LMFDB - Embedded newform 784.2.x.p.765.13

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			765.13
Character	$\chi$	$=$	784.765
Dual form			784.2.x.p.165.13

$q$-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} +(-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} + 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 $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

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

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	$-0.948270\pi$
$3$	−0.0888704	+	0.331669i	−0.0513093	+	0.191489i	0.935514	+	0.353289i	$0.114937\pi$
$4$	−1.56902	+	1.24023i	−0.784510	+	0.620116i
$5$	0.613128	+	2.28822i	0.274199	+	1.02332i	0.956376	+	0.292138i	$0.0943666\pi$
$5$	0.613128	+	2.28822i	0.274199	+	1.02332i	−0.682177	+	0.731187i	$0.738967\pi$
$6$	−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	−0.147712	−	0.989030i	$-0.547191\pi$
$11$	−2.55430	−	0.684421i	−0.770149	−	0.206361i	−0.622437	+	0.782670i	$0.713857\pi$
$12$	−0.271906	−	0.630615i	−0.0784926	−	0.182043i
$13$	2.24784	+	2.24784i	0.623439	+	0.623439i	0.946409	−	0.322970i	$-0.104681\pi$
$13$	2.24784	+	2.24784i	0.623439	+	0.623439i	−0.322970	+	0.946409i	$0.604681\pi$
$14$		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	0.985694	+	0.168544i	$0.0539066\pi$
$17$	2.63388	+	4.56202i	0.638811	+	1.10645i	−0.346883	+	0.937908i	$0.612760\pi$
$18$	−0.766383	+	4.00320i	−0.180638	+	0.943564i
$19$	−7.09898	+	1.90217i	−1.62862	+	0.436387i	−0.953517	−	0.301339i	$-0.902567\pi$
$19$	−7.09898	+	1.90217i	−1.62862	+	0.436387i	−0.675101	+	0.737726i	$0.735900\pi$
$20$	−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	$-0.330297\pi$
$23$	0.0792419	+	0.0457503i	0.0165231	+	0.00953960i	−0.491716	+	0.870756i	$0.663630\pi$
$24$	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	−0.968903	−	0.247439i	$-0.920411\pi$
$29$	−6.55020	−	6.55020i	−1.21634	−	1.21634i	−0.247439	−	0.968903i	$-0.579589\pi$
$30$	−0.377597	−	1.08661i	−0.0689395	−	0.198388i
$31$	0.331648	+	0.574432i	0.0595658	+	0.103171i	0.894271	−	0.447527i	$-0.147695\pi$
$31$	0.331648	+	0.574432i	0.0595658	+	0.103171i	−0.834705	+	0.550698i	$0.814362\pi$
$32$	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	0.984579	−	0.174940i	$-0.0559732\pi$
$37$	0.270309	+	1.00881i	0.0444385	+	0.165847i	−0.940141	+	0.340787i	$0.889307\pi$
$38$	−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	−0.125683	−	0.992070i	$-0.540112\pi$
$43$	5.68128	−	5.68128i	0.866388	−	0.866388i	0.992070	+	0.125683i	$0.0401122\pi$
$44$	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	$-0.959746\pi$
$47$	−2.65163	+	4.59276i	−0.386780	+	0.669923i	0.605234	+	0.796047i	$0.293079\pi$
$48$	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	0.198479	−	0.980105i	$-0.436400\pi$
$53$	−0.871326	−	0.233471i	−0.119686	−	0.0320697i	−0.318165	+	0.948035i	$0.603067\pi$
$54$	−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	$-0.201740\pi$
$59$	9.27519	+	2.48528i	1.20753	+	0.323556i	0.401736	+	0.915756i	$0.368407\pi$
$60$	1.27627	−	1.00883i	0.164766	−	0.130239i
$61$	−2.09296	+	0.560807i	−0.267976	+	0.0718040i	−0.390305	−	0.920686i	$-0.627630\pi$
$61$	−2.09296	+	0.560807i	−0.267976	+	0.0718040i	0.122329	+	0.992490i	$0.460964\pi$
$62$	−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	−0.644810	−	0.764343i	$-0.723063\pi$
$67$	2.42109	−	9.03564i	0.295783	−	1.10388i	0.940593	−	0.339536i	$-0.110270\pi$
$68$	−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	$0.357589\pi$
$71$			15.1936i			1.80315i	−0.432621	+	0.901576i	$0.642411\pi$
$72$	−3.76243	−	7.23160i	−0.443406	−	0.852252i
$73$	−4.17280	+	2.40917i	−0.488390	+	0.281972i	−0.723906	−	0.689899i	$-0.757655\pi$
$73$	−4.17280	+	2.40917i	−0.488390	+	0.281972i	0.235517	+	0.971870i	$0.424322\pi$
$74$	−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	0.366869	+	0.930272i	$0.380430\pi$
$79$	−5.53028	+	9.57872i	−0.622205	+	1.07769i	−0.989074	+	0.147418i	$0.952904\pi$
$80$	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	−0.973541	−	0.228512i	$-0.926614\pi$
$83$	−10.9512	−	10.9512i	−1.20205	−	1.20205i	−0.228512	−	0.973541i	$-0.573386\pi$
$84$		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	$-0.371738\pi$
$89$	−1.96668	−	1.13547i	−0.208468	−	0.120359i	−0.600599	+	0.799550i	$0.705071\pi$
$90$	−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	$-0.151945\pi$
$97$	17.4958			1.77643			0.888215	+	0.459427i	$0.151945\pi$
$98$		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	$-0.122613\pi$
$101$	15.4911	+	4.15082i	1.54142	+	0.413022i	0.614694	+	0.788766i	$0.289279\pi$
$102$	−1.43642	−	2.11663i	−0.142227	−	0.209577i
$103$	10.5828	+	6.10999i	1.04276	+	0.602035i	0.920613	−	0.390477i	$-0.127690\pi$
$103$	10.5828	+	6.10999i	1.04276	+	0.602035i	0.122143	+	0.992513i	$0.461023\pi$
$104$	−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	0.993746	+	0.111661i	$0.0356171\pi$
$107$	1.95469	+	7.29501i	0.188967	+	0.705236i	−0.804779	+	0.593575i	$0.797716\pi$
$108$	0.469566	−	4.01207i	0.0451840	−	0.386062i
$109$	−1.13501	+	4.23590i	−0.108714	+	0.405726i	−0.998740	−	0.0501838i	$-0.984019\pi$
$109$	−1.13501	+	4.23590i	−0.108714	+	0.405726i	0.890026	+	0.455910i	$0.150686\pi$
$110$	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	$-0.725262\pi$
$131$	−9.53546	+	2.55502i	−0.833117	+	0.223233i	−0.183044	+	0.983105i	$0.558595\pi$
$132$	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	−0.970675	−	0.240396i	$-0.922723\pi$
$137$	−14.6054	+	8.43243i	−1.24782	+	0.720431i	−0.277148	+	0.960827i	$0.589389\pi$
$138$	−0.0399906	−	0.0193647i	−0.00340423	−	0.00164843i
$139$	6.01333	−	6.01333i	0.510044	−	0.510044i	−0.404496	−	0.914540i	$-0.632553\pi$
$139$	6.01333	−	6.01333i	0.510044	−	0.510044i	0.914540	+	0.404496i	$0.132553\pi$
$140$		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	0.926988	−	0.375092i	$-0.122389\pi$
$149$	−0.773325	−	2.88609i	−0.0633533	−	0.236438i	−0.990341	+	0.138655i	$0.955722\pi$
$150$	0.245862	−	0.166851i	0.0200746	−	0.0136234i
$151$	18.9197	−	10.9233i	1.53966	−	0.888925i	0.540806	−	0.841147i	$-0.318119\pi$
$151$	18.9197	−	10.9233i	1.53966	−	0.888925i	0.998858	−	0.0477779i	$-0.0152140\pi$
$152$	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	$-0.879274\pi$
$157$	0.760181	−	2.83703i	0.0606690	−	0.226420i	0.989603	+	0.143825i	$0.0459403\pi$
$158$	−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	0.136451	−	0.990647i	$-0.456430\pi$
$163$	9.57465	−	2.56552i	0.749944	−	0.200947i	0.613493	+	0.789700i	$0.289764\pi$
$164$	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	$-0.586296\pi$
$173$	−0.236519	+	0.0633750i	−0.0179822	+	0.00481831i	0.249817	+	0.968293i	$0.419630\pi$
$174$	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	−0.963262	−	0.268562i	$-0.913452\pi$
$179$	0.0699503	−	0.261058i	0.00522833	−	0.0195124i	0.968491	+	0.249050i	$0.0801182\pi$
$180$	−5.40657	−	12.5391i	−0.402982	−	0.934610i
$181$	−0.745744	+	0.745744i	−0.0554307	+	0.0554307i	−0.734279	−	0.678848i	$-0.762479\pi$
$181$	−0.745744	+	0.745744i	−0.0554307	+	0.0554307i	0.678848	+	0.734279i	$0.262479\pi$
$182$		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	−0.785509	−	0.618851i	$-0.787599\pi$
$191$	1.97887	−	3.42751i	0.143186	−	0.248006i	0.928695	+	0.370845i	$0.120932\pi$
$192$	−2.70544	+	0.475762i	−0.195248	+	0.0343352i
$193$	−0.444328	−	0.769598i	−0.0319834	−	0.0553969i	0.849591	−	0.527443i	$-0.176849\pi$
$193$	−0.444328	−	0.769598i	−0.0319834	−	0.0553969i	−0.881574	+	0.472046i	$0.843516\pi$
$194$	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	−0.858165	−	0.513374i	$-0.828395\pi$
$197$	−4.83936	+	4.83936i	−0.344790	+	0.344790i	0.513374	+	0.858165i	$0.328395\pi$
$198$	4.69745	−	9.70084i	0.333833	−	0.689408i
$199$	7.57734	−	4.37478i	0.537144	−	0.310120i	−0.206777	−	0.978388i	$-0.566297\pi$
$199$	7.57734	−	4.37478i	0.537144	−	0.310120i	0.743920	+	0.668268i	$0.232964\pi$
$200$	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	0.936860	−	0.349704i	$-0.113718\pi$
$211$	8.52893	+	8.52893i	0.587156	+	0.587156i	−0.349704	+	0.936860i	$0.613718\pi$
$212$	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	$-0.822287\pi$
$223$	−25.3314			−1.69631			−0.848156	+	0.529746i	$0.822287\pi$
$224$		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	$-0.924510\pi$
$227$	−0.192153	+	0.717124i	−0.0127536	+	0.0475972i	0.959256	+	0.282539i	$0.0911767\pi$
$228$	3.12979	+	3.95951i	0.207276	+	0.262225i
$229$	4.16121	+	15.5299i	0.274981	+	1.02624i	0.955854	+	0.293841i	$0.0949337\pi$
$229$	4.16121	+	15.5299i	0.274981	+	1.02624i	−0.680873	+	0.732401i	$0.738400\pi$
$230$	−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	$-0.218732\pi$
$233$	9.31438	+	5.37766i	0.610206	+	0.352302i	−0.162840	+	0.986652i	$0.552066\pi$
$234$	−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	−0.957810	−	0.287401i	$-0.907209\pi$
$241$	−11.2985	−	19.5696i	−0.727802	−	1.26059i	0.230009	−	0.973189i	$-0.426125\pi$
$242$	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	$-0.784731\pi$
$251$	−2.43982	+	2.43982i	−0.154000	+	0.154000i	0.625902	+	0.779902i	$0.284731\pi$
$252$		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	−0.419770	−	0.907631i	$-0.637889\pi$
$257$	9.23633	−	15.9978i	0.576147	−	0.997915i	0.995916	−	0.0902843i	$-0.0287776\pi$
$258$	−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	−0.735407	−	0.677626i	$-0.763009\pi$
$263$	−8.37247	+	4.83385i	−0.516269	+	0.298068i	0.219138	+	0.975694i	$0.429676\pi$
$264$	−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	0.462162	+	0.886796i	$0.347074\pi$
$269$	−6.25673	+	23.3504i	−0.381480	+	1.42370i	−0.843642	+	0.536906i	$0.819593\pi$
$270$	1.27229	−	6.64579i	0.0774289	−	0.404450i
$271$	14.3220	−	24.8064i	0.869999	−	1.50688i	0.00800296	−	0.999968i	$-0.497453\pi$
$271$	14.3220	−	24.8064i	0.869999	−	1.50688i	0.861996	−	0.506915i	$-0.169214\pi$
$272$	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	0.703053	−	0.711138i	$-0.251820\pi$
$277$	15.9168	+	4.26488i	0.956345	+	0.256252i	0.253293	+	0.967390i	$0.418486\pi$
$278$	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	$-0.801466\pi$
$281$		−	19.5811i		−	1.16811i	0.811715	−	0.584054i	$-0.198534\pi$
$282$	1.12235	−	2.31780i	0.0668352	−	0.138023i
$283$	0.491997	+	0.131830i	0.0292462	+	0.00783649i	0.273412	−	0.961897i	$-0.411848\pi$
$283$	0.491997	+	0.131830i	0.0292462	+	0.00783649i	−0.244166	+	0.969733i	$0.578514\pi$
$284$	−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	$-0.937073\pi$
$293$	−13.4219	+	13.4219i	−0.784117	+	0.784117i	0.196406	+	0.980523i	$0.437073\pi$
$294$		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	−0.999307	−	0.0372355i	$-0.988145\pi$
$307$	−18.1617	−	18.1617i	−1.03654	−	1.03654i	−0.0372355	−	0.999307i	$-0.511855\pi$
$308$		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	0.541440	−	0.840739i	$-0.317879\pi$
$311$	27.1628	−	15.6825i	1.54026	−	0.889271i	0.998822	−	0.0485315i	$-0.0154541\pi$
$312$	3.08438	+	0.135376i	0.174619	+	0.00766413i
$313$	−11.6376	−	6.71895i	−0.657794	−	0.379777i	0.133642	−	0.991030i	$-0.457333\pi$
$313$	−11.6376	−	6.71895i	−0.657794	−	0.379777i	−0.791436	+	0.611252i	$0.790666\pi$
$314$	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	0.445499	−	0.895282i	$-0.353026\pi$
$317$	22.7711	−	6.10150i	1.27895	−	0.342695i	0.833455	+	0.552588i	$0.186360\pi$
$318$	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	0.999585	−	0.0288201i	$-0.00917498\pi$
$331$	2.17427	+	8.11450i	0.119509	+	0.446013i	−0.880076	+	0.474833i	$0.842508\pi$
$332$	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	0.558849	−	0.829269i	$-0.311243\pi$
$347$	11.7019	+	3.13552i	0.628193	+	0.168324i	0.0693432	+	0.997593i	$0.477910\pi$
$348$	−2.34961	+	5.91170i	−0.125953	+	0.316900i
$349$	−18.6177	−	18.6177i	−0.996582	−	0.996582i	0.00341200	−	0.999994i	$-0.498914\pi$
$349$	−18.6177	−	18.6177i	−0.996582	−	0.996582i	−0.999994	+	0.00341200i	$0.998914\pi$
$350$		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	−0.991824	−	0.127615i	$-0.959268\pi$
$353$	−11.3938	−	19.7346i	−0.606430	−	1.05037i	0.385394	−	0.922752i	$-0.374066\pi$
$354$	−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	0.448122	−	0.893973i	$-0.352093\pi$
$359$	−1.93301	−	1.11602i	−0.102020	−	0.0589014i	−0.550142	+	0.835071i	$0.685426\pi$
$360$	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	−0.998972	−	0.0453208i	$-0.985569\pi$
$367$	−10.3207	−	17.8759i	−0.538735	−	0.933117i	0.460237	−	0.887796i	$-0.347764\pi$
$368$	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	−0.924865	−	0.380295i	$-0.875823\pi$
$373$	−6.06542	−	22.6365i	−0.314056	−	1.17207i	0.610810	−	0.791777i	$-0.290844\pi$
$374$	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	−0.554777	−	0.831999i	$-0.687196\pi$
$379$	5.39695	−	5.39695i	0.277223	−	0.277223i	0.831999	+	0.554777i	$0.187196\pi$
$380$	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	$-0.990955\pi$
$383$	−9.29971	+	16.1076i	−0.475193	+	0.823058i	0.524403	+	0.851470i	$0.324288\pi$
$384$	−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	0.353052	−	0.935604i	$-0.385144\pi$
$389$	3.76716	+	1.00941i	0.191003	+	0.0511790i	−0.162050	+	0.986783i	$0.551810\pi$
$390$	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	$-0.696747\pi$
$397$	−13.4263	+	3.59757i	−0.673848	+	0.180557i	−0.0943605	+	0.995538i	$0.530081\pi$
$398$	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	−0.700060	−	0.714084i	$-0.746843\pi$
$401$	5.37440	−	9.30874i	0.268385	−	0.464856i	0.968445	+	0.249228i	$0.0801768\pi$
$402$	−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	$-0.735447\pi$
$409$	−7.51025	+	4.33605i	−0.371358	+	0.214404i	0.302694	+	0.953088i	$0.402114\pi$
$410$	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	$-0.293712\pi$
$419$	−3.96286	−	3.96286i	−0.193598	−	0.193598i	−0.797249	+	0.603651i	$0.793712\pi$
$420$		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	$0.438553\pi$
$422$	−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	0.872750	−	0.488167i	$-0.162334\pi$
$431$	0.282550	+	0.489392i	0.0136100	+	0.0235732i	−0.859140	+	0.511740i	$0.829001\pi$
$432$	4.23914	+	6.87740i	0.203956	+	0.330889i
$433$	−14.8949			−0.715801			−0.357900	−	0.933760i	$-0.616507\pi$
$433$	−14.8949			−0.715801			−0.357900	+	0.933760i	$0.616507\pi$
$434$		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	$-0.550136\pi$
$439$	−22.8504	−	13.1927i	−1.09059	−	0.629652i	−0.933733	+	0.357970i	$0.883469\pi$
$440$	−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	−0.999994	−	0.00334579i	$-0.998935\pi$
$443$	−2.85503	−	10.6551i	−0.135647	−	0.506241i	0.864348	−	0.502895i	$-0.167732\pi$
$444$	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	0.335488	−	0.942045i	$-0.391099\pi$
$457$	−6.68269	−	3.85825i	−0.312603	−	0.180482i	−0.648091	+	0.761563i	$0.724432\pi$
$458$	−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	$-0.216632\pi$
$461$	3.17728	+	3.17728i	0.147980	+	0.147980i	−0.629235	+	0.777215i	$0.716632\pi$
$462$		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	$-0.399495\pi$
$467$	22.7929	−	6.10734i	1.05473	−	0.282614i	0.744205	+	0.667952i	$0.232829\pi$
$468$	−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	0.935972	+	0.352075i	$0.114524\pi$
$479$	16.9156	+	29.2986i	0.772892	+	1.33869i	−0.163080	+	0.986613i	$0.552143\pi$
$480$	−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	−0.281435	−	0.959580i	$-0.590810\pi$
$487$	9.02294	−	5.20940i	0.408868	−	0.236060i	0.690303	+	0.723520i	$0.257477\pi$
$488$	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	−0.868875	−	0.495031i	$-0.835157\pi$
$491$	−8.28383	+	8.28383i	−0.373844	+	0.373844i	0.495031	+	0.868875i	$0.335157\pi$
$492$	−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	0.0126342	−	0.999920i	$-0.495978\pi$
$499$	11.6949	−	3.13364i	0.523536	−	0.140281i	0.510902	+	0.859639i	$0.329312\pi$
$500$	−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	$-0.848421\pi$
$509$	−32.2445	+	8.63990i	−1.42921	+	0.382957i	−0.540471	+	0.841363i	$0.681754\pi$
$510$	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	$-0.663285\pi$
$521$	0.420026	−	0.242502i	0.0184017	−	0.0106242i	0.509173	+	0.860664i	$0.329951\pi$
$522$	31.2418	−	21.2018i	1.36741	−	0.927979i
$523$	−5.31716	−	19.8439i	−0.232503	−	0.867714i	−0.979259	−	0.202615i	$-0.935056\pi$
$523$	−5.31716	−	19.8439i	−0.232503	−	0.867714i	0.746755	−	0.665099i	$-0.231611\pi$
$524$	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	−0.511984	−	0.858995i	$-0.671089\pi$
$541$	−12.2316	+	3.27745i	−0.525878	+	0.140909i	−0.0138940	+	0.999903i	$0.504423\pi$
$542$	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	−0.990754	−	0.135668i	$-0.956682\pi$
$547$	−26.3448	−	26.3448i	−1.12642	−	1.12642i	−0.135668	−	0.990754i	$-0.543318\pi$
$548$	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	−0.801776	−	0.597624i	$-0.796112\pi$
$557$	4.51707	−	16.8579i	0.191394	−	0.714293i	0.993171	−	0.116669i	$-0.0372218\pi$
$558$	−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	0.849363	+	0.527809i	$0.176986\pi$
$563$	−3.56178	+	13.2928i	−0.150111	+	0.560223i	−0.999475	+	0.0324143i	$0.989680\pi$
$564$	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	0.624340	−	0.781153i	$-0.285368\pi$
$569$	6.20226	+	3.58088i	0.260012	+	0.150118i	−0.364328	+	0.931271i	$0.618701\pi$
$570$	4.74747	+	6.99559i	0.198850	+	0.293013i
$571$	32.6720	+	8.75442i	1.36728	+	0.366361i	0.866484	−	0.499205i	$-0.166375\pi$
$571$	32.6720	+	8.75442i	1.36728	+	0.366361i	0.500795	+	0.865566i	$0.333041\pi$
$572$	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	1.00000		0.000868882i	$0.000276574\pi$
$577$	12.0285	+	20.8339i	0.500752	+	0.867328i	−0.499247	+	0.866460i	$0.666390\pi$
$578$	−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	$-0.734834\pi$
$587$	1.63189	−	1.63189i	0.0673551	−	0.0673551i	0.739982	+	0.672627i	$0.234834\pi$
$588$		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	$-0.777472\pi$
$593$	4.25167	−	7.36410i	0.174595	−	0.302408i	0.940021	+	0.341116i	$0.110805\pi$
$594$	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	−0.690435	−	0.723394i	$-0.742581\pi$
$599$	−10.0144	+	5.78179i	−0.409176	+	0.236238i	0.281260	+	0.959632i	$0.409248\pi$
$600$	−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	$-0.828409\pi$
$607$	0.381118	−	0.660116i	0.0154691	−	0.0267933i	0.873656	+	0.486544i	$0.161743\pi$
$608$	−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	−0.276332	−	0.961062i	$-0.589119\pi$
$613$	−24.6641	−	6.60873i	−0.996174	−	0.266924i	−0.719842	+	0.694138i	$0.755786\pi$
$614$	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	$-0.751935\pi$
$617$		−	34.9141i		−	1.40559i	0.711392	−	0.702795i	$-0.248065\pi$
$618$	−5.34078	−	2.58617i	−0.214837	−	0.104031i
$619$	28.7392	+	7.70066i	1.15513	+	0.309516i	0.785018	−	0.619473i	$-0.212654\pi$
$619$	28.7392	+	7.70066i	1.15513	+	0.309516i	0.370109	+	0.928988i	$0.379320\pi$
$620$	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	$-0.974110\pi$
$631$		−	4.08175i		−	0.162492i	0.996694	−	0.0812460i	$-0.0258900\pi$
$632$	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	0.828467	−	0.560037i	$-0.189213\pi$
$641$	−1.79183	−	3.10354i	−0.0707730	−	0.122582i	−0.899240	+	0.437455i	$0.855880\pi$
$642$	−1.20381	−	3.46420i	−0.0475104	−	0.136721i
$643$	15.8733	+	15.8733i	0.625982	+	0.625982i	0.947055	−	0.321072i	$-0.104043\pi$
$643$	15.8733	+	15.8733i	0.625982	+	0.625982i	−0.321072	+	0.947055i	$0.604043\pi$
$644$		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	$-0.835111\pi$
$647$	−22.2411	+	12.8409i	−0.874388	+	0.504828i	−0.00558405	+	0.999984i	$0.501777\pi$
$648$	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	−0.785261	−	0.619165i	$-0.787471\pi$
$653$	−29.5335	+	7.91347i	−1.15573	+	0.309678i	−0.370473	+	0.928843i	$0.620805\pi$
$654$	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	0.763650	−	0.645631i	$-0.223405\pi$
$659$	3.02967	+	3.02967i	0.118019	+	0.118019i	−0.645631	+	0.763650i	$0.723405\pi$
$660$	−3.95045	+	1.70334i	−0.153771	+	0.0663025i
$661$	37.2677	+	9.98584i	1.44954	+	0.388404i	0.895865	−	0.444326i	$-0.146557\pi$
$661$	37.2677	+	9.98584i	1.44954	+	0.388404i	0.553679	+	0.832730i	$0.313223\pi$
$662$	−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	−0.955309	−	0.295608i	$-0.904478\pi$
$677$	−7.17588	−	26.7807i	−0.275791	−	1.02927i	0.679518	−	0.733659i	$-0.262189\pi$
$678$	−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	0.298879	−	0.954291i	$-0.403387\pi$
$683$	2.10565	+	0.564208i	0.0805705	+	0.0215888i	−0.218309	+	0.975880i	$0.570054\pi$
$684$	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	$-0.394359\pi$
$691$	28.4084	−	7.61200i	1.08071	−	0.289574i	0.754885	+	0.655858i	$0.227693\pi$
$692$	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	0.997308	+	0.0733289i	$0.0233623\pi$
$701$	28.3466	+	28.3466i	1.07064	+	1.07064i	0.0733289	+	0.997308i	$0.476638\pi$
$702$	−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	−0.941490	−	0.337042i	$-0.890574\pi$
$709$	−7.84584	−	29.2811i	−0.294657	−	1.09967i	0.646833	−	0.762632i	$-0.276093\pi$
$710$	−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	$-0.825077\pi$
$719$	0.695395	−	1.20446i	0.0259338	−	0.0449187i	0.878701	+	0.477372i	$0.158411\pi$
$720$	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	$-0.500725\pi$
$733$	13.4219	−	3.59639i	0.495750	−	0.132836i	0.498027	+	0.867162i	$0.334058\pi$
$734$	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	−0.773433	−	0.633878i	$-0.781462\pi$
$739$	5.79897	−	21.6421i	0.213319	−	0.796116i	0.986752	−	0.162238i	$-0.0518712\pi$
$740$	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	$0.264213\pi$
$743$			40.2309i			1.47593i	−0.674839	+	0.737965i	$0.735787\pi$
$744$	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	−0.930021	−	0.367507i	$-0.880212\pi$
$751$	−4.02133	+	6.96514i	−0.146740	+	0.254162i	0.783281	+	0.621668i	$0.213545\pi$
$752$	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	−0.436372	−	0.899766i	$-0.643737\pi$
$757$	12.7497	−	12.7497i	0.463394	−	0.463394i	0.899766	+	0.436372i	$0.143737\pi$
$758$	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	$-0.210822\pi$
$761$	17.9392	+	10.3572i	0.650297	+	0.375449i	−0.138273	+	0.990394i	$0.544155\pi$
$762$	−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	$-0.646051\pi$
$769$	−24.5641			−0.885805			−0.442902	+	0.896570i	$0.646051\pi$
$770$		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	$-0.638845\pi$
$773$	−34.5191	−	9.24937i	−1.24157	−	0.332677i	−0.819073	+	0.573689i	$0.805512\pi$
$774$	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	0.820740	+	0.571302i	$0.193561\pi$
$787$	−4.92879	+	18.3945i	−0.175693	+	0.655693i	−0.996433	+	0.0843917i	$0.973105\pi$
$788$	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	$-0.276066\pi$
$797$	−3.26569	−	3.26569i	−0.115677	−	0.115677i	−0.762576	+	0.646899i	$0.776066\pi$
$798$		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	0.0148891	−	0.999889i	$-0.495260\pi$
$809$	25.2648	−	14.5866i	0.888263	−	0.512839i	0.873374	+	0.487050i	$0.161927\pi$
$810$	−23.9799	−	11.6118i	−0.842566	−	0.407997i
$811$	32.8375	−	32.8375i	1.15308	−	1.15308i	0.167148	−	0.985932i	$-0.446544\pi$
$811$	32.8375	−	32.8375i	1.15308	−	1.15308i	0.985932	−	0.167148i	$-0.0534558\pi$
$812$		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	0.952821	+	0.303534i	$0.0981666\pi$
$821$	8.00627	+	29.8798i	0.279421	+	1.04281i	−0.673400	+	0.739279i	$0.735167\pi$
$822$	6.77642	−	4.59873i	0.236355	−	0.160399i
$823$	−24.4402	+	14.1106i	−0.851932	+	0.491863i	−0.861302	−	0.508093i	$-0.830351\pi$
$823$	−24.4402	+	14.1106i	−0.851932	+	0.491863i	0.00937002	+	0.999956i	$0.497017\pi$
$824$	−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	−0.976778	−	0.214256i	$-0.931267\pi$
$827$	−21.9283	+	21.9283i	−0.762522	+	0.762522i	0.214256	+	0.976778i	$0.431267\pi$
$828$	−0.490134	−	0.194804i	−0.0170333	−	0.00676992i
$829$	0.365814	−	1.36524i	0.0127052	−	0.0474166i	−0.959282	−	0.282449i	$-0.908853\pi$
$829$	0.365814	−	1.36524i	0.0127052	−	0.0474166i	0.971987	+	0.235033i	$0.0755198\pi$
$830$	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	$-0.618980\pi$
$853$	16.5250	−	16.5250i	0.565806	−	0.565806i	0.930951	+	0.365144i	$0.118980\pi$
$854$		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	$-0.518249\pi$
$857$	22.7948	−	13.1606i	0.778655	−	0.449556i	0.835953	+	0.548801i	$0.184915\pi$
$858$	2.29226	+	3.37774i	0.0782564	+	0.115314i
$859$	12.5923	+	46.9949i	0.429642	+	1.60345i	0.753572	+	0.657365i	$0.228329\pi$
$859$	12.5923	+	46.9949i	0.429642	+	1.60345i	−0.323930	+	0.946081i	$0.605004\pi$
$860$	−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	−0.769445	−	0.638714i	$-0.779467\pi$
$863$	4.94765	−	8.56957i	0.168420	−	0.291712i	0.937864	+	0.347002i	$0.112800\pi$
$864$	−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	0.342333	−	0.939579i	$-0.388783\pi$
$877$	32.8300	−	8.79678i	1.10859	−	0.297046i	0.766258	+	0.642533i	$0.222116\pi$
$878$	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	$-0.358597\pi$
$881$	25.5121			0.859526			0.429763	+	0.902942i	$0.358597\pi$
$882$		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	$0.568573\pi$
$884$	−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	−0.995533	−	0.0944105i	$-0.969903\pi$
$887$	−46.9094	−	27.0831i	−1.57506	−	0.909362i	−0.579529	−	0.814952i	$-0.696763\pi$
$888$	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	0.0414881	−	0.999139i	$-0.486790\pi$
$907$	−12.7137	−	3.40663i	−0.422152	−	0.113115i	−0.463640	+	0.886024i	$0.653457\pi$
$908$	−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	0.831078	−	0.556156i	$-0.187724\pi$
$919$	23.1901	+	13.3888i	0.764972	+	0.441657i	−0.0661060	+	0.997813i	$0.521058\pi$
$920$	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	$-0.972828\pi$
$929$	−12.9337	+	22.4019i	−0.424342	+	0.734982i	0.572017	+	0.820242i	$0.306161\pi$
$930$	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	$-0.911780\pi$
$941$	0.243750	−	0.909688i	0.00794603	−	0.0296550i	0.969785	+	0.243961i	$0.0784469\pi$
$942$	−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	−0.532173	−	0.846636i	$-0.678624\pi$
$947$	−17.5325	+	4.69782i	−0.569730	+	0.152659i	−0.0375571	+	0.999294i	$0.511958\pi$
$948$	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	$-0.795906\pi$
$953$		−	36.9302i		−	1.19629i	0.801390	−	0.598143i	$-0.204094\pi$
$954$	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	$-0.917688\pi$
$967$		−	15.9039i		−	0.511436i	0.966751	−	0.255718i	$-0.0823119\pi$
$968$	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	$-0.148156\pi$
$971$	−3.26217	−	12.1746i	−0.104688	−	0.390701i	−0.998310	+	0.0581203i	$0.981489\pi$
$972$	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	−0.980016	−	0.198918i	$-0.936257\pi$
$977$	−20.7008	−	35.8548i	−0.662276	−	1.14710i	0.317740	−	0.948178i	$-0.397076\pi$
$978$	−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	$-0.678227\pi$
$983$	−1.97172	+	1.13838i	−0.0628882	+	0.0363085i	0.468226	+	0.883609i	$0.344893\pi$
$984$	−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	0.991918	+	0.126883i	$0.0404973\pi$
$991$	19.0720	+	33.0337i	0.605843	+	1.04935i	−0.386075	+	0.922468i	$0.626169\pi$
$992$	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	$-0.224465\pi$
$997$	34.6346	+	9.28031i	1.09689	+	0.293911i	0.335392	+	0.942079i	$0.391131\pi$
$998$	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.765.13		96
7.2	even	3		784.2.m.l.589.19	yes	48
7.3	odd	6	inner	784.2.x.p.557.1		96
7.4	even	3	inner	784.2.x.p.557.2		96
7.5	odd	6		784.2.m.l.589.20	yes	48
7.6	odd	2	inner	784.2.x.p.765.14		96
16.5	even	4	inner	784.2.x.p.373.2		96
112.5	odd	12		784.2.m.l.197.20	yes	48
112.37	even	12		784.2.m.l.197.19	✓	48
112.53	even	12	inner	784.2.x.p.165.13		96
112.69	odd	4	inner	784.2.x.p.373.1		96
112.101	odd	12	inner	784.2.x.p.165.14		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
784.2.m.l.197.19	✓	48	112.37	even	12
784.2.m.l.197.20	yes	48	112.5	odd	12
784.2.m.l.589.19	yes	48	7.2	even	3
784.2.m.l.589.20	yes	48	7.5	odd	6
784.2.x.p.165.13		96	112.53	even	12	inner
784.2.x.p.165.14		96	112.101	odd	12	inner
784.2.x.p.373.1		96	112.69	odd	4	inner
784.2.x.p.373.2		96	16.5	even	4	inner
784.2.x.p.557.1		96	7.3	odd	6	inner
784.2.x.p.557.2		96	7.4	even	3	inner
784.2.x.p.765.13		96	1.1	even	1	trivial
784.2.x.p.765.14		96	7.6	odd	2	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} +(-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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 4 q^{4} + 8 q^{11} + 64 q^{15} - 36 q^{16} - 20 q^{18} - 56 q^{22} - 32 q^{29} - 96 q^{30} - 40 q^{32} + 80 q^{36} + 16 q^{37} + 16 q^{43} - 4 q^{44} - 64 q^{46} - 56 q^{50} - 16 q^{53} + 20 q^{58}+ \cdots - 80 q^{99}+O(q^{100}) \) 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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