92313i	−0.686238	−	0.357033i
$377$		−	29.4476i		−	1.51663i
$378$		0			0
$379$	5.39695	+	5.39695i	0.277223	+	0.277223i	0.831999	−	0.554777i	$-0.187196\pi$
$379$	5.39695	+	5.39695i	0.277223	+	0.277223i	−0.554777	+	0.831999i	$0.687196\pi$
$380$	32.3585	−	12.8609i	1.65996	−	0.659752i
$381$	1.62857	+	6.07791i	0.0834342	+	0.311381i
$382$	5.49727	−	1.05241i	0.281265	−	0.0538460i
$383$	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
$387$	22.3673	+	5.99331i	1.13699	+	0.304657i
$388$	27.4513	+	21.6989i	1.39363	+	1.10159i
$389$	3.76716	−	1.00941i	0.191003	−	0.0511790i	−0.162050	−	0.986783i	$-0.551810\pi$
$389$	3.76716	−	1.00941i	0.191003	−	0.0511790i	0.353052	+	0.935604i	$0.385144\pi$
$390$	−1.59376	−	3.29131i	−0.0807029	−	0.166662i
$391$			0.482004i			0.0243760i
$392$		0			0
$393$			3.38968i			0.170987i
$394$	−8.71116	+	4.21822i	−0.438862	+	0.212511i
$395$	25.3090	−	6.78153i	1.27344	−	0.341216i
$396$	15.1395	−	1.77190i	0.760789	−	0.0890414i
$397$	13.4263	+	3.59757i	0.673848	+	0.180557i	0.579488	−	0.814981i	$-0.303253\pi$
$397$	13.4263	+	3.59757i	0.673848	+	0.180557i	0.0943605	+	0.995538i	$0.469919\pi$
$398$	−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	$0.746843\pi$
$402$	0.854108	+	4.46144i	0.0425991	+	0.222516i
$403$	−0.545739	−	2.03672i	−0.0271852	−	0.101456i
$404$	29.4538	+	12.6998i	1.46538	+	0.631837i
$405$	13.3217	+	13.3217i	0.661959	+	0.661959i
$406$		0			0
$407$			2.76179i			0.136897i
$408$	4.87888	−	1.53954i	0.241541	−	0.0762184i
$409$	7.51025	+	4.33605i	0.371358	+	0.214404i	0.674052	−	0.738684i	$-0.264553\pi$
$409$	7.51025	+	4.33605i	0.371358	+	0.214404i	−0.302694	+	0.953088i	$0.597886\pi$
$410$	4.58379	−	6.75440i	0.226377	−	0.333576i
$411$	1.49879	−	5.59354i	0.0739297	−	0.275909i
$412$	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
$416$	−13.9379	+	11.3628i	−0.683361	+	0.557108i
$417$	1.46003	−	2.52884i	0.0714979	−	0.123838i
$418$	−9.02179	+	25.9621i	−0.441270	+	1.26985i
$419$	3.96286	−	3.96286i	0.193598	−	0.193598i	−0.603651	−	0.797249i	$-0.706288\pi$
$419$	3.96286	−	3.96286i	0.193598	−	0.193598i	0.797249	+	0.603651i	$0.206288\pi$
$420$		0			0
$421$	−16.2008	−	16.2008i	−0.789580	−	0.789580i	0.191845	−	0.981425i	$-0.438553\pi$
$421$	−16.2008	−	16.2008i	−0.789580	−	0.789580i	−0.981425	+	0.191845i	$0.938553\pi$
$422$	−7.43422	−	15.3526i	−0.361892	−	0.747354i
$423$	13.2368	+	7.64226i	0.643594	+	0.371579i
$424$	1.72328	−	1.88150i	0.0836900	−	0.0913736i
$425$	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
$429$	2.78813	+	0.747076i	0.134612	+	0.0360692i
$430$	5.06120	+	26.4372i	0.244073	+	1.27491i
$431$	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	$0.162334\pi$
$432$	−4.23914	+	6.87740i	−0.203956	+	0.330889i
$433$	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
$436$	−3.47265	+	8.05389i	−0.166310	+	0.385711i
$437$	0.649561	−	0.174049i	0.0310727	−	0.00832591i
$438$	1.93604	+	1.31387i	0.0925077	+	0.0627792i
$439$	22.8504	−	13.1927i	1.09059	−	0.629652i	0.156855	−	0.987622i	$-0.449864\pi$
$439$	22.8504	−	13.1927i	1.09059	−	0.629652i	0.933733	+	0.357970i	$0.116531\pi$
$440$	9.52357	+	14.9415i	0.454018	+	0.712306i
$441$		0			0
$442$	−23.6197	−	1.71890i	−1.12348	−	0.0817595i
$443$	−2.85503	+	10.6551i	−0.135647	+	0.506241i	0.864348	+	0.502895i	$0.167732\pi$
$443$	−2.85503	+	10.6551i	−0.135647	+	0.506241i	−0.999994	+	0.00334579i	$0.998935\pi$
$444$	−0.562669	−	0.444761i	−0.0267031	−	0.0211074i
$445$	1.39237	+	5.19640i	0.0660047	+	0.246333i
$446$	11.7590	−	33.8390i	0.556806	−	1.60232i
$447$	−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	$0.232306\pi$
$450$	−0.818646	+	2.35582i	−0.0385913	+	0.111054i
$451$	1.66763	+	6.22366i	0.0785254	+	0.293061i
$452$	−19.9422	−	15.7633i	−0.938001	−	0.741442i
$453$	−1.94152	+	7.24583i	−0.0912203	+	0.340439i
$454$	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	−0.648091	−	0.761563i	$-0.724432\pi$
$457$	−6.68269	+	3.85825i	−0.312603	+	0.180482i	0.335488	+	0.942045i	$0.391099\pi$
$458$	18.8140	+	12.7679i	0.879120	+	0.596604i
$459$	−10.2769	+	2.75370i	−0.479686	+	0.128531i
$460$	0.171647	−	0.398091i	0.00800310	−	0.0185611i
$461$	−3.17728	+	3.17728i	−0.147980	+	0.147980i	−0.777215	−	0.629235i	$-0.783368\pi$
$461$	−3.17728	+	3.17728i	−0.147980	+	0.147980i	0.629235	+	0.777215i	$0.283368\pi$
$462$		0			0
$463$	−7.90920			−0.367571			−0.183786	−	0.982966i	$-0.558835\pi$
$463$	−7.90920			−0.367571			−0.183786	+	0.982966i	$0.558835\pi$
$464$	−31.5428	−	19.4426i	−1.46434	−	0.902600i
$465$	0.269770	−	0.467255i	0.0125103	−	0.0216684i
$466$	−2.85996	−	14.9390i	−0.132485	−	0.692037i
$467$	−22.7929	−	6.10734i	−1.05473	−	0.282614i	−0.310524	−	0.950565i	$-0.600505\pi$
$467$	−22.7929	−	6.10734i	−1.05473	−	0.282614i	−0.744205	+	0.667952i	$0.767171\pi$
$468$	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
$472$	18.3442	−	20.0284i	0.844360	−	0.921881i
$473$	−18.4001	−	10.6233i	−0.846036	−	0.488459i
$474$	−2.34080	−	4.83405i	−0.107516	−	0.222035i
$475$	−3.17988	−	3.17988i	−0.145903	−	0.145903i
$476$		0			0
$477$	−1.83836	+	1.83836i	−0.0841727	+	0.0841727i
$478$	1.39282	−	4.00813i	0.0637061	−	0.183328i
$479$	−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	$0.885476\pi$
$480$	−4.57776	−	0.465915i	−0.208945	−	0.0212660i
$481$	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
$485$	10.7272	−	40.0343i	0.487096	−	1.81787i
$486$	6.98039	−	10.2859i	0.316637	−	0.466578i
$487$	9.02294	+	5.20940i	0.408868	+	0.236060i	0.690303	−	0.723520i	$-0.257477\pi$
$487$	9.02294	+	5.20940i	0.408868	+	0.236060i	−0.281435	+	0.959580i	$0.590810\pi$
$488$	−5.84454	+	1.84425i	−0.264570	+	0.0834853i
$489$			3.40361i			0.153917i
$490$		0			0
$491$	−8.28383	−	8.28383i	−0.373844	−	0.373844i	0.495031	−	0.868875i	$-0.335157\pi$
$491$	−8.28383	−	8.28383i	−0.373844	−	0.373844i	−0.868875	+	0.495031i	$0.835157\pi$
$492$	−1.53652	−	0.662513i	−0.0692718	−	0.0298684i
$493$	−12.6297	−	47.1346i	−0.568813	−	2.12284i
$494$	6.21255	+	32.4513i	0.279516	+	1.46005i
$495$	−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
$499$	11.6949	+	3.13364i	0.523536	+	0.140281i	0.510902	−	0.859639i	$-0.329312\pi$
$499$	11.6949	+	3.13364i	0.523536	+	0.140281i	0.0126342	+	0.999920i	$0.495978\pi$
$500$	20.6494	−	2.41677i	0.923470	−	0.108081i
$501$	−5.64694	+	1.51309i	−0.252287	+	0.0676000i
$502$	4.39183	−	2.12666i	0.196017	−	0.0949174i
$503$			26.5226i			1.18258i	0.806458	+	0.591292i	$0.201382\pi$
$503$			26.5226i			1.18258i	−0.806458	+	0.591292i	$0.798618\pi$
$504$		0			0
$505$		−	37.9920i		−	1.69062i
$506$	0.149134	+	0.307981i	0.00662982	+	0.0136914i
$507$	−0.959990	+	0.257229i	−0.0426347	+	0.0114239i
$508$	−28.7527	−	22.7275i	−1.27569	−	1.00837i
$509$	32.2445	+	8.63990i	1.42921	+	0.382957i	0.888743	−	0.458406i	$-0.151579\pi$
$509$	32.2445	+	8.63990i	1.42921	+	0.382957i	0.540471	+	0.841363i	$0.318246\pi$
$510$	−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
$514$	−25.6583	+	4.91209i	−1.13174	+	0.216663i
$515$	−7.49241	−	27.9620i	−0.330155	−	1.23215i
$516$	5.12748	−	2.03792i	0.225725	−	0.0897146i
$517$	−9.91643	−	9.91643i	−0.436124	−	0.436124i
$518$		0			0
$519$			0.0840780i			0.00369062i
$520$	18.8956	+	9.83093i	0.828627	+	0.431115i
$521$	−0.420026	−	0.242502i	−0.0184017	−	0.0106242i	0.490771	−	0.871289i	$-0.336715\pi$
$521$	−0.420026	−	0.242502i	−0.0184017	−	0.0106242i	−0.509173	+	0.860664i	$0.670049\pi$
$522$	31.2418	+	21.2018i	1.36741	+	0.927979i
$523$	5.31716	−	19.8439i	0.232503	−	0.867714i	−0.746755	−	0.665099i	$-0.768389\pi$
$523$	5.31716	−	19.8439i	0.232503	−	0.867714i	0.979259	−	0.202615i	$-0.0649439\pi$
$524$	−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
$528$	2.64107	−	2.49325i	0.114938	−	0.108505i
$529$	−11.4958	+	19.9113i	−0.499818	+	0.865710i
$530$	−2.85464	−	0.991984i	−0.123998	−	0.0430890i
$531$	−19.5692	+	19.5692i	−0.849230	+	0.849230i
$532$		0			0
$533$	5.47697	+	5.47697i	0.237234	+	0.237234i
$534$	0.992516	−	0.480607i	0.0429504	−	0.0207979i
$535$	15.4941	+	8.94555i	0.669870	+	0.386750i
$536$	−19.5111	−	17.8704i	−0.842752	−	0.771885i
$537$	−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
$541$	−12.2316	−	3.27745i	−0.525878	−	0.140909i	−0.0138940	−	0.999903i	$-0.504423\pi$
$541$	−12.2316	−	3.27745i	−0.525878	−	0.140909i	−0.511984	+	0.858995i	$0.671089\pi$
$542$	−39.7862	+	7.61676i	−1.70896	+	0.327168i
$543$	−0.181066	+	0.313615i	−0.00777027	+	0.0134585i
$544$	−17.4360	+	24.1654i	−0.747561	+	1.03608i
$545$	10.3886			0.444998
$546$		0			0
$547$	−26.3448	+	26.3448i	−1.12642	+	1.12642i	−0.135668	+	0.990754i	$0.543318\pi$
$547$	−26.3448	+	26.3448i	−1.12642	+	1.12642i	−0.990754	+	0.135668i	$0.956682\pi$
$548$	12.4580	+	31.3447i	0.532180	+	1.33898i
$549$	6.03212	−	1.61630i	0.257445	−	0.0689821i
$550$	1.28498	−	1.89347i	0.0547917	−	0.0807378i
$551$	−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
$555$	−0.219875	+	0.820584i	−0.00933316	+	0.0348318i
$556$	1.97712	+	16.8930i	0.0838487	+	0.716422i
$557$	4.51707	+	16.8579i	0.191394	+	0.714293i	0.993171	+	0.116669i	$0.0372218\pi$
$557$	4.51707	+	16.8579i	0.191394	+	0.714293i	−0.801776	+	0.597624i	$0.796112\pi$
$558$	2.55374	+	0.887421i	0.108108	+	0.0375675i
$559$	−25.5412			−1.08028
$560$		0			0
$561$	4.78316			0.201945
$562$	26.1575	+	9.08970i	1.10339	+	0.383426i
$563$	3.56178	+	13.2928i	0.150111	+	0.560223i	0.999475	+	0.0324143i	$0.0103196\pi$
$563$	3.56178	+	13.2928i	0.150111	+	0.560223i	−0.849363	+	0.527809i	$0.823014\pi$
$564$	3.61726	−	0.423357i	0.152314	−	0.0178266i
$565$	−7.79282	+	29.0832i	−0.327846	+	1.22354i
$566$	−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	−0.364328	−	0.931271i	$-0.618701\pi$
$569$	6.20226	−	3.58088i	0.260012	−	0.150118i	0.624340	+	0.781153i	$0.285368\pi$
$570$	−4.74747	+	6.99559i	−0.198850	+	0.293013i
$571$	32.6720	−	8.75442i	1.36728	−	0.366361i	0.500795	−	0.865566i	$-0.333041\pi$
$571$	32.6720	−	8.75442i	1.36728	−	0.366361i	0.866484	+	0.499205i	$0.166375\pi$
$572$	−15.6239	+	6.20975i	−0.653268	+	0.259643i
$573$	−0.960934	+	0.960934i	−0.0401436	+	0.0401436i
$574$		0			0
$575$	−0.0559884			−0.00233488
$576$	−2.02006	−	22.9681i	−0.0841693	−	0.957005i
$577$	−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	$0.999723\pi$
$578$	−14.9308	+	2.85838i	−0.621038	+	0.118893i
$579$	−0.294739	−	0.0789751i	−0.0122489	−	0.00328209i
$580$	−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
$584$	−13.6152	+	0.597580i	−0.563401	+	0.0247280i
$585$	−18.7964	−	10.8521i	−0.777135	−	0.448679i
$586$	24.1603	−	11.6992i	0.998054	−	0.483289i
$587$	−1.63189	−	1.63189i	−0.0673551	−	0.0673551i	0.672627	−	0.739982i	$-0.265166\pi$
$587$	−1.63189	−	1.63189i	−0.0673551	−	0.0673551i	−0.739982	+	0.672627i	$0.765166\pi$
$588$		0			0
$589$	−3.44703	+	3.44703i	−0.142032	+	0.142032i
$590$	−30.3874	−	10.5596i	−1.25103	−	0.434731i
$591$	1.17499	−	2.03514i	0.0483326	−	0.0837145i
$592$	4.17584	+	0.120227i	0.171626	+	0.00494130i
$593$	−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
$597$	0.777577	−	2.90196i	0.0318241	−	0.118769i
$598$	0.340378	+	0.230993i	0.0139191	+	0.00944602i
$599$	−10.0144	−	5.78179i	−0.409176	−	0.236238i	0.281260	−	0.959632i	$-0.409248\pi$
$599$	−10.0144	−	5.78179i	−0.409176	−	0.236238i	−0.690435	+	0.723394i	$0.742581\pi$
$600$	0.178829	+	0.566719i	0.00730065	+	0.0231362i
$601$			4.27752i			0.174484i	0.996187	+	0.0872418i	$0.0278053\pi$
$601$			4.27752i			0.174484i	−0.996187	+	0.0872418i	$0.972195\pi$
$602$		0			0
$603$	19.0638	+	19.0638i	0.776337	+	0.776337i
$604$	−16.1380	−	40.6037i	−0.656646	−	1.65214i
$605$	−2.45689	−	9.16923i	−0.0998867	−	0.372782i
$606$	−7.64886	+	1.46432i	−0.310714	+	0.0594838i
$607$	−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
$611$	−16.2842	−	4.36335i	−0.658790	−	0.176522i
$612$	18.8295	−	23.8212i	0.761136	−	0.962916i
$613$	−24.6641	+	6.60873i	−0.996174	+	0.266924i	−0.719842	−	0.694138i	$-0.755786\pi$
$613$	−24.6641	+	6.60873i	−0.996174	+	0.266924i	−0.276332	+	0.961062i	$0.589119\pi$
$614$	−15.8306	−	32.6922i	−0.638870	−	1.31935i
$615$			1.98194i			0.0799195i
$616$		0			0
$617$			34.9141i			1.40559i	0.711392	+	0.702795i	$0.248065\pi$
$617$			34.9141i			1.40559i	−0.711392	+	0.702795i	$0.751935\pi$
$618$	−5.34078	+	2.58617i	−0.214837	+	0.104031i
$619$	−28.7392	+	7.70066i	−1.15513	+	0.309516i	−0.785018	−	0.619473i	$-0.787346\pi$
$619$	−28.7392	+	7.70066i	−1.15513	+	0.309516i	−0.370109	+	0.928988i	$0.620680\pi$
$620$	0.365314	+	3.12132i	0.0146713	+	0.125355i
$621$	0.178509	+	0.0478314i	0.00716333	+	0.00191941i
$622$	−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
$626$	−3.57329	−	18.6651i	−0.142817	−	0.746007i
$627$	−1.72718	−	6.44591i	−0.0689768	−	0.257425i
$628$	−2.32584	+	5.39416i	−0.0928110	+	0.215251i
$629$	3.89023	+	3.89023i	0.155114	+	0.155114i
$630$		0			0
$631$			4.08175i			0.162492i	0.996694	+	0.0812460i	$0.0258900\pi$
$631$			4.08175i			0.162492i	−0.996694	+	0.0812460i	$0.974110\pi$
$632$	27.7525	+	14.4390i	1.10394	+	0.574351i
$633$	3.58675	+	2.07081i	0.142561	+	0.0823074i
$634$	18.7213	−	27.5866i	0.743517	−	1.09560i
$635$	−11.2357	+	41.9322i	−0.445875	+	1.66403i
$636$	−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
$640$	23.0061	−	13.7492i	0.909396	−	0.543486i
$641$	−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	$0.189213\pi$
$642$	1.20381	−	3.46420i	0.0475104	−	0.136721i
$643$	−15.8733	+	15.8733i	−0.625982	+	0.625982i	−0.947055	−	0.321072i	$-0.895957\pi$
$643$	−15.8733	+	15.8733i	−0.625982	+	0.625982i	0.321072	+	0.947055i	$0.395957\pi$
$644$		0			0
$645$	−4.62128	−	4.62128i	−0.181963	−	0.181963i
$646$	23.8619	+	49.2779i	0.938833	+	1.93881i
$647$	22.2411	+	12.8409i	0.874388	+	0.504828i	0.868804	−	0.495156i	$-0.164889\pi$
$647$	22.2411	+	12.8409i	0.874388	+	0.504828i	0.00558405	+	0.999984i	$0.498223\pi$
$648$	0.986320	+	22.4722i	0.0387463	+	0.882793i
$649$	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
$653$	−29.5335	−	7.91347i	−1.15573	−	0.309678i	−0.370473	−	0.928843i	$-0.620805\pi$
$653$	−29.5335	−	7.91347i	−1.15573	−	0.309678i	−0.785261	+	0.619165i	$0.787471\pi$
$654$	−0.400405	−	2.09152i	−0.0156571	−	0.0817848i
$655$	−11.6929	+	20.2527i	−0.456880	+	0.791339i
$656$	9.48280	−	2.25053i	0.370241	−	0.0878683i
$657$	13.8869			0.541780
$658$		0			0
$659$	3.02967	−	3.02967i	0.118019	−	0.118019i	−0.645631	−	0.763650i	$-0.723405\pi$
$659$	3.02967	−	3.02967i	0.118019	−	0.118019i	0.763650	+	0.645631i	$0.223405\pi$
$660$	−3.95045	−	1.70334i	−0.153771	−	0.0663025i
$661$	−37.2677	+	9.98584i	−1.44954	+	0.388404i	−0.895865	−	0.444326i	$-0.853443\pi$
$661$	−37.2677	+	9.98584i	−1.44954	+	0.388404i	−0.553679	+	0.832730i	$0.686777\pi$
$662$	−9.83049	−	6.67134i	−0.382073	−	0.259289i
$663$	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
$667$	−0.219376	+	0.818724i	−0.00849429	+	0.0317011i
$668$	21.1160	−	26.7139i	0.817001	−	1.03359i
$669$	2.25121	+	8.40162i	0.0870367	+	0.324825i
$670$	−10.2869	+	29.6026i	−0.397416	+	1.14365i
$671$	−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	$0.379044\pi$
$674$	−2.68198	+	7.71794i	−0.103306	+	0.297284i
$675$	−0.319863	−	1.19374i	−0.0123115	−	0.0459472i
$676$	3.58975	−	4.54141i	0.138067	−	0.174670i
$677$	7.17588	−	26.7807i	0.275791	−	1.02927i	−0.679518	−	0.733659i	$-0.737811\pi$
$677$	7.17588	−	26.7807i	0.275791	−	1.02927i	0.955309	−	0.295608i	$-0.0955224\pi$
$678$	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
$682$	−2.05254	−	1.39293i	−0.0785959	−	0.0533382i
$683$	2.10565	−	0.564208i	0.0805705	−	0.0215888i	−0.218309	−	0.975880i	$-0.570054\pi$
$683$	2.10565	−	0.564208i	0.0805705	−	0.0215888i	0.298879	+	0.954291i	$0.403387\pi$
$684$	−38.9013	−	16.7733i	−1.48743	−	0.641345i
$685$	28.2502	−	28.2502i	1.07939	−	1.07939i
$686$		0			0
$687$	−5.52058			−0.210623
$688$	−16.8634	+	27.3585i	−0.642912	+	1.04303i
$689$	1.43380	−	2.48341i	0.0546233	−	0.0946103i
$690$	0.0197914	+	0.103380i	0.000753446	+	0.00393563i
$691$	−28.4084	−	7.61200i	−1.08071	−	0.289574i	−0.325820	−	0.945432i	$-0.605641\pi$
$691$	−28.4084	−	7.61200i	−1.08071	−	0.289574i	−0.754885	+	0.655858i	$0.772307\pi$
$692$	−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
$696$	8.98789	−	0.394484i	0.340685	−	0.0149529i
$697$	11.1156	+	6.41759i	0.421033	+	0.243083i
$698$	−16.2281	−	33.5130i	−0.614241	−	1.26849i
$699$	2.61138	+	2.61138i	0.0987713	+	0.0987713i
$700$		0			0
$701$	28.3466	−	28.3466i	1.07064	−	1.07064i	0.0733289	−	0.997308i	$-0.476638\pi$
$701$	28.3466	−	28.3466i	1.07064	−	1.07064i	0.997308	−	0.0733289i	$-0.0233623\pi$
$702$	−2.98048	+	8.57695i	−0.112491	+	0.323716i
$703$	3.83783	−	6.64732i	0.144747	−	0.250708i
$704$	−3.66401	+	20.8355i	−0.138093	+	0.785267i
$705$	−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
$709$	−7.84584	+	29.2811i	−0.294657	+	1.09967i	0.646833	+	0.762632i	$0.276093\pi$
$709$	−7.84584	+	29.2811i	−0.294657	+	1.09967i	−0.941490	+	0.337042i	$0.890574\pi$
$710$	28.5832	−	42.1185i	1.07271	−	1.58068i
$711$	−27.6068	−	15.9388i	−1.03534	−	0.597752i
$712$	−2.96458	+	5.69809i	−0.111102	+	0.213545i
$713$			0.0606921i			0.00227294i
$714$		0			0
$715$	14.0815	+	14.0815i	0.526617	+	0.526617i
$716$	0.214019	−	0.496360i	0.00799826	−	0.0185498i
$717$	0.266649	+	0.995146i	0.00995817	+	0.0371644i
$718$	0.593526	+	3.10029i	0.0221502	+	0.115702i
$719$	−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
$723$	7.49473	+	2.00821i	0.278732	+	0.0746861i
$724$	−0.245193	−	2.09498i	−0.00911253	−	0.0778595i
$725$	5.47505	−	1.46703i	0.203338	−	0.0544843i
$726$	−1.75133	+	0.848049i	−0.0649980	+	0.0314741i
$727$		−	19.9346i		−	0.739332i	−0.929165	−	0.369666i	$-0.879472\pi$
$727$		−	19.9346i		−	0.739332i	0.929165	−	0.369666i	$-0.120528\pi$
$728$		0			0
$729$		−	20.8402i		−	0.771858i
$730$	7.03522	+	14.5286i	0.260385	+	0.537729i
$731$	−40.8820	+	10.9543i	−1.51207	+	0.405159i
$732$	0.922743	−	1.16737i	0.0341056	−	0.0431471i
$733$	−13.4219	−	3.59639i	−0.495750	−	0.132836i	0.00227682	−	0.999997i	$-0.499275\pi$
$733$	−13.4219	−	3.59639i	−0.495750	−	0.132836i	−0.498027	+	0.867162i	$0.665942\pi$
$734$	−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
$738$	−9.75400	+	1.86733i	−0.359050	+	0.0687373i
$739$	5.79897	+	21.6421i	0.213319	+	0.796116i	0.986752	+	0.162238i	$0.0518712\pi$
$739$	5.79897	+	21.6421i	0.213319	+	0.796116i	−0.773433	+	0.633878i	$0.781462\pi$
$740$	−1.82761	−	4.59833i	−0.0671844	−	0.169038i
$741$	−5.67255	−	5.67255i	−0.208386	−	0.208386i
$742$		0			0
$743$		−	40.2309i		−	1.47593i	−0.674839	−	0.737965i	$-0.735787\pi$
$743$		−	40.2309i		−	1.47593i	0.674839	−	0.737965i	$-0.264213\pi$
$744$	0.614330	−	0.193852i	0.0225224	−	0.00710697i
$745$	−6.12987	−	3.53908i	−0.224581	−	0.129662i
$746$	27.4234	+	18.6106i	1.00404	+	0.681382i
$747$	11.5527	−	43.1152i	0.422690	−	1.57750i
$748$	−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	$0.880212\pi$
$752$	−15.4254	+	14.5620i	−0.562505	+	0.531021i
$753$	−0.592384	+	1.02604i	−0.0215877	+	0.0373909i
$754$	−39.3378	−	13.6698i	−1.43260	−	0.497826i
$755$	−36.5951	+	36.5951i	−1.33183	+	1.33183i
$756$		0			0
$757$	12.7497	+	12.7497i	0.463394	+	0.463394i	0.899766	−	0.436372i	$-0.143737\pi$
$757$	12.7497	+	12.7497i	0.463394	+	0.463394i	−0.436372	+	0.899766i	$0.643737\pi$
$758$	9.71485	−	4.70424i	0.352859	−	0.170866i
$759$	−0.0719520	−	0.0415415i	−0.00261169	−	0.00150786i
$760$	−2.15926	−	49.1965i	−0.0783248	−	1.78454i
$761$	−17.9392	+	10.3572i	−0.650297	+	0.375449i	−0.788570	−	0.614945i	$-0.789178\pi$
$761$	−17.9392	+	10.3572i	−0.650297	+	0.375449i	0.138273	+	0.990394i	$0.455845\pi$
$762$	8.87520	+	0.645881i	0.321515	+	0.0233978i
$763$		0			0
$764$	1.14601	−	7.83209i	0.0414612	−	0.283355i
$765$	−34.7403	−	9.30864i	−1.25604	−	0.336555i
$766$	25.8344	−	4.94580i	0.933435	−	0.178699i
$767$	15.2626	−	26.4357i	0.551102	−	0.954536i
$768$	−3.65483	−	4.10185i	−0.131882	−	0.148013i
$769$	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
$772$	1.65164	−	0.656446i	0.0594438	−	0.0236260i
$773$	34.5191	−	9.24937i	1.24157	−	0.332677i	0.422494	−	0.906366i	$-0.361155\pi$
$773$	34.5191	−	9.24937i	1.24157	−	0.332677i	0.819073	+	0.573689i	$0.194488\pi$
$774$	18.3893	−	27.0974i	0.660989	−	0.973995i
$775$	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
$779$	4.63472	−	17.2970i	0.166056	−	0.619730i
$780$	−5.13655	+	0.601173i	−0.183918	+	0.0215254i
$781$	10.3988	+	38.8090i	0.372100	+	1.38870i
$782$	0.643888	+	0.223750i	0.0230254	+	0.00800130i
$783$	−18.7095			−0.668624
$784$		0			0
$785$	6.95785			0.248336
$786$	4.52812	+	1.57352i	0.161513	+	0.0561255i
$787$	4.92879	+	18.3945i	0.175693	+	0.655693i	0.996433	+	0.0843917i	$0.0268947\pi$
$787$	4.92879	+	18.3945i	0.175693	+	0.655693i	−0.820740	+	0.571302i	$0.806439\pi$
$788$	1.59113	+	13.5950i	0.0566818	+	0.484302i
$789$	0.859172	−	3.20647i	0.0305873	−	0.114153i
$790$	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
$794$	11.0385	−	16.2656i	0.391740	−	0.577245i
$795$	0.708755	−	0.189910i	0.0251369	−	0.00673542i
$796$	6.46327	+	16.2618i	0.229085	+	0.576383i
$797$	3.26569	−	3.26569i	0.115677	−	0.115677i	−0.646899	−	0.762576i	$-0.723934\pi$
$797$	3.26569	−	3.26569i	0.115677	−	0.115677i	0.762576	+	0.646899i	$0.223934\pi$
$798$		0			0
$799$	−27.9364			−0.988317
$800$	−2.80699	−	2.02532i	−0.0992422	−	0.0716059i
$801$	3.27252	−	5.66818i	0.115629	−	0.200275i
$802$	14.9300	−	2.85823i	0.527196	−	0.100928i
$803$	−12.3075	−	3.29777i	−0.434321	−	0.116376i
$804$	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
$808$	30.6378	−	33.4506i	1.07783	−	1.17679i
$809$	25.2648	+	14.5866i	0.888263	+	0.512839i	0.873374	−	0.487050i	$-0.161927\pi$
$809$	25.2648	+	14.5866i	0.888263	+	0.512839i	0.0148891	+	0.999889i	$0.495260\pi$
$810$	23.9799	−	11.6118i	0.842566	−	0.407997i
$811$	−32.8375	−	32.8375i	−1.15308	−	1.15308i	−0.985932	−	0.167148i	$-0.946544\pi$
$811$	−32.8375	−	32.8375i	−1.15308	−	1.15308i	−0.167148	−	0.985932i	$-0.553456\pi$
$812$		0			0
$813$	6.95471	−	6.95471i	0.243912	−	0.243912i
$814$	3.68936	+	1.28205i	0.129312	+	0.0449358i
$815$	−11.7410	+	20.3359i	−0.411268	+	0.712337i
$816$	0.208222	−	7.23215i	0.00728921	−	0.253176i
$817$	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
$821$	8.00627	−	29.8798i	0.279421	−	1.04281i	−0.673400	−	0.739279i	$-0.735167\pi$
$821$	8.00627	−	29.8798i	0.279421	−	1.04281i	0.952821	−	0.303534i	$-0.0981666\pi$
$822$	−6.77642	−	4.59873i	−0.236355	−	0.160399i
$823$	−24.4402	−	14.1106i	−0.851932	−	0.491863i	0.00937002	−	0.999956i	$-0.497017\pi$
$823$	−24.4402	−	14.1106i	−0.851932	−	0.491863i	−0.861302	+	0.508093i	$0.830351\pi$
$824$	15.9525	−	30.6617i	0.555733	−	1.06815i
$825$			0.555600i			0.0193435i
$826$		0			0
$827$	−21.9283	−	21.9283i	−0.762522	−	0.762522i	0.214256	−	0.976778i	$-0.431267\pi$
$827$	−21.9283	−	21.9283i	−0.762522	−	0.762522i	−0.976778	+	0.214256i	$0.931267\pi$
$828$	−0.490134	+	0.194804i	−0.0170333	+	0.00676992i
$829$	−0.365814	−	1.36524i	−0.0127052	−	0.0474166i	0.959282	−	0.282449i	$-0.0911469\pi$
$829$	−0.365814	−	1.36524i	−0.0127052	−	0.0474166i	−0.971987	+	0.235033i	$0.924480\pi$
$830$	50.9602	−	9.75595i	1.76885	−	0.338634i
$831$	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
$835$	−38.9589	−	10.4390i	−1.34823	−	0.361257i
$836$	30.4936	+	24.1036i	1.05464	+	0.833641i
$837$	−1.29403	+	0.346735i	−0.0447283	+	0.0119849i
$838$	−3.45422	−	7.13340i	−0.119324	−	0.246419i
$839$		−	4.25867i		−	0.147026i	−0.997294	−	0.0735128i	$-0.976579\pi$
$839$		−	4.25867i		−	0.147026i	0.997294	−	0.0735128i	$-0.0234210\pi$
$840$		0			0
$841$		−	56.8104i		−	1.95898i
$842$	−29.1625	+	14.1214i	−1.00501	+	0.486656i
$843$	−6.49443	+	1.74018i	−0.223680	+	0.0599349i
$844$	−23.9599	+	2.80423i	−0.824735	+	0.0965254i
$845$	−6.62309	−	1.77465i	−0.227841	−	0.0610499i
$846$	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
$850$	−0.857112	−	4.47713i	−0.0293987	−	0.153564i
$851$	−0.0247334	−	0.0923063i	−0.000847850	−	0.00316422i
$852$	−9.58133	−	4.13124i	−0.328251	−	0.141534i
$853$	−16.5250	−	16.5250i	−0.565806	−	0.565806i	0.365144	−	0.930951i	$-0.381020\pi$
$853$	−16.5250	−	16.5250i	−0.565806	−	0.565806i	−0.930951	+	0.365144i	$0.881020\pi$
$854$		0			0
$855$			50.1783i			1.71606i
$856$	6.42813	+	20.3711i	0.219709	+	0.696271i
$857$	−22.7948	−	13.1606i	−0.778655	−	0.449556i	0.0572986	−	0.998357i	$-0.481751\pi$
$857$	−22.7948	−	13.1606i	−0.778655	−	0.449556i	−0.835953	+	0.548801i	$0.815085\pi$
$858$	2.29226	−	3.37774i	0.0782564	−	0.115314i
$859$	−12.5923	+	46.9949i	−0.429642	+	1.60345i	0.323930	+	0.946081i	$0.394996\pi$
$859$	−12.5923	+	46.9949i	−0.429642	+	1.60345i	−0.753572	+	0.657365i	$0.771671\pi$
$860$	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	$0.779467\pi$
$864$	7.21936	+	8.85542i	0.245608	+	0.301268i
$865$	−0.290032	+	0.502351i	−0.00986139	+	0.0170804i
$866$	6.91432	−	19.8974i	0.234958	−	0.676140i
$867$	2.60993	−	2.60993i	0.0886379	−	0.0886379i
$868$		0			0
$869$	20.6819	+	20.6819i	0.701584	+	0.701584i
$870$	−4.64420	−	9.59088i	−0.157453	−	0.325161i
$871$	−25.7529	−	14.8684i	−0.872604	−	0.503798i
$872$	9.14680	+	8.37764i	0.309750	+	0.283703i
$873$	−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
$877$	32.8300	+	8.79678i	1.10859	+	0.297046i	0.766258	−	0.642533i	$-0.222116\pi$
$877$	32.8300	+	8.79678i	1.10859	+	0.297046i	0.342333	+	0.939579i	$0.388783\pi$
$878$	−7.01616	−	36.6489i	−0.236784	−	1.23684i
$879$	−3.25882	+	5.64444i	−0.109917	+	0.190382i
$880$	24.3805	−	5.78617i	0.821868	−	0.195052i
$881$	−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	−0.213765	−	0.976885i	$-0.568573\pi$
$883$	22.6764	−	22.6764i	0.763120	−	0.763120i	0.976885	+	0.213765i	$0.0685727\pi$
$884$	−13.2607	+	30.7546i	−0.446005	+	1.03439i
$885$	7.54463	−	2.02158i	0.253610	−	0.0679546i
$886$	12.9084	+	8.76012i	0.433666	+	0.294302i
$887$	46.9094	−	27.0831i	1.57506	−	0.909362i	0.579529	−	0.814952i	$-0.303237\pi$
$887$	46.9094	−	27.0831i	1.57506	−	0.909362i	0.995533	−	0.0944105i	$-0.0300966\pi$
$888$	−0.855333	+	0.545183i	−0.0287031	+	0.0182951i
$889$		0			0
$890$	7.58799	+	0.552206i	0.254350	+	0.0185100i
$891$	−5.44305	+	20.3138i	−0.182349	+	0.680536i
$892$	−39.7454	−	31.4167i	−1.33078	−	1.05191i
$893$	10.0877	+	37.6478i	0.337572	+	1.25983i
$894$	−0.476255	+	1.37052i	−0.0159284	+	0.0458371i
$895$	−0.640248			−0.0214011
$896$		0			0
$897$	−0.0998770			−0.00333479
$898$	14.6622	−	42.1934i	0.489283	−	1.40801i
$899$	−1.59028	−	5.93501i	−0.0530389	−	0.197944i
$900$	2.76702	+	2.18718i	0.0922338	+	0.0729062i
$901$	1.22987	−	4.58994i	0.0409729	−	0.152913i
$902$	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
$906$	8.77812	+	5.95716i	0.291633	+	0.197913i
$907$	−12.7137	+	3.40663i	−0.422152	+	0.113115i	−0.463640	−	0.886024i	$-0.653457\pi$
$907$	−12.7137	+	3.40663i	−0.422152	+	0.113115i	0.0414881	+	0.999139i	$0.486790\pi$
$908$	0.587907	−	1.36350i	0.0195104	−	0.0452492i
$909$	−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	$0.366734\pi$
$912$	−9.82142	+	2.33089i	−0.325220	+	0.0771835i
$913$	−20.4774	+	35.4679i	−0.677704	+	1.17382i
$914$	2.05191	+	10.7181i	0.0678711	+	0.354525i
$915$	−1.70246	−	0.456172i	−0.0562815	−	0.0150806i
$916$	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	−0.0661060	−	0.997813i	$-0.521058\pi$
$919$	23.1901	−	13.3888i	0.764972	−	0.441657i	0.831078	+	0.556156i	$0.187724\pi$
$920$	−0.452112	−	0.414093i	−0.0149057	−	0.0136523i
$921$	7.63770	+	4.40963i	0.251671	+	0.145302i
$922$	2.76946	+	5.71930i	0.0912074	+	0.188355i
$923$	34.1528	+	34.1528i	1.12415	+	1.12415i
$924$		0			0
$925$	−0.451880	+	0.451880i	−0.0148577	+	0.0148577i
$926$	−3.67152	+	10.5655i	−0.120654	+	0.347205i
$927$	−17.6096	+	30.5007i	−0.578375	+	1.00177i
$928$	−40.6150	+	33.1113i	−1.33325	+	1.08693i
$929$	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
$933$	2.78741	−	10.4028i	0.0912558	−	0.340571i
$934$	−18.7392	+	27.6129i	−0.613165	+	0.903523i
$935$	28.5785	+	16.4998i	0.934617	+	0.539601i
$936$	−7.79815	−	24.7128i	−0.254891	−	0.807764i
$937$		−	19.6850i		−	0.643080i	−0.946896	−	0.321540i	$-0.895800\pi$
$937$		−	19.6850i		−	0.643080i	0.946896	−	0.321540i	$-0.104200\pi$
$938$		0			0
$939$	3.26270	+	3.26270i	0.106474	+	0.106474i
$940$	23.0728	+	9.94847i	0.752553	+	0.324483i
$941$	−0.243750	−	0.909688i	−0.00794603	−	0.0296550i	0.961839	−	0.273616i	$-0.0882198\pi$
$941$	−0.243750	−	0.909688i	−0.00794603	−	0.0296550i	−0.969785	+	0.243961i	$0.921553\pi$
$942$	−0.268175	−	1.40081i	−0.00873762	−	0.0456410i
$943$	−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
$947$	−17.5325	−	4.69782i	−0.569730	−	0.152659i	−0.0375571	−	0.999294i	$-0.511958\pi$
$947$	−17.5325	−	4.69782i	−0.569730	−	0.152659i	−0.532173	+	0.846636i	$0.678624\pi$
$948$	−7.54421	+	0.882960i	−0.245024	+	0.0286772i
$949$	−14.7952	+	3.96437i	−0.480273	+	0.128689i
$950$	−5.72400	+	2.77174i	−0.185711	+	0.0899270i
$951$			8.09471i			0.262489i
$952$		0			0
$953$			36.9302i			1.19629i	0.801390	+	0.598143i	$0.204094\pi$
$953$			36.9302i			1.19629i	−0.801390	+	0.598143i	$0.795906\pi$
$954$	1.60240	+	3.30917i	0.0518796	+	0.107138i
$955$	−9.05621	+	2.42660i	−0.293052	+	0.0785230i
$956$	−4.70772	−	3.72122i	−0.152259	−	0.120353i
$957$	8.12460	+	2.17698i	0.262631	+	0.0703717i
$958$	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
$962$	4.61151	−	0.882839i	0.148681	−	0.0284639i
$963$	−5.63362	−	21.0249i	−0.181541	−	0.677519i
$964$	−41.9985	+	16.6924i	−1.35268	+	0.537625i
$965$	−1.48858	−	1.48858i	−0.0479192	−	0.0479192i
$966$		0			0
$967$			15.9039i			0.511436i	0.966751	+	0.255718i	$0.0823119\pi$
$967$			15.9039i			0.511436i	−0.966751	+	0.255718i	$0.917688\pi$
$968$	5.23111	−	10.0545i	0.168134	−	0.323164i
$969$	−11.5125	−	6.64675i	−0.369835	−	0.213525i
$970$	−48.5004	−	32.9142i	−1.55726	−	1.05681i
$971$	3.26217	−	12.1746i	0.104688	−	0.390701i	−0.893622	−	0.448821i	$-0.851844\pi$
$971$	3.26217	−	12.1746i	0.104688	−	0.390701i	0.998310	+	0.0581203i	$0.0185107\pi$
$972$	−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
$976$	−0.249434	+	8.66358i	−0.00798419	+	0.277314i
$977$	−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	$0.936257\pi$
$978$	4.54673	+	1.57998i	0.145388	+	0.0505223i
$979$	−4.24636	+	4.24636i	−0.135714	+	0.135714i
$980$		0			0
$981$	−8.93708	−	8.93708i	−0.285339	−	0.285339i
$982$	−14.9114	+	7.22057i	−0.475843	+	0.230418i
$983$	1.97172	+	1.13838i	0.0628882	+	0.0363085i	0.531114	−	0.847300i	$-0.321773\pi$
$983$	1.97172	+	1.13838i	0.0628882	+	0.0363085i	−0.468226	+	0.883609i	$0.655107\pi$
$984$	−1.59829	+	1.74503i	−0.0509516	+	0.0556295i
$985$	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
$989$	0.710116	+	0.190275i	0.0225804	+	0.00605039i
$990$	−25.0778	+	4.80096i	−0.797025	+	0.152584i
$991$	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	$-0.0404973\pi$
$992$	−2.19547	+	3.04281i	−0.0697063	+	0.0966094i
$993$	2.88456			0.0915386
$994$		0			0
$995$	14.6564	−	14.6564i	0.464638	−	0.464638i
$996$	−3.92830	−	9.88372i	−0.124473	−	0.313178i
$997$	−34.6346	+	9.28031i	−1.09689	+	0.293911i	−0.761497	−	0.648168i	$-0.775535\pi$
$997$	−34.6346	+	9.28031i	−1.09689	+	0.293911i	−0.335392	+	0.942079i	$0.608869\pi$
$998$	9.61497	−	14.1680i	0.304356	−	0.448482i
$999$	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.165.14		96
7.2	even	3	inner	784.2.x.p.373.1		96
7.3	odd	6		784.2.m.l.197.19	✓	48
7.4	even	3		784.2.m.l.197.20	yes	48
7.5	odd	6	inner	784.2.x.p.373.2		96
7.6	odd	2	inner	784.2.x.p.165.13		96
16.13	even	4	inner	784.2.x.p.557.1		96
112.13	odd	4	inner	784.2.x.p.557.2		96
112.45	odd	12		784.2.m.l.589.19	yes	48
112.61	odd	12	inner	784.2.x.p.765.13		96
112.93	even	12	inner	784.2.x.p.765.14		96
112.109	even	12		784.2.m.l.589.20	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
784.2.m.l.197.19	✓	48	7.3	odd	6
784.2.m.l.197.20	yes	48	7.4	even	3
784.2.m.l.589.19	yes	48	112.45	odd	12
784.2.m.l.589.20	yes	48	112.109	even	12
784.2.x.p.165.13		96	7.6	odd	2	inner
784.2.x.p.165.14		96	1.1	even	1	trivial
784.2.x.p.373.1		96	7.2	even	3	inner
784.2.x.p.373.2		96	7.5	odd	6	inner
784.2.x.p.557.1		96	16.13	even	4	inner
784.2.x.p.557.2		96	112.13	odd	4	inner
784.2.x.p.765.13		96	112.61	odd	12	inner
784.2.x.p.765.14		96	112.93	even	12	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)

\(f(q)\)	\(=\)	\(q+(0.464209 - 1.33586i) q^{2} +(0.0888704 + 0.331669i) q^{3} +(-1.56902 - 1.24023i) q^{4} +(-0.613128 + 2.28822i) q^{5} +(0.484316 + 0.0352455i) q^{6} +(-2.38512 + 1.52026i) q^{8} +(2.49597 - 1.44105i) q^{9} +O(q^{10})\)	\(q+(0.464209 - 1.33586i) q^{2} +(0.0888704 + 0.331669i) q^{3} +(-1.56902 - 1.24023i) q^{4} +(-0.613128 + 2.28822i) q^{5} +(0.484316 + 0.0352455i) q^{6} +(-2.38512 + 1.52026i) q^{8} +(2.49597 - 1.44105i) q^{9} +(2.77212 + 1.88126i) q^{10} +(-2.55430 + 0.684421i) q^{11} +(0.271906 - 0.630615i) q^{12} +(-2.24784 + 2.24784i) q^{13} -0.813421 q^{15} +(0.923653 + 3.89190i) q^{16} +(-2.63388 + 4.56202i) q^{17} +(-0.766383 - 4.00320i) q^{18} +(7.09898 + 1.90217i) q^{19} +(3.79994 - 2.82985i) q^{20} +(-0.271438 + 3.72988i) q^{22} +(0.0792419 - 0.0457503i) q^{23} +(-0.716189 - 0.655965i) q^{24} +(-0.529913 - 0.305946i) q^{25} +(1.95932 + 4.04626i) q^{26} +(1.42816 + 1.42816i) q^{27} +(-6.55020 + 6.55020i) q^{29} +(-0.377597 + 1.08661i) q^{30} +(-0.331648 + 0.574432i) q^{31} +(5.62778 + 0.572785i) q^{32} +(-0.454002 - 0.786355i) q^{33} +(4.87153 + 5.63622i) q^{34} +(-5.70346 - 0.834544i) q^{36} +(0.270309 - 1.00881i) q^{37} +(5.83643 - 8.60021i) q^{38} +(-0.945305 - 0.545772i) q^{39} +(-2.01631 - 6.38981i) q^{40} -2.43655i q^{41} +(5.68128 + 5.68128i) q^{43} +(4.85658 + 2.09405i) q^{44} +(1.76709 + 6.59488i) q^{45} +(-0.0243311 - 0.127093i) q^{46} +(2.65163 + 4.59276i) q^{47} +(-1.20874 + 0.652221i) q^{48} +(-0.654689 + 0.565865i) q^{50} +(-1.74715 - 0.468149i) q^{51} +(6.31475 - 0.739067i) q^{52} +(-0.871326 + 0.233471i) q^{53} +(2.57079 - 1.24486i) q^{54} -6.26444i q^{55} +2.52356i q^{57} +(5.70947 + 11.7908i) q^{58} +(-9.27519 + 2.48528i) q^{59} +(1.27627 + 1.00883i) q^{60} +(2.09296 + 0.560807i) q^{61} +(0.613404 + 0.709691i) q^{62} +(3.37762 - 7.25201i) q^{64} +(-3.76535 - 6.52177i) q^{65} +(-1.26121 + 0.241449i) q^{66} +(2.42109 + 9.03564i) q^{67} +(9.79058 - 3.89128i) q^{68} +(0.0222162 + 0.0222162i) q^{69} -15.1936i q^{71} +(-3.76243 + 7.23160i) q^{72} +(4.17280 + 2.40917i) q^{73} +(-1.22214 - 0.829390i) q^{74} +(0.0543790 - 0.202945i) q^{75} +(-8.77932 - 11.7889i) q^{76} +(-1.16789 + 1.00944i) q^{78} +(-5.53028 - 9.57872i) q^{79} +(-9.47185 - 0.272705i) q^{80} +(3.97639 - 6.88731i) q^{81} +(-3.25488 - 1.13107i) q^{82} +(10.9512 - 10.9512i) q^{83} +(-8.82402 - 8.82402i) q^{85} +(10.2267 - 4.95207i) q^{86} +(-2.75462 - 1.59038i) q^{87} +(5.05181 - 5.51562i) q^{88} +(1.96668 - 1.13547i) q^{89} +(9.63011 + 0.700819i) q^{90} +(-0.181073 - 0.0264950i) q^{92} +(-0.219995 - 0.0589474i) q^{93} +(7.36617 - 1.41020i) q^{94} +(-8.70516 + 15.0778i) q^{95} +(0.310168 + 1.91746i) q^{96} -17.4958 q^{97} +(-5.38916 + 5.38916i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 4 q^{4}+O(q^{10}) \) 96 * q + 4 * q^4	\( 96 q + 4 q^{4} + 8 q^{11} + 64 q^{15} - 36 q^{16} - 20 q^{18} - 56 q^{22} - 32 q^{29} - 96 q^{30} - 40 q^{32} + 80 q^{36} + 16 q^{37} + 16 q^{43} - 4 q^{44} - 64 q^{46} - 56 q^{50} - 16 q^{53} + 20 q^{58} - 8 q^{60} + 88 q^{64} - 40 q^{67} + 196 q^{72} + 28 q^{74} + 112 q^{78} - 80 q^{79} + 48 q^{81} + 108 q^{86} + 100 q^{88} + 128 q^{95} - 80 q^{99}+O(q^{100}) \) 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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