LMFDB - Embedded newform 201.3.h.a.172.8

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:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			172.8
Character	$\chi$	$=$	201.172
Dual form			201.3.h.a.97.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.57301 + 0.908176i) q^{2} +1.73205i q^{3} +(-0.350432 - 0.606966i) q^{4} -5.97048i q^{5} +(-1.57301 + 2.72453i) q^{6} +(6.73988 - 3.89127i) q^{7} -8.53843i q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(1.57301 + 0.908176i) q^{2} +1.73205i q^{3} +(-0.350432 - 0.606966i) q^{4} -5.97048i q^{5} +(-1.57301 + 2.72453i) q^{6} +(6.73988 - 3.89127i) q^{7} -8.53843i q^{8} -3.00000 q^{9} +(5.42225 - 9.39162i) q^{10} +(3.44158 - 1.98700i) q^{11} +(1.05130 - 0.606966i) q^{12} +(4.64727 + 2.68310i) q^{13} +14.1358 q^{14} +10.3412 q^{15} +(6.35267 - 11.0031i) q^{16} +(-6.53128 + 11.3125i) q^{17} +(-4.71902 - 2.72453i) q^{18} +(-6.51703 + 11.2878i) q^{19} +(-3.62388 + 2.09225i) q^{20} +(6.73988 + 11.6738i) q^{21} +7.21817 q^{22} +(14.7763 - 25.5933i) q^{23} +14.7890 q^{24} -10.6467 q^{25} +(4.87346 + 8.44108i) q^{26} -5.19615i q^{27} +(-4.72374 - 2.72725i) q^{28} +(16.8172 + 29.1282i) q^{29} +(16.2668 + 9.39162i) q^{30} +(-24.0841 + 13.9050i) q^{31} +(-9.59239 + 5.53817i) q^{32} +(3.44158 + 5.96099i) q^{33} +(-20.5475 + 11.8631i) q^{34} +(-23.2328 - 40.2404i) q^{35} +(1.05130 + 1.82090i) q^{36} +(2.99353 - 5.18494i) q^{37} +(-20.5027 + 11.8372i) q^{38} +(-4.64727 + 8.04931i) q^{39} -50.9785 q^{40} +(30.7167 - 17.7343i) q^{41} +24.4840i q^{42} +35.0077i q^{43} +(-2.41208 - 1.39261i) q^{44} +17.9115i q^{45} +(46.4865 - 26.8390i) q^{46} +(-13.1152 - 22.7162i) q^{47} +(19.0580 + 11.0031i) q^{48} +(5.78402 - 10.0182i) q^{49} +(-16.7473 - 9.66906i) q^{50} +(-19.5938 - 11.3125i) q^{51} -3.76098i q^{52} -58.9526i q^{53} +(4.71902 - 8.17359i) q^{54} +(-11.8633 - 20.5479i) q^{55} +(-33.2253 - 57.5480i) q^{56} +(-19.5511 - 11.2878i) q^{57} +61.0919i q^{58} -47.4856 q^{59} +(-3.62388 - 6.27674i) q^{60} +(60.5107 + 34.9359i) q^{61} -50.5127 q^{62} +(-20.2197 + 11.6738i) q^{63} -70.9399 q^{64} +(16.0194 - 27.7465i) q^{65} +12.5022i q^{66} +(31.1180 + 59.3352i) q^{67} +9.15507 q^{68} +(44.3289 + 25.5933i) q^{69} -84.3979i q^{70} +(31.8812 + 55.2199i) q^{71} +25.6153i q^{72} +(-46.7763 + 81.0189i) q^{73} +(9.41767 - 5.43730i) q^{74} -18.4406i q^{75} +9.13510 q^{76} +(15.4639 - 26.7843i) q^{77} +(-14.6204 + 8.44108i) q^{78} +(11.8603 - 6.84756i) q^{79} +(-65.6941 - 37.9285i) q^{80} +9.00000 q^{81} +64.4234 q^{82} +(-23.3392 + 40.4247i) q^{83} +(4.72374 - 8.18176i) q^{84} +(67.5411 + 38.9949i) q^{85} +(-31.7931 + 55.0673i) q^{86} +(-50.4516 + 29.1282i) q^{87} +(-16.9658 - 29.3857i) q^{88} -89.7813 q^{89} +(-16.2668 + 28.1748i) q^{90} +41.7628 q^{91} -20.7123 q^{92} +(-24.0841 - 41.7149i) q^{93} -47.6436i q^{94} +(67.3938 + 38.9098i) q^{95} +(-9.59239 - 16.6145i) q^{96} +(-4.03037 - 2.32694i) q^{97} +(18.1966 - 10.5058i) q^{98} +(-10.3247 + 5.96099i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 26 q^{4} - 15 q^{7} - 66 q^{9}+O(q^{10}) $ 22 * q + 26 * q^4 - 15 * q^7 - 66 * q^9	$ 22 q + 26 q^{4} - 15 q^{7} - 66 q^{9} + 6 q^{10} + 30 q^{11} - 78 q^{12} - 27 q^{13} + 6 q^{14} - 6 q^{15} - 58 q^{16} - 8 q^{17} + q^{19} - 12 q^{20} - 15 q^{21} + 14 q^{22} - q^{23} - 56 q^{25} + 71 q^{26} - 75 q^{28} + 42 q^{29} + 18 q^{30} + 120 q^{31} - 105 q^{32} + 30 q^{33} - 24 q^{34} + 3 q^{35} - 78 q^{36} + 13 q^{37} + 108 q^{38} + 27 q^{39} + 82 q^{40} - 159 q^{41} + 189 q^{44} + 372 q^{46} - 35 q^{47} - 174 q^{48} - 40 q^{49} + 285 q^{50} - 24 q^{51} - 212 q^{55} - 113 q^{56} + 3 q^{57} + 136 q^{59} - 12 q^{60} + 63 q^{61} - 150 q^{62} + 45 q^{63} - 284 q^{64} - 20 q^{65} + 94 q^{67} + 154 q^{68} - 3 q^{69} - 41 q^{71} - 16 q^{73} + 441 q^{74} - 390 q^{76} - 84 q^{77} - 213 q^{78} - 615 q^{79} + 267 q^{80} + 198 q^{81} - 302 q^{82} - 154 q^{83} + 75 q^{84} + 633 q^{85} + 221 q^{86} - 126 q^{87} + 410 q^{88} + 56 q^{89} - 18 q^{90} + 272 q^{91} + 636 q^{92} + 120 q^{93} + 588 q^{95} - 105 q^{96} - 441 q^{97} + 780 q^{98} - 90 q^{99}+O(q^{100}) $ 22 * q + 26 * q^4 - 15 * q^7 - 66 * q^9 + 6 * q^10 + 30 * q^11 - 78 * q^12 - 27 * q^13 + 6 * q^14 - 6 * q^15 - 58 * q^16 - 8 * q^17 + q^19 - 12 * q^20 - 15 * q^21 + 14 * q^22 - q^23 - 56 * q^25 + 71 * q^26 - 75 * q^28 + 42 * q^29 + 18 * q^30 + 120 * q^31 - 105 * q^32 + 30 * q^33 - 24 * q^34 + 3 * q^35 - 78 * q^36 + 13 * q^37 + 108 * q^38 + 27 * q^39 + 82 * q^40 - 159 * q^41 + 189 * q^44 + 372 * q^46 - 35 * q^47 - 174 * q^48 - 40 * q^49 + 285 * q^50 - 24 * q^51 - 212 * q^55 - 113 * q^56 + 3 * q^57 + 136 * q^59 - 12 * q^60 + 63 * q^61 - 150 * q^62 + 45 * q^63 - 284 * q^64 - 20 * q^65 + 94 * q^67 + 154 * q^68 - 3 * q^69 - 41 * q^71 - 16 * q^73 + 441 * q^74 - 390 * q^76 - 84 * q^77 - 213 * q^78 - 615 * q^79 + 267 * q^80 + 198 * q^81 - 302 * q^82 - 154 * q^83 + 75 * q^84 + 633 * q^85 + 221 * q^86 - 126 * q^87 + 410 * q^88 + 56 * q^89 - 18 * q^90 + 272 * q^91 + 636 * q^92 + 120 * q^93 + 588 * q^95 - 105 * q^96 - 441 * q^97 + 780 * q^98 - 90 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	1.57301	+	0.908176i	0.786504	+	0.454088i	0.838730	−	0.544547i	$-0.183298\pi$
$2$	1.57301	+	0.908176i	0.786504	+	0.454088i	−0.0522266	+	0.998635i	$0.516632\pi$
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	−0.350432	−	0.606966i	−0.0876080	−	0.151741i
$5$		−	5.97048i		−	1.19410i	−0.802205	−	0.597048i	$-0.796340\pi$
$5$		−	5.97048i		−	1.19410i	0.802205	−	0.597048i	$-0.203660\pi$
$6$	−1.57301	+	2.72453i	−0.262168	+	0.454088i
$7$	6.73988	−	3.89127i	0.962841	−	0.555896i	0.0657944	−	0.997833i	$-0.479042\pi$
$7$	6.73988	−	3.89127i	0.962841	−	0.555896i	0.897046	+	0.441937i	$0.145709\pi$
$8$		−	8.53843i		−	1.06730i
$9$	−3.00000			−0.333333
$10$	5.42225	−	9.39162i	0.542225	−	0.939162i
$11$	3.44158	−	1.98700i	0.312871	−	0.180636i	−0.335340	−	0.942097i	$-0.608851\pi$
$11$	3.44158	−	1.98700i	0.312871	−	0.180636i	0.648210	+	0.761461i	$0.275518\pi$
$12$	1.05130	−	0.606966i	0.0876080	−	0.0505805i
$13$	4.64727	+	2.68310i	0.357482	+	0.206393i	0.667976	−	0.744183i	$-0.267161\pi$
$13$	4.64727	+	2.68310i	0.357482	+	0.206393i	−0.310493	+	0.950576i	$0.600494\pi$
$14$	14.1358			1.00970
$15$	10.3412			0.689412
$16$	6.35267	−	11.0031i	0.397042	−	0.687696i
$17$	−6.53128	+	11.3125i	−0.384193	+	0.665441i	−0.991657	−	0.128906i	$-0.958854\pi$
$17$	−6.53128	+	11.3125i	−0.384193	+	0.665441i	0.607464	+	0.794347i	$0.292187\pi$
$18$	−4.71902	−	2.72453i	−0.262168	−	0.151363i
$19$	−6.51703	+	11.2878i	−0.343002	+	0.594096i	−0.984989	−	0.172619i	$-0.944777\pi$
$19$	−6.51703	+	11.2878i	−0.343002	+	0.594096i	0.641987	+	0.766715i	$0.278110\pi$
$20$	−3.62388	+	2.09225i	−0.181194	+	0.104612i
$21$	6.73988	+	11.6738i	0.320947	+	0.555896i
$22$	7.21817			0.328099
$23$	14.7763	−	25.5933i	0.642448	−	1.11275i	−0.342437	−	0.939541i	$-0.611252\pi$
$23$	14.7763	−	25.5933i	0.642448	−	1.11275i	0.984885	−	0.173212i	$-0.0554144\pi$
$24$	14.7890			0.616208
$25$	−10.6467			−0.425867
$26$	4.87346	+	8.44108i	0.187441	+	0.324657i
$27$		−	5.19615i		−	0.192450i
$28$	−4.72374	−	2.72725i	−0.168705	−	0.0974019i
$29$	16.8172	+	29.1282i	0.579903	+	1.00442i	0.995490	+	0.0948679i	$0.0302429\pi$
$29$	16.8172	+	29.1282i	0.579903	+	1.00442i	−0.415587	+	0.909553i	$0.636424\pi$
$30$	16.2668	+	9.39162i	0.542225	+	0.313054i
$31$	−24.0841	+	13.9050i	−0.776907	+	0.448548i	−0.835333	−	0.549744i	$-0.814725\pi$
$31$	−24.0841	+	13.9050i	−0.776907	+	0.448548i	0.0584257	+	0.998292i	$0.481392\pi$
$32$	−9.59239	+	5.53817i	−0.299762	+	0.173068i
$33$	3.44158	+	5.96099i	0.104290	+	0.180636i
$34$	−20.5475	+	11.8631i	−0.604338	+	0.348915i
$35$	−23.2328	−	40.2404i	−0.663794	−	1.14972i
$36$	1.05130	+	1.82090i	0.0292027	+	0.0505805i
$37$	2.99353	−	5.18494i	0.0809061	−	0.140133i	−0.822733	−	0.568428i	$-0.807552\pi$
$37$	2.99353	−	5.18494i	0.0809061	−	0.140133i	0.903639	+	0.428294i	$0.140885\pi$
$38$	−20.5027	+	11.8372i	−0.539544	+	0.311506i
$39$	−4.64727	+	8.04931i	−0.119161	+	0.206393i
$40$	−50.9785			−1.27446
$41$	30.7167	−	17.7343i	0.749187	−	0.432543i	−0.0762129	−	0.997092i	$-0.524283\pi$
$41$	30.7167	−	17.7343i	0.749187	−	0.432543i	0.825400	+	0.564548i	$0.190950\pi$
$42$			24.4840i			0.582953i
$43$			35.0077i			0.814132i	0.913399	+	0.407066i	$0.133448\pi$
$43$			35.0077i			0.814132i	−0.913399	+	0.407066i	$0.866552\pi$
$44$	−2.41208	−	1.39261i	−0.0548200	−	0.0316503i
$45$			17.9115i			0.398032i
$46$	46.4865	−	26.8390i	1.01058	−	0.583456i
$47$	−13.1152	−	22.7162i	−0.279046	−	0.483323i	0.692102	−	0.721800i	$-0.256685\pi$
$47$	−13.1152	−	22.7162i	−0.279046	−	0.483323i	−0.971148	+	0.238478i	$0.923352\pi$
$48$	19.0580	+	11.0031i	0.397042	+	0.229232i
$49$	5.78402	−	10.0182i	0.118041	−	0.204453i
$50$	−16.7473	−	9.66906i	−0.334946	−	0.193381i
$51$	−19.5938	−	11.3125i	−0.384193	−	0.221814i
$52$		−	3.76098i		−	0.0723265i
$53$		−	58.9526i		−	1.11231i	−0.831077	−	0.556157i	$-0.812275\pi$
$53$		−	58.9526i		−	1.11231i	0.831077	−	0.556157i	$-0.187725\pi$
$54$	4.71902	−	8.17359i	0.0873893	−	0.151363i
$55$	−11.8633	−	20.5479i	−0.215697	−	0.373598i
$56$	−33.2253	−	57.5480i	−0.593310	−	1.02764i
$57$	−19.5511	−	11.2878i	−0.343002	−	0.198032i
$58$			61.0919i			1.05331i
$59$	−47.4856			−0.804841			−0.402421	−	0.915455i	$-0.631831\pi$
$59$	−47.4856			−0.804841			−0.402421	+	0.915455i	$0.631831\pi$
$60$	−3.62388	−	6.27674i	−0.0603980	−	0.104612i
$61$	60.5107	+	34.9359i	0.991979	+	0.572719i	0.905865	−	0.423566i	$-0.139222\pi$
$61$	60.5107	+	34.9359i	0.991979	+	0.572719i	0.0861137	+	0.996285i	$0.472555\pi$
$62$	−50.5127			−0.814721
$63$	−20.2197	+	11.6738i	−0.320947	+	0.185299i
$64$	−70.9399			−1.10844
$65$	16.0194	−	27.7465i	0.246453	−	0.426869i
$66$			12.5022i			0.189428i
$67$	31.1180	+	59.3352i	0.464448	+	0.885600i
$67$	31.1180	+	59.3352i	0.464448	+	0.885600i
$68$	9.15507			0.134633
$69$	44.3289	+	25.5933i	0.642448	+	0.370917i
$70$		−	84.3979i		−	1.20568i
$71$	31.8812	+	55.2199i	0.449032	+	0.777745i	0.998323	−	0.0578852i	$-0.0184357\pi$
$71$	31.8812	+	55.2199i	0.449032	+	0.777745i	−0.549292	+	0.835631i	$0.685102\pi$
$72$			25.6153i			0.355768i
$73$	−46.7763	+	81.0189i	−0.640771	+	1.10985i	0.344490	+	0.938790i	$0.388052\pi$
$73$	−46.7763	+	81.0189i	−0.640771	+	1.10985i	−0.985261	+	0.171058i	$0.945282\pi$
$74$	9.41767	−	5.43730i	0.127266	−	0.0734770i
$75$		−	18.4406i		−	0.245875i
$76$	9.13510			0.120199
$77$	15.4639	−	26.7843i	0.200830	−	0.347847i
$78$	−14.6204	+	8.44108i	−0.187441	+	0.108219i
$79$	11.8603	−	6.84756i	0.150131	−	0.0866780i	−0.423053	−	0.906105i	$-0.639042\pi$
$79$	11.8603	−	6.84756i	0.150131	−	0.0866780i	0.573184	+	0.819427i	$0.305708\pi$
$80$	−65.6941	−	37.9285i	−0.821176	−	0.474106i
$81$	9.00000			0.111111
$82$	64.4234			0.785651
$83$	−23.3392	+	40.4247i	−0.281195	+	0.487045i	−0.971679	−	0.236303i	$-0.924064\pi$
$83$	−23.3392	+	40.4247i	−0.281195	+	0.487045i	0.690484	+	0.723348i	$0.257398\pi$
$84$	4.72374	−	8.18176i	0.0562350	−	0.0974019i
$85$	67.5411	+	38.9949i	0.794601	+	0.458763i
$86$	−31.7931	+	55.0673i	−0.369687	+	0.640317i
$87$	−50.4516	+	29.1282i	−0.579903	+	0.334807i
$88$	−16.9658	−	29.3857i	−0.192793	−	0.333928i
$89$	−89.7813			−1.00878			−0.504390	−	0.863476i	$-0.668282\pi$
$89$	−89.7813			−1.00878			−0.504390	+	0.863476i	$0.668282\pi$
$90$	−16.2668	+	28.1748i	−0.180742	+	0.313054i
$91$	41.7628			0.458931
$92$	−20.7123			−0.225134
$93$	−24.0841	−	41.7149i	−0.258969	−	0.448548i
$94$		−	47.6436i		−	0.506847i
$95$	67.3938	+	38.9098i	0.709408	+	0.409577i
$96$	−9.59239	−	16.6145i	−0.0999207	−	0.173068i
$97$	−4.03037	−	2.32694i	−0.0415502	−	0.0239890i	0.479081	−	0.877771i	$-0.340970\pi$
$97$	−4.03037	−	2.32694i	−0.0415502	−	0.0239890i	−0.520631	+	0.853782i	$0.674303\pi$
$98$	18.1966	−	10.5058i	0.185680	−	0.107202i
$99$	−10.3247	+	5.96099i	−0.104290	+	0.0602120i
$100$	3.73094	+	6.46217i	0.0373094	+	0.0646217i
$101$	101.207	−	58.4317i	1.00205	−	0.578531i	0.0931926	−	0.995648i	$-0.470293\pi$
$101$	101.207	−	58.4317i	1.00205	−	0.578531i	0.908853	+	0.417117i	$0.136959\pi$
$102$	−20.5475	−	35.5893i	−0.201446	−	0.348915i
$103$	81.5553	+	141.258i	0.791799	+	1.37144i	0.924852	+	0.380328i	$0.124189\pi$
$103$	81.5553	+	141.258i	0.791799	+	1.37144i	−0.133052	+	0.991109i	$0.542478\pi$
$104$	22.9095	−	39.6804i	0.220283	−	0.381542i
$105$	69.6984	−	40.2404i	0.663794	−	0.383242i
$106$	53.5394	−	92.7329i	0.505089	−	0.874839i
$107$	−200.798			−1.87662			−0.938310	−	0.345795i	$-0.887609\pi$
$107$	−200.798			−1.87662			−0.938310	+	0.345795i	$0.887609\pi$
$108$	−3.15389	+	1.82090i	−0.0292027	+	0.0168602i
$109$			162.421i			1.49010i	0.667008	+	0.745050i	$0.267575\pi$
$109$			162.421i			1.49010i	−0.667008	+	0.745050i	$0.732425\pi$
$110$		−	43.0960i		−	0.391782i
$111$	8.98058	+	5.18494i	0.0809061	+	0.0467111i
$112$		−	98.8799i		−	0.882856i
$113$	90.3559	−	52.1670i	0.799610	−	0.461655i	−0.0437251	−	0.999044i	$-0.513923\pi$
$113$	90.3559	−	52.1670i	0.799610	−	0.461655i	0.843335	+	0.537389i	$0.180589\pi$
$114$	−20.5027	−	35.5117i	−0.179848	−	0.311506i
$115$	−152.804	−	88.2217i	−1.32873	−	0.767145i
$116$	11.7866	−	20.4149i	0.101608	−	0.175991i
$117$	−13.9418	−	8.04931i	−0.119161	−	0.0687975i
$118$	−74.6952	−	43.1253i	−0.633011	−	0.365469i
$119$			101.660i			0.854285i
$120$		−	88.2974i		−	0.735812i
$121$	−52.6037	+	91.1123i	−0.434741	+	0.752994i
$122$	63.4559	+	109.909i	0.520130	+	0.900892i
$123$	30.7167	+	53.2028i	0.249729	+	0.432543i
$124$	16.8797	+	9.74550i	0.136127	+	0.0785927i
$125$		−	85.6963i		−	0.685570i
$126$	−42.4075			−0.336568
$127$	−18.6778	−	32.3508i	−0.147069	−	0.254731i	0.783074	−	0.621929i	$-0.213651\pi$
$127$	−18.6778	−	32.3508i	−0.147069	−	0.254731i	−0.930143	+	0.367198i	$0.880317\pi$
$128$	−73.2194	−	42.2732i	−0.572026	−	0.330260i
$129$	−60.6350			−0.470039
$130$	50.3974	−	29.0969i	0.387672	−	0.223822i
$131$	194.713			1.48636			0.743181	−	0.669091i	$-0.233316\pi$
$131$	194.713			1.48636			0.743181	+	0.669091i	$0.233316\pi$
$132$	2.41208	−	4.17784i	0.0182733	−	0.0316503i
$133$			101.438i			0.762693i
$134$	−4.93795	+	121.595i	−0.0368504	+	0.907428i
$135$	−31.0235			−0.229804
$136$	96.5910	+	55.7668i	0.710228	+	0.410050i
$137$		−	109.677i		−	0.800563i	−0.916392	−	0.400281i	$-0.868912\pi$
$137$		−	109.677i		−	0.800563i	0.916392	−	0.400281i	$-0.131088\pi$
$138$	46.4865	+	80.5169i	0.336858	+	0.583456i
$139$		−	44.0031i		−	0.316569i	−0.987394	−	0.158285i	$-0.949404\pi$
$139$		−	44.0031i		−	0.316569i	0.987394	−	0.158285i	$-0.0505964\pi$
$140$	−16.2830	+	28.2030i	−0.116307	+	0.201450i
$141$	39.3455	−	22.7162i	0.279046	−	0.161108i
$142$			115.815i			0.815600i
$143$	21.3253			0.149128
$144$	−19.0580	+	33.0094i	−0.132347	+	0.229232i
$145$	173.910	−	100.407i	1.19938	−	0.692460i
$146$	−147.159	+	84.9622i	−1.00794	+	0.581933i
$147$	17.3521	+	10.0182i	0.118041	+	0.0681511i
$148$	−4.19611			−0.0283521
$149$	163.773			1.09915			0.549575	−	0.835444i	$-0.314790\pi$
$149$	163.773			1.09915			0.549575	+	0.835444i	$0.314790\pi$
$150$	16.7473	−	29.0072i	0.111649	−	0.193381i
$151$	20.6661	−	35.7948i	0.136862	−	0.237051i	−0.789445	−	0.613821i	$-0.789632\pi$
$151$	20.6661	−	35.7948i	0.136862	−	0.237051i	0.926307	+	0.376769i	$0.122965\pi$
$152$	96.3803	+	55.6452i	0.634081	+	0.366087i
$153$	19.5938	−	33.9375i	0.128064	−	0.221814i
$154$	48.6496	−	28.0879i	0.315907	−	0.182389i
$155$	83.0195	+	143.794i	0.535609	+	0.927703i
$156$	6.51421			0.0417577
$157$	99.4113	−	172.185i	0.633193	−	1.09672i	−0.353702	−	0.935358i	$-0.615077\pi$
$157$	99.4113	−	172.185i	0.633193	−	1.09672i	0.986895	−	0.161364i	$-0.0515894\pi$
$158$	24.8752			0.157438
$159$	102.109			0.642195
$160$	33.0655	+	57.2712i	0.206660	+	0.357945i
$161$		−	229.995i		−	1.42854i
$162$	14.1571	+	8.17359i	0.0873893	+	0.0504542i
$163$	−67.4213	−	116.777i	−0.413628	−	0.716424i	0.581656	−	0.813435i	$-0.302405\pi$
$163$	−67.4213	−	116.777i	−0.413628	−	0.716424i	−0.995283	+	0.0970111i	$0.969072\pi$
$164$	−21.5282	−	12.4293i	−0.131270	−	0.0757885i
$165$	35.5900	−	20.5479i	0.215697	−	0.124533i
$166$	−73.4255	+	42.3922i	−0.442322	+	0.255375i
$167$	103.838	+	179.852i	0.621783	+	1.07696i	0.989154	+	0.146885i	$0.0469248\pi$
$167$	103.838	+	179.852i	0.621783	+	1.07696i	−0.367370	+	0.930075i	$0.619742\pi$
$168$	99.6760	−	57.5480i	0.593310	−	0.342548i
$169$	−70.1019	−	121.420i	−0.414804	−	0.718462i
$170$	70.8285	+	122.678i	0.416638	+	0.721638i
$171$	19.5511	−	33.8635i	0.114334	−	0.198032i
$172$	21.2485	−	12.2678i	0.123538	−	0.0713244i
$173$	−33.9070	+	58.7286i	−0.195994	+	0.339472i	−0.947226	−	0.320567i	$-0.896127\pi$
$173$	−33.9070	+	58.7286i	−0.195994	+	0.339472i	0.751232	+	0.660038i	$0.229460\pi$
$174$	−105.814			−0.608128
$175$	−71.7574	+	41.4292i	−0.410042	+	0.236738i
$176$		−	50.4909i		−	0.286880i
$177$		−	82.2475i		−	0.464675i
$178$	−141.227	−	81.5373i	−0.793409	−	0.458075i
$179$		−	206.537i		−	1.15384i	−0.816801	−	0.576919i	$-0.804255\pi$
$179$		−	206.537i		−	1.15384i	0.816801	−	0.576919i	$-0.195745\pi$
$180$	10.8716	−	6.27674i	0.0603980	−	0.0348708i
$181$	−65.6455	−	113.701i	−0.362682	−	0.628184i	0.625719	−	0.780049i	$-0.284806\pi$
$181$	−65.6455	−	113.701i	−0.362682	−	0.628184i	−0.988401	+	0.151864i	$0.951472\pi$
$182$	65.6931	+	37.9279i	0.360951	+	0.208395i
$183$	−60.5107	+	104.808i	−0.330660	+	0.572719i
$184$	−218.527	−	126.166i	−1.18764	−	0.685687i
$185$	−30.9566	−	17.8728i	−0.167333	−	0.0966097i
$186$		−	87.4905i		−	0.470379i
$187$			51.9105i			0.277596i
$188$	−9.19196	+	15.9209i	−0.0488934	+	0.0846858i
$189$	−20.2197	−	35.0215i	−0.106982	−	0.185299i
$190$	70.6739	+	122.411i	0.371968	+	0.644268i
$191$	−176.739	−	102.040i	−0.925334	−	0.534242i	−0.0400012	−	0.999200i	$-0.512736\pi$
$191$	−176.739	−	102.040i	−0.925334	−	0.534242i	−0.885333	+	0.464958i	$0.846070\pi$
$192$		−	122.871i		−	0.639956i
$193$	7.23162			0.0374695			0.0187348	−	0.999824i	$-0.494036\pi$
$193$	7.23162			0.0374695			0.0187348	+	0.999824i	$0.494036\pi$
$194$	−4.22654	−	7.32058i	−0.0217863	−	0.0377349i
$195$	48.0583	+	27.7465i	0.246453	+	0.142290i
$196$	−8.10762			−0.0413654
$197$	2.84991	−	1.64540i	0.0144666	−	0.00835227i	−0.492749	−	0.870171i	$-0.664008\pi$
$197$	2.84991	−	1.64540i	0.0144666	−	0.00835227i	0.507216	+	0.861819i	$0.330675\pi$
$198$	−21.6545			−0.109366
$199$	−125.120	+	216.714i	−0.628742	+	1.08901i	0.359063	+	0.933313i	$0.383096\pi$
$199$	−125.120	+	216.714i	−0.628742	+	1.08901i	−0.987805	+	0.155699i	$0.950237\pi$
$200$			90.9059i			0.454530i
$201$	−102.772	+	53.8980i	−0.511302	+	0.268149i
$202$	212.265			1.05082
$203$	226.692	+	130.881i	1.11671	+	0.644732i
$204$			15.8570i			0.0777306i
$205$	−105.882	−	183.393i	−0.516499	−	0.894602i
$206$			296.266i			1.43819i
$207$	−44.3289	+	76.7799i	−0.214149	+	0.370917i
$208$	59.0451	−	34.0897i	0.283871	−	0.163893i
$209$			51.7973i			0.247834i
$210$	146.181			0.696102
$211$	196.081	−	339.622i	0.929292	−	1.60958i	0.144783	−	0.989463i	$-0.453752\pi$
$211$	196.081	−	339.622i	0.929292	−	1.60958i	0.784509	−	0.620118i	$-0.212915\pi$
$212$	−35.7822	+	20.6589i	−0.168784	+	0.0974476i
$213$	−95.6437	+	55.2199i	−0.449032	+	0.259248i
$214$	−315.857	−	182.360i	−1.47597	−	0.852151i
$215$	209.013			0.972152
$216$	−44.3670			−0.205403
$217$	−108.216	+	187.436i	−0.498692	+	0.863760i
$218$	−147.507	+	255.489i	−0.676637	+	1.17197i
$219$	−140.329	−	81.0189i	−0.640771	−	0.369949i
$220$	−8.31458	+	14.4013i	−0.0377936	+	0.0654604i
$221$	−60.7052	+	35.0482i	−0.274684	+	0.158589i
$222$	9.41767	+	16.3119i	0.0424220	+	0.0734770i
$223$	−39.2391			−0.175960			−0.0879801	−	0.996122i	$-0.528041\pi$
$223$	−39.2391			−0.175960			−0.0879801	+	0.996122i	$0.528041\pi$
$224$	−43.1011	+	74.6532i	−0.192415	+	0.333273i
$225$	31.9401			0.141956
$226$	189.507			0.838528
$227$	203.282	+	352.095i	0.895515	+	1.55108i	0.833166	+	0.553023i	$0.186526\pi$
$227$	203.282	+	352.095i	0.895515	+	1.55108i	0.0623495	+	0.998054i	$0.480141\pi$
$228$			15.8225i			0.0693967i
$229$	−69.5960	−	40.1813i	−0.303913	−	0.175464i	0.340287	−	0.940322i	$-0.389476\pi$
$229$	−69.5960	−	40.1813i	−0.303913	−	0.175464i	−0.644199	+	0.764858i	$0.722809\pi$
$230$	−160.242	−	277.547i	−0.696703	−	1.20672i
$231$	46.3917	+	26.7843i	0.200830	+	0.115949i
$232$	248.709	−	143.592i	1.07202	−	0.618932i
$233$	122.481	−	70.7145i	0.525670	−	0.303496i	−0.213581	−	0.976925i	$-0.568513\pi$
$233$	122.481	−	70.7145i	0.525670	−	0.303496i	0.739252	+	0.673429i	$0.235179\pi$
$234$	−14.6204	−	25.3232i	−0.0624803	−	0.108219i
$235$	−135.626	+	78.3040i	−0.577134	+	0.333208i
$236$	16.6405	+	28.8222i	0.0705105	+	0.122128i
$237$	11.8603	+	20.5427i	0.0500435	+	0.0866780i
$238$	−92.3251	+	159.912i	−0.387921	+	0.671898i
$239$	−288.274	+	166.435i	−1.20617	+	0.696382i	−0.961920	−	0.273331i	$-0.911875\pi$
$239$	−288.274	+	166.435i	−1.20617	+	0.696382i	−0.244249	+	0.969713i	$0.578541\pi$
$240$	65.6941	−	113.786i	0.273725	−	0.474106i
$241$	−418.276			−1.73559			−0.867793	−	0.496925i	$-0.834462\pi$
$241$	−418.276			−1.73559			−0.867793	+	0.496925i	$0.834462\pi$
$242$	−165.492	+	95.5468i	−0.683851	+	0.394822i
$243$			15.5885i			0.0641500i
$244$		−	48.9706i		−	0.200699i
$245$	−59.8136	−	34.5334i	−0.244137	−	0.140953i
$246$			111.585i			0.453596i
$247$	−60.5728	+	34.9717i	−0.245234	+	0.141586i
$248$	118.727	+	205.641i	0.478736	+	0.829196i
$249$	−70.0177	−	40.4247i	−0.281195	−	0.162348i
$250$	77.8273	−	134.801i	0.311309	−	0.539203i
$251$	−236.203	−	136.372i	−0.941046	−	0.543313i	−0.0507579	−	0.998711i	$-0.516164\pi$
$251$	−236.203	−	136.372i	−0.941046	−	0.543313i	−0.890288	+	0.455398i	$0.849497\pi$
$252$	14.1712	+	8.18176i	0.0562350	+	0.0324673i
$253$		−	117.442i		−	0.464197i
$254$		−	67.8508i		−	0.267129i
$255$	−67.5411	+	116.985i	−0.264867	+	0.458763i
$256$	65.0967	+	112.751i	0.254284	+	0.440432i
$257$	10.9172	+	18.9092i	0.0424796	+	0.0735768i	0.886483	−	0.462760i	$-0.153141\pi$
$257$	10.9172	+	18.9092i	0.0424796	+	0.0735768i	−0.844004	+	0.536337i	$0.819808\pi$
$258$	−95.3794	−	55.0673i	−0.369687	−	0.213439i
$259$		−	46.5945i		−	0.179902i
$260$	−22.4549			−0.0863649
$261$	−50.4516	−	87.3847i	−0.193301	−	0.334807i
$262$	306.286	+	176.834i	1.16903	+	0.674939i
$263$	−259.874			−0.988115			−0.494057	−	0.869429i	$-0.664487\pi$
$263$	−259.874			−0.988115			−0.494057	+	0.869429i	$0.664487\pi$
$264$	50.8975	−	29.3857i	0.192793	−	0.111309i
$265$	−351.976			−1.32821
$266$	−92.1237	+	159.563i	−0.346330	+	0.599861i
$267$		−	155.506i		−	0.582419i
$268$	25.1097	−	39.6805i	0.0936929	−	0.148062i
$269$	−401.437			−1.49233			−0.746165	−	0.665761i	$-0.768107\pi$
$269$	−401.437			−1.49233			−0.746165	+	0.665761i	$0.768107\pi$
$270$	−48.8003	−	28.1748i	−0.180742	−	0.104351i
$271$		−	128.921i		−	0.475722i	−0.971299	−	0.237861i	$-0.923554\pi$
$271$		−	128.921i		−	0.475722i	0.971299	−	0.237861i	$-0.0764463\pi$
$272$	82.9821	+	143.729i	0.305081	+	0.528416i
$273$			72.3352i			0.264964i
$274$	99.6061	−	172.523i	0.363526	−	0.629646i
$275$	−36.6414	+	21.1549i	−0.133241	+	0.0769270i
$276$		−	35.8748i		−	0.129981i
$277$	−79.4164			−0.286702			−0.143351	−	0.989672i	$-0.545788\pi$
$277$	−79.4164			−0.286702			−0.143351	+	0.989672i	$0.545788\pi$
$278$	39.9626	−	69.2173i	0.143750	−	0.248983i
$279$	72.2524	−	41.7149i	0.258969	−	0.149516i
$280$	−343.589	+	198.371i	−1.22710	+	0.708469i
$281$	92.9957	+	53.6911i	0.330946	+	0.191072i	0.656261	−	0.754534i	$-0.272137\pi$
$281$	92.9957	+	53.6911i	0.330946	+	0.191072i	−0.325315	+	0.945606i	$0.605470\pi$
$282$	82.5211			0.292628
$283$	−216.343			−0.764464			−0.382232	−	0.924066i	$-0.624844\pi$
$283$	−216.343			−0.764464			−0.382232	+	0.924066i	$0.624844\pi$
$284$	22.3444	−	38.7016i	0.0786775	−	0.136273i
$285$	−67.3938	+	116.729i	−0.236469	+	0.409577i
$286$	33.5448	+	19.3671i	0.117290	+	0.0677172i
$287$	138.018	−	239.054i	0.480899	−	0.832941i
$288$	28.7772	−	16.6145i	0.0999207	−	0.0576893i
$289$	59.1849	+	102.511i	0.204792	+	0.354710i
$290$	364.748			1.25775
$291$	4.03037	−	6.98081i	0.0138501	−	0.0239890i
$292$	65.5676			0.224547
$293$	7.59217			0.0259118			0.0129559	−	0.999916i	$-0.495876\pi$
$293$	7.59217			0.0259118			0.0129559	+	0.999916i	$0.495876\pi$
$294$	18.1966	+	31.5175i	0.0618932	+	0.107202i
$295$			283.512i			0.961058i
$296$	−44.2712	−	25.5600i	−0.149565	−	0.0863513i
$297$	−10.3247	−	17.8830i	−0.0347634	−	0.0602120i
$298$	257.617	+	148.735i	0.864486	+	0.499111i
$299$	137.339	−	79.2927i	0.459328	−	0.265193i
$300$	−11.1928	+	6.46217i	−0.0373094	+	0.0215406i
$301$	136.224	+	235.948i	0.452573	+	0.783879i
$302$	65.0159	−	37.5370i	0.215285	−	0.124295i
$303$	101.207	+	175.295i	0.334015	+	0.578531i
$304$	82.8010	+	143.416i	0.272372	+	0.471762i
$305$	208.584	−	361.278i	0.683882	−	1.18452i
$306$	61.6425	−	35.5893i	0.201446	−	0.116305i
$307$	−263.316	+	456.076i	−0.857706	+	1.48559i	0.0164060	+	0.999865i	$0.494778\pi$
$307$	−263.316	+	456.076i	−0.857706	+	1.48559i	−0.874112	+	0.485725i	$0.838556\pi$
$308$	−21.6762			−0.0703772
$309$	−244.666	+	141.258i	−0.791799	+	0.457146i
$310$			301.585i			0.972856i
$311$			18.2044i			0.0585351i	0.999572	+	0.0292676i	$0.00931749\pi$
$311$			18.2044i			0.0585351i	−0.999572	+	0.0292676i	$0.990683\pi$
$312$	68.7284	+	39.6804i	0.220283	+	0.127181i
$313$		−	397.602i		−	1.27030i	−0.772391	−	0.635148i	$-0.780939\pi$
$313$		−	397.602i		−	1.27030i	0.772391	−	0.635148i	$-0.219061\pi$
$314$	312.749	−	180.566i	0.996017	−	0.575051i
$315$	69.6984	+	120.721i	0.221265	+	0.383242i
$316$	−8.31247	−	4.79921i	−0.0263053	−	0.0151874i
$317$	263.438	−	456.288i	0.831035	−	1.43939i	−0.0661835	−	0.997807i	$-0.521082\pi$
$317$	263.438	−	456.288i	0.831035	−	1.43939i	0.897218	−	0.441587i	$-0.145584\pi$
$318$	160.618	+	92.7329i	0.505089	+	0.291613i
$319$	115.755	+	66.8314i	0.362869	+	0.209503i
$320$			423.545i			1.32358i
$321$		−	347.793i		−	1.08347i
$322$	208.876	−	361.783i	0.648682	−	1.12355i
$323$	−85.1290	−	147.448i	−0.263557	−	0.456495i
$324$	−3.15389	−	5.46269i	−0.00973422	−	0.0168602i
$325$	−49.4780	−	28.5662i	−0.152240	−	0.0878959i
$326$		−	244.922i		−	0.751293i
$327$	−281.321			−0.860310
$328$	−151.423	−	262.272i	−0.461655	−	0.799610i
$329$	−176.790	−	102.070i	−0.537354	−	0.310242i
$330$	74.6444			0.226195
$331$	533.905	−	308.250i	1.61301	−	0.931270i	0.624339	−	0.781154i	$-0.285369\pi$
$331$	533.905	−	308.250i	1.61301	−	0.931270i	0.988668	−	0.150116i	$-0.0479648\pi$
$332$	32.7152			0.0985398
$333$	−8.98058	+	15.5548i	−0.0269687	+	0.0467111i
$334$			377.212i			1.12938i
$335$	354.260	−	185.790i	1.05749	−	0.554596i
$336$	171.265			0.509717
$337$	78.4864	+	45.3141i	0.232897	+	0.134463i	0.611908	−	0.790929i	$-0.290402\pi$
$337$	78.4864	+	45.3141i	0.232897	+	0.134463i	−0.379011	+	0.925392i	$0.623736\pi$
$338$		−	254.660i		−	0.753431i
$339$	90.3559	+	156.501i	0.266537	+	0.461655i
$340$		−	54.6602i		−	0.160765i
$341$	−55.2583	+	95.7102i	−0.162048	+	0.280675i
$342$	61.5080	−	35.5117i	0.179848	−	0.103835i
$343$			291.316i			0.849318i
$344$	298.910			0.868925
$345$	152.804	−	264.665i	0.442911	−	0.767145i
$346$	−106.672	+	61.5870i	−0.308300	+	0.177997i
$347$	−141.075	+	81.4497i	−0.406556	+	0.234725i	−0.689309	−	0.724467i	$-0.742086\pi$
$347$	−141.075	+	81.4497i	−0.406556	+	0.234725i	0.282753	+	0.959193i	$0.408752\pi$
$348$	35.3597	+	20.4149i	0.101608	+	0.0586636i
$349$	−198.838			−0.569738			−0.284869	−	0.958566i	$-0.591950\pi$
$349$	−198.838			−0.569738			−0.284869	+	0.958566i	$0.591950\pi$
$350$	−150.500			−0.430000
$351$	13.9418	−	24.1479i	0.0397203	−	0.0687975i
$352$	−22.0086	+	38.1201i	−0.0625246	+	0.108296i
$353$	67.7369	+	39.1079i	0.191889	+	0.110787i	0.592867	−	0.805301i	$-0.297996\pi$
$353$	67.7369	+	39.1079i	0.191889	+	0.110787i	−0.400977	+	0.916088i	$0.631329\pi$
$354$	74.6952	−	129.376i	0.211004	−	0.365469i
$355$	329.690	−	190.346i	0.928703	−	0.536187i
$356$	31.4622	+	54.4942i	0.0883771	+	0.153074i
$357$	−176.080			−0.493222
$358$	187.572	−	324.884i	0.523944	−	0.907498i
$359$	−518.721			−1.44491			−0.722453	−	0.691420i	$-0.756985\pi$
$359$	−518.721			−1.44491			−0.722453	+	0.691420i	$0.756985\pi$
$360$	152.936			0.424821
$361$	95.5567	+	165.509i	0.264700	+	0.458474i
$362$		−	238.471i		−	0.658759i
$363$	−157.811	−	91.1123i	−0.434741	−	0.250998i
$364$	−14.6350	−	25.3486i	−0.0402061	−	0.0696389i
$365$	483.722	+	279.277i	1.32527	+	0.765142i
$366$	−190.368	+	109.909i	−0.520130	+	0.300297i
$367$	405.751	−	234.260i	1.10559	−	0.638312i	0.167905	−	0.985803i	$-0.446300\pi$
$367$	405.751	−	234.260i	1.10559	−	0.638312i	0.937683	+	0.347492i	$0.112966\pi$
$368$	−187.738	−	325.172i	−0.510157	−	0.883618i
$369$	−92.1500	+	53.2028i	−0.249729	+	0.144181i
$370$	−32.4633	−	56.2281i	−0.0877386	−	0.151968i
$371$	−229.401	−	397.334i	−0.618331	−	1.07098i
$372$	−16.8797	+	29.2365i	−0.0453755	+	0.0785927i
$373$	385.209	−	222.400i	1.03273	−	0.596247i	0.114965	−	0.993370i	$-0.463324\pi$
$373$	385.209	−	222.400i	1.03273	−	0.596247i	0.917766	+	0.397122i	$0.129991\pi$
$374$	−47.1439	+	81.6556i	−0.126053	+	0.218330i
$375$	148.430			0.395814
$376$	−193.960	+	111.983i	−0.515852	+	0.297827i
$377$			180.489i			0.478751i
$378$		−	73.4520i		−	0.194318i
$379$	373.924	+	215.885i	0.986607	+	0.569618i	0.904258	−	0.426986i	$-0.140425\pi$
$379$	373.924	+	215.885i	0.986607	+	0.569618i	0.0823487	+	0.996604i	$0.473758\pi$
$380$		−	54.5410i		−	0.143529i
$381$	56.0333	−	32.3508i	0.147069	−	0.0849103i
$382$	−185.341	−	321.020i	−0.485186	−	0.840366i
$383$	−353.004	−	203.807i	−0.921683	−	0.532134i	−0.0375111	−	0.999296i	$-0.511943\pi$
$383$	−353.004	−	203.807i	−0.921683	−	0.532134i	−0.884171	+	0.467163i	$0.845276\pi$
$384$	73.2194	−	126.820i	0.190675	−	0.330260i
$385$	−159.915	−	92.3270i	−0.415364	−	0.239810i
$386$	11.3754	+	6.56758i	0.0294699	+	0.0170145i
$387$		−	105.023i		−	0.271377i
$388$			3.26173i			0.00840653i
$389$	−8.71981	+	15.1032i	−0.0224160	+	0.0388256i	−0.877016	−	0.480462i	$-0.840469\pi$
$389$	−8.71981	+	15.1032i	−0.0224160	+	0.0388256i	0.854600	+	0.519287i	$0.173802\pi$
$390$	50.3974	+	87.2908i	0.129224	+	0.223822i
$391$	193.016	+	334.314i	0.493648	+	0.855023i
$392$	−85.5398	−	49.3864i	−0.218214	−	0.125986i
$393$			337.253i			0.858151i
$394$	5.97724			0.0151707
$395$	−40.8832	−	70.8118i	−0.103502	−	0.179270i
$396$	7.23624	+	4.17784i	0.0182733	+	0.0105501i
$397$	638.855			1.60921			0.804604	−	0.593812i	$-0.202378\pi$
$397$	638.855			1.60921			0.804604	+	0.593812i	$0.202378\pi$
$398$	−393.628	+	227.261i	−0.989015	+	0.571008i
$399$	−175.696			−0.440341
$400$	−67.6348	+	117.147i	−0.169087	+	0.292867i
$401$		−	604.174i		−	1.50667i	−0.657638	−	0.753334i	$-0.728444\pi$
$401$		−	604.174i		−	1.50667i	0.657638	−	0.753334i	$-0.271556\pi$
$402$	−210.609	−	8.55278i	−0.523904	−	0.0212756i
$403$	−149.234			−0.370308
$404$	−70.9320	−	40.9526i	−0.175574	−	0.101368i
$405$		−	53.7344i		−	0.132677i
$406$	237.725	+	411.752i	0.585530	+	1.01417i
$407$		−	23.7925i		−	0.0584582i
$408$	−96.5910	+	167.300i	−0.236743	+	0.410050i
$409$	6.22090	−	3.59164i	0.0152100	−	0.00878151i	−0.492376	−	0.870383i	$-0.663871\pi$
$409$	6.22090	−	3.59164i	0.0152100	−	0.00878151i	0.507586	+	0.861601i	$0.330538\pi$
$410$		−	384.639i		−	0.938144i
$411$	189.966			0.462205
$412$	57.1592	−	99.0026i	0.138736	−	0.240298i
$413$	−320.048	+	184.780i	−0.774934	+	0.447408i
$414$	−139.459	+	80.5169i	−0.336858	+	0.194485i
$415$	241.355	+	139.346i	0.581579	+	0.335775i
$416$	−59.4379			−0.142880
$417$	76.2157			0.182771
$418$	−47.0410	+	81.4775i	−0.112538	+	0.194922i
$419$	−362.716	+	628.242i	−0.865670	+	1.49938i	0.000710832		1.00000i	$0.499774\pi$
$419$	−362.716	+	628.242i	−0.865670	+	1.49938i	−0.866381	+	0.499384i	$0.833560\pi$
$420$	−48.8491	−	28.2030i	−0.116307	−	0.0671500i
$421$	353.069	−	611.533i	0.838643	−	1.45257i	−0.0523860	−	0.998627i	$-0.516683\pi$
$421$	353.069	−	611.533i	0.838643	−	1.45257i	0.891029	−	0.453946i	$-0.149984\pi$
$422$	616.873	−	356.152i	1.46178	−	0.843961i
$423$	39.3455	+	68.1485i	0.0930155	+	0.161108i
$424$	−503.363			−1.18718
$425$	69.5364	−	120.441i	0.163615	−	0.283390i
$426$	−200.598			−0.470887
$427$	543.780			1.27349
$428$	70.3662	+	121.878i	0.164407	+	0.284761i
$429$			36.9365i			0.0860990i
$430$	328.778	+	189.820i	0.764601	+	0.441443i
$431$	−25.6996	−	44.5131i	−0.0596279	−	0.103279i	0.834671	−	0.550750i	$-0.185658\pi$
$431$	−25.6996	−	44.5131i	−0.0596279	−	0.103279i	−0.894298	+	0.447471i	$0.852325\pi$
$432$	−57.1740	−	33.0094i	−0.132347	−	0.0764107i
$433$	−199.625	+	115.254i	−0.461028	+	0.266175i	−0.712476	−	0.701696i	$-0.752426\pi$
$433$	−199.625	+	115.254i	−0.461028	+	0.266175i	0.251448	+	0.967871i	$0.419093\pi$
$434$	−340.450	+	196.559i	−0.784446	+	0.452900i
$435$	173.910	+	301.220i	0.399792	+	0.692460i
$436$	98.5840	−	56.9175i	0.226110	−	0.130545i
$437$	192.595	+	333.585i	0.440721	+	0.763352i
$438$	−147.159	−	254.887i	−0.335979	−	0.581933i
$439$	−327.564	+	567.357i	−0.746159	+	1.29239i	0.203492	+	0.979077i	$0.434771\pi$
$439$	−327.564	+	567.357i	−0.746159	+	1.29239i	−0.949651	+	0.313309i	$0.898562\pi$
$440$	−175.447	+	101.294i	−0.398742	+	0.230214i
$441$	−17.3521	+	30.0547i	−0.0393471	+	0.0681511i
$442$	−127.320			−0.288054
$443$	6.08326	−	3.51217i	0.0137320	−	0.00792816i	−0.493118	−	0.869962i	$-0.664143\pi$
$443$	6.08326	−	3.51217i	0.0137320	−	0.00792816i	0.506850	+	0.862034i	$0.330810\pi$
$444$		−	7.26787i		−	0.0163691i
$445$			536.038i			1.20458i
$446$	−61.7234	−	35.6360i	−0.138393	−	0.0799014i
$447$			283.664i			0.634595i
$448$	−478.126	+	276.046i	−1.06725	+	0.616175i
$449$	72.6008	+	125.748i	0.161694	+	0.280063i	0.935476	−	0.353389i	$-0.114971\pi$
$449$	72.6008	+	125.748i	0.161694	+	0.280063i	−0.773782	+	0.633452i	$0.781637\pi$
$450$	50.2419	+	29.0072i	0.111649	+	0.0644604i
$451$	70.4759	−	122.068i	0.156266	−	0.270661i
$452$	−63.3272	−	36.5620i	−0.140104	−	0.0808893i
$453$	61.9984	+	35.7948i	0.136862	+	0.0790172i
$454$			738.463i			1.62657i
$455$		−	249.344i		−	0.548009i
$456$	−96.3803	+	166.935i	−0.211360	+	0.366087i
$457$	−368.880	−	638.919i	−0.807178	−	1.39807i	−0.914811	−	0.403882i	$-0.867661\pi$
$457$	−368.880	−	638.919i	−0.807178	−	1.39807i	0.107633	−	0.994191i	$-0.465673\pi$
$458$	−72.9833	−	126.411i	−0.159352	−	0.276006i
$459$	58.7815	+	33.9375i	0.128064	+	0.0739379i
$460$			123.663i			0.268832i
$461$	397.021			0.861217			0.430608	−	0.902539i	$-0.358299\pi$
$461$	397.021			0.861217			0.430608	+	0.902539i	$0.358299\pi$
$462$	48.6496	+	84.2637i	0.105302	+	0.182389i
$463$	−491.510	−	283.774i	−1.06158	−	0.612902i	−0.135709	−	0.990749i	$-0.543331\pi$
$463$	−491.510	−	283.774i	−1.06158	−	0.612902i	−0.925868	+	0.377847i	$0.876665\pi$
$464$	427.336			0.920983
$465$	−249.058	+	143.794i	−0.535609	+	0.309234i
$466$	256.885			0.551255
$467$	−212.678	+	368.369i	−0.455413	+	0.788798i	−0.998712	−	0.0507412i	$-0.983842\pi$
$467$	−212.678	+	368.369i	−0.455413	+	0.788798i	0.543299	+	0.839539i	$0.317175\pi$
$468$			11.2829i			0.0241088i
$469$	440.621	+	278.824i	0.939491	+	0.594507i
$470$	−284.455			−0.605224
$471$	298.234	+	172.185i	0.633193	+	0.365574i
$472$			405.452i			0.859010i
$473$	69.5601	+	120.482i	0.147062	+	0.254718i
$474$			43.0850i			0.0908967i
$475$	69.3847	−	120.178i	0.146073	−	0.253006i
$476$	61.7041	−	35.6249i	0.129630	−	0.0748422i
$477$			176.858i			0.370771i
$478$	−604.610			−1.26487
$479$	−87.0954	+	150.854i	−0.181827	+	0.314934i	−0.942503	−	0.334198i	$-0.891535\pi$
$479$	−87.0954	+	150.854i	−0.181827	+	0.314934i	0.760675	+	0.649132i	$0.224868\pi$
$480$	−99.1966	+	57.2712i	−0.206660	+	0.119315i
$481$	27.8234	−	16.0639i	0.0578450	−	0.0333968i
$482$	−657.952	−	379.869i	−1.36505	−	0.788109i
$483$	398.362			0.824766
$484$	73.7360			0.152347
$485$	−13.8929	+	24.0633i	−0.0286452	+	0.0496150i
$486$	−14.1571	+	24.5208i	−0.0291298	+	0.0504542i
$487$	−514.438	−	297.011i	−1.05634	−	0.609878i	−0.131922	−	0.991260i	$-0.542115\pi$
$487$	−514.438	−	297.011i	−1.05634	−	0.609878i	−0.924418	+	0.381382i	$0.875448\pi$
$488$	298.297	−	516.666i	0.611265	−	1.05874i
$489$	202.264	−	116.777i	0.413628	−	0.238808i
$490$	−62.7248	−	108.643i	−0.128010	−	0.221720i
$491$	−703.546			−1.43288			−0.716442	−	0.697647i	$-0.754231\pi$
$491$	−703.546			−1.43288			−0.716442	+	0.697647i	$0.754231\pi$
$492$	21.5282	−	37.2879i	0.0437565	−	0.0757885i
$493$	−439.351			−0.891178
$494$	−127.042			−0.257170
$495$	35.5900	+	61.6437i	0.0718990	+	0.124533i
$496$			353.335i			0.712369i
$497$	429.752	+	248.117i	0.864692	+	0.499230i
$498$	−73.4255	−	127.177i	−0.147441	−	0.255375i
$499$	−657.565	−	379.645i	−1.31776	−	0.760812i	−0.334396	−	0.942433i	$-0.608532\pi$
$499$	−657.565	−	379.645i	−1.31776	−	0.760812i	−0.983369	+	0.181621i	$0.941866\pi$
$500$	−52.0147	+	30.0307i	−0.104029	+	0.0600614i
$501$	−311.513	+	179.852i	−0.621783	+	0.358987i
$502$	−247.699	−	429.027i	−0.493424	−	0.854636i
$503$	−5.85675	+	3.38140i	−0.0116436	+	0.00672246i	−0.505811	−	0.862645i	$-0.668807\pi$
$503$	−5.85675	+	3.38140i	−0.0116436	+	0.00672246i	0.494167	+	0.869367i	$0.335473\pi$
$504$	99.6760	+	172.644i	0.197770	+	0.342548i
$505$	−348.865	−	604.252i	−0.690822	−	1.19654i
$506$	106.658	−	184.737i	0.210786	−	0.365093i
$507$	210.306	−	121.420i	0.414804	−	0.239487i
$508$	−13.0906	+	22.6735i	−0.0257688	+	0.0446329i
$509$	−225.834			−0.443682			−0.221841	−	0.975083i	$-0.571207\pi$
$509$	−225.834			−0.443682			−0.221841	+	0.975083i	$0.571207\pi$
$510$	−212.485	+	122.678i	−0.416638	+	0.240546i
$511$			728.077i			1.42481i
$512$			574.663i			1.12239i
$513$	58.6533	+	33.8635i	0.114334	+	0.0660107i
$514$			39.6591i			0.0771579i
$515$	843.379	−	486.925i	1.63763	−	0.945485i
$516$	21.2485	+	36.8034i	0.0411792	+	0.0713244i
$517$	−90.2739	−	52.1197i	−0.174611	−	0.100812i
$518$	42.3160	−	73.2935i	0.0816912	−	0.141493i
$519$	−101.721	−	58.7286i	−0.195994	−	0.113157i
$520$	−236.911	−	136.781i	−0.455598	−	0.263040i
$521$		−	714.297i		−	1.37101i	−0.728068	−	0.685505i	$-0.759581\pi$
$521$		−	714.297i		−	1.37101i	0.728068	−	0.685505i	$-0.240419\pi$
$522$		−	183.276i		−	0.351103i
$523$	251.393	−	435.425i	0.480675	−	0.832553i	−0.519079	−	0.854726i	$-0.673725\pi$
$523$	251.393	−	435.425i	0.480675	−	0.832553i	0.999754	+	0.0221728i	$0.00705839\pi$
$524$	−68.2338	−	118.184i	−0.130217	−	0.225543i
$525$	−71.7574	−	124.287i	−0.136681	−	0.236738i
$526$	−408.784	−	236.012i	−0.777156	−	0.448691i
$527$		−	363.269i		−	0.689315i
$528$	87.4528			0.165630
$529$	−172.178	−	298.221i	−0.325479	−	0.563745i
$530$	−553.661	−	319.656i	−1.04464	−	0.603125i
$531$	142.457			0.268280
$532$	61.5695	−	35.5472i	0.115732	−	0.0668180i
$533$	190.332			0.357095
$534$	141.227	−	244.612i	0.264470	−	0.458075i
$535$			1198.86i			2.24087i
$536$	506.629	−	265.699i	0.945204	−	0.495707i
$537$	357.733			0.666169
$538$	−631.463	−	364.575i	−1.17372	−	0.677649i
$539$		−	45.9713i		−	0.0852900i
$540$	10.8716	+	18.8302i	0.0201327	+	0.0348708i
$541$			313.616i			0.579696i	0.957073	+	0.289848i	$0.0936048\pi$
$541$			313.616i			0.579696i	−0.957073	+	0.289848i	$0.906395\pi$
$542$	117.083	−	202.793i	0.216020	−	0.374157i
$543$	196.936	−	113.701i	0.362682	−	0.209395i
$544$		−	144.685i		−	0.265965i
$545$	969.732			1.77932
$546$	−65.6931	+	113.784i	−0.120317	+	0.208395i
$547$	−338.951	+	195.693i	−0.619654	+	0.357757i	−0.776734	−	0.629829i	$-0.783125\pi$
$547$	−338.951	+	195.693i	−0.619654	+	0.357757i	0.157081	+	0.987586i	$0.449792\pi$
$548$	−66.5703	+	38.4344i	−0.121479	+	0.0701357i
$549$	−181.532	−	104.808i	−0.330660	−	0.190906i
$550$	−76.8496			−0.139727
$551$	−438.392			−0.795630
$552$	218.527	−	378.499i	0.395881	−	0.685687i
$553$	53.2914	−	92.3035i	0.0963679	−	0.166914i
$554$	−124.923	−	72.1241i	−0.225492	−	0.130188i
$555$	30.9566	−	53.6184i	0.0557776	−	0.0966097i
$556$	−26.7084	+	15.4201i	−0.0480367	+	0.0277340i
$557$	198.409	+	343.654i	0.356209	+	0.616973i	0.987324	−	0.158717i	$-0.0507356\pi$
$557$	198.409	+	343.654i	0.356209	+	0.616973i	−0.631115	+	0.775690i	$0.717402\pi$
$558$	151.538			0.271574
$559$	−93.9292	+	162.690i	−0.168031	+	0.291038i
$560$	−590.361			−1.05422
$561$	−89.9116			−0.160270
$562$	97.5220	+	168.913i	0.173527	+	0.300557i
$563$			1010.23i			1.79437i	0.441657	+	0.897184i	$0.354391\pi$
$563$			1010.23i			1.79437i	−0.441657	+	0.897184i	$0.645609\pi$
$564$	−27.5759	−	15.9209i	−0.0488934	−	0.0282286i
$565$	−311.462	−	539.468i	−0.551261	−	0.954811i
$566$	−340.310	−	196.478i	−0.601254	−	0.347134i
$567$	60.6590	−	35.0215i	0.106982	−	0.0617662i
$568$	471.491	−	272.216i	0.830090	−	0.479253i
$569$	250.279	+	433.496i	0.439858	+	0.761857i	0.997678	−	0.0681052i	$-0.0216954\pi$
$569$	250.279	+	433.496i	0.439858	+	0.761857i	−0.557820	+	0.829962i	$0.688362\pi$
$570$	−212.022	+	122.411i	−0.371968	+	0.214756i
$571$	181.054	+	313.595i	0.317083	+	0.549204i	0.979878	−	0.199597i	$-0.0639633\pi$
$571$	181.054	+	313.595i	0.317083	+	0.549204i	−0.662795	+	0.748801i	$0.730630\pi$
$572$	−7.47306	−	12.9437i	−0.0130648	−	0.0226289i
$573$	176.739	−	306.121i	0.308445	−	0.534242i
$574$	434.206	−	250.689i	0.756457	−	0.436741i
$575$	−157.319	+	272.484i	−0.273598	+	0.473885i
$576$	212.820			0.369478
$577$	772.349	−	445.916i	1.33856	−	0.772818i	0.351967	−	0.936013i	$-0.385513\pi$
$577$	772.349	−	445.916i	1.33856	−	0.772818i	0.986594	+	0.163194i	$0.0521797\pi$
$578$			215.001i			0.371974i
$579$			12.5255i			0.0216330i
$580$	−121.887	−	70.3715i	−0.210150	−	0.121330i
$581$			363.277i			0.625262i
$582$	12.6796	−	7.32058i	0.0217863	−	0.0125783i
$583$	−117.139	−	202.890i	−0.200924	−	0.348011i
$584$	691.774	+	399.396i	1.18454	+	0.683897i
$585$	−48.0583	+	83.2394i	−0.0821509	+	0.142290i
$586$	11.9425	+	6.89503i	0.0203798	+	0.0117663i
$587$	365.471	+	211.005i	0.622608	+	0.359463i	0.777884	−	0.628408i	$-0.216293\pi$
$587$	365.471	+	211.005i	0.622608	+	0.359463i	−0.155276	+	0.987871i	$0.549627\pi$
$588$		−	14.0428i		−	0.0238823i
$589$		−	362.477i		−	0.615410i
$590$	−257.479	+	445.967i	−0.436405	+	0.755876i
$591$	2.84991	+	4.93619i	0.00482218	+	0.00835227i
$592$	−38.0337	−	65.8764i	−0.0642462	−	0.111278i
$593$	680.170	+	392.696i	1.14700	+	0.662219i	0.948154	−	0.317812i	$-0.102948\pi$
$593$	680.170	+	392.696i	1.14700	+	0.662219i	0.198844	+	0.980031i	$0.436281\pi$
$594$		−	37.5067i		−	0.0631426i
$595$	606.959			1.02010
$596$	−57.3914	−	99.4049i	−0.0962943	−	0.166787i
$597$	−375.359	−	216.714i	−0.628742	−	0.363004i
$598$	288.047			0.481684
$599$	−367.317	+	212.070i	−0.613217	+	0.354041i	−0.774223	−	0.632912i	$-0.781859\pi$
$599$	−367.317	+	212.070i	−0.613217	+	0.354041i	0.161007	+	0.986953i	$0.448526\pi$
$600$	−157.454			−0.262423
$601$	−476.944	+	826.092i	−0.793585	+	1.37453i	0.130149	+	0.991494i	$0.458454\pi$
$601$	−476.944	+	826.092i	−0.793585	+	1.37453i	−0.923734	+	0.383035i	$0.874879\pi$
$602$			494.863i			0.822032i
$603$	−93.3541	−	178.006i	−0.154816	−	0.295200i
$604$	−28.9683			−0.0479607
$605$	543.984	+	314.069i	0.899148	+	0.519123i
$606$			367.654i			0.606689i
$607$	−85.9371	−	148.847i	−0.141577	−	0.245218i	0.786514	−	0.617573i	$-0.211884\pi$
$607$	−85.9371	−	148.847i	−0.141577	−	0.245218i	−0.928091	+	0.372355i	$0.878551\pi$
$608$		−	144.370i		−	0.237450i
$609$	−226.692	+	392.642i	−0.372236	+	0.644732i
$610$	656.209	−	378.862i	1.07575	−	0.621086i
$611$		−	140.758i		−	0.230372i
$612$	−27.4652			−0.0448778
$613$	576.179	−	997.971i	0.939933	−	1.62801i	0.174340	−	0.984685i	$-0.444221\pi$
$613$	576.179	−	997.971i	0.939933	−	1.62801i	0.765592	−	0.643326i	$-0.222446\pi$
$614$	−828.395	+	478.274i	−1.34918	+	0.778948i
$615$	317.647	−	183.393i	0.516499	−	0.298201i
$616$	−228.695	−	132.037i	−0.371259	−	0.214346i
$617$	−346.448			−0.561505			−0.280752	−	0.959780i	$-0.590584\pi$
$617$	−346.448			−0.561505			−0.280752	+	0.959780i	$0.590584\pi$
$618$	−513.149			−0.830338
$619$	75.3971	−	130.592i	0.121805	−	0.210972i	−0.798675	−	0.601763i	$-0.794465\pi$
$619$	75.3971	−	130.592i	0.121805	−	0.210972i	0.920479	+	0.390791i	$0.127799\pi$
$620$	58.1853	−	100.780i	0.0938473	−	0.162548i
$621$	−132.987	−	76.7799i	−0.214149	−	0.123639i
$622$	−16.5328	+	28.6357i	−0.0265801	+	0.0460381i
$623$	−605.116	+	349.364i	−0.971293	+	0.560777i
$624$	59.0451	+	102.269i	0.0946236	+	0.163893i
$625$	−777.815			−1.24450
$626$	361.093	−	625.431i	0.576826	−	0.999092i
$627$	−89.7155			−0.143087
$628$	−139.348			−0.221891
$629$	39.1031	+	67.7285i	0.0621671	+	0.107677i
$630$			253.194i			0.401895i
$631$	10.2189	+	5.89991i	0.0161948	+	0.00935010i	0.508076	−	0.861312i	$-0.330357\pi$
$631$	10.2189	+	5.89991i	0.0161948	+	0.00935010i	−0.491881	+	0.870663i	$0.663690\pi$
$632$	−58.4674	−	101.268i	−0.0925117	−	0.160235i
$633$	588.242	+	339.622i	0.929292	+	0.536527i
$634$	828.780	−	478.496i	1.30722	−	0.754726i
$635$	−193.150	+	111.515i	−0.304173	+	0.175615i
$636$	−35.7822	−	61.9767i	−0.0562614	−	0.0974476i
$637$	53.7598	−	31.0383i	0.0843953	−	0.0487257i
$638$	121.389	+	210.253i	0.190265	+	0.329549i
$639$	−95.6437	−	165.660i	−0.149677	−	0.259248i
$640$	−252.392	+	437.155i	−0.394362	+	0.683055i
$641$	−278.003	+	160.505i	−0.433702	+	0.250398i	−0.700922	−	0.713238i	$-0.747228\pi$
$641$	−278.003	+	160.505i	−0.433702	+	0.250398i	0.267221	+	0.963635i	$0.413895\pi$
$642$	315.857	−	547.081i	0.491990	−	0.852151i
$643$	−10.5656			−0.0164317			−0.00821584	−	0.999966i	$-0.502615\pi$
$643$	−10.5656			−0.0164317			−0.00821584	+	0.999966i	$0.502615\pi$
$644$	−139.599	+	80.5974i	−0.216768	+	0.125151i
$645$			362.021i			0.561272i
$646$		−	309.249i		−	0.478713i
$647$	−373.037	−	215.373i	−0.576563	−	0.332879i	0.183203	−	0.983075i	$-0.441353\pi$
$647$	−373.037	−	215.373i	−0.576563	−	0.332879i	−0.759766	+	0.650196i	$0.774687\pi$
$648$		−	76.8458i		−	0.118589i
$649$	−163.426	+	94.3538i	−0.251811	+	0.145383i
$650$	−51.8862	−	89.8695i	−0.0798249	−	0.138261i
$651$	−324.648	−	187.436i	−0.498692	−	0.287920i
$652$	−47.2531	+	81.8448i	−0.0724741	+	0.125529i
$653$	−32.5889	−	18.8152i	−0.0499064	−	0.0288135i	0.474839	−	0.880073i	$-0.342506\pi$
$653$	−32.5889	−	18.8152i	−0.0499064	−	0.0288135i	−0.524746	+	0.851259i	$0.675840\pi$
$654$	−442.521	−	255.489i	−0.676637	−	0.390657i
$655$		−	1162.53i		−	1.77486i
$656$		−	450.640i		−	0.686951i
$657$	140.329	−	243.057i	0.213590	−	0.369949i
$658$	−185.394	−	321.112i	−0.281754	−	0.488012i
$659$	−205.353	−	355.682i	−0.311613	−	0.539730i	0.667098	−	0.744970i	$-0.267536\pi$
$659$	−205.353	−	355.682i	−0.311613	−	0.539730i	−0.978712	+	0.205239i	$0.934203\pi$
$660$	−24.9437	−	14.4013i	−0.0377936	−	0.0218201i
$661$			603.251i			0.912633i	0.889817	+	0.456317i	$0.150832\pi$
$661$			603.251i			0.912633i	−0.889817	+	0.456317i	$0.849168\pi$
$662$	1119.78			1.69151
$663$	−60.7052	−	105.145i	−0.0915614	−	0.158589i
$664$	345.163	+	199.280i	0.519824	+	0.300121i
$665$	605.635			0.910729
$666$	−28.2530	+	16.3119i	−0.0424220	+	0.0244923i
$667$	993.983			1.49023
$668$	72.7762	−	126.052i	0.108946	−	0.188701i
$669$		−	67.9642i		−	0.101591i
$670$	725.983	+	29.4819i	1.08356	+	0.0440029i
$671$	277.670			0.413815
$672$	−129.303	−	74.6532i	−0.192415	−	0.111091i
$673$			1132.56i			1.68285i	0.540375	+	0.841424i	$0.318282\pi$
$673$			1132.56i			1.68285i	−0.540375	+	0.841424i	$0.681718\pi$
$674$	82.3064	+	142.559i	0.122116	+	0.211512i
$675$			55.3218i			0.0819582i
$676$	−49.1319	+	85.0989i	−0.0726803	+	0.125886i
$677$	573.799	−	331.283i	0.847561	−	0.489340i	−0.0122659	−	0.999925i	$-0.503904\pi$
$677$	573.799	−	331.283i	0.847561	−	0.489340i	0.859827	+	0.510585i	$0.170571\pi$
$678$			328.236i			0.484124i
$679$	−36.2190			−0.0533417
$680$	332.955	−	576.695i	0.489640	−	0.848081i
$681$	−609.846	+	352.095i	−0.895515	+	0.517026i
$682$	−173.843	+	100.369i	−0.254902	+	0.147168i
$683$	1040.04	+	600.466i	1.52275	+	0.879160i	0.999638	+	0.0268947i	$0.00856190\pi$
$683$	1040.04	+	600.466i	1.52275	+	0.879160i	0.523111	+	0.852265i	$0.324771\pi$
$684$	−27.4053			−0.0400662
$685$	−654.825			−0.955950
$686$	−264.566	+	458.242i	−0.385665	+	0.667992i
$687$	69.5960	−	120.544i	0.101304	−	0.175464i
$688$	385.194	+	222.392i	0.559875	+	0.323244i
$689$	158.176	−	273.969i	0.229573	−	0.397633i
$690$	480.725	−	277.547i	0.696703	−	0.402242i
$691$	191.110	+	331.012i	0.276570	+	0.479033i	0.970530	−	0.240980i	$-0.0774690\pi$
$691$	191.110	+	331.012i	0.276570	+	0.479033i	−0.693960	+	0.720013i	$0.744136\pi$
$692$	47.5283			0.0686826
$693$	−46.3917	+	80.3528i	−0.0669433	+	0.115949i
$694$	−295.883			−0.426344
$695$	−262.720			−0.378014
$696$	248.709	+	430.777i	0.357341	+	0.618932i
$697$			463.310i			0.664720i
$698$	−312.774	−	180.580i	−0.448101	−	0.258711i
$699$	122.481	+	212.144i	0.175223	+	0.303496i
$700$	50.2922	+	29.0362i	0.0718460	+	0.0414803i
$701$	−1052.86	+	607.866i	−1.50193	+	0.867141i	−0.501935	+	0.864905i	$0.667379\pi$
$701$	−1052.86	+	607.866i	−1.50193	+	0.867141i	−0.999997	+	0.00223635i	$0.999288\pi$
$702$	43.8612	−	25.3232i	0.0624803	−	0.0360730i
$703$	39.0178	+	67.5808i	0.0555018	+	0.0961320i
$704$	−244.145	+	140.957i	−0.346797	+	0.200223i
$705$	−135.626	−	234.912i	−0.192378	−	0.333208i
$706$	71.0338	+	123.034i	0.100614	+	0.174269i
$707$	454.747	−	787.645i	0.643207	−	1.11407i
$708$	−49.9214	+	28.8222i	−0.0705105	+	0.0407093i
$709$	662.360	−	1147.24i	0.934217	−	1.61811i	0.158194	−	0.987408i	$-0.449433\pi$
$709$	662.360	−	1147.24i	0.934217	−	1.61811i	0.776024	−	0.630704i	$-0.217234\pi$
$710$	691.472			0.973905
$711$	−35.5810	+	20.5427i	−0.0500435	+	0.0288927i
$712$			766.591i			1.07667i
$713$			821.857i			1.15267i
$714$	−276.975	−	159.912i	−0.387921	−	0.223966i
$715$		−	127.322i		−	0.178073i
$716$	−125.361	+	72.3772i	−0.175085	+	0.101085i
$717$	−288.274	−	499.306i	−0.402056	−	0.696382i
$718$	−815.952	−	471.090i	−1.13642	−	0.656115i
$719$	177.394	−	307.255i	0.246723	−	0.427337i	−0.715892	−	0.698211i	$-0.753980\pi$
$719$	177.394	−	307.255i	0.246723	−	0.427337i	0.962615	+	0.270875i	$0.0873129\pi$
$720$	197.082	+	113.786i	0.273725	+	0.158035i
$721$	1099.35	+	634.708i	1.52475	+	0.880317i
$722$			347.129i			0.480788i
$723$		−	724.476i		−	1.00204i
$724$	−46.0086	+	79.6892i	−0.0635477	+	0.110068i
$725$	−179.047	−	310.119i	−0.246962	−	0.427750i
$726$	−165.492	−	286.641i	−0.227950	−	0.394822i
$727$	−175.613	−	101.390i	−0.241558	−	0.139463i	0.374335	−	0.927294i	$-0.377871\pi$
$727$	−175.613	−	101.390i	−0.241558	−	0.139463i	−0.615893	+	0.787830i	$0.711204\pi$
$728$		−	356.588i		−	0.489819i
$729$	−27.0000			−0.0370370
$730$	507.265	+	878.609i	0.694884	+	1.20357i
$731$	−396.024	−	228.645i	−0.541757	−	0.312783i
$732$	84.8195			0.115874
$733$	−420.054	+	242.518i	−0.573062	+	0.330857i	−0.758371	−	0.651823i	$-0.774005\pi$
$733$	−420.054	+	242.518i	−0.573062	+	0.330857i	0.185310	+	0.982680i	$0.440671\pi$
$734$	850.999			1.15940
$735$	59.8136	−	103.600i	0.0813791	−	0.140953i
$736$			327.335i			0.444748i
$737$	224.994	+	142.375i	0.305284	+	0.193182i
$738$	−193.270			−0.261884
$739$	−592.509	−	342.085i	−0.801771	−	0.462903i	0.0423190	−	0.999104i	$-0.486525\pi$
$739$	−592.509	−	342.085i	−0.801771	−	0.462903i	−0.844090	+	0.536201i	$0.819859\pi$
$740$			25.0528i			0.0338551i
$741$	−60.5728	−	104.915i	−0.0817447	−	0.141586i
$742$		−	833.346i		−	1.12311i
$743$	279.710	−	484.472i	0.376460	−	0.652048i	−0.614084	−	0.789240i	$-0.710475\pi$
$743$	279.710	−	484.472i	0.376460	−	0.652048i	0.990544	+	0.137192i	$0.0438079\pi$
$744$	−356.180	+	205.641i	−0.478736	+	0.276399i
$745$		−	977.806i		−	1.31249i
$746$	807.915			1.08300
$747$	70.0177	−	121.274i	0.0937318	−	0.162348i
$748$	31.5079	−	18.1911i	0.0421229	−	0.0243196i
$749$	−1353.36	+	781.361i	−1.80689	+	1.04321i
$750$	233.482	+	134.801i	0.311309	+	0.179734i
$751$	−546.411			−0.727577			−0.363789	−	0.931482i	$-0.618517\pi$
$751$	−546.411			−0.727577			−0.363789	+	0.931482i	$0.618517\pi$
$752$	−333.266			−0.443172
$753$	236.203	−	409.115i	0.313682	−	0.543313i
$754$	−163.916	+	283.911i	−0.217395	+	0.376539i
$755$	−213.712	−	123.387i	−0.283062	−	0.163426i
$756$	−14.1712	+	24.5453i	−0.0187450	+	0.0324673i
$757$	−954.770	+	551.237i	−1.26125	+	0.728186i	−0.973317	−	0.229463i	$-0.926303\pi$
$757$	−954.770	+	551.237i	−1.26125	+	0.728186i	−0.287938	+	0.957649i	$0.592970\pi$
$758$	392.124	+	679.178i	0.517313	+	0.896013i
$759$	203.415			0.268004
$760$	332.229	−	575.437i	0.437143	−	0.757154i
$761$	−716.305			−0.941268			−0.470634	−	0.882329i	$-0.655975\pi$
$761$	−716.305			−0.941268			−0.470634	+	0.882329i	$0.655975\pi$
$762$	117.521			0.154227
$763$	632.025	+	1094.70i	0.828342	+	1.43473i
$764$			143.033i			0.187215i
$765$	−202.623	−	116.985i	−0.264867	−	0.152921i
$766$	−370.186	−	641.180i	−0.483271	−	0.837050i
$767$	−220.679	−	127.409i	−0.287717	−	0.166113i
$768$	−195.290	+	112.751i	−0.254284	+	0.146811i
$769$	910.596	−	525.733i	1.18413	−	0.683658i	0.227163	−	0.973857i	$-0.427055\pi$
$769$	910.596	−	525.733i	1.18413	−	0.683658i	0.956966	+	0.290199i	$0.0937215\pi$
$770$	−167.698	−	290.462i	−0.217790	−	0.377223i
$771$	−32.7517	+	18.9092i	−0.0424796	+	0.0245256i
$772$	−2.53419	−	4.38935i	−0.00328263	−	0.00568568i
$773$	272.646	+	472.237i	0.352712	+	0.610915i	0.986724	−	0.162408i	$-0.0519262\pi$
$773$	272.646	+	472.237i	0.352712	+	0.610915i	−0.634012	+	0.773324i	$0.718593\pi$
$774$	95.3794	−	165.202i	0.123229	−	0.213439i
$775$	256.416	−	148.042i	0.330860	−	0.191022i
$776$	−19.8684	+	34.4130i	−0.0256036	+	0.0443467i
$777$	80.7040			0.103866
$778$	−27.4327	+	15.8383i	−0.0352605	+	0.0203577i
$779$			462.299i			0.593452i
$780$		−	38.8930i		−	0.0498628i
$781$	219.444	+	126.696i	0.280978	+	0.162223i
$782$			701.171i			0.896638i
$783$	151.355	−	87.3847i	0.193301	−	0.111602i
$784$	−73.4879	−	127.285i	−0.0937346	−	0.162353i
$785$	−1028.03	−	593.534i	−1.30959	−	0.756094i
$786$	−306.286	+	530.502i	−0.389676	+	0.674939i
$787$	534.507	+	308.598i	0.679170	+	0.392119i	0.799542	−	0.600610i	$-0.205075\pi$
$787$	534.507	+	308.598i	0.679170	+	0.392119i	−0.120372	+	0.992729i	$0.538409\pi$
$788$	−1.99740	−	1.15320i	−0.00253477	−	0.00146345i
$789$		−	450.115i		−	0.570488i
$790$		−	148.517i		−	0.187996i
$791$	405.992	−	703.199i	0.513264	−	0.889000i
$792$	50.8975	+	88.1570i	0.0642645	+	0.111309i
$793$	187.473	+	324.713i	0.236410	+	0.409474i
$794$	1004.92	+	580.193i	1.26565	+	0.730722i
$795$		−	609.640i		−	0.766843i
$796$	175.384			0.220331
$797$	−72.0672	−	124.824i	−0.0904231	−	0.156617i	0.817266	−	0.576260i	$-0.195489\pi$
$797$	−72.0672	−	124.824i	−0.0904231	−	0.156617i	−0.907689	+	0.419643i	$0.862155\pi$
$798$	−276.371	−	159.563i	−0.346330	−	0.199954i
$799$	342.636			0.428830
$800$	102.127	−	58.9631i	0.127659	−	0.0737039i
$801$	269.344			0.336260
$802$	548.696	−	950.370i	0.684160	−	1.18500i
$803$			371.777i			0.462985i
$804$	68.7287	+	43.4913i	0.0854835	+	0.0540936i
$805$	−1373.18			−1.70581
$806$	−234.746	−	135.531i	−0.291248	−	0.168152i
$807$		−	695.309i		−	0.861597i
$808$	−498.914	−	864.145i	−0.617468	−	1.06949i
$809$			1450.05i			1.79240i	0.443649	+	0.896201i	$0.353684\pi$
$809$			1450.05i			1.79240i	−0.443649	+	0.896201i	$0.646316\pi$
$810$	48.8003	−	84.5245i	0.0602472	−	0.104351i
$811$	177.288	−	102.357i	0.218604	−	0.126211i	−0.386700	−	0.922206i	$-0.626385\pi$
$811$	177.288	−	102.357i	0.218604	−	0.126211i	0.605304	+	0.795995i	$0.293052\pi$
$812$		−	183.459i		−	0.225935i
$813$	223.297			0.274658
$814$	21.6078	−	37.4258i	0.0265452	−	0.0459776i
$815$	−697.216	+	402.538i	−0.855480	+	0.493911i
$816$	−248.946	+	143.729i	−0.305081	+	0.176139i
$817$	−395.160	−	228.146i	−0.483672	−	0.279248i
$818$	13.0474			0.0159503
$819$	−125.288			−0.152977
$820$	−74.2090	+	128.534i	−0.0904988	+	0.156749i
$821$	238.987	−	413.937i	0.291092	−	0.504186i	−0.682976	−	0.730441i	$-0.739315\pi$
$821$	238.987	−	413.937i	0.291092	−	0.504186i	0.974068	+	0.226254i	$0.0726481\pi$
$822$	298.818	+	172.523i	0.363526	+	0.209882i
$823$	514.077	−	890.408i	0.624638	−	1.08191i	−0.363972	−	0.931410i	$-0.618580\pi$
$823$	514.077	−	890.408i	0.624638	−	1.08191i	0.988611	−	0.150496i	$-0.0480869\pi$
$824$	1206.12	−	696.354i	1.46374	−	0.845090i
$825$	−36.6414	−	63.4648i	−0.0444138	−	0.0769270i
$826$	−671.250			−0.812651
$827$	−114.329	+	198.024i	−0.138245	+	0.239448i	−0.926833	−	0.375475i	$-0.877480\pi$
$827$	−114.329	+	198.024i	−0.138245	+	0.239448i	0.788587	+	0.614923i	$0.210813\pi$
$828$	62.1370			0.0750447
$829$	−194.136			−0.234181			−0.117091	−	0.993121i	$-0.537357\pi$
$829$	−194.136			−0.234181			−0.117091	+	0.993121i	$0.537357\pi$
$830$	253.102	+	438.386i	0.304942	+	0.528176i
$831$		−	137.553i		−	0.165527i
$832$	−329.677	−	190.339i	−0.396246	−	0.228773i
$833$	75.5541	+	130.864i	0.0907012	+	0.157099i
$834$	119.888	+	69.2173i	0.143750	+	0.0829943i
$835$	1073.81	−	619.962i	1.28599	−	0.742469i
$836$	31.4392	−	18.1514i	0.0376067	−	0.0217122i
$837$	72.2524	+	125.145i	0.0863231	+	0.149516i
$838$	−1141.11	+	658.819i	−1.36170	+	0.786181i
$839$	−181.058	−	313.602i	−0.215803	−	0.373781i	0.737718	−	0.675109i	$-0.235903\pi$
$839$	−181.058	−	313.602i	−0.215803	−	0.373781i	−0.953521	+	0.301328i	$0.902570\pi$
$840$	−343.589	−	595.114i	−0.409035	−	0.708469i
$841$	−145.135	+	251.382i	−0.172575	+	0.298909i
$842$	1110.76	−	641.297i	1.31919	−	0.761636i
$843$	−92.9957	+	161.073i	−0.110315	+	0.191072i
$844$	−274.852			−0.325654
$845$	−724.937	+	418.542i	−0.857913	+	0.495316i
$846$			142.931i			0.168949i
$847$			818.781i			0.966684i
$848$	−648.664	−	374.506i	−0.764934	−	0.441635i
$849$		−	374.717i		−	0.441363i
$850$	218.763	−	126.303i	0.257368	−	0.148591i
$851$	−88.4665	−	153.228i	−0.103956	−	0.180057i
$852$	67.0332	+	38.7016i	0.0786775	+	0.0454245i
$853$	−230.648	+	399.494i	−0.270396	+	0.468340i	−0.968963	−	0.247205i	$-0.920488\pi$
$853$	−230.648	+	399.494i	−0.270396	+	0.468340i	0.698567	+	0.715544i	$0.253821\pi$
$854$	855.370	+	493.848i	1.00160	+	0.578277i
$855$	−202.181	−	116.729i	−0.236469	−	0.136526i
$856$			1714.50i			2.00292i
$857$		−	590.535i		−	0.689072i	−0.938773	−	0.344536i	$-0.888036\pi$
$857$		−	590.535i		−	0.689072i	0.938773	−	0.344536i	$-0.111964\pi$
$858$	−33.5448	+	58.1013i	−0.0390965	+	0.0677172i
$859$	−55.0647	−	95.3749i	−0.0641033	−	0.111030i	0.832193	−	0.554487i	$-0.187085\pi$
$859$	−55.0647	−	95.3749i	−0.0641033	−	0.111030i	−0.896296	+	0.443457i	$0.853752\pi$
$860$	−73.2447	−	126.864i	−0.0851683	−	0.147516i
$861$	414.054	+	239.054i	0.480899	+	0.277647i
$862$		−	93.3592i		−	0.108305i
$863$	−1002.74			−1.16192			−0.580959	−	0.813933i	$-0.697322\pi$
$863$	−1002.74			−1.16192			−0.580959	+	0.813933i	$0.697322\pi$
$864$	28.7772	+	49.8435i	0.0333069	+	0.0576893i
$865$	350.638	+	202.441i	0.405362	+	0.234036i
$866$	−418.682			−0.483467
$867$	−177.555	+	102.511i	−0.204792	+	0.118237i
$868$	151.690			0.174758
$869$	27.2122	−	47.1328i	0.0313143	−	0.0542380i
$870$			631.762i			0.726163i
$871$	−14.5886	+	359.240i	−0.0167493	+	0.412445i
$872$	1386.82			1.59039
$873$	12.0911	+	6.98081i	0.0138501	+	0.00799635i
$874$			699.641i			0.800505i
$875$	−333.468	−	577.583i	−0.381106	−	0.660095i
$876$			113.566i			0.129642i
$877$	436.252	−	755.611i	0.497437	−	0.861586i	−0.502559	−	0.864543i	$-0.667608\pi$
$877$	436.252	−	755.611i	0.497437	−	0.861586i	0.999996	+	0.00295715i	$0.000941292\pi$
$878$	−1030.52	+	594.972i	−1.17371	+	0.677644i
$879$			13.1500i			0.0149602i
$880$	−301.455			−0.342563
$881$	205.875	−	356.586i	0.233683	−	0.404751i	−0.725206	−	0.688532i	$-0.758255\pi$
$881$	205.875	−	356.586i	0.233683	−	0.404751i	0.958889	+	0.283781i	$0.0915888\pi$
$882$	−54.5898	+	31.5175i	−0.0618932	+	0.0357341i
$883$	84.9757	−	49.0607i	0.0962352	−	0.0555614i	−0.451110	−	0.892468i	$-0.648972\pi$
$883$	84.9757	−	49.0607i	0.0962352	−	0.0555614i	0.547345	+	0.836907i	$0.315638\pi$
$884$	42.5461	+	24.5640i	0.0481291	+	0.0277873i
$885$	−491.058			−0.554867
$886$	12.7587			0.0144003
$887$	−369.026	+	639.171i	−0.416038	+	0.720599i	−0.995537	−	0.0943744i	$-0.969915\pi$
$887$	−369.026	+	639.171i	−0.416038	+	0.720599i	0.579499	+	0.814973i	$0.303248\pi$
$888$	44.2712	−	76.6800i	0.0498550	−	0.0863513i
$889$	−251.772	−	145.361i	−0.283208	−	0.163510i
$890$	−486.817	+	843.192i	−0.546985	+	0.947407i
$891$	30.9742	−	17.8830i	0.0347634	−	0.0200707i
$892$	13.7506	+	23.8168i	0.0154155	+	0.0267005i
$893$	341.888			0.382853
$894$	−257.617	+	446.205i	−0.288162	+	0.499111i
$895$	−1233.13			−1.37779
$896$	−657.987			−0.734360
$897$	137.339	+	237.878i	0.153109	+	0.265193i
$898$			263.737i			0.293694i
$899$	−810.055	−	467.685i	−0.901062	−	0.520228i
$900$	−11.1928	−	19.3865i	−0.0124365	−	0.0215406i
$901$	666.902	+	385.036i	0.740180	+	0.427343i
$902$	221.718	−	128.009i	0.245807	−	0.141917i
$903$	−408.673	+	235.948i	−0.452573	+	0.261293i
$904$	−445.424	−	771.497i	−0.492726	−	0.853426i
$905$	−678.852	+	391.935i	−0.750113	+	0.433078i
$906$	65.0159	+	112.611i	0.0717615	+	0.124295i
$907$	138.052	+	239.112i	0.152207	+	0.263630i	0.932038	−	0.362359i	$-0.118029\pi$
$907$	138.052	+	239.112i	0.152207	+	0.263630i	−0.779832	+	0.625989i	$0.784695\pi$
$908$	142.473	−	246.770i	0.156909	−	0.271774i
$909$	−303.620	+	175.295i	−0.334015	+	0.192844i
$910$	226.448	−	392.220i	0.248844	−	0.431011i
$911$	−885.726			−0.972256			−0.486128	−	0.873888i	$-0.661591\pi$
$911$	−885.726			−0.972256			−0.486128	+	0.873888i	$0.661591\pi$
$912$	−248.403	+	143.416i	−0.272372	+	0.157254i
$913$			185.500i			0.203176i
$914$		−	1340.03i		−	1.46612i
$915$	625.752	+	361.278i	0.683882	+	0.394840i
$916$			56.3232i			0.0614882i
$917$	1312.35	−	757.683i	1.43113	−	0.826263i
$918$	61.6425	+	106.768i	0.0671487	+	0.116305i
$919$	−836.759	−	483.103i	−0.910510	−	0.525683i	−0.0299149	−	0.999552i	$-0.509524\pi$
$919$	−836.759	−	483.103i	−0.910510	−	0.525683i	−0.880595	+	0.473869i	$0.842857\pi$
$920$	−753.274	+	1304.71i	−0.818776	+	1.41816i
$921$	−789.947	−	456.076i	−0.857706	−	0.495197i
$922$	624.517	+	360.565i	0.677350	+	0.391068i
$923$			342.163i			0.370707i
$924$		−	37.5442i		−	0.0406323i
$925$	−31.8711	+	55.2024i	−0.0344553	+	0.0596783i
$926$	−515.433	−	892.756i	−0.556623	−	0.964099i
$927$	−244.666	−	423.774i	−0.263933	−	0.457146i
$928$	−322.634	−	186.273i	−0.347666	−	0.200725i
$929$		−	1416.22i		−	1.52446i	−0.647305	−	0.762231i	$-0.724104\pi$
$929$		−	1416.22i		−	1.52446i	0.647305	−	0.762231i	$-0.275896\pi$
$930$	−522.361			−0.561678
$931$	75.3893	+	130.578i	0.0809767	+	0.140256i
$932$	−85.8426	−	49.5613i	−0.0921058	−	0.0531773i
$933$	−31.5310			−0.0337953
$934$	−669.087	+	386.298i	−0.716368	+	0.413595i
$935$	309.931			0.331477
$936$	−68.7284	+	119.041i	−0.0734278	+	0.127181i
$937$			1323.45i			1.41244i	0.707994	+	0.706219i	$0.249600\pi$
$937$			1323.45i			1.41244i	−0.707994	+	0.706219i	$0.750400\pi$
$938$	439.880	+	838.754i	0.468955	+	0.894194i
$939$	688.668			0.733405
$940$	95.0557	+	54.8804i	0.101123	+	0.0583834i
$941$			1567.20i			1.66547i	0.553675	+	0.832733i	$0.313225\pi$
$941$			1567.20i			1.66547i	−0.553675	+	0.832733i	$0.686775\pi$
$942$	312.749	+	541.698i	0.332006	+	0.575051i
$943$		−	1048.19i		−	1.11155i
$944$	−301.660	+	522.491i	−0.319556	+	0.553486i
$945$	−209.095	+	120.721i	−0.221265	+	0.127747i
$946$			252.691i			0.267116i
$947$	−136.791			−0.144447			−0.0722234	−	0.997388i	$-0.523009\pi$
$947$	−136.791			−0.144447			−0.0722234	+	0.997388i	$0.523009\pi$
$948$	8.31247	−	14.3976i	0.00876843	−	0.0151874i
$949$	−434.764	+	251.011i	−0.458129	+	0.264501i
$950$	218.285	−	126.027i	0.229774	−	0.132660i
$951$	790.314	+	456.288i	0.831035	+	0.479798i
$952$	868.016			0.911781
$953$	−110.171			−0.115605			−0.0578023	−	0.998328i	$-0.518409\pi$
$953$	−110.171			−0.115605			−0.0578023	+	0.998328i	$0.518409\pi$
$954$	−160.618	+	278.199i	−0.168363	+	0.291613i
$955$	−609.229	+	1055.22i	−0.637937	+	1.10494i
$956$	202.041	+	116.648i	0.211340	+	0.122017i
$957$	−115.755	+	200.494i	−0.120956	+	0.209503i
$958$	−274.003	+	158.196i	−0.286016	+	0.165131i
$959$	−426.784	−	739.211i	−0.445030	−	0.770814i
$960$	−733.602			−0.764169
$961$	−93.8031	+	162.472i	−0.0976098	+	0.169065i
$962$	58.3553			0.0606604
$963$	602.395			0.625540
$964$	146.577	+	253.879i	0.152051	+	0.263360i
$965$		−	43.1763i		−	0.0447422i
$966$	626.627	+	361.783i	0.648682	+	0.374517i
$967$	210.205	+	364.086i	0.217379	+	0.376511i	0.954006	−	0.299788i	$-0.0969161\pi$
$967$	210.205	+	364.086i	0.217379	+	0.376511i	−0.736627	+	0.676299i	$0.763583\pi$
$968$	777.955	+	449.153i	0.803673	+	0.464001i
$969$	255.387	−	147.448i	0.263557	−	0.152165i
$970$	−43.7074	+	25.2345i	−0.0450592	+	0.0260149i
$971$	−624.917	−	1082.39i	−0.643581	−	1.11472i	−0.984627	−	0.174669i	$-0.944114\pi$
$971$	−624.917	−	1082.39i	−0.643581	−	1.11472i	0.341046	−	0.940047i	$-0.389219\pi$
$972$	9.46166	−	5.46269i	0.00973422	−	0.00562005i
$973$	−171.228	−	296.576i	−0.175980	−	0.304806i
$974$	−539.476	−	934.400i	−0.553877	−	0.959343i
$975$	49.4780	−	85.6985i	0.0507467	−	0.0878959i
$976$	768.809	−	443.872i	0.787714	−	0.454787i
$977$	−126.492	+	219.091i	−0.129470	+	0.224249i	−0.923471	−	0.383667i	$-0.874661\pi$
$977$	−126.492	+	219.091i	−0.129470	+	0.224249i	0.794001	+	0.607916i	$0.207994\pi$
$978$	424.217			0.433759
$979$	−308.990	+	178.395i	−0.315618	+	0.182222i
$980$			48.4064i			0.0493943i
$981$		−	487.263i		−	0.496700i
$982$	−1106.68	−	638.944i	−1.12697	−	0.650656i
$983$			874.747i			0.889875i	0.895562	+	0.444937i	$0.146774\pi$
$983$			874.747i			0.889875i	−0.895562	+	0.444937i	$0.853226\pi$
$984$	454.269	−	262.272i	0.461655	−	0.266537i
$985$	−9.82381	−	17.0153i	−0.00997342	−	0.0172745i
$986$	−691.102	−	399.008i	−0.700915	−	0.404673i
$987$	176.790	−	306.209i	0.179118	−	0.310242i
$988$	42.4533	+	24.5104i	0.0429689	+	0.0248081i
$989$	895.962	+	517.284i	0.905927	+	0.523037i
$990$			129.288i			0.130594i
$991$		−	537.549i		−	0.542431i	−0.962519	−	0.271216i	$-0.912574\pi$
$991$		−	537.549i		−	0.542431i	0.962519	−	0.271216i	$-0.0874256\pi$
$992$	154.016	−	266.764i	0.155258	−	0.268915i
$993$	533.905	+	924.751i	0.537669	+	0.931270i
$994$	450.668	+	780.581i	0.453389	+	0.785292i
$995$	1293.88	+	747.025i	1.30039	+	0.750779i
$996$			56.6644i			0.0568920i
$997$	172.805			0.173325			0.0866627	−	0.996238i	$-0.472380\pi$
$997$	172.805			0.173325			0.0866627	+	0.996238i	$0.472380\pi$
$998$	−689.569	−	1194.37i	−0.690951	−	1.19676i
$999$	−26.9417	−	15.5548i	−0.0269687	−	0.0155704i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.h.a.172.8	yes	22
67.30	odd	6	inner	201.3.h.a.97.8	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.h.a.97.8	✓	22	67.30	odd	6	inner
201.3.h.a.172.8	yes	22	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(1.57301 + 0.908176i) q^{2} +1.73205i q^{3} +(-0.350432 - 0.606966i) q^{4} -5.97048i q^{5} +(-1.57301 + 2.72453i) q^{6} +(6.73988 - 3.89127i) q^{7} -8.53843i q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(1.57301 + 0.908176i) q^{2} +1.73205i q^{3} +(-0.350432 - 0.606966i) q^{4} -5.97048i q^{5} +(-1.57301 + 2.72453i) q^{6} +(6.73988 - 3.89127i) q^{7} -8.53843i q^{8} -3.00000 q^{9} +(5.42225 - 9.39162i) q^{10} +(3.44158 - 1.98700i) q^{11} +(1.05130 - 0.606966i) q^{12} +(4.64727 + 2.68310i) q^{13} +14.1358 q^{14} +10.3412 q^{15} +(6.35267 - 11.0031i) q^{16} +(-6.53128 + 11.3125i) q^{17} +(-4.71902 - 2.72453i) q^{18} +(-6.51703 + 11.2878i) q^{19} +(-3.62388 + 2.09225i) q^{20} +(6.73988 + 11.6738i) q^{21} +7.21817 q^{22} +(14.7763 - 25.5933i) q^{23} +14.7890 q^{24} -10.6467 q^{25} +(4.87346 + 8.44108i) q^{26} -5.19615i q^{27} +(-4.72374 - 2.72725i) q^{28} +(16.8172 + 29.1282i) q^{29} +(16.2668 + 9.39162i) q^{30} +(-24.0841 + 13.9050i) q^{31} +(-9.59239 + 5.53817i) q^{32} +(3.44158 + 5.96099i) q^{33} +(-20.5475 + 11.8631i) q^{34} +(-23.2328 - 40.2404i) q^{35} +(1.05130 + 1.82090i) q^{36} +(2.99353 - 5.18494i) q^{37} +(-20.5027 + 11.8372i) q^{38} +(-4.64727 + 8.04931i) q^{39} -50.9785 q^{40} +(30.7167 - 17.7343i) q^{41} +24.4840i q^{42} +35.0077i q^{43} +(-2.41208 - 1.39261i) q^{44} +17.9115i q^{45} +(46.4865 - 26.8390i) q^{46} +(-13.1152 - 22.7162i) q^{47} +(19.0580 + 11.0031i) q^{48} +(5.78402 - 10.0182i) q^{49} +(-16.7473 - 9.66906i) q^{50} +(-19.5938 - 11.3125i) q^{51} -3.76098i q^{52} -58.9526i q^{53} +(4.71902 - 8.17359i) q^{54} +(-11.8633 - 20.5479i) q^{55} +(-33.2253 - 57.5480i) q^{56} +(-19.5511 - 11.2878i) q^{57} +61.0919i q^{58} -47.4856 q^{59} +(-3.62388 - 6.27674i) q^{60} +(60.5107 + 34.9359i) q^{61} -50.5127 q^{62} +(-20.2197 + 11.6738i) q^{63} -70.9399 q^{64} +(16.0194 - 27.7465i) q^{65} +12.5022i q^{66} +(31.1180 + 59.3352i) q^{67} +9.15507 q^{68} +(44.3289 + 25.5933i) q^{69} -84.3979i q^{70} +(31.8812 + 55.2199i) q^{71} +25.6153i q^{72} +(-46.7763 + 81.0189i) q^{73} +(9.41767 - 5.43730i) q^{74} -18.4406i q^{75} +9.13510 q^{76} +(15.4639 - 26.7843i) q^{77} +(-14.6204 + 8.44108i) q^{78} +(11.8603 - 6.84756i) q^{79} +(-65.6941 - 37.9285i) q^{80} +9.00000 q^{81} +64.4234 q^{82} +(-23.3392 + 40.4247i) q^{83} +(4.72374 - 8.18176i) q^{84} +(67.5411 + 38.9949i) q^{85} +(-31.7931 + 55.0673i) q^{86} +(-50.4516 + 29.1282i) q^{87} +(-16.9658 - 29.3857i) q^{88} -89.7813 q^{89} +(-16.2668 + 28.1748i) q^{90} +41.7628 q^{91} -20.7123 q^{92} +(-24.0841 - 41.7149i) q^{93} -47.6436i q^{94} +(67.3938 + 38.9098i) q^{95} +(-9.59239 - 16.6145i) q^{96} +(-4.03037 - 2.32694i) q^{97} +(18.1966 - 10.5058i) q^{98} +(-10.3247 + 5.96099i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 26 q^{4} - 15 q^{7} - 66 q^{9}+O(q^{10}) \) 22 * q + 26 * q^4 - 15 * q^7 - 66 * q^9	\( 22 q + 26 q^{4} - 15 q^{7} - 66 q^{9} + 6 q^{10} + 30 q^{11} - 78 q^{12} - 27 q^{13} + 6 q^{14} - 6 q^{15} - 58 q^{16} - 8 q^{17} + q^{19} - 12 q^{20} - 15 q^{21} + 14 q^{22} - q^{23} - 56 q^{25} + 71 q^{26} - 75 q^{28} + 42 q^{29} + 18 q^{30} + 120 q^{31} - 105 q^{32} + 30 q^{33} - 24 q^{34} + 3 q^{35} - 78 q^{36} + 13 q^{37} + 108 q^{38} + 27 q^{39} + 82 q^{40} - 159 q^{41} + 189 q^{44} + 372 q^{46} - 35 q^{47} - 174 q^{48} - 40 q^{49} + 285 q^{50} - 24 q^{51} - 212 q^{55} - 113 q^{56} + 3 q^{57} + 136 q^{59} - 12 q^{60} + 63 q^{61} - 150 q^{62} + 45 q^{63} - 284 q^{64} - 20 q^{65} + 94 q^{67} + 154 q^{68} - 3 q^{69} - 41 q^{71} - 16 q^{73} + 441 q^{74} - 390 q^{76} - 84 q^{77} - 213 q^{78} - 615 q^{79} + 267 q^{80} + 198 q^{81} - 302 q^{82} - 154 q^{83} + 75 q^{84} + 633 q^{85} + 221 q^{86} - 126 q^{87} + 410 q^{88} + 56 q^{89} - 18 q^{90} + 272 q^{91} + 636 q^{92} + 120 q^{93} + 588 q^{95} - 105 q^{96} - 441 q^{97} + 780 q^{98} - 90 q^{99}+O(q^{100}) \) 22 * q + 26 * q^4 - 15 * q^7 - 66 * q^9 + 6 * q^10 + 30 * q^11 - 78 * q^12 - 27 * q^13 + 6 * q^14 - 6 * q^15 - 58 * q^16 - 8 * q^17 + q^19 - 12 * q^20 - 15 * q^21 + 14 * q^22 - q^23 - 56 * q^25 + 71 * q^26 - 75 * q^28 + 42 * q^29 + 18 * q^30 + 120 * q^31 - 105 * q^32 + 30 * q^33 - 24 * q^34 + 3 * q^35 - 78 * q^36 + 13 * q^37 + 108 * q^38 + 27 * q^39 + 82 * q^40 - 159 * q^41 + 189 * q^44 + 372 * q^46 - 35 * q^47 - 174 * q^48 - 40 * q^49 + 285 * q^50 - 24 * q^51 - 212 * q^55 - 113 * q^56 + 3 * q^57 + 136 * q^59 - 12 * q^60 + 63 * q^61 - 150 * q^62 + 45 * q^63 - 284 * q^64 - 20 * q^65 + 94 * q^67 + 154 * q^68 - 3 * q^69 - 41 * q^71 - 16 * q^73 + 441 * q^74 - 390 * q^76 - 84 * q^77 - 213 * q^78 - 615 * q^79 + 267 * q^80 + 198 * q^81 - 302 * q^82 - 154 * q^83 + 75 * q^84 + 633 * q^85 + 221 * q^86 - 126 * q^87 + 410 * q^88 + 56 * q^89 - 18 * q^90 + 272 * q^91 + 636 * q^92 + 120 * q^93 + 588 * q^95 - 105 * q^96 - 441 * q^97 + 780 * q^98 - 90 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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