LMFDB - Embedded newform 201.3.l.a.43.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,3,Mod(43,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("201.43");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	201.l (of order $22$, degree $10$, 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:	$220$
Relative dimension:	$22$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			43.10
Character	$\chi$	$=$	201.43
Dual form			201.3.l.a.187.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.736337 - 0.336274i) q^{2} +(-0.936417 - 1.45709i) q^{3} +(-2.19033 - 2.52778i) q^{4} +(5.35256 + 0.769582i) q^{5} +(0.199536 + 1.38780i) q^{6} +(8.86602 + 4.04898i) q^{7} +(1.67503 + 5.70464i) q^{8} +(-1.24625 + 2.72890i) q^{9} +O(q^{10})$	\(q+(-0.736337 - 0.336274i) q^{2} +(-0.936417 - 1.45709i) q^{3} +(-2.19033 - 2.52778i) q^{4} +(5.35256 + 0.769582i) q^{5} +(0.199536 + 1.38780i) q^{6} +(8.86602 + 4.04898i) q^{7} +(1.67503 + 5.70464i) q^{8} +(-1.24625 + 2.72890i) q^{9} +(-3.68250 - 2.36660i) q^{10} +(1.00498 + 0.144495i) q^{11} +(-1.63214 + 5.55857i) q^{12} +(3.64330 - 12.4079i) q^{13} +(-5.16681 - 5.96282i) q^{14} +(-3.89088 - 8.51983i) q^{15} +(-1.21909 + 8.47893i) q^{16} +(8.87592 - 10.2434i) q^{17} +(1.83531 - 1.59031i) q^{18} +(-9.13637 - 20.0059i) q^{19} +(-9.77855 - 15.2157i) q^{20} +(-2.40256 - 16.7102i) q^{21} +(-0.691415 - 0.444346i) q^{22} +(22.1978 - 14.2657i) q^{23} +(6.74366 - 7.78260i) q^{24} +(4.07031 + 1.19515i) q^{25} +(-6.85515 + 7.91127i) q^{26} +(5.14326 - 0.739490i) q^{27} +(-9.18461 - 31.2799i) q^{28} +4.18489 q^{29} +7.58186i q^{30} +(13.3424 + 45.4399i) q^{31} +(16.6064 - 25.8400i) q^{32} +(-0.730541 - 1.59966i) q^{33} +(-9.98024 + 4.55782i) q^{34} +(44.3399 + 28.4955i) q^{35} +(9.62773 - 2.82696i) q^{36} -46.2465 q^{37} +17.8034i q^{38} +(-21.4912 + 6.31038i) q^{39} +(4.57553 + 31.8235i) q^{40} +(11.6386 + 10.0849i) q^{41} +(-3.85009 + 13.1122i) q^{42} +(-38.2784 - 33.1684i) q^{43} +(-1.83599 - 2.85686i) q^{44} +(-8.77071 + 13.6475i) q^{45} +(-21.1423 + 3.03980i) q^{46} +(46.3777 - 29.8051i) q^{47} +(13.4962 - 6.16350i) q^{48} +(30.1239 + 34.7649i) q^{49} +(-2.59522 - 2.24877i) q^{50} +(-23.2371 - 3.34099i) q^{51} +(-39.3445 + 17.9680i) q^{52} +(15.0526 - 13.0432i) q^{53} +(-4.03584 - 1.18503i) q^{54} +(5.26803 + 1.54683i) q^{55} +(-8.24707 + 57.3596i) q^{56} +(-20.5950 + 32.0464i) q^{57} +(-3.08149 - 1.40727i) q^{58} +(29.4044 - 8.63390i) q^{59} +(-13.0139 + 28.4965i) q^{60} +(-26.9747 + 3.87838i) q^{61} +(5.45578 - 37.9458i) q^{62} +(-22.0985 + 19.1484i) q^{63} +(7.90794 - 5.08213i) q^{64} +(29.0499 - 63.6104i) q^{65} +1.42355i q^{66} +(-8.47305 + 66.4621i) q^{67} -45.3341 q^{68} +(-41.5729 - 18.9857i) q^{69} +(-23.0668 - 35.8926i) q^{70} +(31.5869 + 36.4533i) q^{71} +(-17.6549 - 2.53839i) q^{72} +(8.80918 + 61.2692i) q^{73} +(34.0530 + 15.5515i) q^{74} +(-2.07006 - 7.04999i) q^{75} +(-30.5587 + 66.9142i) q^{76} +(8.32514 + 5.35024i) q^{77} +(17.9467 + 2.58035i) q^{78} +(16.7254 - 56.9615i) q^{79} +(-13.0505 + 44.4458i) q^{80} +(-5.89375 - 6.80175i) q^{81} +(-5.17865 - 11.3397i) q^{82} +(-17.9942 + 125.153i) q^{83} +(-36.9771 + 42.6739i) q^{84} +(55.3920 - 47.9974i) q^{85} +(17.0321 + 37.2951i) q^{86} +(-3.91880 - 6.09778i) q^{87} +(0.859089 + 5.97509i) q^{88} +(-1.26749 - 0.814564i) q^{89} +(11.0475 - 7.09979i) q^{90} +(82.5410 - 95.2574i) q^{91} +(-84.6811 - 24.8646i) q^{92} +(53.7162 - 61.9918i) q^{93} +(-44.1723 + 6.35102i) q^{94} +(-33.5068 - 114.114i) q^{95} -53.2018 q^{96} +71.6785i q^{97} +(-10.4908 - 35.7285i) q^{98} +(-1.64676 + 2.56242i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 220 q + 52 q^{4} + 66 q^{8} + 66 q^{9}+O(q^{10}) $ 220 * q + 52 * q^4 + 66 * q^8 + 66 * q^9	$ 220 q + 52 q^{4} + 66 q^{8} + 66 q^{9} - 162 q^{10} - 72 q^{14} + 54 q^{15} - 116 q^{16} + 14 q^{17} - 84 q^{19} - 48 q^{21} + 78 q^{22} + 82 q^{23} - 36 q^{24} + 62 q^{25} + 100 q^{26} - 154 q^{28} + 52 q^{29} - 88 q^{31} + 770 q^{32} - 36 q^{33} + 180 q^{35} + 42 q^{36} - 304 q^{37} + 72 q^{39} - 1066 q^{40} + 330 q^{41} + 770 q^{43} - 242 q^{46} - 616 q^{47} - 146 q^{49} + 858 q^{50} + 264 q^{52} - 286 q^{53} - 62 q^{55} - 1484 q^{56} - 660 q^{57} - 352 q^{58} - 634 q^{59} - 504 q^{60} - 352 q^{61} + 124 q^{62} - 132 q^{63} - 1226 q^{64} + 196 q^{65} + 156 q^{67} - 192 q^{68} + 66 q^{69} + 1144 q^{70} + 280 q^{71} + 264 q^{72} + 552 q^{73} + 352 q^{74} + 396 q^{75} + 400 q^{76} - 176 q^{77} + 528 q^{78} + 682 q^{79} + 1848 q^{80} - 198 q^{81} + 728 q^{82} + 246 q^{83} - 1320 q^{84} - 1120 q^{86} + 1120 q^{88} + 448 q^{89} + 486 q^{90} - 128 q^{91} + 604 q^{92} + 72 q^{93} + 704 q^{94} - 462 q^{95} + 144 q^{96} - 176 q^{98}+O(q^{100}) $ 220 * q + 52 * q^4 + 66 * q^8 + 66 * q^9 - 162 * q^10 - 72 * q^14 + 54 * q^15 - 116 * q^16 + 14 * q^17 - 84 * q^19 - 48 * q^21 + 78 * q^22 + 82 * q^23 - 36 * q^24 + 62 * q^25 + 100 * q^26 - 154 * q^28 + 52 * q^29 - 88 * q^31 + 770 * q^32 - 36 * q^33 + 180 * q^35 + 42 * q^36 - 304 * q^37 + 72 * q^39 - 1066 * q^40 + 330 * q^41 + 770 * q^43 - 242 * q^46 - 616 * q^47 - 146 * q^49 + 858 * q^50 + 264 * q^52 - 286 * q^53 - 62 * q^55 - 1484 * q^56 - 660 * q^57 - 352 * q^58 - 634 * q^59 - 504 * q^60 - 352 * q^61 + 124 * q^62 - 132 * q^63 - 1226 * q^64 + 196 * q^65 + 156 * q^67 - 192 * q^68 + 66 * q^69 + 1144 * q^70 + 280 * q^71 + 264 * q^72 + 552 * q^73 + 352 * q^74 + 396 * q^75 + 400 * q^76 - 176 * q^77 + 528 * q^78 + 682 * q^79 + 1848 * q^80 - 198 * q^81 + 728 * q^82 + 246 * q^83 - 1320 * q^84 - 1120 * q^86 + 1120 * q^88 + 448 * q^89 + 486 * q^90 - 128 * q^91 + 604 * q^92 + 72 * q^93 + 704 * q^94 - 462 * q^95 + 144 * q^96 - 176 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$68$	$136$
$\chi(n)$	$1$	$e\left(\frac{3}{22}\right)$

Coefficient data

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

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

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

$2$	−0.736337	−	0.336274i	−0.368168	−	0.168137i	0.222735	−	0.974879i	$-0.428501\pi$
$2$	−0.736337	−	0.336274i	−0.368168	−	0.168137i	−0.590904	+	0.806742i	$0.701229\pi$
$3$	−0.936417	−	1.45709i	−0.312139	−	0.485698i
$3$	−0.936417	−	1.45709i	−0.312139	−	0.485698i
$4$	−2.19033	−	2.52778i	−0.547583	−	0.631944i
$5$	5.35256	+	0.769582i	1.07051	+	0.153916i	0.654968	−	0.755657i	$-0.272682\pi$
$5$	5.35256	+	0.769582i	1.07051	+	0.153916i	0.415544	+	0.909573i	$0.363591\pi$
$6$	0.199536	+	1.38780i	0.0332560	+	0.231301i
$7$	8.86602	+	4.04898i	1.26657	+	0.578425i	0.931491	−	0.363764i	$-0.118508\pi$
$7$	8.86602	+	4.04898i	1.26657	+	0.578425i	0.335083	+	0.942189i	$0.391236\pi$
$8$	1.67503	+	5.70464i	0.209379	+	0.713080i
$9$	−1.24625	+	2.72890i	−0.138472	+	0.303211i
$10$	−3.68250	−	2.36660i	−0.368250	−	0.236660i
$11$	1.00498	+	0.144495i	0.0913620	+	0.0131359i	0.187844	−	0.982199i	$-0.439850\pi$
$11$	1.00498	+	0.144495i	0.0913620	+	0.0131359i	−0.0964822	+	0.995335i	$0.530759\pi$
$12$	−1.63214	+	5.55857i	−0.136012	+	0.463214i
$13$	3.64330	−	12.4079i	0.280254	−	0.954456i	−0.692267	−	0.721641i	$-0.743388\pi$
$13$	3.64330	−	12.4079i	0.280254	−	0.954456i	0.972521	−	0.232815i	$-0.0747937\pi$
$14$	−5.16681	−	5.96282i	−0.369058	−	0.425916i
$15$	−3.89088	−	8.51983i	−0.259392	−	0.567989i
$16$	−1.21909	+	8.47893i	−0.0761929	+	0.529933i
$17$	8.87592	−	10.2434i	0.522113	−	0.602551i	−0.432046	−	0.901852i	$-0.642208\pi$
$17$	8.87592	−	10.2434i	0.522113	−	0.602551i	0.954159	+	0.299301i	$0.0967535\pi$
$18$	1.83531	−	1.59031i	0.101962	−	0.0883504i
$19$	−9.13637	−	20.0059i	−0.480862	−	1.05294i	−0.982226	−	0.187704i	$-0.939896\pi$
$19$	−9.13637	−	20.0059i	−0.480862	−	1.05294i	0.501364	−	0.865236i	$-0.332832\pi$
$20$	−9.77855	−	15.2157i	−0.488927	−	0.760786i
$21$	−2.40256	−	16.7102i	−0.114407	−	0.795722i
$22$	−0.691415	−	0.444346i	−0.0314280	−	0.0201975i
$23$	22.1978	−	14.2657i	0.965123	−	0.620247i	0.0397119	−	0.999211i	$-0.487356\pi$
$23$	22.1978	−	14.2657i	0.965123	−	0.620247i	0.925411	+	0.378964i	$0.123720\pi$
$24$	6.74366	−	7.78260i	0.280986	−	0.324275i
$25$	4.07031	+	1.19515i	0.162813	+	0.0478061i
$26$	−6.85515	+	7.91127i	−0.263660	+	0.304280i
$27$	5.14326	−	0.739490i	0.190491	−	0.0273885i
$28$	−9.18461	−	31.2799i	−0.328022	−	1.11714i
$29$	4.18489			0.144307			0.0721533	−	0.997394i	$-0.477013\pi$
$29$	4.18489			0.144307			0.0721533	+	0.997394i	$0.477013\pi$
$30$			7.58186i			0.252729i
$31$	13.3424	+	45.4399i	0.430399	+	1.46580i	0.834458	+	0.551071i	$0.185781\pi$
$31$	13.3424	+	45.4399i	0.430399	+	1.46580i	−0.404060	+	0.914733i	$0.632401\pi$
$32$	16.6064	−	25.8400i	0.518949	−	0.807500i
$33$	−0.730541	−	1.59966i	−0.0221376	−	0.0484746i
$34$	−9.98024	+	4.55782i	−0.293536	+	0.134054i
$35$	44.3399	+	28.4955i	1.26685	+	0.814157i
$36$	9.62773	−	2.82696i	0.267437	−	0.0785266i
$37$	−46.2465			−1.24991			−0.624953	−	0.780663i	$-0.714882\pi$
$37$	−46.2465			−1.24991			−0.624953	+	0.780663i	$0.714882\pi$
$38$			17.8034i			0.468510i
$39$	−21.4912	+	6.31038i	−0.551056	+	0.161805i
$40$	4.57553	+	31.8235i	0.114388	+	0.795587i
$41$	11.6386	+	10.0849i	0.283869	+	0.245974i	0.785143	−	0.619315i	$-0.212590\pi$
$41$	11.6386	+	10.0849i	0.283869	+	0.245974i	−0.501274	+	0.865289i	$0.667135\pi$
$42$	−3.85009	+	13.1122i	−0.0916689	+	0.312196i
$43$	−38.2784	−	33.1684i	−0.890195	−	0.771359i	0.0841416	−	0.996454i	$-0.473185\pi$
$43$	−38.2784	−	33.1684i	−0.890195	−	0.771359i	−0.974337	+	0.225095i	$0.927731\pi$
$44$	−1.83599	−	2.85686i	−0.0417271	−	0.0649287i
$45$	−8.77071	+	13.6475i	−0.194905	+	0.303278i
$46$	−21.1423	+	3.03980i	−0.459614	+	0.0660825i
$47$	46.3777	−	29.8051i	0.986760	−	0.634152i	0.0554811	−	0.998460i	$-0.482331\pi$
$47$	46.3777	−	29.8051i	0.986760	−	0.634152i	0.931279	+	0.364308i	$0.118694\pi$
$48$	13.4962	−	6.16350i	0.281170	−	0.128406i
$49$	30.1239	+	34.7649i	0.614774	+	0.709487i
$50$	−2.59522	−	2.24877i	−0.0519045	−	0.0449755i
$51$	−23.2371	−	3.34099i	−0.455629	−	0.0655096i
$52$	−39.3445	+	17.9680i	−0.756625	+	0.345539i
$53$	15.0526	−	13.0432i	0.284011	−	0.246097i	−0.501191	−	0.865337i	$-0.667104\pi$
$53$	15.0526	−	13.0432i	0.284011	−	0.246097i	0.785202	+	0.619240i	$0.212559\pi$
$54$	−4.03584	−	1.18503i	−0.0747378	−	0.0219450i
$55$	5.26803	+	1.54683i	0.0957823	+	0.0281242i
$56$	−8.24707	+	57.3596i	−0.147269	+	1.02428i
$57$	−20.5950	+	32.0464i	−0.361315	+	0.562217i
$58$	−3.08149	−	1.40727i	−0.0531291	−	0.0242633i
$59$	29.4044	−	8.63390i	0.498379	−	0.146337i	−0.0228758	−	0.999738i	$-0.507282\pi$
$59$	29.4044	−	8.63390i	0.498379	−	0.146337i	0.521255	+	0.853401i	$0.325464\pi$
$60$	−13.0139	+	28.4965i	−0.216899	+	0.474942i
$61$	−26.9747	+	3.87838i	−0.442208	+	0.0635800i	−0.359823	−	0.933021i	$-0.617163\pi$
$61$	−26.9747	+	3.87838i	−0.442208	+	0.0635800i	−0.0823853	+	0.996601i	$0.526254\pi$
$62$	5.45578	−	37.9458i	0.0879964	−	0.612028i
$63$	−22.0985	+	19.1484i	−0.350769	+	0.303943i
$64$	7.90794	−	5.08213i	0.123562	−	0.0794082i
$65$	29.0499	−	63.6104i	0.446921	−	0.978621i
$66$			1.42355i			0.0215689i
$67$	−8.47305	+	66.4621i	−0.126463	+	0.991971i
$67$	−8.47305	+	66.4621i	−0.126463	+	0.991971i
$68$	−45.3341			−0.666679
$69$	−41.5729	−	18.9857i	−0.602505	−	0.275155i
$70$	−23.0668	−	35.8926i	−0.329525	−	0.512752i
$71$	31.5869	+	36.4533i	0.444886	+	0.513426i	0.933257	−	0.359210i	$-0.116954\pi$
$71$	31.5869	+	36.4533i	0.444886	+	0.513426i	−0.488370	+	0.872637i	$0.662408\pi$
$72$	−17.6549	−	2.53839i	−0.245207	−	0.0352554i
$73$	8.80918	+	61.2692i	0.120674	+	0.839304i	0.956796	+	0.290761i	$0.0939084\pi$
$73$	8.80918	+	61.2692i	0.120674	+	0.839304i	−0.836122	+	0.548543i	$0.815183\pi$
$74$	34.0530	+	15.5515i	0.460175	+	0.210155i
$75$	−2.07006	−	7.04999i	−0.0276009	−	0.0939999i
$76$	−30.5587	+	66.9142i	−0.402088	+	0.880450i
$77$	8.32514	+	5.35024i	0.108119	+	0.0694836i
$78$	17.9467	+	2.58035i	0.230087	+	0.0330814i
$79$	16.7254	−	56.9615i	0.211714	−	0.721032i	−0.783331	−	0.621605i	$-0.786481\pi$
$79$	16.7254	−	56.9615i	0.211714	−	0.721032i	0.995045	−	0.0994270i	$-0.0317010\pi$
$80$	−13.0505	+	44.4458i	−0.163131	+	0.555573i
$81$	−5.89375	−	6.80175i	−0.0727623	−	0.0839722i
$82$	−5.17865	−	11.3397i	−0.0631543	−	0.138289i
$83$	−17.9942	+	125.153i	−0.216798	+	1.50786i	0.532954	+	0.846144i	$0.321082\pi$
$83$	−17.9942	+	125.153i	−0.216798	+	1.50786i	−0.749752	+	0.661719i	$0.769827\pi$
$84$	−36.9771	+	42.6739i	−0.440204	+	0.508023i
$85$	55.3920	−	47.9974i	0.651671	−	0.564676i
$86$	17.0321	+	37.2951i	0.198048	+	0.433664i
$87$	−3.91880	−	6.09778i	−0.0450437	−	0.0700894i
$88$	0.859089	+	5.97509i	0.00976237	+	0.0678988i
$89$	−1.26749	−	0.814564i	−0.0142414	−	0.00915241i	0.533501	−	0.845800i	$-0.320876\pi$
$89$	−1.26749	−	0.814564i	−0.0142414	−	0.00915241i	−0.547742	+	0.836647i	$0.684513\pi$
$90$	11.0475	−	7.09979i	0.122750	−	0.0788865i
$91$	82.5410	−	95.2574i	0.907044	−	1.04678i
$92$	−84.6811	−	24.8646i	−0.920446	−	0.270267i
$93$	53.7162	−	61.9918i	0.577594	−	0.666578i
$94$	−44.1723	+	6.35102i	−0.469918	+	0.0675640i
$95$	−33.5068	−	114.114i	−0.352703	−	1.20120i
$96$	−53.2018			−0.554185
$97$			71.6785i			0.738954i	0.929240	+	0.369477i	$0.120463\pi$
$97$			71.6785i			0.738954i	−0.929240	+	0.369477i	$0.879537\pi$
$98$	−10.4908	−	35.7285i	−0.107049	−	0.364577i
$99$	−1.64676	+	2.56242i	−0.0166340	+	0.0258830i
$100$	−5.89426	−	12.9066i	−0.0589426	−	0.129066i
$101$	−118.869	+	54.2856i	−1.17692	+	0.537481i	−0.905238	−	0.424906i	$-0.860307\pi$
$101$	−118.869	+	54.2856i	−1.17692	+	0.537481i	−0.271682	+	0.962387i	$0.587580\pi$
$102$	15.9868	+	10.2741i	0.156734	+	0.100727i
$103$	161.012	−	47.2773i	1.56322	−	0.459002i	0.618201	−	0.786020i	$-0.287862\pi$
$103$	161.012	−	47.2773i	1.56322	−	0.459002i	0.945018	+	0.327018i	$0.106044\pi$
$104$	76.8854			0.739283
$105$		−	91.2911i		−	0.869439i
$106$	−15.4699	+	4.54236i	−0.145942	+	0.0428524i
$107$	28.0501	+	195.093i	0.262151	+	1.82330i	0.516618	+	0.856216i	$0.327191\pi$
$107$	28.0501	+	195.093i	0.262151	+	1.82330i	−0.254467	+	0.967081i	$0.581900\pi$
$108$	−13.1347	−	11.3813i	−0.121618	−	0.105382i
$109$	−2.39351	+	8.15156i	−0.0219588	+	0.0747849i	−0.969744	−	0.244126i	$-0.921499\pi$
$109$	−2.39351	+	8.15156i	−0.0219588	+	0.0747849i	0.947785	+	0.318911i	$0.103317\pi$
$110$	−3.35888	−	2.91049i	−0.0305353	−	0.0264590i
$111$	43.3060	+	67.3855i	0.390144	+	0.607076i
$112$	−45.1394	+	70.2383i	−0.403031	+	0.627128i
$113$	−116.036	+	16.6835i	−1.02687	+	0.147641i	−0.635106	−	0.772425i	$-0.719044\pi$
$113$	−116.036	+	16.6835i	−1.02687	+	0.147641i	−0.391763	+	0.920066i	$0.628135\pi$
$114$	25.9412	−	16.6714i	0.227554	−	0.146240i
$115$	129.794	−	59.2749i	1.12864	−	0.515434i
$116$	−9.16630	−	10.5785i	−0.0790198	−	0.0911937i
$117$	29.3195	+	25.4055i	0.250594	+	0.217141i
$118$	−24.5549	−	3.53046i	−0.208092	−	0.0299191i
$119$	120.169	−	54.8794i	1.00983	−	0.461172i
$120$	42.0852	−	36.4670i	0.350710	−	0.303892i
$121$	−115.110	−	33.7992i	−0.951319	−	0.279332i
$122$	21.1667	+	6.21509i	0.173497	+	0.0509434i
$123$	3.79608	−	26.4023i	0.0308624	−	0.214653i
$124$	85.6378	−	133.255i	0.690627	−	1.07464i
$125$	−102.106	−	46.6304i	−0.816851	−	0.373043i
$126$	22.7110	−	6.66856i	0.180246	−	0.0529251i
$127$	27.9714	−	61.2489i	0.220248	−	0.482275i	−0.766964	−	0.641690i	$-0.778234\pi$
$127$	27.9714	−	61.2489i	0.220248	−	0.482275i	0.987212	+	0.159415i	$0.0509609\pi$
$128$	−129.146	+	18.5683i	−1.00895	+	0.145065i
$129$	−12.4849	+	86.8347i	−0.0967825	+	0.673137i
$130$	−42.7810	+	37.0699i	−0.329085	+	0.285153i
$131$	212.557	−	136.602i	1.62258	−	1.04277i	0.668276	−	0.743914i	$-0.267033\pi$
$131$	212.557	−	136.602i	1.62258	−	1.04277i	0.954299	−	0.298852i	$-0.0966038\pi$
$132$	−2.44346	+	5.35043i	−0.0185111	+	0.0405336i
$133$		−	214.365i		−	1.61177i
$134$	28.5885	−	46.0892i	0.213347	−	0.343949i
$135$	28.0987			0.208139
$136$	73.3021	+	33.4760i	0.538986	+	0.246147i
$137$	−13.6450	−	21.2320i	−0.0995984	−	0.154978i	0.787878	−	0.615831i	$-0.211180\pi$
$137$	−13.6450	−	21.2320i	−0.0995984	−	0.154978i	−0.887476	+	0.460853i	$0.847543\pi$
$138$	24.2272	+	27.9597i	0.175560	+	0.202607i
$139$	−131.959	−	18.9729i	−0.949348	−	0.136496i	−0.349791	−	0.936828i	$-0.613747\pi$
$139$	−131.959	−	18.9729i	−0.949348	−	0.136496i	−0.599557	+	0.800332i	$0.704656\pi$
$140$	−25.0887	−	174.496i	−0.179205	−	1.24640i
$141$	−86.8578	−	39.6666i	−0.616013	−	0.281324i
$142$	−11.0003	−	37.4637i	−0.0774672	−	0.263829i
$143$	5.45433	−	11.9433i	0.0381422	−	0.0835197i
$144$	−21.6188	−	13.8936i	−0.150131	−	0.0964832i
$145$	22.3999	+	3.22062i	0.154482	+	0.0222111i
$146$	14.1167	−	48.0771i	0.0966897	−	0.329295i
$147$	22.4471	−	76.4478i	0.152701	−	0.520053i
$148$	101.295	+	116.901i	0.684427	+	0.789870i
$149$	−82.8378	−	181.389i	−0.555958	−	1.21738i	−0.953943	−	0.299987i	$-0.903018\pi$
$149$	−82.8378	−	181.389i	−0.555958	−	1.21738i	0.397985	−	0.917392i	$-0.369710\pi$
$150$	−0.846462	+	5.88727i	−0.00564308	+	0.0392485i
$151$	−93.2763	+	107.647i	−0.617724	+	0.712891i	−0.975273	−	0.221003i	$-0.929067\pi$
$151$	−93.2763	+	107.647i	−0.617724	+	0.712891i	0.357549	+	0.933894i	$0.383612\pi$
$152$	98.8225	−	85.6302i	0.650148	−	0.563356i
$153$	16.8915	+	36.9872i	0.110402	+	0.241746i
$154$	−4.33096	−	6.73910i	−0.0281231	−	0.0437604i
$155$	36.4461	+	253.488i	0.235136	+	1.63541i
$156$	63.0240	+	40.5031i	0.404000	+	0.259635i
$157$	−89.0278	+	57.2147i	−0.567056	+	0.364425i	−0.792538	−	0.609823i	$-0.791241\pi$
$157$	−89.0278	+	57.2147i	−0.567056	+	0.364425i	0.225482	+	0.974247i	$0.427604\pi$
$158$	−31.4702	+	36.3186i	−0.199179	+	0.229864i
$159$	−33.1006	−	9.71922i	−0.208180	−	0.0611272i
$160$	108.773	−	125.530i	0.679828	−	0.784564i
$161$	254.568	−	36.6013i	1.58117	−	0.227337i
$162$	2.05253	+	6.99029i	0.0126700	+	0.0431499i
$163$	−162.599			−0.997538			−0.498769	−	0.866735i	$-0.666214\pi$
$163$	−162.599			−0.997538			−0.498769	+	0.866735i	$0.666214\pi$
$164$		−	51.5092i		−	0.314081i
$165$	−2.67919	−	9.12449i	−0.0162375	−	0.0552999i
$166$	55.3353	−	86.1035i	0.333345	−	0.518696i
$167$	19.1022	+	41.8279i	0.114384	+	0.250466i	0.958162	−	0.286226i	$-0.0924008\pi$
$167$	19.1022	+	41.8279i	0.114384	+	0.250466i	−0.843778	+	0.536692i	$0.819674\pi$
$168$	91.3010	−	41.6958i	0.543459	−	0.248189i
$169$	1.48865	+	0.956694i	0.00880855	+	0.00566091i
$170$	−56.9274	+	16.7154i	−0.334867	+	0.0983259i
$171$	65.9801			0.385848
$172$			169.409i			0.984936i
$173$	138.425	−	40.6452i	0.800143	−	0.234943i	0.143998	−	0.989578i	$-0.454004\pi$
$173$	138.425	−	40.6452i	0.800143	−	0.234943i	0.656145	+	0.754635i	$0.272186\pi$
$174$	0.835037	+	5.80781i	0.00479906	+	0.0333782i
$175$	31.2483	+	27.0768i	0.178562	+	0.154725i
$176$	−2.45032	+	8.34502i	−0.0139223	+	0.0474149i
$177$	−40.1152	−	34.7600i	−0.226639	−	0.196384i
$178$	0.659380	+	1.02602i	0.00370438	+	0.00576413i
$179$	−176.968	+	275.368i	−0.988649	+	1.53837i	−0.153644	+	0.988126i	$0.549101\pi$
$179$	−176.968	+	275.368i	−0.988649	+	1.53837i	−0.835005	+	0.550242i	$0.814535\pi$
$180$	53.7086	−	7.72213i	0.298381	−	0.0429007i
$181$	−196.068	+	126.005i	−1.08325	+	0.696162i	−0.955306	−	0.295619i	$-0.904474\pi$
$181$	−196.068	+	126.005i	−1.08325	+	0.696162i	−0.127944	+	0.991781i	$0.540838\pi$
$182$	−92.8105	+	42.3851i	−0.509948	+	0.232885i
$183$	30.9107	+	35.6729i	0.168911	+	0.194934i
$184$	118.563	+	102.735i	0.644362	+	0.558343i
$185$	−247.537	−	35.5905i	−1.33804	−	0.192381i
$186$	−60.3994	+	27.5835i	−0.324728	+	0.148298i
$187$	10.4003	−	9.01187i	0.0556163	−	0.0481918i
$188$	−176.923	−	51.9494i	−0.941081	−	0.276326i
$189$	48.5944	+	14.2686i	0.257113	+	0.0754953i
$190$	−13.7011	+	95.2936i	−0.0721113	+	0.501545i
$191$	0.902196	−	1.40384i	0.00472354	−	0.00734997i	−0.838884	−	0.544311i	$-0.816791\pi$
$191$	0.902196	−	1.40384i	0.00472354	−	0.00734997i	0.843607	+	0.536961i	$0.180428\pi$
$192$	−14.8103	−	6.76362i	−0.0771368	−	0.0352272i
$193$	170.731	−	50.1312i	0.884617	−	0.259747i	0.192296	−	0.981337i	$-0.438407\pi$
$193$	170.731	−	50.1312i	0.884617	−	0.259747i	0.692321	+	0.721590i	$0.256588\pi$
$194$	24.1036	−	52.7795i	0.124245	−	0.272059i
$195$	−119.889	+	17.2375i	−0.614816	+	0.0883972i
$196$	21.8964	−	152.293i	0.111717	−	0.777006i
$197$	−203.862	+	176.648i	−1.03483	+	0.896689i	−0.994732	−	0.102506i	$-0.967314\pi$
$197$	−203.862	+	176.648i	−1.03483	+	0.896689i	−0.0401024	+	0.999196i	$0.512768\pi$
$198$	2.07425	−	1.33304i	0.0104760	−	0.00673251i
$199$	−9.89759	+	21.6727i	−0.0497366	+	0.108908i	−0.932869	−	0.360216i	$-0.882703\pi$
$199$	−9.89759	+	21.6727i	−0.0497366	+	0.108908i	0.883132	+	0.469124i	$0.155430\pi$
$200$			25.2216i			0.126108i
$201$	104.776	−	49.8902i	0.521273	−	0.248210i
$202$	105.782			0.523675
$203$	37.1033	+	16.9445i	0.182775	+	0.0834705i
$204$	42.4517	+	66.0561i	0.208096	+	0.323804i
$205$	54.5353	+	62.9371i	0.266026	+	0.307010i
$206$	−134.457	−	19.3320i	−0.652703	−	0.0938445i
$207$	11.2656	+	78.3541i	0.0544233	+	0.378522i
$208$	100.765	+	46.0176i	0.484445	+	0.221239i
$209$	−6.29115	−	21.4257i	−0.0301012	−	0.102515i
$210$	−30.6988	+	67.2209i	−0.146185	+	0.320100i
$211$	105.178	+	67.5935i	0.498472	+	0.320348i	0.765605	−	0.643311i	$-0.222440\pi$
$211$	105.178	+	67.5935i	0.498472	+	0.320348i	−0.267133	+	0.963660i	$0.586076\pi$
$212$	−65.9404	−	9.48079i	−0.311040	−	0.0447207i
$213$	23.5373	−	80.1606i	0.110504	−	0.376341i
$214$	44.9503	−	153.087i	0.210048	−	0.715357i
$215$	−179.362	−	206.994i	−0.834240	−	0.962764i
$216$	12.8337	+	28.1018i	0.0594151	+	0.130101i
$217$	−65.6914	+	456.894i	−0.302726	+	2.10550i
$218$	4.50359	−	5.19741i	0.0206586	−	0.0238414i
$219$	81.0259	−	70.2094i	0.369981	−	0.320591i
$220$	−7.62868	−	16.7045i	−0.0346758	−	0.0759294i
$221$	−94.7613	−	147.451i	−0.428784	−	0.667201i
$222$	−9.22784	−	64.1811i	−0.0415669	−	0.289104i
$223$	−43.7557	−	28.1201i	−0.196214	−	0.126099i	0.438845	−	0.898563i	$-0.355388\pi$
$223$	−43.7557	−	28.1201i	−0.196214	−	0.126099i	−0.635059	+	0.772464i	$0.719024\pi$
$224$	251.858	−	161.859i	1.12437	−	0.722586i
$225$	−8.33405	+	9.61801i	−0.0370402	+	0.0427467i
$226$	91.0519	+	26.7353i	0.402885	+	0.118298i
$227$	−43.5108	+	50.2141i	−0.191677	+	0.221207i	−0.843451	−	0.537206i	$-0.819480\pi$
$227$	−43.5108	+	50.2141i	−0.191677	+	0.221207i	0.651774	+	0.758414i	$0.274025\pi$
$228$	126.116	−	18.1327i	0.553140	−	0.0795295i
$229$	−83.2176	−	283.413i	−0.363396	−	1.23761i	−0.914982	−	0.403494i	$-0.867795\pi$
$229$	−83.2176	−	283.413i	−0.363396	−	1.23761i	0.551586	−	0.834118i	$-0.314023\pi$
$230$	−115.505			−0.502194
$231$		−	17.1406i		−	0.0742016i
$232$	7.00983	+	23.8733i	0.0302148	+	0.102902i
$233$	−168.716	+	262.527i	−0.724103	+	1.12673i	0.262712	+	0.964874i	$0.415383\pi$
$233$	−168.716	+	262.527i	−0.724103	+	1.12673i	−0.986815	+	0.161852i	$0.948253\pi$
$234$	−13.0458	−	28.5664i	−0.0557514	−	0.122079i
$235$	271.177	−	123.842i	1.15394	−	0.526989i
$236$	−86.2299	−	55.4166i	−0.365381	−	0.234816i
$237$	−98.6603	+	28.9693i	−0.416288	+	0.122233i
$238$	−106.939			−0.449326
$239$			304.471i			1.27394i	0.770890	+	0.636968i	$0.219812\pi$
$239$			304.471i			1.27394i	−0.770890	+	0.636968i	$0.780188\pi$
$240$	76.9824	−	22.6041i	0.320760	−	0.0941836i
$241$	−30.2332	−	210.277i	−0.125449	−	0.872518i	−0.951220	−	0.308513i	$-0.900169\pi$
$241$	−30.2332	−	210.277i	−0.125449	−	0.872518i	0.825771	−	0.564005i	$-0.190740\pi$
$242$	73.3936	+	63.5959i	0.303279	+	0.262793i
$243$	−4.39178	+	14.9570i	−0.0180732	+	0.0615515i
$244$	68.8872	+	59.6911i	0.282325	+	0.244636i
$245$	134.486	+	209.264i	0.548921	+	0.854138i
$246$	−11.6736	+	18.1645i	−0.0474536	+	0.0738392i
$247$	−281.518	+	40.4762i	−1.13975	+	0.163871i
$248$	−236.869	+	152.227i	−0.955119	+	0.613817i
$249$	199.209	−	90.9758i	0.800037	−	0.365365i
$250$	59.5041	+	68.6713i	0.238016	+	0.274685i
$251$	226.840	+	196.558i	0.903744	+	0.783098i	0.976783	−	0.214231i	$-0.0687244\pi$
$251$	226.840	+	196.558i	0.903744	+	0.783098i	−0.0730393	+	0.997329i	$0.523270\pi$
$252$	96.8059	+	13.9186i	0.384150	+	0.0552325i
$253$	24.3697	−	11.1293i	0.0963231	−	0.0439893i
$254$	−41.1928	+	35.6938i	−0.162176	+	0.140527i
$255$	−121.807	−	35.7657i	−0.477674	−	0.140258i
$256$	65.2610	+	19.1624i	0.254926	+	0.0748530i
$257$	−56.3346	+	391.816i	−0.219201	+	1.52458i	0.521798	+	0.853069i	$0.325262\pi$
$257$	−56.3346	+	391.816i	−0.219201	+	1.52458i	−0.740999	+	0.671506i	$0.765648\pi$
$258$	38.3933	−	59.7412i	0.148811	−	0.231555i
$259$	−410.022	−	187.251i	−1.58310	−	0.722976i
$260$	−224.422	+	65.8962i	−0.863161	+	0.253447i
$261$	−5.21540	+	11.4201i	−0.0199824	+	0.0437553i
$262$	−202.450	+	29.1078i	−0.772708	+	0.111099i
$263$	46.5327	−	323.642i	0.176930	−	1.23058i	−0.686884	−	0.726767i	$-0.741022\pi$
$263$	46.5327	−	323.642i	0.176930	−	1.23058i	0.863814	−	0.503810i	$-0.168069\pi$
$264$	7.90181	−	6.84695i	0.0299311	−	0.0259354i
$265$	90.6077	−	58.2301i	0.341916	−	0.219736i
$266$	−72.0854	+	157.845i	−0.270998	+	0.593402i
$267$			2.60962i			0.00977385i
$268$	186.560	−	124.156i	0.696120	−	0.463269i
$269$	−50.8925			−0.189191			−0.0945957	−	0.995516i	$-0.530156\pi$
$269$	−50.8925			−0.189191			−0.0945957	+	0.995516i	$0.530156\pi$
$270$	−20.6901	−	9.44886i	−0.0766301	−	0.0349958i
$271$	63.7467	+	99.1918i	0.235228	+	0.366021i	0.938720	−	0.344682i	$-0.112013\pi$
$271$	63.7467	+	99.1918i	0.235228	+	0.366021i	−0.703492	+	0.710703i	$0.748377\pi$
$272$	76.0322	+	87.7459i	0.279530	+	0.322595i
$273$	−216.092	−	31.0693i	−0.791545	−	0.113807i
$274$	2.90754	+	20.2224i	0.0106114	+	0.0738042i
$275$	3.91790	+	1.78925i	0.0142469	+	0.00650635i
$276$	43.0668	+	146.672i	0.156039	+	0.531420i
$277$	−143.857	+	315.002i	−0.519338	+	1.13719i	0.450351	+	0.892852i	$0.351299\pi$
$277$	−143.857	+	315.002i	−0.519338	+	1.13719i	−0.969689	+	0.244341i	$0.921428\pi$
$278$	90.7864	+	58.3449i	0.326570	+	0.209874i
$279$	−140.629	−	20.2193i	−0.504045	−	0.0724708i
$280$	−88.2858	+	300.674i	−0.315307	+	1.07384i
$281$	128.760	−	438.515i	0.458219	−	1.56055i	−0.329278	−	0.944233i	$-0.606805\pi$
$281$	128.760	−	438.515i	0.458219	−	1.56055i	0.787497	−	0.616318i	$-0.211377\pi$
$282$	50.6177	+	58.4160i	0.179495	+	0.207149i
$283$	108.009	+	236.507i	0.381657	+	0.835712i	0.998805	+	0.0488654i	$0.0155605\pi$
$283$	108.009	+	236.507i	0.381657	+	0.835712i	−0.617148	+	0.786847i	$0.711712\pi$
$284$	22.9599	−	159.689i	0.0808447	−	0.562287i
$285$	−134.898	+	155.681i	−0.473327	+	0.546248i
$286$	−8.03244	+	6.96015i	−0.0280855	+	0.0243362i
$287$	62.3547	+	136.538i	0.217264	+	0.475741i
$288$	49.8191	+	77.5200i	0.172983	+	0.269167i
$289$	14.9846	+	104.220i	0.0518497	+	0.360622i
$290$	−15.4108	−	9.90395i	−0.0531408	−	0.0341515i
$291$	104.442	−	67.1210i	0.358908	−	0.230656i
$292$	135.580	−	156.468i	0.464315	−	0.535848i
$293$	475.233	+	139.541i	1.62196	+	0.476249i	0.961543	−	0.274654i	$-0.0885634\pi$
$293$	475.233	+	139.541i	1.62196	+	0.476249i	0.660412	+	0.750903i	$0.270382\pi$
$294$	−42.2360	+	48.7429i	−0.143660	+	0.165792i
$295$	164.033	−	23.5844i	0.556045	−	0.0799471i
$296$	−77.4644	−	263.820i	−0.261704	−	0.891282i
$297$	5.27574			0.0177634
$298$			161.420i			0.541677i
$299$	−96.1343	−	327.403i	−0.321519	−	1.09499i
$300$	−13.2867	+	20.6745i	−0.0442889	+	0.0689149i
$301$	−205.079	−	449.060i	−0.681325	−	1.49189i
$302$	104.881	−	47.8977i	0.347290	−	0.158602i
$303$	190.410	+	122.369i	0.628416	+	0.403859i
$304$	180.766	−	53.0778i	0.594626	−	0.174598i
$305$	−147.368			−0.483175
$306$		−	32.9152i		−	0.107566i
$307$	−432.511	+	126.997i	−1.40883	+	0.413670i	−0.895707	−	0.444644i	$-0.853330\pi$
$307$	−432.511	+	126.997i	−1.40883	+	0.413670i	−0.513124	+	0.858314i	$0.671512\pi$
$308$	−4.71059	−	32.7629i	−0.0152941	−	0.106373i
$309$	−219.661	−	190.338i	−0.710878	−	0.615980i
$310$	58.4047	−	198.908i	0.188402	−	0.641639i
$311$	−178.470	−	154.645i	−0.573858	−	0.497251i	0.318900	−	0.947789i	$-0.396687\pi$
$311$	−178.470	−	154.645i	−0.573858	−	0.497251i	−0.892757	+	0.450538i	$0.851232\pi$
$312$	−71.9969	−	112.029i	−0.230759	−	0.359068i
$313$	127.956	−	199.103i	0.408805	−	0.636113i	−0.574409	−	0.818568i	$-0.694768\pi$
$313$	127.956	−	199.103i	0.408805	−	0.636113i	0.983214	+	0.182456i	$0.0584046\pi$
$314$	84.7942	−	12.1916i	0.270045	−	0.0388267i
$315$	−133.020	+	85.4865i	−0.422285	+	0.271386i
$316$	−180.620	+	82.4865i	−0.571583	+	0.261033i
$317$	−86.8400	−	100.219i	−0.273943	−	0.316148i	0.602062	−	0.798450i	$-0.294346\pi$
$317$	−86.8400	−	100.219i	−0.273943	−	0.316148i	−0.876005	+	0.482302i	$0.839801\pi$
$318$	21.1049	+	18.2875i	0.0663675	+	0.0575078i
$319$	4.20574	+	0.604694i	0.0131841	+	0.00189559i
$320$	46.2388	−	21.1166i	0.144496	−	0.0659893i
$321$	258.002	−	223.560i	0.803744	−	0.696448i
$322$	−199.756	−	58.6536i	−0.620359	−	0.182154i
$323$	−286.021	−	83.9833i	−0.885514	−	0.260010i
$324$	−4.28404	+	29.7962i	−0.0132223	+	0.0919634i
$325$	29.6587	−	46.1499i	0.0912577	−	0.142000i
$326$	119.727	+	54.6777i	0.367262	+	0.167723i
$327$	14.1189	−	4.14569i	0.0431771	−	0.0126779i
$328$	−38.0358	+	83.2868i	−0.115963	+	0.253923i
$329$	531.866	−	76.4708i	1.61661	−	0.232434i
$330$	−1.09554	+	7.61964i	−0.00331981	+	0.0230898i
$331$	376.048	−	325.847i	1.13610	−	0.984433i	0.136116	−	0.990693i	$-0.456538\pi$
$331$	376.048	−	325.847i	1.13610	−	0.984433i	0.999980	+	0.00626013i	$0.00199267\pi$
$332$	355.771	−	228.640i	1.07160	−	0.688676i
$333$	57.6345	−	126.202i	0.173076	−	0.378985i
$334$		−	37.2230i		−	0.111446i
$335$	−96.5005	+	349.222i	−0.288061	+	1.04245i
$336$	144.613			0.430396
$337$	133.983	+	61.1879i	0.397575	+	0.181566i	0.604161	−	0.796862i	$-0.293508\pi$
$337$	133.983	+	61.1879i	0.397575	+	0.181566i	−0.206587	+	0.978428i	$0.566236\pi$
$338$	−0.774433	−	1.20504i	−0.00229122	−	0.00356521i
$339$	132.968	+	153.453i	0.392235	+	0.452663i
$340$	−242.654	−	34.8883i	−0.713687	−	0.102613i
$341$	6.84301	+	47.5942i	0.0200675	+	0.139572i
$342$	−48.5835	−	22.1874i	−0.142057	−	0.0648753i
$343$	−8.23664	−	28.0514i	−0.0240135	−	0.0817825i
$344$	125.096	−	273.923i	0.363652	−	0.796287i
$345$	−207.910	−	133.616i	−0.602638	−	0.387292i
$346$	−115.595	−	16.6201i	−0.334090	−	0.0480349i
$347$	48.8107	−	166.234i	0.140665	−	0.479060i	−0.858781	−	0.512342i	$-0.828778\pi$
$347$	48.8107	−	166.234i	0.140665	−	0.479060i	0.999446	+	0.0332823i	$0.0105960\pi$
$348$	−6.83035	+	23.2620i	−0.0196274	+	0.0668449i
$349$	−218.241	−	251.864i	−0.625332	−	0.721672i	0.351378	−	0.936234i	$-0.385713\pi$
$349$	−218.241	−	251.864i	−0.625332	−	0.721672i	−0.976710	+	0.214562i	$0.931168\pi$
$350$	−13.9041	−	30.4457i	−0.0397259	−	0.0869876i
$351$	9.56290	−	66.5114i	0.0272447	−	0.189491i
$352$	20.4228	−	23.5692i	0.0580194	−	0.0669580i
$353$	−60.6293	+	52.5356i	−0.171754	+	0.148826i	−0.736496	−	0.676442i	$-0.763521\pi$
$353$	−60.6293	+	52.5356i	−0.171754	+	0.148826i	0.564742	+	0.825268i	$0.308976\pi$
$354$	17.8494	+	39.0847i	0.0504220	+	0.110409i
$355$	141.017	+	219.427i	0.397232	+	0.618104i
$356$	0.717179	+	4.98809i	0.00201455	+	0.0140115i
$357$	−192.493	−	123.708i	−0.539196	−	0.346520i
$358$	222.907	−	143.254i	0.622646	−	0.400150i
$359$	328.722	−	379.365i	0.915659	−	1.05673i	−0.0825311	−	0.996588i	$-0.526300\pi$
$359$	328.722	−	379.365i	0.915659	−	1.05673i	0.998190	−	0.0601382i	$-0.0191542\pi$
$360$	−92.5452	−	27.1737i	−0.257070	−	0.0754826i
$361$	−80.3564	+	92.7362i	−0.222594	+	0.256887i
$362$	186.744	−	26.8498i	0.515869	−	0.0741707i
$363$	58.5419	+	199.376i	0.161273	+	0.549244i
$364$	−421.581			−1.15819
$365$			334.726i			0.917059i
$366$	−10.7649	−	36.6617i	−0.0294122	−	0.100169i
$367$	−108.728	+	169.184i	−0.296261	+	0.460991i	−0.957191	−	0.289456i	$-0.906525\pi$
$367$	−108.728	+	169.184i	−0.296261	+	0.460991i	0.660930	+	0.750447i	$0.270162\pi$
$368$	93.8967	+	205.605i	0.255154	+	0.558709i
$369$	−42.0253	+	19.1923i	−0.113890	+	0.0520117i
$370$	170.302	+	109.447i	0.460277	+	0.295802i
$371$	186.268	−	54.6932i	0.502070	−	0.147421i
$372$	−274.358			−0.737521
$373$		−	94.0539i		−	0.252155i	−0.992020	−	0.126078i	$-0.959761\pi$
$373$		−	94.0539i		−	0.252155i	0.992020	−	0.126078i	$-0.0402388\pi$
$374$	−10.6885	+	3.13844i	−0.0285790	+	0.00839155i
$375$	27.6693	+	192.444i	0.0737847	+	0.513184i
$376$	247.712	+	214.643i	0.658808	+	0.570860i
$377$	15.2468	−	51.9259i	0.0404425	−	0.137734i
$378$	−30.9837	−	26.8475i	−0.0819675	−	0.0710252i
$379$	357.019	+	555.533i	0.942004	+	1.46579i	0.884009	+	0.467470i	$0.154834\pi$
$379$	357.019	+	555.533i	0.942004	+	1.46579i	0.0579949	+	0.998317i	$0.481529\pi$
$380$	−215.063	+	334.645i	−0.565955	+	0.880644i
$381$	−115.438	+	16.5975i	−0.302988	+	0.0435631i
$382$	−1.13640	+	0.730317i	−0.00297486	+	0.00191182i
$383$	−246.533	+	112.588i	−0.643690	+	0.293963i	−0.710389	−	0.703810i	$-0.751481\pi$
$383$	−246.533	+	112.588i	−0.643690	+	0.293963i	0.0666983	+	0.997773i	$0.478753\pi$
$384$	147.990	+	170.790i	0.385391	+	0.444764i
$385$	40.4433	+	35.0444i	0.105048	+	0.0910243i
$386$	−142.573	−	20.4989i	−0.369361	−	0.0531061i
$387$	138.217	−	63.1218i	0.357151	−	0.163105i
$388$	181.187	−	157.000i	0.466978	−	0.404638i
$389$	−3.32996	−	0.977765i	−0.00856031	−	0.00251353i	0.277450	−	0.960740i	$-0.410511\pi$
$389$	−3.32996	−	0.977765i	−0.00856031	−	0.00251353i	−0.286010	+	0.958227i	$0.592329\pi$
$390$	94.0753	+	27.6230i	0.241219	+	0.0708282i
$391$	50.8977	−	354.001i	0.130173	−	0.905375i
$392$	−147.862	+	230.078i	−0.377200	+	0.586935i
$393$	−398.085	−	181.799i	−1.01294	−	0.462593i
$394$	209.513	−	61.5187i	0.531760	−	0.156139i
$395$	133.360	−	292.019i	0.337621	−	0.739287i
$396$	10.0842	−	1.44989i	0.0254651	−	0.00366133i
$397$	110.563	−	768.986i	0.278497	−	1.93699i	−0.0651097	−	0.997878i	$-0.520740\pi$
$397$	110.563	−	768.986i	0.278497	−	1.93699i	0.343607	−	0.939114i	$-0.388351\pi$
$398$	14.5759	−	12.6301i	0.0366229	−	0.0317339i
$399$	−312.350	+	200.735i	−0.782833	+	0.503096i
$400$	−15.0957	+	33.0549i	−0.0377392	+	0.0826373i
$401$			408.965i			1.01986i	0.860215	+	0.509931i	$0.170329\pi$
$401$			408.965i			1.01986i	−0.860215	+	0.509931i	$0.829671\pi$
$402$	−93.9270	+	1.50265i	−0.233649	+	0.00373794i
$403$	612.426			1.51967
$404$	397.584	+	181.571i	0.984119	+	0.449432i
$405$	−26.3121	−	40.9425i	−0.0649682	−	0.101093i
$406$	−21.6225	−	24.9537i	−0.0532575	−	0.0614624i
$407$	−46.4769	−	6.68237i	−0.114194	−	0.0164186i
$408$	−19.8638	−	138.156i	−0.0486857	−	0.338617i
$409$	−133.458	−	60.9484i	−0.326304	−	0.149018i	0.245526	−	0.969390i	$-0.421039\pi$
$409$	−133.458	−	60.9484i	−0.326304	−	0.149018i	−0.571830	+	0.820372i	$0.693766\pi$
$410$	−18.9923	−	64.6817i	−0.0463226	−	0.157760i
$411$	−18.1596	+	39.7640i	−0.0441840	+	0.0967495i
$412$	−472.175	−	303.448i	−1.14606	−	0.736525i
$413$	295.658	+	42.5092i	0.715879	+	0.102928i
$414$	18.0531	−	61.4833i	0.0436066	−	0.148510i
$415$	−192.630	+	656.039i	−0.464170	+	1.58082i
$416$	−260.119	−	300.193i	−0.625286	−	0.721619i
$417$	95.9237	+	210.044i	0.230033	+	0.503702i
$418$	−2.57249	+	17.8921i	−0.00615428	+	0.0428040i
$419$	119.927	−	138.403i	0.286222	−	0.330317i	−0.594371	−	0.804191i	$-0.702599\pi$
$419$	119.927	−	138.403i	0.286222	−	0.330317i	0.880593	+	0.473873i	$0.157145\pi$
$420$	−230.763	+	199.958i	−0.549437	+	0.476090i
$421$	−171.424	−	375.367i	−0.407183	−	0.891607i	−0.996491	−	0.0836987i	$-0.973327\pi$
$421$	−171.424	−	375.367i	−0.407183	−	0.891607i	0.589308	−	0.807909i	$-0.299401\pi$
$422$	−54.7161	−	85.1400i	−0.129659	−	0.201753i
$423$	23.5371	+	163.704i	0.0556434	+	0.387008i
$424$	99.6201	+	64.0220i	0.234953	+	0.150995i
$425$	48.3702	−	31.0856i	0.113812	−	0.0731426i
$426$	−44.2873	+	51.1102i	−0.103961	+	0.119977i
$427$	−254.862	−	74.8342i	−0.596866	−	0.175256i
$428$	431.712	−	498.222i	1.00867	−	1.16407i
$429$	−22.5101	+	3.23646i	−0.0524710	+	0.00754419i
$430$	62.4638	+	212.732i	0.145265	+	0.494726i
$431$	545.799			1.26636			0.633178	−	0.774006i	$-0.281750\pi$
$431$	545.799			1.26636			0.633178	+	0.774006i	$0.281750\pi$
$432$			44.5109i			0.103034i
$433$	−50.3452	−	171.460i	−0.116271	−	0.395981i	0.880708	−	0.473660i	$-0.157067\pi$
$433$	−50.3452	−	171.460i	−0.116271	−	0.395981i	−0.996978	+	0.0776786i	$0.975249\pi$
$434$	202.012	−	314.337i	0.465466	−	0.724280i
$435$	−16.2829	−	35.6546i	−0.0374319	−	0.0819645i
$436$	25.8479	−	11.8043i	0.0592842	−	0.0270742i
$437$	−488.205	−	313.750i	−1.11717	−	0.717964i
$438$	−83.2719	+	24.4508i	−0.190118	+	0.0558238i
$439$	427.806			0.974501			0.487251	−	0.873262i	$-0.338000\pi$
$439$	427.806			0.974501			0.487251	+	0.873262i	$0.338000\pi$
$440$			32.6432i			0.0741891i
$441$	−132.411	+	38.8795i	−0.300253	+	0.0881622i
$442$	20.1922	+	140.440i	0.0456836	+	0.317737i
$443$	−464.790	−	402.743i	−1.04919	−	0.909127i	−0.0531974	−	0.998584i	$-0.516941\pi$
$443$	−464.790	−	402.743i	−1.04919	−	0.909127i	−0.995991	+	0.0894574i	$0.971487\pi$
$444$	75.4809	−	257.064i	0.170002	−	0.578974i
$445$	−6.15742	−	5.33544i	−0.0138369	−	0.0119897i
$446$	22.7629	+	35.4197i	0.0510379	+	0.0794165i
$447$	−186.731	+	290.559i	−0.417742	+	0.650020i
$448$	90.6894	−	13.0392i	0.202432	−	0.0291053i
$449$	468.764	−	301.256i	1.04402	−	0.670949i	0.0980397	−	0.995183i	$-0.468743\pi$
$449$	468.764	−	301.256i	1.04402	−	0.670949i	0.945977	+	0.324234i	$0.105106\pi$
$450$	9.37095	−	4.27957i	0.0208243	−	0.00951016i
$451$	10.2394	+	11.8169i	0.0227038	+	0.0262015i
$452$	296.330	+	256.771i	0.655597	+	0.568078i
$453$	244.197	+	35.1102i	0.539066	+	0.0775059i
$454$	48.9242	−	22.3429i	0.107763	−	0.0492135i
$455$	515.114	−	446.349i	1.13212	−	0.980986i
$456$	−217.310	−	63.8081i	−0.476558	−	0.139930i
$457$	−704.139	−	206.754i	−1.54079	−	0.452416i	−0.602455	−	0.798153i	$-0.705811\pi$
$457$	−704.139	−	206.754i	−1.54079	−	0.452416i	−0.938331	+	0.345738i	$0.887629\pi$
$458$	−34.0282	+	236.671i	−0.0742974	+	0.516750i
$459$	38.0763	−	59.2479i	0.0829550	−	0.129080i
$460$	−434.125	−	198.258i	−0.943750	−	0.430996i
$461$	−88.3765	+	25.9497i	−0.191706	+	0.0562900i	−0.376176	−	0.926548i	$-0.622761\pi$
$461$	−88.3765	+	25.9497i	−0.191706	+	0.0562900i	0.184470	+	0.982838i	$0.440943\pi$
$462$	−5.76392	+	12.6212i	−0.0124760	+	0.0273187i
$463$	−760.628	+	109.362i	−1.64282	+	0.236203i	−0.900820	−	0.434192i	$-0.857034\pi$
$463$	−760.628	+	109.362i	−1.64282	+	0.236203i	−0.742005	+	0.670395i	$0.766125\pi$
$464$	−5.10174	+	35.4834i	−0.0109951	+	0.0764729i
$465$	335.227	−	290.476i	0.720918	−	0.624679i
$466$	212.513	−	136.574i	0.456036	−	0.293076i
$467$	−275.909	+	604.156i	−0.590811	+	1.29370i	0.344140	+	0.938919i	$0.388171\pi$
$467$	−275.909	+	604.156i	−0.590811	+	1.29370i	−0.934951	+	0.354778i	$0.884557\pi$
$468$		−	129.760i		−	0.277264i
$469$	−344.226	+	554.947i	−0.733956	+	1.18326i
$470$	−241.322			−0.513452
$471$	166.734	+	76.1450i	0.354001	+	0.161667i
$472$	98.5066	+	153.279i	0.208700	+	0.324744i
$473$	−33.6764	−	38.8647i	−0.0711976	−	0.0821664i
$474$	82.3888	+	11.8457i	0.173816	+	0.0249910i
$475$	−13.2779	−	92.3495i	−0.0279534	−	0.194420i
$476$	−401.933	−	183.557i	−0.844398	−	0.385624i
$477$	16.8342	+	57.3320i	0.0352918	+	0.120193i
$478$	102.386	−	224.193i	0.214196	−	0.469023i
$479$	694.103	+	446.073i	1.44907	+	0.931259i	0.999273	+	0.0381269i	$0.0121391\pi$
$479$	694.103	+	446.073i	1.44907	+	0.931259i	0.449794	+	0.893132i	$0.351497\pi$
$480$	−284.766	−	40.9431i	−0.593262	−	0.0852982i
$481$	−168.490	+	573.823i	−0.350291	+	1.19298i
$482$	−48.4487	+	165.001i	−0.100516	+	0.342326i
$483$	−291.713	−	336.655i	−0.603961	−	0.697008i
$484$	166.691	+	365.003i	0.344403	+	0.754138i
$485$	−55.1625	+	383.663i	−0.113737	+	0.791059i
$486$	8.26348	−	9.53656i	0.0170030	−	0.0196225i
$487$	443.310	−	384.130i	0.910287	−	0.788768i	−0.0676411	−	0.997710i	$-0.521547\pi$
$487$	443.310	−	384.130i	0.910287	−	0.788768i	0.977928	+	0.208941i	$0.0670018\pi$
$488$	−67.3083	−	147.385i	−0.137927	−	0.302018i
$489$	152.260	+	236.922i	0.311371	+	0.484502i
$490$	−28.6568	−	199.313i	−0.0584833	−	0.406760i
$491$	−674.647	−	433.570i	−1.37403	−	0.883034i	−0.374996	−	0.927027i	$-0.622356\pi$
$491$	−674.647	−	433.570i	−1.37403	−	0.883034i	−0.999032	+	0.0439928i	$0.985992\pi$
$492$	−75.0538	+	48.2341i	−0.152548	+	0.0980368i
$493$	37.1448	−	42.8673i	0.0753444	−	0.0869520i
$494$	220.903	+	64.8630i	0.447172	+	0.131302i
$495$	−10.7864	+	12.4482i	−0.0217907	+	0.0251478i
$496$	−401.547	+	57.7338i	−0.809571	+	0.116399i
$497$	132.452	+	451.090i	0.266503	+	0.907626i
$498$	−177.278			−0.355980
$499$			541.644i			1.08546i	0.839908	+	0.542730i	$0.182609\pi$
$499$			541.644i			1.08546i	−0.839908	+	0.542730i	$0.817391\pi$
$500$	105.775	+	360.238i	0.211551	+	0.720476i
$501$	43.0596	−	67.0020i	0.0859472	−	0.133737i
$502$	−100.933	−	221.013i	−0.201062	−	0.440265i
$503$	−476.459	+	217.592i	−0.947235	+	0.432588i	−0.828282	−	0.560312i	$-0.810681\pi$
$503$	−476.459	+	217.592i	−0.947235	+	0.432588i	−0.118953	+	0.992900i	$0.537954\pi$
$504$	−146.251	−	93.9895i	−0.290180	−	0.186487i
$505$	−678.030	+	199.088i	−1.34263	+	0.394233i
$506$	−21.6868			−0.0428593
$507$		−	3.06496i		−	0.00604529i
$508$	−216.090	+	63.4498i	−0.425375	+	0.124901i
$509$	36.6459	+	254.878i	0.0719958	+	0.500742i	0.993631	+	0.112684i	$0.0359448\pi$
$509$	36.6459	+	254.878i	0.0719958	+	0.500742i	−0.921635	+	0.388058i	$0.873146\pi$
$510$	77.6637	+	67.2960i	0.152282	+	0.131953i
$511$	−169.975	+	578.882i	−0.332632	+	1.13284i
$512$	352.811	+	305.713i	0.689084	+	0.597095i
$513$	−61.7849	−	96.1391i	−0.120438	−	0.187406i
$514$	173.239	−	269.565i	0.337040	−	0.524445i
$515$	898.208	−	129.143i	1.74409	−	0.250763i
$516$	246.845	−	158.638i	0.478382	−	0.307437i
$517$	50.9154	−	23.2523i	0.0984825	−	0.0449754i
$518$	238.947	+	275.759i	0.461287	+	0.532354i
$519$	−188.847	−	163.637i	−0.363867	−	0.315293i
$520$	411.534	+	59.1696i	0.791411	+	0.113788i
$521$	−360.619	+	164.689i	−0.692168	+	0.316102i	−0.730258	−	0.683172i	$-0.760600\pi$
$521$	−360.619	+	164.689i	−0.692168	+	0.316102i	0.0380899	+	0.999274i	$0.487873\pi$
$522$	7.68058	−	6.65526i	0.0147138	−	0.0127495i
$523$	−259.058	−	76.0662i	−0.495330	−	0.145442i	0.0245204	−	0.999699i	$-0.492194\pi$
$523$	−259.058	−	76.0662i	−0.495330	−	0.145442i	−0.519850	+	0.854257i	$0.674012\pi$
$524$	−810.871	−	238.093i	−1.54746	−	0.454376i
$525$	10.1920	−	70.8870i	0.0194134	−	0.135023i
$526$	−143.096	+	222.662i	−0.272045	+	0.423311i
$527$	583.883	+	266.650i	1.10794	+	0.505978i
$528$	14.4540	−	4.24408i	0.0273750	−	0.00803803i
$529$	69.4796	−	152.139i	0.131341	−	0.287598i
$530$	−86.2990	+	12.4079i	−0.162828	+	0.0234112i
$531$	−13.0840	+	91.0014i	−0.0246404	+	0.171377i
$532$	−541.868	+	469.531i	−1.01855	+	0.882577i
$533$	167.536	−	107.669i	0.314327	−	0.202006i
$534$	0.877546	−	1.92156i	0.00164334	−	0.00359842i
$535$			1065.83i			1.99221i
$536$	−393.335	+	62.9905i	−0.733834	+	0.117520i
$537$	566.953			1.05578
$538$	37.4740	+	17.1138i	0.0696542	+	0.0318100i
$539$	25.2507	+	39.2908i	0.0468472	+	0.0728957i
$540$	−61.5455	−	71.0273i	−0.113973	−	0.131532i
$541$	691.157	+	99.3734i	1.27755	+	0.183685i	0.747490	−	0.664273i	$-0.231259\pi$
$541$	691.157	+	99.3734i	1.27755	+	0.183685i	0.530064	+	0.847957i	$0.322168\pi$
$542$	−13.5834	−	94.4748i	−0.0250617	−	0.174308i
$543$	367.203	+	167.696i	0.676249	+	0.308833i
$544$	−117.292	−	399.459i	−0.215610	−	0.734299i
$545$	−19.0847	+	41.7897i	−0.0350178	+	0.0766783i
$546$	148.668	+	95.5434i	0.272287	+	0.174988i
$547$	519.159	+	74.6438i	0.949103	+	0.136460i	0.599444	−	0.800417i	$-0.295388\pi$
$547$	519.159	+	74.6438i	0.949103	+	0.136460i	0.349659	+	0.936877i	$0.386297\pi$
$548$	−23.7827	+	80.9966i	−0.0433992	+	0.147804i
$549$	23.0334	−	78.4446i	0.0419552	−	0.142886i
$550$	−2.28322	−	2.63497i	−0.00415130	−	0.00479086i
$551$	−38.2347	−	83.7223i	−0.0693915	−	0.151946i
$552$	38.6706	−	268.960i	0.0700554	−	0.487246i
$553$	378.924	−	437.301i	0.685215	−	0.790780i
$554$	211.854	−	183.572i	0.382408	−	0.331358i
$555$	179.939	+	394.012i	0.324215	+	0.709932i
$556$	241.075	+	375.121i	0.433589	+	0.674678i
$557$	30.9517	+	215.274i	0.0555686	+	0.386488i	0.998559	+	0.0536679i	$0.0170912\pi$
$557$	30.9517	+	215.274i	0.0555686	+	0.386488i	−0.942990	+	0.332821i	$0.892000\pi$
$558$	96.7508	+	62.1780i	0.173388	+	0.111430i
$559$	−551.011	+	354.113i	−0.985709	+	0.633476i
$560$	−295.666	+	341.216i	−0.527974	+	0.609315i
$561$	−22.8701	−	6.71527i	−0.0407667	−	0.0119702i
$562$	−242.271	+	279.596i	−0.431088	+	0.497502i
$563$	547.575	−	78.7294i	0.972603	−	0.139839i	0.362347	−	0.932043i	$-0.381976\pi$
$563$	547.575	−	78.7294i	0.972603	−	0.139839i	0.610256	+	0.792204i	$0.291067\pi$
$564$	89.9789	+	306.440i	0.159537	+	0.543334i
$565$	−633.930			−1.12200
$566$		−	210.469i		−	0.371853i
$567$	−24.7140	−	84.1680i	−0.0435872	−	0.148445i
$568$	−155.044	+	241.253i	−0.272964	+	0.424740i
$569$	−210.458	−	460.838i	−0.369873	−	0.809908i	−0.999456	−	0.0329753i	$-0.989502\pi$
$569$	−210.458	−	460.838i	−0.369873	−	0.809908i	0.629584	−	0.776933i	$-0.283226\pi$
$570$	151.682	−	69.2707i	0.266108	−	0.121528i
$571$	−296.216	−	190.366i	−0.518767	−	0.333391i	0.254917	−	0.966963i	$-0.417952\pi$
$571$	−296.216	−	190.366i	−0.518767	−	0.333391i	−0.773684	+	0.633572i	$0.781588\pi$
$572$	−42.1368	+	12.3725i	−0.0736658	+	0.0216302i
$573$	−2.89036			−0.00504426
$574$		−	121.506i		−	0.211683i
$575$	107.402	−	31.5360i	0.186786	−	0.0548453i
$576$	4.01336	+	27.9135i	0.00696764	+	0.0484610i
$577$	−52.0864	−	45.1332i	−0.0902711	−	0.0782204i	0.608556	−	0.793511i	$-0.291749\pi$
$577$	−52.0864	−	45.1332i	−0.0902711	−	0.0782204i	−0.698827	+	0.715290i	$0.746294\pi$
$578$	24.0127	−	81.7798i	0.0415445	−	0.141488i
$579$	−232.921	−	201.827i	−0.402282	−	0.348579i
$580$	−40.9222	−	63.6761i	−0.0705554	−	0.109786i
$581$	−666.277	+	1036.75i	−1.14678	+	1.78442i
$582$	−99.4757	+	14.3024i	−0.170920	+	0.0245747i
$583$	17.0123	−	10.9331i	0.0291806	−	0.0187532i
$584$	−334.763	+	152.881i	−0.573224	+	0.261783i
$585$	137.383	+	158.548i	0.234842	+	0.271023i
$586$	−303.007	−	262.557i	−0.517078	−	0.448050i
$587$	−8.99840	−	1.29378i	−0.0153295	−	0.00220405i	0.134646	−	0.990894i	$-0.457010\pi$
$587$	−8.99840	−	1.29378i	−0.0153295	−	0.00220405i	−0.149975	+	0.988690i	$0.547919\pi$
$588$	−242.410	+	110.705i	−0.412261	+	0.188273i
$589$	787.164	−	682.081i	1.33644	−	1.15803i
$590$	−128.714	−	37.7940i	−0.218160	−	0.0640576i
$591$	448.293	+	131.631i	0.758533	+	0.222725i
$592$	56.3785	−	392.121i	0.0952339	−	0.662366i
$593$	−75.2616	+	117.109i	−0.126917	+	0.197486i	−0.898897	−	0.438161i	$-0.855630\pi$
$593$	−75.2616	+	117.109i	−0.126917	+	0.197486i	0.771980	+	0.635647i	$0.219266\pi$
$594$	−3.88472	−	1.77409i	−0.00653993	−	0.00298669i
$595$	685.447	−	201.265i	1.15201	−	0.338261i
$596$	−277.070	+	606.699i	−0.464882	+	1.01795i
$597$	40.8474	−	5.87297i	0.0684212	−	0.00983748i
$598$	−39.3099	+	273.407i	−0.0657357	+	0.457202i
$599$	614.156	−	532.169i	1.02530	−	0.888430i	0.0314906	−	0.999504i	$-0.489975\pi$
$599$	614.156	−	532.169i	1.02530	−	0.888430i	0.993812	+	0.111074i	$0.0354291\pi$
$600$	36.7502	−	23.6179i	0.0612504	−	0.0393632i
$601$	82.2289	−	180.056i	0.136820	−	0.299594i	−0.828803	−	0.559541i	$-0.810978\pi$
$601$	82.2289	−	180.056i	0.136820	−	0.299594i	0.965623	+	0.259946i	$0.0837049\pi$
$602$			399.622i			0.663824i
$603$	−170.809	−	105.950i	−0.283265	−	0.175705i
$604$	476.412			0.788762
$605$	−590.119	−	269.499i	−0.975404	−	0.445452i
$606$	−99.0564	−	154.135i	−0.163459	−	0.254348i
$607$	174.711	+	201.628i	0.287828	+	0.332171i	0.881188	−	0.472766i	$-0.156745\pi$
$607$	174.711	+	201.628i	0.287828	+	0.332171i	−0.593360	+	0.804937i	$0.702199\pi$
$608$	−668.673	−	96.1407i	−1.09979	−	0.158126i
$609$	−10.0544	−	69.9302i	−0.0165098	−	0.114828i
$610$	108.513	+	49.5561i	0.177890	+	0.0812396i
$611$	−200.852	−	684.040i	−0.328727	−	1.11954i
$612$	56.4974	−	123.712i	0.0923161	−	0.202144i
$613$	273.177	+	175.560i	0.445639	+	0.286395i	0.744151	−	0.668011i	$-0.232854\pi$
$613$	273.177	+	175.560i	0.445639	+	0.286395i	−0.298513	+	0.954406i	$0.596490\pi$
$614$	361.180	+	51.9298i	0.588240	+	0.0845762i
$615$	40.6374	−	138.398i	0.0660771	−	0.225038i
$616$	−16.5763	+	56.4537i	−0.0269096	+	0.0916457i
$617$	−289.794	−	334.440i	−0.469683	−	0.542043i	0.470641	−	0.882325i	$-0.344023\pi$
$617$	−289.794	−	334.440i	−0.469683	−	0.542043i	−0.940323	+	0.340282i	$0.889477\pi$
$618$	97.7392	+	214.019i	0.158154	+	0.346309i
$619$	152.560	−	1061.08i	0.246463	−	1.71419i	−0.371883	−	0.928280i	$-0.621288\pi$
$619$	152.560	−	1061.08i	0.246463	−	1.71419i	0.618346	−	0.785906i	$-0.287803\pi$
$620$	560.932	−	647.350i	0.904729	−	1.04411i
$621$	103.620	−	89.7872i	0.166860	−	0.144585i
$622$	79.4108	+	173.885i	0.127670	+	0.279559i
$623$	−7.93941	−	12.3540i	−0.0127438	−	0.0198298i
$624$	−27.3057	−	189.915i	−0.0437591	−	0.304351i
$625$	−599.863	−	385.508i	−0.959780	−	0.616813i
$626$	−161.172	+	103.579i	−0.257463	+	0.165461i
$627$	−25.3281	+	29.2302i	−0.0403957	+	0.0466191i
$628$	339.626	+	99.7233i	0.540806	+	0.158795i
$629$	−410.480	+	473.719i	−0.652592	+	0.753131i
$630$	126.694	−	18.2159i	0.201102	−	0.0289141i
$631$	−37.9361	−	129.199i	−0.0601207	−	0.204752i	0.923955	−	0.382500i	$-0.124937\pi$
$631$	−37.9361	−	129.199i	−0.0601207	−	0.204752i	−0.984076	+	0.177748i	$0.943119\pi$
$632$	352.961			0.558482
$633$		−	216.549i		−	0.342100i
$634$	30.2426	+	102.997i	0.0477012	+	0.162455i
$635$	196.855	−	306.312i	0.310008	−	0.482381i
$636$	47.9333	+	104.959i	0.0753668	+	0.165030i
$637$	541.110	−	247.117i	0.849467	−	0.387939i
$638$	−2.89350	−	1.85954i	−0.00453526	−	0.00291464i
$639$	−138.842	+	40.7678i	−0.217281	+	0.0637993i
$640$	−705.549			−1.10242
$641$			410.143i			0.639849i	0.947443	+	0.319924i	$0.103657\pi$
$641$			410.143i			0.639849i	−0.947443	+	0.319924i	$0.896343\pi$
$642$	−265.154	+	77.8561i	−0.413012	+	0.121271i
$643$	−72.0064	−	500.816i	−0.111985	−	0.778874i	−0.965985	−	0.258600i	$-0.916739\pi$
$643$	−72.0064	−	500.816i	−0.111985	−	0.778874i	0.853999	−	0.520274i	$-0.174170\pi$
$644$	−650.108	−	563.322i	−1.00948	−	0.874723i
$645$	−133.653	+	455.180i	−0.207214	+	0.705705i
$646$	182.366	+	158.021i	0.282301	+	0.244615i
$647$	−322.895	−	502.435i	−0.499066	−	0.776561i	0.496755	−	0.867891i	$-0.334525\pi$
$647$	−322.895	−	502.435i	−0.499066	−	0.776561i	−0.995821	+	0.0913295i	$0.970888\pi$
$648$	28.9293	−	45.0148i	0.0446440	−	0.0694674i
$649$	30.7984	−	4.42814i	0.0474552	−	0.00682303i
$650$	−37.3578	+	24.0084i	−0.0574735	+	0.0369360i
$651$	727.252	−	332.125i	1.11713	−	0.510176i
$652$	356.145	+	411.013i	0.546235	+	0.630389i
$653$	299.696	+	259.688i	0.458952	+	0.397684i	0.853419	−	0.521226i	$-0.174525\pi$
$653$	299.696	+	259.688i	0.458952	+	0.397684i	−0.394466	+	0.918910i	$0.629071\pi$
$654$	−11.7904	−	1.69520i	−0.0180281	−	0.00259204i
$655$	1242.85	−	567.592i	1.89748	−	0.866552i
$656$	−99.6980	+	86.3888i	−0.151979	+	0.131690i
$657$	−178.176	−	52.3171i	−0.271196	−	0.0796303i
$658$	−417.347	−	122.544i	−0.634267	−	0.186237i
$659$	82.1843	−	571.604i	0.124711	−	0.867381i	−0.827397	−	0.561618i	$-0.810179\pi$
$659$	82.1843	−	571.604i	0.124711	−	0.867381i	0.952107	−	0.305764i	$-0.0989118\pi$
$660$	−17.1964	+	26.7581i	−0.0260551	+	0.0405425i
$661$	323.661	+	147.811i	0.489653	+	0.223617i	0.644912	−	0.764257i	$-0.276894\pi$
$661$	323.661	+	147.811i	0.489653	+	0.223617i	−0.155259	+	0.987874i	$0.549621\pi$
$662$	−386.472	+	113.478i	−0.583794	+	0.171417i
$663$	−126.114	+	276.152i	−0.190218	+	0.416519i
$664$	−744.091	+	106.984i	−1.12062	+	0.161121i
$665$	164.972	−	1147.40i	0.248078	−	1.72542i
$666$	−84.8767	+	73.5461i	−0.127443	+	0.110430i
$667$	92.8955	−	59.7003i	0.139274	−	0.0895057i
$668$	63.8915	−	139.903i	0.0956460	−	0.209436i
$669$			90.0883i			0.134661i
$670$	188.491	−	224.694i	0.281330	−	0.335364i
$671$	−27.6695			−0.0412362
$672$	−471.688	−	215.413i	−0.701917	−	0.320555i
$673$	−577.202	−	898.144i	−0.857655	−	1.33454i	−0.941136	−	0.338028i	$-0.890240\pi$
$673$	−577.202	−	898.144i	−0.857655	−	1.33454i	0.0834809	−	0.996509i	$-0.473396\pi$
$674$	−78.0805	−	90.1097i	−0.115846	−	0.133694i
$675$	21.8185	+	3.13703i	0.0323237	+	0.00464745i
$676$	−0.842317	−	5.85844i	−0.00124603	−	0.00866633i
$677$	222.768	+	101.735i	0.329051	+	0.150273i	0.573089	−	0.819493i	$-0.305745\pi$
$677$	222.768	+	101.735i	0.329051	+	0.150273i	−0.244038	+	0.969766i	$0.578472\pi$
$678$	−46.3068	−	157.707i	−0.0682991	−	0.232605i
$679$	−290.224	+	635.503i	−0.427429	+	0.935940i
$680$	366.592	+	235.594i	0.539105	+	0.346462i
$681$	113.911	+	16.3779i	0.167270	+	0.0240498i
$682$	10.9659	−	37.3465i	0.0160791	−	0.0547602i
$683$	340.047	−	1158.09i	0.497872	−	1.69560i	−0.200357	−	0.979723i	$-0.564210\pi$
$683$	340.047	−	1158.09i	0.497872	−	1.69560i	0.698229	−	0.715874i	$-0.253972\pi$
$684$	−144.518	−	166.783i	−0.211284	−	0.243835i
$685$	−56.6958	−	124.147i	−0.0827676	−	0.181236i
$686$	−3.36801	+	23.4250i	−0.00490964	+	0.0341473i
$687$	−335.033	+	386.649i	−0.487676	+	0.562808i
$688$	327.897	−	284.125i	0.476595	−	0.412972i
$689$	−106.997	−	234.292i	−0.155294	−	0.340046i
$690$	108.160	+	168.301i	0.156754	+	0.243914i
$691$	−54.0080	−	375.634i	−0.0781592	−	0.543609i	−0.990851	−	0.134961i	$-0.956909\pi$
$691$	−54.0080	−	375.634i	−0.0781592	−	0.543609i	0.912692	−	0.408649i	$-0.134000\pi$
$692$	−405.938	−	260.880i	−0.586615	−	0.376995i
$693$	−24.9754	+	16.0507i	−0.0360395	+	0.0231612i
$694$	−91.8412	+	105.990i	−0.132336	+	0.152724i
$695$	−691.719	−	203.107i	−0.995279	−	0.292240i
$696$	28.2215	−	32.5694i	0.0405481	−	0.0467950i
$697$	206.607	−	29.7056i	0.296424	−	0.0426193i
$698$	76.0037	+	258.845i	0.108888	+	0.370838i
$699$	540.515			0.773269
$700$		−	138.296i		−	0.197566i
$701$	79.6602	+	271.298i	0.113638	+	0.387015i	0.996596	−	0.0824358i	$-0.0262700\pi$
$701$	79.6602	+	271.298i	0.113638	+	0.387015i	−0.882958	+	0.469451i	$0.844452\pi$
$702$	−29.4076	+	45.7591i	−0.0418911	+	0.0651838i
$703$	422.525	+	925.201i	0.601031	+	1.31607i
$704$	8.68168	−	3.96479i	0.0123319	−	0.00563180i
$705$	−434.385	−	279.162i	−0.616149	−	0.395975i
$706$	62.3099	−	18.2958i	0.0882577	−	0.0259148i
$707$	−1273.70			−1.80155
$708$			177.538i			0.250760i
$709$	534.806	−	157.033i	0.754310	−	0.221485i	0.118100	−	0.993002i	$-0.462320\pi$
$709$	534.806	−	157.033i	0.754310	−	0.221485i	0.636210	+	0.771516i	$0.280501\pi$
$710$	−30.0486	−	208.993i	−0.0423220	−	0.294356i
$711$	134.598	+	116.630i	0.189308	+	0.164037i
$712$	2.52371	−	8.59497i	0.00354454	−	0.0120716i
$713$	944.403	+	818.330i	1.32455	+	1.14773i
$714$	100.140	+	155.821i	0.140252	+	0.218237i
$715$	38.3860	−	59.7298i	0.0536867	−	0.0835381i
$716$	1083.69	−	155.811i	1.51353	−	0.217613i
$717$	443.643	−	285.112i	0.618749	−	0.397646i
$718$	−369.620	+	168.800i	−0.514791	+	0.235097i
$719$	−356.769	−	411.733i	−0.496201	−	0.572647i	0.451311	−	0.892367i	$-0.350957\pi$
$719$	−356.769	−	411.733i	−0.496201	−	0.572647i	−0.947512	+	0.319720i	$0.896411\pi$
$720$	−105.024	−	91.0037i	−0.145867	−	0.126394i
$721$	1618.96	+	232.771i	2.24543	+	0.322844i
$722$	90.3541	−	41.2633i	0.125144	−	0.0571514i
$723$	−278.082	+	240.960i	−0.384623	+	0.333277i
$724$	747.968	+	219.623i	1.03310	+	0.303347i
$725$	17.0338	+	5.00158i	0.0234949	+	0.00689873i
$726$	23.9382	−	166.494i	0.0329727	−	0.229330i
$727$	−697.826	+	1085.84i	−0.959871	+	1.49359i	−0.0926302	+	0.995701i	$0.529527\pi$
$727$	−697.826	+	1085.84i	−0.959871	+	1.49359i	−0.867241	+	0.497888i	$0.834109\pi$
$728$	681.668	+	311.307i	0.936357	+	0.427620i
$729$	25.9063	−	7.60678i	0.0355368	−	0.0104345i
$730$	112.560	−	246.471i	0.154191	−	0.337632i
$731$	−679.512	+	97.6991i	−0.929565	+	0.133651i
$732$	22.4684	−	156.271i	0.0306945	−	0.213485i
$733$	417.346	−	361.632i	0.569367	−	0.493359i	−0.321940	−	0.946760i	$-0.604335\pi$
$733$	417.346	−	361.632i	0.569367	−	0.493359i	0.891307	+	0.453401i	$0.149789\pi$
$734$	136.952	−	88.0138i	0.186583	−	0.119910i
$735$	178.982	−	391.916i	0.243513	−	0.533220i
$736$		−	810.493i		−	1.10121i
$737$	−18.1187	+	65.5689i	−0.0245844	+	0.0889673i
$738$	37.3987			0.0506757
$739$	−1094.21	−	499.707i	−1.48066	−	0.676194i	−0.498957	−	0.866627i	$-0.666284\pi$
$739$	−1094.21	−	499.707i	−1.48066	−	0.676194i	−0.981700	+	0.190433i	$0.939011\pi$
$740$	452.223	+	703.673i	0.611113	+	0.950910i
$741$	322.596	+	372.295i	0.435352	+	0.502423i
$742$	−155.548	−	22.3644i	−0.209633	−	0.0301407i
$743$	−119.470	−	830.931i	−0.160794	−	1.11835i	−0.897142	−	0.441743i	$-0.854360\pi$
$743$	−119.470	−	830.931i	−0.160794	−	1.11835i	0.736348	−	0.676603i	$-0.236549\pi$
$744$	443.617	+	202.593i	0.596260	+	0.272303i
$745$	−303.800	−	1034.65i	−0.407786	−	1.38879i
$746$	−31.6278	+	69.2553i	−0.0423966	+	0.0928355i
$747$	−319.103	−	205.075i	−0.427180	−	0.274532i
$748$	−45.5600	−	6.55054i	−0.0609091	−	0.00875741i
$749$	−541.233	+	1843.27i	−0.722608	+	2.46098i
$750$	44.3400	−	151.008i	0.0591199	−	0.201344i
$751$	680.355	+	785.171i	0.905932	+	1.04550i	0.998758	+	0.0498188i	$0.0158644\pi$
$751$	680.355	+	785.171i	0.905932	+	1.04550i	−0.0928264	+	0.995682i	$0.529590\pi$
$752$	196.177	+	429.568i	0.260874	+	0.571235i
$753$	73.9864	−	514.587i	0.0982555	−	0.683382i
$754$	−28.6881	+	33.1078i	−0.0380478	+	0.0439096i
$755$	−582.110	+	504.401i	−0.771006	+	0.668081i
$756$	−70.3701	−	154.089i	−0.0930821	−	0.203821i
$757$	721.998	+	1123.45i	0.953763	+	1.48408i	0.873216	+	0.487333i	$0.162030\pi$
$757$	721.998	+	1123.45i	0.953763	+	1.48408i	0.0805465	+	0.996751i	$0.474333\pi$
$758$	−76.0753	−	529.116i	−0.100363	−	0.698042i
$759$	−39.0367	−	25.0873i	−0.0514317	−	0.0330532i
$760$	594.853	−	382.289i	0.782701	−	0.503011i
$761$	379.607	−	438.090i	0.498827	−	0.575677i	−0.449376	−	0.893343i	$-0.648354\pi$
$761$	379.607	−	438.090i	0.498827	−	0.575677i	0.948203	+	0.317666i	$0.102899\pi$
$762$	90.5828	+	26.5975i	0.118875	+	0.0349049i
$763$	−54.2264	+	62.5806i	−0.0710700	+	0.0820191i
$764$	−5.52471	+	0.794334i	−0.00723130	+	0.00103970i
$765$	61.9480	+	210.976i	0.0809778	+	0.275785i
$766$	219.392			0.286412
$767$		−	396.303i		−	0.516693i
$768$	−33.1902	−	113.035i	−0.0432164	−	0.147181i
$769$	−511.236	+	795.499i	−0.664807	+	1.03446i	0.331058	+	0.943610i	$0.392594\pi$
$769$	−511.236	+	795.499i	−0.664807	+	1.03446i	−0.995865	+	0.0908490i	$0.971042\pi$
$770$	−17.9954	−	39.4045i	−0.0233707	−	0.0511746i
$771$	623.665	−	284.818i	0.808904	−	0.369414i
$772$	−500.678	−	321.766i	−0.648547	−	0.416796i
$773$	−1337.02	+	392.583i	−1.72965	+	0.507870i	−0.986849	−	0.161648i	$-0.948319\pi$
$773$	−1337.02	+	392.583i	−1.72965	+	0.507870i	−0.742797	+	0.669517i	$0.766501\pi$
$774$	−123.001			−0.158916
$775$			200.901i			0.259227i
$776$	−408.900	+	120.064i	−0.526933	+	0.154721i
$777$	111.110	+	772.786i	0.142999	+	0.994576i
$778$	2.12318	+	1.83974i	0.00272902	+	0.00236471i
$779$	95.4229	−	324.981i	0.122494	−	0.417177i
$780$	306.169	+	265.297i	0.392525	+	0.340125i
$781$	26.4770	+	41.1990i	0.0339014	+	0.0527516i
$782$	−156.519	+	243.549i	−0.200152	+	0.311443i
$783$	21.5240	−	3.09468i	0.0274891	−	0.00395234i
$784$	−331.492	+	213.037i	−0.422822	+	0.271731i
$785$	−520.558	+	237.731i	−0.663131	+	0.302842i
$786$	231.990	+	267.731i	0.295153	+	0.340624i
$787$	−671.735	−	582.061i	−0.853538	−	0.739595i	0.113687	−	0.993517i	$-0.463734\pi$
$787$	−671.735	−	582.061i	−0.853538	−	0.739595i	−0.967225	+	0.253922i	$0.918279\pi$
$788$	893.053	+	128.402i	1.13332	+	0.162946i
$789$	−515.150	+	235.261i	−0.652916	+	0.298177i
$790$	−196.396	+	170.178i	−0.248603	+	0.215416i
$791$	−1096.33	−	321.912i	−1.38601	−	0.406968i
$792$	−17.3760	−	5.10207i	−0.0219395	−	0.00644200i
$793$	−50.1542	+	348.830i	−0.0632462	+	0.439887i
$794$	−340.002	+	529.053i	−0.428214	+	0.666313i
$795$	−169.693	−	77.4963i	−0.213451	−	0.0974797i
$796$	76.4628	−	22.4515i	0.0960587	−	0.0282054i
$797$	421.314	−	922.550i	0.528625	−	1.15753i	−0.437444	−	0.899246i	$-0.644116\pi$
$797$	421.314	−	922.550i	0.528625	−	1.15753i	0.966069	−	0.258283i	$-0.0831565\pi$
$798$	297.497	−	42.7736i	0.372803	−	0.0536010i
$799$	106.340	−	739.612i	0.133091	−	0.925672i
$800$	98.4758	−	85.3298i	0.123095	−	0.106662i
$801$	3.80246	−	2.44369i	0.00474714	−	0.00305080i
$802$	137.524	−	301.136i	0.171476	−	0.375481i
$803$			62.8473i			0.0782657i
$804$	−355.605	−	155.574i	−0.442295	−	0.193500i
$805$	1390.76			1.72765
$806$	−450.951	−	205.943i	−0.559493	−	0.255512i
$807$	47.6566	+	74.1551i	0.0590540	+	0.0918898i
$808$	−508.789	−	587.174i	−0.629690	−	0.726701i
$809$	1010.19	+	145.243i	1.24869	+	0.179534i	0.734776	−	0.678310i	$-0.237287\pi$
$809$	1010.19	+	145.243i	1.24869	+	0.179534i	0.513911	+	0.857844i	$0.328196\pi$
$810$	5.60671	+	38.9955i	0.00692186	+	0.0481426i
$811$	478.817	+	218.668i	0.590403	+	0.269628i	0.688133	−	0.725585i	$-0.258431\pi$
$811$	478.817	+	218.668i	0.590403	+	0.269628i	−0.0977295	+	0.995213i	$0.531158\pi$
$812$	−38.4366	−	130.903i	−0.0473357	−	0.161211i
$813$	84.8382	−	185.770i	0.104352	−	0.228499i
$814$	31.9755	+	20.5494i	0.0392820	+	0.0252450i
$815$	−870.319	−	125.133i	−1.06788	−	0.153537i
$816$	56.6561	−	192.953i	0.0694315	−	0.236462i
$817$	−313.837	+	1068.83i	−0.384134	+	1.30824i
$818$	77.7749	+	89.7570i	0.0950793	+	0.109727i
$819$	157.081	+	343.960i	0.191796	+	0.419975i
$820$	39.6406	−	275.706i	0.0483421	−	0.336227i
$821$	−265.593	+	306.510i	−0.323499	+	0.373338i	−0.894083	−	0.447902i	$-0.852171\pi$
$821$	−265.593	+	306.510i	−0.323499	+	0.373338i	0.570584	+	0.821239i	$0.306717\pi$
$822$	26.7432	−	23.1731i	0.0325343	−	0.0281911i
$823$	221.211	+	484.383i	0.268786	+	0.588558i	0.995108	−	0.0987962i	$-0.0314992\pi$
$823$	221.211	+	484.383i	0.268786	+	0.588558i	−0.726322	+	0.687354i	$0.758772\pi$
$824$	539.399	+	839.322i	0.654611	+	1.01859i
$825$	−1.06169	−	7.38423i	−0.00128690	−	0.00895058i
$826$	−203.409	−	130.723i	−0.246258	−	0.158260i
$827$	−1221.47	+	784.994i	−1.47699	+	0.949206i	−0.479568	+	0.877505i	$0.659207\pi$
$827$	−1221.47	+	784.994i	−1.47699	+	0.949206i	−0.997426	+	0.0717017i	$0.977157\pi$
$828$	173.386	−	200.098i	0.209404	−	0.241665i
$829$	413.583	+	121.439i	0.498894	+	0.146489i	0.521492	−	0.853256i	$-0.325376\pi$
$829$	413.583	+	121.439i	0.498894	+	0.146489i	−0.0225980	+	0.999745i	$0.507194\pi$
$830$	362.449	−	418.289i	0.436686	−	0.503962i
$831$	593.698	−	85.3608i	0.714438	−	0.102721i
$832$	−34.2477	−	116.637i	−0.0411631	−	0.140189i
$833$	623.486			0.748483
$834$		−	186.919i		−	0.224124i
$835$	70.0554	+	238.587i	0.0838987	+	0.285733i
$836$	−40.3797	+	62.8320i	−0.0483010	+	0.0751579i
$837$	102.226	+	223.843i	0.122133	+	0.267435i
$838$	−134.848	+	61.5829i	−0.160916	+	0.0734880i
$839$	532.581	+	342.269i	0.634781	+	0.407949i	0.818077	−	0.575109i	$-0.195040\pi$
$839$	532.581	+	342.269i	0.634781	+	0.407949i	−0.183296	+	0.983058i	$0.558677\pi$
$840$	520.783	−	152.916i	0.619979	−	0.182042i
$841$	−823.487			−0.979176
$842$			334.042i			0.396724i
$843$	−759.530	+	223.018i	−0.900985	+	0.264553i
$844$	−59.5123	−	413.917i	−0.0705122	−	0.490423i
$845$	7.23181	+	6.26640i	0.00855835	+	0.00741586i
$846$	37.7182	−	128.456i	0.0445842	−	0.151840i
$847$	−883.711	−	765.740i	−1.04334	−	0.904062i
$848$	92.2416	+	143.531i	0.108775	+	0.169258i
$849$	243.471	−	378.848i	0.286774	−	0.446228i
$850$	−46.0700	+	6.62387i	−0.0542000	+	0.00779278i
$851$	−1026.57	+	659.738i	−1.20631	+	0.775250i
$852$	−254.183	+	116.081i	−0.298336	+	0.136246i
$853$	−373.971	−	431.585i	−0.438418	−	0.505962i	0.492941	−	0.870063i	$-0.335922\pi$
$853$	−373.971	−	431.585i	−0.438418	−	0.505962i	−0.931359	+	0.364101i	$0.881376\pi$
$854$	162.499	+	140.806i	0.190280	+	0.164879i
$855$	353.162	+	50.7771i	0.413055	+	0.0593884i
$856$	−1065.95	+	486.803i	−1.24527	+	0.568695i
$857$	−330.644	+	286.505i	−0.385816	+	0.334311i	−0.826076	−	0.563559i	$-0.809432\pi$
$857$	−330.644	+	286.505i	−0.385816	+	0.334311i	0.440260	+	0.897870i	$0.354886\pi$
$858$	17.6633	+	5.18642i	0.0205866	+	0.00604478i
$859$	−1103.97	−	324.156i	−1.28519	−	0.377365i	−0.433375	−	0.901214i	$-0.642677\pi$
$859$	−1103.97	−	324.156i	−1.28519	−	0.377365i	−0.851811	+	0.523849i	$0.824496\pi$
$860$	−130.374	+	906.772i	−0.151598	+	1.05439i
$861$	140.558	−	218.713i	0.163250	−	0.254022i
$862$	−401.892	−	183.538i	−0.466232	−	0.212921i
$863$	141.951	−	41.6805i	0.164485	−	0.0482973i	−0.198453	−	0.980110i	$-0.563592\pi$
$863$	141.951	−	41.6805i	0.164485	−	0.0482973i	0.362938	+	0.931813i	$0.381774\pi$
$864$	66.3025	−	145.182i	0.0767390	−	0.168035i
$865$	772.206	−	111.027i	0.892724	−	0.128354i
$866$	−20.5865	+	143.182i	−0.0237719	+	0.165337i
$867$	137.826	−	119.427i	0.158969	−	0.137748i
$868$	1298.81	−	834.696i	1.49633	−	0.961631i
$869$	25.0394	−	54.8286i	0.0288140	−	0.0630939i
$870$			31.7293i			0.0364704i
$871$	793.787	+	347.274i	0.911352	+	0.398707i
$872$	−50.5109			−0.0579254
$873$	−195.603	−	89.3290i	−0.224059	−	0.102324i
$874$	253.977	+	395.196i	0.290592	+	0.452170i
$875$	−716.471	−	826.852i	−0.818825	−	0.944974i
$876$	−354.947	−	51.0337i	−0.405191	−	0.0582577i
$877$	43.6496	+	303.589i	0.0497714	+	0.346168i	0.999457	+	0.0329619i	$0.0104940\pi$
$877$	43.6496	+	303.589i	0.0497714	+	0.346168i	−0.949685	+	0.313206i	$0.898597\pi$
$878$	−315.009	−	143.860i	−0.358780	−	0.163850i
$879$	−241.692	−	823.128i	−0.274963	−	0.936436i
$880$	−19.5377	+	42.7815i	−0.0222019	+	0.0486154i
$881$	−93.6977	−	60.2159i	−0.106354	−	0.0683494i	0.486383	−	0.873746i	$-0.338316\pi$
$881$	−93.6977	−	60.2159i	−0.106354	−	0.0683494i	−0.592737	+	0.805396i	$0.701952\pi$
$882$	110.574	+	15.8981i	0.125367	+	0.0180250i
$883$	−428.542	+	1459.48i	−0.485325	+	1.65287i	0.244817	+	0.969569i	$0.421272\pi$
$883$	−428.542	+	1459.48i	−0.485325	+	1.65287i	−0.730142	+	0.683296i	$0.760546\pi$
$884$	−165.166	+	562.503i	−0.186839	+	0.636316i
$885$	−187.968	−	216.927i	−0.212393	−	0.245115i
$886$	206.810	+	452.851i	0.233420	+	0.511119i
$887$	−84.3696	+	586.804i	−0.0951180	+	0.661560i	0.885356	+	0.464913i	$0.153914\pi$
$887$	−84.3696	+	586.804i	−0.0951180	+	0.661560i	−0.980474	+	0.196647i	$0.936995\pi$
$888$	−311.871	+	359.918i	−0.351206	+	0.405313i
$889$	495.991	−	429.778i	0.557920	−	0.483440i
$890$	2.73977	+	5.99926i	0.00307839	+	0.00674074i
$891$	−4.94029	−	7.68725i	−0.00554466	−	0.00862766i
$892$	24.7582	+	172.197i	0.0277558	+	0.193046i
$893$	−1020.00	−	655.515i	−1.14222	−	0.734059i
$894$	235.204	−	151.156i	0.263092	−	0.169079i
$895$	−1159.15	+	1337.73i	−1.29514	+	1.49467i
$896$	−1220.19	−	358.280i	−1.36182	−	0.399866i
$897$	−387.036	+	446.663i	−0.431478	+	0.497952i
$898$	−446.472	+	64.1930i	−0.497185	+	0.0714844i
$899$	55.8363	+	190.161i	0.0621094	+	0.211525i
$900$	42.5665			0.0472961
$901$		−	269.959i		−	0.299622i
$902$	−3.56593	−	12.1445i	−0.00395336	−	0.0134639i
$903$	−462.283	+	719.327i	−0.511942	+	0.796597i
$904$	−289.538	−	633.999i	−0.320285	−	0.701327i
$905$	−1146.44	+	523.561i	−1.26678	+	0.578520i
$906$	−168.004	−	107.970i	−0.185435	−	0.119172i
$907$	1080.12	−	317.150i	1.19087	−	0.349670i	0.374512	−	0.927222i	$-0.377810\pi$
$907$	1080.12	−	317.150i	1.19087	−	0.349670i	0.816354	+	0.577552i	$0.195992\pi$
$908$	222.233			0.244750
$909$		−	392.034i		−	0.431281i
$910$	−529.392	+	155.444i	−0.581750	+	0.170817i
$911$	175.131	+	1218.06i	0.192241	+	1.33706i	0.826060	+	0.563582i	$0.190577\pi$
$911$	175.131	+	1218.06i	0.192241	+	1.33706i	−0.633819	+	0.773481i	$0.718514\pi$
$912$	−246.612	−	213.691i	−0.270408	−	0.234310i
$913$	−36.1678	+	123.176i	−0.0396142	+	0.134914i
$914$	448.958	+	389.024i	0.491201	+	0.425628i
$915$	137.998	+	214.730i	0.150818	+	0.234677i
$916$	−534.131	+	831.124i	−0.583113	+	0.907341i
$917$	2437.64	−	350.479i	2.65827	−	0.382202i
$918$	−47.9605	+	30.8224i	−0.0522446	+	0.0335756i
$919$	766.131	−	349.880i	0.833657	−	0.380718i	0.0475956	−	0.998867i	$-0.484844\pi$
$919$	766.131	−	349.880i	0.833657	−	0.380718i	0.786062	+	0.618148i	$0.212117\pi$
$920$	555.551	+	641.140i	0.603859	+	0.696891i
$921$	590.057	+	511.287i	0.640670	+	0.555144i
$922$	73.8011	+	10.6110i	0.0800446	+	0.0115087i
$923$	567.390	−	259.119i	0.614724	−	0.280735i
$924$	−43.3275	+	37.5435i	−0.0468913	+	0.0406315i
$925$	−188.238	−	55.2716i	−0.203500	−	0.0597531i
$926$	596.854	+	175.252i	0.644550	+	0.189257i
$927$	−71.6451	+	498.303i	−0.0772871	+	0.537544i
$928$	69.4958	−	108.138i	0.0748877	−	0.116528i
$929$	−26.4977	−	12.1011i	−0.0285229	−	0.0130259i	0.401103	−	0.916033i	$-0.368627\pi$
$929$	−26.4977	−	12.1011i	−0.0285229	−	0.0130259i	−0.429625	+	0.903007i	$0.641354\pi$
$930$	−344.519	+	101.160i	−0.370451	+	0.108774i
$931$	420.278	−	920.279i	0.451426	−	0.988485i
$932$	1033.15	−	148.545i	1.10853	−	0.159383i
$933$	−58.2100	+	404.859i	−0.0623901	+	0.433933i
$934$	406.324	−	352.081i	0.435036	−	0.376961i
$935$	62.6033	−	40.2327i	0.0669555	−	0.0430297i
$936$	−95.8181	+	209.812i	−0.102370	+	0.224158i
$937$			580.863i			0.619918i	0.950750	+	0.309959i	$0.100315\pi$
$937$			580.863i			0.619918i	−0.950750	+	0.309959i	$0.899685\pi$
$938$	440.080	−	292.874i	0.469168	−	0.312232i
$939$	−409.932			−0.436562
$940$	−907.013	−	414.219i	−0.964908	−	0.440659i
$941$	−548.641	−	853.702i	−0.583040	−	0.907228i	0.416958	−	0.908926i	$-0.363096\pi$
$941$	−548.641	−	853.702i	−0.583040	−	0.907228i	−0.999999	+	0.00169738i	$0.999460\pi$
$942$	−97.1671	−	112.137i	−0.103150	−	0.119041i
$943$	402.221	+	57.8306i	0.426533	+	0.0613262i
$944$	37.3598	+	259.843i	0.0395761	+	0.275258i
$945$	249.124	+	113.771i	0.263623	+	0.120393i
$946$	11.7280	+	39.9420i	0.0123975	+	0.0422220i
$947$	679.077	−	1486.97i	0.717082	−	1.57019i	−0.100867	−	0.994900i	$-0.532162\pi$
$947$	679.077	−	1486.97i	0.717082	−	1.57019i	0.817949	−	0.575291i	$-0.195111\pi$
$948$	289.327	+	185.939i	0.305197	+	0.196138i
$949$	792.319	+	113.918i	0.834899	+	0.120040i
$950$	−21.2777	+	72.4653i	−0.0223976	+	0.0762793i
$951$	−64.7096	+	220.381i	−0.0680438	+	0.231736i
$952$	514.355	+	593.597i	0.540289	+	0.623526i
$953$	188.171	+	412.036i	0.197451	+	0.432357i	0.982296	−	0.187335i	$-0.0599849\pi$
$953$	188.171	+	412.036i	0.197451	+	0.432357i	−0.784845	+	0.619692i	$0.787258\pi$
$954$	6.88360	−	47.8765i	0.00721552	−	0.0501850i
$955$	5.90943	−	6.81984i	0.00618788	−	0.00714120i
$956$	769.635	−	666.892i	0.805057	−	0.697586i
$957$	−3.05723	−	6.69441i	−0.00319460	−	0.00699520i
$958$	−361.091	−	561.869i	−0.376922	−	0.586502i
$959$	−35.0088	−	243.492i	−0.0365055	−	0.253902i
$960$	−74.0677	−	47.6004i	−0.0771538	−	0.0495838i
$961$	−1078.32	+	692.996i	−1.12208	+	0.721119i
$962$	317.027	−	365.868i	0.329550	−	0.380321i
$963$	−567.345	−	166.588i	−0.589144	−	0.172988i
$964$	−465.312	+	536.999i	−0.482689	+	0.557053i
$965$	952.428	−	136.938i	0.986972	−	0.141905i
$966$	101.591	+	345.987i	0.105167	+	0.358165i
$967$	−40.5611			−0.0419453			−0.0209727	−	0.999780i	$-0.506676\pi$
$967$	−40.5611			−0.0419453			−0.0209727	+	0.999780i	$0.506676\pi$
$968$		−	713.273i		−	0.736852i
$969$	145.463	+	495.403i	0.150117	+	0.511252i
$970$	169.634	−	263.956i	0.174880	−	0.272119i
$971$	−218.767	−	479.032i	−0.225300	−	0.493339i	0.762898	−	0.646519i	$-0.223776\pi$
$971$	−218.767	−	479.032i	−0.225300	−	0.493339i	−0.988198	+	0.153180i	$0.951049\pi$
$972$	47.4274	−	21.6594i	0.0487937	−	0.0222833i
$973$	−1093.13	−	702.514i	−1.12347	−	0.722008i
$974$	−455.598	+	133.776i	−0.467760	+	0.137347i
$975$	−95.0177			−0.0974540
$976$		−	233.445i		−	0.239185i
$977$	1294.28	−	380.034i	1.32475	−	0.388980i	0.458542	−	0.888672i	$-0.348372\pi$
$977$	1294.28	−	380.034i	1.32475	−	0.388980i	0.866203	+	0.499692i	$0.166554\pi$
$978$	−32.4443	−	225.655i	−0.0331741	−	0.230731i
$979$	−1.15610	−	1.00177i	−0.00118090	−	0.00102326i
$980$	234.404	−	798.307i	0.239188	−	0.814599i
$981$	−19.2618	−	16.6905i	−0.0196349	−	0.0170137i
$982$	350.970	+	546.119i	0.357403	+	0.556130i
$983$	−796.036	+	1238.66i	−0.809803	+	1.26008i	0.152556	+	0.988295i	$0.451250\pi$
$983$	−796.036	+	1238.66i	−0.809803	+	1.26008i	−0.962359	+	0.271783i	$0.912387\pi$
$984$	156.974	−	22.5695i	0.159527	−	0.0229364i
$985$	−1227.13	+	788.629i	−1.24582	+	0.800639i
$986$	−41.7662	+	19.0740i	−0.0423592	+	0.0193448i
$987$	−609.474	−	703.370i	−0.617501	−	0.712634i
$988$	718.932	+	622.958i	0.727664	+	0.630525i
$989$	−1322.87	−	190.200i	−1.33758	−	0.192315i
$990$	12.1284	−	5.53886i	0.0122509	−	0.00559481i
$991$	2.81219	−	2.43678i	0.00283773	−	0.00245891i	−0.653441	−	0.756978i	$-0.726675\pi$
$991$	2.81219	−	2.43678i	0.00283773	−	0.00245891i	0.656278	+	0.754519i	$0.272130\pi$
$992$	1395.74	+	409.825i	1.40699	+	0.413130i
$993$	−826.928	−	242.808i	−0.832757	−	0.244520i
$994$	54.1605	−	376.694i	0.0544874	−	0.378968i
$995$	−69.6564	+	108.387i	−0.0700064	+	0.108932i
$996$	−666.301	−	304.289i	−0.668977	−	0.305511i
$997$	−989.845	+	290.645i	−0.992824	+	0.291519i	−0.737508	−	0.675338i	$-0.763998\pi$
$997$	−989.845	+	290.645i	−0.992824	+	0.291519i	−0.255316	+	0.966858i	$0.582179\pi$
$998$	182.141	−	398.832i	0.182506	−	0.399632i
$999$	−237.858	+	34.1988i	−0.238096	+	0.0342330i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.l.a.43.10	✓	220
67.53	odd	22	inner	201.3.l.a.187.10	yes	220

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.l.a.43.10	✓	220	1.1	even	1	trivial
201.3.l.a.187.10	yes	220	67.53	odd	22	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.l (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.736337 - 0.336274i) q^{2} +(-0.936417 - 1.45709i) q^{3} +(-2.19033 - 2.52778i) q^{4} +(5.35256 + 0.769582i) q^{5} +(0.199536 + 1.38780i) q^{6} +(8.86602 + 4.04898i) q^{7} +(1.67503 + 5.70464i) q^{8} +(-1.24625 + 2.72890i) q^{9} +O(q^{10})\)	\(q+(-0.736337 - 0.336274i) q^{2} +(-0.936417 - 1.45709i) q^{3} +(-2.19033 - 2.52778i) q^{4} +(5.35256 + 0.769582i) q^{5} +(0.199536 + 1.38780i) q^{6} +(8.86602 + 4.04898i) q^{7} +(1.67503 + 5.70464i) q^{8} +(-1.24625 + 2.72890i) q^{9} +(-3.68250 - 2.36660i) q^{10} +(1.00498 + 0.144495i) q^{11} +(-1.63214 + 5.55857i) q^{12} +(3.64330 - 12.4079i) q^{13} +(-5.16681 - 5.96282i) q^{14} +(-3.89088 - 8.51983i) q^{15} +(-1.21909 + 8.47893i) q^{16} +(8.87592 - 10.2434i) q^{17} +(1.83531 - 1.59031i) q^{18} +(-9.13637 - 20.0059i) q^{19} +(-9.77855 - 15.2157i) q^{20} +(-2.40256 - 16.7102i) q^{21} +(-0.691415 - 0.444346i) q^{22} +(22.1978 - 14.2657i) q^{23} +(6.74366 - 7.78260i) q^{24} +(4.07031 + 1.19515i) q^{25} +(-6.85515 + 7.91127i) q^{26} +(5.14326 - 0.739490i) q^{27} +(-9.18461 - 31.2799i) q^{28} +4.18489 q^{29} +7.58186i q^{30} +(13.3424 + 45.4399i) q^{31} +(16.6064 - 25.8400i) q^{32} +(-0.730541 - 1.59966i) q^{33} +(-9.98024 + 4.55782i) q^{34} +(44.3399 + 28.4955i) q^{35} +(9.62773 - 2.82696i) q^{36} -46.2465 q^{37} +17.8034i q^{38} +(-21.4912 + 6.31038i) q^{39} +(4.57553 + 31.8235i) q^{40} +(11.6386 + 10.0849i) q^{41} +(-3.85009 + 13.1122i) q^{42} +(-38.2784 - 33.1684i) q^{43} +(-1.83599 - 2.85686i) q^{44} +(-8.77071 + 13.6475i) q^{45} +(-21.1423 + 3.03980i) q^{46} +(46.3777 - 29.8051i) q^{47} +(13.4962 - 6.16350i) q^{48} +(30.1239 + 34.7649i) q^{49} +(-2.59522 - 2.24877i) q^{50} +(-23.2371 - 3.34099i) q^{51} +(-39.3445 + 17.9680i) q^{52} +(15.0526 - 13.0432i) q^{53} +(-4.03584 - 1.18503i) q^{54} +(5.26803 + 1.54683i) q^{55} +(-8.24707 + 57.3596i) q^{56} +(-20.5950 + 32.0464i) q^{57} +(-3.08149 - 1.40727i) q^{58} +(29.4044 - 8.63390i) q^{59} +(-13.0139 + 28.4965i) q^{60} +(-26.9747 + 3.87838i) q^{61} +(5.45578 - 37.9458i) q^{62} +(-22.0985 + 19.1484i) q^{63} +(7.90794 - 5.08213i) q^{64} +(29.0499 - 63.6104i) q^{65} +1.42355i q^{66} +(-8.47305 + 66.4621i) q^{67} -45.3341 q^{68} +(-41.5729 - 18.9857i) q^{69} +(-23.0668 - 35.8926i) q^{70} +(31.5869 + 36.4533i) q^{71} +(-17.6549 - 2.53839i) q^{72} +(8.80918 + 61.2692i) q^{73} +(34.0530 + 15.5515i) q^{74} +(-2.07006 - 7.04999i) q^{75} +(-30.5587 + 66.9142i) q^{76} +(8.32514 + 5.35024i) q^{77} +(17.9467 + 2.58035i) q^{78} +(16.7254 - 56.9615i) q^{79} +(-13.0505 + 44.4458i) q^{80} +(-5.89375 - 6.80175i) q^{81} +(-5.17865 - 11.3397i) q^{82} +(-17.9942 + 125.153i) q^{83} +(-36.9771 + 42.6739i) q^{84} +(55.3920 - 47.9974i) q^{85} +(17.0321 + 37.2951i) q^{86} +(-3.91880 - 6.09778i) q^{87} +(0.859089 + 5.97509i) q^{88} +(-1.26749 - 0.814564i) q^{89} +(11.0475 - 7.09979i) q^{90} +(82.5410 - 95.2574i) q^{91} +(-84.6811 - 24.8646i) q^{92} +(53.7162 - 61.9918i) q^{93} +(-44.1723 + 6.35102i) q^{94} +(-33.5068 - 114.114i) q^{95} -53.2018 q^{96} +71.6785i q^{97} +(-10.4908 - 35.7285i) q^{98} +(-1.64676 + 2.56242i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 220 q + 52 q^{4} + 66 q^{8} + 66 q^{9}+O(q^{10}) \) 220 * q + 52 * q^4 + 66 * q^8 + 66 * q^9	\( 220 q + 52 q^{4} + 66 q^{8} + 66 q^{9} - 162 q^{10} - 72 q^{14} + 54 q^{15} - 116 q^{16} + 14 q^{17} - 84 q^{19} - 48 q^{21} + 78 q^{22} + 82 q^{23} - 36 q^{24} + 62 q^{25} + 100 q^{26} - 154 q^{28} + 52 q^{29} - 88 q^{31} + 770 q^{32} - 36 q^{33} + 180 q^{35} + 42 q^{36} - 304 q^{37} + 72 q^{39} - 1066 q^{40} + 330 q^{41} + 770 q^{43} - 242 q^{46} - 616 q^{47} - 146 q^{49} + 858 q^{50} + 264 q^{52} - 286 q^{53} - 62 q^{55} - 1484 q^{56} - 660 q^{57} - 352 q^{58} - 634 q^{59} - 504 q^{60} - 352 q^{61} + 124 q^{62} - 132 q^{63} - 1226 q^{64} + 196 q^{65} + 156 q^{67} - 192 q^{68} + 66 q^{69} + 1144 q^{70} + 280 q^{71} + 264 q^{72} + 552 q^{73} + 352 q^{74} + 396 q^{75} + 400 q^{76} - 176 q^{77} + 528 q^{78} + 682 q^{79} + 1848 q^{80} - 198 q^{81} + 728 q^{82} + 246 q^{83} - 1320 q^{84} - 1120 q^{86} + 1120 q^{88} + 448 q^{89} + 486 q^{90} - 128 q^{91} + 604 q^{92} + 72 q^{93} + 704 q^{94} - 462 q^{95} + 144 q^{96} - 176 q^{98}+O(q^{100}) \) 220 * q + 52 * q^4 + 66 * q^8 + 66 * q^9 - 162 * q^10 - 72 * q^14 + 54 * q^15 - 116 * q^16 + 14 * q^17 - 84 * q^19 - 48 * q^21 + 78 * q^22 + 82 * q^23 - 36 * q^24 + 62 * q^25 + 100 * q^26 - 154 * q^28 + 52 * q^29 - 88 * q^31 + 770 * q^32 - 36 * q^33 + 180 * q^35 + 42 * q^36 - 304 * q^37 + 72 * q^39 - 1066 * q^40 + 330 * q^41 + 770 * q^43 - 242 * q^46 - 616 * q^47 - 146 * q^49 + 858 * q^50 + 264 * q^52 - 286 * q^53 - 62 * q^55 - 1484 * q^56 - 660 * q^57 - 352 * q^58 - 634 * q^59 - 504 * q^60 - 352 * q^61 + 124 * q^62 - 132 * q^63 - 1226 * q^64 + 196 * q^65 + 156 * q^67 - 192 * q^68 + 66 * q^69 + 1144 * q^70 + 280 * q^71 + 264 * q^72 + 552 * q^73 + 352 * q^74 + 396 * q^75 + 400 * q^76 - 176 * q^77 + 528 * q^78 + 682 * q^79 + 1848 * q^80 - 198 * q^81 + 728 * q^82 + 246 * q^83 - 1320 * q^84 - 1120 * q^86 + 1120 * q^88 + 448 * q^89 + 486 * q^90 - 128 * q^91 + 604 * q^92 + 72 * q^93 + 704 * q^94 - 462 * q^95 + 144 * q^96 - 176 * q^98

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