LMFDB - Embedded newform 403.2.v.a.36.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(36,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 4]))

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

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

chi := DirichletCharacter("403.36");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.v (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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$70$
Relative dimension:	$35$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			36.18
Character	$\chi$	$=$	403.36
Dual form			403.2.v.a.56.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0898111 + 0.0518525i) q^{2} -0.467545 q^{3} +(-0.994623 + 1.72274i) q^{4} +(1.88817 - 1.09014i) q^{5} +(0.0419908 - 0.0242434i) q^{6} +(-2.42419 + 1.39960i) q^{7} -0.413704i q^{8} -2.78140 q^{9} +O(q^{10})$	\(q+(-0.0898111 + 0.0518525i) q^{2} -0.467545 q^{3} +(-0.994623 + 1.72274i) q^{4} +(1.88817 - 1.09014i) q^{5} +(0.0419908 - 0.0242434i) q^{6} +(-2.42419 + 1.39960i) q^{7} -0.413704i q^{8} -2.78140 q^{9} +(-0.113053 + 0.195813i) q^{10} +(2.24155 + 1.29416i) q^{11} +(0.465031 - 0.805457i) q^{12} +(-0.248332 + 3.59699i) q^{13} +(0.145146 - 0.251400i) q^{14} +(-0.882807 + 0.509689i) q^{15} +(-1.96779 - 3.40832i) q^{16} +(1.32604 + 2.29677i) q^{17} +(0.249801 - 0.144223i) q^{18} +(-6.58957 + 3.80449i) q^{19} +4.33710i q^{20} +(1.13342 - 0.654379i) q^{21} -0.268422 q^{22} +(-3.60890 - 6.25080i) q^{23} +0.193426i q^{24} +(-0.123198 + 0.213385i) q^{25} +(-0.164210 - 0.335926i) q^{26} +2.70307 q^{27} -5.56831i q^{28} +(4.67329 + 8.09438i) q^{29} +(0.0528573 - 0.0915514i) q^{30} +(-5.23399 - 1.89878i) q^{31} +(1.07002 + 0.617774i) q^{32} +(-1.04803 - 0.605079i) q^{33} +(-0.238186 - 0.137517i) q^{34} +(-3.05153 + 5.28540i) q^{35} +(2.76644 - 4.79162i) q^{36} +1.96464i q^{37} +(0.394544 - 0.683371i) q^{38} +(0.116106 - 1.68176i) q^{39} +(-0.450995 - 0.781146i) q^{40} +(-0.383246 - 0.221267i) q^{41} +(-0.0678623 + 0.117541i) q^{42} +(3.17167 + 5.49349i) q^{43} +(-4.45900 + 2.57441i) q^{44} +(-5.25177 + 3.03211i) q^{45} +(0.648239 + 0.374261i) q^{46} +1.47978i q^{47} +(0.920032 + 1.59354i) q^{48} +(0.417788 - 0.723630i) q^{49} -0.0255524i q^{50} +(-0.619983 - 1.07384i) q^{51} +(-5.94967 - 4.00546i) q^{52} +(-0.238168 - 0.412519i) q^{53} +(-0.242765 + 0.140161i) q^{54} +5.64326 q^{55} +(0.579023 + 1.00290i) q^{56} +(3.08092 - 1.77877i) q^{57} +(-0.839427 - 0.484643i) q^{58} +(7.19608 - 4.15466i) q^{59} -2.02779i q^{60} +(0.841967 - 1.45833i) q^{61} +(0.568527 - 0.100864i) q^{62} +(6.74264 - 3.89286i) q^{63} +7.74304 q^{64} +(3.45232 + 7.06246i) q^{65} +0.125499 q^{66} +(4.58340 + 2.64623i) q^{67} -5.27564 q^{68} +(1.68733 + 2.92253i) q^{69} -0.632917i q^{70} -14.2493i q^{71} +1.15068i q^{72} +(6.54975 - 3.78150i) q^{73} +(-0.101871 - 0.176446i) q^{74} +(0.0576005 - 0.0997670i) q^{75} -15.1361i q^{76} -7.24526 q^{77} +(0.0767755 + 0.157061i) q^{78} +(2.92619 - 5.06831i) q^{79} +(-7.43108 - 4.29033i) q^{80} +7.08040 q^{81} +0.0458930 q^{82} +(-1.39500 + 0.805406i) q^{83} +2.60344i q^{84} +(5.00759 + 2.89113i) q^{85} +(-0.569702 - 0.328918i) q^{86} +(-2.18497 - 3.78449i) q^{87} +(0.535401 - 0.927341i) q^{88} +(7.89148 - 4.55615i) q^{89} +(0.314445 - 0.544635i) q^{90} +(-4.43236 - 9.06734i) q^{91} +14.3580 q^{92} +(2.44713 + 0.887765i) q^{93} +(-0.0767301 - 0.132901i) q^{94} +(-8.29483 + 14.3671i) q^{95} +(-0.500281 - 0.288837i) q^{96} +(-0.625592 - 0.361186i) q^{97} +0.0866533i q^{98} +(-6.23466 - 3.59958i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 70 q - 6 q^{2} + 4 q^{3} + 30 q^{4} + 6 q^{6} - 12 q^{7} + 58 q^{9}+O(q^{10}) $ 70 * q - 6 * q^2 + 4 * q^3 + 30 * q^4 + 6 * q^6 - 12 * q^7 + 58 * q^9	$ 70 q - 6 q^{2} + 4 q^{3} + 30 q^{4} + 6 q^{6} - 12 q^{7} + 58 q^{9} - q^{10} - 6 q^{11} + 13 q^{12} - 14 q^{13} - 14 q^{14} - 15 q^{15} - 28 q^{16} + 6 q^{17} + 12 q^{19} + 9 q^{21} - 8 q^{22} + 10 q^{23} + 19 q^{25} + 34 q^{27} - 18 q^{29} - 31 q^{30} + 2 q^{31} + 36 q^{32} - 12 q^{33} - 9 q^{34} - 12 q^{35} + 8 q^{36} - 21 q^{38} - 30 q^{39} + 5 q^{40} + 18 q^{41} - 49 q^{42} + 19 q^{43} - 42 q^{44} - 63 q^{45} - 6 q^{46} - 27 q^{48} + 9 q^{49} - 7 q^{51} - 43 q^{52} - 22 q^{53} + 18 q^{54} + 30 q^{55} + 25 q^{56} - 15 q^{57} - 12 q^{58} + 33 q^{59} - 13 q^{61} - 17 q^{62} - 6 q^{63} - 38 q^{64} + 9 q^{65} - 52 q^{66} + 30 q^{67} + 88 q^{68} - 16 q^{69} + 9 q^{73} - 19 q^{74} + 25 q^{75} + 34 q^{77} + 14 q^{78} + 6 q^{79} + 6 q^{80} + 22 q^{81} - 78 q^{82} + 54 q^{83} - 33 q^{85} + 24 q^{86} - 14 q^{87} + 16 q^{88} - 6 q^{89} - 11 q^{90} - 70 q^{91} - 6 q^{92} + 7 q^{93} - 43 q^{94} + 25 q^{95} - 36 q^{96} - 75 q^{97} - 93 q^{99}+O(q^{100}) $ 70 * q - 6 * q^2 + 4 * q^3 + 30 * q^4 + 6 * q^6 - 12 * q^7 + 58 * q^9 - q^10 - 6 * q^11 + 13 * q^12 - 14 * q^13 - 14 * q^14 - 15 * q^15 - 28 * q^16 + 6 * q^17 + 12 * q^19 + 9 * q^21 - 8 * q^22 + 10 * q^23 + 19 * q^25 + 34 * q^27 - 18 * q^29 - 31 * q^30 + 2 * q^31 + 36 * q^32 - 12 * q^33 - 9 * q^34 - 12 * q^35 + 8 * q^36 - 21 * q^38 - 30 * q^39 + 5 * q^40 + 18 * q^41 - 49 * q^42 + 19 * q^43 - 42 * q^44 - 63 * q^45 - 6 * q^46 - 27 * q^48 + 9 * q^49 - 7 * q^51 - 43 * q^52 - 22 * q^53 + 18 * q^54 + 30 * q^55 + 25 * q^56 - 15 * q^57 - 12 * q^58 + 33 * q^59 - 13 * q^61 - 17 * q^62 - 6 * q^63 - 38 * q^64 + 9 * q^65 - 52 * q^66 + 30 * q^67 + 88 * q^68 - 16 * q^69 + 9 * q^73 - 19 * q^74 + 25 * q^75 + 34 * q^77 + 14 * q^78 + 6 * q^79 + 6 * q^80 + 22 * q^81 - 78 * q^82 + 54 * q^83 - 33 * q^85 + 24 * q^86 - 14 * q^87 + 16 * q^88 - 6 * q^89 - 11 * q^90 - 70 * q^91 - 6 * q^92 + 7 * q^93 - 43 * q^94 + 25 * q^95 - 36 * q^96 - 75 * q^97 - 93 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.0898111	+	0.0518525i	−0.0635060	+	0.0366652i	−0.531417	−	0.847110i	$-0.678340\pi$
$2$	−0.0898111	+	0.0518525i	−0.0635060	+	0.0366652i	0.467911	+	0.883776i	$0.345007\pi$
$3$	−0.467545			−0.269937			−0.134969	−	0.990850i	$-0.543093\pi$
$3$	−0.467545			−0.269937			−0.134969	+	0.990850i	$0.543093\pi$
$4$	−0.994623	+	1.72274i	−0.497311	+	0.861368i
$5$	1.88817	−	1.09014i	0.844417	−	0.487525i	−0.0143459	−	0.999897i	$-0.504567\pi$
$5$	1.88817	−	1.09014i	0.844417	−	0.487525i	0.858763	+	0.512372i	$0.171233\pi$
$6$	0.0419908	−	0.0242434i	0.0171427	−	0.00989732i
$7$	−2.42419	+	1.39960i	−0.916256	+	0.529001i	−0.882439	−	0.470427i	$-0.844100\pi$
$7$	−2.42419	+	1.39960i	−0.916256	+	0.529001i	−0.0338176	+	0.999428i	$0.510767\pi$
$8$		−	0.413704i		−	0.146267i
$9$	−2.78140			−0.927134
$10$	−0.113053	+	0.195813i	−0.0357504	+	0.0619215i
$11$	2.24155	+	1.29416i	0.675854	+	0.390205i	0.798291	−	0.602272i	$-0.205738\pi$
$11$	2.24155	+	1.29416i	0.675854	+	0.390205i	−0.122437	+	0.992476i	$0.539071\pi$
$12$	0.465031	−	0.805457i	0.134243	−	0.232516i
$13$	−0.248332	+	3.59699i	−0.0688749	+	0.997625i
$13$	−0.248332	+	3.59699i	−0.0688749	+	0.997625i
$14$	0.145146	−	0.251400i	0.0387919	−	0.0671895i
$15$	−0.882807	+	0.509689i	−0.227940	+	0.131601i
$16$	−1.96779	−	3.40832i	−0.491948	−	0.852080i
$17$	1.32604	+	2.29677i	0.321612	+	0.557048i	0.980821	−	0.194912i	$-0.0624420\pi$
$17$	1.32604	+	2.29677i	0.321612	+	0.557048i	−0.659209	+	0.751960i	$0.729109\pi$
$18$	0.249801	−	0.144223i	0.0588786	−	0.0339936i
$19$	−6.58957	+	3.80449i	−1.51175	+	0.872809i	−0.511845	+	0.859078i	$0.671038\pi$
$19$	−6.58957	+	3.80449i	−1.51175	+	0.872809i	−0.999906	+	0.0137313i	$0.995629\pi$
$20$			4.33710i			0.969806i
$21$	1.13342	−	0.654379i	0.247332	−	0.142797i
$22$	−0.268422			−0.0572278
$23$	−3.60890	−	6.25080i	−0.752508	−	1.30338i	−0.946603	−	0.322400i	$-0.895510\pi$
$23$	−3.60890	−	6.25080i	−0.752508	−	1.30338i	0.194095	−	0.980983i	$-0.437823\pi$
$24$			0.193426i			0.0394828i
$25$	−0.123198	+	0.213385i	−0.0246395	+	0.0426769i
$26$	−0.164210	−	0.335926i	−0.0322042	−	0.0658806i
$27$	2.70307			0.520205
$28$		−	5.56831i		−	1.05231i
$29$	4.67329	+	8.09438i	0.867808	+	1.50309i	0.864232	+	0.503094i	$0.167805\pi$
$29$	4.67329	+	8.09438i	0.867808	+	1.50309i	0.00357667	+	0.999994i	$0.498862\pi$
$30$	0.0528573	−	0.0915514i	0.00965037	−	0.0167149i
$31$	−5.23399	−	1.89878i	−0.940052	−	0.341031i
$31$	−5.23399	−	1.89878i	−0.940052	−	0.341031i
$32$	1.07002	+	0.617774i	0.189154	+	0.109208i
$33$	−1.04803	−	0.605079i	−0.182438	−	0.105331i
$34$	−0.238186	−	0.137517i	−0.0408486	−	0.0235839i
$35$	−3.05153	+	5.28540i	−0.515802	+	0.893395i
$36$	2.76644	−	4.79162i	0.461074	−	0.798604i
$37$			1.96464i			0.322984i	0.986874	+	0.161492i	$0.0516306\pi$
$37$			1.96464i			0.322984i	−0.986874	+	0.161492i	$0.948369\pi$
$38$	0.394544	−	0.683371i	0.0640035	−	0.110857i
$39$	0.116106	−	1.68176i	0.0185919	−	0.269296i
$40$	−0.450995	−	0.781146i	−0.0713086	−	0.123510i
$41$	−0.383246	−	0.221267i	−0.0598530	−	0.0345561i	0.469775	−	0.882786i	$-0.344335\pi$
$41$	−0.383246	−	0.221267i	−0.0598530	−	0.0345561i	−0.529628	+	0.848230i	$0.677668\pi$
$42$	−0.0678623	+	0.117541i	−0.0104714	+	0.0181370i
$43$	3.17167	+	5.49349i	0.483675	+	0.837749i	0.999824	−	0.0187494i	$-0.00596847\pi$
$43$	3.17167	+	5.49349i	0.483675	+	0.837749i	−0.516150	+	0.856498i	$0.672635\pi$
$44$	−4.45900	+	2.57441i	−0.672220	+	0.388106i
$45$	−5.25177	+	3.03211i	−0.782888	+	0.452001i
$46$	0.648239	+	0.374261i	0.0955777	+	0.0551818i
$47$			1.47978i			0.215848i	0.994159	+	0.107924i	$0.0344203\pi$
$47$			1.47978i			0.215848i	−0.994159	+	0.107924i	$0.965580\pi$
$48$	0.920032	+	1.59354i	0.132795	+	0.230008i
$49$	0.417788	−	0.723630i	0.0596840	−	0.103376i
$50$		−	0.0255524i		−	0.00361366i
$51$	−0.619983	−	1.07384i	−0.0868151	−	0.150368i
$52$	−5.94967	−	4.00546i	−0.825071	−	0.555457i
$53$	−0.238168	−	0.412519i	−0.0327149	−	0.0566639i	0.849204	−	0.528064i	$-0.177082\pi$
$53$	−0.238168	−	0.412519i	−0.0327149	−	0.0566639i	−0.881919	+	0.471400i	$0.843749\pi$
$54$	−0.242765	+	0.140161i	−0.0330362	+	0.0190735i
$55$	5.64326			0.760937
$56$	0.579023	+	1.00290i	0.0773752	+	0.134018i
$57$	3.08092	−	1.77877i	0.408078	−	0.235604i
$58$	−0.839427	−	0.484643i	−0.110222	−	0.0636368i
$59$	7.19608	−	4.15466i	0.936850	−	0.540891i	0.0478787	−	0.998853i	$-0.484754\pi$
$59$	7.19608	−	4.15466i	0.936850	−	0.540891i	0.888972	+	0.457962i	$0.151421\pi$
$60$		−	2.02779i		−	0.261787i
$61$	0.841967	−	1.45833i	0.107803	−	0.186720i	−0.807077	−	0.590446i	$-0.798952\pi$
$61$	0.841967	−	1.45833i	0.107803	−	0.186720i	0.914880	+	0.403726i	$0.132285\pi$
$62$	0.568527	−	0.100864i	0.0722030	−	0.0128097i
$63$	6.74264	−	3.89286i	0.849492	−	0.490455i
$64$	7.74304			0.967880
$65$	3.45232	+	7.06246i	0.428208	+	0.875990i
$66$	0.125499			0.0154479
$67$	4.58340	+	2.64623i	0.559952	+	0.323288i	0.753126	−	0.657876i	$-0.228545\pi$
$67$	4.58340	+	2.64623i	0.559952	+	0.323288i	−0.193174	+	0.981164i	$0.561878\pi$
$68$	−5.27564			−0.639765
$69$	1.68733	+	2.92253i	0.203130	+	0.351832i
$70$		−	0.632917i		−	0.0756480i
$71$		−	14.2493i		−	1.69108i	−0.533913	−	0.845539i	$-0.679279\pi$
$71$		−	14.2493i		−	1.69108i	0.533913	−	0.845539i	$-0.320721\pi$
$72$			1.15068i			0.135609i
$73$	6.54975	−	3.78150i	0.766590	−	0.442591i	−0.0650665	−	0.997881i	$-0.520726\pi$
$73$	6.54975	−	3.78150i	0.766590	−	0.442591i	0.831657	+	0.555290i	$0.187393\pi$
$74$	−0.101871	−	0.176446i	−0.0118423	−	0.0205114i
$75$	0.0576005	−	0.0997670i	0.00665113	−	0.0115201i
$76$		−	15.1361i		−	1.73623i
$77$	−7.24526			−0.825674
$78$	0.0767755	+	0.157061i	0.00869311	+	0.0177836i
$79$	2.92619	−	5.06831i	0.329222	−	0.570229i	−0.653136	−	0.757241i	$-0.726547\pi$
$79$	2.92619	−	5.06831i	0.329222	−	0.570229i	0.982358	+	0.187012i	$0.0598802\pi$
$80$	−7.43108	−	4.29033i	−0.830820	−	0.479674i
$81$	7.08040			0.786711
$82$	0.0458930			0.00506804
$83$	−1.39500	+	0.805406i	−0.153122	+	0.0884048i	−0.574603	−	0.818432i	$-0.694844\pi$
$83$	−1.39500	+	0.805406i	−0.153122	+	0.0884048i	0.421482	+	0.906837i	$0.361510\pi$
$84$			2.60344i			0.284058i
$85$	5.00759	+	2.89113i	0.543149	+	0.313587i
$86$	−0.569702	−	0.328918i	−0.0614325	−	0.0354681i
$87$	−2.18497	−	3.78449i	−0.234254	−	0.405740i
$88$	0.535401	−	0.927341i	0.0570739	−	0.0988549i
$89$	7.89148	−	4.55615i	0.836495	−	0.482951i	−0.0195761	−	0.999808i	$-0.506232\pi$
$89$	7.89148	−	4.55615i	0.836495	−	0.482951i	0.856071	+	0.516858i	$0.172898\pi$
$90$	0.314445	−	0.544635i	0.0331454	−	0.0574095i
$91$	−4.43236	−	9.06734i	−0.464638	−	0.950516i
$92$	14.3580			1.49692
$93$	2.44713	+	0.887765i	0.253755	+	0.0920569i
$94$	−0.0767301	−	0.132901i	−0.00791411	−	0.0137076i
$95$	−8.29483	+	14.3671i	−0.851032	+	1.47403i
$96$	−0.500281	−	0.288837i	−0.0510597	−	0.0294793i
$97$	−0.625592	−	0.361186i	−0.0635192	−	0.0366728i	0.467904	−	0.883779i	$-0.345009\pi$
$97$	−0.625592	−	0.361186i	−0.0635192	−	0.0366728i	−0.531423	+	0.847106i	$0.678343\pi$
$98$			0.0866533i			0.00875331i
$99$	−6.23466	−	3.59958i	−0.626607	−	0.361772i
$100$	−0.245070	−	0.424474i	−0.0245070	−	0.0424474i
$101$	2.05050	+	3.55157i	0.204033	+	0.353395i	0.949824	−	0.312785i	$-0.101262\pi$
$101$	2.05050	+	3.55157i	0.204033	+	0.353395i	−0.745792	+	0.666179i	$0.767928\pi$
$102$	0.111363	+	0.0642954i	0.0110266	+	0.00636619i
$103$	4.96396	+	8.59783i	0.489113	+	0.847169i	0.999922	−	0.0125256i	$-0.00398714\pi$
$103$	4.96396	+	8.59783i	0.489113	+	0.847169i	−0.510808	+	0.859695i	$0.670654\pi$
$104$	1.48809	+	0.102736i	0.145919	+	0.0100741i
$105$	1.42673	−	2.47116i	0.139234	−	0.241161i
$106$	0.0427803	+	0.0246992i	0.00415519	+	0.00239900i
$107$	−10.6631			−1.03084			−0.515419	−	0.856939i	$-0.672364\pi$
$107$	−10.6631			−1.03084			−0.515419	+	0.856939i	$0.672364\pi$
$108$	−2.68853	+	4.65667i	−0.258704	+	0.448089i
$109$			8.55112i			0.819049i	0.912299	+	0.409524i	$0.134305\pi$
$109$			8.55112i			0.819049i	−0.912299	+	0.409524i	$0.865695\pi$
$110$	−0.506828	+	0.292617i	−0.0483241	+	0.0278999i
$111$		−	0.918556i		−	0.0871855i
$112$	9.54060	+	5.50827i	0.901502	+	0.520482i
$113$	5.98570			0.563087			0.281543	−	0.959548i	$-0.409154\pi$
$113$	5.98570			0.563087			0.281543	+	0.959548i	$0.409154\pi$
$114$	−0.184467	+	0.319507i	−0.0172769	+	0.0299245i
$115$	−13.6285	−	7.86841i	−1.27086	−	0.733733i
$116$	−18.5926			−1.72628
$117$	0.690711	−	10.0047i	0.0638563	−	0.924932i
$118$	−0.430859	+	0.746269i	−0.0396638	+	0.0686997i
$119$	−6.42914	−	3.71186i	−0.589358	−	0.340266i
$120$	0.210861	+	0.365221i	0.0192488	+	0.0333400i
$121$	−2.15029	−	3.72441i	−0.195481	−	0.338583i
$122$			0.174632i			0.0158105i
$123$	0.179185	+	0.103452i	0.0161566	+	0.00932799i
$124$	8.47694	−	7.12822i	0.761252	−	0.640133i
$125$			11.4386i			1.02310i
$126$	−0.403709	+	0.699245i	−0.0359653	+	0.0622937i
$127$	−3.97793			−0.352985			−0.176492	−	0.984302i	$-0.556475\pi$
$127$	−3.97793			−0.352985			−0.176492	+	0.984302i	$0.556475\pi$
$128$	−2.83544	+	1.63704i	−0.250620	+	0.144696i
$129$	−1.48290	−	2.56845i	−0.130562	−	0.226140i
$130$	−0.676263	−	0.455276i	−0.0593122	−	0.0399304i
$131$	−1.93144	+	3.34535i	−0.168751	+	0.292285i	−0.937981	−	0.346687i	$-0.887307\pi$
$131$	−1.93144	+	3.34535i	−0.168751	+	0.292285i	0.769230	+	0.638972i	$0.220640\pi$
$132$	2.08478	−	1.20365i	0.181457	−	0.104764i
$133$	10.6496	−	18.4456i	0.923434	−	1.59943i
$134$	−0.548854			−0.0474138
$135$	5.10386	−	2.94672i	0.439270	−	0.253613i
$136$	0.950183	−	0.548589i	0.0814775	−	0.0470411i
$137$			1.13091i			0.0966201i	0.998832	+	0.0483100i	$0.0153836\pi$
$137$			1.13091i			0.0966201i	−0.998832	+	0.0483100i	$0.984616\pi$
$138$	−0.303081	−	0.174984i	−0.0258000	−	0.0148956i
$139$	−4.10740	+	7.11422i	−0.348385	+	0.603420i	−0.985963	−	0.166966i	$-0.946603\pi$
$139$	−4.10740	+	7.11422i	−0.348385	+	0.603420i	0.637578	+	0.770386i	$0.279936\pi$
$140$	−6.07023	−	10.5140i	−0.513028	−	0.888591i
$141$		−	0.691863i		−	0.0582654i
$142$	0.738860	+	1.27974i	0.0620038	+	0.107394i
$143$	−5.21174	+	7.74147i	−0.435827	+	0.647374i
$144$	5.47322	+	9.47990i	0.456102	+	0.789992i
$145$	17.6480	+	10.1891i	1.46558	+	0.846156i
$146$	−0.392160	+	0.679242i	−0.0324554	+	0.0562144i
$147$	−0.195335	+	0.338330i	−0.0161109	+	0.0279050i
$148$	−3.38455	−	1.95407i	−0.278208	−	0.160624i
$149$	−2.59359	+	1.49741i	−0.212475	+	0.122673i	−0.602461	−	0.798148i	$-0.705813\pi$
$149$	−2.59359	+	1.49741i	−0.212475	+	0.122673i	0.389986	+	0.920821i	$0.372480\pi$
$150$			0.0119469i			0.000975461i
$151$			2.07619i			0.168958i	0.996425	+	0.0844791i	$0.0269226\pi$
$151$			2.07619i			0.168958i	−0.996425	+	0.0844791i	$0.973077\pi$
$152$	1.57393	+	2.72613i	0.127663	+	0.221119i
$153$	−3.68825	−	6.38823i	−0.298177	−	0.516458i
$154$	0.650705	−	0.375685i	0.0524353	−	0.0302735i
$155$	−11.9526	+	2.12054i	−0.960057	+	0.170326i
$156$	2.78174	+	1.87273i	0.222717	+	0.149939i
$157$	22.9115			1.82854			0.914269	−	0.405107i	$-0.132766\pi$
$157$	22.9115			1.82854			0.914269	+	0.405107i	$0.132766\pi$
$158$			0.606921i			0.0482840i
$159$	0.111354	+	0.192871i	0.00883098	+	0.0152957i
$160$	2.69384			0.212967
$161$	17.4973	+	10.1021i	1.37898	+	0.796155i
$162$	−0.635898	+	0.367136i	−0.0499609	+	0.0288449i
$163$	19.4002	+	11.2007i	1.51954	+	0.877307i	0.999735	+	0.0230216i	$0.00732866\pi$
$163$	19.4002	+	11.2007i	1.51954	+	0.877307i	0.519805	+	0.854285i	$0.326005\pi$
$164$	0.762371	−	0.440155i	0.0595311	−	0.0343703i
$165$	−2.63848			−0.205405
$166$	0.0835245	−	0.144669i	0.00648276	−	0.0112285i
$167$			14.0524i			1.08740i	0.839278	+	0.543702i	$0.182978\pi$
$167$			14.0524i			1.08740i	−0.839278	+	0.543702i	$0.817022\pi$
$168$	−0.270719	−	0.468900i	−0.0208864	−	0.0361764i
$169$	−12.8767	−	1.78650i	−0.990512	−	0.137423i
$170$	−0.599650			−0.0459910
$171$	18.3282	−	10.5818i	1.40159	−	0.809211i
$172$	−12.6184			−0.962148
$173$	−9.12665			−0.693886			−0.346943	−	0.937886i	$-0.612780\pi$
$173$	−9.12665			−0.693886			−0.346943	+	0.937886i	$0.612780\pi$
$174$	0.392470	+	0.226593i	0.0297531	+	0.0171779i
$175$		−	0.689712i		−	0.0521373i
$176$		−	10.1866i		−	0.767842i
$177$	−3.36449	+	1.94249i	−0.252891	+	0.146007i
$178$	−0.472495	+	0.818385i	−0.0354150	+	0.0613406i
$179$	−21.9819			−1.64300			−0.821502	−	0.570206i	$-0.806863\pi$
$179$	−21.9819			−1.64300			−0.821502	+	0.570206i	$0.806863\pi$
$180$		−	12.0632i		−	0.899140i
$181$	−4.10222	−	7.10525i	−0.304916	−	0.528129i	0.672327	−	0.740254i	$-0.265295\pi$
$181$	−4.10222	−	7.10525i	−0.304916	−	0.528129i	−0.977243	+	0.212125i	$0.931962\pi$
$182$	0.868239	+	0.584519i	0.0643582	+	0.0433274i
$183$	−0.393658	+	0.681835i	−0.0291000	+	0.0504027i
$184$	−2.58599	+	1.49302i	−0.190641	+	0.110067i
$185$	2.14172	+	3.70958i	0.157463	+	0.272733i
$186$	−0.265812	+	0.0471584i	−0.0194903	+	0.00345782i
$187$			6.86444i			0.501978i
$188$	−2.54927	−	1.47182i	−0.185924	−	0.107344i
$189$	−6.55274	+	3.78323i	−0.476642	+	0.275189i
$190$		−	1.72043i		−	0.124813i
$191$	−4.68493			−0.338990			−0.169495	−	0.985531i	$-0.554214\pi$
$191$	−4.68493			−0.338990			−0.169495	+	0.985531i	$0.554214\pi$
$192$	−3.62022			−0.261267
$193$			22.8543i			1.64509i	0.568702	+	0.822544i	$0.307446\pi$
$193$			22.8543i			1.64509i	−0.568702	+	0.822544i	$0.692554\pi$
$194$	0.0749134			0.00537847
$195$	−1.61412	−	3.30202i	−0.115589	−	0.236463i
$196$	0.831083	+	1.43948i	0.0593630	+	0.102820i
$197$	11.7868	+	6.80512i	0.839775	+	0.484844i	0.857188	−	0.515004i	$-0.172210\pi$
$197$	11.7868	+	6.80512i	0.839775	+	0.484844i	−0.0174127	+	0.999848i	$0.505543\pi$
$198$	0.746589			0.0530578
$199$	−5.71576			−0.405179			−0.202590	−	0.979264i	$-0.564936\pi$
$199$	−5.71576			−0.405179			−0.202590	+	0.979264i	$0.564936\pi$
$200$	0.0882782	+	0.0509674i	0.00624221	+	0.00360394i
$201$	−2.14295	−	1.23723i	−0.151152	−	0.0872676i
$202$	−0.368316	−	0.212647i	−0.0259146	−	0.0149618i
$203$	−22.6579	−	13.0815i	−1.59027	−	0.918143i
$204$	2.46660			0.172696
$205$	−0.964847			−0.0673879
$206$	−0.891637	−	0.514787i	−0.0621233	−	0.0358669i
$207$	10.0378	+	17.3860i	0.697676	+	1.20841i
$208$	12.7484	−	6.23174i	0.883939	−	0.432093i
$209$	−19.6945			−1.36230
$210$			0.295917i			0.0204202i
$211$	−14.1177			−0.971904			−0.485952	−	0.873986i	$-0.661527\pi$
$211$	−14.1177			−0.971904			−0.485952	+	0.873986i	$0.661527\pi$
$212$	0.947550			0.0650780
$213$			6.66218i			0.456485i
$214$	0.957662	−	0.552906i	0.0654644	−	0.0377959i
$215$	11.9773	+	6.91511i	0.816847	+	0.471607i
$216$		−	1.11827i		−	0.0760887i
$217$	15.3457	−	2.72252i	1.04173	−	0.184817i
$218$	−0.443397	−	0.767986i	−0.0300306	−	0.0520145i
$219$	−3.06231	+	1.76802i	−0.206931	+	0.119472i
$220$	−5.61292	+	9.72186i	−0.378423	+	0.655447i
$221$	−8.59075	+	4.19939i	−0.577876	+	0.282481i
$222$	0.0476294	+	0.0824965i	0.00319668	+	0.00553680i
$223$		−	18.3161i		−	1.22653i	−0.789876	−	0.613267i	$-0.789855\pi$
$223$		−	18.3161i		−	1.22653i	0.789876	−	0.613267i	$-0.210145\pi$
$224$	−3.45856			−0.231085
$225$	0.342662	−	0.593508i	0.0228441	−	0.0395672i
$226$	−0.537582	+	0.310373i	−0.0357594	+	0.0206457i
$227$		−	9.06698i		−	0.601797i	−0.953656	−	0.300898i	$-0.902714\pi$
$227$		−	9.06698i		−	0.601797i	0.953656	−	0.300898i	$-0.0972865\pi$
$228$			7.07682i			0.468674i
$229$	−22.9448	−	13.2472i	−1.51624	−	0.875400i	−0.999818	−	0.0190631i	$-0.993932\pi$
$229$	−22.9448	−	13.2472i	−1.51624	−	0.875400i	−0.516418	−	0.856337i	$-0.672735\pi$
$230$	1.63199			0.107610
$231$	3.38749			0.222880
$232$	3.34868	−	1.93336i	0.219852	−	0.126931i
$233$	−6.83119			−0.447526			−0.223763	−	0.974644i	$-0.571834\pi$
$233$	−6.83119			−0.447526			−0.223763	+	0.974644i	$0.571834\pi$
$234$	0.456733	+	0.934346i	0.0298576	+	0.0610801i
$235$	1.61316	+	2.79408i	0.105231	+	0.182266i
$236$			16.5293i			1.07596i
$237$	−1.36813	+	2.36966i	−0.0888693	+	0.153926i
$238$	0.769877			0.0499037
$239$	−20.5168	+	11.8454i	−1.32712	+	0.766215i	−0.984854	−	0.173387i	$-0.944529\pi$
$239$	−20.5168	+	11.8454i	−1.32712	+	0.766215i	−0.342269	+	0.939602i	$0.611195\pi$
$240$	3.47436	+	2.00592i	0.224269	+	0.129482i
$241$	1.56891	−	0.905812i	0.101063	−	0.0583485i	−0.448617	−	0.893724i	$-0.648083\pi$
$241$	1.56891	−	0.905812i	0.101063	−	0.0583485i	0.549679	+	0.835376i	$0.314750\pi$
$242$	0.386240	+	0.222996i	0.0248284	+	0.0143347i
$243$	−11.4196			−0.732568
$244$	1.67488	+	2.90098i	0.107223	+	0.185716i
$245$		−	1.82179i		−	0.116390i
$246$	−0.0214571			−0.00136805
$247$	−12.0483	−	24.6474i	−0.766615	−	1.56827i
$248$	−0.785533	+	2.16532i	−0.0498814	+	0.137498i
$249$	0.652227	−	0.376564i	0.0413332	−	0.0238637i
$250$	−0.593119	−	1.02731i	−0.0375122	−	0.0649730i
$251$	12.5396	+	21.7192i	0.791493	+	1.37091i	0.925042	+	0.379864i	$0.124029\pi$
$251$	12.5396	+	21.7192i	0.791493	+	1.37091i	−0.133549	+	0.991042i	$0.542637\pi$
$252$			15.4877i			0.975635i
$253$		−	18.6820i		−	1.17453i
$254$	0.357263	−	0.206266i	0.0224167	−	0.0129423i
$255$	−2.34127	−	1.35174i	−0.146616	−	0.0846489i
$256$	−7.57327	+	13.1173i	−0.473330	+	0.819831i
$257$	−7.87380	+	13.6378i	−0.491154	+	0.850704i	−0.999948	−	0.0101843i	$-0.996758\pi$
$257$	−7.87380	+	13.6378i	−0.491154	+	0.850704i	0.508794	+	0.860888i	$0.330092\pi$
$258$	0.266361	+	0.153784i	0.0165829	+	0.00957416i
$259$	−2.74971	−	4.76264i	−0.170859	−	0.295936i
$260$	−15.6005	−	1.07704i	−0.967503	−	0.0667953i
$261$	−12.9983	−	22.5137i	−0.804574	−	1.39356i
$262$		−	0.400599i		−	0.0247491i
$263$	5.76508	+	9.98541i	0.355490	+	0.615727i	0.987202	−	0.159477i	$-0.0509807\pi$
$263$	5.76508	+	9.98541i	0.355490	+	0.615727i	−0.631712	+	0.775203i	$0.717647\pi$
$264$	−0.250324	+	0.433574i	−0.0154064	+	0.0266846i
$265$	−0.899406	−	0.519272i	−0.0552501	−	0.0318987i
$266$			2.20882i			0.135432i
$267$	−3.68962	+	2.13021i	−0.225801	+	0.130366i
$268$	−9.11751	+	5.26400i	−0.556941	+	0.321550i
$269$	16.2051			0.988042			0.494021	−	0.869450i	$-0.335527\pi$
$269$	16.2051			0.988042			0.494021	+	0.869450i	$0.335527\pi$
$270$	−0.305589	+	0.529296i	−0.0185976	+	0.0322119i
$271$	18.4205	−	10.6351i	1.11896	−	0.646035i	0.177828	−	0.984061i	$-0.443093\pi$
$271$	18.4205	−	10.6351i	1.11896	−	0.646035i	0.941137	+	0.338027i	$0.109759\pi$
$272$	5.21875	−	9.03913i	0.316433	−	0.548078i
$273$	2.07233	+	4.23939i	0.125423	+	0.256580i
$274$	−0.0586404	−	0.101568i	−0.00354260	−	0.00613596i
$275$	−0.552309	+	0.318876i	−0.0333055	+	0.0192289i
$276$	−6.71301			−0.404076
$277$	−13.7122	+	23.7503i	−0.823889	+	1.42702i	0.0788762	+	0.996884i	$0.474867\pi$
$277$	−13.7122	+	23.7503i	−0.823889	+	1.42702i	−0.902765	+	0.430133i	$0.858467\pi$
$278$		−	0.851915i		−	0.0510945i
$279$	14.5578	+	5.28127i	0.871554	+	0.316181i
$280$	2.18659	+	1.26243i	0.130674	+	0.0754446i
$281$		−	27.1552i		−	1.61994i	−0.586468	−	0.809972i	$-0.699482\pi$
$281$		−	27.1552i		−	1.61994i	0.586468	−	0.809972i	$-0.300518\pi$
$282$	0.0358748	+	0.0621370i	0.00213631	+	0.00370020i
$283$	12.6713	+	21.9473i	0.753228	+	1.30463i	0.946250	+	0.323436i	$0.104838\pi$
$283$	12.6713	+	21.9473i	0.753228	+	1.30463i	−0.193022	+	0.981194i	$0.561829\pi$
$284$	24.5478	+	14.1727i	1.45664	+	0.840992i
$285$	3.87821	−	6.71726i	0.229725	−	0.397896i
$286$	0.0666578	−	0.965511i	0.00394156	−	0.0570919i
$287$	1.23875			0.0731209
$288$	−2.97615	−	1.71828i	−0.175371	−	0.101251i
$289$	4.98324	−	8.63122i	0.293132	−	0.507719i
$290$	−2.11331			−0.124098
$291$	0.292492	+	0.168871i	0.0171462	+	0.00989937i
$292$			15.0447i			0.880423i
$293$	24.9323	−	14.3947i	1.45656	−	0.840946i	0.457720	−	0.889096i	$-0.348666\pi$
$293$	24.9323	−	14.3947i	1.45656	−	0.840946i	0.998840	+	0.0481508i	$0.0153328\pi$
$294$		−	0.0405143i		−	0.00236284i
$295$	9.05831	−	15.6894i	0.527395	−	0.913475i
$296$	0.812778			0.0472418
$297$	6.05907	+	3.49821i	0.351583	+	0.202987i
$298$	0.155289	−	0.268968i	0.00899565	−	0.0155809i
$299$	23.3803	−	11.4289i	1.35212	−	0.660951i
$300$	0.114581	+	0.198461i	0.00661537	+	0.0114581i
$301$	−15.3774	−	8.87816i	−0.886340	−	0.511729i
$302$	−0.107656	−	0.186465i	−0.00619489	−	0.0107299i
$303$	−0.958702	−	1.66052i	−0.0550760	−	0.0953944i
$304$	25.9338	+	14.9729i	1.48741	+	0.858754i
$305$		−	3.67144i		−	0.210226i
$306$	0.662491	+	0.382490i	0.0378721	+	0.0218655i
$307$	6.10713	+	3.52595i	0.348552	+	0.201237i	0.664047	−	0.747690i	$-0.268837\pi$
$307$	6.10713	+	3.52595i	0.348552	+	0.201237i	−0.315495	+	0.948927i	$0.602171\pi$
$308$	7.20630	−	12.4817i	0.410617	−	0.711210i
$309$	−2.32087	−	4.01987i	−0.132030	−	0.228683i
$310$	0.963522	−	0.810221i	0.0547244	−	0.0460175i
$311$	−15.9658			−0.905335			−0.452668	−	0.891679i	$-0.649528\pi$
$311$	−15.9658			−0.905335			−0.452668	+	0.891679i	$0.649528\pi$
$312$	−0.695750	−	0.0480338i	−0.0393891	−	0.00271938i
$313$	5.47484	−	9.48271i	0.309456	−	0.535994i	−0.668787	−	0.743454i	$-0.733186\pi$
$313$	5.47484	−	9.48271i	0.309456	−	0.535994i	0.978244	+	0.207460i	$0.0665196\pi$
$314$	−2.05771	+	1.18802i	−0.116123	+	0.0670438i
$315$	8.48752	−	14.7008i	0.478217	−	0.828297i
$316$	5.82091	+	10.0821i	0.327452	+	0.567163i
$317$	15.2919	+	8.82876i	0.858877	+	0.495873i	0.863636	−	0.504116i	$-0.168182\pi$
$317$	15.2919	+	8.82876i	0.858877	+	0.495873i	−0.00475939	+	0.999989i	$0.501515\pi$
$318$	−0.0200017	−	0.0115480i	−0.00112164	−	0.000647580i
$319$			24.1920i			1.35449i
$320$	14.6202	−	8.44099i	0.817295	−	0.471865i
$321$	4.98546			0.278261
$322$	−2.09527			−0.116765
$323$	−17.4761	−	10.0898i	−0.972394	−	0.561412i
$324$	−7.04232	+	12.1977i	−0.391240	+	0.677648i
$325$	−0.736948	−	0.496131i	−0.0408785	−	0.0275204i
$326$	−2.32314			−0.128667
$327$		−	3.99803i		−	0.221092i
$328$	−0.0915392	+	0.158551i	−0.00505441	+	0.00875449i
$329$	−2.07110	−	3.58726i	−0.114184	−	0.197772i
$330$	0.236965	−	0.136812i	0.0130445	−	0.00753124i
$331$		−	6.27388i		−	0.344844i	−0.985023	−	0.172422i	$-0.944841\pi$
$331$		−	6.27388i		−	0.344844i	0.985023	−	0.172422i	$-0.0551592\pi$
$332$		−	3.20430i		−	0.175859i
$333$		−	5.46444i		−	0.299449i
$334$	−0.728650	−	1.26206i	−0.0398699	−	0.0690567i
$335$	11.5390			0.630444
$336$	−4.46066	−	2.57536i	−0.243349	−	0.140498i
$337$	−15.1703			−0.826381			−0.413190	−	0.910645i	$-0.635586\pi$
$337$	−15.1703			−0.826381			−0.413190	+	0.910645i	$0.635586\pi$
$338$	1.24910	−	0.507240i	0.0679422	−	0.0275902i
$339$	−2.79858			−0.151998
$340$	−9.96132	+	5.75117i	−0.540229	+	0.311901i
$341$	−9.27494	−	11.0298i	−0.502266	−	0.597300i
$342$	−1.09739	+	1.90073i	−0.0593398	+	0.102780i
$343$		−	17.2555i		−	0.931710i
$344$	2.27268	−	1.31213i	0.122535	−	0.0707455i
$345$	6.37193	+	3.67884i	0.343053	+	0.198062i
$346$	0.819675	−	0.473239i	0.0440660	−	0.0254415i
$347$	−5.61177	−	9.71987i	−0.301256	−	0.521790i	0.675165	−	0.737667i	$-0.264072\pi$
$347$	−5.61177	−	9.71987i	−0.301256	−	0.521790i	−0.976421	+	0.215877i	$0.930739\pi$
$348$	8.69290			0.465988
$349$	−1.33978	+	0.773523i	−0.0717168	+	0.0414057i	−0.535430	−	0.844580i	$-0.679850\pi$
$349$	−1.33978	+	0.773523i	−0.0717168	+	0.0414057i	0.463713	+	0.885986i	$0.346517\pi$
$350$	0.0357633	+	0.0619438i	0.00191163	+	0.00331104i
$351$	−0.671258	+	9.72290i	−0.0358291	+	0.518970i
$352$	1.59900	+	2.76955i	0.0852270	+	0.147618i
$353$		−	18.4041i		−	0.979550i	−0.871849	−	0.489775i	$-0.837079\pi$
$353$		−	18.4041i		−	0.979550i	0.871849	−	0.489775i	$-0.162921\pi$
$354$	0.201446	−	0.348915i	0.0107067	−	0.0185446i
$355$	−15.5337	−	26.9051i	−0.824442	−	1.42798i
$356$			18.1266i			0.960707i
$357$	3.00591	+	1.73546i	0.159090	+	0.0918505i
$358$	1.97422	−	1.13982i	0.104341	−	0.0602411i
$359$	25.8896	−	14.9473i	1.36640	−	0.788890i	0.375932	−	0.926647i	$-0.377323\pi$
$359$	25.8896	−	14.9473i	1.36640	−	0.788890i	0.990466	+	0.137757i	$0.0439892\pi$
$360$	1.25440	+	2.17268i	0.0661126	+	0.114510i
$361$	19.4483	−	33.6854i	1.02359	−	1.77291i
$362$	0.736850	+	0.425420i	0.0387280	+	0.0223596i
$363$	1.00536	+	1.74133i	0.0527676	+	0.0913961i
$364$	20.0292	+	1.38279i	1.04981	+	0.0724780i
$365$	8.24472	−	14.2803i	0.431548	−	0.747463i
$366$		−	0.0816485i		−	0.00426784i
$367$	−18.0857	+	31.3254i	−0.944068	+	1.63517i	−0.186462	+	0.982462i	$0.559702\pi$
$367$	−18.0857	+	31.3254i	−0.944068	+	1.63517i	−0.757606	+	0.652712i	$0.773631\pi$
$368$	−14.2032	+	24.6006i	−0.740391	+	1.28239i
$369$	1.06596	+	0.615433i	0.0554917	+	0.0320382i
$370$	−0.384701	−	0.222107i	−0.0199997	−	0.0115468i
$371$	1.15473	+	0.666683i	0.0599505	+	0.0346124i
$372$	−3.96335	+	3.33276i	−0.205490	+	0.172796i
$373$	−18.9713	+	32.8593i	−0.982299	+	1.70139i	−0.328924	+	0.944356i	$0.606686\pi$
$373$	−18.9713	+	32.8593i	−0.982299	+	1.70139i	−0.653374	+	0.757035i	$0.726647\pi$
$374$	−0.355938	−	0.616503i	−0.0184051	−	0.0318786i
$375$		−	5.34806i		−	0.276173i
$376$	0.612191			0.0315713
$377$	−30.2759	+	14.7997i	−1.55929	+	0.762222i
$378$	0.392339	−	0.679551i	0.0201797	−	0.0349523i
$379$		−	3.14272i		−	0.161430i	−0.996737	−	0.0807152i	$-0.974280\pi$
$379$		−	3.14272i		−	0.161430i	0.996737	−	0.0807152i	$-0.0257204\pi$
$380$	−16.5005	−	28.5796i	−0.846456	−	1.46610i
$381$	1.85986			0.0952837
$382$	0.420759	−	0.242925i	0.0215279	−	0.0124291i
$383$			19.2381i			0.983022i	0.870871	+	0.491511i	$0.163555\pi$
$383$			19.2381i			0.983022i	−0.870871	+	0.491511i	$0.836445\pi$
$384$	1.32570	−	0.765392i	0.0676518	−	0.0390588i
$385$	−13.6803	+	7.89834i	−0.697214	+	0.402537i
$386$	−1.18505	−	2.05257i	−0.0603175	−	0.104473i
$387$	−8.82168	−	15.2796i	−0.448431	−	0.776706i
$388$	1.24446	−	0.718487i	0.0631776	−	0.0364756i
$389$	18.4669	−	31.9855i	0.936307	−	1.62173i	0.164019	−	0.986457i	$-0.447554\pi$
$389$	18.4669	−	31.9855i	0.936307	−	1.62173i	0.772287	−	0.635273i	$-0.219113\pi$
$390$	0.316183	+	0.212862i	0.0160106	+	0.0107787i
$391$	9.57110	−	16.5776i	0.484031	−	0.838367i
$392$	−0.299369	−	0.172841i	−0.0151204	−	0.00872977i
$393$	0.903035	−	1.56410i	0.0455521	−	0.0788985i
$394$	−1.41145			−0.0711077
$395$		−	12.7598i		−	0.642015i
$396$	12.4023	−	7.16046i	0.623238	−	0.359826i
$397$	2.54433	−	1.46897i	0.127696	−	0.0737254i	−0.434791	−	0.900531i	$-0.643178\pi$
$397$	2.54433	−	1.46897i	0.127696	−	0.0737254i	0.562487	+	0.826806i	$0.309845\pi$
$398$	0.513339	−	0.296376i	0.0257313	−	0.0148560i
$399$	−4.97915	+	8.62414i	−0.249269	+	0.431747i
$400$	0.969710			0.0484855
$401$	−0.530530	+	0.306302i	−0.0264934	+	0.0152960i	−0.513188	−	0.858276i	$-0.671536\pi$
$401$	−0.530530	+	0.306302i	−0.0264934	+	0.0152960i	0.486695	+	0.873572i	$0.338202\pi$
$402$	0.256614			0.0127987
$403$	8.12965	−	18.3551i	0.404967	−	0.914331i
$404$	−8.15790			−0.405871
$405$	13.3690	−	7.71861i	0.664312	−	0.383541i
$406$	2.71324			0.134656
$407$	−2.54256	+	4.40384i	−0.126030	+	0.218290i
$408$	−0.444254	+	0.256490i	−0.0219938	+	0.0126981i
$409$	−20.4261	+	11.7930i	−1.01001	+	0.583128i	−0.911194	−	0.411978i	$-0.864838\pi$
$409$	−20.4261	+	11.7930i	−1.01001	+	0.583128i	−0.0988140	+	0.995106i	$0.531505\pi$
$410$	0.0866540	−	0.0500297i	0.00427954	−	0.00247079i
$411$		−	0.528751i		−	0.0260814i
$412$	−19.7491			−0.972966
$413$	−11.6298	+	20.1433i	−0.572263	+	0.991189i
$414$	−1.80301	−	1.04097i	−0.0886133	−	0.0511609i
$415$	−1.75601	+	3.04149i	−0.0861990	+	0.149301i
$416$	−2.48785	+	3.69542i	−0.121977	+	0.181183i
$417$	1.92039	−	3.32622i	0.0940421	−	0.162886i
$418$	1.76878	−	1.02121i	0.0865141	−	0.0499489i
$419$	17.4783	+	30.2732i	0.853869	+	1.47894i	0.877690	+	0.479228i	$0.159083\pi$
$419$	17.4783	+	30.2732i	0.853869	+	1.47894i	−0.0238216	+	0.999716i	$0.507583\pi$
$420$	2.83811	+	4.91575i	0.138485	+	0.239864i
$421$	−4.35059	+	2.51181i	−0.212035	+	0.122418i	−0.602257	−	0.798303i	$-0.705732\pi$
$421$	−4.35059	+	2.51181i	−0.212035	+	0.122418i	0.390222	+	0.920721i	$0.372398\pi$
$422$	1.26793	−	0.732039i	0.0617218	−	0.0356351i
$423$		−	4.11586i		−	0.200120i
$424$	−0.170661	+	0.0985312i	−0.00828804	+	0.00478510i
$425$	−0.653460			−0.0316975
$426$	−0.345451	−	0.598338i	−0.0167371	−	0.0289896i
$427$			4.71369i			0.228111i
$428$	10.6057	−	18.3697i	0.512647	−	0.887931i
$429$	2.43672	−	3.61949i	0.117646	−	0.174750i
$430$	−1.43426			−0.0691663
$431$		−	8.65847i		−	0.417064i	−0.978016	−	0.208532i	$-0.933131\pi$
$431$		−	8.65847i		−	0.417064i	0.978016	−	0.208532i	$-0.0668685\pi$
$432$	−5.31908	−	9.21291i	−0.255914	−	0.443256i
$433$	7.58986	−	13.1460i	0.364746	−	0.631758i	−0.623990	−	0.781433i	$-0.714489\pi$
$433$	7.58986	−	13.1460i	0.364746	−	0.631758i	0.988735	+	0.149675i	$0.0478226\pi$
$434$	−1.23705	+	1.04023i	−0.0593801	+	0.0499324i
$435$	−8.25123	−	4.76385i	−0.395616	−	0.228409i
$436$	−14.7313	−	8.50514i	−0.705503	−	0.407322i
$437$	47.5622	+	27.4601i	2.27521	+	1.31359i
$438$	0.183353	−	0.317576i	0.00876093	−	0.0151744i
$439$	8.60356	−	14.9018i	0.410625	−	0.711224i	−0.584333	−	0.811514i	$-0.698644\pi$
$439$	8.60356	−	14.9018i	0.410625	−	0.711224i	0.994958	+	0.100290i	$0.0319771\pi$
$440$		−	2.33464i		−	0.111300i
$441$	−1.16204	+	2.01271i	−0.0553350	+	0.0958431i
$442$	0.553796	−	0.822603i	0.0263414	−	0.0391273i
$443$	15.5018	+	26.8499i	0.736513	+	1.27568i	0.954057	+	0.299627i	$0.0968621\pi$
$443$	15.5018	+	26.8499i	0.736513	+	1.27568i	−0.217544	+	0.976051i	$0.569805\pi$
$444$	1.58243	+	0.913617i	0.0750988	+	0.0433583i
$445$	9.93366	−	17.2056i	0.470901	−	0.815624i
$446$	0.949733	+	1.64499i	0.0449711	+	0.0778923i
$447$	1.21262	−	0.700107i	0.0573550	−	0.0331139i
$448$	−18.7706	+	10.8372i	−0.886827	+	0.512010i
$449$	29.3791	+	16.9620i	1.38648	+	0.800487i	0.992917	−	0.118809i	$-0.0379077\pi$
$449$	29.3791	+	16.9620i	1.38648	+	0.800487i	0.393567	+	0.919296i	$0.371241\pi$
$450$			0.0710715i			0.00335034i
$451$	−0.572711	−	0.991965i	−0.0269679	−	0.0467098i
$452$	−5.95351	+	10.3118i	−0.280029	+	0.485025i
$453$		−	0.970714i		−	0.0456081i
$454$	0.470145	+	0.814316i	0.0220650	+	0.0382177i
$455$	−18.2537	−	12.2888i	−0.855748	−	0.576110i
$456$	−0.735885	−	1.27459i	−0.0344610	−	0.0596882i
$457$	15.9304	−	9.19741i	0.745192	−	0.430237i	−0.0787622	−	0.996893i	$-0.525097\pi$
$457$	15.9304	−	9.19741i	0.745192	−	0.430237i	0.823954	+	0.566657i	$0.191763\pi$
$458$	2.74760			0.128387
$459$	3.58437	+	6.20832i	0.167304	+	0.289779i
$460$	27.1104	−	15.6522i	1.26403	−	0.729787i
$461$	6.32830	+	3.65365i	0.294738	+	0.170167i	0.640077	−	0.768311i	$-0.278903\pi$
$461$	6.32830	+	3.65365i	0.294738	+	0.170167i	−0.345338	+	0.938478i	$0.612236\pi$
$462$	−0.304234	+	0.175650i	−0.0141542	+	0.00817196i
$463$		−	29.9774i		−	1.39317i	−0.717475	−	0.696584i	$-0.754702\pi$
$463$		−	29.9774i		−	1.39317i	0.717475	−	0.696584i	$-0.245298\pi$
$464$	18.3921	−	31.8561i	0.853834	−	1.47888i
$465$	5.58839	−	0.991451i	0.259155	−	0.0459774i
$466$	0.613517	−	0.354214i	0.0284206	−	0.0164087i
$467$	−16.9517			−0.784432			−0.392216	−	0.919873i	$-0.628291\pi$
$467$	−16.9517			−0.784432			−0.392216	+	0.919873i	$0.628291\pi$
$468$	16.5484	+	11.1408i	0.764951	+	0.514983i
$469$	−14.8147			−0.684079
$470$	−0.289760	−	0.167293i	−0.0133656	−	0.00771665i
$471$	−10.7122			−0.493591
$472$	−1.71880	−	2.97705i	−0.0791143	−	0.137030i
$473$			16.4186i			0.754928i
$474$		−	0.283763i		−	0.0130337i
$475$		−	1.87482i		−	0.0860225i
$476$	12.7891	−	7.38381i	0.586189	−	0.338436i
$477$	0.662441	+	1.14738i	0.0303311	+	0.0525350i
$478$	1.22843	−	2.12770i	0.0561869	−	0.0973185i
$479$		−	22.7292i		−	1.03852i	−0.854615	−	0.519262i	$-0.826207\pi$
$479$		−	22.7292i		−	1.03852i	0.854615	−	0.519262i	$-0.173793\pi$
$480$	−1.25949			−0.0574876
$481$	−7.06677	−	0.487882i	−0.322217	−	0.0222455i
$482$	−0.0939372	+	0.162704i	−0.00427872	+	0.00741096i
$483$	−8.18079	−	4.72318i	−0.372239	−	0.214912i
$484$	8.55490			0.388859
$485$	−1.57497			−0.0715156
$486$	1.02561	−	0.592135i	0.0465225	−	0.0268598i
$487$		−	5.80554i		−	0.263074i	−0.991311	−	0.131537i	$-0.958009\pi$
$487$		−	5.80554i		−	0.263074i	0.991311	−	0.131537i	$-0.0419913\pi$
$488$	−0.603318	−	0.348326i	−0.0273109	−	0.0157680i
$489$	−9.07046	−	5.23683i	−0.410181	−	0.236818i
$490$	0.0944641	+	0.163617i	0.00426745	+	0.00739145i
$491$	−3.07021	+	5.31776i	−0.138557	+	0.239987i	−0.926951	−	0.375184i	$-0.877580\pi$
$491$	−3.07021	+	5.31776i	−0.138557	+	0.239987i	0.788394	+	0.615171i	$0.210913\pi$
$492$	−0.356443	+	0.205792i	−0.0160697	+	0.00927783i
$493$	−12.3939	+	21.4669i	−0.558195	+	0.966822i
$494$	2.36010	+	1.58887i	0.106186	+	0.0714868i
$495$	−15.6962			−0.705491
$496$	3.82777	+	21.5755i	0.171872	+	0.968769i
$497$	19.9434	+	34.5429i	0.894582	+	1.54946i
$498$	−0.0390515	+	0.0676392i	−0.00174994	+	0.00303098i
$499$	−10.9066	−	6.29691i	−0.488245	−	0.281889i	0.235601	−	0.971850i	$-0.424294\pi$
$499$	−10.9066	−	6.29691i	−0.488245	−	0.281889i	−0.723846	+	0.689961i	$0.757628\pi$
$500$	−19.7057	−	11.3771i	−0.881265	−	0.508799i
$501$		−	6.57011i		−	0.293531i
$502$	−2.25239	−	1.30042i	−0.100529	−	0.0580405i
$503$	8.60682	+	14.9075i	0.383759	+	0.664690i	0.991596	−	0.129371i	$-0.0412959\pi$
$503$	8.60682	+	14.9075i	0.383759	+	0.664690i	−0.607837	+	0.794062i	$0.707963\pi$
$504$	−1.61049	−	2.78946i	−0.0717371	−	0.124252i
$505$	7.74341	+	4.47066i	0.344577	+	0.198942i
$506$	0.968709	+	1.67785i	0.0430644	+	0.0745897i
$507$	6.02042	+	0.835268i	0.267376	+	0.0370955i
$508$	3.95654	−	6.85293i	0.175543	−	0.304050i
$509$	−11.6945	−	6.75181i	−0.518349	−	0.299269i	0.217910	−	0.975969i	$-0.430076\pi$
$509$	−11.6945	−	6.75181i	−0.518349	−	0.299269i	−0.736259	+	0.676700i	$0.763409\pi$
$510$	0.280363			0.0124147
$511$	−10.5852	+	18.3341i	−0.468262	+	0.811054i
$512$		−	8.11895i		−	0.358810i
$513$	−17.8120	+	10.2838i	−0.786421	+	0.454040i
$514$		−	1.63310i		−	0.0720331i
$515$	18.7456	+	10.8228i	0.826031	+	0.476909i
$516$	5.89969			0.259720
$517$	−1.91507	+	3.31700i	−0.0842248	+	0.145882i
$518$	0.493910	+	0.285159i	0.0217011	+	0.0125292i
$519$	4.26712			0.187306
$520$	2.92177	−	1.42824i	0.128128	−	0.0626325i
$521$	−17.6142	+	30.5087i	−0.771692	+	1.33661i	0.164943	+	0.986303i	$0.447256\pi$
$521$	−17.6142	+	30.5087i	−0.771692	+	1.33661i	−0.936635	+	0.350307i	$0.886077\pi$
$522$	2.33478	+	1.34799i	0.102191	+	0.0589998i
$523$	−0.930339	−	1.61139i	−0.0406809	−	0.0704613i	0.844968	−	0.534817i	$-0.179619\pi$
$523$	−0.930339	−	1.61139i	−0.0406809	−	0.0704613i	−0.885649	+	0.464355i	$0.846286\pi$
$524$	−3.84211	−	6.65472i	−0.167843	−	0.290713i
$525$			0.322472i			0.0140738i
$526$	−1.03554	−	0.597867i	−0.0451515	−	0.0260682i
$527$	−2.57942	−	14.5391i	−0.112361	−	0.633334i
$528$			4.76268i			0.207269i
$529$	−14.5484	+	25.1985i	−0.632538	+	1.09559i
$530$	0.107702			0.00467829
$531$	−20.0152	+	11.5558i	−0.868586	+	0.501478i
$532$	21.1846	+	36.6928i	0.918468	+	1.59083i
$533$	0.891068	−	1.32358i	0.0385964	−	0.0573308i
$534$	0.220913	−	0.382632i	0.00955983	−	0.0165581i
$535$	−20.1337	+	11.6242i	−0.870457	+	0.502559i
$536$	1.09476	−	1.89617i	0.0472863	−	0.0819022i
$537$	10.2775			0.443508
$538$	−1.45540	+	0.840274i	−0.0627466	+	0.0362268i
$539$	1.87299	−	1.08137i	0.0806753	−	0.0465779i
$540$			11.7235i			0.504498i
$541$	10.4785	+	6.04975i	0.450505	+	0.260099i	0.708043	−	0.706169i	$-0.249578\pi$
$541$	10.4785	+	6.04975i	0.450505	+	0.260099i	−0.257538	+	0.966268i	$0.582911\pi$
$542$	−1.10291	+	1.91030i	−0.0473740	+	0.0820542i
$543$	1.91797	+	3.32203i	0.0823081	+	0.142562i
$544$			3.27677i			0.140490i
$545$	9.32190	+	16.1460i	0.399306	+	0.691619i
$546$	−0.405941	−	0.273289i	−0.0173727	−	0.0116957i
$547$	11.7886	+	20.4185i	0.504045	+	0.873032i	0.999989	+	0.00467729i	$0.00148883\pi$
$547$	11.7886	+	20.4185i	0.504045	+	0.873032i	−0.495944	+	0.868355i	$0.665178\pi$
$548$	−1.94826	−	1.12483i	−0.0832255	−	0.0480503i
$549$	−2.34185	+	4.05620i	−0.0999477	+	0.173114i
$550$	0.0330690	−	0.0572771i	0.00141007	−	0.00244231i
$551$	−61.5899	−	35.5590i	−2.62382	−	1.51486i
$552$	1.20907	−	0.698054i	0.0514612	−	0.0297112i
$553$			16.3820i			0.696635i
$554$		−	2.84406i		−	0.120832i
$555$	−1.00135	−	1.73439i	−0.0425051	−	0.0736209i
$556$	−8.17062	−	14.1519i	−0.346512	−	0.600176i
$557$	29.7725	−	17.1891i	1.26150	−	0.728327i	0.288135	−	0.957590i	$-0.406965\pi$
$557$	29.7725	−	17.1891i	1.26150	−	0.728327i	0.973365	+	0.229263i	$0.0736315\pi$
$558$	−1.58130	+	0.280543i	−0.0669418	+	0.0118763i
$559$	−20.5476	+	10.0442i	−0.869073	+	0.424826i
$560$	24.0191			1.01499
$561$		−	3.20944i		−	0.135503i
$562$	1.40807	+	2.43884i	0.0593956	+	0.102876i
$563$	17.4321			0.734676			0.367338	−	0.930087i	$-0.380269\pi$
$563$	17.4321			0.734676			0.367338	+	0.930087i	$0.380269\pi$
$564$	1.19190	+	0.688143i	0.0501880	+	0.0289760i
$565$	11.3020	−	6.52523i	0.475480	−	0.274519i
$566$	−2.27604	−	1.31407i	−0.0956691	−	0.0552346i
$567$	−17.1642	+	9.90976i	−0.720829	+	0.416171i
$568$	−5.89499			−0.247348
$569$	−6.50800	+	11.2722i	−0.272829	+	0.472554i	−0.969585	−	0.244754i	$-0.921293\pi$
$569$	−6.50800	+	11.2722i	−0.272829	+	0.472554i	0.696756	+	0.717308i	$0.254626\pi$
$570$			0.804379i			0.0336917i
$571$	−13.1084	−	22.7045i	−0.548571	−	0.950152i	−0.998373	−	0.0570239i	$-0.981839\pi$
$571$	−13.1084	−	22.7045i	−0.548571	−	0.950152i	0.449802	−	0.893128i	$-0.351494\pi$
$572$	−8.15280	−	16.6783i	−0.340886	−	0.697354i
$573$	2.19042			0.0915060
$574$	−0.111253	+	0.0642321i	−0.00464362	+	0.00268100i
$575$	1.77843			0.0741658
$576$	−21.5365			−0.897355
$577$	−1.77482	−	1.02469i	−0.0738866	−	0.0426585i	0.462602	−	0.886566i	$-0.346916\pi$
$577$	−1.77482	−	1.02469i	−0.0738866	−	0.0426585i	−0.536488	+	0.843908i	$0.680249\pi$
$578$			1.03357i			0.0429910i
$579$		−	10.6854i		−	0.444070i
$580$	−35.1062	+	20.2685i	−1.45770	+	0.841606i
$581$	2.25450	−	3.90491i	0.0935324	−	0.162003i
$582$	−0.0350254			−0.00145185
$583$		−	1.23291i		−	0.0510620i
$584$	−1.56442	−	2.70966i	−0.0647363	−	0.112127i
$585$	−9.60229	−	19.6435i	−0.397006	−	0.812160i
$586$	−1.49280	+	2.58560i	−0.0616669	+	0.106810i
$587$	10.7148	−	6.18621i	0.442248	−	0.255332i	−0.262303	−	0.964986i	$-0.584482\pi$
$587$	10.7148	−	6.18621i	0.442248	−	0.255332i	0.704551	+	0.709654i	$0.251149\pi$
$588$	−0.388569	−	0.673021i	−0.0160243	−	0.0277549i
$589$	41.7136	−	7.40052i	1.71878	−	0.304933i
$590$			1.87878i			0.0773483i
$591$	−5.51086	−	3.18170i	−0.226687	−	0.130878i
$592$	6.69610	−	3.86600i	0.275208	−	0.158892i
$593$		−	4.14808i		−	0.170341i	−0.996366	−	0.0851705i	$-0.972856\pi$
$593$		−	4.14808i		−	0.170341i	0.996366	−	0.0851705i	$-0.0271435\pi$
$594$	−0.725563			−0.0297702
$595$	−16.1858			−0.663552
$596$		−	5.95744i		−	0.244026i
$597$	2.67238			0.109373
$598$	−1.50719	+	2.23877i	−0.0616337	+	0.0915501i
$599$	−7.66485	−	13.2759i	−0.313177	−	0.542439i	0.665871	−	0.746067i	$-0.268060\pi$
$599$	−7.66485	−	13.2759i	−0.313177	−	0.542439i	−0.979048	+	0.203628i	$0.934727\pi$
$600$	−0.0412740	−	0.0238296i	−0.00168501	−	0.000972838i
$601$	15.1788			0.619156			0.309578	−	0.950874i	$-0.399812\pi$
$601$	15.1788			0.619156			0.309578	+	0.950874i	$0.399812\pi$
$602$	1.84142			0.0750506
$603$	−12.7483	−	7.36022i	−0.519150	−	0.299732i
$604$	−3.57674	−	2.06503i	−0.145535	−	0.0840248i
$605$	−8.12024	−	4.68822i	−0.330135	−	0.190603i
$606$	0.172204	+	0.0994222i	0.00699532	+	0.00403875i
$607$	−18.4662			−0.749519			−0.374760	−	0.927122i	$-0.622275\pi$
$607$	−18.4662			−0.749519			−0.374760	+	0.927122i	$0.622275\pi$
$608$	−9.40126			−0.381271
$609$	10.5936	+	6.11620i	0.429273	+	0.247841i
$610$	0.190373	+	0.329736i	0.00770799	+	0.0133506i
$611$	−5.32275	−	0.367476i	−0.215335	−	0.0148665i
$612$	14.6737			0.593148
$613$			21.4990i			0.868336i	0.900832	+	0.434168i	$0.142958\pi$
$613$			21.4990i			0.868336i	−0.900832	+	0.434168i	$0.857042\pi$
$614$	−0.731317			−0.0295136
$615$	0.451110			0.0181905
$616$			2.99740i			0.120769i
$617$	−18.3888	+	10.6168i	−0.740304	+	0.427415i	−0.822180	−	0.569228i	$-0.807242\pi$
$617$	−18.3888	+	10.6168i	−0.740304	+	0.427415i	0.0818761	+	0.996643i	$0.473909\pi$
$618$	0.416881	+	0.240686i	0.0167694	+	0.00968182i
$619$			23.8119i			0.957080i	0.878066	+	0.478540i	$0.158834\pi$
$619$			23.8119i			0.957080i	−0.878066	+	0.478540i	$0.841166\pi$
$620$	8.23520	−	22.7004i	0.330734	−	0.911668i
$621$	−9.75511	−	16.8963i	−0.391459	−	0.678027i
$622$	1.43390	−	0.827864i	0.0574943	−	0.0331943i
$623$	−12.7536	+	22.0899i	−0.510963	+	0.885014i
$624$	−5.96043	+	2.91362i	−0.238608	+	0.116638i
$625$	11.8537	+	20.5311i	0.474146	+	0.821245i
$626$			1.13554i			0.0453852i
$627$	9.20807			0.367735
$628$	−22.7883	+	39.4705i	−0.909353	+	1.57505i
$629$	−4.51231	+	2.60518i	−0.179918	+	0.103876i
$630$			1.76039i			0.0701358i
$631$		−	15.0376i		−	0.598636i	−0.954153	−	0.299318i	$-0.903241\pi$
$631$		−	15.0376i		−	0.598636i	0.954153	−	0.299318i	$-0.0967592\pi$
$632$	−2.09678	−	1.21058i	−0.0834055	−	0.0481542i
$633$	6.60067			0.262353
$634$	−1.83117			−0.0727251
$635$	−7.51103	+	4.33650i	−0.298066	+	0.172089i
$636$	−0.443022			−0.0175670
$637$	2.49914	+	1.68248i	0.0990195	+	0.0666622i
$638$	−1.25441	−	2.17271i	−0.0496627	−	0.0860184i
$639$			39.6330i			1.56786i
$640$	−3.56921	+	6.18205i	−0.141085	+	0.244367i
$641$	−2.91588			−0.115170			−0.0575852	−	0.998341i	$-0.518340\pi$
$641$	−2.91588			−0.115170			−0.0575852	+	0.998341i	$0.518340\pi$
$642$	−0.447750	+	0.258509i	−0.0176713	+	0.0102025i
$643$	21.2276	+	12.2557i	0.837133	+	0.483319i	0.856289	−	0.516497i	$-0.172764\pi$
$643$	21.2276	+	12.2557i	0.837133	+	0.483319i	−0.0191555	+	0.999817i	$0.506098\pi$
$644$	−34.8065	+	20.0955i	−1.37157	+	0.791874i
$645$	−5.59994	−	3.23313i	−0.220497	−	0.127304i
$646$	2.09273			0.0823372
$647$	5.89770	+	10.2151i	0.231862	+	0.401598i	0.958356	−	0.285576i	$-0.0921847\pi$
$647$	5.89770	+	10.2151i	0.231862	+	0.401598i	−0.726494	+	0.687173i	$0.758851\pi$
$648$		−	2.92919i		−	0.115070i
$649$	21.5072			0.844232
$650$	0.0919118	+	0.00634549i	0.00360508	+	0.000248890i
$651$	−7.17481	+	1.27290i	−0.281203	+	0.0498890i
$652$	−38.5917	+	22.2809i	−1.51137	+	0.872589i
$653$	−15.3868	−	26.6507i	−0.602131	−	1.04292i	−0.992498	−	0.122262i	$-0.960985\pi$
$653$	−15.3868	−	26.6507i	−0.602131	−	1.04292i	0.390367	−	0.920659i	$-0.372348\pi$
$654$	0.207308	+	0.359068i	0.00810638	+	0.0140407i
$655$			8.42214i			0.329080i
$656$			1.74163i			0.0679993i
$657$	−18.2175	+	10.5179i	−0.710732	+	0.410341i
$658$	0.372016	+	0.214784i	0.0145027	+	0.00837314i
$659$	9.30223	−	16.1119i	0.362364	−	0.627632i	−0.625986	−	0.779834i	$-0.715303\pi$
$659$	9.30223	−	16.1119i	0.362364	−	0.627632i	0.988349	+	0.152202i	$0.0486365\pi$
$660$	2.62429	−	4.54541i	0.102150	−	0.176930i
$661$	−23.9085	−	13.8036i	−0.929934	−	0.536898i	−0.0431435	−	0.999069i	$-0.513737\pi$
$661$	−23.9085	−	13.8036i	−0.929934	−	0.536898i	−0.886791	+	0.462171i	$0.847071\pi$
$662$	0.325316	+	0.563464i	0.0126438	+	0.0218997i
$663$	4.01656	−	1.96340i	0.155990	−	0.0762523i
$664$	0.333200	+	0.577119i	0.0129307	+	0.0223966i
$665$		−	46.4380i		−	1.80079i
$666$	0.283345	+	0.490767i	0.0109794	+	0.0190169i
$667$	33.7309	−	58.4237i	1.30607	−	2.26217i
$668$	−24.2085	−	13.9768i	−0.936656	−	0.540778i
$669$			8.56358i			0.331087i
$670$	−1.03633	+	0.598327i	−0.0400370	+	0.0231154i
$671$	3.77463	−	2.17928i	0.145718	−	0.0841303i
$672$	1.61703			0.0623784
$673$	−12.0777	+	20.9192i	−0.465562	+	0.806377i	−0.999227	−	0.0393194i	$-0.987481\pi$
$673$	−12.0777	+	20.9192i	−0.465562	+	0.806377i	0.533665	+	0.845696i	$0.320814\pi$
$674$	1.36246	−	0.786619i	0.0524802	−	0.0302994i
$675$	−0.333012	+	0.576793i	−0.0128176	+	0.0222008i
$676$	15.8851	−	20.4062i	0.610965	−	0.784854i
$677$	19.0345	+	32.9687i	0.731554	+	1.26709i	0.956219	+	0.292653i	$0.0945379\pi$
$677$	19.0345	+	32.9687i	0.731554	+	1.26709i	−0.224665	+	0.974436i	$0.572129\pi$
$678$	0.251344	−	0.145113i	0.00965280	−	0.00557305i
$679$	2.02207			0.0775999
$680$	1.19607	−	2.07166i	0.0458674	−	0.0794446i
$681$			4.23922i			0.162447i
$682$	1.40492	+	0.509674i	0.0537971	+	0.0195164i
$683$	−9.71900	−	5.61127i	−0.371887	−	0.214709i	0.302395	−	0.953183i	$-0.402214\pi$
$683$	−9.71900	−	5.61127i	−0.371887	−	0.214709i	−0.674283	+	0.738473i	$0.735547\pi$
$684$			42.0996i			1.60972i
$685$	1.23285	+	2.13535i	0.0471047	+	0.0815877i
$686$	0.894741	+	1.54974i	0.0341614	+	0.0591692i
$687$	10.7277	+	6.19366i	0.409289	+	0.236303i
$688$	12.4824	−	21.6201i	0.475886	−	0.824259i
$689$	1.54297	−	0.754247i	0.0587826	−	0.0287345i
$690$	−0.763027			−0.0290479
$691$	18.3109	+	10.5718i	0.696579	+	0.402170i	0.806072	−	0.591817i	$-0.201589\pi$
$691$	18.3109	+	10.5718i	0.696579	+	0.402170i	−0.109493	+	0.993988i	$0.534923\pi$
$692$	9.07757	−	15.7228i	0.345078	−	0.597692i
$693$	20.1520			0.765511
$694$	1.00800	+	0.581968i	0.0382631	+	0.0220912i
$695$			17.9105i			0.679385i
$696$	−1.56566	+	0.903934i	−0.0593461	+	0.0342635i
$697$		−	1.17364i		−	0.0444547i
$698$	0.0802181	−	0.138942i	0.00303630	−	0.00525903i
$699$	3.19389			0.120804
$700$	1.18819	+	0.686003i	0.0449095	+	0.0259285i
$701$	23.9382	−	41.4621i	0.904132	−	1.56600i	0.0820542	−	0.996628i	$-0.473852\pi$
$701$	23.9382	−	41.4621i	0.904132	−	1.56600i	0.822078	−	0.569375i	$-0.192815\pi$
$702$	−0.443870	−	0.908031i	−0.0167528	−	0.0342714i
$703$	−7.47443	−	12.9461i	−0.281904	−	0.488271i
$704$	17.3565	+	10.0208i	0.654146	+	0.377671i
$705$	−0.754226	−	1.30636i	−0.0284058	−	0.0492003i
$706$	0.954297	+	1.65289i	0.0359154	+	0.0622074i
$707$	−9.94160	−	5.73978i	−0.373892	−	0.215867i
$708$		−	7.72818i		−	0.290443i
$709$	−32.9655	−	19.0326i	−1.23804	−	0.714785i	−0.269350	−	0.963042i	$-0.586809\pi$
$709$	−32.9655	−	19.0326i	−1.23804	−	0.714785i	−0.968694	+	0.248257i	$0.920142\pi$
$710$	2.79019	+	1.61092i	0.104714	+	0.0604567i
$711$	−8.13891	+	14.0970i	−0.305233	+	0.528679i
$712$	−1.88490	−	3.26474i	−0.0706396	−	0.122351i
$713$	7.02007	+	39.5692i	0.262904	+	1.48188i
$714$	−0.359952			−0.0134709
$715$	−1.40140	+	20.2988i	−0.0524095	+	0.759130i
$716$	21.8637	−	37.8690i	0.817084	−	1.41523i
$717$	9.59254	−	5.53826i	0.358240	−	0.206830i
$718$	−1.55011	+	2.68487i	−0.0578497	+	0.100199i
$719$	11.6617	+	20.1987i	0.434908	+	0.753283i	0.997288	−	0.0735958i	$-0.0234475\pi$
$719$	11.6617	+	20.1987i	0.434908	+	0.753283i	−0.562380	+	0.826879i	$0.690114\pi$
$720$	20.6688	+	11.9331i	0.770281	+	0.444722i
$721$	−24.0671	−	13.8952i	−0.896306	−	0.517483i
$722$			4.03376i			0.150121i
$723$	−0.733537	+	0.423508i	−0.0272805	+	0.0157504i
$724$	16.3206			0.606552
$725$	−2.30295			−0.0855296
$726$	−0.180584	−	0.104260i	−0.00670212	−	0.00386947i
$727$	−10.9626	+	18.9878i	−0.406580	+	0.704218i	−0.994504	−	0.104698i	$-0.966612\pi$
$727$	−10.9626	+	18.9878i	−0.406580	+	0.704218i	0.587924	+	0.808917i	$0.299946\pi$
$728$	−3.75120	+	1.83369i	−0.139029	+	0.0679610i
$729$	−15.9020			−0.588963
$730$			1.71004i			0.0632913i
$731$	−8.41151	+	14.5692i	−0.311111	+	0.538860i
$732$	−0.783082	−	1.35634i	−0.0289435	−	0.0501317i
$733$	9.42650	−	5.44239i	0.348176	−	0.201019i	−0.315706	−	0.948857i	$-0.602241\pi$
$733$	9.42650	−	5.44239i	0.348176	−	0.201019i	0.663881	+	0.747838i	$0.268908\pi$
$734$		−	3.75116i		−	0.138458i
$735$			0.851767i			0.0314179i
$736$		−	8.91795i		−	0.328720i
$737$	6.84930	+	11.8633i	0.252297	+	0.436991i
$738$	−0.127647			−0.00469875
$739$	−3.12715	−	1.80546i	−0.115034	−	0.0664149i	0.441379	−	0.897321i	$-0.354489\pi$
$739$	−3.12715	−	1.80546i	−0.115034	−	0.0664149i	−0.556413	+	0.830906i	$0.687823\pi$
$740$	−8.52083			−0.313232
$741$	5.63313	+	11.5238i	0.206938	+	0.423336i
$742$	−0.138277			−0.00507629
$743$	−14.0619	+	8.11867i	−0.515883	+	0.297845i	−0.735248	−	0.677798i	$-0.762935\pi$
$743$	−14.0619	+	8.11867i	−0.515883	+	0.297845i	0.219366	+	0.975643i	$0.429601\pi$
$744$	0.367272	−	1.01239i	0.0134649	−	0.0371159i
$745$	−3.26477	+	5.65475i	−0.119612	+	0.207174i
$746$		−	3.93484i		−	0.144065i
$747$	3.88006	−	2.24016i	0.141964	−	0.0819630i
$748$	−11.8256	−	6.82753i	−0.432388	−	0.249639i
$749$	25.8493	−	14.9241i	0.944511	−	0.545314i
$750$	0.277310	+	0.480315i	0.0101259	+	0.0175386i
$751$	42.6465			1.55619			0.778097	−	0.628144i	$-0.216185\pi$
$751$	42.6465			1.55619			0.778097	+	0.628144i	$0.216185\pi$
$752$	5.04356	−	2.91190i	0.183920	−	0.106186i
$753$	−5.86283	−	10.1547i	−0.213654	−	0.370059i
$754$	1.95171	−	2.89906i	0.0710772	−	0.105577i
$755$	2.26334	+	3.92022i	0.0823713	+	0.142671i
$756$		−	15.0515i		−	0.547419i
$757$	15.5666	−	26.9622i	0.565779	−	0.979958i	−0.431198	−	0.902257i	$-0.641909\pi$
$757$	15.5666	−	26.9622i	0.565779	−	0.979958i	0.996977	−	0.0777003i	$-0.0247577\pi$
$758$	0.162958	+	0.282251i	0.00591889	+	0.0102518i
$759$			8.73469i			0.317049i
$760$	5.94372	+	3.43161i	0.215601	+	0.124478i
$761$	−20.2526	+	11.6929i	−0.734157	+	0.423866i	−0.819941	−	0.572448i	$-0.805994\pi$
$761$	−20.2526	+	11.6929i	−0.734157	+	0.423866i	0.0857837	+	0.996314i	$0.472661\pi$
$762$	−0.167036	+	0.0964385i	−0.00605109	+	0.00349360i
$763$	−11.9682	−	20.7295i	−0.433278	−	0.750459i
$764$	4.65974	−	8.07091i	0.168583	−	0.291995i
$765$	−13.9281	−	8.04140i	−0.503572	−	0.290737i
$766$	−0.997544	−	1.72780i	−0.0360427	−	0.0624278i
$767$	13.1573	+	26.9160i	0.475081	+	0.971879i
$768$	3.54085	−	6.13293i	0.127769	−	0.221303i
$769$			26.0099i			0.937939i	0.883214	+	0.468970i	$0.155375\pi$
$769$			26.0099i			0.937939i	−0.883214	+	0.468970i	$0.844625\pi$
$770$	0.819097	−	1.41872i	0.0295182	−	0.0511270i
$771$	3.68136	−	6.37630i	0.132581	−	0.229637i
$772$	−39.3719	−	22.7314i	−1.41703	−	0.818121i
$773$	0.261577	+	0.151021i	0.00940825	+	0.00543186i	0.504697	−	0.863297i	$-0.331604\pi$
$773$	0.261577	+	0.151021i	0.00940825	+	0.00543186i	−0.495288	+	0.868729i	$0.664938\pi$
$774$	1.58457	+	0.914852i	0.0569562	+	0.0328837i
$775$	1.04999	−	0.882928i	0.0377166	−	0.0317157i
$776$	−0.149424	+	0.258810i	−0.00536401	+	0.00929074i
$777$	1.28562	+	2.22675i	0.0461212	+	0.0798843i
$778$			3.83021i			0.137320i
$779$	3.36723			0.120644
$780$	7.29395	+	0.503566i	0.261165	+	0.0180306i
$781$	18.4409	−	31.9405i	0.659867	−	1.14292i
$782$			1.98514i			0.0709885i
$783$	12.6322	+	21.8796i	0.451439	+	0.781914i
$784$	−3.28848			−0.117446
$785$	43.2610	−	24.9767i	1.54405	−	0.891458i
$786$			0.187298i			0.00668071i
$787$	44.0171	−	25.4133i	1.56904	−	0.905885i	0.572758	−	0.819725i	$-0.305874\pi$
$787$	44.0171	−	25.4133i	1.56904	−	0.905885i	0.996281	−	0.0861604i	$-0.0274598\pi$
$788$	−23.4468	+	13.5370i	−0.835259	+	0.482237i
$789$	−2.69543	−	4.66863i	−0.0959600	−	0.166208i
$790$	0.661627	+	1.14597i	0.0235396	+	0.0407719i
$791$	−14.5104	+	8.37761i	−0.515932	+	0.297873i
$792$	−1.48916	+	2.57931i	−0.0529151	+	0.0916517i
$793$	5.03651	+	3.39070i	0.178852	+	0.120407i
$794$	−0.152339	+	0.263859i	−0.00540631	+	0.00936401i
$795$	0.420513	+	0.242783i	0.0149141	+	0.00861064i
$796$	5.68502	−	9.84675i	0.201500	−	0.349009i
$797$	−22.6631			−0.802769			−0.401384	−	0.915910i	$-0.631471\pi$
$797$	−22.6631			−0.802769			−0.401384	+	0.915910i	$0.631471\pi$
$798$		−	1.03273i		−	0.0365581i
$799$	−3.39871	+	1.96224i	−0.120238	+	0.0694192i
$800$	−0.263647	+	0.152217i	−0.00932133	+	0.00538167i
$801$	−21.9494	+	12.6725i	−0.775543	+	0.447760i
$802$	0.0317650	−	0.0550186i	0.00112166	−	0.00194277i
$803$	19.5755			0.690804
$804$	4.26285	−	2.46116i	0.150339	−	0.0867983i
$805$	44.0506			1.55258
$806$	0.221623	+	2.07003i	0.00780632	+	0.0729138i
$807$	−7.57661			−0.266709
$808$	1.46930	−	0.848302i	0.0516898	−	0.0298431i
$809$	−18.4758			−0.649573			−0.324786	−	0.945787i	$-0.605292\pi$
$809$	−18.4758			−0.649573			−0.324786	+	0.945787i	$0.605292\pi$
$810$	−0.800458	+	1.38643i	−0.0281252	+	0.0487143i
$811$	26.3465	−	15.2112i	0.925152	−	0.534137i	0.0398772	−	0.999205i	$-0.487303\pi$
$811$	26.3465	−	15.2112i	0.925152	−	0.534137i	0.885275	+	0.465068i	$0.153970\pi$
$812$	45.0720	−	26.0224i	1.58172	−	0.913206i
$813$	−8.61241	+	4.97238i	−0.302050	+	0.174389i
$814$		−	0.527351i		−	0.0184837i
$815$	48.8412			1.71083
$816$	−2.44000	+	4.22620i	−0.0854171	+	0.147947i
$817$	−41.7998	−	24.1331i	−1.46239	−	0.844312i
$818$	1.22300	−	2.11829i	0.0427611	−	0.0740644i
$819$	12.3282	+	25.2199i	0.430781	+	0.881255i
$820$	0.959659	−	1.66218i	0.0335127	−	0.0580458i
$821$	18.2519	−	10.5377i	0.636995	−	0.367769i	−0.146461	−	0.989216i	$-0.546788\pi$
$821$	18.2519	−	10.5377i	0.636995	−	0.367769i	0.783456	+	0.621447i	$0.213455\pi$
$822$	0.0274171	+	0.0474877i	0.000956280	+	0.00165632i
$823$	−15.2994	−	26.4993i	−0.533303	−	0.923707i	−0.999243	−	0.0388914i	$-0.987617\pi$
$823$	−15.2994	−	26.4993i	−0.533303	−	0.923707i	0.465941	−	0.884816i	$-0.345716\pi$
$824$	3.55696	−	2.05361i	0.123913	−	0.0715409i
$825$	0.258229	−	0.149089i	0.00899039	−	0.00519060i
$826$		−	2.41213i		−	0.0839287i
$827$	−22.3862	+	12.9247i	−0.778444	+	0.449435i	−0.835878	−	0.548915i	$-0.815041\pi$
$827$	−22.3862	+	12.9247i	−0.778444	+	0.449435i	0.0574347	+	0.998349i	$0.481708\pi$
$828$	−39.9353			−1.38785
$829$	11.9374	+	20.6762i	0.414604	+	0.718114i	0.995387	−	0.0959439i	$-0.0305869\pi$
$829$	11.9374	+	20.6762i	0.414604	+	0.718114i	−0.580783	+	0.814058i	$0.697254\pi$
$830$		−	0.364213i		−	0.0126420i
$831$	6.41110	−	11.1043i	0.222398	−	0.385205i
$832$	−1.92285	+	27.8516i	−0.0666627	+	0.965582i
$833$	2.21601			0.0767803
$834$			0.398309i			0.0137923i
$835$	15.3190	+	26.5333i	0.530136	+	0.918223i
$836$	19.5886	−	33.9284i	0.677486	−	1.17344i
$837$	−14.1478	−	5.13253i	−0.489020	−	0.177406i
$838$	−3.13948	−	1.81258i	−0.108452	−	0.0626146i
$839$	−11.7974	−	6.81121i	−0.407290	−	0.235149i	0.282335	−	0.959316i	$-0.408891\pi$
$839$	−11.7974	−	6.81121i	−0.407290	−	0.235149i	−0.689625	+	0.724167i	$0.742224\pi$
$840$	−1.02233	−	0.590243i	−0.0352738	−	0.0203653i
$841$	−29.1793	+	50.5400i	−1.00618	+	1.74276i
$842$	0.260488	−	0.451178i	0.00897699	−	0.0155486i
$843$			12.6963i			0.437284i
$844$	14.0418	−	24.3211i	0.483339	−	0.837167i
$845$	−26.2609	+	10.6641i	−0.903403	+	0.366857i
$846$	0.213417	+	0.369650i	0.00733744	+	0.0127088i
$847$	10.4254	+	6.01911i	0.358221	+	0.206819i
$848$	−0.937332	+	1.62351i	−0.0321881	+	0.0557514i
$849$	−5.92439	−	10.2613i	−0.203325	−	0.352168i
$850$	0.0586880	−	0.0338835i	0.00201298	−	0.00116220i
$851$	12.2806	−	7.09018i	0.420972	−	0.243048i
$852$	−11.4772	−	6.62636i	−0.393202	−	0.227015i
$853$		−	16.4565i		−	0.563461i	−0.959494	−	0.281730i	$-0.909092\pi$
$853$		−	16.4565i		−	0.563461i	0.959494	−	0.281730i	$-0.0909084\pi$
$854$	−0.244416	−	0.423341i	−0.00836375	−	0.0144864i
$855$	23.0713	−	39.9606i	0.789021	−	1.36662i
$856$			4.41136i			0.150777i
$857$	−11.1650	−	19.3384i	−0.381390	−	0.660587i	0.609871	−	0.792501i	$-0.291221\pi$
$857$	−11.1650	−	19.3384i	−0.381390	−	0.660587i	−0.991261	+	0.131913i	$0.957888\pi$
$858$	−0.0311655	+	0.451420i	−0.00106397	+	0.0154112i
$859$	−7.31382	−	12.6679i	−0.249544	−	0.432223i	0.713855	−	0.700293i	$-0.246947\pi$
$859$	−7.31382	−	12.6679i	−0.249544	−	0.432223i	−0.963399	+	0.268070i	$0.913614\pi$
$860$	−23.8258	+	13.7558i	−0.812454	+	0.469071i
$861$	−0.579170			−0.0197381
$862$	0.448963	+	0.777627i	0.0152917	+	0.0264861i
$863$	34.9230	−	20.1628i	1.18879	−	0.686350i	0.230761	−	0.973011i	$-0.425879\pi$
$863$	34.9230	−	20.1628i	1.18879	−	0.686350i	0.958032	+	0.286661i	$0.0925453\pi$
$864$	2.89233	+	1.66989i	0.0983989	+	0.0568106i
$865$	−17.2327	+	9.94931i	−0.585930	+	0.338287i
$866$			1.57421i			0.0534939i
$867$	−2.32989	+	4.03549i	−0.0791272	+	0.137052i
$868$	−10.5730	+	29.1445i	−0.358871	+	0.989229i
$869$	13.1184	−	7.57393i	0.445012	−	0.256928i
$870$	0.988069			0.0334987
$871$	−10.6567	+	15.8293i	−0.361087	+	0.536356i
$872$	3.53764			0.119799
$873$	1.74002	+	1.00460i	0.0588908	+	0.0340006i
$874$	−5.69549			−0.192653
$875$	−16.0095	−	27.7293i	−0.541220	−	0.937421i
$876$		−	7.03406i		−	0.237659i
$877$		−	5.34331i		−	0.180431i	−0.995922	−	0.0902155i	$-0.971244\pi$
$877$		−	5.34331i		−	0.180431i	0.995922	−	0.0902155i	$-0.0287556\pi$
$878$			1.78446i			0.0602227i
$879$	−11.6570	+	6.73016i	−0.393180	+	0.227003i
$880$	−11.1048	−	19.2340i	−0.374342	−	0.648379i
$881$	−23.3510	+	40.4451i	−0.786716	+	1.36263i	0.141253	+	0.989974i	$0.454887\pi$
$881$	−23.3510	+	40.4451i	−0.786716	+	1.36263i	−0.927969	+	0.372658i	$0.878446\pi$
$882$		−	0.241018i		−	0.00811549i
$883$	−47.0864			−1.58458			−0.792292	−	0.610142i	$-0.791112\pi$
$883$	−47.0864			−1.58458			−0.792292	+	0.610142i	$0.791112\pi$
$884$	1.31011	−	18.9764i	0.0440638	−	0.638246i
$885$	−4.23517	+	7.33553i	−0.142364	+	0.246581i
$886$	−2.78447	−	1.60761i	−0.0935460	−	0.0540088i
$887$	23.4408			0.787067			0.393533	−	0.919310i	$-0.371253\pi$
$887$	23.4408			0.787067			0.393533	+	0.919310i	$0.371253\pi$
$888$	−0.380011			−0.0127523
$889$	9.64325	−	5.56754i	0.323424	−	0.186729i
$890$			2.06034i			0.0690627i
$891$	15.8711	+	9.16318i	0.531702	+	0.306978i
$892$	31.5537	+	18.2176i	1.05650	+	0.609969i
$893$	−5.62980	−	9.75110i	−0.188394	−	0.326308i
$894$	−0.0726046	+	0.125755i	−0.00242826	+	0.00420587i
$895$	−41.5057	+	23.9633i	−1.38738	+	0.801005i
$896$	4.58243	−	7.93700i	0.153088	−	0.265157i
$897$	−10.9313	+	5.34353i	−0.364987	+	0.178415i
$898$	−3.51809			−0.117400
$899$	−9.09052	−	51.2394i	−0.303186	−	1.70893i
$900$	0.681639	+	1.18063i	0.0227213	+	0.0393545i
$901$	0.631641	−	1.09403i	0.0210430	−	0.0364476i
$902$	0.102872	+	0.0593930i	0.00342525	+	0.00197757i
$903$	7.18964	+	4.15094i	0.239256	+	0.138135i
$904$		−	2.47631i		−	0.0823608i
$905$	−15.4914	−	8.94397i	−0.514952	−	0.297308i
$906$	0.0503339	+	0.0871809i	0.00167223	+	0.00289639i
$907$	−6.89580	−	11.9439i	−0.228971	−	0.396590i	0.728532	−	0.685011i	$-0.240203\pi$
$907$	−6.89580	−	11.9439i	−0.228971	−	0.396590i	−0.957503	+	0.288422i	$0.906870\pi$
$908$	15.6200	+	9.01822i	0.518369	+	0.299280i
$909$	−5.70327	−	9.87835i	−0.189165	−	0.327644i
$910$	2.27659	+	0.157174i	0.0754684	+	0.00521025i
$911$	−22.0568	+	38.2035i	−0.730774	+	1.26574i	0.225779	+	0.974178i	$0.427507\pi$
$911$	−22.0568	+	38.2035i	−0.730774	+	1.26574i	−0.956553	+	0.291559i	$0.905826\pi$
$912$	−12.1252	−	7.00051i	−0.401506	−	0.231810i
$913$	−4.16930			−0.137984
$914$	−0.953817	+	1.65206i	−0.0315495	+	0.0546453i
$915$			1.71657i			0.0567479i
$916$	45.6429	−	26.3519i	1.50808	−	0.870692i
$917$		−	10.8130i		−	0.357077i
$918$	−0.643833	−	0.371717i	−0.0212497	−	0.0122685i
$919$	6.06988			0.200227			0.100113	−	0.994976i	$-0.468079\pi$
$919$	6.06988			0.200227			0.100113	+	0.994976i	$0.468079\pi$
$920$	−3.25520	+	5.63816i	−0.107321	+	0.185885i
$921$	−2.85536	−	1.64854i	−0.0940873	−	0.0543213i
$922$	−0.757802			−0.0249569
$923$	51.2545	+	3.53855i	1.68706	+	0.116473i
$924$	−3.36927	+	5.83575i	−0.110841	+	0.191982i
$925$	−0.419223	−	0.242039i	−0.0137840	−	0.00795818i
$926$	1.55440	+	2.69230i	0.0510808	+	0.0884746i
$927$	−13.8068	−	23.9140i	−0.453473	−	0.785439i
$928$			11.5482i			0.379087i
$929$	−17.5619	−	10.1394i	−0.576187	−	0.332662i	0.183430	−	0.983033i	$-0.441280\pi$
$929$	−17.5619	−	10.1394i	−0.576187	−	0.332662i	−0.759616	+	0.650371i	$0.774613\pi$
$930$	−0.450490	+	0.378815i	−0.0147722	+	0.0124218i
$931$			6.35788i			0.208371i
$932$	6.79446	−	11.7684i	0.222560	−	0.385485i
$933$	7.46471			0.244384
$934$	1.52245	−	0.878988i	0.0498162	−	0.0287614i
$935$	7.48319	+	12.9613i	0.244726	+	0.423879i
$936$	−4.13898	−	0.285750i	−0.135287	−	0.00934004i
$937$	−15.2106	+	26.3454i	−0.496907	+	0.860668i	−0.999994	−	0.00356773i	$-0.998864\pi$
$937$	−15.2106	+	26.3454i	−0.496907	+	0.860668i	0.503087	+	0.864236i	$0.332198\pi$
$938$	1.33052	−	0.768179i	0.0434432	−	0.0250819i
$939$	−2.55974	+	4.43359i	−0.0835339	+	0.144685i
$940$	−6.41795			−0.209331
$941$	34.1033	−	19.6895i	1.11174	−	0.641861i	0.172457	−	0.985017i	$-0.444829\pi$
$941$	34.1033	−	19.6895i	1.11174	−	0.641861i	0.939278	+	0.343156i	$0.111496\pi$
$942$	0.962072	−	0.555453i	0.0313460	−	0.0180976i
$943$			3.19413i			0.104015i
$944$	−28.3208	−	16.3510i	−0.921764	−	0.532181i
$945$	−8.24848	+	14.2868i	−0.268323	+	0.464749i
$946$	−0.851345	−	1.47457i	−0.0276796	−	0.0479425i
$947$		−	26.9349i		−	0.875267i	−0.899154	−	0.437633i	$-0.855817\pi$
$947$		−	26.9349i		−	0.875267i	0.899154	−	0.437633i	$-0.144183\pi$
$948$	−2.72154	−	4.71384i	−0.0883914	−	0.153098i
$949$	11.9755	+	24.4985i	0.388741	+	0.795254i
$950$	0.0972139	+	0.168379i	0.00315403	+	0.00546295i
$951$	−7.14964	−	4.12784i	−0.231843	−	0.133855i
$952$	−1.53561	+	2.65976i	−0.0497695	+	0.0862034i
$953$	20.5754	−	35.6377i	0.666503	−	1.15442i	−0.312372	−	0.949960i	$-0.601124\pi$
$953$	20.5754	−	35.6377i	0.666503	−	1.15442i	0.978875	−	0.204458i	$-0.0655431\pi$
$954$	−0.118989	−	0.0686984i	−0.00385242	−	0.00222419i
$955$	−8.84597	+	5.10722i	−0.286249	+	0.165266i
$956$		−	47.1268i		−	1.52419i
$957$		−	11.3108i		−	0.365628i
$958$	1.17857	+	2.04133i	0.0380777	+	0.0659525i
$959$	−1.58283	−	2.74154i	−0.0511121	−	0.0885288i
$960$	−6.83561	+	3.94654i	−0.220618	+	0.127374i
$961$	23.7893	+	19.8764i	0.767396	+	0.641173i
$962$	0.659973	−	0.322612i	0.0212784	−	0.0104014i
$963$	29.6583			0.955724
$964$			3.60376i			0.116069i
$965$	24.9143	+	43.1529i	0.802021	+	1.38914i
$966$	0.979634			0.0315192
$967$	−33.7786	−	19.5021i	−1.08625	−	0.627145i	−0.153672	−	0.988122i	$-0.549110\pi$
$967$	−33.7786	−	19.5021i	−1.08625	−	0.627145i	−0.932575	+	0.360977i	$0.882443\pi$
$968$	−1.54080	+	0.889584i	−0.0495233	+	0.0285923i
$969$	8.17084	+	4.71744i	0.262485	+	0.151546i
$970$	0.141450	−	0.0816660i	0.00454168	−	0.00262214i
$971$	53.1186			1.70466			0.852329	−	0.523006i	$-0.175190\pi$
$971$	53.1186			1.70466			0.852329	+	0.523006i	$0.175190\pi$
$972$	11.3582	−	19.6730i	0.364314	−	0.631011i
$973$		−	22.9949i		−	0.737184i
$974$	0.301032	+	0.521402i	0.00964568	+	0.0167068i
$975$	0.344557	+	0.231964i	0.0110346	+	0.00742878i
$976$	−6.62727			−0.212134
$977$	−26.2866	+	15.1766i	−0.840982	+	0.485541i	−0.857598	−	0.514321i	$-0.828044\pi$
$977$	−26.2866	+	15.1766i	−0.840982	+	0.485541i	0.0166160	+	0.999862i	$0.494711\pi$
$978$	1.08617			0.0347319
$979$	23.5856			0.753798
$980$	3.13846	+	1.81199i	0.100254	+	0.0578819i
$981$		−	23.7841i		−	0.759368i
$982$		−	0.636792i		−	0.0203209i
$983$	26.1649	−	15.1063i	0.834530	−	0.481816i	−0.0208714	−	0.999782i	$-0.506644\pi$
$983$	26.1649	−	15.1063i	0.834530	−	0.481816i	0.855401	+	0.517966i	$0.173311\pi$
$984$	0.0427987	−	0.0741296i	0.00136437	−	0.00236316i
$985$	29.6741			0.945494
$986$		−	2.57062i		−	0.0818654i
$987$	0.968335	+	1.67721i	0.0308224	+	0.0533860i
$988$	54.4445	+	3.75878i	1.73211	+	0.119583i
$989$	22.8925	−	39.6509i	0.727939	−	1.26083i
$990$	1.40969	−	0.813886i	0.0448029	−	0.0258670i
$991$	−3.07036	−	5.31801i	−0.0975331	−	0.168932i	0.813130	−	0.582082i	$-0.197762\pi$
$991$	−3.07036	−	5.31801i	−0.0975331	−	0.168932i	−0.910663	+	0.413150i	$0.864429\pi$
$992$	−4.42744	−	5.26515i	−0.140571	−	0.167169i
$993$			2.93332i			0.0930862i
$994$	−3.58227	−	2.06823i	−0.113623	−	0.0656001i
$995$	−10.7924	+	6.23097i	−0.342141	+	0.197535i
$996$			1.49815i			0.0474708i
$997$	0.350010			0.0110849			0.00554246	−	0.999985i	$-0.498236\pi$
$997$	0.350010			0.0110849			0.00554246	+	0.999985i	$0.498236\pi$
$998$	1.30604			0.0413420
$999$			5.31054i			0.168018i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.v.a.36.18	yes	70
13.4	even	6		403.2.s.a.160.18	✓	70
31.25	even	3		403.2.s.a.335.18	yes	70
403.56	even	6	inner	403.2.v.a.56.18	yes	70

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.s.a.160.18	✓	70	13.4	even	6
403.2.s.a.335.18	yes	70	31.25	even	3
403.2.v.a.36.18	yes	70	1.1	even	1	trivial
403.2.v.a.56.18	yes	70	403.56	even	6	inner

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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.v (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0898111 + 0.0518525i) q^{2} -0.467545 q^{3} +(-0.994623 + 1.72274i) q^{4} +(1.88817 - 1.09014i) q^{5} +(0.0419908 - 0.0242434i) q^{6} +(-2.42419 + 1.39960i) q^{7} -0.413704i q^{8} -2.78140 q^{9} +O(q^{10})\)	\(q+(-0.0898111 + 0.0518525i) q^{2} -0.467545 q^{3} +(-0.994623 + 1.72274i) q^{4} +(1.88817 - 1.09014i) q^{5} +(0.0419908 - 0.0242434i) q^{6} +(-2.42419 + 1.39960i) q^{7} -0.413704i q^{8} -2.78140 q^{9} +(-0.113053 + 0.195813i) q^{10} +(2.24155 + 1.29416i) q^{11} +(0.465031 - 0.805457i) q^{12} +(-0.248332 + 3.59699i) q^{13} +(0.145146 - 0.251400i) q^{14} +(-0.882807 + 0.509689i) q^{15} +(-1.96779 - 3.40832i) q^{16} +(1.32604 + 2.29677i) q^{17} +(0.249801 - 0.144223i) q^{18} +(-6.58957 + 3.80449i) q^{19} +4.33710i q^{20} +(1.13342 - 0.654379i) q^{21} -0.268422 q^{22} +(-3.60890 - 6.25080i) q^{23} +0.193426i q^{24} +(-0.123198 + 0.213385i) q^{25} +(-0.164210 - 0.335926i) q^{26} +2.70307 q^{27} -5.56831i q^{28} +(4.67329 + 8.09438i) q^{29} +(0.0528573 - 0.0915514i) q^{30} +(-5.23399 - 1.89878i) q^{31} +(1.07002 + 0.617774i) q^{32} +(-1.04803 - 0.605079i) q^{33} +(-0.238186 - 0.137517i) q^{34} +(-3.05153 + 5.28540i) q^{35} +(2.76644 - 4.79162i) q^{36} +1.96464i q^{37} +(0.394544 - 0.683371i) q^{38} +(0.116106 - 1.68176i) q^{39} +(-0.450995 - 0.781146i) q^{40} +(-0.383246 - 0.221267i) q^{41} +(-0.0678623 + 0.117541i) q^{42} +(3.17167 + 5.49349i) q^{43} +(-4.45900 + 2.57441i) q^{44} +(-5.25177 + 3.03211i) q^{45} +(0.648239 + 0.374261i) q^{46} +1.47978i q^{47} +(0.920032 + 1.59354i) q^{48} +(0.417788 - 0.723630i) q^{49} -0.0255524i q^{50} +(-0.619983 - 1.07384i) q^{51} +(-5.94967 - 4.00546i) q^{52} +(-0.238168 - 0.412519i) q^{53} +(-0.242765 + 0.140161i) q^{54} +5.64326 q^{55} +(0.579023 + 1.00290i) q^{56} +(3.08092 - 1.77877i) q^{57} +(-0.839427 - 0.484643i) q^{58} +(7.19608 - 4.15466i) q^{59} -2.02779i q^{60} +(0.841967 - 1.45833i) q^{61} +(0.568527 - 0.100864i) q^{62} +(6.74264 - 3.89286i) q^{63} +7.74304 q^{64} +(3.45232 + 7.06246i) q^{65} +0.125499 q^{66} +(4.58340 + 2.64623i) q^{67} -5.27564 q^{68} +(1.68733 + 2.92253i) q^{69} -0.632917i q^{70} -14.2493i q^{71} +1.15068i q^{72} +(6.54975 - 3.78150i) q^{73} +(-0.101871 - 0.176446i) q^{74} +(0.0576005 - 0.0997670i) q^{75} -15.1361i q^{76} -7.24526 q^{77} +(0.0767755 + 0.157061i) q^{78} +(2.92619 - 5.06831i) q^{79} +(-7.43108 - 4.29033i) q^{80} +7.08040 q^{81} +0.0458930 q^{82} +(-1.39500 + 0.805406i) q^{83} +2.60344i q^{84} +(5.00759 + 2.89113i) q^{85} +(-0.569702 - 0.328918i) q^{86} +(-2.18497 - 3.78449i) q^{87} +(0.535401 - 0.927341i) q^{88} +(7.89148 - 4.55615i) q^{89} +(0.314445 - 0.544635i) q^{90} +(-4.43236 - 9.06734i) q^{91} +14.3580 q^{92} +(2.44713 + 0.887765i) q^{93} +(-0.0767301 - 0.132901i) q^{94} +(-8.29483 + 14.3671i) q^{95} +(-0.500281 - 0.288837i) q^{96} +(-0.625592 - 0.361186i) q^{97} +0.0866533i q^{98} +(-6.23466 - 3.59958i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 70 q - 6 q^{2} + 4 q^{3} + 30 q^{4} + 6 q^{6} - 12 q^{7} + 58 q^{9}+O(q^{10}) \) 70 * q - 6 * q^2 + 4 * q^3 + 30 * q^4 + 6 * q^6 - 12 * q^7 + 58 * q^9	\( 70 q - 6 q^{2} + 4 q^{3} + 30 q^{4} + 6 q^{6} - 12 q^{7} + 58 q^{9} - q^{10} - 6 q^{11} + 13 q^{12} - 14 q^{13} - 14 q^{14} - 15 q^{15} - 28 q^{16} + 6 q^{17} + 12 q^{19} + 9 q^{21} - 8 q^{22} + 10 q^{23} + 19 q^{25} + 34 q^{27} - 18 q^{29} - 31 q^{30} + 2 q^{31} + 36 q^{32} - 12 q^{33} - 9 q^{34} - 12 q^{35} + 8 q^{36} - 21 q^{38} - 30 q^{39} + 5 q^{40} + 18 q^{41} - 49 q^{42} + 19 q^{43} - 42 q^{44} - 63 q^{45} - 6 q^{46} - 27 q^{48} + 9 q^{49} - 7 q^{51} - 43 q^{52} - 22 q^{53} + 18 q^{54} + 30 q^{55} + 25 q^{56} - 15 q^{57} - 12 q^{58} + 33 q^{59} - 13 q^{61} - 17 q^{62} - 6 q^{63} - 38 q^{64} + 9 q^{65} - 52 q^{66} + 30 q^{67} + 88 q^{68} - 16 q^{69} + 9 q^{73} - 19 q^{74} + 25 q^{75} + 34 q^{77} + 14 q^{78} + 6 q^{79} + 6 q^{80} + 22 q^{81} - 78 q^{82} + 54 q^{83} - 33 q^{85} + 24 q^{86} - 14 q^{87} + 16 q^{88} - 6 q^{89} - 11 q^{90} - 70 q^{91} - 6 q^{92} + 7 q^{93} - 43 q^{94} + 25 q^{95} - 36 q^{96} - 75 q^{97} - 93 q^{99}+O(q^{100}) \) 70 * q - 6 * q^2 + 4 * q^3 + 30 * q^4 + 6 * q^6 - 12 * q^7 + 58 * q^9 - q^10 - 6 * q^11 + 13 * q^12 - 14 * q^13 - 14 * q^14 - 15 * q^15 - 28 * q^16 + 6 * q^17 + 12 * q^19 + 9 * q^21 - 8 * q^22 + 10 * q^23 + 19 * q^25 + 34 * q^27 - 18 * q^29 - 31 * q^30 + 2 * q^31 + 36 * q^32 - 12 * q^33 - 9 * q^34 - 12 * q^35 + 8 * q^36 - 21 * q^38 - 30 * q^39 + 5 * q^40 + 18 * q^41 - 49 * q^42 + 19 * q^43 - 42 * q^44 - 63 * q^45 - 6 * q^46 - 27 * q^48 + 9 * q^49 - 7 * q^51 - 43 * q^52 - 22 * q^53 + 18 * q^54 + 30 * q^55 + 25 * q^56 - 15 * q^57 - 12 * q^58 + 33 * q^59 - 13 * q^61 - 17 * q^62 - 6 * q^63 - 38 * q^64 + 9 * q^65 - 52 * q^66 + 30 * q^67 + 88 * q^68 - 16 * q^69 + 9 * q^73 - 19 * q^74 + 25 * q^75 + 34 * q^77 + 14 * q^78 + 6 * q^79 + 6 * q^80 + 22 * q^81 - 78 * q^82 + 54 * q^83 - 33 * q^85 + 24 * q^86 - 14 * q^87 + 16 * q^88 - 6 * q^89 - 11 * q^90 - 70 * q^91 - 6 * q^92 + 7 * q^93 - 43 * q^94 + 25 * q^95 - 36 * q^96 - 75 * q^97 - 93 * q^99

Introduction

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