LMFDB - Embedded newform 130.2.s.a.33.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [130,2,Mod(33,130)] 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("130.33"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(130, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 11])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 130 = 2 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	130.s (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$1.03805522628$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			33.3
Root			$-1.55227i$ of defining polynomial
Character	$\chi$	$=$	130.33
Dual form			130.2.s.a.67.3

$q$-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} +(-0.709753 + 2.12044i) q^{5} +(-0.776134 + 2.89657i) q^{6} +(-1.10671 + 0.638961i) q^{7} +1.00000 q^{8} +(5.18966 - 2.99625i) q^{9} +(-1.48148 - 1.67488i) q^{10} +(-0.228853 - 0.854091i) q^{11} +(-2.12044 - 2.12044i) q^{12} +(-1.42488 - 3.31205i) q^{13} -1.27792i q^{14} +(-0.410108 + 6.69286i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.160684 - 0.599680i) q^{17} +5.99250i q^{18} +(-3.26251 - 0.874187i) q^{19} +(2.19123 - 0.445554i) q^{20} +(-2.70975 + 2.70975i) q^{21} +(0.854091 + 0.228853i) q^{22} +(2.16292 + 8.07211i) q^{23} +(2.89657 - 0.776134i) q^{24} +(-3.99250 - 3.00997i) q^{25} +(3.58077 + 0.422042i) q^{26} +(6.34541 - 6.34541i) q^{27} +(1.10671 + 0.638961i) q^{28} +(-5.53601 - 3.19622i) q^{29} +(-5.59113 - 3.70159i) q^{30} +(-7.30303 - 7.30303i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.32578 - 2.29631i) q^{33} +(0.438997 + 0.438997i) q^{34} +(-0.569383 - 2.80022i) q^{35} +(-5.18966 - 2.99625i) q^{36} +(7.93494 + 4.58124i) q^{37} +(2.38832 - 2.38832i) q^{38} +(-6.69787 - 8.48770i) q^{39} +(-0.709753 + 2.12044i) q^{40} +(8.36236 - 2.24069i) q^{41} +(-0.991839 - 3.70159i) q^{42} +(-1.97169 - 0.528312i) q^{43} +(-0.625238 + 0.625238i) q^{44} +(2.66998 + 13.1309i) q^{45} +(-8.07211 - 2.16292i) q^{46} +2.55866i q^{47} +(-0.776134 + 2.89657i) q^{48} +(-2.68346 + 4.64788i) q^{49} +(4.60296 - 1.95262i) q^{50} -1.86173i q^{51} +(-2.15588 + 2.89001i) q^{52} +(2.67655 + 2.67655i) q^{53} +(2.32258 + 8.66799i) q^{54} +(1.97348 + 0.120926i) q^{55} +(-1.10671 + 0.638961i) q^{56} -10.1286 q^{57} +(5.53601 - 3.19622i) q^{58} +(0.288254 - 1.07578i) q^{59} +(6.00124 - 2.99126i) q^{60} +(3.53771 + 6.12749i) q^{61} +(9.97612 - 2.67309i) q^{62} +(-3.82898 + 6.63198i) q^{63} +1.00000 q^{64} +(8.03432 - 0.670633i) q^{65} +2.65156 q^{66} +(1.29025 - 2.23477i) q^{67} +(-0.599680 + 0.160684i) q^{68} +(12.5301 + 21.7027i) q^{69} +(2.70975 + 0.907010i) q^{70} +(-1.80066 + 6.72017i) q^{71} +(5.18966 - 2.99625i) q^{72} +4.86934 q^{73} +(-7.93494 + 4.58124i) q^{74} +(-13.9007 - 5.61988i) q^{75} +(0.874187 + 3.26251i) q^{76} +(0.799006 + 0.799006i) q^{77} +(10.6995 - 1.55668i) q^{78} -11.2172i q^{79} +(-1.48148 - 1.67488i) q^{80} +(4.46628 - 7.73583i) q^{81} +(-2.24069 + 8.36236i) q^{82} -1.75068i q^{83} +(3.70159 + 0.991839i) q^{84} +(1.15754 + 0.766345i) q^{85} +(1.44337 - 1.44337i) q^{86} +(-18.5161 - 4.96138i) q^{87} +(-0.228853 - 0.854091i) q^{88} +(6.08837 - 1.63137i) q^{89} +(-12.7067 - 4.25320i) q^{90} +(3.69321 + 2.75505i) q^{91} +(5.90920 - 5.90920i) q^{92} +(-26.8219 - 15.4856i) q^{93} +(-2.21587 - 1.27933i) q^{94} +(4.16923 - 6.29749i) q^{95} +(-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^{15} - 6 q^{16} - 36 q^{19} - 24 q^{21} + 6 q^{23} + 12 q^{25} + 6 q^{26} - 12 q^{27} - 6 q^{28} - 6 q^{29} - 18 q^{30}+ \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^15 - 6 * q^16 - 36 * q^19 - 24 * q^21 + 6 * q^23 + 12 * q^25 + 6 * q^26 - 12 * q^27 - 6 * q^28 - 6 * q^29 - 18 * q^30 - 24 * q^31 - 6 * q^32 + 18 * q^33 + 12 * q^34 - 12 * q^35 - 24 * q^36 + 6 * q^37 + 6 * q^38 - 6 * q^39 + 18 * q^41 + 18 * q^42 - 6 * q^44 - 18 * q^45 - 6 * q^46 + 6 * q^50 + 18 * q^53 + 6 * q^54 - 6 * q^55 + 6 * q^56 + 6 * q^58 - 18 * q^59 + 24 * q^60 + 18 * q^61 + 36 * q^62 + 12 * q^64 + 42 * q^65 - 36 * q^66 + 24 * q^67 - 12 * q^68 + 42 * q^69 + 24 * q^70 + 18 * q^71 + 24 * q^72 - 12 * q^73 - 6 * q^74 + 24 * q^75 + 30 * q^76 - 30 * q^77 + 30 * q^78 + 30 * q^81 - 18 * q^82 + 6 * q^84 - 42 * q^85 - 60 * q^87 + 6 * q^88 - 6 * q^89 + 12 * q^90 - 6 * q^91 - 30 * q^93 - 24 * q^94 - 24 * q^95 + 6 * q^97 - 54 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/130\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{11}{12}\right)$

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	0.706597	−	0.707617i	$-0.250230\pi$
$3$	2.89657	−	0.776134i	1.67234	−	0.448101i	0.965739	+	0.259516i	$0.0835629\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.709753	+	2.12044i	−0.317411	+	0.948288i
$5$	−0.709753	+	2.12044i	−0.317411	+	0.948288i
$6$	−0.776134	+	2.89657i	−0.316855	+	1.18252i
$7$	−1.10671	+	0.638961i	−0.418298	+	0.241505i	−0.694349	−	0.719638i	$-0.744308\pi$
$7$	−1.10671	+	0.638961i	−0.418298	+	0.241505i	0.276051	+	0.961143i	$0.410974\pi$
$8$	1.00000			0.353553
$9$	5.18966	−	2.99625i	1.72989	−	0.998750i
$10$	−1.48148	−	1.67488i	−0.468484	−	0.529644i
$11$	−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
$15$	−0.410108	+	6.69286i	−0.105889	+	1.72809i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.160684	−	0.599680i	0.0389716	−	0.145444i	−0.943699	−	0.330806i	$-0.892679\pi$
$17$	0.160684	−	0.599680i	0.0389716	−	0.145444i	0.982670	+	0.185363i	$0.0593460\pi$
$18$			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	$0.709973\pi$
$20$	2.19123	−	0.445554i	0.489974	−	0.0996289i
$21$	−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	$0.253366\pi$
$23$	2.16292	+	8.07211i	0.450999	+	1.68315i	−0.248591	+	0.968608i	$0.579968\pi$
$24$	2.89657	−	0.776134i	0.591260	−	0.158428i
$25$	−3.99250	−	3.00997i	−0.798500	−	0.601995i
$26$	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	$0.868930\pi$
$30$	−5.59113	−	3.70159i	−1.02080	−	0.675815i
$31$	−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
$35$	−0.569383	−	2.80022i	−0.0962433	−	0.473324i
$36$	−5.18966	−	2.99625i	−0.864943	−	0.499375i
$37$	7.93494	+	4.58124i	1.30450	+	0.753151i	0.981172	−	0.193137i	$-0.0618661\pi$
$37$	7.93494	+	4.58124i	1.30450	+	0.753151i	0.323325	+	0.946288i	$0.395199\pi$
$38$	2.38832	−	2.38832i	0.387437	−	0.387437i
$39$	−6.69787	−	8.48770i	−1.07252	−	1.35912i
$40$	−0.709753	+	2.12044i	−0.112222	+	0.335270i
$41$	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	0.105325	−	0.994438i	$-0.466412\pi$
$43$	−1.97169	−	0.528312i	−0.300679	−	0.0805668i	−0.406005	+	0.913871i	$0.633078\pi$
$44$	−0.625238	+	0.625238i	−0.0942582	+	0.0942582i
$45$	2.66998	+	13.1309i	0.398017	+	1.95744i
$46$	−8.07211	−	2.16292i	−1.19017	−	0.318905i
$47$			2.55866i			0.373219i	0.982434	+	0.186610i	$0.0597500\pi$
$47$			2.55866i			0.373219i	−0.982434	+	0.186610i	$0.940250\pi$
$48$	−0.776134	+	2.89657i	−0.112025	+	0.418084i
$49$	−2.68346	+	4.64788i	−0.383351	+	0.663983i
$50$	4.60296	−	1.95262i	0.650957	−	0.276142i
$51$		−	1.86173i		−	0.260694i
$52$	−2.15588	+	2.89001i	−0.298967	+	0.400773i
$53$	2.67655	+	2.67655i	0.367653	+	0.367653i	0.866621	−	0.498968i	$-0.166287\pi$
$53$	2.67655	+	2.67655i	0.367653	+	0.367653i	−0.498968	+	0.866621i	$0.666287\pi$
$54$	2.32258	+	8.66799i	0.316063	+	1.17956i
$55$	1.97348	+	0.120926i	0.266103	+	0.0163056i
$56$	−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	$0.0602364\pi$
$60$	6.00124	−	2.99126i	0.774756	−	0.386170i
$61$	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
$65$	8.03432	−	0.670633i	0.996534	−	0.0831817i
$66$	2.65156			0.326384
$67$	1.29025	−	2.23477i	0.157629	−	0.273021i	−0.776384	−	0.630260i	$-0.782948\pi$
$67$	1.29025	−	2.23477i	0.157629	−	0.273021i	0.934013	+	0.357239i	$0.116282\pi$
$68$	−0.599680	+	0.160684i	−0.0727219	+	0.0194858i
$69$	12.5301	+	21.7027i	1.50844	+	2.61270i
$70$	2.70975	+	0.907010i	0.323877	+	0.108408i
$71$	−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	$-0.408021\pi$
$73$	4.86934			0.569913			0.284957	+	0.958540i	$0.408021\pi$
$74$	−7.93494	+	4.58124i	−0.922418	+	0.532558i
$75$	−13.9007	−	5.61988i	−1.60511	−	0.648928i
$76$	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	$-0.217362\pi$
$80$	−1.48148	−	1.67488i	−0.165634	−	0.187258i
$81$	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	$-0.969369\pi$
$83$		−	1.75068i		−	0.192162i	0.995374	−	0.0960809i	$-0.0306307\pi$
$84$	3.70159	+	0.991839i	0.403877	+	0.108218i
$85$	1.15754	+	0.766345i	0.125553	+	0.0831218i
$86$	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	$0.308246\pi$
$90$	−12.7067	−	4.25320i	−1.33941	−	0.448326i
$91$	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
$95$	4.16923	−	6.29749i	0.427754	−	0.646109i
$96$	−2.12044	−	2.12044i	−0.216416	−	0.216416i
$97$	4.99081	+	8.64434i	0.506740	+	0.877700i	0.999970	+	0.00780033i	$0.00248295\pi$
$97$	4.99081	+	8.64434i	0.506740	+	0.877700i	−0.493230	+	0.869899i	$0.664184\pi$
$98$	−2.68346	−	4.64788i	−0.271070	−	0.469507i
$99$	−3.74674	−	3.74674i	−0.376562	−	0.376562i
$100$	−0.610463	+	4.96259i	−0.0610463	+	0.496259i
$101$	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	−0.853505	−	0.521085i	$-0.825528\pi$
$103$	−3.37370	+	3.37370i	−0.332420	+	0.332420i	0.521085	+	0.853505i	$0.325528\pi$
$104$	−1.42488	−	3.31205i	−0.139721	−	0.324774i
$105$	−3.82260	−	7.66912i	−0.373048	−	0.748429i
$106$	−3.65624	+	0.979686i	−0.355125	+	0.0951555i
$107$	3.77105	+	14.0737i	0.364561	+	1.36056i	0.868015	+	0.496538i	$0.165396\pi$
$107$	3.77105	+	14.0737i	0.364561	+	1.36056i	−0.503454	+	0.864022i	$0.667938\pi$
$108$	−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	$0.155140\pi$
$110$	−1.09146	+	1.64862i	−0.104067	+	0.157189i
$111$	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	$0.173614\pi$
$113$	−1.53983	+	5.74674i	−0.144855	+	0.540608i	−0.999762	+	0.0218255i	$0.993052\pi$
$114$	5.06429	−	8.77160i	0.474314	−	0.821536i
$115$	−18.6515	−	1.14288i	−1.73927	−	0.106574i
$116$			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
$120$	−0.410108	+	6.69286i	−0.0374376	+	0.610971i
$121$	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
$125$	9.21615	−	6.32950i	0.824317	−	0.566128i
$126$	−3.82898	−	6.63198i	−0.341112	−	0.590824i
$127$	12.5862	−	3.37246i	1.11684	−	0.299257i	0.347238	−	0.937777i	$-0.387119\pi$
$127$	12.5862	−	3.37246i	1.11684	−	0.299257i	0.769606	+	0.638519i	$0.220453\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−6.12117			−0.538939
$130$	−3.43637	+	7.29324i	−0.301390	+	0.639659i
$131$	−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
$135$	8.95136	+	17.9587i	0.770410	+	1.54564i
$136$	0.160684	−	0.599680i	0.0137785	−	0.0514222i
$137$	−10.6066	+	6.12370i	−0.906179	+	0.523183i	−0.879200	−	0.476453i	$-0.841922\pi$
$137$	−10.6066	+	6.12370i	−0.906179	+	0.523183i	−0.0269793	+	0.999636i	$0.508589\pi$
$138$	−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	$0.320300\pi$
$140$	−2.14037	+	1.89321i	−0.180894	+	0.160005i
$141$	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
$145$	10.7066	−	9.47023i	0.889132	−	0.786459i
$146$	−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	$0.623997\pi$
$150$	11.8173	−	9.22842i	0.964879	−	0.753497i
$151$	−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
$155$	20.6690	−	10.3023i	1.66017	−	0.827497i
$156$	−4.00163	+	10.0444i	−0.320387	+	0.804194i
$157$	8.47200	−	8.47200i	0.676139	−	0.676139i	−0.282985	−	0.959124i	$-0.591325\pi$
$157$	8.47200	−	8.47200i	0.676139	−	0.676139i	0.959124	+	0.282985i	$0.0913248\pi$
$158$	9.71436	+	5.60859i	0.772833	+	0.446195i
$159$	9.83018	+	5.67546i	0.779584	+	0.450093i
$160$	2.19123	−	0.445554i	0.173232	−	0.0352241i
$161$	−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	$-0.863719\pi$
$163$	−10.3979	−	18.0097i	−0.814426	−	1.41063i	0.0953137	−	0.995447i	$-0.469615\pi$
$164$	−6.12167	−	6.12167i	−0.478022	−	0.478022i
$165$	5.81016	−	1.18141i	0.452321	−	0.0919727i
$166$	1.51613	+	0.875338i	0.117675	+	0.0679394i
$167$	−10.3056	−	5.94992i	−0.797469	−	0.460419i	0.0451166	−	0.998982i	$-0.485634\pi$
$167$	−10.3056	−	5.94992i	−0.797469	−	0.460419i	−0.842585	+	0.538563i	$0.818967\pi$
$168$	−2.70975	+	2.70975i	−0.209062	+	0.209062i
$169$	−8.93941	+	9.43858i	−0.687647	+	0.726045i
$170$	−1.24244	+	0.619285i	−0.0952911	+	0.0474970i
$171$	−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	−0.357807	−	0.933796i	$-0.616475\pi$
$173$	−14.9230	−	3.99861i	−1.13457	−	0.304008i	−0.776768	+	0.629787i	$0.783142\pi$
$174$	13.5547	−	13.5547i	1.02758	−	1.02758i
$175$	6.34181	+	0.780124i	0.479396	+	0.0589719i
$176$	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	$0.189195\pi$
$180$	10.0367	−	8.87774i	0.748094	−	0.661708i
$181$		−	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
$185$	−15.3461	+	13.5740i	−1.12827	+	0.997980i
$186$	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
$190$	3.36917	+	6.75941i	0.244425	+	0.490379i
$191$	−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	−0.823910	−	0.566720i	$-0.808212\pi$
$193$	1.09527	−	1.89706i	0.0788392	−	0.136553i	0.902749	+	0.430167i	$0.141545\pi$
$194$	−9.98162			−0.716639
$195$	22.7515	−	8.17824i	1.62927	−	0.585656i
$196$	5.36691			0.383351
$197$	0.759889	−	1.31617i	0.0541398	−	0.0937729i	−0.837685	−	0.546153i	$-0.816092\pi$
$197$	0.759889	−	1.31617i	0.0541398	−	0.0937729i	0.891825	+	0.452380i	$0.149425\pi$
$198$	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	$0.765056\pi$
$200$	−3.99250	−	3.00997i	−0.282312	−	0.212837i
$201$	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
$205$	−1.18398	+	19.3222i	−0.0826926	+	1.34952i
$206$	−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
$210$	8.55295	+	0.524086i	0.590210	+	0.0361654i
$211$	−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
$215$	2.51966	−	3.80586i	0.171840	−	0.259558i
$216$	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
$220$	−0.882013	−	1.76954i	−0.0594653	−	0.119303i
$221$	−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	0.701349	−	0.712818i	$-0.252582\pi$
$223$	6.49152	+	3.74788i	0.434704	+	0.250976i	−0.266645	+	0.963795i	$0.585915\pi$
$224$	1.10671	+	0.638961i	0.0739454	+	0.0426924i
$225$	−29.7383	−	3.65820i	−1.98256	−	0.243880i
$226$	−4.20691	−	4.20691i	−0.279839	−	0.279839i
$227$	−6.65757	−	11.5313i	−0.441879	−	0.765356i	0.555950	−	0.831215i	$-0.312354\pi$
$227$	−6.65757	−	11.5313i	−0.441879	−	0.765356i	−0.997829	+	0.0658594i	$0.979021\pi$
$228$	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	$0.710620\pi$
$230$	10.3155	−	15.5813i	0.680186	−	1.02740i
$231$	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	−0.946244	−	0.323454i	$-0.895156\pi$
$233$	−9.50648	+	9.50648i	−0.622790	+	0.622790i	0.323454	+	0.946244i	$0.395156\pi$
$234$	19.8475	−	8.53861i	1.29747	−	0.558187i
$235$	−5.42548	−	1.81602i	−0.353919	−	0.118464i
$236$	−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	$0.409512\pi$
$240$	−5.59113	−	3.70159i	−0.360906	−	0.238937i
$241$	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
$245$	−7.95095	−	8.98895i	−0.507968	−	0.574283i
$246$			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
$250$	0.873438	+	11.1462i	0.0552411	+	0.704946i
$251$	−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
$255$	3.94768	+	1.32137i	0.247213	+	0.0827473i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−2.30049	+	0.616415i	−0.143501	+	0.0384509i	−0.329854	−	0.944032i	$-0.607000\pi$
$257$	−2.30049	+	0.616415i	−0.143501	+	0.0384509i	0.186354	+	0.982483i	$0.440333\pi$
$258$	3.06058	−	5.30109i	0.190544	−	0.330031i
$259$	−11.7089			−0.727558
$260$	−4.59794	−	6.62261i	−0.285152	−	0.410717i
$261$	−38.3066			−2.37112
$262$	2.95320	−	5.11508i	0.182449	−	0.316011i
$263$	−23.0654	+	6.18036i	−1.42228	+	0.381098i	−0.886290	−	0.463130i	$-0.846726\pi$
$263$	−23.0654	+	6.18036i	−1.42228	+	0.381098i	−0.535985	+	0.844227i	$0.680060\pi$
$264$	−1.32578	−	2.29631i	−0.0815960	−	0.141328i
$265$	−7.57515	+	3.77577i	−0.465338	+	0.231944i
$266$	−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	$-0.0621295\pi$
$270$	−20.0284	−	1.22725i	−1.21889	−	0.0746880i
$271$	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
$275$	−1.65710	+	4.09880i	−0.0999266	+	0.247167i
$276$	12.5301	−	21.7027i	0.754222	−	1.30635i
$277$	7.96424	−	29.7230i	0.478525	−	1.78588i	−0.129073	−	0.991635i	$-0.541200\pi$
$277$	7.96424	−	29.7230i	0.478525	−	1.78588i	0.607598	−	0.794245i	$-0.292133\pi$
$278$			0.965186i			0.0578880i
$279$	−59.7819	−	16.0185i	−3.57905	−	0.959003i
$280$	−0.569383	−	2.80022i	−0.0340272	−	0.167345i
$281$	−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	$-0.948456\pi$
$283$	−3.58042	−	13.3623i	−0.212834	−	0.794307i	0.774084	−	0.633083i	$-0.218211\pi$
$284$	6.72017	−	1.80066i	0.398769	−	0.106850i
$285$	7.18879	−	21.4770i	0.425827	−	1.27219i
$286$	−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
$290$	2.84817	+	14.0073i	0.167250	+	0.822535i
$291$	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	0.775989	−	0.630746i	$-0.217251\pi$
$293$	−2.70877	−	4.69172i	−0.158248	−	0.274093i	−0.934237	+	0.356653i	$0.883918\pi$
$294$	−11.3802	−	11.3802i	−0.663707	−	0.663707i
$295$	2.07653	+	1.37476i	0.120900	+	0.0800417i
$296$	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
$300$	2.08339	+	14.8483i	0.120284	+	0.857267i
$301$	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
$305$	−15.5039	+	3.15248i	−0.887749	+	0.180511i
$306$	3.59358	+	0.962898i	0.205432	+	0.0550452i
$307$			1.34151i			0.0765638i	0.999267	+	0.0382819i	$0.0121885\pi$
$307$			1.34151i			0.0765638i	−0.999267	+	0.0382819i	$0.987812\pi$
$308$	0.292456	−	1.09146i	0.0166643	−	0.0621918i
$309$	−7.15371	+	12.3906i	−0.406960	+	0.704876i
$310$	−1.41246	+	23.0510i	−0.0802223	+	1.30921i
$311$			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	0.608554	−	0.793512i	$-0.291750\pi$
$313$	−3.27224	−	3.27224i	−0.184958	−	0.184958i	−0.793512	+	0.608554i	$0.791750\pi$
$314$	3.10097	+	11.5730i	0.174998	+	0.653100i
$315$	−11.3451	−	12.8262i	−0.639222	−	0.722673i
$316$	−9.71436	+	5.60859i	−0.546475	+	0.315508i
$317$	3.50975			0.197127			0.0985635	−	0.995131i	$-0.468575\pi$
$317$	3.50975			0.197127			0.0985635	+	0.995131i	$0.468575\pi$
$318$	−9.83018	+	5.67546i	−0.551249	+	0.318264i
$319$	−1.46293	+	5.45972i	−0.0819082	+	0.305686i
$320$	−0.709753	+	2.12044i	−0.0396764	+	0.118536i
$321$	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
$325$	−4.28035	+	17.5122i	−0.237431	+	0.971404i
$326$	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
$330$	−1.88195	+	5.62246i	−0.103598	+	0.309506i
$331$	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
$335$	3.82294	+	4.32202i	0.208869	+	0.236137i
$336$	−0.991839	−	3.70159i	−0.0541092	−	0.201938i
$337$	6.40557	+	6.40557i	0.348934	+	0.348934i	0.859712	−	0.510779i	$-0.170643\pi$
$337$	6.40557	+	6.40557i	0.348934	+	0.348934i	−0.510779	+	0.859712i	$0.670643\pi$
$338$	−3.70435	−	12.4611i	−0.201490	−	0.677792i
$339$			17.8410i			0.968988i
$340$	0.0849052	−	1.38563i	0.00460463	−	0.0751463i
$341$	−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
$345$	−54.9125	+	11.1656i	−2.95639	+	0.601138i
$346$	10.9244	−	10.9244i	0.587299	−	0.587299i
$347$	−18.2716	−	4.89586i	−0.980871	−	0.262824i	−0.267460	−	0.963569i	$-0.586184\pi$
$347$	−18.2716	−	4.89586i	−0.980871	−	0.262824i	−0.713412	+	0.700745i	$0.752851\pi$
$348$	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	$0.621251\pi$
$350$	−3.84651	+	5.10211i	−0.205605	+	0.272719i
$351$	−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	0.999282	−	0.0378892i	$-0.0120634\pi$
$353$	27.5457	+	15.9035i	1.46611	+	0.846459i	0.466828	+	0.884348i	$0.345397\pi$
$354$	2.89234	+	1.66990i	0.153726	+	0.0887540i
$355$	−12.9717	−	8.58785i	−0.688464	−	0.455796i
$356$	−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	$0.646644\pi$
$360$	2.66998	+	13.1309i	0.140720	+	0.692061i
$361$	−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
$365$	−3.45603	+	10.3251i	−0.180897	+	0.540442i
$366$	−20.4944	+	5.49147i	−1.07126	+	0.287044i
$367$	0.788653	+	2.94329i	0.0411674	+	0.153639i	0.983450	−	0.181180i	$-0.0579916\pi$
$367$	0.788653	+	2.94329i	0.0411674	+	0.153639i	−0.942283	+	0.334819i	$0.891325\pi$
$368$	−8.07211	−	2.16292i	−0.420788	−	0.112750i
$369$	36.6841	−	36.6841i	1.90970	−	1.90970i
$370$	−4.08238	−	20.0771i	−0.212233	−	1.04376i
$371$	−4.67239	−	1.25196i	−0.242578	−	0.0649987i
$372$			30.9712i			1.60578i
$373$	0.996016	−	3.71718i	0.0515717	−	0.192468i	−0.935334	−	0.353766i	$-0.884901\pi$
$373$	0.996016	−	3.71718i	0.0515717	−	0.192468i	0.986906	+	0.161297i	$0.0515678\pi$
$374$	0.274477	−	0.475409i	0.0141929	−	0.0245828i
$375$	21.7827	−	25.4868i	1.12485	−	1.31613i
$376$			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	$0.984882\pi$
$380$	−7.53840	−	0.461919i	−0.386712	−	0.0236960i
$381$	33.8393	−	19.5371i	1.73364	−	1.00092i
$382$	20.3169			1.03950
$383$	−3.78044	+	2.18264i	−0.193172	+	0.111528i	−0.593466	−	0.804859i	$-0.702241\pi$
$383$	−3.78044	+	2.18264i	−0.193172	+	0.111528i	0.400295	+	0.916386i	$0.368908\pi$
$384$	−0.776134	+	2.89657i	−0.0396069	+	0.147815i
$385$	−2.26134	+	1.12714i	−0.115248	+	0.0574446i
$386$	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	$0.452593\pi$
$390$	−4.29317	+	23.7925i	−0.217393	+	1.20478i
$391$	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
$395$	23.7853	+	7.96143i	1.19677	+	0.400583i
$396$	−1.37140	+	5.11814i	−0.0689156	+	0.257196i
$397$	12.0807	−	6.97482i	0.606315	−	0.350056i	−0.165207	−	0.986259i	$-0.552829\pi$
$397$	12.0807	−	6.97482i	0.606315	−	0.350056i	0.771522	+	0.636203i	$0.219496\pi$
$398$	−6.00544			−0.301026
$399$	11.2094	−	6.47177i	0.561173	−	0.323994i
$400$	4.60296	−	1.95262i	0.230148	−	0.0976310i
$401$	−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
$405$	13.2334	+	14.9610i	0.657571	+	0.743418i
$406$	−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	$0.361841\pi$
$410$	−16.1415	−	10.6864i	−0.797173	−	0.527766i
$411$	−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
$415$	3.71220	+	1.24255i	0.182225	+	0.0609943i
$416$	−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	$0.498582\pi$
$420$	−4.73035	+	7.14503i	−0.230817	+	0.348642i
$421$	−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
$425$	−2.44655	+	1.91057i	−0.118675	+	0.0926763i
$426$	−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
$430$	2.03614	+	4.08502i	0.0981916	+	0.196997i
$431$	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	0.873338	−	0.487114i	$-0.161951\pi$
$433$	28.8432	+	7.72850i	1.38611	+	0.371408i	0.512776	+	0.858523i	$0.328617\pi$
$434$	−9.33270	+	9.33270i	−0.447984	+	0.447984i
$435$	23.6622	−	35.7409i	1.13451	−	1.71364i
$436$	−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	$0.291446\pi$
$440$	1.97348	+	0.120926i	0.0940818	+	0.00576491i
$441$			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	$0.00952930\pi$
$443$	21.6681	+	21.6681i	1.02948	+	1.02948i	0.0299327	+	0.999552i	$0.490471\pi$
$444$	−7.11131	−	26.5398i	−0.337488	−	1.25952i
$445$	−0.862017	+	14.0679i	−0.0408635	+	0.666882i
$446$	−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	$0.0155620\pi$
$450$	18.0373	−	23.9251i	0.850285	−	1.12784i
$451$	−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
$455$	−8.46318	+	5.87582i	−0.396760	+	0.275462i
$456$	−10.1286			−0.474314
$457$	−12.2784	+	21.2668i	−0.574360	+	0.994820i	0.421751	+	0.906712i	$0.361416\pi$
$457$	−12.2784	+	21.2668i	−0.574360	+	0.994820i	−0.996111	+	0.0881087i	$0.971918\pi$
$458$	−3.60754	+	0.966636i	−0.168569	+	0.0451679i
$459$	−2.78561	−	4.82482i	−0.130021	−	0.225203i
$460$	8.33601	+	16.7242i	0.388668	+	0.779768i
$461$	−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	$-0.724364\pi$
$463$	−27.8834			−1.29585			−0.647926	+	0.761703i	$0.724364\pi$
$464$	5.53601	−	3.19622i	0.257003	−	0.148381i
$465$	51.8731	−	45.8831i	2.40556	−	2.12778i
$466$	−3.47961	−	12.9861i	−0.161190	−	0.601569i
$467$	−22.3548	−	22.3548i	−1.03446	−	1.03446i	−0.999385	−	0.0350738i	$-0.988833\pi$
$467$	−22.3548	−	22.3548i	−1.03446	−	1.03446i	−0.0350738	−	0.999385i	$-0.511167\pi$
$468$	−2.52909	+	21.4577i	−0.116907	+	0.991884i
$469$			3.29767i			0.152272i
$470$	4.28546	−	3.79059i	0.197673	−	0.174847i
$471$	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
$475$	10.3943	+	13.3103i	0.476923	+	0.610717i
$476$	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	$0.432986\pi$
$480$	6.00124	−	2.99126i	0.273918	−	0.136532i
$481$	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
$485$	−21.8720	+	4.44735i	−0.993157	+	0.201944i
$486$	−0.0952932	−	0.0952932i	−0.00432259	−	0.00432259i
$487$	11.5045	+	19.9264i	0.521319	+	0.902951i	0.999693	+	0.0247947i	$0.00789322\pi$
$487$	11.5045	+	19.9264i	0.521319	+	0.902951i	−0.478373	+	0.878157i	$0.658773\pi$
$488$	3.53771	+	6.12749i	0.160145	+	0.277379i
$489$	−44.0961	−	44.0961i	−1.99410	−	1.99410i
$490$	11.7601	−	2.39125i	0.531269	−	0.108026i
$491$	−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
$495$	10.6040	−	5.28546i	0.476614	−	0.237564i
$496$	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	$0.181875\pi$
$500$	−10.0896	−	4.81667i	−0.451220	−	0.215408i
$501$	−34.4687	−	9.23587i	−1.53995	−	0.412628i
$502$		−	7.88510i		−	0.351929i
$503$	2.94883	−	11.0052i	0.131482	−	0.490697i	−0.868506	−	0.495679i	$-0.834919\pi$
$503$	2.94883	−	11.0052i	0.131482	−	0.490697i	0.999988	+	0.00498191i	$0.00158580\pi$
$504$	−3.82898	+	6.63198i	−0.170556	+	0.295412i
$505$	−1.76253	+	1.55900i	−0.0784317	+	0.0693748i
$506$			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	$-0.429950\pi$
$510$	−3.11818	+	2.75810i	−0.138075	+	0.122131i
$511$	−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
$515$	−4.75922	−	9.54820i	−0.209716	−	0.420744i
$516$	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
$520$	8.03432	−	0.670633i	0.352328	−	0.0294092i
$521$	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	0.328593	−	0.944472i	$-0.393426\pi$
$523$	24.8222	−	6.65109i	1.08540	−	0.290832i	0.756806	+	0.653640i	$0.226759\pi$
$524$	2.95320	+	5.11508i	0.129011	+	0.223453i
$525$	18.9750	−	2.66241i	0.828136	−	0.116197i
$526$	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
$530$	0.517665	−	8.44816i	0.0224859	−	0.366964i
$531$	−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
$535$	−32.5190	−	1.99262i	−1.40592	−	0.0861484i
$536$	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
$540$	11.0770	−	16.7315i	0.476679	−	0.720007i
$541$	−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
$545$	6.11568	+	12.2696i	0.261967	+	0.525573i
$546$	−10.8466	+	8.55936i	−0.464193	+	0.366307i
$547$	−22.0342	+	22.0342i	−0.942115	+	0.942115i	−0.998414	−	0.0562990i	$-0.982070\pi$
$547$	−22.0342	+	22.0342i	−0.942115	+	0.942115i	0.0562990	+	0.998414i	$0.482070\pi$
$548$	10.6066	+	6.12370i	0.453090	+	0.261591i
$549$	36.7190	+	21.1997i	1.56713	+	0.904782i
$550$	−2.72112	−	3.48449i	−0.116029	−	0.148579i
$551$	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
$555$	−33.9158	+	51.2286i	−1.43964	+	2.17453i
$556$	−0.835876	−	0.482593i	−0.0354490	−	0.0204665i
$557$	24.7384	+	14.2827i	1.04820	+	0.605179i	0.922145	−	0.386844i	$-0.126435\pi$
$557$	24.7384	+	14.2827i	1.04820	+	0.605179i	0.126055	+	0.992023i	$0.459768\pi$
$558$	43.7634	−	43.7634i	1.85265	−	1.85265i
$559$	1.05963	+	7.28312i	0.0448174	+	0.308043i
$560$	2.70975	+	0.907010i	0.114508	+	0.0383282i
$561$	−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	0.298188	−	0.954507i	$-0.403618\pi$
$563$	1.87859	+	0.503366i	0.0791731	+	0.0212144i	−0.219015	+	0.975721i	$0.570284\pi$
$564$	5.42548	−	5.42548i	0.228454	−	0.228454i
$565$	−11.0927	−	7.34389i	−0.466673	−	0.308960i
$566$	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	$0.972690\pi$
$570$	15.0052	+	16.9642i	0.628500	+	0.710551i
$571$			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
$575$	15.6614	−	38.7382i	0.653126	−	1.61550i
$576$	5.18966	−	2.99625i	0.216236	−	0.124844i
$577$	−22.1256			−0.921103			−0.460551	−	0.887633i	$-0.652348\pi$
$577$	−22.1256			−0.921103			−0.460551	+	0.887633i	$0.652348\pi$
$578$	−14.3886	+	8.30728i	−0.598488	+	0.345537i
$579$	1.70015	−	6.34504i	0.0706558	−	0.263691i
$580$	−13.5547	−	4.53705i	−0.562830	−	0.188391i
$581$	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
$585$	39.6860	−	27.5532i	1.64081	−	1.13918i
$586$	5.41754			0.223796
$587$	16.6364	−	28.8151i	0.686657	−	1.18932i	−0.286256	−	0.958153i	$-0.592411\pi$
$587$	16.6364	−	28.8151i	0.686657	−	1.18932i	0.972913	−	0.231172i	$-0.0742559\pi$
$588$	15.5456	−	4.16544i	0.641091	−	0.171780i
$589$	17.4420	+	30.2104i	0.718685	+	1.24480i
$590$	−2.22884	+	1.11095i	−0.0917601	+	0.0457370i
$591$	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	$-0.492255\pi$
$593$	1.18487			0.0486567			0.0243283	+	0.999704i	$0.492255\pi$
$594$	6.87172	−	3.96739i	0.281950	−	0.162784i
$595$	−1.77073	−	0.108502i	−0.0725928	−	0.00444816i
$596$	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	$-0.00616098\pi$
$600$	−13.9007	−	5.61988i	−0.567494	−	0.229431i
$601$	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
$605$	4.55274	+	22.3903i	0.185095	+	0.910296i
$606$	−2.23140	+	2.23140i	−0.0906446	+	0.0906446i
$607$	−18.7294	−	5.01853i	−0.760204	−	0.203696i	−0.142164	−	0.989843i	$-0.545406\pi$
$607$	−18.7294	−	5.01853i	−0.760204	−	0.203696i	−0.618039	+	0.786147i	$0.712073\pi$
$608$	0.874187	+	3.26251i	0.0354530	+	0.132312i
$609$	23.6622	−	6.34026i	0.958839	−	0.256920i
$610$	5.02180	−	15.0030i	0.203327	−	0.607453i
$611$	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	0.376770	−	0.926307i	$-0.377035\pi$
$613$	−5.86909	−	3.38852i	−0.237050	−	0.136861i	−0.613820	+	0.789446i	$0.710368\pi$
$614$	−1.16178	−	0.670753i	−0.0468856	−	0.0270694i
$615$	11.5671	+	56.8870i	0.466432	+	2.29391i
$616$	0.799006	+	0.799006i	0.0321929	+	0.0321929i
$617$	4.57750	+	7.92846i	0.184283	+	0.319188i	0.943335	−	0.331843i	$-0.107670\pi$
$617$	4.57750	+	7.92846i	0.184283	+	0.319188i	−0.759052	+	0.651030i	$0.774337\pi$
$618$	−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	$0.796336\pi$
$620$	−19.2565	−	12.7487i	−0.773359	−	0.512000i
$621$	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
$625$	6.88012	+	24.0346i	0.275205	+	0.961386i
$626$	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
$630$	16.7803	−	3.41203i	0.668544	−	0.135939i
$631$	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
$635$	−1.78200	+	29.0818i	−0.0707167	+	1.15408i
$636$		−	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
$640$	−1.48148	−	1.67488i	−0.0585604	−	0.0662055i
$641$	−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	−0.564537	−	0.825408i	$-0.690945\pi$
$643$	−3.34673	+	1.93223i	−0.131982	+	0.0761998i	0.432555	+	0.901607i	$0.357612\pi$
$644$	−2.76404	+	10.3155i	−0.108918	+	0.406489i
$645$	4.34452	−	12.9795i	0.171065	−	0.511069i
$646$	−1.04847	−	1.81600i	−0.0412513	−	0.0714494i
$647$	2.16676	−	0.580581i	0.0851841	−	0.0228250i	−0.215975	−	0.976399i	$-0.569293\pi$
$647$	2.16676	−	0.580581i	0.0851841	−	0.0228250i	0.301159	+	0.953574i	$0.402626\pi$
$648$	4.46628	−	7.73583i	0.175452	−	0.303892i
$649$	−0.984781			−0.0386560
$650$	−13.0259	−	12.4630i	−0.510917	−	0.488840i
$651$	39.5788			1.55122
$652$	−10.3979	+	18.0097i	−0.407213	+	0.705313i
$653$	−21.0761	+	5.64733i	−0.824773	+	0.220997i	−0.646432	−	0.762972i	$-0.723740\pi$
$653$	−21.0761	+	5.64733i	−0.824773	+	0.220997i	−0.178341	+	0.983969i	$0.557073\pi$
$654$	9.19265	+	15.9221i	0.359461	+	0.622605i
$655$	4.19208	−	12.5241i	0.163798	−	0.489358i
$656$	−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	$-0.00921424\pi$
$660$	−3.92821	−	4.44104i	−0.152906	−	0.172867i
$661$	−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
$665$	−0.590297	+	9.63349i	−0.0228907	+	0.373571i
$666$	−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
$670$	−5.65445	+	1.14975i	−0.218450	+	0.0444187i
$671$	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	$-0.730099\pi$
$673$	−12.0264	−	44.8831i	−0.463583	−	1.73012i	0.197961	−	0.980210i	$-0.436568\pi$
$674$	−8.75017	+	2.34460i	−0.337044	+	0.0903107i
$675$	−44.4335	+	6.23454i	−1.71025	+	0.239967i
$676$	12.6438	+	3.02247i	0.486298	+	0.116249i
$677$	−19.7486	+	19.7486i	−0.758999	+	0.758999i	−0.976140	−	0.217141i	$-0.930327\pi$
$677$	−19.7486	+	19.7486i	−0.758999	+	0.758999i	0.217141	+	0.976140i	$0.430327\pi$
$678$	−15.4507	−	8.92048i	−0.593381	−	0.342589i
$679$	−11.0468	−	6.37787i	−0.423937	−	0.244760i
$680$	1.15754	+	0.766345i	0.0443896	+	0.0293880i
$681$	−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	0.942668	−	0.333733i	$-0.108308\pi$
$683$	4.76460	+	8.25253i	0.182312	+	0.315774i	−0.760355	+	0.649508i	$0.774975\pi$
$684$	14.3120	+	14.3120i	0.547234	+	0.547234i
$685$	−5.45687	−	26.8368i	−0.208496	−	1.02538i
$686$	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
$690$	17.7865	−	53.1385i	0.677122	−	2.02295i
$691$	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
$695$	0.430042	+	2.11494i	0.0163124	+	0.0802244i
$696$	−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
$700$	−2.49530	−	5.88223i	−0.0943134	−	0.222327i
$701$		−	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
$705$	−17.1248	−	1.04933i	−0.644956	−	0.0395200i
$706$	−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	$-0.0405053\pi$
$710$	13.9231	−	6.93986i	0.522526	−	0.260448i
$711$	−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
$715$	−2.41146	−	6.70856i	−0.0901835	−	0.250886i
$716$	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	$0.933523\pi$
$720$	−12.7067	−	4.25320i	−0.473551	−	0.158507i
$721$	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
$725$	12.4820	+	29.4241i	0.463569	+	1.09278i
$726$	7.93065	+	29.5976i	0.294334	+	1.09847i
$727$	−3.52264	−	3.52264i	−0.130648	−	0.130648i	0.638759	−	0.769407i	$-0.279448\pi$
$727$	−3.52264	−	3.52264i	−0.130648	−	0.130648i	−0.769407	+	0.638759i	$0.779448\pi$
$728$	3.69321	+	2.75505i	0.136880	+	0.102109i
$729$			27.2018i			1.00747i
$730$	−7.21381	−	8.15557i	−0.266995	−	0.301851i
$731$	−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	$0.0576213\pi$
$733$			9.74855i			0.360071i	−0.983660	+	0.180035i	$0.942379\pi$
$734$	−2.94329	−	0.788653i	−0.108639	−	0.0291097i
$735$	−30.0071	−	19.8661i	−1.10683	−	0.732773i
$736$	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	$0.473397\pi$
$740$	19.4285	+	6.50310i	0.714204	+	0.239059i
$741$	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	$0.113968\pi$
$743$	46.5667	+	26.8853i	1.70837	+	0.986326i	0.771782	+	0.635888i	$0.219366\pi$
$744$	−26.8219	−	15.4856i	−0.983337	−	0.567730i
$745$	3.83925	−	5.79906i	0.140659	−	0.212461i
$746$	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
$750$	11.1809	+	31.6078i	0.408268	+	1.15415i
$751$	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
$755$	−15.3319	−	30.7597i	−0.557984	−	1.11946i
$756$	11.0770	−	2.96808i	0.402867	−	0.107948i
$757$	12.6177	+	47.0899i	0.458598	+	1.71151i	0.677290	+	0.735716i	$0.263154\pi$
$757$	12.6177	+	47.0899i	0.458598	+	1.71151i	−0.218692	+	0.975794i	$0.570179\pi$
$758$	7.99821	+	2.14311i	0.290508	+	0.0778414i
$759$	15.6686	−	15.6686i	0.568733	−	0.568733i
$760$	4.16923	−	6.29749i	0.151234	−	0.228434i
$761$	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
$765$	8.30339	+	0.508794i	0.300210	+	0.0183955i
$766$		−	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	$0.701271\pi$
$770$	0.154534	−	2.52195i	0.00556901	−	0.0908847i
$771$	−6.18511	+	3.57098i	−0.222751	+	0.128606i
$772$	−2.19054			−0.0788392
$773$	−17.9285	+	10.3510i	−0.644843	+	0.372300i	−0.786478	−	0.617619i	$-0.788097\pi$
$773$	−17.9285	+	10.3510i	−0.644843	+	0.372300i	0.141635	+	0.989919i	$0.454764\pi$
$774$	3.16591	−	11.8153i	0.113796	−	0.424693i
$775$	7.17542	+	51.1393i	0.257749	+	1.83698i
$776$	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
$780$	−18.4583	−	15.6142i	−0.660913	−	0.559079i
$781$	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
$785$	11.9513	+	23.9774i	0.426560	+	0.855788i
$786$	4.58415	−	17.1083i	0.163511	−	0.610232i
$787$	18.3969	−	10.6214i	0.655777	−	0.378613i	−0.134889	−	0.990861i	$-0.543068\pi$
$787$	18.3969	−	10.6214i	0.655777	−	0.378613i	0.790666	+	0.612248i	$0.209734\pi$
$788$	−1.51978			−0.0541398
$789$	−62.0139	+	35.8037i	−2.20775	+	1.27465i
$790$	−18.7875	+	16.6180i	−0.668428	+	0.591241i
$791$	−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
$795$	−19.0115	+	16.8161i	−0.674267	+	0.596406i
$796$	3.00272	−	5.20086i	0.106429	−	0.184340i
$797$	4.09634	−	15.2878i	0.145100	−	0.541520i	−0.854651	−	0.519203i	$-0.826229\pi$
$797$	4.09634	−	15.2878i	0.145100	−	0.541520i	0.999751	−	0.0223172i	$-0.00710438\pi$
$798$			12.9435i			0.458196i
$799$	1.53438	+	0.411136i	0.0542825	+	0.0145449i
$800$	−0.610463	+	4.96259i	−0.0215831	+	0.175454i
$801$	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
$805$	21.3722	−	10.6528i	0.753270	−	0.375461i
$806$	−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	$0.710824\pi$
$810$	−19.5733	+	3.97994i	−0.687735	+	0.139841i
$811$	−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
$815$	45.5683	−	9.26564i	1.59619	−	0.324561i
$816$	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
$820$	17.3255	−	8.63574i	0.605033	−	0.301573i
$821$	−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	0.0462212	−	0.998931i	$-0.485282\pi$
$823$	−11.8543	−	3.17636i	−0.413216	−	0.110721i	−0.459437	+	0.888210i	$0.651949\pi$
$824$	−3.37370	+	3.37370i	−0.117528	+	0.117528i
$825$	−1.61868	+	13.1586i	−0.0563551	+	0.458123i
$826$	−1.37476	−	0.368366i	−0.0478341	−	0.0128171i
$827$			33.6098i			1.16873i	0.811492	+	0.584364i	$0.198656\pi$
$827$			33.6098i			1.16873i	−0.811492	+	0.584364i	$0.801344\pi$
$828$	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	$0.00753590\pi$
$830$	−2.93218	+	2.59358i	−0.101777	+	0.0900246i
$831$		−	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
$835$	19.9308	−	17.6293i	0.689735	−	0.610088i
$836$	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	$-0.131719\pi$
$840$	−3.82260	−	7.66912i	−0.131892	−	0.264610i
$841$	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
$845$	−13.6691	−	25.6545i	−0.470233	−	0.882543i
$846$	−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
$850$	−0.431326	−	3.07406i	−0.0147944	−	0.105439i
$851$	−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	$-0.374712\pi$
$853$	22.4023			0.767041			0.383520	+	0.923532i	$0.374712\pi$
$854$	7.83046	−	4.52092i	0.267953	−	0.154703i
$855$	2.76805	−	45.1739i	0.0946654	−	1.54491i
$856$	3.77105	+	14.0737i	0.128892	+	0.481031i
$857$	−31.7108	−	31.7108i	−1.08322	−	1.08322i	−0.996207	−	0.0870141i	$-0.972267\pi$
$857$	−31.7108	−	31.7108i	−1.08322	−	1.08322i	−0.0870141	−	0.996207i	$-0.527733\pi$
$858$	−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	$-0.324315\pi$
$860$	−4.55581	−	0.279159i	−0.155352	−	0.00951926i
$861$	−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	$0.138020\pi$
$863$			24.6850i			0.840288i	−0.907457	+	0.420144i	$0.861980\pi$
$864$	−8.66799	−	2.32258i	−0.294891	−	0.0790158i
$865$	19.0704	−	28.8052i	0.648414	−	0.979408i
$866$	−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
$870$	19.1214	+	38.3625i	0.648278	+	1.30061i
$871$	−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
$875$	−6.15532	+	12.8937i	−0.208088	+	0.435887i
$876$	−10.3251	−	10.3251i	−0.348854	−	0.348854i
$877$	−6.52548	−	11.3025i	−0.220350	−	0.381657i	0.734564	−	0.678539i	$-0.237387\pi$
$877$	−6.52548	−	11.3025i	−0.220350	−	0.381657i	−0.954914	+	0.296882i	$0.904053\pi$
$878$	−8.00470	−	13.8645i	−0.270145	−	0.467906i
$879$	−11.4875	−	11.4875i	−0.387465	−	0.387465i
$880$	−1.09146	+	1.64862i	−0.0367932	+	0.0555749i
$881$	−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	$0.512671\pi$
$883$	−30.8743	+	30.8743i	−1.03900	+	1.03900i	−0.999208	+	0.0397956i	$0.987329\pi$
$884$	1.38667	+	1.75722i	0.0466387	+	0.0591017i
$885$	7.08182	+	2.37043i	0.238053	+	0.0796811i
$886$	−29.5992	+	7.93109i	−0.994406	+	0.266450i
$887$	−0.823779	−	3.07438i	−0.0276598	−	0.103228i	0.950716	−	0.310063i	$-0.100350\pi$
$887$	−0.823779	−	3.07438i	−0.0276598	−	0.103228i	−0.978376	+	0.206835i	$0.933684\pi$
$888$	26.5398	+	7.11131i	0.890616	+	0.238640i
$889$	−11.7744	+	11.7744i	−0.394902	+	0.394902i
$890$	−11.7521	−	7.78047i	−0.393932	−	0.260802i
$891$	−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
$895$	−2.80324	−	3.16920i	−0.0937019	−	0.105935i
$896$		−	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
$900$	11.7011	+	27.5833i	0.390036	+	0.919442i
$901$	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
$905$	43.3589	+	14.5131i	1.44130	+	0.482433i
$906$	−23.0458	−	39.9164i	−0.765644	−	1.32614i
$907$	−36.5384	+	9.79045i	−1.21324	+	0.325086i	−0.808032	−	0.589138i	$-0.799467\pi$
$907$	−36.5384	+	9.79045i	−1.21324	+	0.325086i	−0.405207	+	0.914225i	$0.632801\pi$
$908$	−6.65757	+	11.5313i	−0.220939	+	0.382678i
$909$	6.30610			0.209160
$910$	−0.857017	−	10.2672i	−0.0284098	−	0.340356i
$911$	−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
$915$	−42.4613	+	21.1644i	−1.40373	+	0.699675i
$916$	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	$0.112384\pi$
$920$	−18.6515	−	1.14288i	−0.614923	−	0.0376797i
$921$	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
$925$	−17.8908	−	42.1746i	−0.588247	−	1.38669i
$926$	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	$0.585959\pi$
$930$	13.7993	+	67.8650i	0.452498	+	2.22538i
$931$	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
$935$	0.389622	−	1.16402i	0.0127420	−	0.0380676i
$936$	−17.3184	−	12.9191i	−0.566070	−	0.422275i
$937$	−9.95025	+	9.95025i	−0.325061	+	0.325061i	−0.850705	−	0.525644i	$-0.823824\pi$
$937$	−9.95025	+	9.95025i	−0.325061	+	0.325061i	0.525644	+	0.850705i	$0.323824\pi$
$938$	−2.85587	−	1.64884i	−0.0932473	−	0.0538364i
$939$	−12.0180	−	6.93858i	−0.392192	−	0.226432i
$940$	1.14002	+	5.60661i	0.0371834	+	0.182868i
$941$	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
$945$	−21.3815	−	14.1556i	−0.695540	−	0.460481i
$946$	−1.56309	−	0.902453i	−0.0508206	−	0.0293413i
$947$	33.7590	+	19.4908i	1.09702	+	0.633365i	0.935437	−	0.353494i	$-0.115007\pi$
$947$	33.7590	+	19.4908i	1.09702	+	0.633365i	0.161583	+	0.986859i	$0.448340\pi$
$948$	−23.7853	+	23.7853i	−0.772511	+	0.772511i
$949$	−6.93824	−	16.1275i	−0.225225	−	0.523522i
$950$	−16.7242	+	2.34659i	−0.542604	+	0.0761335i
$951$	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	−0.820798	−	0.571219i	$-0.806471\pi$
$953$	−56.0994	−	15.0318i	−1.81724	−	0.486928i	−0.996441	+	0.0842907i	$0.973138\pi$
$954$	−16.0392	+	16.0392i	−0.519290	+	0.519290i
$955$	44.5189	−	9.05226i	1.44060	−	0.292924i
$956$	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
$960$	−0.410108	+	6.69286i	−0.0132362	+	0.216011i
$961$			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
$965$	3.24523	+	3.66889i	0.104468	+	0.118106i
$966$	27.7344	−	16.0125i	0.892340	−	0.515193i
$967$	51.5834			1.65881			0.829405	−	0.558648i	$-0.188680\pi$
$967$	51.5834			1.65881			0.829405	+	0.558648i	$0.188680\pi$
$968$	8.84918	−	5.10908i	0.284423	−	0.164212i
$969$	−1.62750	+	6.07391i	−0.0522828	+	0.195122i
$970$	7.08449	−	21.1654i	0.227469	−	0.679580i
$971$	−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
$975$	1.19351	+	54.0476i	0.0382229	+	1.73091i
$976$	−7.07542			−0.226479
$977$	−20.1158	+	34.8416i	−0.643562	+	1.11468i	0.341070	+	0.940038i	$0.389211\pi$
$977$	−20.1158	+	34.8416i	−0.643562	+	1.11468i	−0.984632	+	0.174644i	$0.944123\pi$
$978$	60.2364	−	16.1403i	1.92615	−	0.516110i
$979$	−2.78669	−	4.82668i	−0.0890629	−	0.154261i
$980$	−3.80918	+	11.3802i	−0.121680	+	0.363527i
$981$	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	$-0.381094\pi$
$983$	22.8830			0.729856			0.364928	+	0.931036i	$0.381094\pi$
$984$	22.4831	−	12.9806i	0.716735	−	0.413807i
$985$	2.25151	+	2.54545i	0.0717391	+	0.0811047i
$986$	−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
$990$	−0.724647	+	11.8261i	−0.0230308	+	0.375857i
$991$	−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
$995$	−13.1593	+	2.67575i	−0.417178	+	0.0848269i
$996$	−3.71220	+	3.71220i	−0.117626	+	0.117626i
$997$	−26.6514	−	7.14123i	−0.844060	−	0.226165i	−0.189222	−	0.981934i	$-0.560596\pi$
$997$	−26.6514	−	7.14123i	−0.844060	−	0.226165i	−0.654838	+	0.755769i	$0.727263\pi$
$998$	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	130.2.s.a.33.3	yes	12
5.2	odd	4		130.2.p.a.7.1	✓	12
5.3	odd	4		650.2.t.e.7.3		12
5.4	even	2		650.2.w.e.293.1		12
13.2	odd	12		130.2.p.a.93.1	yes	12
65.2	even	12	inner	130.2.s.a.67.3	yes	12
65.28	even	12		650.2.w.e.457.1		12
65.54	odd	12		650.2.t.e.93.3		12

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

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:	\( N \)	\(=\)	\( 130 = 2 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	130.s (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} +(-0.709753 + 2.12044i) q^{5} +(-0.776134 + 2.89657i) q^{6} +(-1.10671 + 0.638961i) q^{7} +1.00000 q^{8} +(5.18966 - 2.99625i) q^{9} +(-1.48148 - 1.67488i) q^{10} +(-0.228853 - 0.854091i) q^{11} +(-2.12044 - 2.12044i) q^{12} +(-1.42488 - 3.31205i) q^{13} -1.27792i q^{14} +(-0.410108 + 6.69286i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.160684 - 0.599680i) q^{17} +5.99250i q^{18} +(-3.26251 - 0.874187i) q^{19} +(2.19123 - 0.445554i) q^{20} +(-2.70975 + 2.70975i) q^{21} +(0.854091 + 0.228853i) q^{22} +(2.16292 + 8.07211i) q^{23} +(2.89657 - 0.776134i) q^{24} +(-3.99250 - 3.00997i) q^{25} +(3.58077 + 0.422042i) q^{26} +(6.34541 - 6.34541i) q^{27} +(1.10671 + 0.638961i) q^{28} +(-5.53601 - 3.19622i) q^{29} +(-5.59113 - 3.70159i) q^{30} +(-7.30303 - 7.30303i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.32578 - 2.29631i) q^{33} +(0.438997 + 0.438997i) q^{34} +(-0.569383 - 2.80022i) q^{35} +(-5.18966 - 2.99625i) q^{36} +(7.93494 + 4.58124i) q^{37} +(2.38832 - 2.38832i) q^{38} +(-6.69787 - 8.48770i) q^{39} +(-0.709753 + 2.12044i) q^{40} +(8.36236 - 2.24069i) q^{41} +(-0.991839 - 3.70159i) q^{42} +(-1.97169 - 0.528312i) q^{43} +(-0.625238 + 0.625238i) q^{44} +(2.66998 + 13.1309i) q^{45} +(-8.07211 - 2.16292i) q^{46} +2.55866i q^{47} +(-0.776134 + 2.89657i) q^{48} +(-2.68346 + 4.64788i) q^{49} +(4.60296 - 1.95262i) q^{50} -1.86173i q^{51} +(-2.15588 + 2.89001i) q^{52} +(2.67655 + 2.67655i) q^{53} +(2.32258 + 8.66799i) q^{54} +(1.97348 + 0.120926i) q^{55} +(-1.10671 + 0.638961i) q^{56} -10.1286 q^{57} +(5.53601 - 3.19622i) q^{58} +(0.288254 - 1.07578i) q^{59} +(6.00124 - 2.99126i) q^{60} +(3.53771 + 6.12749i) q^{61} +(9.97612 - 2.67309i) q^{62} +(-3.82898 + 6.63198i) q^{63} +1.00000 q^{64} +(8.03432 - 0.670633i) q^{65} +2.65156 q^{66} +(1.29025 - 2.23477i) q^{67} +(-0.599680 + 0.160684i) q^{68} +(12.5301 + 21.7027i) q^{69} +(2.70975 + 0.907010i) q^{70} +(-1.80066 + 6.72017i) q^{71} +(5.18966 - 2.99625i) q^{72} +4.86934 q^{73} +(-7.93494 + 4.58124i) q^{74} +(-13.9007 - 5.61988i) q^{75} +(0.874187 + 3.26251i) q^{76} +(0.799006 + 0.799006i) q^{77} +(10.6995 - 1.55668i) q^{78} -11.2172i q^{79} +(-1.48148 - 1.67488i) q^{80} +(4.46628 - 7.73583i) q^{81} +(-2.24069 + 8.36236i) q^{82} -1.75068i q^{83} +(3.70159 + 0.991839i) q^{84} +(1.15754 + 0.766345i) q^{85} +(1.44337 - 1.44337i) q^{86} +(-18.5161 - 4.96138i) q^{87} +(-0.228853 - 0.854091i) q^{88} +(6.08837 - 1.63137i) q^{89} +(-12.7067 - 4.25320i) q^{90} +(3.69321 + 2.75505i) q^{91} +(5.90920 - 5.90920i) q^{92} +(-26.8219 - 15.4856i) q^{93} +(-2.21587 - 1.27933i) q^{94} +(4.16923 - 6.29749i) q^{95} +(-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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} - 6 q^{4} + 6 q^{7} + 12 q^{8} + 24 q^{9} + 6 q^{11} - 6 q^{13} - 6 q^{15} - 6 q^{16} - 36 q^{19} - 24 q^{21} + 6 q^{23} + 12 q^{25} + 6 q^{26} - 12 q^{27} - 6 q^{28} - 6 q^{29} - 18 q^{30}+ \cdots - 54 q^{99}+O(q^{100}) \) 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^15 - 6 * q^16 - 36 * q^19 - 24 * q^21 + 6 * q^23 + 12 * q^25 + 6 * q^26 - 12 * q^27 - 6 * q^28 - 6 * q^29 - 18 * q^30 - 24 * q^31 - 6 * q^32 + 18 * q^33 + 12 * q^34 - 12 * q^35 - 24 * q^36 + 6 * q^37 + 6 * q^38 - 6 * q^39 + 18 * q^41 + 18 * q^42 - 6 * q^44 - 18 * q^45 - 6 * q^46 + 6 * q^50 + 18 * q^53 + 6 * q^54 - 6 * q^55 + 6 * q^56 + 6 * q^58 - 18 * q^59 + 24 * q^60 + 18 * q^61 + 36 * q^62 + 12 * q^64 + 42 * q^65 - 36 * q^66 + 24 * q^67 - 12 * q^68 + 42 * q^69 + 24 * q^70 + 18 * q^71 + 24 * q^72 - 12 * q^73 - 6 * q^74 + 24 * q^75 + 30 * q^76 - 30 * q^77 + 30 * q^78 + 30 * q^81 - 18 * q^82 + 6 * q^84 - 42 * q^85 - 60 * q^87 + 6 * q^88 - 6 * q^89 + 12 * q^90 - 6 * q^91 - 30 * q^93 - 24 * q^94 - 24 * q^95 + 6 * q^97 - 54 * q^99

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