LMFDB - Embedded newform 126.4.f.a.43.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [126,4,Mod(43,126)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("126.43"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(126, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	126.f (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.43424066072$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			43.3
Root			$0.500000 - 0.224437i$ of defining polynomial
Character	$\chi$	$=$	126.43
Dual form			126.4.f.a.85.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 - 1.73205i) q^{2} +(1.04944 - 5.08907i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-4.60507 - 7.97622i) q^{5} +(-7.76509 - 6.90676i) q^{6} +(-3.50000 + 6.06218i) q^{7} -8.00000 q^{8} +(-24.7973 - 10.6814i) q^{9} -18.4203 q^{10} +(6.63526 - 11.4926i) q^{11} +(-19.7280 + 6.54277i) q^{12} +(8.49862 + 14.7200i) q^{13} +(7.00000 + 12.1244i) q^{14} +(-45.4243 + 15.0650i) q^{15} +(-8.00000 + 13.8564i) q^{16} +16.3035 q^{17} +(-43.2980 + 32.2689i) q^{18} -26.2762 q^{19} +(-18.4203 + 31.9049i) q^{20} +(27.1778 + 24.1737i) q^{21} +(-13.2705 - 22.9852i) q^{22} +(-46.0617 - 79.7812i) q^{23} +(-8.39554 + 40.7126i) q^{24} +(20.0866 - 34.7910i) q^{25} +33.9945 q^{26} +(-80.3817 + 114.986i) q^{27} +28.0000 q^{28} +(87.6755 - 151.858i) q^{29} +(-19.3310 + 93.7422i) q^{30} +(2.55846 + 4.43139i) q^{31} +(16.0000 + 27.7128i) q^{32} +(-51.5234 - 45.8281i) q^{33} +(16.3035 - 28.2385i) q^{34} +64.4710 q^{35} +(12.5933 + 107.263i) q^{36} -284.652 q^{37} +(-26.2762 + 45.5117i) q^{38} +(83.8302 - 27.8023i) q^{39} +(36.8406 + 63.8098i) q^{40} +(7.78519 + 13.4843i) q^{41} +(69.0478 - 22.8997i) q^{42} +(146.918 - 254.470i) q^{43} -53.0821 q^{44} +(28.9966 + 246.978i) q^{45} -184.247 q^{46} +(309.331 - 535.777i) q^{47} +(62.1207 + 55.2541i) q^{48} +(-24.5000 - 42.4352i) q^{49} +(-40.1732 - 69.5820i) q^{50} +(17.1096 - 82.9698i) q^{51} +(33.9945 - 58.8802i) q^{52} +666.814 q^{53} +(118.780 + 254.211i) q^{54} -122.223 q^{55} +(28.0000 - 48.4974i) q^{56} +(-27.5753 + 133.721i) q^{57} +(-175.351 - 303.717i) q^{58} +(150.534 + 260.732i) q^{59} +(143.035 + 127.225i) q^{60} +(-69.3057 + 120.041i) q^{61} +10.2339 q^{62} +(151.543 - 112.941i) q^{63} +64.0000 q^{64} +(78.2736 - 135.574i) q^{65} +(-130.900 + 43.4130i) q^{66} +(102.582 + 177.677i) q^{67} +(-32.6070 - 56.4771i) q^{68} +(-454.351 + 150.686i) q^{69} +(64.4710 - 111.667i) q^{70} +953.646 q^{71} +(198.379 + 85.4510i) q^{72} -589.387 q^{73} +(-284.652 + 493.032i) q^{74} +(-155.974 - 138.733i) q^{75} +(52.5524 + 91.0234i) q^{76} +(46.4468 + 80.4482i) q^{77} +(35.6753 - 173.000i) q^{78} +(433.022 - 750.016i) q^{79} +147.362 q^{80} +(500.816 + 529.740i) q^{81} +31.1408 q^{82} +(-230.294 + 398.881i) q^{83} +(29.3844 - 142.494i) q^{84} +(-75.0789 - 130.041i) q^{85} +(-293.836 - 508.940i) q^{86} +(-680.809 - 605.554i) q^{87} +(-53.0821 + 91.9408i) q^{88} +138.382 q^{89} +(456.774 + 196.754i) q^{90} -118.981 q^{91} +(-184.247 + 319.125i) q^{92} +(25.2366 - 8.36972i) q^{93} +(-618.662 - 1071.55i) q^{94} +(121.004 + 209.585i) q^{95} +(157.824 - 52.3422i) q^{96} +(-448.941 + 777.589i) q^{97} -98.0000 q^{98} +(-287.294 + 214.112i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} - 12 q^{3} - 12 q^{4} - 9 q^{5} - 12 q^{6} - 21 q^{7} - 48 q^{8} - 36 q^{9} - 36 q^{10} - 48 q^{11} + 24 q^{12} + 57 q^{13} + 42 q^{14} - 63 q^{15} - 48 q^{16} + 48 q^{17} - 144 q^{18} - 282 q^{19}+ \cdots + 1512 q^{99}+O(q^{100}) $ 6 * q + 6 * q^2 - 12 * q^3 - 12 * q^4 - 9 * q^5 - 12 * q^6 - 21 * q^7 - 48 * q^8 - 36 * q^9 - 36 * q^10 - 48 * q^11 + 24 * q^12 + 57 * q^13 + 42 * q^14 - 63 * q^15 - 48 * q^16 + 48 * q^17 - 144 * q^18 - 282 * q^19 - 36 * q^20 + 42 * q^21 + 96 * q^22 + 30 * q^23 + 96 * q^24 + 210 * q^25 + 228 * q^26 - 189 * q^27 + 168 * q^28 - 117 * q^29 - 126 * q^30 + 165 * q^31 + 96 * q^32 - 342 * q^33 + 48 * q^34 + 126 * q^35 - 144 * q^36 - 798 * q^37 - 282 * q^38 + 102 * q^39 + 72 * q^40 + 384 * q^41 - 84 * q^42 + 771 * q^43 + 384 * q^44 + 189 * q^45 + 120 * q^46 - 81 * q^47 + 96 * q^48 - 147 * q^49 - 420 * q^50 - 675 * q^51 + 228 * q^52 + 1044 * q^53 + 54 * q^54 + 156 * q^55 + 168 * q^56 + 183 * q^57 + 234 * q^58 - 21 * q^59 + 780 * q^61 + 660 * q^62 + 504 * q^63 + 384 * q^64 - 531 * q^65 - 1386 * q^66 + 384 * q^67 - 96 * q^68 - 1809 * q^69 + 126 * q^70 + 114 * q^71 + 288 * q^72 - 234 * q^73 - 798 * q^74 - 147 * q^75 + 564 * q^76 - 336 * q^77 - 1212 * q^78 + 1383 * q^79 + 288 * q^80 + 2592 * q^81 + 1536 * q^82 - 12 * q^83 - 336 * q^84 + 1095 * q^85 - 1542 * q^86 - 27 * q^87 + 384 * q^88 - 1296 * q^89 + 2106 * q^90 - 798 * q^91 + 120 * q^92 - 1707 * q^93 + 162 * q^94 + 1314 * q^95 - 192 * q^96 - 741 * q^97 - 588 * q^98 + 1512 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	1.00000	−	1.73205i	0.353553	−	0.612372i
$2$	1.00000	−	1.73205i	0.353553	−	0.612372i
$3$	1.04944	−	5.08907i	0.201965	−	0.979393i
$3$	1.04944	−	5.08907i	0.201965	−	0.979393i
$4$	−2.00000	−	3.46410i	−0.250000	−	0.433013i
$5$	−4.60507	−	7.97622i	−0.411890	−	0.713415i	0.583206	−	0.812324i	$-0.301798\pi$
$5$	−4.60507	−	7.97622i	−0.411890	−	0.713415i	−0.995096	+	0.0989092i	$0.968465\pi$
$6$	−7.76509	−	6.90676i	−0.528348	−	0.469946i
$7$	−3.50000	+	6.06218i	−0.188982	+	0.327327i
$7$	−3.50000	+	6.06218i	−0.188982	+	0.327327i
$8$	−8.00000			−0.353553
$9$	−24.7973	−	10.6814i	−0.918420	−	0.395607i
$10$	−18.4203			−0.582501
$11$	6.63526	−	11.4926i	0.181873	−	0.315014i	−0.760645	−	0.649168i	$-0.775117\pi$
$11$	6.63526	−	11.4926i	0.181873	−	0.315014i	0.942518	+	0.334154i	$0.108451\pi$
$12$	−19.7280	+	6.54277i	−0.474581	+	0.157395i
$13$	8.49862	+	14.7200i	0.181315	+	0.314047i	0.942329	−	0.334689i	$-0.108631\pi$
$13$	8.49862	+	14.7200i	0.181315	+	0.314047i	−0.761014	+	0.648736i	$0.775298\pi$
$14$	7.00000	+	12.1244i	0.133631	+	0.231455i
$15$	−45.4243	+	15.0650i	−0.781901	+	0.259317i
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	16.3035			0.232599			0.116300	−	0.993214i	$-0.462897\pi$
$17$	16.3035			0.232599			0.116300	+	0.993214i	$0.462897\pi$
$18$	−43.2980	+	32.2689i	−0.566969	+	0.422547i
$19$	−26.2762			−0.317272			−0.158636	−	0.987337i	$-0.550710\pi$
$19$	−26.2762			−0.317272			−0.158636	+	0.987337i	$0.550710\pi$
$20$	−18.4203	+	31.9049i	−0.205945	+	0.356708i
$21$	27.1778	+	24.1737i	0.282414	+	0.251196i
$22$	−13.2705	−	22.9852i	−0.128604	−	0.222748i
$23$	−46.0617	−	79.7812i	−0.417588	−	0.723283i	0.578108	−	0.815960i	$-0.303791\pi$
$23$	−46.0617	−	79.7812i	−0.417588	−	0.723283i	−0.995696	+	0.0926765i	$0.970458\pi$
$24$	−8.39554	+	40.7126i	−0.0714055	+	0.346268i
$25$	20.0866	−	34.7910i	0.160693	−	0.278328i
$26$	33.9945			0.256418
$27$	−80.3817	+	114.986i	−0.572943	+	0.819595i
$28$	28.0000			0.188982
$29$	87.6755	−	151.858i	0.561412	−	0.972394i	−0.435962	−	0.899965i	$-0.643592\pi$
$29$	87.6755	−	151.858i	0.561412	−	0.972394i	0.997374	−	0.0724284i	$-0.0230749\pi$
$30$	−19.3310	+	93.7422i	−0.117645	+	0.570497i
$31$	2.55846	+	4.43139i	0.0148230	+	0.0256742i	0.873342	−	0.487108i	$-0.161948\pi$
$31$	2.55846	+	4.43139i	0.0148230	+	0.0256742i	−0.858519	+	0.512782i	$0.828615\pi$
$32$	16.0000	+	27.7128i	0.0883883	+	0.153093i
$33$	−51.5234	−	45.8281i	−0.271790	−	0.241747i
$34$	16.3035	−	28.2385i	0.0822362	−	0.142437i
$35$	64.4710			0.311360
$36$	12.5933	+	107.263i	0.0583023	+	0.496589i
$37$	−284.652			−1.26477			−0.632385	−	0.774654i	$-0.717924\pi$
$37$	−284.652			−1.26477			−0.632385	+	0.774654i	$0.717924\pi$
$38$	−26.2762	+	45.5117i	−0.112173	+	0.194289i
$39$	83.8302	−	27.8023i	0.344194	−	0.114152i
$40$	36.8406	+	63.8098i	0.145625	+	0.252230i
$41$	7.78519	+	13.4843i	0.0296547	+	0.0513634i	0.880472	−	0.474098i	$-0.157226\pi$
$41$	7.78519	+	13.4843i	0.0296547	+	0.0513634i	−0.850817	+	0.525462i	$0.823893\pi$
$42$	69.0478	−	22.8997i	0.253674	−	0.0841310i
$43$	146.918	−	254.470i	0.521042	−	0.902472i	−0.478658	−	0.878001i	$-0.658877\pi$
$43$	146.918	−	254.470i	0.521042	−	0.902472i	0.999701	−	0.0244705i	$-0.00778998\pi$
$44$	−53.0821			−0.181873
$45$	28.9966	+	246.978i	0.0960567	+	0.818161i
$46$	−184.247			−0.590558
$47$	309.331	−	535.777i	0.960011	−	1.66279i	0.237552	−	0.971375i	$-0.423655\pi$
$47$	309.331	−	535.777i	0.960011	−	1.66279i	0.722459	−	0.691414i	$-0.243012\pi$
$48$	62.1207	+	55.2541i	0.186799	+	0.166151i
$49$	−24.5000	−	42.4352i	−0.0714286	−	0.123718i
$50$	−40.1732	−	69.5820i	−0.113627	−	0.196808i
$51$	17.1096	−	82.9698i	0.0469769	−	0.227806i
$52$	33.9945	−	58.8802i	0.0906575	−	0.157023i
$53$	666.814			1.72819			0.864094	−	0.503330i	$-0.167892\pi$
$53$	666.814			1.72819			0.864094	+	0.503330i	$0.167892\pi$
$54$	118.780	+	254.211i	0.299331	+	0.640625i
$55$	−122.223			−0.299647
$56$	28.0000	−	48.4974i	0.0668153	−	0.115728i
$57$	−27.5753	+	133.721i	−0.0640779	+	0.310734i
$58$	−175.351	−	303.717i	−0.396978	−	0.687586i
$59$	150.534	+	260.732i	0.332167	+	0.575330i	0.982936	−	0.183946i	$-0.0588870\pi$
$59$	150.534	+	260.732i	0.332167	+	0.575330i	−0.650770	+	0.759275i	$0.725554\pi$
$60$	143.035	+	127.225i	0.307763	+	0.273744i
$61$	−69.3057	+	120.041i	−0.145470	+	0.251962i	−0.929548	−	0.368700i	$-0.879803\pi$
$61$	−69.3057	+	120.041i	−0.145470	+	0.251962i	0.784078	+	0.620662i	$0.213136\pi$
$62$	10.2339			0.0209629
$63$	151.543	−	112.941i	0.303058	−	0.225861i
$64$	64.0000			0.125000
$65$	78.2736	−	135.574i	0.149364	−	0.258706i
$66$	−130.900	+	43.4130i	−0.244132	+	0.0809662i
$67$	102.582	+	177.677i	0.187050	+	0.323980i	0.944265	−	0.329185i	$-0.106774\pi$
$67$	102.582	+	177.677i	0.187050	+	0.323980i	−0.757215	+	0.653165i	$0.773441\pi$
$68$	−32.6070	−	56.4771i	−0.0581498	−	0.100718i
$69$	−454.351	+	150.686i	−0.792717	+	0.262904i
$70$	64.4710	−	111.667i	0.110082	−	0.190668i
$71$	953.646			1.59404			0.797021	−	0.603952i	$-0.206408\pi$
$71$	953.646			1.59404			0.797021	+	0.603952i	$0.206408\pi$
$72$	198.379	+	85.4510i	0.324711	+	0.139868i
$73$	−589.387			−0.944967			−0.472483	−	0.881340i	$-0.656642\pi$
$73$	−589.387			−0.944967			−0.472483	+	0.881340i	$0.656642\pi$
$74$	−284.652	+	493.032i	−0.447164	+	0.774510i
$75$	−155.974	−	138.733i	−0.240138	−	0.213594i
$76$	52.5524	+	91.0234i	0.0793180	+	0.137383i
$77$	46.4468	+	80.4482i	0.0687416	+	0.119064i
$78$	35.6753	−	173.000i	0.0517875	−	0.251134i
$79$	433.022	−	750.016i	0.616694	−	1.06814i	−0.373391	−	0.927674i	$-0.621805\pi$
$79$	433.022	−	750.016i	0.616694	−	1.06814i	0.990085	−	0.140471i	$-0.0448616\pi$
$80$	147.362			0.205945
$81$	500.816	+	529.740i	0.686991	+	0.726666i
$82$	31.1408			0.0419381
$83$	−230.294	+	398.881i	−0.304555	+	0.527505i	−0.977162	−	0.212495i	$-0.931841\pi$
$83$	−230.294	+	398.881i	−0.304555	+	0.527505i	0.672607	+	0.740000i	$0.265174\pi$
$84$	29.3844	−	142.494i	0.0381678	−	0.185088i
$85$	−75.0789	−	130.041i	−0.0958053	−	0.165940i
$86$	−293.836	−	508.940i	−0.368433	−	0.638144i
$87$	−680.809	−	605.554i	−0.838969	−	0.746232i
$88$	−53.0821	+	91.9408i	−0.0643019	+	0.111374i
$89$	138.382			0.164814			0.0824072	−	0.996599i	$-0.473739\pi$
$89$	138.382			0.164814			0.0824072	+	0.996599i	$0.473739\pi$
$90$	456.774	+	196.754i	0.534981	+	0.230441i
$91$	−118.981			−0.137061
$92$	−184.247	+	319.125i	−0.208794	+	0.361642i
$93$	25.2366	−	8.36972i	0.0281389	−	0.00933226i
$94$	−618.662	−	1071.55i	−0.678831	−	1.17577i
$95$	121.004	+	209.585i	0.130681	+	0.226347i
$96$	157.824	−	52.3422i	0.167790	−	0.0556474i
$97$	−448.941	+	777.589i	−0.469929	+	0.813941i	−0.999409	−	0.0343818i	$-0.989054\pi$
$97$	−448.941	+	777.589i	−0.469929	+	0.813941i	0.529480	+	0.848322i	$0.322387\pi$
$98$	−98.0000			−0.101015
$99$	−287.294	+	214.112i	−0.291658	+	0.217365i
$100$	−160.693			−0.160693
$101$	−603.468	+	1045.24i	−0.594527	+	1.02975i	0.399086	+	0.916914i	$0.369328\pi$
$101$	−603.468	+	1045.24i	−0.594527	+	1.02975i	−0.993613	+	0.112838i	$0.964006\pi$
$102$	−126.598	−	112.605i	−0.122893	−	0.109309i
$103$	197.662	+	342.361i	0.189090	+	0.327513i	0.944947	−	0.327223i	$-0.106113\pi$
$103$	197.662	+	342.361i	0.189090	+	0.327513i	−0.755857	+	0.654736i	$0.772780\pi$
$104$	−67.9890	−	117.760i	−0.0641045	−	0.111032i
$105$	67.6586	−	328.098i	0.0628839	−	0.304944i
$106$	666.814	−	1154.96i	0.611007	−	1.05830i
$107$	−50.7643			−0.0458652			−0.0229326	−	0.999737i	$-0.507300\pi$
$107$	−50.7643			−0.0458652			−0.0229326	+	0.999737i	$0.507300\pi$
$108$	559.087	+	48.4783i	0.498131	+	0.0431929i
$109$	−2191.18			−1.92548			−0.962738	−	0.270437i	$-0.912832\pi$
$109$	−2191.18			−1.92548			−0.962738	+	0.270437i	$0.912832\pi$
$110$	−122.223	+	211.697i	−0.105941	+	0.183496i
$111$	−298.726	+	1448.61i	−0.255440	+	1.23871i
$112$	−56.0000	−	96.9948i	−0.0472456	−	0.0818317i
$113$	−352.980	−	611.380i	−0.293855	−	0.508971i	0.680863	−	0.732411i	$-0.261605\pi$
$113$	−352.980	−	611.380i	−0.293855	−	0.508971i	−0.974718	+	0.223439i	$0.928272\pi$
$114$	204.037	+	181.483i	0.167630	+	0.149101i
$115$	−424.235	+	734.796i	−0.344001	+	0.595827i
$116$	−701.404			−0.561412
$117$	−53.5129	−	455.795i	−0.0422843	−	0.360156i
$118$	602.135			0.469755
$119$	−57.0623	+	98.8349i	−0.0439571	+	0.0761359i
$120$	363.395	−	120.520i	0.276444	−	0.0916825i
$121$	577.447	+	1000.17i	0.433844	+	0.751440i
$122$	138.611	+	240.082i	0.102863	+	0.178164i
$123$	76.7930	−	25.4684i	0.0562942	−	0.0186700i
$124$	10.2339	−	17.7256i	0.00741151	−	0.0128371i
$125$	−1521.27			−1.08853
$126$	−44.0766	−	375.421i	−0.0311639	−	0.265438i
$127$	825.927			0.577080			0.288540	−	0.957468i	$-0.406830\pi$
$127$	825.927			0.577080			0.288540	+	0.957468i	$0.406830\pi$
$128$	64.0000	−	110.851i	0.0441942	−	0.0765466i
$129$	−1140.83	−	1014.73i	−0.778642	−	0.692573i
$130$	−156.547	−	271.148i	−0.105616	−	0.182932i
$131$	−629.241	−	1089.88i	−0.419672	−	0.726893i	0.576235	−	0.817284i	$-0.304521\pi$
$131$	−629.241	−	1089.88i	−0.419672	−	0.726893i	−0.995906	+	0.0903915i	$0.971188\pi$
$132$	−55.7066	+	270.139i	−0.0367321	+	0.178125i
$133$	91.9666	−	159.291i	0.0599588	−	0.103852i
$134$	410.327			0.264529
$135$	1287.32	+	111.623i	0.820701	+	0.0711629i
$136$	−130.428			−0.0822362
$137$	310.413	−	537.651i	0.193579	−	0.335289i	−0.752855	−	0.658187i	$-0.771324\pi$
$137$	310.413	−	537.651i	0.193579	−	0.335289i	0.946434	+	0.322898i	$0.104657\pi$
$138$	−193.356	+	937.645i	−0.119272	+	0.578389i
$139$	1259.41	+	2181.36i	0.768501	+	1.33108i	0.938376	+	0.345617i	$0.112330\pi$
$139$	1259.41	+	2181.36i	0.768501	+	1.33108i	−0.169874	+	0.985466i	$0.554336\pi$
$140$	−128.942	−	223.334i	−0.0778400	−	0.134823i
$141$	−2401.98	−	2136.47i	−1.43463	−	1.27605i
$142$	953.646	−	1651.76i	0.563579	−	0.976147i
$143$	225.562			0.131905
$144$	346.384	−	258.151i	0.200454	−	0.149393i
$145$	−1615.01			−0.924960
$146$	−589.387	+	1020.85i	−0.334096	+	0.578672i
$147$	−241.667	+	80.1490i	−0.135595	+	0.0449699i
$148$	569.304	+	986.063i	0.316193	+	0.547662i
$149$	−657.564	−	1138.93i	−0.361542	−	0.626209i	0.626673	−	0.779282i	$-0.284416\pi$
$149$	−657.564	−	1138.93i	−0.361542	−	0.626209i	−0.988215	+	0.153074i	$0.951083\pi$
$150$	−396.267	+	131.422i	−0.215701	+	0.0715370i
$151$	−519.646	+	900.054i	−0.280055	+	0.485069i	−0.971398	−	0.237458i	$-0.923686\pi$
$151$	−519.646	+	900.054i	−0.280055	+	0.485069i	0.691343	+	0.722526i	$0.257019\pi$
$152$	210.209			0.112173
$153$	−404.284	−	174.144i	−0.213624	−	0.0920177i
$154$	185.787			0.0972153
$155$	23.5638	−	40.8137i	0.0122109	−	0.0211499i
$156$	−263.970	−	234.792i	−0.135478	−	0.120503i
$157$	1402.48	+	2429.17i	0.712932	+	1.23483i	0.963752	+	0.266801i	$0.0859665\pi$
$157$	1402.48	+	2429.17i	0.712932	+	1.23483i	−0.250820	+	0.968034i	$0.580700\pi$
$158$	−866.044	−	1500.03i	−0.436068	−	0.755292i
$159$	699.783	−	3393.47i	0.349034	−	1.69258i
$160$	147.362	−	255.239i	0.0728126	−	0.126115i
$161$	644.863			0.315667
$162$	1418.35	−	337.700i	0.687878	−	0.163779i
$163$	4016.56			1.93007			0.965035	−	0.262120i	$-0.0844218\pi$
$163$	4016.56			1.93007			0.965035	+	0.262120i	$0.0844218\pi$
$164$	31.1408	−	53.9374i	0.0148274	−	0.0256817i
$165$	−128.266	+	622.004i	−0.0605184	+	0.293472i
$166$	460.588	+	797.762i	0.215353	+	0.373002i
$167$	1541.79	+	2670.46i	0.714415	+	1.23740i	0.963185	+	0.268840i	$0.0866403\pi$
$167$	1541.79	+	2670.46i	0.714415	+	1.23740i	−0.248770	+	0.968563i	$0.580026\pi$
$168$	−217.423	−	193.389i	−0.0998483	−	0.0888114i
$169$	954.047	−	1652.46i	0.434250	−	0.752143i
$170$	−300.316			−0.135489
$171$	651.579	+	280.666i	0.291389	+	0.125515i
$172$	−1175.35			−0.521042
$173$	920.469	−	1594.30i	0.404520	−	0.700649i	−0.589745	−	0.807589i	$-0.700772\pi$
$173$	920.469	−	1594.30i	0.404520	−	0.700649i	0.994265	+	0.106940i	$0.0341053\pi$
$174$	−1729.66	+	573.641i	−0.753593	+	0.249929i
$175$	140.606	+	243.537i	0.0607361	+	0.105198i
$176$	106.164	+	183.882i	0.0454683	+	0.0787534i
$177$	1484.86	−	492.454i	0.630560	−	0.209125i
$178$	138.382	−	239.685i	0.0582707	−	0.100928i
$179$	−655.758			−0.273819			−0.136910	−	0.990584i	$-0.543717\pi$
$179$	−655.758			−0.273819			−0.136910	+	0.990584i	$0.543717\pi$
$180$	797.563	−	594.402i	0.330260	−	0.246134i
$181$	−380.429			−0.156227			−0.0781134	−	0.996944i	$-0.524890\pi$
$181$	−380.429			−0.156227			−0.0781134	+	0.996944i	$0.524890\pi$
$182$	−118.981	+	206.081i	−0.0484584	+	0.0839325i
$183$	538.165	+	478.678i	0.217390	+	0.193360i
$184$	368.493	+	638.249i	0.147640	+	0.255719i
$185$	1310.84	+	2270.45i	0.520947	+	0.902306i
$186$	10.7398	−	52.0808i	0.00423378	−	0.0205309i
$187$	108.178	−	187.370i	0.0423036	−	0.0732719i
$188$	−2474.65			−0.960011
$189$	−415.730	−	889.739i	−0.159999	−	0.342429i
$190$	484.015			0.184811
$191$	1400.19	−	2425.20i	0.530440	−	0.918750i	−0.468929	−	0.883236i	$-0.655360\pi$
$191$	1400.19	−	2425.20i	0.530440	−	0.918750i	0.999369	−	0.0355138i	$-0.0113068\pi$
$192$	67.1643	−	325.701i	0.0252457	−	0.122424i
$193$	2259.67	+	3913.87i	0.842771	+	1.45972i	0.887543	+	0.460726i	$0.152411\pi$
$193$	2259.67	+	3913.87i	0.842771	+	1.45972i	−0.0447712	+	0.998997i	$0.514256\pi$
$194$	897.883	+	1555.18i	0.332290	+	0.575543i
$195$	−607.802	−	540.617i	−0.223208	−	0.198535i
$196$	−98.0000	+	169.741i	−0.0357143	+	0.0618590i
$197$	−895.383			−0.323824			−0.161912	−	0.986805i	$-0.551766\pi$
$197$	−895.383			−0.323824			−0.161912	+	0.986805i	$0.551766\pi$
$198$	83.5598	+	711.719i	0.0299916	+	0.255453i
$199$	4115.94			1.46619			0.733094	−	0.680127i	$-0.238075\pi$
$199$	4115.94			1.46619			0.733094	+	0.680127i	$0.238075\pi$
$200$	−160.693	+	278.328i	−0.0568134	+	0.0984038i
$201$	1011.86	−	335.584i	0.355081	−	0.117763i
$202$	1206.94	+	2090.47i	0.420394	+	0.728144i
$203$	613.729	+	1063.01i	0.212194	+	0.367530i
$204$	−321.635	+	106.670i	−0.110387	+	0.0366099i
$205$	71.7028	−	124.193i	0.0244290	−	0.0423122i
$206$	790.649			0.267413
$207$	290.034	+	2470.36i	0.0973854	+	0.829479i
$208$	−271.956			−0.0906575
$209$	−174.349	+	301.982i	−0.0577033	+	0.0999450i
$210$	−500.624	−	445.286i	−0.164506	−	0.146322i
$211$	−189.903	−	328.922i	−0.0619596	−	0.107317i	0.833382	−	0.552698i	$-0.186402\pi$
$211$	−189.903	−	328.922i	−0.0619596	−	0.107317i	−0.895341	+	0.445381i	$0.853068\pi$
$212$	−1333.63	−	2309.91i	−0.432047	−	0.748328i
$213$	1000.80	−	4853.17i	0.321941	−	1.56119i
$214$	−50.7643	+	87.9264i	−0.0162158	+	0.0280866i
$215$	−2706.28			−0.858449
$216$	643.054	−	919.888i	0.202566	−	0.289771i
$217$	−35.8185			−0.0112051
$218$	−2191.18	+	3795.23i	−0.680758	+	1.17911i
$219$	−618.528	+	2999.44i	−0.190850	+	0.925493i
$220$	244.447	+	423.394i	0.0749118	+	0.129751i
$221$	138.557	+	239.989i	0.0421737	+	0.0730470i
$222$	2210.35	+	1966.02i	0.668238	+	0.594373i
$223$	2593.64	−	4492.32i	0.778849	−	1.34901i	−0.153757	−	0.988109i	$-0.549137\pi$
$223$	2593.64	−	4492.32i	0.778849	−	1.34901i	0.932606	−	0.360897i	$-0.117529\pi$
$224$	−224.000			−0.0668153
$225$	−869.709	+	648.171i	−0.257692	+	0.192051i
$226$	−1411.92			−0.415573
$227$	−853.663	+	1478.59i	−0.249602	+	0.432323i	−0.963415	−	0.268013i	$-0.913633\pi$
$227$	−853.663	+	1478.59i	−0.249602	+	0.432323i	0.713814	+	0.700336i	$0.246966\pi$
$228$	518.375	−	171.919i	0.150571	−	0.0499369i
$229$	−2443.45	−	4232.17i	−0.705098	−	1.22127i	−0.966656	−	0.256078i	$-0.917570\pi$
$229$	−2443.45	−	4232.17i	−0.705098	−	1.22127i	0.261558	−	0.965188i	$-0.415764\pi$
$230$	848.470	+	1469.59i	0.243245	+	0.421313i
$231$	458.150	−	151.945i	0.130494	−	0.0432783i
$232$	−701.404	+	1214.87i	−0.198489	+	0.343793i
$233$	−3829.40			−1.07671			−0.538353	−	0.842720i	$-0.680953\pi$
$233$	−3829.40			−1.07671			−0.538353	+	0.842720i	$0.680953\pi$
$234$	−842.973	−	363.108i	−0.235499	−	0.101441i
$235$	−5697.97			−1.58168
$236$	602.135	−	1042.93i	0.166083	−	0.287665i
$237$	−3362.46	−	2990.78i	−0.921582	−	0.819713i
$238$	114.125	+	197.670i	0.0310824	+	0.0538362i
$239$	−2241.09	−	3881.68i	−0.606544	−	1.05057i	−0.991805	−	0.127758i	$-0.959222\pi$
$239$	−2241.09	−	3881.68i	−0.606544	−	1.05057i	0.385261	−	0.922808i	$-0.374111\pi$
$240$	154.648	−	749.938i	0.0415938	−	0.201701i
$241$	1029.02	−	1782.32i	0.275042	−	0.476386i	−0.695104	−	0.718909i	$-0.744642\pi$
$241$	1029.02	−	1782.32i	0.275042	−	0.476386i	0.970146	+	0.242523i	$0.0779750\pi$
$242$	2309.79			0.613548
$243$	3221.46	−	1992.76i	0.850440	−	0.526073i
$244$	554.446			0.145470
$245$	−225.649	+	390.835i	−0.0588415	+	0.101916i
$246$	32.6804	−	158.478i	0.00847003	−	0.0410738i
$247$	−223.311	−	386.787i	−0.0575262	−	0.0996382i
$248$	−20.4677	−	35.4511i	−0.00524073	−	0.00907721i
$249$	1788.25	+	1590.59i	0.455125	+	0.404816i
$250$	−1521.27	+	2634.92i	−0.384854	+	0.666587i
$251$	−5910.35			−1.48629			−0.743143	−	0.669132i	$-0.766666\pi$
$251$	−5910.35			−1.48629			−0.743143	+	0.669132i	$0.766666\pi$
$252$	−694.326	−	299.079i	−0.173565	−	0.0747626i
$253$	−1222.52			−0.303792
$254$	825.927	−	1430.55i	0.204029	−	0.353388i
$255$	−740.577	+	245.612i	−0.181869	+	0.0603170i
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	3280.82	+	5682.54i	0.796310	+	1.37925i	0.922004	+	0.387180i	$0.126551\pi$
$257$	3280.82	+	5682.54i	0.796310	+	1.37925i	−0.125694	+	0.992069i	$0.540116\pi$
$258$	−2898.40	+	961.253i	−0.699404	+	0.231957i
$259$	996.282	−	1725.61i	0.239019	−	0.413993i
$260$	−626.189			−0.149364
$261$	−3796.18	+	2829.19i	−0.900297	+	0.670968i
$262$	−2516.96			−0.593506
$263$	3540.83	−	6132.90i	0.830179	−	1.43791i	−0.0677175	−	0.997705i	$-0.521572\pi$
$263$	3540.83	−	6132.90i	0.830179	−	1.43791i	0.897896	−	0.440207i	$-0.145095\pi$
$264$	412.187	+	366.625i	0.0960923	+	0.0854705i
$265$	−3070.73	−	5318.66i	−0.711824	−	1.23292i
$266$	−183.933	−	318.582i	−0.0423973	−	0.0734342i
$267$	145.224	−	704.237i	0.0332868	−	0.161418i
$268$	410.327	−	710.707i	0.0935250	−	0.161990i
$269$	2665.66			0.604193			0.302097	−	0.953277i	$-0.402313\pi$
$269$	2665.66			0.604193			0.302097	+	0.953277i	$0.402313\pi$
$270$	1480.65	−	2118.08i	0.333740	−	0.477415i
$271$	−7097.49			−1.59093			−0.795465	−	0.606000i	$-0.792773\pi$
$271$	−7097.49			−1.59093			−0.795465	+	0.606000i	$0.792773\pi$
$272$	−130.428	+	225.908i	−0.0290749	+	0.0503592i
$273$	−124.863	+	605.502i	−0.0276816	+	0.134237i
$274$	−620.826	−	1075.30i	−0.136881	−	0.237085i
$275$	−266.559	−	461.694i	−0.0584514	−	0.101241i
$276$	1430.69	+	1272.55i	0.312020	+	0.277530i
$277$	−2627.29	+	4550.60i	−0.569886	+	0.987072i	0.426690	+	0.904398i	$0.359679\pi$
$277$	−2627.29	+	4550.60i	−0.569886	+	0.987072i	−0.996577	+	0.0826743i	$0.973654\pi$
$278$	5037.63			1.08682
$279$	−16.1098	−	137.215i	−0.00345687	−	0.0294438i
$280$	−515.768			−0.110082
$281$	−680.160	+	1178.07i	−0.144395	+	0.250099i	−0.929147	−	0.369711i	$-0.879457\pi$
$281$	−680.160	+	1178.07i	−0.144395	+	0.250099i	0.784752	+	0.619810i	$0.212790\pi$
$282$	−6102.46	+	2023.88i	−1.28864	+	0.427377i
$283$	13.1963	+	22.8567i	0.00277188	+	0.00480103i	0.867408	−	0.497598i	$-0.165784\pi$
$283$	13.1963	+	22.8567i	0.00277188	+	0.00480103i	−0.864636	+	0.502399i	$0.832451\pi$
$284$	−1907.29	−	3303.53i	−0.398510	−	0.690240i
$285$	1193.58	−	395.850i	0.248075	−	0.0822742i
$286$	225.562	−	390.685i	0.0466356	−	0.0807752i
$287$	−108.993			−0.0224168
$288$	−100.746	−	858.106i	−0.0206130	−	0.175571i
$289$	−4647.20			−0.945898
$290$	−1615.01	+	2797.28i	−0.327023	+	0.566420i
$291$	3486.07	+	3100.73i	0.702258	+	0.624633i
$292$	1178.77	+	2041.70i	0.236242	+	0.409183i
$293$	1987.12	+	3441.79i	0.396207	+	0.686250i	0.993254	−	0.115955i	$-0.0369930\pi$
$293$	1987.12	+	3441.79i	0.396207	+	0.686250i	−0.597048	+	0.802206i	$0.703660\pi$
$294$	−102.845	+	498.729i	−0.0204016	+	0.0989336i
$295$	1386.44	−	2401.38i	0.273633	−	0.473945i
$296$	2277.22			0.447164
$297$	788.135	+	1686.76i	0.153981	+	0.329547i
$298$	−2630.25			−0.511297
$299$	782.921	−	1356.06i	0.151430	−	0.262284i
$300$	−168.638	+	817.777i	−0.0324543	+	0.157381i
$301$	1028.43	+	1781.29i	0.196936	+	0.341102i
$302$	1039.29	+	1800.11i	0.198028	+	0.342995i
$303$	4685.98	+	4168.01i	0.888457	+	0.790250i
$304$	210.209	−	364.093i	0.0396590	−	0.0686914i
$305$	1276.63			0.239671
$306$	−705.910	+	526.096i	−0.131877	+	0.0982841i
$307$	4596.06			0.854434			0.427217	−	0.904149i	$-0.359494\pi$
$307$	4596.06			0.854434			0.427217	+	0.904149i	$0.359494\pi$
$308$	185.787	−	321.793i	0.0343708	−	0.0595320i
$309$	1949.74	−	646.630i	0.358953	−	0.119047i
$310$	−47.1277	−	81.6275i	−0.00863442	−	0.0149553i
$311$	784.679	+	1359.10i	0.143071	+	0.247806i	0.928652	−	0.370953i	$-0.120969\pi$
$311$	784.679	+	1359.10i	0.143071	+	0.247806i	−0.785581	+	0.618759i	$0.787636\pi$
$312$	−670.642	+	222.418i	−0.121691	+	0.0403588i
$313$	−1619.60	+	2805.23i	−0.292477	+	0.506585i	−0.974395	−	0.224844i	$-0.927813\pi$
$313$	−1619.60	+	2805.23i	−0.292477	+	0.506585i	0.681918	+	0.731429i	$0.261146\pi$
$314$	5609.93			1.00824
$315$	−1598.71	−	688.640i	−0.285959	−	0.123176i
$316$	−3464.18			−0.616694
$317$	−1646.40	+	2851.66i	−0.291708	+	0.505252i	−0.974214	−	0.225628i	$-0.927557\pi$
$317$	−1646.40	+	2851.66i	−0.291708	+	0.505252i	0.682506	+	0.730880i	$0.260890\pi$
$318$	−5177.88	−	4605.53i	−0.913084	−	0.812155i
$319$	−1163.50	−	2015.24i	−0.204212	−	0.353705i
$320$	−294.725	−	510.478i	−0.0514863	−	0.0891769i
$321$	−53.2742	+	258.343i	−0.00926317	+	0.0449200i
$322$	644.863	−	1116.94i	0.111605	−	0.193306i
$323$	−428.394			−0.0737972
$324$	833.439	−	2794.36i	0.142908	−	0.479142i
$325$	682.833			0.116544
$326$	4016.56	−	6956.89i	0.682383	−	1.18192i
$327$	−2299.51	+	11151.1i	−0.388879	+	1.88580i
$328$	−62.2815	−	107.875i	−0.0104845	−	0.0181597i
$329$	2165.32	+	3750.44i	0.362850	+	0.628475i
$330$	949.076	+	844.168i	0.158318	+	0.140818i
$331$	−1445.06	+	2502.92i	−0.239963	+	0.415628i	−0.960703	−	0.277577i	$-0.910469\pi$
$331$	−1445.06	+	2502.92i	−0.239963	+	0.415628i	0.720741	+	0.693205i	$0.243802\pi$
$332$	1842.35			0.304555
$333$	7058.61	+	3040.48i	1.16159	+	0.500351i
$334$	6167.16			1.01033
$335$	944.793	−	1636.43i	0.154088	−	0.266889i
$336$	−552.383	+	183.198i	−0.0896873	+	0.0297448i
$337$	2587.21	+	4481.17i	0.418202	+	0.724347i	0.995759	−	0.0920033i	$-0.0293270\pi$
$337$	2587.21	+	4481.17i	0.418202	+	0.724347i	−0.577557	+	0.816351i	$0.695994\pi$
$338$	−1908.09	−	3304.92i	−0.307061	−	0.531845i
$339$	−3481.79	+	1154.73i	−0.557831	+	0.185005i
$340$	−300.316	+	520.162i	−0.0479027	+	0.0829699i
$341$	67.9043			0.0107836
$342$	1137.71	−	847.903i	0.179883	−	0.134062i
$343$	343.000			0.0539949
$344$	−1175.35	+	2035.76i	−0.184216	+	0.319072i
$345$	3294.22	+	2930.09i	0.514072	+	0.457248i
$346$	−1840.94	−	3188.60i	−0.286039	−	0.495434i
$347$	−3055.70	−	5292.63i	−0.472734	−	0.818800i	0.526779	−	0.850002i	$-0.323400\pi$
$347$	−3055.70	−	5292.63i	−0.472734	−	0.818800i	−0.999513	+	0.0312028i	$0.990066\pi$
$348$	−736.083	+	3569.50i	−0.113386	+	0.549842i
$349$	5398.38	−	9350.27i	0.827990	−	1.43412i	−0.0716218	−	0.997432i	$-0.522817\pi$
$349$	5398.38	−	9350.27i	0.827990	−	1.43412i	0.899612	−	0.436690i	$-0.143849\pi$
$350$	562.424			0.0858938
$351$	−2375.73	−	206.000i	−0.361274	−	0.0313260i
$352$	424.657			0.0643019
$353$	438.245	−	759.062i	0.0660776	−	0.114450i	−0.831094	−	0.556132i	$-0.812285\pi$
$353$	438.245	−	759.062i	0.0660776	−	0.114450i	0.897172	+	0.441682i	$0.145618\pi$
$354$	631.906	−	3064.31i	0.0948741	−	0.460074i
$355$	−4391.61	−	7606.49i	−0.656570	−	1.13721i
$356$	−276.764	−	479.370i	−0.0412036	−	0.0713668i
$357$	443.094	+	394.116i	0.0656892	+	0.0584281i
$358$	−655.758	+	1135.81i	−0.0968097	+	0.167679i
$359$	3013.12			0.442970			0.221485	−	0.975164i	$-0.428910\pi$
$359$	3013.12			0.442970			0.221485	+	0.975164i	$0.428910\pi$
$360$	−231.972	−	1975.82i	−0.0339612	−	0.289264i
$361$	−6168.56			−0.899338
$362$	−380.429	+	658.922i	−0.0552345	+	0.0956690i
$363$	5695.92	−	1889.05i	0.823577	−	0.273139i
$364$	237.961	+	412.161i	0.0342653	+	0.0593492i
$365$	2714.17	+	4701.08i	0.389223	+	0.674153i
$366$	1367.26	−	453.452i	0.195267	−	0.0647604i
$367$	2513.15	−	4352.90i	0.357453	−	0.619127i	−0.630081	−	0.776529i	$-0.716978\pi$
$367$	2513.15	−	4352.90i	0.357453	−	0.619127i	0.987535	+	0.157402i	$0.0503118\pi$
$368$	1473.97			0.208794
$369$	−49.0207	−	417.533i	−0.00691575	−	0.0589048i
$370$	5243.37			0.736730
$371$	−2333.85	+	4042.35i	−0.326597	+	0.565683i
$372$	−79.4668	−	70.6828i	−0.0110757	−	0.00985143i
$373$	−2696.02	−	4669.64i	−0.374248	−	0.648217i	0.615966	−	0.787773i	$-0.288766\pi$
$373$	−2696.02	−	4669.64i	−0.374248	−	0.648217i	−0.990214	+	0.139556i	$0.955433\pi$
$374$	−216.356	−	374.740i	−0.0299131	−	0.0518111i
$375$	−1596.48	+	7741.85i	−0.219846	+	1.06610i
$376$	−2474.65	+	4286.21i	−0.339415	+	0.587885i
$377$	2980.49			0.407169
$378$	−1956.80	−	169.674i	−0.266262	−	0.0230876i
$379$	10989.7			1.48945			0.744724	−	0.667373i	$-0.232581\pi$
$379$	10989.7			1.48945			0.744724	+	0.667373i	$0.232581\pi$
$380$	484.015	−	838.339i	0.0653407	−	0.113173i
$381$	866.763	−	4203.20i	0.116550	−	0.565188i
$382$	−2800.38	−	4850.40i	−0.375078	−	0.649654i
$383$	−6943.29	−	12026.1i	−0.926333	−	1.60446i	−0.789404	−	0.613874i	$-0.789610\pi$
$383$	−6943.29	−	12026.1i	−0.926333	−	1.60446i	−0.136929	−	0.990581i	$-0.543723\pi$
$384$	−496.966	−	442.033i	−0.0660434	−	0.0587432i
$385$	427.782	−	740.940i	0.0566280	−	0.0980826i
$386$	9038.70			1.19186
$387$	−6361.27	+	4740.89i	−0.835560	+	0.622720i
$388$	3591.53			0.469929
$389$	7095.63	−	12290.0i	0.924840	−	1.60187i	0.133021	−	0.991113i	$-0.457532\pi$
$389$	7095.63	−	12290.0i	0.924840	−	1.60187i	0.791819	−	0.610756i	$-0.209135\pi$
$390$	−1544.18	+	512.126i	−0.200493	+	0.0664936i
$391$	−750.967	−	1300.71i	−0.0971306	−	0.168235i
$392$	196.000	+	339.482i	0.0252538	+	0.0437409i
$393$	−6206.81	+	2058.49i	−0.796673	+	0.264216i
$394$	−895.383	+	1550.85i	−0.114489	+	0.198301i
$395$	−7976.40			−1.01604
$396$	1316.29	+	566.990i	0.167036	+	0.0719502i
$397$	−2502.53			−0.316369			−0.158185	−	0.987410i	$-0.550564\pi$
$397$	−2502.53			−0.316369			−0.158185	+	0.987410i	$0.550564\pi$
$398$	4115.94	−	7129.02i	0.518376	−	0.897853i
$399$	−714.129	−	635.192i	−0.0896020	−	0.0796976i
$400$	321.385	+	556.656i	0.0401732	+	0.0695820i
$401$	2826.36	+	4895.39i	0.351974	+	0.609636i	0.986595	−	0.163187i	$-0.0521773\pi$
$401$	2826.36	+	4895.39i	0.351974	+	0.609636i	−0.634621	+	0.772823i	$0.718844\pi$
$402$	430.614	−	2088.18i	0.0534256	−	0.259077i
$403$	−43.4868	+	75.3214i	−0.00537527	+	0.00931024i
$404$	4827.74			0.594527
$405$	1919.02	−	6434.11i	0.235450	−	0.789416i
$406$	2454.91			0.300087
$407$	−1888.74	+	3271.39i	−0.230028	+	0.398420i
$408$	−136.877	+	663.759i	−0.0166089	+	0.0805415i
$409$	−453.580	−	785.623i	−0.0548364	−	0.0949794i	0.837304	−	0.546737i	$-0.184130\pi$
$409$	−453.580	−	785.623i	−0.0548364	−	0.0949794i	−0.892141	+	0.451758i	$0.850797\pi$
$410$	−143.406	−	248.386i	−0.0172739	−	0.0299193i
$411$	−2410.39	−	2143.95i	−0.289284	−	0.257307i
$412$	790.649	−	1369.44i	0.0945449	−	0.163757i
$413$	−2107.47			−0.251094
$414$	4568.83	+	1968.01i	0.542381	+	0.233629i
$415$	4242.09			0.501773
$416$	−271.956	+	471.041i	−0.0320523	+	0.0555161i
$417$	12422.8	−	4120.01i	1.45886	−	0.483832i
$418$	348.698	+	603.963i	0.0408024	+	0.0706718i
$419$	4203.95	+	7281.45i	0.490158	+	0.848978i	0.999936	−	0.0113276i	$-0.00360576\pi$
$419$	4203.95	+	7281.45i	0.490158	+	0.848978i	−0.509778	+	0.860306i	$0.670272\pi$
$420$	−1271.88	+	421.819i	−0.147765	+	0.0490064i
$421$	−2876.51	+	4982.27i	−0.332999	+	0.576772i	−0.983098	−	0.183078i	$-0.941394\pi$
$421$	−2876.51	+	4982.27i	−0.332999	+	0.576772i	0.650099	+	0.759849i	$0.274727\pi$
$422$	−759.613			−0.0876242
$423$	−13393.4	+	9981.76i	−1.53950	+	1.14735i
$424$	−5334.52			−0.611007
$425$	327.482	−	567.216i	0.0373770	−	0.0647388i
$426$	−7405.15	−	6586.60i	−0.842208	−	0.749113i
$427$	−485.140	−	840.287i	−0.0549826	−	0.0952327i
$428$	101.529	+	175.853i	0.0114663	+	0.0198602i
$429$	236.715	−	1147.90i	0.0266403	−	0.129187i
$430$	−2706.28	+	4687.41i	−0.303508	+	0.525691i
$431$	−2151.82			−0.240486			−0.120243	−	0.992744i	$-0.538367\pi$
$431$	−2151.82			−0.240486			−0.120243	+	0.992744i	$0.538367\pi$
$432$	−950.239	−	2033.69i	−0.105830	−	0.226495i
$433$	10561.9			1.17222			0.586112	−	0.810230i	$-0.300658\pi$
$433$	10561.9			1.17222			0.586112	+	0.810230i	$0.300658\pi$
$434$	−35.8185	+	62.0394i	−0.00396162	+	0.00686172i
$435$	−1694.86	+	8218.90i	−0.186810	+	0.905899i
$436$	4382.36	+	7590.46i	0.481369	+	0.833755i
$437$	1210.32	+	2096.34i	0.132489	+	0.229478i
$438$	4576.65	+	4070.76i	0.499271	+	0.444083i
$439$	−5085.89	+	8809.02i	−0.552930	+	0.957703i	0.445131	+	0.895465i	$0.353157\pi$
$439$	−5085.89	+	8809.02i	−0.552930	+	0.957703i	−0.998061	+	0.0622376i	$0.980176\pi$
$440$	977.787			0.105941
$441$	154.268	+	1313.98i	0.0166578	+	0.141883i
$442$	554.230			0.0596426
$443$	−4425.62	+	7665.40i	−0.474645	+	0.822109i	−0.999578	−	0.0290345i	$-0.990757\pi$
$443$	−4425.62	+	7665.40i	−0.474645	+	0.822109i	0.524934	+	0.851143i	$0.324090\pi$
$444$	5615.60	−	1862.41i	0.600236	−	0.199068i
$445$	−637.260	−	1103.77i	−0.0678855	−	0.117581i
$446$	−5187.29	−	8984.64i	−0.550729	−	0.953891i
$447$	−6486.19	+	2151.14i	−0.686323	+	0.227619i
$448$	−224.000	+	387.979i	−0.0236228	+	0.0409159i
$449$	171.152			0.0179893			0.00899463	−	0.999960i	$-0.497137\pi$
$449$	171.152			0.0179893			0.00899463	+	0.999960i	$0.497137\pi$
$450$	252.956	+	2154.55i	0.0264989	+	0.225703i
$451$	206.627			0.0215736
$452$	−1411.92	+	2445.52i	−0.146927	+	0.254486i
$453$	4035.10	+	3589.07i	0.418511	+	0.372250i
$454$	1707.33	+	2957.17i	0.176495	+	0.305698i
$455$	547.915	+	949.017i	0.0564542	+	0.0977815i
$456$	220.603	−	1069.77i	0.0226550	−	0.109861i
$457$	−7882.57	+	13653.0i	−0.806851	+	1.39751i	0.108183	+	0.994131i	$0.465497\pi$
$457$	−7882.57	+	13653.0i	−0.806851	+	1.39751i	−0.915034	+	0.403377i	$0.867836\pi$
$458$	−9773.79			−0.997160
$459$	−1310.50	+	1874.68i	−0.133266	+	0.190637i
$460$	3393.88			0.344001
$461$	3597.48	−	6231.02i	0.363452	−	0.629518i	−0.625074	−	0.780565i	$-0.714931\pi$
$461$	3597.48	−	6231.02i	0.363452	−	0.629518i	0.988527	+	0.151047i	$0.0482646\pi$
$462$	194.973	−	945.485i	0.0196341	−	0.0952120i
$463$	2213.67	+	3834.20i	0.222199	+	0.384860i	0.955475	−	0.295071i	$-0.0953432\pi$
$463$	2213.67	+	3834.20i	0.222199	+	0.384860i	−0.733276	+	0.679931i	$0.762010\pi$
$464$	1402.81	+	2429.74i	0.140353	+	0.243098i
$465$	−182.975	−	162.750i	−0.0182479	−	0.0162308i
$466$	−3829.40	+	6632.72i	−0.380673	+	0.659345i
$467$	−4861.63			−0.481733			−0.240866	−	0.970558i	$-0.577432\pi$
$467$	−4861.63			−0.481733			−0.240866	+	0.970558i	$0.577432\pi$
$468$	−1471.89	+	1096.96i	−0.145381	+	0.108349i
$469$	−1436.14			−0.141397
$470$	−5697.97	+	9869.17i	−0.559208	+	0.968576i
$471$	13834.1	−	4588.06i	1.35338	−	0.448847i
$472$	−1204.27	−	2085.86i	−0.117439	−	0.203410i
$473$	−1949.68	−	3376.95i	−0.189527	−	0.328271i
$474$	−8542.64	+	2833.17i	−0.827798	+	0.274539i
$475$	−527.799	+	914.174i	−0.0509833	+	0.0883056i
$476$	456.499			0.0439571
$477$	−16535.2	−	7122.50i	−1.58720	−	0.683683i
$478$	−8964.36			−0.857783
$479$	−1762.81	+	3053.27i	−0.168152	+	0.291247i	−0.937770	−	0.347257i	$-0.887113\pi$
$479$	−1762.81	+	3053.27i	−0.168152	+	0.291247i	0.769618	+	0.638504i	$0.220447\pi$
$480$	−1144.28	−	1017.80i	−0.108811	−	0.0967830i
$481$	−2419.15	−	4190.09i	−0.229322	−	0.397197i
$482$	−2058.04	−	3564.63i	−0.194484	−	0.336856i
$483$	676.747	−	3281.76i	0.0637537	−	0.309162i
$484$	2309.79	−	4000.67i	0.216922	−	0.375720i
$485$	8269.64			0.774237
$486$	−230.101	−	7572.50i	−0.0214765	−	0.706781i
$487$	−238.866			−0.0222259			−0.0111130	−	0.999938i	$-0.503537\pi$
$487$	−238.866			−0.0222259			−0.0111130	+	0.999938i	$0.503537\pi$
$488$	554.446	−	960.329i	0.0514315	−	0.0890820i
$489$	4215.15	−	20440.6i	0.389807	−	1.89030i
$490$	451.297	+	781.670i	0.0416072	+	0.0720658i
$491$	−6393.92	−	11074.6i	−0.587685	−	1.01790i	−0.994535	−	0.104406i	$-0.966706\pi$
$491$	−6393.92	−	11074.6i	−0.587685	−	1.01790i	0.406849	−	0.913495i	$-0.366627\pi$
$492$	−241.811	−	215.082i	−0.0221579	−	0.0197086i
$493$	1429.42	−	2475.83i	0.130584	−	0.226178i
$494$	−893.245			−0.0813543
$495$	3030.82	+	1305.51i	0.275202	+	0.118542i
$496$	−81.8708			−0.00741151
$497$	−3337.76	+	5781.17i	−0.301245	+	0.521772i
$498$	4543.23	−	1506.76i	0.408809	−	0.135582i
$499$	−2826.45	−	4895.56i	−0.253566	−	0.439189i	0.710939	−	0.703254i	$-0.248270\pi$
$499$	−2826.45	−	4895.56i	−0.253566	−	0.439189i	−0.964505	+	0.264064i	$0.914937\pi$
$500$	3042.54	+	5269.83i	0.272133	+	0.471348i
$501$	15208.2	−	5043.79i	1.35619	−	0.449780i
$502$	−5910.35	+	10237.0i	−0.525482	+	0.910161i
$503$	−14539.3			−1.28882			−0.644411	−	0.764679i	$-0.722897\pi$
$503$	−14539.3			−1.28882			−0.644411	+	0.764679i	$0.722897\pi$
$504$	−1212.34	+	903.529i	−0.107147	+	0.0798539i
$505$	11116.1			0.979520
$506$	−1222.52	+	2117.47i	−0.107407	+	0.186034i
$507$	−7408.26	−	6589.37i	−0.648940	−	0.577208i
$508$	−1651.85	−	2861.10i	−0.144270	−	0.249883i
$509$	−2087.08	−	3614.94i	−0.181745	−	0.314792i	0.760730	−	0.649069i	$-0.224841\pi$
$509$	−2087.08	−	3614.94i	−0.181745	−	0.314792i	−0.942475	+	0.334277i	$0.891508\pi$
$510$	−315.164	+	1528.33i	−0.0273641	+	0.132697i
$511$	2062.86	−	3572.97i	0.178582	−	0.309313i
$512$	−512.000			−0.0441942
$513$	2112.12	−	3021.39i	0.181779	−	0.260035i
$514$	13123.3			1.12615
$515$	1820.50	−	3153.20i	0.155769	−	0.269799i
$516$	−1233.46	+	5981.42i	−0.105232	+	0.510305i
$517$	−4104.98	−	7110.03i	−0.349201	−	0.604833i
$518$	−1992.56	−	3451.22i	−0.169012	−	0.292737i
$519$	−7147.53	−	6357.46i	−0.604512	−	0.537691i
$520$	−626.189	+	1084.59i	−0.0528081	+	0.0914662i
$521$	1279.75			0.107614			0.0538068	−	0.998551i	$-0.482864\pi$
$521$	1279.75			0.107614			0.0538068	+	0.998551i	$0.482864\pi$
$522$	1104.12	+	9404.36i	0.0925790	+	0.788540i
$523$	17049.4			1.42547			0.712734	−	0.701435i	$-0.247457\pi$
$523$	17049.4			1.42547			0.712734	+	0.701435i	$0.247457\pi$
$524$	−2516.96	+	4359.51i	−0.209836	+	0.363446i
$525$	1386.93	−	459.977i	0.115297	−	0.0382382i
$526$	−7081.66	−	12265.8i	−0.587025	−	1.01676i
$527$	41.7120	+	72.2473i	0.00344782	+	0.00597180i
$528$	1047.20	−	347.304i	0.0863135	−	0.0286259i
$529$	1840.15	−	3187.23i	0.151241	−	0.261957i
$530$	−12282.9			−1.00667
$531$	−947.859	−	8073.38i	−0.0774644	−	0.659802i
$532$	−735.733			−0.0599588
$533$	−132.327	+	229.197i	−0.0107537	+	0.0186259i
$534$	−1074.55	−	955.773i	−0.0870793	−	0.0774538i
$535$	233.774	+	404.908i	0.0188914	+	0.0327209i
$536$	−820.654	−	1421.41i	−0.0661322	−	0.114544i
$537$	−688.180	+	3337.20i	−0.0553020	+	0.268176i
$538$	2665.66	−	4617.05i	0.213615	−	0.369991i
$539$	−650.255			−0.0519638
$540$	−2187.96	−	4682.65i	−0.174361	−	0.373165i
$541$	−21420.3			−1.70227			−0.851137	−	0.524943i	$-0.824087\pi$
$541$	−21420.3			−1.70227			−0.851137	+	0.524943i	$0.824087\pi$
$542$	−7097.49	+	12293.2i	−0.562478	+	0.974241i
$543$	−399.238	+	1936.03i	−0.0315524	+	0.153007i
$544$	260.856	+	451.816i	0.0205591	+	0.0356093i
$545$	10090.5	+	17477.3i	0.793085	+	1.37366i
$546$	923.896	+	821.771i	0.0724159	+	0.0644113i
$547$	−3018.69	+	5228.52i	−0.235959	+	0.408693i	−0.959551	−	0.281535i	$-0.909157\pi$
$547$	−3018.69	+	5228.52i	−0.235959	+	0.408693i	0.723592	+	0.690228i	$0.242490\pi$
$548$	−2483.30			−0.193579
$549$	3000.80	−	2236.42i	0.233281	−	0.173858i
$550$	−1066.24			−0.0826627
$551$	−2303.78	+	3990.26i	−0.178120	+	0.308513i
$552$	3634.81	−	1205.48i	0.280268	−	0.0929507i
$553$	3031.15	+	5250.11i	0.233088	+	0.403721i
$554$	5254.58	+	9101.20i	0.402971	+	0.697965i
$555$	12930.1	−	4288.28i	0.988925	−	0.327977i
$556$	5037.63	−	8725.44i	0.384251	−	0.665541i
$557$	−13190.0			−1.00337			−0.501684	−	0.865051i	$-0.667286\pi$
$557$	−13190.0			−1.00337			−0.501684	+	0.865051i	$0.667286\pi$
$558$	−253.772	−	109.312i	−0.0192528	−	0.00829307i
$559$	4994.41			0.377891
$560$	−515.768	+	893.337i	−0.0389200	+	0.0674114i
$561$	−840.013	−	747.160i	−0.0632181	−	0.0562302i
$562$	1360.32	+	2356.14i	0.102103	+	0.176847i
$563$	−2034.55	−	3523.94i	−0.152302	−	0.263794i	0.779771	−	0.626064i	$-0.215335\pi$
$563$	−2034.55	−	3523.94i	−0.152302	−	0.263794i	−0.932073	+	0.362270i	$0.882002\pi$
$564$	−2597.00	+	12593.7i	−0.193889	+	0.940228i
$565$	−3251.00	+	5630.90i	−0.242072	+	0.419281i
$566$	52.7854			0.00392003
$567$	−4964.23	+	1181.95i	−0.367686	+	0.0875436i
$568$	−7629.17			−0.563579
$569$	−3579.01	+	6199.03i	−0.263691	+	0.456726i	−0.967220	−	0.253941i	$-0.918273\pi$
$569$	−3579.01	+	6199.03i	−0.263691	+	0.456726i	0.703529	+	0.710666i	$0.251606\pi$
$570$	507.946	−	2463.19i	0.0373255	−	0.181003i
$571$	5038.25	+	8726.50i	0.369254	+	0.639567i	0.989449	−	0.144881i	$-0.0462798\pi$
$571$	5038.25	+	8726.50i	0.369254	+	0.639567i	−0.620195	+	0.784448i	$0.712947\pi$
$572$	−451.124	−	781.370i	−0.0329763	−	0.0571167i
$573$	−10872.6	−	9670.77i	−0.792686	−	0.705065i
$574$	−108.993	+	188.781i	−0.00792555	+	0.0137275i
$575$	−3700.89			−0.268413
$576$	−1587.03	−	683.608i	−0.114803	−	0.0494508i
$577$	18349.2			1.32390			0.661948	−	0.749549i	$-0.269730\pi$
$577$	18349.2			1.32390			0.661948	+	0.749549i	$0.269730\pi$
$578$	−4647.20	+	8049.18i	−0.334425	+	0.579242i
$579$	22289.4	−	7392.27i	1.59985	−	0.530591i
$580$	3230.02	+	5594.56i	0.231240	+	0.400520i
$581$	−1612.06	−	2792.17i	−0.115111	−	0.199378i
$582$	8856.70	−	2937.32i	0.630794	−	0.209203i
$583$	4424.49	−	7663.43i	0.314311	−	0.544403i
$584$	4715.10			0.334096
$585$	−3389.09	+	2525.80i	−0.239524	+	0.178511i
$586$	7948.47			0.560321
$587$	−12274.1	+	21259.4i	−0.863045	+	1.49484i	0.00593027	+	0.999982i	$0.498112\pi$
$587$	−12274.1	+	21259.4i	−0.863045	+	1.49484i	−0.868975	+	0.494855i	$0.835221\pi$
$588$	760.979	+	676.863i	0.0533712	+	0.0474717i
$589$	−67.2266	−	116.440i	−0.00470293	−	0.00814571i
$590$	−2772.88	−	4802.77i	−0.193487	−	0.335130i
$591$	−939.653	+	4556.67i	−0.0654013	+	0.317151i
$592$	2277.22	−	3944.25i	0.158096	−	0.273831i
$593$	21383.6			1.48081			0.740404	−	0.672162i	$-0.234634\pi$
$593$	21383.6			1.48081			0.740404	+	0.672162i	$0.234634\pi$
$594$	3709.68	+	321.666i	0.256246	+	0.0222191i
$595$	1051.11			0.0724220
$596$	−2630.25	+	4555.73i	−0.180771	+	0.313104i
$597$	4319.44	−	20946.3i	0.296119	−	1.43597i
$598$	−1565.84	−	2712.12i	−0.107077	−	0.185463i
$599$	−3700.86	−	6410.08i	−0.252443	−	0.437244i	0.711755	−	0.702428i	$-0.247901\pi$
$599$	−3700.86	−	6410.08i	−0.252443	−	0.437244i	−0.964198	+	0.265184i	$0.914567\pi$
$600$	1247.79	+	1109.87i	0.0849016	+	0.0755168i
$601$	−12051.6	+	20874.1i	−0.817965	+	1.41676i	0.0892149	+	0.996012i	$0.471564\pi$
$601$	−12051.6	+	20874.1i	−0.817965	+	1.41676i	−0.907179	+	0.420744i	$0.861769\pi$
$602$	4113.71			0.278509
$603$	−645.922	−	5501.63i	−0.0436218	−	0.371548i
$604$	4157.17			0.280055
$605$	5318.37	−	9211.69i	0.357393	−	0.619022i
$606$	11905.2	−	3948.35i	0.798044	−	0.264671i
$607$	3136.92	+	5433.31i	0.209759	+	0.363313i	0.951639	−	0.307220i	$-0.0993987\pi$
$607$	3136.92	+	5433.31i	0.209759	+	0.363313i	−0.741880	+	0.670533i	$0.766065\pi$
$608$	−420.419	−	728.187i	−0.0280432	−	0.0485722i
$609$	6053.81	−	2007.74i	0.402812	−	0.133593i
$610$	1276.63	−	2211.19i	0.0847366	−	0.146768i
$611$	10515.5			0.696258
$612$	205.315	+	1748.77i	0.0135611	+	0.115506i
$613$	−7269.75			−0.478992			−0.239496	−	0.970897i	$-0.576982\pi$
$613$	−7269.75			−0.478992			−0.239496	+	0.970897i	$0.576982\pi$
$614$	4596.06	−	7960.62i	0.302088	−	0.523232i
$615$	−556.779	−	495.234i	−0.0365065	−	0.0324712i
$616$	−371.574	−	643.586i	−0.0243038	−	0.0420955i
$617$	5956.71	+	10317.3i	0.388668	+	0.673193i	0.992271	−	0.124093i	$-0.0396020\pi$
$617$	5956.71	+	10317.3i	0.388668	+	0.673193i	−0.603603	+	0.797285i	$0.706269\pi$
$618$	829.741	−	4023.67i	0.0540082	−	0.261903i
$619$	9802.19	−	16977.9i	0.636483	−	1.10242i	−0.349715	−	0.936856i	$-0.613722\pi$
$619$	9802.19	−	16977.9i	0.636483	−	1.10242i	0.986199	−	0.165566i	$-0.0529450\pi$
$620$	−188.511			−0.0122109
$621$	12876.2	+	1116.50i	0.832054	+	0.0721473i
$622$	3138.72			0.202333
$623$	−484.338	+	838.898i	−0.0311470	+	0.0539482i
$624$	−285.402	+	1384.00i	−0.0183097	+	0.0887892i
$625$	4494.74	+	7785.11i	0.287663	+	0.498247i
$626$	3239.20	+	5610.46i	0.206812	+	0.358209i
$627$	1353.84	+	1204.19i	0.0862314	+	0.0766996i
$628$	5609.93	−	9716.69i	0.356466	−	0.617417i
$629$	−4640.83			−0.294184
$630$	−2791.47	+	2080.41i	−0.176531	+	0.131564i
$631$	19282.8			1.21654			0.608269	−	0.793731i	$-0.291864\pi$
$631$	19282.8			1.21654			0.608269	+	0.793731i	$0.291864\pi$
$632$	−3464.18	+	6000.13i	−0.218034	+	0.377646i
$633$	−1873.20	+	621.247i	−0.117619	+	0.0390085i
$634$	3292.81	+	5703.31i	0.206268	+	0.357267i
$635$	−3803.46	−	6587.78i	−0.237694	−	0.411698i
$636$	−13154.9	+	4362.82i	−0.820165	+	0.272008i
$637$	416.433	−	721.282i	0.0259021	−	0.0448638i
$638$	−4654.00			−0.288799
$639$	−23647.9	−	10186.3i	−1.46400	−	0.630613i
$640$	−1178.90			−0.0728126
$641$	12089.1	−	20938.9i	0.744914	−	1.29023i	−0.205321	−	0.978695i	$-0.565824\pi$
$641$	12089.1	−	20938.9i	0.744914	−	1.29023i	0.950235	−	0.311535i	$-0.100843\pi$
$642$	394.190	+	350.617i	0.0242328	+	0.0215541i
$643$	−1526.21	−	2643.47i	−0.0936047	−	0.162128i	0.815421	−	0.578869i	$-0.196506\pi$
$643$	−1526.21	−	2643.47i	−0.0936047	−	0.162128i	−0.909025	+	0.416741i	$0.863172\pi$
$644$	−1289.73	−	2233.87i	−0.0789167	−	0.136688i
$645$	−2840.08	+	13772.4i	−0.173377	+	0.840759i
$646$	−428.394	+	742.001i	−0.0260913	+	0.0451914i
$647$	9110.78			0.553604			0.276802	−	0.960927i	$-0.410725\pi$
$647$	9110.78			0.553604			0.276802	+	0.960927i	$0.410725\pi$
$648$	−4006.53	−	4237.92i	−0.242888	−	0.256915i
$649$	3995.32			0.241649
$650$	682.833	−	1182.70i	0.0412045	−	0.0713683i
$651$	−37.5894	+	182.283i	−0.00226305	+	0.0109742i
$652$	−8033.13	−	13913.8i	−0.482518	−	0.835745i
$653$	−6388.35	−	11064.9i	−0.382841	−	0.663100i	0.608626	−	0.793457i	$-0.291721\pi$
$653$	−6388.35	−	11064.9i	−0.382841	−	0.663100i	−0.991467	+	0.130357i	$0.958388\pi$
$654$	17014.7	+	15133.9i	1.01732	+	0.904869i
$655$	−5795.40	+	10037.9i	−0.345718	+	0.598800i
$656$	−249.126			−0.0148274
$657$	14615.2	+	6295.47i	0.867876	+	0.373835i
$658$	8661.26			0.513148
$659$	7580.50	−	13129.8i	0.448095	−	0.776123i	−0.550167	−	0.835054i	$-0.685436\pi$
$659$	7580.50	−	13129.8i	0.448095	−	0.776123i	0.998262	+	0.0589316i	$0.0187694\pi$
$660$	2411.22	−	799.680i	0.142207	−	0.0471629i
$661$	12031.5	+	20839.3i	0.707977	+	1.22625i	0.965606	+	0.260009i	$0.0837254\pi$
$661$	12031.5	+	20839.3i	0.707977	+	1.22625i	−0.257629	+	0.966244i	$0.582941\pi$
$662$	2890.12	+	5005.84i	0.169679	+	0.293893i
$663$	1366.73	−	453.275i	0.0800593	−	0.0265517i
$664$	1842.35	−	3191.05i	0.107676	−	0.186501i
$665$	−1694.05			−0.0987858
$666$	12324.9	−	9185.40i	0.717086	−	0.534425i
$667$	−16153.9			−0.937755
$668$	6167.16	−	10681.8i	0.357207	−	0.618701i
$669$	−20139.9	−	17913.7i	−1.16391	−	1.03525i
$670$	−1889.59	−	3272.86i	−0.108957	−	0.188719i
$671$	919.723	+	1593.01i	0.0529143	+	0.0916503i
$672$	−235.075	+	1139.95i	−0.0134944	+	0.0654384i
$673$	−8484.28	+	14695.2i	−0.485951	+	0.841692i	−0.999870	−	0.0161472i	$-0.994860\pi$
$673$	−8484.28	+	14695.2i	−0.485951	+	0.841692i	0.513919	+	0.857839i	$0.328193\pi$
$674$	10348.8			0.591427
$675$	2385.88	+	5106.23i	0.136048	+	0.291169i
$676$	−7632.37			−0.434250
$677$	−7891.34	+	13668.2i	−0.447990	+	0.775941i	−0.998255	−	0.0590489i	$-0.981193\pi$
$677$	−7891.34	+	13668.2i	−0.447990	+	0.775941i	0.550265	+	0.834990i	$0.314527\pi$
$678$	−1481.73	+	7185.37i	−0.0839314	+	0.407009i
$679$	−3142.59	−	5443.13i	−0.177616	−	0.307641i
$680$	600.631	+	1040.32i	0.0338723	+	0.0586686i
$681$	6628.77	+	5896.04i	0.373003	+	0.331772i
$682$	67.9043	−	117.614i	0.00381259	−	0.00660361i
$683$	11169.1			0.625728			0.312864	−	0.949798i	$-0.398712\pi$
$683$	11169.1			0.625728			0.312864	+	0.949798i	$0.398712\pi$
$684$	−330.904	−	2818.47i	−0.0184977	−	0.157554i
$685$	−5717.90			−0.318934
$686$	343.000	−	594.093i	0.0190901	−	0.0330650i
$687$	−24102.1	+	7993.46i	−1.33850	+	0.443915i
$688$	2350.69	+	4071.52i	0.130261	+	0.225618i
$689$	5667.00	+	9815.54i	0.313346	+	0.542732i
$690$	8369.28	−	2775.67i	0.461758	−	0.153142i
$691$	−5052.70	+	8751.53i	−0.278167	+	0.481800i	−0.970929	−	0.239366i	$-0.923060\pi$
$691$	−5052.70	+	8751.53i	−0.278167	+	0.481800i	0.692762	+	0.721166i	$0.256394\pi$
$692$	−7363.75			−0.404520
$693$	−292.459	−	2491.02i	−0.0160312	−	0.136545i
$694$	−12222.8			−0.668547
$695$	11599.3	−	20090.6i	0.633076	−	1.09652i
$696$	5446.47	+	4844.43i	0.296620	+	0.263833i
$697$	126.926	+	219.842i	0.00689766	+	0.0119471i
$698$	−10796.8	−	18700.5i	−0.585478	−	1.01408i
$699$	−4018.73	+	19488.1i	−0.217457	+	1.05452i
$700$	562.424	−	974.147i	0.0303681	−	0.0525990i
$701$	16988.8			0.915347			0.457673	−	0.889120i	$-0.348683\pi$
$701$	16988.8			0.915347			0.457673	+	0.889120i	$0.348683\pi$
$702$	−2732.53	+	3908.89i	−0.146913	+	0.210159i
$703$	7479.57			0.401276
$704$	424.657	−	735.527i	0.0227342	−	0.0393767i
$705$	−5979.69	+	28997.4i	−0.319444	+	1.54908i
$706$	−876.489	−	1518.12i	−0.0467239	−	0.0809283i
$707$	−4224.27	−	7316.66i	−0.224710	−	0.389210i
$708$	−4675.64	−	4158.80i	−0.248194	−	0.220759i
$709$	−1246.94	+	2159.76i	−0.0660504	+	0.114403i	−0.897159	−	0.441707i	$-0.854373\pi$
$709$	−1246.94	+	2159.76i	−0.0660504	+	0.114403i	0.831109	+	0.556110i	$0.187706\pi$
$710$	−17566.4			−0.928531
$711$	−18749.0	+	13973.1i	−0.988949	+	0.737037i
$712$	−1107.06			−0.0582707
$713$	235.694	−	408.234i	0.0123798	−	0.0214425i
$714$	1125.72	−	373.346i	0.0590044	−	0.0195688i
$715$	−1038.73	−	1799.13i	−0.0543305	−	0.0941032i
$716$	1311.52	+	2271.61i	0.0684548	+	0.118567i
$717$	−22106.1	+	7331.47i	−1.15142	+	0.381867i
$718$	3013.12	−	5218.87i	0.156614	−	0.271263i
$719$	4036.74			0.209381			0.104691	−	0.994505i	$-0.466615\pi$
$719$	4036.74			0.209381			0.104691	+	0.994505i	$0.466615\pi$
$720$	−3654.20	−	1574.03i	−0.189144	−	0.0814733i
$721$	−2767.27			−0.142938
$722$	−6168.56	+	10684.3i	−0.317964	+	0.550730i
$723$	−7990.44	−	7107.20i	−0.411020	−	0.365587i
$724$	760.858	+	1317.84i	0.0390567	+	0.0676482i
$725$	−3522.20	−	6100.64i	−0.180429	−	0.312513i
$726$	2423.99	−	11754.7i	0.123915	−	0.600905i
$727$	−14478.6	+	25077.6i	−0.738624	+	1.27933i	0.214491	+	0.976726i	$0.431191\pi$
$727$	−14478.6	+	25077.6i	−0.738624	+	1.27933i	−0.953115	+	0.302609i	$0.902143\pi$
$728$	951.846			0.0484584
$729$	−6760.57	−	18485.5i	−0.343472	−	0.939163i
$730$	10856.7			0.550444
$731$	2395.28	−	4148.76i	0.121194	−	0.209914i
$732$	581.859	−	2821.62i	0.0293800	−	0.142473i
$733$	−17611.3	−	30503.6i	−0.887431	−	1.53708i	−0.842902	−	0.538068i	$-0.819155\pi$
$733$	−17611.3	−	30503.6i	−0.887431	−	1.53708i	−0.0445293	−	0.999008i	$-0.514179\pi$
$734$	−5026.30	−	8705.81i	−0.252758	−	0.437789i
$735$	1752.18	+	1558.50i	0.0879323	+	0.0782125i
$736$	1473.97	−	2553.00i	0.0738198	−	0.127860i
$737$	2722.62			0.136078
$738$	−772.208	−	332.626i	−0.0385168	−	0.0165910i
$739$	−11455.8			−0.570241			−0.285121	−	0.958492i	$-0.592034\pi$
$739$	−11455.8			−0.570241			−0.285121	+	0.958492i	$0.592034\pi$
$740$	5243.37	−	9081.79i	0.260473	−	0.451153i
$741$	−2202.74	+	730.538i	−0.109203	+	0.0362172i
$742$	4667.70	+	8084.70i	0.230939	+	0.399998i
$743$	−69.2081	−	119.872i	−0.00341723	−	0.00591881i	0.864312	−	0.502956i	$-0.167754\pi$
$743$	−69.2081	−	119.872i	−0.00341723	−	0.00591881i	−0.867729	+	0.497038i	$0.834421\pi$
$744$	−201.893	+	66.9578i	−0.00994860	+	0.00329945i
$745$	−6056.26	+	10489.7i	−0.297831	+	0.515859i
$746$	−10784.1			−0.529267
$747$	9971.28	−	7431.33i	0.488394	−	0.363987i
$748$	−865.425			−0.0423036
$749$	177.675	−	307.742i	0.00866770	−	0.0150129i
$750$	11812.8	+	10507.0i	0.575123	+	0.511551i
$751$	−5802.38	−	10050.0i	−0.281933	−	0.488323i	0.689928	−	0.723878i	$-0.257642\pi$
$751$	−5802.38	−	10050.0i	−0.281933	−	0.488323i	−0.971861	+	0.235556i	$0.924309\pi$
$752$	4949.29	+	8572.43i	0.240003	+	0.415697i
$753$	−6202.57	+	30078.2i	−0.300178	+	1.45566i
$754$	2980.49	−	5162.35i	0.143956	−	0.249339i
$755$	9572.04			0.461407
$756$	−2250.69	+	3219.61i	−0.108276	+	0.154889i
$757$	10192.7			0.489377			0.244689	−	0.969602i	$-0.421314\pi$
$757$	10192.7			0.489377			0.244689	+	0.969602i	$0.421314\pi$
$758$	10989.7	−	19034.6i	0.526599	−	0.912097i
$759$	−1282.97	+	6221.52i	−0.0613555	+	0.297532i
$760$	−968.030	−	1676.68i	−0.0462028	−	0.0800256i
$761$	14615.8	+	25315.4i	0.696220	+	1.20589i	0.969768	+	0.244030i	$0.0784696\pi$
$761$	14615.8	+	25315.4i	0.696220	+	1.20589i	−0.273548	+	0.961858i	$0.588197\pi$
$762$	−6413.40	−	5704.48i	−0.304899	−	0.271196i
$763$	7669.12	−	13283.3i	0.363881	−	0.630260i
$764$	−11201.5			−0.530440
$765$	472.746	+	4026.61i	0.0223427	+	0.190304i
$766$	−27773.2			−1.31003
$767$	−2558.66	+	4431.73i	−0.120454	+	0.208632i
$768$	−1262.59	+	418.737i	−0.0593226	+	0.0196743i
$769$	−6290.17	−	10894.9i	−0.294967	−	0.510897i	0.680011	−	0.733202i	$-0.261975\pi$
$769$	−6290.17	−	10894.9i	−0.294967	−	0.510897i	−0.974977	+	0.222305i	$0.928642\pi$
$770$	−855.564	−	1481.88i	−0.0400421	−	0.0693549i
$771$	32361.9	−	10732.8i	1.51165	−	0.501340i
$772$	9038.70	−	15655.5i	0.421386	−	0.729861i
$773$	−16234.1			−0.755369			−0.377685	−	0.925934i	$-0.623280\pi$
$773$	−16234.1			−0.755369			−0.377685	+	0.925934i	$0.623280\pi$
$774$	1850.19	+	15758.9i	0.0859219	+	0.731839i
$775$	205.563			0.00952780
$776$	3591.53	−	6220.72i	0.166145	−	0.287771i
$777$	−7736.22	−	6881.08i	−0.357188	−	0.317706i
$778$	−14191.3	−	24580.0i	−0.653961	−	1.13269i
$779$	−204.565	−	354.317i	−0.00940861	−	0.0162962i
$780$	−657.149	+	3186.72i	−0.0301663	+	0.146286i
$781$	6327.69	−	10959.9i	0.289913	−	0.502145i
$782$	−3003.87			−0.137363
$783$	10414.1	+	22288.1i	0.475312	+	1.01726i
$784$	784.000			0.0357143
$785$	12917.1	−	22373.0i	0.587300	−	1.01723i
$786$	−2641.41	+	12809.0i	−0.119867	+	0.581275i
$787$	2893.33	+	5011.39i	0.131050	+	0.226985i	0.924081	−	0.382196i	$-0.124832\pi$
$787$	2893.33	+	5011.39i	0.131050	+	0.226985i	−0.793032	+	0.609180i	$0.791499\pi$
$788$	1790.77	+	3101.70i	0.0809561	+	0.140220i
$789$	−27494.9	−	24455.7i	−1.24061	−	1.10348i
$790$	−7976.40	+	13815.5i	−0.359225	+	0.622195i
$791$	4941.72			0.222133
$792$	2298.35	−	1712.90i	0.103117	−	0.0768500i
$793$	−2356.01			−0.105504
$794$	−2502.53	+	4334.52i	−0.111853	+	0.193736i
$795$	−30289.6	+	10045.5i	−1.35127	+	0.448149i
$796$	−8231.89	−	14258.0i	−0.366547	−	0.634878i
$797$	11539.7	+	19987.3i	0.512868	+	0.888314i	0.999889	+	0.0149231i	$0.00475036\pi$
$797$	11539.7	+	19987.3i	0.512868	+	0.888314i	−0.487021	+	0.873391i	$0.661916\pi$
$798$	−1814.31	+	601.717i	−0.0804837	+	0.0266924i
$799$	5043.18	−	8735.05i	0.223298	−	0.386763i
$800$	1285.54			0.0568134
$801$	−3431.51	−	1478.11i	−0.151369	−	0.0652017i
$802$	11305.4			0.497766
$803$	−3910.74	+	6773.60i	−0.171864	+	0.297677i
$804$	−3186.23	−	2834.03i	−0.139763	−	0.124314i
$805$	−2969.64	−	5143.57i	−0.130020	−	0.225201i
$806$	86.9737	+	150.643i	0.00380089	+	0.00658333i
$807$	2797.45	−	13565.7i	0.122026	−	0.591742i
$808$	4827.74	−	8361.89i	0.210197	−	0.364072i
$809$	−19604.2			−0.851973			−0.425986	−	0.904730i	$-0.640073\pi$
$809$	−19604.2			−0.851973			−0.425986	+	0.904730i	$0.640073\pi$
$810$	−9225.19	−	9757.96i	−0.400173	−	0.423284i
$811$	−37188.0			−1.61017			−0.805086	−	0.593159i	$-0.797881\pi$
$811$	−37188.0			−1.61017			−0.805086	+	0.593159i	$0.797881\pi$
$812$	2454.91	−	4252.04i	0.106097	−	0.183765i
$813$	−7448.41	+	36119.7i	−0.321312	+	1.55814i
$814$	3777.48	+	6542.79i	0.162654	+	0.281725i
$815$	−18496.6	−	32037.0i	−0.794977	−	1.37694i
$816$	1012.79	+	900.836i	0.0434493	+	0.0386465i
$817$	−3860.45	+	6686.50i	−0.165312	+	0.286329i
$818$	−1814.32			−0.0775503
$819$	2950.41	+	1270.88i	0.125880	+	0.0542223i
$820$	−573.622			−0.0244290
$821$	−7747.41	+	13418.9i	−0.329338	+	0.570430i	−0.982381	−	0.186891i	$-0.940159\pi$
$821$	−7747.41	+	13418.9i	−0.329338	+	0.570430i	0.653043	+	0.757321i	$0.273492\pi$
$822$	−6123.81	+	2030.96i	−0.259845	+	0.0861775i
$823$	20445.9	+	35413.3i	0.865975	+	1.49991i	0.866076	+	0.499913i	$0.166635\pi$
$823$	20445.9	+	35413.3i	0.865975	+	1.49991i	−0.000100432		1.00000i	$0.500032\pi$
$824$	−1581.30	−	2738.89i	−0.0668533	−	0.115793i
$825$	−2629.33	+	872.019i	−0.110960	+	0.0367997i
$826$	−2107.47	+	3650.25i	−0.0887753	+	0.153763i
$827$	11679.5			0.491095			0.245548	−	0.969385i	$-0.421032\pi$
$827$	11679.5			0.491095			0.245548	+	0.969385i	$0.421032\pi$
$828$	7977.52	−	5945.43i	0.334828	−	0.249539i
$829$	−32752.5			−1.37219			−0.686093	−	0.727514i	$-0.740676\pi$
$829$	−32752.5			−1.37219			−0.686093	+	0.727514i	$0.740676\pi$
$830$	4242.09	−	7347.51i	0.177404	−	0.307272i
$831$	20401.1	+	18146.1i	0.851634	+	0.757497i
$832$	543.912	+	942.083i	0.0226644	+	0.0392558i
$833$	−399.436	−	691.844i	−0.0166142	−	0.0287767i
$834$	5286.71	−	25636.9i	0.219501	−	1.06443i
$835$	14200.1	−	24595.3i	0.588521	−	1.01935i
$836$	1394.79			0.0577033
$837$	−715.201	−	62.0150i	−0.0295352	−	0.00256100i
$838$	16815.8			0.693188
$839$	−3791.12	+	6566.40i	−0.156000	+	0.270200i	−0.933423	−	0.358779i	$-0.883193\pi$
$839$	−3791.12	+	6566.40i	−0.156000	+	0.270200i	0.777423	+	0.628978i	$0.216527\pi$
$840$	−541.269	+	2624.78i	−0.0222328	+	0.107814i
$841$	−3179.50	−	5507.05i	−0.130366	−	0.225801i
$842$	5753.03	+	9964.53i	0.235466	+	0.407839i
$843$	5281.50	+	4697.70i	0.215783	+	0.191931i
$844$	−759.613	+	1315.69i	−0.0309798	+	0.0536586i
$845$	−17573.8			−0.715453
$846$	3895.50	+	33179.8i	0.158310	+	1.34840i
$847$	−8084.25			−0.327955
$848$	−5334.52	+	9239.65i	−0.216024	+	0.374164i
$849$	130.168	−	43.1703i	0.00526192	−	0.00174511i
$850$	−654.964	−	1134.43i	−0.0264295	−	0.0457773i
$851$	13111.5	+	22709.9i	0.528153	+	0.914787i
$852$	−18813.5	+	6239.49i	−0.756501	+	0.250894i
$853$	9768.24	−	16919.1i	0.392096	−	0.679131i	−0.600629	−	0.799528i	$-0.705083\pi$
$853$	9768.24	−	16919.1i	0.392096	−	0.679131i	0.992726	+	0.120397i	$0.0384166\pi$
$854$	−1940.56			−0.0777572
$855$	−761.919	−	6489.63i	−0.0304761	−	0.259580i
$856$	406.115			0.0162158
$857$	15657.5	−	27119.5i	0.624094	−	1.08096i	−0.364621	−	0.931156i	$-0.618801\pi$
$857$	15657.5	−	27119.5i	0.624094	−	1.08096i	0.988715	−	0.149807i	$-0.0478652\pi$
$858$	−1751.51	−	1557.90i	−0.0696919	−	0.0619883i
$859$	−9550.43	−	16541.8i	−0.379344	−	0.657043i	0.611623	−	0.791149i	$-0.290517\pi$
$859$	−9550.43	−	16541.8i	−0.379344	−	0.657043i	−0.990967	+	0.134106i	$0.957184\pi$
$860$	5412.56	+	9374.82i	0.214612	+	0.371719i
$861$	−114.382	+	554.672i	−0.00452742	+	0.0219549i
$862$	−2151.82	+	3727.06i	−0.0850247	+	0.147267i
$863$	34822.8			1.37356			0.686779	−	0.726866i	$-0.259024\pi$
$863$	34822.8			1.37356			0.686779	+	0.726866i	$0.259024\pi$
$864$	−4472.69	−	387.827i	−0.176116	−	0.0152710i
$865$	−16955.3			−0.666472
$866$	10561.9	−	18293.8i	0.414444	−	0.717838i
$867$	−4876.96	+	23649.9i	−0.191038	+	0.926405i
$868$	71.6370	+	124.079i	0.00280129	+	0.00485197i
$869$	−5746.43	−	9953.10i	−0.224320	−	0.388534i
$870$	12540.7	+	11154.5i	0.488700	+	0.434681i
$871$	−1743.61	+	3020.02i	−0.0678299	+	0.117485i
$872$	17529.4			0.680758
$873$	19438.3	−	14486.8i	0.753592	−	0.561633i
$874$	4841.30			0.187368
$875$	5324.44	−	9222.21i	0.205713	−	0.356306i
$876$	11627.4	−	3856.23i	0.448463	−	0.148733i
$877$	5648.90	+	9784.19i	0.217503	+	0.376726i	0.954044	−	0.299667i	$-0.0968756\pi$
$877$	5648.90	+	9784.19i	0.217503	+	0.376726i	−0.736541	+	0.676393i	$0.763542\pi$
$878$	10171.8	+	17618.0i	0.390981	+	0.677198i
$879$	19600.9	−	6500.63i	0.752129	−	0.249443i
$880$	977.787	−	1693.58i	0.0374559	−	0.0648756i
$881$	3346.43			0.127973			0.0639864	−	0.997951i	$-0.479619\pi$
$881$	3346.43			0.127973			0.0639864	+	0.997951i	$0.479619\pi$
$882$	2430.14	+	1046.78i	0.0927744	+	0.0399623i
$883$	14001.0			0.533603			0.266801	−	0.963752i	$-0.414033\pi$
$883$	14001.0			0.533603			0.266801	+	0.963752i	$0.414033\pi$
$884$	554.230	−	959.954i	0.0210868	−	0.0365235i
$885$	−10765.8	−	9575.80i	−0.408914	−	0.363714i
$886$	8851.24	+	15330.8i	0.335624	+	0.581319i
$887$	5947.09	+	10300.7i	0.225123	+	0.389924i	0.956356	−	0.292203i	$-0.0943884\pi$
$887$	5947.09	+	10300.7i	0.225123	+	0.389924i	−0.731234	+	0.682127i	$0.761055\pi$
$888$	2389.81	−	11588.9i	0.0903115	−	0.437949i
$889$	−2890.74	+	5006.92i	−0.109058	+	0.188894i
$890$	−2549.04			−0.0960046
$891$	9411.13	−	2240.73i	0.353855	−	0.0842504i
$892$	−20749.1			−0.778849
$893$	−8128.03	+	14078.2i	−0.304585	+	0.527556i
$894$	−2760.30	+	13385.6i	−0.103264	+	0.500761i
$895$	3019.81	+	5230.47i	0.112783	+	0.195347i
$896$	448.000	+	775.959i	0.0167038	+	0.0289319i
$897$	−6079.46	−	5407.45i	−0.226296	−	0.201282i
$898$	171.152	−	296.444i	0.00636016	−	0.0110161i
$899$	897.259			0.0332873
$900$	3984.75	+	1716.42i	0.147583	+	0.0635711i
$901$	10871.4			0.401975
$902$	206.627	−	357.889i	0.00762741	−	0.0132111i
$903$	10144.4	−	3364.38i	0.373847	−	0.123986i
$904$	2823.84	+	4891.04i	0.103893	+	0.179949i
$905$	1751.90	+	3034.39i	0.0643483	+	0.111455i
$906$	10251.6	−	3399.93i	0.375922	−	0.124674i
$907$	16776.1	−	29057.1i	0.614158	−	1.06375i	−0.376373	−	0.926468i	$-0.622829\pi$
$907$	16776.1	−	29057.1i	0.614158	−	1.06375i	0.990532	−	0.137286i	$-0.0438378\pi$
$908$	6829.30			0.249602
$909$	26129.0	−	19473.2i	0.953402	−	0.710546i
$910$	2191.66			0.0798383
$911$	27055.7	−	46861.9i	0.983969	−	1.70428i	0.337538	−	0.941312i	$-0.390406\pi$
$911$	27055.7	−	46861.9i	0.983969	−	1.70428i	0.646431	−	0.762972i	$-0.276261\pi$
$912$	−1632.30	−	1451.87i	−0.0592661	−	0.0527150i
$913$	3056.12	+	5293.36i	0.110781	+	0.191878i
$914$	15765.1	+	27306.0i	0.570530	+	0.988187i
$915$	1339.75	−	6496.88i	0.0484053	−	0.234732i
$916$	−9773.79	+	16928.7i	−0.352549	+	0.610633i
$917$	8809.37			0.317242
$918$	1936.53	+	4144.54i	0.0696242	+	0.149009i
$919$	662.276			0.0237720			0.0118860	−	0.999929i	$-0.496216\pi$
$919$	662.276			0.0237720			0.0118860	+	0.999929i	$0.496216\pi$
$920$	3393.88	−	5878.37i	0.121623	−	0.210657i
$921$	4823.30	−	23389.7i	0.172566	−	0.836826i
$922$	−7194.97	−	12462.0i	−0.257000	−	0.445136i
$923$	8104.68	+	14037.7i	0.289023	+	0.500603i
$924$	−1442.65	−	1283.19i	−0.0513635	−	0.0456859i
$925$	−5717.69	+	9903.32i	−0.203239	+	0.352021i
$926$	8854.70			0.314237
$927$	−1244.61	−	10601.0i	−0.0440975	−	0.375600i
$928$	5611.23			0.198489
$929$	−23513.5	+	40726.5i	−0.830411	+	1.43831i	0.0673014	+	0.997733i	$0.478561\pi$
$929$	−23513.5	+	40726.5i	−0.830411	+	1.43831i	−0.897713	+	0.440582i	$0.854772\pi$
$930$	−464.866	+	154.173i	−0.0163909	+	0.00543605i
$931$	643.766	+	1115.04i	0.0226623	+	0.0392522i
$932$	7658.80	+	13265.4i	0.269176	+	0.466227i
$933$	7740.05	−	2566.99i	0.271595	−	0.0900744i
$934$	−4861.63	+	8420.58i	−0.170318	+	0.295000i
$935$	−1992.67			−0.0696977
$936$	428.103	+	3646.36i	0.0149498	+	0.127334i
$937$	17852.7			0.622437			0.311218	−	0.950338i	$-0.399263\pi$
$937$	17852.7			0.622437			0.311218	+	0.950338i	$0.399263\pi$
$938$	−1436.14	+	2487.47i	−0.0499912	+	0.0865873i
$939$	12576.3	+	11186.2i	0.437075	+	0.388762i
$940$	11395.9	+	19738.3i	0.395419	+	0.684887i
$941$	−18652.4	−	32306.9i	−0.646175	−	1.11921i	−0.984029	−	0.178010i	$-0.943034\pi$
$941$	−18652.4	−	32306.9i	−0.646175	−	1.11921i	0.337853	−	0.941199i	$-0.390299\pi$
$942$	5887.30	−	28549.4i	0.203629	−	0.987461i
$943$	717.198	−	1242.22i	0.0247669	−	0.0428975i
$944$	−4817.08			−0.166083
$945$	−5182.29	+	7413.27i	−0.178391	+	0.255189i
$946$	−7798.72			−0.268032
$947$	−17476.9	+	30270.8i	−0.599706	+	1.03872i	0.393158	+	0.919471i	$0.371383\pi$
$947$	−17476.9	+	30270.8i	−0.599706	+	1.03872i	−0.992864	+	0.119251i	$0.961951\pi$
$948$	−3635.45	+	17629.5i	−0.124551	+	0.603985i
$949$	−5008.98	−	8675.81i	−0.171337	−	0.296764i
$950$	1055.60	+	1828.35i	0.0360506	+	0.0624415i
$951$	12784.5	+	11371.3i	0.435926	+	0.387740i
$952$	456.499	−	790.679i	0.0155412	−	0.0269181i
$953$	−19162.4			−0.651343			−0.325671	−	0.945483i	$-0.605590\pi$
$953$	−19162.4			−0.651343			−0.325671	+	0.945483i	$0.605590\pi$
$954$	−28871.8	+	21517.4i	−0.979830	+	0.730241i
$955$	−25791.9			−0.873933
$956$	−8964.36	+	15526.7i	−0.303272	+	0.525283i
$957$	−11476.7	+	3806.26i	−0.387659	+	0.128567i
$958$	3525.61	+	6106.54i	0.118901	+	0.205943i
$959$	2172.89	+	3763.56i	0.0731661	+	0.126727i
$960$	−2907.16	+	964.159i	−0.0977376	+	0.0324147i
$961$	14882.4	−	25777.1i	0.499561	−	0.865264i
$962$	−9676.60			−0.324310
$963$	1258.82	+	542.233i	0.0421235	+	0.0181446i
$964$	−8232.16			−0.275042
$965$	20811.9	−	36047.3i	0.694259	−	1.20249i
$966$	−5007.42	−	4453.92i	−0.166782	−	0.148346i
$967$	8822.46	+	15280.9i	0.293393	+	0.508172i	0.974610	−	0.223910i	$-0.0718822\pi$
$967$	8822.46	+	15280.9i	0.293393	+	0.508172i	−0.681217	+	0.732082i	$0.738549\pi$
$968$	−4619.57	−	8001.34i	−0.153387	−	0.265674i
$969$	−449.575	+	2180.13i	−0.0149045	+	0.0722764i
$970$	8269.64	−	14323.4i	0.273734	−	0.474121i
$971$	48568.3			1.60518			0.802590	−	0.596530i	$-0.203454\pi$
$971$	48568.3			1.60518			0.802590	+	0.596530i	$0.203454\pi$
$972$	−13346.0	−	7173.95i	−0.440406	−	0.236733i
$973$	−17631.7			−0.580932
$974$	−238.866	+	413.727i	−0.00785805	+	0.0136105i
$975$	716.594	−	3474.99i	0.0235378	−	0.114142i
$976$	−1108.89	−	1920.66i	−0.0363676	−	0.0629905i
$977$	4478.17	+	7756.41i	0.146642	+	0.253991i	0.929984	−	0.367599i	$-0.119820\pi$
$977$	4478.17	+	7756.41i	0.146642	+	0.253991i	−0.783342	+	0.621591i	$0.786487\pi$
$978$	−31189.0	−	27741.4i	−1.01975	−	0.907028i
$979$	918.202	−	1590.37i	0.0299753	−	0.0519188i
$980$	1805.19			0.0588415
$981$	54335.4	+	23404.8i	1.76840	+	0.761731i
$982$	−25575.7			−0.831113
$983$	−26235.8	+	45441.8i	−0.851264	+	1.47443i	0.0288038	+	0.999585i	$0.490830\pi$
$983$	−26235.8	+	45441.8i	−0.851264	+	1.47443i	−0.880068	+	0.474848i	$0.842503\pi$
$984$	−614.344	+	203.747i	−0.0199030	+	0.00660083i
$985$	4123.31	+	7141.78i	0.133380	+	0.231021i
$986$	−2858.84	−	4951.66i	−0.0923367	−	0.159932i
$987$	21358.6	−	7083.58i	0.688807	−	0.228443i
$988$	−893.245	+	1547.15i	−0.0287631	+	0.0498191i
$989$	−27069.2			−0.870324
$990$	5292.03	−	3944.01i	0.169891	−	0.126615i
$991$	8829.03			0.283010			0.141505	−	0.989938i	$-0.454806\pi$
$991$	8829.03			0.283010			0.141505	+	0.989938i	$0.454806\pi$
$992$	−81.8708	+	141.804i	−0.00262036	+	0.00453860i
$993$	11221.0	+	9980.68i	0.358599	+	0.318960i
$994$	6675.52	+	11562.3i	0.213013	+	0.368949i
$995$	−18954.2	−	32829.7i	−0.603909	−	1.04600i
$996$	1933.44	−	9375.87i	0.0615095	−	0.298279i
$997$	19800.7	−	34295.9i	0.628983	−	1.08943i	−0.358774	−	0.933425i	$-0.616805\pi$
$997$	19800.7	−	34295.9i	0.628983	−	1.08943i	0.987756	−	0.156005i	$-0.0498617\pi$
$998$	−11305.8			−0.358597
$999$	22880.8	−	32731.0i	0.724641	−	1.03660i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.4.f.a.43.3	✓	6
3.2	odd	2		378.4.f.a.127.3		6
9.2	odd	6		1134.4.a.h.1.1		3
9.4	even	3	inner	126.4.f.a.85.3	yes	6
9.5	odd	6		378.4.f.a.253.3		6
9.7	even	3		1134.4.a.g.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.4.f.a.43.3	✓	6	1.1	even	1	trivial
126.4.f.a.85.3	yes	6	9.4	even	3	inner
378.4.f.a.127.3		6	3.2	odd	2
378.4.f.a.253.3		6	9.5	odd	6
1134.4.a.g.1.3		3	9.7	even	3
1134.4.a.h.1.1		3	9.2	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	126.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{2} +(1.04944 - 5.08907i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-4.60507 - 7.97622i) q^{5} +(-7.76509 - 6.90676i) q^{6} +(-3.50000 + 6.06218i) q^{7} -8.00000 q^{8} +(-24.7973 - 10.6814i) q^{9} -18.4203 q^{10} +(6.63526 - 11.4926i) q^{11} +(-19.7280 + 6.54277i) q^{12} +(8.49862 + 14.7200i) q^{13} +(7.00000 + 12.1244i) q^{14} +(-45.4243 + 15.0650i) q^{15} +(-8.00000 + 13.8564i) q^{16} +16.3035 q^{17} +(-43.2980 + 32.2689i) q^{18} -26.2762 q^{19} +(-18.4203 + 31.9049i) q^{20} +(27.1778 + 24.1737i) q^{21} +(-13.2705 - 22.9852i) q^{22} +(-46.0617 - 79.7812i) q^{23} +(-8.39554 + 40.7126i) q^{24} +(20.0866 - 34.7910i) q^{25} +33.9945 q^{26} +(-80.3817 + 114.986i) q^{27} +28.0000 q^{28} +(87.6755 - 151.858i) q^{29} +(-19.3310 + 93.7422i) q^{30} +(2.55846 + 4.43139i) q^{31} +(16.0000 + 27.7128i) q^{32} +(-51.5234 - 45.8281i) q^{33} +(16.3035 - 28.2385i) q^{34} +64.4710 q^{35} +(12.5933 + 107.263i) q^{36} -284.652 q^{37} +(-26.2762 + 45.5117i) q^{38} +(83.8302 - 27.8023i) q^{39} +(36.8406 + 63.8098i) q^{40} +(7.78519 + 13.4843i) q^{41} +(69.0478 - 22.8997i) q^{42} +(146.918 - 254.470i) q^{43} -53.0821 q^{44} +(28.9966 + 246.978i) q^{45} -184.247 q^{46} +(309.331 - 535.777i) q^{47} +(62.1207 + 55.2541i) q^{48} +(-24.5000 - 42.4352i) q^{49} +(-40.1732 - 69.5820i) q^{50} +(17.1096 - 82.9698i) q^{51} +(33.9945 - 58.8802i) q^{52} +666.814 q^{53} +(118.780 + 254.211i) q^{54} -122.223 q^{55} +(28.0000 - 48.4974i) q^{56} +(-27.5753 + 133.721i) q^{57} +(-175.351 - 303.717i) q^{58} +(150.534 + 260.732i) q^{59} +(143.035 + 127.225i) q^{60} +(-69.3057 + 120.041i) q^{61} +10.2339 q^{62} +(151.543 - 112.941i) q^{63} +64.0000 q^{64} +(78.2736 - 135.574i) q^{65} +(-130.900 + 43.4130i) q^{66} +(102.582 + 177.677i) q^{67} +(-32.6070 - 56.4771i) q^{68} +(-454.351 + 150.686i) q^{69} +(64.4710 - 111.667i) q^{70} +953.646 q^{71} +(198.379 + 85.4510i) q^{72} -589.387 q^{73} +(-284.652 + 493.032i) q^{74} +(-155.974 - 138.733i) q^{75} +(52.5524 + 91.0234i) q^{76} +(46.4468 + 80.4482i) q^{77} +(35.6753 - 173.000i) q^{78} +(433.022 - 750.016i) q^{79} +147.362 q^{80} +(500.816 + 529.740i) q^{81} +31.1408 q^{82} +(-230.294 + 398.881i) q^{83} +(29.3844 - 142.494i) q^{84} +(-75.0789 - 130.041i) q^{85} +(-293.836 - 508.940i) q^{86} +(-680.809 - 605.554i) q^{87} +(-53.0821 + 91.9408i) q^{88} +138.382 q^{89} +(456.774 + 196.754i) q^{90} -118.981 q^{91} +(-184.247 + 319.125i) q^{92} +(25.2366 - 8.36972i) q^{93} +(-618.662 - 1071.55i) q^{94} +(121.004 + 209.585i) q^{95} +(157.824 - 52.3422i) q^{96} +(-448.941 + 777.589i) q^{97} -98.0000 q^{98} +(-287.294 + 214.112i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} - 12 q^{3} - 12 q^{4} - 9 q^{5} - 12 q^{6} - 21 q^{7} - 48 q^{8} - 36 q^{9} - 36 q^{10} - 48 q^{11} + 24 q^{12} + 57 q^{13} + 42 q^{14} - 63 q^{15} - 48 q^{16} + 48 q^{17} - 144 q^{18} - 282 q^{19}+ \cdots + 1512 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 - 12 * q^3 - 12 * q^4 - 9 * q^5 - 12 * q^6 - 21 * q^7 - 48 * q^8 - 36 * q^9 - 36 * q^10 - 48 * q^11 + 24 * q^12 + 57 * q^13 + 42 * q^14 - 63 * q^15 - 48 * q^16 + 48 * q^17 - 144 * q^18 - 282 * q^19 - 36 * q^20 + 42 * q^21 + 96 * q^22 + 30 * q^23 + 96 * q^24 + 210 * q^25 + 228 * q^26 - 189 * q^27 + 168 * q^28 - 117 * q^29 - 126 * q^30 + 165 * q^31 + 96 * q^32 - 342 * q^33 + 48 * q^34 + 126 * q^35 - 144 * q^36 - 798 * q^37 - 282 * q^38 + 102 * q^39 + 72 * q^40 + 384 * q^41 - 84 * q^42 + 771 * q^43 + 384 * q^44 + 189 * q^45 + 120 * q^46 - 81 * q^47 + 96 * q^48 - 147 * q^49 - 420 * q^50 - 675 * q^51 + 228 * q^52 + 1044 * q^53 + 54 * q^54 + 156 * q^55 + 168 * q^56 + 183 * q^57 + 234 * q^58 - 21 * q^59 + 780 * q^61 + 660 * q^62 + 504 * q^63 + 384 * q^64 - 531 * q^65 - 1386 * q^66 + 384 * q^67 - 96 * q^68 - 1809 * q^69 + 126 * q^70 + 114 * q^71 + 288 * q^72 - 234 * q^73 - 798 * q^74 - 147 * q^75 + 564 * q^76 - 336 * q^77 - 1212 * q^78 + 1383 * q^79 + 288 * q^80 + 2592 * q^81 + 1536 * q^82 - 12 * q^83 - 336 * q^84 + 1095 * q^85 - 1542 * q^86 - 27 * q^87 + 384 * q^88 - 1296 * q^89 + 2106 * q^90 - 798 * q^91 + 120 * q^92 - 1707 * q^93 + 162 * q^94 + 1314 * q^95 - 192 * q^96 - 741 * q^97 - 588 * q^98 + 1512 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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