LMFDB - Embedded newform 105.3.n.a.31.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,3,Mod(31,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("105.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.n (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:	$2.86104277578$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.523596960000.16
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 13x^{6} - 2x^{5} + 91x^{4} - 50x^{3} + 190x^{2} + 100x + 100 $ x^8 - 2x^7 + 13x^6 - 2x^5 + 91x^4 - 50x^3 + 190x^2 + 100*x + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.4
Root			$1.76021 + 3.04878i$ of defining polynomial
Character	$\chi$	$=$	105.31
Dual form			105.3.n.a.61.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.76021 + 3.04878i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-4.19671 + 7.26891i) q^{4} +(-1.93649 + 1.11803i) q^{5} -6.09756i q^{6} +(0.244004 + 6.99575i) q^{7} -15.4667 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(1.76021 + 3.04878i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-4.19671 + 7.26891i) q^{4} +(-1.93649 + 1.11803i) q^{5} -6.09756i q^{6} +(0.244004 + 6.99575i) q^{7} -15.4667 q^{8} +(1.50000 + 2.59808i) q^{9} +(-6.81728 - 3.93596i) q^{10} +(-1.29685 + 2.24621i) q^{11} +(12.5901 - 7.26891i) q^{12} -11.5763i q^{13} +(-20.8990 + 13.0579i) q^{14} +3.87298 q^{15} +(-10.4379 - 18.0789i) q^{16} +(20.0957 + 11.6023i) q^{17} +(-5.28064 + 9.14634i) q^{18} +(25.9538 - 14.9844i) q^{19} -18.7682i q^{20} +(5.69249 - 10.7049i) q^{21} -9.13094 q^{22} +(17.5542 + 30.4048i) q^{23} +(23.2000 + 13.3945i) q^{24} +(2.50000 - 4.33013i) q^{25} +(35.2936 - 20.3768i) q^{26} -5.19615i q^{27} +(-51.8754 - 27.5854i) q^{28} -24.4905 q^{29} +(6.81728 + 11.8079i) q^{30} +(-32.4355 - 18.7266i) q^{31} +(5.81233 - 10.0673i) q^{32} +(3.89055 - 2.24621i) q^{33} +81.6898i q^{34} +(-8.29399 - 13.2744i) q^{35} -25.1802 q^{36} +(-12.8743 - 22.2990i) q^{37} +(91.3685 + 52.7516i) q^{38} +(-10.0254 + 17.3645i) q^{39} +(29.9511 - 17.2923i) q^{40} -3.71113i q^{41} +(42.6570 - 1.48783i) q^{42} +74.2225 q^{43} +(-10.8850 - 18.8534i) q^{44} +(-5.80948 - 3.35410i) q^{45} +(-61.7983 + 107.038i) q^{46} +(2.92646 - 1.68959i) q^{47} +36.1578i q^{48} +(-48.8809 + 3.41398i) q^{49} +17.6021 q^{50} +(-20.0957 - 34.8068i) q^{51} +(84.1471 + 48.5823i) q^{52} +(20.0193 - 34.6744i) q^{53} +(15.8419 - 9.14634i) q^{54} -5.79969i q^{55} +(-3.77394 - 108.201i) q^{56} -51.9076 q^{57} +(-43.1085 - 74.6661i) q^{58} +(-42.7180 - 24.6632i) q^{59} +(-16.2538 + 28.1524i) q^{60} +(-0.765094 + 0.441727i) q^{61} -131.852i q^{62} +(-17.8095 + 11.1276i) q^{63} -42.5790 q^{64} +(12.9427 + 22.4174i) q^{65} +(13.6964 + 7.90763i) q^{66} +(32.5272 - 56.3388i) q^{67} +(-168.671 + 97.3825i) q^{68} -60.8096i q^{69} +(25.8715 - 48.6523i) q^{70} +86.0786 q^{71} +(-23.2000 - 40.1836i) q^{72} +(-53.3274 - 30.7886i) q^{73} +(45.3231 - 78.5019i) q^{74} +(-7.50000 + 4.33013i) q^{75} +251.541i q^{76} +(-16.0304 - 8.52436i) q^{77} -70.5872 q^{78} +(-13.7718 - 23.8534i) q^{79} +(40.4256 + 23.3397i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(11.3144 - 6.53239i) q^{82} +131.445i q^{83} +(53.9235 + 86.3036i) q^{84} -51.8869 q^{85} +(130.648 + 226.288i) q^{86} +(36.7357 + 21.2094i) q^{87} +(20.0580 - 34.7415i) q^{88} +(-56.5108 + 32.6265i) q^{89} -23.6157i q^{90} +(80.9849 - 2.82467i) q^{91} -294.679 q^{92} +(32.4355 + 56.1799i) q^{93} +(10.3024 + 5.94809i) q^{94} +(-33.5062 + 58.0345i) q^{95} +(-17.4370 + 10.0673i) q^{96} -42.2375i q^{97} +(-96.4494 - 143.018i) q^{98} -7.78111 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 12 q^{3} - 6 q^{4} - 16 q^{7} - 32 q^{8} + 12 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 - 12 * q^3 - 6 * q^4 - 16 * q^7 - 32 * q^8 + 12 * q^9	$ 8 q + 2 q^{2} - 12 q^{3} - 6 q^{4} - 16 q^{7} - 32 q^{8} + 12 q^{9} + 20 q^{11} + 18 q^{12} - 16 q^{14} - 2 q^{16} - 18 q^{17} - 6 q^{18} + 48 q^{21} - 16 q^{22} + 62 q^{23} + 48 q^{24} + 20 q^{25} + 120 q^{26} - 120 q^{28} - 100 q^{29} - 126 q^{31} + 36 q^{32} - 60 q^{33} - 36 q^{36} - 80 q^{37} + 114 q^{38} - 12 q^{39} + 90 q^{40} + 90 q^{42} + 352 q^{43} - 18 q^{44} - 82 q^{46} - 72 q^{47} + 38 q^{49} + 20 q^{50} + 18 q^{51} - 48 q^{52} - 76 q^{53} + 18 q^{54} + 196 q^{56} - 40 q^{58} - 54 q^{59} - 60 q^{60} - 396 q^{61} - 96 q^{63} - 4 q^{64} - 60 q^{65} + 24 q^{66} + 184 q^{67} - 312 q^{68} + 164 q^{71} - 48 q^{72} + 348 q^{73} - 140 q^{74} - 60 q^{75} + 152 q^{77} - 240 q^{78} - 206 q^{79} - 36 q^{81} + 204 q^{82} + 132 q^{84} - 60 q^{85} + 178 q^{86} + 150 q^{87} + 124 q^{88} + 282 q^{89} - 114 q^{91} - 288 q^{92} + 126 q^{93} + 30 q^{94} - 120 q^{95} - 108 q^{96} - 592 q^{98} + 120 q^{99}+O(q^{100}) $ 8 * q + 2 * q^2 - 12 * q^3 - 6 * q^4 - 16 * q^7 - 32 * q^8 + 12 * q^9 + 20 * q^11 + 18 * q^12 - 16 * q^14 - 2 * q^16 - 18 * q^17 - 6 * q^18 + 48 * q^21 - 16 * q^22 + 62 * q^23 + 48 * q^24 + 20 * q^25 + 120 * q^26 - 120 * q^28 - 100 * q^29 - 126 * q^31 + 36 * q^32 - 60 * q^33 - 36 * q^36 - 80 * q^37 + 114 * q^38 - 12 * q^39 + 90 * q^40 + 90 * q^42 + 352 * q^43 - 18 * q^44 - 82 * q^46 - 72 * q^47 + 38 * q^49 + 20 * q^50 + 18 * q^51 - 48 * q^52 - 76 * q^53 + 18 * q^54 + 196 * q^56 - 40 * q^58 - 54 * q^59 - 60 * q^60 - 396 * q^61 - 96 * q^63 - 4 * q^64 - 60 * q^65 + 24 * q^66 + 184 * q^67 - 312 * q^68 + 164 * q^71 - 48 * q^72 + 348 * q^73 - 140 * q^74 - 60 * q^75 + 152 * q^77 - 240 * q^78 - 206 * q^79 - 36 * q^81 + 204 * q^82 + 132 * q^84 - 60 * q^85 + 178 * q^86 + 150 * q^87 + 124 * q^88 + 282 * q^89 - 114 * q^91 - 288 * q^92 + 126 * q^93 + 30 * q^94 - 120 * q^95 - 108 * q^96 - 592 * q^98 + 120 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	1.76021	+	3.04878i	0.880107	+	1.52439i	0.851221	+	0.524807i	$0.175863\pi$
$2$	1.76021	+	3.04878i	0.880107	+	1.52439i	0.0288858	+	0.999583i	$0.490804\pi$
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$4$	−4.19671	+	7.26891i	−1.04918	+	1.81723i
$5$	−1.93649	+	1.11803i	−0.387298	+	0.223607i
$5$	−1.93649	+	1.11803i	−0.387298	+	0.223607i
$6$		−	6.09756i		−	1.01626i
$7$	0.244004	+	6.99575i	0.0348577	+	0.999392i
$7$	0.244004	+	6.99575i	0.0348577	+	0.999392i
$8$	−15.4667			−1.93334
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$	−6.81728	−	3.93596i	−0.681728	−	0.393596i
$11$	−1.29685	+	2.24621i	−0.117896	+	0.204201i	−0.918934	−	0.394412i	$-0.870948\pi$
$11$	−1.29685	+	2.24621i	−0.117896	+	0.204201i	0.801038	+	0.598614i	$0.204281\pi$
$12$	12.5901	−	7.26891i	1.04918	−	0.605742i
$13$		−	11.5763i		−	0.890485i	−0.895410	−	0.445242i	$-0.853117\pi$
$13$		−	11.5763i		−	0.890485i	0.895410	−	0.445242i	$-0.146883\pi$
$14$	−20.8990	+	13.0579i	−1.49278	+	0.932709i
$15$	3.87298			0.258199
$16$	−10.4379	−	18.0789i	−0.652366	−	1.12993i
$17$	20.0957	+	11.6023i	1.18210	+	0.682486i	0.956499	−	0.291734i	$-0.0942323\pi$
$17$	20.0957	+	11.6023i	1.18210	+	0.682486i	0.225600	+	0.974220i	$0.427566\pi$
$18$	−5.28064	+	9.14634i	−0.293369	+	0.508130i
$19$	25.9538	−	14.9844i	1.36599	−	0.788654i	0.375576	−	0.926791i	$-0.377445\pi$
$19$	25.9538	−	14.9844i	1.36599	−	0.788654i	0.990413	+	0.138137i	$0.0441115\pi$
$20$		−	18.7682i		−	0.938412i
$21$	5.69249	−	10.7049i	0.271071	−	0.509759i
$22$	−9.13094			−0.415043
$23$	17.5542	+	30.4048i	0.763226	+	1.32195i	0.941179	+	0.337908i	$0.109719\pi$
$23$	17.5542	+	30.4048i	0.763226	+	1.32195i	−0.177953	+	0.984039i	$0.556947\pi$
$24$	23.2000	+	13.3945i	0.966668	+	0.558106i
$25$	2.50000	−	4.33013i	0.100000	−	0.173205i
$26$	35.2936	−	20.3768i	1.35745	−	0.783722i
$27$		−	5.19615i		−	0.192450i
$28$	−51.8754	−	27.5854i	−1.85269	−	0.985194i
$29$	−24.4905			−0.844499			−0.422250	−	0.906480i	$-0.638759\pi$
$29$	−24.4905			−0.844499			−0.422250	+	0.906480i	$0.638759\pi$
$30$	6.81728	+	11.8079i	0.227243	+	0.393596i
$31$	−32.4355	−	18.7266i	−1.04631	−	0.604085i	−0.124693	−	0.992195i	$-0.539795\pi$
$31$	−32.4355	−	18.7266i	−1.04631	−	0.604085i	−0.921613	+	0.388110i	$0.873128\pi$
$32$	5.81233	−	10.0673i	0.181635	−	0.314602i
$33$	3.89055	−	2.24621i	0.117896	−	0.0680670i
$34$			81.6898i			2.40264i
$35$	−8.29399	−	13.2744i	−0.236971	−	0.379269i
$36$	−25.1802			−0.699451
$37$	−12.8743	−	22.2990i	−0.347954	−	0.602675i	0.637932	−	0.770093i	$-0.279790\pi$
$37$	−12.8743	−	22.2990i	−0.347954	−	0.602675i	−0.985886	+	0.167418i	$0.946457\pi$
$38$	91.3685	+	52.7516i	2.40443	+	1.38820i
$39$	−10.0254	+	17.3645i	−0.257061	+	0.445242i
$40$	29.9511	−	17.2923i	0.748778	−	0.432307i
$41$		−	3.71113i		−	0.0905155i	−0.998975	−	0.0452577i	$-0.985589\pi$
$41$		−	3.71113i		−	0.0905155i	0.998975	−	0.0452577i	$-0.0144109\pi$
$42$	42.6570	−	1.48783i	1.01564	−	0.0354245i
$43$	74.2225			1.72611			0.863053	−	0.505114i	$-0.168549\pi$
$43$	74.2225			1.72611			0.863053	+	0.505114i	$0.168549\pi$
$44$	−10.8850	−	18.8534i	−0.247386	−	0.428486i
$45$	−5.80948	−	3.35410i	−0.129099	−	0.0745356i
$46$	−61.7983	+	107.038i	−1.34344	+	2.32691i
$47$	2.92646	−	1.68959i	0.0622652	−	0.0359488i	−0.468544	−	0.883440i	$-0.655221\pi$
$47$	2.92646	−	1.68959i	0.0622652	−	0.0359488i	0.530809	+	0.847491i	$0.321888\pi$
$48$			36.1578i			0.753287i
$49$	−48.8809	+	3.41398i	−0.997570	+	0.0696731i
$50$	17.6021			0.352043
$51$	−20.0957	−	34.8068i	−0.394033	−	0.682486i
$52$	84.1471	+	48.5823i	1.61821	+	0.934276i
$53$	20.0193	−	34.6744i	0.377722	−	0.654234i	−0.613008	−	0.790076i	$-0.710041\pi$
$53$	20.0193	−	34.6744i	0.377722	−	0.654234i	0.990730	+	0.135843i	$0.0433741\pi$
$54$	15.8419	−	9.14634i	0.293369	−	0.169377i
$55$		−	5.79969i		−	0.105449i
$56$	−3.77394	−	108.201i	−0.0673917	−	1.93216i
$57$	−51.9076			−0.910660
$58$	−43.1085	−	74.6661i	−0.743250	−	1.28735i
$59$	−42.7180	−	24.6632i	−0.724033	−	0.418021i	0.0922022	−	0.995740i	$-0.470609\pi$
$59$	−42.7180	−	24.6632i	−0.724033	−	0.418021i	−0.816235	+	0.577720i	$0.803943\pi$
$60$	−16.2538	+	28.1524i	−0.270896	+	0.469206i
$61$	−0.765094	+	0.441727i	−0.0125425	+	0.00724143i	−0.506258	−	0.862382i	$-0.668972\pi$
$61$	−0.765094	+	0.441727i	−0.0125425	+	0.00724143i	0.493716	+	0.869623i	$0.335638\pi$
$62$		−	131.852i		−	2.12664i
$63$	−17.8095	+	11.1276i	−0.282690	+	0.176628i
$64$	−42.5790			−0.665297
$65$	12.9427	+	22.4174i	0.199118	+	0.344883i
$66$	13.6964	+	7.90763i	0.207521	+	0.119813i
$67$	32.5272	−	56.3388i	0.485481	−	0.840877i	−0.514380	−	0.857562i	$-0.671978\pi$
$67$	32.5272	−	56.3388i	0.485481	−	0.840877i	0.999861	+	0.0166850i	$0.00531125\pi$
$68$	−168.671	+	97.3825i	−2.48046	+	1.43210i
$69$		−	60.8096i		−	0.881298i
$70$	25.8715	−	48.6523i	0.369593	−	0.695033i
$71$	86.0786			1.21237			0.606187	−	0.795322i	$-0.292698\pi$
$71$	86.0786			1.21237			0.606187	+	0.795322i	$0.292698\pi$
$72$	−23.2000	−	40.1836i	−0.322223	−	0.558106i
$73$	−53.3274	−	30.7886i	−0.730512	−	0.421761i	0.0880974	−	0.996112i	$-0.471921\pi$
$73$	−53.3274	−	30.7886i	−0.730512	−	0.421761i	−0.818609	+	0.574350i	$0.805255\pi$
$74$	45.3231	−	78.5019i	0.612474	−	1.06084i
$75$	−7.50000	+	4.33013i	−0.100000	+	0.0577350i
$76$			251.541i			3.30975i
$77$	−16.0304	−	8.52436i	−0.208187	−	0.110706i
$78$	−70.5872			−0.904964
$79$	−13.7718	−	23.8534i	−0.174326	−	0.301942i	0.765602	−	0.643315i	$-0.222441\pi$
$79$	−13.7718	−	23.8534i	−0.174326	−	0.301942i	−0.939928	+	0.341373i	$0.889108\pi$
$80$	40.4256	+	23.3397i	0.505320	+	0.291747i
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	11.3144	−	6.53239i	0.137981	−	0.0796633i
$83$			131.445i			1.58367i	0.610732	+	0.791837i	$0.290875\pi$
$83$			131.445i			1.58367i	−0.610732	+	0.791837i	$0.709125\pi$
$84$	53.9235	+	86.3036i	0.641946	+	1.02742i
$85$	−51.8869			−0.610434
$86$	130.648	+	226.288i	1.51916	+	2.63126i
$87$	36.7357	+	21.2094i	0.422250	+	0.243786i
$88$	20.0580	−	34.7415i	0.227932	−	0.394789i
$89$	−56.5108	+	32.6265i	−0.634953	+	0.366590i	−0.782668	−	0.622440i	$-0.786142\pi$
$89$	−56.5108	+	32.6265i	−0.634953	+	0.366590i	0.147715	+	0.989030i	$0.452808\pi$
$90$		−	23.6157i		−	0.262397i
$91$	80.9849	−	2.82467i	0.889944	−	0.0310403i
$92$	−294.679			−3.20304
$93$	32.4355	+	56.1799i	0.348769	+	0.604085i
$94$	10.3024	+	5.94809i	0.109600	+	0.0632776i
$95$	−33.5062	+	58.0345i	−0.352697	+	0.610889i
$96$	−17.4370	+	10.0673i	−0.181635	+	0.104867i
$97$		−	42.2375i		−	0.435438i	−0.976011	−	0.217719i	$-0.930138\pi$
$97$		−	42.2375i		−	0.435438i	0.976011	−	0.217719i	$-0.0698616\pi$
$98$	−96.4494	−	143.018i	−0.984177	−	1.45937i
$99$	−7.78111			−0.0785970
$100$	20.9835	+	36.3445i	0.209835	+	0.363445i
$101$	−129.874	−	74.9830i	−1.28589	−	0.742406i	−0.307968	−	0.951397i	$-0.599649\pi$
$101$	−129.874	−	74.9830i	−1.28589	−	0.742406i	−0.977918	+	0.208991i	$0.932982\pi$
$102$	70.7454	−	122.535i	0.693583	−	1.20132i
$103$	120.964	−	69.8388i	1.17441	−	0.678047i	0.219697	−	0.975568i	$-0.429493\pi$
$103$	120.964	−	69.8388i	1.17441	−	0.678047i	0.954715	+	0.297521i	$0.0961599\pi$
$104$			179.047i			1.72161i
$105$	0.945024	+	27.0944i	0.00900023	+	0.258042i
$106$	140.953			1.32974
$107$	90.6198	+	156.958i	0.846914	+	1.46690i	0.883949	+	0.467584i	$0.154875\pi$
$107$	90.6198	+	156.958i	0.846914	+	1.46690i	−0.0370350	+	0.999314i	$0.511791\pi$
$108$	37.7703	+	21.8067i	0.349725	+	0.201914i
$109$	36.9049	−	63.9212i	0.338577	−	0.586433i	−0.645588	−	0.763686i	$-0.723388\pi$
$109$	36.9049	−	63.9212i	0.338577	−	0.586433i	0.984165	+	0.177253i	$0.0567211\pi$
$110$	17.6820	−	10.2087i	0.160745	−	0.0928064i
$111$			44.5979i			0.401783i
$112$	123.928	−	77.4319i	1.10650	−	0.691356i
$113$	7.38562			0.0653595			0.0326797	−	0.999466i	$-0.489596\pi$
$113$	7.38562			0.0653595			0.0326797	+	0.999466i	$0.489596\pi$
$114$	−91.3685	−	158.255i	−0.801478	−	1.38820i
$115$	−67.9872	−	39.2524i	−0.591193	−	0.341325i
$116$	102.779	−	178.019i	0.886029	−	1.53465i
$117$	30.0761	−	17.3645i	0.257061	−	0.148414i
$118$		−	173.650i		−	1.47161i
$119$	−76.2630	+	143.415i	−0.640866	+	1.20517i
$120$	−59.9022			−0.499185
$121$	57.1364	+	98.9631i	0.472201	+	0.817877i
$122$	−2.69346	−	1.55507i	−0.0220775	−	0.0127465i
$123$	−3.21394	+	5.56670i	−0.0261296	+	0.0452577i
$124$	272.244	−	157.180i	2.19552	−	1.26758i
$125$			11.1803i			0.0894427i
$126$	−65.2740	−	34.7103i	−0.518047	−	0.275478i
$127$	−208.640			−1.64283			−0.821416	−	0.570329i	$-0.806816\pi$
$127$	−208.640			−1.64283			−0.821416	+	0.570329i	$0.806816\pi$
$128$	−98.1975	−	170.083i	−0.767168	−	1.32877i
$129$	−111.334	−	64.2786i	−0.863053	−	0.498284i
$130$	−45.5638	+	78.9189i	−0.350491	+	0.607068i
$131$	94.8997	−	54.7904i	0.724425	−	0.418247i	−0.0919540	−	0.995763i	$-0.529311\pi$
$131$	94.8997	−	54.7904i	0.724425	−	0.418247i	0.816379	+	0.577516i	$0.195978\pi$
$132$			37.7068i			0.285657i
$133$	111.160	+	177.910i	0.835790	+	1.33767i
$134$	229.019			1.70910
$135$	5.80948	+	10.0623i	0.0430331	+	0.0745356i
$136$	−310.814	−	179.448i	−2.28540	−	1.31947i
$137$	88.7262	−	153.678i	0.647637	−	1.12174i	−0.336049	−	0.941844i	$-0.609091\pi$
$137$	88.7262	−	153.678i	0.647637	−	1.12174i	0.983686	−	0.179895i	$-0.0575758\pi$
$138$	185.395	−	107.038i	1.34344	−	0.775636i
$139$			169.894i			1.22226i	0.791532	+	0.611128i	$0.209284\pi$
$139$			169.894i			1.22226i	−0.791532	+	0.611128i	$0.790716\pi$
$140$	131.298	−	4.57953i	0.937842	−	0.0327109i
$141$	−5.85293			−0.0415101
$142$	151.517	+	262.435i	1.06702	+	1.84813i
$143$	26.0028	+	15.0127i	0.181838	+	0.104984i
$144$	31.3136	−	54.2367i	0.217455	−	0.376644i
$145$	47.4256	−	27.3812i	0.327073	−	0.188836i
$146$		−	216.778i		−	1.48478i
$147$	76.2780	+	37.2111i	0.518898	+	0.253137i
$148$	216.119			1.46026
$149$	−42.6928	−	73.9461i	−0.286529	−	0.496283i	0.686450	−	0.727177i	$-0.259168\pi$
$149$	−42.6928	−	73.9461i	−0.286529	−	0.496283i	−0.972979	+	0.230894i	$0.925835\pi$
$150$	−26.4032	−	15.2439i	−0.176021	−	0.101626i
$151$	68.9977	−	119.507i	0.456938	−	0.791440i	−0.541859	−	0.840469i	$-0.682279\pi$
$151$	68.9977	−	119.507i	0.456938	−	0.791440i	0.998797	+	0.0490293i	$0.0156128\pi$
$152$	−401.419	+	231.760i	−2.64092	+	1.52473i
$153$			69.6135i			0.454990i
$154$	−2.22799	−	63.8777i	−0.0144675	−	0.414791i
$155$	83.7481			0.540310
$156$	−84.1471	−	145.747i	−0.539404	−	0.934276i
$157$	5.94674	+	3.43335i	0.0378773	+	0.0218685i	0.518819	−	0.854884i	$-0.326372\pi$
$157$	5.94674	+	3.43335i	0.0378773	+	0.0218685i	−0.480942	+	0.876753i	$0.659705\pi$
$158$	48.4825	−	83.9742i	0.306851	−	0.531482i
$159$	−60.0578	+	34.6744i	−0.377722	+	0.218078i
$160$			25.9935i			0.162460i
$161$	−208.421	+	130.224i	−1.29454	+	0.808843i
$162$	−31.6838			−0.195579
$163$	138.363	+	239.652i	0.848854	+	1.47026i	0.882231	+	0.470816i	$0.156040\pi$
$163$	138.363	+	239.652i	0.848854	+	1.47026i	−0.0333772	+	0.999443i	$0.510626\pi$
$164$	26.9759	+	15.5745i	0.164487	+	0.0949667i
$165$	−5.02268	+	8.69954i	−0.0304405	+	0.0527245i
$166$	−400.747	+	231.371i	−2.41414	+	1.39380i
$167$			42.3799i			0.253772i	0.991917	+	0.126886i	$0.0404982\pi$
$167$			42.3799i			0.253772i	−0.991917	+	0.126886i	$0.959502\pi$
$168$	−88.0439	+	165.570i	−0.524071	+	0.985535i
$169$	34.9892			0.207036
$170$	−91.3320	−	158.192i	−0.537247	−	0.930539i
$171$	77.8614	+	44.9533i	0.455330	+	0.262885i
$172$	−311.490	+	539.517i	−1.81099	+	3.13673i
$173$	25.5999	−	14.7801i	0.147976	−	0.0854342i	−0.424184	−	0.905576i	$-0.639439\pi$
$173$	25.5999	−	14.7801i	0.147976	−	0.0854342i	0.572160	+	0.820142i	$0.306106\pi$
$174$			149.332i			0.858231i
$175$	30.9025	+	16.4328i	0.176586	+	0.0939017i
$176$	54.1454			0.307644
$177$	42.7180	+	73.9897i	0.241344	+	0.418021i
$178$	−198.942	−	114.859i	−1.11765	−	0.645277i
$179$	74.3408	−	128.762i	0.415312	−	0.719341i	−0.580149	−	0.814510i	$-0.697006\pi$
$179$	74.3408	−	128.762i	0.415312	−	0.719341i	0.995461	+	0.0951690i	$0.0303392\pi$
$180$	48.7613	−	28.1524i	0.270896	−	0.156402i
$181$		−	257.302i		−	1.42156i	−0.703414	−	0.710780i	$-0.748342\pi$
$181$		−	257.302i		−	1.42156i	0.703414	−	0.710780i	$-0.251658\pi$
$182$	151.163	+	241.933i	0.830563	+	1.32930i
$183$	1.53019			0.00836168
$184$	−271.505	−	470.261i	−1.47557	−	2.55577i
$185$	49.8620	+	28.7878i	0.269524	+	0.155610i
$186$	−114.187	+	197.777i	−0.613908	+	1.06332i
$187$	−52.1223	+	30.0928i	−0.278729	+	0.160924i
$188$			28.3629i			0.150867i
$189$	36.3510	−	1.26788i	0.192333	−	0.00670837i
$190$	−235.912			−1.24164
$191$	−60.8021	−	105.312i	−0.318336	−	0.551373i	0.661805	−	0.749676i	$-0.269791\pi$
$191$	−60.8021	−	105.312i	−0.318336	−	0.551373i	−0.980141	+	0.198302i	$0.936457\pi$
$192$	63.8685	+	36.8745i	0.332649	+	0.192055i
$193$	−121.266	+	210.039i	−0.628323	+	1.08829i	0.359566	+	0.933120i	$0.382925\pi$
$193$	−121.266	+	210.039i	−0.628323	+	1.08829i	−0.987888	+	0.155167i	$0.950408\pi$
$194$	128.773	−	74.3470i	0.663777	−	0.383232i
$195$		−	44.8348i		−	0.229922i
$196$	180.323	−	369.638i	0.920015	−	1.88591i
$197$	−98.9929			−0.502502			−0.251251	−	0.967922i	$-0.580842\pi$
$197$	−98.9929			−0.502502			−0.251251	+	0.967922i	$0.580842\pi$
$198$	−13.6964	−	23.7229i	−0.0691738	−	0.119813i
$199$	68.2115	+	39.3819i	0.342772	+	0.197899i	0.661497	−	0.749948i	$-0.269921\pi$
$199$	68.2115	+	39.3819i	0.342772	+	0.197899i	−0.318725	+	0.947847i	$0.603255\pi$
$200$	−38.6667	+	66.9727i	−0.193334	+	0.334864i
$201$	−97.5816	+	56.3388i	−0.485481	+	0.280292i
$202$		−	527.945i		−	2.61359i
$203$	−5.97578	−	171.329i	−0.0294373	−	0.843986i
$204$	337.343			1.65364
$205$	4.14917	+	7.18658i	0.0202399	+	0.0350565i
$206$	425.846	+	245.863i	2.06722	+	1.19351i
$207$	−52.6626	+	91.2143i	−0.254409	+	0.440649i
$208$	−209.287	+	120.832i	−1.00619	+	0.580922i
$209$			77.7303i			0.371915i
$210$	−80.9414	+	50.5731i	−0.385435	+	0.240824i
$211$	−107.144			−0.507790			−0.253895	−	0.967232i	$-0.581712\pi$
$211$	−107.144			−0.507790			−0.253895	+	0.967232i	$0.581712\pi$
$212$	168.030	+	291.036i	0.792594	+	1.37281i
$213$	−129.118	−	74.5462i	−0.606187	−	0.349982i
$214$	−319.020	+	552.559i	−1.49075	+	2.58205i
$215$	−143.731	+	82.9833i	−0.668518	+	0.385969i
$216$			80.3673i			0.372071i
$217$	123.092	−	231.480i	0.567246	−	1.06673i
$218$	259.842			1.19194
$219$	53.3274	+	92.3657i	0.243504	+	0.421761i
$220$	42.1574	+	24.3396i	0.191625	+	0.110635i
$221$	134.311	−	232.634i	0.607743	−	1.05264i
$222$	−135.969	+	78.5019i	−0.612474	+	0.353612i
$223$			8.72021i			0.0391041i	0.999809	+	0.0195520i	$0.00622400\pi$
$223$			8.72021i			0.0391041i	−0.999809	+	0.0195520i	$0.993776\pi$
$224$	71.8462	+	38.2051i	0.320742	+	0.170559i
$225$	15.0000			0.0666667
$226$	13.0003	+	22.5171i	0.0575233	+	0.0996333i
$227$	−219.123	−	126.511i	−0.965299	−	0.557316i	−0.0674992	−	0.997719i	$-0.521502\pi$
$227$	−219.123	−	126.511i	−0.965299	−	0.557316i	−0.897800	+	0.440404i	$0.854835\pi$
$228$	217.841	−	377.312i	0.955443	−	1.65488i
$229$	125.988	−	72.7394i	0.550167	−	0.317639i	−0.199022	−	0.979995i	$-0.563777\pi$
$229$	125.988	−	72.7394i	0.550167	−	0.317639i	0.749189	+	0.662356i	$0.230443\pi$
$230$		−	276.370i		−	1.20161i
$231$	16.6632	+	26.6692i	0.0721352	+	0.115451i
$232$	378.787			1.63270
$233$	−128.758	−	223.015i	−0.552609	−	0.957146i	−0.998085	−	0.0618526i	$-0.980299\pi$
$233$	−128.758	−	223.015i	−0.552609	−	0.957146i	0.445477	−	0.895294i	$-0.353034\pi$
$234$	105.881	+	61.1303i	0.452482	+	0.261241i
$235$	−3.77805	+	6.54377i	−0.0160768	+	0.0278458i
$236$	358.549	−	207.009i	1.51928	−	0.877155i
$237$			47.7068i			0.201295i
$238$	−571.481	+	19.9326i	−2.40118	+	0.0837506i
$239$	−128.682			−0.538418			−0.269209	−	0.963082i	$-0.586762\pi$
$239$	−128.682			−0.538418			−0.269209	+	0.963082i	$0.586762\pi$
$240$	−40.4256	−	70.0192i	−0.168440	−	0.291747i
$241$	−8.02227	−	4.63166i	−0.0332874	−	0.0192185i	0.483264	−	0.875475i	$-0.339451\pi$
$241$	−8.02227	−	4.63166i	−0.0332874	−	0.0192185i	−0.516551	+	0.856256i	$0.672784\pi$
$242$	−201.144	+	348.392i	−0.831175	+	1.43964i
$243$	13.5000	−	7.79423i	0.0555556	−	0.0320750i
$244$		−	7.41519i		−	0.0303901i
$245$	90.8406	−	61.2617i	0.370778	−	0.250048i
$246$	−22.6289			−0.0919872
$247$	−173.464	−	300.449i	−0.702285	−	1.21639i
$248$	501.670	+	289.639i	2.02286	+	1.16790i
$249$	113.835	−	197.167i	0.457167	−	0.791837i
$250$	−34.0864	+	19.6798i	−0.136346	+	0.0787192i
$251$			29.9212i			0.119208i	0.998222	+	0.0596040i	$0.0189838\pi$
$251$			29.9212i			0.119208i	−0.998222	+	0.0596040i	$0.981016\pi$
$252$	−6.14408	−	176.155i	−0.0243813	−	0.699026i
$253$	−91.0608			−0.359924
$254$	−367.251	−	636.097i	−1.44587	−	2.50432i
$255$	77.8303	+	44.9353i	0.305217	+	0.176217i
$256$	260.539	−	451.267i	1.01773	−	1.76276i
$257$	83.7338	−	48.3438i	0.325813	−	0.188108i	−0.328168	−	0.944619i	$-0.606431\pi$
$257$	83.7338	−	48.3438i	0.325813	−	0.188108i	0.653980	+	0.756511i	$0.273098\pi$
$258$		−	452.576i		−	1.75417i
$259$	152.857	−	95.5065i	0.590180	−	0.368751i
$260$	−217.267			−0.835642
$261$	−36.7357	−	63.6281i	−0.140750	−	0.243786i
$262$	334.088	+	192.886i	1.27514	+	0.736204i
$263$	−32.1231	+	55.6388i	−0.122141	+	0.211554i	−0.920612	−	0.390479i	$-0.872309\pi$
$263$	−32.1231	+	55.6388i	−0.122141	+	0.211554i	0.798471	+	0.602034i	$0.205643\pi$
$264$	−60.1740	+	34.7415i	−0.227932	+	0.131596i
$265$			89.5289i			0.337845i
$266$	−346.743	+	652.062i	−1.30354	+	2.45136i
$267$	113.022			0.423302
$268$	273.014	+	472.875i	1.01871	+	1.76446i
$269$	−171.096	−	98.7823i	−0.636044	−	0.367220i	0.147045	−	0.989130i	$-0.453024\pi$
$269$	−171.096	−	98.7823i	−0.636044	−	0.367220i	−0.783089	+	0.621910i	$0.786357\pi$
$270$	−20.4518	+	35.4236i	−0.0757475	+	0.131199i
$271$	−133.483	+	77.0667i	−0.492559	+	0.284379i	−0.725635	−	0.688080i	$-0.758454\pi$
$271$	−133.483	+	77.0667i	−0.492559	+	0.284379i	0.233077	+	0.972458i	$0.425121\pi$
$272$		−	484.410i		−	1.78092i
$273$	−123.924	−	65.8980i	−0.453932	−	0.241385i
$274$	624.708			2.27996
$275$	6.48426	+	11.2311i	0.0235791	+	0.0408402i
$276$	442.019	+	255.200i	1.60152	+	0.924637i
$277$	−169.602	+	293.758i	−0.612280	+	1.06050i	0.378575	+	0.925570i	$0.376414\pi$
$277$	−169.602	+	293.758i	−0.612280	+	1.06050i	−0.990855	+	0.134929i	$0.956919\pi$
$278$	−517.968	+	299.049i	−1.86320	+	1.07572i
$279$		−	112.360i		−	0.402724i
$280$	128.281	+	205.311i	0.458145	+	0.733253i
$281$	−111.976			−0.398492			−0.199246	−	0.979949i	$-0.563849\pi$
$281$	−111.976			−0.398492			−0.199246	+	0.979949i	$0.563849\pi$
$282$	−10.3024	−	17.8443i	−0.0365333	−	0.0632776i
$283$	−56.6453	−	32.7042i	−0.200160	−	0.115563i	0.396570	−	0.918004i	$-0.370200\pi$
$283$	−56.6453	−	32.7042i	−0.200160	−	0.115563i	−0.596730	+	0.802442i	$0.703534\pi$
$284$	−361.246	+	625.697i	−1.27199	+	2.20316i
$285$	100.519	−	58.0345i	0.352697	−	0.203630i
$286$			105.703i			0.369589i
$287$	25.9622	−	0.905532i	0.0904605	−	0.00315516i
$288$	34.8740			0.121090
$289$	124.725	+	216.029i	0.431573	+	0.747507i
$290$	166.958	+	96.3935i	0.575719	+	0.332391i
$291$	−36.5787	+	63.3562i	−0.125700	+	0.217719i
$292$	447.599	−	258.421i	1.53287	−	0.885004i
$293$			100.992i			0.344681i	0.985037	+	0.172341i	$0.0551330\pi$
$293$			100.992i			0.344681i	−0.985037	+	0.172341i	$0.944867\pi$
$294$	20.8170	+	298.054i	0.0708060	+	1.01379i
$295$	110.297			0.373889
$296$	199.123	+	344.891i	0.672713	+	1.16517i
$297$	11.6717	+	6.73864i	0.0392985	+	0.0226890i
$298$	150.297	−	260.322i	0.504352	−	0.873564i
$299$	351.975	−	203.213i	1.17717	−	0.679642i
$300$		−	72.6891i		−	0.242297i
$301$	18.1106	+	519.242i	0.0601681	+	1.72506i
$302$	485.802			1.60862
$303$	129.874	+	224.949i	0.428628	+	0.742406i
$304$	−541.804	−	312.811i	−1.78225	−	1.02898i
$305$	0.987732	−	1.71080i	0.00323846	−	0.00560918i
$306$	−212.236	+	122.535i	−0.693583	+	0.400440i
$307$		−	400.388i		−	1.30420i	−0.758135	−	0.652098i	$-0.773889\pi$
$307$		−	400.388i		−	1.30420i	0.758135	−	0.652098i	$-0.226111\pi$
$308$	129.237	−	80.7490i	0.419602	−	0.262172i
$309$	−241.929			−0.782941
$310$	147.415	+	255.330i	0.475531	+	0.823644i
$311$	−31.1758	−	17.9993i	−0.100244	−	0.0578757i	0.449040	−	0.893512i	$-0.351766\pi$
$311$	−31.1758	−	17.9993i	−0.100244	−	0.0578757i	−0.549284	+	0.835636i	$0.685099\pi$
$312$	155.059	−	268.571i	0.496985	−	0.860803i
$313$	−99.1558	+	57.2476i	−0.316792	+	0.182900i	−0.649962	−	0.759967i	$-0.725215\pi$
$313$	−99.1558	+	57.2476i	−0.316792	+	0.182900i	0.333170	+	0.942867i	$0.391882\pi$
$314$			24.1737i			0.0769864i
$315$	22.0469	−	41.4600i	0.0699902	−	0.131619i
$316$	231.184			0.731596
$317$	−2.01608	−	3.49195i	−0.00635987	−	0.0110156i	0.862828	−	0.505498i	$-0.168691\pi$
$317$	−2.01608	−	3.49195i	−0.00635987	−	0.0110156i	−0.869188	+	0.494482i	$0.835358\pi$
$318$	−211.429	−	122.069i	−0.664872	−	0.383864i
$319$	31.7605	−	55.0108i	0.0995627	−	0.172448i
$320$	82.4539	−	47.6048i	0.257669	−	0.148765i
$321$		−	313.916i		−	0.977932i
$322$	−763.888	−	406.208i	−2.37232	−	1.26151i
$323$	695.413			2.15298
$324$	−37.7703	−	65.4202i	−0.116575	−	0.201914i
$325$	−50.1269	−	28.9408i	−0.154237	−	0.0890485i
$326$	−487.098	+	843.678i	−1.49417	+	2.58797i
$327$	−110.715	+	63.9212i	−0.338577	+	0.195478i
$328$			57.3989i			0.174997i
$329$	12.5340	+	20.0605i	0.0380974	+	0.0609742i
$330$	−35.3640			−0.107164
$331$	−253.691	−	439.406i	−0.766439	−	1.32751i	−0.939482	−	0.342598i	$-0.888693\pi$
$331$	−253.691	−	439.406i	−0.766439	−	1.32751i	0.173043	−	0.984914i	$-0.444640\pi$
$332$	−955.461	−	551.636i	−2.87790	−	1.66155i
$333$	38.6229	−	66.8969i	0.115985	−	0.200892i
$334$	−129.207	+	74.5976i	−0.386847	+	0.223346i
$335$			145.466i			0.434227i
$336$	−252.951	+	8.82265i	−0.752829	+	0.0262579i
$337$	−264.279			−0.784210			−0.392105	−	0.919921i	$-0.628253\pi$
$337$	−264.279			−0.784210			−0.392105	+	0.919921i	$0.628253\pi$
$338$	61.5884	+	106.674i	0.182214	+	0.315604i
$339$	−11.0784	−	6.39614i	−0.0326797	−	0.0188677i
$340$	217.754	−	377.161i	0.640453	−	1.10930i
$341$	84.1280	−	48.5713i	0.246710	−	0.142438i
$342$			316.510i			0.925467i
$343$	−35.8105	−	341.126i	−0.104404	−	0.994535i
$344$	−1147.98			−3.33714
$345$	67.9872	+	117.757i	0.197064	+	0.341325i
$346$	90.1226	+	52.0323i	0.260470	+	0.150382i
$347$	117.234	−	203.055i	0.337849	−	0.585172i	−0.646179	−	0.763186i	$-0.723634\pi$
$347$	117.234	−	203.055i	0.337849	−	0.585172i	0.984028	+	0.178014i	$0.0569673\pi$
$348$	−308.338	+	178.019i	−0.886029	+	0.511549i
$349$		−	54.2133i		−	0.155339i	−0.996979	−	0.0776695i	$-0.975252\pi$
$349$		−	54.2133i		−	0.155339i	0.996979	−	0.0776695i	$-0.0247479\pi$
$350$	4.29499	+	123.140i	0.0122714	+	0.351829i
$351$	−60.1522			−0.171374
$352$	15.0755	+	26.1115i	0.0428280	+	0.0741803i
$353$	−451.914	−	260.913i	−1.28021	−	0.739129i	−0.303322	−	0.952888i	$-0.598096\pi$
$353$	−451.914	−	260.913i	−1.28021	−	0.739129i	−0.976886	+	0.213759i	$0.931429\pi$
$354$	−150.385	+	260.475i	−0.424818	+	0.735806i
$355$	−166.690	+	96.2388i	−0.469551	+	0.271095i
$356$		−	547.696i		−	1.53847i
$357$	238.596	−	149.077i	0.668336	−	0.417584i
$358$	523.423			1.46208
$359$	233.973	+	405.253i	0.651735	+	1.12884i	0.982702	+	0.185196i	$0.0592919\pi$
$359$	233.973	+	405.253i	0.651735	+	1.12884i	−0.330967	+	0.943642i	$0.607375\pi$
$360$	89.8533	+	51.8768i	0.249593	+	0.144102i
$361$	268.566	−	465.171i	0.743951	−	1.28856i
$362$	784.458	−	452.907i	2.16701	−	1.25112i
$363$		−	197.926i		−	0.545251i
$364$	−319.337	+	600.526i	−0.877301	+	1.64980i
$365$	137.691			0.377235
$366$	2.69346	+	4.66520i	0.00735917	+	0.0127465i
$367$	−149.151	−	86.1123i	−0.406406	−	0.234638i	0.282839	−	0.959168i	$-0.408724\pi$
$367$	−149.151	−	86.1123i	−0.406406	−	0.234638i	−0.689244	+	0.724529i	$0.742057\pi$
$368$	366.456	−	634.721i	0.995806	−	1.72479i
$369$	9.64181	−	5.56670i	0.0261296	−	0.0150859i
$370$			202.691i			0.547814i
$371$	247.458	+	131.589i	0.667003	+	0.354687i
$372$	−544.489			−1.46368
$373$	230.486	+	399.213i	0.617924	+	1.07028i	0.989864	+	0.142019i	$0.0453593\pi$
$373$	230.486	+	399.213i	0.617924	+	1.07028i	−0.371940	+	0.928257i	$0.621307\pi$
$374$	−183.493	−	105.940i	−0.490622	−	0.283261i
$375$	9.68246	−	16.7705i	0.0258199	−	0.0447214i
$376$	−45.2627	+	26.1324i	−0.120379	+	0.0695011i
$377$			283.509i			0.752014i
$378$	67.8510	+	108.594i	0.179500	+	0.287287i
$379$	444.638			1.17319			0.586594	−	0.809881i	$-0.300468\pi$
$379$	444.638			1.17319			0.586594	+	0.809881i	$0.300468\pi$
$380$	−281.231	−	487.107i	−0.740083	−	1.28186i
$381$	312.960	+	180.687i	0.821416	+	0.474245i
$382$	214.049	−	370.744i	0.560339	−	0.970535i
$383$	−458.528	+	264.731i	−1.19720	+	0.691205i	−0.959930	−	0.280239i	$-0.909586\pi$
$383$	−458.528	+	264.731i	−1.19720	+	0.691205i	−0.237271	+	0.971443i	$0.576253\pi$
$384$			340.166i			0.885849i
$385$	40.5732	−	1.41515i	0.105385	−	0.00367571i
$386$	−853.818			−2.21196
$387$	111.334	+	192.836i	0.287684	+	0.498284i
$388$	307.020	+	177.258i	0.791290	+	0.456851i
$389$	−97.7554	+	169.317i	−0.251299	+	0.435263i	−0.963884	−	0.266323i	$-0.914191\pi$
$389$	−97.7554	+	169.317i	−0.251299	+	0.435263i	0.712585	+	0.701586i	$0.247524\pi$
$390$	136.692	−	78.9189i	0.350491	−	0.202356i
$391$			814.674i			2.08356i
$392$	756.026	−	52.8030i	1.92864	−	0.134701i
$393$	−189.799			−0.482950
$394$	−174.249	−	301.808i	−0.442256	−	0.766009i
$395$	53.3378	+	30.7946i	0.135032	+	0.0779610i
$396$	32.6550	−	56.5601i	0.0824622	−	0.142829i
$397$	25.3358	−	14.6276i	0.0638181	−	0.0368454i	−0.467751	−	0.883860i	$-0.654936\pi$
$397$	25.3358	−	14.6276i	0.0638181	−	0.0368454i	0.531570	+	0.847015i	$0.321602\pi$
$398$			277.283i			0.696690i
$399$	−12.6657	−	363.132i	−0.0317435	−	0.910106i
$400$	−104.379			−0.260946
$401$	−105.396	−	182.551i	−0.262833	−	0.455241i	0.704160	−	0.710041i	$-0.251324\pi$
$401$	−105.396	−	182.551i	−0.262833	−	0.455241i	−0.966994	+	0.254800i	$0.917990\pi$
$402$	−343.529	−	198.337i	−0.854550	−	0.493375i
$403$	−216.785	+	375.483i	−0.537929	+	0.931720i
$404$	1090.09	−	629.363i	2.69824	−	1.55783i
$405$		−	20.1246i		−	0.0496904i
$406$	511.826	−	319.795i	1.26066	−	0.787672i
$407$	66.7843			0.164089
$408$	310.814	+	538.345i	0.761799	+	1.31947i
$409$	281.014	+	162.244i	0.687077	+	0.396684i	0.802516	−	0.596631i	$-0.203494\pi$
$409$	281.014	+	162.244i	0.687077	+	0.396684i	−0.115439	+	0.993315i	$0.536828\pi$
$410$	−14.6069	+	25.2998i	−0.0356265	+	0.0617069i
$411$	−266.179	+	153.678i	−0.647637	+	0.373913i
$412$			1172.37i			2.84556i
$413$	162.114	−	304.862i	0.392529	−	0.738164i
$414$	−370.790			−0.895628
$415$	−146.960	−	254.542i	−0.354120	−	0.613355i
$416$	−116.542	−	67.2853i	−0.280148	−	0.161744i
$417$	147.132	−	254.841i	0.352835	−	0.611128i
$418$	−236.983	+	136.822i	−0.566944	+	0.327325i
$419$			693.958i			1.65622i	0.560563	+	0.828112i	$0.310585\pi$
$419$			693.958i			1.65622i	−0.560563	+	0.828112i	$0.689415\pi$
$420$	−200.913	−	106.838i	−0.478364	−	0.254376i
$421$	−341.554			−0.811292			−0.405646	−	0.914030i	$-0.632953\pi$
$421$	−341.554			−0.811292			−0.405646	+	0.914030i	$0.632953\pi$
$422$	−188.596	−	326.657i	−0.446909	−	0.774070i
$423$	8.77939	+	5.06878i	0.0207551	+	0.0119829i
$424$	−309.632	+	536.298i	−0.730264	+	1.26485i
$425$	100.478	−	58.0113i	0.236420	−	0.136497i
$426$		−	524.869i		−	1.23209i
$427$	−3.27690	−	5.24462i	−0.00767423	−	0.0122825i
$428$	−1521.22			−3.55425
$429$	−26.0028	−	45.0382i	−0.0606127	−	0.104984i
$430$	−505.996	−	292.137i	−1.17673	−	0.679388i
$431$	205.726	−	356.328i	0.477323	−	0.826748i	−0.522339	−	0.852738i	$-0.674941\pi$
$431$	205.726	−	356.328i	0.477323	−	0.826748i	0.999662	+	0.0259902i	$0.00827387\pi$
$432$	−93.9407	+	54.2367i	−0.217455	+	0.125548i
$433$			443.458i			1.02415i	0.858940	+	0.512077i	$0.171124\pi$
$433$			443.458i			1.02415i	−0.858940	+	0.512077i	$0.828876\pi$
$434$	922.400	−	32.1723i	2.12535	−	0.0741298i
$435$	−94.8512			−0.218049
$436$	309.758	+	536.517i	0.710454	+	1.23054i
$437$	911.197	+	526.080i	2.08512	+	1.20384i
$438$	−187.735	+	325.167i	−0.428619	+	0.742390i
$439$	−268.002	+	154.731i	−0.610484	+	0.352463i	−0.773155	−	0.634217i	$-0.781322\pi$
$439$	−268.002	+	154.731i	−0.610484	+	0.352463i	0.162671	+	0.986680i	$0.447989\pi$
$440$			89.7021i			0.203868i
$441$	−82.1912	−	121.875i	−0.186375	−	0.276361i
$442$	945.666			2.13952
$443$	−409.330	−	708.981i	−0.923996	−	1.60041i	−0.793167	−	0.609004i	$-0.791569\pi$
$443$	−409.330	−	708.981i	−0.923996	−	1.60041i	−0.130829	−	0.991405i	$-0.541764\pi$
$444$	−324.178	−	187.164i	−0.730131	−	0.421541i
$445$	72.9552	−	126.362i	0.163944	−	0.283960i
$446$	−26.5860	+	15.3494i	−0.0596099	+	0.0344158i
$447$			147.892i			0.330855i
$448$	−10.3895	−	297.872i	−0.0231908	−	0.664893i
$449$	315.756			0.703243			0.351621	−	0.936142i	$-0.385630\pi$
$449$	315.756			0.703243			0.351621	+	0.936142i	$0.385630\pi$
$450$	26.4032	+	45.7317i	0.0586738	+	0.101626i
$451$	8.33600	+	4.81279i	0.0184834	+	0.0106714i
$452$	−30.9953	+	53.6854i	−0.0685736	+	0.118773i
$453$	−206.993	+	119.507i	−0.456938	+	0.263813i
$454$		−	890.743i		−	1.96199i
$455$	−153.668	+	96.0138i	−0.337733	+	0.211019i
$456$	802.839			1.76061
$457$	93.6533	+	162.212i	0.204931	+	0.354950i	0.950111	−	0.311913i	$-0.100970\pi$
$457$	93.6533	+	162.212i	0.204931	+	0.354950i	−0.745180	+	0.666863i	$0.767636\pi$
$458$	443.533	+	256.074i	0.968412	+	0.559113i
$459$	60.2871	−	104.420i	0.131344	−	0.227495i
$460$	570.644	−	329.462i	1.24053	−	0.716221i
$461$			8.27599i			0.0179523i	0.999960	+	0.00897613i	$0.00285723\pi$
$461$			8.27599i			0.0179523i	−0.999960	+	0.00897613i	$0.997143\pi$
$462$	−51.9778	+	97.7461i	−0.112506	+	0.211572i
$463$	−472.925			−1.02144			−0.510718	−	0.859748i	$-0.670620\pi$
$463$	−472.925			−1.02144			−0.510718	+	0.859748i	$0.670620\pi$
$464$	255.628	+	442.761i	0.550922	+	0.954226i
$465$	−125.622	−	72.5280i	−0.270155	−	0.155974i
$466$	453.283	−	785.108i	0.972709	−	1.68478i
$467$	−620.865	+	358.456i	−1.32948	+	0.767573i	−0.985218	−	0.171303i	$-0.945202\pi$
$467$	−620.865	+	358.456i	−1.32948	+	0.767573i	−0.344257	+	0.938876i	$0.611869\pi$
$468$			291.494i			0.622851i
$469$	402.069	+	213.805i	0.857289	+	0.455875i
$470$	−26.6007			−0.0565972
$471$	−5.94674	−	10.3001i	−0.0126258	−	0.0218685i
$472$	660.705	+	381.458i	1.39980	+	0.808174i
$473$	−96.2556	+	166.720i	−0.203500	+	0.352473i
$474$	−145.448	+	83.9742i	−0.306851	+	0.177161i
$475$		−	149.844i		−	0.315462i
$476$	−722.420	−	1156.22i	−1.51769	−	2.42904i
$477$	120.116			0.251815
$478$	−226.508	−	392.323i	−0.473866	−	0.820759i
$479$	178.320	+	102.953i	0.372276	+	0.214933i	0.674452	−	0.738319i	$-0.264380\pi$
$479$	178.320	+	102.953i	0.372276	+	0.214933i	−0.302177	+	0.953252i	$0.597713\pi$
$480$	22.5111	−	38.9903i	0.0468981	−	0.0812298i
$481$	−258.140	+	149.037i	−0.536673	+	0.309848i
$482$		−	32.6108i		−	0.0676573i
$483$	425.408	−	14.8378i	0.880762	−	0.0307201i
$484$	−959.138			−1.98169
$485$	47.2230	+	81.7926i	0.0973669	+	0.168644i
$486$	47.5258	+	27.4390i	0.0977897	+	0.0564589i
$487$	−161.439	+	279.621i	−0.331498	+	0.574171i	−0.982806	−	0.184643i	$-0.940887\pi$
$487$	−161.439	+	279.621i	−0.331498	+	0.574171i	0.651308	+	0.758813i	$0.274221\pi$
$488$	11.8335	−	6.83205i	0.0242489	−	0.0140001i
$489$		−	479.304i		−	0.980172i
$490$	346.672	+	169.119i	0.707494	+	0.345141i
$491$	272.380			0.554745			0.277372	−	0.960763i	$-0.410536\pi$
$491$	272.380			0.554745			0.277372	+	0.960763i	$0.410536\pi$
$492$	−26.9759	−	46.7236i	−0.0548290	−	0.0949667i
$493$	−492.153	−	284.145i	−0.998282	−	0.576359i
$494$	610.669	−	1057.71i	1.23617	−	2.14111i
$495$	15.0680	−	8.69954i	0.0304405	−	0.0175748i
$496$			781.864i			1.57634i
$497$	21.0035	+	602.184i	0.0422606	+	1.21164i
$498$	801.494			1.60943
$499$	−264.597	−	458.296i	−0.530255	−	0.918429i	−0.999377	−	0.0352954i	$-0.988763\pi$
$499$	−264.597	−	458.296i	−0.530255	−	0.918429i	0.469122	−	0.883134i	$-0.344571\pi$
$500$	−81.2689	−	46.9206i	−0.162538	−	0.0938412i
$501$	36.7020	−	63.5698i	0.0732576	−	0.126886i
$502$	−91.2231	+	52.6677i	−0.181719	+	0.104916i
$503$			204.695i			0.406948i	0.979080	+	0.203474i	$0.0652232\pi$
$503$			204.695i			0.406948i	−0.979080	+	0.203474i	$0.934777\pi$
$504$	275.454	−	172.106i	0.546535	−	0.341481i
$505$	335.334			0.664028
$506$	−160.286	−	277.624i	−0.316772	−	0.548665i
$507$	−52.4837	−	30.3015i	−0.103518	−	0.0597663i
$508$	875.599	−	1516.58i	1.72362	−	2.98540i
$509$	−473.892	+	273.602i	−0.931026	+	0.537528i	−0.887136	−	0.461508i	$-0.847309\pi$
$509$	−473.892	+	273.602i	−0.931026	+	0.537528i	−0.0438903	+	0.999036i	$0.513975\pi$
$510$			316.383i			0.620359i
$511$	202.377	−	380.577i	0.396041	−	0.744770i
$512$	1048.84			2.04851
$513$	−77.8614	−	134.860i	−0.151777	−	0.262885i
$514$	294.779	+	170.191i	0.573500	+	0.331110i
$515$	−156.164	+	270.485i	−0.303232	+	0.525213i
$516$	934.470	−	539.517i	1.81099	−	1.04558i
$517$			8.76461i			0.0169528i
$518$	560.238	+	297.914i	1.08154	+	0.575124i
$519$	−51.1998			−0.0986509
$520$	−200.181	−	346.723i	−0.384963	−	0.666775i
$521$	30.1482	+	17.4061i	0.0578660	+	0.0334090i	0.528654	−	0.848837i	$-0.322697\pi$
$521$	30.1482	+	17.4061i	0.0578660	+	0.0334090i	−0.470788	+	0.882246i	$0.656030\pi$
$522$	129.325	−	223.998i	0.247750	−	0.429115i
$523$	720.290	−	415.860i	1.37723	−	0.795143i	0.385403	−	0.922748i	$-0.374062\pi$
$523$	720.290	−	415.860i	1.37723	−	0.795143i	0.991825	+	0.127606i	$0.0407292\pi$
$524$			919.756i			1.75526i
$525$	−32.1225	−	51.4115i	−0.0611857	−	0.0979267i
$526$	−226.174			−0.429989
$527$	−434.543	−	752.650i	−0.824559	−	1.42818i
$528$	−81.2180	−	46.8913i	−0.153822	−	0.0888092i
$529$	−351.800	+	609.336i	−0.665029	+	1.15186i
$530$	−272.954	+	157.590i	−0.515007	+	0.297340i
$531$		−	147.979i		−	0.278680i
$532$	−1759.72	+	61.3770i	−3.30774	+	0.115370i
$533$	−42.9612			−0.0806027
$534$	198.942	+	344.578i	0.372551	+	0.645277i
$535$	−350.969	−	202.632i	−0.656017	−	0.378751i
$536$	−503.088	+	871.374i	−0.938597	+	1.62570i
$537$	−223.022	+	128.762i	−0.415312	+	0.239780i
$538$		−	695.512i		−	1.29277i
$539$	55.7228	−	114.224i	0.103382	−	0.211919i
$540$	−97.5226			−0.180597
$541$	112.177	+	194.296i	0.207351	+	0.359143i	0.950879	−	0.309562i	$-0.100182\pi$
$541$	112.177	+	194.296i	0.207351	+	0.359143i	−0.743528	+	0.668705i	$0.766849\pi$
$542$	−469.919	−	271.308i	−0.867008	−	0.500568i
$543$	−222.830	+	385.954i	−0.410369	+	0.710780i
$544$	233.606	−	134.872i	0.429422	−	0.247927i
$545$			165.044i			0.302833i
$546$	−17.2236	−	493.810i	−0.0315450	−	0.904414i
$547$	−456.739			−0.834989			−0.417495	−	0.908679i	$-0.637092\pi$
$547$	−456.739			−0.834989			−0.417495	+	0.908679i	$0.637092\pi$
$548$	744.716	+	1289.89i	1.35897	+	2.35381i
$549$	−2.29528	−	1.32518i	−0.00418084	−	0.00241381i
$550$	−22.8274	+	39.5381i	−0.0415043	+	0.0718875i
$551$	−635.621	+	366.976i	−1.15358	+	0.666018i
$552$			940.522i			1.70384i
$553$	163.512	−	102.164i	0.295682	−	0.184745i
$554$	−1194.14			−2.15549
$555$	−49.8620	−	86.3635i	−0.0898414	−	0.155610i
$556$	−1234.94	−	712.994i	−2.22112	−	1.28236i
$557$	388.525	−	672.945i	0.697532	−	1.20816i	−0.271788	−	0.962357i	$-0.587615\pi$
$557$	388.525	−	672.945i	0.697532	−	1.20816i	0.969320	−	0.245803i	$-0.0790516\pi$
$558$	342.561	−	197.777i	0.613908	−	0.354440i
$559$		−	859.223i		−	1.53707i
$560$	−153.415	+	288.502i	−0.273955	+	0.515183i
$561$	104.245			0.185819
$562$	−197.102	−	341.391i	−0.350716	−	0.607457i
$563$	−72.2428	−	41.7094i	−0.128318	−	0.0740842i	0.434467	−	0.900688i	$-0.356937\pi$
$563$	−72.2428	−	41.7094i	−0.128318	−	0.0740842i	−0.562785	+	0.826603i	$0.690270\pi$
$564$	24.5630	−	42.5444i	0.0435514	−	0.0754333i
$565$	−14.3022	+	8.25738i	−0.0253136	+	0.0146148i
$566$		−	230.265i		−	0.406829i
$567$	−55.6245	−	29.5790i	−0.0981031	−	0.0521676i
$568$	−1331.35			−2.34393
$569$	111.671	+	193.421i	0.196259	+	0.339931i	0.947313	−	0.320311i	$-0.103787\pi$
$569$	111.671	+	193.421i	0.196259	+	0.339931i	−0.751053	+	0.660241i	$0.770454\pi$
$570$	353.869	+	204.306i	0.620822	+	0.358432i
$571$	−88.3631	+	153.049i	−0.154751	+	0.268037i	−0.932969	−	0.359958i	$-0.882791\pi$
$571$	−88.3631	+	153.049i	−0.154751	+	0.268037i	0.778217	+	0.627995i	$0.216124\pi$
$572$	−218.252	+	126.008i	−0.381560	+	0.220294i
$573$			210.625i			0.367582i
$574$	48.4597	+	77.5590i	0.0844246	+	0.135120i
$575$	175.542			0.305291
$576$	−63.8685	−	110.624i	−0.110883	−	0.192055i
$577$	780.812	+	450.802i	1.35323	+	0.781286i	0.988700	−	0.149907i	$-0.0478975\pi$
$577$	780.812	+	450.802i	1.35323	+	0.781286i	0.364527	+	0.931193i	$0.381231\pi$
$578$	−439.084	+	760.516i	−0.759661	+	1.31577i
$579$	363.799	−	210.039i	0.628323	−	0.362762i
$580$			459.643i			0.792488i
$581$	−919.556	+	32.0731i	−1.58271	+	0.0552033i
$582$	−257.546			−0.442518
$583$	51.9240	+	89.9351i	0.0890635	+	0.154263i
$584$	824.798	+	476.197i	1.41233	+	0.815406i
$585$	−38.8281	+	67.2523i	−0.0663728	+	0.114961i
$586$	−307.901	+	177.767i	−0.525429	+	0.303356i
$587$			163.544i			0.278610i	0.990250	+	0.139305i	$0.0444868\pi$
$587$			163.544i			0.278610i	−0.990250	+	0.139305i	$0.955513\pi$
$588$	−590.601	+	398.293i	−1.00442	+	0.677370i
$589$	−1122.43			−1.90566
$590$	194.147	+	336.272i	0.329062	+	0.569953i
$591$	148.489	+	85.7304i	0.251251	+	0.145060i
$592$	−268.760	+	465.507i	−0.453987	+	0.786329i
$593$	1004.47	−	579.932i	1.69388	−	0.977964i	0.742554	−	0.669786i	$-0.233614\pi$
$593$	1004.47	−	579.932i	1.69388	−	0.977964i	0.951329	−	0.308177i	$-0.0997190\pi$
$594$			47.4458i			0.0798750i
$595$	−12.6606	−	362.987i	−0.0212783	−	0.610063i
$596$	716.677			1.20248
$597$	−68.2115	−	118.146i	−0.114257	−	0.197899i
$598$	1239.10	+	715.396i	2.07208	+	1.19631i
$599$	−16.3990	+	28.4039i	−0.0273773	+	0.0474188i	−0.879389	−	0.476103i	$-0.842049\pi$
$599$	−16.3990	+	28.4039i	−0.0273773	+	0.0474188i	0.852012	+	0.523522i	$0.175382\pi$
$600$	116.000	−	66.9727i	0.193334	−	0.111621i
$601$			796.834i			1.32585i	0.748687	+	0.662924i	$0.230685\pi$
$601$			796.834i			1.32585i	−0.748687	+	0.662924i	$0.769315\pi$
$602$	−1551.18	+	969.192i	−2.57670	+	1.60995i
$603$	195.163			0.323654
$604$	579.126	+	1003.08i	0.958817	+	1.66072i
$605$	−221.288	−	127.761i	−0.365766	−	0.211175i
$606$	−457.214	+	791.917i	−0.754478	+	1.30679i
$607$	−453.877	+	262.046i	−0.747739	+	0.431707i	−0.824876	−	0.565313i	$-0.808755\pi$
$607$	−453.877	+	262.046i	−0.747739	+	0.431707i	0.0771375	+	0.997020i	$0.475422\pi$
$608$		−	348.378i		−	0.572990i
$609$	−139.412	+	262.169i	−0.228919	+	0.430491i
$610$	6.95448			0.0114008
$611$	−19.5593	−	33.8776i	−0.0320119	−	0.0554462i
$612$	−506.014	−	292.147i	−0.826821	−	0.477365i
$613$	126.866	−	219.738i	0.206959	−	0.358463i	−0.743796	−	0.668406i	$-0.766977\pi$
$613$	126.866	−	219.738i	0.206959	−	0.358463i	0.950755	+	0.309944i	$0.100310\pi$
$614$	1220.69	−	704.769i	1.98810	−	1.14783i
$615$		−	14.3732i		−	0.0233710i
$616$	247.937	+	131.844i	0.402495	+	0.214032i
$617$	620.813			1.00618			0.503090	−	0.864234i	$-0.332196\pi$
$617$	620.813			1.00618			0.503090	+	0.864234i	$0.332196\pi$
$618$	−425.846	−	737.588i	−0.689072	−	1.19351i
$619$	555.643	+	320.801i	0.897647	+	0.518257i	0.876436	−	0.481519i	$-0.159915\pi$
$619$	555.643	+	320.801i	0.897647	+	0.518257i	0.0212107	+	0.999775i	$0.493248\pi$
$620$	−351.466	+	608.757i	−0.566881	+	0.981866i
$621$	157.988	−	91.2143i	0.254409	−	0.146883i
$622$		−	126.731i		−	0.203747i
$623$	−242.036	−	387.374i	−0.388501	−	0.621789i
$624$	418.573			0.670791
$625$	−12.5000	−	21.6506i	−0.0200000	−	0.0346410i
$626$	−349.071	−	201.536i	−0.557621	−	0.321943i
$627$	67.3164	−	116.595i	0.107363	−	0.185958i
$628$	−49.9134	+	28.8175i	−0.0794800	+	0.0458878i
$629$		−	597.484i		−	0.949896i
$630$	165.210	−	5.76234i	0.262238	−	0.00914657i
$631$	−166.338			−0.263610			−0.131805	−	0.991276i	$-0.542077\pi$
$631$	−166.338			−0.263610			−0.131805	+	0.991276i	$0.542077\pi$
$632$	213.004	+	368.933i	0.337031	+	0.583755i
$633$	160.715	+	92.7891i	0.253895	+	0.146586i
$634$	7.09746	−	12.2932i	0.0111947	−	0.0193899i
$635$	404.029	−	233.266i	0.636266	−	0.367348i
$636$		−	582.073i		−	0.915209i
$637$	39.5213	+	565.860i	0.0620429	+	0.888321i
$638$	223.621			0.350503
$639$	129.118	+	223.639i	0.202062	+	0.349982i
$640$	380.317	+	219.576i	0.594246	+	0.343088i
$641$	−68.5302	+	118.698i	−0.106911	+	0.185176i	−0.914518	−	0.404546i	$-0.867429\pi$
$641$	−68.5302	+	118.698i	−0.106911	+	0.185176i	0.807606	+	0.589722i	$0.200763\pi$
$642$	957.061	−	552.559i	1.49075	−	0.860685i
$643$		−	812.010i		−	1.26285i	−0.775438	−	0.631423i	$-0.782471\pi$
$643$		−	812.010i		−	1.26285i	0.775438	−	0.631423i	$-0.217529\pi$
$644$	−71.9030	−	2061.50i	−0.111651	−	3.20109i
$645$	287.463			0.445679
$646$	1224.08	+	2120.16i	1.89485	+	3.28198i
$647$	−197.709	−	114.148i	−0.305579	−	0.176426i	0.339368	−	0.940654i	$-0.389787\pi$
$647$	−197.709	−	114.148i	−0.305579	−	0.176426i	−0.644946	+	0.764228i	$0.723120\pi$
$648$	69.6001	−	120.551i	0.107408	−	0.186035i
$649$	110.798	−	63.9691i	0.170721	−	0.0985656i
$650$		−	203.768i		−	0.313489i
$651$	−385.106	+	240.619i	−0.591561	+	0.369614i
$652$	−2322.68			−3.56239
$653$	435.557	+	754.406i	0.667009	+	1.15529i	0.978736	+	0.205122i	$0.0657590\pi$
$653$	435.557	+	754.406i	0.667009	+	1.15529i	−0.311728	+	0.950171i	$0.600908\pi$
$654$	−389.763	−	225.030i	−0.595968	−	0.344082i
$655$	−122.515	+	212.202i	−0.187046	+	0.323973i
$656$	−67.0932	+	38.7363i	−0.102276	+	0.0590492i
$657$		−	184.731i		−	0.281174i
$658$	−39.0975	+	73.5243i	−0.0594187	+	0.111739i
$659$	−677.945			−1.02875			−0.514374	−	0.857566i	$-0.671976\pi$
$659$	−677.945			−1.02875			−0.514374	+	0.857566i	$0.671976\pi$
$660$	−42.1574	−	73.0188i	−0.0638749	−	0.110635i
$661$	608.681	+	351.422i	0.920849	+	0.531652i	0.883906	−	0.467665i	$-0.154905\pi$
$661$	608.681	+	351.422i	0.920849	+	0.531652i	0.0369430	+	0.999317i	$0.488238\pi$
$662$	893.102	−	1546.90i	1.34910	−	2.33670i
$663$	−402.934	+	232.634i	−0.607743	+	0.350881i
$664$		−	2033.02i		−	3.06177i
$665$	−414.170	−	220.240i	−0.622812	−	0.331188i
$666$	271.939			0.408316
$667$	−429.911	−	744.628i	−0.644544	−	1.11638i
$668$	−308.055	−	177.856i	−0.461161	−	0.266251i
$669$	7.55192	−	13.0803i	0.0112884	−	0.0195520i
$670$	−443.494	+	256.051i	−0.661932	+	0.382166i
$671$		−	2.29142i		−	0.00341493i
$672$	−74.6827	−	119.528i	−0.111135	−	0.177870i
$673$	612.283			0.909782			0.454891	−	0.890547i	$-0.349678\pi$
$673$	612.283			0.909782			0.454891	+	0.890547i	$0.349678\pi$
$674$	−465.187	−	805.727i	−0.690188	−	1.19544i
$675$	−22.5000	−	12.9904i	−0.0333333	−	0.0192450i
$676$	−146.839	+	254.333i	−0.217218	+	0.376232i
$677$	−5.01270	+	2.89408i	−0.00740428	+	0.00427487i	−0.503698	−	0.863880i	$-0.668027\pi$
$677$	−5.01270	+	2.89408i	−0.00740428	+	0.00427487i	0.496293	+	0.868155i	$0.334694\pi$
$678$		−	45.0343i		−	0.0664222i
$679$	295.483	−	10.3061i	0.435173	−	0.0151784i
$680$	802.518			1.18017
$681$	219.123	+	379.532i	0.321766	+	0.557316i
$682$	296.167	+	170.992i	0.434262	+	0.250721i
$683$	58.3832	−	101.123i	0.0854806	−	0.148057i	−0.820115	−	0.572198i	$-0.806091\pi$
$683$	58.3832	−	101.123i	0.0854806	−	0.148057i	0.905596	+	0.424142i	$0.139424\pi$
$684$	−653.523	+	377.312i	−0.955443	+	0.551625i
$685$			396.796i			0.579264i
$686$	976.982	−	709.632i	1.42417	−	1.03445i
$687$	−251.977			−0.366778
$688$	−774.724	−	1341.86i	−1.12605	−	1.95038i
$689$	−401.401	−	231.749i	−0.582585	−	0.336356i
$690$	−239.344	+	414.556i	−0.346875	+	0.600805i
$691$	820.541	−	473.740i	1.18747	−	0.685585i	0.229738	−	0.973252i	$-0.426213\pi$
$691$	820.541	−	473.740i	1.18747	−	0.685585i	0.957730	+	0.287667i	$0.0928796\pi$
$692$			248.111i			0.358542i
$693$	−1.89862	−	54.4346i	−0.00273971	−	0.0785493i
$694$	825.425			1.18937
$695$	−189.947	−	328.998i	−0.273305	−	0.473378i
$696$	−568.180	−	328.039i	−0.816350	−	0.471320i
$697$	43.0575	−	74.5778i	0.0617755	−	0.106998i
$698$	165.284	−	95.4270i	0.236797	−	0.136715i
$699$			446.030i			0.638097i
$700$	−249.137	+	155.664i	−0.355910	+	0.222377i
$701$	1168.56			1.66700			0.833498	−	0.552523i	$-0.186335\pi$
$701$	1168.56			1.66700			0.833498	+	0.552523i	$0.186335\pi$
$702$	−105.881	−	183.391i	−0.150827	−	0.261241i
$703$	−668.275	−	385.829i	−0.950604	−	0.548832i
$704$	55.2187	−	95.6415i	0.0784356	−	0.135854i
$705$	11.3341	−	6.54377i	0.0160768	−	0.00928194i
$706$		−	1837.05i		−	2.60205i
$707$	492.872	−	926.865i	0.697132	−	1.31098i
$708$	−717.099			−1.01285
$709$	−334.781	−	579.857i	−0.472187	−	0.817852i	0.527306	−	0.849675i	$-0.323202\pi$
$709$	−334.781	−	579.857i	−0.472187	−	0.817852i	−0.999494	+	0.0318230i	$0.989869\pi$
$710$	−586.822	−	338.802i	−0.826509	−	0.477185i
$711$	41.3153	−	71.5602i	0.0581087	−	0.100647i
$712$	874.035	−	504.625i	1.22758	−	0.708742i
$713$		−	1314.93i		−	1.84422i
$714$	874.484	+	465.018i	1.22477	+	0.651286i
$715$	−67.1390			−0.0939008
$716$	623.973	+	1080.75i	0.871471	+	1.50943i
$717$	193.023	+	111.442i	0.269209	+	0.155428i
$718$	−823.685	+	1426.66i	−1.14719	+	1.98700i
$719$	−805.983	+	465.334i	−1.12098	+	0.647196i	−0.941650	−	0.336593i	$-0.890725\pi$
$719$	−805.983	+	465.334i	−1.12098	+	0.647196i	−0.179327	+	0.983790i	$0.557392\pi$
$720$			140.038i			0.194498i
$721$	518.091	+	829.195i	0.718572	+	1.15006i
$722$	1890.94			2.61903
$723$	8.02227	+	13.8950i	0.0110958	+	0.0192185i
$724$	1870.31	+	1079.82i	2.58330	+	1.49147i
$725$	−61.2262	+	106.047i	−0.0844499	+	0.146272i
$726$	603.433	−	348.392i	0.831175	−	0.479879i
$727$			290.932i			0.400182i	0.979777	+	0.200091i	$0.0641238\pi$
$727$			290.932i			0.400182i	−0.979777	+	0.200091i	$0.935876\pi$
$728$	−1252.57	+	43.6882i	−1.72056	+	0.0600113i
$729$	−27.0000			−0.0370370
$730$	242.365	+	419.789i	0.332007	+	0.575053i
$731$	1491.55	+	861.149i	2.04043	+	1.17804i
$732$	−6.42174	+	11.1228i	−0.00877288	+	0.0151951i
$733$	−0.836082	+	0.482712i	−0.00114063	+	0.000658543i	−0.500570	−	0.865696i	$-0.666876\pi$
$733$	−0.836082	+	0.482712i	−0.00114063	+	0.000658543i	0.499430	+	0.866354i	$0.333543\pi$
$734$		−	606.304i		−	0.826027i
$735$	−189.315	+	13.2223i	−0.257571	+	0.0179895i
$736$	408.124			0.554516
$737$	84.3659	+	146.126i	0.114472	+	0.198271i
$738$	33.9433	+	19.5972i	0.0459936	+	0.0265544i
$739$	49.9365	−	86.4925i	0.0675731	−	0.117040i	−0.830259	−	0.557377i	$-0.811808\pi$
$739$	49.9365	−	86.4925i	0.0675731	−	0.117040i	0.897832	+	0.440337i	$0.145141\pi$
$740$	−418.512	+	241.628i	−0.565557	+	0.326525i
$741$			600.898i			0.810929i
$742$	34.3931	+	986.070i	0.0463518	+	1.32894i
$743$	890.635			1.19870			0.599351	−	0.800486i	$-0.295425\pi$
$743$	890.635			1.19870			0.599351	+	0.800486i	$0.295425\pi$
$744$	−501.670	−	868.917i	−0.674287	−	1.16790i
$745$	165.349	+	95.4640i	0.221944	+	0.128140i
$746$	−811.408	+	1405.40i	−1.08768	+	1.88391i
$747$	−341.504	+	197.167i	−0.457167	+	0.263946i
$748$		−	505.162i		−	0.675351i
$749$	−1075.93	+	672.251i	−1.43648	+	0.897532i
$750$	68.1728			0.0908971
$751$	−310.537	−	537.867i	−0.413499	−	0.716200i	0.581771	−	0.813353i	$-0.302360\pi$
$751$	−310.537	−	537.867i	−0.413499	−	0.716200i	−0.995270	+	0.0971521i	$0.969027\pi$
$752$	−61.0920	−	35.2715i	−0.0812393	−	0.0469035i
$753$	25.9125	−	44.8818i	0.0344124	−	0.0596040i
$754$	−864.357	+	499.037i	−1.14636	+	0.661853i
$755$			308.567i			0.408698i
$756$	−143.338	+	269.553i	−0.189601	+	0.356551i
$757$	675.637			0.892519			0.446259	−	0.894904i	$-0.352756\pi$
$757$	675.637			0.892519			0.446259	+	0.894904i	$0.352756\pi$
$758$	782.658	+	1355.60i	1.03253	+	1.78840i
$759$	136.591	+	78.8609i	0.179962	+	0.103901i
$760$	518.230	−	897.601i	0.681882	−	1.18105i
$761$	549.336	−	317.159i	0.721861	−	0.416766i	−0.0935765	−	0.995612i	$-0.529830\pi$
$761$	549.336	−	317.159i	0.721861	−	0.416766i	0.815437	+	0.578846i	$0.196497\pi$
$762$			1272.19i			1.66954i
$763$	456.181	+	242.580i	0.597878	+	0.317930i
$764$	1020.67			1.33596
$765$	−77.8303	−	134.806i	−0.101739	−	0.176217i
$766$	−1614.22	−	931.967i	−2.10733	−	1.21667i
$767$	−285.509	+	494.516i	−0.372241	+	0.644741i
$768$	−781.618	+	451.267i	−1.01773	+	0.587587i
$769$		−	17.8434i		−	0.0232033i	−0.999933	−	0.0116017i	$-0.996307\pi$
$769$		−	17.8434i		−	0.0232033i	0.999933	−	0.0116017i	$-0.00369301\pi$
$770$	75.7320	+	121.208i	0.0983532	+	0.157413i
$771$	−167.468			−0.217208
$772$	−1017.84	−	1762.95i	−1.31844	−	2.28361i
$773$	−223.935	−	129.289i	−0.289697	−	0.167256i	0.348108	−	0.937454i	$-0.386824\pi$
$773$	−223.935	−	129.289i	−0.289697	−	0.167256i	−0.637805	+	0.770198i	$0.720157\pi$
$774$	−391.943	+	678.865i	−0.506386	+	0.877086i
$775$	−162.178	+	93.6332i	−0.209261	+	0.120817i
$776$			653.274i			0.841848i
$777$	−311.996	+	10.8821i	−0.401539	+	0.0140053i
$778$	−688.281			−0.884680
$779$	−55.6092	−	96.3180i	−0.0713854	−	0.123643i
$780$	325.900	+	188.159i	0.417821	+	0.241229i
$781$	−111.631	+	193.351i	−0.142934	+	0.247568i
$782$	−2483.76	+	1434.00i	−3.17616	+	1.83376i
$783$			127.256i			0.162524i
$784$	571.933	+	848.078i	0.729506	+	1.08173i
$785$	−15.3544			−0.0195598
$786$	−334.088	−	578.657i	−0.425048	−	0.736204i
$787$	936.494	+	540.685i	1.18995	+	0.687020i	0.958296	−	0.285777i	$-0.0922517\pi$
$787$	936.494	+	540.685i	1.18995	+	0.687020i	0.231658	+	0.972797i	$0.425585\pi$
$788$	415.444	−	719.570i	0.527213	−	0.913160i
$789$	96.3693	−	55.6388i	0.122141	−	0.0705182i
$790$			216.820i			0.274456i
$791$	1.80212	+	51.6679i	0.00227828	+	0.0653198i
$792$	120.348			0.151954
$793$	5.11357	+	8.85696i	0.00644838	+	0.0111689i
$794$	89.1928	+	51.4955i	0.112333	+	0.0648558i
$795$	77.5343	−	134.293i	0.0975274	−	0.168922i
$796$	−572.527	+	330.549i	−0.719256	+	0.415262i
$797$		−	145.723i		−	0.182839i	−0.995812	−	0.0914195i	$-0.970860\pi$
$797$		−	145.723i		−	0.182839i	0.995812	−	0.0914195i	$-0.0291404\pi$
$798$	1084.82	−	677.805i	1.35942	−	0.849380i
$799$	78.4124			0.0981382
$800$	−29.0617	−	50.3363i	−0.0363271	−	0.0629203i
$801$	−169.533	−	97.8796i	−0.211651	−	0.122197i
$802$	371.040	−	642.659i	0.462643	−	0.801321i
$803$	138.315	−	79.8564i	0.172248	−	0.0994476i
$804$		−	945.749i		−	1.17630i
$805$	258.011	−	485.199i	0.320510	−	0.602731i
$806$	−1526.35			−1.89374
$807$	171.096	+	296.347i	0.212015	+	0.367220i
$808$	2008.73	+	1159.74i	2.48605	+	1.43532i
$809$	108.425	−	187.797i	0.134023	−	0.232134i	−0.791201	−	0.611556i	$-0.790544\pi$
$809$	108.425	−	187.797i	0.134023	−	0.232134i	0.925224	+	0.379422i	$0.123877\pi$
$810$	61.3555	−	35.4236i	0.0757475	−	0.0437329i
$811$			8.20233i			0.0101139i	0.999987	+	0.00505693i	$0.00160968\pi$
$811$			8.20233i			0.0101139i	−0.999987	+	0.00505693i	$0.998390\pi$
$812$	1270.45	+	675.581i	1.56460	+	0.831996i
$813$	266.967			0.328372
$814$	117.555	+	203.611i	0.144416	+	0.250136i
$815$	−535.879	−	309.390i	−0.657520	−	0.379619i
$816$	−419.512	+	726.616i	−0.514108	+	0.890460i
$817$	1926.36	−	1112.18i	2.35784	−	1.36130i
$818$			1142.33i			1.39650i
$819$	128.816	+	206.168i	0.157285	+	0.251731i
$820$	−69.6514			−0.0849408
$821$	−786.474	−	1362.21i	−0.957946	−	1.65921i	−0.727477	−	0.686132i	$-0.759307\pi$
$821$	−786.474	−	1362.21i	−0.957946	−	1.65921i	−0.230469	−	0.973080i	$-0.574026\pi$
$822$	−937.063	−	541.013i	−1.13998	−	0.658167i
$823$	−499.339	+	864.881i	−0.606731	+	1.05089i	0.385045	+	0.922898i	$0.374186\pi$
$823$	−499.339	+	864.881i	−0.606731	+	1.05089i	−0.991775	+	0.127991i	$0.959147\pi$
$824$	−1870.92	+	1080.18i	−2.27053	+	1.31089i
$825$		−	22.4621i		−	0.0272268i
$826$	1214.81	−	42.3714i	1.47072	−	0.0512970i
$827$	−1344.24			−1.62544			−0.812718	−	0.582658i	$-0.802013\pi$
$827$	−1344.24			−1.62544			−0.812718	+	0.582658i	$0.802013\pi$
$828$	−442.019	−	765.599i	−0.533839	−	0.924637i
$829$	−1312.22	−	757.611i	−1.58290	−	0.913885i	−0.994434	−	0.105360i	$-0.966400\pi$
$829$	−1312.22	−	757.611i	−1.58290	−	0.913885i	−0.588462	−	0.808525i	$-0.700266\pi$
$830$	517.362	−	896.097i	0.623328	−	1.07964i
$831$	508.805	−	293.758i	0.612280	−	0.353500i
$832$			492.908i			0.592437i
$833$	−1021.91	−	498.523i	−1.22678	−	0.598467i
$834$	1035.94			1.24213
$835$	−47.3821	−	82.0682i	−0.0567451	−	0.0982853i
$836$	−565.014	−	326.211i	−0.675855	−	0.390205i
$837$	−97.3065	+	168.540i	−0.116256	+	0.201362i
$838$	−2115.72	+	1221.51i	−2.52473	+	1.45765i
$839$		−	439.769i		−	0.524159i	−0.965046	−	0.262079i	$-0.915592\pi$
$839$		−	439.769i		−	0.524159i	0.965046	−	0.262079i	$-0.0844082\pi$
$840$	−14.6164	−	419.061i	−0.0174005	−	0.498882i
$841$	−241.217			−0.286821
$842$	−601.208	−	1041.32i	−0.714024	−	1.23673i
$843$	167.964	+	96.9743i	0.199246	+	0.115035i
$844$	449.650	−	778.817i	0.532761	−	0.922769i
$845$	−67.7562	+	39.1191i	−0.0801849	+	0.0462948i
$846$			35.6886i			0.0421851i
$847$	−678.379	+	423.859i	−0.800920	+	0.500424i
$848$	−835.833			−0.985652
$849$	56.6453	+	98.1126i	0.0667201	+	0.115563i
$850$	353.727	+	204.224i	0.416150	+	0.240264i
$851$	451.997	−	782.881i	0.531136	−	0.919955i
$852$	1083.74	−	625.697i	1.27199	−	0.734386i
$853$		−	222.026i		−	0.260288i	−0.991495	−	0.130144i	$-0.958456\pi$
$853$		−	222.026i		−	0.260288i	0.991495	−	0.130144i	$-0.0415439\pi$
$854$	10.2216	−	19.2222i	0.0119691	−	0.0225084i
$855$	−201.037			−0.235131
$856$	−1401.59	−	2427.62i	−1.63737	−	2.83601i
$857$	−902.699	−	521.173i	−1.05332	−	0.608137i	−0.129746	−	0.991547i	$-0.541416\pi$
$857$	−902.699	−	521.173i	−1.05332	−	0.608137i	−0.923578	+	0.383410i	$0.874750\pi$
$858$	91.5411	−	158.554i	0.106691	−	0.184795i
$859$	132.904	−	76.7321i	0.154719	−	0.0893272i	−0.420642	−	0.907227i	$-0.638195\pi$
$859$	132.904	−	76.7321i	0.154719	−	0.0893272i	0.575361	+	0.817900i	$0.304862\pi$
$860$		−	1393.03i		−	1.61980i
$861$	−39.7274	−	21.1256i	−0.0461410	−	0.0245361i
$862$	1448.49			1.68038
$863$	401.493	+	695.406i	0.465229	+	0.805800i	0.999212	−	0.0396949i	$-0.0126386\pi$
$863$	401.493	+	695.406i	0.465229	+	0.805800i	−0.533983	+	0.845495i	$0.679305\pi$
$864$	−52.3110	−	30.2018i	−0.0605451	−	0.0349557i
$865$	−33.0493	+	57.2431i	−0.0382073	+	0.0661770i
$866$	−1352.01	+	780.582i	−1.56121	+	0.901365i
$867$		−	432.059i		−	0.498338i
$868$	1166.02	+	1866.20i	1.34334	+	2.15000i
$869$	71.4397			0.0822091
$870$	−166.958	−	289.180i	−0.191906	−	0.332391i
$871$	−652.195	−	376.545i	−0.748789	−	0.432313i
$872$	−570.797	+	988.649i	−0.654583	+	1.13377i
$873$	109.736	−	63.3562i	0.125700	−	0.0725730i
$874$			3704.05i			4.23804i
$875$	−78.2148	+	2.72805i	−0.0893884	+	0.00311777i
$876$	−895.197			−1.02191
$877$	672.328	+	1164.51i	0.766622	+	1.32783i	0.939385	+	0.342865i	$0.111397\pi$
$877$	672.328	+	1164.51i	0.766622	+	1.32783i	−0.172763	+	0.984963i	$0.555269\pi$
$878$	−943.483	−	544.720i	−1.07458	−	0.620410i
$879$	87.4613	−	151.487i	0.0995009	−	0.172341i
$880$	−104.852	+	60.5364i	−0.119150	+	0.0687913i
$881$			1052.91i			1.19513i	0.801822	+	0.597563i	$0.203864\pi$
$881$			1052.91i			1.19513i	−0.801822	+	0.597563i	$0.796136\pi$
$882$	226.897	−	465.110i	0.257253	−	0.527335i
$883$	1372.84			1.55475			0.777375	−	0.629037i	$-0.216551\pi$
$883$	1372.84			1.55475			0.777375	+	0.629037i	$0.216551\pi$
$884$	1127.33	+	1952.59i	1.27526	+	2.20881i
$885$	−165.446	−	95.5202i	−0.186945	−	0.107932i
$886$	1441.02	−	2495.92i	1.62643	−	2.81706i
$887$	−544.825	+	314.555i	−0.614233	+	0.354628i	−0.774620	−	0.632427i	$-0.782059\pi$
$887$	−544.825	+	314.555i	−0.614233	+	0.354628i	0.160387	+	0.987054i	$0.448726\pi$
$888$		−	689.782i		−	0.776782i
$889$	−50.9090	−	1459.59i	−0.0572654	−	1.64183i
$890$	513.667			0.577154
$891$	−11.6717	−	20.2159i	−0.0130995	−	0.0226890i
$892$	−63.3864	−	36.5962i	−0.0710610	−	0.0410271i
$893$	50.6352	−	87.7028i	0.0567024	−	0.0982114i
$894$	−450.891	+	260.322i	−0.504352	+	0.291188i
$895$			332.462i			0.371466i
$896$	1165.90	−	728.466i	1.30122	−	0.813020i
$897$	−703.950			−0.784783
$898$	555.798	+	962.671i	0.618929	+	1.07202i
$899$	794.361	+	458.624i	0.883605	+	0.510150i
$900$	−62.9506	+	109.034i	−0.0699451	+	0.121148i
$901$	804.602	−	464.537i	0.893010	−	0.515580i
$902$			33.8862i			0.0375678i
$903$	422.511	−	794.547i	0.467897	−	0.879897i
$904$	−114.231			−0.126362
$905$	287.673	+	498.264i	0.317870	+	0.550568i
$906$	−728.704	−	420.717i	−0.804309	−	0.464368i
$907$	29.8954	−	51.7804i	0.0329608	−	0.0570897i	−0.849074	−	0.528273i	$-0.822840\pi$
$907$	29.8954	−	51.7804i	0.0329608	−	0.0570897i	0.882035	+	0.471183i	$0.156173\pi$
$908$	1839.19	−	1061.86i	2.02554	−	1.16944i
$909$		−	449.898i		−	0.494938i
$910$	−563.214	−	299.497i	−0.618917	−	0.329117i
$911$	−850.964			−0.934099			−0.467050	−	0.884231i	$-0.654683\pi$
$911$	−850.964			−0.934099			−0.467050	+	0.884231i	$0.654683\pi$
$912$	541.804	+	938.432i	0.594083	+	1.02898i
$913$	−295.253	−	170.465i	−0.323388	−	0.186708i
$914$	−329.700	+	571.057i	−0.360722	+	0.624788i
$915$	−2.96319	+	1.71080i	−0.00323846	+	0.00186973i
$916$			1221.06i			1.33304i
$917$	406.455	+	650.525i	0.443245	+	0.709406i
$918$	424.473			0.462389
$919$	−330.505	−	572.452i	−0.359636	−	0.622908i	0.628264	−	0.778000i	$-0.283766\pi$
$919$	−330.505	−	572.452i	−0.359636	−	0.622908i	−0.987900	+	0.155093i	$0.950432\pi$
$920$	1051.54	+	607.105i	1.14297	+	0.659896i
$921$	−346.746	+	600.582i	−0.376489	+	0.652098i
$922$	−25.2317	+	14.5675i	−0.0273662	+	0.0157999i
$923$		−	996.472i		−	1.07960i
$924$	−263.787	+	9.20061i	−0.285484	+	0.00995737i
$925$	−128.743			−0.139182
$926$	−832.448	−	1441.84i	−0.898972	−	1.55707i
$927$	362.893	+	209.517i	0.391471	+	0.226016i
$928$	−142.347	+	246.552i	−0.153391	+	0.265681i
$929$	−231.638	+	133.736i	−0.249341	+	0.143957i	−0.619462	−	0.785026i	$-0.712649\pi$
$929$	−231.638	+	133.736i	−0.249341	+	0.143957i	0.370122	+	0.928983i	$0.379316\pi$
$930$		−	510.659i		−	0.549096i
$931$	−1217.49	+	821.059i	−1.30772	+	0.881911i
$932$	2161.43			2.31914
$933$	31.1758	+	53.9980i	0.0334145	+	0.0578757i
$934$	−2185.71	−	1261.92i	−2.34016	−	1.35109i
$935$	67.2895	−	116.549i	0.0719674	−	0.124651i
$936$	−465.178	+	268.571i	−0.496985	+	0.286934i
$937$		−	1625.83i		−	1.73515i	−0.497309	−	0.867573i	$-0.665679\pi$
$937$		−	1625.83i		−	1.73515i	0.497309	−	0.867573i	$-0.334321\pi$
$938$	55.8817	+	1602.16i	0.0595754	+	1.70806i
$939$	198.312			0.211194
$940$	−31.7107	−	54.9245i	−0.0337348	−	0.0584304i
$941$	−257.993	−	148.952i	−0.274168	−	0.158291i	0.356612	−	0.934253i	$-0.383932\pi$
$941$	−257.993	−	148.952i	−0.274168	−	0.158291i	−0.630780	+	0.775961i	$0.717265\pi$
$942$	20.9351	−	36.2606i	0.0222241	−	0.0384932i
$943$	112.836	−	65.1460i	0.119657	−	0.0690838i
$944$			1029.72i			1.09081i
$945$	−68.9758	+	43.0969i	−0.0729903	+	0.0456051i
$946$	−677.722			−0.716408
$947$	456.876	+	791.333i	0.482446	+	0.835621i	0.999797	−	0.0201524i	$-0.00641516\pi$
$947$	456.876	+	791.333i	0.482446	+	0.835621i	−0.517351	+	0.855773i	$0.673082\pi$
$948$	−346.776	−	200.211i	−0.365798	−	0.211193i
$949$	−356.418	+	617.334i	−0.375572	+	0.650510i
$950$	456.842	−	263.758i	0.480887	−	0.277640i
$951$			6.98391i			0.00734375i
$952$	1179.54	−	2218.16i	1.23901	−	2.33000i
$953$	−1451.89			−1.52349			−0.761746	−	0.647875i	$-0.775658\pi$
$953$	−1451.89			−1.52349			−0.761746	+	0.647875i	$0.775658\pi$
$954$	211.429	+	366.206i	0.221624	+	0.383864i
$955$	235.486	+	135.958i	0.246582	+	0.142364i
$956$	540.040	−	935.377i	0.564896	−	0.978428i
$957$	−95.2815	+	55.0108i	−0.0995627	+	0.0574826i
$958$			724.878i			0.756657i
$959$	1096.74	+	583.208i	1.14363	+	0.608142i
$960$	−164.908			−0.171779
$961$	220.874	+	382.566i	0.229838	+	0.398091i
$962$	−908.762	−	524.674i	−0.944659	−	0.545399i
$963$	−271.859	+	470.874i	−0.282305	+	0.488966i
$964$	67.3342	−	38.8754i	0.0698487	−	0.0403272i
$965$		−	542.319i		−	0.561989i
$966$	794.047	+	1270.86i	0.821994	+	1.31559i
$967$	235.985			0.244039			0.122019	−	0.992528i	$-0.461063\pi$
$967$	235.985			0.244039			0.122019	+	0.992528i	$0.461063\pi$
$968$	−883.710	−	1530.63i	−0.912924	−	1.58123i
$969$	−1043.12	−	602.245i	−1.07649	−	0.621512i
$970$	−166.245	+	287.945i	−0.171387	+	0.296850i
$971$	−555.872	+	320.933i	−0.572474	+	0.330518i	−0.758137	−	0.652096i	$-0.773890\pi$
$971$	−555.872	+	320.933i	−0.572474	+	0.330518i	0.185663	+	0.982613i	$0.440557\pi$
$972$			130.840i			0.134609i
$973$	−1188.53	+	41.4548i	−1.22151	+	0.0426051i
$974$	−1136.67			−1.16701
$975$	50.1269	+	86.8223i	0.0514122	+	0.0890485i
$976$	15.9719	+	9.22136i	0.0163646	+	0.00944812i
$977$	−320.423	+	554.990i	−0.327967	+	0.568055i	−0.982108	−	0.188317i	$-0.939697\pi$
$977$	−320.423	+	554.990i	−0.327967	+	0.568055i	0.654142	+	0.756372i	$0.273030\pi$
$978$	1461.29	−	843.678i	1.49417	−	0.862657i
$979$		−	169.247i		−	0.172878i
$980$	64.0744	+	917.409i	0.0653821	+	0.936131i
$981$	221.429			0.225718
$982$	479.446	+	830.425i	0.488235	+	0.845647i
$983$	−368.692	−	212.865i	−0.375068	−	0.216546i	0.300602	−	0.953750i	$-0.402812\pi$
$983$	−368.692	−	212.865i	−0.375068	−	0.216546i	−0.675670	+	0.737204i	$0.736146\pi$
$984$	49.7089	−	86.0984i	0.0505172	−	0.0874984i
$985$	191.699	−	110.677i	0.194618	−	0.112363i
$986$		−	2000.62i		−	2.02903i
$987$	−1.42814	−	40.9456i	−0.00144695	−	0.0414849i
$988$	2911.92			2.94728
$989$	1302.92	+	2256.72i	1.31741	+	2.28182i
$990$	53.0460	+	30.6261i	0.0535818	+	0.0309355i
$991$	548.625	−	950.247i	0.553608	−	0.958877i	−0.444402	−	0.895827i	$-0.646584\pi$
$991$	548.625	−	950.247i	0.553608	−	0.958877i	0.998010	−	0.0630498i	$-0.0200827\pi$
$992$	−377.052	+	217.691i	−0.380093	+	0.219447i
$993$			878.813i			0.885008i
$994$	−1798.96	+	1124.01i	−1.80981	+	1.13079i
$995$	−176.121			−0.177006
$996$	955.461	+	1654.91i	0.959299	+	1.66155i
$997$	−1104.16	−	637.487i	−1.10748	−	0.639405i	−0.169306	−	0.985564i	$-0.554153\pi$
$997$	−1104.16	−	637.487i	−1.10748	−	0.639405i	−0.938176	+	0.346159i	$0.887486\pi$
$998$	931.496	−	1613.40i	0.933362	−	1.61663i
$999$	−115.869	+	66.8969i	−0.115985	+	0.0669639i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.n.a.31.4	✓	8
3.2	odd	2		315.3.w.a.136.1		8
5.2	odd	4		525.3.s.h.199.1		16
5.3	odd	4		525.3.s.h.199.8		16
5.4	even	2		525.3.o.l.451.1		8
7.3	odd	6		735.3.h.a.391.1		8
7.4	even	3		735.3.h.a.391.2		8
7.5	odd	6	inner	105.3.n.a.61.4	yes	8
21.5	even	6		315.3.w.a.271.1		8
35.12	even	12		525.3.s.h.124.8		16
35.19	odd	6		525.3.o.l.376.1		8
35.33	even	12		525.3.s.h.124.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.n.a.31.4	✓	8	1.1	even	1	trivial
105.3.n.a.61.4	yes	8	7.5	odd	6	inner
315.3.w.a.136.1		8	3.2	odd	2
315.3.w.a.271.1		8	21.5	even	6
525.3.o.l.376.1		8	35.19	odd	6
525.3.o.l.451.1		8	5.4	even	2
525.3.s.h.124.1		16	35.33	even	12
525.3.s.h.124.8		16	35.12	even	12
525.3.s.h.199.1		16	5.2	odd	4
525.3.s.h.199.8		16	5.3	odd	4
735.3.h.a.391.1		8	7.3	odd	6
735.3.h.a.391.2		8	7.4	even	3

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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.76021 + 3.04878i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-4.19671 + 7.26891i) q^{4} +(-1.93649 + 1.11803i) q^{5} -6.09756i q^{6} +(0.244004 + 6.99575i) q^{7} -15.4667 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.76021 + 3.04878i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-4.19671 + 7.26891i) q^{4} +(-1.93649 + 1.11803i) q^{5} -6.09756i q^{6} +(0.244004 + 6.99575i) q^{7} -15.4667 q^{8} +(1.50000 + 2.59808i) q^{9} +(-6.81728 - 3.93596i) q^{10} +(-1.29685 + 2.24621i) q^{11} +(12.5901 - 7.26891i) q^{12} -11.5763i q^{13} +(-20.8990 + 13.0579i) q^{14} +3.87298 q^{15} +(-10.4379 - 18.0789i) q^{16} +(20.0957 + 11.6023i) q^{17} +(-5.28064 + 9.14634i) q^{18} +(25.9538 - 14.9844i) q^{19} -18.7682i q^{20} +(5.69249 - 10.7049i) q^{21} -9.13094 q^{22} +(17.5542 + 30.4048i) q^{23} +(23.2000 + 13.3945i) q^{24} +(2.50000 - 4.33013i) q^{25} +(35.2936 - 20.3768i) q^{26} -5.19615i q^{27} +(-51.8754 - 27.5854i) q^{28} -24.4905 q^{29} +(6.81728 + 11.8079i) q^{30} +(-32.4355 - 18.7266i) q^{31} +(5.81233 - 10.0673i) q^{32} +(3.89055 - 2.24621i) q^{33} +81.6898i q^{34} +(-8.29399 - 13.2744i) q^{35} -25.1802 q^{36} +(-12.8743 - 22.2990i) q^{37} +(91.3685 + 52.7516i) q^{38} +(-10.0254 + 17.3645i) q^{39} +(29.9511 - 17.2923i) q^{40} -3.71113i q^{41} +(42.6570 - 1.48783i) q^{42} +74.2225 q^{43} +(-10.8850 - 18.8534i) q^{44} +(-5.80948 - 3.35410i) q^{45} +(-61.7983 + 107.038i) q^{46} +(2.92646 - 1.68959i) q^{47} +36.1578i q^{48} +(-48.8809 + 3.41398i) q^{49} +17.6021 q^{50} +(-20.0957 - 34.8068i) q^{51} +(84.1471 + 48.5823i) q^{52} +(20.0193 - 34.6744i) q^{53} +(15.8419 - 9.14634i) q^{54} -5.79969i q^{55} +(-3.77394 - 108.201i) q^{56} -51.9076 q^{57} +(-43.1085 - 74.6661i) q^{58} +(-42.7180 - 24.6632i) q^{59} +(-16.2538 + 28.1524i) q^{60} +(-0.765094 + 0.441727i) q^{61} -131.852i q^{62} +(-17.8095 + 11.1276i) q^{63} -42.5790 q^{64} +(12.9427 + 22.4174i) q^{65} +(13.6964 + 7.90763i) q^{66} +(32.5272 - 56.3388i) q^{67} +(-168.671 + 97.3825i) q^{68} -60.8096i q^{69} +(25.8715 - 48.6523i) q^{70} +86.0786 q^{71} +(-23.2000 - 40.1836i) q^{72} +(-53.3274 - 30.7886i) q^{73} +(45.3231 - 78.5019i) q^{74} +(-7.50000 + 4.33013i) q^{75} +251.541i q^{76} +(-16.0304 - 8.52436i) q^{77} -70.5872 q^{78} +(-13.7718 - 23.8534i) q^{79} +(40.4256 + 23.3397i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(11.3144 - 6.53239i) q^{82} +131.445i q^{83} +(53.9235 + 86.3036i) q^{84} -51.8869 q^{85} +(130.648 + 226.288i) q^{86} +(36.7357 + 21.2094i) q^{87} +(20.0580 - 34.7415i) q^{88} +(-56.5108 + 32.6265i) q^{89} -23.6157i q^{90} +(80.9849 - 2.82467i) q^{91} -294.679 q^{92} +(32.4355 + 56.1799i) q^{93} +(10.3024 + 5.94809i) q^{94} +(-33.5062 + 58.0345i) q^{95} +(-17.4370 + 10.0673i) q^{96} -42.2375i q^{97} +(-96.4494 - 143.018i) q^{98} -7.78111 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 12 q^{3} - 6 q^{4} - 16 q^{7} - 32 q^{8} + 12 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 - 12 * q^3 - 6 * q^4 - 16 * q^7 - 32 * q^8 + 12 * q^9	\( 8 q + 2 q^{2} - 12 q^{3} - 6 q^{4} - 16 q^{7} - 32 q^{8} + 12 q^{9} + 20 q^{11} + 18 q^{12} - 16 q^{14} - 2 q^{16} - 18 q^{17} - 6 q^{18} + 48 q^{21} - 16 q^{22} + 62 q^{23} + 48 q^{24} + 20 q^{25} + 120 q^{26} - 120 q^{28} - 100 q^{29} - 126 q^{31} + 36 q^{32} - 60 q^{33} - 36 q^{36} - 80 q^{37} + 114 q^{38} - 12 q^{39} + 90 q^{40} + 90 q^{42} + 352 q^{43} - 18 q^{44} - 82 q^{46} - 72 q^{47} + 38 q^{49} + 20 q^{50} + 18 q^{51} - 48 q^{52} - 76 q^{53} + 18 q^{54} + 196 q^{56} - 40 q^{58} - 54 q^{59} - 60 q^{60} - 396 q^{61} - 96 q^{63} - 4 q^{64} - 60 q^{65} + 24 q^{66} + 184 q^{67} - 312 q^{68} + 164 q^{71} - 48 q^{72} + 348 q^{73} - 140 q^{74} - 60 q^{75} + 152 q^{77} - 240 q^{78} - 206 q^{79} - 36 q^{81} + 204 q^{82} + 132 q^{84} - 60 q^{85} + 178 q^{86} + 150 q^{87} + 124 q^{88} + 282 q^{89} - 114 q^{91} - 288 q^{92} + 126 q^{93} + 30 q^{94} - 120 q^{95} - 108 q^{96} - 592 q^{98} + 120 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - 12 * q^3 - 6 * q^4 - 16 * q^7 - 32 * q^8 + 12 * q^9 + 20 * q^11 + 18 * q^12 - 16 * q^14 - 2 * q^16 - 18 * q^17 - 6 * q^18 + 48 * q^21 - 16 * q^22 + 62 * q^23 + 48 * q^24 + 20 * q^25 + 120 * q^26 - 120 * q^28 - 100 * q^29 - 126 * q^31 + 36 * q^32 - 60 * q^33 - 36 * q^36 - 80 * q^37 + 114 * q^38 - 12 * q^39 + 90 * q^40 + 90 * q^42 + 352 * q^43 - 18 * q^44 - 82 * q^46 - 72 * q^47 + 38 * q^49 + 20 * q^50 + 18 * q^51 - 48 * q^52 - 76 * q^53 + 18 * q^54 + 196 * q^56 - 40 * q^58 - 54 * q^59 - 60 * q^60 - 396 * q^61 - 96 * q^63 - 4 * q^64 - 60 * q^65 + 24 * q^66 + 184 * q^67 - 312 * q^68 + 164 * q^71 - 48 * q^72 + 348 * q^73 - 140 * q^74 - 60 * q^75 + 152 * q^77 - 240 * q^78 - 206 * q^79 - 36 * q^81 + 204 * q^82 + 132 * q^84 - 60 * q^85 + 178 * q^86 + 150 * q^87 + 124 * q^88 + 282 * q^89 - 114 * q^91 - 288 * q^92 + 126 * q^93 + 30 * q^94 - 120 * q^95 - 108 * q^96 - 592 * q^98 + 120 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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