LMFDB - Embedded newform 650.2.w.f.357.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,2,Mod(193,650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(650, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 7]))

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

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

chi := DirichletCharacter("650.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.w (of order $12$, degree $4$, 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:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 28x^{14} + 294x^{12} + 1516x^{10} + 4147x^{8} + 6012x^{6} + 4338x^{4} + 1296x^{2} + 81 $ x^16 + 28x^14 + 294x^12 + 1516x^10 + 4147x^8 + 6012x^6 + 4338x^4 + 1296*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			357.4
Root			$-3.38585i$ of defining polynomial
Character	$\chi$	$=$	650.357
Dual form			650.2.w.f.193.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.876322 + 3.27048i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-3.27048 - 0.876322i) q^{6} +(-3.61605 + 2.08773i) q^{7} +1.00000 q^{8} +(-7.33001 + 4.23198i) q^{9} +(-0.732472 + 0.196265i) q^{11} +(2.39416 - 2.39416i) q^{12} +(3.59012 + 0.333218i) q^{13} -4.17546i q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.47178 + 0.662311i) q^{17} -8.46396i q^{18} +(1.24990 - 4.66470i) q^{19} +(-9.99670 - 9.99670i) q^{21} +(0.196265 - 0.732472i) q^{22} +(-2.01011 + 0.538606i) q^{23} +(0.876322 + 3.27048i) q^{24} +(-2.08364 + 2.94253i) q^{26} +(-13.0816 - 13.0816i) q^{27} +(3.61605 + 2.08773i) q^{28} +(4.35399 + 2.51378i) q^{29} +(-1.70293 + 1.70293i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.28376 - 2.22354i) q^{33} +(-1.80947 + 1.80947i) q^{34} +(7.33001 + 4.23198i) q^{36} +(-1.55098 - 0.895461i) q^{37} +(3.41480 + 3.41480i) q^{38} +(2.05632 + 12.0334i) q^{39} +(0.417770 + 1.55914i) q^{41} +(13.6557 - 3.65905i) q^{42} +(-2.44221 + 9.11447i) q^{43} +(0.536207 + 0.536207i) q^{44} +(0.538606 - 2.01011i) q^{46} -4.89371i q^{47} +(-3.27048 - 0.876322i) q^{48} +(5.21723 - 9.03650i) q^{49} +8.66429i q^{51} +(-1.50648 - 3.27574i) q^{52} +(-3.87316 + 3.87316i) q^{53} +(17.8698 - 4.78819i) q^{54} +(-3.61605 + 2.08773i) q^{56} +16.3511 q^{57} +(-4.35399 + 2.51378i) q^{58} +(-12.6359 - 3.38578i) q^{59} +(-0.00936317 - 0.0162175i) q^{61} +(-0.623315 - 2.32624i) q^{62} +(17.6705 - 30.6061i) q^{63} +1.00000 q^{64} +2.56753 q^{66} +(-5.67984 + 9.83777i) q^{67} +(-0.662311 - 2.47178i) q^{68} +(-3.52300 - 6.10202i) q^{69} +(7.24992 + 1.94261i) q^{71} +(-7.33001 + 4.23198i) q^{72} +2.26886 q^{73} +(1.55098 - 0.895461i) q^{74} +(-4.66470 + 1.24990i) q^{76} +(2.23891 - 2.23891i) q^{77} +(-11.4494 - 4.23588i) q^{78} +4.98569i q^{79} +(18.6234 - 32.2567i) q^{81} +(-1.55914 - 0.417770i) q^{82} +2.56023i q^{83} +(-3.65905 + 13.6557i) q^{84} +(-6.67225 - 6.67225i) q^{86} +(-4.40575 + 16.4425i) q^{87} +(-0.732472 + 0.196265i) q^{88} +(-1.73597 - 6.47873i) q^{89} +(-13.6777 + 6.29026i) q^{91} +(1.47150 + 1.47150i) q^{92} +(-7.06170 - 4.07708i) q^{93} +(4.23808 + 2.44685i) q^{94} +(2.39416 - 2.39416i) q^{96} +(3.50956 + 6.07874i) q^{97} +(5.21723 + 9.03650i) q^{98} +(4.53844 - 4.53844i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{2} - 8 q^{4} - 12 q^{7} + 16 q^{8} - 24 q^{9} - 4 q^{11} - 8 q^{13} - 8 q^{16} + 8 q^{17} + 16 q^{19} - 4 q^{21} - 4 q^{22} + 4 q^{23} + 4 q^{26} - 36 q^{27} + 12 q^{28} + 36 q^{29} - 8 q^{31}+ \cdots - 36 q^{99}+O(q^{100}) $ 16 * q - 8 * q^2 - 8 * q^4 - 12 * q^7 + 16 * q^8 - 24 * q^9 - 4 * q^11 - 8 * q^13 - 8 * q^16 + 8 * q^17 + 16 * q^19 - 4 * q^21 - 4 * q^22 + 4 * q^23 + 4 * q^26 - 36 * q^27 + 12 * q^28 + 36 * q^29 - 8 * q^31 - 8 * q^32 - 16 * q^34 + 24 * q^36 + 36 * q^37 + 4 * q^38 + 32 * q^41 + 8 * q^42 + 36 * q^43 + 8 * q^44 + 4 * q^46 + 16 * q^49 + 4 * q^52 - 44 * q^53 + 36 * q^54 - 12 * q^56 + 48 * q^57 - 36 * q^58 - 24 * q^59 - 20 * q^61 - 8 * q^62 + 36 * q^63 + 16 * q^64 + 12 * q^67 + 8 * q^68 + 24 * q^69 + 16 * q^71 - 24 * q^72 - 36 * q^74 - 20 * q^76 - 16 * q^77 - 60 * q^78 + 16 * q^81 - 16 * q^82 - 4 * q^84 - 36 * q^86 - 12 * q^87 - 4 * q^88 - 28 * q^89 - 44 * q^91 - 8 * q^92 + 24 * q^93 + 24 * q^94 + 8 * q^97 + 16 * q^98 - 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{12}\right)$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	0.876322	+	3.27048i	0.505945	+	1.88821i	0.457123	+	0.889404i	$0.348880\pi$
$3$	0.876322	+	3.27048i	0.505945	+	1.88821i	0.0488219	+	0.998808i	$0.484453\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−3.27048	−	0.876322i	−1.33517	−	0.357757i
$7$	−3.61605	+	2.08773i	−1.36674	+	0.789087i	−0.990510	−	0.137439i	$-0.956113\pi$
$7$	−3.61605	+	2.08773i	−1.36674	+	0.789087i	−0.376229	+	0.926527i	$0.622780\pi$
$8$	1.00000			0.353553
$9$	−7.33001	+	4.23198i	−2.44334	+	1.41066i
$10$		0			0
$11$	−0.732472	+	0.196265i	−0.220849	+	0.0591762i	−0.367547	−	0.930005i	$-0.619802\pi$
$11$	−0.732472	+	0.196265i	−0.220849	+	0.0591762i	0.146698	+	0.989181i	$0.453135\pi$
$12$	2.39416	−	2.39416i	0.691133	−	0.691133i
$13$	3.59012	+	0.333218i	0.995720	+	0.0924181i
$13$	3.59012	+	0.333218i	0.995720	+	0.0924181i
$14$		−	4.17546i		−	1.11594i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.47178	+	0.662311i	0.599494	+	0.160634i	0.545789	−	0.837923i	$-0.316230\pi$
$17$	2.47178	+	0.662311i	0.599494	+	0.160634i	0.0537056	+	0.998557i	$0.482897\pi$
$18$		−	8.46396i		−	1.99498i
$19$	1.24990	−	4.66470i	0.286747	−	1.07016i	−0.660805	−	0.750557i	$-0.729785\pi$
$19$	1.24990	−	4.66470i	0.286747	−	1.07016i	0.947553	−	0.319599i	$-0.103548\pi$
$20$		0			0
$21$	−9.99670	−	9.99670i	−2.18146	−	2.18146i
$22$	0.196265	−	0.732472i	0.0418439	−	0.156164i
$23$	−2.01011	+	0.538606i	−0.419136	+	0.112307i	−0.462222	−	0.886764i	$-0.652948\pi$
$23$	−2.01011	+	0.538606i	−0.419136	+	0.112307i	0.0430860	+	0.999071i	$0.486281\pi$
$24$	0.876322	+	3.27048i	0.178878	+	0.667583i
$25$		0			0
$26$	−2.08364	+	2.94253i	−0.408635	+	0.577077i
$27$	−13.0816	−	13.0816i	−2.51755	−	2.51755i
$28$	3.61605	+	2.08773i	0.683370	+	0.394544i
$29$	4.35399	+	2.51378i	0.808515	+	0.466796i	0.846440	−	0.532484i	$-0.178741\pi$
$29$	4.35399	+	2.51378i	0.808515	+	0.466796i	−0.0379250	+	0.999281i	$0.512075\pi$
$30$		0			0
$31$	−1.70293	+	1.70293i	−0.305855	+	0.305855i	−0.843299	−	0.537444i	$-0.819390\pi$
$31$	−1.70293	+	1.70293i	−0.305855	+	0.305855i	0.537444	+	0.843299i	$0.319390\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−1.28376	−	2.22354i	−0.223474	−	0.387069i
$34$	−1.80947	+	1.80947i	−0.310321	+	0.310321i
$35$		0			0
$36$	7.33001	+	4.23198i	1.22167	+	0.705330i
$37$	−1.55098	−	0.895461i	−0.254980	−	0.147213i	0.367062	−	0.930196i	$-0.380364\pi$
$37$	−1.55098	−	0.895461i	−0.254980	−	0.147213i	−0.622042	+	0.782983i	$0.713697\pi$
$38$	3.41480	+	3.41480i	0.553954	+	0.553954i
$39$	2.05632	+	12.0334i	0.329274	+	1.92689i
$40$		0			0
$41$	0.417770	+	1.55914i	0.0652446	+	0.243496i	0.990845	−	0.135007i	$-0.0431056\pi$
$41$	0.417770	+	1.55914i	0.0652446	+	0.243496i	−0.925600	+	0.378503i	$0.876439\pi$
$42$	13.6557	−	3.65905i	2.10713	−	0.564603i
$43$	−2.44221	+	9.11447i	−0.372434	+	1.38994i	0.484624	+	0.874723i	$0.338957\pi$
$43$	−2.44221	+	9.11447i	−0.372434	+	1.38994i	−0.857058	+	0.515220i	$0.827710\pi$
$44$	0.536207	+	0.536207i	0.0808362	+	0.0808362i
$45$		0			0
$46$	0.538606	−	2.01011i	0.0794132	−	0.296374i
$47$		−	4.89371i		−	0.713821i	−0.934139	−	0.356910i	$-0.883830\pi$
$47$		−	4.89371i		−	0.713821i	0.934139	−	0.356910i	$-0.116170\pi$
$48$	−3.27048	−	0.876322i	−0.472053	−	0.126486i
$49$	5.21723	−	9.03650i	0.745318	−	1.29093i
$50$		0			0
$51$			8.66429i			1.21324i
$52$	−1.50648	−	3.27574i	−0.208912	−	0.454264i
$53$	−3.87316	+	3.87316i	−0.532019	+	0.532019i	−0.921173	−	0.389153i	$-0.872768\pi$
$53$	−3.87316	+	3.87316i	−0.532019	+	0.532019i	0.389153	+	0.921173i	$0.372768\pi$
$54$	17.8698	−	4.78819i	2.43177	−	0.651590i
$55$		0			0
$56$	−3.61605	+	2.08773i	−0.483215	+	0.278985i
$57$	16.3511			2.16576
$58$	−4.35399	+	2.51378i	−0.571706	+	0.330075i
$59$	−12.6359	−	3.38578i	−1.64506	−	0.440792i	−0.686834	−	0.726814i	$-0.741000\pi$
$59$	−12.6359	−	3.38578i	−1.64506	−	0.440792i	−0.958223	+	0.286023i	$0.907667\pi$
$60$		0			0
$61$	−0.00936317	−	0.0162175i	−0.00119883	−	0.00207644i	0.865425	−	0.501038i	$-0.167048\pi$
$61$	−0.00936317	−	0.0162175i	−0.00119883	−	0.00207644i	−0.866624	+	0.498961i	$0.833715\pi$
$62$	−0.623315	−	2.32624i	−0.0791611	−	0.295433i
$63$	17.6705	−	30.6061i	2.22627	−	3.85601i
$64$	1.00000			0.125000
$65$		0			0
$66$	2.56753			0.316041
$67$	−5.67984	+	9.83777i	−0.693903	+	1.20187i	0.276647	+	0.960972i	$0.410777\pi$
$67$	−5.67984	+	9.83777i	−0.693903	+	1.20187i	−0.970549	+	0.240903i	$0.922556\pi$
$68$	−0.662311	−	2.47178i	−0.0803170	−	0.299747i
$69$	−3.52300	−	6.10202i	−0.424119	−	0.734596i
$70$		0			0
$71$	7.24992	+	1.94261i	0.860407	+	0.230545i	0.661935	−	0.749561i	$-0.269735\pi$
$71$	7.24992	+	1.94261i	0.860407	+	0.230545i	0.198472	+	0.980107i	$0.436402\pi$
$72$	−7.33001	+	4.23198i	−0.863850	+	0.498744i
$73$	2.26886			0.265549			0.132775	−	0.991146i	$-0.457611\pi$
$73$	2.26886			0.265549			0.132775	+	0.991146i	$0.457611\pi$
$74$	1.55098	−	0.895461i	0.180298	−	0.104095i
$75$		0			0
$76$	−4.66470	+	1.24990i	−0.535078	+	0.143374i
$77$	2.23891	−	2.23891i	0.255147	−	0.255147i
$78$	−11.4494	−	4.23588i	−1.29639	−	0.479619i
$79$			4.98569i			0.560934i	0.959864	+	0.280467i	$0.0904894\pi$
$79$			4.98569i			0.560934i	−0.959864	+	0.280467i	$0.909511\pi$
$80$		0			0
$81$	18.6234	−	32.2567i	2.06927	−	3.58407i
$82$	−1.55914	−	0.417770i	−0.172178	−	0.0461349i
$83$			2.56023i			0.281021i	0.990079	+	0.140511i	$0.0448744\pi$
$83$			2.56023i			0.281021i	−0.990079	+	0.140511i	$0.955126\pi$
$84$	−3.65905	+	13.6557i	−0.399235	+	1.48996i
$85$		0			0
$86$	−6.67225	−	6.67225i	−0.719487	−	0.719487i
$87$	−4.40575	+	16.4425i	−0.472346	+	1.76282i
$88$	−0.732472	+	0.196265i	−0.0780818	+	0.0209220i
$89$	−1.73597	−	6.47873i	−0.184013	−	0.686744i	−0.994840	−	0.101459i	$-0.967649\pi$
$89$	−1.73597	−	6.47873i	−0.184013	−	0.686744i	0.810827	−	0.585286i	$-0.199018\pi$
$90$		0			0
$91$	−13.6777	+	6.29026i	−1.43382	+	0.659399i
$92$	1.47150	+	1.47150i	0.153414	+	0.153414i
$93$	−7.06170	−	4.07708i	−0.732264	−	0.422773i
$94$	4.23808	+	2.44685i	0.437124	+	0.252374i
$95$		0			0
$96$	2.39416	−	2.39416i	0.244352	−	0.244352i
$97$	3.50956	+	6.07874i	0.356342	+	0.617203i	0.987347	−	0.158577i	$-0.0506905\pi$
$97$	3.50956	+	6.07874i	0.356342	+	0.617203i	−0.631005	+	0.775779i	$0.717357\pi$
$98$	5.21723	+	9.03650i	0.527020	+	0.912825i
$99$	4.53844	−	4.53844i	0.456130	−	0.456130i
$100$		0			0
$101$	11.6709	+	6.73818i	1.16129	+	0.670474i	0.951614	−	0.307296i	$-0.0994243\pi$
$101$	11.6709	+	6.73818i	1.16129	+	0.670474i	0.209680	+	0.977770i	$0.432758\pi$
$102$	−7.50350	−	4.33215i	−0.742957	−	0.428946i
$103$	5.59931	+	5.59931i	0.551716	+	0.551716i	0.926936	−	0.375220i	$-0.122433\pi$
$103$	5.59931	+	5.59931i	0.551716	+	0.551716i	−0.375220	+	0.926936i	$0.622433\pi$
$104$	3.59012	+	0.333218i	0.352040	+	0.0326747i
$105$		0			0
$106$	−1.41768	−	5.29084i	−0.137697	−	0.513891i
$107$	−0.794439	+	0.212869i	−0.0768013	+	0.0205788i	−0.297015	−	0.954873i	$-0.595991\pi$
$107$	−0.794439	+	0.212869i	−0.0768013	+	0.0205788i	0.220214	+	0.975452i	$0.429324\pi$
$108$	−4.78819	+	17.8698i	−0.460744	+	1.71952i
$109$	2.20036	+	2.20036i	0.210757	+	0.210757i	0.804589	−	0.593832i	$-0.202386\pi$
$109$	2.20036	+	2.20036i	0.210757	+	0.210757i	−0.593832	+	0.804589i	$0.702386\pi$
$110$		0			0
$111$	1.56942	−	5.85717i	0.148963	−	0.555938i
$112$		−	4.17546i		−	0.394544i
$113$	−7.42029	−	1.98826i	−0.698042	−	0.187040i	−0.107689	−	0.994185i	$-0.534345\pi$
$113$	−7.42029	−	1.98826i	−0.698042	−	0.187040i	−0.590353	+	0.807145i	$0.701012\pi$
$114$	−8.17556	+	14.1605i	−0.765711	+	1.32625i
$115$		0			0
$116$		−	5.02755i		−	0.466796i
$117$	−27.7258	+	12.7508i	−2.56325	+	1.17881i
$118$	9.25014	−	9.25014i	0.851544	−	0.851544i
$119$	−10.3208	+	2.76545i	−0.946107	+	0.253509i
$120$		0			0
$121$	−9.02828	+	5.21248i	−0.820753	+	0.473862i
$122$	0.0187263			0.00169540
$123$	−4.73302	+	2.73261i	−0.426762	+	0.246391i
$124$	2.32624	+	0.623315i	0.208903	+	0.0559753i
$125$		0			0
$126$	17.6705	+	30.6061i	1.57421	+	2.72661i
$127$	3.75739	+	14.0228i	0.333415	+	1.24432i	0.905577	+	0.424181i	$0.139438\pi$
$127$	3.75739	+	14.0228i	0.333415	+	1.24432i	−0.572163	+	0.820140i	$0.693895\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−31.9488			−2.81294
$130$		0			0
$131$	−18.7853			−1.64128			−0.820639	−	0.571447i	$-0.806382\pi$
$131$	−18.7853			−1.64128			−0.820639	+	0.571447i	$0.806382\pi$
$132$	−1.28376	+	2.22354i	−0.111737	+	0.193535i
$133$	5.21892	+	19.4773i	0.452538	+	1.68889i
$134$	−5.67984	−	9.83777i	−0.490663	−	0.849854i
$135$		0			0
$136$	2.47178	+	0.662311i	0.211953	+	0.0567927i
$137$	7.54859	−	4.35818i	0.644920	−	0.372344i	−0.141588	−	0.989926i	$-0.545221\pi$
$137$	7.54859	−	4.35818i	0.644920	−	0.372344i	0.786507	+	0.617581i	$0.211887\pi$
$138$	7.04600			0.599795
$139$	2.72940	−	1.57582i	0.231504	−	0.133659i	−0.379761	−	0.925084i	$-0.623994\pi$
$139$	2.72940	−	1.57582i	0.231504	−	0.133659i	0.611266	+	0.791425i	$0.290661\pi$
$140$		0			0
$141$	16.0048	−	4.28846i	1.34784	−	0.361154i
$142$	−5.30731	+	5.30731i	−0.445379	+	0.445379i
$143$	−2.69506	+	0.460543i	−0.225373	+	0.0385126i
$144$		−	8.46396i		−	0.705330i
$145$		0			0
$146$	−1.13443	+	1.96489i	−0.0938859	+	0.162615i
$147$	34.1256	+	9.14394i	2.81464	+	0.754179i
$148$			1.79092i			0.147213i
$149$	5.18428	−	19.3480i	0.424713	−	1.58505i	−0.339836	−	0.940485i	$-0.610372\pi$
$149$	5.18428	−	19.3480i	0.424713	−	1.58505i	0.764549	−	0.644566i	$-0.222962\pi$
$150$		0			0
$151$	4.48760	+	4.48760i	0.365195	+	0.365195i	0.865721	−	0.500526i	$-0.166860\pi$
$151$	4.48760	+	4.48760i	0.365195	+	0.365195i	−0.500526	+	0.865721i	$0.666860\pi$
$152$	1.24990	−	4.66470i	0.101381	−	0.378357i
$153$	−20.9210	+	5.60578i	−1.69137	+	0.453200i
$154$	0.819498	+	3.05841i	0.0660370	+	0.246454i
$155$		0			0
$156$	9.39308	−	7.79753i	0.752049	−	0.624302i
$157$	15.7067	+	15.7067i	1.25353	+	1.25353i	0.954125	+	0.299408i	$0.0967893\pi$
$157$	15.7067	+	15.7067i	1.25353	+	1.25353i	0.299408	+	0.954125i	$0.403211\pi$
$158$	−4.31774	−	2.49285i	−0.343501	−	0.198320i
$159$	−16.0612	−	9.27295i	−1.27374	−	0.735393i
$160$		0			0
$161$	6.14419	−	6.14419i	0.484230	−	0.484230i
$162$	18.6234	+	32.2567i	1.46319	+	2.53432i
$163$	−3.63070	−	6.28855i	−0.284378	−	0.492557i	0.688080	−	0.725635i	$-0.258454\pi$
$163$	−3.63070	−	6.28855i	−0.284378	−	0.492557i	−0.972458	+	0.233077i	$0.925120\pi$
$164$	1.14137	−	1.14137i	0.0891258	−	0.0891258i
$165$		0			0
$166$	−2.21722	−	1.28011i	−0.172090	−	0.0993560i
$167$	−13.9752	−	8.06856i	−1.08143	−	0.624364i	−0.150149	−	0.988663i	$-0.547975\pi$
$167$	−13.9752	−	8.06856i	−1.08143	−	0.624364i	−0.931282	+	0.364299i	$0.881309\pi$
$168$	−9.99670	−	9.99670i	−0.771262	−	0.771262i
$169$	12.7779	+	2.39259i	0.982918	+	0.184045i
$170$		0			0
$171$	10.5791	+	39.4819i	0.809007	+	3.01925i
$172$	9.11447	−	2.44221i	0.694971	−	0.186217i
$173$	2.50223	−	9.33846i	0.190241	−	0.709990i	−0.803206	−	0.595701i	$-0.796874\pi$
$173$	2.50223	−	9.33846i	0.190241	−	0.709990i	0.993448	−	0.114289i	$-0.0364590\pi$
$174$	−12.0367	−	12.0367i	−0.912503	−	0.912503i
$175$		0			0
$176$	0.196265	−	0.732472i	0.0147941	−	0.0552122i
$177$		−	44.2925i		−	3.32923i
$178$	6.47873	+	1.73597i	0.485601	+	0.130117i
$179$	−2.15547	+	3.73338i	−0.161107	+	0.279046i	−0.935266	−	0.353946i	$-0.884840\pi$
$179$	−2.15547	+	3.73338i	−0.161107	+	0.279046i	0.774159	+	0.632991i	$0.218173\pi$
$180$		0			0
$181$			9.62668i			0.715545i	0.933809	+	0.357773i	$0.116464\pi$
$181$			9.62668i			0.715545i	−0.933809	+	0.357773i	$0.883536\pi$
$182$	1.39134	−	14.9904i	0.103133	−	1.11116i
$183$	0.0448338	−	0.0448338i	0.00331421	−	0.00331421i
$184$	−2.01011	+	0.538606i	−0.148187	+	0.0397066i
$185$		0			0
$186$	7.06170	−	4.07708i	0.517789	−	0.298946i
$187$	−1.94050			−0.141903
$188$	−4.23808	+	2.44685i	−0.309093	+	0.178455i
$189$	74.6145	+	19.9929i	5.42741	+	1.45427i
$190$		0			0
$191$	11.3481	+	19.6555i	0.821119	+	1.42222i	0.904849	+	0.425732i	$0.139983\pi$
$191$	11.3481	+	19.6555i	0.821119	+	1.42222i	−0.0837303	+	0.996488i	$0.526683\pi$
$192$	0.876322	+	3.27048i	0.0632431	+	0.236026i
$193$	−1.22466	+	2.12118i	−0.0881533	+	0.152686i	−0.906731	−	0.421711i	$-0.861430\pi$
$193$	−1.22466	+	2.12118i	−0.0881533	+	0.152686i	0.818577	+	0.574396i	$0.194763\pi$
$194$	−7.01912			−0.503944
$195$		0			0
$196$	−10.4345			−0.745318
$197$	−9.34032	+	16.1779i	−0.665470	+	1.15263i	0.313687	+	0.949526i	$0.398436\pi$
$197$	−9.34032	+	16.1779i	−0.665470	+	1.15263i	−0.979158	+	0.203102i	$0.934898\pi$
$198$	1.66118	+	6.19962i	0.118055	+	0.440588i
$199$	8.52723	+	14.7696i	0.604479	+	1.04699i	0.992134	+	0.125184i	$0.0399521\pi$
$199$	8.52723	+	14.7696i	0.604479	+	1.04699i	−0.387654	+	0.921805i	$0.626715\pi$
$200$		0			0
$201$	−37.1516	−	9.95473i	−2.62047	−	0.702153i
$202$	−11.6709	+	6.73818i	−0.821159	+	0.474096i
$203$	−20.9923			−1.47337
$204$	7.50350	−	4.33215i	0.525350	−	0.303311i
$205$		0			0
$206$	−7.64880	+	2.04949i	−0.532917	+	0.142795i
$207$	12.4547	−	12.4547i	0.865663	−	0.865663i
$208$	−2.08364	+	2.94253i	−0.144474	+	0.204027i
$209$			3.66208i			0.253311i
$210$		0			0
$211$	9.88824	−	17.1269i	0.680735	−	1.17907i	−0.294022	−	0.955799i	$-0.594994\pi$
$211$	9.88824	−	17.1269i	0.680735	−	1.17907i	0.974757	−	0.223269i	$-0.0716727\pi$
$212$	5.29084	+	1.41768i	0.363376	+	0.0973663i
$213$			25.4130i			1.74127i
$214$	0.212869	−	0.794439i	0.0145514	−	0.0543067i
$215$		0			0
$216$	−13.0816	−	13.0816i	−0.890089	−	0.890089i
$217$	2.60263	−	9.71313i	0.176678	−	0.659370i
$218$	−3.00575	+	0.805389i	−0.203575	+	0.0545478i
$219$	1.98825	+	7.42024i	0.134353	+	0.501413i
$220$		0			0
$221$	8.65329	+	3.20142i	0.582083	+	0.215351i
$222$	4.28775	+	4.28775i	0.287775	+	0.287775i
$223$	13.0781	+	7.55064i	0.875773	+	0.505628i	0.869263	−	0.494351i	$-0.164594\pi$
$223$	13.0781	+	7.55064i	0.875773	+	0.505628i	0.00651091	+	0.999979i	$0.497927\pi$
$224$	3.61605	+	2.08773i	0.241608	+	0.139492i
$225$		0			0
$226$	5.43203	−	5.43203i	0.361333	−	0.361333i
$227$	−10.0811	−	17.4610i	−0.669106	−	1.15893i	−0.978154	−	0.207880i	$-0.933344\pi$
$227$	−10.0811	−	17.4610i	−0.669106	−	1.15893i	0.309048	−	0.951046i	$-0.399990\pi$
$228$	−8.17556	−	14.1605i	−0.541440	−	0.937801i
$229$	−1.26351	+	1.26351i	−0.0834950	+	0.0834950i	−0.747621	−	0.664126i	$-0.768804\pi$
$229$	−1.26351	+	1.26351i	−0.0834950	+	0.0834950i	0.664126	+	0.747621i	$0.268804\pi$
$230$		0			0
$231$	9.28431	+	5.36030i	0.610863	+	0.352682i
$232$	4.35399	+	2.51378i	0.285853	+	0.165037i
$233$	−5.75348	−	5.75348i	−0.376923	−	0.376923i	0.493068	−	0.869991i	$-0.335875\pi$
$233$	−5.75348	−	5.75348i	−0.376923	−	0.376923i	−0.869991	+	0.493068i	$0.835875\pi$
$234$	2.82035	−	30.3866i	0.184372	−	1.98644i
$235$		0			0
$236$	3.38578	+	12.6359i	0.220396	+	0.822528i
$237$	−16.3056	+	4.36907i	−1.05916	+	0.283802i
$238$	2.76545	−	10.3208i	0.179258	−	0.668999i
$239$	2.44600	+	2.44600i	0.158219	+	0.158219i	0.781777	−	0.623558i	$-0.214314\pi$
$239$	2.44600	+	2.44600i	0.158219	+	0.158219i	−0.623558	+	0.781777i	$0.714314\pi$
$240$		0			0
$241$	−1.92172	+	7.17197i	−0.123789	+	0.461987i	−0.999794	−	0.0203158i	$-0.993533\pi$
$241$	−1.92172	+	7.17197i	−0.123789	+	0.461987i	0.876005	+	0.482303i	$0.160200\pi$
$242$		−	10.4250i		−	0.670142i
$243$	68.2055	+	18.2756i	4.37538	+	1.17238i
$244$	−0.00936317	+	0.0162175i	−0.000599416	+	0.00103822i
$245$		0			0
$246$		−	5.46522i		−	0.348450i
$247$	6.04167	−	16.3304i	0.384422	−	1.03908i
$248$	−1.70293	+	1.70293i	−0.108136	+	0.108136i
$249$	−8.37316	+	2.24358i	−0.530628	+	0.142181i
$250$		0			0
$251$	20.7305	−	11.9688i	1.30850	−	0.755462i	0.326653	−	0.945144i	$-0.394079\pi$
$251$	20.7305	−	11.9688i	1.30850	−	0.755462i	0.981845	+	0.189683i	$0.0607459\pi$
$252$	−35.3409			−2.22627
$253$	1.36664	−	0.789029i	0.0859198	−	0.0496058i
$254$	−14.0228	−	3.75739i	−0.879868	−	0.235760i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.47635	+	12.9739i	0.216849	+	0.809291i	0.985507	+	0.169632i	$0.0542579\pi$
$257$	3.47635	+	12.9739i	0.216849	+	0.809291i	−0.768659	+	0.639659i	$0.779075\pi$
$258$	15.9744	−	27.6685i	0.994523	−	1.72256i
$259$	7.47792			0.464655
$260$		0			0
$261$	−42.5530			−2.63396
$262$	9.39264	−	16.2685i	0.580279	−	1.00507i
$263$	−2.54798	−	9.50920i	−0.157115	−	0.586362i	−0.998915	−	0.0465722i	$-0.985170\pi$
$263$	−2.54798	−	9.50920i	−0.157115	−	0.586362i	0.841800	−	0.539790i	$-0.181496\pi$
$264$	−1.28376	−	2.22354i	−0.0790102	−	0.136850i
$265$		0			0
$266$	−19.4773	−	5.21892i	−1.19423	−	0.319992i
$267$	19.6673	−	11.3549i	1.20362	−	0.694909i
$268$	11.3597			0.693903
$269$	−2.37390	+	1.37057i	−0.144739	+	0.0835654i	−0.570621	−	0.821214i	$-0.693297\pi$
$269$	−2.37390	+	1.37057i	−0.144739	+	0.0835654i	0.425881	+	0.904779i	$0.359964\pi$
$270$		0			0
$271$	6.31118	−	1.69108i	0.383377	−	0.102726i	−0.0619830	−	0.998077i	$-0.519742\pi$
$271$	6.31118	−	1.69108i	0.383377	−	0.102726i	0.445360	+	0.895352i	$0.353076\pi$
$272$	−1.80947	+	1.80947i	−0.109715	+	0.109715i
$273$	−32.5583	−	39.2204i	−1.97052	−	2.37373i
$274$			8.71636i			0.526575i
$275$		0			0
$276$	−3.52300	+	6.10202i	−0.212060	+	0.367298i
$277$	−13.9628	−	3.74132i	−0.838943	−	0.224794i	−0.186332	−	0.982487i	$-0.559660\pi$
$277$	−13.9628	−	3.74132i	−0.838943	−	0.224794i	−0.652611	+	0.757693i	$0.726327\pi$
$278$			3.15164i			0.189023i
$279$	5.27572	−	19.6892i	0.315849	−	1.17876i
$280$		0			0
$281$	9.15879	+	9.15879i	0.546368	+	0.546368i	0.925388	−	0.379021i	$-0.123739\pi$
$281$	9.15879	+	9.15879i	0.546368	+	0.546368i	−0.379021	+	0.925388i	$0.623739\pi$
$282$	−4.28846	+	16.0048i	−0.255374	+	0.953070i
$283$	−12.0424	+	3.22674i	−0.715844	+	0.191810i	−0.598316	−	0.801260i	$-0.704163\pi$
$283$	−12.0424	+	3.22674i	−0.715844	+	0.191810i	−0.117527	+	0.993070i	$0.537497\pi$
$284$	−1.94261	−	7.24992i	−0.115273	−	0.430203i
$285$		0			0
$286$	0.948690	−	2.56426i	0.0560972	−	0.151628i
$287$	−4.76573	−	4.76573i	−0.281312	−	0.281312i
$288$	7.33001	+	4.23198i	0.431925	+	0.249372i
$289$	−9.05140	−	5.22583i	−0.532435	−	0.307402i
$290$		0			0
$291$	−16.8049	+	16.8049i	−0.985119	+	0.985119i
$292$	−1.13443	−	1.96489i	−0.0663874	−	0.114986i
$293$	−15.2652	−	26.4401i	−0.891801	−	1.54464i	−0.837715	−	0.546108i	$-0.816109\pi$
$293$	−15.2652	−	26.4401i	−0.891801	−	1.54464i	−0.0540863	−	0.998536i	$-0.517225\pi$
$294$	−24.9817	+	24.9817i	−1.45696	+	1.45696i
$295$		0			0
$296$	−1.55098	−	0.895461i	−0.0901491	−	0.0520476i
$297$	12.1494	+	7.01443i	0.704977	+	0.407019i
$298$	14.1637	+	14.1637i	0.820483	+	0.820483i
$299$	−7.39600	+	1.26386i	−0.427722	+	0.0730908i
$300$		0			0
$301$	−10.1974	−	38.0571i	−0.587766	−	2.19357i
$302$	−6.13017	+	1.64257i	−0.352752	+	0.0945195i
$303$	−11.8096	+	44.0741i	−0.678445	+	2.53199i
$304$	3.41480	+	3.41480i	0.195852	+	0.195852i
$305$		0			0
$306$	5.60578	−	20.9210i	0.320461	−	1.19598i
$307$			11.3407i			0.647249i	0.946186	+	0.323625i	$0.104901\pi$
$307$			11.3407i			0.647249i	−0.946186	+	0.323625i	$0.895099\pi$
$308$	−3.05841	−	0.819498i	−0.174269	−	0.0466952i
$309$	−13.4056	+	23.2192i	−0.762619	+	1.32089i
$310$		0			0
$311$		−	18.0460i		−	1.02330i	−0.859195	−	0.511649i	$-0.829035\pi$
$311$		−	18.0460i		−	1.02330i	0.859195	−	0.511649i	$-0.170965\pi$
$312$	2.05632	+	12.0334i	0.116416	+	0.681258i
$313$	9.49544	−	9.49544i	0.536714	−	0.536714i	−0.385848	−	0.922562i	$-0.626091\pi$
$313$	9.49544	−	9.49544i	0.536714	−	0.536714i	0.922562	+	0.385848i	$0.126091\pi$
$314$	−21.4558	+	5.74906i	−1.21082	+	0.324438i
$315$		0			0
$316$	4.31774	−	2.49285i	0.242892	−	0.140234i
$317$	14.7891			0.830636			0.415318	−	0.909676i	$-0.363670\pi$
$317$	14.7891			0.830636			0.415318	+	0.909676i	$0.363670\pi$
$318$	16.0612	−	9.27295i	0.900668	−	0.520001i
$319$	−3.68254	−	0.986734i	−0.206183	−	0.0552465i
$320$		0			0
$321$	−1.39237	−	2.41165i	−0.0777144	−	0.134605i
$322$	2.24893	+	8.39312i	0.125328	+	0.467730i
$323$	6.17897	−	10.7023i	0.343807	−	0.595491i
$324$	−37.2468			−2.06927
$325$		0			0
$326$	7.26139			0.402171
$327$	−5.26801	+	9.12447i	−0.291322	+	0.504584i
$328$	0.417770	+	1.55914i	0.0230675	+	0.0860889i
$329$	10.2167	+	17.6959i	0.563267	+	0.975607i
$330$		0			0
$331$	31.2960	+	8.38573i	1.72018	+	0.460922i	0.977884	−	0.209148i	$-0.0670690\pi$
$331$	31.2960	+	8.38573i	1.72018	+	0.460922i	0.742299	+	0.670069i	$0.233736\pi$
$332$	2.21722	−	1.28011i	0.121686	−	0.0702553i
$333$	15.1583			0.830669
$334$	13.9752	−	8.06856i	0.764687	−	0.441492i
$335$		0			0
$336$	13.6557	−	3.65905i	0.744982	−	0.199617i
$337$	−15.3618	+	15.3618i	−0.836810	+	0.836810i	−0.988438	−	0.151628i	$-0.951548\pi$
$337$	−15.3618	+	15.3618i	−0.836810	+	0.836810i	0.151628	+	0.988438i	$0.451548\pi$
$338$	−8.46101	+	9.86972i	−0.460218	+	0.536842i
$339$		−	26.0102i		−	1.41268i
$340$		0			0
$341$	0.913122	−	1.58157i	0.0494483	−	0.0856470i
$342$	−39.4819	−	10.5791i	−2.13494	−	0.572054i
$343$			14.3404i			0.774310i
$344$	−2.44221	+	9.11447i	−0.131675	+	0.491419i
$345$		0			0
$346$	6.83623	+	6.83623i	0.367518	+	0.367518i
$347$	−0.970881	+	3.62338i	−0.0521196	+	0.194513i	−0.987077	−	0.160247i	$-0.948771\pi$
$347$	−0.970881	+	3.62338i	−0.0521196	+	0.194513i	0.934957	+	0.354760i	$0.115438\pi$
$348$	16.4425	−	4.40575i	0.881410	−	0.236173i
$349$	2.88458	+	10.7654i	0.154408	+	0.576258i	0.999155	+	0.0410929i	$0.0130839\pi$
$349$	2.88458	+	10.7654i	0.154408	+	0.576258i	−0.844747	+	0.535165i	$0.820249\pi$
$350$		0			0
$351$	−42.6054	−	51.3235i	−2.27411	−	2.73944i
$352$	0.536207	+	0.536207i	0.0285799	+	0.0285799i
$353$	11.0688	+	6.39060i	0.589135	+	0.340137i	0.764755	−	0.644321i	$-0.222860\pi$
$353$	11.0688	+	6.39060i	0.589135	+	0.340137i	−0.175620	+	0.984458i	$0.556193\pi$
$354$	38.3585	+	22.1463i	2.03873	+	1.17706i
$355$		0			0
$356$	−4.74276	+	4.74276i	−0.251366	+	0.251366i
$357$	−18.0887	−	31.3305i	−0.957356	−	1.65819i
$358$	−2.15547	−	3.73338i	−0.113920	−	0.197315i
$359$	−5.32657	+	5.32657i	−0.281126	+	0.281126i	−0.833558	−	0.552432i	$-0.813700\pi$
$359$	−5.32657	+	5.32657i	−0.281126	+	0.281126i	0.552432	+	0.833558i	$0.313700\pi$
$360$		0			0
$361$	−3.74271	−	2.16085i	−0.196985	−	0.113729i
$362$	−8.33695	−	4.81334i	−0.438180	−	0.252983i
$363$	−24.9590	−	24.9590i	−1.31001	−	1.31001i
$364$	12.2864	+	8.70014i	0.643982	+	0.456011i
$365$		0			0
$366$	0.0164103	+	0.0612441i	0.000857780	+	0.00320128i
$367$	0.0995368	−	0.0266708i	0.00519578	−	0.00139221i	−0.256220	−	0.966618i	$-0.582477\pi$
$367$	0.0995368	−	0.0266708i	0.00519578	−	0.00139221i	0.261416	+	0.965226i	$0.415811\pi$
$368$	0.538606	−	2.01011i	0.0280768	−	0.104784i
$369$	−9.66049	−	9.66049i	−0.502905	−	0.502905i
$370$		0			0
$371$	5.91944	−	22.0917i	0.307322	−	1.14694i
$372$			8.15415i			0.422773i
$373$	13.4883	+	3.61418i	0.698397	+	0.187135i	0.590513	−	0.807028i	$-0.298926\pi$
$373$	13.4883	+	3.61418i	0.698397	+	0.187135i	0.107885	+	0.994163i	$0.465592\pi$
$374$	0.970249	−	1.68052i	0.0501704	−	0.0868977i
$375$		0			0
$376$		−	4.89371i		−	0.252374i
$377$	14.7937	+	10.4756i	0.761914	+	0.539520i
$378$	−54.6216	+	54.6216i	−2.80943	+	2.80943i
$379$	28.4375	−	7.61981i	1.46074	−	0.391403i	0.560993	−	0.827821i	$-0.310419\pi$
$379$	28.4375	−	7.61981i	1.46074	−	0.391403i	0.899744	+	0.436417i	$0.143753\pi$
$380$		0			0
$381$	−42.5685	+	24.5770i	−2.18085	+	1.25912i
$382$	−22.6962			−1.16124
$383$	18.0719	−	10.4338i	0.923433	−	0.533144i	0.0387045	−	0.999251i	$-0.487677\pi$
$383$	18.0719	−	10.4338i	0.923433	−	0.533144i	0.884729	+	0.466106i	$0.154344\pi$
$384$	−3.27048	−	0.876322i	−0.166896	−	0.0447196i
$385$		0			0
$386$	−1.22466	−	2.12118i	−0.0623338	−	0.107965i
$387$	−20.6708	−	77.1445i	−1.05076	−	3.92148i
$388$	3.50956	−	6.07874i	0.178171	−	0.308601i
$389$	17.6286			0.893804			0.446902	−	0.894583i	$-0.352527\pi$
$389$	17.6286			0.893804			0.446902	+	0.894583i	$0.352527\pi$
$390$		0			0
$391$	−5.32526			−0.269310
$392$	5.21723	−	9.03650i	0.263510	−	0.456412i
$393$	−16.4619	−	61.4368i	−0.830395	−	3.09908i
$394$	−9.34032	−	16.1779i	−0.470559	−	0.815032i
$395$		0			0
$396$	−6.19962	−	1.66118i	−0.311543	−	0.0834776i
$397$	−25.0432	+	14.4587i	−1.25688	+	0.725661i	−0.972467	−	0.233040i	$-0.925133\pi$
$397$	−25.0432	+	14.4587i	−1.25688	+	0.725661i	−0.284415	+	0.958701i	$0.591799\pi$
$398$	−17.0545			−0.854863
$399$	−59.1265	+	34.1367i	−2.96003	+	1.70897i
$400$		0			0
$401$	−8.22656	+	2.20430i	−0.410815	+	0.110078i	−0.458307	−	0.888794i	$-0.651544\pi$
$401$	−8.22656	+	2.20430i	−0.410815	+	0.110078i	0.0474918	+	0.998872i	$0.484877\pi$
$402$	27.1968	−	27.1968i	1.35645	−	1.35645i
$403$	−6.68116	+	5.54627i	−0.332812	+	0.276279i
$404$		−	13.4764i		−	0.670474i
$405$		0			0
$406$	10.4962	−	18.1799i	0.520916	−	0.902253i
$407$	1.31180	+	0.351496i	0.0650235	+	0.0174230i
$408$			8.66429i			0.428946i
$409$	6.49840	−	24.2524i	0.321325	−	1.19920i	−0.596629	−	0.802517i	$-0.703494\pi$
$409$	6.49840	−	24.2524i	0.321325	−	1.19920i	0.917955	−	0.396685i	$-0.129840\pi$
$410$		0			0
$411$	20.8683	+	20.8683i	1.02936	+	1.02936i
$412$	2.04949	−	7.64880i	0.100971	−	0.376829i
$413$	52.7608	−	14.1372i	2.59619	−	0.695646i
$414$	4.55874	+	17.0135i	0.224050	+	0.836166i
$415$		0			0
$416$	−1.50648	−	3.27574i	−0.0738615	−	0.160607i
$417$	7.54551	+	7.54551i	0.369505	+	0.369505i
$418$	−3.17145	−	1.83104i	−0.155121	−	0.0895591i
$419$	23.2032	+	13.3964i	1.13355	+	0.654456i	0.944826	−	0.327574i	$-0.106231\pi$
$419$	23.2032	+	13.3964i	1.13355	+	0.654456i	0.188726	+	0.982030i	$0.439564\pi$
$420$		0			0
$421$	5.47935	−	5.47935i	0.267047	−	0.267047i	−0.560862	−	0.827909i	$-0.689530\pi$
$421$	5.47935	−	5.47935i	0.267047	−	0.267047i	0.827909	+	0.560862i	$0.189530\pi$
$422$	9.88824	+	17.1269i	0.481352	+	0.833726i
$423$	20.7101	+	35.8709i	1.00696	+	1.74410i
$424$	−3.87316	+	3.87316i	−0.188097	+	0.188097i
$425$		0			0
$426$	−22.0083	−	12.7065i	−1.06631	−	0.615633i
$427$	0.0677154	+	0.0390955i	0.00327698	+	0.00189197i
$428$	0.581570	+	0.581570i	0.0281112	+	0.0281112i
$429$	−3.86794	−	8.41056i	−0.186746	−	0.406066i
$430$		0			0
$431$	1.63759	+	6.11158i	0.0788800	+	0.294384i	0.994085	−	0.108604i	$-0.0346381\pi$
$431$	1.63759	+	6.11158i	0.0788800	+	0.294384i	−0.915205	+	0.402989i	$0.867971\pi$
$432$	17.8698	−	4.78819i	0.859760	−	0.230372i
$433$	6.30725	−	23.5390i	0.303107	−	1.13121i	−0.631455	−	0.775412i	$-0.717542\pi$
$433$	6.30725	−	23.5390i	0.303107	−	1.13121i	0.934562	−	0.355799i	$-0.115791\pi$
$434$	7.11051	+	7.11051i	0.341315	+	0.341315i
$435$		0			0
$436$	0.805389	−	3.00575i	0.0385711	−	0.143949i
$437$			10.0498i			0.480745i
$438$	−7.42024	−	1.98825i	−0.354553	−	0.0950021i
$439$	8.74647	−	15.1493i	0.417446	−	0.723038i	−0.578235	−	0.815870i	$-0.696258\pi$
$439$	8.74647	−	15.1493i	0.417446	−	0.723038i	0.995682	+	0.0928316i	$0.0295918\pi$
$440$		0			0
$441$			88.3168i			4.20556i
$442$	−7.09915	+	5.89326i	−0.337672	+	0.280314i
$443$	20.0146	−	20.0146i	0.950923	−	0.950923i	−0.0479276	−	0.998851i	$-0.515262\pi$
$443$	20.0146	−	20.0146i	0.950923	−	0.950923i	0.998851	+	0.0479276i	$0.0152617\pi$
$444$	−5.85717	+	1.56942i	−0.277969	+	0.0744816i
$445$		0			0
$446$	−13.0781	+	7.55064i	−0.619265	+	0.357533i
$447$	67.8203			3.20779
$448$	−3.61605	+	2.08773i	−0.170842	+	0.0986359i
$449$	−17.1530	−	4.59612i	−0.809498	−	0.216904i	−0.169748	−	0.985488i	$-0.554295\pi$
$449$	−17.1530	−	4.59612i	−0.809498	−	0.216904i	−0.639750	+	0.768583i	$0.720962\pi$
$450$		0			0
$451$	−0.612009	−	1.06003i	−0.0288184	−	0.0499149i
$452$	1.98826	+	7.42029i	0.0935199	+	0.349021i
$453$	−10.7440	+	18.6092i	−0.504797	+	0.874334i
$454$	20.1622			0.946259
$455$		0			0
$456$	16.3511			0.765711
$457$	8.49845	−	14.7198i	0.397541	−	0.688561i	−0.595881	−	0.803073i	$-0.703197\pi$
$457$	8.49845	−	14.7198i	0.397541	−	0.688561i	0.993422	+	0.114512i	$0.0365304\pi$
$458$	−0.462476	−	1.72598i	−0.0216101	−	0.0806500i
$459$	−23.6707	−	40.9988i	−1.10485	−	1.91366i
$460$		0			0
$461$	13.2125	+	3.54027i	0.615366	+	0.164887i	0.553020	−	0.833168i	$-0.313475\pi$
$461$	13.2125	+	3.54027i	0.615366	+	0.164887i	0.0623456	+	0.998055i	$0.480142\pi$
$462$	−9.28431	+	5.36030i	−0.431945	+	0.249384i
$463$	−7.68919			−0.357347			−0.178674	−	0.983908i	$-0.557181\pi$
$463$	−7.68919			−0.357347			−0.178674	+	0.983908i	$0.557181\pi$
$464$	−4.35399	+	2.51378i	−0.202129	+	0.116699i
$465$		0			0
$466$	7.85940	−	2.10592i	0.364080	−	0.0975548i
$467$	25.0177	−	25.0177i	1.15768	−	1.15768i	0.172709	−	0.984973i	$-0.444748\pi$
$467$	25.0177	−	25.0177i	1.15768	−	1.15768i	0.984973	−	0.172709i	$-0.0552520\pi$
$468$	24.9054	+	17.6358i	1.15125	+	0.815216i
$469$		−	47.4319i		−	2.19020i
$470$		0			0
$471$	−37.6044	+	65.1327i	−1.73272	+	3.00115i
$472$	−12.6359	−	3.38578i	−0.581615	−	0.155843i
$473$		−	7.15542i		−	0.329006i
$474$	4.36907	−	16.3056i	0.200678	−	0.748941i
$475$		0			0
$476$	7.55536	+	7.55536i	0.346299	+	0.346299i
$477$	11.9991	−	44.7814i	0.549403	−	2.05040i
$478$	−3.34130	+	0.895298i	−0.152827	+	0.0409500i
$479$	10.8240	+	40.3955i	0.494559	+	1.84572i	0.532486	+	0.846439i	$0.321258\pi$
$479$	10.8240	+	40.3955i	0.494559	+	1.84572i	−0.0379268	+	0.999281i	$0.512075\pi$
$480$		0			0
$481$	−5.26983	−	3.73163i	−0.240284	−	0.170148i
$482$	−5.25025	−	5.25025i	−0.239142	−	0.239142i
$483$	25.4787	+	14.7101i	1.15932	+	0.669335i
$484$	9.02828	+	5.21248i	0.410377	+	0.236931i
$485$		0			0
$486$	−49.9299	+	49.9299i	−2.26487	+	2.26487i
$487$	9.91755	+	17.1777i	0.449407	+	0.778396i	0.998347	−	0.0574656i	$-0.0183020\pi$
$487$	9.91755	+	17.1777i	0.449407	+	0.778396i	−0.548940	+	0.835861i	$0.684969\pi$
$488$	−0.00936317	−	0.0162175i	−0.000423851	−	0.000734131i
$489$	17.3849	−	17.3849i	0.786173	−	0.786173i
$490$		0			0
$491$	−16.5596	−	9.56070i	−0.747325	−	0.431469i	0.0774013	−	0.997000i	$-0.475338\pi$
$491$	−16.5596	−	9.56070i	−0.747325	−	0.431469i	−0.824727	+	0.565532i	$0.808671\pi$
$492$	4.73302	+	2.73261i	0.213381	+	0.123196i
$493$	9.09719	+	9.09719i	0.409717	+	0.409717i
$494$	11.1217	+	13.3974i	0.500387	+	0.602778i
$495$		0			0
$496$	−0.623315	−	2.32624i	−0.0279877	−	0.104451i
$497$	−30.2717	+	8.11128i	−1.35787	+	0.363841i
$498$	2.24358	−	8.37316i	0.100537	−	0.375210i
$499$	8.31578	+	8.31578i	0.372266	+	0.372266i	0.868302	−	0.496036i	$-0.165212\pi$
$499$	8.31578	+	8.31578i	0.372266	+	0.372266i	−0.496036	+	0.868302i	$0.665212\pi$
$500$		0			0
$501$	14.1413	−	52.7761i	0.631787	−	2.35786i
$502$			23.9375i			1.06838i
$503$	−13.8375	−	3.70775i	−0.616984	−	0.165320i	−0.0632279	−	0.997999i	$-0.520139\pi$
$503$	−13.8375	−	3.70775i	−0.616984	−	0.165320i	−0.553757	+	0.832679i	$0.686806\pi$
$504$	17.6705	−	30.6061i	0.787105	−	1.36331i
$505$		0			0
$506$			1.57806i			0.0701532i
$507$	3.37267	+	43.8866i	0.149786	+	1.94907i
$508$	10.2654	−	10.2654i	0.455453	−	0.455453i
$509$	20.5496	−	5.50625i	0.910845	−	0.244060i	0.227177	−	0.973853i	$-0.427050\pi$
$509$	20.5496	−	5.50625i	0.910845	−	0.244060i	0.683668	+	0.729793i	$0.260384\pi$
$510$		0			0
$511$	−8.20430	+	4.73676i	−0.362937	+	0.209542i
$512$	1.00000			0.0441942
$513$	−77.3724	+	44.6710i	−3.41607	+	1.97227i
$514$	−12.9739	−	3.47635i	−0.572255	−	0.153335i
$515$		0			0
$516$	15.9744	+	27.6685i	0.703234	+	1.21804i
$517$	0.960465	+	3.58451i	0.0422412	+	0.157646i
$518$	−3.73896	+	6.47607i	−0.164280	+	0.284542i
$519$	32.7340			1.43686
$520$		0			0
$521$	12.9481			0.567266			0.283633	−	0.958933i	$-0.408460\pi$
$521$	12.9481			0.567266			0.283633	+	0.958933i	$0.408460\pi$
$522$	21.2765	−	36.8520i	0.931247	−	1.61297i
$523$	8.93236	+	33.3360i	0.390585	+	1.45768i	0.829172	+	0.558994i	$0.188812\pi$
$523$	8.93236	+	33.3360i	0.390585	+	1.45768i	−0.438587	+	0.898689i	$0.644521\pi$
$524$	9.39264	+	16.2685i	0.410319	+	0.710694i
$525$		0			0
$526$	9.50920	+	2.54798i	0.414621	+	0.111097i
$527$	−5.33713	+	3.08139i	−0.232489	+	0.134228i
$528$	2.56753			0.111737
$529$	−16.1682	+	9.33469i	−0.702963	+	0.405856i
$530$		0			0
$531$	106.950	−	28.6572i	4.64123	−	1.24361i
$532$	14.2584	−	14.2584i	0.618178	−	0.618178i
$533$	0.980310	+	5.73670i	0.0424619	+	0.248484i
$534$			22.7098i			0.982750i
$535$		0			0
$536$	−5.67984	+	9.83777i	−0.245332	+	0.424927i
$537$	−14.0988	−	3.77777i	−0.608409	−	0.163023i
$538$		−	2.74115i		−	0.118179i
$539$	−2.04792	+	7.64295i	−0.0882102	+	0.329205i
$540$		0			0
$541$	7.10819	+	7.10819i	0.305605	+	0.305605i	0.843202	−	0.537597i	$-0.180668\pi$
$541$	7.10819	+	7.10819i	0.305605	+	0.305605i	−0.537597	+	0.843202i	$0.680668\pi$
$542$	−1.69108	+	6.31118i	−0.0726379	+	0.271088i
$543$	−31.4838	+	8.43607i	−1.35110	+	0.362026i
$544$	−0.662311	−	2.47178i	−0.0283964	−	0.105977i
$545$		0			0
$546$	50.2450	−	8.58607i	2.15029	−	0.367450i
$547$	−12.8526	−	12.8526i	−0.549536	−	0.549536i	0.376771	−	0.926307i	$-0.377034\pi$
$547$	−12.8526	−	12.8526i	−0.549536	−	0.549536i	−0.926307	+	0.376771i	$0.877034\pi$
$548$	−7.54859	−	4.35818i	−0.322460	−	0.186172i
$549$	0.137264	+	0.0792495i	0.00585829	+	0.00338229i
$550$		0			0
$551$	17.1681	−	17.1681i	0.731385	−	0.731385i
$552$	−3.52300	−	6.10202i	−0.149949	−	0.259719i
$553$	−10.4088	−	18.0285i	−0.442626	−	0.766651i
$554$	10.2215	−	10.2215i	0.434269	−	0.434269i
$555$		0			0
$556$	−2.72940	−	1.57582i	−0.115752	−	0.0668296i
$557$	37.4945	+	21.6475i	1.58869	+	0.917233i	0.993523	+	0.113635i	$0.0362494\pi$
$557$	37.4945	+	21.6475i	1.58869	+	0.917233i	0.595172	+	0.803598i	$0.297084\pi$
$558$	14.4135	+	14.4135i	0.610173	+	0.610173i
$559$	−11.8049	+	31.9082i	−0.499296	+	1.34957i
$560$		0			0
$561$	−1.70050	−	6.34636i	−0.0717952	−	0.267943i
$562$	−12.5111	+	3.35235i	−0.527751	+	0.141410i
$563$	−4.76983	+	17.8012i	−0.201024	+	0.750232i	0.789601	+	0.613621i	$0.210288\pi$
$563$	−4.76983	+	17.8012i	−0.201024	+	0.750232i	−0.990625	+	0.136611i	$0.956379\pi$
$564$	−11.7163	−	11.7163i	−0.493345	−	0.493345i
$565$		0			0
$566$	3.22674	−	12.0424i	0.135630	−	0.506178i
$567$			155.522i			6.53133i
$568$	7.24992	+	1.94261i	0.304200	+	0.0815101i
$569$	−17.0518	+	29.5346i	−0.714849	+	1.23815i	0.248169	+	0.968717i	$0.420171\pi$
$569$	−17.0518	+	29.5346i	−0.714849	+	1.23815i	−0.963018	+	0.269438i	$0.913162\pi$
$570$		0			0
$571$		−	11.8871i		−	0.497460i	−0.968573	−	0.248730i	$-0.919987\pi$
$571$		−	11.8871i		−	0.497460i	0.968573	−	0.248730i	$-0.0800132\pi$
$572$	1.74637	+	2.10372i	0.0730196	+	0.0879610i
$573$	−54.3382	+	54.3382i	−2.27001	+	2.27001i
$574$	6.51011	−	1.74438i	0.271727	−	0.0728090i
$575$		0			0
$576$	−7.33001	+	4.23198i	−0.305417	+	0.176333i
$577$	−31.4791			−1.31049			−0.655247	−	0.755415i	$-0.727435\pi$
$577$	−31.4791			−1.31049			−0.655247	+	0.755415i	$0.727435\pi$
$578$	9.05140	−	5.22583i	0.376489	−	0.217366i
$579$	−8.01047	−	2.14640i	−0.332904	−	0.0892013i
$580$		0			0
$581$	−5.34506	−	9.25791i	−0.221750	−	0.384083i
$582$	−6.15101	−	22.9559i	−0.254968	−	0.951552i
$583$	2.07682	−	3.59715i	0.0860129	−	0.148979i
$584$	2.26886			0.0938859
$585$		0			0
$586$	30.5303			1.26120
$587$	−3.14505	+	5.44739i	−0.129810	+	0.224838i	−0.923603	−	0.383350i	$-0.874770\pi$
$587$	−3.14505	+	5.44739i	−0.129810	+	0.224838i	0.793793	+	0.608188i	$0.208103\pi$
$588$	−9.14394	−	34.1256i	−0.377090	−	1.40732i
$589$	5.81516	+	10.0721i	0.239609	+	0.415016i
$590$		0			0
$591$	−61.0946	−	16.3703i	−2.51310	−	0.673382i
$592$	1.55098	−	0.895461i	0.0637450	−	0.0368032i
$593$	−26.1184			−1.07255			−0.536277	−	0.844042i	$-0.680170\pi$
$593$	−26.1184			−1.07255			−0.536277	+	0.844042i	$0.680170\pi$
$594$	−12.1494	+	7.01443i	−0.498494	+	0.287806i
$595$		0			0
$596$	−19.3480	+	5.18428i	−0.792525	+	0.212357i
$597$	−40.8310	+	40.8310i	−1.67110	+	1.67110i
$598$	2.60347	−	7.03705i	0.106464	−	0.287766i
$599$		−	15.9858i		−	0.653161i	−0.945169	−	0.326581i	$-0.894104\pi$
$599$		−	15.9858i		−	0.653161i	0.945169	−	0.326581i	$-0.105896\pi$
$600$		0			0
$601$	3.86818	−	6.69989i	0.157787	−	0.273294i	−0.776284	−	0.630384i	$-0.782898\pi$
$601$	3.86818	−	6.69989i	0.157787	−	0.273294i	0.934070	+	0.357089i	$0.116231\pi$
$602$	38.0571	+	10.1974i	1.55109	+	0.415613i
$603$		−	96.1479i		−	3.91544i
$604$	1.64257	−	6.13017i	0.0668354	−	0.249433i
$605$		0			0
$606$	−32.2645	−	32.2645i	−1.31066	−	1.31066i
$607$	10.8949	−	40.6602i	0.442209	−	1.65035i	−0.280992	−	0.959710i	$-0.590664\pi$
$607$	10.8949	−	40.6602i	0.442209	−	1.65035i	0.723202	−	0.690637i	$-0.242670\pi$
$608$	−4.66470	+	1.24990i	−0.189179	+	0.0506903i
$609$	−18.3960	−	68.6549i	−0.745445	−	2.78204i
$610$		0			0
$611$	1.63067	−	17.5690i	0.0659700	−	0.710766i
$612$	15.3153	+	15.3153i	0.619083	+	0.619083i
$613$	−1.31674	−	0.760221i	−0.0531827	−	0.0307051i	0.473173	−	0.880970i	$-0.343109\pi$
$613$	−1.31674	−	0.760221i	−0.0531827	−	0.0307051i	−0.526356	+	0.850265i	$0.676442\pi$
$614$	−9.82135	−	5.67036i	−0.396358	−	0.228837i
$615$		0			0
$616$	2.23891	−	2.23891i	0.0902083	−	0.0902083i
$617$	−19.8314	−	34.3490i	−0.798381	−	1.38284i	−0.920670	−	0.390343i	$-0.872357\pi$
$617$	−19.8314	−	34.3490i	−0.798381	−	1.38284i	0.122288	−	0.992495i	$-0.460977\pi$
$618$	−13.4056	−	23.2192i	−0.539253	−	0.934014i
$619$	−2.88094	+	2.88094i	−0.115795	+	0.115795i	−0.762630	−	0.646835i	$-0.776092\pi$
$619$	−2.88094	+	2.88094i	−0.115795	+	0.115795i	0.646835	+	0.762630i	$0.276092\pi$
$620$		0			0
$621$	33.3412	+	19.2495i	1.33794	+	0.772458i
$622$	15.6283	+	9.02302i	0.626639	+	0.361790i
$623$	19.8032	+	19.8032i	0.793399	+	0.793399i
$624$	−11.4494	−	4.23588i	−0.458343	−	0.169571i
$625$		0			0
$626$	3.47557	+	12.9710i	0.138912	+	0.518426i
$627$	−11.9767	+	3.20916i	−0.478305	+	0.128161i
$628$	5.74906	−	21.4558i	0.229413	−	0.856179i
$629$	−3.24061	−	3.24061i	−0.129212	−	0.129212i
$630$		0			0
$631$	−7.40223	+	27.6255i	−0.294678	+	1.09975i	0.646794	+	0.762664i	$0.276109\pi$
$631$	−7.40223	+	27.6255i	−0.294678	+	1.09975i	−0.941473	+	0.337090i	$0.890557\pi$
$632$			4.98569i			0.198320i
$633$	64.6786	+	17.3306i	2.57074	+	0.688828i
$634$	−7.39453	+	12.8077i	−0.293674	+	0.508659i
$635$		0			0
$636$			18.5459i			0.735393i
$637$	21.7416	−	30.7037i	0.861434	−	1.21652i
$638$	2.69581	−	2.69581i	0.106728	−	0.106728i
$639$	−61.3630	+	16.4422i	−2.42748	+	0.650442i
$640$		0			0
$641$	−10.4012	+	6.00513i	−0.410822	+	0.237188i	−0.691143	−	0.722718i	$-0.742893\pi$
$641$	−10.4012	+	6.00513i	−0.410822	+	0.237188i	0.280321	+	0.959906i	$0.409559\pi$
$642$	2.78474			0.109905
$643$	−16.0043	+	9.24008i	−0.631148	+	0.364393i	−0.781196	−	0.624285i	$-0.785390\pi$
$643$	−16.0043	+	9.24008i	−0.631148	+	0.364393i	0.150049	+	0.988679i	$0.452057\pi$
$644$	−8.39312	−	2.24893i	−0.330735	−	0.0886202i
$645$		0			0
$646$	6.17897	+	10.7023i	0.243108	+	0.421076i
$647$	6.38555	+	23.8312i	0.251042	+	0.936901i	0.970250	+	0.242106i	$0.0778381\pi$
$647$	6.38555	+	23.8312i	0.251042	+	0.936901i	−0.719208	+	0.694795i	$0.755495\pi$
$648$	18.6234	−	32.2567i	0.731596	−	1.26716i
$649$	9.91998			0.389393
$650$		0			0
$651$	34.0473			1.33442
$652$	−3.63070	+	6.28855i	−0.142189	+	0.246279i
$653$	−0.991306	−	3.69960i	−0.0387928	−	0.144777i	0.943813	−	0.330480i	$-0.107210\pi$
$653$	−0.991306	−	3.69960i	−0.0387928	−	0.144777i	−0.982606	+	0.185703i	$0.940544\pi$
$654$	−5.26801	−	9.12447i	−0.205996	−	0.356795i
$655$		0			0
$656$	−1.55914	−	0.417770i	−0.0608741	−	0.0163112i
$657$	−16.6307	+	9.60176i	−0.648827	+	0.374600i
$658$	−20.4335			−0.796580
$659$	−9.13583	+	5.27458i	−0.355882	+	0.205468i	−0.667273	−	0.744814i	$-0.732538\pi$
$659$	−9.13583	+	5.27458i	−0.355882	+	0.205468i	0.311391	+	0.950282i	$0.399205\pi$
$660$		0			0
$661$	11.0424	−	2.95880i	0.429500	−	0.115084i	−0.0375915	−	0.999293i	$-0.511969\pi$
$661$	11.0424	−	2.95880i	0.429500	−	0.115084i	0.467091	+	0.884209i	$0.345302\pi$
$662$	−22.9102	+	22.9102i	−0.890432	+	0.890432i
$663$	−2.88710	+	31.1059i	−0.112126	+	1.20805i
$664$			2.56023i			0.0993560i
$665$		0			0
$666$	−7.57915	+	13.1275i	−0.293686	+	0.508679i
$667$	−10.1059	−	2.70787i	−0.391302	−	0.104849i
$668$			16.1371i			0.624364i
$669$	−13.2336	+	49.3884i	−0.511640	+	1.90946i
$670$		0			0
$671$	0.0100412	+	0.0100412i	0.000387636	+	0.000387636i
$672$	−3.65905	+	13.6557i	−0.141151	+	0.526782i
$673$	48.2133	−	12.9187i	1.85849	−	0.497980i	0.858594	−	0.512656i	$-0.171338\pi$
$673$	48.2133	−	12.9187i	1.85849	−	0.497980i	0.999892	+	0.0146758i	$0.00467162\pi$
$674$	−5.62280	−	20.9846i	−0.216582	−	0.808296i
$675$		0			0
$676$	−4.31692	−	12.2623i	−0.166036	−	0.471627i
$677$	12.0185	+	12.0185i	0.461909	+	0.461909i	0.899281	−	0.437372i	$-0.144091\pi$
$677$	12.0185	+	12.0185i	0.461909	+	0.461909i	−0.437372	+	0.899281i	$0.644091\pi$
$678$	22.5255	+	13.0051i	0.865088	+	0.499459i
$679$	−25.3815	−	14.6540i	−0.974054	−	0.562370i
$680$		0			0
$681$	48.2715	−	48.2715i	1.84977	−	1.84977i
$682$	0.913122	+	1.58157i	0.0349652	+	0.0605616i
$683$	−12.8174	−	22.2004i	−0.490444	−	0.849475i	0.509495	−	0.860474i	$-0.329832\pi$
$683$	−12.8174	−	22.2004i	−0.490444	−	0.849475i	−0.999940	+	0.0109989i	$0.996499\pi$
$684$	28.9027	−	28.9027i	1.10512	−	1.10512i
$685$		0			0
$686$	−12.4192	−	7.17021i	−0.474166	−	0.273760i
$687$	−5.23952	−	3.02504i	−0.199900	−	0.115412i
$688$	−6.67225	−	6.67225i	−0.254377	−	0.254377i
$689$	−15.1957	+	12.6145i	−0.578911	+	0.480574i
$690$		0			0
$691$	0.460873	+	1.72000i	0.0175324	+	0.0654320i	0.974138	−	0.225955i	$-0.0725501\pi$
$691$	0.460873	+	1.72000i	0.0175324	+	0.0654320i	−0.956605	+	0.291387i	$0.905883\pi$
$692$	−9.33846	+	2.50223i	−0.354995	+	0.0951206i
$693$	−6.93620	+	25.8863i	−0.263484	+	0.983337i
$694$	−2.65250	−	2.65250i	−0.100687	−	0.100687i
$695$		0			0
$696$	−4.40575	+	16.4425i	−0.167000	+	0.623251i
$697$			4.13053i			0.156455i
$698$	−10.7654	−	2.88458i	−0.407476	−	0.109183i
$699$	13.7747	−	23.8585i	0.521008	−	0.902412i
$700$		0			0
$701$			1.74194i			0.0657923i	0.999459	+	0.0328961i	$0.0104731\pi$
$701$			1.74194i			0.0657923i	−0.999459	+	0.0328961i	$0.989527\pi$
$702$	65.7501	−	11.2356i	2.48158	−	0.424062i
$703$	−6.11564	+	6.11564i	−0.230656	+	0.230656i
$704$	−0.732472	+	0.196265i	−0.0276061	+	0.00739703i
$705$		0			0
$706$	−11.0688	+	6.39060i	−0.416581	+	0.240513i
$707$	−56.2699			−2.11625
$708$	−38.3585	+	22.1463i	−1.44160	+	0.832308i
$709$	−17.1644	−	4.59918i	−0.644622	−	0.172726i	−0.0783257	−	0.996928i	$-0.524957\pi$
$709$	−17.1644	−	4.59918i	−0.644622	−	0.172726i	−0.566296	+	0.824202i	$0.691624\pi$
$710$		0			0
$711$	−21.0994	−	36.5452i	−0.791288	−	1.37055i
$712$	−1.73597	−	6.47873i	−0.0650583	−	0.242801i
$713$	2.50586	−	4.34027i	0.0938451	−	0.162545i
$714$	36.1774			1.35391
$715$		0			0
$716$	4.31093			0.161107
$717$	−5.85610	+	10.1431i	−0.218700	+	0.378800i
$718$	−1.94966	−	7.27623i	−0.0727607	−	0.271547i
$719$	−14.7761	−	25.5929i	−0.551054	−	0.954453i	−0.998199	−	0.0599917i	$-0.980893\pi$
$719$	−14.7761	−	25.5929i	−0.551054	−	0.954453i	0.447145	−	0.894461i	$-0.352441\pi$
$720$		0			0
$721$	−31.9372	−	8.55756i	−1.18940	−	0.318700i
$722$	3.74271	−	2.16085i	0.139289	−	0.0804186i
$723$	−25.1398			−0.934960
$724$	8.33695	−	4.81334i	0.309840	−	0.178886i
$725$		0			0
$726$	34.0946	−	9.13562i	1.26537	−	0.339055i
$727$	−21.2487	+	21.2487i	−0.788072	+	0.788072i	−0.981178	−	0.193106i	$-0.938144\pi$
$727$	−21.2487	+	21.2487i	−0.788072	+	0.788072i	0.193106	+	0.981178i	$0.438144\pi$
$728$	−13.6777	+	6.29026i	−0.506931	+	0.233133i
$729$			127.339i			4.71627i
$730$		0			0
$731$	−12.0732	+	20.9114i	−0.446544	+	0.773437i
$732$	−0.0612441	−	0.0164103i	−0.00226365	−	0.000606542i
$733$			24.2362i			0.895183i	0.894238	+	0.447592i	$0.147718\pi$
$733$			24.2362i			0.895183i	−0.894238	+	0.447592i	$0.852282\pi$
$734$	−0.0266708	+	0.0995368i	−0.000984438	+	0.00367397i
$735$		0			0
$736$	1.47150	+	1.47150i	0.0542402	+	0.0542402i
$737$	2.22951	−	8.32065i	0.0821251	−	0.306495i
$738$	13.1965	−	3.53599i	0.485769	−	0.130161i
$739$	12.5644	+	46.8911i	0.462190	+	1.72492i	0.666041	+	0.745916i	$0.267988\pi$
$739$	12.5644	+	46.8911i	0.462190	+	1.72492i	−0.203850	+	0.979002i	$0.565346\pi$
$740$		0			0
$741$	58.7025	+	5.44849i	2.15649	+	0.200155i
$742$	16.1722	+	16.1722i	0.593701	+	0.593701i
$743$	−29.9017	−	17.2637i	−1.09699	−	0.633345i	−0.161558	−	0.986863i	$-0.551652\pi$
$743$	−29.9017	−	17.2637i	−1.09699	−	0.633345i	−0.935428	+	0.353518i	$0.884985\pi$
$744$	−7.06170	−	4.07708i	−0.258895	−	0.149473i
$745$		0			0
$746$	−9.87411	+	9.87411i	−0.361517	+	0.361517i
$747$	−10.8348	−	18.7665i	−0.396426	−	0.686629i
$748$	0.970249	+	1.68052i	0.0354758	+	0.0614459i
$749$	2.42832	−	2.42832i	0.0887289	−	0.0887289i
$750$		0			0
$751$	6.61675	+	3.82018i	0.241449	+	0.139400i	0.615842	−	0.787869i	$-0.288816\pi$
$751$	6.61675	+	3.82018i	0.241449	+	0.139400i	−0.374394	+	0.927270i	$0.622149\pi$
$752$	4.23808	+	2.44685i	0.154547	+	0.0892276i
$753$	57.3102	+	57.3102i	2.08850	+	2.08850i
$754$	−16.4690	+	7.57393i	−0.599765	+	0.275826i
$755$		0			0
$756$	−19.9929	−	74.6145i	−0.727134	−	2.71370i
$757$	−33.4967	+	8.97541i	−1.21746	+	0.326217i	−0.809684	−	0.586866i	$-0.800362\pi$
$757$	−33.4967	+	8.97541i	−1.21746	+	0.326217i	−0.407774	+	0.913083i	$0.633695\pi$
$758$	−7.61981	+	28.4375i	−0.276764	+	1.03290i
$759$	3.77811	+	3.77811i	0.137137	+	0.137137i
$760$		0			0
$761$	−1.66206	+	6.20288i	−0.0602495	+	0.224854i	−0.989485	−	0.144633i	$-0.953800\pi$
$761$	−1.66206	+	6.20288i	−0.0602495	+	0.224854i	0.929236	+	0.369487i	$0.120467\pi$
$762$		−	49.1539i		−	1.78066i
$763$	−12.5504	−	3.36287i	−0.454355	−	0.121744i
$764$	11.3481	−	19.6555i	0.410560	−	0.711110i
$765$		0			0
$766$			20.8677i			0.753980i
$767$	−44.2363	−	16.3659i	−1.59728	−	0.590938i
$768$	2.39416	−	2.39416i	0.0863917	−	0.0863917i
$769$	29.2963	−	7.84993i	1.05645	−	0.283076i	0.311537	−	0.950234i	$-0.399156\pi$
$769$	29.2963	−	7.84993i	1.05645	−	0.283076i	0.744916	+	0.667158i	$0.232489\pi$
$770$		0			0
$771$	−39.3845	+	22.7387i	−1.41840	+	0.818913i
$772$	2.44933			0.0881533
$773$	29.5519	−	17.0618i	1.06291	−	0.613670i	0.136673	−	0.990616i	$-0.456359\pi$
$773$	29.5519	−	17.0618i	1.06291	−	0.613670i	0.926235	+	0.376946i	$0.123026\pi$
$774$	77.1445	+	20.6708i	2.77290	+	0.742997i
$775$		0			0
$776$	3.50956	+	6.07874i	0.125986	+	0.218214i
$777$	6.55306	+	24.4564i	0.235090	+	0.877367i
$778$	−8.81428	+	15.2668i	−0.316007	+	0.547341i
$779$	7.79508			0.279288
$780$		0			0
$781$	−5.69163			−0.203663
$782$	2.66263	−	4.61181i	0.0952155	−	0.164918i
$783$	−24.0729	−	89.8412i	−0.860294	−	3.21066i
$784$	5.21723	+	9.03650i	0.186330	+	0.322732i
$785$		0			0
$786$	61.4368	+	16.4619i	2.19138	+	0.587178i
$787$	38.7940	−	22.3977i	1.38285	−	0.798392i	0.390358	−	0.920663i	$-0.372351\pi$
$787$	38.7940	−	22.3977i	1.38285	−	0.798392i	0.992497	+	0.122271i	$0.0390178\pi$
$788$	18.6806			0.665470
$789$	28.8668	−	16.6662i	1.02768	−	0.593334i
$790$		0			0
$791$	30.9831	−	8.30190i	1.10163	−	0.295182i
$792$	4.53844	−	4.53844i	0.161266	−	0.161266i
$793$	−0.0282109	−	0.0613427i	−0.00100180	−	0.00217834i
$794$		−	28.9174i		−	1.02624i
$795$		0			0
$796$	8.52723	−	14.7696i	0.302240	−	0.523494i
$797$	45.5195	+	12.1969i	1.61238	+	0.432037i	0.948752	−	0.316022i	$-0.102347\pi$
$797$	45.5195	+	12.1969i	1.61238	+	0.432037i	0.663632	+	0.748059i	$0.269014\pi$
$798$		−	68.2734i		−	2.41685i
$799$	3.24116	−	12.0962i	0.114664	−	0.427931i
$800$		0			0
$801$	40.1426	+	40.1426i	1.41837	+	1.41837i
$802$	2.20430	−	8.22656i	0.0778366	−	0.290490i
$803$	−1.66187	+	0.445298i	−0.0586463	+	0.0157142i
$804$	9.95473	+	37.1516i	0.351076	+	1.31023i
$805$		0			0
$806$	−1.46263	−	8.55919i	−0.0515189	−	0.301485i
$807$	−6.56274	−	6.56274i	−0.231019	−	0.231019i
$808$	11.6709	+	6.73818i	0.410580	+	0.237048i
$809$	29.4427	+	16.9988i	1.03515	+	0.597645i	0.918456	−	0.395523i	$-0.129437\pi$
$809$	29.4427	+	16.9988i	1.03515	+	0.597645i	0.116695	+	0.993168i	$0.462770\pi$
$810$		0			0
$811$	−26.3564	+	26.3564i	−0.925498	+	0.925498i	−0.997411	−	0.0719129i	$-0.977090\pi$
$811$	−26.3564	+	26.3564i	−0.925498	+	0.925498i	0.0719129	+	0.997411i	$0.477090\pi$
$812$	10.4962	+	18.1799i	0.368343	+	0.637989i
$813$	11.0612	+	19.1586i	0.387935	+	0.671923i
$814$	−0.960305	+	0.960305i	−0.0336587	+	0.0336587i
$815$		0			0
$816$	−7.50350	−	4.33215i	−0.262675	−	0.151655i
$817$	39.4637	+	22.7844i	1.38066	+	0.797125i
$818$	17.7540	+	17.7540i	0.620753	+	0.620753i
$819$	73.6376	−	103.992i	2.57311	−	3.63376i
$820$		0			0
$821$	−10.1687	−	37.9502i	−0.354891	−	1.32447i	−0.880621	−	0.473821i	$-0.842874\pi$
$821$	−10.1687	−	37.9502i	−0.354891	−	1.32447i	0.525730	−	0.850651i	$-0.323792\pi$
$822$	−28.5067	+	7.63834i	−0.994284	+	0.266418i
$823$	8.71449	−	32.5229i	0.303768	−	1.13368i	−0.630233	−	0.776406i	$-0.717041\pi$
$823$	8.71449	−	32.5229i	0.303768	−	1.13368i	0.934001	−	0.357271i	$-0.116293\pi$
$824$	5.59931	+	5.59931i	0.195061	+	0.195061i
$825$		0			0
$826$	−14.1372	+	52.7608i	−0.491896	+	1.83578i
$827$		−	26.5912i		−	0.924666i	−0.886706	−	0.462333i	$-0.847013\pi$
$827$		−	26.5912i		−	0.924666i	0.886706	−	0.462333i	$-0.152987\pi$
$828$	−17.0135	−	4.55874i	−0.591259	−	0.158427i
$829$	2.49475	−	4.32104i	0.0866463	−	0.150076i	−0.819445	−	0.573157i	$-0.805718\pi$
$829$	2.49475	−	4.32104i	0.0866463	−	0.150076i	0.906092	+	0.423082i	$0.139052\pi$
$830$		0			0
$831$		−	48.9436i		−	1.69784i
$832$	3.59012	+	0.333218i	0.124465	+	0.0115523i
$833$	18.8808	−	18.8808i	0.654181	−	0.654181i
$834$	−10.3074	+	2.76185i	−0.356915	+	0.0956350i
$835$		0			0
$836$	3.17145	−	1.83104i	0.109687	−	0.0633278i
$837$	44.5540			1.54001
$838$	−23.2032	+	13.3964i	−0.801542	+	0.462770i
$839$	−10.8926	−	2.91865i	−0.376053	−	0.100763i	0.0658415	−	0.997830i	$-0.479027\pi$
$839$	−10.8926	−	2.91865i	−0.376053	−	0.100763i	−0.441895	+	0.897067i	$0.645694\pi$
$840$		0			0
$841$	−1.86187	−	3.22485i	−0.0642024	−	0.111202i
$842$	2.00558	+	7.48493i	0.0691169	+	0.257948i
$843$	−21.9276	+	37.9797i	−0.755226	+	1.30809i
$844$	−19.7765			−0.680735
$845$		0			0
$846$	−41.4202			−1.42405
$847$	21.7645	−	37.6972i	0.747837	−	1.29529i
$848$	−1.41768	−	5.29084i	−0.0486832	−	0.181688i
$849$	−21.1060	−	36.5566i	−0.724355	−	1.25462i
$850$		0			0
$851$	3.59994	+	0.964602i	0.123404	+	0.0330661i
$852$	22.0083	−	12.7065i	0.753993	−	0.435318i
$853$	−30.1746			−1.03316			−0.516579	−	0.856239i	$-0.672795\pi$
$853$	−30.1746			−1.03316			−0.516579	+	0.856239i	$0.672795\pi$
$854$	−0.0677154	+	0.0390955i	−0.00231717	+	0.00133782i
$855$		0			0
$856$	−0.794439	+	0.212869i	−0.0271534	+	0.00727572i
$857$	18.4882	−	18.4882i	0.631546	−	0.631546i	−0.316910	−	0.948456i	$-0.602645\pi$
$857$	18.4882	−	18.4882i	0.631546	−	0.631546i	0.948456	+	0.316910i	$0.102645\pi$
$858$	9.21773	+	0.855547i	0.314688	+	0.0292079i
$859$			2.76088i			0.0941999i	0.998890	+	0.0471000i	$0.0149979\pi$
$859$			2.76088i			0.0941999i	−0.998890	+	0.0471000i	$0.985002\pi$
$860$		0			0
$861$	11.4099	−	19.7625i	0.388849	−	0.673505i
$862$	−6.11158	−	1.63759i	−0.208161	−	0.0557766i
$863$			45.2712i			1.54105i	0.637411	+	0.770524i	$0.280006\pi$
$863$			45.2712i			1.54105i	−0.637411	+	0.770524i	$0.719994\pi$
$864$	−4.78819	+	17.8698i	−0.162898	+	0.607942i
$865$		0			0
$866$	17.2317	+	17.2317i	0.585558	+	0.585558i
$867$	9.15901	−	34.1819i	0.311056	−	1.16088i
$868$	−9.71313	+	2.60263i	−0.329685	+	0.0883389i
$869$	−0.978519	−	3.65188i	−0.0331940	−	0.123882i
$870$		0			0
$871$	−23.6694	+	33.4261i	−0.802008	+	1.13260i
$872$	2.20036	+	2.20036i	0.0745137	+	0.0745137i
$873$	−51.4502	−	29.7048i	−1.74133	−	1.00536i
$874$	−8.70334	−	5.02488i	−0.294395	−	0.169969i
$875$		0			0
$876$	5.43199	−	5.43199i	0.183530	−	0.183530i
$877$	19.1871	+	33.2331i	0.647903	+	1.12220i	0.983623	+	0.180239i	$0.0576872\pi$
$877$	19.1871	+	33.2331i	0.647903	+	1.12220i	−0.335719	+	0.941962i	$0.608979\pi$
$878$	8.74647	+	15.1493i	0.295179	+	0.511265i
$879$	73.0944	−	73.0944i	2.46541	−	2.46541i
$880$		0			0
$881$	−43.2499	−	24.9703i	−1.45713	−	0.841272i	−0.458257	−	0.888820i	$-0.651526\pi$
$881$	−43.2499	−	24.9703i	−1.45713	−	0.841272i	−0.998869	+	0.0475474i	$0.984859\pi$
$882$	−76.4846	−	44.1584i	−2.57537	−	1.48689i
$883$	−23.5749	−	23.5749i	−0.793358	−	0.793358i	0.188680	−	0.982039i	$-0.439579\pi$
$883$	−23.5749	−	23.5749i	−0.793358	−	0.793358i	−0.982039	+	0.188680i	$0.939579\pi$
$884$	−1.55413	−	9.09468i	−0.0522712	−	0.305887i
$885$		0			0
$886$	7.32586	+	27.3405i	0.246117	+	0.918521i
$887$	−9.49544	+	2.54430i	−0.318826	+	0.0854291i	−0.414683	−	0.909966i	$-0.636107\pi$
$887$	−9.49544	+	2.54430i	−0.318826	+	0.0854291i	0.0958571	+	0.995395i	$0.469441\pi$
$888$	1.56942	−	5.85717i	0.0526664	−	0.196554i
$889$	−42.8627	−	42.8627i	−1.43757	−	1.43757i
$890$		0			0
$891$	−7.31026	+	27.2822i	−0.244903	+	0.913990i
$892$		−	15.1013i		−	0.505628i
$893$	−22.8277	−	6.11666i	−0.763900	−	0.204686i
$894$	−33.9102	+	58.7341i	−1.13413	+	1.96436i
$895$		0			0
$896$		−	4.17546i		−	0.139492i
$897$	−10.6147	−	23.0809i	−0.354414	−	0.770649i
$898$	12.5568	−	12.5568i	0.419027	−	0.419027i
$899$	−11.6953	+	3.13375i	−0.390060	+	0.104516i
$900$		0			0
$901$	−12.1388	+	7.00836i	−0.404403	+	0.233482i
$902$	1.22402			0.0407554
$903$	115.529	−	66.7005i	3.84455	−	2.21965i
$904$	−7.42029	−	1.98826i	−0.246795	−	0.0661286i
$905$		0			0
$906$	−10.7440	−	18.6092i	−0.356946	−	0.618248i
$907$	2.44703	+	9.13246i	0.0812525	+	0.303238i	0.994578	−	0.103992i	$-0.0331615\pi$
$907$	2.44703	+	9.13246i	0.0812525	+	0.303238i	−0.913326	+	0.407230i	$0.866495\pi$
$908$	−10.0811	+	17.4610i	−0.334553	+	0.579463i
$909$	−114.063			−3.78324
$910$		0			0
$911$	−20.0662			−0.664822			−0.332411	−	0.943135i	$-0.607862\pi$
$911$	−20.0662			−0.664822			−0.332411	+	0.943135i	$0.607862\pi$
$912$	−8.17556	+	14.1605i	−0.270720	+	0.468901i
$913$	−0.502484	−	1.87529i	−0.0166298	−	0.0620632i
$914$	8.49845	+	14.7198i	0.281104	+	0.486886i
$915$		0			0
$916$	1.72598	+	0.462476i	0.0570281	+	0.0152806i
$917$	67.9286	−	39.2186i	2.24320	−	1.29511i
$918$	47.3414			1.56250
$919$	−6.83105	+	3.94391i	−0.225336	+	0.130098i	−0.608418	−	0.793616i	$-0.708196\pi$
$919$	−6.83105	+	3.94391i	−0.225336	+	0.130098i	0.383083	+	0.923714i	$0.374862\pi$
$920$		0			0
$921$	−37.0896	+	9.93812i	−1.22214	+	0.327472i
$922$	−9.67220	+	9.67220i	−0.318537	+	0.318537i
$923$	25.3808	+	9.39001i	0.835418	+	0.309076i
$924$		−	10.7206i		−	0.352682i
$925$		0			0
$926$	3.84460	−	6.65903i	0.126341	−	0.218829i
$927$	−64.7391	−	17.3468i	−2.12631	−	0.569744i
$928$		−	5.02755i		−	0.165037i
$929$	−6.71229	+	25.0506i	−0.220223	+	0.821884i	0.764039	+	0.645170i	$0.223213\pi$
$929$	−6.71229	+	25.0506i	−0.220223	+	0.821884i	−0.984262	+	0.176714i	$0.943453\pi$
$930$		0			0
$931$	−35.6316	−	35.6316i	−1.16778	−	1.16778i
$932$	−2.10592	+	7.85940i	−0.0689817	+	0.257443i
$933$	59.0192	−	15.8141i	1.93220	−	0.517732i
$934$	9.15712	+	34.1748i	0.299630	+	1.11823i
$935$		0			0
$936$	−27.7258	+	12.7508i	−0.906246	+	0.416774i
$937$	5.05649	+	5.05649i	0.165188	+	0.165188i	0.784861	−	0.619672i	$-0.212734\pi$
$937$	5.05649	+	5.05649i	0.165188	+	0.165188i	−0.619672	+	0.784861i	$0.712734\pi$
$938$	41.0772	+	23.7159i	1.34122	+	0.774352i
$939$	39.3757	+	22.7336i	1.28498	+	0.741881i
$940$		0			0
$941$	−22.6650	+	22.6650i	−0.738859	+	0.738859i	−0.972357	−	0.233498i	$-0.924983\pi$
$941$	−22.6650	+	22.6650i	−0.738859	+	0.738859i	0.233498	+	0.972357i	$0.424983\pi$
$942$	−37.6044	−	65.1327i	−1.22522	−	2.12214i
$943$	−1.67952	−	2.90902i	−0.0546928	−	0.0947307i
$944$	9.25014	−	9.25014i	0.301066	−	0.301066i
$945$		0			0
$946$	6.19677	+	3.57771i	0.201474	+	0.116321i
$947$	−29.0597	−	16.7776i	−0.944314	−	0.545200i	−0.0530042	−	0.998594i	$-0.516880\pi$
$947$	−29.0597	−	16.7776i	−0.944314	−	0.545200i	−0.891310	+	0.453394i	$0.850213\pi$
$948$	11.9365	+	11.9365i	0.387680	+	0.387680i
$949$	8.14546	+	0.756024i	0.264413	+	0.0245416i
$950$		0			0
$951$	12.9600	+	48.3673i	0.420256	+	1.56842i
$952$	−10.3208	+	2.76545i	−0.334499	+	0.0896288i
$953$	−1.53795	+	5.73970i	−0.0498190	+	0.185927i	−0.986351	−	0.164654i	$-0.947349\pi$
$953$	−1.53795	+	5.73970i	−0.0498190	+	0.185927i	0.936532	+	0.350581i	$0.114016\pi$
$954$	32.7823	+	32.7823i	1.06137	+	1.06137i
$955$		0			0
$956$	0.895298	−	3.34130i	0.0289560	−	0.108065i
$957$		−	12.9084i		−	0.417268i
$958$	−40.3955	−	10.8240i	−1.30512	−	0.349706i
$959$	−18.1974	+	31.5188i	−0.587625	+	1.01780i
$960$		0			0
$961$			25.2001i			0.812906i
$962$	5.86660	−	2.69800i	0.189147	−	0.0869869i
$963$	4.92238	−	4.92238i	0.158622	−	0.158622i
$964$	7.17197	−	1.92172i	0.230994	−	0.0618945i
$965$		0			0
$966$	−25.4787	+	14.7101i	−0.819764	+	0.473291i
$967$	−17.2907			−0.556030			−0.278015	−	0.960577i	$-0.589677\pi$
$967$	−17.2907			−0.556030			−0.278015	+	0.960577i	$0.589677\pi$
$968$	−9.02828	+	5.21248i	−0.290180	+	0.167536i
$969$	40.4164	+	10.8295i	1.29836	+	0.347895i
$970$		0			0
$971$	8.22692	+	14.2494i	0.264014	+	0.457286i	0.967305	−	0.253616i	$-0.0816200\pi$
$971$	8.22692	+	14.2494i	0.264014	+	0.457286i	−0.703291	+	0.710903i	$0.748287\pi$
$972$	−18.2756	−	68.2055i	−0.586190	−	2.18769i
$973$	−6.57976	+	11.3965i	−0.210938	+	0.365355i
$974$	−19.8351			−0.635558
$975$		0			0
$976$	0.0187263			0.000599416
$977$	−1.64582	+	2.85064i	−0.0526545	+	0.0912002i	−0.891151	−	0.453706i	$-0.850102\pi$
$977$	−1.64582	+	2.85064i	−0.0526545	+	0.0912002i	0.838497	+	0.544906i	$0.183435\pi$
$978$	6.36332	+	23.7482i	0.203476	+	0.759384i
$979$	2.54310	+	4.40478i	0.0812779	+	0.140777i
$980$		0			0
$981$	−25.4406	−	6.81678i	−0.812255	−	0.217643i
$982$	16.5596	−	9.56070i	0.528439	−	0.305094i
$983$	−18.4925			−0.589818			−0.294909	−	0.955525i	$-0.595289\pi$
$983$	−18.4925			−0.589818			−0.294909	+	0.955525i	$0.595289\pi$
$984$	−4.73302	+	2.73261i	−0.150883	+	0.0871125i
$985$		0			0
$986$	−12.4270	+	3.32980i	−0.395756	+	0.106043i
$987$	−48.9209	+	48.9209i	−1.55717	+	1.55717i
$988$	−17.1633	+	2.93294i	−0.546038	+	0.0933092i
$989$		−	19.6364i		−	0.624402i
$990$		0			0
$991$	16.1179	−	27.9170i	0.512002	−	0.886813i	−0.487902	−	0.872899i	$-0.662238\pi$
$991$	16.1179	−	27.9170i	0.512002	−	0.886813i	0.999903	−	0.0139141i	$-0.00442913\pi$
$992$	2.32624	+	0.623315i	0.0738583	+	0.0197903i
$993$			109.701i			3.48127i
$994$	8.11128	−	30.2717i	0.257274	−	0.960161i
$995$		0			0
$996$	6.12958	+	6.12958i	0.194223	+	0.194223i
$997$	13.3302	−	49.7491i	0.422173	−	1.57557i	−0.347847	−	0.937551i	$-0.613087\pi$
$997$	13.3302	−	49.7491i	0.422173	−	1.57557i	0.770020	−	0.638020i	$-0.220246\pi$
$998$	−11.3596	+	3.04379i	−0.359581	+	0.0963494i
$999$	8.57527	+	32.0034i	0.271310	+	1.01254i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.w.f.357.4	yes	16
5.2	odd	4		650.2.t.f.643.4	yes	16
5.3	odd	4		650.2.t.h.643.1	yes	16
5.4	even	2		650.2.w.h.357.1	yes	16
13.11	odd	12		650.2.t.h.557.1	yes	16
65.24	odd	12		650.2.t.f.557.4	✓	16
65.37	even	12		650.2.w.h.193.1	yes	16
65.63	even	12	inner	650.2.w.f.193.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
650.2.t.f.557.4	✓	16	65.24	odd	12
650.2.t.f.643.4	yes	16	5.2	odd	4
650.2.t.h.557.1	yes	16	13.11	odd	12
650.2.t.h.643.1	yes	16	5.3	odd	4
650.2.w.f.193.4	yes	16	65.63	even	12	inner
650.2.w.f.357.4	yes	16	1.1	even	1	trivial
650.2.w.h.193.1	yes	16	65.37	even	12
650.2.w.h.357.1	yes	16	5.4	even	2

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:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.876322 + 3.27048i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-3.27048 - 0.876322i) q^{6} +(-3.61605 + 2.08773i) q^{7} +1.00000 q^{8} +(-7.33001 + 4.23198i) q^{9} +(-0.732472 + 0.196265i) q^{11} +(2.39416 - 2.39416i) q^{12} +(3.59012 + 0.333218i) q^{13} -4.17546i q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.47178 + 0.662311i) q^{17} -8.46396i q^{18} +(1.24990 - 4.66470i) q^{19} +(-9.99670 - 9.99670i) q^{21} +(0.196265 - 0.732472i) q^{22} +(-2.01011 + 0.538606i) q^{23} +(0.876322 + 3.27048i) q^{24} +(-2.08364 + 2.94253i) q^{26} +(-13.0816 - 13.0816i) q^{27} +(3.61605 + 2.08773i) q^{28} +(4.35399 + 2.51378i) q^{29} +(-1.70293 + 1.70293i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.28376 - 2.22354i) q^{33} +(-1.80947 + 1.80947i) q^{34} +(7.33001 + 4.23198i) q^{36} +(-1.55098 - 0.895461i) q^{37} +(3.41480 + 3.41480i) q^{38} +(2.05632 + 12.0334i) q^{39} +(0.417770 + 1.55914i) q^{41} +(13.6557 - 3.65905i) q^{42} +(-2.44221 + 9.11447i) q^{43} +(0.536207 + 0.536207i) q^{44} +(0.538606 - 2.01011i) q^{46} -4.89371i q^{47} +(-3.27048 - 0.876322i) q^{48} +(5.21723 - 9.03650i) q^{49} +8.66429i q^{51} +(-1.50648 - 3.27574i) q^{52} +(-3.87316 + 3.87316i) q^{53} +(17.8698 - 4.78819i) q^{54} +(-3.61605 + 2.08773i) q^{56} +16.3511 q^{57} +(-4.35399 + 2.51378i) q^{58} +(-12.6359 - 3.38578i) q^{59} +(-0.00936317 - 0.0162175i) q^{61} +(-0.623315 - 2.32624i) q^{62} +(17.6705 - 30.6061i) q^{63} +1.00000 q^{64} +2.56753 q^{66} +(-5.67984 + 9.83777i) q^{67} +(-0.662311 - 2.47178i) q^{68} +(-3.52300 - 6.10202i) q^{69} +(7.24992 + 1.94261i) q^{71} +(-7.33001 + 4.23198i) q^{72} +2.26886 q^{73} +(1.55098 - 0.895461i) q^{74} +(-4.66470 + 1.24990i) q^{76} +(2.23891 - 2.23891i) q^{77} +(-11.4494 - 4.23588i) q^{78} +4.98569i q^{79} +(18.6234 - 32.2567i) q^{81} +(-1.55914 - 0.417770i) q^{82} +2.56023i q^{83} +(-3.65905 + 13.6557i) q^{84} +(-6.67225 - 6.67225i) q^{86} +(-4.40575 + 16.4425i) q^{87} +(-0.732472 + 0.196265i) q^{88} +(-1.73597 - 6.47873i) q^{89} +(-13.6777 + 6.29026i) q^{91} +(1.47150 + 1.47150i) q^{92} +(-7.06170 - 4.07708i) q^{93} +(4.23808 + 2.44685i) q^{94} +(2.39416 - 2.39416i) q^{96} +(3.50956 + 6.07874i) q^{97} +(5.21723 + 9.03650i) q^{98} +(4.53844 - 4.53844i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{2} - 8 q^{4} - 12 q^{7} + 16 q^{8} - 24 q^{9} - 4 q^{11} - 8 q^{13} - 8 q^{16} + 8 q^{17} + 16 q^{19} - 4 q^{21} - 4 q^{22} + 4 q^{23} + 4 q^{26} - 36 q^{27} + 12 q^{28} + 36 q^{29} - 8 q^{31}+ \cdots - 36 q^{99}+O(q^{100}) \) 16 * q - 8 * q^2 - 8 * q^4 - 12 * q^7 + 16 * q^8 - 24 * q^9 - 4 * q^11 - 8 * q^13 - 8 * q^16 + 8 * q^17 + 16 * q^19 - 4 * q^21 - 4 * q^22 + 4 * q^23 + 4 * q^26 - 36 * q^27 + 12 * q^28 + 36 * q^29 - 8 * q^31 - 8 * q^32 - 16 * q^34 + 24 * q^36 + 36 * q^37 + 4 * q^38 + 32 * q^41 + 8 * q^42 + 36 * q^43 + 8 * q^44 + 4 * q^46 + 16 * q^49 + 4 * q^52 - 44 * q^53 + 36 * q^54 - 12 * q^56 + 48 * q^57 - 36 * q^58 - 24 * q^59 - 20 * q^61 - 8 * q^62 + 36 * q^63 + 16 * q^64 + 12 * q^67 + 8 * q^68 + 24 * q^69 + 16 * q^71 - 24 * q^72 - 36 * q^74 - 20 * q^76 - 16 * q^77 - 60 * q^78 + 16 * q^81 - 16 * q^82 - 4 * q^84 - 36 * q^86 - 12 * q^87 - 4 * q^88 - 28 * q^89 - 44 * q^91 - 8 * q^92 + 24 * q^93 + 24 * q^94 + 8 * q^97 + 16 * q^98 - 36 * q^99

Introduction

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