LMFDB - Embedded newform 201.4.e.b.37.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,4,Mod(37,201)]

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, 2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("201.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	201.e (of order $3$, 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:	$11.8593839112$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.3
Character	$\chi$	$=$	201.37
Dual form			201.4.e.b.163.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.37227 - 4.10889i) q^{2} -3.00000 q^{3} +(-7.25534 + 12.5666i) q^{4} -19.3810 q^{5} +(7.11681 + 12.3267i) q^{6} +(3.13332 - 5.42707i) q^{7} +30.8902 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+(-2.37227 - 4.10889i) q^{2} -3.00000 q^{3} +(-7.25534 + 12.5666i) q^{4} -19.3810 q^{5} +(7.11681 + 12.3267i) q^{6} +(3.13332 - 5.42707i) q^{7} +30.8902 q^{8} +9.00000 q^{9} +(45.9769 + 79.6344i) q^{10} +(-35.1900 + 60.9509i) q^{11} +(21.7660 - 37.6998i) q^{12} +(-5.95611 - 10.3163i) q^{13} -29.7323 q^{14} +58.1430 q^{15} +(-15.2371 - 26.3915i) q^{16} +(-6.64784 - 11.5144i) q^{17} +(-21.3504 - 36.9800i) q^{18} +(-25.0373 - 43.3659i) q^{19} +(140.616 - 243.553i) q^{20} +(-9.39995 + 16.2812i) q^{21} +333.921 q^{22} +(-96.4457 - 167.049i) q^{23} -92.6705 q^{24} +250.623 q^{25} +(-28.2590 + 48.9460i) q^{26} -27.0000 q^{27} +(45.4666 + 78.7504i) q^{28} +(-77.2548 + 133.809i) q^{29} +(-137.931 - 238.903i) q^{30} +(-15.7344 + 27.2528i) q^{31} +(51.2674 - 88.7978i) q^{32} +(105.570 - 182.853i) q^{33} +(-31.5410 + 54.6306i) q^{34} +(-60.7268 + 105.182i) q^{35} +(-65.2980 + 113.100i) q^{36} +(-156.046 - 270.279i) q^{37} +(-118.791 + 205.751i) q^{38} +(17.8683 + 30.9488i) q^{39} -598.682 q^{40} +(-14.2832 + 24.7392i) q^{41} +89.1969 q^{42} +241.452 q^{43} +(-510.631 - 884.438i) q^{44} -174.429 q^{45} +(-457.591 + 792.571i) q^{46} +(-8.73759 + 15.1340i) q^{47} +(45.7114 + 79.1745i) q^{48} +(151.865 + 263.037i) q^{49} +(-594.545 - 1029.78i) q^{50} +(19.9435 + 34.5432i) q^{51} +172.854 q^{52} -73.5001 q^{53} +(64.0513 + 110.940i) q^{54} +(682.017 - 1181.29i) q^{55} +(96.7887 - 167.643i) q^{56} +(75.1120 + 130.098i) q^{57} +733.077 q^{58} +882.980 q^{59} +(-421.847 + 730.660i) q^{60} +(144.933 + 251.032i) q^{61} +149.305 q^{62} +(28.1999 - 48.8436i) q^{63} -730.275 q^{64} +(115.435 + 199.940i) q^{65} -1001.76 q^{66} +(-276.751 + 473.468i) q^{67} +192.929 q^{68} +(289.337 + 501.147i) q^{69} +576.241 q^{70} +(443.444 - 768.067i) q^{71} +278.012 q^{72} +(-259.013 - 448.624i) q^{73} +(-740.365 + 1282.35i) q^{74} -751.868 q^{75} +726.617 q^{76} +(220.523 + 381.957i) q^{77} +(84.7770 - 146.838i) q^{78} +(-312.696 + 541.606i) q^{79} +(295.311 + 511.493i) q^{80} +81.0000 q^{81} +135.534 q^{82} +(181.045 + 313.579i) q^{83} +(-136.400 - 236.251i) q^{84} +(128.842 + 223.160i) q^{85} +(-572.790 - 992.101i) q^{86} +(231.764 - 401.428i) q^{87} +(-1087.03 + 1882.78i) q^{88} +1289.83 q^{89} +(413.793 + 716.710i) q^{90} -74.6495 q^{91} +2798.99 q^{92} +(47.2033 - 81.7584i) q^{93} +82.9117 q^{94} +(485.248 + 840.474i) q^{95} +(-153.802 + 266.393i) q^{96} +(577.666 + 1000.55i) q^{97} +(720.528 - 1247.99i) q^{98} +(-316.710 + 548.558i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 2 q^{2} - 108 q^{3} - 90 q^{4} - 4 q^{5} - 6 q^{6} + 22 q^{7} + 48 q^{8} + 324 q^{9}+O(q^{10}) $ 36 * q + 2 * q^2 - 108 * q^3 - 90 * q^4 - 4 * q^5 - 6 * q^6 + 22 * q^7 + 48 * q^8 + 324 * q^9	\( 36 q + 2 q^{2} - 108 q^{3} - 90 q^{4} - 4 q^{5} - 6 q^{6} + 22 q^{7} + 48 q^{8} + 324 q^{9} + 14 q^{10} - 16 q^{11} + 270 q^{12} - 46 q^{13} + 14 q^{14} + 12 q^{15} - 346 q^{16} - 8 q^{17} + 18 q^{18} - 154 q^{19} - 180 q^{20} - 66 q^{21} + 214 q^{22} - 104 q^{23} - 144 q^{24} + 1032 q^{25} - 333 q^{26} - 972 q^{27} - 473 q^{28} + 76 q^{29} - 42 q^{30} + 498 q^{31} - 285 q^{32} + 48 q^{33} + 26 q^{34} - 392 q^{35} - 810 q^{36} - 124 q^{37} + 20 q^{38} + 138 q^{39} + 638 q^{40} - 508 q^{41} - 42 q^{42} - 1400 q^{43} - 333 q^{44} - 36 q^{45} - 1372 q^{46} + 18 q^{47} + 1038 q^{48} - 238 q^{49} - 337 q^{50} + 24 q^{51} + 3640 q^{52} + 724 q^{53} - 54 q^{54} - 178 q^{55} - 829 q^{56} + 462 q^{57} - 1472 q^{58} + 720 q^{59} + 540 q^{60} + 232 q^{61} - 3882 q^{62} + 198 q^{63} + 3628 q^{64} - 1428 q^{65} - 642 q^{66} - 1164 q^{67} + 1634 q^{68} + 312 q^{69} + 2550 q^{70} + 406 q^{71} + 432 q^{72} - 2120 q^{73} + 1375 q^{74} - 3096 q^{75} + 4190 q^{76} - 800 q^{77} + 999 q^{78} + 1306 q^{79} - 1927 q^{80} + 2916 q^{81} - 794 q^{82} - 1010 q^{83} + 1419 q^{84} + 472 q^{85} + 737 q^{86} - 228 q^{87} - 1838 q^{88} + 1904 q^{89} + 126 q^{90} + 7340 q^{91} + 7368 q^{92} - 1494 q^{93} - 9862 q^{94} + 1678 q^{95} + 855 q^{96} - 2358 q^{97} - 2610 q^{98} - 144 q^{99}+O(q^{100}) \) 36 * q + 2 * q^2 - 108 * q^3 - 90 * q^4 - 4 * q^5 - 6 * q^6 + 22 * q^7 + 48 * q^8 + 324 * q^9 + 14 * q^10 - 16 * q^11 + 270 * q^12 - 46 * q^13 + 14 * q^14 + 12 * q^15 - 346 * q^16 - 8 * q^17 + 18 * q^18 - 154 * q^19 - 180 * q^20 - 66 * q^21 + 214 * q^22 - 104 * q^23 - 144 * q^24 + 1032 * q^25 - 333 * q^26 - 972 * q^27 - 473 * q^28 + 76 * q^29 - 42 * q^30 + 498 * q^31 - 285 * q^32 + 48 * q^33 + 26 * q^34 - 392 * q^35 - 810 * q^36 - 124 * q^37 + 20 * q^38 + 138 * q^39 + 638 * q^40 - 508 * q^41 - 42 * q^42 - 1400 * q^43 - 333 * q^44 - 36 * q^45 - 1372 * q^46 + 18 * q^47 + 1038 * q^48 - 238 * q^49 - 337 * q^50 + 24 * q^51 + 3640 * q^52 + 724 * q^53 - 54 * q^54 - 178 * q^55 - 829 * q^56 + 462 * q^57 - 1472 * q^58 + 720 * q^59 + 540 * q^60 + 232 * q^61 - 3882 * q^62 + 198 * q^63 + 3628 * q^64 - 1428 * q^65 - 642 * q^66 - 1164 * q^67 + 1634 * q^68 + 312 * q^69 + 2550 * q^70 + 406 * q^71 + 432 * q^72 - 2120 * q^73 + 1375 * q^74 - 3096 * q^75 + 4190 * q^76 - 800 * q^77 + 999 * q^78 + 1306 * q^79 - 1927 * q^80 + 2916 * q^81 - 794 * q^82 - 1010 * q^83 + 1419 * q^84 + 472 * q^85 + 737 * q^86 - 228 * q^87 - 1838 * q^88 + 1904 * q^89 + 126 * q^90 + 7340 * q^91 + 7368 * q^92 - 1494 * q^93 - 9862 * q^94 + 1678 * q^95 + 855 * q^96 - 2358 * q^97 - 2610 * q^98 - 144 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−2.37227	−	4.10889i	−0.838724	−	1.45271i	−0.890962	−	0.454079i	$-0.849969\pi$
$2$	−2.37227	−	4.10889i	−0.838724	−	1.45271i	0.0522373	−	0.998635i	$-0.483365\pi$
$3$	−3.00000			−0.577350
$3$	−3.00000			−0.577350
$4$	−7.25534	+	12.5666i	−0.906917	+	1.57083i
$5$	−19.3810			−1.73349			−0.866744	−	0.498753i	$-0.833791\pi$
$5$	−19.3810			−1.73349			−0.866744	+	0.498753i	$0.833791\pi$
$6$	7.11681	+	12.3267i	0.484238	+	0.838724i
$7$	3.13332	−	5.42707i	0.169183	−	0.293034i	−0.768950	−	0.639309i	$-0.779220\pi$
$7$	3.13332	−	5.42707i	0.169183	−	0.293034i	0.938133	+	0.346275i	$0.112554\pi$
$8$	30.8902			1.36517
$9$	9.00000			0.333333
$10$	45.9769	+	79.6344i	1.45392	+	2.51826i
$11$	−35.1900	+	60.9509i	−0.964562	+	1.67067i	−0.253777	+	0.967263i	$0.581673\pi$
$11$	−35.1900	+	60.9509i	−0.964562	+	1.67067i	−0.710786	+	0.703408i	$0.751661\pi$
$12$	21.7660	−	37.6998i	0.523609	−	0.906917i
$13$	−5.95611	−	10.3163i	−0.127071	−	0.220094i	0.795469	−	0.605994i	$-0.207224\pi$
$13$	−5.95611	−	10.3163i	−0.127071	−	0.220094i	−0.922541	+	0.385900i	$0.873891\pi$
$14$	−29.7323			−0.567592
$15$	58.1430			1.00083
$16$	−15.2371	−	26.3915i	−0.238080	−	0.412367i
$17$	−6.64784	−	11.5144i	−0.0948435	−	0.164274i	0.814700	−	0.579883i	$-0.196902\pi$
$17$	−6.64784	−	11.5144i	−0.0948435	−	0.164274i	−0.909543	+	0.415609i	$0.863568\pi$
$18$	−21.3504	−	36.9800i	−0.279575	−	0.484238i
$19$	−25.0373	−	43.3659i	−0.302314	−	0.523622i	0.674346	−	0.738415i	$-0.264426\pi$
$19$	−25.0373	−	43.3659i	−0.302314	−	0.523622i	−0.976660	+	0.214793i	$0.931092\pi$
$20$	140.616	−	243.553i	1.57213	−	2.72301i
$21$	−9.39995	+	16.2812i	−0.0976780	+	0.169183i
$22$	333.921			3.23601
$23$	−96.4457	−	167.049i	−0.874362	−	1.51444i	−0.857441	−	0.514583i	$-0.827947\pi$
$23$	−96.4457	−	167.049i	−0.874362	−	1.51444i	−0.0169212	−	0.999857i	$-0.505386\pi$
$24$	−92.6705			−0.788179
$25$	250.623			2.00498
$26$	−28.2590	+	48.9460i	−0.213156	+	0.369196i
$27$	−27.0000			−0.192450
$28$	45.4666	+	78.7504i	0.306870	+	0.531515i
$29$	−77.2548	+	133.809i	−0.494685	+	0.856819i	−0.999981	−	0.00612671i	$-0.998050\pi$
$29$	−77.2548	+	133.809i	−0.494685	+	0.856819i	0.505297	+	0.862946i	$0.331383\pi$
$30$	−137.931	−	238.903i	−0.839420	−	1.45392i
$31$	−15.7344	+	27.2528i	−0.0911608	+	0.157895i	−0.908000	−	0.418971i	$-0.862391\pi$
$31$	−15.7344	+	27.2528i	−0.0911608	+	0.157895i	0.816839	+	0.576866i	$0.195724\pi$
$32$	51.2674	−	88.7978i	0.283215	−	0.490543i
$33$	105.570	−	182.853i	0.556890	−	0.964562i
$34$	−31.5410	+	54.6306i	−0.159095	+	0.275561i
$35$	−60.7268	+	105.182i	−0.293277	+	0.507971i
$36$	−65.2980	+	113.100i	−0.302306	+	0.523609i
$37$	−156.046	−	270.279i	−0.693345	−	1.20091i	−0.970736	−	0.240151i	$-0.922803\pi$
$37$	−156.046	−	270.279i	−0.693345	−	1.20091i	0.277391	−	0.960757i	$-0.410530\pi$
$38$	−118.791	+	205.751i	−0.507116	+	0.878350i
$39$	17.8683	+	30.9488i	0.0733646	+	0.127071i
$40$	−598.682			−2.36650
$41$	−14.2832	+	24.7392i	−0.0544063	+	0.0942344i	−0.891946	−	0.452142i	$-0.850660\pi$
$41$	−14.2832	+	24.7392i	−0.0544063	+	0.0942344i	0.837540	+	0.546377i	$0.183993\pi$
$42$	89.1969			0.327700
$43$	241.452			0.856305			0.428152	−	0.903707i	$-0.359165\pi$
$43$	241.452			0.856305			0.428152	+	0.903707i	$0.359165\pi$
$44$	−510.631	−	884.438i	−1.74956	−	3.03032i
$45$	−174.429			−0.577829
$46$	−457.591	+	792.571i	−1.46670	+	2.54039i
$47$	−8.73759	+	15.1340i	−0.0271172	+	0.0469684i	−0.879266	−	0.476332i	$-0.841966\pi$
$47$	−8.73759	+	15.1340i	−0.0271172	+	0.0469684i	0.852148	+	0.523300i	$0.175299\pi$
$48$	45.7114	+	79.1745i	0.137456	+	0.238080i
$49$	151.865	+	263.037i	0.442754	+	0.766873i
$50$	−594.545	−	1029.78i	−1.68163	−	2.91266i
$51$	19.9435	+	34.5432i	0.0547579	+	0.0948435i
$52$	172.854			0.460972
$53$	−73.5001			−0.190491			−0.0952454	−	0.995454i	$-0.530364\pi$
$53$	−73.5001			−0.190491			−0.0952454	+	0.995454i	$0.530364\pi$
$54$	64.0513	+	110.940i	0.161413	+	0.279575i
$55$	682.017	−	1181.29i	1.67206	−	2.89609i
$56$	96.7887	−	167.643i	0.230963	−	0.400040i
$57$	75.1120	+	130.098i	0.174541	+	0.302314i
$58$	733.077			1.65962
$59$	882.980			1.94838			0.974188	−	0.225738i	$-0.0724794\pi$
$59$	882.980			1.94838			0.974188	+	0.225738i	$0.0724794\pi$
$60$	−421.847	+	730.660i	−0.907670	+	1.57213i
$61$	144.933	+	251.032i	0.304210	+	0.526907i	0.977085	−	0.212849i	$-0.0682742\pi$
$61$	144.933	+	251.032i	0.304210	+	0.526907i	−0.672875	+	0.739756i	$0.734941\pi$
$62$	149.305			0.305835
$63$	28.1999	−	48.8436i	0.0563944	−	0.0976780i
$64$	−730.275			−1.42632
$65$	115.435	+	199.940i	0.220277	+	0.381530i
$66$	−1001.76			−1.86831
$67$	−276.751	+	473.468i	−0.504634	+	0.863333i
$67$	−276.751	+	473.468i	−0.504634	+	0.863333i
$68$	192.929			0.344061
$69$	289.337	+	501.147i	0.504813	+	0.874362i
$70$	576.241			0.983915
$71$	443.444	−	768.067i	0.741227	−	1.28384i	−0.210710	−	0.977549i	$-0.567578\pi$
$71$	443.444	−	768.067i	0.741227	−	1.28384i	0.951937	−	0.306294i	$-0.0990891\pi$
$72$	278.012			0.455055
$73$	−259.013	−	448.624i	−0.415276	−	0.719280i	0.580181	−	0.814488i	$-0.302982\pi$
$73$	−259.013	−	448.624i	−0.415276	−	0.719280i	−0.995457	+	0.0952077i	$0.969648\pi$
$74$	−740.365	+	1282.35i	−1.16305	+	2.01446i
$75$	−751.868			−1.15758
$76$	726.617			1.09669
$77$	220.523	+	381.957i	0.326376	+	0.565299i
$78$	84.7770	−	146.838i	0.123065	−	0.213156i
$79$	−312.696	+	541.606i	−0.445330	+	0.771334i	−0.998075	−	0.0620162i	$-0.980247\pi$
$79$	−312.696	+	541.606i	−0.445330	+	0.771334i	0.552745	+	0.833350i	$0.313580\pi$
$80$	295.311	+	511.493i	0.412709	+	0.714834i
$81$	81.0000			0.111111
$82$	135.534			0.182527
$83$	181.045	+	313.579i	0.239425	+	0.414696i	0.960549	−	0.278109i	$-0.0897078\pi$
$83$	181.045	+	313.579i	0.239425	+	0.414696i	−0.721125	+	0.692805i	$0.756374\pi$
$84$	−136.400	−	236.251i	−0.177172	−	0.306870i
$85$	128.842	+	223.160i	0.164410	+	0.284766i
$86$	−572.790	−	992.101i	−0.718204	−	1.24397i
$87$	231.764	−	401.428i	0.285606	−	0.494685i
$88$	−1087.03	+	1882.78i	−1.31679	+	2.28074i
$89$	1289.83			1.53620			0.768102	−	0.640328i	$-0.221202\pi$
$89$	1289.83			1.53620			0.768102	+	0.640328i	$0.221202\pi$
$90$	413.793	+	716.710i	0.484640	+	0.839420i
$91$	−74.6495			−0.0859933
$92$	2798.99			3.17190
$93$	47.2033	−	81.7584i	0.0526317	−	0.0911608i
$94$	82.9117			0.0909755
$95$	485.248	+	840.474i	0.524057	+	0.907693i
$96$	−153.802	+	266.393i	−0.163514	+	0.283215i
$97$	577.666	+	1000.55i	0.604671	+	1.04732i	0.992103	+	0.125423i	$0.0400287\pi$
$97$	577.666	+	1000.55i	0.604671	+	1.04732i	−0.387432	+	0.921898i	$0.626638\pi$
$98$	720.528	−	1247.99i	0.742697	−	1.28639i
$99$	−316.710	+	548.558i	−0.321521	+	0.556890i
$100$	−1818.35	+	3149.48i	−1.81835	+	3.14948i
$101$	97.0374	−	168.074i	0.0955999	−	0.165584i	−0.814259	−	0.580502i	$-0.802856\pi$
$101$	97.0374	−	168.074i	0.0955999	−	0.165584i	0.909859	+	0.414918i	$0.136190\pi$
$102$	94.6229	−	163.892i	0.0918536	−	0.159095i
$103$	511.067	−	885.194i	0.488902	−	0.846803i	−0.511016	−	0.859571i	$-0.670731\pi$
$103$	511.067	−	885.194i	0.488902	−	0.846803i	0.999918	+	0.0127676i	$0.00406417\pi$
$104$	−183.985	−	318.672i	−0.173473	−	0.300465i
$105$	182.180	−	315.546i	0.169324	−	0.293277i
$106$	174.362	+	302.004i	0.159769	+	0.276728i
$107$	951.532			0.859701			0.429851	−	0.902900i	$-0.358566\pi$
$107$	951.532			0.859701			0.429851	+	0.902900i	$0.358566\pi$
$108$	195.894	−	339.299i	0.174536	−	0.302306i
$109$	386.591			0.339713			0.169857	−	0.985469i	$-0.445670\pi$
$109$	386.591			0.339713			0.169857	+	0.985469i	$0.445670\pi$
$110$	−6471.72			−5.60958
$111$	468.137	+	810.837i	0.400303	+	0.693345i
$112$	−190.971			−0.161117
$113$	−57.6624	+	99.8742i	−0.0480037	+	0.0831449i	−0.889029	−	0.457851i	$-0.848619\pi$
$113$	−57.6624	+	99.8742i	−0.0480037	+	0.0831449i	0.841025	+	0.540996i	$0.181953\pi$
$114$	356.372	−	617.254i	0.292783	−	0.507116i
$115$	1869.21	+	3237.57i	1.51570	+	2.62526i
$116$	−1121.02	−	1941.66i	−0.897276	−	1.55413i
$117$	−53.6050	−	92.8465i	−0.0423571	−	0.0733646i
$118$	−2094.67	−	3628.07i	−1.63415	−	2.83043i
$119$	−83.3192			−0.0641837
$120$	1796.05			1.36630
$121$	−1811.17	−	3137.04i	−1.36076	−	2.35691i
$122$	687.642	−	1191.03i	0.510297	−	0.883860i
$123$	42.8495	−	74.2175i	0.0314115	−	0.0544063i
$124$	−228.317	−	395.457i	−0.165351	−	0.286396i
$125$	−2434.69			−1.74212
$126$	−267.591			−0.189197
$127$	−1099.39	+	1904.20i	−0.768153	+	1.33048i	0.170411	+	0.985373i	$0.445490\pi$
$127$	−1099.39	+	1904.20i	−0.768153	+	1.33048i	−0.938564	+	0.345106i	$0.887843\pi$
$128$	1322.27	+	2290.24i	0.913073	+	1.58149i
$129$	−724.356			−0.494388
$130$	547.687	−	948.622i	0.369503	−	0.639997i
$131$	−2278.78			−1.51983			−0.759915	−	0.650023i	$-0.774759\pi$
$131$	−2278.78			−1.51983			−0.759915	+	0.650023i	$0.774759\pi$
$132$	1531.89	+	2653.32i	1.01011	+	1.74956i
$133$	−313.800			−0.204586
$134$	2601.96	+	13.9455i	1.67742	+	0.00899036i
$135$	523.287			0.333610
$136$	−205.353	−	355.682i	−0.129477	−	0.224261i
$137$	1794.88			1.11932			0.559662	−	0.828721i	$-0.310931\pi$
$137$	1794.88			1.11932			0.559662	+	0.828721i	$0.310931\pi$
$138$	1372.77	−	2377.71i	0.846798	−	1.46670i
$139$	123.504			0.0753629			0.0376814	−	0.999290i	$-0.488003\pi$
$139$	123.504			0.0753629			0.0376814	+	0.999290i	$0.488003\pi$
$140$	−881.187	−	1526.26i	−0.531956	−	0.921375i
$141$	26.2128	−	45.4019i	0.0156561	−	0.0271172i
$142$	−4207.88			−2.48674
$143$	838.382			0.490273
$144$	−137.134	−	237.524i	−0.0793601	−	0.137456i
$145$	1497.27	−	2593.36i	0.857530	−	1.48529i
$146$	−1228.90	+	2128.51i	−0.696605	+	1.20656i
$147$	−455.594	−	789.112i	−0.255624	−	0.442754i
$148$	4528.66			2.51523
$149$	−1324.73			−0.728365			−0.364182	−	0.931328i	$-0.618651\pi$
$149$	−1324.73			−0.728365			−0.364182	+	0.931328i	$0.618651\pi$
$150$	1783.63	+	3089.34i	0.970887	+	1.68163i
$151$	−1159.55	−	2008.41i	−0.624922	−	1.08240i	−0.988556	−	0.150854i	$-0.951798\pi$
$151$	−1159.55	−	2008.41i	−0.624922	−	1.08240i	0.363635	−	0.931542i	$-0.381536\pi$
$152$	−773.407	−	1339.58i	−0.412708	−	0.714831i
$153$	−59.8306	−	103.630i	−0.0316145	−	0.0547579i
$154$	1046.28	−	1812.21i	0.547478	−	0.948260i
$155$	304.949	−	528.186i	0.158026	−	0.273709i
$156$	−518.563			−0.266143
$157$	−443.827	−	768.731i	−0.225613	−	0.390773i	0.730890	−	0.682495i	$-0.239105\pi$
$157$	−443.827	−	768.731i	−0.225613	−	0.390773i	−0.956503	+	0.291722i	$0.905772\pi$
$158$	2967.20			1.49404
$159$	220.500			0.109980
$160$	−993.613	+	1720.99i	−0.490950	+	0.850350i
$161$	−1208.78			−0.591710
$162$	−192.154	−	332.820i	−0.0931916	−	0.161413i
$163$	530.158	−	918.261i	0.254756	−	0.441250i	−0.710073	−	0.704128i	$-0.751338\pi$
$163$	530.158	−	918.261i	0.254756	−	0.441250i	0.964829	+	0.262878i	$0.0846716\pi$
$164$	−207.258	−	358.982i	−0.0986840	−	0.170926i
$165$	−2046.05	+	3543.86i	−0.965363	+	1.67206i
$166$	858.975	−	1487.79i	0.401623	−	0.695631i
$167$	−643.913	+	1115.29i	−0.298368	+	0.516789i	−0.975763	−	0.218831i	$-0.929776\pi$
$167$	−643.913	+	1115.29i	−0.298368	+	0.516789i	0.677394	+	0.735620i	$0.263109\pi$
$168$	−290.366	+	502.929i	−0.133347	+	0.230963i
$169$	1027.55	−	1779.77i	0.467706	−	0.810090i
$170$	611.295	−	1058.79i	0.275789	−	0.477681i
$171$	−225.336	−	390.293i	−0.100771	−	0.174541i
$172$	−1751.82	+	3034.24i	−0.776597	+	1.34511i
$173$	1404.08	+	2431.94i	0.617053	+	1.06877i	0.990021	+	0.140923i	$0.0450070\pi$
$173$	1404.08	+	2431.94i	0.617053	+	1.06877i	−0.372967	+	0.927844i	$0.621660\pi$
$174$	−2199.23			−0.958180
$175$	785.280	−	1360.15i	0.339209	−	0.587528i
$176$	2144.78			0.918574
$177$	−2648.94			−1.12490
$178$	−3059.83	−	5299.79i	−1.28845	−	2.23166i
$179$	−4341.67			−1.81291			−0.906457	−	0.422298i	$-0.861224\pi$
$179$	−4341.67			−1.81291			−0.906457	+	0.422298i	$0.861224\pi$
$180$	1265.54	−	2191.98i	0.524043	−	0.907670i
$181$	−1240.88	+	2149.27i	−0.509580	+	0.882618i	0.490359	+	0.871521i	$0.336866\pi$
$181$	−1240.88	+	2149.27i	−0.509580	+	0.882618i	−0.999938	+	0.0110972i	$0.996468\pi$
$182$	177.089	+	306.727i	0.0721247	+	0.124924i
$183$	−434.800	−	753.095i	−0.175636	−	0.304210i
$184$	−2979.22	−	5160.17i	−1.19365	−	2.06746i
$185$	3024.32	+	5238.28i	1.20190	+	2.08176i
$186$	−447.916			−0.176574
$187$	935.751			0.365930
$188$	−126.788	−	219.604i	−0.0491861	−	0.0851929i
$189$	−84.5996	+	146.531i	−0.0325593	+	0.0563944i
$190$	2302.28	−	3987.67i	0.879079	−	1.52261i
$191$	139.802	+	242.145i	0.0529620	+	0.0917328i	0.891291	−	0.453432i	$-0.149800\pi$
$191$	139.802	+	242.145i	0.0529620	+	0.0917328i	−0.838329	+	0.545165i	$0.816467\pi$
$192$	2190.83			0.823485
$193$	1588.75			0.592544			0.296272	−	0.955104i	$-0.404257\pi$
$193$	1588.75			0.592544			0.296272	+	0.955104i	$0.404257\pi$
$194$	2740.76	−	4747.14i	1.01430	−	1.75683i
$195$	−346.306	−	599.819i	−0.127177	−	0.220277i
$196$	−4407.32			−1.60617
$197$	208.692	−	361.465i	0.0754755	−	0.130727i	−0.825817	−	0.563938i	$-0.809286\pi$
$197$	208.692	−	361.465i	0.0754755	−	0.130727i	0.901293	+	0.433210i	$0.142619\pi$
$198$	3005.29			1.07867
$199$	2181.21	+	3777.97i	0.776995	+	1.34579i	0.933666	+	0.358144i	$0.116590\pi$
$199$	2181.21	+	3777.97i	0.776995	+	1.34579i	−0.156671	+	0.987651i	$0.550076\pi$
$200$	7741.77			2.73713
$201$	830.253	−	1420.40i	0.291351	−	0.498446i
$202$	−920.796			−0.320728
$203$	484.128	+	838.534i	0.167385	+	0.289919i
$204$	−578.788			−0.198644
$205$	276.822	−	479.470i	0.0943126	−	0.163354i
$206$	−4849.56			−1.64022
$207$	−868.012	−	1503.44i	−0.291454	−	0.504813i
$208$	−181.508	+	314.381i	−0.0605064	+	0.104800i
$209$	3524.26			1.16640
$210$	−1728.72			−0.568063
$211$	1865.29	+	3230.78i	0.608588	+	1.05411i	0.991473	+	0.130310i	$0.0415971\pi$
$211$	1865.29	+	3230.78i	0.608588	+	1.05411i	−0.382885	+	0.923796i	$0.625070\pi$
$212$	533.268	−	923.647i	0.172759	−	0.299228i
$213$	−1330.33	+	2304.20i	−0.427948	+	0.741227i
$214$	−2257.29	−	3909.74i	−0.721052	−	1.24890i
$215$	−4679.58			−1.48439
$216$	−834.035			−0.262726
$217$	98.6018	+	170.783i	0.0308458	+	0.0534264i
$218$	−917.099	−	1588.46i	−0.284926	−	0.493506i
$219$	777.039	+	1345.87i	0.239760	+	0.415276i
$220$	9896.53	+	17141.3i	3.03284	+	5.25303i
$221$	−79.1905	+	137.162i	−0.0241038	+	0.0417489i
$222$	2221.10	−	3847.05i	0.671487	−	1.16305i
$223$	−5993.95			−1.79993			−0.899966	−	0.435960i	$-0.856409\pi$
$223$	−5993.95			−1.79993			−0.899966	+	0.435960i	$0.856409\pi$
$224$	−321.274	−	556.463i	−0.0958305	−	0.165983i
$225$	2255.60			0.668327
$226$	547.163			0.161048
$227$	924.514	−	1601.31i	0.270318	−	0.468204i	−0.698625	−	0.715488i	$-0.746205\pi$
$227$	924.514	−	1601.31i	0.270318	−	0.468204i	0.968943	+	0.247283i	$0.0795378\pi$
$228$	−2179.85			−0.633176
$229$	127.150	+	220.231i	0.0366914	+	0.0635514i	0.883788	−	0.467888i	$-0.154985\pi$
$229$	127.150	+	220.231i	0.0366914	+	0.0635514i	−0.847097	+	0.531439i	$0.821651\pi$
$230$	8868.56	−	15360.8i	2.54250	−	4.40374i
$231$	−661.569	−	1145.87i	−0.188433	−	0.326376i
$232$	−2386.41	+	4133.39i	−0.675326	+	1.16970i
$233$	−726.372	+	1258.11i	−0.204233	+	0.353741i	−0.949888	−	0.312591i	$-0.898803\pi$
$233$	−726.372	+	1258.11i	−0.204233	+	0.353741i	0.745655	+	0.666332i	$0.232137\pi$
$234$	−254.331	+	440.514i	−0.0710519	+	0.123065i
$235$	169.343	−	293.311i	0.0470074	−	0.0814191i
$236$	−6406.32	+	11096.1i	−1.76702	+	3.06056i
$237$	938.088	−	1624.82i	0.257111	−	0.445330i
$238$	197.656	+	342.350i	0.0538324	+	0.0932405i
$239$	2443.57	−	4232.39i	0.661345	−	1.14548i	−0.318918	−	0.947782i	$-0.603319\pi$
$239$	2443.57	−	4232.39i	0.661345	−	1.14548i	0.980263	−	0.197700i	$-0.0633473\pi$
$240$	−885.933	−	1534.48i	−0.238278	−	0.412709i
$241$	6241.62			1.66829			0.834146	−	0.551544i	$-0.185961\pi$
$241$	6241.62			1.66829			0.834146	+	0.551544i	$0.185961\pi$
$242$	−8593.19	+	14883.8i	−2.28261	+	3.95359i
$243$	−243.000			−0.0641500
$244$	−4206.16			−1.10357
$245$	−2943.29	−	5097.92i	−0.767509	−	1.32936i
$246$	−406.603			−0.105382
$247$	−298.250	+	516.584i	−0.0768307	+	0.133075i
$248$	−486.039	+	841.844i	−0.124450	+	0.215553i
$249$	−543.135	−	940.737i	−0.138232	−	0.239425i
$250$	5775.74	+	10003.9i	1.46116	+	2.53080i
$251$	946.097	+	1638.69i	0.237917	+	0.412084i	0.960116	−	0.279601i	$-0.0902021\pi$
$251$	946.097	+	1638.69i	0.237917	+	0.412084i	−0.722199	+	0.691685i	$0.756869\pi$
$252$	409.199	+	708.753i	0.102290	+	0.177172i
$253$	13575.7			3.37351
$254$	10432.2			2.57707
$255$	−386.525	−	669.481i	−0.0949222	−	0.164410i
$256$	3352.47	−	5806.65i	0.818474	−	1.41764i
$257$	1284.11	−	2224.15i	0.311677	−	0.539840i	−0.667049	−	0.745014i	$-0.732443\pi$
$257$	1284.11	−	2224.15i	0.311677	−	0.539840i	0.978725	+	0.205174i	$0.0657761\pi$
$258$	1718.37	+	2976.30i	0.414655	+	0.718204i
$259$	−1955.76			−0.469209
$260$	−3350.09			−0.799090
$261$	−695.293	+	1204.28i	−0.164895	+	0.285606i
$262$	5405.88	+	9363.25i	1.27472	+	2.20788i
$263$	−2343.05			−0.549348			−0.274674	−	0.961537i	$-0.588570\pi$
$263$	−2343.05			−0.549348			−0.274674	+	0.961537i	$0.588570\pi$
$264$	3261.08	−	5648.35i	0.760248	−	1.31679i
$265$	1424.50			0.330214
$266$	744.418	+	1289.37i	0.171591	+	0.297204i
$267$	−3869.50			−0.886927
$268$	−3941.97	−	6912.99i	−0.898485	−	1.57566i
$269$	−954.321			−0.216305			−0.108152	−	0.994134i	$-0.534493\pi$
$269$	−954.321			−0.216305			−0.108152	+	0.994134i	$0.534493\pi$
$270$	−1241.38	−	2150.13i	−0.279807	−	0.484640i
$271$	−5735.51			−1.28564			−0.642818	−	0.766019i	$-0.722235\pi$
$271$	−5735.51			−1.28564			−0.642818	+	0.766019i	$0.722235\pi$
$272$	−202.588	+	350.893i	−0.0451607	+	0.0782207i
$273$	223.948			0.0496483
$274$	−4257.95	−	7374.99i	−0.938804	−	1.62606i
$275$	−8819.41	+	15275.7i	−1.93393	+	3.34966i
$276$	−8396.96			−1.83129
$277$	2119.03			0.459639			0.229820	−	0.973233i	$-0.426186\pi$
$277$	2119.03			0.459639			0.229820	+	0.973233i	$0.426186\pi$
$278$	−292.984	−	507.463i	−0.0632087	−	0.109481i
$279$	−141.610	+	245.275i	−0.0303869	+	0.0526317i
$280$	−1875.86	+	3249.09i	−0.400372	+	0.693464i
$281$	−2714.48	−	4701.62i	−0.576272	−	0.998132i	−0.995902	−	0.0904371i	$-0.971174\pi$
$281$	−2714.48	−	4701.62i	−0.576272	−	0.998132i	0.419630	−	0.907695i	$-0.362160\pi$
$282$	−248.735			−0.0525247
$283$	3773.41			0.792600			0.396300	−	0.918121i	$-0.370294\pi$
$283$	3773.41			0.792600			0.396300	+	0.918121i	$0.370294\pi$
$284$	6434.67	+	11145.2i	1.34446	+	2.32868i
$285$	−1455.74	−	2521.42i	−0.302564	−	0.524057i
$286$	−1988.87	−	3444.82i	−0.411204	−	0.712226i
$287$	89.5074	+	155.031i	0.0184093	+	0.0318858i
$288$	461.407	−	799.180i	0.0944050	−	0.163514i
$289$	2368.11	−	4101.69i	0.482009	−	0.834865i
$290$	−14207.8			−2.87693
$291$	−1733.00	−	3001.64i	−0.349107	−	0.604671i
$292$	7516.91			1.50649
$293$	4307.88			0.858939			0.429470	−	0.903081i	$-0.358701\pi$
$293$	4307.88			0.858939			0.429470	+	0.903081i	$0.358701\pi$
$294$	−2161.58	+	3743.97i	−0.428796	+	0.742697i
$295$	−17113.0			−3.37749
$296$	−4820.28	−	8348.97i	−0.946530	−	1.63944i
$297$	950.130	−	1645.67i	0.185630	−	0.321521i
$298$	3142.62	+	5443.18i	0.610897	+	1.05810i
$299$	−1148.88	+	1989.92i	−0.222213	+	0.384883i
$300$	5455.05	−	9448.43i	1.04983	−	1.81835i
$301$	756.546	−	1310.38i	0.144872	−	0.250926i
$302$	−5501.55	+	9528.97i	−1.04827	+	1.81566i
$303$	−291.112	+	504.221i	−0.0551946	+	0.0955999i
$304$	−762.995	+	1321.55i	−0.143950	+	0.249328i
$305$	−2808.95	−	4865.24i	−0.527344	−	0.913387i
$306$	−283.869	+	491.675i	−0.0530317	+	0.0918536i
$307$	−4503.41	−	7800.14i	−0.837209	−	1.45009i	−0.892219	−	0.451603i	$-0.850852\pi$
$307$	−4503.41	−	7800.14i	−0.837209	−	1.45009i	0.0550093	−	0.998486i	$-0.482481\pi$
$308$	−6399.87			−1.18398
$309$	−1533.20	+	2655.58i	−0.282268	+	0.488902i
$310$	−2893.68			−0.530162
$311$	5578.04			1.01705			0.508523	−	0.861048i	$-0.330192\pi$
$311$	5578.04			1.01705			0.508523	+	0.861048i	$0.330192\pi$
$312$	551.955	+	956.015i	0.100155	+	0.173473i
$313$	654.265			0.118151			0.0590754	−	0.998254i	$-0.481185\pi$
$313$	654.265			0.118151			0.0590754	+	0.998254i	$0.481185\pi$
$314$	−2105.76	+	3647.28i	−0.378454	+	0.655502i
$315$	−546.541	+	946.637i	−0.0977590	+	0.169324i
$316$	−4537.43	−	7859.06i	−0.807755	−	1.39907i
$317$	934.936	+	1619.36i	0.165651	+	0.286915i	0.936886	−	0.349635i	$-0.113694\pi$
$317$	934.936	+	1619.36i	0.165651	+	0.286915i	−0.771236	+	0.636550i	$0.780361\pi$
$318$	−523.086	−	906.012i	−0.0922428	−	0.159769i
$319$	−5437.19	−	9417.50i	−0.954309	−	1.65291i
$320$	14153.4			2.47251
$321$	−2854.59			−0.496349
$322$	2867.55	+	4966.75i	0.496281	+	0.859584i
$323$	−332.889	+	576.580i	−0.0573449	+	0.0993243i
$324$	−587.682	+	1017.90i	−0.100769	+	0.174536i
$325$	−1492.73	−	2585.49i	−0.254775	−	0.441284i
$326$	−5030.72			−0.854680
$327$	−1159.77			−0.196133
$328$	−441.210	+	764.197i	−0.0742736	+	0.128646i
$329$	54.7553	+	94.8390i	0.00917555	+	0.0158925i
$330$	19415.2			3.23869
$331$	−4508.79	+	7809.46i	−0.748718	+	1.29682i	0.199719	+	0.979853i	$0.435997\pi$
$331$	−4508.79	+	7809.46i	−0.748718	+	1.29682i	−0.948437	+	0.316965i	$0.897336\pi$
$332$	−5254.17			−0.868554
$333$	−1404.41	−	2432.51i	−0.231115	−	0.400303i
$334$	6110.15			1.00100
$335$	5363.70	−	9176.28i	0.874778	−	1.49658i
$336$	572.914			0.0930208
$337$	3675.62	+	6366.36i	0.594135	+	1.02907i	0.993668	+	0.112354i	$0.0358390\pi$
$337$	3675.62	+	6366.36i	0.594135	+	1.02907i	−0.399533	+	0.916719i	$0.630828\pi$
$338$	−9750.50			−1.56910
$339$	172.987	−	299.623i	0.0277150	−	0.0480037i
$340$	−3739.16			−0.596425
$341$	−1107.39	−	1918.05i	−0.175861	−	0.304599i
$342$	−1069.12	+	1851.76i	−0.169039	+	0.292783i
$343$	4052.82			0.637993
$344$	7458.50			1.16900
$345$	−5607.64	−	9712.72i	−0.875088	−	1.51570i
$346$	6661.71	−	11538.4i	1.03508	−	1.79280i
$347$	1089.16	−	1886.48i	0.168499	−	0.291848i	−0.769393	−	0.638775i	$-0.779441\pi$
$347$	1089.16	−	1886.48i	0.168499	−	0.291848i	0.937892	+	0.346927i	$0.112775\pi$
$348$	3363.06	+	5824.99i	0.518043	+	0.897276i
$349$	8325.81			1.27699			0.638496	−	0.769625i	$-0.279557\pi$
$349$	8325.81			1.27699			0.638496	+	0.769625i	$0.279557\pi$
$350$	−7451.59			−1.13801
$351$	160.815	+	278.540i	0.0244549	+	0.0423571i
$352$	3608.20	+	6249.59i	0.546357	+	0.946319i
$353$	5003.81	+	8666.85i	0.754464	+	1.30677i	0.945640	+	0.325215i	$0.105437\pi$
$353$	5003.81	+	8666.85i	0.754464	+	1.30677i	−0.191176	+	0.981556i	$0.561230\pi$
$354$	6284.00	+	10884.2i	0.943477	+	1.63415i
$355$	−8594.38	+	14885.9i	−1.28491	+	2.22553i
$356$	−9358.18	+	16208.8i	−1.39321	+	2.41311i
$357$	249.958			0.0370565
$358$	10299.6	+	17839.5i	1.52054	+	2.63364i
$359$	12705.7			1.86792			0.933958	−	0.357383i	$-0.116331\pi$
$359$	12705.7			1.86792			0.933958	+	0.357383i	$0.116331\pi$
$360$	−5388.14			−0.788833
$361$	2175.76	−	3768.53i	0.317213	−	0.549429i
$362$	11774.8			1.70959
$363$	5433.52	+	9411.13i	0.785636	+	1.36076i
$364$	541.607	−	938.091i	0.0779888	−	0.135081i
$365$	5019.93	+	8694.77i	0.719877	+	1.24686i
$366$	−2062.93	+	3573.09i	−0.294620	+	0.510297i
$367$	−437.661	+	758.050i	−0.0622499	+	0.107820i	−0.895471	−	0.445120i	$-0.853161\pi$
$367$	−437.661	+	758.050i	−0.0622499	+	0.107820i	0.833221	+	0.552940i	$0.186494\pi$
$368$	−2939.12	+	5090.70i	−0.416337	+	0.721117i
$369$	−128.549	+	222.653i	−0.0181354	+	0.0314115i
$370$	14349.0	−	24853.2i	2.01613	−	3.49205i
$371$	−230.299	+	398.890i	−0.0322278	+	0.0558203i
$372$	684.951	+	1186.37i	0.0954652	+	0.165351i
$373$	5505.83	−	9536.37i	0.764292	−	1.32379i	−0.176328	−	0.984331i	$-0.556422\pi$
$373$	5505.83	−	9536.37i	0.764292	−	1.32379i	0.940620	−	0.339461i	$-0.110245\pi$
$374$	−2219.85	−	3844.90i	−0.306914	−	0.531591i
$375$	7304.07			1.00581
$376$	−269.906	+	467.490i	−0.0370195	+	0.0641196i
$377$	1840.55			0.251441
$378$	802.772			0.109233
$379$	−394.962	−	684.095i	−0.0535300	−	0.0927166i	0.838019	−	0.545641i	$-0.183714\pi$
$379$	−394.962	−	684.095i	−0.0535300	−	0.0927166i	−0.891549	+	0.452925i	$0.850381\pi$
$380$	−14082.6			−1.90111
$381$	3298.18	−	5712.61i	0.443493	−	0.768153i
$382$	663.297	−	1148.86i	0.0888410	−	0.153877i
$383$	−4211.25	−	7294.09i	−0.561840	−	0.973135i	−0.997336	−	0.0729447i	$-0.976760\pi$
$383$	−4211.25	−	7294.09i	−0.561840	−	0.973135i	0.435496	−	0.900191i	$-0.356573\pi$
$384$	−3966.81	−	6870.72i	−0.527163	−	0.913073i
$385$	−4273.95	−	7402.70i	−0.565768	−	0.979939i
$386$	−3768.95	−	6528.01i	−0.496981	−	0.860796i
$387$	2173.07			0.285435
$388$	−16764.6			−2.19355
$389$	−15.5877	−	26.9987i	−0.00203169	−	0.00351900i	0.865008	−	0.501758i	$-0.167313\pi$
$389$	−15.5877	−	26.9987i	−0.00203169	−	0.00351900i	−0.867039	+	0.498239i	$0.833980\pi$
$390$	−1643.06	+	2845.87i	−0.213332	+	0.369503i
$391$	−1282.31	+	2221.03i	−0.165855	+	0.287269i
$392$	4691.12	+	8125.27i	0.604433	+	1.04691i
$393$	6836.33			0.877474
$394$	−1980.29			−0.253213
$395$	6060.36	−	10496.9i	0.771974	−	1.33710i
$396$	−4595.68	−	7959.95i	−0.583186	−	1.01011i
$397$	−2829.48			−0.357702			−0.178851	−	0.983876i	$-0.557238\pi$
$397$	−2829.48			−0.357702			−0.178851	+	0.983876i	$0.557238\pi$
$398$	10348.8	−	17924.7i	1.30337	−	2.25750i
$399$	941.399			0.118118
$400$	−3818.77	−	6614.31i	−0.477347	−	0.826789i
$401$	3516.07			0.437866			0.218933	−	0.975740i	$-0.429742\pi$
$401$	3516.07			0.437866			0.218933	+	0.975740i	$0.429742\pi$
$402$	−7805.87	−	41.8365i	−0.968462	−	0.00519059i
$403$	374.863			0.0463357
$404$	1408.08	+	2438.86i	0.173402	+	0.300342i
$405$	−1569.86			−0.192610
$406$	2296.96	−	3978.46i	0.280779	−	0.486324i
$407$	21965.0			2.67510
$408$	616.059	+	1067.05i	0.0747536	+	0.129477i
$409$	−4325.82	+	7492.53i	−0.522978	+	0.905824i	0.476665	+	0.879085i	$0.341846\pi$
$409$	−4325.82	+	7492.53i	−0.522978	+	0.905824i	−0.999642	+	0.0267388i	$0.991488\pi$
$410$	−2626.79			−0.316409
$411$	−5384.65			−0.646242
$412$	7415.93	+	12844.8i	0.886788	+	1.53596i
$413$	2766.66	−	4791.99i	0.329633	−	0.570940i
$414$	−4118.32	+	7133.13i	−0.488899	+	0.846798i
$415$	−3508.83	−	6077.47i	−0.415040	−	0.718870i
$416$	−1221.42			−0.143954
$417$	−370.511			−0.0435108
$418$	−8360.49	−	14480.8i	−0.978289	−	1.69445i
$419$	−4311.82	−	7468.29i	−0.502735	−	0.870763i	−0.999995	−	0.00316125i	$-0.998994\pi$
$419$	−4311.82	−	7468.29i	−0.502735	−	0.870763i	0.497260	−	0.867602i	$-0.334340\pi$
$420$	2643.56	+	4578.78i	0.307125	+	0.531956i
$421$	−4058.55	−	7029.61i	−0.469837	−	0.813782i	0.529568	−	0.848267i	$-0.322354\pi$
$421$	−4058.55	−	7029.61i	−0.469837	−	0.813782i	−0.999405	+	0.0344856i	$0.989021\pi$
$422$	8849.96	−	15328.6i	1.02088	−	1.76821i
$423$	−78.6383	+	136.206i	−0.00903907	+	0.0156561i
$424$	−2270.43			−0.260051
$425$	−1666.10	−	2885.77i	−0.190159	−	0.329366i
$426$	12623.6			1.43572
$427$	1816.49			0.205869
$428$	−6903.68	+	11957.5i	−0.779678	+	1.35044i
$429$	−2515.15			−0.283059
$430$	11101.2	+	19227.9i	1.24500	+	2.15640i
$431$	−3973.72	+	6882.68i	−0.444100	+	0.769204i	−0.997989	−	0.0633863i	$-0.979810\pi$
$431$	−3973.72	+	6882.68i	−0.444100	+	0.769204i	0.553889	+	0.832591i	$0.313143\pi$
$432$	411.403	+	712.571i	0.0458186	+	0.0793601i
$433$	814.343	−	1410.48i	0.0903807	−	0.156544i	−0.817291	−	0.576226i	$-0.804525\pi$
$433$	814.343	−	1410.48i	0.0903807	−	0.156544i	0.907671	+	0.419682i	$0.137858\pi$
$434$	467.821	−	810.289i	0.0517422	−	0.0896201i
$435$	−4491.82	+	7780.07i	−0.495095	+	0.857530i
$436$	−2804.85	+	4858.14i	−0.308092	+	0.533630i
$437$	−4829.49	+	8364.92i	−0.528663	+	0.915671i
$438$	3686.69	−	6385.54i	0.402185	−	0.696605i
$439$	−1860.94	−	3223.24i	−0.202318	−	0.350425i	0.746957	−	0.664873i	$-0.231514\pi$
$439$	−1860.94	−	3223.24i	−0.202318	−	0.350425i	−0.949275	+	0.314447i	$0.898181\pi$
$440$	21067.6	−	36490.2i	2.28264	−	3.95364i
$441$	1366.78	+	2367.34i	0.147585	+	0.255624i
$442$	751.445			0.0808656
$443$	−6209.96	+	10756.0i	−0.666014	+	1.15357i	0.312996	+	0.949755i	$0.398667\pi$
$443$	−6209.96	+	10756.0i	−0.666014	+	1.15357i	−0.979009	+	0.203815i	$0.934666\pi$
$444$	−13586.0			−1.45217
$445$	−24998.2			−2.66299
$446$	14219.3	+	24628.5i	1.50965	+	2.61479i
$447$	3974.20			0.420521
$448$	−2288.18	+	3963.25i	−0.241309	+	0.417960i
$449$	2850.87	−	4937.85i	0.299646	−	0.519001i	−0.676409	−	0.736526i	$-0.736465\pi$
$449$	2850.87	−	4937.85i	0.299646	−	0.519001i	0.976055	+	0.217525i	$0.0697982\pi$
$450$	−5350.90	−	9268.03i	−0.560542	−	0.970887i
$451$	−1005.25	−	1741.14i	−0.104956	−	0.181790i
$452$	−836.720	−	1449.24i	−0.0870708	−	0.150811i
$453$	3478.66	+	6025.22i	0.360799	+	0.624922i
$454$	−8772.79			−0.906889
$455$	1446.78			0.149068
$456$	2320.22	+	4018.74i	0.238277	+	0.412708i
$457$	3554.88	−	6157.24i	0.363874	−	0.630248i	−0.624721	−	0.780848i	$-0.714787\pi$
$457$	3554.88	−	6157.24i	0.363874	−	0.630248i	0.988595	+	0.150600i	$0.0481206\pi$
$458$	603.270	−	1044.90i	0.0615480	−	0.106604i
$459$	179.492	+	310.889i	0.0182526	+	0.0316145i
$460$	−54247.1			−5.49844
$461$	823.471			0.0831950			0.0415975	−	0.999134i	$-0.486755\pi$
$461$	823.471			0.0831950			0.0415975	+	0.999134i	$0.486755\pi$
$462$	−3138.84	+	5436.63i	−0.316087	+	0.547478i
$463$	−7706.56	−	13348.2i	−0.773552	−	1.33983i	−0.935605	−	0.353049i	$-0.885145\pi$
$463$	−7706.56	−	13348.2i	−0.773552	−	1.33983i	0.162053	−	0.986782i	$-0.448188\pi$
$464$	4708.57			0.471099
$465$	−914.846	+	1584.56i	−0.0912364	+	0.158026i
$466$	6892.60			0.685179
$467$	8755.43	+	15164.9i	0.867566	+	1.50267i	0.864477	+	0.502672i	$0.167650\pi$
$467$	8755.43	+	15164.9i	0.867566	+	1.50267i	0.00308850	+	0.999995i	$0.499017\pi$
$468$	1555.69			0.153657
$469$	1702.39	+	2985.47i	0.167610	+	0.293937i
$470$	−1606.91			−0.157705
$471$	1331.48	+	2306.19i	0.130258	+	0.225613i
$472$	27275.4			2.65986
$473$	−8496.70	+	14716.7i	−0.825959	+	1.43060i
$474$	−8901.60			−0.862582
$475$	−6274.92	−	10868.5i	−0.606133	−	1.04985i
$476$	604.509	−	1047.04i	0.0582093	−	0.100821i
$477$	−661.501			−0.0634969
$478$	−23187.2			−2.21874
$479$	1235.95	+	2140.73i	0.117896	+	0.204201i	0.918934	−	0.394412i	$-0.129052\pi$
$479$	1235.95	+	2140.73i	0.117896	+	0.204201i	−0.801038	+	0.598614i	$0.795719\pi$
$480$	2980.84	−	5162.96i	0.283450	−	0.490950i
$481$	−1858.85	+	3219.62i	−0.176208	+	0.305202i
$482$	−14806.8	−	25646.2i	−1.39924	−	2.42355i
$483$	3626.34			0.341624
$484$	52562.7			4.93639
$485$	−11195.7	−	19391.6i	−1.04819	−	1.81552i
$486$	576.462	+	998.461i	0.0538042	+	0.0931916i
$487$	−1263.68	−	2188.75i	−0.117583	−	0.203659i	0.801227	−	0.598361i	$-0.204181\pi$
$487$	−1263.68	−	2188.75i	−0.117583	−	0.203659i	−0.918809	+	0.394702i	$0.870848\pi$
$488$	4477.01	+	7754.41i	0.415297	+	0.719315i
$489$	−1590.47	+	2754.78i	−0.147083	+	0.254756i
$490$	−13964.5	+	24187.3i	−1.28746	+	2.22994i
$491$	17577.7			1.61562			0.807812	−	0.589440i	$-0.200652\pi$
$491$	17577.7			1.61562			0.807812	+	0.589440i	$0.200652\pi$
$492$	621.775	+	1076.95i	0.0569752	+	0.0986840i
$493$	2054.31			0.187670
$494$	2830.12			0.257759
$495$	6138.15	−	10631.6i	0.557353	−	0.965363i
$496$	958.990			0.0868144
$497$	−2778.90	−	4813.20i	−0.250806	−	0.434409i
$498$	−2576.93	+	4463.37i	−0.231877	+	0.401623i
$499$	3104.87	+	5377.80i	0.278543	+	0.482451i	0.971023	−	0.238986i	$-0.0768150\pi$
$499$	3104.87	+	5377.80i	0.278543	+	0.482451i	−0.692480	+	0.721438i	$0.743482\pi$
$500$	17664.5	−	30595.8i	1.57996	−	2.73657i
$501$	1931.74	−	3345.87i	0.172263	−	0.298368i
$502$	4488.80	−	7774.83i	0.399093	−	0.691250i
$503$	−3716.79	+	6437.66i	−0.329470	+	0.570658i	−0.982407	−	0.186754i	$-0.940203\pi$
$503$	−3716.79	+	6437.66i	−0.329470	+	0.570658i	0.652937	+	0.757412i	$0.273537\pi$
$504$	871.098	−	1508.79i	0.0769877	−	0.133347i
$505$	−1880.68	+	3257.44i	−0.165721	+	0.287038i
$506$	−32205.3	−	55781.1i	−2.82944	−	4.90074i
$507$	−3082.65	+	5339.30i	−0.270030	+	0.467706i
$508$	−15952.9	−	27631.3i	−1.39330	−	2.41327i
$509$	13155.7			1.14561			0.572806	−	0.819691i	$-0.305855\pi$
$509$	13155.7			1.14561			0.572806	+	0.819691i	$0.305855\pi$
$510$	−1833.89	+	3176.38i	−0.159227	+	0.275789i
$511$	−3246.28			−0.281031
$512$	−10655.5			−0.919750
$513$	676.008	+	1170.88i	0.0581803	+	0.100771i
$514$	−12185.1			−1.04564
$515$	−9904.98	+	17155.9i	−0.847506	+	1.46792i
$516$	5255.45	−	9102.71i	0.448369	−	0.776597i
$517$	−614.952	−	1065.13i	−0.0523125	−	0.0906079i
$518$	4639.60	+	8036.02i	0.393537	+	0.681627i
$519$	−4212.24	−	7295.81i	−0.356256	−	0.617053i
$520$	3565.81	+	6176.17i	0.300714	+	0.520852i
$521$	−12800.5			−1.07640			−0.538198	−	0.842819i	$-0.680895\pi$
$521$	−12800.5			−1.07640			−0.538198	+	0.842819i	$0.680895\pi$
$522$	6597.70			0.553206
$523$	6362.20	+	11019.7i	0.531930	+	0.921330i	0.999305	+	0.0372710i	$0.0118665\pi$
$523$	6362.20	+	11019.7i	0.531930	+	0.921330i	−0.467375	+	0.884059i	$0.654800\pi$
$524$	16533.3	−	28636.5i	1.37836	−	2.38739i
$525$	−2355.84	+	4080.44i	−0.195843	+	0.339209i
$526$	5558.34	+	9627.34i	0.460752	+	0.798045i
$527$	418.400			0.0345840
$528$	−6434.34			−0.530339
$529$	−12520.1	+	21685.4i	−1.02902	+	1.78231i
$530$	−3379.31	−	5853.13i	−0.276958	−	0.479706i
$531$	7946.82			0.649459
$532$	2276.72	−	3943.40i	0.185542	−	0.321368i
$533$	340.288			0.0276539
$534$	9179.50	+	15899.4i	0.743888	+	1.28845i
$535$	−18441.6			−1.49028
$536$	−8548.88	+	14625.5i	−0.688909	+	1.17859i
$537$	13025.0			1.04669
$538$	2263.91	+	3921.20i	0.181420	+	0.314229i
$539$	−21376.5			−1.70826
$540$	−3796.62	+	6575.94i	−0.302557	+	0.524043i
$541$	12177.3			0.967729			0.483864	−	0.875143i	$-0.339233\pi$
$541$	12177.3			0.967729			0.483864	+	0.875143i	$0.339233\pi$
$542$	13606.2	+	23566.6i	1.07829	+	1.86766i
$543$	3722.64	−	6447.80i	0.294206	−	0.509580i
$544$	−1363.27			−0.107444
$545$	−7492.52			−0.588888
$546$	−531.266	−	920.180i	−0.0416412	−	0.0721247i
$547$	−8523.30	+	14762.8i	−0.666234	+	1.15395i	0.312716	+	0.949847i	$0.398761\pi$
$547$	−8523.30	+	14762.8i	−0.666234	+	1.15395i	−0.978949	+	0.204104i	$0.934572\pi$
$548$	−13022.5	+	22555.6i	−1.01513	+	1.75826i
$549$	1304.40	+	2259.29i	0.101403	+	0.175636i
$550$	83688.1			6.48813
$551$	7737.02			0.598200
$552$	8937.67	+	15480.5i	0.689153	+	1.19365i
$553$	1959.55	+	3394.04i	0.150685	+	0.260994i
$554$	−5026.91	−	8706.86i	−0.385511	−	0.667724i
$555$	−9072.96	−	15714.8i	−0.693920	−	1.20190i
$556$	−896.060	+	1552.02i	−0.0683479	+	0.118382i
$557$	−4489.02	+	7775.21i	−0.341483	+	0.591466i	−0.984708	−	0.174211i	$-0.944262\pi$
$557$	−4489.02	+	7775.21i	−0.341483	+	0.591466i	0.643226	+	0.765677i	$0.277596\pi$
$558$	1343.75			0.101945
$559$	−1438.11	−	2490.89i	−0.108812	−	0.188467i
$560$	3701.21			0.279294
$561$	−2807.25			−0.211270
$562$	−12879.0	+	22307.0i	−0.966667	+	1.67432i
$563$	10540.5			0.789042			0.394521	−	0.918887i	$-0.370911\pi$
$563$	10540.5			0.789042			0.394521	+	0.918887i	$0.370911\pi$
$564$	380.365	+	658.812i	0.0283976	+	0.0491861i
$565$	1117.55	−	1935.66i	0.0832139	−	0.144131i
$566$	−8951.54	−	15504.5i	−0.664773	−	1.15142i
$567$	253.799	−	439.592i	0.0187981	−	0.0325593i
$568$	13698.1	−	23725.7i	1.01190	−	1.75266i
$569$	8672.57	−	15021.3i	0.638968	−	1.10673i	−0.346691	−	0.937979i	$-0.612695\pi$
$569$	8672.57	−	15021.3i	0.638968	−	1.10673i	0.985660	−	0.168746i	$-0.0539718\pi$
$570$	−6906.84	+	11963.0i	−0.507536	+	0.879079i
$571$	2778.40	−	4812.33i	0.203630	−	0.352697i	−0.746066	−	0.665872i	$-0.768060\pi$
$571$	2778.40	−	4812.33i	0.203630	−	0.352697i	0.949695	+	0.313176i	$0.101393\pi$
$572$	−6082.74	+	10535.6i	−0.444637	+	0.770133i
$573$	−419.407	−	726.434i	−0.0305776	−	0.0529620i
$574$	424.672	−	735.553i	0.0308806	−	0.0534867i
$575$	−24171.5	−	41866.2i	−1.75308	−	3.03642i
$576$	−6572.48			−0.475439
$577$	4137.10	−	7165.66i	0.298491	−	0.517002i	−0.677300	−	0.735707i	$-0.736850\pi$
$577$	4137.10	−	7165.66i	0.298491	−	0.517002i	0.975791	+	0.218705i	$0.0701832\pi$
$578$	−22471.2			−1.61709
$579$	−4766.26			−0.342105
$580$	21726.5	+	37631.3i	1.55542	+	2.69406i
$581$	2269.08			0.162027
$582$	−8222.28	+	14241.4i	−0.585609	+	1.01430i
$583$	2586.47	−	4479.89i	0.183740	−	0.318247i
$584$	−8000.96	−	13858.1i	−0.566921	−	0.981936i
$585$	1038.92	+	1799.46i	0.0734255	+	0.127177i
$586$	−10219.5	−	17700.6i	−0.720413	−	1.24779i
$587$	4829.44	+	8364.84i	0.339578	+	0.588167i	0.984353	−	0.176205i	$-0.0563823\pi$
$587$	4829.44	+	8364.84i	0.339578	+	0.588167i	−0.644775	+	0.764372i	$0.723049\pi$
$588$	13222.0			0.927320
$589$	1575.79			0.110237
$590$	40596.7	+	70315.6i	2.83278	+	4.90652i
$591$	−626.075	+	1084.39i	−0.0435758	+	0.0754755i
$592$	−4755.38	+	8236.56i	−0.330144	+	0.571825i
$593$	−3565.03	−	6174.81i	−0.246877	−	0.427604i	0.715781	−	0.698325i	$-0.246071\pi$
$593$	−3565.03	−	6174.81i	−0.246877	−	0.427604i	−0.962658	+	0.270722i	$0.912738\pi$
$594$	−9015.87			−0.622770
$595$	1614.81			0.111262
$596$	9611.38	−	16647.4i	0.660566	−	1.14413i
$597$	−6543.64	−	11333.9i	−0.448598	−	0.776995i
$598$	10901.8			0.745500
$599$	−11477.6	+	19879.8i	−0.782909	+	1.35604i	0.147331	+	0.989087i	$0.452932\pi$
$599$	−11477.6	+	19879.8i	−0.782909	+	1.35604i	−0.930240	+	0.366952i	$0.880401\pi$
$600$	−23225.3			−1.58028
$601$	−7383.21	−	12788.1i	−0.501110	−	0.867949i	−0.999999	−	0.00128263i	$-0.999592\pi$
$601$	−7383.21	−	12788.1i	−0.501110	−	0.867949i	0.498889	−	0.866666i	$-0.333742\pi$
$602$	−7178.93			−0.486032
$603$	−2490.76	+	4261.21i	−0.168211	+	0.287778i
$604$	33651.8			2.26701
$605$	35102.3	+	60799.0i	2.35886	+	4.08567i
$606$	2762.39			0.185172
$607$	−12840.2	+	22239.9i	−0.858596	+	1.48713i	0.0146716	+	0.999892i	$0.495330\pi$
$607$	−12840.2	+	22239.9i	−0.858596	+	1.48713i	−0.873268	+	0.487240i	$0.838004\pi$
$608$	−5134.40			−0.342479
$609$	−1452.38	−	2515.60i	−0.0966396	−	0.167385i
$610$	−13327.2	+	23083.4i	−0.884593	+	1.53216i
$611$	208.168			0.0137833
$612$	1736.36			0.114687
$613$	−3433.03	−	5946.19i	−0.226197	−	0.391785i	0.730481	−	0.682933i	$-0.239296\pi$
$613$	−3433.03	−	5946.19i	−0.226197	−	0.391785i	−0.956678	+	0.291148i	$0.905963\pi$
$614$	−21366.6	+	37008.1i	−1.40438	+	2.43245i
$615$	−830.466	+	1438.41i	−0.0544514	+	0.0943126i
$616$	6811.99	+	11798.7i	0.445557	+	0.771727i
$617$	−18558.9			−1.21095			−0.605473	−	0.795866i	$-0.707016\pi$
$617$	−18558.9			−1.21095			−0.605473	+	0.795866i	$0.707016\pi$
$618$	14548.7			0.946980
$619$	4515.99	+	7821.93i	0.293236	+	0.507900i	0.974573	−	0.224070i	$-0.0719345\pi$
$619$	4515.99	+	7821.93i	0.293236	+	0.507900i	−0.681337	+	0.731970i	$0.738601\pi$
$620$	4425.01	+	7664.34i	0.286633	+	0.496463i
$621$	2604.03	+	4510.32i	0.168271	+	0.291454i
$622$	−13232.6	−	22919.6i	−0.853021	−	1.47748i
$623$	4041.46	−	7000.01i	0.259900	−	0.450160i
$624$	544.524	−	943.144i	0.0349334	−	0.0605064i
$625$	15858.9			1.01497
$626$	−1552.09	−	2688.30i	−0.0990960	−	0.171639i
$627$	−10572.8			−0.673422
$628$	12880.5			0.818449
$629$	−2074.73	+	3593.55i	−0.131518	+	0.227797i
$630$	5186.17			0.327972
$631$	5187.65	+	8985.27i	0.327285	+	0.566875i	0.981972	−	0.189025i	$-0.0605328\pi$
$631$	5187.65	+	8985.27i	0.327285	+	0.566875i	−0.654687	+	0.755900i	$0.727199\pi$
$632$	−9659.24	+	16730.3i	−0.607949	+	1.05300i
$633$	−5595.88	−	9692.35i	−0.351368	−	0.608588i
$634$	4435.84	−	7683.10i	0.277870	−	0.481285i
$635$	21307.3	−	36905.4i	1.33158	−	2.30637i
$636$	−1599.80	+	2770.94i	−0.0997427	+	0.172759i
$637$	1809.04	−	3133.36i	0.112523	−	0.194895i
$638$	−25797.0	+	44681.7i	−1.60080	+	2.77267i
$639$	3991.00	−	6912.61i	0.247076	−	0.427948i
$640$	−25626.9	−	44387.1i	−1.58280	−	2.74149i
$641$	8635.98	−	14958.0i	0.532139	−	0.921691i	−0.467157	−	0.884174i	$-0.654722\pi$
$641$	8635.98	−	14958.0i	0.532139	−	0.921691i	0.999296	−	0.0375170i	$-0.0119448\pi$
$642$	6771.87	+	11729.2i	0.416300	+	0.721052i
$643$	−25240.9			−1.54806			−0.774031	−	0.633147i	$-0.781763\pi$
$643$	−25240.9			−1.54806			−0.774031	+	0.633147i	$0.781763\pi$
$644$	8770.11	−	15190.3i	0.536632	−	0.929473i
$645$	14038.7			0.857015
$646$	3158.81			0.192386
$647$	3158.26	+	5470.27i	0.191907	+	0.332393i	0.945882	−	0.324510i	$-0.105199\pi$
$647$	3158.26	+	5470.27i	0.191907	+	0.332393i	−0.753975	+	0.656903i	$0.771866\pi$
$648$	2502.10			0.151685
$649$	−31072.1	+	53818.4i	−1.87933	+	3.25510i
$650$	−7082.34	+	12267.0i	−0.427373	+	0.740231i
$651$	−295.806	−	512.350i	−0.0178088	−	0.0308458i
$652$	7692.95	+	13324.6i	0.462085	+	0.800355i
$653$	−7320.55	−	12679.6i	−0.438706	−	0.759861i	0.558884	−	0.829246i	$-0.311230\pi$
$653$	−7320.55	−	12679.6i	−0.438706	−	0.759861i	−0.997590	+	0.0693846i	$0.977896\pi$
$654$	2751.30	+	4765.39i	0.164502	+	0.284926i
$655$	44165.0			2.63461
$656$	870.539			0.0518123
$657$	−2331.12	−	4037.61i	−0.138425	−	0.239760i
$658$	259.789	−	449.967i	0.0153915	−	0.0266589i
$659$	6284.15	−	10884.5i	0.371465	−	0.643397i	−0.618326	−	0.785922i	$-0.712189\pi$
$659$	6284.15	−	10884.5i	0.371465	−	0.643397i	0.989791	+	0.142525i	$0.0455221\pi$
$660$	−29689.6	−	51423.9i	−1.75101	−	3.03284i
$661$	24591.3			1.44703			0.723517	−	0.690307i	$-0.242524\pi$
$661$	24591.3			1.44703			0.723517	+	0.690307i	$0.242524\pi$
$662$	42784.3			2.51187
$663$	237.572	−	411.486i	0.0139163	−	0.0241038i
$664$	5592.51	+	9686.51i	0.326854	+	0.566129i
$665$	6081.75			0.354647
$666$	−6663.29	+	11541.2i	−0.387683	+	0.671487i
$667$	29803.6			1.73013
$668$	−9343.62	−	16183.6i	−0.541191	−	0.937370i
$669$	17981.9			1.03919
$670$	−50428.5	−	270.278i	−2.90780	−	0.0155847i
$671$	−20400.8			−1.17372
$672$	963.822	+	1669.39i	0.0553278	+	0.0958305i
$673$	5961.10			0.341432			0.170716	−	0.985320i	$-0.445392\pi$
$673$	5961.10			0.341432			0.170716	+	0.985320i	$0.445392\pi$
$674$	17439.1	−	30205.4i	0.996632	−	1.72622i
$675$	−6766.81			−0.385859
$676$	14910.4	+	25825.6i	0.848341	+	1.46937i
$677$	4279.77	−	7412.77i	0.242961	−	0.420821i	−0.718595	−	0.695429i	$-0.755215\pi$
$677$	4279.77	−	7412.77i	0.242961	−	0.420821i	0.961556	+	0.274607i	$0.0885479\pi$
$678$	−1641.49			−0.0929809
$679$	7240.04			0.409201
$680$	3979.94	+	6893.46i	0.224447	+	0.388753i
$681$	−2773.54	+	4803.92i	−0.156068	+	0.270318i
$682$	−5254.05	+	9100.28i	−0.294997	+	0.510950i
$683$	−4144.34	−	7178.21i	−0.232180	−	0.402147i	0.726270	−	0.687410i	$-0.241252\pi$
$683$	−4144.34	−	7178.21i	−0.232180	−	0.402147i	−0.958449	+	0.285263i	$0.907919\pi$
$684$	6539.55			0.365564
$685$	−34786.6			−1.94033
$686$	−9614.38	−	16652.6i	−0.535100	−	0.926821i
$687$	−381.451	−	660.693i	−0.0211838	−	0.0366914i
$688$	−3679.04	−	6372.28i	−0.203869	−	0.353112i
$689$	437.774	+	758.247i	0.0242059	+	0.0419259i
$690$	−26605.7	+	46082.4i	−1.46791	+	2.54250i
$691$	−6609.23	+	11447.5i	−0.363859	+	0.630223i	−0.988592	−	0.150616i	$-0.951874\pi$
$691$	−6609.23	+	11447.5i	−0.363859	+	0.630223i	0.624733	+	0.780838i	$0.285208\pi$
$692$	−40748.3			−2.23846
$693$	1984.71	+	3437.61i	0.108792	+	0.188433i
$694$	−10335.1			−0.565296
$695$	−2393.62			−0.130641
$696$	7159.24	−	12400.2i	0.389900	−	0.675326i
$697$	379.809			0.0206403
$698$	−19751.1	−	34209.9i	−1.07104	−	1.85510i
$699$	2179.12	−	3774.34i	0.117914	−	0.204233i
$700$	11394.9	+	19736.6i	0.615269	+	1.06568i
$701$	10313.2	−	17863.1i	0.555672	−	0.962451i	−0.442179	−	0.896927i	$-0.645795\pi$
$701$	10313.2	−	17863.1i	0.555672	−	0.962451i	0.997851	−	0.0655247i	$-0.0208721\pi$
$702$	762.993	−	1321.54i	0.0410218	−	0.0710519i
$703$	−7813.94	+	13534.1i	−0.419215	+	0.726102i
$704$	25698.4	−	44510.9i	1.37577	−	2.38291i
$705$	−508.029	+	879.933i	−0.0271397	+	0.0470074i
$706$	23740.8	−	41120.2i	1.26558	−	2.19204i
$707$	−608.098	−	1053.26i	−0.0323478	−	0.0560280i
$708$	19219.0	−	33288.2i	1.02019	−	1.76702i
$709$	−4184.47	−	7247.72i	−0.221652	−	0.383912i	0.733658	−	0.679519i	$-0.237812\pi$
$709$	−4184.47	−	7247.72i	−0.221652	−	0.383912i	−0.955310	+	0.295607i	$0.904478\pi$
$710$	81552.8			4.31073
$711$	−2814.27	+	4874.45i	−0.148443	+	0.257111i
$712$	39843.2			2.09717
$713$	6070.07			0.318830
$714$	−592.967	−	1027.05i	−0.0310802	−	0.0538324i
$715$	−16248.7			−0.849882
$716$	31500.3	−	54560.1i	1.64416	−	2.84777i
$717$	−7330.71	+	12697.2i	−0.381828	+	0.661345i
$718$	−30141.4	−	52206.4i	−1.56667	−	2.71355i
$719$	10313.7	+	17863.8i	0.534959	+	0.926577i	0.999165	+	0.0408496i	$0.0130065\pi$
$719$	10313.7	+	17863.8i	0.534959	+	0.926577i	−0.464206	+	0.885727i	$0.653660\pi$
$720$	2657.80	+	4603.44i	0.137570	+	0.238278i
$721$	−3202.67	−	5547.19i	−0.165428	−	0.286530i
$722$	−20646.0			−1.06422
$723$	−18724.9			−0.963189
$724$	−18006.0	−	31187.3i	−0.924293	−	1.60092i
$725$	−19361.8	+	33535.6i	−0.991833	+	1.71791i
$726$	25779.6	−	44651.5i	1.31786	−	2.28261i
$727$	9469.15	+	16401.0i	0.483069	+	0.836700i	0.999811	−	0.0194411i	$-0.00618868\pi$
$727$	9469.15	+	16401.0i	0.483069	+	0.836700i	−0.516742	+	0.856141i	$0.672855\pi$
$728$	−2305.94			−0.117395
$729$	729.000			0.0370370
$730$	23817.3	−	41252.7i	1.20756	−	2.09155i
$731$	−1605.14	−	2780.18i	−0.0812149	−	0.140668i
$732$	12618.5			0.637148
$733$	8308.69	−	14391.1i	0.418674	−	0.725165i	−0.577132	−	0.816651i	$-0.695828\pi$
$733$	8308.69	−	14391.1i	0.418674	−	0.725165i	0.995806	+	0.0914855i	$0.0291615\pi$
$734$	4153.00			0.208842
$735$	8829.86	+	15293.8i	0.443121	+	0.767509i
$736$	−19778.1			−0.990530
$737$	−19119.4	−	33529.6i	−0.955595	−	1.67582i
$738$	1219.81			0.0608425
$739$	−10270.0	−	17788.1i	−0.511213	−	0.885447i	−0.999916	−	0.0129965i	$-0.995863\pi$
$739$	−10270.0	−	17788.1i	−0.511213	−	0.885447i	0.488702	−	0.872451i	$-0.337470\pi$
$740$	−87769.8			−4.36011
$741$	894.750	−	1549.75i	0.0443582	−	0.0768307i
$742$	2185.33			0.108121
$743$	−10869.8	−	18827.1i	−0.536711	−	0.929610i	−0.999078	−	0.0429220i	$-0.986333\pi$
$743$	−10869.8	−	18827.1i	−0.536711	−	0.929610i	0.462368	−	0.886688i	$-0.347000\pi$
$744$	1458.12	−	2525.53i	0.0718510	−	0.124450i
$745$	25674.6			1.26261
$746$	−52245.2			−2.56412
$747$	1629.40	+	2822.21i	0.0798083	+	0.138232i
$748$	−6789.19	+	11759.2i	−0.331868	+	0.574812i
$749$	2981.45	−	5164.02i	0.145447	−	0.251922i
$750$	−17327.2	−	30011.6i	−0.843601	−	1.46116i
$751$	6344.89			0.308293			0.154147	−	0.988048i	$-0.450737\pi$
$751$	6344.89			0.308293			0.154147	+	0.988048i	$0.450737\pi$
$752$	532.544			0.0258243
$753$	−2838.29	−	4916.07i	−0.137361	−	0.237917i
$754$	−4366.29	−	7562.63i	−0.210890	−	0.365271i
$755$	22473.3	+	38924.9i	1.08329	+	1.87632i
$756$	−1227.60	−	2126.26i	−0.0590572	−	0.102290i
$757$	333.090	−	576.929i	0.0159926	−	0.0276999i	−0.857918	−	0.513786i	$-0.828243\pi$
$757$	333.090	−	576.929i	0.0159926	−	0.0276999i	0.873911	+	0.486086i	$0.161576\pi$
$758$	−1873.92	+	3245.72i	−0.0897938	+	0.155527i
$759$	−40727.1			−1.94770
$760$	14989.4	+	25962.4i	0.715424	+	1.23915i
$761$	30627.1			1.45891			0.729457	−	0.684027i	$-0.239773\pi$
$761$	30627.1			1.45891			0.729457	+	0.684027i	$0.239773\pi$
$762$	−31296.7			−1.48787
$763$	1211.31	−	2098.06i	0.0574738	−	0.0995475i
$764$	−4057.25			−0.192128
$765$	1159.58	+	2008.44i	0.0548033	+	0.0949222i
$766$	−19980.4	+	34607.1i	−0.942458	+	1.63238i
$767$	−5259.12	−	9109.07i	−0.247583	−	0.428826i
$768$	−10057.4	+	17419.9i	−0.472546	+	0.818474i
$769$	4256.37	−	7372.25i	0.199595	−	0.345709i	−0.748802	−	0.662794i	$-0.769371\pi$
$769$	4256.37	−	7372.25i	0.199595	−	0.345709i	0.948397	+	0.317085i	$0.102704\pi$
$770$	−20277.9	+	35122.4i	−0.949047	+	1.64380i
$771$	−3852.34	+	6672.46i	−0.179947	+	0.311677i
$772$	−11526.9	+	19965.2i	−0.537388	+	0.930783i
$773$	7526.57	−	13036.4i	0.350210	−	0.606581i	−0.636076	−	0.771626i	$-0.719444\pi$
$773$	7526.57	−	13036.4i	0.350210	−	0.606581i	0.986286	+	0.165045i	$0.0527770\pi$
$774$	−5155.11	−	8928.91i	−0.239401	−	0.414655i
$775$	−3943.40	+	6830.17i	−0.182776	+	0.316577i
$776$	17844.2	+	30907.1i	0.825476	+	1.42977i
$777$	5867.29			0.270898
$778$	−73.9566	+	128.097i	−0.00340806	+	0.00590294i
$779$	1430.45			0.0657910
$780$	10050.3			0.461355
$781$	31209.6	+	54056.6i	1.42992	+	2.47669i
$782$	12168.0			0.556427
$783$	2085.88	−	3612.85i	0.0952021	−	0.164895i
$784$	4627.97	−	8015.87i	0.210822	−	0.365155i
$785$	8601.80	+	14898.8i	0.391098	+	0.677401i
$786$	−16217.6	−	28089.8i	−0.735959	−	1.27472i
$787$	10123.3	+	17534.0i	0.458521	+	0.794181i	0.998883	−	0.0472512i	$-0.0150461\pi$
$787$	10123.3	+	17534.0i	0.458521	+	0.794181i	−0.540362	+	0.841432i	$0.681713\pi$
$788$	3028.26	+	5245.10i	0.136900	+	0.237118i
$789$	7029.14			0.317166
$790$	−57507.3			−2.58989
$791$	361.349	+	625.875i	0.0162429	+	0.0281335i
$792$	−9783.23	+	16945.0i	−0.438929	+	0.760248i
$793$	1726.48	−	2990.34i	0.0773127	−	0.133910i
$794$	6712.30	+	11626.0i	0.300014	+	0.519639i
$795$	−4273.51			−0.190649
$796$	−63301.7			−2.81868
$797$	−1949.74	+	3377.06i	−0.0866543	+	0.150090i	−0.906095	−	0.423074i	$-0.860951\pi$
$797$	−1949.74	+	3377.06i	−0.0866543	+	0.150090i	0.819441	+	0.573164i	$0.194284\pi$
$798$	−2233.25	−	3868.11i	−0.0990681	−	0.171591i
$799$	232.345			0.0102876
$800$	12848.8	−	22254.7i	0.567841	−	0.983529i
$801$	11608.5			0.512068
$802$	−8341.08	−	14447.2i	−0.367249	−	0.636094i
$803$	36458.7			1.60224
$804$	11825.9	+	20739.0i	0.518741	+	0.909710i
$805$	23427.4			1.02572
$806$	−889.278	−	1540.27i	−0.0388629	−	0.0673124i
$807$	2862.96			0.124884
$808$	2997.50	−	5191.83i	0.130510	−	0.226049i
$809$	12252.1			0.532461			0.266230	−	0.963909i	$-0.414222\pi$
$809$	12252.1			0.532461			0.266230	+	0.963909i	$0.414222\pi$
$810$	3724.13	+	6450.39i	0.161547	+	0.279807i
$811$	9015.05	−	15614.5i	0.390334	−	0.676079i	−0.602159	−	0.798376i	$-0.705693\pi$
$811$	9015.05	−	15614.5i	0.390334	−	0.676079i	0.992494	+	0.122297i	$0.0390261\pi$
$812$	−14050.0			−0.607216
$813$	17206.5			0.742263
$814$	−52106.9	−	90251.8i	−2.24367	−	3.88615i
$815$	−10275.0	+	17796.8i	−0.441616	+	0.764902i
$816$	607.765	−	1052.68i	0.0260736	−	0.0451607i
$817$	−6045.32	−	10470.8i	−0.258873	−	0.448380i
$818$	41048.0			1.75454
$819$	−671.845			−0.0286644
$820$	4016.87	+	6957.43i	0.171067	+	0.296298i
$821$	18203.5	+	31529.4i	0.773820	+	1.34030i	0.935455	+	0.353445i	$0.114990\pi$
$821$	18203.5	+	31529.4i	0.773820	+	1.34030i	−0.161636	+	0.986851i	$0.551677\pi$
$822$	12773.9	+	22125.0i	0.542019	+	0.938804i
$823$	−8357.86	−	14476.2i	−0.353993	−	0.613135i	0.632952	−	0.774191i	$-0.281843\pi$
$823$	−8357.86	−	14476.2i	−0.353993	−	0.613135i	−0.986945	+	0.161057i	$0.948510\pi$
$824$	15786.9	−	27343.8i	0.667432	−	1.15603i
$825$	26458.2	−	45827.0i	1.11655	−	1.93393i
$826$	−26253.0			−1.10588
$827$	−1384.79	−	2398.52i	−0.0582270	−	0.100852i	0.835443	−	0.549578i	$-0.185211\pi$
$827$	−1384.79	−	2398.52i	−0.0582270	−	0.100852i	−0.893670	+	0.448726i	$0.851878\pi$
$828$	25190.9			1.05730
$829$	9851.53			0.412735			0.206368	−	0.978475i	$-0.433836\pi$
$829$	9851.53			0.412735			0.206368	+	0.978475i	$0.433836\pi$
$830$	−16647.8	+	28834.8i	−0.696208	+	1.20587i
$831$	−6357.08			−0.265373
$832$	4349.60	+	7533.72i	0.181244	+	0.313924i
$833$	2019.14	−	3497.26i	0.0839847	−	0.145466i
$834$	878.952	+	1522.39i	0.0364936	+	0.0632087i
$835$	12479.7	−	21615.4i	0.517218	−	0.895848i
$836$	−25569.7	+	44288.0i	−1.05783	+	1.83221i
$837$	424.829	−	735.826i	0.0175439	−	0.0303869i
$838$	−20457.6	+	35433.6i	−0.843313	+	1.46066i
$839$	15312.7	−	26522.4i	0.630099	−	1.09136i	−0.357432	−	0.933939i	$-0.616348\pi$
$839$	15312.7	−	26522.4i	0.630099	−	1.09136i	0.987531	−	0.157424i	$-0.0503189\pi$
$840$	5627.58	−	9747.26i	0.231155	−	0.400372i
$841$	257.890	+	446.679i	0.0105740	+	0.0183148i
$842$	−19255.9	+	33352.3i	−0.788128	+	1.36508i
$843$	8143.45	+	14104.9i	0.332711	+	0.576272i
$844$	−54133.3			−2.20776
$845$	−19914.9	+	34493.7i	−0.810762	+	1.40428i
$846$	746.206			0.0303252
$847$	−22699.9			−0.920872
$848$	1119.93	+	1939.78i	0.0453521	+	0.0785522i
$849$	−11320.2			−0.457608
$850$	−7904.88	+	13691.7i	−0.318983	+	0.552494i
$851$	−30099.9	+	52134.5i	−1.21247	+	2.10006i
$852$	−19304.0	−	33435.5i	−0.776226	−	1.34446i
$853$	−5657.80	−	9799.60i	−0.227104	−	0.393355i	0.729845	−	0.683613i	$-0.239592\pi$
$853$	−5657.80	−	9799.60i	−0.227104	−	0.393355i	−0.956948	+	0.290258i	$0.906259\pi$
$854$	−4309.20	−	7463.76i	−0.172667	−	0.299068i
$855$	4367.23	+	7564.27i	0.174686	+	0.302564i
$856$	29393.0			1.17363
$857$	15901.0			0.633800			0.316900	−	0.948459i	$-0.397358\pi$
$857$	15901.0			0.633800			0.316900	+	0.948459i	$0.397358\pi$
$858$	5966.61	+	10334.5i	0.237409	+	0.411204i
$859$	−2348.95	+	4068.50i	−0.0933005	+	0.161601i	−0.908898	−	0.417018i	$-0.863075\pi$
$859$	−2348.95	+	4068.50i	−0.0933005	+	0.161601i	0.815598	+	0.578620i	$0.196408\pi$
$860$	33951.9	−	58806.5i	1.34622	−	2.33173i
$861$	−268.522	−	465.094i	−0.0106286	−	0.0184093i
$862$	37706.9			1.48991
$863$	42715.1			1.68487			0.842433	−	0.538802i	$-0.181123\pi$
$863$	42715.1			1.68487			0.842433	+	0.538802i	$0.181123\pi$
$864$	−1384.22	+	2397.54i	−0.0545048	+	0.0944050i
$865$	−27212.5	−	47133.3i	−1.06965	−	1.85270i
$866$	−7727.37			−0.303218
$867$	−7104.34	+	12305.1i	−0.278288	+	0.482009i
$868$	−2861.56			−0.111898
$869$	−22007.6	−	38118.2i	−0.859097	−	1.48800i
$870$	42623.3			1.66099
$871$	6532.79	+	35.0132i	0.254139	+	0.00136209i
$872$	11941.9			0.463764
$873$	5198.99	+	9004.92i	0.201557	+	0.349107i
$874$	45827.4			1.77361
$875$	−7628.66	+	13213.2i	−0.294738	+	0.510501i
$876$	−22550.7			−0.869770
$877$	−14367.8	−	24885.7i	−0.553210	−	0.958188i	−0.998040	−	0.0625732i	$-0.980069\pi$
$877$	−14367.8	−	24885.7i	−0.553210	−	0.958188i	0.444830	−	0.895615i	$-0.353264\pi$
$878$	−8829.29	+	15292.8i	−0.339378	+	0.587820i
$879$	−12923.6			−0.495909
$880$	−41568.0			−1.59234
$881$	−2748.64	−	4760.79i	−0.105113	−	0.182060i	0.808672	−	0.588260i	$-0.200187\pi$
$881$	−2748.64	−	4760.79i	−0.105113	−	0.182060i	−0.913784	+	0.406200i	$0.866854\pi$
$882$	6484.75	−	11231.9i	0.247566	−	0.428796i
$883$	20228.4	−	35036.6i	0.770940	−	1.33531i	−0.166108	−	0.986108i	$-0.553120\pi$
$883$	20228.4	−	35036.6i	0.770940	−	1.33531i	0.937048	−	0.349200i	$-0.113547\pi$
$884$	−1149.11	−	1990.31i	−0.0437202	−	0.0757257i
$885$	51339.1			1.94999
$886$	58926.8			2.23441
$887$	6664.85	+	11543.9i	0.252293	+	0.436984i	0.964157	−	0.265334i	$-0.0854821\pi$
$887$	6664.85	+	11543.9i	0.252293	+	0.436984i	−0.711864	+	0.702317i	$0.752149\pi$
$888$	14460.8	+	25046.9i	0.546480	+	0.946530i
$889$	6889.50	+	11933.0i	0.259917	+	0.450190i
$890$	59302.6	+	102715.i	2.23351	+	3.86856i
$891$	−2850.39	+	4937.02i	−0.107174	+	0.185630i
$892$	43488.2	−	75323.7i	1.63239	−	2.82738i
$893$	875.064			0.0327916
$894$	−9427.87	−	16329.6i	−0.352702	−	0.610897i
$895$	84145.8			3.14267
$896$	16572.4			0.617907
$897$	3446.65	−	5969.77i	0.128294	−	0.222213i
$898$	−27052.1			−1.00528
$899$	−2431.12	−	4210.82i	−0.0901917	−	0.156217i
$900$	−16365.2	+	28345.3i	−0.606117	+	1.04983i
$901$	488.617	+	846.309i	0.0180668	+	0.0312926i
$902$	−4769.45	+	8260.93i	−0.176059	+	0.304943i
$903$	−2269.64	+	3931.13i	−0.0836421	+	0.144872i
$904$	−1781.20	+	3085.13i	−0.0655331	+	0.113507i
$905$	24049.5	−	41654.9i	0.883350	−	1.53001i
$906$	16504.7	−	28586.9i	0.605221	−	1.04827i
$907$	6815.72	−	11805.2i	0.249517	−	0.432177i	−0.713875	−	0.700274i	$-0.753061\pi$
$907$	6815.72	−	11805.2i	0.249517	−	0.432177i	0.963392	+	0.268097i	$0.0863947\pi$
$908$	13415.3	+	23236.0i	0.490312	+	0.849245i
$909$	873.337	−	1512.66i	0.0318666	−	0.0551946i
$910$	−3432.16	−	5944.67i	−0.125027	−	0.216554i
$911$	−13970.0			−0.508063			−0.254032	−	0.967196i	$-0.581757\pi$
$911$	−13970.0			−0.508063			−0.254032	+	0.967196i	$0.581757\pi$
$912$	2288.98	−	3964.64i	0.0831095	−	0.143950i
$913$	−25483.9			−0.923761
$914$	−33732.6			−1.22076
$915$	8426.85	+	14595.7i	0.304462	+	0.527344i
$916$	−3690.08			−0.133104
$917$	−7140.13	+	12367.1i	−0.257130	+	0.445362i
$918$	851.606	−	1475.03i	0.0306179	−	0.0530317i
$919$	1811.39	+	3137.42i	0.0650187	+	0.112616i	0.896702	−	0.442634i	$-0.145956\pi$
$919$	1811.39	+	3137.42i	0.0650187	+	0.112616i	−0.831684	+	0.555250i	$0.812623\pi$
$920$	57740.3	+	100009.i	2.06918	+	3.58392i
$921$	13510.2	+	23400.4i	0.483363	+	0.837209i
$922$	−1953.50	−	3383.56i	−0.0697776	−	0.120858i
$923$	−10564.8			−0.376755
$924$	19199.6			0.683573
$925$	−39108.6	−	67738.0i	−1.39014	−	2.40780i
$926$	−36564.1	+	63330.9i	−1.29759	+	2.24750i
$927$	4599.60	−	7966.75i	0.162967	−	0.282268i
$928$	7921.31	+	13720.1i	0.280204	+	0.485328i
$929$	−11087.5			−0.391570			−0.195785	−	0.980647i	$-0.562725\pi$
$929$	−11087.5			−0.391570			−0.195785	+	0.980647i	$0.562725\pi$
$930$	8681.05			0.306089
$931$	7604.57	−	13171.5i	0.267701	−	0.463672i
$932$	−10540.1	−	18256.1i	−0.370444	−	0.641628i
$933$	−16734.1			−0.587192
$934$	41540.5	−	71950.3i	1.45530	−	2.52065i
$935$	−18135.8			−0.634335
$936$	−1655.87	−	2868.04i	−0.0578244	−	0.100155i
$937$	51594.9			1.79886			0.899430	−	0.437065i	$-0.143982\pi$
$937$	51594.9			1.79886			0.899430	+	0.437065i	$0.143982\pi$
$938$	8228.44	−	14077.3i	0.286427	−	0.490021i
$939$	−1962.79			−0.0682144
$940$	2457.28	+	4256.14i	0.0852636	+	0.147681i
$941$	−50280.0			−1.74185			−0.870925	−	0.491416i	$-0.836479\pi$
$941$	−50280.0			−1.74185			−0.870925	+	0.491416i	$0.836479\pi$
$942$	6317.27	−	10941.8i	0.218501	−	0.378454i
$943$	5510.20			0.190283
$944$	−13454.1	−	23303.2i	−0.463870	−	0.803447i
$945$	1639.62	−	2839.91i	0.0564412	−	0.0977590i
$946$	80625.9			2.77101
$947$	2844.03			0.0975908			0.0487954	−	0.998809i	$-0.484462\pi$
$947$	2844.03			0.0975908			0.0487954	+	0.998809i	$0.484462\pi$
$948$	13612.3	+	23577.2i	0.466357	+	0.807755i
$949$	−3085.42	+	5344.10i	−0.105539	+	0.182800i
$950$	−29771.6	+	51566.0i	−1.01676	+	1.76107i
$951$	−2804.81	−	4858.07i	−0.0956384	−	0.165651i
$952$	−2573.74			−0.0876214
$953$	−52076.2			−1.77011			−0.885054	−	0.465489i	$-0.845879\pi$
$953$	−52076.2			−1.77011			−0.885054	+	0.465489i	$0.845879\pi$
$954$	1569.26	+	2718.04i	0.0532564	+	0.0922428i
$955$	−2709.50	−	4693.00i	−0.0918089	−	0.159018i
$956$	35457.8	+	61414.8i	1.19957	+	2.07772i
$957$	16311.6	+	28252.5i	0.550970	+	0.954309i
$958$	5864.02	−	10156.8i	0.197764	−	0.342537i
$959$	5623.94	−	9740.96i	0.189371	−	0.328000i
$960$	−42460.3			−1.42750
$961$	14400.4	+	24942.1i	0.483379	+	0.837238i
$962$	17638.8			0.591161
$963$	8563.78			0.286567
$964$	−45285.1	+	78436.1i	−1.51300	+	2.62060i
$965$	−30791.6			−1.02717
$966$	−8602.66	−	14900.3i	−0.286528	−	0.496281i
$967$	−3689.09	+	6389.70i	−0.122682	+	0.212491i	−0.920824	−	0.389978i	$-0.872483\pi$
$967$	−3689.09	+	6389.70i	−0.122682	+	0.212491i	0.798143	+	0.602469i	$0.205816\pi$
$968$	−55947.5	−	96903.8i	−1.85766	−	3.21757i
$969$	998.666	−	1729.74i	0.0331081	−	0.0573449i
$970$	−53118.6	+	92004.2i	−1.75828	+	3.04544i
$971$	−11559.8	+	20022.2i	−0.382052	+	0.661734i	−0.991355	−	0.131204i	$-0.958116\pi$
$971$	−11559.8	+	20022.2i	−0.382052	+	0.661734i	0.609303	+	0.792937i	$0.291449\pi$
$972$	1763.05	−	3053.69i	0.0581788	−	0.100769i
$973$	386.976	−	670.262i	0.0127501	−	0.0220839i
$974$	−5995.57	+	10384.6i	−0.197239	+	0.341627i
$975$	4478.20	+	7756.48i	0.147095	+	0.254775i
$976$	4416.74	−	7650.02i	0.144853	−	0.250892i
$977$	−950.673	−	1646.61i	−0.0311307	−	0.0539200i	0.850040	−	0.526718i	$-0.176577\pi$
$977$	−950.673	−	1646.61i	−0.0311307	−	0.0539200i	−0.881171	+	0.472798i	$0.843244\pi$
$978$	15092.1			0.493450
$979$	−45389.3	+	78616.5i	−1.48176	+	2.56649i
$980$	85418.1			2.78427
$981$	3479.32			0.113238
$982$	−41699.1	−	72225.0i	−1.35506	−	2.34704i
$983$	−10669.3			−0.346182			−0.173091	−	0.984906i	$-0.555376\pi$
$983$	−10669.3			−0.346182			−0.173091	+	0.984906i	$0.555376\pi$
$984$	1323.63	−	2292.59i	0.0428819	−	0.0742736i
$985$	−4044.65	+	7005.54i	−0.130836	+	0.226614i
$986$	−4873.38	−	8440.95i	−0.157404	−	0.272631i
$987$	−164.266	−	284.517i	−0.00529751	−	0.00917555i
$988$	−4327.81	−	7495.98i	−0.139358	−	0.241376i
$989$	−23287.0	−	40334.3i	−0.748720	−	1.29682i
$990$	−58245.5			−1.86986
$991$	−34354.5			−1.10122			−0.550609	−	0.834763i	$-0.685605\pi$
$991$	−34354.5			−1.10122			−0.550609	+	0.834763i	$0.685605\pi$
$992$	1613.33	+	2794.36i	0.0516362	+	0.0894366i
$993$	13526.4	−	23428.4i	0.432273	−	0.748718i
$994$	−13184.6	+	22836.4i	−0.420715	+	0.728699i
$995$	−42274.0	−	73220.8i	−1.34691	−	2.33292i
$996$	15762.5			0.501460
$997$	28387.4			0.901742			0.450871	−	0.892589i	$-0.351114\pi$
$997$	28387.4			0.901742			0.450871	+	0.892589i	$0.351114\pi$
$998$	14731.2	−	25515.2i	0.467242	−	0.809288i
$999$	4213.23	+	7297.54i	0.133434	+	0.231115i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.4.e.b.37.3	✓	36
67.29	even	3	inner	201.4.e.b.163.3	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.4.e.b.37.3	✓	36	1.1	even	1	trivial
201.4.e.b.163.3	yes	36	67.29	even	3	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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	201.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.37227 - 4.10889i) q^{2} -3.00000 q^{3} +(-7.25534 + 12.5666i) q^{4} -19.3810 q^{5} +(7.11681 + 12.3267i) q^{6} +(3.13332 - 5.42707i) q^{7} +30.8902 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+(-2.37227 - 4.10889i) q^{2} -3.00000 q^{3} +(-7.25534 + 12.5666i) q^{4} -19.3810 q^{5} +(7.11681 + 12.3267i) q^{6} +(3.13332 - 5.42707i) q^{7} +30.8902 q^{8} +9.00000 q^{9} +(45.9769 + 79.6344i) q^{10} +(-35.1900 + 60.9509i) q^{11} +(21.7660 - 37.6998i) q^{12} +(-5.95611 - 10.3163i) q^{13} -29.7323 q^{14} +58.1430 q^{15} +(-15.2371 - 26.3915i) q^{16} +(-6.64784 - 11.5144i) q^{17} +(-21.3504 - 36.9800i) q^{18} +(-25.0373 - 43.3659i) q^{19} +(140.616 - 243.553i) q^{20} +(-9.39995 + 16.2812i) q^{21} +333.921 q^{22} +(-96.4457 - 167.049i) q^{23} -92.6705 q^{24} +250.623 q^{25} +(-28.2590 + 48.9460i) q^{26} -27.0000 q^{27} +(45.4666 + 78.7504i) q^{28} +(-77.2548 + 133.809i) q^{29} +(-137.931 - 238.903i) q^{30} +(-15.7344 + 27.2528i) q^{31} +(51.2674 - 88.7978i) q^{32} +(105.570 - 182.853i) q^{33} +(-31.5410 + 54.6306i) q^{34} +(-60.7268 + 105.182i) q^{35} +(-65.2980 + 113.100i) q^{36} +(-156.046 - 270.279i) q^{37} +(-118.791 + 205.751i) q^{38} +(17.8683 + 30.9488i) q^{39} -598.682 q^{40} +(-14.2832 + 24.7392i) q^{41} +89.1969 q^{42} +241.452 q^{43} +(-510.631 - 884.438i) q^{44} -174.429 q^{45} +(-457.591 + 792.571i) q^{46} +(-8.73759 + 15.1340i) q^{47} +(45.7114 + 79.1745i) q^{48} +(151.865 + 263.037i) q^{49} +(-594.545 - 1029.78i) q^{50} +(19.9435 + 34.5432i) q^{51} +172.854 q^{52} -73.5001 q^{53} +(64.0513 + 110.940i) q^{54} +(682.017 - 1181.29i) q^{55} +(96.7887 - 167.643i) q^{56} +(75.1120 + 130.098i) q^{57} +733.077 q^{58} +882.980 q^{59} +(-421.847 + 730.660i) q^{60} +(144.933 + 251.032i) q^{61} +149.305 q^{62} +(28.1999 - 48.8436i) q^{63} -730.275 q^{64} +(115.435 + 199.940i) q^{65} -1001.76 q^{66} +(-276.751 + 473.468i) q^{67} +192.929 q^{68} +(289.337 + 501.147i) q^{69} +576.241 q^{70} +(443.444 - 768.067i) q^{71} +278.012 q^{72} +(-259.013 - 448.624i) q^{73} +(-740.365 + 1282.35i) q^{74} -751.868 q^{75} +726.617 q^{76} +(220.523 + 381.957i) q^{77} +(84.7770 - 146.838i) q^{78} +(-312.696 + 541.606i) q^{79} +(295.311 + 511.493i) q^{80} +81.0000 q^{81} +135.534 q^{82} +(181.045 + 313.579i) q^{83} +(-136.400 - 236.251i) q^{84} +(128.842 + 223.160i) q^{85} +(-572.790 - 992.101i) q^{86} +(231.764 - 401.428i) q^{87} +(-1087.03 + 1882.78i) q^{88} +1289.83 q^{89} +(413.793 + 716.710i) q^{90} -74.6495 q^{91} +2798.99 q^{92} +(47.2033 - 81.7584i) q^{93} +82.9117 q^{94} +(485.248 + 840.474i) q^{95} +(-153.802 + 266.393i) q^{96} +(577.666 + 1000.55i) q^{97} +(720.528 - 1247.99i) q^{98} +(-316.710 + 548.558i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 2 q^{2} - 108 q^{3} - 90 q^{4} - 4 q^{5} - 6 q^{6} + 22 q^{7} + 48 q^{8} + 324 q^{9}+O(q^{10}) \) 36 * q + 2 * q^2 - 108 * q^3 - 90 * q^4 - 4 * q^5 - 6 * q^6 + 22 * q^7 + 48 * q^8 + 324 * q^9	\( 36 q + 2 q^{2} - 108 q^{3} - 90 q^{4} - 4 q^{5} - 6 q^{6} + 22 q^{7} + 48 q^{8} + 324 q^{9} + 14 q^{10} - 16 q^{11} + 270 q^{12} - 46 q^{13} + 14 q^{14} + 12 q^{15} - 346 q^{16} - 8 q^{17} + 18 q^{18} - 154 q^{19} - 180 q^{20} - 66 q^{21} + 214 q^{22} - 104 q^{23} - 144 q^{24} + 1032 q^{25} - 333 q^{26} - 972 q^{27} - 473 q^{28} + 76 q^{29} - 42 q^{30} + 498 q^{31} - 285 q^{32} + 48 q^{33} + 26 q^{34} - 392 q^{35} - 810 q^{36} - 124 q^{37} + 20 q^{38} + 138 q^{39} + 638 q^{40} - 508 q^{41} - 42 q^{42} - 1400 q^{43} - 333 q^{44} - 36 q^{45} - 1372 q^{46} + 18 q^{47} + 1038 q^{48} - 238 q^{49} - 337 q^{50} + 24 q^{51} + 3640 q^{52} + 724 q^{53} - 54 q^{54} - 178 q^{55} - 829 q^{56} + 462 q^{57} - 1472 q^{58} + 720 q^{59} + 540 q^{60} + 232 q^{61} - 3882 q^{62} + 198 q^{63} + 3628 q^{64} - 1428 q^{65} - 642 q^{66} - 1164 q^{67} + 1634 q^{68} + 312 q^{69} + 2550 q^{70} + 406 q^{71} + 432 q^{72} - 2120 q^{73} + 1375 q^{74} - 3096 q^{75} + 4190 q^{76} - 800 q^{77} + 999 q^{78} + 1306 q^{79} - 1927 q^{80} + 2916 q^{81} - 794 q^{82} - 1010 q^{83} + 1419 q^{84} + 472 q^{85} + 737 q^{86} - 228 q^{87} - 1838 q^{88} + 1904 q^{89} + 126 q^{90} + 7340 q^{91} + 7368 q^{92} - 1494 q^{93} - 9862 q^{94} + 1678 q^{95} + 855 q^{96} - 2358 q^{97} - 2610 q^{98} - 144 q^{99}+O(q^{100}) \) 36 * q + 2 * q^2 - 108 * q^3 - 90 * q^4 - 4 * q^5 - 6 * q^6 + 22 * q^7 + 48 * q^8 + 324 * q^9 + 14 * q^10 - 16 * q^11 + 270 * q^12 - 46 * q^13 + 14 * q^14 + 12 * q^15 - 346 * q^16 - 8 * q^17 + 18 * q^18 - 154 * q^19 - 180 * q^20 - 66 * q^21 + 214 * q^22 - 104 * q^23 - 144 * q^24 + 1032 * q^25 - 333 * q^26 - 972 * q^27 - 473 * q^28 + 76 * q^29 - 42 * q^30 + 498 * q^31 - 285 * q^32 + 48 * q^33 + 26 * q^34 - 392 * q^35 - 810 * q^36 - 124 * q^37 + 20 * q^38 + 138 * q^39 + 638 * q^40 - 508 * q^41 - 42 * q^42 - 1400 * q^43 - 333 * q^44 - 36 * q^45 - 1372 * q^46 + 18 * q^47 + 1038 * q^48 - 238 * q^49 - 337 * q^50 + 24 * q^51 + 3640 * q^52 + 724 * q^53 - 54 * q^54 - 178 * q^55 - 829 * q^56 + 462 * q^57 - 1472 * q^58 + 720 * q^59 + 540 * q^60 + 232 * q^61 - 3882 * q^62 + 198 * q^63 + 3628 * q^64 - 1428 * q^65 - 642 * q^66 - 1164 * q^67 + 1634 * q^68 + 312 * q^69 + 2550 * q^70 + 406 * q^71 + 432 * q^72 - 2120 * q^73 + 1375 * q^74 - 3096 * q^75 + 4190 * q^76 - 800 * q^77 + 999 * q^78 + 1306 * q^79 - 1927 * q^80 + 2916 * q^81 - 794 * q^82 - 1010 * q^83 + 1419 * q^84 + 472 * q^85 + 737 * q^86 - 228 * q^87 - 1838 * q^88 + 1904 * q^89 + 126 * q^90 + 7340 * q^91 + 7368 * q^92 - 1494 * q^93 - 9862 * q^94 + 1678 * q^95 + 855 * q^96 - 2358 * q^97 - 2610 * q^98 - 144 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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