LMFDB - Embedded newform 240.2.bc.e.43.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(43,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0, 3]))

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

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

chi := DirichletCharacter("240.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.bc (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 14 x^{14} - 10 x^{13} - 26 x^{12} + 78 x^{11} - 66 x^{10} - 74 x^{9} + 233 x^{8} + \cdots + 256 $ x^16 - 6x^15 + 14x^14 - 10x^13 - 26x^12 + 78x^11 - 66x^10 - 74x^9 + 233x^8 - 148x^7 - 264x^6 + 624x^5 - 416x^4 - 320x^3 + 896x^2 - 768*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.8
Root			$0.237728 - 1.39409i$ of defining polynomial
Character	$\chi$	$=$	240.43
Dual form			240.2.bc.e.67.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.34756 - 0.429059i) q^{2} +1.00000i q^{3} +(1.63182 - 1.15636i) q^{4} +(-0.0583995 + 2.23531i) q^{5} +(0.429059 + 1.34756i) q^{6} +(0.747384 - 0.747384i) q^{7} +(1.70282 - 2.25841i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(1.34756 - 0.429059i) q^{2} +1.00000i q^{3} +(1.63182 - 1.15636i) q^{4} +(-0.0583995 + 2.23531i) q^{5} +(0.429059 + 1.34756i) q^{6} +(0.747384 - 0.747384i) q^{7} +(1.70282 - 2.25841i) q^{8} -1.00000 q^{9} +(0.880380 + 3.03726i) q^{10} +(-0.920311 + 0.920311i) q^{11} +(1.15636 + 1.63182i) q^{12} +0.996441 q^{13} +(0.686471 - 1.32781i) q^{14} +(-2.23531 - 0.0583995i) q^{15} +(1.32566 - 3.77394i) q^{16} +(-0.982332 + 0.982332i) q^{17} +(-1.34756 + 0.429059i) q^{18} +(1.03458 - 1.03458i) q^{19} +(2.48952 + 3.71514i) q^{20} +(0.747384 + 0.747384i) q^{21} +(-0.845304 + 1.63504i) q^{22} +(-4.77394 - 4.77394i) q^{23} +(2.25841 + 1.70282i) q^{24} +(-4.99318 - 0.261081i) q^{25} +(1.34276 - 0.427532i) q^{26} -1.00000i q^{27} +(0.355348 - 2.08384i) q^{28} +(2.95516 + 2.95516i) q^{29} +(-3.03726 + 0.880380i) q^{30} -10.4545i q^{31} +(0.167155 - 5.65438i) q^{32} +(-0.920311 - 0.920311i) q^{33} +(-0.902270 + 1.74523i) q^{34} +(1.62698 + 1.71428i) q^{35} +(-1.63182 + 1.15636i) q^{36} -8.22694 q^{37} +(0.950259 - 1.83805i) q^{38} +0.996441i q^{39} +(4.94879 + 3.93821i) q^{40} +5.70040i q^{41} +(1.32781 + 0.686471i) q^{42} -5.22869 q^{43} +(-0.437567 + 2.56599i) q^{44} +(0.0583995 - 2.23531i) q^{45} +(-8.48146 - 4.38486i) q^{46} +(-0.0548243 - 0.0548243i) q^{47} +(3.77394 + 1.32566i) q^{48} +5.88283i q^{49} +(-6.84061 + 1.79054i) q^{50} +(-0.982332 - 0.982332i) q^{51} +(1.62601 - 1.15225i) q^{52} +5.13957i q^{53} +(-0.429059 - 1.34756i) q^{54} +(-2.00343 - 2.11092i) q^{55} +(-0.415238 - 2.96056i) q^{56} +(1.03458 + 1.03458i) q^{57} +(5.25018 + 2.71431i) q^{58} +(2.30403 + 2.30403i) q^{59} +(-3.71514 + 2.48952i) q^{60} +(10.8244 - 10.8244i) q^{61} +(-4.48559 - 14.0880i) q^{62} +(-0.747384 + 0.747384i) q^{63} +(-2.20081 - 7.69132i) q^{64} +(-0.0581916 + 2.22735i) q^{65} +(-1.63504 - 0.845304i) q^{66} +8.99029 q^{67} +(-0.467056 + 2.73892i) q^{68} +(4.77394 - 4.77394i) q^{69} +(2.92798 + 1.61201i) q^{70} -14.1421 q^{71} +(-1.70282 + 2.25841i) q^{72} +(-6.35840 + 6.35840i) q^{73} +(-11.0863 + 3.52984i) q^{74} +(0.261081 - 4.99318i) q^{75} +(0.491897 - 2.88459i) q^{76} +1.37565i q^{77} +(0.427532 + 1.34276i) q^{78} +8.76588 q^{79} +(8.35849 + 3.18364i) q^{80} +1.00000 q^{81} +(2.44581 + 7.68161i) q^{82} +12.3589i q^{83} +(2.08384 + 0.355348i) q^{84} +(-2.13845 - 2.25318i) q^{85} +(-7.04595 + 2.24341i) q^{86} +(-2.95516 + 2.95516i) q^{87} +(0.511314 + 3.64556i) q^{88} +18.0456 q^{89} +(-0.880380 - 3.03726i) q^{90} +(0.744724 - 0.744724i) q^{91} +(-13.3106 - 2.26980i) q^{92} +10.4545 q^{93} +(-0.0974017 - 0.0503560i) q^{94} +(2.25218 + 2.37302i) q^{95} +(5.65438 + 0.167155i) q^{96} +(1.29787 - 1.29787i) q^{97} +(2.52408 + 7.92745i) q^{98} +(0.920311 - 0.920311i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{2} + 8 q^{4} - 8 q^{5} + 2 q^{6} - 4 q^{7} + 8 q^{8} - 16 q^{9}+O(q^{10}) $ 16 * q + 2 * q^2 + 8 * q^4 - 8 * q^5 + 2 * q^6 - 4 * q^7 + 8 * q^8 - 16 * q^9	$ 16 q + 2 q^{2} + 8 q^{4} - 8 q^{5} + 2 q^{6} - 4 q^{7} + 8 q^{8} - 16 q^{9} - 2 q^{10} - 4 q^{12} - 8 q^{13} + 4 q^{14} + 4 q^{15} - 8 q^{16} - 8 q^{17} - 2 q^{18} - 8 q^{19} + 4 q^{20} - 4 q^{21} + 4 q^{24} - 32 q^{25} + 20 q^{26} + 12 q^{28} - 12 q^{29} + 2 q^{30} - 28 q^{32} + 12 q^{35} - 8 q^{36} - 24 q^{37} + 16 q^{38} + 16 q^{40} + 24 q^{42} + 24 q^{43} - 52 q^{44} + 8 q^{45} - 16 q^{46} + 32 q^{47} - 16 q^{48} + 6 q^{50} - 8 q^{51} + 24 q^{52} - 2 q^{54} - 4 q^{55} + 20 q^{56} - 8 q^{57} + 12 q^{58} + 24 q^{59} + 24 q^{60} + 40 q^{61} + 28 q^{62} + 4 q^{63} + 8 q^{64} - 4 q^{65} - 8 q^{66} + 16 q^{67} - 8 q^{68} + 12 q^{70} - 8 q^{72} - 8 q^{73} - 64 q^{74} + 24 q^{75} + 16 q^{76} + 12 q^{78} + 48 q^{79} + 16 q^{81} - 32 q^{82} - 12 q^{84} - 8 q^{85} - 8 q^{86} + 12 q^{87} + 24 q^{88} + 2 q^{90} - 40 q^{91} - 16 q^{92} - 32 q^{93} + 20 q^{94} - 8 q^{95} - 28 q^{96} + 48 q^{97} + 62 q^{98}+O(q^{100}) $ 16 * q + 2 * q^2 + 8 * q^4 - 8 * q^5 + 2 * q^6 - 4 * q^7 + 8 * q^8 - 16 * q^9 - 2 * q^10 - 4 * q^12 - 8 * q^13 + 4 * q^14 + 4 * q^15 - 8 * q^16 - 8 * q^17 - 2 * q^18 - 8 * q^19 + 4 * q^20 - 4 * q^21 + 4 * q^24 - 32 * q^25 + 20 * q^26 + 12 * q^28 - 12 * q^29 + 2 * q^30 - 28 * q^32 + 12 * q^35 - 8 * q^36 - 24 * q^37 + 16 * q^38 + 16 * q^40 + 24 * q^42 + 24 * q^43 - 52 * q^44 + 8 * q^45 - 16 * q^46 + 32 * q^47 - 16 * q^48 + 6 * q^50 - 8 * q^51 + 24 * q^52 - 2 * q^54 - 4 * q^55 + 20 * q^56 - 8 * q^57 + 12 * q^58 + 24 * q^59 + 24 * q^60 + 40 * q^61 + 28 * q^62 + 4 * q^63 + 8 * q^64 - 4 * q^65 - 8 * q^66 + 16 * q^67 - 8 * q^68 + 12 * q^70 - 8 * q^72 - 8 * q^73 - 64 * q^74 + 24 * q^75 + 16 * q^76 + 12 * q^78 + 48 * q^79 + 16 * q^81 - 32 * q^82 - 12 * q^84 - 8 * q^85 - 8 * q^86 + 12 * q^87 + 24 * q^88 + 2 * q^90 - 40 * q^91 - 16 * q^92 - 32 * q^93 + 20 * q^94 - 8 * q^95 - 28 * q^96 + 48 * q^97 + 62 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	1.34756	−	0.429059i	0.952866	−	0.303390i
$2$	1.34756	−	0.429059i	0.952866	−	0.303390i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	1.63182	−	1.15636i	0.815909	−	0.578181i
$5$	−0.0583995	+	2.23531i	−0.0261170	+	0.999659i
$5$	−0.0583995	+	2.23531i	−0.0261170	+	0.999659i
$6$	0.429059	+	1.34756i	0.175162	+	0.550138i
$7$	0.747384	−	0.747384i	0.282485	−	0.282485i	−0.551615	−	0.834099i	$-0.685988\pi$
$7$	0.747384	−	0.747384i	0.282485	−	0.282485i	0.834099	+	0.551615i	$0.185988\pi$
$8$	1.70282	−	2.25841i	0.602038	−	0.798468i
$9$	−1.00000			−0.333333
$10$	0.880380	+	3.03726i	0.278401	+	0.960465i
$11$	−0.920311	+	0.920311i	−0.277484	+	0.277484i	−0.832104	−	0.554620i	$-0.812864\pi$
$11$	−0.920311	+	0.920311i	−0.277484	+	0.277484i	0.554620	+	0.832104i	$0.312864\pi$
$12$	1.15636	+	1.63182i	0.333813	+	0.471065i
$13$	0.996441			0.276363			0.138182	−	0.990407i	$-0.455874\pi$
$13$	0.996441			0.276363			0.138182	+	0.990407i	$0.455874\pi$
$14$	0.686471	−	1.32781i	0.183467	−	0.354873i
$15$	−2.23531	−	0.0583995i	−0.577153	−	0.0150787i
$16$	1.32566	−	3.77394i	0.331414	−	0.943485i
$17$	−0.982332	+	0.982332i	−0.238251	+	0.238251i	−0.816125	−	0.577875i	$-0.803882\pi$
$17$	−0.982332	+	0.982332i	−0.238251	+	0.238251i	0.577875	+	0.816125i	$0.303882\pi$
$18$	−1.34756	+	0.429059i	−0.317622	+	0.101130i
$19$	1.03458	−	1.03458i	0.237349	−	0.237349i	−0.578403	−	0.815751i	$-0.696324\pi$
$19$	1.03458	−	1.03458i	0.237349	−	0.237349i	0.815751	+	0.578403i	$0.196324\pi$
$20$	2.48952	+	3.71514i	0.556674	+	0.830731i
$21$	0.747384	+	0.747384i	0.163093	+	0.163093i
$22$	−0.845304	+	1.63504i	−0.180219	+	0.348591i
$23$	−4.77394	−	4.77394i	−0.995436	−	0.995436i	0.00455400	−	0.999990i	$-0.498550\pi$
$23$	−4.77394	−	4.77394i	−0.995436	−	0.995436i	−0.999990	+	0.00455400i	$0.998550\pi$
$24$	2.25841	+	1.70282i	0.460996	+	0.347587i
$25$	−4.99318	−	0.261081i	−0.998636	−	0.0522163i
$26$	1.34276	−	0.427532i	0.263337	−	0.0838458i
$27$		−	1.00000i		−	0.192450i
$28$	0.355348	−	2.08384i	0.0671545	−	0.393809i
$29$	2.95516	+	2.95516i	0.548760	+	0.548760i	0.926082	−	0.377322i	$-0.123155\pi$
$29$	2.95516	+	2.95516i	0.548760	+	0.548760i	−0.377322	+	0.926082i	$0.623155\pi$
$30$	−3.03726	+	0.880380i	−0.554525	+	0.160735i
$31$		−	10.4545i		−	1.87768i	−0.344351	−	0.938841i	$-0.611901\pi$
$31$		−	10.4545i		−	1.87768i	0.344351	−	0.938841i	$-0.388099\pi$
$32$	0.167155	−	5.65438i	0.0295491	−	0.999563i
$33$	−0.920311	−	0.920311i	−0.160206	−	0.160206i
$34$	−0.902270	+	1.74523i	−0.154738	+	0.299304i
$35$	1.62698	+	1.71428i	0.275011	+	0.289766i
$36$	−1.63182	+	1.15636i	−0.271970	+	0.192727i
$37$	−8.22694			−1.35250			−0.676251	−	0.736672i	$-0.736396\pi$
$37$	−8.22694			−1.35250			−0.676251	+	0.736672i	$0.736396\pi$
$38$	0.950259	−	1.83805i	0.154152	−	0.298171i
$39$			0.996441i			0.159558i
$40$	4.94879	+	3.93821i	0.782472	+	0.622686i
$41$			5.70040i			0.890253i	0.895468	+	0.445127i	$0.146841\pi$
$41$			5.70040i			0.890253i	−0.895468	+	0.445127i	$0.853159\pi$
$42$	1.32781	+	0.686471i	0.204886	+	0.105925i
$43$	−5.22869			−0.797368			−0.398684	−	0.917088i	$-0.630533\pi$
$43$	−5.22869			−0.797368			−0.398684	+	0.917088i	$0.630533\pi$
$44$	−0.437567	+	2.56599i	−0.0659658	+	0.386838i
$45$	0.0583995	−	2.23531i	0.00870568	−	0.333220i
$46$	−8.48146	−	4.38486i	−1.25052	−	0.646512i
$47$	−0.0548243	−	0.0548243i	−0.00799695	−	0.00799695i	0.703097	−	0.711094i	$-0.251800\pi$
$47$	−0.0548243	−	0.0548243i	−0.00799695	−	0.00799695i	−0.711094	+	0.703097i	$0.751800\pi$
$48$	3.77394	+	1.32566i	0.544722	+	0.191342i
$49$			5.88283i			0.840405i
$50$	−6.84061	+	1.79054i	−0.967408	+	0.253221i
$51$	−0.982332	−	0.982332i	−0.137554	−	0.137554i
$52$	1.62601	−	1.15225i	0.225487	−	0.159788i
$53$			5.13957i			0.705974i	0.935628	+	0.352987i	$0.114834\pi$
$53$			5.13957i			0.705974i	−0.935628	+	0.352987i	$0.885166\pi$
$54$	−0.429059	−	1.34756i	−0.0583875	−	0.183379i
$55$	−2.00343	−	2.11092i	−0.270142	−	0.284637i
$56$	−0.415238	−	2.96056i	−0.0554885	−	0.395621i
$57$	1.03458	+	1.03458i	0.137033	+	0.137033i
$58$	5.25018	+	2.71431i	0.689383	+	0.356406i
$59$	2.30403	+	2.30403i	0.299959	+	0.299959i	0.840998	−	0.541039i	$-0.181969\pi$
$59$	2.30403	+	2.30403i	0.299959	+	0.299959i	−0.541039	+	0.840998i	$0.681969\pi$
$60$	−3.71514	+	2.48952i	−0.479623	+	0.321396i
$61$	10.8244	−	10.8244i	1.38592	−	1.38592i	0.552234	−	0.833689i	$-0.313776\pi$
$61$	10.8244	−	10.8244i	1.38592	−	1.38592i	0.833689	−	0.552234i	$-0.186224\pi$
$62$	−4.48559	−	14.0880i	−0.569670	−	1.78918i
$63$	−0.747384	+	0.747384i	−0.0941615	+	0.0941615i
$64$	−2.20081	−	7.69132i	−0.275101	−	0.961415i
$65$	−0.0581916	+	2.22735i	−0.00721778	+	0.276269i
$66$	−1.63504	−	0.845304i	−0.201259	−	0.104050i
$67$	8.99029			1.09834			0.549169	−	0.835711i	$-0.314944\pi$
$67$	8.99029			1.09834			0.549169	+	0.835711i	$0.314944\pi$
$68$	−0.467056	+	2.73892i	−0.0566388	+	0.332143i
$69$	4.77394	−	4.77394i	0.574715	−	0.574715i
$70$	2.92798	+	1.61201i	0.349960	+	0.192673i
$71$	−14.1421			−1.67836			−0.839180	−	0.543853i	$-0.816965\pi$
$71$	−14.1421			−1.67836			−0.839180	+	0.543853i	$0.816965\pi$
$72$	−1.70282	+	2.25841i	−0.200679	+	0.266156i
$73$	−6.35840	+	6.35840i	−0.744195	+	0.744195i	−0.973382	−	0.229188i	$-0.926393\pi$
$73$	−6.35840	+	6.35840i	−0.744195	+	0.744195i	0.229188	+	0.973382i	$0.426393\pi$
$74$	−11.0863	+	3.52984i	−1.28875	+	0.410336i
$75$	0.261081	−	4.99318i	0.0301471	−	0.576563i
$76$	0.491897	−	2.88459i	0.0564245	−	0.330886i
$77$			1.37565i			0.156770i
$78$	0.427532	+	1.34276i	0.0484084	+	0.152038i
$79$	8.76588			0.986238			0.493119	−	0.869962i	$-0.335857\pi$
$79$	8.76588			0.986238			0.493119	+	0.869962i	$0.335857\pi$
$80$	8.35849	+	3.18364i	0.934508	+	0.355942i
$81$	1.00000			0.111111
$82$	2.44581	+	7.68161i	0.270094	+	0.848292i
$83$			12.3589i			1.35657i	0.734800	+	0.678284i	$0.237276\pi$
$83$			12.3589i			1.35657i	−0.734800	+	0.678284i	$0.762724\pi$
$84$	2.08384	+	0.355348i	0.227366	+	0.0387717i
$85$	−2.13845	−	2.25318i	−0.231947	−	0.244392i
$86$	−7.04595	+	2.24341i	−0.759785	+	0.241914i
$87$	−2.95516	+	2.95516i	−0.316827	+	0.316827i
$88$	0.511314	+	3.64556i	0.0545062	+	0.388618i
$89$	18.0456			1.91283			0.956414	−	0.292014i	$-0.0943254\pi$
$89$	18.0456			1.91283			0.956414	+	0.292014i	$0.0943254\pi$
$90$	−0.880380	−	3.03726i	−0.0928002	−	0.320155i
$91$	0.744724	−	0.744724i	0.0780683	−	0.0780683i
$92$	−13.3106	−	2.26980i	−1.38773	−	0.236643i
$93$	10.4545			1.08408
$94$	−0.0974017	−	0.0503560i	−0.0100462	−	0.00519383i
$95$	2.25218	+	2.37302i	0.231069	+	0.243467i
$96$	5.65438	+	0.167155i	0.577098	+	0.0170602i
$97$	1.29787	−	1.29787i	0.131779	−	0.131779i	−0.638141	−	0.769920i	$-0.720296\pi$
$97$	1.29787	−	1.29787i	0.131779	−	0.131779i	0.769920	+	0.638141i	$0.220296\pi$
$98$	2.52408	+	7.92745i	0.254971	+	0.800794i
$99$	0.920311	−	0.920311i	0.0924947	−	0.0924947i
$100$	−8.44986	+	5.34788i	−0.844986	+	0.534788i
$101$	4.25125	+	4.25125i	0.423015	+	0.423015i	0.886241	−	0.463225i	$-0.153308\pi$
$101$	4.25125	+	4.25125i	0.423015	+	0.423015i	−0.463225	+	0.886241i	$0.653308\pi$
$102$	−1.74523	−	0.902270i	−0.172803	−	0.0893381i
$103$	−5.92346	−	5.92346i	−0.583656	−	0.583656i	0.352250	−	0.935906i	$-0.385417\pi$
$103$	−5.92346	−	5.92346i	−0.583656	−	0.583656i	−0.935906	+	0.352250i	$0.885417\pi$
$104$	1.69676	−	2.25037i	0.166381	−	0.220667i
$105$	−1.71428	+	1.62698i	−0.167296	+	0.158777i
$106$	2.20518	+	6.92586i	0.214186	+	0.672699i
$107$			0.0554707i			0.00536256i	0.999996	+	0.00268128i	$0.000853478\pi$
$107$			0.0554707i			0.00536256i	−0.999996	+	0.00268128i	$0.999147\pi$
$108$	−1.15636	−	1.63182i	−0.111271	−	0.157022i
$109$	0.947769	+	0.947769i	0.0907798	+	0.0907798i	0.751038	−	0.660259i	$-0.229553\pi$
$109$	0.947769	+	0.947769i	0.0907798	+	0.0907798i	−0.660259	+	0.751038i	$0.729553\pi$
$110$	−3.60544	−	1.98500i	−0.343766	−	0.189262i
$111$		−	8.22694i		−	0.780867i
$112$	−1.82981	−	3.81136i	−0.172901	−	0.360139i
$113$	−10.8801	−	10.8801i	−1.02351	−	1.02351i	−0.999717	−	0.0237977i	$-0.992424\pi$
$113$	−10.8801	−	10.8801i	−1.02351	−	1.02351i	−0.0237977	−	0.999717i	$-0.507576\pi$
$114$	1.83805	+	0.950259i	0.172149	+	0.0889999i
$115$	10.9500	−	10.3924i	1.02109	−	0.969098i
$116$	8.23952	+	1.40505i	0.765020	+	0.130456i
$117$	−0.996441			−0.0921210
$118$	4.09337	+	2.11624i	0.376825	+	0.194816i
$119$			1.46836i			0.134604i
$120$	−3.93821	+	4.94879i	−0.359508	+	0.451760i
$121$			9.30606i			0.846005i
$122$	9.94219	−	19.2308i	0.900124	−	1.74107i
$123$	−5.70040			−0.513988
$124$	−12.0892	−	17.0598i	−1.08564	−	1.53202i
$125$	0.875196	−	11.1460i	0.0782799	−	0.996931i
$126$	−0.686471	+	1.32781i	−0.0611557	+	0.118291i
$127$	9.61338	+	9.61338i	0.853050	+	0.853050i	0.990508	−	0.137458i	$-0.0438931\pi$
$127$	9.61338	+	9.61338i	0.853050	+	0.853050i	−0.137458	+	0.990508i	$0.543893\pi$
$128$	−6.26575	−	9.42021i	−0.553819	−	0.832637i
$129$		−	5.22869i		−	0.460360i
$130$	0.877247	+	3.02645i	0.0769397	+	0.265437i
$131$	5.60184	+	5.60184i	0.489435	+	0.489435i	0.908128	−	0.418693i	$-0.137512\pi$
$131$	5.60184	+	5.60184i	0.489435	+	0.489435i	−0.418693	+	0.908128i	$0.637512\pi$
$132$	−2.56599	−	0.437567i	−0.223341	−	0.0380854i
$133$		−	1.54646i		−	0.134095i
$134$	12.1149	−	3.85736i	1.04657	−	0.333225i
$135$	2.23531	+	0.0583995i	0.192384	+	0.00502623i
$136$	0.545772	+	3.89124i	0.0467996	+	0.333671i
$137$	4.68373	+	4.68373i	0.400158	+	0.400158i	0.878289	−	0.478130i	$-0.158685\pi$
$137$	4.68373	+	4.68373i	0.400158	+	0.400158i	−0.478130	+	0.878289i	$0.658685\pi$
$138$	4.38486	−	8.48146i	0.373264	−	0.721990i
$139$	1.64971	+	1.64971i	0.139926	+	0.139926i	0.773600	−	0.633674i	$-0.218454\pi$
$139$	1.64971	+	1.64971i	0.139926	+	0.139926i	−0.633674	+	0.773600i	$0.718454\pi$
$140$	4.63727	+	0.916007i	0.391921	+	0.0774167i
$141$	0.0548243	−	0.0548243i	0.00461704	−	0.00461704i
$142$	−19.0573	+	6.06780i	−1.59925	+	0.509198i
$143$	−0.917036	+	0.917036i	−0.0766864	+	0.0766864i
$144$	−1.32566	+	3.77394i	−0.110471	+	0.314495i
$145$	−6.77827	+	6.43311i	−0.562905	+	0.534241i
$146$	−5.84018	+	11.2964i	−0.483337	+	0.934899i
$147$	−5.88283			−0.485208
$148$	−13.4249	+	9.51332i	−1.10352	+	0.781990i
$149$	12.0813	−	12.0813i	0.989742	−	0.989742i	−0.0102058	−	0.999948i	$-0.503249\pi$
$149$	12.0813	−	12.0813i	0.989742	−	0.989742i	0.999948	+	0.0102058i	$0.00324866\pi$
$150$	−1.79054	−	6.84061i	−0.146197	−	0.558533i
$151$	12.6503			1.02947			0.514735	−	0.857350i	$-0.327890\pi$
$151$	12.6503			1.02947			0.514735	+	0.857350i	$0.327890\pi$
$152$	−0.574800	−	4.09821i	−0.0466225	−	0.332408i
$153$	0.982332	−	0.982332i	0.0794169	−	0.0794169i
$154$	0.590235	+	1.85377i	0.0475625	+	0.149381i
$155$	23.3690	+	0.610537i	1.87704	+	0.0490395i
$156$	1.15225	+	1.62601i	0.0922535	+	0.130185i
$157$			6.31279i			0.503816i	0.967751	+	0.251908i	$0.0810580\pi$
$157$			6.31279i			0.503816i	−0.967751	+	0.251908i	$0.918942\pi$
$158$	11.8125	−	3.76107i	0.939753	−	0.299215i
$159$	−5.13957			−0.407595
$160$	12.6295	+	0.703856i	0.998451	+	0.0556447i
$161$	−7.13593			−0.562390
$162$	1.34756	−	0.429059i	0.105874	−	0.0337100i
$163$			14.6329i			1.14613i	0.819508	+	0.573067i	$0.194247\pi$
$163$			14.6329i			1.14613i	−0.819508	+	0.573067i	$0.805753\pi$
$164$	6.59172	+	9.30201i	0.514727	+	0.726365i
$165$	2.11092	−	2.00343i	0.164335	−	0.155967i
$166$	5.30270	+	16.6543i	0.411569	+	1.29263i
$167$	5.31380	−	5.31380i	0.411194	−	0.411194i	−0.470960	−	0.882155i	$-0.656092\pi$
$167$	5.31380	−	5.31380i	0.411194	−	0.411194i	0.882155	+	0.470960i	$0.156092\pi$
$168$	2.96056	−	0.415238i	0.228412	−	0.0320363i
$169$	−12.0071			−0.923623
$170$	−3.84842	−	2.11877i	−0.295161	−	0.162502i
$171$	−1.03458	+	1.03458i	−0.0791163	+	0.0791163i
$172$	−8.53227	+	6.04625i	−0.650579	+	0.461023i
$173$	−13.1537			−1.00006			−0.500029	−	0.866008i	$-0.666678\pi$
$173$	−13.1537			−1.00006			−0.500029	+	0.866008i	$0.666678\pi$
$174$	−2.71431	+	5.25018i	−0.205771	+	0.398015i
$175$	−3.92695	+	3.53669i	−0.296849	+	0.267349i
$176$	2.25318	+	4.69322i	0.169840	+	0.353764i
$177$	−2.30403	+	2.30403i	−0.173181	+	0.173181i
$178$	24.3174	−	7.74261i	1.82267	−	0.580333i
$179$	−12.2215	+	12.2215i	−0.913479	+	0.913479i	−0.996544	−	0.0830647i	$-0.973529\pi$
$179$	−12.2215	+	12.2215i	−0.913479	+	0.913479i	0.0830647	+	0.996544i	$0.473529\pi$
$180$	−2.48952	−	3.71514i	−0.185558	−	0.276910i
$181$	7.77734	+	7.77734i	0.578085	+	0.578085i	0.934375	−	0.356290i	$-0.115959\pi$
$181$	7.77734	+	7.77734i	0.578085	+	0.578085i	−0.356290	+	0.934375i	$0.615959\pi$
$182$	0.684027	−	1.32309i	0.0507035	−	0.0980738i
$183$	10.8244	+	10.8244i	0.800163	+	0.800163i
$184$	−18.9107	+	2.65235i	−1.39411	+	0.195534i
$185$	0.480449	−	18.3897i	0.0353233	−	1.35204i
$186$	14.0880	−	4.48559i	1.03298	−	0.328899i
$187$		−	1.80810i		−	0.132222i
$188$	−0.152860	−	0.0260665i	−0.0111485	−	0.00190110i
$189$	−0.747384	−	0.747384i	−0.0543642	−	0.0543642i
$190$	4.05311	+	2.23146i	0.294043	+	0.161887i
$191$		−	18.2743i		−	1.32228i	−0.750262	−	0.661141i	$-0.770073\pi$
$191$		−	18.2743i		−	1.32228i	0.750262	−	0.661141i	$-0.229927\pi$
$192$	7.69132	−	2.20081i	0.555073	−	0.158830i
$193$	−11.3061	−	11.3061i	−0.813832	−	0.813832i	0.171374	−	0.985206i	$-0.445179\pi$
$193$	−11.3061	−	11.3061i	−0.813832	−	0.813832i	−0.985206	+	0.171374i	$0.945179\pi$
$194$	1.19209	−	2.30582i	0.0855873	−	0.165548i
$195$	−2.22735	−	0.0581916i	−0.159504	−	0.00416719i
$196$	6.80268	+	9.59971i	0.485906	+	0.685694i
$197$	−11.1767			−0.796305			−0.398153	−	0.917319i	$-0.630349\pi$
$197$	−11.1767			−0.796305			−0.398153	+	0.917319i	$0.630349\pi$
$198$	0.845304	−	1.63504i	0.0600731	−	0.116197i
$199$			18.8869i			1.33886i	0.742877	+	0.669428i	$0.233461\pi$
$199$			18.8869i			1.33886i	−0.742877	+	0.669428i	$0.766539\pi$
$200$	−9.09211	+	10.8321i	−0.642909	+	0.765942i
$201$			8.99029i			0.634126i
$202$	7.55284	+	3.90477i	0.531416	+	0.274738i
$203$	4.41728			0.310032
$204$	−2.73892	−	0.467056i	−0.191763	−	0.0327005i
$205$	−12.7421	−	0.332900i	−0.889949	−	0.0232508i
$206$	−10.5237	−	5.44069i	−0.733222	−	0.379071i
$207$	4.77394	+	4.77394i	0.331812	+	0.331812i
$208$	1.32094	−	3.76051i	0.0915906	−	0.260744i
$209$			1.90427i			0.131721i
$210$	−1.61201	+	2.92798i	−0.111240	+	0.202050i
$211$	−7.95311	−	7.95311i	−0.547514	−	0.547514i	0.378207	−	0.925721i	$-0.376541\pi$
$211$	−7.95311	−	7.95311i	−0.547514	−	0.547514i	−0.925721	+	0.378207i	$0.876541\pi$
$212$	5.94320	+	8.38684i	0.408181	+	0.576011i
$213$		−	14.1421i		−	0.969002i
$214$	0.0238002	+	0.0747499i	0.00162695	+	0.00510980i
$215$	0.305353	−	11.6877i	0.0208249	−	0.797096i
$216$	−2.25841	−	1.70282i	−0.153665	−	0.115862i
$217$	−7.81352	−	7.81352i	−0.530416	−	0.530416i
$218$	1.68382	+	0.870524i	0.114043	+	0.0589593i
$219$	−6.35840	−	6.35840i	−0.429661	−	0.429661i
$220$	−5.71022	−	1.12795i	−0.384983	−	0.0760463i
$221$	−0.978836	+	0.978836i	−0.0658437	+	0.0658437i
$222$	−3.52984	−	11.0863i	−0.236907	−	0.744062i
$223$	−4.22843	+	4.22843i	−0.283157	+	0.283157i	−0.834367	−	0.551210i	$-0.814166\pi$
$223$	−4.22843	+	4.22843i	−0.283157	+	0.283157i	0.551210	+	0.834367i	$0.314166\pi$
$224$	−4.10107	−	4.35092i	−0.274014	−	0.290708i
$225$	4.99318	+	0.261081i	0.332879	+	0.0174054i
$226$	−19.3298	−	9.99336i	−1.28580	−	0.664748i
$227$	−15.7654			−1.04639			−0.523193	−	0.852214i	$-0.675259\pi$
$227$	−15.7654			−1.04639			−0.523193	+	0.852214i	$0.675259\pi$
$228$	2.88459	+	0.491897i	0.191037	+	0.0325767i
$229$	0.746140	−	0.746140i	0.0493063	−	0.0493063i	−0.682024	−	0.731330i	$-0.738900\pi$
$229$	0.746140	−	0.746140i	0.0493063	−	0.0493063i	0.731330	+	0.682024i	$0.238900\pi$
$230$	10.2968	−	18.7026i	0.678951	−	1.23321i
$231$	−1.37565			−0.0905112
$232$	11.7061	−	1.64185i	0.768541	−	0.107793i
$233$	5.74517	−	5.74517i	0.376379	−	0.376379i	−0.493415	−	0.869794i	$-0.664252\pi$
$233$	5.74517	−	5.74517i	0.376379	−	0.376379i	0.869794	+	0.493415i	$0.164252\pi$
$234$	−1.34276	+	0.427532i	−0.0877790	+	0.0279486i
$235$	0.125751	−	0.119347i	0.00820308	−	0.00778536i
$236$	6.42404	+	1.09546i	0.418169	+	0.0713086i
$237$			8.76588i			0.569405i
$238$	0.630012	+	1.97870i	0.0408376	+	0.128260i
$239$	−27.9736			−1.80946			−0.904729	−	0.425987i	$-0.859927\pi$
$239$	−27.9736			−1.80946			−0.904729	+	0.425987i	$0.859927\pi$
$240$	−3.18364	+	8.35849i	−0.205503	+	0.539538i
$241$	−7.01072			−0.451600			−0.225800	−	0.974174i	$-0.572500\pi$
$241$	−7.01072			−0.451600			−0.225800	+	0.974174i	$0.572500\pi$
$242$	3.99284	+	12.5404i	0.256670	+	0.806130i
$243$			1.00000i			0.0641500i
$244$	5.14653	−	30.1804i	0.329473	−	1.93210i
$245$	−13.1499	−	0.343555i	−0.840118	−	0.0219489i
$246$	−7.68161	+	2.44581i	−0.489762	+	0.155939i
$247$	1.03090	−	1.03090i	0.0655945	−	0.0655945i
$248$	−23.6105	−	17.8021i	−1.49927	−	1.13044i
$249$	−12.3589			−0.783215
$250$	−3.60293	−	15.3954i	−0.227869	−	0.973692i
$251$	−5.41619	+	5.41619i	−0.341867	+	0.341867i	−0.857069	−	0.515202i	$-0.827717\pi$
$251$	−5.41619	+	5.41619i	−0.341867	+	0.341867i	0.515202	+	0.857069i	$0.327717\pi$
$252$	−0.355348	+	2.08384i	−0.0223848	+	0.131270i
$253$	8.78702			0.552435
$254$	17.0793	+	8.82987i	1.07165	+	0.554036i
$255$	2.25318	−	2.13845i	0.141100	−	0.133915i
$256$	−12.4853	−	10.0059i	−0.780329	−	0.625369i
$257$	17.0268	−	17.0268i	1.06210	−	1.06210i	0.0641616	−	0.997940i	$-0.479563\pi$
$257$	17.0268	−	17.0268i	1.06210	−	1.06210i	0.997940	−	0.0641616i	$-0.0204373\pi$
$258$	−2.24341	−	7.04595i	−0.139669	−	0.438662i
$259$	−6.14869	+	6.14869i	−0.382061	+	0.382061i
$260$	2.48066	+	3.70192i	0.153844	+	0.229583i
$261$	−2.95516	−	2.95516i	−0.182920	−	0.182920i
$262$	9.95232	+	5.14528i	0.614856	+	0.317877i
$263$	7.04662	+	7.04662i	0.434513	+	0.434513i	0.890160	−	0.455647i	$-0.150592\pi$
$263$	7.04662	+	7.04662i	0.434513	+	0.434513i	−0.455647	+	0.890160i	$0.650592\pi$
$264$	−3.64556	+	0.511314i	−0.224369	+	0.0314692i
$265$	−11.4885	−	0.300148i	−0.705734	−	0.0184380i
$266$	−0.663520	−	2.08394i	−0.0406830	−	0.127774i
$267$			18.0456i			1.10437i
$268$	14.6705	−	10.3960i	0.896144	−	0.635038i
$269$	−13.1762	−	13.1762i	−0.803366	−	0.803366i	0.180254	−	0.983620i	$-0.442308\pi$
$269$	−13.1762	−	13.1762i	−0.803366	−	0.803366i	−0.983620	+	0.180254i	$0.942308\pi$
$270$	3.03726	−	0.880380i	0.184842	−	0.0535782i
$271$		−	2.01115i		−	0.122169i	−0.998133	−	0.0610845i	$-0.980544\pi$
$271$		−	2.01115i		−	0.122169i	0.998133	−	0.0610845i	$-0.0194559\pi$
$272$	2.40503	+	5.00950i	0.145826	+	0.303746i
$273$	0.744724	+	0.744724i	0.0450727	+	0.0450727i
$274$	8.32119	+	4.30200i	0.502702	+	0.259893i
$275$	4.83555	−	4.35500i	0.291595	−	0.262616i
$276$	2.26980	−	13.3106i	0.136626	−	0.801204i
$277$	−5.15280			−0.309602			−0.154801	−	0.987946i	$-0.549474\pi$
$277$	−5.15280			−0.309602			−0.154801	+	0.987946i	$0.549474\pi$
$278$	2.93089	+	1.51525i	0.175783	+	0.0908787i
$279$			10.4545i			0.625894i
$280$	6.64200	−	0.755288i	0.396935	−	0.0451371i
$281$		−	14.7480i		−	0.879791i	−0.898049	−	0.439895i	$-0.855016\pi$
$281$		−	14.7480i		−	0.879791i	0.898049	−	0.439895i	$-0.144984\pi$
$282$	0.0503560	−	0.0974017i	0.00299866	−	0.00580019i
$283$	−7.82068			−0.464891			−0.232446	−	0.972609i	$-0.574673\pi$
$283$	−7.82068			−0.464891			−0.232446	+	0.972609i	$0.574673\pi$
$284$	−23.0774	+	16.3534i	−1.36939	+	0.970396i
$285$	−2.37302	+	2.25218i	−0.140566	+	0.133408i
$286$	−0.842295	+	1.62922i	−0.0498060	+	0.0963378i
$287$	4.26039	+	4.26039i	0.251483	+	0.251483i
$288$	−0.167155	+	5.65438i	−0.00984970	+	0.333188i
$289$			15.0700i			0.886473i
$290$	−6.37392	+	11.5773i	−0.374289	+	0.679840i
$291$	1.29787	+	1.29787i	0.0760826	+	0.0760826i
$292$	−3.02314	+	17.7284i	−0.176916	+	1.03747i
$293$			19.1115i			1.11651i	0.829670	+	0.558254i	$0.188529\pi$
$293$			19.1115i			1.11651i	−0.829670	+	0.558254i	$0.811471\pi$
$294$	−7.92745	+	2.52408i	−0.462338	+	0.147207i
$295$	−5.28476	+	5.01565i	−0.307690	+	0.292022i
$296$	−14.0090	+	18.5798i	−0.814257	+	1.07993i
$297$	0.920311	+	0.920311i	0.0534019	+	0.0534019i
$298$	11.0967	−	21.4639i	0.642814	−	1.24337i
$299$	−4.75695	−	4.75695i	−0.275102	−	0.275102i
$300$	−5.34788	−	8.44986i	−0.308760	−	0.487853i
$301$	−3.90784	+	3.90784i	−0.225244	+	0.225244i
$302$	17.0470	−	5.42773i	0.980947	−	0.312331i
$303$	−4.25125	+	4.25125i	−0.244228	+	0.244228i
$304$	−2.53295	−	5.27594i	−0.145274	−	0.302596i
$305$	23.5637	+	24.8280i	1.34925	+	1.42165i
$306$	0.902270	−	1.74523i	0.0515794	−	0.0997680i
$307$	3.29048			0.187798			0.0938988	−	0.995582i	$-0.470067\pi$
$307$	3.29048			0.187798			0.0938988	+	0.995582i	$0.470067\pi$
$308$	1.59075	+	2.24481i	0.0906414	+	0.127910i
$309$	5.92346	−	5.92346i	0.336974	−	0.336974i
$310$	31.7530	−	9.20393i	1.80345	−	0.522748i
$311$	−10.6744			−0.605292			−0.302646	−	0.953103i	$-0.597870\pi$
$311$	−10.6744			−0.605292			−0.302646	+	0.953103i	$0.597870\pi$
$312$	2.25037	+	1.69676i	0.127402	+	0.0960601i
$313$	21.5451	−	21.5451i	1.21780	−	1.21780i	0.249401	−	0.968400i	$-0.419766\pi$
$313$	21.5451	−	21.5451i	1.21780	−	1.21780i	0.968400	−	0.249401i	$-0.0802336\pi$
$314$	2.70856	+	8.50684i	0.152853	+	0.480069i
$315$	−1.62698	−	1.71428i	−0.0916702	−	0.0965886i
$316$	14.3043	−	10.1365i	0.804680	−	0.570224i
$317$			16.1238i			0.905603i	0.891611	+	0.452801i	$0.149575\pi$
$317$			16.1238i			0.905603i	−0.891611	+	0.452801i	$0.850425\pi$
$318$	−6.92586	+	2.20518i	−0.388383	+	0.123660i
$319$	−5.43934			−0.304544
$320$	17.3210	−	4.47032i	0.968272	−	0.249898i
$321$	−0.0554707			−0.00309607
$322$	−9.61607	+	3.06173i	−0.535883	+	0.170624i
$323$			2.03260i			0.113097i
$324$	1.63182	−	1.15636i	0.0906565	−	0.0642423i
$325$	−4.97541	−	0.260152i	−0.275986	−	0.0144306i
$326$	6.27835	+	19.7186i	0.347726	+	1.09211i
$327$	−0.947769	+	0.947769i	−0.0524117	+	0.0524117i
$328$	12.8738	+	9.70675i	0.710838	+	0.535966i
$329$	−0.0819496			−0.00451803
$330$	1.98500	−	3.60544i	0.109271	−	0.198473i
$331$	1.97876	−	1.97876i	0.108762	−	0.108762i	−0.650631	−	0.759394i	$-0.725496\pi$
$331$	1.97876	−	1.97876i	0.108762	−	0.108762i	0.759394	+	0.650631i	$0.225496\pi$
$332$	14.2914	+	20.1675i	0.784341	+	1.10684i
$333$	8.22694			0.450834
$334$	4.88072	−	9.44058i	0.267061	−	0.516566i
$335$	−0.525028	+	20.0960i	−0.0286854	+	1.09796i
$336$	3.81136	−	1.82981i	0.207927	−	0.0998243i
$337$	25.2423	−	25.2423i	1.37503	−	1.37503i	0.522229	−	0.852806i	$-0.325101\pi$
$337$	25.2423	−	25.2423i	1.37503	−	1.37503i	0.852806	−	0.522229i	$-0.174899\pi$
$338$	−16.1803	+	5.15175i	−0.880090	+	0.280218i
$339$	10.8801	−	10.8801i	0.590926	−	0.590926i
$340$	−6.09504	−	1.20396i	−0.330550	−	0.0652941i
$341$	9.62138	+	9.62138i	0.521027	+	0.521027i
$342$	−0.950259	+	1.83805i	−0.0513841	+	0.0993904i
$343$	9.62842	+	9.62842i	0.519886	+	0.519886i
$344$	−8.90351	+	11.8085i	−0.480045	+	0.636672i
$345$	10.3924	+	10.9500i	0.559509	+	0.589529i
$346$	−17.7254	+	5.64372i	−0.952923	+	0.303408i
$347$		−	24.1967i		−	1.29895i	−0.760383	−	0.649475i	$-0.774989\pi$
$347$		−	24.1967i		−	1.29895i	0.760383	−	0.649475i	$-0.225011\pi$
$348$	−1.40505	+	8.23952i	−0.0753186	+	0.441685i
$349$	−2.28867	−	2.28867i	−0.122510	−	0.122510i	0.643194	−	0.765704i	$-0.277609\pi$
$349$	−2.28867	−	2.28867i	−0.122510	−	0.122510i	−0.765704	+	0.643194i	$0.777609\pi$
$350$	−3.77434	+	6.45079i	−0.201747	+	0.344809i
$351$		−	0.996441i		−	0.0531861i
$352$	5.04996	+	5.35763i	0.269164	+	0.285562i
$353$	−9.70578	−	9.70578i	−0.516587	−	0.516587i	0.399950	−	0.916537i	$-0.369027\pi$
$353$	−9.70578	−	9.70578i	−0.516587	−	0.516587i	−0.916537	+	0.399950i	$0.869027\pi$
$354$	−2.11624	+	4.09337i	−0.112477	+	0.217560i
$355$	0.825893	−	31.6120i	0.0438338	−	1.67779i
$356$	29.4471	−	20.8672i	1.56069	−	1.10596i
$357$	−1.46836			−0.0777138
$358$	−11.2254	+	21.7129i	−0.593283	+	1.14756i
$359$		−	27.1463i		−	1.43273i	−0.697726	−	0.716365i	$-0.745805\pi$
$359$		−	27.1463i		−	1.43273i	0.697726	−	0.716365i	$-0.254195\pi$
$360$	−4.94879	−	3.93821i	−0.260824	−	0.207562i
$361$			16.8593i			0.887331i
$362$	13.8173	+	7.14347i	0.726223	+	0.375452i
$363$	−9.30606			−0.488441
$364$	0.354083	−	2.07642i	0.0185590	−	0.108834i
$365$	−13.8416	−	14.5843i	−0.724505	−	0.763377i
$366$	19.2308	+	9.94219i	1.00521	+	0.519687i
$367$	16.3750	+	16.3750i	0.854769	+	0.854769i	0.990716	−	0.135947i	$-0.0434078\pi$
$367$	16.3750	+	16.3750i	0.854769	+	0.854769i	−0.135947	+	0.990716i	$0.543408\pi$
$368$	−24.3452	+	11.6880i	−1.26908	+	0.609278i
$369$		−	5.70040i		−	0.296751i
$370$	−7.24284	−	24.9873i	−0.376537	−	1.29903i
$371$	3.84123	+	3.84123i	0.199427	+	0.199427i
$372$	17.0598	−	12.0892i	0.884510	−	0.626794i
$373$		−	29.7473i		−	1.54026i	−0.637888	−	0.770129i	$-0.720192\pi$
$373$		−	29.7473i		−	1.54026i	0.637888	−	0.770129i	$-0.279808\pi$
$374$	−0.775782	−	2.43652i	−0.0401147	−	0.125989i
$375$	11.1460	+	0.875196i	0.575579	+	0.0451949i
$376$	−0.217172	+	0.0304597i	−0.0111998	+	0.00157084i
$377$	2.94464	+	2.94464i	0.151657	+	0.151657i
$378$	−1.32781	−	0.686471i	−0.0682954	−	0.0353082i
$379$	11.0584	+	11.0584i	0.568031	+	0.568031i	0.931576	−	0.363546i	$-0.118434\pi$
$379$	11.0584	+	11.0584i	0.568031	+	0.568031i	−0.363546	+	0.931576i	$0.618434\pi$
$380$	6.41922	+	1.26800i	0.329299	+	0.0650470i
$381$	−9.61338	+	9.61338i	−0.492509	+	0.492509i
$382$	−7.84074	−	24.6256i	−0.401167	−	1.25996i
$383$	16.2297	−	16.2297i	0.829298	−	0.829298i	−0.158122	−	0.987420i	$-0.550544\pi$
$383$	16.2297	−	16.2297i	0.829298	−	0.829298i	0.987420	+	0.158122i	$0.0505439\pi$
$384$	9.42021	−	6.26575i	0.480723	−	0.319747i
$385$	−3.07500	−	0.0803373i	−0.156717	−	0.00409437i
$386$	−20.0866	−	10.3846i	−1.02238	−	0.528565i
$387$	5.22869			0.265789
$388$	0.617081	−	3.61870i	0.0313276	−	0.183712i
$389$	−12.6341	+	12.6341i	−0.640575	+	0.640575i	−0.950697	−	0.310122i	$-0.899630\pi$
$389$	−12.6341	+	12.6341i	−0.640575	+	0.640575i	0.310122	+	0.950697i	$0.399630\pi$
$390$	−3.02645	+	0.877247i	−0.153250	+	0.0444211i
$391$	9.37920			0.474326
$392$	13.2858	+	10.0174i	0.671036	+	0.505955i
$393$	−5.60184	+	5.60184i	−0.282576	+	0.282576i
$394$	−15.0612	+	4.79545i	−0.758773	+	0.241591i
$395$	−0.511923	+	19.5944i	−0.0257576	+	0.985902i
$396$	0.437567	−	2.56599i	0.0219886	−	0.128946i
$397$			5.42044i			0.272044i	0.990706	+	0.136022i	$0.0434318\pi$
$397$			5.42044i			0.272044i	−0.990706	+	0.136022i	$0.956568\pi$
$398$	8.10358	+	25.4512i	0.406196	+	1.27575i
$399$	1.54646			0.0774197
$400$	−7.60455	+	18.4979i	−0.380227	+	0.924893i
$401$	15.7550			0.786765			0.393382	−	0.919375i	$-0.371305\pi$
$401$	15.7550			0.786765			0.393382	+	0.919375i	$0.371305\pi$
$402$	3.85736	+	12.1149i	0.192388	+	0.604238i
$403$		−	10.4173i		−	0.518922i
$404$	11.8533	+	2.02128i	0.589721	+	0.100563i
$405$	−0.0583995	+	2.23531i	−0.00290189	+	0.111073i
$406$	5.95254	−	1.89527i	0.295419	−	0.0940608i
$407$	7.57135	−	7.57135i	0.375298	−	0.375298i
$408$	−3.89124	+	0.545772i	−0.192645	+	0.0270198i
$409$	30.9442			1.53009			0.765046	−	0.643976i	$-0.222716\pi$
$409$	30.9442			1.53009			0.765046	+	0.643976i	$0.222716\pi$
$410$	−17.3136	+	5.01852i	−0.855057	+	0.247847i
$411$	−4.68373	+	4.68373i	−0.231032	+	0.231032i
$412$	−16.5157	−	2.81635i	−0.813669	−	0.138751i
$413$	3.44398			0.169467
$414$	8.48146	+	4.38486i	0.416841	+	0.215504i
$415$	−27.6260	−	0.721754i	−1.35610	−	0.0354295i
$416$	0.166560	−	5.63426i	0.00816628	−	0.276242i
$417$	−1.64971	+	1.64971i	−0.0807864	+	0.0807864i
$418$	0.817043	+	2.56611i	0.0399629	+	0.125513i
$419$	15.2385	−	15.2385i	0.744451	−	0.744451i	−0.228980	−	0.973431i	$-0.573539\pi$
$419$	15.2385	−	15.2385i	0.744451	−	0.744451i	0.973431	+	0.228980i	$0.0735391\pi$
$420$	−0.916007	+	4.63727i	−0.0446966	+	0.226275i
$421$	14.4008	+	14.4008i	0.701852	+	0.701852i	0.964808	−	0.262956i	$-0.0846974\pi$
$421$	14.4008	+	14.4008i	0.701852	+	0.701852i	−0.262956	+	0.964808i	$0.584697\pi$
$422$	−14.1296	−	7.30491i	−0.687819	−	0.355598i
$423$	0.0548243	+	0.0548243i	0.00266565	+	0.00266565i
$424$	11.6072	+	8.75176i	0.563698	+	0.425023i
$425$	5.16143	−	4.64849i	0.250366	−	0.225485i
$426$	−6.06780	−	19.0573i	−0.293986	−	0.923330i
$427$		−	16.1800i		−	0.783004i
$428$	0.0641442	+	0.0905181i	0.00310053	+	0.00437536i
$429$	−0.917036	−	0.917036i	−0.0442749	−	0.0442749i
$430$	−4.60323	−	15.8809i	−0.221988	−	0.765844i
$431$			4.47310i			0.215461i	0.994180	+	0.107731i	$0.0343584\pi$
$431$			4.47310i			0.215461i	−0.994180	+	0.107731i	$0.965642\pi$
$432$	−3.77394	−	1.32566i	−0.181574	−	0.0637807i
$433$	20.8589	+	20.8589i	1.00242	+	1.00242i	0.999997	+	0.00241793i	$0.000769652\pi$
$433$	20.8589	+	20.8589i	1.00242	+	1.00242i	0.00241793	+	0.999997i	$0.499230\pi$
$434$	−13.8816	−	7.17670i	−0.666339	−	0.344493i
$435$	−6.43311	−	6.77827i	−0.308444	−	0.324993i
$436$	2.64255	+	0.450622i	0.126555	+	0.0215809i
$437$	−9.87805			−0.472531
$438$	−11.2964	−	5.84018i	−0.539764	−	0.279055i
$439$		−	0.257771i		−	0.0123027i	−0.999981	−	0.00615136i	$-0.998042\pi$
$439$		−	0.257771i		−	0.0123027i	0.999981	−	0.00615136i	$-0.00195805\pi$
$440$	−8.17880	+	0.930044i	−0.389909	+	0.0443381i
$441$		−	5.88283i		−	0.280135i
$442$	−0.899059	+	1.73902i	−0.0427639	+	0.0827165i
$443$	27.8275			1.32212			0.661062	−	0.750331i	$-0.270106\pi$
$443$	27.8275			1.32212			0.661062	+	0.750331i	$0.270106\pi$
$444$	−9.51332	−	13.4249i	−0.451482	−	0.637116i
$445$	−1.05385	+	40.3374i	−0.0499574	+	1.91218i
$446$	−3.88380	+	7.51229i	−0.183903	+	0.355717i
$447$	12.0813	+	12.0813i	0.571428	+	0.571428i
$448$	−7.39322	−	4.10352i	−0.349297	−	0.193873i
$449$		−	7.32170i		−	0.345533i	−0.984963	−	0.172766i	$-0.944729\pi$
$449$		−	7.32170i		−	0.345533i	0.984963	−	0.172766i	$-0.0552705\pi$
$450$	6.84061	−	1.79054i	0.322469	−	0.0844071i
$451$	−5.24614	−	5.24614i	−0.247031	−	0.247031i
$452$	−30.3357	−	5.17301i	−1.42687	−	0.243318i
$453$			12.6503i			0.594364i
$454$	−21.2448	+	6.76428i	−0.997066	+	0.317463i
$455$	1.62119	+	1.70818i	0.0760027	+	0.0800806i
$456$	4.09821	−	0.574800i	0.191916	−	0.0269175i
$457$	−13.1962	−	13.1962i	−0.617293	−	0.617293i	0.327543	−	0.944836i	$-0.393779\pi$
$457$	−13.1962	−	13.1962i	−0.617293	−	0.617293i	−0.944836	+	0.327543i	$0.893779\pi$
$458$	0.685328	−	1.32560i	0.0320233	−	0.0619414i
$459$	0.982332	+	0.982332i	0.0458514	+	0.0458514i
$460$	5.85103	−	29.6207i	0.272806	−	1.38107i
$461$	−19.6030	+	19.6030i	−0.913002	+	0.913002i	−0.996507	−	0.0835057i	$-0.973388\pi$
$461$	−19.6030	+	19.6030i	−0.913002	+	0.913002i	0.0835057	+	0.996507i	$0.473388\pi$
$462$	−1.85377	+	0.590235i	−0.0862451	+	0.0274602i
$463$	17.2918	−	17.2918i	0.803619	−	0.803619i	−0.180040	−	0.983659i	$-0.557623\pi$
$463$	17.2918	−	17.2918i	0.803619	−	0.803619i	0.983659	+	0.180040i	$0.0576227\pi$
$464$	15.0701	−	7.23508i	0.699614	−	0.335880i
$465$	−0.610537	+	23.3690i	−0.0283130	+	1.08371i
$466$	5.27693	−	10.2070i	0.244449	−	0.472828i
$467$	−31.3895			−1.45253			−0.726267	−	0.687413i	$-0.758746\pi$
$467$	−31.3895			−1.45253			−0.726267	+	0.687413i	$0.758746\pi$
$468$	−1.62601	+	1.15225i	−0.0751623	+	0.0532626i
$469$	6.71920	−	6.71920i	0.310264	−	0.310264i
$470$	0.118249	−	0.214782i	0.00545443	−	0.00990714i
$471$	−6.31279			−0.290878
$472$	9.12677	−	1.28009i	0.420094	−	0.0589209i
$473$	4.81202	−	4.81202i	0.221257	−	0.221257i
$474$	3.76107	+	11.8125i	0.172752	+	0.542567i
$475$	−5.43595	+	4.89573i	−0.249419	+	0.224632i
$476$	1.69795	+	2.39609i	0.0778256	+	0.109825i
$477$		−	5.13957i		−	0.235325i
$478$	−37.6959	+	12.0023i	−1.72417	+	0.548972i
$479$	−10.4863			−0.479133			−0.239566	−	0.970880i	$-0.577005\pi$
$479$	−10.4863			−0.479133			−0.239566	+	0.970880i	$0.577005\pi$
$480$	−0.703856	+	12.6295i	−0.0321265	+	0.576456i
$481$	−8.19767			−0.373781
$482$	−9.44735	+	3.00801i	−0.430315	+	0.137011i
$483$		−	7.13593i		−	0.324696i
$484$	10.7612	+	15.1858i	0.489144	+	0.690263i
$485$	2.82535	+	2.97694i	0.128292	+	0.135176i
$486$	0.429059	+	1.34756i	0.0194625	+	0.0611264i
$487$	4.72750	−	4.72750i	0.214224	−	0.214224i	−0.591835	−	0.806059i	$-0.701596\pi$
$487$	4.72750	−	4.72750i	0.214224	−	0.214224i	0.806059	+	0.591835i	$0.201596\pi$
$488$	−6.01391	−	42.8779i	−0.272237	−	1.94099i
$489$	−14.6329			−0.661721
$490$	−17.8677	+	5.17913i	−0.807180	+	0.233969i
$491$	−3.00877	+	3.00877i	−0.135784	+	0.135784i	−0.771732	−	0.635948i	$-0.780609\pi$
$491$	−3.00877	+	3.00877i	−0.135784	+	0.135784i	0.635948	+	0.771732i	$0.280609\pi$
$492$	−9.30201	+	6.59172i	−0.419367	+	0.297178i
$493$	−5.80590			−0.261485
$494$	0.946877	−	1.83151i	0.0426020	−	0.0824035i
$495$	2.00343	+	2.11092i	0.0900475	+	0.0948789i
$496$	−39.4546	−	13.8591i	−1.77157	−	0.622290i
$497$	−10.5696	+	10.5696i	−0.474111	+	0.474111i
$498$	−16.6543	+	5.30270i	−0.746299	+	0.237620i
$499$	8.75769	−	8.75769i	0.392048	−	0.392048i	−0.483369	−	0.875417i	$-0.660587\pi$
$499$	8.75769	−	8.75769i	0.392048	−	0.392048i	0.875417	+	0.483369i	$0.160587\pi$
$500$	−11.4607	−	19.2003i	−0.512537	−	0.858665i
$501$	5.31380	+	5.31380i	0.237403	+	0.237403i
$502$	−4.97476	+	9.62249i	−0.222034	+	0.429473i
$503$	−3.79393	−	3.79393i	−0.169163	−	0.169163i	0.617448	−	0.786611i	$-0.288166\pi$
$503$	−3.79393	−	3.79393i	−0.169163	−	0.169163i	−0.786611	+	0.617448i	$0.788166\pi$
$504$	0.415238	+	2.96056i	0.0184962	+	0.131874i
$505$	−9.75112	+	9.25457i	−0.433919	+	0.411823i
$506$	11.8410	−	3.77015i	0.526397	−	0.167603i
$507$		−	12.0071i		−	0.533254i
$508$	26.8038	+	4.57074i	1.18923	+	0.202794i
$509$	9.92183	+	9.92183i	0.439777	+	0.439777i	0.891937	−	0.452160i	$-0.149346\pi$
$509$	9.92183	+	9.92183i	0.439777	+	0.439777i	−0.452160	+	0.891937i	$0.649346\pi$
$510$	2.11877	−	3.84842i	0.0938207	−	0.170411i
$511$			9.50433i			0.420447i
$512$	−21.1177	−	8.12660i	−0.933280	−	0.359149i
$513$	−1.03458	−	1.03458i	−0.0456778	−	0.0456778i
$514$	15.6391	−	30.2500i	0.689809	−	1.33427i
$515$	13.5867	−	12.8948i	0.598701	−	0.568214i
$516$	−6.04625	−	8.53227i	−0.266171	−	0.375612i
$517$	0.100911			0.00443805
$518$	−5.64756	+	10.9238i	−0.248139	+	0.479966i
$519$		−	13.1537i		−	0.577384i
$520$	4.93117	+	3.92420i	0.216246	+	0.172087i
$521$		−	31.9555i		−	1.39999i	−0.714146	−	0.699997i	$-0.753185\pi$
$521$		−	31.9555i		−	1.39999i	0.714146	−	0.699997i	$-0.246815\pi$
$522$	−5.25018	−	2.71431i	−0.229794	−	0.118802i
$523$	−24.3222			−1.06354			−0.531768	−	0.846890i	$-0.678472\pi$
$523$	−24.3222			−1.06354			−0.531768	+	0.846890i	$0.678472\pi$
$524$	15.6189	+	2.66343i	0.682317	+	0.116352i
$525$	−3.53669	−	3.92695i	−0.154354	−	0.171386i
$526$	12.5191	+	6.47231i	0.545860	+	0.282206i
$527$	10.2698	+	10.2698i	0.447359	+	0.447359i
$528$	−4.69322	+	2.25318i	−0.204246	+	0.0980572i
$529$			22.5810i			0.981784i
$530$	−15.6102	+	4.52478i	−0.678064	+	0.196544i
$531$	−2.30403	−	2.30403i	−0.0999862	−	0.0999862i
$532$	−1.78826	−	2.52353i	−0.0775310	−	0.109409i
$533$			5.68011i			0.246033i
$534$	7.74261	+	24.3174i	0.335056	+	1.05232i
$535$	−0.123994	−	0.00323946i	−0.00536073	−	0.000140054i
$536$	15.3088	−	20.3037i	0.661241	−	0.876988i
$537$	−12.2215	−	12.2215i	−0.527398	−	0.527398i
$538$	−23.4090	−	12.1023i	−1.00923	−	0.521767i
$539$	−5.41404	−	5.41404i	−0.233199	−	0.233199i
$540$	3.71514	−	2.48952i	0.159874	−	0.107132i
$541$	24.3708	−	24.3708i	1.04778	−	1.04778i	0.0489835	−	0.998800i	$-0.484402\pi$
$541$	24.3708	−	24.3708i	1.04778	−	1.04778i	0.998800	−	0.0489835i	$-0.0155982\pi$
$542$	−0.862903	−	2.71015i	−0.0370649	−	0.116411i
$543$	−7.77734	+	7.77734i	−0.333758	+	0.333758i
$544$	5.39028	+	5.71869i	0.231106	+	0.245187i
$545$	−2.17390	+	2.06320i	−0.0931197	+	0.0883779i
$546$	1.32309	+	0.684027i	0.0566229	+	0.0292737i
$547$	−46.2500			−1.97751			−0.988754	−	0.149550i	$-0.952218\pi$
$547$	−46.2500			−1.97751			−0.988754	+	0.149550i	$0.952218\pi$
$548$	13.0591	+	2.22691i	0.557857	+	0.0951289i
$549$	−10.8244	+	10.8244i	−0.461974	+	0.461974i
$550$	4.64763	−	7.94335i	0.198176	−	0.338705i
$551$	6.11470			0.260495
$552$	−2.65235	−	18.9107i	−0.112891	−	0.804891i
$553$	6.55147	−	6.55147i	0.278597	−	0.278597i
$554$	−6.94369	+	2.21085i	−0.295009	+	0.0939301i
$555$	18.3897	+	0.480449i	0.780601	+	0.0203939i
$556$	4.59967	+	0.784362i	0.195070	+	0.0332644i
$557$			3.18081i			0.134775i	0.997727	+	0.0673876i	$0.0214664\pi$
$557$			3.18081i			0.134775i	−0.997727	+	0.0673876i	$0.978534\pi$
$558$	4.48559	+	14.0880i	0.189890	+	0.596393i
$559$	−5.21008			−0.220363
$560$	8.62641	−	3.86760i	0.364532	−	0.163436i
$561$	1.80810			0.0763382
$562$	−6.32775	−	19.8737i	−0.266920	−	0.838323i
$563$		−	26.5795i		−	1.12019i	−0.828427	−	0.560096i	$-0.810764\pi$
$563$		−	26.5795i		−	1.12019i	0.828427	−	0.560096i	$-0.189236\pi$
$564$	0.0260665	−	0.152860i	0.00109760	−	0.00643657i
$565$	24.9558	−	23.6850i	1.04990	−	0.996434i
$566$	−10.5388	+	3.35553i	−0.442979	+	0.141044i
$567$	0.747384	−	0.747384i	0.0313872	−	0.0313872i
$568$	−24.0815	+	31.9387i	−1.01044	+	1.34012i
$569$	6.17442			0.258845			0.129423	−	0.991590i	$-0.458688\pi$
$569$	6.17442			0.258845			0.129423	+	0.991590i	$0.458688\pi$
$570$	−2.23146	+	4.05311i	−0.0934656	+	0.169766i
$571$	−22.1640	+	22.1640i	−0.927533	+	0.927533i	−0.997546	−	0.0700130i	$-0.977696\pi$
$571$	−22.1640	+	22.1640i	−0.927533	+	0.927533i	0.0700130	+	0.997546i	$0.477696\pi$
$572$	−0.436010	+	2.55686i	−0.0182305	+	0.106908i
$573$	18.2743			0.763419
$574$	7.56907	+	3.91316i	0.315927	+	0.163332i
$575$	22.5908	+	25.0835i	0.942100	+	1.04606i
$576$	2.20081	+	7.69132i	0.0917005	+	0.320472i
$577$	16.5888	−	16.5888i	0.690601	−	0.690601i	−0.271764	−	0.962364i	$-0.587607\pi$
$577$	16.5888	−	16.5888i	0.690601	−	0.690601i	0.962364	+	0.271764i	$0.0876068\pi$
$578$	6.46593	+	20.3077i	0.268947	+	0.844691i
$579$	11.3061	−	11.3061i	0.469866	−	0.469866i
$580$	−3.62190	+	18.3358i	−0.150391	+	0.761352i
$581$	9.23686	+	9.23686i	0.383209	+	0.383209i
$582$	2.30582	+	1.19209i	0.0955793	+	0.0494139i
$583$	−4.73000	−	4.73000i	−0.195897	−	0.195897i
$584$	3.53265	+	25.1871i	0.146182	+	1.04225i
$585$	0.0581916	−	2.22735i	0.00240593	−	0.0920896i
$586$	8.19997	+	25.7539i	0.338738	+	1.06388i
$587$		−	4.69495i		−	0.193781i	−0.995295	−	0.0968907i	$-0.969110\pi$
$587$		−	4.69495i		−	0.193781i	0.995295	−	0.0968907i	$-0.0308897\pi$
$588$	−9.59971	+	6.80268i	−0.395885	+	0.280538i
$589$	−10.8160	−	10.8160i	−0.445666	−	0.445666i
$590$	−4.96950	+	9.02634i	−0.204591	+	0.371609i
$591$		−	11.1767i		−	0.459747i
$592$	−10.9061	+	31.0480i	−0.448238	+	1.27607i
$593$	16.7482	+	16.7482i	0.687765	+	0.687765i	0.961738	−	0.273972i	$-0.0883376\pi$
$593$	16.7482	+	16.7482i	0.687765	+	0.687765i	−0.273972	+	0.961738i	$0.588338\pi$
$594$	1.63504	+	0.845304i	0.0670864	+	0.0346832i
$595$	−3.28223	−	0.0857514i	−0.134558	−	0.00351546i
$596$	5.74415	−	33.6849i	0.235289	−	1.37979i
$597$	−18.8869			−0.772989
$598$	−8.45127	−	4.36925i	−0.345598	−	0.178672i
$599$		−	3.09289i		−	0.126372i	−0.998002	−	0.0631860i	$-0.979874\pi$
$599$		−	3.09289i		−	0.126372i	0.998002	−	0.0631860i	$-0.0201261\pi$
$600$	−10.8321	−	9.09211i	−0.442217	−	0.371184i
$601$			23.3900i			0.954099i	0.878876	+	0.477050i	$0.158294\pi$
$601$			23.3900i			0.954099i	−0.878876	+	0.477050i	$0.841706\pi$
$602$	−3.58934	+	6.94272i	−0.146291	+	0.282964i
$603$	−8.99029			−0.366113
$604$	20.6430	−	14.6284i	0.839953	−	0.595219i
$605$	−20.8019	−	0.543469i	−0.845716	−	0.0220952i
$606$	−3.90477	+	7.55284i	−0.158620	+	0.306813i
$607$	−25.7183	−	25.7183i	−1.04387	−	1.04387i	−0.998992	−	0.0448798i	$-0.985710\pi$
$607$	−25.7183	−	25.7183i	−1.04387	−	1.04387i	−0.0448798	−	0.998992i	$-0.514290\pi$
$608$	−5.67698	−	6.02285i	−0.230232	−	0.244259i
$609$			4.41728i			0.178997i
$610$	42.4061	+	23.3469i	1.71697	+	0.945289i
$611$	−0.0546292	−	0.0546292i	−0.00221006	−	0.00221006i
$612$	0.467056	−	2.73892i	0.0188796	−	0.110714i
$613$			35.2830i			1.42507i	0.701639	+	0.712533i	$0.252452\pi$
$613$			35.2830i			1.42507i	−0.701639	+	0.712533i	$0.747548\pi$
$614$	4.43411	−	1.41181i	0.178946	−	0.0569760i
$615$	0.332900	−	12.7421i	0.0134238	−	0.513813i
$616$	3.10678	+	2.34249i	0.125176	+	0.0943814i
$617$	−4.50814	−	4.50814i	−0.181491	−	0.181491i	0.610514	−	0.792005i	$-0.290963\pi$
$617$	−4.50814	−	4.50814i	−0.181491	−	0.181491i	−0.792005	+	0.610514i	$0.790963\pi$
$618$	5.44069	−	10.5237i	0.218857	−	0.423326i
$619$	−1.70323	−	1.70323i	−0.0684586	−	0.0684586i	0.672048	−	0.740507i	$-0.265415\pi$
$619$	−1.70323	−	1.70323i	−0.0684586	−	0.0684586i	−0.740507	+	0.672048i	$0.765415\pi$
$620$	38.8399	−	26.0267i	1.55985	−	1.04526i
$621$	−4.77394	+	4.77394i	−0.191572	+	0.191572i
$622$	−14.3844	+	4.57996i	−0.576763	+	0.183640i
$623$	13.4870	−	13.4870i	0.540344	−	0.540344i
$624$	3.76051	+	1.32094i	0.150541	+	0.0528799i
$625$	24.8637	+	2.60725i	0.994547	+	0.104290i
$626$	19.7891	−	38.2774i	0.790933	−	1.52987i
$627$	−1.90427			−0.0760492
$628$	7.29987	+	10.3013i	0.291296	+	0.411068i
$629$	8.08159	−	8.08159i	0.322234	−	0.322234i
$630$	−2.92798	−	1.61201i	−0.116653	−	0.0642242i
$631$	16.8799			0.671980			0.335990	−	0.941866i	$-0.390929\pi$
$631$	16.8799			0.671980			0.335990	+	0.941866i	$0.390929\pi$
$632$	14.9267	−	19.7969i	0.593752	−	0.787479i
$633$	7.95311	−	7.95311i	0.316108	−	0.316108i
$634$	6.91805	+	21.7277i	0.274751	+	0.862918i
$635$	−22.0503	+	20.9274i	−0.875038	+	0.830480i
$636$	−8.38684	+	5.94320i	−0.332560	+	0.235663i
$637$			5.86190i			0.232257i
$638$	−7.32981	+	2.33379i	−0.290190	+	0.0923958i
$639$	14.1421			0.559454
$640$	21.4230	−	13.4557i	0.846817	−	0.531884i
$641$	−36.2647			−1.43237			−0.716185	−	0.697911i	$-0.754113\pi$
$641$	−36.2647			−1.43237			−0.716185	+	0.697911i	$0.754113\pi$
$642$	−0.0747499	+	0.0238002i	−0.00295014	+	0.000939319i
$643$			43.9474i			1.73312i	0.499074	+	0.866559i	$0.333673\pi$
$643$			43.9474i			1.73312i	−0.499074	+	0.866559i	$0.666327\pi$
$644$	−11.6445	+	8.25172i	−0.458859	+	0.325163i
$645$	11.6877	+	0.305353i	0.460203	+	0.0120233i
$646$	0.872106	+	2.73905i	0.0343125	+	0.107766i
$647$	−2.77825	+	2.77825i	−0.109224	+	0.109224i	−0.759607	−	0.650382i	$-0.774609\pi$
$647$	−2.77825	+	2.77825i	−0.109224	+	0.109224i	0.650382	+	0.759607i	$0.274609\pi$
$648$	1.70282	−	2.25841i	0.0668931	−	0.0887186i
$649$	−4.24084			−0.166468
$650$	−6.81626	+	1.78417i	−0.267356	+	0.0699810i
$651$	7.81352	−	7.81352i	0.306236	−	0.306236i
$652$	16.9209	+	23.8782i	0.662673	+	0.935141i
$653$	15.8532			0.620384			0.310192	−	0.950674i	$-0.399607\pi$
$653$	15.8532			0.620384			0.310192	+	0.950674i	$0.399607\pi$
$654$	−0.870524	+	1.68382i	−0.0340402	+	0.0658426i
$655$	−12.8490	+	12.1947i	−0.502051	+	0.476486i
$656$	21.5130	+	7.55677i	0.839941	+	0.295042i
$657$	6.35840	−	6.35840i	0.248065	−	0.248065i
$658$	−0.110432	+	0.0351612i	−0.00430508	+	0.00137073i
$659$	−3.02357	+	3.02357i	−0.117781	+	0.117781i	−0.763541	−	0.645759i	$-0.776541\pi$
$659$	−3.02357	+	3.02357i	−0.117781	+	0.117781i	0.645759	+	0.763541i	$0.276541\pi$
$660$	1.12795	−	5.71022i	0.0439054	−	0.222270i
$661$	−14.5980	−	14.5980i	−0.567797	−	0.567797i	0.363714	−	0.931511i	$-0.381509\pi$
$661$	−14.5980	−	14.5980i	−0.567797	−	0.567797i	−0.931511	+	0.363714i	$0.881509\pi$
$662$	1.81749	−	3.51549i	0.0706386	−	0.136634i
$663$	−0.978836	−	0.978836i	−0.0380149	−	0.0380149i
$664$	27.9115	+	21.0450i	1.08318	+	0.816705i
$665$	3.45680	+	0.0903123i	0.134049	+	0.00350216i
$666$	11.0863	−	3.52984i	0.429584	−	0.136779i
$667$		−	28.2155i		−	1.09251i
$668$	2.52648	−	14.8158i	0.0977524	−	0.573242i
$669$	−4.22843	−	4.22843i	−0.163480	−	0.163480i
$670$	7.91488	+	27.3058i	0.305778	+	1.05492i
$671$			19.9236i			0.769143i
$672$	4.35092	−	4.10107i	0.167841	−	0.158202i
$673$	−11.2973	−	11.2973i	−0.435481	−	0.435481i	0.455007	−	0.890488i	$-0.349637\pi$
$673$	−11.2973	−	11.2973i	−0.435481	−	0.435481i	−0.890488	+	0.455007i	$0.849637\pi$
$674$	23.1850	−	44.8458i	0.893052	−	1.72740i
$675$	−0.261081	+	4.99318i	−0.0100490	+	0.192188i
$676$	−19.5934	+	13.8846i	−0.753592	+	0.534021i
$677$	9.23434			0.354905			0.177452	−	0.984129i	$-0.443214\pi$
$677$	9.23434			0.354905			0.177452	+	0.984129i	$0.443214\pi$
$678$	9.99336	−	19.3298i	0.383793	−	0.742355i
$679$		−	1.94002i		−	0.0744510i
$680$	−8.72999	+	0.992721i	−0.334780	+	0.0380691i
$681$		−	15.7654i		−	0.604131i
$682$	17.0935	+	8.83722i	0.654544	+	0.338395i
$683$	10.8971			0.416967			0.208483	−	0.978026i	$-0.433147\pi$
$683$	10.8971			0.416967			0.208483	+	0.978026i	$0.433147\pi$
$684$	−0.491897	+	2.88459i	−0.0188082	+	0.110295i
$685$	−10.7431	+	10.1960i	−0.410473	+	0.389571i
$686$	17.1060	+	8.84369i	0.653110	+	0.337654i
$687$	0.746140	+	0.746140i	0.0284670	+	0.0284670i
$688$	−6.93144	+	19.7328i	−0.264259	+	0.752305i
$689$			5.12128i			0.195105i
$690$	18.7026	+	10.2968i	0.711995	+	0.391993i
$691$	−12.7458	−	12.7458i	−0.484873	−	0.484873i	0.421811	−	0.906684i	$-0.361395\pi$
$691$	−12.7458	−	12.7458i	−0.484873	−	0.484873i	−0.906684	+	0.421811i	$0.861395\pi$
$692$	−21.4645	+	15.2105i	−0.815957	+	0.578215i
$693$		−	1.37565i		−	0.0522567i
$694$	−10.3818	−	32.6065i	−0.394089	−	1.23773i
$695$	−3.78394	+	3.59125i	−0.143533	+	0.136224i
$696$	1.64185	+	11.7061i	0.0622343	+	0.443717i
$697$	−5.59969	−	5.59969i	−0.212103	−	0.212103i
$698$	−4.06609	−	2.10214i	−0.153904	−	0.0795673i
$699$	5.74517	+	5.74517i	0.217302	+	0.217302i
$700$	−2.31837	+	10.3122i	−0.0876261	+	0.389765i
$701$	28.0269	−	28.0269i	1.05856	−	1.05856i	0.0603853	−	0.998175i	$-0.480767\pi$
$701$	28.0269	−	28.0269i	1.05856	−	1.05856i	0.998175	−	0.0603853i	$-0.0192329\pi$
$702$	−0.427532	−	1.34276i	−0.0161361	−	0.0506792i
$703$	−8.51143	+	8.51143i	−0.321015	+	0.321015i
$704$	9.10384	+	5.05298i	0.343114	+	0.190441i
$705$	0.119347	+	0.125751i	0.00449488	+	0.00473605i
$706$	−17.2434	−	8.91474i	−0.648965	−	0.335511i
$707$	6.35463			0.238991
$708$	−1.09546	+	6.42404i	−0.0411700	+	0.241430i
$709$	−6.39995	+	6.39995i	−0.240355	+	0.240355i	−0.816997	−	0.576642i	$-0.804363\pi$
$709$	−6.39995	+	6.39995i	−0.240355	+	0.240355i	0.576642	+	0.816997i	$0.304363\pi$
$710$	−12.4504	−	42.9533i	−0.467257	−	1.61201i
$711$	−8.76588			−0.328746
$712$	30.7284	−	40.7543i	1.15159	−	1.52733i
$713$	−49.9091	+	49.9091i	−1.86911	+	1.86911i
$714$	−1.97870	+	0.630012i	−0.0740509	+	0.0235776i
$715$	−1.99630	−	2.10341i	−0.0746574	−	0.0786630i
$716$	−5.81080	+	34.0758i	−0.217160	+	1.27347i
$717$		−	27.9736i		−	1.04469i
$718$	−11.6474	−	36.5812i	−0.434676	−	1.36520i
$719$	−11.7136			−0.436843			−0.218422	−	0.975854i	$-0.570091\pi$
$719$	−11.7136			−0.436843			−0.218422	+	0.975854i	$0.570091\pi$
$720$	−8.35849	−	3.18364i	−0.311503	−	0.118647i
$721$	−8.85420			−0.329748
$722$	7.23362	+	22.7188i	0.269208	+	0.845508i
$723$		−	7.01072i		−	0.260732i
$724$	21.6846	+	3.69778i	0.805902	+	0.137427i
$725$	−13.9841	−	15.5272i	−0.519357	−	0.576665i
$726$	−12.5404	+	3.99284i	−0.465419	+	0.148188i
$727$	−7.19783	+	7.19783i	−0.266953	+	0.266953i	−0.827871	−	0.560918i	$-0.810448\pi$
$727$	−7.19783	+	7.19783i	−0.266953	+	0.266953i	0.560918	+	0.827871i	$0.310448\pi$
$728$	−0.413760	−	2.95002i	−0.0153350	−	0.109335i
$729$	−1.00000			−0.0370370
$730$	−24.9099	−	13.7143i	−0.921957	−	0.507589i
$731$	5.13631	−	5.13631i	0.189973	−	0.189973i
$732$	30.1804	+	5.14653i	1.11550	+	0.190221i
$733$	−10.6158			−0.392103			−0.196052	−	0.980594i	$-0.562812\pi$
$733$	−10.6158			−0.392103			−0.196052	+	0.980594i	$0.562812\pi$
$734$	29.0921	+	15.0404i	1.07381	+	0.555152i
$735$	0.343555	−	13.1499i	0.0126722	−	0.485043i
$736$	−27.7917	+	26.1957i	−1.02442	+	0.965587i
$737$	−8.27386	+	8.27386i	−0.304772	+	0.304772i
$738$	−2.44581	−	7.68161i	−0.0900314	−	0.282764i
$739$	−30.4725	+	30.4725i	−1.12095	+	1.12095i	−0.129349	+	0.991599i	$0.541289\pi$
$739$	−30.4725	+	30.4725i	−1.12095	+	1.12095i	−0.991599	+	0.129349i	$0.958711\pi$
$740$	−20.4812	−	30.5643i	−0.752903	−	1.12356i
$741$	1.03090	+	1.03090i	0.0378710	+	0.0378710i
$742$	6.82439	+	3.52816i	0.250531	+	0.129523i
$743$	6.20995	+	6.20995i	0.227821	+	0.227821i	0.811782	−	0.583961i	$-0.198498\pi$
$743$	6.20995	+	6.20995i	0.227821	+	0.227821i	−0.583961	+	0.811782i	$0.698498\pi$
$744$	17.8021	−	23.6105i	0.652657	−	0.865603i
$745$	26.2999	+	27.7110i	0.963555	+	1.01525i
$746$	−12.7634	−	40.0862i	−0.467299	−	1.46766i
$747$		−	12.3589i		−	0.452189i
$748$	−2.09082	−	2.95049i	−0.0764480	−	0.107881i
$749$	0.0414579	+	0.0414579i	0.00151484	+	0.00151484i
$750$	15.3954	−	3.60293i	0.562161	−	0.131560i
$751$		−	11.3219i		−	0.413143i	−0.978432	−	0.206571i	$-0.933769\pi$
$751$		−	11.3219i		−	0.413143i	0.978432	−	0.206571i	$-0.0662305\pi$
$752$	−0.279582	+	0.134226i	−0.0101953	+	0.00489470i
$753$	−5.41619	−	5.41619i	−0.197377	−	0.197377i
$754$	5.23150	+	2.70465i	0.190520	+	0.0984975i
$755$	−0.738773	+	28.2774i	−0.0268867	+	1.02912i
$756$	−2.08384	−	0.355348i	−0.0757885	−	0.0129239i
$757$	11.1139			0.403942			0.201971	−	0.979391i	$-0.435265\pi$
$757$	11.1139			0.403942			0.201971	+	0.979391i	$0.435265\pi$
$758$	19.6465	+	10.1571i	0.713592	+	0.368922i
$759$			8.78702i			0.318949i
$760$	9.19431	−	1.04552i	0.333513	−	0.0379250i
$761$			4.08171i			0.147962i	0.997260	+	0.0739810i	$0.0235704\pi$
$761$			4.08171i			0.147962i	−0.997260	+	0.0739810i	$0.976430\pi$
$762$	−8.82987	+	17.0793i	−0.319873	+	0.618717i
$763$	1.41669			0.0512878
$764$	−21.1317	−	29.8203i	−0.764518	−	1.07886i
$765$	2.13845	+	2.25318i	0.0773156	+	0.0814639i
$766$	14.9069	−	28.8339i	0.538609	−	1.04181i
$767$	2.29583	+	2.29583i	0.0828975	+	0.0828975i
$768$	10.0059	−	12.4853i	0.361057	−	0.450523i
$769$		−	31.6143i		−	1.14004i	−0.821631	−	0.570020i	$-0.806935\pi$
$769$		−	31.6143i		−	1.14004i	0.821631	−	0.570020i	$-0.193065\pi$
$770$	−4.17821	+	1.21110i	−0.150572	+	0.0436449i
$771$	17.0268	+	17.0268i	0.613204	+	0.613204i
$772$	−31.5235	−	5.37556i	−1.13455	−	0.193471i
$773$			22.3964i			0.805542i	0.915301	+	0.402771i	$0.131953\pi$
$773$			22.3964i			0.805542i	−0.915301	+	0.402771i	$0.868047\pi$
$774$	7.04595	−	2.24341i	0.253262	−	0.0806378i
$775$	−2.72947	+	52.2011i	−0.0980455	+	1.87512i
$776$	−0.721083	−	5.14117i	−0.0258854	−	0.184557i
$777$	−6.14869	−	6.14869i	−0.220583	−	0.220583i
$778$	−11.6044	+	22.4460i	−0.416038	+	0.804727i
$779$	5.89752	+	5.89752i	0.211301	+	0.211301i
$780$	−3.70192	+	2.48066i	−0.132550	+	0.0888220i
$781$	13.0151	−	13.0151i	0.465719	−	0.465719i
$782$	12.6390	−	4.02422i	0.451970	−	0.143906i
$783$	2.95516	−	2.95516i	0.105609	−	0.105609i
$784$	22.2015	+	7.79862i	0.792910	+	0.278522i
$785$	−14.1110	−	0.368664i	−0.503644	−	0.0131582i
$786$	−5.14528	+	9.95232i	−0.183526	+	0.354987i
$787$	45.2339			1.61242			0.806208	−	0.591633i	$-0.201516\pi$
$787$	45.2339			1.61242			0.806208	+	0.591633i	$0.201516\pi$
$788$	−18.2383	+	12.9243i	−0.649713	+	0.460408i
$789$	−7.04662	+	7.04662i	−0.250866	+	0.250866i
$790$	7.71730	+	26.6242i	0.274569	+	0.947247i
$791$	−16.2632			−0.578254
$792$	−0.511314	−	3.64556i	−0.0181687	−	0.129539i
$793$	10.7859	−	10.7859i	0.383018	−	0.383018i
$794$	2.32569	+	7.30435i	0.0825356	+	0.259222i
$795$	0.300148	−	11.4885i	0.0106452	−	0.407456i
$796$	21.8401	+	30.8200i	0.774101	+	1.09238i
$797$			33.6337i			1.19137i	0.803219	+	0.595684i	$0.203119\pi$
$797$			33.6337i			1.19137i	−0.803219	+	0.595684i	$0.796881\pi$
$798$	2.08394	−	0.663520i	0.0737706	−	0.0234884i
$799$	0.107711			0.00381056
$800$	−2.31089	+	28.1897i	−0.0817023	+	0.996657i
$801$	−18.0456			−0.637609
$802$	21.2307	−	6.75980i	0.749682	−	0.238697i
$803$		−	11.7034i		−	0.413004i
$804$	10.3960	+	14.6705i	0.366640	+	0.517389i
$805$	0.416735	−	15.9510i	0.0146880	−	0.562199i
$806$	−4.46962	−	14.0379i	−0.157436	−	0.494463i
$807$	13.1762	−	13.1762i	0.463823	−	0.463823i
$808$	16.8402	−	2.36195i	0.592435	−	0.0830929i
$809$	−7.75023			−0.272483			−0.136242	−	0.990676i	$-0.543502\pi$
$809$	−7.75023			−0.272483			−0.136242	+	0.990676i	$0.543502\pi$
$810$	0.880380	+	3.03726i	0.0309334	+	0.106718i
$811$	15.5679	−	15.5679i	0.546661	−	0.546661i	−0.378812	−	0.925474i	$-0.623667\pi$
$811$	15.5679	−	15.5679i	0.546661	−	0.546661i	0.925474	+	0.378812i	$0.123667\pi$
$812$	7.20820	−	5.10797i	0.252958	−	0.179255i
$813$	2.01115			0.0705343
$814$	6.95427	−	13.4514i	0.243747	−	0.471470i
$815$	−32.7089	−	0.854552i	−1.14574	−	0.0299336i
$816$	−5.00950	+	2.40503i	−0.175368	+	0.0841929i
$817$	−5.40950	+	5.40950i	−0.189254	+	0.189254i
$818$	41.6990	−	13.2769i	1.45797	−	0.464215i
$819$	−0.744724	+	0.744724i	−0.0260228	+	0.0260228i
$820$	−21.1778	+	14.1913i	−0.739561	+	0.495581i
$821$	−25.2360	−	25.2360i	−0.880741	−	0.880741i	0.112869	−	0.993610i	$-0.463996\pi$
$821$	−25.2360	−	25.2360i	−0.880741	−	0.880741i	−0.993610	+	0.112869i	$0.963996\pi$
$822$	−4.30200	+	8.32119i	−0.150049	+	0.290235i
$823$	−24.2751	−	24.2751i	−0.846178	−	0.846178i	0.143476	−	0.989654i	$-0.454172\pi$
$823$	−24.2751	−	24.2751i	−0.846178	−	0.846178i	−0.989654	+	0.143476i	$0.954172\pi$
$824$	−23.4642	+	3.29101i	−0.817414	+	0.114648i
$825$	4.35500	+	4.83555i	0.151622	+	0.168352i
$826$	4.64096	−	1.47767i	0.161480	−	0.0514147i
$827$			8.03445i			0.279385i	0.990195	+	0.139693i	$0.0446115\pi$
$827$			8.03445i			0.279385i	−0.990195	+	0.139693i	$0.955389\pi$
$828$	13.3106	+	2.26980i	0.462575	+	0.0788810i
$829$	−17.2385	−	17.2385i	−0.598718	−	0.598718i	0.341254	−	0.939971i	$-0.389148\pi$
$829$	−17.2385	−	17.2385i	−0.598718	−	0.598718i	−0.939971	+	0.341254i	$0.889148\pi$
$830$	−37.5372	+	10.8805i	−1.30294	+	0.377669i
$831$		−	5.15280i		−	0.178749i
$832$	−2.19298	−	7.66395i	−0.0760279	−	0.265700i
$833$	−5.77890	−	5.77890i	−0.200227	−	0.200227i
$834$	−1.51525	+	2.93089i	−0.0524689	+	0.101488i
$835$	11.5676	+	12.1883i	0.400315	+	0.421793i
$836$	2.20202	+	3.10742i	0.0761586	+	0.107472i
$837$	−10.4545			−0.361360
$838$	13.9966	−	27.0730i	0.483503	−	0.935221i
$839$			23.0026i			0.794136i	0.917789	+	0.397068i	$0.129972\pi$
$839$			23.0026i			0.794136i	−0.917789	+	0.397068i	$0.870028\pi$
$840$	0.755288	+	6.64200i	0.0260599	+	0.229171i
$841$		−	11.5340i		−	0.397726i
$842$	25.5847	+	13.2271i	0.881706	+	0.455836i
$843$	14.7480			0.507947
$844$	−22.1747	−	3.78135i	−0.763284	−	0.130160i
$845$	0.701209	−	26.8395i	0.0241223	−	0.923308i
$846$	0.0974017	+	0.0503560i	0.00334874	+	0.00173128i
$847$	6.95520	+	6.95520i	0.238983	+	0.238983i
$848$	19.3964	+	6.81331i	0.666077	+	0.233970i
$849$		−	7.82068i		−	0.268405i
$850$	4.96084	−	8.47866i	0.170156	−	0.290816i
$851$	39.2750	+	39.2750i	1.34633	+	1.34633i
$852$	−16.3534	−	23.0774i	−0.560258	−	0.790617i
$853$		−	17.9417i		−	0.614312i	−0.951659	−	0.307156i	$-0.900623\pi$
$853$		−	17.9417i		−	0.614312i	0.951659	−	0.307156i	$-0.0993773\pi$
$854$	−6.94216	−	21.8034i	−0.237556	−	0.746098i
$855$	−2.25218	−	2.37302i	−0.0770230	−	0.0811556i
$856$	0.125276	+	0.0944566i	0.00428183	+	0.00322846i
$857$	27.5741	+	27.5741i	0.941914	+	0.941914i	0.998403	−	0.0564890i	$-0.0179906\pi$
$857$	27.5741	+	27.5741i	0.941914	+	0.941914i	−0.0564890	+	0.998403i	$0.517991\pi$
$858$	−1.62922	−	0.842295i	−0.0556206	−	0.0287555i
$859$	22.0003	+	22.0003i	0.750640	+	0.750640i	0.974599	−	0.223959i	$-0.0718981\pi$
$859$	22.0003	+	22.0003i	0.750640	+	0.750640i	−0.223959	+	0.974599i	$0.571898\pi$
$860$	−13.0169	−	19.4253i	−0.443874	−	0.662398i
$861$	−4.26039	+	4.26039i	−0.145194	+	0.145194i
$862$	1.91922	+	6.02775i	0.0653689	+	0.205306i
$863$	16.4456	−	16.4456i	0.559814	−	0.559814i	−0.369440	−	0.929254i	$-0.620451\pi$
$863$	16.4456	−	16.4456i	0.559814	−	0.559814i	0.929254	+	0.369440i	$0.120451\pi$
$864$	−5.65438	−	0.167155i	−0.192366	−	0.00568673i
$865$	0.768171	−	29.4026i	0.0261186	−	0.999718i
$866$	37.0582	+	19.1589i	1.25929	+	0.651045i
$867$	−15.0700			−0.511806
$868$	−21.7855	−	3.71498i	−0.739447	−	0.126095i
$869$	−8.06733	+	8.06733i	−0.273665	+	0.273665i
$870$	−11.5773	−	6.37392i	−0.392506	−	0.216096i
$871$	8.95830			0.303540
$872$	3.75433	−	0.526569i	0.127138	−	0.0178319i
$873$	−1.29787	+	1.29787i	−0.0439263	+	0.0439263i
$874$	−13.3112	+	4.23826i	−0.450259	+	0.143361i
$875$	−7.67626	−	8.98447i	−0.259505	−	0.303731i
$876$	−17.7284	−	3.02314i	−0.598986	−	0.102142i
$877$		−	6.59281i		−	0.222623i	−0.993786	−	0.111312i	$-0.964495\pi$
$877$		−	6.59281i		−	0.222623i	0.993786	−	0.111312i	$-0.0355052\pi$
$878$	−0.110599	−	0.347360i	−0.00373252	−	0.0117228i
$879$	−19.1115			−0.644617
$880$	−10.6224	+	4.76247i	−0.358080	+	0.160543i
$881$	22.1698			0.746920			0.373460	−	0.927646i	$-0.378171\pi$
$881$	22.1698			0.746920			0.373460	+	0.927646i	$0.378171\pi$
$882$	−2.52408	−	7.92745i	−0.0849902	−	0.266931i
$883$			38.7205i			1.30305i	0.758628	+	0.651524i	$0.225870\pi$
$883$			38.7205i			1.30305i	−0.758628	+	0.651524i	$0.774130\pi$
$884$	−0.465394	+	2.72917i	−0.0156529	+	0.0917920i
$885$	−5.01565	−	5.28476i	−0.168599	−	0.177645i
$886$	37.4991	−	11.9396i	1.25981	−	0.401120i
$887$	−25.2413	+	25.2413i	−0.847518	+	0.847518i	−0.989823	−	0.142305i	$-0.954549\pi$
$887$	−25.2413	+	25.2413i	−0.847518	+	0.847518i	0.142305	+	0.989823i	$0.454549\pi$
$888$	−18.5798	−	14.0090i	−0.623497	−	0.470111i
$889$	14.3698			0.481947
$890$	15.8870	+	54.8091i	0.532533	+	1.83720i
$891$	−0.920311	+	0.920311i	−0.0308316	+	0.0308316i
$892$	−2.01043	+	11.7896i	−0.0673142	+	0.394746i
$893$	−0.113440			−0.00379613
$894$	21.4639	+	11.0967i	0.717860	+	0.371129i
$895$	−26.6051	−	28.0326i	−0.889310	−	0.937025i
$896$	−11.7234	−	2.35760i	−0.391652	−	0.0787619i
$897$	4.75695	−	4.75695i	0.158830	−	0.158830i
$898$	−3.14144	−	9.86641i	−0.104831	−	0.329246i
$899$	30.8947	−	30.8947i	1.03040	−	1.03040i
$900$	8.44986	−	5.34788i	0.281662	−	0.178263i
$901$	−5.04877	−	5.04877i	−0.168199	−	0.168199i
$902$	−9.32037	−	4.81857i	−0.310335	−	0.160441i
$903$	−3.90784	−	3.90784i	−0.130045	−	0.130045i
$904$	−43.0986	+	6.04486i	−1.43344	+	0.201049i
$905$	−17.8389	+	16.9305i	−0.592986	+	0.562790i
$906$	5.42773	+	17.0470i	0.180324	+	0.566350i
$907$		−	9.44895i		−	0.313747i	−0.987619	−	0.156874i	$-0.949858\pi$
$907$		−	9.44895i		−	0.313747i	0.987619	−	0.156874i	$-0.0501415\pi$
$908$	−25.7262	+	18.2305i	−0.853755	+	0.605000i
$909$	−4.25125	−	4.25125i	−0.141005	−	0.141005i
$910$	2.91756	+	1.60628i	0.0967161	+	0.0532476i
$911$		−	36.1798i		−	1.19869i	−0.800490	−	0.599346i	$-0.795427\pi$
$911$		−	36.1798i		−	1.19869i	0.800490	−	0.599346i	$-0.204573\pi$
$912$	5.27594	−	2.53295i	0.174704	−	0.0838742i
$913$	−11.3740	−	11.3740i	−0.376426	−	0.376426i
$914$	−23.4446	−	12.1207i	−0.775478	−	0.400917i
$915$	−24.8280	+	23.5637i	−0.820788	+	0.778992i
$916$	0.354757	−	2.08037i	0.0117215	−	0.0687374i
$917$	8.37345			0.276516
$918$	1.74523	+	0.902270i	0.0576011	+	0.0297794i
$919$		−	45.3587i		−	1.49624i	−0.663561	−	0.748122i	$-0.730956\pi$
$919$		−	45.3587i		−	1.49624i	0.663561	−	0.748122i	$-0.269044\pi$
$920$	−4.82443	−	42.4260i	−0.159057	−	1.39874i
$921$			3.29048i			0.108425i
$922$	−18.0053	+	34.8269i	−0.592973	+	1.14696i
$923$	−14.0918			−0.463837
$924$	−2.24481	+	1.59075i	−0.0738489	+	0.0523318i
$925$	41.0786	+	2.14790i	1.35066	+	0.0706226i
$926$	15.8825	−	30.7209i	0.521932	−	1.00955i
$927$	5.92346	+	5.92346i	0.194552	+	0.194552i
$928$	17.2036	−	16.2156i	0.564735	−	0.532305i
$929$			0.551101i			0.0180810i	0.999959	+	0.00904052i	$0.00287773\pi$
$929$			0.551101i			0.0180810i	−0.999959	+	0.00904052i	$0.997122\pi$
$930$	9.20393	+	31.7530i	0.301809	+	1.04122i
$931$	6.08626	+	6.08626i	0.199469	+	0.199469i
$932$	2.73158	−	16.0186i	0.0894758	−	0.524706i
$933$		−	10.6744i		−	0.349466i
$934$	−42.2992	+	13.4679i	−1.38407	+	0.440685i
$935$	4.04166	+	0.105592i	0.132176	+	0.00345324i
$936$	−1.69676	+	2.25037i	−0.0554603	+	0.0735556i
$937$	10.4271	+	10.4271i	0.340639	+	0.340639i	0.856607	−	0.515969i	$-0.172568\pi$
$937$	10.4271	+	10.4271i	0.340639	+	0.340639i	−0.515969	+	0.856607i	$0.672568\pi$
$938$	6.17157	−	11.9374i	0.201509	−	0.389771i
$939$	21.5451	+	21.5451i	0.703098	+	0.703098i
$940$	0.0671936	−	0.340166i	0.00219161	−	0.0110950i
$941$	7.44442	−	7.44442i	0.242681	−	0.242681i	−0.575277	−	0.817958i	$-0.695106\pi$
$941$	7.44442	−	7.44442i	0.242681	−	0.242681i	0.817958	+	0.575277i	$0.195106\pi$
$942$	−8.50684	+	2.70856i	−0.277168	+	0.0882496i
$943$	27.2134	−	27.2134i	0.886190	−	0.886190i
$944$	11.7496	−	5.64091i	0.382417	−	0.183596i
$945$	1.71428	−	1.62698i	0.0557655	−	0.0529258i
$946$	4.41983	−	8.54911i	0.143701	−	0.277955i
$947$	15.8341			0.514539			0.257270	−	0.966340i	$-0.417177\pi$
$947$	15.8341			0.514539			0.257270	+	0.966340i	$0.417177\pi$
$948$	10.1365	+	14.3043i	0.329219	+	0.464582i
$949$	−6.33577	+	6.33577i	−0.205668	+	0.205668i
$950$	−5.22470	+	8.92962i	−0.169512	+	0.289715i
$951$	−16.1238			−0.522850
$952$	3.31615	+	2.50035i	0.107477	+	0.0810368i
$953$	−14.8928	+	14.8928i	−0.482424	+	0.482424i	−0.905905	−	0.423481i	$-0.860808\pi$
$953$	−14.8928	+	14.8928i	−0.482424	+	0.482424i	0.423481	+	0.905905i	$0.360808\pi$
$954$	−2.20518	−	6.92586i	−0.0713953	−	0.224233i
$955$	40.8486	+	1.06721i	1.32183	+	0.0345341i
$956$	−45.6477	+	32.3475i	−1.47635	+	1.04619i
$957$		−	5.43934i		−	0.175829i
$958$	−14.1309	+	4.49925i	−0.456549	+	0.145364i
$959$	7.00109			0.226077
$960$	4.47032	+	17.3210i	0.144279	+	0.559032i
$961$	−78.2963			−2.52569
$962$	−11.0468	+	3.51728i	−0.356164	+	0.113402i
$963$		−	0.0554707i		−	0.00178752i
$964$	−11.4402	+	8.10693i	−0.368465	+	0.261107i
$965$	25.9329	−	24.6123i	0.834809	−	0.792300i
$966$	−3.06173	−	9.61607i	−0.0985097	−	0.309392i
$967$	−27.8728	+	27.8728i	−0.896330	+	0.896330i	−0.995109	−	0.0987795i	$-0.968506\pi$
$967$	−27.8728	+	27.8728i	−0.896330	+	0.896330i	0.0987795	+	0.995109i	$0.468506\pi$
$968$	21.0169	+	15.8465i	0.675508	+	0.509327i
$969$	−2.03260			−0.0652966
$970$	5.08459	+	2.79935i	0.163256	+	0.0898817i
$971$	−30.0958	+	30.0958i	−0.965819	+	0.965819i	−0.999435	−	0.0336155i	$-0.989298\pi$
$971$	−30.0958	+	30.0958i	−0.965819	+	0.965819i	0.0336155	+	0.999435i	$0.489298\pi$
$972$	1.15636	+	1.63182i	0.0370903	+	0.0523406i
$973$	2.46593			0.0790540
$974$	4.34220	−	8.39895i	0.139133	−	0.269120i
$975$	0.260152	−	4.97541i	0.00833154	−	0.159341i
$976$	−26.5012	−	55.2001i	−0.848284	−	1.76691i
$977$	−9.03427	+	9.03427i	−0.289032	+	0.289032i	−0.836697	−	0.547666i	$-0.815517\pi$
$977$	−9.03427	+	9.03427i	−0.289032	+	0.289032i	0.547666	+	0.836697i	$0.315517\pi$
$978$	−19.7186	+	6.27835i	−0.630532	+	0.200760i
$979$	−16.6075	+	16.6075i	−0.530780	+	0.530780i
$980$	−21.8556	+	14.6455i	−0.698150	+	0.467832i
$981$	−0.947769	−	0.947769i	−0.0302599	−	0.0302599i
$982$	−2.76355	+	5.34543i	−0.0881884	+	0.170579i
$983$	24.5191	+	24.5191i	0.782039	+	0.782039i	0.980175	−	0.198135i	$-0.0634886\pi$
$983$	24.5191	+	24.5191i	0.782039	+	0.782039i	−0.198135	+	0.980175i	$0.563489\pi$
$984$	−9.70675	+	12.8738i	−0.309440	+	0.410403i
$985$	0.652712	−	24.9833i	0.0207971	−	0.796034i
$986$	−7.82378	+	2.49107i	−0.249160	+	0.0793319i
$987$		−	0.0819496i		−	0.00260848i
$988$	0.490147	−	2.87433i	0.0155936	−	0.0914445i
$989$	24.9615	+	24.9615i	0.793728	+	0.793728i
$990$	3.60544	+	1.98500i	0.114589	+	0.0630874i
$991$			25.8872i			0.822334i	0.911560	+	0.411167i	$0.134879\pi$
$991$			25.8872i			0.822334i	−0.911560	+	0.411167i	$0.865121\pi$
$992$	−59.1137	−	1.74752i	−1.87686	−	0.0554838i
$993$	1.97876	+	1.97876i	0.0627940	+	0.0627940i
$994$	−9.70815	+	18.7781i	−0.307924	+	0.595605i
$995$	−42.2180	−	1.10298i	−1.33840	−	0.0349670i
$996$	−20.1675	+	14.2914i	−0.639032	+	0.452840i
$997$	16.7546			0.530624			0.265312	−	0.964163i	$-0.414525\pi$
$997$	16.7546			0.530624			0.265312	+	0.964163i	$0.414525\pi$
$998$	8.04392	−	15.5591i	0.254626	−	0.492513i
$999$			8.22694i			0.260289i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.bc.e.43.8	yes	16
3.2	odd	2		720.2.bd.f.523.1		16
4.3	odd	2		960.2.bc.e.463.6		16
5.2	odd	4		240.2.y.e.187.5	yes	16
8.3	odd	2		1920.2.bc.j.1183.3		16
8.5	even	2		1920.2.bc.i.1183.3		16
15.2	even	4		720.2.z.f.667.4		16
16.3	odd	4		240.2.y.e.163.5	✓	16
16.5	even	4		1920.2.y.j.223.1		16
16.11	odd	4		1920.2.y.i.223.1		16
16.13	even	4		960.2.y.e.943.8		16
20.7	even	4		960.2.y.e.847.8		16
40.27	even	4		1920.2.y.j.1567.1		16
40.37	odd	4		1920.2.y.i.1567.1		16
48.35	even	4		720.2.z.f.163.4		16
80.27	even	4		1920.2.bc.i.607.3		16
80.37	odd	4		1920.2.bc.j.607.3		16
80.67	even	4	inner	240.2.bc.e.67.8	yes	16
80.77	odd	4		960.2.bc.e.367.6		16
240.227	odd	4		720.2.bd.f.307.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.y.e.163.5	✓	16	16.3	odd	4
240.2.y.e.187.5	yes	16	5.2	odd	4
240.2.bc.e.43.8	yes	16	1.1	even	1	trivial
240.2.bc.e.67.8	yes	16	80.67	even	4	inner
720.2.z.f.163.4		16	48.35	even	4
720.2.z.f.667.4		16	15.2	even	4
720.2.bd.f.307.1		16	240.227	odd	4
720.2.bd.f.523.1		16	3.2	odd	2
960.2.y.e.847.8		16	20.7	even	4
960.2.y.e.943.8		16	16.13	even	4
960.2.bc.e.367.6		16	80.77	odd	4
960.2.bc.e.463.6		16	4.3	odd	2
1920.2.y.i.223.1		16	16.11	odd	4
1920.2.y.i.1567.1		16	40.37	odd	4
1920.2.y.j.223.1		16	16.5	even	4
1920.2.y.j.1567.1		16	40.27	even	4
1920.2.bc.i.607.3		16	80.27	even	4
1920.2.bc.i.1183.3		16	8.5	even	2
1920.2.bc.j.607.3		16	80.37	odd	4
1920.2.bc.j.1183.3		16	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.bc (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.34756 - 0.429059i) q^{2} +1.00000i q^{3} +(1.63182 - 1.15636i) q^{4} +(-0.0583995 + 2.23531i) q^{5} +(0.429059 + 1.34756i) q^{6} +(0.747384 - 0.747384i) q^{7} +(1.70282 - 2.25841i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(1.34756 - 0.429059i) q^{2} +1.00000i q^{3} +(1.63182 - 1.15636i) q^{4} +(-0.0583995 + 2.23531i) q^{5} +(0.429059 + 1.34756i) q^{6} +(0.747384 - 0.747384i) q^{7} +(1.70282 - 2.25841i) q^{8} -1.00000 q^{9} +(0.880380 + 3.03726i) q^{10} +(-0.920311 + 0.920311i) q^{11} +(1.15636 + 1.63182i) q^{12} +0.996441 q^{13} +(0.686471 - 1.32781i) q^{14} +(-2.23531 - 0.0583995i) q^{15} +(1.32566 - 3.77394i) q^{16} +(-0.982332 + 0.982332i) q^{17} +(-1.34756 + 0.429059i) q^{18} +(1.03458 - 1.03458i) q^{19} +(2.48952 + 3.71514i) q^{20} +(0.747384 + 0.747384i) q^{21} +(-0.845304 + 1.63504i) q^{22} +(-4.77394 - 4.77394i) q^{23} +(2.25841 + 1.70282i) q^{24} +(-4.99318 - 0.261081i) q^{25} +(1.34276 - 0.427532i) q^{26} -1.00000i q^{27} +(0.355348 - 2.08384i) q^{28} +(2.95516 + 2.95516i) q^{29} +(-3.03726 + 0.880380i) q^{30} -10.4545i q^{31} +(0.167155 - 5.65438i) q^{32} +(-0.920311 - 0.920311i) q^{33} +(-0.902270 + 1.74523i) q^{34} +(1.62698 + 1.71428i) q^{35} +(-1.63182 + 1.15636i) q^{36} -8.22694 q^{37} +(0.950259 - 1.83805i) q^{38} +0.996441i q^{39} +(4.94879 + 3.93821i) q^{40} +5.70040i q^{41} +(1.32781 + 0.686471i) q^{42} -5.22869 q^{43} +(-0.437567 + 2.56599i) q^{44} +(0.0583995 - 2.23531i) q^{45} +(-8.48146 - 4.38486i) q^{46} +(-0.0548243 - 0.0548243i) q^{47} +(3.77394 + 1.32566i) q^{48} +5.88283i q^{49} +(-6.84061 + 1.79054i) q^{50} +(-0.982332 - 0.982332i) q^{51} +(1.62601 - 1.15225i) q^{52} +5.13957i q^{53} +(-0.429059 - 1.34756i) q^{54} +(-2.00343 - 2.11092i) q^{55} +(-0.415238 - 2.96056i) q^{56} +(1.03458 + 1.03458i) q^{57} +(5.25018 + 2.71431i) q^{58} +(2.30403 + 2.30403i) q^{59} +(-3.71514 + 2.48952i) q^{60} +(10.8244 - 10.8244i) q^{61} +(-4.48559 - 14.0880i) q^{62} +(-0.747384 + 0.747384i) q^{63} +(-2.20081 - 7.69132i) q^{64} +(-0.0581916 + 2.22735i) q^{65} +(-1.63504 - 0.845304i) q^{66} +8.99029 q^{67} +(-0.467056 + 2.73892i) q^{68} +(4.77394 - 4.77394i) q^{69} +(2.92798 + 1.61201i) q^{70} -14.1421 q^{71} +(-1.70282 + 2.25841i) q^{72} +(-6.35840 + 6.35840i) q^{73} +(-11.0863 + 3.52984i) q^{74} +(0.261081 - 4.99318i) q^{75} +(0.491897 - 2.88459i) q^{76} +1.37565i q^{77} +(0.427532 + 1.34276i) q^{78} +8.76588 q^{79} +(8.35849 + 3.18364i) q^{80} +1.00000 q^{81} +(2.44581 + 7.68161i) q^{82} +12.3589i q^{83} +(2.08384 + 0.355348i) q^{84} +(-2.13845 - 2.25318i) q^{85} +(-7.04595 + 2.24341i) q^{86} +(-2.95516 + 2.95516i) q^{87} +(0.511314 + 3.64556i) q^{88} +18.0456 q^{89} +(-0.880380 - 3.03726i) q^{90} +(0.744724 - 0.744724i) q^{91} +(-13.3106 - 2.26980i) q^{92} +10.4545 q^{93} +(-0.0974017 - 0.0503560i) q^{94} +(2.25218 + 2.37302i) q^{95} +(5.65438 + 0.167155i) q^{96} +(1.29787 - 1.29787i) q^{97} +(2.52408 + 7.92745i) q^{98} +(0.920311 - 0.920311i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{2} + 8 q^{4} - 8 q^{5} + 2 q^{6} - 4 q^{7} + 8 q^{8} - 16 q^{9}+O(q^{10}) \) 16 * q + 2 * q^2 + 8 * q^4 - 8 * q^5 + 2 * q^6 - 4 * q^7 + 8 * q^8 - 16 * q^9	\( 16 q + 2 q^{2} + 8 q^{4} - 8 q^{5} + 2 q^{6} - 4 q^{7} + 8 q^{8} - 16 q^{9} - 2 q^{10} - 4 q^{12} - 8 q^{13} + 4 q^{14} + 4 q^{15} - 8 q^{16} - 8 q^{17} - 2 q^{18} - 8 q^{19} + 4 q^{20} - 4 q^{21} + 4 q^{24} - 32 q^{25} + 20 q^{26} + 12 q^{28} - 12 q^{29} + 2 q^{30} - 28 q^{32} + 12 q^{35} - 8 q^{36} - 24 q^{37} + 16 q^{38} + 16 q^{40} + 24 q^{42} + 24 q^{43} - 52 q^{44} + 8 q^{45} - 16 q^{46} + 32 q^{47} - 16 q^{48} + 6 q^{50} - 8 q^{51} + 24 q^{52} - 2 q^{54} - 4 q^{55} + 20 q^{56} - 8 q^{57} + 12 q^{58} + 24 q^{59} + 24 q^{60} + 40 q^{61} + 28 q^{62} + 4 q^{63} + 8 q^{64} - 4 q^{65} - 8 q^{66} + 16 q^{67} - 8 q^{68} + 12 q^{70} - 8 q^{72} - 8 q^{73} - 64 q^{74} + 24 q^{75} + 16 q^{76} + 12 q^{78} + 48 q^{79} + 16 q^{81} - 32 q^{82} - 12 q^{84} - 8 q^{85} - 8 q^{86} + 12 q^{87} + 24 q^{88} + 2 q^{90} - 40 q^{91} - 16 q^{92} - 32 q^{93} + 20 q^{94} - 8 q^{95} - 28 q^{96} + 48 q^{97} + 62 q^{98}+O(q^{100}) \) 16 * q + 2 * q^2 + 8 * q^4 - 8 * q^5 + 2 * q^6 - 4 * q^7 + 8 * q^8 - 16 * q^9 - 2 * q^10 - 4 * q^12 - 8 * q^13 + 4 * q^14 + 4 * q^15 - 8 * q^16 - 8 * q^17 - 2 * q^18 - 8 * q^19 + 4 * q^20 - 4 * q^21 + 4 * q^24 - 32 * q^25 + 20 * q^26 + 12 * q^28 - 12 * q^29 + 2 * q^30 - 28 * q^32 + 12 * q^35 - 8 * q^36 - 24 * q^37 + 16 * q^38 + 16 * q^40 + 24 * q^42 + 24 * q^43 - 52 * q^44 + 8 * q^45 - 16 * q^46 + 32 * q^47 - 16 * q^48 + 6 * q^50 - 8 * q^51 + 24 * q^52 - 2 * q^54 - 4 * q^55 + 20 * q^56 - 8 * q^57 + 12 * q^58 + 24 * q^59 + 24 * q^60 + 40 * q^61 + 28 * q^62 + 4 * q^63 + 8 * q^64 - 4 * q^65 - 8 * q^66 + 16 * q^67 - 8 * q^68 + 12 * q^70 - 8 * q^72 - 8 * q^73 - 64 * q^74 + 24 * q^75 + 16 * q^76 + 12 * q^78 + 48 * q^79 + 16 * q^81 - 32 * q^82 - 12 * q^84 - 8 * q^85 - 8 * q^86 + 12 * q^87 + 24 * q^88 + 2 * q^90 - 40 * q^91 - 16 * q^92 - 32 * q^93 + 20 * q^94 - 8 * q^95 - 28 * q^96 + 48 * q^97 + 62 * q^98

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