LMFDB - Embedded newform 35.3.i.a.24.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,3,Mod(19,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("35.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	35.i (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:	$0.953680925261$
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} - 15x^{10} + 180x^{8} - 669x^{6} + 1980x^{4} - 135x^{2} + 9 $ x^12 - 15x^10 + 180x^8 - 669x^6 + 1980x^4 - 135*x^2 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			24.5
Root			$1.74002 - 1.00460i$ of defining polynomial
Character	$\chi$	$=$	35.24
Dual form			35.3.i.a.19.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.74002 - 1.00460i) q^{2} +(0.784824 - 1.35935i) q^{3} +(0.0184439 - 0.0319457i) q^{4} +(-3.93275 + 3.08763i) q^{5} -3.15374i q^{6} +(-1.38623 - 6.86137i) q^{7} +7.96269i q^{8} +(3.26810 + 5.66052i) q^{9} +O(q^{10})$	\(q+(1.74002 - 1.00460i) q^{2} +(0.784824 - 1.35935i) q^{3} +(0.0184439 - 0.0319457i) q^{4} +(-3.93275 + 3.08763i) q^{5} -3.15374i q^{6} +(-1.38623 - 6.86137i) q^{7} +7.96269i q^{8} +(3.26810 + 5.66052i) q^{9} +(-3.74123 + 9.32338i) q^{10} +(4.78655 - 8.29054i) q^{11} +(-0.0289503 - 0.0501435i) q^{12} -13.9463 q^{13} +(-9.30499 - 10.5463i) q^{14} +(1.11066 + 7.76925i) q^{15} +(8.07310 + 13.9830i) q^{16} +(8.97665 - 15.5480i) q^{17} +(11.3731 + 6.56628i) q^{18} +(-9.91497 + 5.72441i) q^{19} +(0.0261013 + 0.182582i) q^{20} +(-10.4150 - 3.50059i) q^{21} -19.2343i q^{22} +(7.35931 - 4.24890i) q^{23} +(10.8241 + 6.24931i) q^{24} +(5.93310 - 24.2858i) q^{25} +(-24.2667 + 14.0104i) q^{26} +24.3864 q^{27} +(-0.244758 - 0.0822662i) q^{28} +26.6824 q^{29} +(9.73757 + 12.4029i) q^{30} +(-1.87157 - 1.08055i) q^{31} +(0.511115 + 0.295092i) q^{32} +(-7.51319 - 13.0132i) q^{33} -36.0718i q^{34} +(26.6370 + 22.7039i) q^{35} +0.241106 q^{36} +(-56.1667 + 32.4279i) q^{37} +(-11.5015 + 19.9212i) q^{38} +(-10.9453 + 18.9579i) q^{39} +(-24.5858 - 31.3153i) q^{40} +23.3267i q^{41} +(-21.6389 + 4.37179i) q^{42} +0.506200i q^{43} +(-0.176565 - 0.305819i) q^{44} +(-30.3302 - 12.1707i) q^{45} +(8.53689 - 14.7863i) q^{46} +(34.3500 + 59.4960i) q^{47} +25.3438 q^{48} +(-45.1568 + 19.0228i) q^{49} +(-14.0738 - 48.2181i) q^{50} +(-14.0902 - 24.4049i) q^{51} +(-0.257223 + 0.445523i) q^{52} +(-47.7045 - 27.5422i) q^{53} +(42.4327 - 24.4986i) q^{54} +(6.77380 + 47.3837i) q^{55} +(54.6349 - 11.0381i) q^{56} +17.9706i q^{57} +(46.4279 - 26.8051i) q^{58} +(54.5751 + 31.5090i) q^{59} +(0.268679 + 0.107814i) q^{60} +(43.9307 - 25.3634i) q^{61} -4.34210 q^{62} +(34.3086 - 30.2704i) q^{63} -63.3990 q^{64} +(54.8472 - 43.0608i) q^{65} +(-26.1462 - 15.0955i) q^{66} +(33.7366 + 19.4779i) q^{67} +(-0.331128 - 0.573531i) q^{68} -13.3385i q^{69} +(69.1573 + 12.7457i) q^{70} +3.47954 q^{71} +(-45.0730 + 26.0229i) q^{72} +(12.3283 - 21.3533i) q^{73} +(-65.1541 + 112.850i) q^{74} +(-28.3565 - 27.1252i) q^{75} +0.422321i q^{76} +(-63.5197 - 21.3497i) q^{77} +43.9828i q^{78} +(-68.8832 - 119.309i) q^{79} +(-74.9238 - 30.0650i) q^{80} +(-10.2739 + 17.7950i) q^{81} +(23.4340 + 40.5889i) q^{82} -110.042 q^{83} +(-0.303921 + 0.268149i) q^{84} +(12.7035 + 88.8631i) q^{85} +(0.508529 + 0.880798i) q^{86} +(20.9410 - 36.2708i) q^{87} +(66.0150 + 38.1138i) q^{88} +(84.0216 - 48.5099i) q^{89} +(-65.0019 + 9.29243i) q^{90} +(19.3326 + 95.6904i) q^{91} -0.313464i q^{92} +(-2.93771 + 1.69609i) q^{93} +(119.539 + 69.0161i) q^{94} +(21.3183 - 53.1265i) q^{95} +(0.802270 - 0.463191i) q^{96} +3.28023 q^{97} +(-59.4633 + 78.4645i) q^{98} +62.5717 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{4} - 18 q^{9}+O(q^{10}) $ 12 * q + 6 * q^4 - 18 * q^9	$ 12 q + 6 q^{4} - 18 q^{9} - 54 q^{10} + 6 q^{11} - 66 q^{14} + 48 q^{15} - 6 q^{16} + 18 q^{19} + 12 q^{21} + 216 q^{24} + 18 q^{25} + 18 q^{26} + 48 q^{30} - 108 q^{31} + 222 q^{35} - 204 q^{36} - 240 q^{39} - 162 q^{40} - 42 q^{44} - 216 q^{45} + 114 q^{46} - 324 q^{49} - 192 q^{50} + 180 q^{51} + 252 q^{54} + 336 q^{56} + 396 q^{59} + 384 q^{60} - 108 q^{61} + 372 q^{64} - 54 q^{65} - 108 q^{66} + 300 q^{70} + 192 q^{71} - 594 q^{74} - 216 q^{75} - 192 q^{79} - 504 q^{80} + 294 q^{81} - 1200 q^{84} - 192 q^{85} - 384 q^{86} + 684 q^{89} - 72 q^{91} + 990 q^{94} + 288 q^{95} - 540 q^{96} + 396 q^{99}+O(q^{100}) $ 12 * q + 6 * q^4 - 18 * q^9 - 54 * q^10 + 6 * q^11 - 66 * q^14 + 48 * q^15 - 6 * q^16 + 18 * q^19 + 12 * q^21 + 216 * q^24 + 18 * q^25 + 18 * q^26 + 48 * q^30 - 108 * q^31 + 222 * q^35 - 204 * q^36 - 240 * q^39 - 162 * q^40 - 42 * q^44 - 216 * q^45 + 114 * q^46 - 324 * q^49 - 192 * q^50 + 180 * q^51 + 252 * q^54 + 336 * q^56 + 396 * q^59 + 384 * q^60 - 108 * q^61 + 372 * q^64 - 54 * q^65 - 108 * q^66 + 300 * q^70 + 192 * q^71 - 594 * q^74 - 216 * q^75 - 192 * q^79 - 504 * q^80 + 294 * q^81 - 1200 * q^84 - 192 * q^85 - 384 * q^86 + 684 * q^89 - 72 * q^91 + 990 * q^94 + 288 * q^95 - 540 * q^96 + 396 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.74002	−	1.00460i	0.870009	−	0.502300i	0.00265807	−	0.999996i	$-0.499154\pi$
$2$	1.74002	−	1.00460i	0.870009	−	0.502300i	0.867351	+	0.497696i	$0.165821\pi$
$3$	0.784824	−	1.35935i	0.261608	−	0.453118i	−0.705061	−	0.709146i	$-0.749081\pi$
$3$	0.784824	−	1.35935i	0.261608	−	0.453118i	0.966669	+	0.256028i	$0.0824139\pi$
$4$	0.0184439	−	0.0319457i	0.00461096	−	0.00798642i
$5$	−3.93275	+	3.08763i	−0.786551	+	0.617526i
$5$	−3.93275	+	3.08763i	−0.786551	+	0.617526i
$6$		−	3.15374i		−	0.525623i
$7$	−1.38623	−	6.86137i	−0.198032	−	0.980196i
$7$	−1.38623	−	6.86137i	−0.198032	−	0.980196i
$8$			7.96269i			0.995336i
$9$	3.26810	+	5.66052i	0.363123	+	0.628947i
$10$	−3.74123	+	9.32338i	−0.374123	+	0.932338i
$11$	4.78655	−	8.29054i	0.435141	−	0.753686i	−0.562166	−	0.827024i	$-0.690032\pi$
$11$	4.78655	−	8.29054i	0.435141	−	0.753686i	0.997307	+	0.0733383i	$0.0233653\pi$
$12$	−0.0289503	−	0.0501435i	−0.00241253	−	0.00417862i
$13$	−13.9463			−1.07279			−0.536394	−	0.843967i	$-0.680214\pi$
$13$	−13.9463			−1.07279			−0.536394	+	0.843967i	$0.680214\pi$
$14$	−9.30499	−	10.5463i	−0.664642	−	0.753308i
$15$	1.11066	+	7.76925i	0.0740442	+	0.517950i
$16$	8.07310	+	13.9830i	0.504568	+	0.873938i
$17$	8.97665	−	15.5480i	0.528038	−	0.914589i	−0.471427	−	0.881905i	$-0.656261\pi$
$17$	8.97665	−	15.5480i	0.528038	−	0.914589i	0.999466	−	0.0326844i	$-0.0104056\pi$
$18$	11.3731	+	6.56628i	0.631840	+	0.364793i
$19$	−9.91497	+	5.72441i	−0.521841	+	0.301285i	−0.737687	−	0.675142i	$-0.764082\pi$
$19$	−9.91497	+	5.72441i	−0.521841	+	0.301285i	0.215847	+	0.976427i	$0.430749\pi$
$20$	0.0261013	+	0.182582i	0.00130506	+	0.00912911i
$21$	−10.4150	−	3.50059i	−0.495951	−	0.166695i
$22$		−	19.2343i		−	0.874285i
$23$	7.35931	−	4.24890i	0.319970	−	0.184735i	−0.331409	−	0.943487i	$-0.607524\pi$
$23$	7.35931	−	4.24890i	0.319970	−	0.184735i	0.651379	+	0.758752i	$0.274191\pi$
$24$	10.8241	+	6.24931i	0.451005	+	0.260388i
$25$	5.93310	−	24.2858i	0.237324	−	0.971431i
$26$	−24.2667	+	14.0104i	−0.933336	+	0.538862i
$27$	24.3864			0.903199
$28$	−0.244758	−	0.0822662i	−0.00874137	−	0.00293808i
$29$	26.6824			0.920083			0.460041	−	0.887897i	$-0.347835\pi$
$29$	26.6824			0.920083			0.460041	+	0.887897i	$0.347835\pi$
$30$	9.73757	+	12.4029i	0.324586	+	0.413429i
$31$	−1.87157	−	1.08055i	−0.0603733	−	0.0348566i	0.469509	−	0.882927i	$-0.344431\pi$
$31$	−1.87157	−	1.08055i	−0.0603733	−	0.0348566i	−0.529883	+	0.848071i	$0.677764\pi$
$32$	0.511115	+	0.295092i	0.0159723	+	0.00922163i
$33$	−7.51319	−	13.0132i	−0.227672	−	0.394340i
$34$		−	36.0718i		−	1.06094i
$35$	26.6370	+	22.7039i	0.761058	+	0.648684i
$36$	0.241106			0.00669738
$37$	−56.1667	+	32.4279i	−1.51802	+	0.876428i	−0.518243	+	0.855233i	$0.673414\pi$
$37$	−56.1667	+	32.4279i	−1.51802	+	0.876428i	−0.999775	+	0.0211951i	$0.993253\pi$
$38$	−11.5015	+	19.9212i	−0.302671	+	0.524241i
$39$	−10.9453	+	18.9579i	−0.280650	+	0.486100i
$40$	−24.5858	−	31.3153i	−0.614646	−	0.782882i
$41$			23.3267i			0.568944i	0.958684	+	0.284472i	$0.0918183\pi$
$41$			23.3267i			0.568944i	−0.958684	+	0.284472i	$0.908182\pi$
$42$	−21.6389	+	4.37179i	−0.515213	+	0.104090i
$43$			0.506200i			0.0117721i	0.999983	+	0.00588605i	$0.00187360\pi$
$43$			0.506200i			0.0117721i	−0.999983	+	0.00588605i	$0.998126\pi$
$44$	−0.176565	−	0.305819i	−0.00401284	−	0.00695043i
$45$	−30.3302	−	12.1707i	−0.674005	−	0.270461i
$46$	8.53689	−	14.7863i	0.185585	−	0.321442i
$47$	34.3500	+	59.4960i	0.730851	+	1.26587i	0.956520	+	0.291667i	$0.0942101\pi$
$47$	34.3500	+	59.4960i	0.730851	+	1.26587i	−0.225668	+	0.974204i	$0.572457\pi$
$48$	25.3438			0.527996
$49$	−45.1568	+	19.0228i	−0.921567	+	0.388220i
$50$	−14.0738	−	48.2181i	−0.281476	−	0.964362i
$51$	−14.0902	−	24.4049i	−0.276278	−	0.478528i
$52$	−0.257223	+	0.445523i	−0.00494659	+	0.00856774i
$53$	−47.7045	−	27.5422i	−0.900085	−	0.519664i	−0.0228569	−	0.999739i	$-0.507276\pi$
$53$	−47.7045	−	27.5422i	−0.900085	−	0.519664i	−0.877228	+	0.480075i	$0.840610\pi$
$54$	42.4327	−	24.4986i	0.785791	−	0.453677i
$55$	6.77380	+	47.3837i	0.123160	+	0.861523i
$56$	54.6349	−	11.0381i	0.975624	−	0.197109i
$57$			17.9706i			0.315274i
$58$	46.4279	−	26.8051i	0.800481	−	0.462158i
$59$	54.5751	+	31.5090i	0.925002	+	0.534050i	0.885227	−	0.465159i	$-0.154003\pi$
$59$	54.5751	+	31.5090i	0.925002	+	0.534050i	0.0397745	+	0.999209i	$0.487336\pi$
$60$	0.268679	+	0.107814i	0.00447798	+	0.00179690i
$61$	43.9307	−	25.3634i	0.720175	−	0.415793i	−0.0946419	−	0.995511i	$-0.530171\pi$
$61$	43.9307	−	25.3634i	0.720175	−	0.415793i	0.814817	+	0.579718i	$0.196837\pi$
$62$	−4.34210			−0.0700338
$63$	34.3086	−	30.2704i	0.544581	−	0.480483i
$64$	−63.3990			−0.990609
$65$	54.8472	−	43.0608i	0.843803	−	0.662475i
$66$	−26.1462	−	15.0955i	−0.396154	−	0.228720i
$67$	33.7366	+	19.4779i	0.503532	+	0.290714i	0.730171	−	0.683265i	$-0.239440\pi$
$67$	33.7366	+	19.4779i	0.503532	+	0.290714i	−0.226639	+	0.973979i	$0.572774\pi$
$68$	−0.331128	−	0.573531i	−0.00486953	−	0.00843428i
$69$		−	13.3385i		−	0.193312i
$70$	69.1573	+	12.7457i	0.987962	+	0.182081i
$71$	3.47954			0.0490076			0.0245038	−	0.999700i	$-0.492199\pi$
$71$	3.47954			0.0490076			0.0245038	+	0.999700i	$0.492199\pi$
$72$	−45.0730	+	26.0229i	−0.626013	+	0.361429i
$73$	12.3283	−	21.3533i	0.168881	−	0.292511i	−0.769146	−	0.639074i	$-0.779318\pi$
$73$	12.3283	−	21.3533i	0.168881	−	0.292511i	0.938027	+	0.346563i	$0.112651\pi$
$74$	−65.1541	+	112.850i	−0.880460	+	1.52500i
$75$	−28.3565	−	27.1252i	−0.378087	−	0.361670i
$76$			0.422321i			0.00555685i
$77$	−63.5197	−	21.3497i	−0.824931	−	0.277269i
$78$			43.9828i			0.563882i
$79$	−68.8832	−	119.309i	−0.871940	−	1.51024i	−0.859987	−	0.510315i	$-0.829529\pi$
$79$	−68.8832	−	119.309i	−0.871940	−	1.51024i	−0.0119524	−	0.999929i	$-0.503805\pi$
$80$	−74.9238	−	30.0650i	−0.936548	−	0.375813i
$81$	−10.2739	+	17.7950i	−0.126839	+	0.219691i
$82$	23.4340	+	40.5889i	0.285781	+	0.494987i
$83$	−110.042			−1.32581			−0.662906	−	0.748703i	$-0.730677\pi$
$83$	−110.042			−1.32581			−0.662906	+	0.748703i	$0.730677\pi$
$84$	−0.303921	+	0.268149i	−0.00361811	+	0.00319225i
$85$	12.7035	+	88.8631i	0.149453	+	1.04545i
$86$	0.508529	+	0.880798i	0.00591313	+	0.0102418i
$87$	20.9410	−	36.2708i	0.240701	−	0.416906i
$88$	66.0150	+	38.1138i	0.750171	+	0.433111i
$89$	84.0216	−	48.5099i	0.944063	−	0.545055i	0.0528312	−	0.998603i	$-0.483175\pi$
$89$	84.0216	−	48.5099i	0.944063	−	0.545055i	0.891232	+	0.453549i	$0.149842\pi$
$90$	−65.0019	+	9.29243i	−0.722244	+	0.103249i
$91$	19.3326	+	95.6904i	0.212447	+	1.05154i
$92$		−	0.313464i		−	0.00340722i
$93$	−2.93771	+	1.69609i	−0.0315883	+	0.0182375i
$94$	119.539	+	69.0161i	1.27170	+	0.734214i
$95$	21.3183	−	53.1265i	0.224403	−	0.559226i
$96$	0.802270	−	0.463191i	0.00835698	−	0.00482490i
$97$	3.28023			0.0338168			0.0169084	−	0.999857i	$-0.494618\pi$
$97$	3.28023			0.0338168			0.0169084	+	0.999857i	$0.494618\pi$
$98$	−59.4633	+	78.4645i	−0.606768	+	0.800659i
$99$	62.5717			0.632038
$100$	−0.666396	−	0.637460i	−0.00666396	−	0.00637460i
$101$	−108.707	−	62.7622i	−1.07631	−	0.621408i	−0.146412	−	0.989224i	$-0.546772\pi$
$101$	−108.707	−	62.7622i	−1.07631	−	0.621408i	−0.929899	+	0.367816i	$0.880106\pi$
$102$	−49.0344	−	28.3100i	−0.480729	−	0.277549i
$103$	−8.47859	−	14.6853i	−0.0823164	−	0.142576i	0.821928	−	0.569591i	$-0.192898\pi$
$103$	−8.47859	−	14.6853i	−0.0823164	−	0.142576i	−0.904245	+	0.427015i	$0.859565\pi$
$104$		−	111.050i		−	1.06779i
$105$	51.7681	−	18.3906i	0.493029	−	0.175149i
$106$	−110.676			−1.04411
$107$	111.108	−	64.1484i	1.03840	−	0.599518i	0.119017	−	0.992892i	$-0.462026\pi$
$107$	111.108	−	64.1484i	1.03840	−	0.599518i	0.919378	+	0.393375i	$0.128692\pi$
$108$	0.449779	−	0.779039i	0.00416462	−	0.00721333i
$109$	−43.3446	+	75.0750i	−0.397657	+	0.688762i	−0.993436	−	0.114386i	$-0.963510\pi$
$109$	−43.3446	+	75.0750i	−0.397657	+	0.688762i	0.595780	+	0.803148i	$0.296843\pi$
$110$	59.3883	+	75.6436i	0.539893	+	0.687670i
$111$			101.801i			0.917122i
$112$	84.7515	−	74.7761i	0.756710	−	0.667644i
$113$		−	102.175i		−	0.904202i	−0.891967	−	0.452101i	$-0.850675\pi$
$113$		−	102.175i		−	0.904202i	0.891967	−	0.452101i	$-0.149325\pi$
$114$	18.0533	+	31.2692i	0.158362	+	0.274291i
$115$	−15.8233	+	39.4327i	−0.137594	+	0.342893i
$116$	0.492126	−	0.852388i	0.00424247	−	0.00734817i
$117$	−45.5778	−	78.9431i	−0.389554	−	0.674727i
$118$	126.616			1.07301
$119$	−119.124	−	40.0391i	−1.00104	−	0.336463i
$120$	−61.8641	+	8.84386i	−0.515534	+	0.0736989i
$121$	14.6779	+	25.4229i	0.121305	+	0.210107i
$122$	50.9602	−	88.2656i	0.417706	−	0.723488i
$123$	31.7093	+	18.3074i	0.257799	+	0.148840i
$124$	−0.0690381	+	0.0398591i	−0.000556758	+	0.000321445i
$125$	51.6520	+	113.829i	0.413216	+	0.910633i
$126$	29.2879	−	87.1375i	0.232444	−	0.691568i
$127$		−	88.5547i		−	0.697281i	−0.937256	−	0.348641i	$-0.886643\pi$
$127$		−	88.5547i		−	0.697281i	0.937256	−	0.348641i	$-0.113357\pi$
$128$	−112.360	+	64.8710i	−0.877811	+	0.506805i
$129$	0.688106	+	0.397278i	0.00533415	+	0.00307967i
$130$	52.1762	−	130.026i	0.401355	−	1.00020i
$131$	−27.8733	+	16.0927i	−0.212774	+	0.122845i	−0.602600	−	0.798044i	$-0.705868\pi$
$131$	−27.8733	+	16.0927i	−0.212774	+	0.122845i	0.389826	+	0.920888i	$0.372535\pi$
$132$	−0.554289			−0.00419916
$133$	53.0217	+	60.0950i	0.398659	+	0.451842i
$134$	78.2698			0.584103
$135$	−95.9056	+	75.2960i	−0.710412	+	0.557748i
$136$	123.804	+	71.4783i	0.910324	+	0.525576i
$137$	3.92636	+	2.26688i	0.0286596	+	0.0165466i	0.514261	−	0.857634i	$-0.328066\pi$
$137$	3.92636	+	2.26688i	0.0286596	+	0.0165466i	−0.485602	+	0.874180i	$0.661399\pi$
$138$	−13.3999	−	23.2093i	−0.0971007	−	0.168183i
$139$		−	84.1243i		−	0.605211i	−0.953116	−	0.302606i	$-0.902144\pi$
$139$		−	84.1243i		−	0.605211i	0.953116	−	0.302606i	$-0.0978565\pi$
$140$	1.21658	−	0.432191i	0.00868987	−	0.00308708i
$141$	107.835			0.764786
$142$	6.05447	−	3.49555i	0.0426371	−	0.0246165i
$143$	−66.7544	+	115.622i	−0.466814	+	0.808546i
$144$	−52.7674	+	91.3959i	−0.366440	+	0.634693i
$145$	−104.935	+	82.3853i	−0.723692	+	0.568175i
$146$		−	49.5401i		−	0.339316i
$147$	−9.58136	+	76.3136i	−0.0651793	+	0.519140i
$148$			2.39238i			0.0161647i
$149$	33.5195	+	58.0575i	0.224963	+	0.389648i	0.956308	−	0.292360i	$-0.0944404\pi$
$149$	33.5195	+	58.0575i	0.224963	+	0.389648i	−0.731345	+	0.682008i	$0.761107\pi$
$150$	−76.5909	−	18.7114i	−0.510606	−	0.124743i
$151$	138.895	−	240.573i	0.919834	−	1.59320i	0.120168	−	0.992754i	$-0.461657\pi$
$151$	138.895	−	240.573i	0.919834	−	1.59320i	0.799666	−	0.600445i	$-0.205010\pi$
$152$	−45.5817	−	78.9498i	−0.299880	−	0.519407i
$153$	117.347			0.766971
$154$	−131.973	+	26.6630i	−0.856970	+	0.173137i
$155$	10.6968	−	1.52917i	0.0690115	−	0.00986563i
$156$	0.403749	+	0.699313i	0.00258813	+	0.00448278i
$157$	−117.857	+	204.134i	−0.750679	+	1.30021i	0.196815	+	0.980441i	$0.436940\pi$
$157$	−117.857	+	204.134i	−0.750679	+	1.30021i	−0.947494	+	0.319773i	$0.896393\pi$
$158$	−239.716	−	138.400i	−1.51719	−	0.875951i
$159$	−74.8792	+	43.2315i	−0.470938	+	0.271896i
$160$	−2.92122	+	0.417607i	−0.0182576	+	0.00261005i
$161$	−39.3549	−	44.6050i	−0.244440	−	0.277050i
$162$			41.2848i			0.254844i
$163$	−91.0392	+	52.5615i	−0.558523	+	0.322463i	−0.752552	−	0.658532i	$-0.771178\pi$
$163$	−91.0392	+	52.5615i	−0.558523	+	0.322463i	0.194030	+	0.980996i	$0.437844\pi$
$164$	0.745188	+	0.430234i	0.00454383	+	0.00262338i
$165$	69.7275	+	27.9799i	0.422591	+	0.169575i
$166$	−191.476	+	110.549i	−1.15347	+	0.665956i
$167$	31.9767			0.191477			0.0957386	−	0.995407i	$-0.469479\pi$
$167$	31.9767			0.191477			0.0957386	+	0.995407i	$0.469479\pi$
$168$	27.8741	−	82.9312i	0.165917	−	0.493638i
$169$	25.4980			0.150875
$170$	111.376	+	141.861i	0.655155	+	0.834479i
$171$	−64.8063	−	37.4160i	−0.378984	−	0.218807i
$172$	0.0161709	+	0.00933628i	9.40170e−5	+	5.42807e-5i
$173$	105.801	+	183.254i	0.611569	+	1.05927i	0.990976	+	0.134039i	$0.0427948\pi$
$173$	105.801	+	183.254i	0.611569	+	1.05927i	−0.379407	+	0.925230i	$0.623872\pi$
$174$		−	84.1493i		−	0.483616i
$175$	−174.858	−	7.04367i	−0.999190	−	0.0402496i
$176$	154.569			0.878233
$177$	85.6637	−	49.4579i	0.483976	−	0.279423i
$178$	97.4661	−	168.816i	0.547562	−	0.948406i
$179$	0.746283	−	1.29260i	0.00416918	−	0.00722123i	−0.863933	−	0.503606i	$-0.832006\pi$
$179$	0.746283	−	1.29260i	0.00416918	−	0.00722123i	0.868102	+	0.496385i	$0.165340\pi$
$180$	−0.948209	+	0.744445i	−0.00526783	+	0.00413580i
$181$		−	67.8351i		−	0.374780i	−0.982286	−	0.187390i	$-0.939997\pi$
$181$		−	67.8351i		−	0.374780i	0.982286	−	0.187390i	$-0.0600027\pi$
$182$	129.770	+	147.081i	0.713021	+	0.808140i
$183$		−	79.6232i		−	0.435099i
$184$	33.8326	+	58.5999i	0.183873	+	0.318477i
$185$	120.765	−	300.953i	0.652782	−	1.62677i
$186$	−3.40778	+	5.90245i	−0.0183214	+	0.0317336i
$187$	−85.9343	−	148.843i	−0.459542	−	0.795950i
$188$	2.53419			0.0134797
$189$	−33.8050	−	167.324i	−0.178862	−	0.885311i
$190$	−16.2766	−	113.857i	−0.0856665	−	0.599250i
$191$	110.030	+	190.578i	0.576074	+	0.997789i	0.995924	+	0.0901956i	$0.0287492\pi$
$191$	110.030	+	190.578i	0.576074	+	0.997789i	−0.419850	+	0.907593i	$0.637917\pi$
$192$	−49.7570	+	86.1817i	−0.259151	+	0.448863i
$193$	200.514	+	115.767i	1.03893	+	0.599829i	0.919531	−	0.393017i	$-0.128569\pi$
$193$	200.514	+	115.767i	1.03893	+	0.599829i	0.119403	+	0.992846i	$0.461902\pi$
$194$	5.70767	−	3.29532i	0.0294210	−	0.0169862i
$195$	−15.4896	−	108.352i	−0.0794338	−	0.555651i
$196$	−0.225168	+	1.79342i	−0.00114882	+	0.00915009i
$197$			223.021i			1.13209i	0.824376	+	0.566043i	$0.191526\pi$
$197$			223.021i			1.13209i	−0.824376	+	0.566043i	$0.808474\pi$
$198$	108.876	−	62.8596i	0.549879	−	0.317473i
$199$	274.861	+	158.691i	1.38121	+	0.797442i	0.992303	−	0.123835i	$-0.0395192\pi$
$199$	274.861	+	158.691i	1.38121	+	0.797442i	0.388907	+	0.921277i	$0.372853\pi$
$200$	193.380	+	47.2434i	0.966900	+	0.236217i
$201$	52.9546	−	30.5734i	0.263456	−	0.152106i
$202$	−252.204			−1.24853
$203$	−36.9878	−	183.078i	−0.182206	−	0.901861i
$204$	−1.03951			−0.00509563
$205$	−72.0242	−	91.7382i	−0.351338	−	0.447503i
$206$	−29.5058	−	17.0352i	−0.143232	−	0.0826951i
$207$	48.1020	+	27.7717i	0.232377	+	0.134163i
$208$	−112.589	−	195.011i	−0.541295	−	0.937551i
$209$			109.601i			0.524405i
$210$	71.6022	−	84.0062i	0.340963	−	0.400030i
$211$	−285.102			−1.35119			−0.675597	−	0.737271i	$-0.736114\pi$
$211$	−285.102			−1.35119			−0.675597	+	0.737271i	$0.736114\pi$
$212$	−1.75971	+	1.01597i	−0.00830051	+	0.00479230i
$213$	2.73083	−	4.72993i	0.0128208	−	0.0222062i
$214$	128.887	−	223.239i	0.602276	−	1.04317i
$215$	−1.56296	−	1.99076i	−0.00726957	−	0.00925935i
$216$			194.181i			0.898986i
$217$	−4.81965	+	14.3394i	−0.0222104	+	0.0660804i
$218$			174.176i			0.798972i
$219$	−19.3511	−	33.5171i	−0.0883612	−	0.153046i
$220$	1.63864	+	0.657545i	0.00744837	+	0.00298884i
$221$	−125.191	+	216.837i	−0.566474	+	0.981161i
$222$	102.269	+	177.135i	0.460671	+	0.797905i
$223$	−170.216			−0.763302			−0.381651	−	0.924306i	$-0.624644\pi$
$223$	−170.216			−0.763302			−0.381651	+	0.924306i	$0.624644\pi$
$224$	1.31622	−	3.91601i	0.00587597	−	0.0174822i
$225$	156.860	−	45.7839i	0.697156	−	0.203484i
$226$	−102.645	−	177.786i	−0.454181	−	0.786664i
$227$	−57.9243	+	100.328i	−0.255173	+	0.441973i	−0.964942	−	0.262461i	$-0.915466\pi$
$227$	−57.9243	+	100.328i	−0.255173	+	0.441973i	0.709770	+	0.704434i	$0.248799\pi$
$228$	0.574084	+	0.331447i	0.00251791	+	0.00145372i
$229$	4.58879	−	2.64934i	0.0200384	−	0.0115692i	−0.489947	−	0.871752i	$-0.662984\pi$
$229$	4.58879	−	2.64934i	0.0200384	−	0.0115692i	0.509986	+	0.860183i	$0.329651\pi$
$230$	12.0812	+	84.5097i	0.0525269	+	0.367433i
$231$	−78.8736	+	69.5900i	−0.341444	+	0.301256i
$232$			212.464i			0.915791i
$233$	64.0256	−	36.9652i	0.274788	−	0.158649i	−0.356274	−	0.934382i	$-0.615953\pi$
$233$	64.0256	−	36.9652i	0.274788	−	0.158649i	0.631061	+	0.775733i	$0.282620\pi$
$234$	−158.612	−	91.5749i	−0.677831	−	0.391346i
$235$	−318.792	−	127.923i	−1.35656	−	0.544353i
$236$	2.01315	−	1.16229i	0.00853030	−	0.00492497i
$237$	−216.245			−0.912425
$238$	−247.502	+	50.0036i	−1.03992	+	0.210099i
$239$	−173.685			−0.726714			−0.363357	−	0.931650i	$-0.618369\pi$
$239$	−173.685			−0.726714			−0.363357	+	0.931650i	$0.618369\pi$
$240$	−99.6710	+	78.2523i	−0.415296	+	0.326051i
$241$	−19.0515	−	10.9994i	−0.0790519	−	0.0456407i	0.459953	−	0.887943i	$-0.347866\pi$
$241$	−19.0515	−	10.9994i	−0.0790519	−	0.0456407i	−0.539005	+	0.842303i	$0.681200\pi$
$242$	51.0797	+	29.4909i	0.211073	+	0.121863i
$243$	125.865	+	218.005i	0.517963	+	0.897139i
$244$		−	1.87120i		−	0.00766883i
$245$	118.855	−	214.239i	0.485123	−	0.874446i
$246$	73.5663			0.299050
$247$	138.277	−	79.8341i	0.559825	−	0.323215i
$248$	8.60411	−	14.9028i	0.0346940	−	0.0600918i
$249$	−86.3639	+	149.587i	−0.346843	+	0.600749i
$250$	204.228	+	146.175i	0.816913	+	0.584701i
$251$		−	284.081i		−	1.13180i	−0.824475	−	0.565899i	$-0.808529\pi$
$251$		−	284.081i		−	1.13180i	0.824475	−	0.565899i	$-0.191471\pi$
$252$	−0.334227	−	1.65432i	−0.00132630	−	0.00656474i
$253$		−	81.3502i		−	0.321542i
$254$	−88.9621	−	154.087i	−0.350245	−	0.606641i
$255$	130.766	+	52.4732i	0.512810	+	0.205777i
$256$	−3.54092	+	6.13305i	−0.0138317	+	0.0239572i
$257$	−135.300	−	234.347i	−0.526459	−	0.911854i	−0.999525	−	0.0308270i	$-0.990186\pi$
$257$	−135.300	−	234.347i	−0.526459	−	0.911854i	0.473065	−	0.881027i	$-0.343147\pi$
$258$	1.59642			0.00618768
$259$	300.359	+	340.428i	1.15969	+	1.31439i
$260$	−0.364015	−	2.54634i	−0.00140006	−	0.00979361i
$261$	87.2008	+	151.036i	0.334103	+	0.578683i
$262$	−32.3334	+	56.0032i	−0.123410	+	0.213752i
$263$	87.6242	+	50.5898i	0.333172	+	0.192357i	0.657248	−	0.753674i	$-0.271720\pi$
$263$	87.6242	+	50.5898i	0.333172	+	0.192357i	−0.324077	+	0.946031i	$0.605054\pi$
$264$	103.620	−	59.8252i	0.392501	−	0.226611i
$265$	272.650	−	38.9770i	1.02887	−	0.147083i
$266$	152.630	+	51.3008i	0.573798	+	0.192860i
$267$		−	152.287i		−	0.570363i
$268$	1.24447	−	0.718493i	0.00464353	−	0.00268095i
$269$	−212.116	−	122.465i	−0.788535	−	0.455261i	0.0509113	−	0.998703i	$-0.483787\pi$
$269$	−212.116	−	122.465i	−0.788535	−	0.455261i	−0.839447	+	0.543442i	$0.817121\pi$
$270$	−91.2351	+	227.363i	−0.337908	+	0.842086i
$271$	290.437	−	167.684i	1.07172	−	0.618759i	0.143070	−	0.989713i	$-0.454303\pi$
$271$	290.437	−	167.684i	1.07172	−	0.618759i	0.928651	+	0.370954i	$0.120969\pi$
$272$	289.877			1.06573
$273$	145.250	+	48.8202i	0.532051	+	0.178828i
$274$	9.10925			0.0332454
$275$	−172.943	−	165.434i	−0.628884	−	0.601577i
$276$	−0.426109	−	0.246014i	−0.00154387	−	0.000891355i
$277$	−267.951	−	154.701i	−0.967330	−	0.558488i	−0.0689091	−	0.997623i	$-0.521952\pi$
$277$	−267.951	−	154.701i	−0.967330	−	0.558488i	−0.898421	+	0.439134i	$0.855285\pi$
$278$	−84.5113	−	146.378i	−0.303998	−	0.526539i
$279$		−	14.1254i		−	0.0506288i
$280$	−180.784	+	212.102i	−0.645658	+	0.757509i
$281$	88.5772			0.315221			0.157611	−	0.987501i	$-0.449621\pi$
$281$	88.5772			0.315221			0.157611	+	0.987501i	$0.449621\pi$
$282$	187.635	−	108.331i	0.665371	−	0.384152i
$283$	86.8005	−	150.343i	0.306716	−	0.531247i	−0.670926	−	0.741524i	$-0.734103\pi$
$283$	86.8005	−	150.343i	0.306716	−	0.531247i	0.977642	+	0.210277i	$0.0674366\pi$
$284$	0.0641761	−	0.111156i	0.000225972	−	0.000391395i
$285$	−55.4866	−	70.6740i	−0.194690	−	0.247979i
$286$			268.246i			0.937923i
$287$	160.053	−	32.3361i	0.557676	−	0.112669i
$288$			3.85757i			0.0133943i
$289$	−16.6606	−	28.8570i	−0.0576491	−	0.0998511i
$290$	−99.8251	+	248.770i	−0.344224	+	0.857828i
$291$	2.57441	−	4.45900i	0.00884675	−	0.0153230i
$292$	−0.454763	−	0.787673i	−0.00155741	−	0.00269751i
$293$	−64.7124			−0.220861			−0.110431	−	0.993884i	$-0.535223\pi$
$293$	−64.7124			−0.220861			−0.110431	+	0.993884i	$0.535223\pi$
$294$	59.9929	+	142.413i	0.204058	+	0.484396i
$295$	−311.918	+	44.5907i	−1.05735	+	0.151155i
$296$	−258.213	−	447.238i	−0.872341	−	1.51094i
$297$	116.726	−	202.176i	0.393019	−	0.680728i
$298$	116.649	+	67.3475i	0.391440	+	0.225998i
$299$	−102.635	+	59.2562i	−0.343260	+	0.198181i
$300$	−1.38954	+	0.405575i	−0.00463179	+	0.00135192i
$301$	3.47323	−	0.701708i	0.0115390	−	0.00233125i
$302$		−	558.135i		−	1.84813i
$303$	−170.632	+	98.5145i	−0.563143	+	0.325131i
$304$	−160.089	−	92.4275i	−0.526609	−	0.304038i
$305$	−94.4559	+	235.390i	−0.309691	+	0.771769i
$306$	204.185	−	117.886i	0.667272	−	0.385250i
$307$	540.515			1.76064			0.880318	−	0.474385i	$-0.157329\pi$
$307$	540.515			1.76064			0.880318	+	0.474385i	$0.157329\pi$
$308$	−1.85358	+	1.63541i	−0.00601811	+	0.00530977i
$309$	−26.6168			−0.0861385
$310$	17.0764	−	13.4068i	0.0550852	−	0.0432477i
$311$	58.5588	+	33.8090i	0.188292	+	0.108710i	0.591183	−	0.806538i	$-0.298661\pi$
$311$	58.5588	+	33.8090i	0.188292	+	0.108710i	−0.402891	+	0.915248i	$0.631995\pi$
$312$	−150.956	−	87.1544i	−0.483833	−	0.279341i
$313$	110.657	+	191.663i	0.353536	+	0.612342i	0.986866	−	0.161539i	$-0.0516459\pi$
$313$	110.657	+	191.663i	0.353536	+	0.612342i	−0.633330	+	0.773882i	$0.718313\pi$
$314$			473.595i			1.50826i
$315$	−41.4635	+	224.978i	−0.131630	+	0.714217i
$316$	−5.08189			−0.0160819
$317$	−392.890	+	226.835i	−1.23940	+	0.715568i	−0.968972	−	0.247172i	$-0.920499\pi$
$317$	−392.890	+	226.835i	−1.23940	+	0.715568i	−0.270428	+	0.962740i	$0.587165\pi$
$318$	−86.8608	+	150.447i	−0.273147	+	0.473105i
$319$	127.717	−	221.212i	0.400365	−	0.693453i
$320$	249.332	−	195.752i	0.779164	−	0.611726i
$321$		−	201.381i		−	0.627354i
$322$	−113.288	−	38.0776i	−0.351828	−	0.118253i
$323$			205.544i			0.636360i
$324$	0.378982	+	0.656416i	0.00116970	+	0.00202598i
$325$	−82.7446	+	338.695i	−0.254599	+	1.04214i
$326$	−105.607	+	182.916i	−0.323947	+	0.561092i
$327$	68.0357	+	117.841i	0.208060	+	0.360371i
$328$	−185.743			−0.566291
$329$	360.607	−	318.163i	1.09607	−	0.967060i
$330$	149.436	−	21.3628i	0.452836	−	0.0647357i
$331$	12.2236	+	21.1720i	0.0369294	+	0.0639636i	0.883899	−	0.467677i	$-0.154909\pi$
$331$	12.2236	+	21.1720i	0.0369294	+	0.0639636i	−0.846970	+	0.531641i	$0.821576\pi$
$332$	−2.02961	+	3.51538i	−0.00611327	+	0.0105885i
$333$	−367.117	−	211.955i	−1.10245	−	0.636502i
$334$	55.6400	−	32.1238i	0.166587	−	0.0961790i
$335$	−192.818	+	27.5646i	−0.575577	+	0.0822823i
$336$	−35.1322	−	173.893i	−0.104560	−	0.517540i
$337$		−	135.815i		−	0.403010i	−0.979487	−	0.201505i	$-0.935417\pi$
$337$		−	135.815i		−	0.403010i	0.979487	−	0.201505i	$-0.0645833\pi$
$338$	44.3669	−	25.6153i	0.131263	−	0.0757848i
$339$	−138.892	−	80.1892i	−0.409710	−	0.236546i
$340$	3.07310	+	1.23315i	0.00903851	+	0.00362693i
$341$	−17.9167	+	10.3442i	−0.0525418	+	0.0303350i
$342$	−150.352			−0.439627
$343$	193.120	+	283.467i	0.563032	+	0.826435i
$344$	−4.03072			−0.0117172
$345$	41.1845	+	52.4572i	0.119375	+	0.152050i
$346$	368.193	+	212.576i	1.06414	+	0.614383i
$347$	234.838	+	135.584i	0.676767	+	0.390731i	0.798636	−	0.601815i	$-0.205555\pi$
$347$	234.838	+	135.584i	0.676767	+	0.390731i	−0.121869	+	0.992546i	$0.538889\pi$
$348$	−0.772465	−	1.33795i	−0.00221973	−	0.00384468i
$349$			164.935i			0.472595i	0.971681	+	0.236297i	$0.0759339\pi$
$349$			164.935i			0.472595i	−0.971681	+	0.236297i	$0.924066\pi$
$350$	−311.333	+	163.406i	−0.889522	+	0.466876i
$351$	−340.098			−0.968941
$352$	4.89295	−	2.82495i	0.0139004	−	0.00802542i
$353$	−50.3135	+	87.1456i	−0.142531	+	0.246871i	−0.928449	−	0.371459i	$-0.878857\pi$
$353$	−50.3135	+	87.1456i	−0.142531	+	0.246871i	0.785918	+	0.618331i	$0.212191\pi$
$354$	99.3709	−	172.116i	0.280709	−	0.486202i
$355$	−13.6842	+	10.7435i	−0.0385470	+	0.0302635i
$356$		−	3.57884i		−	0.0100529i
$357$	−147.919	+	130.509i	−0.414339	+	0.365570i
$358$		−	2.99887i		−	0.00837672i
$359$	62.9543	+	109.040i	0.175360	+	0.303733i	0.940286	−	0.340386i	$-0.110558\pi$
$359$	62.9543	+	109.040i	0.175360	+	0.303733i	−0.764926	+	0.644119i	$0.777224\pi$
$360$	96.9119	−	241.510i	0.269200	−	0.670862i
$361$	−114.962	+	199.120i	−0.318455	+	0.551580i
$362$	−68.1472	−	118.034i	−0.188252	−	0.326062i
$363$	46.0783			0.126938
$364$	3.41346	+	1.14730i	0.00937765	+	0.00315194i
$365$	17.4467	+	122.042i	0.0477993	+	0.334363i
$366$	−79.9895	−	138.546i	−0.218550	−	0.378541i
$367$	249.172	−	431.578i	0.678942	−	1.17596i	−0.296358	−	0.955077i	$-0.595772\pi$
$367$	249.172	−	431.578i	0.678942	−	1.17596i	0.975300	−	0.220885i	$-0.0708945\pi$
$368$	118.825	+	68.6035i	0.322893	+	0.186423i
$369$	−132.041	+	76.2341i	−0.357836	+	0.206596i
$370$	−92.2044	−	644.983i	−0.249201	−	1.74320i
$371$	−122.848	+	365.498i	−0.331127	+	0.985169i
$372$			0.125130i			0.000336370i
$373$	219.874	−	126.944i	0.589473	−	0.340333i	−0.175416	−	0.984494i	$-0.556127\pi$
$373$	219.874	−	126.944i	0.589473	−	0.340333i	0.764889	+	0.644162i	$0.222794\pi$
$374$	−299.055	−	172.659i	−0.799612	−	0.461656i
$375$	195.272	+	19.1225i	0.520725	+	0.0509932i
$376$	−473.748	+	273.518i	−1.25997	+	0.727443i
$377$	−372.119			−0.987054
$378$	−226.915	−	257.186i	−0.600304	−	0.680387i
$379$	−132.243			−0.348926			−0.174463	−	0.984664i	$-0.555819\pi$
$379$	−132.243			−0.348926			−0.174463	+	0.984664i	$0.555819\pi$
$380$	−1.30397	−	1.66088i	−0.00343150	−	0.00437075i
$381$	−120.377	−	69.4998i	−0.315951	−	0.182414i
$382$	382.909	+	221.073i	1.00238	+	0.578724i
$383$	−225.067	−	389.827i	−0.587642	−	1.01783i	−0.994540	−	0.104352i	$-0.966723\pi$
$383$	−225.067	−	389.827i	−0.587642	−	1.01783i	0.406899	−	0.913473i	$-0.366610\pi$
$384$			203.649i			0.530336i
$385$	315.727	−	112.162i	0.820071	−	0.291330i
$386$	465.198			1.20518
$387$	−2.86536	+	1.65432i	−0.00740403	+	0.00427472i
$388$	0.0605002	−	0.104789i	0.000155928	−	0.000270076i
$389$	162.154	−	280.859i	0.416849	−	0.722004i	−0.578771	−	0.815490i	$-0.696468\pi$
$389$	162.154	−	280.859i	0.416849	−	0.722004i	0.995621	+	0.0934859i	$0.0298010\pi$
$390$	−135.803	−	172.974i	−0.348212	−	0.443522i
$391$		−	152.563i		−	0.390188i
$392$	−151.473	−	359.569i	−0.386410	−	0.917268i
$393$			50.5197i			0.128549i
$394$	224.047	+	388.061i	0.568647	+	0.984925i
$395$	639.283	+	256.528i	1.61844	+	0.649438i
$396$	1.15406	−	1.99890i	0.00291430	−	0.00504772i
$397$	287.389	+	497.772i	0.723902	+	1.25383i	0.959424	+	0.281966i	$0.0909866\pi$
$397$	287.389	+	497.772i	0.723902	+	1.25383i	−0.235522	+	0.971869i	$0.575680\pi$
$398$	637.684			1.60222
$399$	123.303	−	24.9113i	0.309030	−	0.0624344i
$400$	387.487	−	113.099i	0.968716	−	0.282747i
$401$	262.640	+	454.906i	0.654963	+	1.13443i	0.981903	+	0.189384i	$0.0606492\pi$
$401$	262.640	+	454.906i	0.654963	+	1.13443i	−0.326940	+	0.945045i	$0.606017\pi$
$402$	61.4280	−	106.396i	0.152806	−	0.264668i
$403$	26.1014	+	15.0697i	0.0647678	+	0.0373937i
$404$	−4.00997	+	2.31515i	−0.00992566	+	0.00573058i
$405$	−14.5394	−	101.705i	−0.0358998	−	0.251124i
$406$	−248.279	−	281.401i	−0.611526	−	0.693105i
$407$			620.870i			1.52548i
$408$	194.329	−	112.196i	0.476296	−	0.274989i
$409$	−368.098	−	212.522i	−0.899995	−	0.519613i	−0.0227968	−	0.999740i	$-0.507257\pi$
$409$	−368.098	−	212.522i	−0.899995	−	0.519613i	−0.877199	+	0.480127i	$0.840590\pi$
$410$	−217.484	−	87.2707i	−0.530448	−	0.212855i
$411$	6.16300	−	3.55821i	0.0149951	−	0.00865744i
$412$	−0.625511			−0.00151823
$413$	140.541	−	418.138i	0.340293	−	1.01244i
$414$	111.598			0.269560
$415$	432.770	−	339.770i	1.04282	−	0.818723i
$416$	−7.12814	−	4.11543i	−0.0171349	−	0.00989286i
$417$	−114.355	−	66.0228i	−0.274232	−	0.158328i
$418$	110.105	+	190.707i	0.263409	+	0.456238i
$419$		−	134.022i		−	0.319861i	−0.987128	−	0.159930i	$-0.948873\pi$
$419$		−	134.022i		−	0.319861i	0.987128	−	0.159930i	$-0.0511270\pi$
$420$	0.367302	−	1.99296i	0.000874529	−	0.00474514i
$421$	41.0706			0.0975548			0.0487774	−	0.998810i	$-0.484468\pi$
$421$	41.0706			0.0975548			0.0487774	+	0.998810i	$0.484468\pi$
$422$	−496.083	+	286.414i	−1.17555	+	0.678705i
$423$	−224.519	+	388.878i	−0.530777	+	0.919333i
$424$	219.310	−	379.856i	0.517240	−	0.895887i
$425$	−324.336	−	310.253i	−0.763144	−	0.730007i
$426$		−	10.9736i		−	0.0257595i
$427$	−234.925	−	266.265i	−0.550177	−	0.623572i
$428$		−	4.73257i		−	0.0110574i
$429$	104.781	+	181.486i	0.244244	+	0.423044i
$430$	−4.71950	−	1.89381i	−0.0109756	−	0.00440422i
$431$	140.380	−	243.145i	0.325708	−	0.564142i	−0.655948	−	0.754806i	$-0.727731\pi$
$431$	140.380	−	243.145i	0.325708	−	0.564142i	0.981655	+	0.190664i	$0.0610641\pi$
$432$	196.873	+	340.995i	0.455726	+	0.789340i
$433$	−671.507			−1.55082			−0.775412	−	0.631456i	$-0.782458\pi$
$433$	−671.507			−1.55082			−0.775412	+	0.631456i	$0.782458\pi$
$434$	6.01912	+	29.7927i	0.0138689	+	0.0686468i
$435$	29.6352	+	207.302i	0.0681268	+	0.476557i
$436$	1.59888	+	2.76934i	0.00366716	+	0.00635171i
$437$	−48.6449	+	84.2554i	−0.111316	+	0.192804i
$438$	−67.3426	−	38.8803i	−0.153750	−	0.0887677i
$439$	−560.999	+	323.893i	−1.27790	+	0.737797i	−0.976462	−	0.215688i	$-0.930800\pi$
$439$	−560.999	+	323.893i	−1.27790	+	0.737797i	−0.301439	+	0.953485i	$0.597467\pi$
$440$	−377.302	+	53.9377i	−0.857505	+	0.122586i
$441$	−255.256	−	193.442i	−0.578812	−	0.438645i
$442$			503.066i			1.13816i
$443$	152.032	−	87.7754i	0.343186	−	0.198139i	−0.318494	−	0.947925i	$-0.603177\pi$
$443$	152.032	−	87.7754i	0.343186	−	0.198139i	0.661680	+	0.749786i	$0.269844\pi$
$444$	3.25209	+	1.87759i	0.00732453	+	0.00422882i
$445$	−180.656	+	450.205i	−0.405968	+	1.01170i
$446$	−296.180	+	170.999i	−0.664080	+	0.383407i
$447$	105.228			0.235409
$448$	87.8852	+	435.004i	0.196172	+	0.970990i
$449$	−10.6253			−0.0236644			−0.0118322	−	0.999930i	$-0.503766\pi$
$449$	−10.6253			−0.0236644			−0.0118322	+	0.999930i	$0.503766\pi$
$450$	226.945	−	237.247i	0.504322	−	0.527215i
$451$	193.391	+	111.654i	0.428805	+	0.247571i
$452$	−3.26404	−	1.88450i	−0.00722134	−	0.00416924i
$453$	−218.016	−	377.615i	−0.481272	−	0.833587i
$454$			232.763i			0.512694i
$455$	−371.487	−	316.635i	−0.816455	−	0.695900i
$456$	−143.094			−0.313804
$457$	−288.743	+	166.706i	−0.631823	+	0.364783i	−0.781458	−	0.623958i	$-0.785524\pi$
$457$	−288.743	+	166.706i	−0.631823	+	0.364783i	0.149635	+	0.988741i	$0.452190\pi$
$458$	5.32306	−	9.21981i	0.0116224	−	0.0201306i
$459$	218.908	−	379.160i	0.476924	−	0.826056i
$460$	0.967861	+	1.23278i	0.00210405	+	0.00267995i
$461$		−	471.684i		−	1.02318i	−0.859231	−	0.511588i	$-0.829057\pi$
$461$		−	471.684i		−	1.02318i	0.859231	−	0.511588i	$-0.170943\pi$
$462$	−67.3314	+	200.324i	−0.145739	+	0.433603i
$463$		−	591.077i		−	1.27662i	−0.769778	−	0.638312i	$-0.779633\pi$
$463$		−	591.077i		−	1.27662i	0.769778	−	0.638312i	$-0.220367\pi$
$464$	215.410	+	373.100i	0.464245	+	0.804095i
$465$	6.31640	−	15.7409i	0.0135837	−	0.0338513i
$466$	74.2705	−	128.640i	0.159379	−	0.276052i
$467$	243.205	+	421.244i	0.520782	+	0.902021i	0.999708	+	0.0241656i	$0.00769291\pi$
$467$	243.205	+	421.244i	0.520782	+	0.902021i	−0.478926	+	0.877855i	$0.658974\pi$
$468$	−3.36252			−0.00718487
$469$	86.8782	−	258.480i	0.185241	−	0.551130i
$470$	−683.215	+	97.6698i	−1.45365	+	0.207808i
$471$	184.993	+	320.418i	0.392767	+	0.680292i
$472$	−250.896	+	434.565i	−0.531559	+	0.920688i
$473$	4.19668	+	2.42295i	0.00887246	+	0.00512252i
$474$	−376.270	+	217.240i	−0.793819	+	0.458311i
$475$	80.1952	+	274.756i	0.168832	+	0.578434i
$476$	−3.47619	+	3.06703i	−0.00730292	+	0.00644335i
$477$		−	360.043i		−	0.754807i
$478$	−302.214	+	174.484i	−0.632248	+	0.365028i
$479$	234.724	+	135.518i	0.490030	+	0.282919i	0.724587	−	0.689184i	$-0.242031\pi$
$479$	234.724	+	135.518i	0.490030	+	0.282919i	−0.234557	+	0.972102i	$0.575364\pi$
$480$	−1.72497	+	4.29873i	−0.00359369	+	0.00895568i
$481$	783.315	−	452.247i	1.62851	−	0.940222i
$482$	−44.2000			−0.0917012
$483$	−91.5206	+	18.4902i	−0.189484	+	0.0382820i
$484$	1.08287			0.00223733
$485$	−12.9004	+	10.1281i	−0.0265987	+	0.0208828i
$486$	438.015	+	252.888i	0.901266	+	0.520346i
$487$	−187.961	−	108.519i	−0.385956	−	0.222832i	0.294450	−	0.955667i	$-0.404863\pi$
$487$	−187.961	−	108.519i	−0.385956	−	0.222832i	−0.680407	+	0.732835i	$0.738197\pi$
$488$	201.961	+	349.806i	0.413854	+	0.716816i
$489$			165.006i			0.337436i
$490$	−8.41480	−	492.182i	−0.0171731	−	1.00445i
$491$	159.467			0.324780			0.162390	−	0.986727i	$-0.448080\pi$
$491$	159.467			0.324780			0.162390	+	0.986727i	$0.448080\pi$
$492$	1.16968	−	0.675316i	0.00237740	−	0.00137259i
$493$	239.519	−	414.858i	0.485839	−	0.841498i
$494$	160.403	−	277.826i	0.324702	−	0.562400i
$495$	−246.079	+	193.198i	−0.497130	+	0.390300i
$496$		−	34.8936i		−	0.0703501i
$497$	−4.82343	−	23.8744i	−0.00970508	−	0.0480370i
$498$			347.045i			0.696877i
$499$	−234.928	−	406.908i	−0.470798	−	0.815447i	0.528644	−	0.848844i	$-0.322701\pi$
$499$	−234.928	−	406.908i	−0.470798	−	0.815447i	−0.999442	+	0.0333970i	$0.989367\pi$
$500$	4.58901	+	0.449390i	0.00917802	+	0.000898780i
$501$	25.0961	−	43.4677i	0.0500919	−	0.0867618i
$502$	−285.388	−	494.307i	−0.568502	−	0.984674i
$503$	725.189			1.44173			0.720864	−	0.693077i	$-0.243745\pi$
$503$	725.189			1.44173			0.720864	+	0.693077i	$0.243745\pi$
$504$	241.034	+	273.189i	0.478242	+	0.542041i
$505$	621.306	−	88.8196i	1.23031	−	0.175880i
$506$	−81.7244	−	141.551i	−0.161511	−	0.279745i
$507$	20.0114	−	34.6608i	0.0394702	−	0.0683644i
$508$	−2.82894	−	1.63329i	−0.00556878	−	0.00321514i
$509$	30.1941	−	17.4326i	0.0593205	−	0.0342487i	−0.470046	−	0.882642i	$-0.655763\pi$
$509$	30.1941	−	17.4326i	0.0593205	−	0.0342487i	0.529367	+	0.848393i	$0.322430\pi$
$510$	280.251	−	40.0636i	0.549511	−	0.0785561i
$511$	−163.603	−	54.9887i	−0.320161	−	0.107610i
$512$		−	504.739i		−	0.985819i
$513$	−241.790	+	139.598i	−0.471326	+	0.272120i
$514$	−470.849	−	271.845i	−0.916049	−	0.528881i
$515$	78.6871	+	31.5751i	0.152790	+	0.0613109i
$516$	0.0253826	−	0.0146547i	4.91912e−5	−	2.84005e-5i
$517$	657.672			1.27209
$518$	864.625	+	290.610i	1.66916	+	0.561024i
$519$	332.142			0.639965
$520$	342.880	+	436.731i	0.659385	+	0.839867i
$521$	−711.157	−	410.587i	−1.36498	−	0.788074i	−0.374702	−	0.927145i	$-0.622255\pi$
$521$	−711.157	−	410.587i	−1.36498	−	0.788074i	−0.990282	+	0.139071i	$0.955588\pi$
$522$	303.462	+	175.204i	0.581345	+	0.335640i
$523$	−341.529	−	591.546i	−0.653019	−	1.13106i	−0.982386	−	0.186861i	$-0.940169\pi$
$523$	−341.529	−	591.546i	−0.653019	−	1.13106i	0.329367	−	0.944202i	$-0.393165\pi$
$524$			1.18724i			0.00226573i
$525$	−146.808	+	232.166i	−0.279634	+	0.442221i
$526$	203.290			0.386483
$527$	−33.6009	+	19.3995i	−0.0637589	+	0.0368112i
$528$	121.309	−	210.114i	0.229753	−	0.397943i
$529$	−228.394	+	395.590i	−0.431746	+	0.747806i
$530$	435.260	−	341.725i	0.821245	−	0.644764i
$531$			411.898i			0.775703i
$532$	2.89770	−	0.585432i	0.00544680	−	0.00110044i
$533$		−	325.320i		−	0.610357i
$534$	−152.987	−	264.982i	−0.286493	−	0.496221i
$535$	−238.895	+	595.341i	−0.446533	+	1.11279i
$536$	−155.096	+	268.634i	−0.289358	+	0.501183i
$537$	−1.17140	−	2.02893i	−0.00218138	−	0.00377826i
$538$	−492.115			−0.914711
$539$	−58.4356	+	465.428i	−0.108415	+	0.863502i
$540$	0.636516	+	4.45252i	0.00117873	+	0.00824541i
$541$	−14.6029	−	25.2930i	−0.0269924	−	0.0467523i	0.852214	−	0.523194i	$-0.175260\pi$
$541$	−14.6029	−	25.2930i	−0.0269924	−	0.0467523i	−0.879206	+	0.476442i	$0.841926\pi$
$542$	336.910	−	583.545i	0.621605	−	1.07665i
$543$	−92.2119	−	53.2386i	−0.169819	−	0.0980453i
$544$	9.17620	−	5.29788i	0.0168680	−	0.00973875i
$545$	−61.3402	−	429.083i	−0.112551	−	0.787309i
$546$	301.782	−	60.9701i	0.552715	−	0.111667i
$547$		−	281.431i		−	0.514499i	−0.966345	−	0.257250i	$-0.917184\pi$
$547$		−	281.431i		−	0.514499i	0.966345	−	0.257250i	$-0.0828163\pi$
$548$	0.144834	−	0.0836202i	0.000264296	−	0.000152592i
$549$	287.140	+	165.780i	0.523024	+	0.301968i
$550$	−467.119	−	114.119i	−0.849307	−	0.207489i
$551$	−264.555	+	152.741i	−0.480137	+	0.277207i
$552$	106.211			0.192411
$553$	−723.137	+	638.023i	−1.30766	+	1.15375i
$554$	−621.652			−1.12212
$555$	−314.322	−	400.357i	−0.566347	−	0.721363i
$556$	−2.68741	−	1.55158i	−0.00483347	−	0.00279061i
$557$	218.792	+	126.320i	0.392805	+	0.226786i	0.683375	−	0.730068i	$-0.260512\pi$
$557$	218.792	+	126.320i	0.392805	+	0.226786i	−0.290570	+	0.956854i	$0.593845\pi$
$558$	−14.1904	−	24.5785i	−0.0254309	−	0.0440476i
$559$		−	7.05960i		−	0.0126290i
$560$	−102.426	+	555.757i	−0.182903	+	0.992423i
$561$	−269.773			−0.480879
$562$	154.126	−	88.9847i	0.274245	−	0.158336i
$563$	−103.317	+	178.950i	−0.183511	+	0.317851i	−0.943074	−	0.332583i	$-0.892080\pi$
$563$	−103.317	+	178.950i	−0.183511	+	0.317851i	0.759562	+	0.650434i	$0.225413\pi$
$564$	1.98889	−	3.44486i	0.00352640	−	0.00610790i
$565$	315.478	+	401.828i	0.558368	+	0.711201i
$566$		−	348.799i		−	0.616253i
$567$	136.340	+	45.8254i	0.240458	+	0.0808208i
$568$			27.7065i			0.0487790i
$569$	−37.7191	−	65.3314i	−0.0662901	−	0.114818i	0.830975	−	0.556309i	$-0.187783\pi$
$569$	−37.7191	−	65.3314i	−0.0662901	−	0.114818i	−0.897266	+	0.441491i	$0.854450\pi$
$570$	−167.547	−	67.2323i	−0.293942	−	0.117951i
$571$	−207.870	+	360.042i	−0.364046	+	0.630547i	−0.988623	−	0.150417i	$-0.951938\pi$
$571$	−207.870	+	360.042i	−0.364046	+	0.630547i	0.624576	+	0.780964i	$0.285272\pi$
$572$	2.46242	+	4.26503i	0.00430492	+	0.00745635i
$573$	345.417			0.602822
$574$	246.011	−	217.055i	0.428590	−	0.378144i
$575$	−59.5242	−	203.936i	−0.103520	−	0.354670i
$576$	−207.194	−	358.871i	−0.359712	−	0.623040i
$577$	35.4974	−	61.4832i	0.0615206	−	0.106557i	−0.833625	−	0.552331i	$-0.813738\pi$
$577$	35.4974	−	61.4832i	0.0615206	−	0.106557i	0.895145	+	0.445775i	$0.147072\pi$
$578$	−57.9794	−	33.4744i	−0.100310	−	0.0579143i
$579$	314.737	−	181.713i	0.543587	−	0.313840i
$580$	0.696445	+	4.87173i	0.00120077	+	0.00839954i
$581$	152.544	+	755.041i	0.262553	+	1.29955i
$582$		−	10.3450i		−	0.0177749i
$583$	−456.680	+	263.664i	−0.783327	+	0.452254i
$584$	170.029	+	98.1666i	0.291146	+	0.168093i
$585$	422.993	+	169.736i	0.723065	+	0.290148i
$586$	−112.601	+	65.0101i	−0.192151	+	0.110939i
$587$	−877.306			−1.49456			−0.747279	−	0.664510i	$-0.768640\pi$
$587$	−877.306			−1.49456			−0.747279	+	0.664510i	$0.768640\pi$
$588$	2.26117	+	1.71360i	0.00384553	+	0.00291429i
$589$	24.7421			0.0420070
$590$	−497.948	+	390.942i	−0.843980	+	0.662614i
$591$	303.164	+	175.032i	0.512969	+	0.296163i
$592$	−906.878	−	523.586i	−1.53189	−	0.884436i
$593$	393.903	+	682.260i	0.664254	+	1.15052i	0.979487	+	0.201508i	$0.0645842\pi$
$593$	393.903	+	682.260i	0.664254	+	1.15052i	−0.315232	+	0.949015i	$0.602082\pi$
$594$		−	469.054i		−	0.789653i
$595$	592.112	−	210.348i	0.995147	−	0.353526i
$596$	2.47292			0.00414919
$597$	431.435	−	249.089i	0.722671	−	0.417234i
$598$	−119.058	+	206.214i	−0.199093	+	0.344839i
$599$	102.833	−	178.113i	0.171675	−	0.297350i	−0.767330	−	0.641252i	$-0.778415\pi$
$599$	102.833	−	178.113i	0.171675	−	0.297350i	0.939006	+	0.343902i	$0.111749\pi$
$600$	215.990	−	225.794i	0.359983	−	0.376324i
$601$			893.863i			1.48729i	0.668573	+	0.743647i	$0.266906\pi$
$601$			893.863i			1.48729i	−0.668573	+	0.743647i	$0.733094\pi$
$602$	5.33854	−	4.71019i	0.00886801	−	0.00782424i
$603$			254.623i			0.422260i
$604$	−5.12351	−	8.87419i	−0.00848264	−	0.0146924i
$605$	−136.221	−	54.6621i	−0.225159	−	0.0903505i
$606$	−197.936	+	342.834i	−0.326626	+	0.565733i
$607$	−256.729	−	444.668i	−0.422948	−	0.732567i	0.573279	−	0.819360i	$-0.305671\pi$
$607$	−256.729	−	444.668i	−0.422948	−	0.732567i	−0.996226	+	0.0867937i	$0.972338\pi$
$608$	−6.75692			−0.0111134
$609$	−277.896	−	93.4042i	−0.456316	−	0.153373i
$610$	72.1176	+	504.473i	0.118226	+	0.827005i
$611$	−479.054	−	829.746i	−0.784049	−	1.35801i
$612$	2.16432	−	3.74872i	0.00353647	−	0.00612535i
$613$	422.091	+	243.694i	0.688565	+	0.397543i	0.803074	−	0.595879i	$-0.203196\pi$
$613$	422.091	+	243.694i	0.688565	+	0.397543i	−0.114509	+	0.993422i	$0.536529\pi$
$614$	940.506	−	543.002i	1.53177	−	0.884367i
$615$	−181.231	+	25.9081i	−0.294685	+	0.0421270i
$616$	170.001	−	505.788i	0.275976	−	0.821084i
$617$			271.341i			0.439775i	0.975525	+	0.219888i	$0.0705690\pi$
$617$			271.341i			0.439775i	−0.975525	+	0.219888i	$0.929431\pi$
$618$	−46.3137	+	26.7392i	−0.0749413	+	0.0432674i
$619$	−450.085	−	259.857i	−0.727116	−	0.419801i	0.0902500	−	0.995919i	$-0.471233\pi$
$619$	−450.085	−	259.857i	−0.727116	−	0.419801i	−0.817366	+	0.576118i	$0.804567\pi$
$620$	0.148439	−	0.369920i	0.000239418	−	0.000596645i
$621$	179.467	−	103.615i	0.288996	−	0.166852i
$622$	135.858			0.218421
$623$	−449.317	−	509.257i	−0.721215	−	0.817428i
$624$	−353.451			−0.566428
$625$	−554.597	−	288.180i	−0.887355	−	0.461088i
$626$	385.090	+	222.332i	0.615159	+	0.355162i
$627$	148.986	+	86.0172i	0.237618	+	0.137189i
$628$	4.34746	+	7.53002i	0.00692270	+	0.0119905i
$629$			1164.37i			1.85115i
$630$	153.866	+	433.121i	0.244232	+	0.687493i
$631$	−215.996			−0.342307			−0.171153	−	0.985244i	$-0.554749\pi$
$631$	−215.996			−0.342307			−0.171153	+	0.985244i	$0.554749\pi$
$632$	950.023	−	548.496i	1.50320	−	0.867873i
$633$	−223.755	+	387.555i	−0.353483	+	0.612251i
$634$	−455.757	+	789.394i	−0.718860	+	1.24510i
$635$	273.424	+	348.264i	0.430589	+	0.548447i
$636$			3.18942i			0.00501482i
$637$	629.768	−	265.297i	0.988646	−	0.416478i
$638$		−	513.216i		−	0.804414i
$639$	11.3715	+	19.6960i	0.0177958	+	0.0308232i
$640$	241.586	−	602.047i	0.377478	−	0.940699i
$641$	81.6625	−	141.444i	0.127399	−	0.220661i	−0.795269	−	0.606256i	$-0.792671\pi$
$641$	81.6625	−	141.444i	0.127399	−	0.220661i	0.922668	+	0.385595i	$0.126004\pi$
$642$	−202.307	−	350.406i	−0.315120	−	0.545804i
$643$	−261.201			−0.406223			−0.203112	−	0.979156i	$-0.565105\pi$
$643$	−261.201			−0.406223			−0.203112	+	0.979156i	$0.565105\pi$
$644$	−2.15079	+	0.434532i	−0.00333974	+	0.000674739i
$645$	−3.93280	+	0.562218i	−0.00609736	+	0.000871656i
$646$	206.490	+	357.651i	0.319644	+	0.553639i
$647$	−198.416	+	343.667i	−0.306671	+	0.531169i	−0.977632	−	0.210323i	$-0.932548\pi$
$647$	−198.416	+	343.667i	−0.306671	+	0.531169i	0.670961	+	0.741492i	$0.265882\pi$
$648$	−141.696	−	81.8082i	−0.218666	−	0.126247i
$649$	522.453	−	301.638i	0.805012	−	0.464774i
$650$	196.276	+	672.462i	0.301964	+	1.03456i
$651$	15.7098	+	17.8056i	0.0241318	+	0.0273511i
$652$			3.87775i			0.00594746i
$653$	1034.53	−	597.284i	1.58427	−	0.914677i	0.590041	−	0.807374i	$-0.299112\pi$
$653$	1034.53	−	597.284i	1.58427	−	0.914677i	0.994226	−	0.107303i	$-0.0342216\pi$
$654$	236.767	+	136.697i	0.362029	+	0.209017i
$655$	59.9308	−	149.351i	0.0914974	−	0.228017i
$656$	−326.178	+	188.319i	−0.497222	+	0.287071i
$657$	161.161			0.245298
$658$	307.836	−	915.875i	0.467836	−	1.39191i
$659$	30.9848			0.0470179			0.0235089	−	0.999724i	$-0.492516\pi$
$659$	30.9848			0.0470179			0.0235089	+	0.999724i	$0.492516\pi$
$660$	2.17988	−	1.71144i	0.00330285	−	0.00259309i
$661$	−947.070	−	546.791i	−1.43278	−	0.827218i	−0.435451	−	0.900212i	$-0.643411\pi$
$661$	−947.070	−	546.791i	−1.43278	−	0.827218i	−0.997332	+	0.0729941i	$0.976745\pi$
$662$	42.5387	+	24.5597i	0.0642579	+	0.0370993i
$663$	196.505	+	340.357i	0.296388	+	0.513359i
$664$		−	876.233i		−	1.31963i
$665$	−394.072	−	72.6274i	−0.592590	−	0.109214i
$666$	−851.721			−1.27886
$667$	196.364	−	113.371i	0.294399	−	0.169971i
$668$	0.589773	−	1.02152i	0.000882894	−	0.00152922i
$669$	−133.590	+	231.384i	−0.199686	+	0.345866i
$670$	−307.816	+	241.668i	−0.459427	+	0.360699i
$671$		−	485.612i		−	0.723715i
$672$	−4.29025	−	4.86258i	−0.00638430	−	0.00723599i
$673$			999.088i			1.48453i	0.670107	+	0.742265i	$0.266248\pi$
$673$			999.088i			1.48453i	−0.670107	+	0.742265i	$0.733752\pi$
$674$	−136.439	−	236.320i	−0.202432	−	0.350623i
$675$	144.687	−	592.242i	0.214351	−	0.877395i
$676$	0.470281	−	0.814550i	0.000695681	−	0.00120496i
$677$	−254.346	−	440.541i	−0.375696	−	0.650725i	0.614735	−	0.788734i	$-0.289263\pi$
$677$	−254.346	−	440.541i	−0.375696	−	0.650725i	−0.990431	+	0.138009i	$0.955930\pi$
$678$	−322.232			−0.475269
$679$	−4.54714	−	22.5069i	−0.00669682	−	0.0331471i
$680$	−707.589	+	101.154i	−1.04057	+	0.148756i
$681$	90.9207	+	157.479i	0.133511	+	0.231247i
$682$	−20.7837	+	35.9983i	−0.0304746	+	0.0527835i
$683$	−216.039	−	124.730i	−0.316309	−	0.182621i	0.333437	−	0.942772i	$-0.391792\pi$
$683$	−216.039	−	124.730i	−0.316309	−	0.182621i	−0.649746	+	0.760151i	$0.725125\pi$
$684$	−2.39056	+	1.38019i	−0.00349497	+	0.00201782i
$685$	−22.4407	+	3.20804i	−0.0327601	+	0.00468327i
$686$	620.804	+	299.230i	0.904962	+	0.436196i
$687$		−	8.31706i		−	0.0121063i
$688$	−7.07820	+	4.08660i	−0.0102881	+	0.00593983i
$689$	665.299	+	384.110i	0.965600	+	0.557490i
$690$	124.360	+	49.9026i	0.180232	+	0.0723226i
$691$	1110.83	−	641.337i	1.60757	−	0.928128i	0.617653	−	0.786451i	$-0.288084\pi$
$691$	1110.83	−	641.337i	1.60757	−	0.928128i	0.989913	−	0.141677i	$-0.0452495\pi$
$692$	7.80555			0.0112797
$693$	−86.7385	−	429.328i	−0.125164	−	0.619521i
$694$	544.830			0.785058
$695$	259.745	+	330.840i	0.373733	+	0.476029i
$696$	288.813	+	166.746i	0.414962	+	0.239578i
$697$	362.684	+	209.396i	0.520350	+	0.300424i
$698$	165.694	+	286.991i	0.237384	+	0.411162i
$699$		−	116.045i		−	0.166015i
$700$	−3.45007	+	5.45605i	−0.00492868	+	0.00779436i
$701$	1114.02			1.58919			0.794596	−	0.607138i	$-0.207683\pi$
$701$	1114.02			1.58919			0.794596	+	0.607138i	$0.207683\pi$
$702$	−591.778	+	341.663i	−0.842988	+	0.486699i
$703$	371.261	−	643.043i	0.528109	−	0.914712i
$704$	−303.462	+	525.612i	−0.431054	+	0.746608i
$705$	−424.088	+	332.954i	−0.601543	+	0.472275i
$706$			202.180i			0.286374i
$707$	−279.942	+	832.884i	−0.395957	+	1.17805i
$708$		−	3.64878i		−	0.00515364i
$709$	−197.068	−	341.332i	−0.277952	−	0.481427i	0.692924	−	0.721011i	$-0.256322\pi$
$709$	−197.068	−	341.332i	−0.277952	−	0.481427i	−0.970876	+	0.239584i	$0.922989\pi$
$710$	−13.0178	+	32.4411i	−0.0183349	+	0.0456916i
$711$	450.235	−	779.830i	0.633242	−	1.09681i
$712$	386.269	+	669.038i	0.542513	+	0.939660i
$713$	−18.3646			−0.0257569
$714$	−126.273	+	375.687i	−0.176852	+	0.526172i
$715$	−94.4692	−	660.826i	−0.132125	−	0.924232i
$716$	−0.0275287	−	0.0476811i	−3.84479e−5	−	6.65937e-5i
$717$	−136.312	+	236.099i	−0.190114	+	0.329287i
$718$	219.083	+	126.488i	0.305130	+	0.176167i
$719$	−707.566	+	408.514i	−0.984098	+	0.568169i	−0.903505	−	0.428578i	$-0.859015\pi$
$719$	−707.566	+	408.514i	−0.984098	+	0.568169i	−0.0805931	+	0.996747i	$0.525681\pi$
$720$	−74.6752	−	522.364i	−0.103715	−	0.725505i
$721$	−89.0083	+	78.5319i	−0.123451	+	0.108921i
$722$			461.964i			0.639840i
$723$	−29.9042	+	17.2652i	−0.0413612	+	0.0238799i
$724$	−2.16704	−	1.25114i	−0.00299315	−	0.00172809i
$725$	158.309	−	648.002i	0.218358	−	0.893796i
$726$	80.1772	−	46.2903i	0.110437	−	0.0637608i
$727$	−984.409			−1.35407			−0.677035	−	0.735951i	$-0.736735\pi$
$727$	−984.409			−1.35407			−0.677035	+	0.735951i	$0.736735\pi$
$728$	−761.953	+	153.940i	−1.04664	+	0.211456i
$729$	210.197			0.288336
$730$	152.962	+	194.829i	0.209536	+	0.266889i
$731$	7.87041	+	4.54398i	0.0107666	+	0.00621612i
$732$	−2.54362	−	1.46856i	−0.00347489	−	0.00200623i
$733$	−142.143	−	246.199i	−0.193920	−	0.335879i	0.752626	−	0.658448i	$-0.228787\pi$
$733$	−142.143	−	246.199i	−0.193920	−	0.335879i	−0.946546	+	0.322569i	$0.895454\pi$
$734$		−	1001.27i		−	1.36413i
$735$	−197.947	−	329.706i	−0.269315	−	0.448580i
$736$	5.01527			0.00681422
$737$	322.964	−	186.463i	0.438214	−	0.253003i
$738$	−153.170	+	265.298i	−0.207547	+	0.359482i
$739$	−561.975	+	973.370i	−0.760454	+	1.31714i	0.182163	+	0.983268i	$0.441690\pi$
$739$	−561.975	+	973.370i	−0.760454	+	1.31714i	−0.942617	+	0.333876i	$0.891643\pi$
$740$	−7.38677	−	9.40863i	−0.00998213	−	0.0127144i
$741$		−	250.623i		−	0.338222i
$742$	153.421	+	759.386i	0.206767	+	1.02343i
$743$			640.618i			0.862205i	0.902303	+	0.431102i	$0.141875\pi$
$743$			640.618i			0.862205i	−0.902303	+	0.431102i	$0.858125\pi$
$744$	−13.5054	−	23.3921i	−0.0181524	−	0.0314410i
$745$	−311.084	−	124.830i	−0.417563	−	0.167557i
$746$	255.056	−	441.770i	0.341898	−	0.592185i
$747$	−359.630	−	622.897i	−0.481432	−	0.833865i
$748$	−6.33984			−0.00847572
$749$	−594.167	−	673.431i	−0.793280	−	0.899106i
$750$	358.987	−	162.897i	0.478649	−	0.217196i
$751$	279.437	+	483.998i	0.372086	+	0.644472i	0.989886	−	0.141863i	$-0.0453093\pi$
$751$	279.437	+	483.998i	0.372086	+	0.644472i	−0.617800	+	0.786335i	$0.711976\pi$
$752$	−554.622	+	960.633i	−0.737529	+	1.27744i
$753$	−386.167	−	222.954i	−0.512838	−	0.296087i
$754$	−647.495	+	373.831i	−0.858747	+	0.495798i
$755$	196.561	+	1374.97i	0.260345	+	1.82115i
$756$	−5.96877	−	2.00617i	−0.00789520	−	0.00265367i
$757$			477.300i			0.630515i	0.949006	+	0.315257i	$0.102091\pi$
$757$			477.300i			0.630515i	−0.949006	+	0.315257i	$0.897909\pi$
$758$	−230.105	+	132.851i	−0.303568	+	0.175265i
$759$	−110.584	−	63.8456i	−0.145697	−	0.0841180i
$760$	423.029	+	169.751i	0.556618	+	0.223356i
$761$	−875.580	+	505.516i	−1.15057	+	0.664279i	−0.949025	−	0.315201i	$-0.897928\pi$
$761$	−875.580	+	505.516i	−1.15057	+	0.664279i	−0.201540	+	0.979480i	$0.564595\pi$
$762$	−279.278			−0.366507
$763$	575.203	+	193.332i	0.753870	+	0.253384i
$764$	8.11751			0.0106250
$765$	−461.495	+	362.322i	−0.603261	+	0.473624i
$766$	−783.241	−	452.204i	−1.02251	−	0.590345i
$767$	−761.118	−	439.432i	−0.992332	−	0.572923i
$768$	5.55799	+	9.62673i	0.00723697	+	0.0125348i
$769$		−	58.9725i		−	0.0766873i	−0.999265	−	0.0383437i	$-0.987792\pi$
$769$		−	58.9725i		−	0.0766873i	0.999265	−	0.0383437i	$-0.0122082\pi$
$770$	436.693	−	512.344i	0.567134	−	0.665382i
$771$	−424.747			−0.550904
$772$	7.39652	−	4.27038i	0.00958098	−	0.00553158i
$773$	447.760	−	775.542i	0.579249	−	1.00329i	−0.416317	−	0.909220i	$-0.636679\pi$
$773$	447.760	−	775.542i	0.579249	−	1.00329i	0.995566	−	0.0940692i	$-0.0299875\pi$
$774$	−3.32385	+	5.75708i	−0.00429438	+	0.00743809i
$775$	−37.3463	+	39.0416i	−0.0481888	+	0.0503762i
$776$			26.1195i			0.0336591i
$777$	698.491	−	141.119i	0.898959	−	0.181620i
$778$		−	651.601i		−	0.837534i
$779$	−133.532	−	231.284i	−0.171414	−	0.296898i
$780$	−3.74706	−	1.50360i	−0.00480393	−	0.00192769i
$781$	16.6550	−	28.8473i	0.0213252	−	0.0369363i
$782$	−153.265	−	265.463i	−0.195991	−	0.339467i
$783$	650.687			0.831018
$784$	−630.551	−	477.855i	−0.804274	−	0.609508i
$785$	−166.788	−	1166.70i	−0.212468	−	1.48625i
$786$	50.7521	+	87.9052i	0.0645701	+	0.111839i
$787$	−412.883	+	715.134i	−0.524629	+	0.908684i	0.474960	+	0.880008i	$0.342463\pi$
$787$	−412.883	+	715.134i	−0.524629	+	0.908684i	−0.999589	+	0.0286766i	$0.990871\pi$
$788$	7.12456	+	4.11337i	0.00904132	+	0.00522001i
$789$	137.539	−	79.4082i	0.174321	−	0.100644i
$790$	1370.07	−	195.861i	1.73427	−	0.247925i
$791$	−701.059	+	141.637i	−0.886295	+	0.179061i
$792$			498.239i			0.629090i
$793$	−612.669	+	353.724i	−0.772596	+	0.446058i
$794$	1000.12	+	577.422i	1.25960	+	0.727232i
$795$	160.999	−	401.218i	0.202514	−	0.504677i
$796$	10.1390	−	5.85375i	0.0127374	−	0.00735395i
$797$	315.810			0.396248			0.198124	−	0.980177i	$-0.436515\pi$
$797$	315.810			0.396248			0.198124	+	0.980177i	$0.436515\pi$
$798$	189.524	−	167.216i	0.237498	−	0.209544i
$799$	1233.39			1.54367
$800$	10.1990	−	10.6620i	0.0127488	−	0.0133275i
$801$	549.182	+	317.071i	0.685621	+	0.395844i
$802$	913.998	+	527.697i	1.13965	+	0.657976i
$803$	−118.020	−	204.417i	−0.146974	−	0.254567i
$804$		−	2.25556i		−	0.00280543i
$805$	292.497	+	53.9071i	0.363350	+	0.0669653i
$806$	60.5560			0.0751315
$807$	−332.947	+	192.227i	−0.412574	+	0.238200i
$808$	499.756	−	865.603i	0.618510	−	1.07129i
$809$	407.907	−	706.515i	0.504211	−	0.873319i	−0.495777	−	0.868450i	$-0.665117\pi$
$809$	407.907	−	706.515i	0.504211	−	0.873319i	0.999988	−	0.00486950i	$-0.00155001\pi$
$810$	−127.472	−	162.363i	−0.157373	−	0.200448i
$811$			567.015i			0.699156i	0.936907	+	0.349578i	$0.113675\pi$
$811$			567.015i			0.699156i	−0.936907	+	0.349578i	$0.886325\pi$
$812$	−6.53074	−	2.19506i	−0.00804279	−	0.00270327i
$813$		−	526.408i		−	0.647489i
$814$	623.726	+	1080.33i	0.766248	+	1.32718i
$815$	195.744	−	487.807i	0.240177	−	0.598536i
$816$	227.503	−	394.046i	0.278802	−	0.482900i
$817$	−2.89770	−	5.01896i	−0.00354676	−	0.00614316i
$818$	−853.997			−1.04401
$819$	−478.476	+	422.159i	−0.584220	+	0.515457i
$820$	−4.25904	+	0.608857i	−0.00519396	+	0.000742509i
$821$	190.825	+	330.519i	0.232430	+	0.402581i	0.958523	−	0.285016i	$-0.0919989\pi$
$821$	190.825	+	330.519i	0.232430	+	0.402581i	−0.726092	+	0.687597i	$0.758666\pi$
$822$	7.14916	−	12.3827i	0.00869727	−	0.0150641i
$823$	879.787	+	507.945i	1.06900	+	0.617187i	0.927908	−	0.372809i	$-0.121605\pi$
$823$	879.787	+	507.945i	1.06900	+	0.617187i	0.141092	+	0.989997i	$0.454939\pi$
$824$	116.935	−	67.5124i	0.141911	−	0.0819325i
$825$	−360.613	+	105.255i	−0.437106	+	0.127582i
$826$	−175.518	−	868.757i	−0.212491	−	1.05176i
$827$		−	643.069i		−	0.777592i	−0.921324	−	0.388796i	$-0.872891\pi$
$827$		−	643.069i		−	0.777592i	0.921324	−	0.388796i	$-0.127109\pi$
$828$	1.77437	−	1.02443i	0.00214296	−	0.00123724i
$829$	1016.88	+	587.094i	1.22663	+	0.708196i	0.966324	−	0.257330i	$-0.0828428\pi$
$829$	1016.88	+	587.094i	1.22663	+	0.708196i	0.260307	+	0.965526i	$0.416176\pi$
$830$	411.694	−	1025.97i	0.496017	−	1.23610i
$831$	−420.588	+	242.826i	−0.506123	+	0.292210i
$832$	884.178			1.06271
$833$	−109.590	+	872.859i	−0.131560	+	1.04785i
$834$	−265.306			−0.318113
$835$	−125.756	+	98.7321i	−0.150607	+	0.118242i
$836$	3.50127	+	2.02146i	0.00418812	+	0.00241801i
$837$	−45.6409	−	26.3508i	−0.0545291	−	0.0314824i
$838$	−134.638	−	233.200i	−0.160666	−	0.278282i
$839$		−	1306.32i		−	1.55700i	−0.627647	−	0.778498i	$-0.715982\pi$
$839$		−	1306.32i		−	1.55700i	0.627647	−	0.778498i	$-0.284018\pi$
$840$	146.439	+	412.213i	0.174332	+	0.490730i
$841$	−129.050			−0.153448
$842$	71.4636	−	41.2595i	0.0848736	−	0.0490018i
$843$	69.5175	−	120.408i	0.0824644	−	0.142832i
$844$	−5.25838	+	9.10778i	−0.00623031	+	0.0107912i
$845$	−100.277	+	78.7282i	−0.118671	+	0.0931695i
$846$			902.207i			1.06644i
$847$	154.089	−	135.953i	0.181923	−	0.160511i
$848$		−	889.403i		−	1.04882i
$849$	−136.246	−	235.985i	−0.160478	−	0.277957i
$850$	−876.031	−	214.018i	−1.03062	−	0.251785i
$851$	−275.565	+	477.293i	−0.323813	+	0.560861i
$852$	−0.100734	−	0.174476i	−0.000118232	−	0.000204784i
$853$	936.388			1.09776			0.548879	−	0.835902i	$-0.315055\pi$
$853$	936.388			1.09776			0.548879	+	0.835902i	$0.315055\pi$
$854$	−676.265	−	227.300i	−0.791879	−	0.266160i
$855$	370.394	−	52.9501i	0.433209	−	0.0619300i
$856$	510.794	+	884.721i	0.596722	+	1.03355i
$857$	216.035	−	374.183i	0.252083	−	0.436620i	−0.712016	−	0.702163i	$-0.752218\pi$
$857$	216.035	−	374.183i	0.252083	−	0.436620i	0.964099	+	0.265543i	$0.0855512\pi$
$858$	364.641	+	210.526i	0.424990	+	0.245368i
$859$	991.760	−	572.593i	1.15455	−	0.666581i	0.204559	−	0.978854i	$-0.434424\pi$
$859$	991.760	−	572.593i	1.15455	−	0.666581i	0.949992	+	0.312274i	$0.101091\pi$
$860$	−0.0924232	+	0.0132125i	−0.000107469	+	1.53633e-5i
$861$	81.6573	−	242.947i	0.0948401	−	0.282168i
$862$		−	564.103i		−	0.654412i
$863$	−22.7062	+	13.1094i	−0.0263107	+	0.0151905i	−0.513098	−	0.858330i	$-0.671502\pi$
$863$	−22.7062	+	13.1094i	−0.0263107	+	0.0151905i	0.486787	+	0.873521i	$0.338169\pi$
$864$	12.4642	+	7.19623i	0.0144262	+	0.00832897i
$865$	−981.910	−	394.015i	−1.13516	−	0.455509i
$866$	−1168.43	+	674.596i	−1.34923	+	0.778979i
$867$	−52.3025			−0.0603258
$868$	0.369191	+	0.418442i	0.000425335	+	0.000482076i
$869$	−1318.85			−1.51767
$870$	259.822	+	330.938i	0.298646	+	0.380389i
$871$	−470.500	−	271.643i	−0.540183	−	0.311875i
$872$	−597.799	−	345.139i	−0.685549	−	0.395802i
$873$	10.7201	+	18.5678i	0.0122797	+	0.0212690i
$874$			195.475i			0.223655i
$875$	709.422	−	512.196i	0.810769	−	0.585367i
$876$	−1.42764			−0.00162972
$877$	204.283	−	117.943i	0.232933	−	0.134484i	−0.378991	−	0.925400i	$-0.623729\pi$
$877$	204.283	−	117.943i	0.232933	−	0.134484i	0.611925	+	0.790916i	$0.290396\pi$
$878$	−650.766	+	1127.16i	−0.741191	+	1.28378i
$879$	−50.7878	+	87.9670i	−0.0577791	+	0.100076i
$880$	−607.882	+	477.252i	−0.690775	+	0.542331i
$881$		−	960.332i		−	1.09005i	−0.838421	−	0.545024i	$-0.816521\pi$
$881$		−	960.332i		−	1.09005i	0.838421	−	0.545024i	$-0.183479\pi$
$882$	−638.482	−	80.1631i	−0.723903	−	0.0908878i
$883$			996.798i			1.12888i	0.825475	+	0.564438i	$0.190907\pi$
$883$			996.798i			1.12888i	−0.825475	+	0.564438i	$0.809093\pi$
$884$	4.61800	+	7.99860i	0.00522398	+	0.00904820i
$885$	−184.186	+	459.004i	−0.208120	+	0.518648i
$886$	176.358	−	305.462i	0.199050	−	0.344765i
$887$	462.180	+	800.519i	0.521059	+	0.902501i	0.999700	+	0.0244904i	$0.00779631\pi$
$887$	462.180	+	800.519i	0.521059	+	0.902501i	−0.478641	+	0.878011i	$0.658870\pi$
$888$	−810.606			−0.912845
$889$	−607.607	+	122.757i	−0.683472	+	0.138084i
$890$	137.932	+	964.852i	0.154979	+	1.08410i
$891$	98.3534	+	170.353i	0.110385	+	0.191193i
$892$	−3.13945	+	5.43768i	−0.00351956	+	0.00609606i
$893$	−681.159	−	393.267i	−0.762776	−	0.440389i
$894$	183.098	−	105.712i	0.204808	−	0.118246i
$895$	1.05612	+	7.38772i	0.00118002	+	0.00825444i
$896$	600.860	+	681.017i	0.670602	+	0.760063i
$897$			186.023i			0.207383i
$898$	−18.4883	+	10.6742i	−0.0205883	+	0.0118866i
$899$	−49.9381	−	28.8318i	−0.0555485	−	0.0320709i
$900$	1.43050	−	5.85544i	0.00158945	−	0.00650604i
$901$	−856.453	+	494.473i	−0.950558	+	0.548805i
$902$	448.672			0.497419
$903$	1.77200	−	5.27206i	0.00196235	−	0.00583839i
$904$	813.586			0.899985
$905$	209.450	+	266.779i	0.231436	+	0.294783i
$906$	−758.704	−	438.038i	−0.837422	−	0.483486i
$907$	−992.959	−	573.285i	−1.09477	−	0.632068i	−0.159930	−	0.987128i	$-0.551127\pi$
$907$	−992.959	−	573.285i	−1.09477	−	0.632068i	−0.934843	+	0.355061i	$0.884460\pi$
$908$	2.13669	+	3.70086i	0.00235319	+	0.00407584i
$909$		−	820.454i		−	0.902589i
$910$	−964.485	−	177.754i	−1.05987	−	0.195335i
$911$	1018.28			1.11776			0.558878	−	0.829250i	$-0.311232\pi$
$911$	1018.28			1.11776			0.558878	+	0.829250i	$0.311232\pi$
$912$	−251.283	+	145.079i	−0.275530	+	0.159077i
$913$	−526.723	+	912.311i	−0.576915	+	0.999246i
$914$	−334.946	+	580.143i	−0.366461	+	0.634729i
$915$	245.847	+	313.138i	0.268685	+	0.342228i
$916$		−	0.195456i		−	0.000213380i
$917$	149.057	+	168.941i	0.162548	+	0.184233i
$918$		−	879.660i		−	0.958235i
$919$	67.5509	+	117.002i	0.0735048	+	0.127314i	0.900435	−	0.434990i	$-0.143248\pi$
$919$	67.5509	+	117.002i	0.0735048	+	0.127314i	−0.826930	+	0.562304i	$0.809915\pi$
$920$	−313.990	−	125.996i	−0.341294	−	0.136952i
$921$	424.209	−	734.751i	0.460596	−	0.797776i
$922$	−473.854	−	820.739i	−0.513941	−	0.890173i
$923$	−48.5265			−0.0525748
$924$	0.768369	+	3.80318i	0.000831568	+	0.00411600i
$925$	454.292	+	1556.45i	0.491127	+	1.68265i
$926$	−593.796	−	1028.48i	−0.641248	−	1.11067i
$927$	55.4178	−	95.9865i	0.0597819	−	0.103545i
$928$	13.6378	+	7.87377i	0.0146959	+	0.00848467i
$929$	−237.895	+	137.349i	−0.256076	+	0.147846i	−0.622543	−	0.782585i	$-0.713901\pi$
$929$	−237.895	+	137.349i	−0.256076	+	0.147846i	0.366467	+	0.930431i	$0.380567\pi$
$930$	−4.82261	−	33.7348i	−0.00518560	−	0.0362740i
$931$	338.834	−	447.107i	0.363946	−	0.480243i
$932$		−	2.72712i		−	0.00292610i
$933$	91.9167	−	53.0681i	0.0985174	−	0.0568790i
$934$	846.363	+	488.648i	0.906171	+	0.523178i
$935$	797.529	+	320.028i	0.852973	+	0.342276i
$936$	628.599	−	362.922i	0.671580	−	0.387737i
$937$	−546.613			−0.583365			−0.291682	−	0.956515i	$-0.594215\pi$
$937$	−546.613			−0.583365			−0.291682	+	0.956515i	$0.594215\pi$
$938$	−108.500	−	537.038i	−0.115671	−	0.572535i
$939$	347.384			0.369951
$940$	−9.96633	+	7.82463i	−0.0106025	+	0.00832407i
$941$	539.855	+	311.685i	0.573703	+	0.331228i	0.758627	−	0.651525i	$-0.225870\pi$
$941$	539.855	+	311.685i	0.573703	+	0.331228i	−0.184924	+	0.982753i	$0.559204\pi$
$942$	643.783	+	371.689i	0.683422	+	0.394574i
$943$	99.1128	+	171.668i	0.105104	+	0.182045i
$944$			1017.50i			1.07786i
$945$	649.581	+	553.666i	0.687387	+	0.585890i
$946$	9.73639			0.0102922
$947$	−11.2372	+	6.48780i	−0.0118661	+	0.00685089i	−0.505921	−	0.862580i	$-0.668847\pi$
$947$	−11.2372	+	6.48780i	−0.0118661	+	0.00685089i	0.494055	+	0.869431i	$0.335514\pi$
$948$	−3.98839	+	6.90809i	−0.00420716	+	0.00728701i
$949$	−171.934	+	297.798i	−0.181174	+	0.313802i
$950$	415.561	+	397.517i	0.437433	+	0.418439i
$951$			712.102i			0.748793i
$952$	318.819	−	948.550i	0.334894	−	0.996376i
$953$			1364.86i			1.43217i	0.698014	+	0.716085i	$0.254068\pi$
$953$			1364.86i			1.43217i	−0.698014	+	0.716085i	$0.745932\pi$
$954$	−361.699	−	626.482i	−0.379140	−	0.656689i
$955$	−1021.15	−	409.763i	−1.06927	−	0.429071i
$956$	−3.20341	+	5.54847i	−0.00335085	+	0.00580384i
$957$	−200.470	−	347.224i	−0.209477	−	0.362826i
$958$	544.566			0.568441
$959$	10.1111	−	30.0826i	0.0105434	−	0.0313687i
$960$	−70.4149	−	492.562i	−0.0733488	−	0.513086i
$961$	−478.165	−	828.206i	−0.497570	−	0.861817i
$962$	908.655	−	1573.84i	0.944548	−	1.63600i
$963$	726.227	+	419.287i	0.754130	+	0.435397i
$964$	−0.702767	+	0.405743i	−0.000729011	+	0.000420895i
$965$	−1146.02	+	163.831i	−1.18758	+	0.169773i
$966$	−140.672	+	124.115i	−0.145624	+	0.128483i
$967$		−	351.163i		−	0.363147i	−0.983377	−	0.181573i	$-0.941881\pi$
$967$		−	351.163i		−	0.363147i	0.983377	−	0.181573i	$-0.0581190\pi$
$968$	−202.435	+	116.876i	−0.209127	+	0.120739i
$969$	279.408	+	161.316i	0.288346	+	0.166477i
$970$	−12.2721	+	30.5829i	−0.0126517	+	0.0315287i
$971$	889.447	−	513.522i	0.916011	−	0.528859i	0.0336509	−	0.999434i	$-0.489287\pi$
$971$	889.447	−	513.522i	0.916011	−	0.528859i	0.882360	+	0.470574i	$0.155953\pi$
$972$	9.28575			0.00955324
$973$	−577.208	+	116.615i	−0.593225	+	0.119851i
$974$	−436.074			−0.447714
$975$	395.467	+	378.295i	0.405607	+	0.387995i
$976$	709.313	+	409.522i	0.726756	+	0.419592i
$977$	946.610	+	546.526i	0.968895	+	0.559392i	0.898899	−	0.438156i	$-0.144368\pi$
$977$	946.610	+	546.526i	0.968895	+	0.559392i	0.0699956	+	0.997547i	$0.477701\pi$
$978$	165.765	+	287.114i	0.169494	+	0.293572i
$979$		−	928.779i		−	0.948702i
$980$	−4.65188	−	7.74831i	−0.00474681	−	0.00790643i
$981$	−566.618			−0.577593
$982$	277.475	−	160.201i	0.282562	−	0.163137i
$983$	102.157	−	176.941i	0.103924	−	0.180001i	−0.809374	−	0.587293i	$-0.800194\pi$
$983$	102.157	−	176.941i	0.103924	−	0.180001i	0.913298	+	0.407292i	$0.133527\pi$
$984$	−145.776	+	252.491i	−0.148146	+	0.256597i
$985$	−688.606	−	877.086i	−0.699092	−	0.890443i
$986$		−	962.482i		−	0.976148i
$987$	−149.483	−	739.894i	−0.151452	−	0.749640i
$988$		−	5.88979i		−	0.00596133i
$989$	2.15079	+	3.72528i	0.00217472	+	0.00376672i
$990$	−234.095	+	583.380i	−0.236460	+	0.589273i
$991$	−194.790	+	337.385i	−0.196559	+	0.340449i	−0.947410	−	0.320021i	$-0.896310\pi$
$991$	−194.790	+	337.385i	−0.196559	+	0.340449i	0.750852	+	0.660471i	$0.229643\pi$
$992$	−0.637726	−	1.10457i	−0.000642869	−	0.00111348i
$993$	38.3736			0.0386441
$994$	−32.3771	−	36.6963i	−0.0325725	−	0.0369178i
$995$	−1570.94	+	224.576i	−1.57883	+	0.225704i
$996$	3.18577	+	5.51791i	0.00319856	+	0.00554007i
$997$	662.752	−	1147.92i	0.664746	−	1.15137i	−0.314608	−	0.949222i	$-0.601873\pi$
$997$	662.752	−	1147.92i	0.664746	−	1.15137i	0.979354	−	0.202153i	$-0.0647937\pi$
$998$	−817.560	−	472.018i	−0.819198	−	0.472964i
$999$	−1369.70	+	790.797i	−1.37107	+	0.791589i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.3.i.a.24.5	yes	12
3.2	odd	2		315.3.bi.c.199.2		12
4.3	odd	2		560.3.br.a.129.3		12
5.2	odd	4		175.3.i.c.101.5		12
5.3	odd	4		175.3.i.c.101.2		12
5.4	even	2	inner	35.3.i.a.24.2	yes	12
7.2	even	3		245.3.i.d.19.2		12
7.3	odd	6		245.3.c.a.244.10		12
7.4	even	3		245.3.c.a.244.9		12
7.5	odd	6	inner	35.3.i.a.19.2	✓	12
7.6	odd	2		245.3.i.d.129.5		12
15.14	odd	2		315.3.bi.c.199.5		12
20.19	odd	2		560.3.br.a.129.4		12
21.5	even	6		315.3.bi.c.19.5		12
28.19	even	6		560.3.br.a.369.4		12
35.4	even	6		245.3.c.a.244.4		12
35.9	even	6		245.3.i.d.19.5		12
35.12	even	12		175.3.i.c.26.5		12
35.19	odd	6	inner	35.3.i.a.19.5	yes	12
35.24	odd	6		245.3.c.a.244.3		12
35.33	even	12		175.3.i.c.26.2		12
35.34	odd	2		245.3.i.d.129.2		12
105.89	even	6		315.3.bi.c.19.2		12
140.19	even	6		560.3.br.a.369.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.3.i.a.19.2	✓	12	7.5	odd	6	inner
35.3.i.a.19.5	yes	12	35.19	odd	6	inner
35.3.i.a.24.2	yes	12	5.4	even	2	inner
35.3.i.a.24.5	yes	12	1.1	even	1	trivial
175.3.i.c.26.2		12	35.33	even	12
175.3.i.c.26.5		12	35.12	even	12
175.3.i.c.101.2		12	5.3	odd	4
175.3.i.c.101.5		12	5.2	odd	4
245.3.c.a.244.3		12	35.24	odd	6
245.3.c.a.244.4		12	35.4	even	6
245.3.c.a.244.9		12	7.4	even	3
245.3.c.a.244.10		12	7.3	odd	6
245.3.i.d.19.2		12	7.2	even	3
245.3.i.d.19.5		12	35.9	even	6
245.3.i.d.129.2		12	35.34	odd	2
245.3.i.d.129.5		12	7.6	odd	2
315.3.bi.c.19.2		12	105.89	even	6
315.3.bi.c.19.5		12	21.5	even	6
315.3.bi.c.199.2		12	3.2	odd	2
315.3.bi.c.199.5		12	15.14	odd	2
560.3.br.a.129.3		12	4.3	odd	2
560.3.br.a.129.4		12	20.19	odd	2
560.3.br.a.369.3		12	140.19	even	6
560.3.br.a.369.4		12	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:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	35.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.74002 - 1.00460i) q^{2} +(0.784824 - 1.35935i) q^{3} +(0.0184439 - 0.0319457i) q^{4} +(-3.93275 + 3.08763i) q^{5} -3.15374i q^{6} +(-1.38623 - 6.86137i) q^{7} +7.96269i q^{8} +(3.26810 + 5.66052i) q^{9} +O(q^{10})\)	\(q+(1.74002 - 1.00460i) q^{2} +(0.784824 - 1.35935i) q^{3} +(0.0184439 - 0.0319457i) q^{4} +(-3.93275 + 3.08763i) q^{5} -3.15374i q^{6} +(-1.38623 - 6.86137i) q^{7} +7.96269i q^{8} +(3.26810 + 5.66052i) q^{9} +(-3.74123 + 9.32338i) q^{10} +(4.78655 - 8.29054i) q^{11} +(-0.0289503 - 0.0501435i) q^{12} -13.9463 q^{13} +(-9.30499 - 10.5463i) q^{14} +(1.11066 + 7.76925i) q^{15} +(8.07310 + 13.9830i) q^{16} +(8.97665 - 15.5480i) q^{17} +(11.3731 + 6.56628i) q^{18} +(-9.91497 + 5.72441i) q^{19} +(0.0261013 + 0.182582i) q^{20} +(-10.4150 - 3.50059i) q^{21} -19.2343i q^{22} +(7.35931 - 4.24890i) q^{23} +(10.8241 + 6.24931i) q^{24} +(5.93310 - 24.2858i) q^{25} +(-24.2667 + 14.0104i) q^{26} +24.3864 q^{27} +(-0.244758 - 0.0822662i) q^{28} +26.6824 q^{29} +(9.73757 + 12.4029i) q^{30} +(-1.87157 - 1.08055i) q^{31} +(0.511115 + 0.295092i) q^{32} +(-7.51319 - 13.0132i) q^{33} -36.0718i q^{34} +(26.6370 + 22.7039i) q^{35} +0.241106 q^{36} +(-56.1667 + 32.4279i) q^{37} +(-11.5015 + 19.9212i) q^{38} +(-10.9453 + 18.9579i) q^{39} +(-24.5858 - 31.3153i) q^{40} +23.3267i q^{41} +(-21.6389 + 4.37179i) q^{42} +0.506200i q^{43} +(-0.176565 - 0.305819i) q^{44} +(-30.3302 - 12.1707i) q^{45} +(8.53689 - 14.7863i) q^{46} +(34.3500 + 59.4960i) q^{47} +25.3438 q^{48} +(-45.1568 + 19.0228i) q^{49} +(-14.0738 - 48.2181i) q^{50} +(-14.0902 - 24.4049i) q^{51} +(-0.257223 + 0.445523i) q^{52} +(-47.7045 - 27.5422i) q^{53} +(42.4327 - 24.4986i) q^{54} +(6.77380 + 47.3837i) q^{55} +(54.6349 - 11.0381i) q^{56} +17.9706i q^{57} +(46.4279 - 26.8051i) q^{58} +(54.5751 + 31.5090i) q^{59} +(0.268679 + 0.107814i) q^{60} +(43.9307 - 25.3634i) q^{61} -4.34210 q^{62} +(34.3086 - 30.2704i) q^{63} -63.3990 q^{64} +(54.8472 - 43.0608i) q^{65} +(-26.1462 - 15.0955i) q^{66} +(33.7366 + 19.4779i) q^{67} +(-0.331128 - 0.573531i) q^{68} -13.3385i q^{69} +(69.1573 + 12.7457i) q^{70} +3.47954 q^{71} +(-45.0730 + 26.0229i) q^{72} +(12.3283 - 21.3533i) q^{73} +(-65.1541 + 112.850i) q^{74} +(-28.3565 - 27.1252i) q^{75} +0.422321i q^{76} +(-63.5197 - 21.3497i) q^{77} +43.9828i q^{78} +(-68.8832 - 119.309i) q^{79} +(-74.9238 - 30.0650i) q^{80} +(-10.2739 + 17.7950i) q^{81} +(23.4340 + 40.5889i) q^{82} -110.042 q^{83} +(-0.303921 + 0.268149i) q^{84} +(12.7035 + 88.8631i) q^{85} +(0.508529 + 0.880798i) q^{86} +(20.9410 - 36.2708i) q^{87} +(66.0150 + 38.1138i) q^{88} +(84.0216 - 48.5099i) q^{89} +(-65.0019 + 9.29243i) q^{90} +(19.3326 + 95.6904i) q^{91} -0.313464i q^{92} +(-2.93771 + 1.69609i) q^{93} +(119.539 + 69.0161i) q^{94} +(21.3183 - 53.1265i) q^{95} +(0.802270 - 0.463191i) q^{96} +3.28023 q^{97} +(-59.4633 + 78.4645i) q^{98} +62.5717 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{4} - 18 q^{9}+O(q^{10}) \) 12 * q + 6 * q^4 - 18 * q^9	\( 12 q + 6 q^{4} - 18 q^{9} - 54 q^{10} + 6 q^{11} - 66 q^{14} + 48 q^{15} - 6 q^{16} + 18 q^{19} + 12 q^{21} + 216 q^{24} + 18 q^{25} + 18 q^{26} + 48 q^{30} - 108 q^{31} + 222 q^{35} - 204 q^{36} - 240 q^{39} - 162 q^{40} - 42 q^{44} - 216 q^{45} + 114 q^{46} - 324 q^{49} - 192 q^{50} + 180 q^{51} + 252 q^{54} + 336 q^{56} + 396 q^{59} + 384 q^{60} - 108 q^{61} + 372 q^{64} - 54 q^{65} - 108 q^{66} + 300 q^{70} + 192 q^{71} - 594 q^{74} - 216 q^{75} - 192 q^{79} - 504 q^{80} + 294 q^{81} - 1200 q^{84} - 192 q^{85} - 384 q^{86} + 684 q^{89} - 72 q^{91} + 990 q^{94} + 288 q^{95} - 540 q^{96} + 396 q^{99}+O(q^{100}) \) 12 * q + 6 * q^4 - 18 * q^9 - 54 * q^10 + 6 * q^11 - 66 * q^14 + 48 * q^15 - 6 * q^16 + 18 * q^19 + 12 * q^21 + 216 * q^24 + 18 * q^25 + 18 * q^26 + 48 * q^30 - 108 * q^31 + 222 * q^35 - 204 * q^36 - 240 * q^39 - 162 * q^40 - 42 * q^44 - 216 * q^45 + 114 * q^46 - 324 * q^49 - 192 * q^50 + 180 * q^51 + 252 * q^54 + 336 * q^56 + 396 * q^59 + 384 * q^60 - 108 * q^61 + 372 * q^64 - 54 * q^65 - 108 * q^66 + 300 * q^70 + 192 * q^71 - 594 * q^74 - 216 * q^75 - 192 * q^79 - 504 * q^80 + 294 * q^81 - 1200 * q^84 - 192 * q^85 - 384 * q^86 + 684 * q^89 - 72 * q^91 + 990 * q^94 + 288 * q^95 - 540 * q^96 + 396 * q^99

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