LMFDB - Embedded newform 650.2.w.e.293.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [650,2,Mod(193,650)] 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("650.193"); S:= CuspForms(chi, 2); N := Newforms(S);

sage: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")

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:traces = [12,6,0,-6,0,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 24x^{10} + 192x^{8} + 680x^{6} + 1104x^{4} + 672x^{2} + 4 $ x^12 + 24x^10 + 192x^8 + 680x^6 + 1104x^4 + 672*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			293.1
Root			$1.55227i$ of defining polynomial
Character	$\chi$	$=$	650.293
Dual form			650.2.w.e.457.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(-2.89657 + 0.776134i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.776134 + 2.89657i) q^{6} +(1.10671 - 0.638961i) q^{7} -1.00000 q^{8} +(5.18966 - 2.99625i) q^{9} +(-0.228853 - 0.854091i) q^{11} +(2.12044 + 2.12044i) q^{12} +(1.42488 + 3.31205i) q^{13} -1.27792i q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.160684 + 0.599680i) q^{17} -5.99250i q^{18} +(-3.26251 - 0.874187i) q^{19} +(-2.70975 + 2.70975i) q^{21} +(-0.854091 - 0.228853i) q^{22} +(-2.16292 - 8.07211i) q^{23} +(2.89657 - 0.776134i) q^{24} +(3.58077 + 0.422042i) q^{26} +(-6.34541 + 6.34541i) q^{27} +(-1.10671 - 0.638961i) q^{28} +(-5.53601 - 3.19622i) q^{29} +(-7.30303 - 7.30303i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.32578 + 2.29631i) q^{33} +(0.438997 + 0.438997i) q^{34} +(-5.18966 - 2.99625i) q^{36} +(-7.93494 - 4.58124i) q^{37} +(-2.38832 + 2.38832i) q^{38} +(-6.69787 - 8.48770i) q^{39} +(8.36236 - 2.24069i) q^{41} +(0.991839 + 3.70159i) q^{42} +(1.97169 + 0.528312i) q^{43} +(-0.625238 + 0.625238i) q^{44} +(-8.07211 - 2.16292i) q^{46} -2.55866i q^{47} +(0.776134 - 2.89657i) q^{48} +(-2.68346 + 4.64788i) q^{49} -1.86173i q^{51} +(2.15588 - 2.89001i) q^{52} +(-2.67655 - 2.67655i) q^{53} +(2.32258 + 8.66799i) q^{54} +(-1.10671 + 0.638961i) q^{56} +10.1286 q^{57} +(-5.53601 + 3.19622i) q^{58} +(0.288254 - 1.07578i) q^{59} +(3.53771 + 6.12749i) q^{61} +(-9.97612 + 2.67309i) q^{62} +(3.82898 - 6.63198i) q^{63} +1.00000 q^{64} +2.65156 q^{66} +(-1.29025 + 2.23477i) q^{67} +(0.599680 - 0.160684i) q^{68} +(12.5301 + 21.7027i) q^{69} +(-1.80066 + 6.72017i) q^{71} +(-5.18966 + 2.99625i) q^{72} -4.86934 q^{73} +(-7.93494 + 4.58124i) q^{74} +(0.874187 + 3.26251i) q^{76} +(-0.799006 - 0.799006i) q^{77} +(-10.6995 + 1.55668i) q^{78} -11.2172i q^{79} +(4.46628 - 7.73583i) q^{81} +(2.24069 - 8.36236i) q^{82} +1.75068i q^{83} +(3.70159 + 0.991839i) q^{84} +(1.44337 - 1.44337i) q^{86} +(18.5161 + 4.96138i) q^{87} +(0.228853 + 0.854091i) q^{88} +(6.08837 - 1.63137i) q^{89} +(3.69321 + 2.75505i) q^{91} +(-5.90920 + 5.90920i) q^{92} +(26.8219 + 15.4856i) q^{93} +(-2.21587 - 1.27933i) q^{94} +(-2.12044 - 2.12044i) q^{96} +(-4.99081 - 8.64434i) q^{97} +(2.68346 + 4.64788i) q^{98} +(-3.74674 - 3.74674i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} - 6 q^{4} - 6 q^{7} - 12 q^{8} + 24 q^{9} + 6 q^{11} + 6 q^{13} - 6 q^{16} - 36 q^{19} - 24 q^{21} - 6 q^{23} + 6 q^{26} + 12 q^{27} + 6 q^{28} - 6 q^{29} - 24 q^{31} + 6 q^{32} - 18 q^{33}+ \cdots - 54 q^{99}+O(q^{100}) $ 12 * q + 6 * q^2 - 6 * q^4 - 6 * q^7 - 12 * q^8 + 24 * q^9 + 6 * q^11 + 6 * q^13 - 6 * q^16 - 36 * q^19 - 24 * q^21 - 6 * q^23 + 6 * q^26 + 12 * q^27 + 6 * q^28 - 6 * q^29 - 24 * q^31 + 6 * q^32 - 18 * q^33 + 12 * q^34 - 24 * q^36 - 6 * q^37 - 6 * q^38 - 6 * q^39 + 18 * q^41 - 18 * q^42 - 6 * q^44 - 6 * q^46 - 18 * q^53 + 6 * q^54 + 6 * q^56 - 6 * q^58 - 18 * q^59 + 18 * q^61 - 36 * q^62 + 12 * q^64 - 36 * q^66 - 24 * q^67 + 12 * q^68 + 42 * q^69 + 18 * q^71 - 24 * q^72 + 12 * q^73 - 6 * q^74 + 30 * q^76 + 30 * q^77 - 30 * q^78 + 30 * q^81 + 18 * q^82 + 6 * q^84 + 60 * q^87 - 6 * q^88 - 6 * q^89 - 6 * q^91 + 30 * q^93 - 24 * q^94 - 6 * q^97 - 54 * q^99

Character values

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

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{11}{12}\right)$

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
$3$	−2.89657	+	0.776134i	−1.67234	+	0.448101i	−0.965739	−	0.259516i	$-0.916437\pi$
$3$	−2.89657	+	0.776134i	−1.67234	+	0.448101i	−0.706597	+	0.707617i	$0.749770\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−0.776134	+	2.89657i	−0.316855	+	1.18252i
$7$	1.10671	−	0.638961i	0.418298	−	0.241505i	−0.276051	−	0.961143i	$-0.589026\pi$
$7$	1.10671	−	0.638961i	0.418298	−	0.241505i	0.694349	+	0.719638i	$0.255692\pi$
$8$	−1.00000			−0.353553
$9$	5.18966	−	2.99625i	1.72989	−	0.998750i
$10$		0			0
$11$	−0.228853	−	0.854091i	−0.0690018	−	0.257518i	0.922805	−	0.385268i	$-0.125891\pi$
$11$	−0.228853	−	0.854091i	−0.0690018	−	0.257518i	−0.991806	+	0.127750i	$0.959224\pi$
$12$	2.12044	+	2.12044i	0.612117	+	0.612117i
$13$	1.42488	+	3.31205i	0.395192	+	0.918599i
$13$	1.42488	+	3.31205i	0.395192	+	0.918599i
$14$		−	1.27792i		−	0.341539i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.160684	+	0.599680i	−0.0389716	+	0.145444i	−0.982670	−	0.185363i	$-0.940654\pi$
$17$	−0.160684	+	0.599680i	−0.0389716	+	0.145444i	0.943699	+	0.330806i	$0.107321\pi$
$18$		−	5.99250i		−	1.41245i
$19$	−3.26251	−	0.874187i	−0.748471	−	0.200552i	−0.135631	−	0.990759i	$-0.543306\pi$
$19$	−3.26251	−	0.874187i	−0.748471	−	0.200552i	−0.612840	+	0.790207i	$0.709973\pi$
$20$		0			0
$21$	−2.70975	+	2.70975i	−0.591317	+	0.591317i
$22$	−0.854091	−	0.228853i	−0.182093	−	0.0487916i
$23$	−2.16292	−	8.07211i	−0.450999	−	1.68315i	−0.699591	−	0.714544i	$-0.746634\pi$
$23$	−2.16292	−	8.07211i	−0.450999	−	1.68315i	0.248591	−	0.968608i	$-0.420032\pi$
$24$	2.89657	−	0.776134i	0.591260	−	0.158428i
$25$		0			0
$26$	3.58077	+	0.422042i	0.702246	+	0.0827693i
$27$	−6.34541	+	6.34541i	−1.22117	+	1.22117i
$28$	−1.10671	−	0.638961i	−0.209149	−	0.120752i
$29$	−5.53601	−	3.19622i	−1.02801	−	0.593522i	−0.111597	−	0.993754i	$-0.535596\pi$
$29$	−5.53601	−	3.19622i	−1.02801	−	0.593522i	−0.916414	+	0.400231i	$0.868930\pi$
$30$		0			0
$31$	−7.30303	−	7.30303i	−1.31166	−	1.31166i	−0.920190	−	0.391473i	$-0.871966\pi$
$31$	−7.30303	−	7.30303i	−1.31166	−	1.31166i	−0.391473	−	0.920190i	$-0.628034\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	1.32578	+	2.29631i	0.230788	+	0.399737i
$34$	0.438997	+	0.438997i	0.0752873	+	0.0752873i
$35$		0			0
$36$	−5.18966	−	2.99625i	−0.864943	−	0.499375i
$37$	−7.93494	−	4.58124i	−1.30450	−	0.753151i	−0.323325	−	0.946288i	$-0.604801\pi$
$37$	−7.93494	−	4.58124i	−1.30450	−	0.753151i	−0.981172	+	0.193137i	$0.938134\pi$
$38$	−2.38832	+	2.38832i	−0.387437	+	0.387437i
$39$	−6.69787	−	8.48770i	−1.07252	−	1.35912i
$40$		0			0
$41$	8.36236	−	2.24069i	1.30598	−	0.349937i	0.462273	−	0.886738i	$-0.347034\pi$
$41$	8.36236	−	2.24069i	1.30598	−	0.349937i	0.843709	+	0.536801i	$0.180367\pi$
$42$	0.991839	+	3.70159i	0.153044	+	0.571168i
$43$	1.97169	+	0.528312i	0.300679	+	0.0805668i	0.406005	−	0.913871i	$-0.366922\pi$
$43$	1.97169	+	0.528312i	0.300679	+	0.0805668i	−0.105325	+	0.994438i	$0.533588\pi$
$44$	−0.625238	+	0.625238i	−0.0942582	+	0.0942582i
$45$		0			0
$46$	−8.07211	−	2.16292i	−1.19017	−	0.318905i
$47$		−	2.55866i		−	0.373219i	−0.982434	−	0.186610i	$-0.940250\pi$
$47$		−	2.55866i		−	0.373219i	0.982434	−	0.186610i	$-0.0597500\pi$
$48$	0.776134	−	2.89657i	0.112025	−	0.418084i
$49$	−2.68346	+	4.64788i	−0.383351	+	0.663983i
$50$		0			0
$51$		−	1.86173i		−	0.260694i
$52$	2.15588	−	2.89001i	0.298967	−	0.400773i
$53$	−2.67655	−	2.67655i	−0.367653	−	0.367653i	0.498968	−	0.866621i	$-0.333713\pi$
$53$	−2.67655	−	2.67655i	−0.367653	−	0.367653i	−0.866621	+	0.498968i	$0.833713\pi$
$54$	2.32258	+	8.66799i	0.316063	+	1.17956i
$55$		0			0
$56$	−1.10671	+	0.638961i	−0.147891	+	0.0853848i
$57$	10.1286			1.34156
$58$	−5.53601	+	3.19622i	−0.726913	+	0.419684i
$59$	0.288254	−	1.07578i	0.0375275	−	0.140054i	−0.944620	−	0.328165i	$-0.893570\pi$
$59$	0.288254	−	1.07578i	0.0375275	−	0.140054i	0.982148	+	0.188111i	$0.0602364\pi$
$60$		0			0
$61$	3.53771	+	6.12749i	0.452957	+	0.784545i	0.998568	−	0.0534935i	$-0.0170356\pi$
$61$	3.53771	+	6.12749i	0.452957	+	0.784545i	−0.545611	+	0.838039i	$0.683702\pi$
$62$	−9.97612	+	2.67309i	−1.26697	+	0.339483i
$63$	3.82898	−	6.63198i	0.482406	−	0.835551i
$64$	1.00000			0.125000
$65$		0			0
$66$	2.65156			0.326384
$67$	−1.29025	+	2.23477i	−0.157629	+	0.273021i	−0.934013	−	0.357239i	$-0.883718\pi$
$67$	−1.29025	+	2.23477i	−0.157629	+	0.273021i	0.776384	+	0.630260i	$0.217052\pi$
$68$	0.599680	−	0.160684i	0.0727219	−	0.0194858i
$69$	12.5301	+	21.7027i	1.50844	+	2.61270i
$70$		0			0
$71$	−1.80066	+	6.72017i	−0.213699	+	0.797537i	0.772921	+	0.634502i	$0.218795\pi$
$71$	−1.80066	+	6.72017i	−0.213699	+	0.797537i	−0.986620	+	0.163035i	$0.947872\pi$
$72$	−5.18966	+	2.99625i	−0.611607	+	0.353111i
$73$	−4.86934			−0.569913			−0.284957	−	0.958540i	$-0.591979\pi$
$73$	−4.86934			−0.569913			−0.284957	+	0.958540i	$0.591979\pi$
$74$	−7.93494	+	4.58124i	−0.922418	+	0.532558i
$75$		0			0
$76$	0.874187	+	3.26251i	0.100276	+	0.374236i
$77$	−0.799006	−	0.799006i	−0.0910552	−	0.0910552i
$78$	−10.6995	+	1.55668i	−1.21148	+	0.176259i
$79$		−	11.2172i		−	1.26203i	−0.775770	−	0.631015i	$-0.782638\pi$
$79$		−	11.2172i		−	1.26203i	0.775770	−	0.631015i	$-0.217362\pi$
$80$		0			0
$81$	4.46628	−	7.73583i	0.496253	−	0.859536i
$82$	2.24069	−	8.36236i	0.247443	−	0.923468i
$83$			1.75068i			0.192162i	0.995374	+	0.0960809i	$0.0306307\pi$
$83$			1.75068i			0.192162i	−0.995374	+	0.0960809i	$0.969369\pi$
$84$	3.70159	+	0.991839i	0.403877	+	0.108218i
$85$		0			0
$86$	1.44337	−	1.44337i	0.155643	−	0.155643i
$87$	18.5161	+	4.96138i	1.98514	+	0.531916i
$88$	0.228853	+	0.854091i	0.0243958	+	0.0910464i
$89$	6.08837	−	1.63137i	0.645366	−	0.172925i	0.0787333	−	0.996896i	$-0.474912\pi$
$89$	6.08837	−	1.63137i	0.645366	−	0.172925i	0.566633	+	0.823970i	$0.308246\pi$
$90$		0			0
$91$	3.69321	+	2.75505i	0.387154	+	0.288808i
$92$	−5.90920	+	5.90920i	−0.616076	+	0.616076i
$93$	26.8219	+	15.4856i	2.78130	+	1.60578i
$94$	−2.21587	−	1.27933i	−0.228549	−	0.131953i
$95$		0			0
$96$	−2.12044	−	2.12044i	−0.216416	−	0.216416i
$97$	−4.99081	−	8.64434i	−0.506740	−	0.877700i	−0.999970	−	0.00780033i	$-0.997517\pi$
$97$	−4.99081	−	8.64434i	−0.506740	−	0.877700i	0.493230	−	0.869899i	$-0.335816\pi$
$98$	2.68346	+	4.64788i	0.271070	+	0.469507i
$99$	−3.74674	−	3.74674i	−0.376562	−	0.376562i
$100$		0			0
$101$	0.911347	+	0.526166i	0.0906824	+	0.0523555i	0.544655	−	0.838660i	$-0.316660\pi$
$101$	0.911347	+	0.526166i	0.0906824	+	0.0523555i	−0.453973	+	0.891015i	$0.649994\pi$
$102$	−1.61230	−	0.930864i	−0.159642	−	0.0921693i
$103$	3.37370	−	3.37370i	0.332420	−	0.332420i	−0.521085	−	0.853505i	$-0.674472\pi$
$103$	3.37370	−	3.37370i	0.332420	−	0.332420i	0.853505	+	0.521085i	$0.174472\pi$
$104$	−1.42488	−	3.31205i	−0.139721	−	0.324774i
$105$		0			0
$106$	−3.65624	+	0.979686i	−0.355125	+	0.0951555i
$107$	−3.77105	−	14.0737i	−0.364561	−	1.36056i	−0.868015	−	0.496538i	$-0.834604\pi$
$107$	−3.77105	−	14.0737i	−0.364561	−	1.36056i	0.503454	−	0.864022i	$-0.332062\pi$
$108$	8.66799	+	2.32258i	0.834077	+	0.223490i
$109$	4.33526	−	4.33526i	0.415243	−	0.415243i	−0.468317	−	0.883560i	$-0.655140\pi$
$109$	4.33526	−	4.33526i	0.415243	−	0.415243i	0.883560	+	0.468317i	$0.155140\pi$
$110$		0			0
$111$	26.5398	+	7.11131i	2.51904	+	0.674976i
$112$			1.27792i			0.120752i
$113$	1.53983	−	5.74674i	0.144855	−	0.540608i	−0.854906	−	0.518782i	$-0.826386\pi$
$113$	1.53983	−	5.74674i	0.144855	−	0.540608i	0.999762	−	0.0218255i	$-0.00694783\pi$
$114$	5.06429	−	8.77160i	0.474314	−	0.821536i
$115$		0			0
$116$			6.39243i			0.593522i
$117$	17.3184	+	12.9191i	1.60109	+	1.19437i
$118$	−0.787525	−	0.787525i	−0.0724975	−	0.0724975i
$119$	0.205342	+	0.766345i	0.0188236	+	0.0702507i
$120$		0			0
$121$	8.84918	−	5.10908i	0.804471	−	0.464462i
$122$	7.07542			0.640578
$123$	−22.4831	+	12.9806i	−2.02723	+	1.17042i
$124$	−2.67309	+	9.97612i	−0.240051	+	0.895882i
$125$		0			0
$126$	−3.82898	−	6.63198i	−0.341112	−	0.590824i
$127$	−12.5862	+	3.37246i	−1.11684	+	0.299257i	−0.769606	−	0.638519i	$-0.779547\pi$
$127$	−12.5862	+	3.37246i	−1.11684	+	0.299257i	−0.347238	+	0.937777i	$0.612881\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−6.12117			−0.538939
$130$		0			0
$131$	−5.90639			−0.516044			−0.258022	−	0.966139i	$-0.583071\pi$
$131$	−5.90639			−0.516044			−0.258022	+	0.966139i	$0.583071\pi$
$132$	1.32578	−	2.29631i	0.115394	−	0.199869i
$133$	−4.16923	+	1.11714i	−0.361518	+	0.0968686i
$134$	1.29025	+	2.23477i	0.111460	+	0.193055i
$135$		0			0
$136$	0.160684	−	0.599680i	0.0137785	−	0.0514222i
$137$	10.6066	−	6.12370i	0.906179	−	0.523183i	0.0269793	−	0.999636i	$-0.491411\pi$
$137$	10.6066	−	6.12370i	0.906179	−	0.523183i	0.879200	+	0.476453i	$0.158078\pi$
$138$	25.0602			2.13326
$139$	0.835876	−	0.482593i	0.0708980	−	0.0409330i	−0.464132	−	0.885766i	$-0.653634\pi$
$139$	0.835876	−	0.482593i	0.0708980	−	0.0409330i	0.535030	+	0.844833i	$0.320300\pi$
$140$		0			0
$141$	1.98586	+	7.41135i	0.167240	+	0.624148i
$142$	4.91950	+	4.91950i	0.412836	+	0.412836i
$143$	2.50271	−	1.97495i	0.209287	−	0.165154i
$144$			5.99250i			0.499375i
$145$		0			0
$146$	−2.43467	+	4.21697i	−0.201495	+	0.348999i
$147$	4.16544	−	15.5456i	0.343560	−	1.28218i
$148$			9.16248i			0.753151i
$149$	−3.00429	−	0.804997i	−0.246121	−	0.0659480i	0.133649	−	0.991029i	$-0.457330\pi$
$149$	−3.00429	−	0.804997i	−0.246121	−	0.0659480i	−0.379771	+	0.925081i	$0.623997\pi$
$150$		0			0
$151$	−10.8684	+	10.8684i	−0.884459	+	0.884459i	−0.993984	−	0.109525i	$-0.965067\pi$
$151$	−10.8684	+	10.8684i	−0.884459	+	0.884459i	0.109525	+	0.993984i	$0.465067\pi$
$152$	3.26251	+	0.874187i	0.264624	+	0.0709059i
$153$	0.962898	+	3.59358i	0.0778457	+	0.290524i
$154$	−1.09146	+	0.292456i	−0.0879526	+	0.0235668i
$155$		0			0
$156$	−4.00163	+	10.0444i	−0.320387	+	0.804194i
$157$	−8.47200	+	8.47200i	−0.676139	+	0.676139i	−0.959124	−	0.282985i	$-0.908675\pi$
$157$	−8.47200	+	8.47200i	−0.676139	+	0.676139i	0.282985	+	0.959124i	$0.408675\pi$
$158$	−9.71436	−	5.60859i	−0.772833	−	0.446195i
$159$	9.83018	+	5.67546i	0.779584	+	0.450093i
$160$		0			0
$161$	−7.55150	−	7.55150i	−0.595141	−	0.595141i
$162$	−4.46628	−	7.73583i	−0.350904	−	0.607784i
$163$	10.3979	+	18.0097i	0.814426	+	1.41063i	0.909739	+	0.415180i	$0.136281\pi$
$163$	10.3979	+	18.0097i	0.814426	+	1.41063i	−0.0953137	+	0.995447i	$0.530385\pi$
$164$	−6.12167	−	6.12167i	−0.478022	−	0.478022i
$165$		0			0
$166$	1.51613	+	0.875338i	0.117675	+	0.0679394i
$167$	10.3056	+	5.94992i	0.797469	+	0.460419i	0.842585	−	0.538563i	$-0.181033\pi$
$167$	10.3056	+	5.94992i	0.797469	+	0.460419i	−0.0451166	+	0.998982i	$0.514366\pi$
$168$	2.70975	−	2.70975i	0.209062	−	0.209062i
$169$	−8.93941	+	9.43858i	−0.687647	+	0.726045i
$170$		0			0
$171$	−19.5506	+	5.23857i	−1.49507	+	0.400603i
$172$	−0.528312	−	1.97169i	−0.0402834	−	0.150340i
$173$	14.9230	+	3.99861i	1.13457	+	0.304008i	0.776768	−	0.629787i	$-0.216858\pi$
$173$	14.9230	+	3.99861i	1.13457	+	0.304008i	0.357807	+	0.933796i	$0.383525\pi$
$174$	13.5547	−	13.5547i	1.02758	−	1.02758i
$175$		0			0
$176$	0.854091	+	0.228853i	0.0643796	+	0.0172504i
$177$			3.33979i			0.251034i
$178$	1.63137	−	6.08837i	0.122277	−	0.456343i
$179$	−0.946097	+	1.63869i	−0.0707146	+	0.122481i	−0.899215	−	0.437508i	$-0.855861\pi$
$179$	−0.946097	+	1.63869i	−0.0707146	+	0.122481i	0.828500	+	0.559989i	$0.189195\pi$
$180$		0			0
$181$		−	20.4481i		−	1.51990i	−0.649983	−	0.759949i	$-0.725224\pi$
$181$		−	20.4481i		−	1.51990i	0.649983	−	0.759949i	$-0.274776\pi$
$182$	4.23255	−	1.82089i	0.313737	−	0.134973i
$183$	−15.0030	−	15.0030i	−1.10905	−	1.10905i
$184$	2.16292	+	8.07211i	0.159452	+	0.595084i
$185$		0			0
$186$	26.8219	−	15.4856i	1.96667	−	1.13546i
$187$	0.548955			0.0401436
$188$	−2.21587	+	1.27933i	−0.161609	+	0.0933048i
$189$	−2.96808	+	11.0770i	−0.215896	+	0.805734i
$190$		0			0
$191$	−10.1584	−	17.5949i	−0.735039	−	1.27312i	−0.954706	−	0.297550i	$-0.903830\pi$
$191$	−10.1584	−	17.5949i	−0.735039	−	1.27312i	0.219667	−	0.975575i	$-0.429503\pi$
$192$	−2.89657	+	0.776134i	−0.209042	+	0.0560126i
$193$	−1.09527	+	1.89706i	−0.0788392	+	0.136553i	−0.902749	−	0.430167i	$-0.858455\pi$
$193$	−1.09527	+	1.89706i	−0.0788392	+	0.136553i	0.823910	+	0.566720i	$0.191788\pi$
$194$	−9.98162			−0.716639
$195$		0			0
$196$	5.36691			0.383351
$197$	−0.759889	+	1.31617i	−0.0541398	+	0.0937729i	−0.891825	−	0.452380i	$-0.850575\pi$
$197$	−0.759889	+	1.31617i	−0.0541398	+	0.0937729i	0.837685	+	0.546153i	$0.183908\pi$
$198$	−5.11814	+	1.37140i	−0.363731	+	0.0974613i
$199$	3.00272	+	5.20086i	0.212857	+	0.368680i	0.952608	−	0.304202i	$-0.0983898\pi$
$199$	3.00272	+	5.20086i	0.212857	+	0.368680i	−0.739750	+	0.672881i	$0.765056\pi$
$200$		0			0
$201$	2.00281	−	7.47458i	0.141267	−	0.527216i
$202$	0.911347	−	0.526166i	0.0641221	−	0.0370209i
$203$	−8.16903			−0.573354
$204$	−1.61230	+	0.930864i	−0.112884	+	0.0651735i
$205$		0			0
$206$	−1.23486	−	4.60855i	−0.0860367	−	0.321093i
$207$	−35.4109	−	35.4109i	−2.46123	−	2.46123i
$208$	−3.58077	−	0.422042i	−0.248281	−	0.0292634i
$209$			2.98654i			0.206583i
$210$		0			0
$211$	−1.36327	+	2.36126i	−0.0938515	+	0.162556i	−0.909129	−	0.416515i	$-0.863251\pi$
$211$	−1.36327	+	2.36126i	−0.0938515	+	0.162556i	0.815277	+	0.579071i	$0.196585\pi$
$212$	−0.979686	+	3.65624i	−0.0672851	+	0.251111i
$213$		−	20.8630i		−	1.42951i
$214$	−14.0737	−	3.77105i	−0.962061	−	0.257784i
$215$		0			0
$216$	6.34541	−	6.34541i	0.431750	−	0.431750i
$217$	−12.7487	−	3.41601i	−0.865439	−	0.231894i
$218$	−1.58682	−	5.92208i	−0.107473	−	0.401094i
$219$	14.1044	−	3.77926i	0.953086	−	0.255379i
$220$		0			0
$221$	−2.21513	+	0.322281i	−0.149006	+	0.0216790i
$222$	19.4285	−	19.4285i	1.30395	−	1.30395i
$223$	−6.49152	−	3.74788i	−0.434704	−	0.250976i	0.266645	−	0.963795i	$-0.414085\pi$
$223$	−6.49152	−	3.74788i	−0.434704	−	0.250976i	−0.701349	+	0.712818i	$0.747418\pi$
$224$	1.10671	+	0.638961i	0.0739454	+	0.0426924i
$225$		0			0
$226$	−4.20691	−	4.20691i	−0.279839	−	0.279839i
$227$	6.65757	+	11.5313i	0.441879	+	0.765356i	0.997829	−	0.0658594i	$-0.0209789\pi$
$227$	6.65757	+	11.5313i	0.441879	+	0.765356i	−0.555950	+	0.831215i	$0.687646\pi$
$228$	−5.06429	−	8.77160i	−0.335391	−	0.580914i
$229$	2.64090	+	2.64090i	0.174516	+	0.174516i	0.788960	−	0.614445i	$-0.210620\pi$
$229$	2.64090	+	2.64090i	0.174516	+	0.174516i	−0.614445	+	0.788960i	$0.710620\pi$
$230$		0			0
$231$	2.93451	+	1.69424i	0.193077	+	0.111473i
$232$	5.53601	+	3.19622i	0.363457	+	0.209842i
$233$	9.50648	−	9.50648i	0.622790	−	0.622790i	−0.323454	−	0.946244i	$-0.604844\pi$
$233$	9.50648	−	9.50648i	0.622790	−	0.622790i	0.946244	+	0.323454i	$0.104844\pi$
$234$	19.8475	−	8.53861i	1.29747	−	0.558187i
$235$		0			0
$236$	−1.07578	+	0.288254i	−0.0700272	+	0.0187637i
$237$	8.70603	+	32.4913i	0.565517	+	2.11054i
$238$	0.766345	+	0.205342i	0.0496748	+	0.0133103i
$239$	−10.5033	+	10.5033i	−0.679400	+	0.679400i	−0.959864	−	0.280464i	$-0.909512\pi$
$239$	−10.5033	+	10.5033i	−0.679400	+	0.679400i	0.280464	+	0.959864i	$0.409512\pi$
$240$		0			0
$241$	1.48479	+	0.397848i	0.0956436	+	0.0256276i	0.306323	−	0.951927i	$-0.400901\pi$
$241$	1.48479	+	0.397848i	0.0956436	+	0.0256276i	−0.210680	+	0.977555i	$0.567568\pi$
$242$		−	10.2182i		−	0.656848i
$243$	0.0348797	−	0.130173i	0.00223753	−	0.00835059i
$244$	3.53771	−	6.12749i	0.226479	−	0.392273i
$245$		0			0
$246$			25.9612i			1.65523i
$247$	−1.75334	−	12.0512i	−0.111562	−	0.766801i
$248$	7.30303	+	7.30303i	0.463743	+	0.463743i
$249$	−1.35876	−	5.07096i	−0.0861078	−	0.321359i
$250$		0			0
$251$	−6.82870	+	3.94255i	−0.431024	+	0.248852i	−0.699783	−	0.714356i	$-0.746720\pi$
$251$	−6.82870	+	3.94255i	−0.431024	+	0.248852i	0.268759	+	0.963207i	$0.413386\pi$
$252$	−7.65795			−0.482406
$253$	−6.39933	+	3.69466i	−0.402323	+	0.232281i
$254$	−3.37246	+	12.5862i	−0.211607	+	0.789728i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	2.30049	−	0.616415i	0.143501	−	0.0384509i	−0.186354	−	0.982483i	$-0.559667\pi$
$257$	2.30049	−	0.616415i	0.143501	−	0.0384509i	0.329854	+	0.944032i	$0.393000\pi$
$258$	−3.06058	+	5.30109i	−0.190544	+	0.330031i
$259$	−11.7089			−0.727558
$260$		0			0
$261$	−38.3066			−2.37112
$262$	−2.95320	+	5.11508i	−0.182449	+	0.316011i
$263$	23.0654	−	6.18036i	1.42228	−	0.381098i	0.535985	−	0.844227i	$-0.319940\pi$
$263$	23.0654	−	6.18036i	1.42228	−	0.381098i	0.886290	+	0.463130i	$0.153274\pi$
$264$	−1.32578	−	2.29631i	−0.0815960	−	0.141328i
$265$		0			0
$266$	−1.11714	+	4.16923i	−0.0684964	+	0.255632i
$267$	−16.3692	+	9.45078i	−1.00178	+	0.578378i
$268$	2.58049			0.157629
$269$	26.8895	−	15.5247i	1.63948	−	0.946555i	0.658470	−	0.752607i	$-0.271204\pi$
$269$	26.8895	−	15.5247i	1.63948	−	0.946555i	0.981012	−	0.193949i	$-0.0621295\pi$
$270$		0			0
$271$	2.52048	+	9.40656i	0.153108	+	0.571408i	0.999260	+	0.0384657i	$0.0122470\pi$
$271$	2.52048	+	9.40656i	0.153108	+	0.571408i	−0.846152	+	0.532942i	$0.821086\pi$
$272$	−0.438997	−	0.438997i	−0.0266181	−	0.0266181i
$273$	−12.8359	−	5.11377i	−0.776866	−	0.309499i
$274$		−	12.2474i		−	0.739892i
$275$		0			0
$276$	12.5301	−	21.7027i	0.754222	−	1.30635i
$277$	−7.96424	+	29.7230i	−0.478525	+	1.78588i	0.129073	+	0.991635i	$0.458800\pi$
$277$	−7.96424	+	29.7230i	−0.478525	+	1.78588i	−0.607598	+	0.794245i	$0.707867\pi$
$278$		−	0.965186i		−	0.0578880i
$279$	−59.7819	−	16.0185i	−3.57905	−	0.959003i
$280$		0			0
$281$	−2.40508	+	2.40508i	−0.143475	+	0.143475i	−0.775196	−	0.631721i	$-0.782349\pi$
$281$	−2.40508	+	2.40508i	−0.143475	+	0.143475i	0.631721	+	0.775196i	$0.282349\pi$
$282$	7.41135	+	1.98586i	0.441339	+	0.118256i
$283$	3.58042	+	13.3623i	0.212834	+	0.794307i	0.986918	+	0.161224i	$0.0515441\pi$
$283$	3.58042	+	13.3623i	0.212834	+	0.794307i	−0.774084	+	0.633083i	$0.781789\pi$
$284$	6.72017	−	1.80066i	0.398769	−	0.106850i
$285$		0			0
$286$	−0.459007	−	3.15489i	−0.0271416	−	0.186552i
$287$	7.82302	−	7.82302i	0.461779	−	0.461779i
$288$	5.18966	+	2.99625i	0.305804	+	0.176556i
$289$	14.3886	+	8.30728i	0.846390	+	0.488664i
$290$		0			0
$291$	21.1654	+	21.1654i	1.24074	+	1.24074i
$292$	2.43467	+	4.21697i	0.142478	+	0.246780i
$293$	2.70877	+	4.69172i	0.158248	+	0.274093i	0.934237	−	0.356653i	$-0.116082\pi$
$293$	2.70877	+	4.69172i	0.158248	+	0.274093i	−0.775989	+	0.630746i	$0.782749\pi$
$294$	−11.3802	−	11.3802i	−0.663707	−	0.663707i
$295$		0			0
$296$	7.93494	+	4.58124i	0.461209	+	0.266279i
$297$	6.87172	+	3.96739i	0.398738	+	0.230211i
$298$	−2.19929	+	2.19929i	−0.127402	+	0.127402i
$299$	23.6534	−	18.6655i	1.36791	−	1.07945i
$300$		0			0
$301$	2.51966	−	0.675142i	0.145231	−	0.0389145i
$302$	3.97811	+	14.8465i	0.228915	+	0.854321i
$303$	−3.04815	−	0.816751i	−0.175112	−	0.0469211i
$304$	2.38832	−	2.38832i	0.136980	−	0.136980i
$305$		0			0
$306$	3.59358	+	0.962898i	0.205432	+	0.0550452i
$307$		−	1.34151i		−	0.0765638i	−0.999267	−	0.0382819i	$-0.987812\pi$
$307$		−	1.34151i		−	0.0765638i	0.999267	−	0.0382819i	$-0.0121885\pi$
$308$	−0.292456	+	1.09146i	−0.0166643	+	0.0621918i
$309$	−7.15371	+	12.3906i	−0.406960	+	0.704876i
$310$		0			0
$311$			2.71377i			0.153884i	0.997036	+	0.0769419i	$0.0245156\pi$
$311$			2.71377i			0.153884i	−0.997036	+	0.0769419i	$0.975484\pi$
$312$	6.69787	+	8.48770i	0.379192	+	0.480521i
$313$	3.27224	+	3.27224i	0.184958	+	0.184958i	0.793512	−	0.608554i	$-0.208250\pi$
$313$	3.27224	+	3.27224i	0.184958	+	0.184958i	−0.608554	+	0.793512i	$0.708250\pi$
$314$	3.10097	+	11.5730i	0.174998	+	0.653100i
$315$		0			0
$316$	−9.71436	+	5.60859i	−0.546475	+	0.315508i
$317$	−3.50975			−0.197127			−0.0985635	−	0.995131i	$-0.531425\pi$
$317$	−3.50975			−0.197127			−0.0985635	+	0.995131i	$0.531425\pi$
$318$	9.83018	−	5.67546i	0.551249	−	0.318264i
$319$	−1.46293	+	5.45972i	−0.0819082	+	0.305686i
$320$		0			0
$321$	21.8462	+	37.8387i	1.21934	+	2.11195i
$322$	−10.3155	+	2.76404i	−0.574862	+	0.154034i
$323$	1.04847	−	1.81600i	0.0583382	−	0.101045i
$324$	−8.93256			−0.496253
$325$		0			0
$326$	20.7958			1.15177
$327$	−9.19265	+	15.9221i	−0.508355	+	0.880496i
$328$	−8.36236	+	2.24069i	−0.461734	+	0.123721i
$329$	−1.63489	−	2.83171i	−0.0901342	−	0.156117i
$330$		0			0
$331$	2.17420	−	8.11424i	0.119505	−	0.445999i	−0.880079	−	0.474827i	$-0.842511\pi$
$331$	2.17420	−	8.11424i	0.119505	−	0.445999i	0.999584	+	0.0288278i	$0.00917745\pi$
$332$	1.51613	−	0.875338i	0.0832085	−	0.0480404i
$333$	−54.9062			−3.00884
$334$	10.3056	−	5.94992i	0.563895	−	0.325565i
$335$		0			0
$336$	−0.991839	−	3.70159i	−0.0541092	−	0.201938i
$337$	−6.40557	−	6.40557i	−0.348934	−	0.348934i	0.510779	−	0.859712i	$-0.329357\pi$
$337$	−6.40557	−	6.40557i	−0.348934	−	0.348934i	−0.859712	+	0.510779i	$0.829357\pi$
$338$	3.70435	+	12.4611i	0.201490	+	0.677792i
$339$			17.8410i			0.968988i
$340$		0			0
$341$	−4.56613	+	7.90877i	−0.247270	+	0.428284i
$342$	−5.23857	+	19.5506i	−0.283269	+	1.05717i
$343$			15.8040i			0.853334i
$344$	−1.97169	−	0.528312i	−0.106306	−	0.0284847i
$345$		0			0
$346$	10.9244	−	10.9244i	0.587299	−	0.587299i
$347$	18.2716	+	4.89586i	0.980871	+	0.262824i	0.713412	−	0.700745i	$-0.247149\pi$
$347$	18.2716	+	4.89586i	0.980871	+	0.262824i	0.267460	+	0.963569i	$0.413816\pi$
$348$	−4.96138	−	18.5161i	−0.265958	−	0.992568i
$349$	−21.6314	+	5.79612i	−1.15790	+	0.310259i	−0.786128	−	0.618064i	$-0.787917\pi$
$349$	−21.6314	+	5.79612i	−1.15790	+	0.310259i	−0.371775	+	0.928323i	$0.621251\pi$
$350$		0			0
$351$	−30.0578	−	11.9749i	−1.60437	−	0.639171i
$352$	0.625238	−	0.625238i	0.0333253	−	0.0333253i
$353$	−27.5457	−	15.9035i	−1.46611	−	0.846459i	−0.466828	−	0.884348i	$-0.654603\pi$
$353$	−27.5457	−	15.9035i	−1.46611	−	0.846459i	−0.999282	+	0.0378892i	$0.987937\pi$
$354$	2.89234	+	1.66990i	0.153726	+	0.0887540i
$355$		0			0
$356$	−4.45700	−	4.45700i	−0.236220	−	0.236220i
$357$	−1.18957	−	2.06040i	−0.0629588	−	0.109048i
$358$	0.946097	+	1.63869i	0.0500028	+	0.0866073i
$359$	8.54852	+	8.54852i	0.451173	+	0.451173i	0.895744	−	0.444570i	$-0.146644\pi$
$359$	8.54852	+	8.54852i	0.451173	+	0.451173i	−0.444570	+	0.895744i	$0.646644\pi$
$360$		0			0
$361$	−6.57472	−	3.79591i	−0.346038	−	0.199785i
$362$	−17.7086	−	10.2241i	−0.930743	−	0.537365i
$363$	−21.6669	+	21.6669i	−1.13722	+	1.13722i
$364$	0.539337	−	4.57594i	0.0282690	−	0.239844i
$365$		0			0
$366$	−20.4944	+	5.49147i	−1.07126	+	0.287044i
$367$	−0.788653	−	2.94329i	−0.0411674	−	0.153639i	0.942283	−	0.334819i	$-0.108675\pi$
$367$	−0.788653	−	2.94329i	−0.0411674	−	0.153639i	−0.983450	+	0.181180i	$0.942008\pi$
$368$	8.07211	+	2.16292i	0.420788	+	0.112750i
$369$	36.6841	−	36.6841i	1.90970	−	1.90970i
$370$		0			0
$371$	−4.67239	−	1.25196i	−0.242578	−	0.0649987i
$372$		−	30.9712i		−	1.60578i
$373$	−0.996016	+	3.71718i	−0.0515717	+	0.192468i	−0.986906	−	0.161297i	$-0.948432\pi$
$373$	−0.996016	+	3.71718i	−0.0515717	+	0.192468i	0.935334	+	0.353766i	$0.115099\pi$
$374$	0.274477	−	0.475409i	0.0141929	−	0.0245828i
$375$		0			0
$376$			2.55866i			0.131953i
$377$	2.69788	−	22.8898i	0.138948	−	1.17888i
$378$	8.10894	+	8.10894i	0.417079	+	0.417079i
$379$	−2.14311	−	7.99821i	−0.110084	−	0.410841i	0.888788	−	0.458319i	$-0.151548\pi$
$379$	−2.14311	−	7.99821i	−0.110084	−	0.410841i	−0.998872	+	0.0474782i	$0.984882\pi$
$380$		0			0
$381$	33.8393	−	19.5371i	1.73364	−	1.00092i
$382$	−20.3169			−1.03950
$383$	3.78044	−	2.18264i	0.193172	−	0.111528i	−0.400295	−	0.916386i	$-0.631092\pi$
$383$	3.78044	−	2.18264i	0.193172	−	0.111528i	0.593466	+	0.804859i	$0.297759\pi$
$384$	−0.776134	+	2.89657i	−0.0396069	+	0.147815i
$385$		0			0
$386$	1.09527	+	1.89706i	0.0557477	+	0.0965579i
$387$	11.8153	−	3.16591i	0.600607	−	0.160932i
$388$	−4.99081	+	8.64434i	−0.253370	+	0.438850i
$389$	5.85321			0.296770			0.148385	−	0.988930i	$-0.452593\pi$
$389$	5.85321			0.296770			0.148385	+	0.988930i	$0.452593\pi$
$390$		0			0
$391$	5.18823			0.262380
$392$	2.68346	−	4.64788i	0.135535	−	0.234754i
$393$	17.1083	−	4.58415i	0.862998	−	0.231240i
$394$	0.759889	+	1.31617i	0.0382826	+	0.0663075i
$395$		0			0
$396$	−1.37140	+	5.11814i	−0.0689156	+	0.257196i
$397$	−12.0807	+	6.97482i	−0.606315	+	0.350056i	−0.771522	−	0.636203i	$-0.780504\pi$
$397$	−12.0807	+	6.97482i	−0.606315	+	0.350056i	0.165207	+	0.986259i	$0.447171\pi$
$398$	6.00544			0.301026
$399$	11.2094	−	6.47177i	0.561173	−	0.323994i
$400$		0			0
$401$	−3.42776	−	12.7926i	−0.171174	−	0.638830i	−0.997172	−	0.0751566i	$-0.976054\pi$
$401$	−3.42776	−	12.7926i	−0.171174	−	0.638830i	0.825998	−	0.563673i	$-0.190612\pi$
$402$	−5.47177	−	5.47177i	−0.272907	−	0.272907i
$403$	13.7821	−	34.5940i	0.686534	−	1.72325i
$404$		−	1.05233i		−	0.0523555i
$405$		0			0
$406$	−4.08452	+	7.07459i	−0.202711	+	0.351106i
$407$	−2.09686	+	7.82560i	−0.103938	+	0.387900i
$408$			1.86173i			0.0921693i
$409$	25.0445	+	6.71066i	1.23837	+	0.331821i	0.817834	−	0.575454i	$-0.195175\pi$
$409$	25.0445	+	6.71066i	1.23837	+	0.331821i	0.420538	+	0.907275i	$0.361841\pi$
$410$		0			0
$411$	−25.9698	+	25.9698i	−1.28100	+	1.28100i
$412$	−4.60855	−	1.23486i	−0.227047	−	0.0608371i
$413$	−0.368366	−	1.37476i	−0.0181261	−	0.0676476i
$414$	−48.3722	+	12.9613i	−2.37736	+	0.637012i
$415$		0			0
$416$	−2.15588	+	2.89001i	−0.105701	+	0.141695i
$417$	−2.04662	+	2.04662i	−0.100223	+	0.100223i
$418$	2.58642	+	1.49327i	0.126506	+	0.0730383i
$419$	17.8637	+	10.3136i	0.872698	+	0.503852i	0.868244	−	0.496138i	$-0.165249\pi$
$419$	17.8637	+	10.3136i	0.872698	+	0.503852i	0.00445381	+	0.999990i	$0.498582\pi$
$420$		0			0
$421$	−21.3596	−	21.3596i	−1.04100	−	1.04100i	−0.999123	−	0.0418813i	$-0.986665\pi$
$421$	−21.3596	−	21.3596i	−1.04100	−	1.04100i	−0.0418813	−	0.999123i	$-0.513335\pi$
$422$	1.36327	+	2.36126i	0.0663630	+	0.114944i
$423$	−7.66639	−	13.2786i	−0.372753	−	0.645627i
$424$	2.67655	+	2.67655i	0.129985	+	0.129985i
$425$		0			0
$426$	−18.0679	−	10.4315i	−0.875392	−	0.505408i
$427$	7.83046	+	4.52092i	0.378943	+	0.218783i
$428$	−10.3027	+	10.3027i	−0.498000	+	0.498000i
$429$	−5.71644	+	7.66303i	−0.275992	+	0.369975i
$430$		0			0
$431$	34.1885	−	9.16078i	1.64680	−	0.441259i	0.688087	−	0.725628i	$-0.258451\pi$
$431$	34.1885	−	9.16078i	1.64680	−	0.441259i	0.958715	+	0.284369i	$0.0917839\pi$
$432$	−2.32258	−	8.66799i	−0.111745	−	0.417039i
$433$	−28.8432	−	7.72850i	−1.38611	−	0.371408i	−0.512776	−	0.858523i	$-0.671383\pi$
$433$	−28.8432	−	7.72850i	−1.38611	−	0.371408i	−0.873338	+	0.487114i	$0.838049\pi$
$434$	−9.33270	+	9.33270i	−0.447984	+	0.447984i
$435$		0			0
$436$	−5.92208	−	1.58682i	−0.283616	−	0.0759947i
$437$			28.2261i			1.35024i
$438$	3.77926	−	14.1044i	0.180580	−	0.673934i
$439$	−8.00470	+	13.8645i	−0.382043	+	0.661718i	−0.991354	−	0.131213i	$-0.958113\pi$
$439$	−8.00470	+	13.8645i	−0.382043	+	0.661718i	0.609311	+	0.792931i	$0.291446\pi$
$440$		0			0
$441$			32.1612i			1.53149i
$442$	−0.828462	+	2.07950i	−0.0394059	+	0.0989117i
$443$	−21.6681	−	21.6681i	−1.02948	−	1.02948i	−0.999552	−	0.0299327i	$-0.990471\pi$
$443$	−21.6681	−	21.6681i	−1.02948	−	1.02948i	−0.0299327	−	0.999552i	$-0.509529\pi$
$444$	−7.11131	−	26.5398i	−0.337488	−	1.25952i
$445$		0			0
$446$	−6.49152	+	3.74788i	−0.307382	+	0.177467i
$447$	9.32692			0.441148
$448$	1.10671	−	0.638961i	0.0522873	−	0.0301881i
$449$	2.31771	−	8.64982i	0.109380	−	0.408210i	−0.889426	−	0.457080i	$-0.848895\pi$
$449$	2.31771	−	8.64982i	0.109380	−	0.408210i	0.998805	+	0.0488699i	$0.0155620\pi$
$450$		0			0
$451$	−3.82750	−	6.62943i	−0.180230	−	0.312168i
$452$	−5.74674	+	1.53983i	−0.270304	+	0.0724277i
$453$	23.0458	−	39.9164i	1.08278	−	1.87544i
$454$	13.3151			0.624911
$455$		0			0
$456$	−10.1286			−0.474314
$457$	12.2784	−	21.2668i	0.574360	−	0.994820i	−0.421751	−	0.906712i	$-0.638584\pi$
$457$	12.2784	−	21.2668i	0.574360	−	0.994820i	0.996111	−	0.0881087i	$-0.0280823\pi$
$458$	3.60754	−	0.966636i	0.168569	−	0.0451679i
$459$	−2.78561	−	4.82482i	−0.130021	−	0.225203i
$460$		0			0
$461$	−2.58880	+	9.66155i	−0.120573	+	0.449983i	−0.999643	−	0.0267083i	$-0.991497\pi$
$461$	−2.58880	+	9.66155i	−0.120573	+	0.449983i	0.879071	+	0.476692i	$0.158164\pi$
$462$	2.93451	−	1.69424i	0.136526	−	0.0788232i
$463$	27.8834			1.29585			0.647926	−	0.761703i	$-0.275636\pi$
$463$	27.8834			1.29585			0.647926	+	0.761703i	$0.275636\pi$
$464$	5.53601	−	3.19622i	0.257003	−	0.148381i
$465$		0			0
$466$	−3.47961	−	12.9861i	−0.161190	−	0.601569i
$467$	22.3548	+	22.3548i	1.03446	+	1.03446i	0.999385	+	0.0350738i	$0.0111666\pi$
$467$	22.3548	+	22.3548i	1.03446	+	1.03446i	0.0350738	+	0.999385i	$0.488833\pi$
$468$	2.52909	−	21.4577i	0.116907	−	0.991884i
$469$			3.29767i			0.152272i
$470$		0			0
$471$	17.9643	−	31.1151i	0.827752	−	1.43371i
$472$	−0.288254	+	1.07578i	−0.0132680	+	0.0495167i
$473$		−	1.80491i		−	0.0829897i
$474$	32.4913	+	8.70603i	1.49238	+	0.399881i
$475$		0			0
$476$	0.561003	−	0.561003i	0.0257136	−	0.0257136i
$477$	−21.9100	−	5.87077i	−1.00319	−	0.268804i
$478$	3.84446	+	14.3477i	0.175842	+	0.656250i
$479$	−2.16670	+	0.580565i	−0.0989990	+	0.0265267i	−0.307978	−	0.951393i	$-0.599652\pi$
$479$	−2.16670	+	0.580565i	−0.0989990	+	0.0265267i	0.208979	+	0.977920i	$0.432986\pi$
$480$		0			0
$481$	3.86695	−	32.8087i	0.176318	−	1.49595i
$482$	1.08694	−	1.08694i	0.0495088	−	0.0495088i
$483$	27.7344	+	16.0125i	1.26196	+	0.728593i
$484$	−8.84918	−	5.10908i	−0.402236	−	0.232231i
$485$		0			0
$486$	−0.0952932	−	0.0952932i	−0.00432259	−	0.00432259i
$487$	−11.5045	−	19.9264i	−0.521319	−	0.902951i	−0.999693	−	0.0247947i	$-0.992107\pi$
$487$	−11.5045	−	19.9264i	−0.521319	−	0.902951i	0.478373	−	0.878157i	$-0.341227\pi$
$488$	−3.53771	−	6.12749i	−0.160145	−	0.277379i
$489$	−44.0961	−	44.0961i	−1.99410	−	1.99410i
$490$		0			0
$491$	−2.22242	−	1.28311i	−0.100296	−	0.0579061i	0.449013	−	0.893525i	$-0.351776\pi$
$491$	−2.22242	−	1.28311i	−0.100296	−	0.0579061i	−0.549309	+	0.835619i	$0.685109\pi$
$492$	22.4831	+	12.9806i	1.01362	+	0.585211i
$493$	2.80625	−	2.80625i	0.126387	−	0.126387i
$494$	−11.3133	−	4.50718i	−0.509011	−	0.202787i
$495$		0			0
$496$	9.97612	−	2.67309i	0.447941	−	0.120025i
$497$	2.30111	+	8.58785i	0.103219	+	0.385218i
$498$	−5.07096	−	1.35876i	−0.227235	−	0.0608874i
$499$	6.70967	−	6.70967i	0.300366	−	0.300366i	−0.540791	−	0.841157i	$-0.681875\pi$
$499$	6.70967	−	6.70967i	0.300366	−	0.300366i	0.841157	+	0.540791i	$0.181875\pi$
$500$		0			0
$501$	−34.4687	−	9.23587i	−1.53995	−	0.412628i
$502$			7.88510i			0.351929i
$503$	−2.94883	+	11.0052i	−0.131482	+	0.490697i	−0.999988	−	0.00498191i	$-0.998414\pi$
$503$	−2.94883	+	11.0052i	−0.131482	+	0.490697i	0.868506	+	0.495679i	$0.165081\pi$
$504$	−3.82898	+	6.63198i	−0.170556	+	0.295412i
$505$		0			0
$506$			7.38931i			0.328495i
$507$	18.5680	−	34.2777i	0.824636	−	1.52233i
$508$	9.21373	+	9.21373i	0.408793	+	0.408793i
$509$	−10.3486	−	38.6216i	−0.458695	−	1.71187i	−0.676991	−	0.735991i	$-0.736716\pi$
$509$	−10.3486	−	38.6216i	−0.458695	−	1.71187i	0.218296	−	0.975883i	$-0.429950\pi$
$510$		0			0
$511$	−5.38896	+	3.11132i	−0.238394	+	0.137637i
$512$	−1.00000			−0.0441942
$513$	26.2490	−	15.1549i	1.15892	−	0.669104i
$514$	0.616415	−	2.30049i	0.0271889	−	0.101470i
$515$		0			0
$516$	3.06058	+	5.30109i	0.134735	+	0.233367i
$517$	−2.18533	+	0.585558i	−0.0961108	+	0.0257528i
$518$	−5.85447	+	10.1402i	−0.257231	+	0.445537i
$519$	−46.3290			−2.03362
$520$		0			0
$521$	20.3944			0.893494			0.446747	−	0.894660i	$-0.352582\pi$
$521$	20.3944			0.893494			0.446747	+	0.894660i	$0.352582\pi$
$522$	−19.1533	+	33.1745i	−0.838318	+	1.45201i
$523$	−24.8222	+	6.65109i	−1.08540	+	0.290832i	−0.756806	−	0.653640i	$-0.773241\pi$
$523$	−24.8222	+	6.65109i	−1.08540	+	0.290832i	−0.328593	+	0.944472i	$0.606574\pi$
$524$	2.95320	+	5.11508i	0.129011	+	0.223453i
$525$		0			0
$526$	6.18036	−	23.0654i	0.269477	−	1.00570i
$527$	5.55296	−	3.20600i	0.241891	−	0.139656i
$528$	−2.65156			−0.115394
$529$	−40.5622	+	23.4186i	−1.76358	+	1.01820i
$530$		0			0
$531$	−1.72736	−	6.44660i	−0.0749611	−	0.279759i
$532$	3.05209	+	3.05209i	0.132325	+	0.132325i
$533$	19.3367	+	24.5039i	0.837564	+	1.06138i
$534$			18.9016i			0.817951i
$535$		0			0
$536$	1.29025	−	2.23477i	0.0557302	−	0.0965275i
$537$	1.46859	−	5.48087i	0.0633746	−	0.236517i
$538$		−	31.0493i		−	1.33863i
$539$	4.58383	+	1.22823i	0.197440	+	0.0529038i
$540$		0			0
$541$	−19.8508	+	19.8508i	−0.853451	+	0.853451i	−0.990557	−	0.137105i	$-0.956220\pi$
$541$	−19.8508	+	19.8508i	−0.853451	+	0.853451i	0.137105	+	0.990557i	$0.456220\pi$
$542$	9.40656	+	2.52048i	0.404046	+	0.108264i
$543$	15.8705	+	59.2294i	0.681067	+	2.54178i
$544$	−0.599680	+	0.160684i	−0.0257111	+	0.00688926i
$545$		0			0
$546$	−10.8466	+	8.55936i	−0.464193	+	0.366307i
$547$	22.0342	−	22.0342i	0.942115	−	0.942115i	−0.0562990	−	0.998414i	$-0.517930\pi$
$547$	22.0342	−	22.0342i	0.942115	−	0.942115i	0.998414	+	0.0562990i	$0.0179300\pi$
$548$	−10.6066	−	6.12370i	−0.453090	−	0.261591i
$549$	36.7190	+	21.1997i	1.56713	+	0.904782i
$550$		0			0
$551$	15.2672	+	15.2672i	0.650404	+	0.650404i
$552$	−12.5301	−	21.7027i	−0.533316	−	0.923730i
$553$	−7.16734	−	12.4142i	−0.304786	−	0.527905i
$554$	21.7587	+	21.7587i	0.924439	+	0.924439i
$555$		0			0
$556$	−0.835876	−	0.482593i	−0.0354490	−	0.0204665i
$557$	−24.7384	−	14.2827i	−1.04820	−	0.605179i	−0.126055	−	0.992023i	$-0.540232\pi$
$557$	−24.7384	−	14.2827i	−1.04820	−	0.605179i	−0.922145	+	0.386844i	$0.873565\pi$
$558$	−43.7634	+	43.7634i	−1.85265	+	1.85265i
$559$	1.05963	+	7.28312i	0.0448174	+	0.308043i
$560$		0			0
$561$	−1.59009	+	0.426062i	−0.0671335	+	0.0179884i
$562$	0.880320	+	3.28540i	0.0371340	+	0.138586i
$563$	−1.87859	−	0.503366i	−0.0791731	−	0.0212144i	0.219015	−	0.975721i	$-0.429716\pi$
$563$	−1.87859	−	0.503366i	−0.0791731	−	0.0212144i	−0.298188	+	0.954507i	$0.596382\pi$
$564$	5.42548	−	5.42548i	0.228454	−	0.228454i
$565$		0			0
$566$	13.3623	+	3.58042i	0.561660	+	0.150496i
$567$		−	11.4151i		−	0.479390i
$568$	1.80066	−	6.72017i	0.0755542	−	0.281972i
$569$	−13.6532	+	23.6481i	−0.572372	+	0.991378i	0.423949	+	0.905686i	$0.360643\pi$
$569$	−13.6532	+	23.6481i	−0.572372	+	0.991378i	−0.996322	+	0.0856922i	$0.972690\pi$
$570$		0			0
$571$			34.7539i			1.45441i	0.686423	+	0.727203i	$0.259180\pi$
$571$			34.7539i			1.45441i	−0.686423	+	0.727203i	$0.740820\pi$
$572$	−2.96171	−	1.17993i	−0.123836	−	0.0493354i
$573$	43.0807	+	43.0807i	1.79972	+	1.79972i
$574$	−2.86343	−	10.6864i	−0.119517	−	0.446044i
$575$		0			0
$576$	5.18966	−	2.99625i	0.216236	−	0.124844i
$577$	22.1256			0.921103			0.460551	−	0.887633i	$-0.347652\pi$
$577$	22.1256			0.921103			0.460551	+	0.887633i	$0.347652\pi$
$578$	14.3886	−	8.30728i	0.598488	−	0.345537i
$579$	1.70015	−	6.34504i	0.0706558	−	0.263691i
$580$		0			0
$581$	1.11861	+	1.93750i	0.0464079	+	0.0803809i
$582$	28.9125	−	7.74707i	1.19846	−	0.321126i
$583$	−1.67348	+	2.89856i	−0.0693086	+	0.120046i
$584$	4.86934			0.201495
$585$		0			0
$586$	5.41754			0.223796
$587$	−16.6364	+	28.8151i	−0.686657	+	1.18932i	0.286256	+	0.958153i	$0.407589\pi$
$587$	−16.6364	+	28.8151i	−0.686657	+	1.18932i	−0.972913	+	0.231172i	$0.925744\pi$
$588$	−15.5456	+	4.16544i	−0.641091	+	0.171780i
$589$	17.4420	+	30.2104i	0.718685	+	1.24480i
$590$		0			0
$591$	1.17955	−	4.40214i	0.0485202	−	0.181080i
$592$	7.93494	−	4.58124i	0.326124	−	0.188288i
$593$	−1.18487			−0.0486567			−0.0243283	−	0.999704i	$-0.507745\pi$
$593$	−1.18487			−0.0486567			−0.0243283	+	0.999704i	$0.507745\pi$
$594$	6.87172	−	3.96739i	0.281950	−	0.162784i
$595$		0			0
$596$	0.804997	+	3.00429i	0.0329740	+	0.123061i
$597$	−12.7342	−	12.7342i	−0.521174	−	0.521174i
$598$	−4.33812	−	29.8172i	−0.177399	−	1.21932i
$599$		−	0.947362i		−	0.0387082i	−0.999813	−	0.0193541i	$-0.993839\pi$
$599$		−	0.947362i		−	0.0387082i	0.999813	−	0.0193541i	$-0.00616098\pi$
$600$		0			0
$601$	9.46190	−	16.3885i	0.385959	−	0.668500i	−0.605943	−	0.795508i	$-0.707204\pi$
$601$	9.46190	−	16.3885i	0.385959	−	0.668500i	0.991902	+	0.127008i	$0.0405373\pi$
$602$	0.675142	−	2.51966i	0.0275167	−	0.102694i
$603$			15.4636i			0.629727i
$604$	14.8465	+	3.97811i	0.604096	+	0.161867i
$605$		0			0
$606$	−2.23140	+	2.23140i	−0.0906446	+	0.0906446i
$607$	18.7294	+	5.01853i	0.760204	+	0.203696i	0.618039	−	0.786147i	$-0.287927\pi$
$607$	18.7294	+	5.01853i	0.760204	+	0.203696i	0.142164	+	0.989843i	$0.454594\pi$
$608$	−0.874187	−	3.26251i	−0.0354530	−	0.132312i
$609$	23.6622	−	6.34026i	0.958839	−	0.256920i
$610$		0			0
$611$	8.47443	−	3.64580i	0.342839	−	0.147493i
$612$	2.63069	−	2.63069i	0.106339	−	0.106339i
$613$	5.86909	+	3.38852i	0.237050	+	0.136861i	0.613820	−	0.789446i	$-0.289632\pi$
$613$	5.86909	+	3.38852i	0.237050	+	0.136861i	−0.376770	+	0.926307i	$0.622965\pi$
$614$	−1.16178	−	0.670753i	−0.0468856	−	0.0270694i
$615$		0			0
$616$	0.799006	+	0.799006i	0.0321929	+	0.0321929i
$617$	−4.57750	−	7.92846i	−0.184283	−	0.319188i	0.759052	−	0.651030i	$-0.225663\pi$
$617$	−4.57750	−	7.92846i	−0.184283	−	0.319188i	−0.943335	+	0.331843i	$0.892330\pi$
$618$	7.15371	+	12.3906i	0.287764	+	0.498422i
$619$	−5.10375	−	5.10375i	−0.205137	−	0.205137i	0.597060	−	0.802197i	$-0.296336\pi$
$619$	−5.10375	−	5.10375i	−0.205137	−	0.205137i	−0.802197	+	0.597060i	$0.796336\pi$
$620$		0			0
$621$	64.9454	+	37.4963i	2.60617	+	1.50467i
$622$	2.35019	+	1.35688i	0.0942341	+	0.0544061i
$623$	5.69570	−	5.69570i	0.228193	−	0.228193i
$624$	10.6995	−	1.55668i	0.428323	−	0.0623170i
$625$		0			0
$626$	4.46996	−	1.19772i	0.178656	−	0.0478706i
$627$	−2.31796	−	8.65073i	−0.0925702	−	0.345477i
$628$	11.5730	+	3.10097i	0.461811	+	0.123742i
$629$	4.02230	−	4.02230i	0.160380	−	0.160380i
$630$		0			0
$631$	9.61001	+	2.57499i	0.382568	+	0.102509i	0.444978	−	0.895542i	$-0.353212\pi$
$631$	9.61001	+	2.57499i	0.382568	+	0.102509i	−0.0624090	+	0.998051i	$0.519878\pi$
$632$			11.2172i			0.446195i
$633$	2.11616	−	7.89762i	0.0841099	−	0.313902i
$634$	−1.75487	+	3.03953i	−0.0696949	+	0.120715i
$635$		0			0
$636$		−	11.3509i		−	0.450093i
$637$	−19.2177	−	2.26506i	−0.761431	−	0.0897451i
$638$	3.99679	+	3.99679i	0.158234	+	0.158234i
$639$	10.7905	+	40.2706i	0.426865	+	1.59308i
$640$		0			0
$641$	−7.80132	+	4.50409i	−0.308134	+	0.177901i	−0.646091	−	0.763260i	$-0.723597\pi$
$641$	−7.80132	+	4.50409i	−0.308134	+	0.177901i	0.337957	+	0.941161i	$0.390264\pi$
$642$	43.6924			1.72440
$643$	3.34673	−	1.93223i	0.131982	−	0.0761998i	−0.432555	−	0.901607i	$-0.642388\pi$
$643$	3.34673	−	1.93223i	0.131982	−	0.0761998i	0.564537	+	0.825408i	$0.309055\pi$
$644$	−2.76404	+	10.3155i	−0.108918	+	0.406489i
$645$		0			0
$646$	−1.04847	−	1.81600i	−0.0412513	−	0.0714494i
$647$	−2.16676	+	0.580581i	−0.0851841	+	0.0228250i	−0.301159	−	0.953574i	$-0.597374\pi$
$647$	−2.16676	+	0.580581i	−0.0851841	+	0.0228250i	0.215975	+	0.976399i	$0.430707\pi$
$648$	−4.46628	+	7.73583i	−0.175452	+	0.303892i
$649$	−0.984781			−0.0386560
$650$		0			0
$651$	39.5788			1.55122
$652$	10.3979	−	18.0097i	0.407213	−	0.705313i
$653$	21.0761	−	5.64733i	0.824773	−	0.220997i	0.178341	−	0.983969i	$-0.442927\pi$
$653$	21.0761	−	5.64733i	0.824773	−	0.220997i	0.646432	+	0.762972i	$0.276260\pi$
$654$	9.19265	+	15.9221i	0.359461	+	0.622605i
$655$		0			0
$656$	−2.24069	+	8.36236i	−0.0874842	+	0.326495i
$657$	−25.2702	+	14.5898i	−0.985885	+	0.569201i
$658$	−3.26977			−0.127469
$659$	39.1338	−	22.5939i	1.52444	−	0.880134i	0.524856	−	0.851191i	$-0.324119\pi$
$659$	39.1338	−	22.5939i	1.52444	−	0.880134i	0.999581	−	0.0289434i	$-0.00921424\pi$
$660$		0			0
$661$	−0.707218	−	2.63937i	−0.0275076	−	0.102660i	0.950807	−	0.309783i	$-0.100256\pi$
$661$	−0.707218	−	2.63937i	−0.0275076	−	0.102660i	−0.978315	+	0.207123i	$0.933590\pi$
$662$	−5.94003	−	5.94003i	−0.230866	−	0.230866i
$663$	6.16615	−	2.65275i	0.239473	−	0.103024i
$664$		−	1.75068i		−	0.0679394i
$665$		0			0
$666$	−27.4531	+	47.5501i	−1.06379	+	1.84253i
$667$	−13.8263	+	51.6004i	−0.535356	+	1.99798i
$668$		−	11.8998i		−	0.460419i
$669$	21.7120	+	5.81771i	0.839434	+	0.224926i
$670$		0			0
$671$	4.42382	−	4.42382i	0.170780	−	0.170780i
$672$	−3.70159	−	0.991839i	−0.142792	−	0.0382610i
$673$	12.0264	+	44.8831i	0.463583	+	1.73012i	0.661544	+	0.749906i	$0.269901\pi$
$673$	12.0264	+	44.8831i	0.463583	+	1.73012i	−0.197961	+	0.980210i	$0.563432\pi$
$674$	−8.75017	+	2.34460i	−0.337044	+	0.0903107i
$675$		0			0
$676$	12.6438	+	3.02247i	0.486298	+	0.116249i
$677$	19.7486	−	19.7486i	0.758999	−	0.758999i	−0.217141	−	0.976140i	$-0.569673\pi$
$677$	19.7486	−	19.7486i	0.758999	−	0.758999i	0.976140	+	0.217141i	$0.0696732\pi$
$678$	15.4507	+	8.92048i	0.593381	+	0.342589i
$679$	−11.0468	−	6.37787i	−0.423937	−	0.244760i
$680$		0			0
$681$	−28.2339	−	28.2339i	−1.08193	−	1.08193i
$682$	4.56613	+	7.90877i	0.174846	+	0.302843i
$683$	−4.76460	−	8.25253i	−0.182312	−	0.315774i	0.760355	−	0.649508i	$-0.225025\pi$
$683$	−4.76460	−	8.25253i	−0.182312	−	0.315774i	−0.942668	+	0.333733i	$0.891692\pi$
$684$	14.3120	+	14.3120i	0.547234	+	0.547234i
$685$		0			0
$686$	13.6866	+	7.90198i	0.522558	+	0.301699i
$687$	−9.69924	−	5.59986i	−0.370049	−	0.213648i
$688$	−1.44337	+	1.44337i	−0.0550281	+	0.0550281i
$689$	5.05111	−	12.6787i	0.192432	−	0.483019i
$690$		0			0
$691$	0.594540	−	0.159306i	0.0226174	−	0.00606030i	−0.247493	−	0.968890i	$-0.579607\pi$
$691$	0.594540	−	0.159306i	0.0226174	−	0.00606030i	0.270110	+	0.962829i	$0.412940\pi$
$692$	−3.99861	−	14.9230i	−0.152004	−	0.567287i
$693$	−6.54059	−	1.75255i	−0.248456	−	0.0665737i
$694$	13.3757	−	13.3757i	0.507736	−	0.507736i
$695$		0			0
$696$	−18.5161	−	4.96138i	−0.701852	−	0.188061i
$697$			5.37479i			0.203585i
$698$	−5.79612	+	21.6314i	−0.219386	+	0.818761i
$699$	−20.1579	+	34.9145i	−0.762441	+	1.32059i
$700$		0			0
$701$		−	18.0552i		−	0.681935i	−0.940075	−	0.340968i	$-0.889245\pi$
$701$		−	18.0552i		−	0.681935i	0.940075	−	0.340968i	$-0.110755\pi$
$702$	−25.3994	+	20.0434i	−0.958640	+	0.756489i
$703$	21.8830	+	21.8830i	0.825332	+	0.825332i
$704$	−0.228853	−	0.854091i	−0.00862522	−	0.0321898i
$705$		0			0
$706$	−27.5457	+	15.9035i	−1.03670	+	0.598537i
$707$	1.34480			0.0505764
$708$	2.89234	−	1.66990i	0.108701	−	0.0627585i
$709$	5.22810	−	19.5115i	0.196345	−	0.732771i	−0.795569	−	0.605863i	$-0.792828\pi$
$709$	5.22810	−	19.5115i	0.196345	−	0.732771i	0.991914	−	0.126908i	$-0.0405053\pi$
$710$		0			0
$711$	−33.6095	−	58.2133i	−1.26045	−	2.18317i
$712$	−6.08837	+	1.63137i	−0.228171	+	0.0611384i
$713$	−43.1550	+	74.7467i	−1.61617	+	2.79929i
$714$	−2.37914			−0.0890372
$715$		0			0
$716$	1.89219			0.0707146
$717$	22.2715	−	38.5754i	0.831745	−	1.44062i
$718$	11.6775	−	3.12897i	0.435800	−	0.116772i
$719$	−8.30123	−	14.3782i	−0.309584	−	0.536215i	0.668688	−	0.743543i	$-0.266856\pi$
$719$	−8.30123	−	14.3782i	−0.309584	−	0.536215i	−0.978271	+	0.207329i	$0.933523\pi$
$720$		0			0
$721$	1.57805	−	5.88938i	0.0587698	−	0.219332i
$722$	−6.57472	+	3.79591i	−0.244686	+	0.141269i
$723$	−4.60957			−0.171432
$724$	−17.7086	+	10.2241i	−0.658135	+	0.379974i
$725$		0			0
$726$	7.93065	+	29.5976i	0.294334	+	1.09847i
$727$	3.52264	+	3.52264i	0.130648	+	0.130648i	0.769407	−	0.638759i	$-0.220552\pi$
$727$	3.52264	+	3.52264i	0.130648	+	0.130648i	−0.638759	+	0.769407i	$0.720552\pi$
$728$	−3.69321	−	2.75505i	−0.136880	−	0.102109i
$729$			27.2018i			1.00747i
$730$		0			0
$731$	−0.633636	+	1.09749i	−0.0234359	+	0.0405922i
$732$	−5.49147	+	20.4944i	−0.202971	+	0.757497i
$733$		−	9.74855i		−	0.360071i	−0.983660	−	0.180035i	$-0.942379\pi$
$733$		−	9.74855i		−	0.360071i	0.983660	−	0.180035i	$-0.0576213\pi$
$734$	−2.94329	−	0.788653i	−0.108639	−	0.0291097i
$735$		0			0
$736$	5.90920	−	5.90920i	0.217816	−	0.217816i
$737$	2.20398	+	0.590554i	0.0811845	+	0.0217533i
$738$	−13.4273	−	50.1115i	−0.494267	−	1.84463i
$739$	−9.31015	+	2.49465i	−0.342479	+	0.0917670i	−0.425959	−	0.904742i	$-0.640063\pi$
$739$	−9.31015	+	2.49465i	−0.342479	+	0.0917670i	0.0834798	+	0.996509i	$0.473397\pi$
$740$		0			0
$741$	14.4320	+	33.5464i	0.530174	+	1.23236i
$742$	−3.42043	+	3.42043i	−0.125568	+	0.125568i
$743$	−46.5667	−	26.8853i	−1.70837	−	0.986326i	−0.936586	−	0.350439i	$-0.886032\pi$
$743$	−46.5667	−	26.8853i	−1.70837	−	0.986326i	−0.771782	−	0.635888i	$-0.780634\pi$
$744$	−26.8219	−	15.4856i	−0.983337	−	0.567730i
$745$		0			0
$746$	2.72117	+	2.72117i	0.0996290	+	0.0996290i
$747$	5.24547	+	9.08541i	0.191922	+	0.332418i
$748$	−0.274477	−	0.475409i	−0.0100359	−	0.0173827i
$749$	−13.1660	−	13.1660i	−0.481077	−	0.481077i
$750$		0			0
$751$	18.9911	+	10.9645i	0.692994	+	0.400100i	0.804733	−	0.593637i	$-0.202309\pi$
$751$	18.9911	+	10.9645i	0.692994	+	0.400100i	−0.111739	+	0.993738i	$0.535642\pi$
$752$	2.21587	+	1.27933i	0.0808043	+	0.0466524i
$753$	16.7199	−	16.7199i	0.609305	−	0.609305i
$754$	−18.4742	−	13.7813i	−0.672791	−	0.501886i
$755$		0			0
$756$	11.0770	−	2.96808i	0.402867	−	0.107948i
$757$	−12.6177	−	47.0899i	−0.458598	−	1.71151i	−0.677290	−	0.735716i	$-0.736846\pi$
$757$	−12.6177	−	47.0899i	−0.458598	−	1.71151i	0.218692	−	0.975794i	$-0.429821\pi$
$758$	−7.99821	−	2.14311i	−0.290508	−	0.0778414i
$759$	15.6686	−	15.6686i	0.568733	−	0.568733i
$760$		0			0
$761$	41.5088	+	11.1222i	1.50469	+	0.403181i	0.914668	−	0.404206i	$-0.132452\pi$
$761$	41.5088	+	11.1222i	1.50469	+	0.403181i	0.590023	+	0.807386i	$0.299119\pi$
$762$		−	39.0743i		−	1.41551i
$763$	2.02783	−	7.56796i	0.0734123	−	0.273978i
$764$	−10.1584	+	17.5949i	−0.367520	+	0.636562i
$765$		0			0
$766$		−	4.36528i		−	0.157724i
$767$	3.97377	−	0.578146i	0.143484	−	0.0208756i
$768$	2.12044	+	2.12044i	0.0765147	+	0.0765147i
$769$	8.98900	+	33.5474i	0.324152	+	1.20975i	0.915162	+	0.403087i	$0.132063\pi$
$769$	8.98900	+	33.5474i	0.324152	+	1.20975i	−0.591010	+	0.806664i	$0.701271\pi$
$770$		0			0
$771$	−6.18511	+	3.57098i	−0.222751	+	0.128606i
$772$	2.19054			0.0788392
$773$	17.9285	−	10.3510i	0.644843	−	0.372300i	−0.141635	−	0.989919i	$-0.545236\pi$
$773$	17.9285	−	10.3510i	0.644843	−	0.372300i	0.786478	+	0.617619i	$0.211903\pi$
$774$	3.16591	−	11.8153i	0.113796	−	0.424693i
$775$		0			0
$776$	4.99081	+	8.64434i	0.179160	+	0.310314i
$777$	33.9158	−	9.08770i	1.21672	−	0.326020i
$778$	2.92660	−	5.06903i	0.104924	−	0.181733i
$779$	−29.2411			−1.04767
$780$		0			0
$781$	6.15173			0.220126
$782$	2.59412	−	4.49314i	0.0927654	−	0.160674i
$783$	55.4095	−	14.8469i	1.98017	−	0.530586i
$784$	−2.68346	−	4.64788i	−0.0958378	−	0.165996i
$785$		0			0
$786$	4.58415	−	17.1083i	0.163511	−	0.610232i
$787$	−18.3969	+	10.6214i	−0.655777	+	0.378613i	−0.790666	−	0.612248i	$-0.790266\pi$
$787$	−18.3969	+	10.6214i	−0.655777	+	0.378613i	0.134889	+	0.990861i	$0.456932\pi$
$788$	1.51978			0.0541398
$789$	−62.0139	+	35.8037i	−2.20775	+	1.27465i
$790$		0			0
$791$	−1.96779	−	7.34389i	−0.0699665	−	0.261119i
$792$	3.74674	+	3.74674i	0.133135	+	0.133135i
$793$	−15.2538	+	20.4481i	−0.541677	+	0.726132i
$794$			13.9496i			0.495054i
$795$		0			0
$796$	3.00272	−	5.20086i	0.106429	−	0.184340i
$797$	−4.09634	+	15.2878i	−0.145100	+	0.541520i	0.854651	+	0.519203i	$0.173771\pi$
$797$	−4.09634	+	15.2878i	−0.145100	+	0.541520i	−0.999751	+	0.0223172i	$0.992896\pi$
$798$		−	12.9435i		−	0.458196i
$799$	1.53438	+	0.411136i	0.0542825	+	0.0145449i
$800$		0			0
$801$	26.7086	−	26.7086i	0.943701	−	0.943701i
$802$	−12.7926	−	3.42776i	−0.451721	−	0.121038i
$803$	1.11436	+	4.15886i	0.0393250	+	0.146763i
$804$	−7.47458	+	2.00281i	−0.263608	+	0.0706336i
$805$		0			0
$806$	−23.0682	−	29.2326i	−0.812544	−	1.02967i
$807$	−65.8381	+	65.8381i	−2.31761	+	2.31761i
$808$	−0.911347	−	0.526166i	−0.0320611	−	0.0185105i
$809$	−6.81229	−	3.93308i	−0.239507	−	0.138280i	0.375443	−	0.926845i	$-0.377491\pi$
$809$	−6.81229	−	3.93308i	−0.239507	−	0.138280i	−0.614950	+	0.788566i	$0.710824\pi$
$810$		0			0
$811$	−13.1134	−	13.1134i	−0.460475	−	0.460475i	0.438336	−	0.898811i	$-0.355568\pi$
$811$	−13.1134	−	13.1134i	−0.460475	−	0.460475i	−0.898811	+	0.438336i	$0.855568\pi$
$812$	4.08452	+	7.07459i	0.143338	+	0.248269i
$813$	−14.6015	−	25.2905i	−0.512097	−	0.886978i
$814$	5.72873	+	5.72873i	0.200792	+	0.200792i
$815$		0			0
$816$	1.61230	+	0.930864i	0.0564419	+	0.0325868i
$817$	−5.97080	−	3.44724i	−0.208892	−	0.120604i
$818$	18.3339	−	18.3339i	0.641028	−	0.641028i
$819$	27.4213	+	3.23198i	0.958179	+	0.112934i
$820$		0			0
$821$	−38.0562	+	10.1971i	−1.32817	+	0.355882i	−0.852032	−	0.523489i	$-0.824630\pi$
$821$	−38.0562	+	10.1971i	−1.32817	+	0.355882i	−0.476137	+	0.879371i	$0.657963\pi$
$822$	9.50561	+	35.4754i	0.331546	+	1.23735i
$823$	11.8543	+	3.17636i	0.413216	+	0.110721i	0.459437	−	0.888210i	$-0.348051\pi$
$823$	11.8543	+	3.17636i	0.413216	+	0.110721i	−0.0462212	+	0.998931i	$0.514718\pi$
$824$	−3.37370	+	3.37370i	−0.117528	+	0.117528i
$825$		0			0
$826$	−1.37476	−	0.368366i	−0.0478341	−	0.0128171i
$827$		−	33.6098i		−	1.16873i	−0.811492	−	0.584364i	$-0.801344\pi$
$827$		−	33.6098i		−	1.16873i	0.811492	−	0.584364i	$-0.198656\pi$
$828$	−12.9613	+	48.3722i	−0.450436	+	1.68105i
$829$	13.8019	−	23.9055i	0.479359	−	0.830274i	−0.520361	−	0.853946i	$-0.674203\pi$
$829$	13.8019	−	23.9055i	0.479359	−	0.830274i	0.999720	+	0.0236725i	$0.00753590\pi$
$830$		0			0
$831$		−	92.2760i		−	3.20102i
$832$	1.42488	+	3.31205i	0.0493989	+	0.114825i
$833$	−2.35606	−	2.35606i	−0.0816325	−	0.0816325i
$834$	0.749113	+	2.79573i	0.0259397	+	0.0968082i
$835$		0			0
$836$	2.58642	−	1.49327i	0.0894532	−	0.0516459i
$837$	92.6814			3.20354
$838$	17.8637	−	10.3136i	0.617090	−	0.356277i
$839$	9.37660	−	34.9939i	0.323716	−	1.20813i	−0.591880	−	0.806026i	$-0.701614\pi$
$839$	9.37660	−	34.9939i	0.323716	−	1.20813i	0.915596	−	0.402099i	$-0.131719\pi$
$840$		0			0
$841$	5.93158	+	10.2738i	0.204537	+	0.354269i
$842$	−29.1778	+	7.81816i	−1.00553	+	0.269432i
$843$	5.09981	−	8.83314i	0.175647	−	0.304229i
$844$	2.72654			0.0938515
$845$		0			0
$846$	−15.3328			−0.527152
$847$	6.52900	−	11.3086i	0.224339	−	0.388567i
$848$	3.65624	−	0.979686i	0.125556	−	0.0336426i
$849$	−20.7419	−	35.9260i	−0.711859	−	1.23298i
$850$		0			0
$851$	−19.8177	+	73.9606i	−0.679341	+	2.53534i
$852$	−18.0679	+	10.4315i	−0.618995	+	0.357377i
$853$	−22.4023			−0.767041			−0.383520	−	0.923532i	$-0.625288\pi$
$853$	−22.4023			−0.767041			−0.383520	+	0.923532i	$0.625288\pi$
$854$	7.83046	−	4.52092i	0.267953	−	0.154703i
$855$		0			0
$856$	3.77105	+	14.0737i	0.128892	+	0.481031i
$857$	31.7108	+	31.7108i	1.08322	+	1.08322i	0.996207	+	0.0870141i	$0.0277325\pi$
$857$	31.7108	+	31.7108i	1.08322	+	1.08322i	0.0870141	+	0.996207i	$0.472267\pi$
$858$	3.77816	+	8.78210i	0.128984	+	0.299816i
$859$		−	49.9135i		−	1.70303i	−0.524332	−	0.851514i	$-0.675685\pi$
$859$		−	49.9135i		−	1.70303i	0.524332	−	0.851514i	$-0.324315\pi$
$860$		0			0
$861$	−16.5882	+	28.7316i	−0.565325	+	0.979172i
$862$	9.16078	−	34.1885i	0.312017	−	1.16447i
$863$		−	24.6850i		−	0.840288i	−0.907457	−	0.420144i	$-0.861980\pi$
$863$		−	24.6850i		−	0.840288i	0.907457	−	0.420144i	$-0.138020\pi$
$864$	−8.66799	−	2.32258i	−0.294891	−	0.0790158i
$865$		0			0
$866$	−21.1147	+	21.1147i	−0.717505	+	0.717505i
$867$	−48.1252	−	12.8951i	−1.63442	−	0.437941i
$868$	3.41601	+	12.7487i	0.115947	+	0.432719i
$869$	−9.58049	+	2.56709i	−0.324996	+	0.0870824i
$870$		0			0
$871$	−9.24014	−	1.08908i	−0.313090	−	0.0369020i
$872$	−4.33526	+	4.33526i	−0.146811	+	0.146811i
$873$	−51.8012	−	29.9074i	−1.75321	−	1.01221i
$874$	24.4446	+	14.1131i	0.826850	+	0.477382i
$875$		0			0
$876$	−10.3251	−	10.3251i	−0.348854	−	0.348854i
$877$	6.52548	+	11.3025i	0.220350	+	0.381657i	0.954914	−	0.296882i	$-0.0959468\pi$
$877$	6.52548	+	11.3025i	0.220350	+	0.381657i	−0.734564	+	0.678539i	$0.762613\pi$
$878$	8.00470	+	13.8645i	0.270145	+	0.467906i
$879$	−11.4875	−	11.4875i	−0.387465	−	0.387465i
$880$		0			0
$881$	−31.4196	−	18.1401i	−1.05855	−	0.611156i	−0.133522	−	0.991046i	$-0.542629\pi$
$881$	−31.4196	−	18.1401i	−1.05855	−	0.611156i	−0.925032	+	0.379890i	$0.875962\pi$
$882$	27.8524	+	16.0806i	0.937841	+	0.541463i
$883$	30.8743	−	30.8743i	1.03900	−	1.03900i	0.0397956	−	0.999208i	$-0.487329\pi$
$883$	30.8743	−	30.8743i	1.03900	−	1.03900i	0.999208	−	0.0397956i	$-0.0126707\pi$
$884$	1.38667	+	1.75722i	0.0466387	+	0.0591017i
$885$		0			0
$886$	−29.5992	+	7.93109i	−0.994406	+	0.266450i
$887$	0.823779	+	3.07438i	0.0276598	+	0.103228i	0.978376	−	0.206835i	$-0.0663165\pi$
$887$	0.823779	+	3.07438i	0.0276598	+	0.103228i	−0.950716	+	0.310063i	$0.899650\pi$
$888$	−26.5398	−	7.11131i	−0.890616	−	0.238640i
$889$	−11.7744	+	11.7744i	−0.394902	+	0.394902i
$890$		0			0
$891$	−7.62922	−	2.04424i	−0.255589	−	0.0684848i
$892$			7.49576i			0.250976i
$893$	−2.23675	+	8.34766i	−0.0748500	+	0.279344i
$894$	4.66346	−	8.07735i	0.155970	−	0.270147i
$895$		0			0
$896$		−	1.27792i		−	0.0426924i
$897$	−54.0267	+	72.4242i	−1.80390	+	2.41817i
$898$	−6.33211	−	6.33211i	−0.211305	−	0.211305i
$899$	17.0876	+	63.7717i	0.569902	+	2.12690i
$900$		0			0
$901$	2.03515	−	1.17500i	0.0678008	−	0.0391448i
$902$	−7.65501			−0.254884
$903$	−6.77438	+	3.91119i	−0.225437	+	0.130156i
$904$	−1.53983	+	5.74674i	−0.0512141	+	0.191134i
$905$		0			0
$906$	−23.0458	−	39.9164i	−0.765644	−	1.32614i
$907$	36.5384	−	9.79045i	1.21324	−	0.325086i	0.405207	−	0.914225i	$-0.367199\pi$
$907$	36.5384	−	9.79045i	1.21324	−	0.325086i	0.808032	+	0.589138i	$0.200533\pi$
$908$	6.65757	−	11.5313i	0.220939	−	0.382678i
$909$	6.30610			0.209160
$910$		0			0
$911$	−3.06450			−0.101531			−0.0507657	−	0.998711i	$-0.516166\pi$
$911$	−3.06450			−0.101531			−0.0507657	+	0.998711i	$0.516166\pi$
$912$	−5.06429	+	8.77160i	−0.167695	+	0.290457i
$913$	1.49524	−	0.400648i	0.0494851	−	0.0132595i
$914$	−12.2784	−	21.2668i	−0.406134	−	0.703444i
$915$		0			0
$916$	0.966636	−	3.60754i	0.0319386	−	0.119196i
$917$	−6.53668	+	3.77395i	−0.215860	+	0.124627i
$918$	−5.57122			−0.183878
$919$	33.5898	−	19.3931i	1.10802	−	0.639718i	0.169708	−	0.985494i	$-0.445718\pi$
$919$	33.5898	−	19.3931i	1.10802	−	0.639718i	0.938317	+	0.345776i	$0.112384\pi$
$920$		0			0
$921$	1.04119	+	3.88577i	0.0343083	+	0.128040i
$922$	7.07275	+	7.07275i	0.232928	+	0.232928i
$923$	−24.8233	+	3.61156i	−0.817069	+	0.118876i
$924$		−	3.38848i		−	0.111473i
$925$		0			0
$926$	13.9417	−	24.1478i	0.458153	−	0.793545i
$927$	7.39989	−	27.6168i	0.243044	−	0.907054i
$928$		−	6.39243i		−	0.209842i
$929$	−0.485719	−	0.130148i	−0.0159359	−	0.00427002i	0.250842	−	0.968028i	$-0.419292\pi$
$929$	−0.485719	−	0.130148i	−0.0159359	−	0.00427002i	−0.266778	+	0.963758i	$0.585959\pi$
$930$		0			0
$931$	12.8179	−	12.8179i	0.420090	−	0.420090i
$932$	−12.9861	−	3.47961i	−0.425374	−	0.113979i
$933$	−2.10625	−	7.86062i	−0.0689554	−	0.257345i
$934$	30.5373	−	8.18244i	0.999210	−	0.267738i
$935$		0			0
$936$	−17.3184	−	12.9191i	−0.566070	−	0.422275i
$937$	9.95025	−	9.95025i	0.325061	−	0.325061i	−0.525644	−	0.850705i	$-0.676176\pi$
$937$	9.95025	−	9.95025i	0.325061	−	0.325061i	0.850705	+	0.525644i	$0.176176\pi$
$938$	2.85587	+	1.64884i	0.0932473	+	0.0538364i
$939$	−12.0180	−	6.93858i	−0.392192	−	0.226432i
$940$		0			0
$941$	23.7430	+	23.7430i	0.774000	+	0.774000i	0.978803	−	0.204803i	$-0.0656555\pi$
$941$	23.7430	+	23.7430i	0.774000	+	0.774000i	−0.204803	+	0.978803i	$0.565655\pi$
$942$	−17.9643	−	31.1151i	−0.585309	−	1.01379i
$943$	−36.1742	−	62.6555i	−1.17799	−	2.04034i
$944$	0.787525	+	0.787525i	0.0256317	+	0.0256317i
$945$		0			0
$946$	−1.56309	−	0.902453i	−0.0508206	−	0.0293413i
$947$	−33.7590	−	19.4908i	−1.09702	−	0.633365i	−0.161583	−	0.986859i	$-0.551660\pi$
$947$	−33.7590	−	19.4908i	−1.09702	−	0.633365i	−0.935437	+	0.353494i	$0.884993\pi$
$948$	23.7853	−	23.7853i	0.772511	−	0.772511i
$949$	−6.93824	−	16.1275i	−0.225225	−	0.523522i
$950$		0			0
$951$	10.1662	−	2.72403i	0.329662	−	0.0883328i
$952$	−0.205342	−	0.766345i	−0.00665516	−	0.0248374i
$953$	56.0994	+	15.0318i	1.81724	+	0.486928i	0.996441	−	0.0842907i	$-0.0268624\pi$
$953$	56.0994	+	15.0318i	1.81724	+	0.486928i	0.820798	+	0.571219i	$0.193529\pi$
$954$	−16.0392	+	16.0392i	−0.519290	+	0.519290i
$955$		0			0
$956$	14.3477	+	3.84446i	0.464039	+	0.124339i
$957$		−	16.9499i		−	0.547912i
$958$	−0.580565	+	2.16670i	−0.0187572	+	0.0700029i
$959$	7.82561	−	13.5544i	0.252702	−	0.437693i
$960$		0			0
$961$			75.6684i			2.44092i
$962$	−26.4797	−	19.7532i	−0.853739	−	0.636870i
$963$	−61.7389	−	61.7389i	−1.98951	−	1.98951i
$964$	−0.397848	−	1.48479i	−0.0128138	−	0.0478218i
$965$		0			0
$966$	27.7344	−	16.0125i	0.892340	−	0.515193i
$967$	−51.5834			−1.65881			−0.829405	−	0.558648i	$-0.811320\pi$
$967$	−51.5834			−1.65881			−0.829405	+	0.558648i	$0.811320\pi$
$968$	−8.84918	+	5.10908i	−0.284423	+	0.164212i
$969$	−1.62750	+	6.07391i	−0.0522828	+	0.195122i
$970$		0			0
$971$	−18.2251	−	31.5668i	−0.584872	−	1.01303i	−0.994891	−	0.100951i	$-0.967811\pi$
$971$	−18.2251	−	31.5668i	−0.584872	−	1.01303i	0.410019	−	0.912077i	$-0.365522\pi$
$972$	−0.130173	+	0.0348797i	−0.00417530	+	0.00111877i
$973$	0.616716	−	1.06818i	0.0197710	−	0.0342444i
$974$	−23.0090			−0.737257
$975$		0			0
$976$	−7.07542			−0.226479
$977$	20.1158	−	34.8416i	0.643562	−	1.11468i	−0.341070	−	0.940038i	$-0.610789\pi$
$977$	20.1158	−	34.8416i	0.643562	−	1.11468i	0.984632	−	0.174644i	$-0.0558774\pi$
$978$	−60.2364	+	16.1403i	−1.92615	+	0.516110i
$979$	−2.78669	−	4.82668i	−0.0890629	−	0.154261i
$980$		0			0
$981$	9.50900	−	35.4881i	0.303599	−	1.13305i
$982$	−2.22242	+	1.28311i	−0.0709203	+	0.0409458i
$983$	−22.8830			−0.729856			−0.364928	−	0.931036i	$-0.618906\pi$
$983$	−22.8830			−0.729856			−0.364928	+	0.931036i	$0.618906\pi$
$984$	22.4831	−	12.9806i	0.716735	−	0.413807i
$985$		0			0
$986$	−1.02716	−	3.83341i	−0.0327115	−	0.122081i
$987$	6.93334	+	6.93334i	0.220691	+	0.220691i
$988$	−9.56000	+	7.54405i	−0.304144	+	0.240008i
$989$		−	17.0584i		−	0.542425i
$990$		0			0
$991$	−2.26574	+	3.92439i	−0.0719738	+	0.124662i	−0.899766	−	0.436372i	$-0.856263\pi$
$991$	−2.26574	+	3.92439i	−0.0719738	+	0.124662i	0.827793	+	0.561034i	$0.189596\pi$
$992$	2.67309	−	9.97612i	0.0848708	−	0.316742i
$993$			25.1909i			0.799410i
$994$	8.58785	+	2.30111i	0.272390	+	0.0729867i
$995$		0			0
$996$	−3.71220	+	3.71220i	−0.117626	+	0.117626i
$997$	26.6514	+	7.14123i	0.844060	+	0.226165i	0.654838	−	0.755769i	$-0.272737\pi$
$997$	26.6514	+	7.14123i	0.844060	+	0.226165i	0.189222	+	0.981934i	$0.439404\pi$
$998$	−2.45591	−	9.16557i	−0.0777404	−	0.290131i
$999$	79.4203	−	21.2806i	2.51275	−	0.673288i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.w.e.293.1		12
5.2	odd	4		650.2.t.e.7.3		12
5.3	odd	4		130.2.p.a.7.1	✓	12
5.4	even	2		130.2.s.a.33.3	yes	12
13.2	odd	12		650.2.t.e.93.3		12
65.2	even	12	inner	650.2.w.e.457.1		12
65.28	even	12		130.2.s.a.67.3	yes	12
65.54	odd	12		130.2.p.a.93.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.p.a.7.1	✓	12	5.3	odd	4
130.2.p.a.93.1	yes	12	65.54	odd	12
130.2.s.a.33.3	yes	12	5.4	even	2
130.2.s.a.67.3	yes	12	65.28	even	12
650.2.t.e.7.3		12	5.2	odd	4
650.2.t.e.93.3		12	13.2	odd	12
650.2.w.e.293.1		12	1.1	even	1	trivial
650.2.w.e.457.1		12	65.2	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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} +(-2.89657 + 0.776134i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.776134 + 2.89657i) q^{6} +(1.10671 - 0.638961i) q^{7} -1.00000 q^{8} +(5.18966 - 2.99625i) q^{9} +(-0.228853 - 0.854091i) q^{11} +(2.12044 + 2.12044i) q^{12} +(1.42488 + 3.31205i) q^{13} -1.27792i q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.160684 + 0.599680i) q^{17} -5.99250i q^{18} +(-3.26251 - 0.874187i) q^{19} +(-2.70975 + 2.70975i) q^{21} +(-0.854091 - 0.228853i) q^{22} +(-2.16292 - 8.07211i) q^{23} +(2.89657 - 0.776134i) q^{24} +(3.58077 + 0.422042i) q^{26} +(-6.34541 + 6.34541i) q^{27} +(-1.10671 - 0.638961i) q^{28} +(-5.53601 - 3.19622i) q^{29} +(-7.30303 - 7.30303i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.32578 + 2.29631i) q^{33} +(0.438997 + 0.438997i) q^{34} +(-5.18966 - 2.99625i) q^{36} +(-7.93494 - 4.58124i) q^{37} +(-2.38832 + 2.38832i) q^{38} +(-6.69787 - 8.48770i) q^{39} +(8.36236 - 2.24069i) q^{41} +(0.991839 + 3.70159i) q^{42} +(1.97169 + 0.528312i) q^{43} +(-0.625238 + 0.625238i) q^{44} +(-8.07211 - 2.16292i) q^{46} -2.55866i q^{47} +(0.776134 - 2.89657i) q^{48} +(-2.68346 + 4.64788i) q^{49} -1.86173i q^{51} +(2.15588 - 2.89001i) q^{52} +(-2.67655 - 2.67655i) q^{53} +(2.32258 + 8.66799i) q^{54} +(-1.10671 + 0.638961i) q^{56} +10.1286 q^{57} +(-5.53601 + 3.19622i) q^{58} +(0.288254 - 1.07578i) q^{59} +(3.53771 + 6.12749i) q^{61} +(-9.97612 + 2.67309i) q^{62} +(3.82898 - 6.63198i) q^{63} +1.00000 q^{64} +2.65156 q^{66} +(-1.29025 + 2.23477i) q^{67} +(0.599680 - 0.160684i) q^{68} +(12.5301 + 21.7027i) q^{69} +(-1.80066 + 6.72017i) q^{71} +(-5.18966 + 2.99625i) q^{72} -4.86934 q^{73} +(-7.93494 + 4.58124i) q^{74} +(0.874187 + 3.26251i) q^{76} +(-0.799006 - 0.799006i) q^{77} +(-10.6995 + 1.55668i) q^{78} -11.2172i q^{79} +(4.46628 - 7.73583i) q^{81} +(2.24069 - 8.36236i) q^{82} +1.75068i q^{83} +(3.70159 + 0.991839i) q^{84} +(1.44337 - 1.44337i) q^{86} +(18.5161 + 4.96138i) q^{87} +(0.228853 + 0.854091i) q^{88} +(6.08837 - 1.63137i) q^{89} +(3.69321 + 2.75505i) q^{91} +(-5.90920 + 5.90920i) q^{92} +(26.8219 + 15.4856i) q^{93} +(-2.21587 - 1.27933i) q^{94} +(-2.12044 - 2.12044i) q^{96} +(-4.99081 - 8.64434i) q^{97} +(2.68346 + 4.64788i) q^{98} +(-3.74674 - 3.74674i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} - 6 q^{4} - 6 q^{7} - 12 q^{8} + 24 q^{9} + 6 q^{11} + 6 q^{13} - 6 q^{16} - 36 q^{19} - 24 q^{21} - 6 q^{23} + 6 q^{26} + 12 q^{27} + 6 q^{28} - 6 q^{29} - 24 q^{31} + 6 q^{32} - 18 q^{33}+ \cdots - 54 q^{99}+O(q^{100}) \) 12 * q + 6 * q^2 - 6 * q^4 - 6 * q^7 - 12 * q^8 + 24 * q^9 + 6 * q^11 + 6 * q^13 - 6 * q^16 - 36 * q^19 - 24 * q^21 - 6 * q^23 + 6 * q^26 + 12 * q^27 + 6 * q^28 - 6 * q^29 - 24 * q^31 + 6 * q^32 - 18 * q^33 + 12 * q^34 - 24 * q^36 - 6 * q^37 - 6 * q^38 - 6 * q^39 + 18 * q^41 - 18 * q^42 - 6 * q^44 - 6 * q^46 - 18 * q^53 + 6 * q^54 + 6 * q^56 - 6 * q^58 - 18 * q^59 + 18 * q^61 - 36 * q^62 + 12 * q^64 - 36 * q^66 - 24 * q^67 + 12 * q^68 + 42 * q^69 + 18 * q^71 - 24 * q^72 + 12 * q^73 - 6 * q^74 + 30 * q^76 + 30 * q^77 - 30 * q^78 + 30 * q^81 + 18 * q^82 + 6 * q^84 + 60 * q^87 - 6 * q^88 - 6 * q^89 - 6 * q^91 + 30 * q^93 - 24 * q^94 - 6 * q^97 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

Properties

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