LMFDB - Embedded newform 56.3.k.d.51.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [56,3,Mod(11,56)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(56, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("56.11");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 56 = 2^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	56.k (of order $6$, 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:	$1.52588948042$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
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} - 3 x^{11} - 4 x^{10} + 3 x^{9} + 86 x^{8} - 163 x^{7} + 155 x^{6} - 166 x^{5} + 164 x^{4} + \cdots + 4 $ x^12 - 3x^11 - 4x^10 + 3x^9 + 86x^8 - 163x^7 + 155x^6 - 166x^5 + 164x^4 - 116x^3 + 60x^2 - 20*x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			51.1
Root			$0.121721 + 0.507075i$ of defining polynomial
Character	$\chi$	$=$	56.51
Dual form			56.3.k.d.11.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.78207 + 0.907869i) q^{2} +(1.99052 + 3.44767i) q^{3} +(2.35155 - 3.23577i) q^{4} +(1.63031 + 0.941260i) q^{5} +(-6.67727 - 4.33687i) q^{6} +(-5.14749 + 4.74377i) q^{7} +(-1.25297 + 7.90127i) q^{8} +(-3.42430 + 5.93106i) q^{9} +O(q^{10})$	\(q+(-1.78207 + 0.907869i) q^{2} +(1.99052 + 3.44767i) q^{3} +(2.35155 - 3.23577i) q^{4} +(1.63031 + 0.941260i) q^{5} +(-6.67727 - 4.33687i) q^{6} +(-5.14749 + 4.74377i) q^{7} +(-1.25297 + 7.90127i) q^{8} +(-3.42430 + 5.93106i) q^{9} +(-3.75987 - 0.197284i) q^{10} +(3.93973 + 6.82381i) q^{11} +(15.8367 + 1.66652i) q^{12} -11.4863i q^{13} +(4.86647 - 13.1270i) q^{14} +7.49437i q^{15} +(-4.94043 - 15.2182i) q^{16} +(1.44921 + 2.51011i) q^{17} +(0.717719 - 13.6784i) q^{18} +(15.0223 - 26.0194i) q^{19} +(6.87946 - 3.06189i) q^{20} +(-26.6011 - 8.30431i) q^{21} +(-13.2160 - 8.58375i) q^{22} +(33.3838 + 19.2741i) q^{23} +(-29.7351 + 11.4078i) q^{24} +(-10.7281 - 18.5815i) q^{25} +(10.4281 + 20.4695i) q^{26} +8.56478 q^{27} +(3.24519 + 27.8113i) q^{28} -27.8701i q^{29} +(-6.80390 - 13.3555i) q^{30} +(-19.4709 + 11.2416i) q^{31} +(22.6203 + 22.6346i) q^{32} +(-15.6842 + 27.1658i) q^{33} +(-4.86145 - 3.15750i) q^{34} +(-12.8571 + 2.88869i) q^{35} +(11.1392 + 25.0274i) q^{36} +(39.4520 + 22.7776i) q^{37} +(-3.14862 + 60.0068i) q^{38} +(39.6011 - 22.8637i) q^{39} +(-9.47988 + 11.7021i) q^{40} -40.6313 q^{41} +(54.9443 - 9.35146i) q^{42} -47.2806 q^{43} +(31.3448 + 3.29846i) q^{44} +(-11.1653 + 6.44632i) q^{45} +(-76.9907 - 4.03978i) q^{46} +(-71.5172 - 41.2905i) q^{47} +(42.6332 - 47.3250i) q^{48} +(3.99327 - 48.8370i) q^{49} +(35.9878 + 23.3739i) q^{50} +(-5.76936 + 9.99283i) q^{51} +(-37.1672 - 27.0107i) q^{52} +(23.2823 - 13.4420i) q^{53} +(-15.2630 + 7.77569i) q^{54} +14.8332i q^{55} +(-31.0322 - 46.6155i) q^{56} +119.609 q^{57} +(25.3024 + 49.6665i) q^{58} +(5.20555 + 9.01627i) q^{59} +(24.2501 + 17.6234i) q^{60} +(19.1932 + 11.0812i) q^{61} +(24.4927 - 37.7103i) q^{62} +(-10.5091 - 46.7742i) q^{63} +(-60.8601 - 19.8001i) q^{64} +(10.8116 - 18.7263i) q^{65} +(3.28734 - 62.6505i) q^{66} +(29.6549 + 51.3639i) q^{67} +(11.5300 + 1.21333i) q^{68} +153.462i q^{69} +(20.2897 - 16.8204i) q^{70} +38.2541i q^{71} +(-42.5724 - 34.4878i) q^{72} +(-6.98890 - 12.1051i) q^{73} +(-90.9852 - 4.77409i) q^{74} +(42.7087 - 73.9737i) q^{75} +(-48.8672 - 109.795i) q^{76} +(-52.6503 - 16.4363i) q^{77} +(-49.8147 + 76.6974i) q^{78} +(-44.3314 - 25.5948i) q^{79} +(6.26980 - 29.4605i) q^{80} +(47.8670 + 82.9081i) q^{81} +(72.4078 - 36.8879i) q^{82} -89.4458 q^{83} +(-89.4247 + 66.5472i) q^{84} +5.45635i q^{85} +(84.2573 - 42.9246i) q^{86} +(96.0871 - 55.4759i) q^{87} +(-58.8531 + 22.5788i) q^{88} +(-52.6288 + 91.1558i) q^{89} +(14.0450 - 21.6245i) q^{90} +(54.4885 + 59.1258i) q^{91} +(140.870 - 62.6982i) q^{92} +(-77.5144 - 44.7530i) q^{93} +(164.935 + 8.65431i) q^{94} +(48.9821 - 28.2798i) q^{95} +(-33.0105 + 123.042i) q^{96} +55.3301 q^{97} +(37.2213 + 90.6564i) q^{98} -53.9633 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} - 6 q^{3} - 4 q^{4} - 56 q^{6} + 8 q^{8} - 40 q^{9}+O(q^{10}) $ 12 * q + 2 * q^2 - 6 * q^3 - 4 * q^4 - 56 * q^6 + 8 * q^8 - 40 * q^9	$ 12 q + 2 q^{2} - 6 q^{3} - 4 q^{4} - 56 q^{6} + 8 q^{8} - 40 q^{9} - 6 q^{10} + 30 q^{11} + 32 q^{12} + 52 q^{14} + 16 q^{16} + 30 q^{17} - 16 q^{18} + 78 q^{19} + 48 q^{20} + 24 q^{22} - 76 q^{24} - 92 q^{25} - 128 q^{26} + 156 q^{27} - 4 q^{28} - 16 q^{30} + 112 q^{32} - 78 q^{33} + 76 q^{34} - 222 q^{35} - 248 q^{36} + 80 q^{38} + 44 q^{40} - 232 q^{41} + 132 q^{42} - 200 q^{43} + 132 q^{44} - 156 q^{46} + 176 q^{48} + 372 q^{49} + 48 q^{50} + 10 q^{51} + 132 q^{52} - 36 q^{54} - 112 q^{56} + 332 q^{57} + 4 q^{58} - 110 q^{59} + 84 q^{60} - 96 q^{62} - 160 q^{64} - 32 q^{65} - 138 q^{66} + 434 q^{67} + 96 q^{68} - 188 q^{70} - 328 q^{72} + 102 q^{73} - 34 q^{74} - 60 q^{75} - 168 q^{76} + 720 q^{78} - 256 q^{80} - 82 q^{81} - 24 q^{82} - 536 q^{83} - 624 q^{84} + 240 q^{86} - 204 q^{88} + 214 q^{89} + 440 q^{90} - 8 q^{91} + 160 q^{92} - 16 q^{94} + 48 q^{96} - 152 q^{97} + 382 q^{98} + 504 q^{99}+O(q^{100}) $ 12 * q + 2 * q^2 - 6 * q^3 - 4 * q^4 - 56 * q^6 + 8 * q^8 - 40 * q^9 - 6 * q^10 + 30 * q^11 + 32 * q^12 + 52 * q^14 + 16 * q^16 + 30 * q^17 - 16 * q^18 + 78 * q^19 + 48 * q^20 + 24 * q^22 - 76 * q^24 - 92 * q^25 - 128 * q^26 + 156 * q^27 - 4 * q^28 - 16 * q^30 + 112 * q^32 - 78 * q^33 + 76 * q^34 - 222 * q^35 - 248 * q^36 + 80 * q^38 + 44 * q^40 - 232 * q^41 + 132 * q^42 - 200 * q^43 + 132 * q^44 - 156 * q^46 + 176 * q^48 + 372 * q^49 + 48 * q^50 + 10 * q^51 + 132 * q^52 - 36 * q^54 - 112 * q^56 + 332 * q^57 + 4 * q^58 - 110 * q^59 + 84 * q^60 - 96 * q^62 - 160 * q^64 - 32 * q^65 - 138 * q^66 + 434 * q^67 + 96 * q^68 - 188 * q^70 - 328 * q^72 + 102 * q^73 - 34 * q^74 - 60 * q^75 - 168 * q^76 + 720 * q^78 - 256 * q^80 - 82 * q^81 - 24 * q^82 - 536 * q^83 - 624 * q^84 + 240 * q^86 - 204 * q^88 + 214 * q^89 + 440 * q^90 - 8 * q^91 + 160 * q^92 - 16 * q^94 + 48 * q^96 - 152 * q^97 + 382 * q^98 + 504 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/56\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$29$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−1.78207	+	0.907869i	−0.891035	+	0.453934i
$2$	−1.78207	+	0.907869i	−0.891035	+	0.453934i
$3$	1.99052	+	3.44767i	0.663505	+	1.14922i	0.979688	+	0.200526i	$0.0642652\pi$
$3$	1.99052	+	3.44767i	0.663505	+	1.14922i	−0.316183	+	0.948698i	$0.602401\pi$
$4$	2.35155	−	3.23577i	0.587887	−	0.808943i
$5$	1.63031	+	0.941260i	0.326062	+	0.188252i	0.654091	−	0.756416i	$-0.273051\pi$
$5$	1.63031	+	0.941260i	0.326062	+	0.188252i	−0.328029	+	0.944668i	$0.606384\pi$
$6$	−6.67727	−	4.33687i	−1.11288	−	0.722812i
$7$	−5.14749	+	4.74377i	−0.735355	+	0.677682i
$7$	−5.14749	+	4.74377i	−0.735355	+	0.677682i
$8$	−1.25297	+	7.90127i	−0.156621	+	0.987659i
$9$	−3.42430	+	5.93106i	−0.380478	+	0.659007i
$10$	−3.75987	−	0.197284i	−0.375987	−	0.0197284i
$11$	3.93973	+	6.82381i	0.358157	+	0.620346i	0.987653	−	0.156658i	$-0.0500719\pi$
$11$	3.93973	+	6.82381i	0.358157	+	0.620346i	−0.629496	+	0.777004i	$0.716739\pi$
$12$	15.8367	+	1.66652i	1.31972	+	0.138877i
$13$		−	11.4863i		−	0.883564i	−0.897122	−	0.441782i	$-0.854346\pi$
$13$		−	11.4863i		−	0.883564i	0.897122	−	0.441782i	$-0.145654\pi$
$14$	4.86647	−	13.1270i	0.347605	−	0.937641i
$15$			7.49437i			0.499625i
$16$	−4.94043	−	15.2182i	−0.308777	−	0.951134i
$17$	1.44921	+	2.51011i	0.0852478	+	0.147654i	0.905497	−	0.424353i	$-0.139498\pi$
$17$	1.44921	+	2.51011i	0.0852478	+	0.147654i	−0.820249	+	0.572007i	$0.806165\pi$
$18$	0.717719	−	13.6784i	0.0398733	−	0.759910i
$19$	15.0223	−	26.0194i	0.790649	−	1.36944i	−0.134916	−	0.990857i	$-0.543077\pi$
$19$	15.0223	−	26.0194i	0.790649	−	1.36944i	0.925566	−	0.378587i	$-0.123590\pi$
$20$	6.87946	−	3.06189i	0.343973	−	0.153095i
$21$	−26.6011	−	8.30431i	−1.26672	−	0.395443i
$22$	−13.2160	−	8.58375i	−0.600727	−	0.390171i
$23$	33.3838	+	19.2741i	1.45147	+	0.838006i	0.998565	−	0.0535530i	$-0.0170546\pi$
$23$	33.3838	+	19.2741i	1.45147	+	0.838006i	0.452904	+	0.891559i	$0.350388\pi$
$24$	−29.7351	+	11.4078i	−1.23896	+	0.475323i
$25$	−10.7281	−	18.5815i	−0.429122	−	0.743262i
$26$	10.4281	+	20.4695i	0.401080	+	0.787287i
$27$	8.56478			0.317214
$28$	3.24519	+	27.8113i	0.115899	+	0.993261i
$29$		−	27.8701i		−	0.961039i	−0.876984	−	0.480519i	$-0.840448\pi$
$29$		−	27.8701i		−	0.961039i	0.876984	−	0.480519i	$-0.159552\pi$
$30$	−6.80390	−	13.3555i	−0.226797	−	0.445183i
$31$	−19.4709	+	11.2416i	−0.628095	+	0.362631i	−0.780014	−	0.625762i	$-0.784788\pi$
$31$	−19.4709	+	11.2416i	−0.628095	+	0.362631i	0.151919	+	0.988393i	$0.451455\pi$
$32$	22.6203	+	22.6346i	0.706884	+	0.707330i
$33$	−15.6842	+	27.1658i	−0.475278	+	0.823206i
$34$	−4.86145	−	3.15750i	−0.142984	−	0.0928676i
$35$	−12.8571	+	2.88869i	−0.367346	+	0.0825341i
$36$	11.1392	+	25.0274i	0.309421	+	0.695207i
$37$	39.4520	+	22.7776i	1.06627	+	0.615611i	0.927160	−	0.374666i	$-0.122243\pi$
$37$	39.4520	+	22.7776i	1.06627	+	0.615611i	0.139109	+	0.990277i	$0.455576\pi$
$38$	−3.14862	+	60.0068i	−0.0828584	+	1.57913i
$39$	39.6011	−	22.8637i	1.01541	−	0.586249i
$40$	−9.47988	+	11.7021i	−0.236997	+	0.292554i
$41$	−40.6313			−0.991007			−0.495503	−	0.868606i	$-0.665016\pi$
$41$	−40.6313			−0.991007			−0.495503	+	0.868606i	$0.665016\pi$
$42$	54.9443	−	9.35146i	1.30820	−	0.222654i
$43$	−47.2806			−1.09955			−0.549774	−	0.835313i	$-0.685286\pi$
$43$	−47.2806			−1.09955			−0.549774	+	0.835313i	$0.685286\pi$
$44$	31.3448	+	3.29846i	0.712381	+	0.0749651i
$45$	−11.1653	+	6.44632i	−0.248119	+	0.143251i
$46$	−76.9907	−	4.03978i	−1.67371	−	0.0878213i
$47$	−71.5172	−	41.2905i	−1.52164	−	0.878520i	−0.999673	−	0.0255554i	$-0.991865\pi$
$47$	−71.5172	−	41.2905i	−1.52164	−	0.878520i	−0.521968	−	0.852965i	$-0.674802\pi$
$48$	42.6332	−	47.3250i	0.888192	−	0.985937i
$49$	3.99327	−	48.8370i	0.0814954	−	0.996674i
$50$	35.9878	+	23.3739i	0.719755	+	0.467479i
$51$	−5.76936	+	9.99283i	−0.113125	+	0.195938i
$52$	−37.1672	−	27.0107i	−0.714753	−	0.519436i
$53$	23.2823	−	13.4420i	0.439288	−	0.253623i	−0.264007	−	0.964521i	$-0.585044\pi$
$53$	23.2823	−	13.4420i	0.439288	−	0.253623i	0.703296	+	0.710897i	$0.251711\pi$
$54$	−15.2630	+	7.77569i	−0.282649	+	0.143994i
$55$			14.8332i			0.269695i
$56$	−31.0322	−	46.6155i	−0.554146	−	0.832420i
$57$	119.609			2.09840
$58$	25.3024	+	49.6665i	0.436249	+	0.856320i
$59$	5.20555	+	9.01627i	0.0882296	+	0.152818i	0.906763	−	0.421641i	$-0.138546\pi$
$59$	5.20555	+	9.01627i	0.0882296	+	0.152818i	−0.818533	+	0.574459i	$0.805212\pi$
$60$	24.2501	+	17.6234i	0.404168	+	0.293723i
$61$	19.1932	+	11.0812i	0.314642	+	0.181659i	0.649002	−	0.760787i	$-0.275187\pi$
$61$	19.1932	+	11.0812i	0.314642	+	0.181659i	−0.334360	+	0.942446i	$0.608520\pi$
$62$	24.4927	−	37.7103i	0.395044	−	0.608231i
$63$	−10.5091	−	46.7742i	−0.166810	−	0.742447i
$64$	−60.8601	−	19.8001i	−0.950939	−	0.309377i
$65$	10.8116	−	18.7263i	0.166333	−	0.288097i
$66$	3.28734	−	62.6505i	0.0498082	−	0.949250i
$67$	29.6549	+	51.3639i	0.442611	+	0.766625i	0.997882	−	0.0650444i	$-0.0207189\pi$
$67$	29.6549	+	51.3639i	0.442611	+	0.766625i	−0.555271	+	0.831669i	$0.687386\pi$
$68$	11.5300	+	1.21333i	0.169559	+	0.0178430i
$69$			153.462i			2.22409i
$70$	20.2897	−	16.8204i	0.289854	−	0.240292i
$71$			38.2541i			0.538791i	0.963030	+	0.269395i	$0.0868238\pi$
$71$			38.2541i			0.538791i	−0.963030	+	0.269395i	$0.913176\pi$
$72$	−42.5724	−	34.4878i	−0.591283	−	0.478997i
$73$	−6.98890	−	12.1051i	−0.0957383	−	0.165824i	0.814178	−	0.580615i	$-0.197188\pi$
$73$	−6.98890	−	12.1051i	−0.0957383	−	0.165824i	−0.909917	+	0.414791i	$0.863855\pi$
$74$	−90.9852	−	4.77409i	−1.22953	−	0.0645147i
$75$	42.7087	−	73.9737i	0.569450	−	0.986316i
$76$	−48.8672	−	109.795i	−0.642990	−	1.44467i
$77$	−52.6503	−	16.4363i	−0.683770	−	0.213459i
$78$	−49.8147	+	76.6974i	−0.638651	+	0.983300i
$79$	−44.3314	−	25.5948i	−0.561157	−	0.323984i	0.192453	−	0.981306i	$-0.438356\pi$
$79$	−44.3314	−	25.5948i	−0.561157	−	0.323984i	−0.753610	+	0.657322i	$0.771689\pi$
$80$	6.26980	−	29.4605i	0.0783725	−	0.368257i
$81$	47.8670	+	82.9081i	0.590951	+	1.02356i
$82$	72.4078	−	36.8879i	0.883022	−	0.449852i
$83$	−89.4458			−1.07766			−0.538830	−	0.842414i	$-0.681134\pi$
$83$	−89.4458			−1.07766			−0.538830	+	0.842414i	$0.681134\pi$
$84$	−89.4247	+	66.5472i	−1.06458	+	0.792228i
$85$			5.45635i			0.0641923i
$86$	84.2573	−	42.9246i	0.979737	−	0.499123i
$87$	96.0871	−	55.4759i	1.10445	−	0.637654i
$88$	−58.8531	+	22.5788i	−0.668786	+	0.256578i
$89$	−52.6288	+	91.1558i	−0.591335	+	1.02422i	0.402718	+	0.915324i	$0.368066\pi$
$89$	−52.6288	+	91.1558i	−0.591335	+	1.02422i	−0.994053	+	0.108898i	$0.965268\pi$
$90$	14.0450	−	21.6245i	0.156056	−	0.240272i
$91$	54.4885	+	59.1258i	0.598775	+	0.649734i
$92$	140.870	−	62.6982i	1.53120	−	0.681502i
$93$	−77.5144	−	44.7530i	−0.833488	−	0.481215i
$94$	164.935	+	8.65431i	1.75463	+	0.0920671i
$95$	48.9821	−	28.2798i	0.515601	−	0.297683i
$96$	−33.0105	+	123.042i	−0.343860	+	1.28168i
$97$	55.3301			0.570413			0.285206	−	0.958466i	$-0.407938\pi$
$97$	55.3301			0.570413			0.285206	+	0.958466i	$0.407938\pi$
$98$	37.2213	+	90.6564i	0.379809	+	0.925065i
$99$	−53.9633			−0.545084
$100$	−85.3532	−	8.98187i	−0.853532	−	0.0898187i
$101$	−27.2216	+	15.7164i	−0.269521	+	0.155608i	−0.628670	−	0.777672i	$-0.716400\pi$
$101$	−27.2216	+	15.7164i	−0.269521	+	0.155608i	0.359149	+	0.933280i	$0.383067\pi$
$102$	1.20923	−	23.0457i	0.0118552	−	0.225939i
$103$	−69.2701	−	39.9931i	−0.672525	−	0.388283i	0.124508	−	0.992219i	$-0.460265\pi$
$103$	−69.2701	−	39.9931i	−0.672525	−	0.388283i	−0.797033	+	0.603936i	$0.793598\pi$
$104$	90.7566	+	14.3920i	0.872660	+	0.138385i
$105$	−35.5516	−	38.5772i	−0.338586	−	0.367402i
$106$	−29.2871	+	45.0919i	−0.276293	+	0.425395i
$107$	−24.3817	+	42.2303i	−0.227866	+	0.394676i	−0.957175	−	0.289508i	$-0.906508\pi$
$107$	−24.3817	+	42.2303i	−0.227866	+	0.394676i	0.729309	+	0.684184i	$0.239842\pi$
$108$	20.1405	−	27.7137i	0.186486	−	0.256608i
$109$	99.6528	−	57.5346i	0.914246	−	0.527840i	0.0324509	−	0.999473i	$-0.489669\pi$
$109$	99.6528	−	57.5346i	0.914246	−	0.527840i	0.881795	+	0.471633i	$0.156335\pi$
$110$	−13.4666	−	26.4339i	−0.122424	−	0.240308i
$111$			181.357i			1.63384i
$112$	97.6222	+	54.8990i	0.871627	+	0.490169i
$113$	−55.7570			−0.493425			−0.246712	−	0.969089i	$-0.579350\pi$
$113$	−55.7570			−0.493425			−0.246712	+	0.969089i	$0.579350\pi$
$114$	−213.151	+	108.589i	−1.86975	+	0.952535i
$115$	36.2840	+	62.8457i	0.315513	+	0.546484i
$116$	−90.1814	−	65.5380i	−0.777426	−	0.564983i
$117$	68.1262	+	39.3327i	0.582275	+	0.336177i
$118$	−17.4622	−	11.3417i	−0.147985	−	0.0961159i
$119$	−19.3672	−	6.04603i	−0.162750	−	0.0508070i
$120$	−59.2150	−	9.39023i	−0.493459	−	0.0782519i
$121$	29.4571	−	51.0212i	0.243447	−	0.421663i
$122$	−44.2639	−	2.32257i	−0.362819	−	0.0190375i
$123$	−80.8772	−	140.083i	−0.657538	−	1.13889i
$124$	−9.41178	+	89.4386i	−0.0759015	+	0.721279i
$125$		−	87.4546i		−	0.699637i
$126$	61.1927	+	73.8140i	0.485656	+	0.585826i
$127$		−	35.6964i		−	0.281074i	−0.990075	−	0.140537i	$-0.955117\pi$
$127$		−	35.6964i		−	0.281074i	0.990075	−	0.140537i	$-0.0448828\pi$
$128$	126.433	−	19.9678i	0.987757	−	0.155998i
$129$	−94.1127	−	163.008i	−0.729556	−	1.26363i
$130$	−2.26607	+	43.1871i	−0.0174313	+	0.332208i
$131$	60.6462	−	105.042i	0.462948	−	0.801849i	−0.536158	−	0.844117i	$-0.680125\pi$
$131$	60.6462	−	105.042i	0.462948	−	0.801849i	0.999106	+	0.0422680i	$0.0134583\pi$
$132$	51.0202	+	114.632i	0.386516	+	0.868425i
$133$	46.1030	+	205.197i	0.346639	+	1.54284i
$134$	−99.4788	−	64.6112i	−0.742379	−	0.482173i
$135$	13.9632	+	8.06168i	0.103431	+	0.0597162i
$136$	−21.6489	+	8.30553i	−0.159183	+	0.0610701i
$137$	4.24835	+	7.35836i	0.0310099	+	0.0537107i	0.881114	−	0.472904i	$-0.156794\pi$
$137$	4.24835	+	7.35836i	0.0310099	+	0.0537107i	−0.850104	+	0.526615i	$0.823461\pi$
$138$	−139.323	−	273.480i	−1.00959	−	1.98174i
$139$	−3.05942			−0.0220102			−0.0110051	−	0.999939i	$-0.503503\pi$
$139$	−3.05942			−0.0220102			−0.0110051	+	0.999939i	$0.503503\pi$
$140$	−20.8870	+	48.3956i	−0.149193	+	0.345683i
$141$		−	328.757i		−	2.33161i
$142$	−34.7297	−	68.1716i	−0.244576	−	0.480081i
$143$	78.3806	−	45.2530i	0.548116	−	0.316455i
$144$	107.177	+	22.8095i	0.744287	+	0.158399i
$145$	26.2330	−	45.4370i	0.180918	−	0.313358i
$146$	23.4446	+	15.2272i	0.160579	+	0.104296i
$147$	176.323	−	83.4433i	1.19947	−	0.567642i
$148$	166.476	−	74.0949i	1.12484	−	0.500641i
$149$	−27.4740	−	15.8621i	−0.184389	−	0.106457i	0.404964	−	0.914333i	$-0.367284\pi$
$149$	−27.4740	−	15.8621i	−0.184389	−	0.106457i	−0.589353	+	0.807876i	$0.700617\pi$
$150$	−8.95157	+	170.600i	−0.0596771	+	1.13733i
$151$	−219.621	+	126.798i	−1.45444	+	0.839723i	−0.998729	−	0.0504039i	$-0.983949\pi$
$151$	−219.621	+	126.798i	−1.45444	+	0.839723i	−0.455713	+	0.890127i	$0.650616\pi$
$152$	186.764	+	151.297i	1.22871	+	0.995376i
$153$	−19.8502			−0.129740
$154$	108.749	−	18.5089i	0.706159	−	0.120188i
$155$	−42.3249			−0.273064
$156$	19.1422	−	181.905i	0.122707	−	1.16606i
$157$	42.7187	−	24.6636i	0.272093	−	0.157093i	−0.357745	−	0.933819i	$-0.616454\pi$
$157$	42.7187	−	24.6636i	0.272093	−	0.157093i	0.629839	+	0.776726i	$0.283121\pi$
$158$	102.238	+	5.36455i	0.647078	+	0.0339529i
$159$	92.6875	+	53.5132i	0.582940	+	0.336561i
$160$	15.5731	+	58.1929i	0.0973317	+	0.363706i
$161$	−263.275	+	59.1516i	−1.63525	+	0.367402i
$162$	−160.572	−	104.291i	−0.991186	−	0.643773i
$163$	−57.8597	+	100.216i	−0.354967	+	0.614821i	−0.987112	−	0.160029i	$-0.948841\pi$
$163$	−57.8597	+	100.216i	−0.354967	+	0.614821i	0.632145	+	0.774850i	$0.282175\pi$
$164$	−95.5465	+	131.474i	−0.582600	+	0.801668i
$165$	−51.1401	+	29.5258i	−0.309940	+	0.178944i
$166$	159.399	−	81.2050i	0.960233	−	0.489187i
$167$		−	32.3859i		−	0.193928i	−0.995288	−	0.0969639i	$-0.969087\pi$
$167$		−	32.3859i		−	0.193928i	0.995288	−	0.0969639i	$-0.0309131\pi$
$168$	98.9450	−	199.778i	0.588959	−	1.18915i
$169$	37.0641			0.219314
$170$	−4.95364	−	9.72359i	−0.0291391	−	0.0571976i
$171$	102.882	+	178.197i	0.601649	+	1.04209i
$172$	−111.183	+	152.989i	−0.646411	+	0.889472i
$173$	−179.479	−	103.622i	−1.03745	−	0.598973i	−0.118341	−	0.992973i	$-0.537758\pi$
$173$	−179.479	−	103.622i	−1.03745	−	0.598973i	−0.919110	+	0.394000i	$0.871091\pi$
$174$	−120.869	+	186.096i	−0.694650	+	1.06952i
$175$	143.369	+	44.7568i	0.819252	+	0.255753i
$176$	84.3818	−	93.6679i	0.479442	−	0.532204i
$177$	−20.7234	+	35.8941i	−0.117082	+	0.202791i
$178$	11.0308	−	210.226i	0.0619707	−	1.18105i
$179$	−87.0837	−	150.833i	−0.486501	−	0.842644i	0.513379	−	0.858162i	$-0.328394\pi$
$179$	−87.0837	−	150.833i	−0.486501	−	0.842644i	−0.999880	+	0.0155178i	$0.995060\pi$
$180$	−5.39706	+	51.2873i	−0.0299837	+	0.284930i
$181$		−	204.244i		−	1.12842i	−0.825632	−	0.564209i	$-0.809181\pi$
$181$		−	204.244i		−	1.12842i	0.825632	−	0.564209i	$-0.190819\pi$
$182$	−150.781	−	55.8979i	−0.828466	−	0.307131i
$183$			88.2291i			0.482126i
$184$	−194.119	+	239.624i	−1.05500	+	1.30231i
$185$	42.8793	+	74.2691i	0.231780	+	0.401455i
$186$	178.766	+	9.38003i	0.961107	+	0.0504303i
$187$	−11.4190	+	19.7783i	−0.0610642	+	0.105766i
$188$	−301.783	+	134.317i	−1.60523	+	0.714450i
$189$	−44.0871	+	40.6293i	−0.233265	+	0.214970i
$190$	−61.6152	+	94.8660i	−0.324291	+	0.499295i
$191$	258.518	+	149.255i	1.35350	+	0.781442i	0.988737	−	0.149660i	$-0.0478180\pi$
$191$	258.518	+	149.255i	1.35350	+	0.781442i	0.364759	+	0.931102i	$0.381151\pi$
$192$	−52.8786	−	249.238i	−0.275410	−	1.29812i
$193$	165.381	+	286.448i	0.856896	+	1.48419i	0.874875	+	0.484349i	$0.160943\pi$
$193$	165.381	+	286.448i	0.856896	+	1.48419i	−0.0179791	+	0.999838i	$0.505723\pi$
$194$	−98.6021	+	50.2324i	−0.508258	+	0.258930i
$195$	86.0828			0.441450
$196$	−148.635	−	127.764i	−0.758342	−	0.651857i
$197$			327.309i			1.66146i	0.556672	+	0.830732i	$0.312078\pi$
$197$			327.309i			1.66146i	−0.556672	+	0.830732i	$0.687922\pi$
$198$	96.1663	−	48.9916i	0.485689	−	0.247432i
$199$	−11.0295	+	6.36789i	−0.0554246	+	0.0319994i	−0.527456	−	0.849582i	$-0.676854\pi$
$199$	−11.0295	+	6.36789i	−0.0554246	+	0.0319994i	0.472032	+	0.881582i	$0.343521\pi$
$200$	160.260	−	61.4832i	0.801299	−	0.307416i
$201$	−118.057	+	204.481i	−0.587349	+	1.01732i
$202$	34.2424	−	52.7214i	0.169517	−	0.260997i
$203$	132.210	+	143.461i	0.651278	+	0.706705i
$204$	18.7676	+	42.1670i	0.0919979	+	0.206701i
$205$	−66.2416	−	38.2446i	−0.323130	−	0.186559i
$206$	159.753	+	8.38239i	0.775498	+	0.0406912i
$207$	−228.632	+	132.001i	−1.10450	+	0.637686i
$208$	−174.801	+	56.7475i	−0.840388	+	0.272824i
$209$	236.736			1.13271
$210$	98.3784	+	36.4711i	0.468469	+	0.173672i
$211$	120.455			0.570875			0.285437	−	0.958397i	$-0.407861\pi$
$211$	120.455			0.570875			0.285437	+	0.958397i	$0.407861\pi$
$212$	11.2541	−	106.946i	0.0530854	−	0.504461i
$213$	−131.888	+	76.1454i	−0.619191	+	0.357490i
$214$	5.11030	−	97.3927i	0.0238799	−	0.455106i
$215$	−77.0820	−	44.5033i	−0.358521	−	0.206992i
$216$	−10.7314	+	67.6726i	−0.0496825	+	0.313299i
$217$	46.8991	−	150.231i	0.216125	−	0.692311i
$218$	−125.354	+	193.002i	−0.575020	+	0.885331i
$219$	27.8230	−	48.1909i	0.127046	−	0.220050i
$220$	47.9970	+	34.8811i	0.218168	+	0.158550i
$221$	28.8320	−	16.6461i	0.130461	−	0.0753219i
$222$	−164.648	−	323.190i	−0.741657	−	1.45581i
$223$		−	372.958i		−	1.67246i	−0.548382	−	0.836228i	$-0.684756\pi$
$223$		−	372.958i		−	1.67246i	0.548382	−	0.836228i	$-0.315244\pi$
$224$	−223.811	−	9.20568i	−0.999155	−	0.0410968i
$225$	146.944			0.653086
$226$	99.3629	−	50.6200i	0.439659	−	0.223982i
$227$	−36.7128	−	63.5885i	−0.161730	−	0.280125i	0.773759	−	0.633480i	$-0.218374\pi$
$227$	−36.7128	−	63.5885i	−0.161730	−	0.280125i	−0.935489	+	0.353355i	$0.885041\pi$
$228$	281.266	−	387.026i	1.23362	−	1.69748i
$229$	367.587	+	212.226i	1.60518	+	0.926752i	0.990428	+	0.138034i	$0.0440783\pi$
$229$	367.587	+	212.226i	1.60518	+	0.926752i	0.614755	+	0.788718i	$0.289255\pi$
$230$	−121.716	−	79.0543i	−0.529201	−	0.343714i
$231$	−48.1342	−	214.238i	−0.208373	−	0.927436i
$232$	220.209	+	34.9205i	0.949179	+	0.150519i
$233$	41.7070	−	72.2386i	0.179000	−	0.310037i	−0.762538	−	0.646943i	$-0.776047\pi$
$233$	41.7070	−	72.2386i	0.179000	−	0.310037i	0.941538	+	0.336906i	$0.109380\pi$
$234$	−157.115	−	8.24396i	−0.671430	−	0.0352306i
$235$	−77.7301	−	134.632i	−0.330766	−	0.572904i
$236$	41.4157	+	4.35825i	0.175490	+	0.0184672i
$237$		−	203.787i		−	0.859861i
$238$	40.0027	−	6.80842i	0.168079	−	0.0286068i
$239$			112.561i			0.470967i	0.971878	+	0.235484i	$0.0756674\pi$
$239$			112.561i			0.470967i	−0.971878	+	0.235484i	$0.924333\pi$
$240$	114.050	−	37.0254i	0.475210	−	0.154273i
$241$	−140.216	−	242.861i	−0.581809	−	1.00772i	−0.995265	−	0.0971992i	$-0.969012\pi$
$241$	−140.216	−	242.861i	−0.581809	−	1.00772i	0.413455	−	0.910524i	$-0.364322\pi$
$242$	−6.17408	+	117.666i	−0.0255127	+	0.486225i
$243$	−152.019	+	263.304i	−0.625591	+	1.08356i
$244$	80.9899	−	36.0468i	0.331926	−	0.147733i
$245$	52.4786	−	75.8608i	0.214198	−	0.309636i
$246$	271.306	+	176.213i	1.10287	+	0.716311i
$247$	−298.868	−	172.552i	−1.20999	−	0.698589i
$248$	−64.4260	−	167.931i	−0.259782	−	0.677139i
$249$	−178.043	−	308.380i	−0.715033	−	1.23847i
$250$	79.3973	+	155.850i	0.317589	+	0.623401i
$251$	−32.9560			−0.131299			−0.0656493	−	0.997843i	$-0.520912\pi$
$251$	−32.9560			−0.131299			−0.0656493	+	0.997843i	$0.520912\pi$
$252$	−176.063	−	75.9869i	−0.698663	−	0.301535i
$253$			303.740i			1.20055i
$254$	32.4076	+	63.6134i	0.127589	+	0.250446i
$255$	−18.8117	+	10.8609i	−0.0737714	+	0.0425919i
$256$	−207.184	+	150.368i	−0.809314	+	0.587377i
$257$	112.109	−	194.179i	0.436223	−	0.755561i	−0.561172	−	0.827700i	$-0.689649\pi$
$257$	112.109	−	194.179i	0.436223	−	0.755561i	0.997395	+	0.0721390i	$0.0229825\pi$
$258$	315.705	+	205.050i	1.22366	+	0.794767i
$259$	−311.130	+	69.9036i	−1.20127	+	0.269898i
$260$	−35.1699	−	79.0197i	−0.135269	−	0.303922i
$261$	165.300	+	95.4357i	0.633332	+	0.365654i
$262$	−12.7112	+	242.252i	−0.0485160	+	0.924624i
$263$	147.190	−	84.9804i	0.559659	−	0.323119i	−0.193350	−	0.981130i	$-0.561935\pi$
$263$	147.190	−	84.9804i	0.559659	−	0.323119i	0.753009	+	0.658011i	$0.228602\pi$
$264$	−194.992	−	157.963i	−0.738608	−	0.598344i
$265$	50.6098			0.190980
$266$	−268.451	−	323.821i	−1.00921	−	1.21737i
$267$	−419.034			−1.56942
$268$	235.937	+	24.8280i	0.880361	+	0.0926420i
$269$	−93.9863	+	54.2630i	−0.349391	+	0.201721i	−0.664417	−	0.747362i	$-0.731320\pi$
$269$	−93.9863	+	54.2630i	−0.349391	+	0.201721i	0.315026	+	0.949083i	$0.397987\pi$
$270$	−32.2024	−	1.68969i	−0.119268	−	0.00625813i
$271$	−16.7690	−	9.68157i	−0.0618781	−	0.0357253i	0.468742	−	0.883335i	$-0.344707\pi$
$271$	−16.7690	−	9.68157i	−0.0618781	−	0.0357253i	−0.530620	+	0.847610i	$0.678041\pi$
$272$	31.0395	−	34.4554i	0.114116	−	0.126674i
$273$	−95.3861	+	305.549i	−0.349400	+	1.11923i
$274$	−14.2513	−	9.25617i	−0.0520120	−	0.0337817i
$275$	84.5313	−	146.412i	0.307386	−	0.532409i
$276$	496.568	+	360.873i	1.79916	+	1.30751i
$277$	−112.104	+	64.7231i	−0.404707	+	0.233658i	−0.688513	−	0.725224i	$-0.741736\pi$
$277$	−112.104	+	64.7231i	−0.404707	+	0.233658i	0.283806	+	0.958882i	$0.408403\pi$
$278$	5.45210	−	2.77755i	0.0196119	−	0.00999120i
$279$		−	153.978i		−	0.551892i
$280$	−6.71474	−	105.207i	−0.0239812	−	0.375739i
$281$	83.3608			0.296658			0.148329	−	0.988938i	$-0.452611\pi$
$281$	83.3608			0.296658			0.148329	+	0.988938i	$0.452611\pi$
$282$	298.468	+	585.868i	1.05840	+	2.07755i
$283$	−14.4646	−	25.0535i	−0.0511118	−	0.0885282i	0.839338	−	0.543611i	$-0.182943\pi$
$283$	−14.4646	−	25.0535i	−0.0511118	−	0.0885282i	−0.890449	+	0.455082i	$0.849610\pi$
$284$	123.782	+	89.9565i	0.435851	+	0.316748i
$285$	194.999	+	112.583i	0.684208	+	0.395028i
$286$	−98.5959	+	151.803i	−0.344741	+	0.530781i
$287$	209.149	−	192.746i	0.728742	−	0.671587i
$288$	−211.706	+	56.6548i	−0.735089	+	0.196718i
$289$	140.300	−	243.006i	0.485466	−	0.840851i
$290$	−5.49833	+	104.788i	−0.0189598	+	0.361338i
$291$	110.135	+	190.760i	0.378472	+	0.655533i
$292$	−55.6042	−	5.85133i	−0.190425	−	0.0200388i
$293$			214.613i			0.732468i	0.930523	+	0.366234i	$0.119353\pi$
$293$			214.613i			0.732468i	−0.930523	+	0.366234i	$0.880647\pi$
$294$	−238.464	+	308.780i	−0.811102	+	1.05027i
$295$			19.5991i			0.0664376i
$296$	−229.404	+	283.181i	−0.775014	+	0.956692i
$297$	33.7429	+	58.4444i	0.113612	+	0.196783i
$298$	63.3612	+	3.32463i	0.212622	+	0.0111565i
$299$	221.389	−	383.457i	0.740432	−	1.28247i
$300$	−138.930	−	312.148i	−0.463101	−	1.04049i
$301$	243.376	−	224.288i	0.808559	−	0.745144i
$302$	276.264	−	425.350i	0.914780	−	1.40844i
$303$	−108.370	−	62.5675i	−0.357657	−	0.206493i
$304$	−470.185	−	100.065i	−1.54666	−	0.329161i
$305$	20.8606	+	36.1316i	0.0683953	+	0.118464i
$306$	35.3744	−	18.0213i	0.115603	−	0.0588933i
$307$	−120.542			−0.392644			−0.196322	−	0.980539i	$-0.562900\pi$
$307$	−120.542			−0.392644			−0.196322	+	0.980539i	$0.562900\pi$
$308$	−176.994	+	131.714i	−0.574656	+	0.427641i
$309$		−	318.427i		−	1.03051i
$310$	75.4259	−	38.4254i	0.243309	−	0.123953i
$311$	−281.771	+	162.681i	−0.906016	+	0.523089i	−0.879147	−	0.476550i	$-0.841887\pi$
$311$	−281.771	+	162.681i	−0.906016	+	0.523089i	−0.0268689	+	0.999639i	$0.508554\pi$
$312$	131.033	+	341.547i	0.419979	+	1.09470i
$313$	−228.378	+	395.562i	−0.729642	+	1.26378i	0.227392	+	0.973803i	$0.426980\pi$
$313$	−228.378	+	395.562i	−0.729642	+	1.26378i	−0.957034	+	0.289974i	$0.906353\pi$
$314$	−53.7363	+	82.7353i	−0.171135	+	0.263488i
$315$	26.8936	−	86.1482i	0.0853767	−	0.273486i
$316$	−187.066	+	83.2590i	−0.591982	+	0.263478i
$317$	−104.980	−	60.6102i	−0.331167	−	0.191199i	0.325192	−	0.945648i	$-0.394571\pi$
$317$	−104.980	−	60.6102i	−0.331167	−	0.191199i	−0.656359	+	0.754449i	$0.727904\pi$
$318$	−213.759	−	11.2161i	−0.672197	−	0.0352709i
$319$	190.180	−	109.801i	0.596177	−	0.344203i
$320$	−80.5838	−	89.5655i	−0.251824	−	0.279892i
$321$	−194.128			−0.604761
$322$	415.472	−	344.431i	1.29029	−	1.06966i
$323$	87.0822			0.269604
$324$	380.833	+	40.0758i	1.17541	+	0.123691i
$325$	−213.434	+	123.226i	−0.656719	+	0.379157i
$326$	12.1271	−	231.121i	0.0371998	−	0.708959i
$327$	396.721	+	229.047i	1.21321	+	0.700449i
$328$	50.9098	−	321.039i	0.155213	−	0.978777i
$329$	564.006	−	126.719i	1.71430	−	0.385164i
$330$	64.3298	−	99.0455i	0.194939	−	0.300138i
$331$	−60.5842	+	104.935i	−0.183034	+	0.317024i	−0.942912	−	0.333041i	$-0.891925\pi$
$331$	−60.5842	+	104.935i	−0.183034	+	0.317024i	0.759878	+	0.650065i	$0.225258\pi$
$332$	−210.336	+	289.426i	−0.633543	+	0.871766i
$333$	−270.191	+	155.995i	−0.811384	+	0.468453i
$334$	29.4022	+	57.7140i	0.0880305	+	0.172797i
$335$			111.652i			0.333290i
$336$	5.04480	+	445.847i	0.0150143	+	1.32693i
$337$	−464.021			−1.37692			−0.688459	−	0.725275i	$-0.741713\pi$
$337$	−464.021			−1.37692			−0.688459	+	0.725275i	$0.741713\pi$
$338$	−66.0509	+	33.6494i	−0.195417	+	0.0995543i
$339$	−110.985	−	192.232i	−0.327390	−	0.567056i
$340$	17.6555	+	12.8309i	0.0519279	+	0.0377378i
$341$	−153.420	−	88.5773i	−0.449913	−	0.259758i
$342$	−345.122	−	224.156i	−1.00913	−	0.655427i
$343$	211.116	+	270.331i	0.615499	+	0.788137i
$344$	59.2412	−	373.577i	0.172213	−	1.08598i
$345$	−144.448	+	250.190i	−0.418688	+	0.725190i
$346$	413.920	+	21.7188i	1.19630	+	0.0627711i
$347$	185.593	+	321.457i	0.534851	+	0.926388i	0.999171	+	0.0407208i	$0.0129654\pi$
$347$	185.593	+	321.457i	0.534851	+	0.926388i	−0.464320	+	0.885667i	$0.653701\pi$
$348$	46.4462	−	441.370i	0.133466	−	1.26831i
$349$		−	207.871i		−	0.595619i	−0.954625	−	0.297809i	$-0.903744\pi$
$349$		−	207.871i		−	0.595619i	0.954625	−	0.297809i	$-0.0962560\pi$
$350$	−296.127	+	50.4005i	−0.846078	+	0.144002i
$351$		−	98.3779i		−	0.280279i
$352$	−65.3361	+	243.530i	−0.185614	+	0.691848i
$353$	307.007	+	531.751i	0.869708	+	1.50638i	0.862296	+	0.506405i	$0.169026\pi$
$353$	307.007	+	531.751i	0.869708	+	1.50638i	0.00741211	+	0.999973i	$0.497641\pi$
$354$	4.34355	−	82.7799i	0.0122699	−	0.233841i
$355$	−36.0071	+	62.3661i	−0.101428	+	0.175679i
$356$	171.200	+	384.652i	0.480899	+	1.08048i
$357$	−17.7060	−	78.8065i	−0.0495965	−	0.220746i
$358$	292.126	+	189.735i	0.815995	+	0.529986i
$359$	93.5930	+	54.0359i	0.260705	+	0.150518i	0.624656	−	0.780900i	$-0.285239\pi$
$359$	93.5930	+	54.0359i	0.260705	+	0.150518i	−0.363951	+	0.931418i	$0.618573\pi$
$360$	−36.9442	−	96.2975i	−0.102623	−	0.267493i
$361$	−270.841	−	469.110i	−0.750252	−	1.29947i
$362$	185.427	+	363.977i	0.512228	+	1.00546i
$363$	234.539			0.646113
$364$	319.450	−	37.2753i	0.877610	−	0.102405i
$365$		−	26.3135i		−	0.0720917i
$366$	−80.1005	−	157.231i	−0.218854	−	0.429592i
$367$	−393.881	+	227.407i	−1.07325	+	0.619639i	−0.929067	−	0.369913i	$-0.879388\pi$
$367$	−393.881	+	227.407i	−1.07325	+	0.619639i	−0.144179	+	0.989552i	$0.546054\pi$
$368$	128.386	−	603.262i	0.348876	−	1.63930i
$369$	139.134	−	240.987i	0.377056	−	0.653081i
$370$	−143.840	−	93.4240i	−0.388758	−	0.252497i
$371$	−56.0794	+	179.639i	−0.151157	+	0.484201i
$372$	−327.089	+	145.580i	−0.879272	+	0.391344i
$373$	−235.344	−	135.876i	−0.630949	−	0.364279i	0.150171	−	0.988660i	$-0.452018\pi$
$373$	−235.344	−	135.876i	−0.630949	−	0.364279i	−0.781119	+	0.624382i	$0.785351\pi$
$374$	2.39338	−	45.6133i	0.00639940	−	0.121961i
$375$	301.515	−	174.080i	0.804039	−	0.464212i
$376$	415.856	−	513.341i	1.10600	−	1.36527i
$377$	−320.126			−0.849140
$378$	41.6802	−	112.430i	0.110265	−	0.297433i
$379$	268.351			0.708051			0.354026	−	0.935236i	$-0.384813\pi$
$379$	268.351			0.708051			0.354026	+	0.935236i	$0.384813\pi$
$380$	23.6768	−	224.996i	0.0623073	−	0.592096i
$381$	123.069	−	71.0541i	0.323017	−	0.186494i
$382$	−596.201	−	31.2833i	−1.56074	−	0.0818934i
$383$	−283.718	−	163.805i	−0.740779	−	0.427689i	0.0815738	−	0.996667i	$-0.474005\pi$
$383$	−283.718	−	163.805i	−0.740779	−	0.427689i	−0.822352	+	0.568979i	$0.807339\pi$
$384$	320.509	+	396.153i	0.834659	+	1.03165i
$385$	−70.3655	−	76.3539i	−0.182767	−	0.198322i
$386$	−554.778	−	360.327i	−1.43725	−	0.933489i
$387$	161.903	−	280.424i	0.418354	−	0.724610i
$388$	130.111	−	179.035i	0.335339	−	0.461431i
$389$	109.380	−	63.1506i	0.281183	−	0.162341i	−0.352776	−	0.935708i	$-0.614762\pi$
$389$	109.380	−	63.1506i	0.281183	−	0.162341i	0.633959	+	0.773367i	$0.281429\pi$
$390$	−153.406	+	78.1519i	−0.393348	+	0.200389i
$391$			111.729i			0.285753i
$392$	380.871	+	92.7433i	0.971610	+	0.236590i
$393$	482.869			1.22867
$394$	−297.153	−	583.287i	−0.754196	−	1.48042i
$395$	−48.1826	−	83.4548i	−0.121981	−	0.211278i
$396$	−126.897	+	174.613i	−0.320448	+	0.440941i
$397$	110.110	+	63.5720i	0.277355	+	0.160131i	0.632225	−	0.774784i	$-0.282142\pi$
$397$	110.110	+	63.5720i	0.277355	+	0.160131i	−0.354870	+	0.934916i	$0.615475\pi$
$398$	13.8741	−	21.3614i	0.0348597	−	0.0536718i
$399$	−615.685	+	567.396i	−1.54307	+	1.42205i
$400$	−229.775	+	255.062i	−0.574439	+	0.637655i
$401$	−30.0751	+	52.0916i	−0.0750003	+	0.129904i	−0.901086	−	0.433640i	$-0.857229\pi$
$401$	−30.0751	+	52.0916i	−0.0750003	+	0.129904i	0.826086	+	0.563544i	$0.190562\pi$
$402$	24.7443	−	471.580i	0.0615530	−	1.17308i
$403$	129.124	+	223.650i	0.320408	+	0.554962i
$404$	−13.1583	+	125.041i	−0.0325700	+	0.309507i
$405$			180.221i			0.444991i
$406$	−365.851	−	135.629i	−0.901110	−	0.334062i
$407$			358.950i			0.881941i
$408$	−71.7272	−	58.1060i	−0.175802	−	0.142417i
$409$	34.8873	+	60.4267i	0.0852991	+	0.147742i	0.905519	−	0.424306i	$-0.139482\pi$
$409$	34.8873	+	60.4267i	0.0852991	+	0.147742i	−0.820220	+	0.572049i	$0.806149\pi$
$410$	152.768	+	8.01591i	0.372605	+	0.0195510i
$411$	−16.9128	+	29.2939i	−0.0411504	+	0.0712746i
$412$	−292.301	+	130.096i	−0.709467	+	0.315768i
$413$	−69.5666	−	21.7172i	−0.168442	−	0.0525841i
$414$	287.599	−	442.803i	0.694685	−	1.06957i
$415$	−145.824	−	84.1918i	−0.351384	−	0.202872i
$416$	259.988	−	259.824i	0.624971	−	0.624577i
$417$	−6.08982	−	10.5479i	−0.0146039	−	0.0252947i
$418$	−421.880	+	214.925i	−1.00928	+	0.514174i
$419$	714.794			1.70595			0.852976	−	0.521950i	$-0.174795\pi$
$419$	714.794			1.70595			0.852976	+	0.521950i	$0.174795\pi$
$420$	−208.428	+	24.3206i	−0.496258	+	0.0579062i
$421$		−	303.440i		−	0.720759i	−0.932806	−	0.360380i	$-0.882647\pi$
$421$		−	303.440i		−	0.720759i	0.932806	−	0.360380i	$-0.117353\pi$
$422$	−214.658	+	109.357i	−0.508669	+	0.259140i
$423$	489.793	−	282.782i	1.15790	−	0.668515i
$424$	77.0371	+	200.802i	0.181691	+	0.473590i
$425$	31.0945	−	53.8572i	0.0731635	−	0.126723i
$426$	165.903	−	255.433i	0.389444	−	0.599609i
$427$	−151.363	+	34.0078i	−0.354481	+	0.0796435i
$428$	79.3129	+	178.200i	0.185310	+	0.416356i
$429$	312.035	+	180.154i	0.727355	+	0.419939i
$430$	177.769	+	9.32771i	0.413416	+	0.0216924i
$431$	−373.685	+	215.747i	−0.867019	+	0.500574i	−0.866357	−	0.499426i	$-0.833544\pi$
$431$	−373.685	+	215.747i	−0.867019	+	0.500574i	−0.000662591		1.00000i	$0.500211\pi$
$432$	−42.3137	−	130.340i	−0.0979484	−	0.301713i
$433$	194.875			0.450057			0.225029	−	0.974352i	$-0.427752\pi$
$433$	194.875			0.450057			0.225029	+	0.974352i	$0.427752\pi$
$434$	52.8129	+	310.301i	0.121689	+	0.714980i
$435$	208.869			0.480159
$436$	48.1697	−	457.749i	0.110481	−	1.04988i
$437$	1003.00	−	579.085i	2.29521	−	1.32514i
$438$	−5.83159	+	111.139i	−0.0133141	+	0.253742i
$439$	264.977	+	152.985i	0.603593	+	0.348485i	0.770454	−	0.637496i	$-0.220030\pi$
$439$	264.977	+	152.985i	0.603593	+	0.348485i	−0.166861	+	0.985980i	$0.553363\pi$
$440$	−117.201	−	18.5856i	−0.266367	−	0.0422400i
$441$	275.981	+	190.917i	0.625808	+	0.432918i
$442$	−36.2681	+	55.8402i	−0.0820545	+	0.126335i
$443$	−125.099	+	216.677i	−0.282390	+	0.489113i	−0.971973	−	0.235093i	$-0.924460\pi$
$443$	−125.099	+	216.677i	−0.282390	+	0.489113i	0.689583	+	0.724206i	$0.257794\pi$
$444$	586.828	+	426.469i	1.32169	+	0.960516i
$445$	−171.603	+	99.0748i	−0.385624	+	0.222640i
$446$	338.597	+	664.637i	0.759185	+	1.49022i
$447$		−	126.295i		−	0.282539i
$448$	407.204	−	186.786i	0.908938	−	0.416932i
$449$	−688.681			−1.53381			−0.766905	−	0.641761i	$-0.778204\pi$
$449$	−688.681			−1.53381			−0.766905	+	0.641761i	$0.778204\pi$
$450$	−261.865	+	133.406i	−0.581923	+	0.296458i
$451$	−160.076	−	277.260i	−0.354936	−	0.614768i
$452$	−131.115	+	180.417i	−0.290078	+	0.399152i
$453$	−874.317	−	504.787i	−1.93006	−	1.11432i
$454$	123.155	+	79.9887i	0.271266	+	0.176187i
$455$	33.1805	+	147.681i	0.0729242	+	0.324574i
$456$	−149.866	+	945.061i	−0.328654	+	2.07250i
$457$	−402.259	+	696.733i	−0.880217	+	1.52458i	−0.0291166	+	0.999576i	$0.509269\pi$
$457$	−402.259	+	696.733i	−0.880217	+	1.52458i	−0.851100	+	0.525004i	$0.824064\pi$
$458$	−847.739	−	44.4817i	−1.85096	−	0.0971217i
$459$	12.4122	+	21.4985i	0.0270418	+	0.0468378i
$460$	288.678	+	30.3781i	0.627560	+	0.0660393i
$461$			693.657i			1.50468i	0.658776	+	0.752339i	$0.271074\pi$
$461$			693.657i			1.50468i	−0.658776	+	0.752339i	$0.728926\pi$
$462$	280.278	+	338.087i	0.606663	+	0.731791i
$463$		−	321.194i		−	0.693724i	−0.937916	−	0.346862i	$-0.887247\pi$
$463$		−	321.194i		−	0.693724i	0.937916	−	0.346862i	$-0.112753\pi$
$464$	−424.132	+	137.690i	−0.914077	+	0.296747i
$465$	−84.2484	−	145.922i	−0.181179	−	0.313812i
$466$	−8.74161	+	166.599i	−0.0187588	+	0.357508i
$467$	−375.937	+	651.142i	−0.805005	+	1.39431i	0.111283	+	0.993789i	$0.464504\pi$
$467$	−375.937	+	651.142i	−0.805005	+	1.39431i	−0.916288	+	0.400521i	$0.868829\pi$
$468$	287.474	−	127.948i	0.614260	−	0.273393i
$469$	−396.307	−	123.719i	−0.845004	−	0.263792i
$470$	260.749	+	169.356i	0.554785	+	0.360332i
$471$	170.064	+	98.1867i	0.361071	+	0.208464i
$472$	−77.7624	+	29.8333i	−0.164751	+	0.0632062i
$473$	−186.273	−	322.634i	−0.393811	−	0.682101i
$474$	185.012	+	363.163i	0.390320	+	0.766166i
$475$	−644.642			−1.35714
$476$	−65.1065	+	48.4503i	−0.136778	+	0.101786i
$477$			184.118i			0.385992i
$478$	−102.191	−	200.592i	−0.213788	−	0.419648i
$479$	625.392	−	361.070i	1.30562	−	0.753800i	0.324257	−	0.945969i	$-0.394886\pi$
$479$	625.392	−	361.070i	1.30562	−	0.753800i	0.981362	+	0.192169i	$0.0615523\pi$
$480$	−169.632	+	169.525i	−0.353399	+	0.353176i
$481$	261.631	−	453.158i	0.543932	−	0.942117i
$482$	470.361	+	305.498i	0.975853	+	0.633814i
$483$	−727.988	−	789.943i	−1.50722	−	1.63549i
$484$	−95.8230	−	215.295i	−0.197981	−	0.444825i
$485$	90.2052	+	52.0800i	0.185990	+	0.107381i
$486$	31.8625	−	607.239i	0.0655606	−	1.24946i
$487$	41.4211	−	23.9145i	0.0850536	−	0.0491057i	−0.456870	−	0.889533i	$-0.651030\pi$
$487$	41.4211	−	23.9145i	0.0850536	−	0.0491057i	0.541924	+	0.840428i	$0.317696\pi$
$488$	−111.604	+	137.766i	−0.228697	+	0.282308i
$489$	−460.682			−0.942090
$490$	−24.6490	+	182.833i	−0.0503040	+	0.373128i
$491$	44.4724			0.0905752			0.0452876	−	0.998974i	$-0.485580\pi$
$491$	44.4724			0.0905752			0.0452876	+	0.998974i	$0.485580\pi$
$492$	−643.465	−	67.7129i	−1.30785	−	0.137628i
$493$	69.9571	−	40.3898i	0.141901	−	0.0819265i
$494$	689.258	+	36.1661i	1.39526	+	0.0732107i
$495$	−87.9769	−	50.7935i	−0.177731	−	0.102613i
$496$	267.271	+	240.774i	0.538852	+	0.485431i
$497$	−181.469	−	196.913i	−0.365128	−	0.396203i
$498$	597.254	+	387.915i	1.19931	+	0.778945i
$499$	250.786	−	434.374i	0.502577	−	0.870489i	−0.497418	−	0.867511i	$-0.665719\pi$
$499$	250.786	−	434.374i	0.502577	−	0.870489i	0.999996	−	0.00297862i	$-0.000948124\pi$
$500$	−282.983	−	205.654i	−0.565966	−	0.411307i
$501$	111.656	−	64.4647i	0.222867	−	0.128672i
$502$	58.7298	−	29.9197i	0.116992	−	0.0596010i
$503$			462.733i			0.919946i	0.887933	+	0.459973i	$0.152141\pi$
$503$			462.733i			0.919946i	−0.887933	+	0.459973i	$0.847859\pi$
$504$	382.743	−	24.4282i	0.759411	−	0.0484686i
$505$	−59.1729			−0.117174
$506$	−275.756	−	541.285i	−0.544971	−	1.06973i
$507$	73.7767	+	127.785i	0.145516	+	0.252041i
$508$	−115.505	−	83.9417i	−0.227372	−	0.165240i
$509$	−408.751	−	235.992i	−0.803046	−	0.463639i	0.0414889	−	0.999139i	$-0.486790\pi$
$509$	−408.751	−	235.992i	−0.803046	−	0.463639i	−0.844535	+	0.535500i	$0.820123\pi$
$510$	23.6635	−	36.4335i	0.0463989	−	0.0714382i
$511$	93.3992	+	29.1573i	0.182777	+	0.0570592i
$512$	232.702	−	456.063i	0.454496	−	0.890749i
$513$	128.663	−	222.851i	0.250805	−	0.434407i
$514$	−23.4976	+	447.821i	−0.0457153	+	0.871248i
$515$	−75.2878	−	130.402i	−0.146190	−	0.253208i
$516$	−748.767	−	78.7941i	−1.45110	−	0.152702i
$517$		−	650.693i		−	1.25859i
$518$	490.993	−	407.038i	0.947862	−	0.785789i
$519$		−	825.047i		−	1.58969i
$520$	134.415	+	108.889i	0.258490	+	0.209402i
$521$	45.3709	+	78.5848i	0.0870843	+	0.150834i	0.906277	−	0.422683i	$-0.138912\pi$
$521$	45.3709	+	78.5848i	0.0870843	+	0.150834i	−0.819193	+	0.573518i	$0.805578\pi$
$522$	−381.218	−	20.0029i	−0.730304	−	0.0383198i
$523$	180.256	−	312.213i	0.344658	−	0.596965i	−0.640634	−	0.767847i	$-0.721328\pi$
$523$	180.256	−	312.213i	0.344658	−	0.596965i	0.985292	+	0.170882i	$0.0546616\pi$
$524$	−197.280	−	443.249i	−0.376489	−	0.845896i
$525$	131.072	+	583.379i	0.249660	+	1.11120i
$526$	−185.152	+	285.070i	−0.352001	+	0.541959i
$527$	−56.4351	−	32.5828i	−0.107087	−	0.0618270i
$528$	490.900	+	104.473i	0.929734	+	0.197866i
$529$	478.485	+	828.760i	0.904509	+	1.56665i
$530$	−90.1902	+	45.9470i	−0.170170	+	0.0866925i
$531$	−71.3014			−0.134278
$532$	772.385	+	333.353i	1.45185	+	0.626603i
$533$			466.705i			0.875618i
$534$	746.748	−	380.428i	1.39840	−	0.712412i
$535$	−79.4994	+	45.8990i	−0.148597	+	0.0857925i
$536$	−442.997	+	169.954i	−0.826486	+	0.317079i
$537$	346.683	−	600.472i	0.645592	−	1.11820i
$538$	118.226	−	182.028i	0.219752	−	0.338341i
$539$	348.987	−	165.155i	0.647471	−	0.306410i
$540$	58.9210	−	26.2244i	0.109113	−	0.0485637i
$541$	485.969	+	280.574i	0.898278	+	0.518621i	0.876641	−	0.481145i	$-0.159779\pi$
$541$	485.969	+	280.574i	0.898278	+	0.518621i	0.0216371	+	0.999766i	$0.493112\pi$
$542$	38.6731	+	2.02922i	0.0713525	+	0.00374394i
$543$	704.166	−	406.550i	1.29681	−	0.748712i
$544$	−24.0336	+	89.5817i	−0.0441795	+	0.164672i
$545$	216.620			0.397468
$546$	−107.414	−	631.109i	−0.196729	−	1.15588i
$547$	1043.62			1.90790			0.953952	−	0.299960i	$-0.0969733\pi$
$547$	1043.62			1.90790			0.953952	+	0.299960i	$0.0969733\pi$
$548$	33.8002	+	3.55685i	0.0616792	+	0.00649061i
$549$	−131.447	+	75.8907i	−0.239429	+	0.138234i
$550$	−17.7174	+	337.661i	−0.0322135	+	0.613928i
$551$	−725.165	−	418.674i	−1.31609	−	0.759845i
$552$	−1212.54	−	192.283i	−2.19664	−	0.348339i
$553$	349.611	−	78.5494i	0.632208	−	0.142042i
$554$	141.017	−	217.117i	0.254543	−	0.391907i
$555$	−170.704	+	295.667i	−0.307574	+	0.532734i
$556$	−7.19438	+	9.89959i	−0.0129395	+	0.0178050i
$557$	−42.1273	+	24.3222i	−0.0756324	+	0.0436664i	−0.537339	−	0.843366i	$-0.680571\pi$
$557$	−42.1273	+	24.3222i	−0.0756324	+	0.0436664i	0.461707	+	0.887033i	$0.347237\pi$
$558$	139.792	+	274.399i	0.250523	+	0.491755i
$559$			543.081i			0.971522i
$560$	107.480	+	181.390i	0.191929	+	0.323911i
$561$	−90.9189			−0.162066
$562$	−148.555	+	75.6807i	−0.264332	+	0.134663i
$563$	−363.015	−	628.761i	−0.644787	−	1.11680i	−0.984351	−	0.176221i	$-0.943613\pi$
$563$	−363.015	−	628.761i	−0.644787	−	1.11680i	0.339563	−	0.940583i	$-0.389721\pi$
$564$	−1063.78	−	773.088i	−1.88614	−	1.37072i
$565$	−90.9012	−	52.4818i	−0.160887	−	0.0928882i
$566$	48.5223	+	31.5151i	0.0857284	+	0.0556804i
$567$	−639.692	−	199.698i	−1.12820	−	0.352202i
$568$	−302.256	−	47.9313i	−0.532141	−	0.0843861i
$569$	240.696	−	416.898i	0.423016	−	0.732685i	−0.573217	−	0.819404i	$-0.694305\pi$
$569$	240.696	−	416.898i	0.423016	−	0.732685i	0.996233	+	0.0867185i	$0.0276381\pi$
$570$	−449.713	−	23.5969i	−0.788970	−	0.0413981i
$571$	−55.0633	−	95.3724i	−0.0964331	−	0.167027i	0.813773	−	0.581183i	$-0.197410\pi$
$571$	−55.0633	−	95.3724i	−0.0964331	−	0.167027i	−0.910206	+	0.414156i	$0.864077\pi$
$572$	37.8873	−	360.036i	0.0662365	−	0.629434i
$573$			1188.38i			2.07396i
$574$	−197.731	+	533.366i	−0.344479	+	0.929209i
$575$		−	827.097i		−	1.43843i
$576$	325.839	−	293.164i	0.565693	−	0.508965i
$577$	101.168	+	175.228i	0.175335	+	0.303688i	0.940277	−	0.340410i	$-0.110566\pi$
$577$	101.168	+	175.228i	0.175335	+	0.303688i	−0.764942	+	0.644099i	$0.777233\pi$
$578$	−29.4062	+	560.427i	−0.0508758	+	0.969597i
$579$	−658.386	+	1140.36i	−1.13711	+	1.96953i
$580$	−85.3353	−	191.731i	−0.147130	−	0.330571i
$581$	460.421	−	424.310i	0.792463	−	0.730310i
$582$	−369.454	−	239.959i	−0.634800	−	0.412301i
$583$	183.452	+	105.916i	0.314669	+	0.181674i
$584$	104.403	−	40.0538i	0.178772	−	0.0685853i
$585$	74.0445	+	128.249i	0.126572	+	0.219229i
$586$	−194.841	−	382.456i	−0.332492	−	0.652655i
$587$	−568.689			−0.968805			−0.484403	−	0.874845i	$-0.660963\pi$
$587$	−568.689			−0.968805			−0.484403	+	0.874845i	$0.660963\pi$
$588$	144.628	−	766.761i	0.245966	−	1.30402i
$589$			675.497i			1.14685i
$590$	−17.7934	−	34.9270i	−0.0301583	−	0.0591982i
$591$	−1128.45	+	651.513i	−1.90940	+	1.10239i
$592$	151.723	−	712.917i	0.256289	−	1.20425i
$593$	342.686	−	593.550i	0.577886	−	1.00093i	−0.417835	−	0.908523i	$-0.637211\pi$
$593$	342.686	−	593.550i	0.577886	−	1.00093i	0.995721	−	0.0924054i	$-0.0294556\pi$
$594$	−113.192	−	73.5179i	−0.190559	−	0.123768i
$595$	−25.8837	−	28.0865i	−0.0435019	−	0.0472042i
$596$	−115.932	+	51.5989i	−0.194518	+	0.0865754i
$597$	−43.9088	−	25.3507i	−0.0735491	−	0.0424636i
$598$	−46.4023	+	884.340i	−0.0775957	+	1.47883i
$599$	−318.077	+	183.642i	−0.531013	+	0.306580i	−0.741429	−	0.671032i	$-0.765851\pi$
$599$	−318.077	+	183.642i	−0.531013	+	0.306580i	0.210416	+	0.977612i	$0.432518\pi$
$600$	530.973	+	430.140i	0.884955	+	0.716900i
$601$	412.344			0.686097			0.343049	−	0.939318i	$-0.388540\pi$
$601$	412.344			0.686097			0.343049	+	0.939318i	$0.388540\pi$
$602$	−230.089	+	620.651i	−0.382208	+	1.03098i
$603$	−406.190			−0.673615
$604$	−106.159	+	1008.81i	−0.175761	+	1.67022i
$605$	96.0484	−	55.4535i	0.158758	−	0.0916588i
$606$	249.926	+	13.1139i	0.412420	+	0.0216401i
$607$	1010.46	+	583.389i	1.66468	+	0.961102i	0.970436	+	0.241359i	$0.0775930\pi$
$607$	1010.46	+	583.389i	1.66468	+	0.961102i	0.694241	+	0.719743i	$0.255740\pi$
$608$	928.748	−	248.543i	1.52755	−	0.408788i
$609$	−231.442	+	741.377i	−0.380036	+	1.21737i
$610$	−69.9777	−	45.4503i	−0.114718	−	0.0745087i
$611$	−474.276	+	821.470i	−0.776229	+	1.34447i
$612$	−46.6787	+	64.2306i	−0.0762723	+	0.104952i
$613$	373.900	−	215.871i	0.609951	−	0.352155i	−0.162995	−	0.986627i	$-0.552115\pi$
$613$	373.900	−	215.871i	0.609951	−	0.352155i	0.772946	+	0.634471i	$0.218782\pi$
$614$	214.814	−	109.436i	0.349860	−	0.178235i
$615$		−	304.506i		−	0.495131i
$616$	195.837	−	395.410i	0.317917	−	0.641899i
$617$	−333.751			−0.540926			−0.270463	−	0.962730i	$-0.587177\pi$
$617$	−333.751			−0.540926			−0.270463	+	0.962730i	$0.587177\pi$
$618$	289.090	+	567.460i	0.467784	+	0.918220i
$619$	488.158	+	845.514i	0.788624	+	1.36594i	0.926810	+	0.375530i	$0.122539\pi$
$619$	488.158	+	845.514i	0.788624	+	1.36594i	−0.138187	+	0.990406i	$0.544127\pi$
$620$	−99.5291	+	136.954i	−0.160531	+	0.220893i
$621$	285.925	+	165.079i	0.460426	+	0.265827i
$622$	354.443	−	545.719i	0.569844	−	0.877362i
$623$	−161.516	−	718.883i	−0.259255	−	1.15390i
$624$	−543.590	−	489.699i	−0.871138	−	0.784775i
$625$	−185.884	+	321.961i	−0.297414	+	0.515137i
$626$	47.8671	−	912.257i	0.0764650	−	1.45728i
$627$	471.226	+	816.187i	0.751556	+	1.30173i
$628$	20.6492	−	196.226i	0.0328808	−	0.312461i
$629$			132.038i			0.209918i
$630$	30.2849	+	177.938i	0.0480712	+	0.282441i
$631$		−	639.885i		−	1.01408i	−0.861922	−	0.507040i	$-0.830739\pi$
$631$		−	639.885i		−	1.01408i	0.861922	−	0.507040i	$-0.169261\pi$
$632$	257.777	−	318.205i	0.407875	−	0.503489i
$633$	239.767	+	415.288i	0.378778	+	0.656063i
$634$	242.108	+	12.7036i	0.381873	+	0.0200373i
$635$	33.5995	−	58.1961i	0.0529127	−	0.0916474i
$636$	391.116	−	174.077i	0.614962	−	0.273706i
$637$	−560.958	−	45.8681i	−0.880625	−	0.0720064i
$638$	−239.230	+	368.332i	−0.374969	+	0.577322i
$639$	−226.888	−	130.994i	−0.355067	−	0.204998i
$640$	224.920	+	86.4526i	0.351437	+	0.135082i
$641$	−10.4295	−	18.0645i	−0.0162707	−	0.0281817i	0.857775	−	0.514025i	$-0.171846\pi$
$641$	−10.4295	−	18.0645i	−0.0162707	−	0.0281817i	−0.874046	+	0.485843i	$0.838513\pi$
$642$	345.950	−	176.243i	0.538864	−	0.274522i
$643$	−69.1348			−0.107519			−0.0537596	−	0.998554i	$-0.517120\pi$
$643$	−69.1348			−0.107519			−0.0537596	+	0.998554i	$0.517120\pi$
$644$	−427.702	+	990.995i	−0.664134	+	1.53881i
$645$		−	354.338i		−	0.549362i
$646$	−155.187	+	79.0592i	−0.240227	+	0.122383i
$647$	−310.868	+	179.480i	−0.480476	+	0.277403i	−0.720615	−	0.693336i	$-0.756140\pi$
$647$	−310.868	+	179.480i	−0.480476	+	0.277403i	0.240139	+	0.970739i	$0.422807\pi$
$648$	−715.056	+	274.329i	−1.10348	+	0.423347i
$649$	−41.0169	+	71.0433i	−0.0632001	+	0.109466i
$650$	268.481	−	413.367i	0.413048	−	0.635950i
$651$	611.302	−	137.345i	0.939021	−	0.210976i
$652$	188.216	+	422.883i	0.288675	+	0.648594i
$653$	−32.1227	−	18.5460i	−0.0491925	−	0.0284013i	0.475202	−	0.879877i	$-0.342375\pi$
$653$	−32.1227	−	18.5460i	−0.0491925	−	0.0284013i	−0.524395	+	0.851475i	$0.675708\pi$
$654$	−914.929	−	48.0073i	−1.39897	−	0.0734056i
$655$	197.744	−	114.168i	0.301900	−	0.174302i
$656$	200.736	+	618.333i	0.306000	+	0.942581i
$657$	95.7284			0.145705
$658$	−890.055	+	737.866i	−1.35267	+	1.12138i
$659$	197.302			0.299396			0.149698	−	0.988732i	$-0.452170\pi$
$659$	197.302			0.299396			0.149698	+	0.988732i	$0.452170\pi$
$660$	−24.7199	+	234.909i	−0.0374544	+	0.355923i
$661$	−938.626	+	541.916i	−1.42001	+	0.819843i	−0.996299	−	0.0859554i	$-0.972606\pi$
$661$	−938.626	+	541.916i	−1.42001	+	0.819843i	−0.423710	+	0.905798i	$0.639272\pi$
$662$	12.6982	−	242.004i	0.0191816	−	0.365565i
$663$	114.781	+	66.2688i	0.173124	+	0.0999530i
$664$	112.073	−	706.735i	0.168785	−	1.06436i
$665$	−117.982	+	377.930i	−0.177416	+	0.568316i
$666$	339.876	−	523.291i	0.510325	−	0.785723i
$667$	537.173	−	930.411i	0.805357	−	1.39492i
$668$	−104.794	−	76.1571i	−0.156877	−	0.114008i
$669$	1285.84	−	742.378i	1.92203	−	1.10968i
$670$	−101.365	−	198.972i	−0.151292	−	0.296973i
$671$			174.628i			0.260250i
$672$	−413.761	−	789.950i	−0.615715	−	1.17552i
$673$	−286.066			−0.425061			−0.212530	−	0.977154i	$-0.568170\pi$
$673$	−286.066			−0.425061			−0.212530	+	0.977154i	$0.568170\pi$
$674$	826.919	−	421.270i	1.22688	−	0.625030i
$675$	−91.8834	−	159.147i	−0.136124	−	0.235773i
$676$	87.1581	−	119.931i	0.128932	−	0.177413i
$677$	−433.324	−	250.180i	−0.640065	−	0.369542i	0.144575	−	0.989494i	$-0.453819\pi$
$677$	−433.324	−	250.180i	−0.640065	−	0.369542i	−0.784640	+	0.619952i	$0.787152\pi$
$678$	372.305	+	241.811i	0.549122	+	0.356653i
$679$	−284.811	+	262.473i	−0.419456	+	0.386558i
$680$	−43.1121	−	6.83664i	−0.0634001	−	0.0100539i
$681$	146.155	−	253.148i	0.214618	−	0.371729i
$682$	353.823	+	18.5654i	0.518801	+	0.0272221i
$683$	−473.225	−	819.650i	−0.692862	−	1.20007i	−0.970896	−	0.239501i	$-0.923016\pi$
$683$	−473.225	−	819.650i	−0.692862	−	1.20007i	0.278034	−	0.960571i	$-0.410317\pi$
$684$	818.536	+	86.1360i	1.19669	+	0.125930i
$685$			15.9952i			0.0233507i
$686$	−621.649	−	290.083i	−0.906194	−	0.422862i
$687$			1689.76i			2.45962i
$688$	233.587	+	719.523i	0.339515	+	1.04582i
$689$	−154.400	−	267.428i	−0.224092	−	0.388140i
$690$	30.2756	−	576.996i	0.0438777	−	0.836227i
$691$	−151.632	+	262.634i	−0.219439	+	0.380079i	−0.954636	−	0.297774i	$-0.903756\pi$
$691$	−151.632	+	262.634i	−0.219439	+	0.380079i	0.735198	+	0.677853i	$0.237089\pi$
$692$	−757.352	+	337.080i	−1.09444	+	0.487111i
$693$	277.775	−	255.989i	0.400830	−	0.369393i
$694$	−622.580	−	404.364i	−0.897090	−	0.582658i
$695$	−4.98781	−	2.87971i	−0.00717670	−	0.00414347i
$696$	317.936	+	828.720i	0.456804	+	1.19069i
$697$	−58.8834	−	101.989i	−0.0844812	−	0.146326i
$698$	188.720	+	370.441i	0.270372	+	0.530717i
$699$	332.074			0.475069
$700$	481.962	−	358.662i	0.688518	−	0.512374i
$701$			390.864i			0.557580i	0.960352	+	0.278790i	$0.0899333\pi$
$701$			390.864i			0.557580i	−0.960352	+	0.278790i	$0.910067\pi$
$702$	89.3142	+	175.316i	0.127228	+	0.249738i
$703$	1185.32	−	684.345i	1.68609	−	0.973464i
$704$	−104.660	−	493.305i	−0.148665	−	0.700717i
$705$	309.446	−	535.976i	0.438930	−	0.760250i
$706$	−1029.87	−	668.897i	−1.45874	−	0.947446i
$707$	65.5679	−	210.033i	0.0927411	−	0.297077i
$708$	67.4128	+	151.463i	0.0952158	+	0.213931i
$709$	−832.393	−	480.582i	−1.17404	−	0.677831i	−0.219410	−	0.975633i	$-0.570413\pi$
$709$	−832.393	−	480.582i	−1.17404	−	0.677831i	−0.954628	+	0.297801i	$0.903747\pi$
$710$	7.54693	−	143.830i	0.0106295	−	0.202578i
$711$	303.608	−	175.288i	0.427016	−	0.246538i
$712$	−654.304	−	530.050i	−0.918967	−	0.744453i
$713$	−866.685			−1.21555
$714$	103.099	+	124.364i	0.144397	+	0.174179i
$715$	170.379			0.238293
$716$	−692.844	−	72.9092i	−0.967659	−	0.101828i
$717$	−388.074	+	224.055i	−0.541247	+	0.312489i
$718$	−215.847	−	11.3257i	−0.300622	−	0.0157740i
$719$	454.773	+	262.563i	0.632507	+	0.365178i	0.781722	−	0.623627i	$-0.214341\pi$
$719$	454.773	+	262.563i	0.632507	+	0.365178i	−0.149215	+	0.988805i	$0.547675\pi$
$720$	153.263	+	138.068i	0.212865	+	0.191762i
$721$	546.285	−	122.737i	0.757677	−	0.170232i
$722$	908.548	+	590.100i	1.25838	+	0.817312i
$723$	558.204	−	966.838i	0.772067	−	1.33726i
$724$	−660.886	−	480.289i	−0.912826	−	0.663383i
$725$	−517.870	+	298.992i	−0.714304	+	0.412403i
$726$	−417.965	+	212.931i	−0.575710	+	0.293293i
$727$			108.633i			0.149426i	0.997205	+	0.0747131i	$0.0238041\pi$
$727$			108.633i			0.149426i	−0.997205	+	0.0747131i	$0.976196\pi$
$728$	−535.441	+	356.446i	−0.735496	+	0.489623i
$729$	−348.775			−0.478429
$730$	23.8892	+	46.8925i	0.0327249	+	0.0642363i
$731$	−68.5197	−	118.680i	−0.0937341	−	0.162352i
$732$	285.489	+	207.475i	0.390013	+	0.283436i
$733$	−34.8609	−	20.1270i	−0.0475593	−	0.0274584i	0.476032	−	0.879428i	$-0.342075\pi$
$733$	−34.8609	−	20.1270i	−0.0475593	−	0.0274584i	−0.523591	+	0.851970i	$0.675408\pi$
$734$	495.468	−	762.849i	0.675025	−	1.03930i
$735$	366.003	+	29.9271i	0.497963	+	0.0407171i
$736$	318.889	+	1191.61i	0.433273	+	1.61904i
$737$	−233.665	+	404.719i	−0.317049	+	0.549144i
$738$	−29.1619	+	555.770i	−0.0395147	+	0.753077i
$739$	−498.602	−	863.603i	−0.674698	−	1.16861i	−0.976557	−	0.215258i	$-0.930941\pi$
$739$	−498.602	−	863.603i	−0.674698	−	1.16861i	0.301859	−	0.953352i	$-0.402393\pi$
$740$	341.151	+	35.8999i	0.461014	+	0.0485134i
$741$		−	1373.87i		−	1.85407i
$742$	−63.1508	−	371.041i	−0.0851089	−	0.500056i
$743$			476.575i			0.641420i	0.947177	+	0.320710i	$0.103922\pi$
$743$			476.575i			0.641420i	−0.947177	+	0.320710i	$0.896078\pi$
$744$	450.729	−	556.388i	0.605818	−	0.747833i
$745$	−29.8607	−	51.7203i	−0.0400815	−	0.0694232i
$746$	542.757	+	28.4790i	0.727556	+	0.0381756i
$747$	306.289	−	530.509i	0.410026	−	0.710186i
$748$	37.1457	+	83.4590i	0.0496600	+	0.111576i
$749$	−74.8265	−	333.041i	−0.0999018	−	0.444648i
$750$	−379.279	+	583.958i	−0.505706	+	0.778611i
$751$	457.691	+	264.248i	0.609442	+	0.351862i	0.772747	−	0.634714i	$-0.218882\pi$
$751$	457.691	+	264.248i	0.609442	+	0.351862i	−0.163305	+	0.986576i	$0.552215\pi$
$752$	−275.039	+	1292.35i	−0.365743	+	1.71855i
$753$	−65.5993	−	113.621i	−0.0871173	−	0.150892i
$754$	570.486	−	290.632i	0.756613	−	0.385454i
$755$	−477.400			−0.632318
$756$	27.7943	+	238.198i	0.0367649	+	0.315076i
$757$		−	455.964i		−	0.602331i	−0.953572	−	0.301165i	$-0.902624\pi$
$757$		−	455.964i		−	0.602331i	0.953572	−	0.301165i	$-0.0973756\pi$
$758$	−478.221	+	243.628i	−0.630898	+	0.321409i
$759$	−1047.19	+	604.598i	−1.37970	+	0.796572i
$760$	162.073	+	422.455i	0.213255	+	0.555862i
$761$	−238.325	+	412.791i	−0.313174	+	0.542433i	−0.979048	−	0.203632i	$-0.934726\pi$
$761$	−238.325	+	412.791i	−0.313174	+	0.542433i	0.665874	+	0.746064i	$0.268059\pi$
$762$	−154.810	+	238.354i	−0.203163	+	0.312801i
$763$	−240.031	+	768.888i	−0.314588	+	1.00772i
$764$	1090.87	−	485.523i	1.42784	−	0.635502i
$765$	−32.3619	−	18.6842i	−0.0423032	−	0.0244238i
$766$	654.319	+	34.3328i	0.854202	+	0.0448209i
$767$	103.564	−	59.7927i	0.135025	−	0.0779565i
$768$	−930.825	−	414.993i	−1.21201	−	0.540355i
$769$	−568.246			−0.738941			−0.369471	−	0.929242i	$-0.620461\pi$
$769$	−568.246			−0.738941			−0.369471	+	0.929242i	$0.620461\pi$
$770$	194.716	+	72.1854i	0.252877	+	0.0937473i
$771$	892.621			1.15774
$772$	1315.78	+	138.462i	1.70438	+	0.179355i
$773$	1036.66	−	598.515i	1.34108	−	0.774275i	0.354118	−	0.935201i	$-0.384781\pi$
$773$	1036.66	−	598.515i	1.34108	−	0.774275i	0.986967	+	0.160925i	$0.0514478\pi$
$774$	−33.9342	+	646.722i	−0.0438426	+	0.835559i
$775$	417.771	+	241.200i	0.539059	+	0.311226i
$776$	−69.3270	+	437.178i	−0.0893389	+	0.563373i
$777$	−860.314	−	933.531i	−1.10723	−	1.20146i
$778$	−137.590	+	211.842i	−0.176852	+	0.272290i
$779$	−610.377	+	1057.20i	−0.783539	+	1.35713i
$780$	202.428	−	278.544i	0.259523	−	0.357108i
$781$	−261.039	+	150.711i	−0.334237	+	0.192972i
$782$	−101.436	−	199.110i	−0.129713	−	0.254616i
$783$		−	238.701i		−	0.304855i
$784$	−762.938	+	180.506i	−0.973135	+	0.230237i
$785$	92.8596			0.118292
$786$	−860.506	+	438.381i	−1.09479	+	0.557737i
$787$	−226.134	−	391.676i	−0.287337	−	0.497682i	0.685836	−	0.727756i	$-0.259437\pi$
$787$	−226.134	−	391.676i	−0.287337	−	0.497682i	−0.973173	+	0.230074i	$0.926103\pi$
$788$	1059.10	+	769.682i	1.34403	+	0.976754i
$789$	585.969	+	338.309i	0.742673	+	0.428783i
$790$	161.631	+	104.979i	0.204596	+	0.132885i
$791$	287.008	−	264.498i	0.362843	−	0.334385i
$792$	67.6144	−	426.378i	0.0853717	−	0.538356i
$793$	127.282	−	220.459i	0.160507	−	0.278007i
$794$	−253.939	−	13.3244i	−0.319822	−	0.0167814i
$795$	100.740	+	174.486i	0.126716	+	0.219479i
$796$	−5.33139	+	50.6633i	−0.00669773	+	0.0636474i
$797$		−	1047.47i		−	1.31426i	−0.753777	−	0.657130i	$-0.771770\pi$
$797$		−	1047.47i		−	1.31426i	0.753777	−	0.657130i	$-0.228230\pi$
$798$	582.072	−	1570.10i	0.729413	−	1.96754i
$799$		−	239.355i		−	0.299568i
$800$	177.913	−	663.145i	0.222392	−	0.828931i
$801$	−360.434	−	624.290i	−0.449980	−	0.779388i
$802$	6.30362	−	120.135i	0.00785987	−	0.149794i
$803$	55.0687	−	95.3818i	0.0685787	−	0.118782i
$804$	384.037	+	862.854i	0.477658	+	1.07320i
$805$	−484.897	−	151.375i	−0.602356	−	0.188043i
$806$	−433.153	−	281.332i	−0.537411	−	0.349047i
$807$	−374.162	−	216.023i	−0.463646	−	0.267686i
$808$	−90.0717	−	234.778i	−0.111475	−	0.290566i
$809$	149.332	+	258.651i	0.184589	+	0.319717i	0.943438	−	0.331549i	$-0.107571\pi$
$809$	149.332	+	258.651i	0.184589	+	0.319717i	−0.758849	+	0.651267i	$0.774238\pi$
$810$	−163.617	−	321.167i	−0.201997	−	0.396502i
$811$	633.054			0.780584			0.390292	−	0.920691i	$-0.372374\pi$
$811$	633.054			0.780584			0.390292	+	0.920691i	$0.372374\pi$
$812$	775.105	−	90.4437i	0.954562	−	0.111384i
$813$		−	77.0852i		−	0.0948158i
$814$	−325.880	−	639.674i	−0.400343	−	0.785841i
$815$	−188.658	+	108.922i	−0.231483	+	0.133647i
$816$	180.575	+	38.4301i	0.221293	+	0.0470957i
$817$	−710.265	+	1230.21i	−0.869357	+	1.50577i
$818$	−117.031	−	76.0114i	−0.143070	−	0.0929235i
$819$	−537.264	+	120.711i	−0.656000	+	0.147388i
$820$	−279.521	+	124.409i	−0.340879	+	0.151718i
$821$	1083.83	+	625.749i	1.32013	+	0.762178i	0.983749	−	0.179547i	$-0.0574632\pi$
$821$	1083.83	+	625.749i	1.32013	+	0.762178i	0.336382	+	0.941725i	$0.390797\pi$
$822$	3.54486	−	67.5583i	0.00431248	−	0.0821878i
$823$	−1062.45	+	613.409i	−1.29095	+	0.745332i	−0.978823	−	0.204707i	$-0.934376\pi$
$823$	−1062.45	+	613.409i	−1.29095	+	0.745332i	−0.312130	+	0.950039i	$0.601043\pi$
$824$	402.790	−	497.211i	0.488822	−	0.603412i
$825$	673.043			0.815810
$826$	143.689	−	24.4557i	0.173958	−	0.0296074i
$827$	−1438.26			−1.73913			−0.869566	−	0.493816i	$-0.835602\pi$
$827$	−1438.26			−1.73913			−0.869566	+	0.493816i	$0.835602\pi$
$828$	−110.515	+	1050.21i	−0.133473	+	1.26837i
$829$	−542.554	+	313.244i	−0.654468	+	0.377858i	−0.790166	−	0.612893i	$-0.790006\pi$
$829$	−542.554	+	313.244i	−0.654468	+	0.377858i	0.135698	+	0.990750i	$0.456672\pi$
$830$	336.304	+	17.6462i	0.405186	+	0.0212605i
$831$	−446.289	−	257.665i	−0.537050	−	0.310066i
$832$	−227.431	+	699.060i	−0.273354	+	0.840216i
$833$	128.373	−	60.7517i	0.154110	−	0.0729312i
$834$	20.4286	+	13.2683i	0.0244947	+	0.0159092i
$835$	30.4836	−	52.7991i	0.0365073	−	0.0632325i
$836$	556.696	−	766.022i	0.665904	−	0.916295i
$837$	−166.764	+	96.2814i	−0.199240	+	0.115032i
$838$	−1273.81	+	648.939i	−1.52006	+	0.774390i
$839$		−	1062.37i		−	1.26624i	−0.774055	−	0.633118i	$-0.781775\pi$
$839$		−	1062.37i		−	1.26624i	0.774055	−	0.633118i	$-0.218225\pi$
$840$	349.354	−	232.566i	0.415897	−	0.276865i
$841$	64.2558			0.0764041
$842$	275.483	+	540.751i	0.327177	+	0.642222i
$843$	165.931	+	287.401i	0.196834	+	0.340926i
$844$	283.255	−	389.763i	0.335610	−	0.461805i
$845$	60.4260	+	34.8870i	0.0715101	+	0.0412864i
$846$	−616.116	+	948.605i	−0.728270	+	1.12128i
$847$	90.4027	+	402.368i	0.106733	+	0.475051i
$848$	−319.588	−	287.904i	−0.376872	−	0.339509i
$849$	57.5842	−	99.7387i	0.0678259	−	0.117478i
$850$	−6.51727	+	124.207i	−0.00766738	+	0.146126i
$851$	878.037	+	1520.80i	1.03177	+	1.78708i
$852$	−63.7514	+	605.818i	−0.0748255	+	0.711054i
$853$			698.388i			0.818743i	0.912368	+	0.409372i	$0.134252\pi$
$853$			698.388i			0.818743i	−0.912368	+	0.409372i	$0.865748\pi$
$854$	238.866	−	198.022i	0.279702	−	0.231876i
$855$			387.355i			0.453047i
$856$	−303.123	−	245.560i	−0.354116	−	0.286869i
$857$	365.162	+	632.479i	0.426094	+	0.738016i	0.996522	−	0.0833317i	$-0.0265561\pi$
$857$	365.162	+	632.479i	0.426094	+	0.738016i	−0.570428	+	0.821347i	$0.693223\pi$
$858$	−719.625	−	37.7595i	−0.838724	−	0.0440087i
$859$	483.130	−	836.805i	0.562433	−	0.974162i	−0.434851	−	0.900502i	$-0.643199\pi$
$859$	483.130	−	836.805i	0.562433	−	0.974162i	0.997283	−	0.0736593i	$-0.0234677\pi$
$860$	−325.265	+	144.768i	−0.378215	+	0.168335i
$861$	1080.84	+	337.415i	1.25533	+	0.391887i
$862$	470.063	−	723.734i	0.545317	−	0.839598i
$863$	255.023	+	147.237i	0.295507	+	0.170611i	0.640423	−	0.768023i	$-0.278759\pi$
$863$	255.023	+	147.237i	0.295507	+	0.170611i	−0.344916	+	0.938634i	$0.612093\pi$
$864$	193.738	+	193.860i	0.224233	+	0.224375i
$865$	−195.071	−	337.873i	−0.225516	−	0.390605i
$866$	−347.281	+	176.921i	−0.401017	+	0.204296i
$867$	1117.07			1.28844
$868$	−375.829	−	505.031i	−0.432983	−	0.581833i
$869$		−	403.346i		−	0.464149i
$870$	−372.219	+	189.626i	−0.427838	+	0.217961i
$871$	589.983	−	340.627i	0.677362	−	0.391075i
$872$	329.734	+	859.473i	0.378135	+	0.985634i
$873$	−189.467	+	328.166i	−0.217030	+	0.375906i
$874$	−1261.69	+	1942.57i	−1.44358	+	2.22262i
$875$	414.864	+	450.171i	0.474131	+	0.514482i
$876$	−90.5075	−	203.352i	−0.103319	−	0.232137i
$877$	818.300	+	472.446i	0.933067	+	0.538706i	0.887780	−	0.460268i	$-0.152247\pi$
$877$	818.300	+	472.446i	0.933067	+	0.538706i	0.0452867	+	0.998974i	$0.485580\pi$
$878$	−611.098	−	32.0650i	−0.696012	−	0.0365205i
$879$	−739.916	+	427.191i	−0.841770	+	0.485996i
$880$	225.734	−	73.2826i	0.256516	−	0.0832757i
$881$	744.098			0.844606			0.422303	−	0.906455i	$-0.361222\pi$
$881$	744.098			0.844606			0.422303	+	0.906455i	$0.361222\pi$
$882$	−665.146	−	89.6728i	−0.754133	−	0.101670i
$883$	23.9032			0.0270704			0.0135352	−	0.999908i	$-0.495691\pi$
$883$	23.9032			0.0270704			0.0135352	+	0.999908i	$0.495691\pi$
$884$	13.9367	−	132.438i	0.0157655	−	0.149817i
$885$	−67.5713	+	39.0123i	−0.0763517	+	0.0440817i
$886$	26.2201	−	499.707i	0.0295938	−	0.564003i
$887$	−820.397	−	473.656i	−0.924912	−	0.533998i	−0.0397129	−	0.999211i	$-0.512644\pi$
$887$	−820.397	−	473.656i	−0.924912	−	0.533998i	−0.885199	+	0.465213i	$0.845978\pi$
$888$	−1432.95	−	227.235i	−1.61368	−	0.255895i
$889$	169.335	+	183.747i	0.190478	+	0.206689i
$890$	215.861	−	332.351i	0.242541	−	0.373428i
$891$	−377.166	+	653.271i	−0.423307	+	0.733189i
$892$	−1206.81	−	877.029i	−1.35292	−	0.983216i
$893$	−2148.71	+	1240.56i	−2.40617	+	1.38920i
$894$	114.659	+	225.067i	0.128254	+	0.251752i
$895$		−	327.874i		−	0.366339i
$896$	−556.089	+	702.553i	−0.620636	+	0.784099i
$897$	1762.71			1.96512
$898$	1227.28	−	625.232i	1.36668	−	0.696249i
$899$	313.304	+	542.658i	0.348502	+	0.603624i
$900$	345.547	−	475.479i	0.383941	−	0.528310i
$901$	67.4820	+	38.9607i	0.0748968	+	0.0432417i
$902$	536.983	+	348.769i	0.595325	+	0.386662i
$903$	1257.72	+	392.633i	1.39282	+	0.434809i
$904$	69.8619	−	440.551i	0.0772809	−	0.487335i
$905$	192.247	−	332.981i	0.212427	−	0.367935i
$906$	2016.37	+	105.801i	2.22558	+	0.116778i
$907$	−275.512	−	477.200i	−0.303761	−	0.526130i	0.673223	−	0.739439i	$-0.264909\pi$
$907$	−275.512	−	477.200i	−0.303761	−	0.526130i	−0.976985	+	0.213309i	$0.931576\pi$
$908$	−292.090	−	30.7371i	−0.321685	−	0.0338515i
$909$		−	215.271i		−	0.236822i
$910$	−193.205	−	233.055i	−0.212313	−	0.256104i
$911$			827.652i			0.908509i	0.890872	+	0.454254i	$0.150094\pi$
$911$			827.652i			0.908509i	−0.890872	+	0.454254i	$0.849906\pi$
$912$	−590.919	−	1820.22i	−0.647937	−	1.99586i
$913$	−352.392	−	610.361i	−0.385972	−	0.668523i
$914$	84.3118	−	1606.83i	0.0922448	−	1.75801i
$915$	−83.0466	+	143.841i	−0.0907613	+	0.157203i
$916$	1551.11	−	690.366i	1.69336	−	0.753675i
$917$	186.121	+	828.396i	0.202967	+	0.903376i
$918$	−41.6372	−	27.0433i	−0.0453565	−	0.0294589i
$919$	309.165	+	178.497i	0.336415	+	0.194229i	0.658685	−	0.752418i	$-0.271113\pi$
$919$	309.165	+	178.497i	0.336415	+	0.194229i	−0.322271	+	0.946648i	$0.604446\pi$
$920$	−542.023	+	207.946i	−0.589156	+	0.226028i
$921$	−239.940	−	415.588i	−0.260521	−	0.451236i
$922$	−629.749	−	1236.14i	−0.683025	−	1.34072i
$923$	439.400			0.476056
$924$	−806.414	−	348.039i	−0.872743	−	0.376666i
$925$		−	977.438i		−	1.05669i
$926$	291.602	+	572.390i	0.314905	+	0.618132i
$927$	474.403	−	273.897i	0.511762	−	0.295466i
$928$	630.828	−	630.430i	0.679771	−	0.679343i
$929$	−484.873	+	839.824i	−0.521930	+	0.904009i	0.477745	+	0.878499i	$0.341454\pi$
$929$	−484.873	+	839.824i	−0.521930	+	0.904009i	−0.999675	+	0.0255102i	$0.991879\pi$
$930$	282.615	+	183.558i	0.303887	+	0.197374i
$931$	−1210.72	−	837.549i	−1.30045	−	0.899623i
$932$	−135.672	−	304.827i	−0.145570	−	0.327068i
$933$	−1121.74	−	647.636i	−1.20229	−	0.694144i
$934$	78.7949	−	1501.68i	0.0843628	−	1.60780i
$935$	−37.2331	+	21.4965i	−0.0398215	+	0.0229909i
$936$	−396.138	+	489.001i	−0.423225	+	0.522437i
$937$	1287.55			1.37412			0.687061	−	0.726600i	$-0.258901\pi$
$937$	1287.55			1.37412			0.687061	+	0.726600i	$0.258901\pi$
$938$	818.567	−	139.319i	0.872673	−	0.148528i
$939$	−1818.36			−1.93649
$940$	−618.426	−	65.0781i	−0.657900	−	0.0692320i
$941$	395.597	−	228.398i	0.420400	−	0.242718i	−0.274848	−	0.961488i	$-0.588628\pi$
$941$	395.597	−	228.398i	0.420400	−	0.242718i	0.695249	+	0.718769i	$0.255294\pi$
$942$	−392.207	−	20.5795i	−0.416356	−	0.0218466i
$943$	−1356.43	−	783.133i	−1.43842	−	0.830470i
$944$	111.493	−	123.763i	0.118107	−	0.131105i
$945$	−110.118	+	24.7410i	−0.116527	+	0.0261810i
$946$	624.860	+	405.845i	0.660529	+	0.429012i
$947$	573.925	−	994.067i	0.606045	−	1.04970i	−0.385840	−	0.922566i	$-0.626088\pi$
$947$	573.925	−	994.067i	0.606045	−	1.04970i	0.991885	−	0.127135i	$-0.0405782\pi$
$948$	−659.408	−	479.215i	−0.695578	−	0.505501i
$949$	−139.044	+	80.2768i	−0.146516	+	0.0845910i
$950$	1148.80	−	585.250i	1.20926	−	0.616053i
$951$		−	482.582i		−	0.507447i
$952$	72.0379	−	145.450i	0.0756700	−	0.152784i
$953$	873.170			0.916232			0.458116	−	0.888892i	$-0.348524\pi$
$953$	873.170			0.916232			0.458116	+	0.888892i	$0.348524\pi$
$954$	−167.155	−	328.112i	−0.175215	−	0.343933i
$955$	280.976	+	486.665i	0.294216	+	0.509597i
$956$	364.222	+	264.693i	0.380986	+	0.276876i
$957$	757.114	+	437.120i	0.791133	+	0.456761i
$958$	−786.688	+	1211.23i	−0.821177	+	1.26433i
$959$	−56.7747	−	17.7239i	−0.0592020	−	0.0184816i
$960$	148.389	−	456.108i	0.154572	−	0.475113i
$961$	−227.755	+	394.483i	−0.236998	+	0.410492i
$962$	−54.8368	+	1045.09i	−0.0570029	+	1.08637i
$963$	−166.980	−	289.219i	−0.173396	−	0.300331i
$964$	−1115.57	−	117.393i	−1.15723	−	0.121777i
$965$			622.666i			0.645249i
$966$	2014.49	+	746.817i	2.08539	+	0.773102i
$967$		−	449.047i		−	0.464372i	−0.972671	−	0.232186i	$-0.925412\pi$
$967$		−	449.047i		−	0.464372i	0.972671	−	0.232186i	$-0.0745878\pi$
$968$	366.223	+	296.676i	0.378330	+	0.306484i
$969$	173.339	+	300.231i	0.178884	+	0.309836i
$970$	−208.034	−	10.9157i	−0.214468	−	0.0112533i
$971$	618.929	−	1072.02i	0.637414	−	1.10403i	−0.348584	−	0.937278i	$-0.613337\pi$
$971$	618.929	−	1072.02i	0.637414	−	1.10403i	0.985998	−	0.166756i	$-0.0533293\pi$
$972$	494.512	+	1111.07i	0.508757	+	1.14308i
$973$	15.7483	−	14.5132i	0.0161853	−	0.0149159i
$974$	−52.1041	+	80.2222i	−0.0534950	+	0.0823636i
$975$	−849.687	−	490.567i	−0.871473	−	0.503145i
$976$	73.8126	−	346.831i	0.0756277	−	0.355359i
$977$	−853.445	−	1478.21i	−0.873536	−	1.51301i	−0.858314	−	0.513125i	$-0.828488\pi$
$977$	−853.445	−	1478.21i	−0.873536	−	1.51301i	−0.0152219	−	0.999884i	$-0.504845\pi$
$978$	820.968	−	418.239i	0.839435	−	0.427647i
$979$	−829.373			−0.847164
$980$	−122.062	−	348.199i	−0.124553	−	0.355305i
$981$			788.063i			0.803326i
$982$	−79.2530	+	40.3751i	−0.0807057	+	0.0411152i
$983$	997.793	−	576.076i	1.01505	−	0.586039i	0.102383	−	0.994745i	$-0.467353\pi$
$983$	997.793	−	576.076i	1.01505	−	0.586039i	0.912666	+	0.408706i	$0.134020\pi$
$984$	1208.17	−	463.512i	1.22782	−	0.471049i
$985$	−308.082	+	533.614i	−0.312774	+	0.541741i
$986$	−87.9999	+	135.489i	−0.0892494	+	0.137413i
$987$	1559.55	+	1692.27i	1.58009	+	1.71456i
$988$	−1261.14	+	561.305i	−1.27646	+	0.568123i
$989$	−1578.41	−	911.293i	−1.59596	−	0.921429i
$990$	202.895	+	10.6461i	0.204944	+	0.0107536i
$991$	357.511	−	206.409i	0.360758	−	0.208283i	−0.308655	−	0.951174i	$-0.599879\pi$
$991$	357.511	−	206.409i	0.360758	−	0.208283i	0.669413	+	0.742890i	$0.266546\pi$
$992$	−694.886	−	186.429i	−0.700490	−	0.187932i
$993$	−482.375			−0.485776
$994$	502.161	+	186.162i	0.505192	+	0.187286i
$995$	−23.9753			−0.0240958
$996$	−1416.52	−	149.063i	−1.42221	−	0.149662i
$997$	−260.805	+	150.576i	−0.261590	+	0.151029i	−0.625060	−	0.780577i	$-0.714925\pi$
$997$	−260.805	+	150.576i	−0.261590	+	0.151029i	0.363470	+	0.931606i	$0.381592\pi$
$998$	−52.5637	+	1001.77i	−0.0526691	+	1.00377i
$999$	337.897	+	195.085i	0.338235	+	0.195280i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	56.3.k.d.51.1	yes	12
4.3	odd	2		224.3.o.d.79.2		12
7.2	even	3		392.3.g.j.99.6		6
7.3	odd	6		392.3.k.l.67.3		12
7.4	even	3	inner	56.3.k.d.11.3	yes	12
7.5	odd	6		392.3.g.i.99.6		6
7.6	odd	2		392.3.k.l.275.1		12
8.3	odd	2	inner	56.3.k.d.51.3	yes	12
8.5	even	2		224.3.o.d.79.1		12
28.11	odd	6		224.3.o.d.207.1		12
28.19	even	6		1568.3.g.l.687.2		6
28.23	odd	6		1568.3.g.j.687.5		6
56.3	even	6		392.3.k.l.67.1		12
56.5	odd	6		1568.3.g.l.687.1		6
56.11	odd	6	inner	56.3.k.d.11.1	✓	12
56.19	even	6		392.3.g.i.99.5		6
56.27	even	2		392.3.k.l.275.3		12
56.37	even	6		1568.3.g.j.687.6		6
56.51	odd	6		392.3.g.j.99.5		6
56.53	even	6		224.3.o.d.207.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.k.d.11.1	✓	12	56.11	odd	6	inner
56.3.k.d.11.3	yes	12	7.4	even	3	inner
56.3.k.d.51.1	yes	12	1.1	even	1	trivial
56.3.k.d.51.3	yes	12	8.3	odd	2	inner
224.3.o.d.79.1		12	8.5	even	2
224.3.o.d.79.2		12	4.3	odd	2
224.3.o.d.207.1		12	28.11	odd	6
224.3.o.d.207.2		12	56.53	even	6
392.3.g.i.99.5		6	56.19	even	6
392.3.g.i.99.6		6	7.5	odd	6
392.3.g.j.99.5		6	56.51	odd	6
392.3.g.j.99.6		6	7.2	even	3
392.3.k.l.67.1		12	56.3	even	6
392.3.k.l.67.3		12	7.3	odd	6
392.3.k.l.275.1		12	7.6	odd	2
392.3.k.l.275.3		12	56.27	even	2
1568.3.g.j.687.5		6	28.23	odd	6
1568.3.g.j.687.6		6	56.37	even	6
1568.3.g.l.687.1		6	56.5	odd	6
1568.3.g.l.687.2		6	28.19	even	6

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:	\( N \)	\(=\)	\( 56 = 2^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	56.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.78207 + 0.907869i) q^{2} +(1.99052 + 3.44767i) q^{3} +(2.35155 - 3.23577i) q^{4} +(1.63031 + 0.941260i) q^{5} +(-6.67727 - 4.33687i) q^{6} +(-5.14749 + 4.74377i) q^{7} +(-1.25297 + 7.90127i) q^{8} +(-3.42430 + 5.93106i) q^{9} +O(q^{10})\)	\(q+(-1.78207 + 0.907869i) q^{2} +(1.99052 + 3.44767i) q^{3} +(2.35155 - 3.23577i) q^{4} +(1.63031 + 0.941260i) q^{5} +(-6.67727 - 4.33687i) q^{6} +(-5.14749 + 4.74377i) q^{7} +(-1.25297 + 7.90127i) q^{8} +(-3.42430 + 5.93106i) q^{9} +(-3.75987 - 0.197284i) q^{10} +(3.93973 + 6.82381i) q^{11} +(15.8367 + 1.66652i) q^{12} -11.4863i q^{13} +(4.86647 - 13.1270i) q^{14} +7.49437i q^{15} +(-4.94043 - 15.2182i) q^{16} +(1.44921 + 2.51011i) q^{17} +(0.717719 - 13.6784i) q^{18} +(15.0223 - 26.0194i) q^{19} +(6.87946 - 3.06189i) q^{20} +(-26.6011 - 8.30431i) q^{21} +(-13.2160 - 8.58375i) q^{22} +(33.3838 + 19.2741i) q^{23} +(-29.7351 + 11.4078i) q^{24} +(-10.7281 - 18.5815i) q^{25} +(10.4281 + 20.4695i) q^{26} +8.56478 q^{27} +(3.24519 + 27.8113i) q^{28} -27.8701i q^{29} +(-6.80390 - 13.3555i) q^{30} +(-19.4709 + 11.2416i) q^{31} +(22.6203 + 22.6346i) q^{32} +(-15.6842 + 27.1658i) q^{33} +(-4.86145 - 3.15750i) q^{34} +(-12.8571 + 2.88869i) q^{35} +(11.1392 + 25.0274i) q^{36} +(39.4520 + 22.7776i) q^{37} +(-3.14862 + 60.0068i) q^{38} +(39.6011 - 22.8637i) q^{39} +(-9.47988 + 11.7021i) q^{40} -40.6313 q^{41} +(54.9443 - 9.35146i) q^{42} -47.2806 q^{43} +(31.3448 + 3.29846i) q^{44} +(-11.1653 + 6.44632i) q^{45} +(-76.9907 - 4.03978i) q^{46} +(-71.5172 - 41.2905i) q^{47} +(42.6332 - 47.3250i) q^{48} +(3.99327 - 48.8370i) q^{49} +(35.9878 + 23.3739i) q^{50} +(-5.76936 + 9.99283i) q^{51} +(-37.1672 - 27.0107i) q^{52} +(23.2823 - 13.4420i) q^{53} +(-15.2630 + 7.77569i) q^{54} +14.8332i q^{55} +(-31.0322 - 46.6155i) q^{56} +119.609 q^{57} +(25.3024 + 49.6665i) q^{58} +(5.20555 + 9.01627i) q^{59} +(24.2501 + 17.6234i) q^{60} +(19.1932 + 11.0812i) q^{61} +(24.4927 - 37.7103i) q^{62} +(-10.5091 - 46.7742i) q^{63} +(-60.8601 - 19.8001i) q^{64} +(10.8116 - 18.7263i) q^{65} +(3.28734 - 62.6505i) q^{66} +(29.6549 + 51.3639i) q^{67} +(11.5300 + 1.21333i) q^{68} +153.462i q^{69} +(20.2897 - 16.8204i) q^{70} +38.2541i q^{71} +(-42.5724 - 34.4878i) q^{72} +(-6.98890 - 12.1051i) q^{73} +(-90.9852 - 4.77409i) q^{74} +(42.7087 - 73.9737i) q^{75} +(-48.8672 - 109.795i) q^{76} +(-52.6503 - 16.4363i) q^{77} +(-49.8147 + 76.6974i) q^{78} +(-44.3314 - 25.5948i) q^{79} +(6.26980 - 29.4605i) q^{80} +(47.8670 + 82.9081i) q^{81} +(72.4078 - 36.8879i) q^{82} -89.4458 q^{83} +(-89.4247 + 66.5472i) q^{84} +5.45635i q^{85} +(84.2573 - 42.9246i) q^{86} +(96.0871 - 55.4759i) q^{87} +(-58.8531 + 22.5788i) q^{88} +(-52.6288 + 91.1558i) q^{89} +(14.0450 - 21.6245i) q^{90} +(54.4885 + 59.1258i) q^{91} +(140.870 - 62.6982i) q^{92} +(-77.5144 - 44.7530i) q^{93} +(164.935 + 8.65431i) q^{94} +(48.9821 - 28.2798i) q^{95} +(-33.0105 + 123.042i) q^{96} +55.3301 q^{97} +(37.2213 + 90.6564i) q^{98} -53.9633 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} - 6 q^{3} - 4 q^{4} - 56 q^{6} + 8 q^{8} - 40 q^{9}+O(q^{10}) \) 12 * q + 2 * q^2 - 6 * q^3 - 4 * q^4 - 56 * q^6 + 8 * q^8 - 40 * q^9	\( 12 q + 2 q^{2} - 6 q^{3} - 4 q^{4} - 56 q^{6} + 8 q^{8} - 40 q^{9} - 6 q^{10} + 30 q^{11} + 32 q^{12} + 52 q^{14} + 16 q^{16} + 30 q^{17} - 16 q^{18} + 78 q^{19} + 48 q^{20} + 24 q^{22} - 76 q^{24} - 92 q^{25} - 128 q^{26} + 156 q^{27} - 4 q^{28} - 16 q^{30} + 112 q^{32} - 78 q^{33} + 76 q^{34} - 222 q^{35} - 248 q^{36} + 80 q^{38} + 44 q^{40} - 232 q^{41} + 132 q^{42} - 200 q^{43} + 132 q^{44} - 156 q^{46} + 176 q^{48} + 372 q^{49} + 48 q^{50} + 10 q^{51} + 132 q^{52} - 36 q^{54} - 112 q^{56} + 332 q^{57} + 4 q^{58} - 110 q^{59} + 84 q^{60} - 96 q^{62} - 160 q^{64} - 32 q^{65} - 138 q^{66} + 434 q^{67} + 96 q^{68} - 188 q^{70} - 328 q^{72} + 102 q^{73} - 34 q^{74} - 60 q^{75} - 168 q^{76} + 720 q^{78} - 256 q^{80} - 82 q^{81} - 24 q^{82} - 536 q^{83} - 624 q^{84} + 240 q^{86} - 204 q^{88} + 214 q^{89} + 440 q^{90} - 8 q^{91} + 160 q^{92} - 16 q^{94} + 48 q^{96} - 152 q^{97} + 382 q^{98} + 504 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 - 6 * q^3 - 4 * q^4 - 56 * q^6 + 8 * q^8 - 40 * q^9 - 6 * q^10 + 30 * q^11 + 32 * q^12 + 52 * q^14 + 16 * q^16 + 30 * q^17 - 16 * q^18 + 78 * q^19 + 48 * q^20 + 24 * q^22 - 76 * q^24 - 92 * q^25 - 128 * q^26 + 156 * q^27 - 4 * q^28 - 16 * q^30 + 112 * q^32 - 78 * q^33 + 76 * q^34 - 222 * q^35 - 248 * q^36 + 80 * q^38 + 44 * q^40 - 232 * q^41 + 132 * q^42 - 200 * q^43 + 132 * q^44 - 156 * q^46 + 176 * q^48 + 372 * q^49 + 48 * q^50 + 10 * q^51 + 132 * q^52 - 36 * q^54 - 112 * q^56 + 332 * q^57 + 4 * q^58 - 110 * q^59 + 84 * q^60 - 96 * q^62 - 160 * q^64 - 32 * q^65 - 138 * q^66 + 434 * q^67 + 96 * q^68 - 188 * q^70 - 328 * q^72 + 102 * q^73 - 34 * q^74 - 60 * q^75 - 168 * q^76 + 720 * q^78 - 256 * q^80 - 82 * q^81 - 24 * q^82 - 536 * q^83 - 624 * q^84 + 240 * q^86 - 204 * q^88 + 214 * q^89 + 440 * q^90 - 8 * q^91 + 160 * q^92 - 16 * q^94 + 48 * q^96 - 152 * q^97 + 382 * q^98 + 504 * q^99

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