LMFDB - Embedded newform 130.2.s.a.67.3

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			67.3
Root			$1.55227i$ of defining polynomial
Character	$\chi$	$=$	130.67
Dual form			130.2.s.a.33.3

$q$-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 $\left(\mathbb{Z}/130\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{12}\right)$

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	$-0.0835629\pi$
$3$	2.89657	+	0.776134i	1.67234	+	0.448101i	0.706597	+	0.707617i	$0.250230\pi$
$4$	−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	0.276051	−	0.961143i	$-0.410974\pi$
$7$	−1.10671	−	0.638961i	−0.418298	−	0.241505i	−0.694349	+	0.719638i	$0.744308\pi$
$8$	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	−0.991806	−	0.127750i	$-0.959224\pi$
$11$	−0.228853	+	0.854091i	−0.0690018	+	0.257518i	0.922805	+	0.385268i	$0.125891\pi$
$12$	−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	0.982670	−	0.185363i	$-0.0593460\pi$
$17$	0.160684	+	0.599680i	0.0389716	+	0.145444i	−0.943699	+	0.330806i	$0.892679\pi$
$18$		−	5.99250i		−	1.41245i
$19$	−3.26251	+	0.874187i	−0.748471	+	0.200552i	−0.612840	−	0.790207i	$-0.709973\pi$
$19$	−3.26251	+	0.874187i	−0.748471	+	0.200552i	−0.135631	+	0.990759i	$0.543306\pi$
$20$	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	−0.248591	−	0.968608i	$-0.579968\pi$
$23$	2.16292	−	8.07211i	0.450999	−	1.68315i	0.699591	−	0.714544i	$-0.253366\pi$
$24$	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	−0.916414	−	0.400231i	$-0.868930\pi$
$29$	−5.53601	+	3.19622i	−1.02801	+	0.593522i	−0.111597	+	0.993754i	$0.535596\pi$
$30$	−5.59113	+	3.70159i	−1.02080	+	0.675815i
$31$	−7.30303	+	7.30303i	−1.31166	+	1.31166i	−0.391473	+	0.920190i	$0.628034\pi$
$31$	−7.30303	+	7.30303i	−1.31166	+	1.31166i	−0.920190	+	0.391473i	$0.871966\pi$
$32$	−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	0.323325	−	0.946288i	$-0.395199\pi$
$37$	7.93494	−	4.58124i	1.30450	−	0.753151i	0.981172	+	0.193137i	$0.0618661\pi$
$38$	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	0.843709	−	0.536801i	$-0.180367\pi$
$41$	8.36236	+	2.24069i	1.30598	+	0.349937i	0.462273	+	0.886738i	$0.347034\pi$
$42$	−0.991839	+	3.70159i	−0.153044	+	0.571168i
$43$	−1.97169	+	0.528312i	−0.300679	+	0.0805668i	−0.406005	−	0.913871i	$-0.633078\pi$
$43$	−1.97169	+	0.528312i	−0.300679	+	0.0805668i	0.105325	+	0.994438i	$0.466412\pi$
$44$	−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	$-0.940250\pi$
$47$		−	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
$50$	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	−0.498968	−	0.866621i	$-0.666287\pi$
$53$	2.67655	−	2.67655i	0.367653	−	0.367653i	0.866621	+	0.498968i	$0.166287\pi$
$54$	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	0.982148	−	0.188111i	$-0.0602364\pi$
$59$	0.288254	+	1.07578i	0.0375275	+	0.140054i	−0.944620	+	0.328165i	$0.893570\pi$
$60$	6.00124	+	2.99126i	0.774756	+	0.386170i
$61$	3.53771	−	6.12749i	0.452957	−	0.784545i	−0.545611	−	0.838039i	$-0.683702\pi$
$61$	3.53771	−	6.12749i	0.452957	−	0.784545i	0.998568	+	0.0534935i	$0.0170356\pi$
$62$	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	0.934013	−	0.357239i	$-0.116282\pi$
$67$	1.29025	+	2.23477i	0.157629	+	0.273021i	−0.776384	+	0.630260i	$0.782948\pi$
$68$	−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	−0.986620	−	0.163035i	$-0.947872\pi$
$71$	−1.80066	−	6.72017i	−0.213699	−	0.797537i	0.772921	−	0.634502i	$-0.218795\pi$
$72$	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	$0.217362\pi$
$79$			11.2172i			1.26203i	−0.775770	+	0.631015i	$0.782638\pi$
$80$	−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	$0.0306307\pi$
$83$			1.75068i			0.192162i	−0.995374	+	0.0960809i	$0.969369\pi$
$84$	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	0.566633	−	0.823970i	$-0.308246\pi$
$89$	6.08837	+	1.63137i	0.645366	+	0.172925i	0.0787333	+	0.996896i	$0.474912\pi$
$90$	−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	−0.493230	−	0.869899i	$-0.664184\pi$
$97$	4.99081	−	8.64434i	0.506740	−	0.877700i	0.999970	−	0.00780033i	$-0.00248295\pi$
$98$	−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	−0.453973	−	0.891015i	$-0.649994\pi$
$101$	0.911347	−	0.526166i	0.0906824	−	0.0523555i	0.544655	+	0.838660i	$0.316660\pi$
$102$	1.61230	−	0.930864i	0.159642	−	0.0921693i
$103$	−3.37370	−	3.37370i	−0.332420	−	0.332420i	0.521085	−	0.853505i	$-0.325528\pi$
$103$	−3.37370	−	3.37370i	−0.332420	−	0.332420i	−0.853505	+	0.521085i	$0.825528\pi$
$104$	−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	−0.503454	−	0.864022i	$-0.667938\pi$
$107$	3.77105	−	14.0737i	0.364561	−	1.36056i	0.868015	−	0.496538i	$-0.165396\pi$
$108$	−8.66799	+	2.32258i	−0.834077	+	0.223490i
$109$	4.33526	+	4.33526i	0.415243	+	0.415243i	0.883560	−	0.468317i	$-0.155140\pi$
$109$	4.33526	+	4.33526i	0.415243	+	0.415243i	−0.468317	+	0.883560i	$0.655140\pi$
$110$	−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	−0.999762	−	0.0218255i	$-0.993052\pi$
$113$	−1.53983	−	5.74674i	−0.144855	−	0.540608i	0.854906	−	0.518782i	$-0.173614\pi$
$114$	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	0.769606	−	0.638519i	$-0.220453\pi$
$127$	12.5862	+	3.37246i	1.11684	+	0.299257i	0.347238	+	0.937777i	$0.387119\pi$
$128$	−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	−0.0269793	−	0.999636i	$-0.508589\pi$
$137$	−10.6066	−	6.12370i	−0.906179	−	0.523183i	−0.879200	+	0.476453i	$0.841922\pi$
$138$	−25.0602			−2.13326
$139$	0.835876	+	0.482593i	0.0708980	+	0.0409330i	0.535030	−	0.844833i	$-0.320300\pi$
$139$	0.835876	+	0.482593i	0.0708980	+	0.0409330i	−0.464132	+	0.885766i	$0.653634\pi$
$140$	−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	−0.379771	−	0.925081i	$-0.623997\pi$
$149$	−3.00429	+	0.804997i	−0.246121	+	0.0659480i	0.133649	+	0.991029i	$0.457330\pi$
$150$	11.8173	+	9.22842i	0.964879	+	0.753497i
$151$	−10.8684	−	10.8684i	−0.884459	−	0.884459i	0.109525	−	0.993984i	$-0.465067\pi$
$151$	−10.8684	−	10.8684i	−0.884459	−	0.884459i	−0.993984	+	0.109525i	$0.965067\pi$
$152$	−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	0.959124	−	0.282985i	$-0.0913248\pi$
$157$	8.47200	+	8.47200i	0.676139	+	0.676139i	−0.282985	+	0.959124i	$0.591325\pi$
$158$	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	0.0953137	+	0.995447i	$0.469615\pi$
$163$	−10.3979	+	18.0097i	−0.814426	+	1.41063i	−0.909739	+	0.415180i	$0.863719\pi$
$164$	−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	−0.842585	−	0.538563i	$-0.818967\pi$
$167$	−10.3056	+	5.94992i	−0.797469	+	0.460419i	0.0451166	+	0.998982i	$0.485634\pi$
$168$	−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	−0.776768	−	0.629787i	$-0.783142\pi$
$173$	−14.9230	+	3.99861i	−1.13457	+	0.304008i	−0.357807	+	0.933796i	$0.616475\pi$
$174$	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	0.828500	−	0.559989i	$-0.189195\pi$
$179$	−0.946097	−	1.63869i	−0.0707146	−	0.122481i	−0.899215	+	0.437508i	$0.855861\pi$
$180$	10.0367	+	8.87774i	0.748094	+	0.661708i
$181$			20.4481i			1.51990i	0.649983	+	0.759949i	$0.274776\pi$
$181$			20.4481i			1.51990i	−0.649983	+	0.759949i	$0.725224\pi$
$182$	−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	0.219667	+	0.975575i	$0.429503\pi$
$191$	−10.1584	+	17.5949i	−0.735039	+	1.27312i	−0.954706	+	0.297550i	$0.903830\pi$
$192$	2.89657	+	0.776134i	0.209042	+	0.0560126i
$193$	1.09527	+	1.89706i	0.0788392	+	0.136553i	0.902749	−	0.430167i	$-0.141545\pi$
$193$	1.09527	+	1.89706i	0.0788392	+	0.136553i	−0.823910	+	0.566720i	$0.808212\pi$
$194$	−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	0.891825	−	0.452380i	$-0.149425\pi$
$197$	0.759889	+	1.31617i	0.0541398	+	0.0937729i	−0.837685	+	0.546153i	$0.816092\pi$
$198$	5.11814	+	1.37140i	0.363731	+	0.0974613i
$199$	3.00272	−	5.20086i	0.212857	−	0.368680i	−0.739750	−	0.672881i	$-0.765056\pi$
$199$	3.00272	−	5.20086i	0.212857	−	0.368680i	0.952608	+	0.304202i	$0.0983898\pi$
$200$	−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	0.815277	−	0.579071i	$-0.196585\pi$
$211$	−1.36327	−	2.36126i	−0.0938515	−	0.162556i	−0.909129	+	0.416515i	$0.863251\pi$
$212$	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	−0.266645	−	0.963795i	$-0.585915\pi$
$223$	6.49152	−	3.74788i	0.434704	−	0.250976i	0.701349	+	0.712818i	$0.252582\pi$
$224$	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	−0.997829	−	0.0658594i	$-0.979021\pi$
$227$	−6.65757	+	11.5313i	−0.441879	+	0.765356i	0.555950	+	0.831215i	$0.312354\pi$
$228$	5.06429	−	8.77160i	0.335391	−	0.580914i
$229$	2.64090	−	2.64090i	0.174516	−	0.174516i	−0.614445	−	0.788960i	$-0.710620\pi$
$229$	2.64090	−	2.64090i	0.174516	−	0.174516i	0.788960	+	0.614445i	$0.210620\pi$
$230$	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	0.323454	−	0.946244i	$-0.395156\pi$
$233$	−9.50648	−	9.50648i	−0.622790	−	0.622790i	−0.946244	+	0.323454i	$0.895156\pi$
$234$	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	0.280464	−	0.959864i	$-0.409512\pi$
$239$	−10.5033	−	10.5033i	−0.679400	−	0.679400i	−0.959864	+	0.280464i	$0.909512\pi$
$240$	−5.59113	+	3.70159i	−0.360906	+	0.238937i
$241$	1.48479	−	0.397848i	0.0956436	−	0.0256276i	−0.210680	−	0.977555i	$-0.567568\pi$
$241$	1.48479	−	0.397848i	0.0956436	−	0.0256276i	0.306323	+	0.951927i	$0.400901\pi$
$242$		−	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	0.268759	−	0.963207i	$-0.413386\pi$
$251$	−6.82870	−	3.94255i	−0.431024	−	0.248852i	−0.699783	+	0.714356i	$0.746720\pi$
$252$	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	0.186354	−	0.982483i	$-0.440333\pi$
$257$	−2.30049	−	0.616415i	−0.143501	−	0.0384509i	−0.329854	+	0.944032i	$0.607000\pi$
$258$	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	−0.535985	−	0.844227i	$-0.680060\pi$
$263$	−23.0654	−	6.18036i	−1.42228	−	0.381098i	−0.886290	+	0.463130i	$0.846726\pi$
$264$	−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	0.981012	+	0.193949i	$0.0621295\pi$
$269$	26.8895	+	15.5247i	1.63948	+	0.946555i	0.658470	+	0.752607i	$0.271204\pi$
$270$	−20.0284	+	1.22725i	−1.21889	+	0.0746880i
$271$	2.52048	−	9.40656i	0.153108	−	0.571408i	−0.846152	−	0.532942i	$-0.821086\pi$
$271$	2.52048	−	9.40656i	0.153108	−	0.571408i	0.999260	−	0.0384657i	$-0.0122470\pi$
$272$	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	0.607598	+	0.794245i	$0.292133\pi$
$277$	7.96424	+	29.7230i	0.478525	+	1.78588i	−0.129073	+	0.991635i	$0.541200\pi$
$278$		−	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	0.631721	−	0.775196i	$-0.282349\pi$
$281$	−2.40508	−	2.40508i	−0.143475	−	0.143475i	−0.775196	+	0.631721i	$0.782349\pi$
$282$	−7.41135	+	1.98586i	−0.441339	+	0.118256i
$283$	−3.58042	+	13.3623i	−0.212834	+	0.794307i	0.774084	+	0.633083i	$0.218211\pi$
$283$	−3.58042	+	13.3623i	−0.212834	+	0.794307i	−0.986918	+	0.161224i	$0.948456\pi$
$284$	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	−0.934237	−	0.356653i	$-0.883918\pi$
$293$	−2.70877	+	4.69172i	−0.158248	+	0.274093i	0.775989	+	0.630746i	$0.217251\pi$
$294$	−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	$-0.987812\pi$
$307$		−	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
$310$	−1.41246	−	23.0510i	−0.0802223	−	1.30921i
$311$		−	2.71377i		−	0.153884i	−0.997036	−	0.0769419i	$-0.975484\pi$
$311$		−	2.71377i		−	0.153884i	0.997036	−	0.0769419i	$-0.0245156\pi$
$312$	−6.69787	+	8.48770i	−0.379192	+	0.480521i
$313$	−3.27224	+	3.27224i	−0.184958	+	0.184958i	−0.793512	−	0.608554i	$-0.791750\pi$
$313$	−3.27224	+	3.27224i	−0.184958	+	0.184958i	0.608554	+	0.793512i	$0.291750\pi$
$314$	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	0.999584	−	0.0288278i	$-0.00917745\pi$
$331$	2.17420	+	8.11424i	0.119505	+	0.445999i	−0.880079	+	0.474827i	$0.842511\pi$
$332$	−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	−0.510779	−	0.859712i	$-0.670643\pi$
$337$	6.40557	−	6.40557i	0.348934	−	0.348934i	0.859712	+	0.510779i	$0.170643\pi$
$338$	−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	−0.713412	−	0.700745i	$-0.752851\pi$
$347$	−18.2716	+	4.89586i	−0.980871	+	0.262824i	−0.267460	+	0.963569i	$0.586184\pi$
$348$	4.96138	−	18.5161i	0.265958	−	0.992568i
$349$	−21.6314	−	5.79612i	−1.15790	−	0.310259i	−0.371775	−	0.928323i	$-0.621251\pi$
$349$	−21.6314	−	5.79612i	−1.15790	−	0.310259i	−0.786128	+	0.618064i	$0.787917\pi$
$350$	−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	0.466828	−	0.884348i	$-0.345397\pi$
$353$	27.5457	−	15.9035i	1.46611	−	0.846459i	0.999282	+	0.0378892i	$0.0120634\pi$
$354$	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	−0.444570	−	0.895744i	$-0.646644\pi$
$359$	8.54852	−	8.54852i	0.451173	−	0.451173i	0.895744	+	0.444570i	$0.146644\pi$
$360$	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	−0.942283	−	0.334819i	$-0.891325\pi$
$367$	0.788653	−	2.94329i	0.0411674	−	0.153639i	0.983450	+	0.181180i	$0.0579916\pi$
$368$	−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	0.986906	−	0.161297i	$-0.0515678\pi$
$373$	0.996016	+	3.71718i	0.0515717	+	0.192468i	−0.935334	+	0.353766i	$0.884901\pi$
$374$	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	−0.998872	−	0.0474782i	$-0.984882\pi$
$379$	−2.14311	+	7.99821i	−0.110084	+	0.410841i	0.888788	+	0.458319i	$0.151548\pi$
$380$	−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	0.400295	−	0.916386i	$-0.368908\pi$
$383$	−3.78044	−	2.18264i	−0.193172	−	0.111528i	−0.593466	+	0.804859i	$0.702241\pi$
$384$	−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	0.771522	−	0.636203i	$-0.219496\pi$
$397$	12.0807	+	6.97482i	0.606315	+	0.350056i	−0.165207	+	0.986259i	$0.552829\pi$
$398$	−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	0.825998	+	0.563673i	$0.190612\pi$
$401$	−3.42776	+	12.7926i	−0.171174	+	0.638830i	−0.997172	+	0.0751566i	$0.976054\pi$
$402$	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	0.420538	−	0.907275i	$-0.361841\pi$
$409$	25.0445	−	6.71066i	1.23837	−	0.331821i	0.817834	+	0.575454i	$0.195175\pi$
$410$	−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	0.00445381	−	0.999990i	$-0.498582\pi$
$419$	17.8637	−	10.3136i	0.872698	−	0.503852i	0.868244	+	0.496138i	$0.165249\pi$
$420$	−4.73035	−	7.14503i	−0.230817	−	0.348642i
$421$	−21.3596	+	21.3596i	−1.04100	+	1.04100i	−0.0418813	+	0.999123i	$0.513335\pi$
$421$	−21.3596	+	21.3596i	−1.04100	+	1.04100i	−0.999123	+	0.0418813i	$0.986665\pi$
$422$	−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	0.958715	−	0.284369i	$-0.0917839\pi$
$431$	34.1885	+	9.16078i	1.64680	+	0.441259i	0.688087	+	0.725628i	$0.258451\pi$
$432$	2.32258	−	8.66799i	0.111745	−	0.417039i
$433$	28.8432	−	7.72850i	1.38611	−	0.371408i	0.512776	−	0.858523i	$-0.328617\pi$
$433$	28.8432	−	7.72850i	1.38611	−	0.371408i	0.873338	+	0.487114i	$0.161951\pi$
$434$	−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	0.609311	−	0.792931i	$-0.291446\pi$
$439$	−8.00470	−	13.8645i	−0.382043	−	0.661718i	−0.991354	+	0.131213i	$0.958113\pi$
$440$	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	0.0299327	−	0.999552i	$-0.490471\pi$
$443$	21.6681	−	21.6681i	1.02948	−	1.02948i	0.999552	−	0.0299327i	$-0.00952930\pi$
$444$	−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	0.998805	−	0.0488699i	$-0.0155620\pi$
$449$	2.31771	+	8.64982i	0.109380	+	0.408210i	−0.889426	+	0.457080i	$0.848895\pi$
$450$	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	−0.996111	−	0.0881087i	$-0.971918\pi$
$457$	−12.2784	−	21.2668i	−0.574360	−	0.994820i	0.421751	−	0.906712i	$-0.361416\pi$
$458$	−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	0.879071	−	0.476692i	$-0.158164\pi$
$461$	−2.58880	−	9.66155i	−0.120573	−	0.449983i	−0.999643	+	0.0267083i	$0.991497\pi$
$462$	−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	−0.0350738	+	0.999385i	$0.511167\pi$
$467$	−22.3548	+	22.3548i	−1.03446	+	1.03446i	−0.999385	+	0.0350738i	$0.988833\pi$
$468$	−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	0.208979	−	0.977920i	$-0.432986\pi$
$479$	−2.16670	−	0.580565i	−0.0989990	−	0.0265267i	−0.307978	+	0.951393i	$0.599652\pi$
$480$	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	−0.478373	−	0.878157i	$-0.658773\pi$
$487$	11.5045	−	19.9264i	0.521319	−	0.902951i	0.999693	−	0.0247947i	$-0.00789322\pi$
$488$	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	−0.549309	−	0.835619i	$-0.685109\pi$
$491$	−2.22242	+	1.28311i	−0.100296	+	0.0579061i	0.449013	+	0.893525i	$0.351776\pi$
$492$	−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	0.841157	−	0.540791i	$-0.181875\pi$
$499$	6.70967	+	6.70967i	0.300366	+	0.300366i	−0.540791	+	0.841157i	$0.681875\pi$
$500$	−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	0.999988	−	0.00498191i	$-0.00158580\pi$
$503$	2.94883	+	11.0052i	0.131482	+	0.490697i	−0.868506	+	0.495679i	$0.834919\pi$
$504$	−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	0.218296	+	0.975883i	$0.429950\pi$
$509$	−10.3486	+	38.6216i	−0.458695	+	1.71187i	−0.676991	+	0.735991i	$0.736716\pi$
$510$	−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	0.756806	−	0.653640i	$-0.226759\pi$
$523$	24.8222	+	6.65109i	1.08540	+	0.290832i	0.328593	+	0.944472i	$0.393426\pi$
$524$	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	0.137105	−	0.990557i	$-0.456220\pi$
$541$	−19.8508	−	19.8508i	−0.853451	−	0.853451i	−0.990557	+	0.137105i	$0.956220\pi$
$542$	−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	0.0562990	−	0.998414i	$-0.482070\pi$
$547$	−22.0342	−	22.0342i	−0.942115	−	0.942115i	−0.998414	+	0.0562990i	$0.982070\pi$
$548$	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	0.126055	−	0.992023i	$-0.459768\pi$
$557$	24.7384	−	14.2827i	1.04820	−	0.605179i	0.922145	+	0.386844i	$0.126435\pi$
$558$	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	−0.219015	−	0.975721i	$-0.570284\pi$
$563$	1.87859	−	0.503366i	0.0791731	−	0.0212144i	0.298188	+	0.954507i	$0.403618\pi$
$564$	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	−0.996322	−	0.0856922i	$-0.972690\pi$
$569$	−13.6532	−	23.6481i	−0.572372	−	0.991378i	0.423949	−	0.905686i	$-0.360643\pi$
$570$	15.0052	−	16.9642i	0.628500	−	0.710551i
$571$		−	34.7539i		−	1.45441i	−0.686423	−	0.727203i	$-0.740820\pi$
$571$		−	34.7539i		−	1.45441i	0.686423	−	0.727203i	$-0.259180\pi$
$572$	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	0.972913	+	0.231172i	$0.0742559\pi$
$587$	16.6364	+	28.8151i	0.686657	+	1.18932i	−0.286256	+	0.958153i	$0.592411\pi$
$588$	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	$0.00616098\pi$
$599$			0.947362i			0.0387082i	−0.999813	+	0.0193541i	$0.993839\pi$
$600$	−13.9007	+	5.61988i	−0.567494	+	0.229431i
$601$	9.46190	+	16.3885i	0.385959	+	0.668500i	0.991902	−	0.127008i	$-0.0405373\pi$
$601$	9.46190	+	16.3885i	0.385959	+	0.668500i	−0.605943	+	0.795508i	$0.707204\pi$
$602$	−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	−0.618039	−	0.786147i	$-0.712073\pi$
$607$	−18.7294	+	5.01853i	−0.760204	+	0.203696i	−0.142164	+	0.989843i	$0.545406\pi$
$608$	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	−0.613820	−	0.789446i	$-0.710368\pi$
$613$	−5.86909	+	3.38852i	−0.237050	+	0.136861i	0.376770	+	0.926307i	$0.377035\pi$
$614$	−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	−0.759052	−	0.651030i	$-0.774337\pi$
$617$	4.57750	−	7.92846i	0.184283	−	0.319188i	0.943335	+	0.331843i	$0.107670\pi$
$618$	−7.15371	+	12.3906i	−0.287764	+	0.498422i
$619$	−5.10375	+	5.10375i	−0.205137	+	0.205137i	−0.802197	−	0.597060i	$-0.796336\pi$
$619$	−5.10375	+	5.10375i	−0.205137	+	0.205137i	0.597060	+	0.802197i	$0.296336\pi$
$620$	−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	−0.0624090	−	0.998051i	$-0.519878\pi$
$631$	9.61001	−	2.57499i	0.382568	−	0.102509i	0.444978	+	0.895542i	$0.353212\pi$
$632$			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	0.337957	−	0.941161i	$-0.390264\pi$
$641$	−7.80132	−	4.50409i	−0.308134	−	0.177901i	−0.646091	+	0.763260i	$0.723597\pi$
$642$	−43.6924			−1.72440
$643$	−3.34673	−	1.93223i	−0.131982	−	0.0761998i	0.432555	−	0.901607i	$-0.357612\pi$
$643$	−3.34673	−	1.93223i	−0.131982	−	0.0761998i	−0.564537	+	0.825408i	$0.690945\pi$
$644$	−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	0.301159	−	0.953574i	$-0.402626\pi$
$647$	2.16676	+	0.580581i	0.0851841	+	0.0228250i	−0.215975	+	0.976399i	$0.569293\pi$
$648$	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	−0.178341	−	0.983969i	$-0.557073\pi$
$653$	−21.0761	−	5.64733i	−0.824773	−	0.220997i	−0.646432	+	0.762972i	$0.723740\pi$
$654$	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	0.999581	+	0.0289434i	$0.00921424\pi$
$659$	39.1338	+	22.5939i	1.52444	+	0.880134i	0.524856	+	0.851191i	$0.324119\pi$
$660$	−3.92821	+	4.44104i	−0.152906	+	0.172867i
$661$	−0.707218	+	2.63937i	−0.0275076	+	0.102660i	−0.978315	−	0.207123i	$-0.933590\pi$
$661$	−0.707218	+	2.63937i	−0.0275076	+	0.102660i	0.950807	+	0.309783i	$0.100256\pi$
$662$	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	0.197961	+	0.980210i	$0.436568\pi$
$673$	−12.0264	+	44.8831i	−0.463583	+	1.73012i	−0.661544	+	0.749906i	$0.730099\pi$
$674$	−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	0.217141	−	0.976140i	$-0.430327\pi$
$677$	−19.7486	−	19.7486i	−0.758999	−	0.758999i	−0.976140	+	0.217141i	$0.930327\pi$
$678$	−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	−0.760355	−	0.649508i	$-0.774975\pi$
$683$	4.76460	−	8.25253i	0.182312	−	0.315774i	0.942668	+	0.333733i	$0.108308\pi$
$684$	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	0.270110	−	0.962829i	$-0.412940\pi$
$691$	0.594540	+	0.159306i	0.0226174	+	0.00606030i	−0.247493	+	0.968890i	$0.579607\pi$
$692$	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	$0.110755\pi$
$701$			18.0552i			0.681935i	−0.940075	+	0.340968i	$0.889245\pi$
$702$	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	0.991914	+	0.126908i	$0.0405053\pi$
$709$	5.22810	+	19.5115i	0.196345	+	0.732771i	−0.795569	+	0.605863i	$0.792828\pi$
$710$	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	−0.978271	−	0.207329i	$-0.933523\pi$
$719$	−8.30123	+	14.3782i	−0.309584	+	0.536215i	0.668688	+	0.743543i	$0.266856\pi$
$720$	−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	−0.769407	−	0.638759i	$-0.779448\pi$
$727$	−3.52264	+	3.52264i	−0.130648	+	0.130648i	0.638759	+	0.769407i	$0.279448\pi$
$728$	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	$-0.942379\pi$
$733$		−	9.74855i		−	0.360071i	0.983660	−	0.180035i	$-0.0576213\pi$
$734$	−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	0.0834798	−	0.996509i	$-0.473397\pi$
$739$	−9.31015	−	2.49465i	−0.342479	−	0.0917670i	−0.425959	+	0.904742i	$0.640063\pi$
$740$	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	0.771782	−	0.635888i	$-0.219366\pi$
$743$	46.5667	−	26.8853i	1.70837	−	0.986326i	0.936586	−	0.350439i	$-0.113968\pi$
$744$	−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	−0.111739	−	0.993738i	$-0.535642\pi$
$751$	18.9911	−	10.9645i	0.692994	−	0.400100i	0.804733	+	0.593637i	$0.202309\pi$
$752$	−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	−0.218692	−	0.975794i	$-0.570179\pi$
$757$	12.6177	−	47.0899i	0.458598	−	1.71151i	0.677290	−	0.735716i	$-0.263154\pi$
$758$	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	0.590023	−	0.807386i	$-0.299119\pi$
$761$	41.5088	−	11.1222i	1.50469	−	0.403181i	0.914668	+	0.404206i	$0.132452\pi$
$762$		−	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	−0.591010	−	0.806664i	$-0.701271\pi$
$769$	8.98900	−	33.5474i	0.324152	−	1.20975i	0.915162	−	0.403087i	$-0.132063\pi$
$770$	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	0.141635	−	0.989919i	$-0.454764\pi$
$773$	−17.9285	−	10.3510i	−0.644843	−	0.372300i	−0.786478	+	0.617619i	$0.788097\pi$
$774$	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	0.790666	−	0.612248i	$-0.209734\pi$
$787$	18.3969	+	10.6214i	0.655777	+	0.378613i	−0.134889	+	0.990861i	$0.543068\pi$
$788$	−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	0.999751	+	0.0223172i	$0.00710438\pi$
$797$	4.09634	+	15.2878i	0.145100	+	0.541520i	−0.854651	+	0.519203i	$0.826229\pi$
$798$		−	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	−0.614950	−	0.788566i	$-0.710824\pi$
$809$	−6.81229	+	3.93308i	−0.239507	+	0.138280i	0.375443	+	0.926845i	$0.377491\pi$
$810$	−19.5733	−	3.97994i	−0.687735	−	0.139841i
$811$	−13.1134	+	13.1134i	−0.460475	+	0.460475i	−0.898811	−	0.438336i	$-0.855568\pi$
$811$	−13.1134	+	13.1134i	−0.460475	+	0.460475i	0.438336	+	0.898811i	$0.355568\pi$
$812$	−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	−0.476137	−	0.879371i	$-0.657963\pi$
$821$	−38.0562	−	10.1971i	−1.32817	−	0.355882i	−0.852032	+	0.523489i	$0.824630\pi$
$822$	−9.50561	+	35.4754i	−0.331546	+	1.23735i
$823$	−11.8543	+	3.17636i	−0.413216	+	0.110721i	−0.459437	−	0.888210i	$-0.651949\pi$
$823$	−11.8543	+	3.17636i	−0.413216	+	0.110721i	0.0462212	+	0.998931i	$0.485282\pi$
$824$	−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	$-0.801344\pi$
$827$		−	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	0.999720	−	0.0236725i	$-0.00753590\pi$
$829$	13.8019	+	23.9055i	0.479359	+	0.830274i	−0.520361	+	0.853946i	$0.674203\pi$
$830$	−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	0.915596	+	0.402099i	$0.131719\pi$
$839$	9.37660	+	34.9939i	0.323716	+	1.20813i	−0.591880	+	0.806026i	$0.701614\pi$
$840$	−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	−0.0870141	+	0.996207i	$0.527733\pi$
$857$	−31.7108	+	31.7108i	−1.08322	+	1.08322i	−0.996207	+	0.0870141i	$0.972267\pi$
$858$	−3.77816	+	8.78210i	−0.128984	+	0.299816i
$859$			49.9135i			1.70303i	0.524332	+	0.851514i	$0.324315\pi$
$859$			49.9135i			1.70303i	−0.524332	+	0.851514i	$0.675685\pi$
$860$	−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	$-0.861980\pi$
$863$		−	24.6850i		−	0.840288i	0.907457	−	0.420144i	$-0.138020\pi$
$864$	−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	−0.954914	−	0.296882i	$-0.904053\pi$
$877$	−6.52548	+	11.3025i	−0.220350	+	0.381657i	0.734564	+	0.678539i	$0.237387\pi$
$878$	−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	−0.925032	−	0.379890i	$-0.875962\pi$
$881$	−31.4196	+	18.1401i	−1.05855	+	0.611156i	−0.133522	+	0.991046i	$0.542629\pi$
$882$	−27.8524	+	16.0806i	−0.937841	+	0.541463i
$883$	−30.8743	−	30.8743i	−1.03900	−	1.03900i	−0.999208	−	0.0397956i	$-0.987329\pi$
$883$	−30.8743	−	30.8743i	−1.03900	−	1.03900i	−0.0397956	−	0.999208i	$-0.512671\pi$
$884$	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	−0.978376	−	0.206835i	$-0.933684\pi$
$887$	−0.823779	+	3.07438i	−0.0276598	+	0.103228i	0.950716	+	0.310063i	$0.100350\pi$
$888$	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	−0.405207	−	0.914225i	$-0.632801\pi$
$907$	−36.5384	−	9.79045i	−1.21324	−	0.325086i	−0.808032	+	0.589138i	$0.799467\pi$
$908$	−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	0.938317	−	0.345776i	$-0.112384\pi$
$919$	33.5898	+	19.3931i	1.10802	+	0.639718i	0.169708	+	0.985494i	$0.445718\pi$
$920$	−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	−0.266778	−	0.963758i	$-0.585959\pi$
$929$	−0.485719	+	0.130148i	−0.0159359	+	0.00427002i	0.250842	+	0.968028i	$0.419292\pi$
$930$	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	0.525644	−	0.850705i	$-0.323824\pi$
$937$	−9.95025	−	9.95025i	−0.325061	−	0.325061i	−0.850705	+	0.525644i	$0.823824\pi$
$938$	−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	−0.204803	−	0.978803i	$-0.565655\pi$
$941$	23.7430	−	23.7430i	0.774000	−	0.774000i	0.978803	+	0.204803i	$0.0656555\pi$
$942$	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	0.161583	−	0.986859i	$-0.448340\pi$
$947$	33.7590	−	19.4908i	1.09702	−	0.633365i	0.935437	+	0.353494i	$0.115007\pi$
$948$	−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	−0.996441	−	0.0842907i	$-0.973138\pi$
$953$	−56.0994	+	15.0318i	−1.81724	+	0.486928i	−0.820798	+	0.571219i	$0.806471\pi$
$954$	−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	0.410019	+	0.912077i	$0.365522\pi$
$971$	−18.2251	+	31.5668i	−0.584872	+	1.01303i	−0.994891	+	0.100951i	$0.967811\pi$
$972$	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	−0.984632	−	0.174644i	$-0.944123\pi$
$977$	−20.1158	−	34.8416i	−0.643562	−	1.11468i	0.341070	−	0.940038i	$-0.389211\pi$
$978$	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	0.827793	−	0.561034i	$-0.189596\pi$
$991$	−2.26574	−	3.92439i	−0.0719738	−	0.124662i	−0.899766	+	0.436372i	$0.856263\pi$
$992$	−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	−0.654838	−	0.755769i	$-0.727263\pi$
$997$	−26.6514	+	7.14123i	−0.844060	+	0.226165i	−0.189222	+	0.981934i	$0.560596\pi$
$998$	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.67.3	yes	12
5.2	odd	4		650.2.t.e.93.3		12
5.3	odd	4		130.2.p.a.93.1	yes	12
5.4	even	2		650.2.w.e.457.1		12
13.7	odd	12		130.2.p.a.7.1	✓	12
65.7	even	12		650.2.w.e.293.1		12
65.33	even	12	inner	130.2.s.a.33.3	yes	12
65.59	odd	12		650.2.t.e.7.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.p.a.7.1	✓	12	13.7	odd	12
130.2.p.a.93.1	yes	12	5.3	odd	4
130.2.s.a.33.3	yes	12	65.33	even	12	inner
130.2.s.a.67.3	yes	12	1.1	even	1	trivial
650.2.t.e.7.3		12	65.59	odd	12
650.2.t.e.93.3		12	5.2	odd	4
650.2.w.e.293.1		12	65.7	even	12
650.2.w.e.457.1		12	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

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