LMFDB - Embedded newform 201.3.h.b.97.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,3,Mod(97,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("201.97");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	201.h (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:	$5.47685331364$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			97.1
Character	$\chi$	$=$	201.97
Dual form			201.3.h.b.172.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.23066 + 1.86522i) q^{2} +1.73205i q^{3} +(4.95809 - 8.58766i) q^{4} -1.91835i q^{5} +(-3.23066 - 5.59566i) q^{6} +(-11.0264 - 6.36611i) q^{7} +22.0700i q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(-3.23066 + 1.86522i) q^{2} +1.73205i q^{3} +(4.95809 - 8.58766i) q^{4} -1.91835i q^{5} +(-3.23066 - 5.59566i) q^{6} +(-11.0264 - 6.36611i) q^{7} +22.0700i q^{8} -3.00000 q^{9} +(3.57814 + 6.19753i) q^{10} +(14.7066 + 8.49088i) q^{11} +(14.8743 + 8.58766i) q^{12} +(3.55480 - 2.05236i) q^{13} +47.4967 q^{14} +3.32268 q^{15} +(-21.3330 - 36.9498i) q^{16} +(-4.51329 - 7.81724i) q^{17} +(9.69197 - 5.59566i) q^{18} +(13.3732 + 23.1631i) q^{19} +(-16.4741 - 9.51135i) q^{20} +(11.0264 - 19.0983i) q^{21} -63.3494 q^{22} +(17.5355 + 30.3723i) q^{23} -38.2263 q^{24} +21.3199 q^{25} +(-7.65621 + 13.2610i) q^{26} -5.19615i q^{27} +(-109.340 + 63.1275i) q^{28} +(-13.4354 + 23.2708i) q^{29} +(-10.7344 + 6.19753i) q^{30} +(10.2737 + 5.93154i) q^{31} +(61.3863 + 35.4414i) q^{32} +(-14.7066 + 25.4726i) q^{33} +(29.1617 + 16.8365i) q^{34} +(-12.2124 + 21.1525i) q^{35} +(-14.8743 + 25.7630i) q^{36} +(-3.10569 - 5.37920i) q^{37} +(-86.4086 - 49.8880i) q^{38} +(3.55480 + 6.15709i) q^{39} +42.3379 q^{40} +(-4.90346 - 2.83101i) q^{41} +82.2668i q^{42} -79.5137i q^{43} +(145.834 - 84.1971i) q^{44} +5.75505i q^{45} +(-113.302 - 65.4150i) q^{46} +(-2.52013 + 4.36499i) q^{47} +(63.9989 - 36.9498i) q^{48} +(56.5546 + 97.9555i) q^{49} +(-68.8774 + 39.7664i) q^{50} +(13.5399 - 7.81724i) q^{51} -40.7032i q^{52} +77.2840i q^{53} +(9.69197 + 16.7870i) q^{54} +(16.2885 - 28.2125i) q^{55} +(140.500 - 243.353i) q^{56} +(-40.1197 + 23.1631i) q^{57} -100.240i q^{58} +60.3136 q^{59} +(16.4741 - 28.5341i) q^{60} +(48.2249 - 27.8426i) q^{61} -44.2545 q^{62} +(33.0793 + 19.0983i) q^{63} -93.7604 q^{64} +(-3.93715 - 6.81934i) q^{65} -109.724i q^{66} +(50.0020 + 44.5960i) q^{67} -89.5091 q^{68} +(-52.6064 + 30.3723i) q^{69} -91.1154i q^{70} +(-1.34649 + 2.33219i) q^{71} -66.2099i q^{72} +(28.9193 + 50.0897i) q^{73} +(20.0668 + 11.5856i) q^{74} +36.9272i q^{75} +265.223 q^{76} +(-108.108 - 187.248i) q^{77} +(-22.9686 - 13.2610i) q^{78} +(37.6533 + 21.7391i) q^{79} +(-70.8826 + 40.9241i) q^{80} +9.00000 q^{81} +21.1219 q^{82} +(-0.640195 - 1.10885i) q^{83} +(-109.340 - 189.382i) q^{84} +(-14.9962 + 8.65806i) q^{85} +(148.311 + 256.881i) q^{86} +(-40.3062 - 23.2708i) q^{87} +(-187.393 + 324.575i) q^{88} +55.9233 q^{89} +(-10.7344 - 18.5926i) q^{90} -52.2622 q^{91} +347.770 q^{92} +(-10.2737 + 17.7946i) q^{93} -18.8024i q^{94} +(44.4350 - 25.6545i) q^{95} +(-61.3863 + 106.324i) q^{96} +(-33.3949 + 19.2806i) q^{97} +(-365.417 - 210.974i) q^{98} +(-44.1199 - 25.4726i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 34 q^{4} + 21 q^{7} - 72 q^{9}+O(q^{10}) $ 24 * q + 34 * q^4 + 21 * q^7 - 72 * q^9	$ 24 q + 34 q^{4} + 21 q^{7} - 72 q^{9} + 30 q^{10} + 12 q^{11} + 102 q^{12} + 30 q^{13} + 6 q^{14} - 6 q^{15} - 98 q^{16} + 4 q^{17} + 39 q^{19} + 108 q^{20} - 21 q^{21} - 82 q^{22} - 13 q^{23} - 36 q^{24} - 222 q^{25} + 29 q^{26} + 189 q^{28} - 90 q^{30} - 93 q^{31} - 33 q^{32} - 12 q^{33} + 72 q^{34} - 93 q^{35} - 102 q^{36} - 33 q^{37} - 210 q^{38} + 30 q^{39} + 274 q^{40} - 15 q^{41} - 9 q^{44} - 228 q^{46} - 131 q^{47} + 294 q^{48} + 295 q^{49} - 423 q^{50} - 12 q^{51} - 56 q^{55} + 349 q^{56} - 117 q^{57} - 116 q^{59} - 108 q^{60} + 120 q^{61} + 282 q^{62} - 63 q^{63} - 276 q^{64} + 136 q^{65} - 25 q^{67} + 10 q^{68} + 39 q^{69} + 169 q^{71} + 187 q^{73} + 849 q^{74} + 386 q^{76} - 348 q^{77} + 87 q^{78} + 51 q^{80} + 216 q^{81} - 14 q^{82} + 104 q^{83} + 189 q^{84} - 243 q^{85} + 641 q^{86} - 766 q^{88} + 152 q^{89} - 90 q^{90} + 32 q^{91} - 216 q^{92} + 93 q^{93} + 762 q^{95} + 33 q^{96} - 84 q^{97} - 1086 q^{98} - 36 q^{99}+O(q^{100}) $ 24 * q + 34 * q^4 + 21 * q^7 - 72 * q^9 + 30 * q^10 + 12 * q^11 + 102 * q^12 + 30 * q^13 + 6 * q^14 - 6 * q^15 - 98 * q^16 + 4 * q^17 + 39 * q^19 + 108 * q^20 - 21 * q^21 - 82 * q^22 - 13 * q^23 - 36 * q^24 - 222 * q^25 + 29 * q^26 + 189 * q^28 - 90 * q^30 - 93 * q^31 - 33 * q^32 - 12 * q^33 + 72 * q^34 - 93 * q^35 - 102 * q^36 - 33 * q^37 - 210 * q^38 + 30 * q^39 + 274 * q^40 - 15 * q^41 - 9 * q^44 - 228 * q^46 - 131 * q^47 + 294 * q^48 + 295 * q^49 - 423 * q^50 - 12 * q^51 - 56 * q^55 + 349 * q^56 - 117 * q^57 - 116 * q^59 - 108 * q^60 + 120 * q^61 + 282 * q^62 - 63 * q^63 - 276 * q^64 + 136 * q^65 - 25 * q^67 + 10 * q^68 + 39 * q^69 + 169 * q^71 + 187 * q^73 + 849 * q^74 + 386 * q^76 - 348 * q^77 + 87 * q^78 + 51 * q^80 + 216 * q^81 - 14 * q^82 + 104 * q^83 + 189 * q^84 - 243 * q^85 + 641 * q^86 - 766 * q^88 + 152 * q^89 - 90 * q^90 + 32 * q^91 - 216 * q^92 + 93 * q^93 + 762 * q^95 + 33 * q^96 - 84 * q^97 - 1086 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−3.23066	+	1.86522i	−1.61533	+	0.932610i	−0.627221	+	0.778841i	$0.715808\pi$
$2$	−3.23066	+	1.86522i	−1.61533	+	0.932610i	−0.988107	+	0.153769i	$0.950859\pi$
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	4.95809	−	8.58766i	1.23952	−	2.14692i
$5$		−	1.91835i		−	0.383670i	−0.981427	−	0.191835i	$-0.938556\pi$
$5$		−	1.91835i		−	0.383670i	0.981427	−	0.191835i	$-0.0614438\pi$
$6$	−3.23066	−	5.59566i	−0.538443	−	0.932610i
$7$	−11.0264	−	6.36611i	−1.57520	−	0.909444i	−0.995515	−	0.0946050i	$-0.969841\pi$
$7$	−11.0264	−	6.36611i	−1.57520	−	0.909444i	−0.579688	−	0.814839i	$-0.696825\pi$
$8$			22.0700i			2.75874i
$9$	−3.00000			−0.333333
$10$	3.57814	+	6.19753i	0.357814	+	0.619753i
$11$	14.7066	+	8.49088i	1.33697	+	0.771898i	0.986356	−	0.164624i	$-0.0526410\pi$
$11$	14.7066	+	8.49088i	1.33697	+	0.771898i	0.350610	+	0.936522i	$0.385974\pi$
$12$	14.8743	+	8.58766i	1.23952	+	0.715639i
$13$	3.55480	−	2.05236i	0.273446	−	0.157874i	−0.357007	−	0.934102i	$-0.616203\pi$
$13$	3.55480	−	2.05236i	0.273446	−	0.157874i	0.630453	+	0.776228i	$0.282869\pi$
$14$	47.4967			3.39262
$15$	3.32268			0.221512
$16$	−21.3330	−	36.9498i	−1.33331	−	2.30936i
$17$	−4.51329	−	7.81724i	−0.265487	−	0.459838i	0.702204	−	0.711976i	$-0.252200\pi$
$17$	−4.51329	−	7.81724i	−0.265487	−	0.459838i	−0.967691	+	0.252138i	$0.918866\pi$
$18$	9.69197	−	5.59566i	0.538443	−	0.310870i
$19$	13.3732	+	23.1631i	0.703854	+	1.21911i	0.967103	+	0.254383i	$0.0818725\pi$
$19$	13.3732	+	23.1631i	0.703854	+	1.21911i	−0.263249	+	0.964728i	$0.584794\pi$
$20$	−16.4741	−	9.51135i	−0.823707	−	0.475568i
$21$	11.0264	−	19.0983i	0.525068	−	0.909444i
$22$	−63.3494			−2.87952
$23$	17.5355	+	30.3723i	0.762412	+	1.32054i	0.941604	+	0.336722i	$0.109318\pi$
$23$	17.5355	+	30.3723i	0.762412	+	1.32054i	−0.179193	+	0.983814i	$0.557349\pi$
$24$	−38.2263			−1.59276
$25$	21.3199			0.852797
$26$	−7.65621	+	13.2610i	−0.294470	+	0.510037i
$27$		−	5.19615i		−	0.192450i
$28$	−109.340	+	63.1275i	−3.90500	+	2.25455i
$29$	−13.4354	+	23.2708i	−0.463290	+	0.802442i	−0.999123	−	0.0418822i	$-0.986665\pi$
$29$	−13.4354	+	23.2708i	−0.463290	+	0.802442i	0.535832	+	0.844324i	$0.319998\pi$
$30$	−10.7344	+	6.19753i	−0.357814	+	0.206584i
$31$	10.2737	+	5.93154i	0.331411	+	0.191340i	0.656467	−	0.754355i	$-0.272050\pi$
$31$	10.2737	+	5.93154i	0.331411	+	0.191340i	−0.325057	+	0.945695i	$0.605383\pi$
$32$	61.3863	+	35.4414i	1.91832	+	1.10754i
$33$	−14.7066	+	25.4726i	−0.445655	+	0.771898i
$34$	29.1617	+	16.8365i	0.857698	+	0.495192i
$35$	−12.2124	+	21.1525i	−0.348926	+	0.604358i
$36$	−14.8743	+	25.7630i	−0.413174	+	0.715639i
$37$	−3.10569	−	5.37920i	−0.0839374	−	0.145384i	0.821001	−	0.570927i	$-0.193416\pi$
$37$	−3.10569	−	5.37920i	−0.0839374	−	0.145384i	−0.904938	+	0.425544i	$0.860083\pi$
$38$	−86.4086	−	49.8880i	−2.27391	−	1.31284i
$39$	3.55480	+	6.15709i	0.0911486	+	0.157874i
$40$	42.3379			1.05845
$41$	−4.90346	−	2.83101i	−0.119597	−	0.0690491i	0.439008	−	0.898483i	$-0.355330\pi$
$41$	−4.90346	−	2.83101i	−0.119597	−	0.0690491i	−0.558605	+	0.829434i	$0.688663\pi$
$42$			82.2668i			1.95873i
$43$		−	79.5137i		−	1.84916i	−0.380993	−	0.924578i	$-0.624418\pi$
$43$		−	79.5137i		−	1.84916i	0.380993	−	0.924578i	$-0.375582\pi$
$44$	145.834	−	84.1971i	3.31440	−	1.91357i
$45$			5.75505i			0.127890i
$46$	−113.302	−	65.4150i	−2.46309	−	1.42207i
$47$	−2.52013	+	4.36499i	−0.0536198	+	0.0928722i	−0.891589	−	0.452845i	$-0.850409\pi$
$47$	−2.52013	+	4.36499i	−0.0536198	+	0.0928722i	0.837970	+	0.545717i	$0.183743\pi$
$48$	63.9989	−	36.9498i	1.33331	−	0.769787i
$49$	56.5546	+	97.9555i	1.15418	+	1.99909i
$50$	−68.8774	+	39.7664i	−1.37755	+	0.795327i
$51$	13.5399	−	7.81724i	0.265487	−	0.153279i
$52$		−	40.7032i		−	0.782754i
$53$			77.2840i			1.45819i	0.684413	+	0.729094i	$0.260058\pi$
$53$			77.2840i			1.45819i	−0.684413	+	0.729094i	$0.739942\pi$
$54$	9.69197	+	16.7870i	0.179481	+	0.310870i
$55$	16.2885	−	28.2125i	0.296154	−	0.512954i
$56$	140.500	−	243.353i	2.50892	−	4.34558i
$57$	−40.1197	+	23.1631i	−0.703854	+	0.406370i
$58$		−	100.240i		−	1.72828i
$59$	60.3136			1.02227			0.511133	−	0.859502i	$-0.329226\pi$
$59$	60.3136			1.02227			0.511133	+	0.859502i	$0.329226\pi$
$60$	16.4741	−	28.5341i	0.274569	−	0.475568i
$61$	48.2249	−	27.8426i	0.790572	−	0.456437i	−0.0495921	−	0.998770i	$-0.515792\pi$
$61$	48.2249	−	27.8426i	0.790572	−	0.456437i	0.840164	+	0.542333i	$0.182459\pi$
$62$	−44.2545			−0.713783
$63$	33.0793	+	19.0983i	0.525068	+	0.303148i
$64$	−93.7604			−1.46501
$65$	−3.93715	−	6.81934i	−0.0605715	−	0.104913i
$66$		−	109.724i		−	1.66249i
$67$	50.0020	+	44.5960i	0.746299	+	0.665611i
$67$	50.0020	+	44.5960i	0.746299	+	0.665611i
$68$	−89.5091			−1.31631
$69$	−52.6064	+	30.3723i	−0.762412	+	0.440179i
$70$		−	91.1154i		−	1.30165i
$71$	−1.34649	+	2.33219i	−0.0189646	+	0.0328477i	−0.875352	−	0.483486i	$-0.839370\pi$
$71$	−1.34649	+	2.33219i	−0.0189646	+	0.0328477i	0.856387	+	0.516334i	$0.172704\pi$
$72$		−	66.2099i		−	0.919582i
$73$	28.9193	+	50.0897i	0.396155	+	0.686160i	0.993248	−	0.116012i	$-0.0370110\pi$
$73$	28.9193	+	50.0897i	0.396155	+	0.686160i	−0.597093	+	0.802172i	$0.703678\pi$
$74$	20.0668	+	11.5856i	0.271173	+	0.156562i
$75$			36.9272i			0.492363i
$76$	265.223			3.48977
$77$	−108.108	−	187.248i	−1.40400	−	2.43179i
$78$	−22.9686	−	13.2610i	−0.294470	−	0.170012i
$79$	37.6533	+	21.7391i	0.476624	+	0.275179i	0.719008	−	0.695001i	$-0.244596\pi$
$79$	37.6533	+	21.7391i	0.476624	+	0.275179i	−0.242385	+	0.970180i	$0.577930\pi$
$80$	−70.8826	+	40.9241i	−0.886032	+	0.511551i
$81$	9.00000			0.111111
$82$	21.1219			0.257584
$83$	−0.640195	−	1.10885i	−0.00771319	−	0.0133596i	0.862143	−	0.506665i	$-0.169122\pi$
$83$	−0.640195	−	1.10885i	−0.00771319	−	0.0133596i	−0.869856	+	0.493305i	$0.835789\pi$
$84$	−109.340	−	189.382i	−1.30167	−	2.25455i
$85$	−14.9962	+	8.65806i	−0.176426	+	0.101860i
$86$	148.311	+	256.881i	1.72454	+	2.98699i
$87$	−40.3062	−	23.2708i	−0.463290	−	0.267481i
$88$	−187.393	+	324.575i	−2.12947	+	3.68835i
$89$	55.9233			0.628351			0.314176	−	0.949365i	$-0.398272\pi$
$89$	55.9233			0.628351			0.314176	+	0.949365i	$0.398272\pi$
$90$	−10.7344	−	18.5926i	−0.119271	−	0.206584i
$91$	−52.2622			−0.574310
$92$	347.770			3.78011
$93$	−10.2737	+	17.7946i	−0.110470	+	0.191340i
$94$		−	18.8024i		−	0.200025i
$95$	44.4350	−	25.6545i	0.467736	−	0.270048i
$96$	−61.3863	+	106.324i	−0.639441	+	1.10754i
$97$	−33.3949	+	19.2806i	−0.344278	+	0.198769i	−0.662162	−	0.749361i	$-0.730361\pi$
$97$	−33.3949	+	19.2806i	−0.344278	+	0.198769i	0.317884	+	0.948129i	$0.397028\pi$
$98$	−365.417	−	210.974i	−3.72874	−	2.15279i
$99$	−44.1199	−	25.4726i	−0.445655	−	0.257299i
$100$	105.706	−	183.088i	1.05706	−	1.83088i
$101$	−169.152	−	97.6598i	−1.67477	−	0.966928i	−0.964909	−	0.262586i	$-0.915425\pi$
$101$	−169.152	−	97.6598i	−1.67477	−	0.966928i	−0.709861	−	0.704342i	$-0.751242\pi$
$102$	−29.1617	+	50.5096i	−0.285899	+	0.495192i
$103$	−46.8713	+	81.1835i	−0.455061	+	0.788189i	−0.998692	−	0.0511353i	$-0.983716\pi$
$103$	−46.8713	+	81.1835i	−0.455061	+	0.788189i	0.543630	+	0.839325i	$0.317049\pi$
$104$	45.2955	+	78.4542i	0.435534	+	0.754367i
$105$	−36.6373	−	21.1525i	−0.348926	−	0.201453i
$106$	−144.152	−	249.678i	−1.35992	−	2.35545i
$107$	85.6252			0.800236			0.400118	−	0.916464i	$-0.368969\pi$
$107$	85.6252			0.800236			0.400118	+	0.916464i	$0.368969\pi$
$108$	−44.6228	−	25.7630i	−0.413174	−	0.238546i
$109$			2.97961i			0.0273358i	0.999907	+	0.0136679i	$0.00435077\pi$
$109$			2.97961i			0.0273358i	−0.999907	+	0.0136679i	$0.995649\pi$
$110$			121.526i			1.10478i
$111$	9.31706	−	5.37920i	0.0839374	−	0.0484613i
$112$			543.232i			4.85028i
$113$	−10.8717	−	6.27678i	−0.0962097	−	0.0555467i	0.451123	−	0.892462i	$-0.351024\pi$
$113$	−10.8717	−	6.27678i	−0.0962097	−	0.0555467i	−0.547333	+	0.836915i	$0.684357\pi$
$114$	86.4086	−	149.664i	0.757970	−	1.31284i
$115$	58.2647	−	33.6392i	0.506650	−	0.292514i
$116$	133.228	+	230.758i	1.14852	+	1.98929i
$117$	−10.6644	+	6.15709i	−0.0911486	+	0.0526247i
$118$	−194.853	+	112.498i	−1.65129	+	0.953375i
$119$			114.928i			0.965783i
$120$			73.3314i			0.611095i
$121$	83.6899	+	144.955i	0.691652	+	1.19798i
$122$	−103.865	+	179.900i	−0.851355	+	1.47459i
$123$	4.90346	−	8.49304i	0.0398655	−	0.0690491i
$124$	101.876	−	58.8182i	0.821582	−	0.474341i
$125$		−	88.8578i		−	0.710863i
$126$	−142.490			−1.13087
$127$	92.3143	−	159.893i	0.726884	−	1.25900i	−0.231310	−	0.972880i	$-0.574301\pi$
$127$	92.3143	−	159.893i	0.726884	−	1.25900i	0.958194	−	0.286120i	$-0.0923656\pi$
$128$	57.3623	−	33.1181i	0.448143	−	0.258735i
$129$	137.722			1.06761
$130$	25.4391	+	14.6873i	0.195686	+	0.112979i
$131$	194.761			1.48673			0.743364	−	0.668887i	$-0.233229\pi$
$131$	194.761			1.48673			0.743364	+	0.668887i	$0.233229\pi$
$132$	145.834	+	252.591i	1.10480	+	1.91357i
$133$		−	340.542i		−	2.56046i
$134$	−244.721	−	50.8094i	−1.82627	−	0.379175i
$135$	−9.96804			−0.0738373
$136$	172.526	−	99.6080i	1.26857	−	0.732412i
$137$			197.297i			1.44012i	0.693910	+	0.720061i	$0.255886\pi$
$137$			197.297i			1.44012i	−0.693910	+	0.720061i	$0.744114\pi$
$138$	113.302	−	196.245i	0.821030	−	1.42207i
$139$		−	34.1364i		−	0.245586i	−0.992432	−	0.122793i	$-0.960815\pi$
$139$		−	34.1364i		−	0.245586i	0.992432	−	0.122793i	$-0.0391851\pi$
$140$	121.101	+	209.752i	0.865004	+	1.49823i
$141$	−7.56039	−	4.36499i	−0.0536198	−	0.0309574i
$142$		−	10.0460i		−	0.0707464i
$143$	69.7054			0.487450
$144$	63.9989	+	110.849i	0.444437	+	0.769787i
$145$	44.6416	+	25.7738i	0.307873	+	0.177751i
$146$	−186.857	−	107.882i	−1.27984	−	0.738916i
$147$	−169.664	+	97.9555i	−1.15418	+	0.666364i
$148$	−61.5931			−0.416169
$149$	−168.369			−1.12999			−0.564995	−	0.825094i	$-0.691122\pi$
$149$	−168.369			−1.12999			−0.564995	+	0.825094i	$0.691122\pi$
$150$	−68.8774	−	119.299i	−0.459182	−	0.795327i
$151$	54.5788	+	94.5333i	0.361449	+	0.626049i	0.988200	−	0.153172i	$-0.0489487\pi$
$151$	54.5788	+	94.5333i	0.361449	+	0.626049i	−0.626750	+	0.779220i	$0.715615\pi$
$152$	−511.209	+	295.147i	−3.36322	+	1.94175i
$153$	13.5399	+	23.4517i	0.0884958	+	0.153279i
$154$	698.517	+	403.289i	4.53582	+	2.61876i
$155$	11.3788	−	19.7086i	0.0734114	−	0.127152i
$156$	70.5000			0.451923
$157$	−74.5394	−	129.106i	−0.474773	−	0.822331i	0.524809	−	0.851220i	$-0.324137\pi$
$157$	−74.5394	−	129.106i	−0.474773	−	0.822331i	−0.999583	+	0.0288885i	$0.990803\pi$
$158$	−162.193			−1.02654
$159$	−133.860			−0.841886
$160$	67.9890	−	117.760i	0.424931	−	0.736003i
$161$		−	446.531i		−	2.77348i
$162$	−29.0759	+	16.7870i	−0.179481	+	0.103623i
$163$	−104.712	+	181.367i	−0.642405	+	1.11268i	0.342489	+	0.939522i	$0.388730\pi$
$163$	−104.712	+	181.367i	−0.642405	+	1.11268i	−0.984894	+	0.173157i	$0.944603\pi$
$164$	−48.6236	+	28.0729i	−0.296485	+	0.171176i
$165$	48.8654	+	28.2125i	0.296154	+	0.170985i
$166$	4.13650	+	2.38821i	0.0249187	+	0.0143868i
$167$	−23.1616	+	40.1171i	−0.138692	+	0.240222i	−0.927002	−	0.375057i	$-0.877623\pi$
$167$	−23.1616	+	40.1171i	−0.138692	+	0.240222i	0.788310	+	0.615279i	$0.210957\pi$
$168$	421.499	+	243.353i	2.50892	+	1.44853i
$169$	−76.0756	+	131.767i	−0.450152	+	0.779685i
$170$	32.2984	−	55.9424i	0.189990	−	0.329073i
$171$	−40.1197	−	69.4893i	−0.234618	−	0.406370i
$172$	−682.837	−	394.236i	−3.96998	−	2.29207i
$173$	−44.6721	−	77.3744i	−0.258220	−	0.447251i	0.707545	−	0.706668i	$-0.249803\pi$
$173$	−44.6721	−	77.3744i	−0.258220	−	0.447251i	−0.965765	+	0.259418i	$0.916469\pi$
$174$	173.621			0.997821
$175$	−235.083	−	135.725i	−1.34333	−	0.775571i
$176$		−	724.542i		−	4.11672i
$177$			104.466i			0.590205i
$178$	−180.669	+	104.309i	−1.01499	+	0.586007i
$179$		−	194.194i		−	1.08488i	−0.840094	−	0.542441i	$-0.817500\pi$
$179$		−	194.194i		−	1.08488i	0.840094	−	0.542441i	$-0.182500\pi$
$180$	49.4224	+	28.5341i	0.274569	+	0.158523i
$181$	40.0021	−	69.2856i	0.221006	−	0.382793i	−0.734108	−	0.679033i	$-0.762399\pi$
$181$	40.0021	−	69.2856i	0.221006	−	0.382793i	0.955114	+	0.296240i	$0.0957327\pi$
$182$	168.841	−	97.4805i	0.927699	−	0.535607i
$183$	48.2249	+	83.5279i	0.263524	+	0.456437i
$184$	−670.316	+	387.007i	−3.64302	+	2.10330i
$185$	−10.3192	+	5.95779i	−0.0557794	+	0.0322043i
$186$		−	76.6511i		−	0.412103i
$187$		−	153.287i		−	0.819717i
$188$	24.9901	+	43.2840i	0.132926	+	0.230234i
$189$	−33.0793	+	57.2950i	−0.175023	+	0.303148i
$190$	−95.7027	+	165.762i	−0.503698	+	0.872431i
$191$	−35.8925	+	20.7226i	−0.187919	+	0.108495i	−0.591008	−	0.806666i	$-0.701270\pi$
$191$	−35.8925	+	20.7226i	−0.187919	+	0.108495i	0.403089	+	0.915161i	$0.367937\pi$
$192$		−	162.398i		−	0.845822i
$193$	115.443			0.598151			0.299075	−	0.954230i	$-0.403322\pi$
$193$	115.443			0.598151			0.299075	+	0.954230i	$0.403322\pi$
$194$	71.9250	−	124.578i	0.370748	−	0.642154i
$195$	11.8114	−	6.81934i	0.0605715	−	0.0349710i
$196$	1121.61			5.72251
$197$	−2.85741	−	1.64973i	−0.0145046	−	0.00837425i	0.492730	−	0.870182i	$-0.335999\pi$
$197$	−2.85741	−	1.64973i	−0.0145046	−	0.00837425i	−0.507235	+	0.861808i	$0.669332\pi$
$198$	190.048			0.959839
$199$	−133.300	−	230.882i	−0.669848	−	1.16021i	−0.977946	−	0.208856i	$-0.933026\pi$
$199$	−133.300	−	230.882i	−0.669848	−	1.16021i	0.308098	−	0.951354i	$-0.400307\pi$
$200$			470.530i			2.35265i
$201$	−77.2425	+	86.6060i	−0.384291	+	0.430876i
$202$	728.628			3.60707
$203$	296.289	−	171.063i	1.45955	−	0.842673i
$204$		−	155.034i		−	0.759972i
$205$	−5.43088	+	9.40655i	−0.0264921	+	0.0458856i
$206$		−	349.701i		−	1.69758i
$207$	−52.6064	−	91.1170i	−0.254137	−	0.440179i
$208$	−151.669	−	87.5659i	−0.729176	−	0.420990i
$209$			454.202i			2.17321i
$210$	157.816			0.751507
$211$	37.1524	+	64.3499i	0.176078	+	0.304976i	0.940534	−	0.339700i	$-0.110326\pi$
$211$	37.1524	+	64.3499i	0.176078	+	0.304976i	−0.764456	+	0.644676i	$0.776992\pi$
$212$	663.689	+	383.181i	3.13061	+	1.80746i
$213$	−4.03946	−	2.33219i	−0.0189646	−	0.0109492i
$214$	−276.626	+	159.710i	−1.29264	+	0.746308i
$215$	−152.535			−0.709465
$216$	114.679			0.530921
$217$	−75.5216	−	130.807i	−0.348026	−	0.602799i
$218$	−5.55762	−	9.62608i	−0.0254937	−	0.0441563i
$219$	−86.7579	+	50.0897i	−0.396155	+	0.228720i
$220$	−161.519	−	279.760i	−0.734179	−	1.27164i
$221$	−32.0876	−	18.5258i	−0.145193	−	0.0838271i
$222$	−20.0668	+	34.7567i	−0.0903910	+	0.156562i
$223$	339.009			1.52022			0.760109	−	0.649796i	$-0.225146\pi$
$223$	339.009			1.52022			0.760109	+	0.649796i	$0.225146\pi$
$224$	−451.248	−	781.584i	−2.01450	−	3.48921i
$225$	−63.9598			−0.284266
$226$	46.8303			0.207214
$227$	−110.370	+	191.167i	−0.486213	+	0.842145i	−0.999874	−	0.0158477i	$-0.994955\pi$
$227$	−110.370	+	191.167i	−0.486213	+	0.842145i	0.513662	+	0.857993i	$0.328289\pi$
$228$			459.379i			2.01482i
$229$	83.9064	−	48.4434i	0.366404	−	0.211543i	−0.305482	−	0.952198i	$-0.598818\pi$
$229$	83.9064	−	48.4434i	0.366404	−	0.211543i	0.671886	+	0.740654i	$0.265484\pi$
$230$	−125.489	+	217.353i	−0.545604	+	0.945013i
$231$	324.323	−	187.248i	1.40400	−	0.810597i
$232$	−513.586	−	296.519i	−2.21373	−	1.27810i
$233$	142.684	+	82.3785i	0.612376	+	0.353556i	0.773895	−	0.633314i	$-0.218306\pi$
$233$	142.684	+	82.3785i	0.612376	+	0.353556i	−0.161519	+	0.986870i	$0.551639\pi$
$234$	22.9686	−	39.7829i	0.0981566	−	0.170012i
$235$	8.37358	+	4.83449i	0.0356323	+	0.0205723i
$236$	299.041	−	517.953i	1.26712	−	2.19472i
$237$	−37.6533	+	65.2174i	−0.158875	+	0.275179i
$238$	−214.366	−	371.294i	−0.900699	−	1.56006i
$239$	13.9668	+	8.06373i	0.0584385	+	0.0337395i	0.528935	−	0.848663i	$-0.322592\pi$
$239$	13.9668	+	8.06373i	0.0584385	+	0.0337395i	−0.470496	+	0.882402i	$0.655925\pi$
$240$	−70.8826	−	122.772i	−0.295344	−	0.511551i
$241$	−390.551			−1.62055			−0.810273	−	0.586053i	$-0.800681\pi$
$241$	−390.551			−1.62055			−0.810273	+	0.586053i	$0.800681\pi$
$242$	−540.747	−	312.200i	−2.23449	−	1.29008i
$243$			15.5885i			0.0641500i
$244$		−	552.185i		−	2.26305i
$245$	187.913	−	108.492i	0.766991	−	0.442823i
$246$			36.5841i			0.148716i
$247$	95.0782	+	54.8934i	0.384932	+	0.222241i
$248$	−130.909	+	226.741i	−0.527858	+	0.914277i
$249$	1.92058	−	1.10885i	0.00771319	−	0.00445321i
$250$	165.739	+	287.069i	0.662958	+	1.14828i
$251$	−71.0869	+	41.0420i	−0.283215	+	0.163514i	−0.634878	−	0.772613i	$-0.718950\pi$
$251$	−71.0869	+	41.0420i	−0.283215	+	0.163514i	0.351663	+	0.936127i	$0.385616\pi$
$252$	328.020	−	189.382i	1.30167	−	0.751517i
$253$			595.566i			2.35402i
$254$			688.746i			2.71160i
$255$	−14.9962	−	25.9742i	−0.0588086	−	0.101860i
$256$	63.9756	−	110.809i	0.249905	−	0.432848i
$257$	78.9625	−	136.767i	0.307247	−	0.532168i	−0.670512	−	0.741899i	$-0.733925\pi$
$257$	78.9625	−	136.767i	0.307247	−	0.532168i	0.977759	+	0.209731i	$0.0672588\pi$
$258$	−444.932	+	256.881i	−1.72454	+	0.995664i
$259$			79.0845i			0.305346i
$260$	−78.0830			−0.300319
$261$	40.3062	−	69.8125i	0.154430	−	0.267481i
$262$	−629.207	+	363.273i	−2.40155	+	1.38654i
$263$	105.457			0.400978			0.200489	−	0.979696i	$-0.435747\pi$
$263$	105.457			0.400978			0.200489	+	0.979696i	$0.435747\pi$
$264$	−562.180	−	324.575i	−2.12947	−	1.22945i
$265$	148.258			0.559463
$266$	635.185	+	1100.17i	2.38791	+	4.13599i
$267$			96.8619i			0.362779i
$268$	630.890	−	208.290i	2.35407	−	0.777200i
$269$	−368.515			−1.36995			−0.684973	−	0.728568i	$-0.740186\pi$
$269$	−368.515			−1.36995			−0.684973	+	0.728568i	$0.740186\pi$
$270$	32.2033	−	18.5926i	0.119271	−	0.0688614i
$271$			76.8875i			0.283718i	0.989887	+	0.141859i	$0.0453079\pi$
$271$			76.8875i			0.283718i	−0.989887	+	0.141859i	$0.954692\pi$
$272$	−192.564	+	333.530i	−0.707954	+	1.22621i
$273$		−	90.5208i		−	0.331578i
$274$	−368.002	−	637.398i	−1.34307	−	2.32627i
$275$	313.544	+	181.025i	1.14016	+	0.658272i
$276$			602.355i			2.18244i
$277$	−485.547			−1.75288			−0.876439	−	0.481512i	$-0.840088\pi$
$277$	−485.547			−1.75288			−0.876439	+	0.481512i	$0.840088\pi$
$278$	63.6719	+	110.283i	0.229036	+	0.396701i
$279$	−30.8212	−	17.7946i	−0.110470	−	0.0637800i
$280$	−466.835	−	269.528i	−1.66727	−	0.962598i
$281$	−390.673	+	225.555i	−1.39029	+	0.802687i	−0.993348	−	0.115155i	$-0.963264\pi$
$281$	−390.673	+	225.555i	−1.39029	+	0.802687i	−0.396947	+	0.917842i	$0.629930\pi$
$282$	32.5667			0.115485
$283$	−33.6535			−0.118917			−0.0594585	−	0.998231i	$-0.518937\pi$
$283$	−33.6535			−0.118917			−0.0594585	+	0.998231i	$0.518937\pi$
$284$	13.3520	+	23.1264i	0.0470141	+	0.0814309i
$285$	44.4350	+	76.9636i	0.155912	+	0.270048i
$286$	−225.194	+	130.016i	−0.787392	+	0.454601i
$287$	36.0451	+	62.4319i	0.125593	+	0.217533i
$288$	−184.159	−	106.324i	−0.639441	−	0.369181i
$289$	103.760	−	179.718i	0.359033	−	0.621863i
$290$	−192.295			−0.663088
$291$	−33.3949	−	57.8417i	−0.114759	−	0.198769i
$292$	573.538			1.96417
$293$	494.201			1.68669			0.843347	−	0.537370i	$-0.180582\pi$
$293$	494.201			1.68669			0.843347	+	0.537370i	$0.180582\pi$
$294$	365.417	−	632.921i	1.24291	−	2.15279i
$295$		−	115.703i		−	0.392212i
$296$	118.719	−	68.5423i	0.401077	−	0.231562i
$297$	44.1199	−	76.4179i	0.148552	−	0.257299i
$298$	543.941	−	314.044i	1.82530	−	1.05384i
$299$	124.670	+	71.9783i	0.416957	+	0.240730i
$300$	317.118	+	183.088i	1.05706	+	0.610295i
$301$	−506.193	+	876.751i	−1.68170	+	2.91279i
$302$	−352.651	−	203.603i	−1.16772	−	0.674182i
$303$	169.152	−	292.979i	0.558256	−	0.966928i
$304$	570.581	−	988.276i	1.87691	−	3.25091i
$305$	−53.4119	−	92.5122i	−0.175121	−	0.303319i
$306$	−87.4852	−	50.5096i	−0.285899	−	0.165064i
$307$	261.686	+	453.253i	0.852397	+	1.47640i	0.879039	+	0.476750i	$0.158185\pi$
$307$	261.686	+	453.253i	0.852397	+	1.47640i	−0.0266416	+	0.999645i	$0.508481\pi$
$308$	−2144.03			−6.96113
$309$	−140.614	−	81.1835i	−0.455061	−	0.262730i
$310$			84.8957i			0.273857i
$311$		−	344.404i		−	1.10741i	−0.832713	−	0.553704i	$-0.813214\pi$
$311$		−	344.404i		−	1.10741i	0.832713	−	0.553704i	$-0.186786\pi$
$312$	−135.887	+	78.4542i	−0.435534	+	0.251456i
$313$			1.31941i			0.00421537i	0.999998	+	0.00210768i	$0.000670897\pi$
$313$			1.31941i			0.00421537i	−0.999998	+	0.00210768i	$0.999329\pi$
$314$	481.622	+	278.065i	1.53383	+	0.885556i
$315$	36.6373	−	63.4576i	0.116309	−	0.201453i
$316$	373.377	−	215.569i	1.18157	−	0.682181i
$317$	−130.180	−	225.479i	−0.410663	−	0.711289i	0.584300	−	0.811538i	$-0.301369\pi$
$317$	−130.180	−	225.479i	−0.410663	−	0.711289i	−0.994962	+	0.100249i	$0.968036\pi$
$318$	432.455	−	249.678i	1.35992	−	0.785151i
$319$	−395.179	+	228.157i	−1.23881	+	0.715225i
$320$			179.865i			0.562079i
$321$			148.307i			0.462016i
$322$	832.878	+	1442.59i	2.58658	+	4.48008i
$323$	120.714	−	209.084i	0.373729	−	0.647317i
$324$	44.6228	−	77.2890i	0.137725	−	0.238546i
$325$	75.7880	−	43.7562i	0.233194	−	0.134635i
$326$		−	781.244i		−	2.39645i
$327$	−5.16083			−0.0157824
$328$	62.4804	−	108.219i	0.190489	−	0.329936i
$329$	55.5760	−	32.0868i	0.168924	−	0.0975283i
$330$	−210.490			−0.637848
$331$	−32.8713	−	18.9783i	−0.0993092	−	0.0573362i	0.449523	−	0.893269i	$-0.351594\pi$
$331$	−32.8713	−	18.9783i	−0.0993092	−	0.0573362i	−0.548832	+	0.835933i	$0.684927\pi$
$332$	−12.6966			−0.0382427
$333$	9.31706	+	16.1376i	0.0279791	+	0.0484613i
$334$		−	172.806i		−	0.517384i
$335$	85.5506	−	95.9213i	0.255375	−	0.286332i
$336$	−940.905			−2.80031
$337$	101.648	−	58.6867i	0.301627	−	0.174145i	−0.341546	−	0.939865i	$-0.610951\pi$
$337$	101.648	−	58.6867i	0.301627	−	0.174145i	0.643174	+	0.765720i	$0.277617\pi$
$338$		−	567.591i		−	1.67926i
$339$	10.8717	−	18.8303i	0.0320699	−	0.0555467i
$340$			171.710i			0.505029i
$341$	100.728	+	174.466i	0.295390	+	0.511630i
$342$	259.226	+	149.664i	0.757970	+	0.437614i
$343$		−	816.252i		−	2.37974i
$344$	1754.86			5.10135
$345$	58.2647	+	100.917i	0.168883	+	0.292514i
$346$	288.641	+	166.647i	0.834221	+	0.481638i
$347$	−185.079	−	106.856i	−0.533370	−	0.307941i	0.209018	−	0.977912i	$-0.432973\pi$
$347$	−185.079	−	106.856i	−0.533370	−	0.307941i	−0.742388	+	0.669970i	$0.766307\pi$
$348$	−399.684	+	230.758i	−1.14852	+	0.663097i
$349$	−635.183			−1.82001			−0.910004	−	0.414600i	$-0.863921\pi$
$349$	−635.183			−1.82001			−0.910004	+	0.414600i	$0.863921\pi$
$350$	1012.63			2.89322
$351$	−10.6644	−	18.4713i	−0.0303829	−	0.0526247i
$352$	601.857	+	1042.45i	1.70982	+	2.96150i
$353$	−130.651	+	75.4312i	−0.370115	+	0.213686i	−0.673509	−	0.739179i	$-0.735214\pi$
$353$	−130.651	+	75.4312i	−0.370115	+	0.213686i	0.303394	+	0.952865i	$0.401880\pi$
$354$	−194.853	−	337.495i	−0.550431	−	0.953375i
$355$	4.47395	+	2.58303i	0.0126027	+	0.00727615i
$356$	277.273	−	480.250i	0.778856	−	1.34902i
$357$	−199.062			−0.557595
$358$	362.214	+	627.374i	1.01177	+	1.75244i
$359$	−497.732			−1.38644			−0.693220	−	0.720726i	$-0.743808\pi$
$359$	−497.732			−1.38644			−0.693220	+	0.720726i	$0.743808\pi$
$360$	−127.014			−0.352816
$361$	−177.187	+	306.896i	−0.490821	+	0.850128i
$362$			298.451i			0.824449i
$363$	−251.070	+	144.955i	−0.691652	+	0.399326i
$364$	−259.121	+	448.810i	−0.711870	+	1.23300i
$365$	96.0896	−	55.4773i	0.263259	−	0.151993i
$366$	−311.596	−	179.900i	−0.851355	−	0.491530i
$367$	118.889	+	68.6407i	0.323949	+	0.187032i	0.653151	−	0.757227i	$-0.273447\pi$
$367$	118.889	+	68.6407i	0.323949	+	0.187032i	−0.329202	+	0.944259i	$0.606780\pi$
$368$	748.167	−	1295.86i	2.03306	−	3.52137i
$369$	14.7104	+	8.49304i	0.0398655	+	0.0230164i
$370$	22.2252	−	38.4951i	0.0600681	−	0.104041i
$371$	491.998	−	852.166i	1.32614	−	2.29694i
$372$	101.876	+	176.455i	0.273861	+	0.474341i
$373$	149.508	+	86.3185i	0.400826	+	0.231417i	0.686840	−	0.726808i	$-0.258997\pi$
$373$	149.508	+	86.3185i	0.400826	+	0.231417i	−0.286014	+	0.958225i	$0.592331\pi$
$374$	285.914	+	495.218i	0.764476	+	1.32411i
$375$	153.906			0.410417
$376$	−96.3352	−	55.6191i	−0.256211	−	0.147923i
$377$			110.297i			0.292566i
$378$		−	246.800i		−	0.652911i
$379$	306.391	−	176.895i	0.808419	−	0.466741i	−0.0379873	−	0.999278i	$-0.512095\pi$
$379$	306.391	−	176.895i	0.808419	−	0.466741i	0.846407	+	0.532537i	$0.178761\pi$
$380$		−	508.790i		−	1.33892i
$381$	276.943	+	159.893i	0.726884	+	0.419667i
$382$	77.3043	−	133.895i	0.202367	−	0.350510i
$383$	119.881	−	69.2135i	0.313006	−	0.180714i	−0.335265	−	0.942124i	$-0.608826\pi$
$383$	119.881	−	69.2135i	0.313006	−	0.180714i	0.648271	+	0.761410i	$0.275492\pi$
$384$	57.3623	+	99.3544i	0.149381	+	0.258735i
$385$	−359.207	+	207.388i	−0.933005	+	0.538671i
$386$	−372.957	+	215.327i	−0.966209	+	0.557841i
$387$			238.541i			0.616385i
$388$			382.379i			0.985514i
$389$	209.071	+	362.122i	0.537458	+	0.930905i	0.999040	+	0.0438072i	$0.0139487\pi$
$389$	209.071	+	362.122i	0.537458	+	0.930905i	−0.461582	+	0.887098i	$0.652718\pi$
$390$	−25.4391	+	44.0619i	−0.0652286	+	0.112979i
$391$	158.285	−	274.158i	0.404821	−	0.701171i
$392$	−2161.87	+	1248.16i	−5.51498	+	3.18408i
$393$			337.336i			0.858363i
$394$	12.3084			0.0312396
$395$	41.7033	−	72.2322i	0.105578	−	0.182866i
$396$	−437.501	+	252.591i	−1.10480	+	0.637856i
$397$	592.780			1.49315			0.746575	−	0.665302i	$-0.231697\pi$
$397$	592.780			1.49315			0.746575	+	0.665302i	$0.231697\pi$
$398$	861.291	+	497.267i	2.16405	+	1.24941i
$399$	589.835			1.47828
$400$	−454.817	−	787.767i	−1.13704	−	1.96942i
$401$		−	77.3113i		−	0.192796i	−0.995343	−	0.0963981i	$-0.969268\pi$
$401$		−	77.3113i		−	0.192796i	0.995343	−	0.0963981i	$-0.0307322\pi$
$402$	88.0045	−	423.868i	0.218917	−	1.05440i
$403$	48.6947			0.120831
$404$	−1677.34	+	968.412i	−4.15183	+	2.39706i
$405$		−	17.2651i		−	0.0426300i
$406$	−638.139	+	1105.29i	−1.57177	+	2.72239i
$407$		−	105.480i		−	0.259164i
$408$	172.526	+	298.824i	0.422858	+	0.732412i
$409$	−211.900	−	122.340i	−0.518092	−	0.299121i	0.218061	−	0.975935i	$-0.430027\pi$
$409$	−211.900	−	122.340i	−0.518092	−	0.299121i	−0.736154	+	0.676814i	$0.763360\pi$
$410$		−	40.5191i		−	0.0988271i
$411$	−341.728			−0.831455
$412$	464.785	+	805.030i	1.12812	+	1.95396i
$413$	−665.044	−	383.963i	−1.61027	−	0.929693i
$414$	339.906	+	196.245i	0.821030	+	0.474022i
$415$	−2.12716	+	1.22812i	−0.00512569	+	0.00295932i
$416$	290.954			0.699410
$417$	59.1260			0.141789
$418$	−847.186	−	1467.37i	−2.02676	−	3.51045i
$419$	56.0262	+	97.0403i	0.133714	+	0.231600i	0.925106	−	0.379710i	$-0.123976\pi$
$419$	56.0262	+	97.0403i	0.133714	+	0.231600i	−0.791391	+	0.611310i	$0.790643\pi$
$420$	−363.302	+	209.752i	−0.865004	+	0.499410i
$421$	96.1951	+	166.615i	0.228492	+	0.395760i	0.957361	−	0.288893i	$-0.0932872\pi$
$421$	96.1951	+	166.615i	0.228492	+	0.395760i	−0.728869	+	0.684653i	$0.759954\pi$
$422$	−240.053	−	138.595i	−0.568847	−	0.328424i
$423$	7.56039	−	13.0950i	0.0178733	−	0.0309574i
$424$	−1705.65			−4.02277
$425$	−96.2230	−	166.663i	−0.226407	−	0.392148i
$426$	17.4002			0.0408454
$427$	−708.997			−1.66041
$428$	424.538	−	735.321i	0.991910	−	1.71804i
$429$			120.733i			0.281430i
$430$	492.788	−	284.511i	1.14602	−	0.661655i
$431$	159.261	−	275.848i	0.369515	−	0.640019i	−0.619975	−	0.784622i	$-0.712857\pi$
$431$	159.261	−	275.848i	0.369515	−	0.640019i	0.989490	+	0.144603i	$0.0461905\pi$
$432$	−191.997	+	110.849i	−0.444437	+	0.256596i
$433$	−299.697	−	173.030i	−0.692140	−	0.399607i	0.112273	−	0.993677i	$-0.464187\pi$
$433$	−299.697	−	173.030i	−0.692140	−	0.399607i	−0.804413	+	0.594070i	$0.797520\pi$
$434$	487.969	+	281.729i	1.12435	+	0.649145i
$435$	−44.6416	+	77.3215i	−0.102624	+	0.177751i
$436$	25.5879	+	14.7732i	0.0586878	+	0.0338834i
$437$	−469.012	+	812.352i	−1.07325	+	1.85893i
$438$	186.857	−	323.645i	0.426613	−	0.738916i
$439$	281.014	+	486.731i	0.640123	+	1.10873i	0.985405	+	0.170227i	$0.0544501\pi$
$439$	281.014	+	486.731i	0.640123	+	1.10873i	−0.345282	+	0.938499i	$0.612217\pi$
$440$	622.648	+	359.486i	1.41511	+	0.817013i
$441$	−169.664	−	293.866i	−0.384725	−	0.666364i
$442$	138.219			0.312712
$443$	−313.913	−	181.238i	−0.708608	−	0.409115i	0.101937	−	0.994791i	$-0.467496\pi$
$443$	−313.913	−	181.238i	−0.708608	−	0.409115i	−0.810545	+	0.585676i	$0.800829\pi$
$444$		−	106.682i		−	0.240276i
$445$		−	107.280i		−	0.241080i
$446$	−1095.22	+	632.326i	−2.45565	+	1.41777i
$447$		−	291.623i		−	0.652400i
$448$	1033.84	+	596.889i	2.30768	+	1.33234i
$449$	66.2402	−	114.731i	0.147528	−	0.255527i	−0.782785	−	0.622292i	$-0.786202\pi$
$449$	66.2402	−	114.731i	0.147528	−	0.255527i	0.930313	+	0.366766i	$0.119535\pi$
$450$	206.632	−	119.299i	0.459182	−	0.265109i
$451$	−48.0756	−	83.2694i	−0.106598	−	0.184633i
$452$	−107.806	+	62.2417i	−0.238508	+	0.137703i
$453$	−163.737	+	94.5333i	−0.361449	+	0.208683i
$454$		−	823.459i		−	1.81379i
$455$			100.257i			0.220346i
$456$	−511.209	−	885.440i	−1.12107	−	1.94175i
$457$	451.520	−	782.056i	0.988009	−	1.71128i	0.360294	−	0.932839i	$-0.382676\pi$
$457$	451.520	−	782.056i	0.988009	−	1.71128i	0.627715	−	0.778443i	$-0.283990\pi$
$458$	−180.715	+	313.008i	−0.394575	+	0.683423i
$459$	−40.6196	+	23.4517i	−0.0884958	+	0.0510931i
$460$		−	667.144i		−	1.45031i
$461$	370.262			0.803171			0.401586	−	0.915822i	$-0.368459\pi$
$461$	370.262			0.803171			0.401586	+	0.915822i	$0.368459\pi$
$462$	−698.517	+	1209.87i	−1.51194	+	2.61876i
$463$	−281.799	+	162.697i	−0.608637	+	0.351397i	−0.772432	−	0.635098i	$-0.780960\pi$
$463$	−281.799	+	162.697i	−0.608637	+	0.351397i	0.163795	+	0.986494i	$0.447627\pi$
$464$	1146.47			2.47084
$465$	34.1363	+	19.7086i	0.0734114	+	0.0423841i
$466$	−614.616			−1.31892
$467$	333.401	+	577.468i	0.713922	+	1.23655i	0.963374	+	0.268162i	$0.0864161\pi$
$467$	333.401	+	577.468i	0.713922	+	1.23655i	−0.249452	+	0.968387i	$0.580251\pi$
$468$			122.110i			0.260918i
$469$	−267.441	−	810.052i	−0.570236	−	1.72719i
$470$	−36.0695			−0.0767437
$471$	223.618	−	129.106i	0.474773	−	0.274110i
$472$			1331.12i			2.82017i
$473$	675.141	−	1169.38i	1.42736	−	2.47226i
$474$		−	280.927i		−	0.592672i
$475$	285.116	+	493.836i	0.600245	+	1.03965i
$476$	986.965	+	569.825i	2.07346	+	1.19711i
$477$		−	231.852i		−	0.486063i
$478$	−60.1625			−0.125863
$479$	145.642	+	252.259i	0.304054	+	0.526637i	0.977050	−	0.213009i	$-0.0683262\pi$
$479$	145.642	+	252.259i	0.304054	+	0.526637i	−0.672996	+	0.739646i	$0.734993\pi$
$480$	203.967	+	117.760i	0.424931	+	0.245334i
$481$	−22.0802	−	12.7480i	−0.0459047	−	0.0265031i
$482$	1261.74	−	728.464i	2.61771	−	1.51134i
$483$	773.414			1.60127
$484$	1659.77			3.42927
$485$	36.9869	+	64.0632i	0.0762616	+	0.132089i
$486$	−29.0759	−	50.3609i	−0.0598270	−	0.103623i
$487$	−283.960	+	163.945i	−0.583081	+	0.336642i	−0.762357	−	0.647157i	$-0.775958\pi$
$487$	−283.960	+	163.945i	−0.583081	+	0.336642i	0.179276	+	0.983799i	$0.442625\pi$
$488$	614.486	+	1064.32i	1.25919	+	2.18099i
$489$	−314.136	−	181.367i	−0.642405	−	0.370893i
$490$	−404.721	+	700.997i	−0.825961	+	1.43061i
$491$	−503.210			−1.02487			−0.512433	−	0.858727i	$-0.671256\pi$
$491$	−503.210			−1.02487			−0.512433	+	0.858727i	$0.671256\pi$
$492$	−48.6236	−	84.2186i	−0.0988285	−	0.171176i
$493$	242.552			0.491991
$494$	−409.553			−0.829055
$495$	−48.8654	+	84.6374i	−0.0987180	+	0.170985i
$496$		−	506.149i		−	1.02046i
$497$	29.6939	−	17.1438i	0.0597462	−	0.0344945i
$498$	−4.13650	+	7.16463i	−0.00830622	+	0.0143868i
$499$	686.681	−	396.456i	1.37611	−	0.794500i	0.384426	−	0.923156i	$-0.374400\pi$
$499$	686.681	−	396.456i	1.37611	−	0.794500i	0.991689	+	0.128656i	$0.0410662\pi$
$500$	−763.081	−	440.565i	−1.52616	−	0.881130i
$501$	−69.4849	−	40.1171i	−0.138692	−	0.0800741i
$502$	153.105	−	265.185i	0.304990	−	0.528258i
$503$	−331.677	−	191.494i	−0.659398	−	0.380704i	0.132650	−	0.991163i	$-0.457652\pi$
$503$	−331.677	−	191.494i	−0.659398	−	0.380704i	−0.792048	+	0.610459i	$0.790985\pi$
$504$	−421.499	+	730.058i	−0.836308	+	1.44853i
$505$	−187.346	+	324.492i	−0.370981	+	0.642559i
$506$	−1110.86	−	1924.07i	−2.19538	−	3.80251i
$507$	−228.227	−	131.767i	−0.450152	−	0.259895i
$508$	−915.405	−	1585.53i	−1.80198	−	3.12112i
$509$	611.731			1.20183			0.600914	−	0.799314i	$-0.294803\pi$
$509$	611.731			1.20183			0.600914	+	0.799314i	$0.294803\pi$
$510$	96.8951	+	55.9424i	0.189990	+	0.109691i
$511$		−	736.413i		−	1.44112i
$512$			742.259i			1.44973i
$513$	120.359	−	69.4893i	0.234618	−	0.135457i
$514$			589.130i			1.14617i
$515$	155.738	+	89.9156i	0.302405	+	0.174593i
$516$	682.837	−	1182.71i	1.32333	−	2.29207i
$517$	−74.1252	+	42.7962i	−0.143376	+	0.0827780i
$518$	−147.510	−	255.495i	−0.284768	−	0.493233i
$519$	134.016	−	77.3744i	0.258220	−	0.149084i
$520$	150.503	−	86.8927i	0.289428	−	0.167101i
$521$			23.8019i			0.0456850i	0.999739	+	0.0228425i	$0.00727162\pi$
$521$			23.8019i			0.0456850i	−0.999739	+	0.0228425i	$0.992728\pi$
$522$			300.720i			0.576092i
$523$	36.2778	+	62.8349i	0.0693647	+	0.120143i	0.898622	−	0.438724i	$-0.144569\pi$
$523$	36.2778	+	62.8349i	0.0693647	+	0.120143i	−0.829257	+	0.558867i	$0.811236\pi$
$524$	965.644	−	1672.54i	1.84283	−	3.19188i
$525$	235.083	−	407.175i	0.447776	−	0.775571i
$526$	−340.696	+	196.701i	−0.647712	+	0.373957i
$527$		−	107.083i		−	0.203194i
$528$	1254.94			2.37679
$529$	−350.485	+	607.058i	−0.662543	+	1.14756i
$530$	−478.970	+	276.533i	−0.903716	+	0.521761i
$531$	−180.941			−0.340755
$532$	−2924.46	−	1688.44i	−5.49710	−	3.17375i
$533$	−23.2411			−0.0436043
$534$	−180.669	−	312.928i	−0.338331	−	0.586007i
$535$		−	164.259i		−	0.307026i
$536$	−984.231	+	1103.54i	−1.83625	+	2.05885i
$537$	336.354			0.626357
$538$	1190.55	−	687.362i	2.21291	−	1.27763i
$539$			1920.79i			3.56362i
$540$	−49.4224	+	85.6022i	−0.0915230	+	0.158523i
$541$			778.499i			1.43900i	0.694492	+	0.719500i	$0.255629\pi$
$541$			778.499i			1.43900i	−0.694492	+	0.719500i	$0.744371\pi$
$542$	−143.412	−	248.397i	−0.264598	−	0.458297i
$543$	120.006	+	69.2856i	0.221006	+	0.127598i
$544$		−	639.829i		−	1.17616i
$545$	5.71593			0.0104879
$546$	168.841	+	292.442i	0.309233	+	0.535607i
$547$	264.274	+	152.579i	0.483133	+	0.278937i	0.721721	−	0.692184i	$-0.243351\pi$
$547$	264.274	+	152.579i	0.483133	+	0.278937i	−0.238588	+	0.971121i	$0.576685\pi$
$548$	1694.32	+	978.216i	3.09182	+	1.78506i
$549$	−144.675	+	83.5279i	−0.263524	+	0.152146i
$550$	−1350.60			−2.45565
$551$	−718.700			−1.30435
$552$	−670.316	−	1161.02i	−1.21434	−	2.10330i
$553$	−276.787	−	479.409i	−0.500519	−	0.866925i
$554$	1568.64	−	905.653i	2.83147	−	1.63475i
$555$	−10.3192	−	17.8734i	−0.0185931	−	0.0322043i
$556$	−293.152	−	169.251i	−0.527252	−	0.304409i
$557$	170.854	−	295.927i	0.306739	−	0.531287i	−0.670908	−	0.741541i	$-0.734095\pi$
$557$	170.854	−	295.927i	0.306739	−	0.531287i	0.977647	+	0.210253i	$0.0674288\pi$
$558$	132.764			0.237928
$559$	−163.191	−	282.655i	−0.291934	−	0.505644i
$560$	1042.11			1.86091
$561$	265.501			0.473264
$562$	841.419	−	1457.38i	1.49719	−	2.59320i
$563$			463.370i			0.823037i	0.911401	+	0.411519i	$0.135002\pi$
$563$			463.370i			0.823037i	−0.911401	+	0.411519i	$0.864998\pi$
$564$	−74.9702	+	43.2840i	−0.132926	+	0.0767448i
$565$	−12.0411	+	20.8557i	−0.0213116	+	0.0369128i
$566$	108.723	−	62.7712i	0.192090	−	0.110903i
$567$	−99.2378	−	57.2950i	−0.175023	−	0.101049i
$568$	−51.4712	−	29.7169i	−0.0906184	−	0.0523185i
$569$	475.480	−	823.556i	0.835642	−	1.44737i	−0.0578655	−	0.998324i	$-0.518429\pi$
$569$	475.480	−	823.556i	0.835642	−	1.44737i	0.893507	−	0.449049i	$-0.148237\pi$
$570$	−287.108	−	165.762i	−0.503698	−	0.290810i
$571$	−57.0847	+	98.8737i	−0.0999733	+	0.173159i	−0.911673	−	0.410916i	$-0.865209\pi$
$571$	−57.0847	+	98.8737i	−0.0999733	+	0.173159i	0.811700	+	0.584074i	$0.198542\pi$
$572$	345.606	−	598.607i	0.604206	−	1.04652i
$573$	−35.8925	−	62.1677i	−0.0626397	−	0.108495i
$574$	−232.898	−	134.464i	−0.405746	−	0.234258i
$575$	373.855	+	647.536i	0.650183	+	1.12615i
$576$	281.281			0.488335
$577$	537.153	+	310.125i	0.930941	+	0.537479i	0.887109	−	0.461560i	$-0.152710\pi$
$577$	537.153	+	310.125i	0.930941	+	0.537479i	0.0438318	+	0.999039i	$0.486043\pi$
$578$			774.145i			1.33935i
$579$			199.953i			0.345342i
$580$	442.674	−	255.578i	0.763231	−	0.440652i
$581$			16.3022i			0.0280589i
$582$	215.775	+	124.578i	0.370748	+	0.214051i
$583$	−656.209	+	1136.59i	−1.12557	+	1.94955i
$584$	−1105.48	+	638.248i	−1.89294	+	1.09289i
$585$	11.8114	+	20.4580i	0.0201905	+	0.0349710i
$586$	−1596.59	+	921.794i	−2.72456	+	1.57303i
$587$	129.883	−	74.9882i	0.221266	−	0.127748i	−0.385270	−	0.922804i	$-0.625892\pi$
$587$	129.883	−	74.9882i	0.221266	−	0.127748i	0.606537	+	0.795056i	$0.292558\pi$
$588$			1942.69i			3.30389i
$589$			317.295i			0.538702i
$590$	215.811	+	373.796i	0.365781	+	0.633552i
$591$	2.85741	−	4.94918i	0.00483487	−	0.00837425i
$592$	−132.507	+	229.509i	−0.223829	+	0.387684i
$593$	−41.6285	+	24.0342i	−0.0701999	+	0.0405299i	−0.534689	−	0.845049i	$-0.679571\pi$
$593$	−41.6285	+	24.0342i	−0.0701999	+	0.0405299i	0.464489	+	0.885579i	$0.346238\pi$
$594$			329.173i			0.554164i
$595$	220.473			0.370542
$596$	−834.787	+	1445.89i	−1.40065	+	2.42599i
$597$	399.899	−	230.882i	0.669848	−	0.386737i
$598$	−537.021			−0.898029
$599$	558.591	+	322.503i	0.932540	+	0.538402i	0.887614	−	0.460588i	$-0.152362\pi$
$599$	558.591	+	322.503i	0.932540	+	0.538402i	0.0449258	+	0.998990i	$0.485695\pi$
$600$	−814.982			−1.35830
$601$	−529.689	−	917.448i	−0.881346	−	1.52654i	−0.849845	−	0.527033i	$-0.823305\pi$
$601$	−529.689	−	917.448i	−0.881346	−	1.52654i	−0.0315012	−	0.999504i	$-0.510029\pi$
$602$		−	3776.64i		−	6.27349i
$603$	−150.006	−	133.788i	−0.248766	−	0.221870i
$604$	1082.43			1.79210
$605$	278.075	−	160.547i	0.459628	−	0.265366i
$606$			1262.02i			2.08254i
$607$	35.9729	−	62.3070i	0.0592635	−	0.102647i	−0.834872	−	0.550445i	$-0.814458\pi$
$607$	35.9729	−	62.3070i	0.0592635	−	0.102647i	0.894135	+	0.447797i	$0.147791\pi$
$608$			1895.86i			3.11820i
$609$	296.289	+	513.188i	0.486517	+	0.842673i
$610$	345.111	+	199.250i	0.565756	+	0.326639i
$611$			20.6889i			0.0338607i
$612$	268.527			0.438770
$613$	−86.2490	−	149.388i	−0.140700	−	0.243699i	0.787060	−	0.616876i	$-0.211602\pi$
$613$	−86.2490	−	149.388i	−0.140700	−	0.243699i	−0.927760	+	0.373176i	$0.878269\pi$
$614$	−1690.83	−	976.204i	−2.75380	−	1.58991i
$615$	−16.2926	−	9.40655i	−0.0264921	−	0.0152952i
$616$	4132.55	−	2385.93i	6.70869	−	3.87326i
$617$	21.7427			0.0352394			0.0176197	−	0.999845i	$-0.494391\pi$
$617$	21.7427			0.0352394			0.0176197	+	0.999845i	$0.494391\pi$
$618$	605.700			0.980098
$619$	−238.629	−	413.317i	−0.385507	−	0.667717i	0.606333	−	0.795211i	$-0.292640\pi$
$619$	−238.629	−	413.317i	−0.385507	−	0.667717i	−0.991839	+	0.127494i	$0.959307\pi$
$620$	−112.834	−	195.434i	−0.181990	−	0.315216i
$621$	157.819	−	91.1170i	0.254137	−	0.146726i
$622$	642.389	+	1112.65i	1.03278	+	1.78883i
$623$	−616.633	−	356.013i	−0.989781	−	0.571450i
$624$	151.669	−	262.698i	0.243059	−	0.420990i
$625$	362.538			0.580061
$626$	−2.46099	−	4.26256i	−0.00393129	−	0.00680920i
$627$	−786.700			−1.25471
$628$	−1478.29			−2.35397
$629$	−28.0337	+	48.5558i	−0.0445687	+	0.0771952i
$630$			273.346i			0.433883i
$631$	134.447	−	77.6233i	0.213070	−	0.123016i	−0.389667	−	0.920956i	$-0.627410\pi$
$631$	134.447	−	77.6233i	0.213070	−	0.123016i	0.602738	+	0.797939i	$0.294077\pi$
$632$	−479.782	+	831.006i	−0.759148	+	1.31488i
$633$	−111.457	+	64.3499i	−0.176078	+	0.101659i
$634$	841.134	+	485.629i	1.32671	+	0.765976i
$635$	−306.731	−	177.091i	−0.483041	−	0.278884i
$636$	−663.689	+	1149.54i	−1.04354	+	1.80746i
$637$	402.080	+	232.141i	0.631209	+	0.364429i
$638$	851.125	−	1474.19i	1.33405	−	2.31065i
$639$	4.03946	−	6.99656i	0.00632154	−	0.0109492i
$640$	−63.5322	−	110.041i	−0.0992690	−	0.171939i
$641$	104.006	+	60.0478i	0.162255	+	0.0936783i	0.578929	−	0.815378i	$-0.303471\pi$
$641$	104.006	+	60.0478i	0.162255	+	0.0936783i	−0.416674	+	0.909056i	$0.636804\pi$
$642$	−276.626	−	479.130i	−0.430881	−	0.746308i
$643$	−873.016			−1.35772			−0.678861	−	0.734266i	$-0.737526\pi$
$643$	−873.016			−1.35772			−0.678861	+	0.734266i	$0.737526\pi$
$644$	−3834.65	−	2213.94i	−5.95443	−	3.43779i
$645$		−	264.198i		−	0.409610i
$646$			900.636i			1.39417i
$647$	−33.6085	+	19.4038i	−0.0519451	+	0.0299905i	−0.525748	−	0.850641i	$-0.676214\pi$
$647$	−33.6085	+	19.4038i	−0.0519451	+	0.0299905i	0.473803	+	0.880631i	$0.342881\pi$
$648$			198.630i			0.306527i
$649$	887.010	+	512.116i	1.36673	+	0.789084i
$650$	−163.230	+	282.723i	−0.251123	+	0.434958i
$651$	226.565	−	130.807i	0.348026	−	0.200933i
$652$	1038.34	+	1798.46i	1.59255	+	2.75838i
$653$	−1049.21	+	605.763i	−1.60676	+	0.927662i	−0.616668	+	0.787224i	$0.711518\pi$
$653$	−1049.21	+	605.763i	−1.60676	+	0.927662i	−0.990089	+	0.140438i	$0.955149\pi$
$654$	16.6729	−	9.62608i	0.0254937	−	0.0147188i
$655$		−	373.620i		−	0.570413i
$656$			241.576i			0.368256i
$657$	−86.7579	−	150.269i	−0.132052	−	0.228720i
$658$	−119.698	+	207.323i	−0.181912	+	0.315080i
$659$	−91.5152	+	158.509i	−0.138870	+	0.240530i	−0.927069	−	0.374891i	$-0.877680\pi$
$659$	−91.5152	+	158.509i	−0.138870	+	0.240530i	0.788199	+	0.615420i	$0.211014\pi$
$660$	484.558	−	279.760i	0.734179	−	0.423879i
$661$			109.100i			0.165054i	0.996589	+	0.0825268i	$0.0262990\pi$
$661$			109.100i			0.165054i	−0.996589	+	0.0825268i	$0.973701\pi$
$662$	141.595			0.213889
$663$	32.0876	−	55.5774i	0.0483976	−	0.0838271i
$664$	24.4723	−	14.1291i	0.0368558	−	0.0212787i
$665$	−653.278			−0.982373
$666$	−60.2004	−	34.7567i	−0.0903910	−	0.0521873i
$667$	−942.385			−1.41287
$668$	229.675	+	397.809i	0.343825	+	0.595522i
$669$			587.180i			0.877698i
$670$	−97.4702	+	469.460i	−0.145478	+	0.700686i
$671$	945.634			1.40929
$672$	1353.74	−	781.584i	2.01450	−	1.16307i
$673$			425.466i			0.632193i	0.948727	+	0.316097i	$0.102372\pi$
$673$			425.466i			0.632193i	−0.948727	+	0.316097i	$0.897628\pi$
$674$	−218.927	+	379.193i	−0.324818	+	0.562601i
$675$		−	110.782i		−	0.164121i
$676$	754.380	+	1306.62i	1.11595	+	1.93288i
$677$	−1036.49	−	598.418i	−1.53101	−	0.883927i	−0.999316	−	0.0369876i	$-0.988224\pi$
$677$	−1036.49	−	598.418i	−1.53101	−	0.883927i	−0.531690	−	0.846939i	$-0.678443\pi$
$678$			81.1124i			0.119635i
$679$	490.969			0.723076
$680$	−191.083	−	330.966i	−0.281004	−	0.486714i
$681$	−331.111	−	191.167i	−0.486213	−	0.280715i
$682$	−650.835	−	375.760i	−0.954303	−	0.550967i
$683$	128.524	−	74.2034i	0.188176	−	0.108643i	−0.402952	−	0.915221i	$-0.632016\pi$
$683$	128.524	−	74.2034i	0.188176	−	0.108643i	0.591128	+	0.806578i	$0.298683\pi$
$684$	−795.668			−1.16326
$685$	378.484			0.552532
$686$	1522.49	+	2637.03i	2.21937	+	3.84407i
$687$	83.9064	+	145.330i	0.122135	+	0.211543i
$688$	−2938.01	+	1696.26i	−4.27037	+	2.46550i
$689$	158.615	+	274.729i	0.230210	+	0.398736i
$690$	−376.467	−	217.353i	−0.545604	−	0.315004i
$691$	428.706	−	742.541i	0.620414	−	1.07459i	−0.368994	−	0.929432i	$-0.620298\pi$
$691$	428.706	−	742.541i	0.620414	−	1.07459i	0.989409	−	0.145157i	$-0.0463688\pi$
$692$	−885.954			−1.28028
$693$	324.323	+	561.744i	0.467998	+	0.810597i
$694$	797.237			1.14876
$695$	−65.4855			−0.0942238
$696$	513.586	−	889.557i	0.737911	−	1.27810i
$697$			51.1087i			0.0733267i
$698$	2052.06	−	1184.76i	2.93991	−	1.69736i
$699$	−142.684	+	247.135i	−0.204125	+	0.353556i
$700$	−2331.12	+	1345.87i	−3.33017	+	1.92268i
$701$	−322.717	−	186.321i	−0.460367	−	0.265793i	0.251832	−	0.967771i	$-0.418967\pi$
$701$	−322.717	−	186.321i	−0.460367	−	0.265793i	−0.712198	+	0.701978i	$0.752300\pi$
$702$	68.9059	+	39.7829i	0.0981566	+	0.0566707i
$703$	83.0661	−	143.875i	0.118159	−	0.204658i
$704$	−1378.90	−	796.108i	−1.95866	−	1.13083i
$705$	−8.37358	+	14.5035i	−0.0118774	+	0.0205723i
$706$	281.391	−	487.384i	0.398571	−	0.690346i
$707$	1243.42	+	2153.68i	1.75873	+	3.04622i
$708$	897.122	+	517.953i	1.26712	+	0.731573i
$709$	234.118	+	405.505i	0.330209	+	0.571939i	0.982553	−	0.185984i	$-0.0595474\pi$
$709$	234.118	+	405.505i	0.330209	+	0.571939i	−0.652344	+	0.757923i	$0.726214\pi$
$710$	−19.2717			−0.0271433
$711$	−112.960	−	65.2174i	−0.158875	−	0.0917263i
$712$			1234.22i			1.73346i
$713$			416.049i			0.583520i
$714$	643.099	−	371.294i	0.900699	−	0.520019i
$715$		−	133.719i		−	0.187020i
$716$	−1667.67	−	962.831i	−2.32915	−	1.34474i
$717$	−13.9668	+	24.1912i	−0.0194795	+	0.0337395i
$718$	1608.00	−	928.379i	2.23955	−	1.29301i
$719$	97.2539	+	168.449i	0.135263	+	0.234282i	0.925698	−	0.378264i	$-0.123479\pi$
$719$	97.2539	+	168.449i	0.135263	+	0.234282i	−0.790435	+	0.612546i	$0.790145\pi$
$720$	212.648	−	122.772i	0.295344	−	0.170517i
$721$	1033.65	−	596.776i	1.43363	−	0.827705i
$722$		−	1321.97i		−	1.83098i
$723$		−	676.455i		−	0.935622i
$724$	−396.668	−	687.049i	−0.547884	−	0.948962i
$725$	−286.442	+	496.132i	−0.395093	+	0.684321i
$726$	540.747	−	936.601i	0.744830	−	1.29008i
$727$	531.241	−	306.712i	0.730730	−	0.421887i	−0.0879590	−	0.996124i	$-0.528034\pi$
$727$	531.241	−	306.712i	0.730730	−	0.421887i	0.818689	+	0.574237i	$0.194701\pi$
$728$		−	1153.42i		−	1.58437i
$729$	−27.0000			−0.0370370
$730$	−206.955	+	358.456i	−0.283500	+	0.491036i
$731$	−621.578	+	358.868i	−0.850312	+	0.490928i
$732$	956.413			1.30658
$733$	1097.78	+	633.804i	1.49765	+	0.864671i	0.999996	−	0.00270326i	$-0.000860475\pi$
$733$	1097.78	+	633.804i	1.49765	+	0.864671i	0.497657	+	0.867374i	$0.334194\pi$
$734$	−512.120			−0.697712
$735$	187.913	+	325.475i	0.255664	+	0.442823i
$736$			2485.93i			3.37762i
$737$	356.702	+	1080.42i	0.483992	+	1.46597i
$738$	−63.3656			−0.0858612
$739$	−99.6181	+	57.5145i	−0.134801	+	0.0778275i	−0.565884	−	0.824485i	$-0.691465\pi$
$739$	−99.6181	+	57.5145i	−0.134801	+	0.0778275i	0.431083	+	0.902312i	$0.358132\pi$
$740$			118.157i			0.159672i
$741$	−95.0782	+	164.680i	−0.128311	+	0.222241i
$742$			3670.74i			4.94709i
$743$	−130.733	−	226.436i	−0.175953	−	0.304759i	0.764538	−	0.644579i	$-0.222967\pi$
$743$	−130.733	−	226.436i	−0.175953	−	0.304759i	−0.940491	+	0.339820i	$0.889634\pi$
$744$	−392.727	−	226.741i	−0.527858	−	0.304759i
$745$			322.990i			0.433543i
$746$	−644.012			−0.863287
$747$	1.92058	+	3.32655i	0.00257106	+	0.00445321i
$748$	−1316.38	−	760.011i	−1.75986	−	1.01606i
$749$	−944.139	−	545.099i	−1.26053	−	0.727769i
$750$	−497.218	+	287.069i	−0.662958	+	0.382759i
$751$	1273.82			1.69617			0.848084	−	0.529862i	$-0.177756\pi$
$751$	1273.82			1.69617			0.848084	+	0.529862i	$0.177756\pi$
$752$	215.047			0.285967
$753$	−71.0869	−	123.126i	−0.0944049	−	0.163514i
$754$	−205.729	−	356.333i	−0.272850	−	0.472590i
$755$	181.348	−	104.701i	0.240196	−	0.138677i
$756$	328.020	+	568.147i	0.433889	+	0.751517i
$757$	−93.5158	−	53.9914i	−0.123535	−	0.0713228i	0.436959	−	0.899481i	$-0.356055\pi$
$757$	−93.5158	−	53.9914i	−0.123535	−	0.0713228i	−0.560494	+	0.828158i	$0.689389\pi$
$758$	−659.896	+	1142.97i	−0.870575	+	1.50788i
$759$	−1031.55			−1.35909
$760$	566.194	+	980.678i	0.744993	+	1.29037i
$761$	−1307.29			−1.71785			−0.858926	−	0.512100i	$-0.828868\pi$
$761$	−1307.29			−1.71785			−0.858926	+	0.512100i	$0.828868\pi$
$762$	−1192.94			−1.56554
$763$	18.9685	−	32.8544i	0.0248604	−	0.0430595i
$764$			410.978i			0.537929i
$765$	44.9886	−	25.9742i	0.0588086	−	0.0339532i
$766$	−258.197	+	447.210i	−0.337072	+	0.583825i
$767$	214.403	−	123.785i	0.279534	−	0.161389i
$768$	191.927	+	110.809i	0.249905	+	0.144283i
$769$	34.7247	+	20.0483i	0.0451557	+	0.0260707i	0.522408	−	0.852696i	$-0.325034\pi$
$769$	34.7247	+	20.0483i	0.0451557	+	0.0260707i	−0.477252	+	0.878766i	$0.658367\pi$
$770$	773.649	−	1340.00i	1.00474	−	1.74026i
$771$	236.888	+	136.767i	0.307247	+	0.177389i
$772$	572.377	−	991.386i	0.741421	−	1.28418i
$773$	209.572	−	362.990i	0.271115	−	0.469586i	−0.698032	−	0.716066i	$-0.745941\pi$
$773$	209.572	−	362.990i	0.271115	−	0.469586i	0.969148	+	0.246481i	$0.0792742\pi$
$774$	−444.932	−	770.644i	−0.574847	−	0.995664i
$775$	219.035	+	126.460i	0.282626	+	0.163174i
$776$	−425.521	−	737.025i	−0.548352	−	0.949774i
$777$	−136.978			−0.176291
$778$	−1350.87	−	779.928i	−1.73634	−	1.00248i
$779$		−	151.439i		−	0.194402i
$780$		−	135.244i		−	0.173389i
$781$	−39.6046	+	22.8657i	−0.0507101	+	0.0292775i
$782$			1180.95i			1.51016i
$783$	120.919	+	69.8125i	0.154430	+	0.0891602i
$784$	2412.95	−	4179.36i	3.07775	−	5.33082i
$785$	−247.670	+	142.993i	−0.315504	+	0.182156i
$786$	−629.207	−	1089.82i	−0.800517	−	1.38654i
$787$	989.944	−	571.545i	1.25787	−	0.726232i	0.285211	−	0.958465i	$-0.407936\pi$
$787$	989.944	−	571.545i	1.25787	−	0.726232i	0.972660	+	0.232233i	$0.0746031\pi$
$788$	−28.3346	+	16.3590i	−0.0359576	+	0.0207601i
$789$			182.657i			0.231505i
$790$			311.143i			0.393852i
$791$	79.9172	+	138.421i	0.101033	+	0.174995i
$792$	562.180	−	973.724i	0.709823	−	1.22945i
$793$	114.286	−	197.950i	0.144119	−	0.249621i
$794$	−1915.07	+	1105.67i	−2.41193	+	1.39253i
$795$			256.790i			0.323006i
$796$	−2643.65			−3.32117
$797$	649.310	−	1124.64i	0.814692	−	1.41109i	−0.0948568	−	0.995491i	$-0.530239\pi$
$797$	649.310	−	1124.64i	0.814692	−	1.41109i	0.909549	−	0.415597i	$-0.136427\pi$
$798$	−1905.55	+	1100.17i	−2.38791	+	1.37866i
$799$	45.4963			0.0569415
$800$	1308.75	+	755.608i	1.63594	+	0.944511i
$801$	−167.770			−0.209450
$802$	144.203	+	249.766i	0.179804	+	0.311429i
$803$			982.201i			1.22316i
$804$	360.768	+	1092.73i	0.448717	+	1.35912i
$805$	−856.602			−1.06410
$806$	−157.316	+	90.8263i	−0.195181	+	0.112688i
$807$		−	638.288i		−	0.790939i
$808$	2155.35	−	3733.17i	2.66751	−	4.62026i
$809$		−	610.373i		−	0.754478i	−0.926116	−	0.377239i	$-0.876874\pi$
$809$		−	610.373i		−	0.754478i	0.926116	−	0.377239i	$-0.123126\pi$
$810$	32.2033	+	55.7777i	0.0397572	+	0.0688614i
$811$	−725.644	−	418.951i	−0.894752	−	0.516585i	−0.0192581	−	0.999815i	$-0.506130\pi$
$811$	−725.644	−	418.951i	−0.894752	−	0.516585i	−0.875494	+	0.483229i	$0.839464\pi$
$812$		−	3392.57i		−	4.17805i
$813$	−133.173			−0.163804
$814$	196.743	+	340.769i	0.241699	+	0.418636i
$815$	347.925	+	200.874i	0.426901	+	0.246472i
$816$	−577.691	−	333.530i	−0.707954	−	0.408737i
$817$	1841.78	−	1063.35i	2.25433	−	1.30154i
$818$	912.767			1.11585
$819$	156.787			0.191437
$820$	53.8536	+	93.2771i	0.0656751	+	0.113753i
$821$	518.134	+	897.434i	0.631101	+	1.09310i	0.987327	+	0.158699i	$0.0507300\pi$
$821$	518.134	+	897.434i	0.631101	+	1.09310i	−0.356226	+	0.934400i	$0.615937\pi$
$822$	1104.01	−	637.398i	1.34307	−	0.775424i
$823$	−39.7793	−	68.8997i	−0.0483344	−	0.0837177i	0.840846	−	0.541274i	$-0.182058\pi$
$823$	−39.7793	−	68.8997i	−0.0483344	−	0.0837177i	−0.889180	+	0.457557i	$0.848725\pi$
$824$	−1791.72	−	1034.45i	−2.17441	−	1.25540i
$825$	−313.544	+	543.075i	−0.380054	+	0.658272i
$826$	2864.70			3.46816
$827$	36.0816	+	62.4951i	0.0436295	+	0.0755684i	0.887015	−	0.461740i	$-0.152775\pi$
$827$	36.0816	+	62.4951i	0.0436295	+	0.0755684i	−0.843386	+	0.537308i	$0.819441\pi$
$828$	−1043.31			−1.26004
$829$	398.238			0.480383			0.240192	−	0.970725i	$-0.422790\pi$
$829$	398.238			0.480383			0.240192	+	0.970725i	$0.422790\pi$
$830$	4.58142	−	7.93525i	0.00551978	−	0.00956054i
$831$		−	840.993i		−	1.01203i
$832$	−333.299	+	192.430i	−0.400600	+	0.231286i
$833$	510.494	−	884.202i	0.612838	−	1.06147i
$834$	−191.016	+	110.283i	−0.229036	+	0.132234i
$835$	76.9587	+	44.4321i	0.0921661	+	0.0532121i
$836$	3900.53	+	2251.97i	4.66571	+	2.69375i
$837$	30.8212	−	53.3839i	0.0368234	−	0.0637800i
$838$	−362.003	−	209.002i	−0.431984	−	0.249406i
$839$	−55.7339	+	96.5339i	−0.0664289	+	0.115058i	−0.897327	−	0.441366i	$-0.854494\pi$
$839$	−55.7339	+	96.5339i	−0.0664289	+	0.115058i	0.830898	+	0.556425i	$0.187827\pi$
$840$	466.835	−	808.583i	0.555756	−	0.962598i
$841$	59.4792	+	103.021i	0.0707244	+	0.122498i
$842$	−621.546	−	358.850i	−0.738179	−	0.426188i
$843$	−390.673	−	676.665i	−0.463432	−	0.802687i
$844$	736.820			0.873010
$845$	252.775	+	145.940i	0.299142	+	0.172710i
$846$			56.4071i			0.0666751i
$847$		−	2131.12i		−	2.51608i
$848$	2855.63	−	1648.70i	3.36748	−	1.94422i
$849$		−	58.2896i		−	0.0686568i
$850$	621.727	+	358.954i	0.731443	+	0.422299i
$851$	108.919	−	188.654i	0.127990	−	0.221685i
$852$	−40.0561	+	23.1264i	−0.0470141	+	0.0271436i
$853$	−423.492	−	733.510i	−0.496474	−	0.859918i	0.503518	−	0.863985i	$-0.332039\pi$
$853$	−423.492	−	733.510i	−0.496474	−	0.859918i	−0.999992	+	0.00406655i	$0.998706\pi$
$854$	2290.52	−	1322.43i	2.68211	−	1.54852i
$855$	−133.305	+	76.9636i	−0.155912	+	0.0900159i
$856$			1889.74i			2.20765i
$857$			1401.80i			1.63571i	0.575427	+	0.817853i	$0.304836\pi$
$857$			1401.80i			1.63571i	−0.575427	+	0.817853i	$0.695164\pi$
$858$	−225.194	−	390.048i	−0.262464	−	0.454601i
$859$	−321.427	+	556.727i	−0.374187	+	0.648111i	−0.990205	−	0.139621i	$-0.955412\pi$
$859$	−321.427	+	556.727i	−0.374187	+	0.648111i	0.616018	+	0.787732i	$0.288745\pi$
$860$	−756.283	+	1309.92i	−0.879398	+	1.52316i
$861$	−108.135	+	62.4319i	−0.125593	+	0.0725109i
$862$			1188.23i			1.37845i
$863$	−337.275			−0.390817			−0.195409	−	0.980722i	$-0.562603\pi$
$863$	−337.275			−0.390817			−0.195409	+	0.980722i	$0.562603\pi$
$864$	184.159	−	318.973i	0.213147	−	0.369181i
$865$	−148.431	+	85.6968i	−0.171597	+	0.0990714i
$866$	1290.96			1.49071
$867$	311.281	+	179.718i	0.359033	+	0.207288i
$868$	−1497.77			−1.72554
$869$	369.168	+	639.419i	0.424820	+	0.735810i
$870$		−	333.065i		−	0.382834i
$871$	269.274	+	55.9073i	0.309155	+	0.0641874i
$872$	−65.7598			−0.0754126
$873$	100.185	−	57.8417i	0.114759	−	0.0662563i
$874$		−	3499.24i		−	4.00371i
$875$	−565.678	+	979.784i	−0.646490	+	1.11975i
$876$			993.397i			1.13401i
$877$	217.678	+	377.030i	0.248208	+	0.429909i	0.963029	−	0.269399i	$-0.0868250\pi$
$877$	217.678	+	377.030i	0.248208	+	0.429909i	−0.714821	+	0.699308i	$0.753492\pi$
$878$	−1815.72	−	1048.31i	−2.06802	−	1.19397i
$879$			855.982i			0.973813i
$880$	−1389.93			−1.57946
$881$	−321.801	−	557.376i	−0.365268	−	0.632663i	0.623551	−	0.781782i	$-0.285689\pi$
$881$	−321.801	−	557.376i	−0.365268	−	0.632663i	−0.988819	+	0.149120i	$0.952356\pi$
$882$	1096.25	+	632.921i	1.24291	+	0.717597i
$883$	−480.476	−	277.403i	−0.544140	−	0.314159i	0.202615	−	0.979258i	$-0.435056\pi$
$883$	−480.476	−	277.403i	−0.544140	−	0.314159i	−0.746755	+	0.665099i	$0.768389\pi$
$884$	−318.187	+	183.705i	−0.359940	+	0.207811i
$885$	200.403			0.226444
$886$	1352.19			1.52618
$887$	−493.090	−	854.058i	−0.555908	−	0.962861i	−0.997832	−	0.0658086i	$-0.979037\pi$
$887$	−493.090	−	854.058i	−0.555908	−	0.962861i	0.441924	−	0.897052i	$-0.354296\pi$
$888$	118.719	+	205.627i	0.133692	+	0.231562i
$889$	−2035.79	+	1175.36i	−2.28998	+	1.32212i
$890$	200.102	+	346.586i	0.224833	+	0.389422i
$891$	132.360	+	76.4179i	0.148552	+	0.0857664i
$892$	1680.84	−	2911.29i	1.88434	−	3.26378i
$893$	−134.809			−0.150962
$894$	543.941	+	942.133i	0.608435	+	1.05384i
$895$	−372.532			−0.416237
$896$	−843.334			−0.941221
$897$	−124.670	+	215.935i	−0.138986	+	0.240730i
$898$			494.210i			0.550346i
$899$	−276.064	+	159.385i	−0.307079	+	0.177292i
$900$	−317.118	+	549.265i	−0.352354	+	0.610295i
$901$	604.148	−	348.805i	0.670530	−	0.387131i
$902$	310.631	+	179.343i	0.344381	+	0.198828i
$903$	−1518.58	−	876.751i	−1.68170	−	0.970932i
$904$	138.528	−	239.938i	0.153239	−	0.265418i
$905$	−132.914	−	76.7380i	−0.146866	−	0.0847933i
$906$	352.651	−	610.809i	0.389239	−	0.674182i
$907$	−564.080	+	977.014i	−0.621918	+	1.07719i	0.367210	+	0.930138i	$0.380313\pi$
$907$	−564.080	+	977.014i	−0.621918	+	1.07719i	−0.989128	+	0.147056i	$0.953020\pi$
$908$	1094.45	+	1895.65i	1.20534	+	2.08772i
$909$	507.455	+	292.979i	0.558256	+	0.322309i
$910$	−187.002	−	323.897i	−0.205496	−	0.355930i
$911$	−1212.93			−1.33143			−0.665715	−	0.746206i	$-0.731873\pi$
$911$	−1212.93			−1.33143			−0.665715	+	0.746206i	$0.731873\pi$
$912$	1711.74	+	988.276i	1.87691	+	1.08364i
$913$		−	21.7433i		−	0.0238152i
$914$			3368.74i			3.68571i
$915$	160.236	−	92.5122i	0.175121	−	0.101106i
$916$		−	960.747i		−	1.04885i
$917$	−2147.52	−	1239.87i	−2.34190	−	1.35209i
$918$	87.4852	−	151.529i	0.0952998	−	0.165064i
$919$	196.187	−	113.269i	0.213479	−	0.123252i	−0.389448	−	0.921048i	$-0.627334\pi$
$919$	196.187	−	113.269i	0.213479	−	0.123252i	0.602927	+	0.797796i	$0.294001\pi$
$920$	742.415	+	1285.90i	0.806973	+	1.39772i
$921$	−785.058	+	453.253i	−0.852397	+	0.492132i
$922$	−1196.19	+	690.620i	−1.29738	+	0.749045i
$923$			11.0539i			0.0119761i
$924$		−	3713.57i		−	4.01901i
$925$	−66.2130	−	114.684i	−0.0715816	−	0.123983i
$926$	606.930	−	1051.23i	0.655432	−	1.13524i
$927$	140.614	−	243.551i	0.151687	−	0.262730i
$928$	−1649.50	+	952.340i	−1.77748	+	1.02623i
$929$			330.440i			0.355694i	0.984058	+	0.177847i	$0.0569132\pi$
$929$			330.440i			0.355694i	−0.984058	+	0.177847i	$0.943087\pi$
$930$	−147.044			−0.158111
$931$	−1512.64	+	2619.96i	−1.62474	+	2.81414i
$932$	1414.88	−	816.880i	1.51811	−	0.876480i
$933$	596.525			0.639362
$934$	−2154.21	−	1243.73i	−2.30644	−	1.33162i
$935$	−294.058			−0.314501
$936$	−135.887	−	235.363i	−0.145178	−	0.251456i
$937$		−	1417.35i		−	1.51264i	−0.654199	−	0.756322i	$-0.726994\pi$
$937$		−	1417.35i		−	1.51264i	0.654199	−	0.756322i	$-0.273006\pi$
$938$	2374.93	+	2118.16i	2.53191	+	2.25817i
$939$	−2.28528			−0.00243374
$940$	83.0339	−	47.9397i	0.0883340	−	0.0509997i
$941$		−	1359.35i		−	1.44459i	−0.691588	−	0.722293i	$-0.743088\pi$
$941$		−	1359.35i		−	1.44459i	0.691588	−	0.722293i	$-0.256912\pi$
$942$	−481.622	+	834.194i	−0.511276	+	0.885556i
$943$		−	198.573i		−	0.210575i
$944$	−1286.67	−	2228.58i	−1.36300	−	2.36078i
$945$	109.912	+	63.4576i	0.116309	+	0.0671509i
$946$			5037.14i			5.32468i
$947$	−1423.31			−1.50297			−0.751483	−	0.659753i	$-0.770661\pi$
$947$	−1423.31			−1.50297			−0.751483	+	0.659753i	$0.770661\pi$
$948$	373.377	+	646.707i	0.393857	+	0.682181i
$949$	205.604	+	118.706i	0.216654	+	0.125085i
$950$	−1842.23	−	1063.61i	−1.93918	−	1.11959i
$951$	390.540	−	225.479i	0.410663	−	0.237096i
$952$	−2536.46			−2.66435
$953$	−279.609			−0.293399			−0.146699	−	0.989181i	$-0.546865\pi$
$953$	−279.609			−0.293399			−0.146699	+	0.989181i	$0.546865\pi$
$954$	432.455	+	749.034i	0.453307	+	0.785151i
$955$	39.7531	+	68.8545i	0.0416263	+	0.0720989i
$956$	138.497	−	79.9614i	0.144872	−	0.0836417i
$957$	−395.179	−	684.471i	−0.412936	−	0.715225i
$958$	−941.038	−	543.309i	−0.982295	−	0.567128i
$959$	1256.01	−	2175.48i	1.30971	−	2.26849i
$960$	−311.536			−0.324516
$961$	−410.134	−	710.372i	−0.426778	−	0.739201i
$962$	95.1112			0.0988682
$963$	−256.876			−0.266745
$964$	−1936.39	+	3353.92i	−2.00870	+	3.47917i
$965$		−	221.460i		−	0.229492i
$966$	−2498.63	+	1442.59i	−2.58658	+	1.49336i
$967$	−266.835	+	462.172i	−0.275941	+	0.477944i	−0.970372	−	0.241615i	$-0.922323\pi$
$967$	−266.835	+	462.172i	−0.275941	+	0.477944i	0.694431	+	0.719559i	$0.255656\pi$
$968$	−3199.15	+	1847.03i	−3.30491	+	1.90809i
$969$	362.143	+	209.084i	0.373729	+	0.215772i
$970$	−238.984	−	137.977i	−0.246375	−	0.142245i
$971$	654.397	−	1133.45i	0.673942	−	1.16730i	−0.302835	−	0.953043i	$-0.597933\pi$
$971$	654.397	−	1133.45i	0.673942	−	1.16730i	0.976777	−	0.214258i	$-0.0687334\pi$
$972$	133.868	+	77.2890i	0.137725	+	0.0795154i
$973$	−217.316	+	376.402i	−0.223346	+	0.386847i
$974$	611.586	−	1059.30i	0.627911	−	1.08757i
$975$	75.7880	+	131.269i	0.0777313	+	0.134635i
$976$	−2057.56	−	1187.93i	−2.10815	−	1.21714i
$977$	−369.139	−	639.368i	−0.377829	−	0.654420i	0.612917	−	0.790147i	$-0.289996\pi$
$977$	−369.139	−	639.368i	−0.377829	−	0.654420i	−0.990746	+	0.135728i	$0.956663\pi$
$978$	1353.15			1.38359
$979$	822.443	+	474.838i	0.840084	+	0.485023i
$980$		−	2151.64i		−	2.19555i
$981$		−	8.93882i		−	0.00911195i
$982$	1625.70	−	938.597i	1.65550	−	0.955801i
$983$			1622.49i			1.65055i	0.564730	+	0.825276i	$0.308980\pi$
$983$			1622.49i			1.65055i	−0.564730	+	0.825276i	$0.691020\pi$
$984$	187.441	+	108.219i	0.190489	+	0.109979i
$985$	−3.16475	+	5.48151i	−0.00321295	+	0.00556499i
$986$	−783.600	+	452.412i	−0.794727	+	0.458836i
$987$	55.5760	+	96.2605i	0.0563080	+	0.0975283i
$988$	942.813	−	544.333i	0.954264	−	0.550944i
$989$	2415.02	−	1394.31i	2.44188	−	1.40982i
$990$		−	364.579i		−	0.368262i
$991$		−	1362.18i		−	1.37455i	−0.726397	−	0.687276i	$-0.758806\pi$
$991$		−	1362.18i		−	1.37455i	0.726397	−	0.687276i	$-0.241194\pi$
$992$	420.444	+	728.231i	0.423835	+	0.734104i
$993$	32.8713	−	56.9348i	0.0331031	−	0.0573362i
$994$	−63.9538	+	110.771i	−0.0643398	+	0.111440i
$995$	−442.912	+	255.716i	−0.445138	+	0.257001i
$996$		−	21.9911i		−	0.0220794i
$997$	−284.836			−0.285693			−0.142847	−	0.989745i	$-0.545626\pi$
$997$	−284.836			−0.285693			−0.142847	+	0.989745i	$0.545626\pi$
$998$	−1478.95	+	2561.62i	−1.48192	+	2.56676i
$999$	−27.9512	+	16.1376i	−0.0279791	+	0.0161538i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.h.b.97.1	✓	24
67.38	odd	6	inner	201.3.h.b.172.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.h.b.97.1	✓	24	1.1	even	1	trivial
201.3.h.b.172.1	yes	24	67.38	odd	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:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	201.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.23066 + 1.86522i) q^{2} +1.73205i q^{3} +(4.95809 - 8.58766i) q^{4} -1.91835i q^{5} +(-3.23066 - 5.59566i) q^{6} +(-11.0264 - 6.36611i) q^{7} +22.0700i q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(-3.23066 + 1.86522i) q^{2} +1.73205i q^{3} +(4.95809 - 8.58766i) q^{4} -1.91835i q^{5} +(-3.23066 - 5.59566i) q^{6} +(-11.0264 - 6.36611i) q^{7} +22.0700i q^{8} -3.00000 q^{9} +(3.57814 + 6.19753i) q^{10} +(14.7066 + 8.49088i) q^{11} +(14.8743 + 8.58766i) q^{12} +(3.55480 - 2.05236i) q^{13} +47.4967 q^{14} +3.32268 q^{15} +(-21.3330 - 36.9498i) q^{16} +(-4.51329 - 7.81724i) q^{17} +(9.69197 - 5.59566i) q^{18} +(13.3732 + 23.1631i) q^{19} +(-16.4741 - 9.51135i) q^{20} +(11.0264 - 19.0983i) q^{21} -63.3494 q^{22} +(17.5355 + 30.3723i) q^{23} -38.2263 q^{24} +21.3199 q^{25} +(-7.65621 + 13.2610i) q^{26} -5.19615i q^{27} +(-109.340 + 63.1275i) q^{28} +(-13.4354 + 23.2708i) q^{29} +(-10.7344 + 6.19753i) q^{30} +(10.2737 + 5.93154i) q^{31} +(61.3863 + 35.4414i) q^{32} +(-14.7066 + 25.4726i) q^{33} +(29.1617 + 16.8365i) q^{34} +(-12.2124 + 21.1525i) q^{35} +(-14.8743 + 25.7630i) q^{36} +(-3.10569 - 5.37920i) q^{37} +(-86.4086 - 49.8880i) q^{38} +(3.55480 + 6.15709i) q^{39} +42.3379 q^{40} +(-4.90346 - 2.83101i) q^{41} +82.2668i q^{42} -79.5137i q^{43} +(145.834 - 84.1971i) q^{44} +5.75505i q^{45} +(-113.302 - 65.4150i) q^{46} +(-2.52013 + 4.36499i) q^{47} +(63.9989 - 36.9498i) q^{48} +(56.5546 + 97.9555i) q^{49} +(-68.8774 + 39.7664i) q^{50} +(13.5399 - 7.81724i) q^{51} -40.7032i q^{52} +77.2840i q^{53} +(9.69197 + 16.7870i) q^{54} +(16.2885 - 28.2125i) q^{55} +(140.500 - 243.353i) q^{56} +(-40.1197 + 23.1631i) q^{57} -100.240i q^{58} +60.3136 q^{59} +(16.4741 - 28.5341i) q^{60} +(48.2249 - 27.8426i) q^{61} -44.2545 q^{62} +(33.0793 + 19.0983i) q^{63} -93.7604 q^{64} +(-3.93715 - 6.81934i) q^{65} -109.724i q^{66} +(50.0020 + 44.5960i) q^{67} -89.5091 q^{68} +(-52.6064 + 30.3723i) q^{69} -91.1154i q^{70} +(-1.34649 + 2.33219i) q^{71} -66.2099i q^{72} +(28.9193 + 50.0897i) q^{73} +(20.0668 + 11.5856i) q^{74} +36.9272i q^{75} +265.223 q^{76} +(-108.108 - 187.248i) q^{77} +(-22.9686 - 13.2610i) q^{78} +(37.6533 + 21.7391i) q^{79} +(-70.8826 + 40.9241i) q^{80} +9.00000 q^{81} +21.1219 q^{82} +(-0.640195 - 1.10885i) q^{83} +(-109.340 - 189.382i) q^{84} +(-14.9962 + 8.65806i) q^{85} +(148.311 + 256.881i) q^{86} +(-40.3062 - 23.2708i) q^{87} +(-187.393 + 324.575i) q^{88} +55.9233 q^{89} +(-10.7344 - 18.5926i) q^{90} -52.2622 q^{91} +347.770 q^{92} +(-10.2737 + 17.7946i) q^{93} -18.8024i q^{94} +(44.4350 - 25.6545i) q^{95} +(-61.3863 + 106.324i) q^{96} +(-33.3949 + 19.2806i) q^{97} +(-365.417 - 210.974i) q^{98} +(-44.1199 - 25.4726i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 34 q^{4} + 21 q^{7} - 72 q^{9}+O(q^{10}) \) 24 * q + 34 * q^4 + 21 * q^7 - 72 * q^9	\( 24 q + 34 q^{4} + 21 q^{7} - 72 q^{9} + 30 q^{10} + 12 q^{11} + 102 q^{12} + 30 q^{13} + 6 q^{14} - 6 q^{15} - 98 q^{16} + 4 q^{17} + 39 q^{19} + 108 q^{20} - 21 q^{21} - 82 q^{22} - 13 q^{23} - 36 q^{24} - 222 q^{25} + 29 q^{26} + 189 q^{28} - 90 q^{30} - 93 q^{31} - 33 q^{32} - 12 q^{33} + 72 q^{34} - 93 q^{35} - 102 q^{36} - 33 q^{37} - 210 q^{38} + 30 q^{39} + 274 q^{40} - 15 q^{41} - 9 q^{44} - 228 q^{46} - 131 q^{47} + 294 q^{48} + 295 q^{49} - 423 q^{50} - 12 q^{51} - 56 q^{55} + 349 q^{56} - 117 q^{57} - 116 q^{59} - 108 q^{60} + 120 q^{61} + 282 q^{62} - 63 q^{63} - 276 q^{64} + 136 q^{65} - 25 q^{67} + 10 q^{68} + 39 q^{69} + 169 q^{71} + 187 q^{73} + 849 q^{74} + 386 q^{76} - 348 q^{77} + 87 q^{78} + 51 q^{80} + 216 q^{81} - 14 q^{82} + 104 q^{83} + 189 q^{84} - 243 q^{85} + 641 q^{86} - 766 q^{88} + 152 q^{89} - 90 q^{90} + 32 q^{91} - 216 q^{92} + 93 q^{93} + 762 q^{95} + 33 q^{96} - 84 q^{97} - 1086 q^{98} - 36 q^{99}+O(q^{100}) \) 24 * q + 34 * q^4 + 21 * q^7 - 72 * q^9 + 30 * q^10 + 12 * q^11 + 102 * q^12 + 30 * q^13 + 6 * q^14 - 6 * q^15 - 98 * q^16 + 4 * q^17 + 39 * q^19 + 108 * q^20 - 21 * q^21 - 82 * q^22 - 13 * q^23 - 36 * q^24 - 222 * q^25 + 29 * q^26 + 189 * q^28 - 90 * q^30 - 93 * q^31 - 33 * q^32 - 12 * q^33 + 72 * q^34 - 93 * q^35 - 102 * q^36 - 33 * q^37 - 210 * q^38 + 30 * q^39 + 274 * q^40 - 15 * q^41 - 9 * q^44 - 228 * q^46 - 131 * q^47 + 294 * q^48 + 295 * q^49 - 423 * q^50 - 12 * q^51 - 56 * q^55 + 349 * q^56 - 117 * q^57 - 116 * q^59 - 108 * q^60 + 120 * q^61 + 282 * q^62 - 63 * q^63 - 276 * q^64 + 136 * q^65 - 25 * q^67 + 10 * q^68 + 39 * q^69 + 169 * q^71 + 187 * q^73 + 849 * q^74 + 386 * q^76 - 348 * q^77 + 87 * q^78 + 51 * q^80 + 216 * q^81 - 14 * q^82 + 104 * q^83 + 189 * q^84 - 243 * q^85 + 641 * q^86 - 766 * q^88 + 152 * q^89 - 90 * q^90 + 32 * q^91 - 216 * q^92 + 93 * q^93 + 762 * q^95 + 33 * q^96 - 84 * q^97 - 1086 * q^98 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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