LMFDB - Embedded newform 784.2.w.f.227.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [784,2,Mod(19,784)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("784.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(784, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 10])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [56,-2,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			227.1
Character	$\chi$	$=$	784.227
Dual form			784.2.w.f.411.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41419 - 0.00846089i) q^{2} +(-1.95777 + 0.524583i) q^{3} +(1.99986 + 0.0239306i) q^{4} +(-0.666898 + 2.48890i) q^{5} +(2.77309 - 0.725295i) q^{6} +(-2.82797 - 0.0507629i) q^{8} +(0.959602 - 0.554026i) q^{9} +(0.964178 - 3.51413i) q^{10} +(5.05213 - 1.35371i) q^{11} +(-3.92781 + 1.00224i) q^{12} +(0.848888 - 0.848888i) q^{13} -5.22253i q^{15} +(3.99885 + 0.0957155i) q^{16} +(2.23951 + 1.29298i) q^{17} +(-1.36174 + 0.775378i) q^{18} +(1.26597 - 4.72466i) q^{19} +(-1.39326 + 4.96148i) q^{20} +(-7.15612 + 1.87166i) q^{22} +(3.15967 + 5.47271i) q^{23} +(5.56315 - 1.38412i) q^{24} +(-1.41973 - 0.819681i) q^{25} +(-1.20767 + 1.19330i) q^{26} +(2.71152 - 2.71152i) q^{27} +(-3.92758 - 3.92758i) q^{29} +(-0.0441873 + 7.38564i) q^{30} +(0.585390 - 1.01392i) q^{31} +(-5.65432 - 0.169194i) q^{32} +(-9.18077 + 5.30052i) q^{33} +(-3.15615 - 1.84747i) q^{34} +(1.93232 - 1.08501i) q^{36} +(-6.04104 - 1.61869i) q^{37} +(-1.83029 + 6.67085i) q^{38} +(-1.21662 + 2.10724i) q^{39} +(2.01231 - 7.00468i) q^{40} +4.77063 q^{41} +(4.80121 + 4.80121i) q^{43} +(10.1359 - 2.58633i) q^{44} +(0.738958 + 2.75783i) q^{45} +(-4.42206 - 7.76617i) q^{46} +(3.39263 + 5.87622i) q^{47} +(-7.87905 + 1.91034i) q^{48} +(2.00083 + 1.17120i) q^{50} +(-5.06272 - 1.35655i) q^{51} +(1.71797 - 1.67734i) q^{52} +(1.97180 + 7.35887i) q^{53} +(-3.85754 + 3.81165i) q^{54} +13.4770i q^{55} +9.91391i q^{57} +(5.52111 + 5.58757i) q^{58} +(0.216856 + 0.809319i) q^{59} +(0.124978 - 10.4443i) q^{60} +(-4.37595 - 1.17253i) q^{61} +(-0.836430 + 1.42893i) q^{62} +(7.99485 + 0.287112i) q^{64} +(1.54667 + 2.67892i) q^{65} +(13.0282 - 7.41826i) q^{66} +(-0.100994 - 0.376913i) q^{67} +(4.44776 + 2.63937i) q^{68} +(-9.05679 - 9.05679i) q^{69} +3.83330 q^{71} +(-2.74185 + 1.51806i) q^{72} +(-4.84591 + 8.39335i) q^{73} +(8.52947 + 2.34025i) q^{74} +(3.20949 + 0.859981i) q^{75} +(2.64482 - 9.41835i) q^{76} +(1.73835 - 2.96974i) q^{78} +(-0.954167 + 0.550889i) q^{79} +(-2.90505 + 9.88891i) q^{80} +(-5.54819 + 9.60974i) q^{81} +(-6.74656 - 0.0403638i) q^{82} +(9.73434 + 9.73434i) q^{83} +(-4.71162 + 4.71162i) q^{85} +(-6.74919 - 6.83044i) q^{86} +(9.74964 + 5.62896i) q^{87} +(-14.3560 + 3.57180i) q^{88} +(7.91117 + 13.7025i) q^{89} +(-1.02169 - 3.90634i) q^{90} +(6.18792 + 11.0202i) q^{92} +(-0.614171 + 2.29212i) q^{93} +(-4.74811 - 8.33878i) q^{94} +(10.9149 + 6.30174i) q^{95} +(11.1586 - 2.63492i) q^{96} -1.12228i q^{97} +(4.09804 - 4.09804i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{2} + 6 q^{3} - 4 q^{4} + 6 q^{5} + 4 q^{8} + 24 q^{10} + 2 q^{11} + 6 q^{12} + 8 q^{16} + 12 q^{17} - 30 q^{18} + 6 q^{19} - 28 q^{22} - 12 q^{23} + 6 q^{24} + 6 q^{26} - 24 q^{29} - 18 q^{30}+ \cdots - 16 q^{99}+O(q^{100}) $ 56 * q - 2 * q^2 + 6 * q^3 - 4 * q^4 + 6 * q^5 + 4 * q^8 + 24 * q^10 + 2 * q^11 + 6 * q^12 + 8 * q^16 + 12 * q^17 - 30 * q^18 + 6 * q^19 - 28 * q^22 - 12 * q^23 + 6 * q^24 + 6 * q^26 - 24 * q^29 - 18 * q^30 - 12 * q^32 + 12 * q^33 + 16 * q^36 + 6 * q^37 + 6 * q^38 - 4 * q^39 + 66 * q^40 + 26 * q^44 - 12 * q^45 + 16 * q^46 - 34 * q^51 - 84 * q^52 + 6 * q^53 - 42 * q^54 + 18 * q^58 - 42 * q^59 + 78 * q^60 + 6 * q^61 - 16 * q^64 - 4 * q^65 - 126 * q^66 + 6 * q^67 - 24 * q^68 - 80 * q^71 - 4 * q^72 + 62 * q^74 - 24 * q^75 + 4 * q^78 - 12 * q^80 - 8 * q^81 - 42 * q^82 - 28 * q^85 + 12 * q^87 + 30 * q^88 - 20 * q^92 + 10 * q^93 + 42 * q^94 - 36 * q^96 - 16 * q^99

Character values

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

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−1.41419	−	0.00846089i	−0.999982	−	0.00598276i
$2$	−1.41419	−	0.00846089i	−0.999982	−	0.00598276i
$3$	−1.95777	+	0.524583i	−1.13032	+	0.302868i	−0.775053	−	0.631897i	$-0.782277\pi$
$3$	−1.95777	+	0.524583i	−1.13032	+	0.302868i	−0.355267	+	0.934765i	$0.615610\pi$
$4$	1.99986	+	0.0239306i	0.999928	+	0.0119653i
$5$	−0.666898	+	2.48890i	−0.298246	+	1.11307i	0.640359	+	0.768075i	$0.278785\pi$
$5$	−0.666898	+	2.48890i	−0.298246	+	1.11307i	−0.938605	+	0.344993i	$0.887881\pi$
$6$	2.77309	−	0.725295i	1.13211	−	0.296100i
$7$		0			0
$7$		0			0
$8$	−2.82797	−	0.0507629i	−0.999839	−	0.0179474i
$9$	0.959602	−	0.554026i	0.319867	−	0.184675i
$10$	0.964178	−	3.51413i	0.304900	−	1.11126i
$11$	5.05213	−	1.35371i	1.52327	−	0.408160i	0.602456	−	0.798152i	$-0.294189\pi$
$11$	5.05213	−	1.35371i	1.52327	−	0.408160i	0.920818	+	0.389992i	$0.127522\pi$
$12$	−3.92781	+	1.00224i	−1.13386	+	0.289322i
$13$	0.848888	−	0.848888i	0.235439	−	0.235439i	−0.579519	−	0.814958i	$-0.696760\pi$
$13$	0.848888	−	0.848888i	0.235439	−	0.235439i	0.814958	+	0.579519i	$0.196760\pi$
$14$		0			0
$15$		−	5.22253i		−	1.34845i
$16$	3.99885	+	0.0957155i	0.999714	+	0.0239289i
$17$	2.23951	+	1.29298i	0.543161	+	0.313594i	0.746359	−	0.665544i	$-0.231800\pi$
$17$	2.23951	+	1.29298i	0.543161	+	0.313594i	−0.203198	+	0.979138i	$0.565134\pi$
$18$	−1.36174	+	0.775378i	−0.320966	+	0.182758i
$19$	1.26597	−	4.72466i	0.290433	−	1.08391i	−0.654343	−	0.756197i	$-0.727055\pi$
$19$	1.26597	−	4.72466i	0.290433	−	1.08391i	0.944777	−	0.327714i	$-0.106278\pi$
$20$	−1.39326	+	4.96148i	−0.311543	+	1.10942i
$21$		0			0
$22$	−7.15612	+	1.87166i	−1.52569	+	0.399039i
$23$	3.15967	+	5.47271i	0.658836	+	1.14114i	0.980917	+	0.194426i	$0.0622844\pi$
$23$	3.15967	+	5.47271i	0.658836	+	1.14114i	−0.322081	+	0.946712i	$0.604382\pi$
$24$	5.56315	−	1.38412i	1.13557	−	0.282533i
$25$	−1.41973	−	0.819681i	−0.283946	−	0.163936i
$26$	−1.20767	+	1.19330i	−0.236843	+	0.234026i
$27$	2.71152	−	2.71152i	0.521831	−	0.521831i
$28$		0			0
$29$	−3.92758	−	3.92758i	−0.729333	−	0.729333i	0.241154	−	0.970487i	$-0.422474\pi$
$29$	−3.92758	−	3.92758i	−0.729333	−	0.729333i	−0.970487	+	0.241154i	$0.922474\pi$
$30$	−0.0441873	+	7.38564i	−0.00806746	+	1.34843i
$31$	0.585390	−	1.01392i	0.105139	−	0.182106i	−0.808656	−	0.588282i	$-0.799805\pi$
$31$	0.585390	−	1.01392i	0.105139	−	0.182106i	0.913795	+	0.406176i	$0.133138\pi$
$32$	−5.65432	−	0.169194i	−0.999553	−	0.0299095i
$33$	−9.18077	+	5.30052i	−1.59817	+	0.922703i
$34$	−3.15615	−	1.84747i	−0.541275	−	0.316838i
$35$		0			0
$36$	1.93232	−	1.08501i	0.322054	−	0.180835i
$37$	−6.04104	−	1.61869i	−0.993141	−	0.266111i	−0.274571	−	0.961567i	$-0.588536\pi$
$37$	−6.04104	−	1.61869i	−0.993141	−	0.266111i	−0.718569	+	0.695455i	$0.755203\pi$
$38$	−1.83029	+	6.67085i	−0.296913	+	1.08215i
$39$	−1.21662	+	2.10724i	−0.194814	+	0.337428i
$40$	2.01231	−	7.00468i	0.318174	−	1.10754i
$41$	4.77063			0.745047			0.372523	−	0.928023i	$-0.378493\pi$
$41$	4.77063			0.745047			0.372523	+	0.928023i	$0.378493\pi$
$42$		0			0
$43$	4.80121	+	4.80121i	0.732177	+	0.732177i	0.971051	−	0.238873i	$-0.0767781\pi$
$43$	4.80121	+	4.80121i	0.732177	+	0.732177i	−0.238873	+	0.971051i	$0.576778\pi$
$44$	10.1359	−	2.58633i	1.52805	−	0.389904i
$45$	0.738958	+	2.75783i	0.110157	+	0.411113i
$46$	−4.42206	−	7.76617i	−0.651998	−	1.14506i
$47$	3.39263	+	5.87622i	0.494867	+	0.857134i	0.999982	−	0.00591740i	$-0.00188358\pi$
$47$	3.39263	+	5.87622i	0.494867	+	0.857134i	−0.505116	+	0.863052i	$0.668550\pi$
$48$	−7.87905	+	1.91034i	−1.13724	+	0.275734i
$49$		0			0
$50$	2.00083	+	1.17120i	0.282960	+	0.165632i
$51$	−5.06272	−	1.35655i	−0.708923	−	0.189955i
$52$	1.71797	−	1.67734i	0.238239	−	0.232605i
$53$	1.97180	+	7.35887i	0.270848	+	1.01082i	0.958573	+	0.284847i	$0.0919429\pi$
$53$	1.97180	+	7.35887i	0.270848	+	1.01082i	−0.687725	+	0.725971i	$0.741390\pi$
$54$	−3.85754	+	3.81165i	−0.524944	+	0.518700i
$55$			13.4770i			1.81724i
$56$		0			0
$57$			9.91391i			1.31313i
$58$	5.52111	+	5.58757i	0.724957	+	0.733683i
$59$	0.216856	+	0.809319i	0.0282323	+	0.105364i	0.978604	−	0.205752i	$-0.0659639\pi$
$59$	0.216856	+	0.809319i	0.0282323	+	0.105364i	−0.950372	+	0.311116i	$0.899297\pi$
$60$	0.124978	−	10.4443i	0.0161346	−	1.34836i
$61$	−4.37595	−	1.17253i	−0.560283	−	0.150127i	−0.0324466	−	0.999473i	$-0.510330\pi$
$61$	−4.37595	−	1.17253i	−0.560283	−	0.150127i	−0.527836	+	0.849346i	$0.676997\pi$
$62$	−0.836430	+	1.42893i	−0.106227	+	0.181474i
$63$		0			0
$64$	7.99485	+	0.287112i	0.999356	+	0.0358890i
$65$	1.54667	+	2.67892i	0.191841	+	0.332279i
$66$	13.0282	−	7.41826i	1.60366	−	0.913125i
$67$	−0.100994	−	0.376913i	−0.0123383	−	0.0460473i	0.959482	−	0.281769i	$-0.0909212\pi$
$67$	−0.100994	−	0.376913i	−0.0123383	−	0.0460473i	−0.971821	+	0.235722i	$0.924255\pi$
$68$	4.44776	+	2.63937i	0.539370	+	0.320071i
$69$	−9.05679	−	9.05679i	−1.09031	−	1.09031i
$70$		0			0
$71$	3.83330			0.454929			0.227465	−	0.973786i	$-0.426956\pi$
$71$	3.83330			0.454929			0.227465	+	0.973786i	$0.426956\pi$
$72$	−2.74185	+	1.51806i	−0.323130	+	0.178905i
$73$	−4.84591	+	8.39335i	−0.567170	+	0.982368i	0.429674	+	0.902984i	$0.358629\pi$
$73$	−4.84591	+	8.39335i	−0.567170	+	0.982368i	−0.996844	+	0.0793836i	$0.974705\pi$
$74$	8.52947	+	2.34025i	0.991531	+	0.272048i
$75$	3.20949	+	0.859981i	0.370600	+	0.0993021i
$76$	2.64482	−	9.41835i	0.303382	−	1.08036i
$77$		0			0
$78$	1.73835	−	2.96974i	0.196830	−	0.336257i
$79$	−0.954167	+	0.550889i	−0.107352	+	0.0619798i	−0.552715	−	0.833370i	$-0.686408\pi$
$79$	−0.954167	+	0.550889i	−0.107352	+	0.0619798i	0.445363	+	0.895350i	$0.353075\pi$
$80$	−2.90505	+	9.88891i	−0.324795	+	1.10561i
$81$	−5.54819	+	9.60974i	−0.616465	+	1.06775i
$82$	−6.74656	−	0.0403638i	−0.745033	−	0.00445743i
$83$	9.73434	+	9.73434i	1.06848	+	1.06848i	0.997476	+	0.0710068i	$0.0226212\pi$
$83$	9.73434	+	9.73434i	1.06848	+	1.06848i	0.0710068	+	0.997476i	$0.477379\pi$
$84$		0			0
$85$	−4.71162	+	4.71162i	−0.511047	+	0.511047i
$86$	−6.74919	−	6.83044i	−0.727784	−	0.736545i
$87$	9.74964	+	5.62896i	1.04527	+	0.603488i
$88$	−14.3560	+	3.57180i	−1.53035	+	0.380756i
$89$	7.91117	+	13.7025i	0.838582	+	1.45247i	0.891080	+	0.453846i	$0.149948\pi$
$89$	7.91117	+	13.7025i	0.838582	+	1.45247i	−0.0524979	+	0.998621i	$0.516718\pi$
$90$	−1.02169	−	3.90634i	−0.107696	−	0.411764i
$91$		0			0
$92$	6.18792	+	11.0202i	0.645135	+	1.14894i
$93$	−0.614171	+	2.29212i	−0.0636866	+	0.237682i
$94$	−4.74811	−	8.33878i	−0.489730	−	0.860079i
$95$	10.9149	+	6.30174i	1.11985	+	0.646544i
$96$	11.1586	−	2.63492i	1.13887	−	0.268925i
$97$		−	1.12228i		−	0.113950i	−0.998376	−	0.0569750i	$-0.981854\pi$
$97$		−	1.12228i		−	0.113950i	0.998376	−	0.0569750i	$-0.0181455\pi$
$98$		0			0
$99$	4.09804	−	4.09804i	0.411868	−	0.411868i
$100$	−2.81964	−	1.67322i	−0.281964	−	0.167322i
$101$	−14.0172	+	3.75591i	−1.39477	+	0.373727i	−0.876463	−	0.481470i	$-0.840103\pi$
$101$	−14.0172	+	3.75591i	−1.39477	+	0.373727i	−0.518304	+	0.855196i	$0.673436\pi$
$102$	7.14816	+	1.96125i	0.707774	+	0.194193i
$103$	−0.741916	+	0.428345i	−0.0731031	+	0.0422061i	−0.536106	−	0.844151i	$-0.680105\pi$
$103$	−0.741916	+	0.428345i	−0.0731031	+	0.0422061i	0.463003	+	0.886357i	$0.346772\pi$
$104$	−2.44372	+	2.35754i	−0.239627	+	0.231176i
$105$		0			0
$106$	−2.72624	−	10.4235i	−0.264796	−	1.01242i
$107$	1.36544	−	5.09589i	0.132002	−	0.492639i	−0.867990	−	0.496581i	$-0.834588\pi$
$107$	1.36544	−	5.09589i	0.132002	−	0.492639i	0.999992	+	0.00394288i	$0.00125506\pi$
$108$	5.48753	−	5.35775i	0.528038	−	0.515550i
$109$	13.3788	−	3.58485i	1.28146	−	0.343367i	0.447050	−	0.894509i	$-0.352475\pi$
$109$	13.3788	−	3.58485i	1.28146	−	0.343367i	0.834411	+	0.551142i	$0.185808\pi$
$110$	0.114028	−	19.0590i	0.0108721	−	1.81721i
$111$	12.6761			1.20316
$112$		0			0
$113$	−8.67774			−0.816333			−0.408167	−	0.912907i	$-0.633832\pi$
$113$	−8.67774			−0.816333			−0.408167	+	0.912907i	$0.633832\pi$
$114$	0.0838806	−	14.0201i	0.00785613	−	1.31311i
$115$	−15.7282	+	4.21435i	−1.46666	+	0.392990i
$116$	−7.76061	−	7.94859i	−0.720554	−	0.738008i
$117$	0.344288	−	1.28490i	0.0318294	−	0.118789i
$118$	−0.299828	−	1.14636i	−0.0276014	−	0.105531i
$119$		0			0
$120$	−0.265111	+	14.7692i	−0.0242012	+	1.34823i
$121$	14.1652	−	8.17828i	1.28774	−	0.743480i
$122$	6.17849	+	1.69521i	0.559375	+	0.153477i
$123$	−9.33979	+	2.50259i	−0.842141	+	0.225651i
$124$	1.19496	−	2.01370i	0.107311	−	0.180835i
$125$	−6.12308	+	6.12308i	−0.547665	+	0.547665i
$126$		0			0
$127$		−	14.0559i		−	1.24726i	−0.781721	−	0.623628i	$-0.785658\pi$
$127$		−	14.0559i		−	1.24726i	0.781721	−	0.623628i	$-0.214342\pi$
$128$	−11.3038	−	0.473674i	−0.999123	−	0.0418673i
$129$	−11.9183	−	6.88103i	−1.04935	−	0.605841i
$130$	−2.16462	−	3.80158i	−0.189850	−	0.333420i
$131$	3.90994	−	14.5921i	0.341613	−	1.27492i	−0.554907	−	0.831913i	$-0.687246\pi$
$131$	3.90994	−	14.5921i	0.341613	−	1.27492i	0.896520	−	0.443004i	$-0.146087\pi$
$132$	−18.4871	+	10.3806i	−1.60909	+	0.903514i
$133$		0			0
$134$	0.139635	+	0.533881i	0.0120626	+	0.0461203i
$135$	4.94038	+	8.55699i	0.425200	+	0.736468i
$136$	−6.26763	−	3.77020i	−0.537445	−	0.323292i
$137$	4.37058	+	2.52336i	0.373404	+	0.215585i	0.674945	−	0.737868i	$-0.264168\pi$
$137$	4.37058	+	2.52336i	0.373404	+	0.215585i	−0.301541	+	0.953453i	$0.597501\pi$
$138$	12.7314	+	12.8846i	1.08377	+	1.09681i
$139$	−3.77959	+	3.77959i	−0.320581	+	0.320581i	−0.848990	−	0.528409i	$-0.822789\pi$
$139$	−3.77959	+	3.77959i	−0.320581	+	0.320581i	0.528409	+	0.848990i	$0.322789\pi$
$140$		0			0
$141$	−9.72456	−	9.72456i	−0.818956	−	0.818956i
$142$	−5.42101	−	0.0324332i	−0.454921	−	0.00272173i
$143$	3.13954	−	5.43784i	0.262541	−	0.454735i
$144$	3.89034	−	2.12362i	0.324195	−	0.176968i
$145$	12.3946	−	7.15605i	1.02932	−	0.594277i
$146$	6.92404	−	11.8288i	0.573037	−	0.978957i
$147$		0			0
$148$	−12.0425	−	3.38172i	−0.989885	−	0.277975i
$149$	−0.263393	−	0.0705758i	−0.0215780	−	0.00578180i	0.248014	−	0.968756i	$-0.420222\pi$
$149$	−0.263393	−	0.0705758i	−0.0215780	−	0.00578180i	−0.269592	+	0.962975i	$0.586889\pi$
$150$	−4.53155	−	1.24333i	−0.370000	−	0.101518i
$151$	−4.58028	+	7.93328i	−0.372738	+	0.645601i	−0.989986	−	0.141168i	$-0.954914\pi$
$151$	−4.58028	+	7.93328i	−0.372738	+	0.645601i	0.617248	+	0.786769i	$0.288248\pi$
$152$	−3.81996	+	13.2969i	−0.309840	+	1.07852i
$153$	2.86538			0.231652
$154$		0			0
$155$	2.13316	+	2.13316i	0.171340	+	0.171340i
$156$	−2.48348	+	4.18506i	−0.198838	+	0.335073i
$157$	−3.85638	−	14.3922i	−0.307772	−	1.14862i	−0.930533	−	0.366209i	$-0.880655\pi$
$157$	−3.85638	−	14.3922i	−0.307772	−	1.14862i	0.622760	−	0.782413i	$-0.286011\pi$
$158$	1.35403	−	0.770987i	0.107721	−	0.0613365i
$159$	−7.72068	−	13.3726i	−0.612290	−	1.06052i
$160$	4.19196	−	13.9602i	0.331404	−	1.10365i
$161$		0			0
$162$	7.92749	−	13.5430i	0.622842	−	1.06404i
$163$	−18.6585	−	4.99953i	−1.46145	−	0.391593i	−0.561457	−	0.827506i	$-0.689759\pi$
$163$	−18.6585	−	4.99953i	−1.46145	−	0.391593i	−0.899989	+	0.435912i	$0.856426\pi$
$164$	9.54057	+	0.114164i	0.744993	+	0.00891470i
$165$	−7.06982	−	26.3849i	−0.550384	−	2.05406i
$166$	−13.6838	−	13.8486i	−1.06207	−	1.07486i
$167$		−	3.48341i		−	0.269554i	−0.990876	−	0.134777i	$-0.956968\pi$
$167$		−	3.48341i		−	0.269554i	0.990876	−	0.134777i	$-0.0430318\pi$
$168$		0			0
$169$			11.5588i			0.889137i
$170$	6.70298	−	6.62325i	0.514095	−	0.507980i
$171$	−1.40276	−	5.23517i	−0.107272	−	0.400344i
$172$	9.48683	+	9.71663i	0.723364	+	0.740886i
$173$	−0.0707438	−	0.0189557i	−0.00537855	−	0.00144118i	0.256129	−	0.966643i	$-0.417553\pi$
$173$	−0.0707438	−	0.0189557i	−0.00537855	−	0.00144118i	−0.261507	+	0.965201i	$0.584220\pi$
$174$	−13.7402	−	8.04290i	−1.04164	−	0.609730i
$175$		0			0
$176$	20.3323	−	4.92974i	1.53260	−	0.371593i
$177$	−0.849110	−	1.47070i	−0.0638230	−	0.110545i
$178$	−11.0719	−	19.4449i	−0.829877	−	1.45746i
$179$	0.805515	+	3.00622i	0.0602070	+	0.224696i	0.989473	−	0.144715i	$-0.0462264\pi$
$179$	0.805515	+	3.00622i	0.0602070	+	0.224696i	−0.929266	+	0.369410i	$0.879560\pi$
$180$	1.41181	+	5.53295i	0.105230	+	0.412401i
$181$	3.34414	+	3.34414i	0.248568	+	0.248568i	0.820383	−	0.571815i	$-0.193760\pi$
$181$	3.34414	+	3.34414i	0.248568	+	0.248568i	−0.571815	+	0.820383i	$0.693760\pi$
$182$		0			0
$183$	9.18219			0.678767
$184$	−8.65764	−	15.6371i	−0.638250	−	1.15278i
$185$	8.05751	−	13.9560i	0.592400	−	1.02607i
$186$	0.887947	−	3.23629i	0.0651074	−	0.237296i
$187$	13.0646	+	3.50065i	0.955379	+	0.255993i
$188$	6.64416	+	11.8328i	0.484575	+	0.862994i
$189$		0			0
$190$	−15.3824	−	9.00419i	−1.11596	−	0.653233i
$191$	−0.271101	+	0.156520i	−0.0196162	+	0.0113254i	−0.509776	−	0.860307i	$-0.670272\pi$
$191$	−0.271101	+	0.156520i	−0.0196162	+	0.0113254i	0.490160	+	0.871633i	$0.336938\pi$
$192$	−15.8027	+	3.63186i	−1.14046	+	0.262107i
$193$	5.17806	−	8.96866i	0.372725	−	0.645578i	−0.617259	−	0.786760i	$-0.711757\pi$
$193$	5.17806	−	8.96866i	0.372725	−	0.645578i	0.989984	+	0.141182i	$0.0450902\pi$
$194$	−0.00949547	+	1.58711i	−0.000681735	+	0.113948i
$195$	−4.43334	−	4.43334i	−0.317478	−	0.317478i
$196$		0			0
$197$	0.112804	−	0.112804i	0.00803695	−	0.00803695i	−0.703077	−	0.711114i	$-0.748191\pi$
$197$	0.112804	−	0.112804i	0.00803695	−	0.00803695i	0.711114	+	0.703077i	$0.248191\pi$
$198$	−5.83007	+	5.76072i	−0.414325	+	0.409397i
$199$	18.4737	+	10.6658i	1.30957	+	0.756078i	0.982023	−	0.188759i	$-0.0604464\pi$
$199$	18.4737	+	10.6658i	1.30957	+	0.756078i	0.327542	+	0.944837i	$0.393780\pi$
$200$	3.97334	+	2.39010i	0.280958	+	0.169006i
$201$	0.395444	+	0.684930i	0.0278925	+	0.0483112i
$202$	19.8548	−	5.19296i	1.39698	−	0.365375i
$203$		0			0
$204$	−10.0923	−	2.83406i	−0.706599	−	0.198424i
$205$	−3.18152	+	11.8736i	−0.222207	+	0.829288i
$206$	1.05283	−	0.599484i	0.0733543	−	0.0417680i
$207$	6.06405	+	3.50108i	0.421480	+	0.243342i
$208$	3.47583	−	3.31333i	0.241005	−	0.229738i
$209$		−	25.5834i		−	1.76964i
$210$		0			0
$211$	7.71946	−	7.71946i	0.531430	−	0.531430i	−0.389568	−	0.920998i	$-0.627376\pi$
$211$	7.71946	−	7.71946i	0.531430	−	0.531430i	0.920998	+	0.389568i	$0.127376\pi$
$212$	3.76722	+	14.7639i	0.258734	+	1.01399i
$213$	−7.50472	+	2.01088i	−0.514215	+	0.137784i
$214$	−1.97411	+	7.19500i	−0.134947	+	0.491840i
$215$	−15.1516	+	8.74780i	−1.03333	+	0.596595i
$216$	−7.80573	+	7.53044i	−0.531113	+	0.512382i
$217$		0			0
$218$	−18.9505	+	4.95646i	−1.28349	+	0.335694i
$219$	5.08416	−	18.9743i	0.343556	−	1.28217i
$220$	−0.322513	+	26.9521i	−0.0217438	+	1.81711i
$221$	2.99869	−	0.803496i	0.201714	−	0.0540490i
$222$	−17.9264	−	0.107251i	−1.20314	−	0.00719823i
$223$	−9.74121			−0.652319			−0.326160	−	0.945315i	$-0.605755\pi$
$223$	−9.74121			−0.652319			−0.326160	+	0.945315i	$0.605755\pi$
$224$		0			0
$225$	−1.81650			−0.121100
$226$	12.2720	+	0.0734215i	0.816319	+	0.00488392i
$227$	−1.00710	+	0.269850i	−0.0668433	+	0.0179106i	−0.292086	−	0.956392i	$-0.594349\pi$
$227$	−1.00710	+	0.269850i	−0.0668433	+	0.0179106i	0.225242	+	0.974303i	$0.427683\pi$
$228$	−0.237246	+	19.8264i	−0.0157120	+	1.31304i
$229$	1.39165	−	5.19372i	0.0919630	−	0.343210i	−0.904579	−	0.426307i	$-0.859814\pi$
$229$	1.39165	−	5.19372i	0.0919630	−	0.343210i	0.996541	+	0.0830966i	$0.0264810\pi$
$230$	22.2783	−	5.82681i	1.46899	−	0.384209i
$231$		0			0
$232$	10.9077	+	11.3065i	0.716126	+	0.742305i
$233$	−11.0720	+	6.39244i	−0.725352	+	0.418782i	−0.816720	−	0.577035i	$-0.804210\pi$
$233$	−11.0720	+	6.39244i	−0.725352	+	0.418782i	0.0913671	+	0.995817i	$0.470876\pi$
$234$	−0.497759	+	1.81418i	−0.0325395	+	0.118596i
$235$	−16.8878	+	4.52508i	−1.10164	+	0.295184i
$236$	0.414314	+	1.62371i	0.0269695	+	0.105695i
$237$	1.57905	−	1.57905i	0.102571	−	0.102571i
$238$		0			0
$239$			26.2285i			1.69658i	0.529530	+	0.848291i	$0.322368\pi$
$239$			26.2285i			1.69658i	−0.529530	+	0.848291i	$0.677632\pi$
$240$	0.499877	−	20.8841i	0.0322669	−	1.34807i
$241$	19.0929	+	11.0233i	1.22988	+	0.710072i	0.967005	−	0.254758i	$-0.0819958\pi$
$241$	19.0929	+	11.0233i	1.22988	+	0.710072i	0.262875	+	0.964830i	$0.415329\pi$
$242$	−20.1014	+	11.4458i	−1.29217	+	0.735762i
$243$	2.84352	−	10.6122i	0.182412	−	0.680771i
$244$	−8.72321	−	2.44962i	−0.558446	−	0.156821i
$245$		0			0
$246$	13.2294	−	3.46011i	0.843475	−	0.220609i
$247$	−2.93604	−	5.08537i	−0.186816	−	0.323575i
$248$	−1.70694	+	2.83763i	−0.108391	+	0.180190i
$249$	−24.1641	−	13.9511i	−1.53134	−	0.884117i
$250$	8.71099	−	8.60738i	0.550932	−	0.544379i
$251$	15.4991	−	15.4991i	0.978295	−	0.978295i	−0.0214744	−	0.999769i	$-0.506836\pi$
$251$	15.4991	−	15.4991i	0.978295	−	0.978295i	0.999769	+	0.0214744i	$0.00683604\pi$
$252$		0			0
$253$	23.3715	+	23.3715i	1.46936	+	1.46936i
$254$	−0.118925	+	19.8776i	−0.00746203	+	1.24723i
$255$	6.75264	−	11.6959i	0.422866	−	0.732426i
$256$	15.9817	+	0.765505i	0.998855	+	0.0478441i
$257$	−1.64001	+	0.946858i	−0.102301	+	0.0590633i	−0.550277	−	0.834982i	$-0.685478\pi$
$257$	−1.64001	+	0.946858i	−0.102301	+	0.0590633i	0.447977	+	0.894045i	$0.352145\pi$
$258$	16.7965	+	9.83191i	1.04570	+	0.612108i
$259$		0			0
$260$	3.02902	+	5.39446i	0.187852	+	0.334550i
$261$	−5.94489	−	1.59293i	−0.367980	−	0.0985998i
$262$	−5.65285	+	20.6029i	−0.349234	+	1.27285i
$263$	4.67609	−	8.09923i	0.288340	−	0.499420i	−0.685073	−	0.728474i	$-0.740230\pi$
$263$	4.67609	−	8.09923i	0.288340	−	0.499420i	0.973414	+	0.229054i	$0.0735633\pi$
$264$	26.2320	−	14.5237i	1.61447	−	0.893871i
$265$	−19.6305			−1.20589
$266$		0			0
$267$	−22.6764	−	22.6764i	−1.38777	−	1.38777i
$268$	−0.192953	−	0.756189i	−0.0117865	−	0.0461916i
$269$	6.90325	+	25.7633i	0.420899	+	1.57082i	0.772719	+	0.634748i	$0.218896\pi$
$269$	6.90325	+	25.7633i	0.420899	+	1.57082i	−0.351820	+	0.936067i	$0.614437\pi$
$270$	−6.91423	−	12.1430i	−0.420786	−	0.738999i
$271$	−4.30075	−	7.44912i	−0.261252	−	0.452502i	0.705323	−	0.708886i	$-0.250802\pi$
$271$	−4.30075	−	7.44912i	−0.261252	−	0.452502i	−0.966575	+	0.256384i	$0.917469\pi$
$272$	8.83171	+	5.38480i	0.535501	+	0.326501i
$273$		0			0
$274$	−6.15948	−	3.60548i	−0.372108	−	0.217815i
$275$	−8.28227	−	2.21923i	−0.499440	−	0.133824i
$276$	−17.8956	−	18.3290i	−1.07719	−	1.10328i
$277$	6.63310	+	24.7551i	0.398544	+	1.48739i	0.815659	+	0.578533i	$0.196375\pi$
$277$	6.63310	+	24.7551i	0.398544	+	1.48739i	−0.417114	+	0.908854i	$0.636959\pi$
$278$	5.37703	−	5.31307i	0.322493	−	0.318657i
$279$		−	1.29729i		−	0.0776664i
$280$		0			0
$281$		−	23.2859i		−	1.38912i	−0.719434	−	0.694561i	$-0.755599\pi$
$281$		−	23.2859i		−	1.38912i	0.719434	−	0.694561i	$-0.244401\pi$
$282$	13.6701	+	13.8346i	0.814042	+	0.823841i
$283$	−2.62772	−	9.80680i	−0.156202	−	0.582954i	−0.998999	−	0.0447228i	$-0.985760\pi$
$283$	−2.62772	−	9.80680i	−0.156202	−	0.582954i	0.842797	−	0.538231i	$-0.180907\pi$
$284$	7.66605	+	0.0917332i	0.454897	+	0.00544336i
$285$	−24.6747	−	6.61157i	−1.46160	−	0.391635i
$286$	−4.48591	+	7.66357i	−0.265257	+	0.453156i
$287$		0			0
$288$	−5.51964	+	2.97028i	−0.325248	+	0.175026i
$289$	−5.15640	−	8.93115i	−0.303318	−	0.525362i
$290$	−17.5889	+	10.0151i	−1.03286	+	0.588108i
$291$	0.588728	+	2.19716i	0.0345118	+	0.128800i
$292$	−9.89197	+	16.6695i	−0.578884	+	0.975511i
$293$	0.0961358	+	0.0961358i	0.00561631	+	0.00561631i	0.709909	−	0.704293i	$-0.248736\pi$
$293$	0.0961358	+	0.0961358i	0.00561631	+	0.00561631i	−0.704293	+	0.709909i	$0.748736\pi$
$294$		0			0
$295$	−2.15893			−0.125698
$296$	17.0017	+	4.88427i	0.988205	+	0.283893i
$297$	10.0283	−	17.3695i	0.581902	−	1.00788i
$298$	0.371890	+	0.102036i	0.0215430	+	0.00591079i
$299$	7.32792	+	1.96351i	0.423784	+	0.113553i
$300$	6.39795	+	1.79664i	0.369386	+	0.103729i
$301$		0			0
$302$	6.54450	−	11.1804i	0.376594	−	0.643360i
$303$	25.4722	−	14.7064i	1.46334	−	0.844861i
$304$	5.51465	−	18.7721i	0.316287	−	1.07665i
$305$	5.83662	−	10.1093i	0.334204	−	0.578858i
$306$	−4.05219	−	0.0242437i	−0.231648	−	0.00138592i
$307$	−16.2451	−	16.2451i	−0.927157	−	0.927157i	0.0703642	−	0.997521i	$-0.477584\pi$
$307$	−16.2451	−	16.2451i	−0.927157	−	0.927157i	−0.997521	+	0.0703642i	$0.977584\pi$
$308$		0			0
$309$	1.22780	−	1.22780i	0.0698470	−	0.0698470i
$310$	−2.99864	−	3.03474i	−0.170311	−	0.172362i
$311$	−12.3134	−	7.10914i	−0.698228	−	0.403122i	0.108459	−	0.994101i	$-0.465408\pi$
$311$	−12.3134	−	7.10914i	−0.698228	−	0.403122i	−0.806687	+	0.590979i	$0.798742\pi$
$312$	3.54752	−	5.89745i	0.200839	−	0.333878i
$313$	13.4403	+	23.2792i	0.759689	+	1.31582i	0.943009	+	0.332766i	$0.107982\pi$
$313$	13.4403	+	23.2792i	0.759689	+	1.31582i	−0.183321	+	0.983053i	$0.558685\pi$
$314$	5.33187	+	20.3859i	0.300895	+	1.15044i
$315$		0			0
$316$	−1.92138	+	1.07886i	−0.108086	+	0.0606909i
$317$	−4.15263	+	15.4978i	−0.233235	+	0.870445i	0.745701	+	0.666280i	$0.232115\pi$
$317$	−4.15263	+	15.4978i	−0.233235	+	0.870445i	−0.978936	+	0.204165i	$0.934552\pi$
$318$	10.8053	+	18.9767i	0.605934	+	1.06416i
$319$	−25.1595	−	14.5258i	−1.40866	−	0.813290i
$320$	−6.04634	+	19.7069i	−0.338001	+	1.10165i
$321$			10.6929i			0.596818i
$322$		0			0
$323$	8.94405	−	8.94405i	0.497660	−	0.497660i
$324$	−11.3255	+	19.0853i	−0.629197	+	1.06030i
$325$	−1.90101	+	0.509373i	−0.105449	+	0.0282549i
$326$	26.3443	+	7.22814i	1.45908	+	0.400330i
$327$	−24.3122	+	14.0366i	−1.34447	+	0.776228i
$328$	−13.4912	−	0.242171i	−0.744927	−	0.0133717i
$329$		0			0
$330$	9.77481	+	37.3730i	0.538086	+	2.05732i
$331$	−4.91579	+	18.3460i	−0.270196	+	1.00839i	0.688796	+	0.724955i	$0.258139\pi$
$331$	−4.91579	+	18.3460i	−0.270196	+	1.00839i	−0.958993	+	0.283431i	$0.908527\pi$
$332$	19.2343	+	19.7002i	1.05562	+	1.08119i
$333$	−6.69379	+	1.79360i	−0.366817	+	0.0982884i
$334$	−0.0294727	+	4.92620i	−0.00161268	+	0.269549i
$335$	1.00545			0.0549336
$336$		0			0
$337$	15.6500			0.852513			0.426256	−	0.904602i	$-0.359832\pi$
$337$	15.6500			0.852513			0.426256	+	0.904602i	$0.359832\pi$
$338$	0.0977976	−	16.3463i	0.00531949	−	0.889121i
$339$	16.9890	−	4.55220i	0.922717	−	0.247241i
$340$	−9.53532	+	9.30982i	−0.517125	+	0.504896i
$341$	1.58490	−	5.91493i	0.0858272	−	0.320311i
$342$	1.93947	+	7.41539i	0.104875	+	0.400978i
$343$		0			0
$344$	−13.3340	−	13.8214i	−0.718919	−	0.745200i
$345$	28.5814	−	16.5015i	1.53877	−	0.888409i
$346$	0.0998847	+	0.0274055i	0.00536983	+	0.00147333i
$347$	18.9357	−	5.07381i	1.01652	−	0.272376i	0.288170	−	0.957579i	$-0.406953\pi$
$347$	18.9357	−	5.07381i	1.01652	−	0.272376i	0.728352	+	0.685203i	$0.240286\pi$
$348$	19.3632	+	11.4904i	1.03798	+	0.615951i
$349$	−7.34147	+	7.34147i	−0.392980	+	0.392980i	−0.875748	−	0.482768i	$-0.839631\pi$
$349$	−7.34147	+	7.34147i	−0.392980	+	0.392980i	0.482768	+	0.875748i	$0.339631\pi$
$350$		0			0
$351$		−	4.60354i		−	0.245719i
$352$	−28.7954	+	6.79955i	−1.53480	+	0.362417i
$353$	−10.4533	−	6.03519i	−0.556371	−	0.321221i	0.195317	−	0.980740i	$-0.437426\pi$
$353$	−10.4533	−	6.03519i	−0.556371	−	0.321221i	−0.751687	+	0.659519i	$0.770760\pi$
$354$	1.18836	+	2.08703i	0.0631605	+	0.110925i
$355$	−2.55642	+	9.54069i	−0.135681	+	0.506367i
$356$	15.4933	+	27.5925i	0.821143	+	1.46240i
$357$		0			0
$358$	−1.11371	−	4.25818i	−0.0588616	−	0.225052i
$359$	0.868374	+	1.50407i	0.0458310	+	0.0793816i	0.888031	−	0.459784i	$-0.152073\pi$
$359$	0.868374	+	1.50407i	0.0458310	+	0.0793816i	−0.842200	+	0.539165i	$0.818740\pi$
$360$	−1.94976	−	7.83657i	−0.102761	−	0.413024i
$361$	−4.26528	−	2.46256i	−0.224488	−	0.129608i
$362$	−4.70095	−	4.75754i	−0.247076	−	0.250051i
$363$	−23.4420	+	23.4420i	−1.23039	+	1.23039i
$364$		0			0
$365$	−17.6585	−	17.6585i	−0.924287	−	0.924287i
$366$	−12.9854	−	0.0776896i	−0.678755	−	0.00406090i
$367$	−5.21754	+	9.03704i	−0.272353	+	0.471730i	−0.969464	−	0.245234i	$-0.921135\pi$
$367$	−5.21754	+	9.03704i	−0.272353	+	0.471730i	0.697111	+	0.716963i	$0.254469\pi$
$368$	12.1112	+	22.1870i	0.631342	+	1.15658i
$369$	4.57790	−	2.64305i	0.238316	−	0.137592i
$370$	−11.5129	+	19.6683i	−0.598528	+	1.02250i
$371$		0			0
$372$	−1.28311	+	4.56921i	−0.0665260	+	0.236903i
$373$	10.6059	+	2.84184i	0.549153	+	0.147145i	0.522718	−	0.852505i	$-0.324918\pi$
$373$	10.6059	+	2.84184i	0.549153	+	0.147145i	0.0264347	+	0.999651i	$0.491585\pi$
$374$	−18.4462	−	5.06112i	−0.953831	−	0.261704i
$375$	8.77552	−	15.1996i	0.453166	−	0.784907i
$376$	−9.29598	−	16.7900i	−0.479404	−	0.865878i
$377$	−6.66815			−0.343427
$378$		0			0
$379$	19.3486	+	19.3486i	0.993870	+	0.993870i	0.999981	−	0.00611151i	$-0.00194537\pi$
$379$	19.3486	+	19.3486i	0.993870	+	0.993870i	−0.00611151	+	0.999981i	$0.501945\pi$
$380$	21.6775	+	12.8638i	1.11203	+	0.659897i
$381$	7.37347	+	27.5182i	0.377754	+	1.40980i
$382$	0.384713	−	0.219056i	0.0196836	−	0.0112079i
$383$	8.91313	+	15.4380i	0.455440	+	0.788844i	0.998713	−	0.0507112i	$-0.0161488\pi$
$383$	8.91313	+	15.4380i	0.455440	+	0.788844i	−0.543274	+	0.839556i	$0.682815\pi$
$384$	22.3787	−	5.00243i	1.14201	−	0.255279i
$385$		0			0
$386$	−7.39863	+	12.6396i	−0.376581	+	0.643337i
$387$	7.26724	+	1.94725i	0.369415	+	0.0989844i
$388$	0.0268568	−	2.24439i	0.00136345	−	0.113942i
$389$	−1.61525	−	6.02818i	−0.0818963	−	0.305641i	0.912812	−	0.408380i	$-0.133906\pi$
$389$	−1.61525	−	6.02818i	−0.0818963	−	0.305641i	−0.994708	+	0.102739i	$0.967239\pi$
$390$	6.23207	+	6.30709i	0.315573	+	0.319372i
$391$			16.3416i			0.826429i
$392$		0			0
$393$			30.6190i			1.54453i
$394$	−0.160480	+	0.158572i	−0.00808489	+	0.00798872i
$395$	−0.734773	−	2.74221i	−0.0369705	−	0.137976i
$396$	8.29356	−	8.09742i	0.416767	−	0.406911i
$397$	6.82155	+	1.82783i	0.342364	+	0.0917361i	0.425904	−	0.904768i	$-0.359956\pi$
$397$	6.82155	+	1.82783i	0.342364	+	0.0917361i	−0.0835403	+	0.996504i	$0.526623\pi$
$398$	−26.0350	−	15.2397i	−1.30502	−	0.763899i
$399$		0			0
$400$	−5.59883	−	3.41367i	−0.279942	−	0.170684i
$401$	10.4950	+	18.1779i	0.524096	+	0.907761i	0.999606	+	0.0280512i	$0.00893014\pi$
$401$	10.4950	+	18.1779i	0.524096	+	0.907761i	−0.475510	+	0.879710i	$0.657737\pi$
$402$	−0.553438	−	0.971966i	−0.0276030	−	0.0484772i
$403$	−0.363778	−	1.35764i	−0.0181211	−	0.0676288i
$404$	−28.1223	+	7.17583i	−1.39914	+	0.357011i
$405$	−20.2176	−	20.2176i	−1.00462	−	1.00462i
$406$		0			0
$407$	−32.7114			−1.62144
$408$	14.2484	+	4.09329i	0.705399	+	0.202648i
$409$	18.0958	−	31.3428i	0.894780	−	1.54980i	0.0607027	−	0.998156i	$-0.480666\pi$
$409$	18.0958	−	31.3428i	0.894780	−	1.54980i	0.834077	−	0.551648i	$-0.186001\pi$
$410$	4.59973	−	16.7646i	0.227164	−	0.827944i
$411$	−9.88031	−	2.64742i	−0.487360	−	0.130588i
$412$	−1.49398	+	0.838875i	−0.0736029	+	0.0413284i
$413$		0			0
$414$	−8.54608	−	5.00249i	−0.420017	−	0.245859i
$415$	−30.7196	+	17.7360i	−1.50797	+	0.870624i
$416$	−4.94351	+	4.65626i	−0.242376	+	0.228292i
$417$	5.41686	−	9.38228i	0.265265	−	0.459452i
$418$	−0.216458	+	36.1797i	−0.0105873	+	1.76961i
$419$	5.15413	+	5.15413i	0.251796	+	0.251796i	0.821707	−	0.569911i	$-0.193022\pi$
$419$	5.15413	+	5.15413i	0.251796	+	0.251796i	−0.569911	+	0.821707i	$0.693022\pi$
$420$		0			0
$421$	−7.75876	+	7.75876i	−0.378139	+	0.378139i	−0.870430	−	0.492292i	$-0.836159\pi$
$421$	−7.75876	+	7.75876i	−0.378139	+	0.378139i	0.492292	+	0.870430i	$0.336159\pi$
$422$	−10.9821	+	10.8515i	−0.534599	+	0.528241i
$423$	6.51116	+	3.75922i	0.316583	+	0.182779i
$424$	−5.20265	−	20.9108i	−0.252663	−	1.01552i
$425$	−2.11966	−	3.67137i	−0.102819	−	0.178087i
$426$	10.6301	−	2.78027i	0.515030	−	0.134705i
$427$		0			0
$428$	2.85263	−	10.1584i	0.137887	−	0.491024i
$429$	−3.29390	+	12.2930i	−0.159031	+	0.593511i
$430$	21.5013	−	12.2428i	1.03688	−	0.590402i
$431$	−21.4746	−	12.3984i	−1.03440	−	0.597209i	−0.116156	−	0.993231i	$-0.537057\pi$
$431$	−21.4746	−	12.3984i	−1.03440	−	0.597209i	−0.918241	+	0.396022i	$0.870391\pi$
$432$	11.1025	−	10.5834i	0.534169	−	0.509195i
$433$			4.84981i			0.233067i	0.993187	+	0.116534i	$0.0371782\pi$
$433$			4.84981i			0.233067i	−0.993187	+	0.116534i	$0.962822\pi$
$434$		0			0
$435$	−20.5119	+	20.5119i	−0.983471	+	0.983471i
$436$	26.8416	−	6.84903i	1.28548	−	0.328009i
$437$	29.8567	−	8.00009i	1.42824	−	0.382696i
$438$	−7.35050	+	26.7903i	−0.351220	+	1.28009i
$439$	32.2458	−	18.6171i	1.53901	−	0.888546i	0.540109	−	0.841595i	$-0.318383\pi$
$439$	32.2458	−	18.6171i	1.53901	−	0.888546i	0.998897	−	0.0469506i	$-0.0149503\pi$
$440$	0.684133	−	38.1126i	0.0326148	−	1.81695i
$441$		0			0
$442$	−4.24751	+	1.11092i	−0.202033	+	0.0528412i
$443$	6.51323	−	24.3077i	0.309453	−	1.15489i	−0.619591	−	0.784925i	$-0.712702\pi$
$443$	6.51323	−	24.3077i	0.309453	−	1.15489i	0.929044	−	0.369969i	$-0.120632\pi$
$444$	25.3504	+	0.303347i	1.20308	+	0.0143962i
$445$	−39.3802	+	10.5519i	−1.86680	+	0.500207i
$446$	13.7759	+	0.0824193i	0.652308	+	0.00390267i
$447$	0.552685			0.0261411
$448$		0			0
$449$	0.885883			0.0418074			0.0209037	−	0.999781i	$-0.493346\pi$
$449$	0.885883			0.0418074			0.0209037	+	0.999781i	$0.493346\pi$
$450$	2.56887	+	0.0153692i	0.121098	+	0.000724511i
$451$	24.1018	−	6.45806i	1.13491	−	0.304098i
$452$	−17.3542	−	0.207664i	−0.816275	−	0.00976767i
$453$	4.80548	−	17.9343i	0.225781	−	0.842626i
$454$	1.42651	−	0.373098i	0.0669492	−	0.0175104i
$455$		0			0
$456$	0.503259	−	28.0363i	0.0235673	−	1.31292i
$457$	30.0308	−	17.3383i	1.40478	−	0.811052i	0.409904	−	0.912129i	$-0.365562\pi$
$457$	30.0308	−	17.3383i	1.40478	−	0.811052i	0.994879	+	0.101077i	$0.0322289\pi$
$458$	−2.01200	+	7.33312i	−0.0940147	+	0.342654i
$459$	9.57840	−	2.56653i	0.447082	−	0.119795i
$460$	−31.5550	+	8.05172i	−1.47126	+	0.375413i
$461$	4.11212	−	4.11212i	0.191520	−	0.191520i	−0.604832	−	0.796353i	$-0.706760\pi$
$461$	4.11212	−	4.11212i	0.191520	−	0.191520i	0.796353	+	0.604832i	$0.206760\pi$
$462$		0			0
$463$			11.6892i			0.543245i	0.962404	+	0.271623i	$0.0875603\pi$
$463$			11.6892i			0.543245i	−0.962404	+	0.271623i	$0.912440\pi$
$464$	−15.3299	−	16.0817i	−0.711672	−	0.746576i
$465$	−5.29526	−	3.05722i	−0.245562	−	0.141775i
$466$	15.7120	−	8.94643i	0.727845	−	0.414435i
$467$	6.51878	−	24.3284i	0.301653	−	1.12579i	−0.634135	−	0.773222i	$-0.718644\pi$
$467$	6.51878	−	24.3284i	0.301653	−	1.12579i	0.935788	−	0.352563i	$-0.114690\pi$
$468$	0.719275	−	2.56138i	0.0332485	−	0.118400i
$469$		0			0
$470$	23.9209	−	6.25643i	1.10339	−	0.288588i
$471$	15.0998	+	26.1536i	0.695762	+	1.20509i
$472$	−0.572180	−	2.29974i	−0.0263367	−	0.105854i
$473$	30.7558	+	17.7569i	1.41415	+	0.816461i
$474$	−2.24644	+	2.21972i	−0.103182	+	0.101955i
$475$	−5.67005	+	5.67005i	−0.260160	+	0.260160i
$476$		0			0
$477$	5.96915	+	5.96915i	0.273309	+	0.273309i
$478$	0.221917	−	37.0921i	0.0101502	−	1.69655i
$479$	−12.1539	+	21.0512i	−0.555328	+	0.961856i	0.442550	+	0.896744i	$0.354074\pi$
$479$	−12.1539	+	21.0512i	−0.555328	+	0.961856i	−0.997878	+	0.0651122i	$0.979259\pi$
$480$	−0.883619	+	29.5299i	−0.0403315	+	1.34785i
$481$	−6.50225	+	3.75408i	−0.296477	+	0.171171i
$482$	−26.9077	−	15.7505i	−1.22561	−	0.717417i
$483$		0			0
$484$	28.5241	−	16.0164i	1.29655	−	0.728018i
$485$	2.79323	+	0.748444i	0.126834	+	0.0339851i
$486$	−4.11106	+	14.9835i	−0.186482	+	0.679667i
$487$	15.5000	−	26.8468i	0.702373	−	1.21655i	−0.265258	−	0.964177i	$-0.585457\pi$
$487$	15.5000	−	26.8468i	0.702373	−	1.21655i	0.967631	−	0.252369i	$-0.0812095\pi$
$488$	12.3155	+	3.53802i	0.557498	+	0.160159i
$489$	39.1517			1.77050
$490$		0			0
$491$	8.29080	+	8.29080i	0.374159	+	0.374159i	0.868989	−	0.494831i	$-0.164770\pi$
$491$	8.29080	+	8.29080i	0.374159	+	0.374159i	−0.494831	+	0.868989i	$0.664770\pi$
$492$	−18.7381	+	4.78131i	−0.844780	+	0.215558i
$493$	−3.71756	−	13.8741i	−0.167431	−	0.624860i
$494$	4.10909	+	7.21652i	0.184877	+	0.324686i
$495$	7.46662	+	12.9326i	0.335600	+	0.581276i
$496$	2.43794	−	3.99851i	0.109467	−	0.179538i
$497$		0			0
$498$	34.0545	+	19.9340i	1.52602	+	0.893263i
$499$	22.9663	+	6.15379i	1.02811	+	0.275482i	0.733178	−	0.680036i	$-0.238036\pi$
$499$	22.9663	+	6.15379i	1.02811	+	0.275482i	0.294933	+	0.955518i	$0.404703\pi$
$500$	−12.3918	+	12.0988i	−0.554179	+	0.541073i
$501$	1.82734	+	6.81971i	0.0816394	+	0.304682i
$502$	−22.0498	+	21.7875i	−0.984130	+	0.972425i
$503$		−	3.42708i		−	0.152806i	−0.997077	−	0.0764029i	$-0.975656\pi$
$503$		−	3.42708i		−	0.152806i	0.997077	−	0.0764029i	$-0.0243435\pi$
$504$		0			0
$505$		−	37.3923i		−	1.66393i
$506$	−32.8540	−	33.2495i	−1.46054	−	1.47812i
$507$	−6.06354	−	22.6294i	−0.269291	−	1.00501i
$508$	0.336365	−	28.1097i	0.0149238	−	1.24717i
$509$	−35.5302	−	9.52030i	−1.57485	−	0.421980i	−0.637523	−	0.770431i	$-0.720041\pi$
$509$	−35.5302	−	9.52030i	−1.57485	−	0.421980i	−0.937327	+	0.348451i	$0.886708\pi$
$510$	−9.64846	+	16.4831i	−0.427241	+	0.729883i
$511$		0			0
$512$	−22.5946	−	1.21779i	−0.998551	−	0.0538191i
$513$	−9.37830	−	16.2437i	−0.414062	−	0.717177i
$514$	2.32729	−	1.32516i	0.102652	−	0.0584503i
$515$	−0.571325	−	2.13221i	−0.0251756	−	0.0939566i
$516$	−23.6702	−	14.0463i	−1.04202	−	0.618353i
$517$	25.0947	+	25.0947i	1.10367	+	1.10367i
$518$		0			0
$519$	0.148444			0.00651597
$520$	−4.23796	−	7.65441i	−0.185847	−	0.335668i
$521$	−6.82432	+	11.8201i	−0.298979	+	0.517846i	−0.975903	−	0.218207i	$-0.929979\pi$
$521$	−6.82432	+	11.8201i	−0.298979	+	0.517846i	0.676924	+	0.736053i	$0.263313\pi$
$522$	8.39372	+	2.30300i	0.367383	+	0.100800i
$523$	−18.4158	−	4.93451i	−0.805269	−	0.215771i	−0.167373	−	0.985894i	$-0.553528\pi$
$523$	−18.4158	−	4.93451i	−0.805269	−	0.215771i	−0.637896	+	0.770123i	$0.720195\pi$
$524$	8.16851	−	29.0885i	0.356843	−	1.27074i
$525$		0			0
$526$	−6.68140	+	11.4143i	−0.291323	+	0.497686i
$527$	2.62197	−	1.51380i	0.114215	−	0.0659420i
$528$	−37.2199	+	20.3173i	−1.61979	+	0.884196i
$529$	−8.46701	+	14.6653i	−0.368131	+	0.637621i
$530$	27.7612	+	0.166091i	1.20587	+	0.00721454i
$531$	0.656479	+	0.656479i	0.0284888	+	0.0284888i
$532$		0			0
$533$	4.04973	−	4.04973i	0.175413	−	0.175413i
$534$	31.8768	+	32.2605i	1.37944	+	1.39605i
$535$	11.7725	+	6.79688i	0.508971	+	0.293855i
$536$	0.266474	+	1.07103i	0.0115099	+	0.0462613i
$537$	−3.15403	−	5.46293i	−0.136106	−	0.235743i
$538$	−9.54452	−	36.4925i	−0.411493	−	1.57331i
$539$		0			0
$540$	9.67528	+	17.2310i	0.416358	+	0.741503i
$541$	−0.122143	+	0.455845i	−0.00525135	+	0.0195983i	−0.968502	−	0.249007i	$-0.919896\pi$
$541$	−0.122143	+	0.455845i	−0.00525135	+	0.0195983i	0.963250	+	0.268605i	$0.0865626\pi$
$542$	6.01905	+	10.5709i	0.258540	+	0.454057i
$543$	−8.30133	−	4.79278i	−0.356244	−	0.205678i
$544$	−12.4441	−	7.68984i	−0.533538	−	0.329699i
$545$			35.6893i			1.52876i
$546$		0			0
$547$	9.02908	−	9.02908i	0.386056	−	0.386056i	−0.487222	−	0.873278i	$-0.661990\pi$
$547$	9.02908	−	9.02908i	0.386056	−	0.386056i	0.873278	+	0.487222i	$0.161990\pi$
$548$	8.68015	+	5.15094i	0.370798	+	0.220037i
$549$	−4.84878	+	1.29923i	−0.206941	+	0.0554497i
$550$	11.6939	+	3.20848i	0.498630	+	0.136810i
$551$	−23.5287	+	13.5843i	−1.00236	+	0.578710i
$552$	25.1526	+	26.0721i	1.07057	+	1.10970i
$553$		0			0
$554$	−9.17100	−	35.0644i	−0.389638	−	1.48975i
$555$	−8.45367	+	31.5495i	−0.358838	+	1.33920i
$556$	−7.64909	+	7.46819i	−0.324394	+	0.316722i
$557$	−6.71669	+	1.79973i	−0.284595	+	0.0762570i	−0.398293	−	0.917258i	$-0.630397\pi$
$557$	−6.71669	+	1.79973i	−0.284595	+	0.0762570i	0.113698	+	0.993515i	$0.463731\pi$
$558$	−0.0109762	+	1.83461i	−0.000464659	+	0.0776651i
$559$	8.15137			0.344766
$560$		0			0
$561$	−27.4139			−1.15742
$562$	−0.197020	+	32.9307i	−0.00831077	+	1.38910i
$563$	−29.7061	+	7.95972i	−1.25196	+	0.335462i	−0.823094	−	0.567905i	$-0.807754\pi$
$563$	−29.7061	+	7.95972i	−1.25196	+	0.335462i	−0.428868	+	0.903367i	$0.641087\pi$
$564$	−19.2150	−	19.6804i	−0.809098	−	0.828696i
$565$	5.78717	−	21.5980i	0.243468	−	0.908635i
$566$	3.63312	+	13.8909i	0.152711	+	0.583878i
$567$		0			0
$568$	−10.8405	−	0.194590i	−0.454856	−	0.00816480i
$569$	−33.8726	+	19.5564i	−1.42002	+	0.819846i	−0.996300	−	0.0859489i	$-0.972608\pi$
$569$	−33.8726	+	19.5564i	−1.42002	+	0.819846i	−0.423716	+	0.905795i	$0.639274\pi$
$570$	34.8387	+	9.55877i	1.45923	+	0.400373i
$571$	−5.29899	+	1.41986i	−0.221756	+	0.0594193i	−0.367986	−	0.929831i	$-0.619953\pi$
$571$	−5.29899	+	1.41986i	−0.221756	+	0.0594193i	0.146230	+	0.989251i	$0.453286\pi$
$572$	6.40876	−	10.7998i	0.267964	−	0.451561i
$573$	0.448646	−	0.448646i	0.0187425	−	0.0187425i
$574$		0			0
$575$		−	10.3597i		−	0.432028i
$576$	7.83093	−	4.15384i	0.326289	−	0.173077i
$577$	−30.0825	−	17.3681i	−1.25235	−	0.723044i	−0.280774	−	0.959774i	$-0.590591\pi$
$577$	−30.0825	−	17.3681i	−1.25235	−	0.723044i	−0.971576	+	0.236729i	$0.923924\pi$
$578$	7.21655	+	12.6739i	0.300169	+	0.527167i
$579$	−5.43264	+	20.2749i	−0.225773	+	0.842596i
$580$	24.9587	−	14.0145i	1.03636	−	0.581919i
$581$		0			0
$582$	−0.813982	−	3.11218i	−0.0337406	−	0.129004i
$583$	19.9236	+	34.5087i	0.825152	+	1.42920i
$584$	14.1302	−	23.4902i	0.584710	−	0.972030i
$585$	2.96838	+	1.71379i	0.122727	+	0.0708567i
$586$	−0.135141	−	0.136768i	−0.00558261	−	0.00564981i
$587$	25.6897	−	25.6897i	1.06033	−	1.06033i	0.0622695	−	0.998059i	$-0.480166\pi$
$587$	25.6897	−	25.6897i	1.06033	−	1.06033i	0.998059	−	0.0622695i	$-0.0198338\pi$
$588$		0			0
$589$	−4.04937	−	4.04937i	−0.166851	−	0.166851i
$590$	3.05314	+	0.0182665i	0.125696	+	0.000752020i
$591$	−0.161669	+	0.280019i	−0.00665018	+	0.0115185i
$592$	−24.0023	−	7.05113i	−0.986489	−	0.289800i
$593$	−21.1335	+	12.2015i	−0.867850	+	0.501054i	−0.866633	−	0.498946i	$-0.833721\pi$
$593$	−21.1335	+	12.2015i	−0.867850	+	0.501054i	−0.00121701	+	0.999999i	$0.500387\pi$
$594$	−14.3289	+	24.4790i	−0.587921	+	1.00438i
$595$		0			0
$596$	−0.525059	−	0.147445i	−0.0215072	−	0.00603957i
$597$	−41.7623	−	11.1902i	−1.70922	−	0.457984i
$598$	−10.3464	−	2.83877i	−0.423097	−	0.116086i
$599$	−13.3779	+	23.1712i	−0.546606	+	0.946750i	0.451898	+	0.892070i	$0.350747\pi$
$599$	−13.3779	+	23.1712i	−0.546606	+	0.946750i	−0.998504	+	0.0546799i	$0.982586\pi$
$600$	−9.03270	−	2.59493i	−0.368759	−	0.105937i
$601$	16.1853			0.660212			0.330106	−	0.943944i	$-0.392915\pi$
$601$	16.1853			0.660212			0.330106	+	0.943944i	$0.392915\pi$
$602$		0			0
$603$	−0.305733	−	0.305733i	−0.0124504	−	0.0124504i
$604$	−9.34976	+	15.7558i	−0.380436	+	0.641095i
$605$	10.9082	+	40.7098i	0.443479	+	1.65509i
$606$	−36.1470	+	20.5821i	−1.46837	+	0.836091i
$607$	2.51647	+	4.35866i	0.102141	+	0.176913i	0.912566	−	0.408929i	$-0.134098\pi$
$607$	2.51647	+	4.35866i	0.102141	+	0.176913i	−0.810426	+	0.585841i	$0.800764\pi$
$608$	−7.95758	+	26.5006i	−0.322723	+	1.07474i
$609$		0			0
$610$	−8.33962	+	14.2471i	−0.337661	+	0.576849i
$611$	7.86821	+	2.10828i	0.318314	+	0.0852919i
$612$	5.73035	+	0.0685703i	0.231636	+	0.00277179i
$613$	−0.117633	−	0.439011i	−0.00475113	−	0.0177315i	0.963510	−	0.267674i	$-0.0862550\pi$
$613$	−0.117633	−	0.439011i	−0.00475113	−	0.0177315i	−0.968261	+	0.249942i	$0.919588\pi$
$614$	22.8362	+	23.1111i	0.921594	+	0.932688i
$615$		−	24.9147i		−	1.00466i
$616$		0			0
$617$			4.35363i			0.175271i	0.996153	+	0.0876353i	$0.0279310\pi$
$617$			4.35363i			0.175271i	−0.996153	+	0.0876353i	$0.972069\pi$
$618$	−1.74673	+	1.72595i	−0.0702636	+	0.0694279i
$619$	1.27148	+	4.74521i	0.0511049	+	0.190726i	0.986759	−	0.162191i	$-0.0518562\pi$
$619$	1.27148	+	4.74521i	0.0511049	+	0.190726i	−0.935654	+	0.352918i	$0.885190\pi$
$620$	4.21497	+	4.31706i	0.169277	+	0.173377i
$621$	23.4068	+	6.27184i	0.939283	+	0.251680i
$622$	17.3533	+	10.1578i	0.695804	+	0.407292i
$623$		0			0
$624$	−5.06676	+	8.31009i	−0.202833	+	0.332670i
$625$	−15.2547	−	26.4218i	−0.610186	−	1.05687i
$626$	−18.8101	−	33.0349i	−0.751803	−	1.32034i
$627$	13.4206	+	50.0864i	0.535967	+	2.00026i
$628$	−7.36779	−	28.8746i	−0.294007	−	1.15222i
$629$	−11.4360	−	11.4360i	−0.455984	−	0.455984i
$630$		0			0
$631$	−22.0158			−0.876434			−0.438217	−	0.898869i	$-0.644390\pi$
$631$	−22.0158			−0.876434			−0.438217	+	0.898869i	$0.644390\pi$
$632$	2.72632	−	1.50946i	0.108447	−	0.0600432i
$633$	−11.0634	+	19.1624i	−0.439732	+	0.761638i
$634$	6.00373	−	21.8817i	0.238439	−	0.869034i
$635$	34.9836	+	9.37383i	1.38828	+	0.371989i
$636$	−15.1202	−	26.9281i	−0.599556	−	1.06777i
$637$		0			0
$638$	35.4573	+	20.7551i	1.40377	+	0.821703i
$639$	3.67844	−	2.12375i	0.145517	−	0.0840142i
$640$	8.71740	−	27.8181i	0.344586	−	1.09961i
$641$	11.9837	−	20.7564i	0.473328	−	0.819828i	−0.526206	−	0.850357i	$-0.676386\pi$
$641$	11.9837	−	20.7564i	0.473328	−	0.819828i	0.999534	+	0.0305295i	$0.00971934\pi$
$642$	0.0904713	−	15.1217i	0.00357062	−	0.596807i
$643$	−30.4232	−	30.4232i	−1.19977	−	1.19977i	−0.974235	−	0.225537i	$-0.927586\pi$
$643$	−30.4232	−	30.4232i	−1.19977	−	1.19977i	−0.225537	−	0.974235i	$-0.572414\pi$
$644$		0			0
$645$	25.0745	−	25.0745i	0.987306	−	0.987306i
$646$	−12.7242	+	12.5729i	−0.500629	+	0.494674i
$647$	−5.45353	−	3.14859i	−0.214400	−	0.123784i	0.388954	−	0.921257i	$-0.372836\pi$
$647$	−5.45353	−	3.14859i	−0.214400	−	0.123784i	−0.603355	+	0.797473i	$0.706170\pi$
$648$	16.1779	−	26.8944i	0.635529	−	1.05651i
$649$	2.19117	+	3.79522i	0.0860110	+	0.148975i
$650$	2.69269	−	0.704266i	0.105616	−	0.0276236i
$651$		0			0
$652$	−37.1947	−	10.4449i	−1.45666	−	0.409052i
$653$	8.24649	−	30.7763i	0.322710	−	1.20437i	−0.593884	−	0.804551i	$-0.702406\pi$
$653$	8.24649	−	30.7763i	0.322710	−	1.20437i	0.916594	−	0.399819i	$-0.130927\pi$
$654$	34.5007	−	19.6447i	1.34909	−	0.768170i
$655$	33.7107	+	19.4629i	1.31719	+	0.760477i
$656$	19.0770	+	0.456623i	0.744833	+	0.0178281i
$657$			10.7390i			0.418970i
$658$		0			0
$659$	−3.27251	+	3.27251i	−0.127479	+	0.127479i	−0.767968	−	0.640489i	$-0.778732\pi$
$659$	−3.27251	+	3.27251i	−0.127479	+	0.127479i	0.640489	+	0.767968i	$0.278732\pi$
$660$	−13.5072	−	52.9352i	−0.525768	−	2.06050i
$661$	14.3283	−	3.83925i	0.557305	−	0.149329i	0.0308372	−	0.999524i	$-0.490183\pi$
$661$	14.3283	−	3.83925i	0.557305	−	0.149329i	0.526468	+	0.850195i	$0.323516\pi$
$662$	7.10707	−	25.9031i	0.276224	−	1.00675i
$663$	−5.44924	+	3.14612i	−0.211631	+	0.122185i
$664$	−27.0343	−	28.0226i	−1.04913	−	1.08749i
$665$		0			0
$666$	9.48145	−	2.47985i	0.367399	−	0.0960921i
$667$	9.08464	−	33.9043i	0.351759	−	1.31278i
$668$	0.0833600	−	6.96632i	0.00322530	−	0.269535i
$669$	19.0710	−	5.11007i	0.737329	−	0.197567i
$670$	−1.42190	−	0.00850701i	−0.0549326	−	0.000328654i
$671$	−23.6951			−0.914740
$672$		0			0
$673$	1.09724			0.0422955			0.0211478	−	0.999776i	$-0.493268\pi$
$673$	1.09724			0.0422955			0.0211478	+	0.999776i	$0.493268\pi$
$674$	−22.1321	−	0.132413i	−0.852497	−	0.00510037i
$675$	−6.07219	+	1.62704i	−0.233719	+	0.0626248i
$676$	−0.276608	+	23.1159i	−0.0106388	+	0.889073i
$677$	−4.30288	+	16.0585i	−0.165373	+	0.617180i	0.832619	+	0.553846i	$0.186840\pi$
$677$	−4.30288	+	16.0585i	−0.165373	+	0.617180i	−0.997992	+	0.0633346i	$0.979826\pi$
$678$	−24.0642	+	6.29392i	−0.924180	+	0.241717i
$679$		0			0
$680$	13.5635	−	13.0852i	0.520137	−	0.501793i
$681$	1.83010	−	1.05661i	0.0701297	−	0.0404894i
$682$	−2.29139	+	8.35142i	−0.0877420	+	0.319792i
$683$	−18.7919	+	5.03528i	−0.719053	+	0.192670i	−0.599749	−	0.800188i	$-0.704733\pi$
$683$	−18.7919	+	5.03528i	−0.719053	+	0.192670i	−0.119304	+	0.992858i	$0.538066\pi$
$684$	−2.68004	−	10.5032i	−0.102474	−	0.401599i
$685$	−9.19511	+	9.19511i	−0.351327	+	0.351327i
$686$		0			0
$687$			10.8981i			0.415790i
$688$	18.7398	+	19.6589i	0.714448	+	0.749488i
$689$	7.92069	+	4.57301i	0.301754	+	0.174218i
$690$	−40.5591	+	23.0944i	−1.54406	+	0.879187i
$691$	0.334331	−	1.24774i	0.0127186	−	0.0474663i	−0.959275	−	0.282474i	$-0.908845\pi$
$691$	0.334331	−	1.24774i	0.0127186	−	0.0474663i	0.971993	+	0.235008i	$0.0755116\pi$
$692$	−0.141024	−	0.0396017i	−0.00536092	−	0.00150543i
$693$		0			0
$694$	−26.8216	+	7.01511i	−1.01813	+	0.266290i
$695$	−6.88641	−	11.9276i	−0.261216	−	0.452440i
$696$	−27.2860	−	16.4135i	−1.03427	−	0.622150i
$697$	10.6839	+	6.16833i	0.404680	+	0.233642i
$698$	10.4443	−	10.3201i	0.395324	−	0.390622i
$699$	18.3231	−	18.3231i	0.693044	−	0.693044i
$700$		0			0
$701$	4.42004	+	4.42004i	0.166942	+	0.166942i	0.785634	−	0.618692i	$-0.212337\pi$
$701$	4.42004	+	4.42004i	0.166942	+	0.166942i	−0.618692	+	0.785634i	$0.712337\pi$
$702$	−0.0389501	+	6.51028i	−0.00147008	+	0.245715i
$703$	−15.2955	+	26.4927i	−0.576882	+	0.999189i
$704$	40.7797	−	9.37221i	1.53694	−	0.353228i
$705$	30.6887	−	17.7181i	1.15580	−	0.667304i
$706$	14.7318	+	8.62334i	0.554439	+	0.324544i
$707$		0			0
$708$	−1.66290	−	2.96151i	−0.0624957	−	0.111300i
$709$	−22.1786	−	5.94273i	−0.832934	−	0.223184i	−0.182941	−	0.983124i	$-0.558562\pi$
$709$	−22.1786	−	5.94273i	−0.832934	−	0.223184i	−0.649993	+	0.759940i	$0.725228\pi$
$710$	3.69598	−	13.4707i	0.138708	−	0.505546i
$711$	−0.610414	+	1.05727i	−0.0228923	+	0.0396506i
$712$	−21.6770	−	39.1520i	−0.812379	−	1.46728i
$713$	7.39855			0.277078
$714$		0			0
$715$	11.4405	+	11.4405i	0.427849	+	0.427849i
$716$	1.53897	+	6.03129i	0.0575142	+	0.225400i
$717$	−13.7590	−	51.3494i	−0.513841	−	1.91768i
$718$	−1.21532	−	2.13438i	−0.0453553	−	0.0796544i
$719$	3.53562	+	6.12387i	0.131856	+	0.228382i	0.924392	−	0.381444i	$-0.124573\pi$
$719$	3.53562	+	6.12387i	0.131856	+	0.228382i	−0.792536	+	0.609825i	$0.791240\pi$
$720$	2.69102	+	11.0989i	0.100288	+	0.413631i
$721$		0			0
$722$	6.01107	+	3.51861i	0.223709	+	0.130949i
$723$	−43.1621	−	11.5652i	−1.60522	−	0.430116i
$724$	6.60777	+	6.76783i	0.245576	+	0.251524i
$725$	2.35674	+	8.79546i	0.0875270	+	0.326655i
$726$	33.3497	−	32.9531i	1.23773	−	1.22300i
$727$			21.2964i			0.789838i	0.918716	+	0.394919i	$0.129227\pi$
$727$			21.2964i			0.789838i	−0.918716	+	0.394919i	$0.870773\pi$
$728$		0			0
$729$		−	11.0213i		−	0.408196i
$730$	24.8230	+	25.1218i	0.918740	+	0.929800i
$731$	4.54448	+	16.9602i	0.168084	+	0.627296i
$732$	18.3631	+	0.219735i	0.678719	+	0.00812165i
$733$	26.8991	+	7.20760i	0.993543	+	0.266219i	0.718738	−	0.695281i	$-0.244720\pi$
$733$	26.8991	+	7.20760i	0.993543	+	0.266219i	0.274805	+	0.961500i	$0.411387\pi$
$734$	7.45504	−	12.7359i	0.275171	−	0.470092i
$735$		0			0
$736$	−16.9398	−	31.4790i	−0.624411	−	1.16033i
$737$	−1.02047	−	1.76750i	−0.0375893	−	0.0651066i
$738$	−6.49638	+	3.69904i	−0.239135	+	0.136164i
$739$	−7.18877	−	26.8289i	−0.264443	−	0.986916i	−0.962590	−	0.270961i	$-0.912658\pi$
$739$	−7.18877	−	26.8289i	−0.264443	−	0.986916i	0.698147	−	0.715954i	$-0.254008\pi$
$740$	16.4478	−	27.7172i	0.604635	−	1.01891i
$741$	8.41580	+	8.41580i	0.309162	+	0.309162i
$742$		0			0
$743$	−4.98267			−0.182796			−0.0913982	−	0.995814i	$-0.529134\pi$
$743$	−4.98267			−0.182796			−0.0913982	+	0.995814i	$0.529134\pi$
$744$	1.85321	−	6.45087i	0.0679421	−	0.236500i
$745$	0.351312	−	0.608490i	0.0128711	−	0.0222934i
$746$	−14.9747	−	4.10864i	−0.548263	−	0.150428i
$747$	14.7342	+	3.94801i	0.539095	+	0.144450i
$748$	26.0436	+	7.31345i	0.952248	+	0.267406i
$749$		0			0
$750$	−12.5388	+	21.4209i	−0.457854	+	0.782181i
$751$	14.1452	−	8.16676i	0.516167	−	0.298009i	−0.219198	−	0.975680i	$-0.570344\pi$
$751$	14.1452	−	8.16676i	0.516167	−	0.298009i	0.735365	+	0.677671i	$0.237011\pi$
$752$	13.0042	+	23.8229i	0.474215	+	0.868730i
$753$	−22.2131	+	38.4743i	−0.809491	+	1.40208i
$754$	9.43001	+	0.0564185i	0.343421	+	0.00205464i
$755$	−16.6905	−	16.6905i	−0.607431	−	0.607431i
$756$		0			0
$757$	38.1458	−	38.1458i	1.38643	−	1.38643i	0.553747	−	0.832685i	$-0.313198\pi$
$757$	38.1458	−	38.1458i	1.38643	−	1.38643i	0.832685	−	0.553747i	$-0.186802\pi$
$758$	−27.1988	−	27.5262i	−0.987906	−	0.999798i
$759$	−58.0164	−	33.4958i	−2.10586	−	1.21582i
$760$	−30.5472	−	18.3752i	−1.10806	−	0.666539i
$761$	−16.5068	−	28.5906i	−0.598371	−	1.03641i	−0.993062	−	0.117595i	$-0.962481\pi$
$761$	−16.5068	−	28.5906i	−0.598371	−	1.03641i	0.394690	−	0.918814i	$-0.370852\pi$
$762$	−10.1946	−	38.9782i	−0.369313	−	1.41203i
$763$		0			0
$764$	−0.545909	+	0.306531i	−0.0197503	+	0.0110899i
$765$	−1.91092	+	7.13164i	−0.0690894	+	0.257845i
$766$	−12.4742	−	21.9076i	−0.450712	−	0.791555i
$767$	0.871107	+	0.502934i	0.0314539	+	0.0181599i
$768$	−31.6900	+	6.88503i	−1.14352	+	0.248442i
$769$		−	18.6850i		−	0.673800i	−0.941540	−	0.336900i	$-0.890622\pi$
$769$		−	18.6850i		−	0.673800i	0.941540	−	0.336900i	$-0.109378\pi$
$770$		0			0
$771$	2.71405	−	2.71405i	0.0977441	−	0.0977441i
$772$	10.5700	−	17.8121i	0.380423	−	0.641072i
$773$	−33.7362	+	9.03958i	−1.21341	+	0.325131i	−0.808097	−	0.589049i	$-0.799503\pi$
$773$	−33.7362	+	9.03958i	−1.21341	+	0.325131i	−0.405309	+	0.914180i	$0.632836\pi$
$774$	−10.2608	−	2.81527i	−0.368816	−	0.101193i
$775$	−1.66219	+	0.959666i	−0.0597076	+	0.0344722i
$776$	−0.0569701	+	3.17377i	−0.00204511	+	0.113932i
$777$		0			0
$778$	2.23326	+	8.53865i	0.0800662	+	0.306126i
$779$	6.03947	−	22.5396i	0.216386	−	0.807565i
$780$	−8.75996	−	8.97214i	−0.313657	−	0.321254i
$781$	19.3663	−	5.18919i	0.692982	−	0.185684i
$782$	0.138264	−	23.1101i	0.00494432	−	0.826414i
$783$	−21.2994			−0.761178
$784$		0			0
$785$	38.3925			1.37029
$786$	0.259065	−	43.3011i	0.00924053	−	1.54450i
$787$	−23.5420	+	6.30807i	−0.839183	+	0.224858i	−0.652716	−	0.757603i	$-0.726370\pi$
$787$	−23.5420	+	6.30807i	−0.839183	+	0.224858i	−0.186467	+	0.982461i	$0.559704\pi$
$788$	0.228291	−	0.222892i	0.00813254	−	0.00794021i
$789$	−4.90600	+	18.3094i	−0.174658	+	0.651833i
$790$	1.01591	+	3.88422i	0.0361443	+	0.138194i
$791$		0			0
$792$	−11.7972	+	11.3811i	−0.419194	+	0.404410i
$793$	−4.71004	+	2.71934i	−0.167258	+	0.0965666i
$794$	−9.63149	−	2.64261i	−0.341809	−	0.0937827i
$795$	38.4319	−	10.2978i	1.36304	−	0.365226i
$796$	36.6895	+	21.7721i	1.30042	+	0.771693i
$797$	25.8769	−	25.8769i	0.916608	−	0.916608i	−0.0801732	−	0.996781i	$-0.525547\pi$
$797$	25.8769	−	25.8769i	0.916608	−	0.916608i	0.996781	+	0.0801732i	$0.0255473\pi$
$798$		0			0
$799$			17.5465i			0.620749i
$800$	7.88892	+	4.87495i	0.278915	+	0.172355i
$801$	15.1831	+	8.76599i	0.536470	+	0.309731i
$802$	−14.6881	−	25.7958i	−0.518656	−	0.910881i
$803$	−13.1199	+	48.9643i	−0.462993	+	1.72791i
$804$	0.774442	+	1.37922i	0.0273124	+	0.0486415i
$805$		0			0
$806$	0.502964	+	1.92303i	0.0177162	+	0.0677360i
$807$	−27.0300	−	46.8173i	−0.951500	−	1.64805i
$808$	39.8310	−	9.91004i	1.40125	−	0.348634i
$809$	−19.9357	−	11.5099i	−0.700901	−	0.404665i	0.106782	−	0.994282i	$-0.465945\pi$
$809$	−19.9357	−	11.5099i	−0.700901	−	0.404665i	−0.807683	+	0.589617i	$0.799279\pi$
$810$	28.4204	+	28.7625i	0.998592	+	1.01061i
$811$	−8.31612	+	8.31612i	−0.292019	+	0.292019i	−0.837877	−	0.545859i	$-0.816204\pi$
$811$	−8.31612	+	8.31612i	−0.292019	+	0.292019i	0.545859	+	0.837877i	$0.316204\pi$
$812$		0			0
$813$	12.3276	+	12.3276i	0.432347	+	0.432347i
$814$	46.2600	+	0.276767i	1.62141	+	0.00970069i
$815$	24.8866	−	43.1049i	0.871741	−	1.50990i
$816$	−20.1152	−	5.90923i	−0.704174	−	0.206865i
$817$	28.7623	−	16.6059i	1.00626	−	0.580967i
$818$	−25.8561	+	44.1716i	−0.904036	+	1.54442i
$819$		0			0
$820$	−6.64673	+	23.6694i	−0.232114	+	0.826570i
$821$	2.17857	+	0.583745i	0.0760325	+	0.0203728i	0.296635	−	0.954991i	$-0.404136\pi$
$821$	2.17857	+	0.583745i	0.0760325	+	0.0203728i	−0.220602	+	0.975364i	$0.570802\pi$
$822$	13.9502	+	3.82755i	0.486570	+	0.133501i
$823$	−4.37272	+	7.57377i	−0.152423	+	0.264005i	−0.932118	−	0.362155i	$-0.882041\pi$
$823$	−4.37272	+	7.57377i	−0.152423	+	0.264005i	0.779694	+	0.626160i	$0.215374\pi$
$824$	2.11986	−	1.17369i	0.0738489	−	0.0408873i
$825$	17.3789			0.605057
$826$		0			0
$827$	−2.25129	−	2.25129i	−0.0782850	−	0.0782850i	0.666880	−	0.745165i	$-0.267629\pi$
$827$	−2.25129	−	2.25129i	−0.0782850	−	0.0782850i	−0.745165	+	0.666880i	$0.767629\pi$
$828$	12.0434	+	7.14677i	0.418538	+	0.248367i
$829$	1.67875	+	6.26518i	0.0583054	+	0.217599i	0.988932	−	0.148373i	$-0.0474035\pi$
$829$	1.67875	+	6.26518i	0.0583054	+	0.217599i	−0.930626	+	0.365971i	$0.880737\pi$
$830$	43.5933	−	24.8221i	1.51315	−	0.861587i
$831$	−25.9722	−	44.9851i	−0.900965	−	1.56052i
$832$	7.03045	−	6.54300i	0.243737	−	0.226838i
$833$		0			0
$834$	−7.73984	+	13.2225i	−0.268009	+	0.457857i
$835$	8.66985	+	2.32308i	0.300032	+	0.0803934i
$836$	0.612225	−	51.1631i	0.0211743	−	1.76951i
$837$	−1.16198	−	4.33657i	−0.0401639	−	0.149894i
$838$	−7.24530	−	7.33252i	−0.250285	−	0.253298i
$839$		−	15.8804i		−	0.548253i	−0.961694	−	0.274126i	$-0.911611\pi$
$839$		−	15.8804i		−	0.548253i	0.961694	−	0.274126i	$-0.0883886\pi$
$840$		0			0
$841$			1.85175i			0.0638536i
$842$	11.0380	−	10.9067i	0.380394	−	0.375870i
$843$	12.2154	+	45.5885i	0.420721	+	1.57015i
$844$	15.6225	−	15.2531i	0.537750	−	0.525033i
$845$	−28.7686	−	7.70853i	−0.989670	−	0.265181i
$846$	−9.17619	−	5.37133i	−0.315484	−	0.184670i
$847$		0			0
$848$	7.18060	+	29.6158i	0.246583	+	1.01701i
$849$	10.2890	+	17.8210i	0.353116	+	0.611615i
$850$	2.96654	+	5.20994i	0.101752	+	0.178699i
$851$	−10.2291	−	38.1754i	−0.350648	−	1.30863i
$852$	−15.0565	+	3.84189i	−0.515827	+	0.131621i
$853$	31.2018	+	31.2018i	1.06833	+	1.06833i	0.997488	+	0.0708400i	$0.0225680\pi$
$853$	31.2018	+	31.2018i	1.06833	+	1.06833i	0.0708400	+	0.997488i	$0.477432\pi$
$854$		0			0
$855$	13.9653			0.477603
$856$	−4.12011	+	14.3417i	−0.140822	+	0.490190i
$857$	0.256772	−	0.444743i	0.00877118	−	0.0151921i	−0.861607	−	0.507577i	$-0.830541\pi$
$857$	0.256772	−	0.444743i	0.00877118	−	0.0151921i	0.870378	+	0.492385i	$0.163875\pi$
$858$	4.76220	−	17.3567i	0.162579	−	0.592549i
$859$	−20.4685	−	5.48453i	−0.698377	−	0.187130i	−0.107874	−	0.994165i	$-0.534404\pi$
$859$	−20.4685	−	5.48453i	−0.698377	−	0.187130i	−0.590504	+	0.807035i	$0.701071\pi$
$860$	−30.5104	+	17.1318i	−1.04040	+	0.584188i
$861$		0			0
$862$	30.2643	+	17.7154i	1.03081	+	0.603387i
$863$	−41.4589	+	23.9363i	−1.41128	+	0.814801i	−0.995509	−	0.0946697i	$-0.969821\pi$
$863$	−41.4589	+	23.9363i	−1.41128	+	0.814801i	−0.415768	+	0.909471i	$0.636487\pi$
$864$	−15.7906	+	14.8730i	−0.537206	+	0.505990i
$865$	0.0943578	−	0.163433i	0.00320826	−	0.00555687i
$866$	0.0410337	−	6.85855i	0.00139438	−	0.233063i
$867$	14.7802	+	14.7802i	0.501961	+	0.501961i
$868$		0			0
$869$	−4.07483	+	4.07483i	−0.138229	+	0.138229i
$870$	29.1813	−	28.8342i	0.989337	−	0.977569i
$871$	−0.405689	−	0.234225i	−0.0137463	−	0.00793640i
$872$	−38.0170	+	9.45871i	−1.28742	+	0.320312i
$873$	−0.621771	−	1.07694i	−0.0210438	−	0.0364489i
$874$	−42.2907	+	11.0610i	−1.43051	+	0.374144i
$875$		0			0
$876$	10.6217	−	37.8243i	0.358873	−	1.27796i
$877$	5.85755	−	21.8607i	0.197795	−	0.738182i	−0.793730	−	0.608270i	$-0.791864\pi$
$877$	5.85755	−	21.8607i	0.197795	−	0.738182i	0.991525	−	0.129912i	$-0.0414696\pi$
$878$	−45.7591	+	26.0553i	−1.54429	+	0.879322i
$879$	−0.238643	−	0.137781i	−0.00804923	−	0.00464722i
$880$	−1.28996	+	53.8926i	−0.0434845	+	1.81672i
$881$			17.7026i			0.596417i	0.954501	+	0.298209i	$0.0963891\pi$
$881$			17.7026i			0.596417i	−0.954501	+	0.298209i	$0.903611\pi$
$882$		0			0
$883$	−13.2141	+	13.2141i	−0.444691	+	0.444691i	−0.893585	−	0.448894i	$-0.851818\pi$
$883$	−13.2141	+	13.2141i	−0.444691	+	0.444691i	0.448894	+	0.893585i	$0.351818\pi$
$884$	6.01617	−	1.53512i	0.202346	−	0.0516315i
$885$	4.22669	−	1.13254i	0.142079	−	0.0380699i
$886$	−9.41660	+	34.3206i	−0.316357	+	1.15302i
$887$	44.3615	−	25.6121i	1.48951	−	0.859970i	0.489584	−	0.871956i	$-0.337149\pi$
$887$	44.3615	−	25.6121i	1.48951	−	0.859970i	0.999928	+	0.0119857i	$0.00381526\pi$
$888$	−35.8477	−	0.643476i	−1.20297	−	0.0215937i
$889$		0			0
$890$	55.7803	−	14.5892i	1.86976	−	0.489030i
$891$	−15.0213	+	56.0603i	−0.503233	+	1.87809i
$892$	−19.4810	−	0.233113i	−0.652273	−	0.00780520i
$893$	32.0581	−	8.58994i	1.07278	−	0.287452i
$894$	−0.781601	−	0.00467621i	−0.0261406	−	0.000156396i
$895$	−8.01938			−0.268058
$896$		0			0
$897$	−15.3764			−0.513403
$898$	−1.25280	−	0.00749536i	−0.0418066	−	0.000250123i
$899$	−6.28144	+	1.68311i	−0.209498	+	0.0561347i
$900$	−3.63274	−	0.0434699i	−0.121091	−	0.00144900i
$901$	−5.09901	+	19.0298i	−0.169873	+	0.633973i
$902$	−34.1391	+	8.92899i	−1.13671	+	0.297303i
$903$		0			0
$904$	24.5404	+	0.440508i	0.816202	+	0.0146511i
$905$	−10.5534	+	6.09302i	−0.350807	+	0.202539i
$906$	−6.94759	+	25.3218i	−0.230818	+	0.841260i
$907$	8.20711	−	2.19909i	0.272512	−	0.0730195i	−0.119975	−	0.992777i	$-0.538281\pi$
$907$	8.20711	−	2.19909i	0.272512	−	0.0730195i	0.392487	+	0.919757i	$0.371615\pi$
$908$	−2.02050	+	0.515562i	−0.0670528	+	0.0171095i
$909$	−11.3701	+	11.3701i	−0.377122	+	0.377122i
$910$		0			0
$911$		−	19.6850i		−	0.652192i	−0.945337	−	0.326096i	$-0.894267\pi$
$911$		−	19.6850i		−	0.652192i	0.945337	−	0.326096i	$-0.105733\pi$
$912$	−0.948915	+	39.6443i	−0.0314217	+	1.31275i
$913$	62.3567	+	36.0016i	2.06370	+	1.19148i
$914$	−42.6159	+	24.2655i	−1.40961	+	0.802633i
$915$	−6.12359	+	22.8535i	−0.202440	+	0.755515i
$916$	2.90739	−	10.3534i	0.0960630	−	0.342086i
$917$		0			0
$918$	−13.5674	+	3.54851i	−0.447790	+	0.117118i
$919$	−17.7313	−	30.7116i	−0.584903	−	1.01308i	−0.994888	−	0.100989i	$-0.967799\pi$
$919$	−17.7313	−	30.7116i	−0.584903	−	1.01308i	0.409985	−	0.912092i	$-0.365534\pi$
$920$	44.6928	−	11.1197i	1.47348	−	0.366604i
$921$	40.3261	+	23.2823i	1.32879	+	0.767177i
$922$	−5.85010	+	5.78052i	−0.192663	+	0.190371i
$923$	3.25404	−	3.25404i	0.107108	−	0.107108i
$924$		0			0
$925$	7.24983	+	7.24983i	0.238373	+	0.238373i
$926$	0.0989015	−	16.5308i	0.00325010	−	0.543236i
$927$	−0.474629	+	0.822082i	−0.0155889	+	0.0270007i
$928$	21.5433	+	22.8723i	0.707193	+	0.750821i
$929$	38.0765	−	21.9835i	1.24925	−	0.721255i	0.278290	−	0.960497i	$-0.410232\pi$
$929$	38.0765	−	21.9835i	1.24925	−	0.721255i	0.970960	+	0.239242i	$0.0768989\pi$
$930$	7.46262	+	4.36828i	0.244709	+	0.143242i
$931$		0			0
$932$	−22.2954	+	12.5190i	−0.730311	+	0.410073i
$933$	27.8361	+	7.45867i	0.911314	+	0.244186i
$934$	−9.42462	+	34.3498i	−0.308383	+	1.12396i
$935$	−17.4255	+	30.1819i	−0.569876	+	0.987054i
$936$	−1.03886	+	3.61618i	−0.0339563	+	0.118199i
$937$	−32.7634			−1.07033			−0.535167	−	0.844746i	$-0.679751\pi$
$937$	−32.7634			−1.07033			−0.535167	+	0.844746i	$0.679751\pi$
$938$		0			0
$939$	−38.5248	−	38.5248i	−1.25721	−	1.25721i
$940$	−33.8815	+	8.64538i	−1.10509	+	0.281981i
$941$	−7.93265	−	29.6051i	−0.258597	−	0.965098i	−0.966054	−	0.258341i	$-0.916824\pi$
$941$	−7.93265	−	29.6051i	−0.258597	−	0.965098i	0.707457	−	0.706757i	$-0.249842\pi$
$942$	−21.1327	−	37.1139i	−0.688540	−	1.20924i
$943$	15.0736	+	26.1082i	0.490864	+	0.850201i
$944$	0.789712	+	3.25710i	0.0257029	+	0.106010i
$945$		0			0
$946$	−43.3442	−	25.3718i	−1.40924	−	0.824907i
$947$	11.1135	+	2.97785i	0.361140	+	0.0967672i	0.434826	−	0.900514i	$-0.356810\pi$
$947$	11.1135	+	2.97785i	0.361140	+	0.0967672i	−0.0736863	+	0.997281i	$0.523476\pi$
$948$	3.19567	−	3.12009i	0.103791	−	0.101336i
$949$	3.01139	+	11.2386i	0.0977537	+	0.364822i
$950$	8.06649	−	7.97054i	0.261712	−	0.258599i
$951$		−	32.5196i		−	1.05452i
$952$		0			0
$953$			31.6828i			1.02631i	0.858297	+	0.513153i	$0.171523\pi$
$953$			31.6828i			1.02631i	−0.858297	+	0.513153i	$0.828477\pi$
$954$	−8.39100	−	8.49201i	−0.271669	−	0.274939i
$955$	−0.208766	−	0.779126i	−0.00675552	−	0.0252119i
$956$	−0.627664	+	52.4533i	−0.0203001	+	1.69646i
$957$	56.8764	+	15.2400i	1.83855	+	0.492639i
$958$	17.3661	−	29.6676i	0.561072	−	0.958516i
$959$		0			0
$960$	1.49945	−	41.7533i	0.0483946	−	1.34758i
$961$	14.8146	+	25.6597i	0.477892	+	0.827732i
$962$	9.22717	−	5.25396i	0.297496	−	0.169394i
$963$	−1.51298	−	5.64652i	−0.0487551	−	0.181956i
$964$	37.9192	+	22.5019i	1.22130	+	0.724737i
$965$	18.8688	+	18.8688i	0.607409	+	0.607409i
$966$		0			0
$967$	15.2574			0.490645			0.245322	−	0.969442i	$-0.421106\pi$
$967$	15.2574			0.490645			0.245322	+	0.969442i	$0.421106\pi$
$968$	−40.4739	+	22.4089i	−1.30088	+	0.720248i
$969$	−12.8185	+	22.2023i	−0.411790	+	0.713240i
$970$	−3.94382	−	1.08207i	−0.126629	−	0.0347433i
$971$	−29.2698	−	7.84283i	−0.939314	−	0.251688i	−0.243492	−	0.969903i	$-0.578293\pi$
$971$	−29.2698	−	7.84283i	−0.939314	−	0.251688i	−0.695822	+	0.718215i	$0.744960\pi$
$972$	5.94059	−	21.1548i	0.190544	−	0.678539i
$973$		0			0
$974$	−22.1471	+	37.8353i	−0.709639	+	1.21232i
$975$	3.45453	−	1.99447i	0.110633	−	0.0638742i
$976$	−17.3866	−	5.10763i	−0.556530	−	0.163491i
$977$	−25.1720	+	43.5992i	−0.805325	+	1.39486i	0.110747	+	0.993849i	$0.464676\pi$
$977$	−25.1720	+	43.5992i	−0.805325	+	1.39486i	−0.916072	+	0.401015i	$0.868658\pi$
$978$	−55.3679	−	0.331259i	−1.77047	−	0.0105925i
$979$	58.5176	+	58.5176i	1.87023	+	1.87023i
$980$		0			0
$981$	10.8523	−	10.8523i	0.346486	−	0.346486i
$982$	−11.6546	−	11.7949i	−0.371913	−	0.376390i
$983$	−8.64540	−	4.99143i	−0.275746	−	0.159202i	0.355750	−	0.934581i	$-0.384225\pi$
$983$	−8.64540	−	4.99143i	−0.275746	−	0.159202i	−0.631496	+	0.775379i	$0.717559\pi$
$984$	26.5397	−	6.60314i	0.846055	−	0.210500i
$985$	0.205529	+	0.355986i	0.00654869	+	0.0113427i
$986$	5.13995	+	19.6521i	0.163689	+	0.625850i
$987$		0			0
$988$	−5.74997	−	10.2403i	−0.182931	−	0.325787i
$989$	−11.1054	+	41.4458i	−0.353130	+	1.31790i
$990$	−10.4498	−	18.3523i	−0.332116	−	0.583273i
$991$	40.8868	+	23.6060i	1.29881	+	0.749869i	0.980199	−	0.198016i	$-0.0634500\pi$
$991$	40.8868	+	23.6060i	1.29881	+	0.749869i	0.318612	+	0.947885i	$0.396783\pi$
$992$	−3.48153	+	5.63402i	−0.110539	+	0.178880i
$993$		−	38.4959i		−	1.22163i
$994$		0			0
$995$	−38.8661	+	38.8661i	−1.23214	+	1.23214i
$996$	−47.9908	−	28.4785i	−1.52065	−	0.902377i
$997$	−33.5965	+	9.00216i	−1.06401	+	0.285101i	−0.748031	−	0.663664i	$-0.769001\pi$
$997$	−33.5965	+	9.00216i	−1.06401	+	0.285101i	−0.315982	+	0.948765i	$0.602334\pi$
$998$	−32.4266	−	8.89694i	−1.02644	−	0.281628i
$999$	−20.7695	+	11.9913i	−0.657117	+	0.379387i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.w.f.227.1		56
7.2	even	3		112.2.v.a.19.10	yes	56
7.3	odd	6		784.2.j.a.195.17		56
7.4	even	3		784.2.j.a.195.18		56
7.5	odd	6	inner	784.2.w.f.19.10		56
7.6	odd	2		112.2.v.a.3.1	✓	56
16.11	odd	4	inner	784.2.w.f.619.10		56
28.23	odd	6		448.2.z.a.47.3		56
28.27	even	2		448.2.z.a.367.3		56
56.13	odd	2		896.2.z.b.479.3		56
56.27	even	2		896.2.z.a.479.12		56
56.37	even	6		896.2.z.b.607.3		56
56.51	odd	6		896.2.z.a.607.12		56
112.11	odd	12		784.2.j.a.587.17		56
112.13	odd	4		896.2.z.a.31.12		56
112.27	even	4		112.2.v.a.59.10	yes	56
112.37	even	12		448.2.z.a.271.3		56
112.51	odd	12		896.2.z.b.159.3		56
112.59	even	12		784.2.j.a.587.18		56
112.69	odd	4		448.2.z.a.143.3		56
112.75	even	12	inner	784.2.w.f.411.1		56
112.83	even	4		896.2.z.b.31.3		56
112.93	even	12		896.2.z.a.159.12		56
112.107	odd	12		112.2.v.a.75.1	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.v.a.3.1	✓	56	7.6	odd	2
112.2.v.a.19.10	yes	56	7.2	even	3
112.2.v.a.59.10	yes	56	112.27	even	4
112.2.v.a.75.1	yes	56	112.107	odd	12
448.2.z.a.47.3		56	28.23	odd	6
448.2.z.a.143.3		56	112.69	odd	4
448.2.z.a.271.3		56	112.37	even	12
448.2.z.a.367.3		56	28.27	even	2
784.2.j.a.195.17		56	7.3	odd	6
784.2.j.a.195.18		56	7.4	even	3
784.2.j.a.587.17		56	112.11	odd	12
784.2.j.a.587.18		56	112.59	even	12
784.2.w.f.19.10		56	7.5	odd	6	inner
784.2.w.f.227.1		56	1.1	even	1	trivial
784.2.w.f.411.1		56	112.75	even	12	inner
784.2.w.f.619.10		56	16.11	odd	4	inner
896.2.z.a.31.12		56	112.13	odd	4
896.2.z.a.159.12		56	112.93	even	12
896.2.z.a.479.12		56	56.27	even	2
896.2.z.a.607.12		56	56.51	odd	6
896.2.z.b.31.3		56	112.83	even	4
896.2.z.b.159.3		56	112.51	odd	12
896.2.z.b.479.3		56	56.13	odd	2
896.2.z.b.607.3		56	56.37	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.41419 - 0.00846089i) q^{2} +(-1.95777 + 0.524583i) q^{3} +(1.99986 + 0.0239306i) q^{4} +(-0.666898 + 2.48890i) q^{5} +(2.77309 - 0.725295i) q^{6} +(-2.82797 - 0.0507629i) q^{8} +(0.959602 - 0.554026i) q^{9} +(0.964178 - 3.51413i) q^{10} +(5.05213 - 1.35371i) q^{11} +(-3.92781 + 1.00224i) q^{12} +(0.848888 - 0.848888i) q^{13} -5.22253i q^{15} +(3.99885 + 0.0957155i) q^{16} +(2.23951 + 1.29298i) q^{17} +(-1.36174 + 0.775378i) q^{18} +(1.26597 - 4.72466i) q^{19} +(-1.39326 + 4.96148i) q^{20} +(-7.15612 + 1.87166i) q^{22} +(3.15967 + 5.47271i) q^{23} +(5.56315 - 1.38412i) q^{24} +(-1.41973 - 0.819681i) q^{25} +(-1.20767 + 1.19330i) q^{26} +(2.71152 - 2.71152i) q^{27} +(-3.92758 - 3.92758i) q^{29} +(-0.0441873 + 7.38564i) q^{30} +(0.585390 - 1.01392i) q^{31} +(-5.65432 - 0.169194i) q^{32} +(-9.18077 + 5.30052i) q^{33} +(-3.15615 - 1.84747i) q^{34} +(1.93232 - 1.08501i) q^{36} +(-6.04104 - 1.61869i) q^{37} +(-1.83029 + 6.67085i) q^{38} +(-1.21662 + 2.10724i) q^{39} +(2.01231 - 7.00468i) q^{40} +4.77063 q^{41} +(4.80121 + 4.80121i) q^{43} +(10.1359 - 2.58633i) q^{44} +(0.738958 + 2.75783i) q^{45} +(-4.42206 - 7.76617i) q^{46} +(3.39263 + 5.87622i) q^{47} +(-7.87905 + 1.91034i) q^{48} +(2.00083 + 1.17120i) q^{50} +(-5.06272 - 1.35655i) q^{51} +(1.71797 - 1.67734i) q^{52} +(1.97180 + 7.35887i) q^{53} +(-3.85754 + 3.81165i) q^{54} +13.4770i q^{55} +9.91391i q^{57} +(5.52111 + 5.58757i) q^{58} +(0.216856 + 0.809319i) q^{59} +(0.124978 - 10.4443i) q^{60} +(-4.37595 - 1.17253i) q^{61} +(-0.836430 + 1.42893i) q^{62} +(7.99485 + 0.287112i) q^{64} +(1.54667 + 2.67892i) q^{65} +(13.0282 - 7.41826i) q^{66} +(-0.100994 - 0.376913i) q^{67} +(4.44776 + 2.63937i) q^{68} +(-9.05679 - 9.05679i) q^{69} +3.83330 q^{71} +(-2.74185 + 1.51806i) q^{72} +(-4.84591 + 8.39335i) q^{73} +(8.52947 + 2.34025i) q^{74} +(3.20949 + 0.859981i) q^{75} +(2.64482 - 9.41835i) q^{76} +(1.73835 - 2.96974i) q^{78} +(-0.954167 + 0.550889i) q^{79} +(-2.90505 + 9.88891i) q^{80} +(-5.54819 + 9.60974i) q^{81} +(-6.74656 - 0.0403638i) q^{82} +(9.73434 + 9.73434i) q^{83} +(-4.71162 + 4.71162i) q^{85} +(-6.74919 - 6.83044i) q^{86} +(9.74964 + 5.62896i) q^{87} +(-14.3560 + 3.57180i) q^{88} +(7.91117 + 13.7025i) q^{89} +(-1.02169 - 3.90634i) q^{90} +(6.18792 + 11.0202i) q^{92} +(-0.614171 + 2.29212i) q^{93} +(-4.74811 - 8.33878i) q^{94} +(10.9149 + 6.30174i) q^{95} +(11.1586 - 2.63492i) q^{96} -1.12228i q^{97} +(4.09804 - 4.09804i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{2} + 6 q^{3} - 4 q^{4} + 6 q^{5} + 4 q^{8} + 24 q^{10} + 2 q^{11} + 6 q^{12} + 8 q^{16} + 12 q^{17} - 30 q^{18} + 6 q^{19} - 28 q^{22} - 12 q^{23} + 6 q^{24} + 6 q^{26} - 24 q^{29} - 18 q^{30}+ \cdots - 16 q^{99}+O(q^{100}) \) 56 * q - 2 * q^2 + 6 * q^3 - 4 * q^4 + 6 * q^5 + 4 * q^8 + 24 * q^10 + 2 * q^11 + 6 * q^12 + 8 * q^16 + 12 * q^17 - 30 * q^18 + 6 * q^19 - 28 * q^22 - 12 * q^23 + 6 * q^24 + 6 * q^26 - 24 * q^29 - 18 * q^30 - 12 * q^32 + 12 * q^33 + 16 * q^36 + 6 * q^37 + 6 * q^38 - 4 * q^39 + 66 * q^40 + 26 * q^44 - 12 * q^45 + 16 * q^46 - 34 * q^51 - 84 * q^52 + 6 * q^53 - 42 * q^54 + 18 * q^58 - 42 * q^59 + 78 * q^60 + 6 * q^61 - 16 * q^64 - 4 * q^65 - 126 * q^66 + 6 * q^67 - 24 * q^68 - 80 * q^71 - 4 * q^72 + 62 * q^74 - 24 * q^75 + 4 * q^78 - 12 * q^80 - 8 * q^81 - 42 * q^82 - 28 * q^85 + 12 * q^87 + 30 * q^88 - 20 * q^92 + 10 * q^93 + 42 * q^94 - 36 * q^96 - 16 * q^99

Introduction

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