LMFDB - Embedded newform 143.4.e.b.100.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,4,Mod(100,143)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(143, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("143.100");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	143.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:	$8.43727313082$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.11
Character	$\chi$	$=$	143.100
Dual form			143.4.e.b.133.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.534214 - 0.925286i) q^{2} +(4.92554 - 8.53128i) q^{3} +(3.42923 + 5.93960i) q^{4} +2.35929 q^{5} +(-5.26259 - 9.11507i) q^{6} +(-6.12528 - 10.6093i) q^{7} +15.8752 q^{8} +(-35.0219 - 60.6597i) q^{9} +O(q^{10})$	\(q+(0.534214 - 0.925286i) q^{2} +(4.92554 - 8.53128i) q^{3} +(3.42923 + 5.93960i) q^{4} +2.35929 q^{5} +(-5.26259 - 9.11507i) q^{6} +(-6.12528 - 10.6093i) q^{7} +15.8752 q^{8} +(-35.0219 - 60.6597i) q^{9} +(1.26037 - 2.18302i) q^{10} +(-5.50000 + 9.52628i) q^{11} +67.5632 q^{12} +(39.1287 - 25.8060i) q^{13} -13.0888 q^{14} +(11.6208 - 20.1278i) q^{15} +(-18.9531 + 32.8277i) q^{16} +(10.6063 + 18.3707i) q^{17} -74.8367 q^{18} +(16.6623 + 28.8600i) q^{19} +(8.09055 + 14.0132i) q^{20} -120.681 q^{21} +(5.87636 + 10.1781i) q^{22} +(55.6369 - 96.3659i) q^{23} +(78.1939 - 135.436i) q^{24} -119.434 q^{25} +(-2.97481 - 49.9911i) q^{26} -424.027 q^{27} +(42.0100 - 72.7634i) q^{28} +(-106.389 + 184.270i) q^{29} +(-12.4160 - 21.5051i) q^{30} +177.548 q^{31} +(83.7508 + 145.061i) q^{32} +(54.1809 + 93.8441i) q^{33} +22.6641 q^{34} +(-14.4513 - 25.0304i) q^{35} +(240.196 - 416.032i) q^{36} +(-90.8672 + 157.387i) q^{37} +35.6050 q^{38} +(-27.4282 - 460.926i) q^{39} +37.4542 q^{40} +(90.7781 - 157.232i) q^{41} +(-64.4696 + 111.665i) q^{42} +(182.437 + 315.990i) q^{43} -75.4431 q^{44} +(-82.6267 - 143.114i) q^{45} +(-59.4440 - 102.960i) q^{46} +180.081 q^{47} +(186.708 + 323.388i) q^{48} +(96.4619 - 167.077i) q^{49} +(-63.8032 + 110.510i) q^{50} +208.967 q^{51} +(287.458 + 143.914i) q^{52} -290.575 q^{53} +(-226.521 + 392.346i) q^{54} +(-12.9761 + 22.4753i) q^{55} +(-97.2400 - 168.425i) q^{56} +328.284 q^{57} +(113.669 + 196.880i) q^{58} +(178.922 + 309.902i) q^{59} +159.401 q^{60} +(285.213 + 494.004i) q^{61} +(94.8486 - 164.283i) q^{62} +(-429.037 + 743.115i) q^{63} -124.286 q^{64} +(92.3159 - 60.8837i) q^{65} +115.777 q^{66} +(-541.149 + 937.297i) q^{67} +(-72.7429 + 125.994i) q^{68} +(-548.083 - 949.308i) q^{69} -30.8804 q^{70} +(-440.021 - 762.139i) q^{71} +(-555.979 - 962.984i) q^{72} +709.422 q^{73} +(97.0851 + 168.156i) q^{74} +(-588.276 + 1018.92i) q^{75} +(-114.278 + 197.935i) q^{76} +134.756 q^{77} +(-441.141 - 220.854i) q^{78} -93.0294 q^{79} +(-44.7158 + 77.4501i) q^{80} +(-1142.97 + 1979.69i) q^{81} +(-96.9899 - 167.991i) q^{82} +1231.90 q^{83} +(-413.844 - 716.798i) q^{84} +(25.0233 + 43.3417i) q^{85} +389.841 q^{86} +(1048.04 + 1815.26i) q^{87} +(-87.3136 + 151.232i) q^{88} +(494.221 - 856.016i) q^{89} -176.562 q^{90} +(-513.457 - 257.059i) q^{91} +763.167 q^{92} +(874.519 - 1514.71i) q^{93} +(96.2019 - 166.626i) q^{94} +(39.3113 + 68.0892i) q^{95} +1650.07 q^{96} +(54.0811 + 93.6712i) q^{97} +(-103.063 - 178.510i) q^{98} +770.481 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 6 q^{3} - 50 q^{4} - 48 q^{5} - 16 q^{6} + 62 q^{7} - 42 q^{8} - 135 q^{9}+O(q^{10}) $ 34 * q + 6 * q^3 - 50 * q^4 - 48 * q^5 - 16 * q^6 + 62 * q^7 - 42 * q^8 - 135 * q^9	\( 34 q + 6 q^{3} - 50 q^{4} - 48 q^{5} - 16 q^{6} + 62 q^{7} - 42 q^{8} - 135 q^{9} - 2 q^{10} - 187 q^{11} - 254 q^{12} + 76 q^{13} + 148 q^{15} - 126 q^{16} + 74 q^{17} + 180 q^{18} + 159 q^{19} + 222 q^{20} - 368 q^{21} + 215 q^{23} - 214 q^{24} + 190 q^{25} + 123 q^{26} - 384 q^{27} + 358 q^{28} + 157 q^{29} - 829 q^{30} - 788 q^{31} + 553 q^{32} + 66 q^{33} - 1404 q^{34} - 58 q^{35} + 700 q^{36} - 88 q^{37} - 2636 q^{38} + 798 q^{39} + 1466 q^{40} + 512 q^{41} - 337 q^{42} - 927 q^{43} + 1100 q^{44} + 1482 q^{45} + 1361 q^{46} - 286 q^{47} + 178 q^{48} - 1835 q^{49} + 583 q^{50} - 1136 q^{51} + 2306 q^{52} + 212 q^{53} + 67 q^{54} + 264 q^{55} - 2059 q^{56} + 2596 q^{57} + 1690 q^{58} + 266 q^{59} + 74 q^{60} + 624 q^{61} - 643 q^{62} + 2360 q^{63} - 3178 q^{64} + 470 q^{65} + 352 q^{66} + 676 q^{67} + 413 q^{68} - 764 q^{69} - 2122 q^{70} + 763 q^{71} + 1366 q^{72} - 4748 q^{73} + 1649 q^{74} - 2420 q^{75} + 2101 q^{76} - 1364 q^{77} - 5848 q^{78} + 4328 q^{79} + 1013 q^{80} - 537 q^{81} - 3152 q^{82} + 1554 q^{83} + 3381 q^{84} + 1690 q^{85} + 5788 q^{86} + 4200 q^{87} + 231 q^{88} + 1687 q^{89} - 10798 q^{90} - 3380 q^{91} + 11084 q^{92} + 4310 q^{93} - 1777 q^{94} - 1124 q^{95} - 6930 q^{96} + 2047 q^{97} - 1553 q^{98} + 2970 q^{99}+O(q^{100}) \) 34 * q + 6 * q^3 - 50 * q^4 - 48 * q^5 - 16 * q^6 + 62 * q^7 - 42 * q^8 - 135 * q^9 - 2 * q^10 - 187 * q^11 - 254 * q^12 + 76 * q^13 + 148 * q^15 - 126 * q^16 + 74 * q^17 + 180 * q^18 + 159 * q^19 + 222 * q^20 - 368 * q^21 + 215 * q^23 - 214 * q^24 + 190 * q^25 + 123 * q^26 - 384 * q^27 + 358 * q^28 + 157 * q^29 - 829 * q^30 - 788 * q^31 + 553 * q^32 + 66 * q^33 - 1404 * q^34 - 58 * q^35 + 700 * q^36 - 88 * q^37 - 2636 * q^38 + 798 * q^39 + 1466 * q^40 + 512 * q^41 - 337 * q^42 - 927 * q^43 + 1100 * q^44 + 1482 * q^45 + 1361 * q^46 - 286 * q^47 + 178 * q^48 - 1835 * q^49 + 583 * q^50 - 1136 * q^51 + 2306 * q^52 + 212 * q^53 + 67 * q^54 + 264 * q^55 - 2059 * q^56 + 2596 * q^57 + 1690 * q^58 + 266 * q^59 + 74 * q^60 + 624 * q^61 - 643 * q^62 + 2360 * q^63 - 3178 * q^64 + 470 * q^65 + 352 * q^66 + 676 * q^67 + 413 * q^68 - 764 * q^69 - 2122 * q^70 + 763 * q^71 + 1366 * q^72 - 4748 * q^73 + 1649 * q^74 - 2420 * q^75 + 2101 * q^76 - 1364 * q^77 - 5848 * q^78 + 4328 * q^79 + 1013 * q^80 - 537 * q^81 - 3152 * q^82 + 1554 * q^83 + 3381 * q^84 + 1690 * q^85 + 5788 * q^86 + 4200 * q^87 + 231 * q^88 + 1687 * q^89 - 10798 * q^90 - 3380 * q^91 + 11084 * q^92 + 4310 * q^93 - 1777 * q^94 - 1124 * q^95 - 6930 * q^96 + 2047 * q^97 - 1553 * q^98 + 2970 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/143\mathbb{Z}\right)^\times$.

$n$	$67$	$79$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.534214	−	0.925286i	0.188873	−	0.327138i	−0.756002	−	0.654570i	$-0.772850\pi$
$2$	0.534214	−	0.925286i	0.188873	−	0.327138i	0.944875	+	0.327432i	$0.106183\pi$
$3$	4.92554	−	8.53128i	0.947920	−	1.64185i	0.198125	−	0.980177i	$-0.436515\pi$
$3$	4.92554	−	8.53128i	0.947920	−	1.64185i	0.749796	−	0.661670i	$-0.230152\pi$
$4$	3.42923	+	5.93960i	0.428654	+	0.742450i
$5$	2.35929			0.211021			0.105511	−	0.994418i	$-0.466352\pi$
$5$	2.35929			0.211021			0.105511	+	0.994418i	$0.466352\pi$
$6$	−5.26259	−	9.11507i	−0.358074	−	0.620202i
$7$	−6.12528	−	10.6093i	−0.330734	−	0.572848i	0.651922	−	0.758286i	$-0.273963\pi$
$7$	−6.12528	−	10.6093i	−0.330734	−	0.572848i	−0.982656	+	0.185438i	$0.940630\pi$
$8$	15.8752			0.701591
$9$	−35.0219	−	60.6597i	−1.29711	−	2.24665i
$10$	1.26037	−	2.18302i	0.0398563	−	0.0690331i
$11$	−5.50000	+	9.52628i	−0.150756	+	0.261116i
$11$	−5.50000	+	9.52628i	−0.150756	+	0.261116i
$12$	67.5632			1.62532
$13$	39.1287	−	25.8060i	0.834795	−	0.550560i
$13$	39.1287	−	25.8060i	0.834795	−	0.550560i
$14$	−13.0888			−0.249867
$15$	11.6208	−	20.1278i	0.200031	−	0.346465i
$16$	−18.9531	+	32.8277i	−0.296142	+	0.512933i
$17$	10.6063	+	18.3707i	0.151318	+	0.262091i	0.931712	−	0.363197i	$-0.118315\pi$
$17$	10.6063	+	18.3707i	0.151318	+	0.262091i	−0.780394	+	0.625288i	$0.784982\pi$
$18$	−74.8367			−0.979955
$19$	16.6623	+	28.8600i	0.201190	+	0.348471i	0.948912	−	0.315541i	$-0.102186\pi$
$19$	16.6623	+	28.8600i	0.201190	+	0.348471i	−0.747722	+	0.664011i	$0.768853\pi$
$20$	8.09055	+	14.0132i	0.0904551	+	0.156673i
$21$	−120.681			−1.25404
$22$	5.87636	+	10.1781i	0.0569474	+	0.0986358i
$23$	55.6369	−	96.3659i	0.504395	−	0.873638i	−0.495592	−	0.868556i	$-0.665049\pi$
$23$	55.6369	−	96.3659i	0.504395	−	0.873638i	0.999987	−	0.00508261i	$-0.00161785\pi$
$24$	78.1939	−	135.436i	0.665053	−	1.15191i
$25$	−119.434			−0.955470
$26$	−2.97481	−	49.9911i	−0.0224388	−	0.377079i
$27$	−424.027			−3.02237
$28$	42.0100	−	72.7634i	0.283541	−	0.491107i
$29$	−106.389	+	184.270i	−0.681237	+	1.17994i	0.293367	+	0.956000i	$0.405224\pi$
$29$	−106.389	+	184.270i	−0.681237	+	1.17994i	−0.974604	+	0.223937i	$0.928109\pi$
$30$	−12.4160	−	21.5051i	−0.0755612	−	0.130876i
$31$	177.548			1.02866			0.514331	−	0.857592i	$-0.328040\pi$
$31$	177.548			1.02866			0.514331	+	0.857592i	$0.328040\pi$
$32$	83.7508	+	145.061i	0.462662	+	0.801355i
$33$	54.1809	+	93.8441i	0.285809	+	0.495035i
$34$	22.6641			0.114320
$35$	−14.4513	−	25.0304i	−0.0697919	−	0.120883i
$36$	240.196	−	416.032i	1.11202	−	1.92607i
$37$	−90.8672	+	157.387i	−0.403743	+	0.699303i	−0.994174	−	0.107785i	$-0.965624\pi$
$37$	−90.8672	+	157.387i	−0.403743	+	0.699303i	0.590432	+	0.807088i	$0.298958\pi$
$38$	35.6050			0.151997
$39$	−27.4282	−	460.926i	−0.112616	−	1.89249i
$40$	37.4542			0.148051
$41$	90.7781	−	157.232i	0.345784	−	0.598916i	−0.639711	−	0.768615i	$-0.720946\pi$
$41$	90.7781	−	157.232i	0.345784	−	0.598916i	0.985496	+	0.169699i	$0.0542795\pi$
$42$	−64.4696	+	111.665i	−0.236854	+	0.410244i
$43$	182.437	+	315.990i	0.647008	+	1.12065i	0.983834	+	0.179084i	$0.0573133\pi$
$43$	182.437	+	315.990i	0.647008	+	1.12065i	−0.336826	+	0.941567i	$0.609353\pi$
$44$	−75.4431			−0.258488
$45$	−82.6267	−	143.114i	−0.273717	−	0.474092i
$46$	−59.4440	−	102.960i	−0.190534	−	0.330014i
$47$	180.081			0.558883			0.279442	−	0.960163i	$-0.409851\pi$
$47$	180.081			0.558883			0.279442	+	0.960163i	$0.409851\pi$
$48$	186.708	+	323.388i	0.561438	+	0.972439i
$49$	96.4619	−	167.077i	0.281230	−	0.487105i
$50$	−63.8032	+	110.510i	−0.180463	+	0.312571i
$51$	208.967			0.573750
$52$	287.458	+	143.914i	0.766602	+	0.383794i
$53$	−290.575			−0.753085			−0.376543	−	0.926399i	$-0.622887\pi$
$53$	−290.575			−0.753085			−0.376543	+	0.926399i	$0.622887\pi$
$54$	−226.521	+	392.346i	−0.570845	+	0.988733i
$55$	−12.9761	+	22.4753i	−0.0318127	+	0.0551011i
$56$	−97.2400	−	168.425i	−0.232040	−	0.401905i
$57$	328.284			0.762847
$58$	113.669	+	196.880i	0.257335	+	0.445717i
$59$	178.922	+	309.902i	0.394808	+	0.683828i	0.993077	−	0.117468i	$-0.0374777\pi$
$59$	178.922	+	309.902i	0.394808	+	0.683828i	−0.598269	+	0.801296i	$0.704144\pi$
$60$	159.401			0.342977
$61$	285.213	+	494.004i	0.598653	+	1.03690i	0.993020	+	0.117944i	$0.0376304\pi$
$61$	285.213	+	494.004i	0.598653	+	1.03690i	−0.394367	+	0.918953i	$0.629036\pi$
$62$	94.8486	−	164.283i	0.194287	−	0.336515i
$63$	−429.037	+	743.115i	−0.857994	+	1.48609i
$64$	−124.286			−0.242746
$65$	92.3159	−	60.8837i	0.176160	−	0.116180i
$66$	115.777			0.215926
$67$	−541.149	+	937.297i	−0.986744	+	1.70909i	−0.352831	+	0.935687i	$0.614781\pi$
$67$	−541.149	+	937.297i	−0.986744	+	1.70909i	−0.633913	+	0.773404i	$0.718552\pi$
$68$	−72.7429	+	125.994i	−0.129726	+	0.224692i
$69$	−548.083	−	949.308i	−0.956253	−	1.65628i
$70$	−30.8804			−0.0527273
$71$	−440.021	−	762.139i	−0.735506	−	1.27393i	−0.954501	−	0.298207i	$-0.903611\pi$
$71$	−440.021	−	762.139i	−0.735506	−	1.27393i	0.218995	−	0.975726i	$-0.429722\pi$
$72$	−555.979	−	962.984i	−0.910039	−	1.57623i
$73$	709.422			1.13742			0.568709	−	0.822539i	$-0.307443\pi$
$73$	709.422			1.13742			0.568709	+	0.822539i	$0.307443\pi$
$74$	97.0851	+	168.156i	0.152512	+	0.264159i
$75$	−588.276	+	1018.92i	−0.905710	+	1.56873i
$76$	−114.278	+	197.935i	−0.172481	+	0.298747i
$77$	134.756			0.199440
$78$	−441.141	−	220.854i	−0.640377	−	0.320600i
$79$	−93.0294			−0.132489			−0.0662444	−	0.997803i	$-0.521102\pi$
$79$	−93.0294			−0.132489			−0.0662444	+	0.997803i	$0.521102\pi$
$80$	−44.7158	+	77.4501i	−0.0624923	+	0.108240i
$81$	−1142.97	+	1979.69i	−1.56786	+	2.71562i
$82$	−96.9899	−	167.991i	−0.130619	−	0.226239i
$83$	1231.90			1.62914			0.814569	−	0.580067i	$-0.196974\pi$
$83$	1231.90			1.62914			0.814569	+	0.580067i	$0.196974\pi$
$84$	−413.844	−	716.798i	−0.537548	−	0.931061i
$85$	25.0233	+	43.3417i	0.0319313	+	0.0553067i
$86$	389.841			0.488810
$87$	1048.04	+	1815.26i	1.29152	+	2.23697i
$88$	−87.3136	+	151.232i	−0.105769	+	0.183197i
$89$	494.221	−	856.016i	0.588622	−	1.01952i	−0.405791	−	0.913966i	$-0.633004\pi$
$89$	494.221	−	856.016i	0.588622	−	1.01952i	0.994413	−	0.105557i	$-0.0336626\pi$
$90$	−176.562			−0.206791
$91$	−513.457	−	257.059i	−0.591483	−	0.296122i
$92$	763.167			0.864844
$93$	874.519	−	1514.71i	0.975090	−	1.68891i
$94$	96.2019	−	166.626i	0.105558	−	0.182832i
$95$	39.3113	+	68.0892i	0.0424553	+	0.0735347i
$96$	1650.07			1.75427
$97$	54.0811	+	93.6712i	0.0566093	+	0.0980502i	0.892941	−	0.450173i	$-0.148638\pi$
$97$	54.0811	+	93.6712i	0.0566093	+	0.0980502i	−0.836332	+	0.548223i	$0.815304\pi$
$98$	−103.063	−	178.510i	−0.106234	−	0.184002i
$99$	770.481			0.782184
$100$	−409.566	−	709.389i	−0.409566	−	0.709389i
$101$	373.660	−	647.199i	0.368125	−	0.637611i	−0.621148	−	0.783694i	$-0.713333\pi$
$101$	373.660	−	647.199i	0.368125	−	0.637611i	0.989272	+	0.146083i	$0.0466666\pi$
$102$	111.633	−	193.354i	0.108366	−	0.187695i
$103$	−995.178			−0.952018			−0.476009	−	0.879441i	$-0.657917\pi$
$103$	−995.178			−0.952018			−0.476009	+	0.879441i	$0.657917\pi$
$104$	621.175	−	409.675i	0.585685	−	0.386268i
$105$	−284.722			−0.264629
$106$	−155.229	+	268.865i	−0.142238	+	0.246363i
$107$	−503.688	+	872.413i	−0.455078	+	0.788218i	−0.998693	−	0.0511166i	$-0.983722\pi$
$107$	−503.688	+	872.413i	−0.455078	+	0.788218i	0.543615	+	0.839335i	$0.317055\pi$
$108$	−1454.09	−	2518.55i	−1.29555	−	2.24396i
$109$	558.653			0.490910			0.245455	−	0.969408i	$-0.421063\pi$
$109$	558.653			0.490910			0.245455	+	0.969408i	$0.421063\pi$
$110$	13.8640	+	24.0132i	0.0120171	+	0.0208143i
$111$	895.140	+	1550.43i	0.765432	+	1.32577i
$112$	464.372			0.391777
$113$	−572.695	−	991.937i	−0.476767	−	0.825784i	0.522879	−	0.852407i	$-0.324858\pi$
$113$	−572.695	−	991.937i	−0.476767	−	0.825784i	−0.999646	+	0.0266228i	$0.991525\pi$
$114$	175.374	−	303.757i	0.144081	−	0.249556i
$115$	131.264	−	227.355i	0.106438	−	0.184356i
$116$	−1459.32			−1.16806
$117$	−2935.74	−	1469.76i	−2.31974	−	1.16136i
$118$	382.331			0.298275
$119$	129.933	−	225.051i	0.100092	−	0.173364i
$120$	184.482	−	319.532i	0.140340	−	0.243077i
$121$	−60.5000	−	104.789i	−0.0454545	−	0.0787296i
$122$	609.460			0.452278
$123$	−894.263	−	1548.91i	−0.655552	−	1.13545i
$124$	608.853	+	1054.56i	0.440940	+	0.763731i
$125$	−576.690			−0.412646
$126$	458.396	+	793.965i	0.324104	+	0.561365i
$127$	−533.768	+	924.513i	−0.372947	+	0.645963i	−0.990017	−	0.140945i	$-0.954986\pi$
$127$	−533.768	+	924.513i	−0.372947	+	0.645963i	0.617071	+	0.786908i	$0.288319\pi$
$128$	−736.402	+	1275.49i	−0.508510	+	0.880766i
$129$	3594.40			2.45325
$130$	−7.01844	−	117.944i	−0.00473506	−	0.0795718i
$131$	−2231.55			−1.48833			−0.744165	−	0.667996i	$-0.767152\pi$
$131$	−2231.55			−1.48833			−0.744165	+	0.667996i	$0.767152\pi$
$132$	−371.598	+	643.626i	−0.245026	+	0.424398i
$133$	204.123	−	353.551i	0.133081	−	0.230502i
$134$	578.179	+	1001.44i	0.372739	+	0.645603i
$135$	−1000.40			−0.637785
$136$	168.377	+	291.638i	0.106163	+	0.183880i
$137$	−261.003	−	452.070i	−0.162766	−	0.281919i	0.773094	−	0.634292i	$-0.218708\pi$
$137$	−261.003	−	452.070i	−0.162766	−	0.281919i	−0.935860	+	0.352373i	$0.885375\pi$
$138$	−1171.18			−0.722442
$139$	−636.085	−	1101.73i	−0.388144	−	0.672285i	0.604056	−	0.796942i	$-0.293550\pi$
$139$	−636.085	−	1101.73i	−0.388144	−	0.672285i	−0.992200	+	0.124657i	$0.960217\pi$
$140$	99.1137	−	171.670i	0.0598331	−	0.103634i
$141$	886.996	−	1536.32i	0.529777	−	0.917601i
$142$	−940.262			−0.555669
$143$	30.6272	+	514.683i	0.0179103	+	0.300979i
$144$	2655.09			1.53651
$145$	−251.002	+	434.747i	−0.143755	+	0.248992i
$146$	378.983	−	656.418i	0.214828	−	0.372093i
$147$	−950.254	−	1645.89i	−0.533167	−	0.923473i
$148$	−1246.42			−0.692263
$149$	300.513	+	520.503i	0.165228	+	0.286183i	0.936736	−	0.350036i	$-0.113831\pi$
$149$	300.513	+	520.503i	0.165228	+	0.286183i	−0.771508	+	0.636219i	$0.780497\pi$
$150$	628.530	+	1088.65i	0.342129	+	0.592584i
$151$	−2338.76			−1.26044			−0.630218	−	0.776418i	$-0.717035\pi$
$151$	−2338.76			−1.26044			−0.630218	+	0.776418i	$0.717035\pi$
$152$	264.518	+	458.159i	0.141153	+	0.244484i
$153$	742.905	−	1286.75i	0.392551	−	0.679918i
$154$	71.9886	−	124.688i	0.0376689	−	0.0652444i
$155$	418.887			0.217070
$156$	2643.66	−	1743.53i	1.35681	−	0.894836i
$157$	−3307.95			−1.68155			−0.840774	−	0.541386i	$-0.817900\pi$
$157$	−3307.95			−1.68155			−0.840774	+	0.541386i	$0.817900\pi$
$158$	−49.6976	+	86.0788i	−0.0250236	+	0.0433422i
$159$	−1431.24	+	2478.98i	−0.713865	+	1.23645i
$160$	197.592	+	342.240i	0.0976316	+	0.169103i
$161$	−1363.17			−0.667283
$162$	1221.18	+	2115.15i	0.592255	+	1.02582i
$163$	−144.981	−	251.114i	−0.0696672	−	0.120667i	0.829088	−	0.559119i	$-0.188860\pi$
$163$	−144.981	−	251.114i	−0.0696672	−	0.120667i	−0.898755	+	0.438452i	$0.855527\pi$
$164$	1245.20			0.592887
$165$	127.829	+	221.405i	0.0603117	+	0.104463i
$166$	658.097	−	1139.86i	0.307700	−	0.532953i
$167$	−22.0453	+	38.1836i	−0.0102151	+	0.0176930i	−0.871088	−	0.491127i	$-0.836585\pi$
$167$	−22.0453	+	38.1836i	−0.0102151	+	0.0176930i	0.860873	+	0.508820i	$0.169918\pi$
$168$	−1915.84			−0.879822
$169$	865.105	−	2019.51i	0.393766	−	0.919211i
$170$	53.4713			0.0241239
$171$	1167.09	−	2021.46i	0.521929	−	0.904007i
$172$	−1251.24	+	2167.20i	−0.554685	+	0.960742i
$173$	−205.996	−	356.795i	−0.0905292	−	0.156801i	0.817205	−	0.576347i	$-0.195523\pi$
$173$	−205.996	−	356.795i	−0.0905292	−	0.156801i	−0.907734	+	0.419546i	$0.862189\pi$
$174$	2239.52			0.975732
$175$	731.565	+	1267.11i	0.316006	+	0.547339i
$176$	−208.484	−	361.105i	−0.0892902	−	0.154655i
$177$	3525.15			1.49699
$178$	−528.040	−	914.592i	−0.222350	−	0.385121i
$179$	509.939	−	883.241i	0.212931	−	0.368807i	−0.739700	−	0.672937i	$-0.765032\pi$
$179$	509.939	−	883.241i	0.212931	−	0.368807i	0.952631	+	0.304130i	$0.0983657\pi$
$180$	566.692	−	981.540i	0.234660	−	0.406443i
$181$	−1211.88			−0.497670			−0.248835	−	0.968546i	$-0.580048\pi$
$181$	−1211.88			−0.497670			−0.248835	+	0.968546i	$0.580048\pi$
$182$	−512.149	+	337.770i	−0.208588	+	0.137567i
$183$	5619.32			2.26990
$184$	883.246	−	1529.83i	0.353879	−	0.612937i
$185$	−214.382	+	371.321i	−0.0851983	+	0.147568i
$186$	−934.361	−	1618.36i	−0.368337	−	0.637978i
$187$	−233.339			−0.0912482
$188$	617.539	+	1069.61i	0.239568	+	0.414943i
$189$	2597.28	+	4498.63i	0.999601	+	1.73136i
$190$	84.0026			0.0320747
$191$	−157.236	−	272.341i	−0.0595665	−	0.103172i	0.834704	−	0.550698i	$-0.185638\pi$
$191$	−157.236	−	272.341i	−0.0595665	−	0.103172i	−0.894271	+	0.447526i	$0.852305\pi$
$192$	−612.175	+	1060.32i	−0.230104	+	0.398551i
$193$	−1688.19	+	2924.04i	−0.629631	+	1.09055i	0.357995	+	0.933724i	$0.383461\pi$
$193$	−1688.19	+	2924.04i	−0.629631	+	1.09055i	−0.987626	+	0.156829i	$0.949873\pi$
$194$	115.564			0.0427679
$195$	−64.7111	−	1087.46i	−0.0237644	−	0.399356i
$196$	1323.16			0.482201
$197$	1723.87	−	2985.83i	0.623454	−	1.07985i	−0.365384	−	0.930857i	$-0.619062\pi$
$197$	1723.87	−	2985.83i	0.623454	−	1.07985i	0.988838	−	0.148997i	$-0.0476045\pi$
$198$	411.602	−	712.915i	0.147734	−	0.255882i
$199$	126.939	+	219.865i	0.0452184	+	0.0783206i	0.887749	−	0.460328i	$-0.152268\pi$
$199$	126.939	+	219.865i	0.0452184	+	0.0783206i	−0.842530	+	0.538649i	$0.818935\pi$
$200$	−1896.03			−0.670350
$201$	5330.90	+	9233.39i	1.87071	+	3.24016i
$202$	−399.229	−	691.485i	−0.139058	−	0.240855i
$203$	2606.64			0.901233
$204$	716.596	+	1241.18i	0.245940	+	0.425981i
$205$	214.172	−	370.957i	0.0729679	−	0.126384i
$206$	−531.638	+	920.824i	−0.179811	+	0.311441i
$207$	−7794.03			−2.61702
$208$	105.542	+	1773.61i	0.0351827	+	0.591238i
$209$	−366.571			−0.121322
$210$	−152.103	+	263.449i	−0.0499813	+	0.0865701i
$211$	−2007.48	+	3477.06i	−0.654980	+	1.13446i	0.326918	+	0.945053i	$0.393990\pi$
$211$	−2007.48	+	3477.06i	−0.654980	+	1.13446i	−0.981899	+	0.189407i	$0.939344\pi$
$212$	−996.448	−	1725.90i	−0.322813	−	0.559128i
$213$	−8669.37			−2.78880
$214$	538.155	+	932.111i	0.171904	+	0.297747i
$215$	430.421	+	745.511i	0.136532	+	0.236481i
$216$	−6731.52			−2.12047
$217$	−1087.53	−	1883.66i	−0.340214	−	0.589267i
$218$	298.440	−	516.913i	0.0927198	−	0.160595i
$219$	3494.28	−	6052.28i	1.07818	−	1.86747i
$220$	−177.992			−0.0545465
$221$	889.083	+	445.113i	0.270616	+	0.135482i
$222$	1912.79			0.578278
$223$	−506.087	+	876.568i	−0.151973	+	0.263226i	−0.931953	−	0.362579i	$-0.881896\pi$
$223$	−506.087	+	876.568i	−0.151973	+	0.263226i	0.779979	+	0.625805i	$0.215230\pi$
$224$	1025.99	−	1777.07i	0.306036	−	0.530070i
$225$	4182.79	+	7244.81i	1.23935	+	2.14661i
$226$	−1223.77			−0.360194
$227$	−2179.76	−	3775.46i	−0.637339	−	1.10390i	−0.986014	−	0.166660i	$-0.946702\pi$
$227$	−2179.76	−	3775.46i	−0.637339	−	1.10390i	0.348675	−	0.937244i	$-0.386632\pi$
$228$	1125.76	+	1949.88i	0.326997	+	0.566376i
$229$	−4087.21			−1.17943			−0.589717	−	0.807610i	$-0.700761\pi$
$229$	−4087.21			−1.17943			−0.589717	+	0.807610i	$0.700761\pi$
$230$	−140.246	−	242.913i	−0.0402066	−	0.0696399i
$231$	663.747	−	1149.64i	0.189053	−	0.327450i
$232$	−1688.94	+	2925.33i	−0.477950	+	0.827833i
$233$	−3417.59			−0.960916			−0.480458	−	0.877018i	$-0.659530\pi$
$233$	−3417.59			−0.960916			−0.480458	+	0.877018i	$0.659530\pi$
$234$	−2928.26	+	1931.23i	−0.818061	+	0.539524i
$235$	424.863			0.117936
$236$	−1227.13	+	2125.45i	−0.338472	+	0.586251i
$237$	−458.220	+	793.660i	−0.125589	+	0.217526i
$238$	−138.824	−	240.451i	−0.0378094	−	0.0654878i
$239$	3900.66			1.05570			0.527850	−	0.849337i	$-0.322998\pi$
$239$	3900.66			1.05570			0.527850	+	0.849337i	$0.322998\pi$
$240$	440.499	+	762.967i	0.118475	+	0.205205i
$241$	−2773.82	−	4804.40i	−0.741401	−	1.28414i	−0.951857	−	0.306541i	$-0.900828\pi$
$241$	−2773.82	−	4804.40i	−0.741401	−	1.28414i	0.210456	−	0.977603i	$-0.432505\pi$
$242$	−129.280			−0.0343406
$243$	5535.14	+	9587.14i	1.46123	+	2.53093i
$244$	−1956.12	+	3388.11i	−0.513230	+	0.888940i
$245$	227.582	−	394.183i	0.0593455	−	0.102789i
$246$	−1910.91			−0.495265
$247$	1396.74	+	699.266i	0.359806	+	0.180135i
$248$	2818.61			0.721701
$249$	6067.76	−	10509.7i	1.54429	−	2.67479i
$250$	−308.076	+	533.603i	−0.0779378	+	0.134992i
$251$	1022.75	+	1771.46i	0.257194	+	0.445472i	0.965489	−	0.260444i	$-0.0838689\pi$
$251$	1022.75	+	1771.46i	0.257194	+	0.445472i	−0.708295	+	0.705916i	$0.750536\pi$
$252$	−5885.07			−1.47113
$253$	612.006	+	1060.02i	0.152081	+	0.263412i
$254$	570.293	+	987.776i	0.140879	+	0.244010i
$255$	493.014			0.121073
$256$	289.649	+	501.687i	0.0707151	+	0.122482i
$257$	−1364.20	+	2362.87i	−0.331115	+	0.573508i	−0.982731	−	0.185041i	$-0.940758\pi$
$257$	−1364.20	+	2362.87i	−0.331115	+	0.573508i	0.651616	+	0.758549i	$0.274091\pi$
$258$	1920.18	−	3325.85i	0.463353	−	0.802551i
$259$	2226.35			0.534126
$260$	678.198	+	339.535i	0.161769	+	0.0809887i
$261$	14903.7			3.53455
$262$	−1192.12	+	2064.82i	−0.281106	+	0.486889i
$263$	2794.03	−	4839.41i	0.655086	−	1.13464i	−0.326787	−	0.945098i	$-0.605966\pi$
$263$	2794.03	−	4839.41i	0.655086	−	1.13464i	0.981872	−	0.189544i	$-0.0607008\pi$
$264$	860.133	+	1489.79i	0.200521	+	0.347312i
$265$	−685.550			−0.158917
$266$	−218.091	−	377.744i	−0.0502707	−	0.0870714i
$267$	−4868.61	−	8432.68i	−1.11593	−	1.93285i
$268$	−7422.90			−1.69189
$269$	−1426.55	−	2470.85i	−0.323338	−	0.560038i	0.657836	−	0.753161i	$-0.271472\pi$
$269$	−1426.55	−	2470.85i	−0.323338	−	0.560038i	−0.981175	+	0.193122i	$0.938139\pi$
$270$	−534.430	+	925.659i	−0.120461	+	0.208644i
$271$	−1623.10	+	2811.29i	−0.363824	+	0.630161i	−0.988587	−	0.150653i	$-0.951862\pi$
$271$	−1623.10	+	2811.29i	−0.363824	+	0.630161i	0.624763	+	0.780815i	$0.285196\pi$
$272$	−804.089			−0.179246
$273$	−4722.09	+	3114.29i	−1.04687	+	0.690424i
$274$	−557.725			−0.122969
$275$	656.886	−	1137.76i	0.144043	−	0.249489i
$276$	3759.01	−	6510.79i	0.819803	−	1.41994i
$277$	2997.37	+	5191.59i	0.650160	+	1.12611i	0.983084	+	0.183156i	$0.0586313\pi$
$277$	2997.37	+	5191.59i	0.650160	+	1.12611i	−0.332924	+	0.942954i	$0.608035\pi$
$278$	−1359.22			−0.293240
$279$	−6218.06	−	10770.0i	−1.33428	−	2.31105i
$280$	−229.417	−	397.363i	−0.0489654	−	0.0848106i
$281$	7043.43			1.49529			0.747644	−	0.664100i	$-0.231185\pi$
$281$	7043.43			1.49529			0.747644	+	0.664100i	$0.231185\pi$
$282$	−947.692	−	1641.45i	−0.200121	−	0.346620i
$283$	818.847	−	1418.28i	0.171998	−	0.297909i	−0.767120	−	0.641503i	$-0.778311\pi$
$283$	818.847	−	1418.28i	0.171998	−	0.297909i	0.939118	+	0.343594i	$0.111644\pi$
$284$	3017.87	−	5227.10i	0.630555	−	1.09215i
$285$	774.517			0.160977
$286$	492.591	+	246.612i	0.101844	+	0.0509877i
$287$	−2224.17			−0.457451
$288$	5866.22	−	10160.6i	1.20024	−	2.07888i
$289$	2231.51	−	3865.09i	0.454206	−	0.786707i
$290$	268.177	+	464.497i	0.0543031	+	0.0940558i
$291$	1065.51			0.214644
$292$	2432.77	+	4213.68i	0.487559	+	0.844476i
$293$	312.033	+	540.457i	0.0622155	+	0.107760i	0.895455	−	0.445151i	$-0.146850\pi$
$293$	312.033	+	540.457i	0.0622155	+	0.107760i	−0.833240	+	0.552912i	$0.813517\pi$
$294$	−2030.56			−0.402804
$295$	422.129	+	731.149i	0.0833129	+	0.144302i
$296$	−1442.54	+	2498.54i	−0.283262	+	0.490625i
$297$	2332.15	−	4039.40i	0.455640	−	0.789191i
$298$	642.152			0.124828
$299$	−309.818	−	5206.43i	−0.0599239	−	1.00701i
$300$	−8069.33			−1.55294
$301$	2234.95	−	3871.05i	0.427975	−	0.741275i
$302$	−1249.40	+	2164.03i	−0.238063	+	0.412337i
$303$	−3680.96	−	6375.60i	−0.697906	−	1.20881i
$304$	−1263.21			−0.238323
$305$	672.901	+	1165.50i	0.126328	+	0.218807i
$306$	−793.741	−	1374.80i	−0.148285	−	0.256837i
$307$	7433.53			1.38193			0.690967	−	0.722886i	$-0.257185\pi$
$307$	7433.53			1.38193			0.690967	+	0.722886i	$0.257185\pi$
$308$	462.110	+	800.398i	0.0854908	+	0.148074i
$309$	−4901.79	+	8490.15i	−0.902437	+	1.56307i
$310$	223.775	−	387.590i	0.0409987	−	0.0710118i
$311$	−4377.50			−0.798152			−0.399076	−	0.916918i	$-0.630669\pi$
$311$	−4377.50			−0.798152			−0.399076	+	0.916918i	$0.630669\pi$
$312$	−435.429	−	7317.29i	−0.0790105	−	1.32776i
$313$	10948.3			1.97712			0.988558	−	0.150842i	$-0.0481983\pi$
$313$	10948.3			1.97712			0.988558	+	0.150842i	$0.0481983\pi$
$314$	−1767.15	+	3060.80i	−0.317600	+	0.550099i
$315$	−1012.22	+	1753.22i	−0.181055	+	0.313597i
$316$	−319.019	−	552.557i	−0.0567919	−	0.0983664i
$317$	1588.82			0.281505			0.140752	−	0.990045i	$-0.455048\pi$
$317$	1588.82			0.281505			0.140752	+	0.990045i	$0.455048\pi$
$318$	1529.17	+	2648.61i	0.269660	+	0.467065i
$319$	−1170.27	−	2026.98i	−0.205401	−	0.355764i
$320$	−293.227			−0.0512246
$321$	4961.87	+	8594.21i	0.862756	+	1.49434i
$322$	−728.222	+	1261.32i	−0.126032	+	0.218293i
$323$	−353.452	+	612.196i	−0.0608872	+	0.105460i
$324$	−15678.1			−2.68828
$325$	−4673.28	+	3082.10i	−0.797622	+	0.526044i
$326$	−309.803			−0.0526331
$327$	2751.67	−	4766.02i	0.465344	−	0.805999i
$328$	1441.12	−	2496.10i	0.242599	−	0.420194i
$329$	−1103.05	−	1910.53i	−0.184842	−	0.320155i
$330$	273.151			0.0455651
$331$	1541.15	+	2669.36i	0.255920	+	0.443266i	0.965145	−	0.261716i	$-0.0842883\pi$
$331$	1541.15	+	2669.36i	0.255920	+	0.443266i	−0.709225	+	0.704982i	$0.750955\pi$
$332$	4224.46	+	7316.98i	0.698336	+	1.20955i
$333$	12729.4			2.09479
$334$	23.5538	+	40.7964i	0.00385870	+	0.00668347i
$335$	−1276.73	+	2211.36i	−0.208224	+	0.360655i
$336$	2287.28	−	3961.69i	0.371373	−	0.643237i
$337$	−1631.13			−0.263660			−0.131830	−	0.991272i	$-0.542085\pi$
$337$	−1631.13			−0.263660			−0.131830	+	0.991272i	$0.542085\pi$
$338$	−1406.47	−	1879.32i	−0.226337	−	0.302430i
$339$	−11283.3			−1.80775
$340$	−171.622	+	297.257i	−0.0273750	+	0.0474148i
$341$	−976.513	+	1691.37i	−0.155077	+	0.268601i
$342$	−1246.95	−	2159.79i	−0.197157	−	0.341485i
$343$	−6565.37			−1.03352
$344$	2896.22	+	5016.40i	0.453935	+	0.786239i
$345$	−1293.09	−	2239.69i	−0.201790	−	0.349510i
$346$	−440.183			−0.0683942
$347$	−5678.30	−	9835.10i	−0.878464	−	1.52154i	−0.853026	−	0.521868i	$-0.825235\pi$
$347$	−5678.30	−	9835.10i	−0.878464	−	1.52154i	−0.0254380	−	0.999676i	$-0.508098\pi$
$348$	−7187.96	+	12449.9i	−1.10723	+	1.91777i
$349$	260.632	−	451.428i	0.0399752	−	0.0692390i	−0.845346	−	0.534220i	$-0.820605\pi$
$349$	260.632	−	451.428i	0.0399752	−	0.0692390i	0.885321	+	0.464981i	$0.153939\pi$
$350$	1563.25			0.238741
$351$	−16591.6	+	10942.4i	−2.52306	+	1.66400i
$352$	−1842.52			−0.278996
$353$	6432.17	−	11140.8i	0.969830	−	1.67979i	0.273793	−	0.961789i	$-0.411722\pi$
$353$	6432.17	−	11140.8i	0.969830	−	1.67979i	0.696037	−	0.718006i	$-0.254945\pi$
$354$	1883.19	−	3261.77i	0.282741	−	0.489721i
$355$	−1038.14	−	1798.11i	−0.155207	−	0.268827i
$356$	6779.19			1.00926
$357$	−1279.98	−	2216.99i	−0.189759	−	0.328671i
$358$	−544.833	−	943.679i	−0.0804339	−	0.139316i
$359$	−13151.0			−1.93339			−0.966693	−	0.255939i	$-0.917615\pi$
$359$	−13151.0			−1.93339			−0.966693	+	0.255939i	$0.917615\pi$
$360$	−1311.72	−	2271.96i	−0.192038	−	0.332619i
$361$	2874.23	−	4978.32i	0.419045	−	0.725808i
$362$	−647.403	+	1121.33i	−0.0939965	+	0.162807i
$363$	−1191.98			−0.172349
$364$	−233.936	−	3931.24i	−0.0336856	−	0.566080i
$365$	1673.73			0.240019
$366$	3001.92	−	5199.48i	0.428723	−	0.742571i
$367$	−6502.13	+	11262.0i	−0.924819	+	1.60183i	−0.132968	+	0.991120i	$0.542451\pi$
$367$	−6502.13	+	11262.0i	−0.924819	+	1.60183i	−0.791852	+	0.610713i	$0.790883\pi$
$368$	2108.98	+	3652.86i	0.298745	+	0.517442i
$369$	−12716.9			−1.79408
$370$	229.052	+	396.730i	0.0321834	+	0.0557432i
$371$	1779.85	+	3082.79i	0.249071	+	0.431403i
$372$	11995.7			1.67190
$373$	5385.45	+	9327.87i	0.747582	+	1.29485i	0.948979	+	0.315340i	$0.102119\pi$
$373$	5385.45	+	9327.87i	0.747582	+	1.29485i	−0.201397	+	0.979510i	$0.564548\pi$
$374$	−124.653	+	215.905i	−0.0172343	+	0.0298508i
$375$	−2840.51	+	4919.91i	−0.391155	+	0.677501i
$376$	2858.82			0.392108
$377$	592.433	+	9955.72i	0.0809333	+	1.36007i
$378$	5550.03			0.755192
$379$	−1935.84	+	3352.97i	−0.262368	+	0.454434i	−0.966871	−	0.255267i	$-0.917837\pi$
$379$	−1935.84	+	3352.97i	−0.262368	+	0.454434i	0.704503	+	0.709701i	$0.251170\pi$
$380$	−269.615	+	466.987i	−0.0363973	+	0.0630419i
$381$	5258.19	+	9107.45i	0.707048	+	1.22464i
$382$	−335.991			−0.0450020
$383$	4263.10	+	7383.90i	0.568757	+	0.985117i	0.996689	+	0.0813057i	$0.0259090\pi$
$383$	4263.10	+	7383.90i	0.568757	+	0.985117i	−0.427932	+	0.903811i	$0.640758\pi$
$384$	7254.35	+	12564.9i	0.964055	+	1.66979i
$385$	317.929			0.0420861
$386$	1803.71	+	3124.12i	0.237841	+	0.411953i
$387$	12778.6	−	22133.1i	1.67848	−	2.90721i
$388$	−370.913	+	642.440i	−0.0485316	+	0.0840592i
$389$	12613.5			1.64403			0.822016	−	0.569464i	$-0.192849\pi$
$389$	12613.5			1.64403			0.822016	+	0.569464i	$0.192849\pi$
$390$	−1040.78	−	521.059i	−0.135133	−	0.0676535i
$391$	2360.41			0.305296
$392$	1531.35	−	2652.38i	0.197309	−	0.341748i
$393$	−10991.6	+	19038.0i	−1.41082	+	2.44361i
$394$	−1841.83	−	3190.14i	−0.235508	−	0.407911i
$395$	−219.483			−0.0279580
$396$	2642.16	+	4576.35i	0.335286	+	0.580733i
$397$	−4214.97	−	7300.54i	−0.532854	−	0.922930i	−0.999264	−	0.0383617i	$-0.987786\pi$
$397$	−4214.97	−	7300.54i	−0.532854	−	0.922930i	0.466410	−	0.884569i	$-0.345547\pi$
$398$	271.250			0.0341622
$399$	−2010.83	−	3482.86i	−0.252299	−	0.436995i
$400$	2263.64	−	3920.74i	0.282955	−	0.490092i
$401$	4074.29	−	7056.87i	0.507382	−	0.878811i	−0.492582	−	0.870266i	$-0.663947\pi$
$401$	4074.29	−	7056.87i	0.507382	−	0.878811i	0.999963	−	0.00854500i	$-0.00271999\pi$
$402$	11391.4			1.41331
$403$	6947.21	−	4581.79i	0.858723	−	0.566341i
$404$	5125.47			0.631192
$405$	−2696.60	+	4670.65i	−0.330852	+	0.573053i
$406$	1392.50	−	2411.89i	0.170219	−	0.294827i
$407$	−999.540	−	1731.25i	−0.121733	−	0.210848i
$408$	3317.39			0.402538
$409$	137.896	+	238.843i	0.0166712	+	0.0288753i	0.874241	−	0.485493i	$-0.161360\pi$
$409$	137.896	+	238.843i	0.0166712	+	0.0288753i	−0.857569	+	0.514368i	$0.828026\pi$
$410$	−228.827	−	396.341i	−0.0275634	−	0.0477411i
$411$	−5142.32			−0.617157
$412$	−3412.70	−	5910.96i	−0.408086	−	0.706826i
$413$	2191.90	−	3796.48i	0.261153	−	0.452330i
$414$	−4163.68	+	7211.71i	−0.494284	+	0.856126i
$415$	2906.40			0.343783
$416$	7020.49	+	3514.76i	0.827422	+	0.414243i
$417$	−12532.2			−1.47172
$418$	−195.828	+	339.183i	−0.0229145	+	0.0396890i
$419$	−409.198	+	708.751i	−0.0477103	+	0.0826367i	−0.888894	−	0.458112i	$-0.848526\pi$
$419$	−409.198	+	708.751i	−0.0477103	+	0.0826367i	0.841184	+	0.540749i	$0.181859\pi$
$420$	−976.377	−	1691.13i	−0.113434	−	0.196474i
$421$	1200.57			0.138984			0.0694918	−	0.997583i	$-0.477862\pi$
$421$	1200.57			0.138984			0.0694918	+	0.997583i	$0.477862\pi$
$422$	2144.85	+	3714.99i	0.247416	+	0.428538i
$423$	−6306.78	−	10923.7i	−0.724931	−	1.25562i
$424$	−4612.93			−0.528358
$425$	−1266.75	−	2194.08i	−0.144580	−	0.250420i
$426$	−4631.30	+	8021.64i	−0.526730	+	0.912324i
$427$	3494.02	−	6051.82i	0.395990	−	0.685874i
$428$	−6909.05			−0.780284
$429$	4541.77	+	2273.80i	0.511139	+	0.255898i
$430$	919.748			0.103149
$431$	−4649.05	+	8052.39i	−0.519575	+	0.899930i	0.480166	+	0.877178i	$0.340576\pi$
$431$	−4649.05	+	8052.39i	−0.519575	+	0.899930i	−0.999741	+	0.0227528i	$0.992757\pi$
$432$	8036.62	−	13919.8i	0.895052	−	1.55027i
$433$	−352.736	−	610.957i	−0.0391488	−	0.0678077i	0.845787	−	0.533521i	$-0.179131\pi$
$433$	−352.736	−	610.957i	−0.0391488	−	0.0678077i	−0.884936	+	0.465713i	$0.845798\pi$
$434$	−2323.90			−0.257029
$435$	2472.64	+	4282.73i	0.272538	+	0.472049i
$436$	1915.75	+	3318.17i	0.210431	+	0.364476i
$437$	3708.16			0.405916
$438$	−3733.39	−	6466.43i	−0.407279	−	0.705429i
$439$	8012.42	−	13877.9i	0.871098	−	1.50879i	0.0102366	−	0.999948i	$-0.496742\pi$
$439$	8012.42	−	13877.9i	0.871098	−	1.50879i	0.860862	−	0.508839i	$-0.169925\pi$
$440$	−205.998	+	356.799i	−0.0223195	+	0.0386585i
$441$	−13513.1			−1.45914
$442$	886.818	−	584.870i	0.0954335	−	0.0629399i
$443$	−12527.4			−1.34356			−0.671779	−	0.740751i	$-0.734470\pi$
$443$	−12527.4			−1.34356			−0.671779	+	0.740751i	$0.734470\pi$
$444$	−6139.28	+	10633.6i	−0.656211	+	1.13659i
$445$	1166.01	−	2019.59i	0.124212	−	0.215141i
$446$	540.718	+	936.550i	0.0574074	+	0.0994326i
$447$	5920.75			0.626491
$448$	761.286	+	1318.59i	0.0802843	+	0.139057i
$449$	−3205.92	−	5552.82i	−0.336964	−	0.583639i	0.646896	−	0.762578i	$-0.276067\pi$
$449$	−3205.92	−	5552.82i	−0.336964	−	0.583639i	−0.983860	+	0.178939i	$0.942733\pi$
$450$	8938.03			0.936317
$451$	998.560	+	1729.56i	0.104258	+	0.180580i
$452$	3927.81	−	6803.16i	0.408736	−	0.707951i
$453$	−11519.7	+	19952.7i	−1.19479	+	2.06944i
$454$	−4657.84			−0.481505
$455$	−1211.39	−	606.476i	−0.124815	−	0.0624880i
$456$	5211.57			0.535207
$457$	3246.61	−	5623.30i	0.332320	−	0.575595i	−0.650646	−	0.759381i	$-0.725502\pi$
$457$	3246.61	−	5623.30i	0.332320	−	0.575595i	0.982966	+	0.183786i	$0.0588353\pi$
$458$	−2183.44	+	3781.84i	−0.222763	+	0.385838i
$459$	−4497.36	−	7789.66i	−0.457340	−	0.792135i
$460$	1800.53			0.182500
$461$	6345.66	+	10991.0i	0.641100	+	1.11042i	0.985188	+	0.171480i	$0.0548549\pi$
$461$	6345.66	+	10991.0i	0.641100	+	1.11042i	−0.344088	+	0.938937i	$0.611812\pi$
$462$	−709.166	−	1228.31i	−0.0714142	−	0.123693i
$463$	16605.5			1.66679			0.833396	−	0.552677i	$-0.186394\pi$
$463$	16605.5			1.66679			0.833396	+	0.552677i	$0.186394\pi$
$464$	−4032.79	−	6984.99i	−0.403486	−	0.698858i
$465$	2063.24	−	3573.64i	0.205765	−	0.356395i
$466$	−1825.72	+	3162.24i	−0.181491	+	0.314352i
$467$	5952.63			0.589839			0.294919	−	0.955522i	$-0.404707\pi$
$467$	5952.63			0.589839			0.294919	+	0.955522i	$0.404707\pi$
$468$	−1337.55	−	22477.3i	−0.132112	−	2.22011i
$469$	13258.8			1.30540
$470$	226.968	−	393.120i	0.0222750	−	0.0385815i
$471$	−16293.4	+	28221.1i	−1.59397	+	2.76084i
$472$	2840.42	+	4919.76i	0.276994	+	0.479768i
$473$	−4013.61			−0.390160
$474$	489.575	+	847.969i	0.0474408	+	0.0821698i
$475$	−1990.05	−	3446.86i	−0.192231	−	0.332953i
$476$	1782.28			0.171619
$477$	10176.5	+	17626.2i	0.976831	+	1.69192i
$478$	2083.79	−	3609.22i	0.199394	−	0.345360i
$479$	−6386.47	+	11061.7i	−0.609197	+	1.05516i	0.382176	+	0.924089i	$0.375175\pi$
$479$	−6386.47	+	11061.7i	−0.609197	+	1.05516i	−0.991373	+	0.131070i	$0.958159\pi$
$480$	3893.00			0.370188
$481$	506.001	+	8503.25i	0.0479660	+	0.806060i
$482$	−5927.26			−0.560123
$483$	−6714.32	+	11629.6i	−0.632531	+	1.09558i
$484$	414.937	−	718.692i	0.0389685	−	0.0674955i
$485$	127.593	+	220.997i	0.0119458	+	0.0206907i
$486$	11827.8			1.10395
$487$	2199.98	+	3810.47i	0.204703	+	0.354556i	0.950038	−	0.312134i	$-0.101044\pi$
$487$	2199.98	+	3810.47i	0.204703	+	0.354556i	−0.745335	+	0.666690i	$0.767710\pi$
$488$	4527.82	+	7842.41i	0.420010	+	0.727478i
$489$	−2856.43			−0.264156
$490$	−243.155	−	421.156i	−0.0224176	−	0.0388284i
$491$	7099.53	−	12296.8i	0.652541	−	1.13023i	−0.329964	−	0.943994i	$-0.607036\pi$
$491$	7099.53	−	12296.8i	0.652541	−	1.13023i	0.982504	−	0.186240i	$-0.0596302\pi$
$492$	6133.26	−	10623.1i	0.562010	−	0.973430i
$493$	−4513.56			−0.412334
$494$	1393.18	−	918.822i	0.126887	−	0.0836837i
$495$	1817.79			0.165058
$496$	−3365.08	+	5828.49i	−0.304630	+	0.527635i
$497$	−5390.50	+	9336.63i	−0.486513	+	0.842666i
$498$	−6482.97	−	11228.8i	−0.583351	−	1.01039i
$499$	−3982.56			−0.357283			−0.178641	−	0.983914i	$-0.557170\pi$
$499$	−3982.56			−0.357283			−0.178641	+	0.983914i	$0.557170\pi$
$500$	−1977.60	−	3425.31i	−0.176882	−	0.306369i
$501$	217.170	+	376.149i	0.0193661	+	0.0335431i
$502$	2185.48			0.194308
$503$	−1203.42	−	2084.38i	−0.106676	−	0.184768i	0.807746	−	0.589531i	$-0.200687\pi$
$503$	−1203.42	−	2084.38i	−0.106676	−	0.184768i	−0.914422	+	0.404763i	$0.867354\pi$
$504$	−6811.06	+	11797.1i	−0.601961	+	1.04263i
$505$	881.573	−	1526.93i	0.0776821	−	0.134549i
$506$	1307.77			0.114896
$507$	−12967.9	−	17327.6i	−1.13594	−	1.51784i
$508$	−7321.65			−0.639460
$509$	−9785.73	+	16949.4i	−0.852151	+	1.47597i	0.0271116	+	0.999632i	$0.491369\pi$
$509$	−9785.73	+	16949.4i	−0.852151	+	1.47597i	−0.879263	+	0.476337i	$0.841964\pi$
$510$	263.375	−	456.179i	0.0228675	−	0.0396077i
$511$	−4345.41	−	7526.46i	−0.376183	−	0.651568i
$512$	−11163.5			−0.963596
$513$	−7065.29	−	12237.4i	−0.608070	−	1.05321i
$514$	1457.55	+	2524.55i	0.125077	+	0.216641i
$515$	−2347.91			−0.200896
$516$	12326.0	+	21349.3i	1.05159	+	1.82141i
$517$	−990.446	+	1715.50i	−0.0842549	+	0.145934i
$518$	1189.35	−	2060.01i	0.100882	−	0.174733i
$519$	−4058.56			−0.343258
$520$	1465.53	−	966.542i	0.123592	−	0.0815109i
$521$	−9383.29			−0.789039			−0.394520	−	0.918888i	$-0.629089\pi$
$521$	−9383.29			−0.789039			−0.394520	+	0.918888i	$0.629089\pi$
$522$	7961.77	−	13790.2i	0.667581	−	1.15628i
$523$	4458.51	−	7722.36i	0.372767	−	0.645651i	−0.617223	−	0.786788i	$-0.711742\pi$
$523$	4458.51	−	7722.36i	0.372767	−	0.645651i	0.989990	+	0.141137i	$0.0450758\pi$
$524$	−7652.49	−	13254.5i	−0.637978	−	1.10501i
$525$	14413.4			1.19820
$526$	−2985.23	−	5170.56i	−0.247456	−	0.428607i
$527$	1883.13	+	3261.67i	0.155655	+	0.269603i
$528$	−4107.58			−0.338560
$529$	−107.423	−	186.062i	−0.00882906	−	0.0152924i
$530$	−366.231	+	634.330i	−0.0300152	+	0.0519878i
$531$	12532.4	−	21706.7i	1.02422	−	1.77399i
$532$	2799.94			0.228182
$533$	−505.505	−	8494.91i	−0.0410804	−	0.690348i
$534$	−10403.5			−0.843080
$535$	−1188.35	+	2058.28i	−0.0960312	+	0.166331i
$536$	−8590.85	+	14879.8i	−0.692291	+	1.19908i
$537$	−5023.45	−	8700.87i	−0.403683	−	0.699200i
$538$	−3048.32			−0.244280
$539$	1061.08	+	1837.85i	0.0847941	+	0.146868i
$540$	−3430.61	−	5942.00i	−0.273389	−	0.473524i
$541$	−10673.0			−0.848187			−0.424094	−	0.905618i	$-0.639407\pi$
$541$	−10673.0			−0.848187			−0.424094	+	0.905618i	$0.639407\pi$
$542$	1734.17	+	3003.66i	0.137433	+	0.238041i
$543$	−5969.16	+	10338.9i	−0.471751	+	0.817098i
$544$	−1776.57	+	3077.11i	−0.140018	+	0.242519i
$545$	1318.02			0.103593
$546$	359.004	+	6032.99i	0.0281391	+	0.472872i
$547$	−11642.2			−0.910029			−0.455014	−	0.890484i	$-0.650366\pi$
$547$	−11642.2			−0.910029			−0.455014	+	0.890484i	$0.650366\pi$
$548$	1790.08	−	3100.50i	0.139541	−	0.241692i
$549$	19977.4	−	34601.9i	1.55303	−	2.68993i
$550$	−701.835	−	1215.61i	−0.0544116	−	0.0942436i
$551$	−7090.73			−0.548231
$552$	−8700.93	−	15070.5i	−0.670899	−	1.16203i
$553$	569.831	+	986.976i	0.0438186	+	0.0758960i
$554$	6404.94			0.491191
$555$	2111.90	+	3657.91i	0.161522	+	0.279765i
$556$	4362.56	−	7556.18i	0.332759	−	0.576355i
$557$	6849.27	−	11863.3i	0.521028	−	0.902447i	−0.478673	−	0.877993i	$-0.658882\pi$
$557$	6849.27	−	11863.3i	0.521028	−	0.902447i	0.999701	−	0.0244539i	$-0.00778469\pi$
$558$	−13287.1			−1.00804
$559$	15292.9	+	7656.30i	1.15711	+	0.579297i
$560$	1095.59			0.0826733
$561$	−1149.32	+	1990.68i	−0.0864960	+	0.149816i
$562$	3762.70	−	6517.19i	0.282420	−	0.489165i
$563$	1010.97	+	1751.05i	0.0756790	+	0.131080i	0.901381	−	0.433026i	$-0.142554\pi$
$563$	1010.97	+	1751.05i	0.0756790	+	0.131080i	−0.825702	+	0.564106i	$0.809221\pi$
$564$	12166.9			0.908364
$565$	−1351.15	−	2340.27i	−0.100608	−	0.174258i
$566$	−874.879	−	1515.34i	−0.0649716	−	0.112534i
$567$	28004.1			2.07418
$568$	−6985.42	−	12099.1i	−0.516024	−	0.893781i
$569$	623.480	−	1079.90i	0.0459361	−	0.0795636i	−0.842143	−	0.539254i	$-0.818706\pi$
$569$	623.480	−	1079.90i	0.0459361	−	0.0795636i	0.888079	+	0.459690i	$0.152040\pi$
$570$	413.758	−	716.650i	0.0304042	−	0.0526617i
$571$	8377.50			0.613988			0.306994	−	0.951711i	$-0.400677\pi$
$571$	8377.50			0.613988			0.306994	+	0.951711i	$0.400677\pi$
$572$	−2951.99	+	1946.88i	−0.215785	+	0.142313i
$573$	−3097.89			−0.225857
$574$	−1188.18	+	2057.99i	−0.0864002	+	0.149650i
$575$	−6644.92	+	11509.3i	−0.481934	+	0.834735i
$576$	4352.72	+	7539.14i	0.314867	+	0.545366i
$577$	21869.2			1.57786			0.788930	−	0.614483i	$-0.210636\pi$
$577$	21869.2			1.57786			0.788930	+	0.614483i	$0.210636\pi$
$578$	−2384.21	−	4129.58i	−0.171575	−	0.297176i
$579$	16630.5	+	28804.9i	1.19368	+	2.06752i
$580$	−3442.97			−0.246485
$581$	−7545.72	−	13069.6i	−0.538811	−	0.933248i
$582$	569.213	−	985.905i	0.0405406	−	0.0702184i
$583$	1598.16	−	2768.10i	0.113532	−	0.196643i
$584$	11262.2			0.798003
$585$	−6926.26	−	3467.59i	−0.489514	−	0.245072i
$586$	666.769			0.0470034
$587$	2078.56	−	3600.17i	0.146152	−	0.253143i	−0.783650	−	0.621203i	$-0.786644\pi$
$587$	2078.56	−	3600.17i	0.146152	−	0.253143i	0.929802	+	0.368059i	$0.119978\pi$
$588$	6517.28	−	11288.3i	0.457088	−	0.791700i
$589$	2958.36	+	5124.04i	0.206956	+	0.358459i
$590$	902.030			0.0629423
$591$	−16982.0	−	29413.6i	−1.18197	−	2.04723i
$592$	−3444.43	−	5965.93i	−0.239130	−	0.414186i
$593$	−23811.5			−1.64894			−0.824469	−	0.565908i	$-0.808526\pi$
$593$	−23811.5			−1.64894			−0.824469	+	0.565908i	$0.808526\pi$
$594$	−2491.73	−	4315.81i	−0.172116	−	0.298114i
$595$	306.550	−	530.960i	0.0211216	−	0.0365836i
$596$	−2061.05	+	3569.85i	−0.141651	+	0.245347i
$597$	2500.97			0.171454
$598$	−4982.95	−	2494.68i	−0.340749	−	0.170594i
$599$	−22974.4			−1.56712			−0.783562	−	0.621314i	$-0.786599\pi$
$599$	−22974.4			−1.56712			−0.783562	+	0.621314i	$0.786599\pi$
$600$	−9338.99	+	16175.6i	−0.635438	+	1.10061i
$601$	881.722	−	1527.19i	0.0598439	−	0.103653i	−0.834551	−	0.550930i	$-0.814273\pi$
$601$	881.722	−	1527.19i	0.0598439	−	0.103653i	0.894395	+	0.447278i	$0.147606\pi$
$602$	−2387.89	−	4135.94i	−0.161666	−	0.280014i
$603$	75808.2			5.11965
$604$	−8020.16	−	13891.3i	−0.540291	−	0.935811i
$605$	−142.737	−	247.228i	−0.00959188	−	0.0166136i
$606$	−7865.68			−0.527263
$607$	2366.56	+	4099.01i	0.158247	+	0.274091i	0.934237	−	0.356654i	$-0.116083\pi$
$607$	2366.56	+	4099.01i	0.158247	+	0.274091i	−0.775990	+	0.630746i	$0.782749\pi$
$608$	−2790.97	+	4834.10i	−0.186166	+	0.322448i
$609$	12839.1	−	22238.0i	0.854297	−	1.47969i
$610$	1437.89			0.0954403
$611$	7046.33	−	4647.17i	0.466553	−	0.307699i
$612$	10190.4			0.673074
$613$	−2849.99	+	4936.34i	−0.187782	+	0.325248i	−0.944510	−	0.328482i	$-0.893463\pi$
$613$	−2849.99	+	4936.34i	−0.187782	+	0.325248i	0.756729	+	0.653729i	$0.226796\pi$
$614$	3971.10	−	6878.14i	0.261010	−	0.452083i
$615$	−2109.82	−	3654.32i	−0.138336	−	0.239604i
$616$	2139.28			0.139925
$617$	−9112.30	−	15783.0i	−0.594566	−	1.02982i	−0.993608	−	0.112886i	$-0.963991\pi$
$617$	−9112.30	−	15783.0i	−0.594566	−	1.02982i	0.399042	−	0.916933i	$-0.369343\pi$
$618$	5237.21	+	9071.11i	0.340892	+	0.590443i
$619$	−10254.3			−0.665840			−0.332920	−	0.942955i	$-0.608034\pi$
$619$	−10254.3			−0.665840			−0.332920	+	0.942955i	$0.608034\pi$
$620$	1436.46	+	2488.02i	0.0930478	+	0.161163i
$621$	−23591.5	+	40861.8i	−1.52447	+	2.64046i
$622$	−2338.52	+	4050.44i	−0.150750	+	0.261106i
$623$	−12109.0			−0.778709
$624$	15651.0	+	7835.56i	1.00407	+	0.502682i
$625$	13568.6			0.868393
$626$	5848.76	−	10130.4i	0.373424	−	0.646790i
$627$	−1805.56	+	3127.33i	−0.115004	+	0.199192i
$628$	−11343.7	−	19647.9i	−0.720802	−	1.24847i
$629$	−3855.06			−0.244374
$630$	1081.49	+	1873.19i	0.0683929	+	0.118460i
$631$	−2277.31	−	3944.42i	−0.143674	−	0.248851i	0.785204	−	0.619238i	$-0.212558\pi$
$631$	−2277.31	−	3944.42i	−0.143674	−	0.248851i	−0.928877	+	0.370387i	$0.879225\pi$
$632$	−1476.86			−0.0929531
$633$	19775.9	+	34252.8i	1.24174	+	2.15075i
$634$	848.769	−	1470.11i	0.0531687	−	0.0920908i
$635$	−1259.31	+	2181.20i	−0.0786997	+	0.136312i
$636$	−19632.2			−1.22400
$637$	−537.155	−	9026.79i	−0.0334111	−	0.561467i
$638$	−2500.71			−0.155179
$639$	−30820.7	+	53383.1i	−1.90806	+	3.30485i
$640$	−1737.39	+	3009.24i	−0.107307	+	0.185860i
$641$	9521.18	+	16491.2i	0.586683	+	1.01616i	0.994663	+	0.103174i	$0.0328999\pi$
$641$	9521.18	+	16491.2i	0.586683	+	1.01616i	−0.407980	+	0.912991i	$0.633767\pi$
$642$	10602.8			0.651806
$643$	10570.4	+	18308.5i	0.648301	+	1.12289i	0.983529	+	0.180753i	$0.0578535\pi$
$643$	10570.4	+	18308.5i	0.648301	+	1.12289i	−0.335227	+	0.942137i	$0.608813\pi$
$644$	−4674.61	−	8096.66i	−0.286033	−	0.495424i
$645$	8480.23			0.517688
$646$	377.638	+	654.088i	0.0229999	+	0.0398371i
$647$	2835.76	−	4911.67i	0.172311	−	0.298451i	−0.766917	−	0.641747i	$-0.778210\pi$
$647$	2835.76	−	4911.67i	0.172311	−	0.298451i	0.939227	+	0.343296i	$0.111543\pi$
$648$	−18144.9	+	31427.9i	−1.10000	+	1.90525i
$649$	−3936.29			−0.238078
$650$	355.293	+	5970.63i	0.0214396	+	0.360288i
$651$	−21426.7			−1.28998
$652$	994.344	−	1722.25i	0.0597262	−	0.103449i
$653$	−3388.12	+	5868.39i	−0.203043	+	0.351681i	−0.949508	−	0.313744i	$-0.898417\pi$
$653$	−3388.12	+	5868.39i	−0.203043	+	0.351681i	0.746464	+	0.665426i	$0.231750\pi$
$654$	−2939.96	−	5092.15i	−0.175782	−	0.304463i
$655$	−5264.87			−0.314069
$656$	3441.05	+	5960.08i	0.204803	+	0.354729i
$657$	−24845.3	−	43033.3i	−1.47535	−	2.55539i
$658$	−2357.05			−0.139647
$659$	5160.95	+	8939.02i	0.305071	+	0.528399i	0.977277	−	0.211965i	$-0.0679864\pi$
$659$	5160.95	+	8939.02i	0.305071	+	0.528399i	−0.672206	+	0.740364i	$0.734653\pi$
$660$	−876.707	+	1518.50i	−0.0517057	+	0.0895569i
$661$	10347.4	−	17922.2i	0.608874	−	1.05460i	−0.382552	−	0.923934i	$-0.624955\pi$
$661$	10347.4	−	17922.2i	0.608874	−	1.05460i	0.991426	−	0.130667i	$-0.0417119\pi$
$662$	3293.23			0.193346
$663$	8176.60	−	5392.60i	0.478964	−	0.315884i
$664$	19556.6			1.14299
$665$	481.585	−	834.130i	0.0280828	−	0.0486409i
$666$	6800.20	−	11778.3i	0.395650	−	0.685285i
$667$	11838.3	+	20504.5i	0.687225	+	1.19031i
$668$	−302.393			−0.0175149
$669$	4985.50	+	8635.14i	0.288118	+	0.499034i
$670$	1364.09	+	2362.68i	0.0786559	+	0.136236i
$671$	−6274.69			−0.361001
$672$	−10107.1	−	17506.1i	−0.580196	−	1.00493i
$673$	4883.78	−	8458.95i	0.279726	−	0.484500i	−0.691590	−	0.722290i	$-0.743090\pi$
$673$	4883.78	−	8458.95i	0.279726	−	0.484500i	0.971317	+	0.237790i	$0.0764229\pi$
$674$	−871.374	+	1509.26i	−0.0497983	+	0.0862532i
$675$	50643.2			2.88779
$676$	14961.7	−	1786.97i	0.851257	−	0.101671i
$677$	−16919.3			−0.960506			−0.480253	−	0.877130i	$-0.659455\pi$
$677$	−16919.3			−0.960506			−0.480253	+	0.877130i	$0.659455\pi$
$678$	−6027.72	+	10440.3i	−0.341435	+	0.591383i
$679$	662.523	−	1147.52i	0.0374452	−	0.0648571i
$680$	397.251	+	688.058i	0.0224027	+	0.0388027i
$681$	−42946.1			−2.41659
$682$	1043.33	+	1807.11i	0.0585797	+	0.101463i
$683$	14506.5	+	25126.0i	0.812702	+	1.40764i	0.910967	+	0.412480i	$0.135337\pi$
$683$	14506.5	+	25126.0i	0.812702	+	1.40764i	−0.0982648	+	0.995160i	$0.531329\pi$
$684$	16008.9			0.894907
$685$	−615.781	−	1066.56i	−0.0343471	−	0.0594910i
$686$	−3507.31	+	6074.84i	−0.195204	+	0.338103i
$687$	−20131.7	+	34869.1i	−1.11801	+	1.93645i
$688$	−13831.0			−0.766425
$689$	−11369.8	+	7498.56i	−0.628672	+	0.414619i
$690$	−2763.14			−0.152451
$691$	10169.5	−	17614.1i	0.559863	−	0.969712i	−0.437644	−	0.899148i	$-0.644187\pi$
$691$	10169.5	−	17614.1i	0.559863	−	0.969712i	0.997507	−	0.0705633i	$-0.0224797\pi$
$692$	1412.81	−	2447.06i	0.0776114	−	0.134427i
$693$	−4719.41	−	8174.26i	−0.258695	−	0.448073i
$694$	−12133.7			−0.663673
$695$	−1500.71	−	2599.30i	−0.0819067	−	0.141867i
$696$	16637.9	+	28817.7i	0.906117	+	1.56944i
$697$	3851.28			0.209294
$698$	−278.467	−	482.319i	−0.0151005	−	0.0261548i
$699$	−16833.5	+	29156.4i	−0.910872	+	1.57768i
$700$	−5017.41	+	8690.41i	−0.270915	+	0.469238i
$701$	−496.855			−0.0267702			−0.0133851	−	0.999910i	$-0.504261\pi$
$701$	−496.855			−0.0267702			−0.0133851	+	0.999910i	$0.504261\pi$
$702$	1261.40	+	21197.6i	0.0678184	+	1.13967i
$703$	−6056.24			−0.324915
$704$	683.572	−	1183.98i	0.0365953	−	0.0633850i
$705$	2092.68	−	3624.63i	0.111794	−	0.193633i
$706$	−6872.31	−	11903.2i	−0.366350	−	0.634536i
$707$	−9155.09			−0.487005
$708$	12088.6	+	20938.0i	0.641689	+	1.11144i
$709$	1401.76	+	2427.92i	0.0742515	+	0.128607i	0.900761	−	0.434316i	$-0.143010\pi$
$709$	1401.76	+	2427.92i	0.0742515	+	0.128607i	−0.826509	+	0.562923i	$0.809677\pi$
$710$	−2218.35			−0.117258
$711$	3258.06	+	5643.13i	0.171852	+	0.297657i
$712$	7845.86	−	13589.4i	0.412972	−	0.715288i
$713$	9878.21	−	17109.6i	0.518853	−	0.898679i
$714$	−2735.14			−0.143361
$715$	72.2583	+	1214.29i	0.00377945	+	0.0635130i
$716$	6994.80			0.365095
$717$	19212.8	−	33277.6i	1.00072	−	1.73330i
$718$	−7025.47	+	12168.5i	−0.365165	+	0.632484i
$719$	−14963.1	−	25916.8i	−0.776118	−	1.34428i	−0.934164	−	0.356844i	$-0.883853\pi$
$719$	−14963.1	−	25916.8i	−0.776118	−	1.34428i	0.158046	−	0.987432i	$-0.449481\pi$
$720$	6264.13			0.324236
$721$	6095.74	+	10558.1i	0.314865	+	0.545361i
$722$	−3070.91	−	5318.98i	−0.158293	−	0.274171i
$723$	−54650.3			−2.81116
$724$	−4155.81	−	7198.08i	−0.213328	−	0.369495i
$725$	12706.4	−	22008.1i	0.650901	−	1.12739i
$726$	−636.773	+	1102.92i	−0.0325521	+	0.0563820i
$727$	11850.0			0.604528			0.302264	−	0.953224i	$-0.402258\pi$
$727$	11850.0			0.604528			0.302264	+	0.953224i	$0.402258\pi$
$728$	−8151.23	−	4080.86i	−0.414979	−	0.207757i
$729$	47333.7			2.40480
$730$	894.131	−	1548.68i	0.0453333	−	0.0785195i
$731$	−3869.96	+	6702.97i	−0.195808	+	0.339149i
$732$	19269.9	+	33376.5i	0.973002	+	1.68529i
$733$	−28928.4			−1.45770			−0.728850	−	0.684674i	$-0.759945\pi$
$733$	−28928.4			−1.45770			−0.728850	+	0.684674i	$0.759945\pi$
$734$	6947.06	+	12032.7i	0.349347	+	0.605087i
$735$	−2241.92	−	3883.13i	−0.112510	−	0.194873i
$736$	18638.5			0.933459
$737$	−5952.64	−	10310.3i	−0.297515	−	0.515310i
$738$	−6793.54	+	11766.8i	−0.338853	+	0.586911i
$739$	−16892.5	+	29258.7i	−0.840867	+	1.45642i	0.0482961	+	0.998833i	$0.484621\pi$
$739$	−16892.5	+	29258.7i	−0.840867	+	1.45642i	−0.889163	+	0.457591i	$0.848712\pi$
$740$	−2940.66			−0.146082
$741$	12845.3	−	8471.69i	0.636821	−	0.419993i
$742$	3803.29			0.188171
$743$	821.045	−	1422.09i	0.0405400	−	0.0702174i	−0.845043	−	0.534698i	$-0.820426\pi$
$743$	821.045	−	1422.09i	0.0405400	−	0.0702174i	0.885583	+	0.464480i	$0.153759\pi$
$744$	13883.2	−	24046.3i	0.684115	−	1.18492i
$745$	708.996	+	1228.02i	0.0348666	+	0.0603907i
$746$	11507.9			0.564793
$747$	−43143.4	−	74726.5i	−2.11316	−	3.66011i
$748$	−800.172	−	1385.94i	−0.0391139	−	0.0677472i
$749$	12340.9			0.602039
$750$	3034.88	+	5256.57i	0.147758	+	0.255924i
$751$	747.449	−	1294.62i	0.0363180	−	0.0629046i	−0.847295	−	0.531122i	$-0.821770\pi$
$751$	747.449	−	1294.62i	0.0363180	−	0.0629046i	0.883613	+	0.468218i	$0.155104\pi$
$752$	−3413.09	+	5911.65i	−0.165509	+	0.286670i
$753$	20150.4			0.975196
$754$	9528.37	+	4770.32i	0.460216	+	0.230404i
$755$	−5517.82			−0.265979
$756$	−17813.4	+	30853.7i	−0.856966	+	1.48431i
$757$	−11370.3	+	19693.9i	−0.545917	+	0.945556i	0.452632	+	0.891698i	$0.350485\pi$
$757$	−11370.3	+	19693.9i	−0.545917	+	0.945556i	−0.998549	+	0.0538585i	$0.982848\pi$
$758$	2068.31	+	3582.41i	0.0991085	+	0.171661i
$759$	12057.8			0.576642
$760$	624.075	+	1080.93i	0.0297863	+	0.0515913i
$761$	11325.3	+	19616.1i	0.539479	+	0.934404i	0.998932	+	0.0462026i	$0.0147120\pi$
$761$	11325.3	+	19616.1i	0.539479	+	0.934404i	−0.459453	+	0.888202i	$0.651955\pi$
$762$	11236.0			0.534170
$763$	−3421.90	−	5926.91i	−0.162361	−	0.281217i
$764$	1078.40	−	1867.84i	0.0510668	−	0.0884503i
$765$	1752.73	−	3035.82i	0.0828367	−	0.143477i
$766$	9109.63			0.429692
$767$	14998.3	+	7508.80i	0.706072	+	0.353490i
$768$	5706.71			0.268129
$769$	19539.0	−	33842.6i	0.916249	−	1.58699i	0.111186	−	0.993800i	$-0.464535\pi$
$769$	19539.0	−	33842.6i	0.916249	−	1.58699i	0.805063	−	0.593190i	$-0.202132\pi$
$770$	169.842	−	294.175i	0.00794894	−	0.0137680i
$771$	13438.8	+	23276.8i	0.627741	+	1.08728i
$772$	−23156.8			−1.07958
$773$	1126.20	+	1950.64i	0.0524018	+	0.0907627i	0.891036	−	0.453932i	$-0.149979\pi$
$773$	1126.20	+	1950.64i	0.0524018	+	0.0907627i	−0.838635	+	0.544694i	$0.816646\pi$
$774$	−13653.0	−	23647.6i	−0.634038	−	1.09819i
$775$	−21205.2			−0.982856
$776$	858.548	+	1487.05i	0.0397166	+	0.0687912i
$777$	10966.0	−	18993.6i	0.506309	−	0.876952i
$778$	6738.30	−	11671.1i	0.310514	−	0.537826i
$779$	6050.31			0.278273
$780$	6237.16	−	4113.50i	0.286316	−	0.188830i
$781$	9680.47			0.443527
$782$	1260.96	−	2184.05i	0.0576623	−	0.0998740i
$783$	45111.7	−	78135.7i	2.05895	−	3.56621i
$784$	3656.50	+	6333.25i	0.166568	+	0.288504i
$785$	−7804.41			−0.354843
$786$	11743.7	+	20340.7i	0.532931	+	0.923064i
$787$	12429.3	+	21528.1i	0.562967	+	0.975088i	0.997236	+	0.0743041i	$0.0236735\pi$
$787$	12429.3	+	21528.1i	0.562967	+	0.975088i	−0.434269	+	0.900783i	$0.642993\pi$
$788$	23646.2			1.06898
$789$	−27524.2	−	47673.4i	−1.24194	−	2.15110i
$790$	−117.251	+	203.085i	−0.00528051	+	0.00914612i
$791$	−7015.84	+	12151.8i	−0.315366	+	0.546230i
$792$	12231.5			0.548774
$793$	23908.3	+	11969.5i	1.07063	+	0.536002i
$794$	−9006.78			−0.402568
$795$	−3376.70	+	5848.62i	−0.150641	+	0.260917i
$796$	−870.606	+	1507.93i	−0.0387661	+	0.0671449i
$797$	7030.63	+	12177.4i	0.312469	+	0.541212i	0.978896	−	0.204358i	$-0.0655107\pi$
$797$	7030.63	+	12177.4i	0.312469	+	0.541212i	−0.666427	+	0.745570i	$0.732177\pi$
$798$	−4296.86			−0.190610
$799$	1909.99	+	3308.21i	0.0845691	+	0.146478i
$800$	−10002.7	−	17325.1i	−0.442060	−	0.765670i
$801$	−69234.2			−3.05402
$802$	−4353.08	−	7539.76i	−0.191662	−	0.331968i
$803$	−3901.82	+	6758.15i	−0.171472	+	0.296999i
$804$	−36561.8	+	63326.8i	−1.60377	+	2.77782i
$805$	−3216.10			−0.140811
$806$	−528.171	−	8875.82i	−0.0230819	−	0.387888i
$807$	−28106.0			−1.22600
$808$	5931.93	−	10274.4i	0.258273	−	0.447342i
$809$	6220.29	−	10773.9i	0.270326	−	0.468219i	−0.698619	−	0.715494i	$-0.746202\pi$
$809$	6220.29	−	10773.9i	0.270326	−	0.468219i	0.968945	+	0.247275i	$0.0795351\pi$
$810$	2881.13	+	4990.26i	0.124978	+	0.216469i
$811$	−3110.40			−0.134674			−0.0673371	−	0.997730i	$-0.521450\pi$
$811$	−3110.40			−0.134674			−0.0673371	+	0.997730i	$0.521450\pi$
$812$	8938.77	+	15482.4i	0.386317	+	0.669120i
$813$	15989.3	+	27694.2i	0.689752	+	1.19469i
$814$	−2135.87			−0.0919684
$815$	−342.051	−	592.450i	−0.0147013	−	0.0254633i
$816$	−3960.57	+	6859.91i	−0.169911	+	0.294295i
$817$	−6079.65	+	10530.3i	−0.260343	+	0.450927i
$818$	294.664			0.0125950
$819$	2389.13	+	40148.8i	0.101933	+	1.71296i
$820$	2937.78			0.125112
$821$	−10445.3	+	18091.8i	−0.444024	+	0.769072i	−0.997984	−	0.0634715i	$-0.979783\pi$
$821$	−10445.3	+	18091.8i	−0.444024	+	0.769072i	0.553960	+	0.832543i	$0.313116\pi$
$822$	−2747.10	+	4758.11i	−0.116565	+	0.201896i
$823$	8649.95	+	14982.2i	0.366365	+	0.634563i	0.988994	−	0.147954i	$-0.0472688\pi$
$823$	8649.95	+	14982.2i	0.366365	+	0.634563i	−0.622629	+	0.782517i	$0.713935\pi$
$824$	−15798.7			−0.667927
$825$	−6471.03	−	11208.2i	−0.273082	−	0.472991i
$826$	−2341.88	−	4056.26i	−0.0986496	−	0.170866i
$827$	7394.58			0.310925			0.155462	−	0.987842i	$-0.450313\pi$
$827$	7394.58			0.310925			0.155462	+	0.987842i	$0.450313\pi$
$828$	−26727.5	−	46293.4i	−1.12179	−	1.94300i
$829$	11385.3	−	19719.9i	0.476994	−	0.826177i	−0.522659	−	0.852542i	$-0.675060\pi$
$829$	11385.3	−	19719.9i	0.476994	−	0.826177i	0.999652	+	0.0263647i	$0.00839311\pi$
$830$	1552.64	−	2689.26i	0.0649313	−	0.112464i
$831$	59054.6			2.46520
$832$	−4863.14	+	3207.32i	−0.202643	+	0.133646i
$833$	4092.42			0.170221
$834$	−6694.90	+	11595.9i	−0.277968	+	0.481455i
$835$	−52.0112	+	90.0861i	−0.00215560	+	0.00373360i
$836$	−1257.06	−	2177.29i	−0.0520051	−	0.0900755i
$837$	−75285.1			−3.10900
$838$	437.198	+	757.250i	0.0180224	+	0.0312157i
$839$	2480.13	+	4295.72i	0.102055	+	0.176764i	0.912531	−	0.409008i	$-0.134125\pi$
$839$	2480.13	+	4295.72i	0.102055	+	0.176764i	−0.810476	+	0.585771i	$0.800792\pi$
$840$	−4520.02			−0.185661
$841$	−10442.6	−	18087.1i	−0.428167	−	0.741607i
$842$	641.360	−	1110.87i	0.0262503	−	0.0454668i
$843$	34692.7	−	60089.5i	1.41741	−	2.45503i
$844$	−27536.5			−1.12304
$845$	2041.03	−	4764.60i	0.0830931	−	0.193973i
$846$	−13476.7			−0.547680
$847$	−741.159	+	1283.72i	−0.0300667	+	0.0520771i
$848$	5507.29	−	9538.90i	0.223020	−	0.386282i
$849$	−8066.52	−	13971.6i	−0.326081	−	0.564788i
$850$	−2706.86			−0.109229
$851$	10111.1	+	17513.0i	0.407292	+	0.705450i
$852$	−29729.3	−	51492.6i	−1.19543	−	2.07055i
$853$	−26084.7			−1.04704			−0.523518	−	0.852015i	$-0.675381\pi$
$853$	−26084.7			−1.04704			−0.523518	+	0.852015i	$0.675381\pi$
$854$	−3733.11	−	6465.94i	−0.149584	−	0.259087i
$855$	2753.51	−	4769.22i	0.110138	−	0.190765i
$856$	−7996.15	+	13849.7i	−0.319279	+	0.553007i
$857$	42203.7			1.68221			0.841104	−	0.540873i	$-0.181906\pi$
$857$	42203.7			1.68221			0.841104	+	0.540873i	$0.181906\pi$
$858$	4530.19	−	2987.73i	0.180254	−	0.118881i
$859$	−6608.73			−0.262499			−0.131250	−	0.991349i	$-0.541899\pi$
$859$	−6608.73			−0.262499			−0.131250	+	0.991349i	$0.541899\pi$
$860$	−2952.03	+	5113.06i	−0.117050	+	0.202737i
$861$	−10955.2	+	18975.0i	−0.433627	+	0.751064i
$862$	4967.18	+	8603.40i	0.196268	+	0.339945i
$863$	23816.7			0.939431			0.469716	−	0.882818i	$-0.344356\pi$
$863$	23816.7			0.939431			0.469716	+	0.882818i	$0.344356\pi$
$864$	−35512.6	−	61509.7i	−1.39834	−	2.42199i
$865$	−486.003	−	841.782i	−0.0191036	−	0.0330884i
$866$	−753.747			−0.0295766
$867$	−21982.8	−	38075.3i	−0.861102	−	1.49147i
$868$	7458.78	−	12919.0i	0.291668	−	0.505183i
$869$	511.662	−	886.224i	0.0199735	−	0.0345950i
$870$	5283.67			0.205900
$871$	3013.43	+	50640.1i	0.117229	+	1.97000i
$872$	8868.72			0.344418
$873$	3788.04	−	6561.08i	0.146857	−	0.254363i
$874$	1980.95	−	3431.11i	0.0766667	−	0.132791i
$875$	3532.39	+	6118.28i	0.136476	+	0.236383i
$876$	47930.8			1.84867
$877$	20403.0	+	35339.1i	0.785588	+	1.36068i	0.928647	+	0.370965i	$0.120973\pi$
$877$	20403.0	+	35339.1i	0.785588	+	1.36068i	−0.143058	+	0.989714i	$0.545694\pi$
$878$	−8560.70	−	14827.6i	−0.329054	−	0.569939i
$879$	6147.72			0.235902
$880$	−491.874	−	851.951i	−0.0188421	−	0.0326355i
$881$	6783.68	−	11749.7i	0.259419	−	0.449327i	−0.706668	−	0.707546i	$-0.749802\pi$
$881$	6783.68	−	11749.7i	0.259419	−	0.449327i	0.966086	+	0.258219i	$0.0831357\pi$
$882$	−7218.89	+	12503.5i	−0.275593	+	0.477341i
$883$	34415.4			1.31163			0.655816	−	0.754921i	$-0.272325\pi$
$883$	34415.4			1.31163			0.655816	+	0.754921i	$0.272325\pi$
$884$	405.074	+	6807.19i	0.0154119	+	0.258994i
$885$	8316.86			0.315896
$886$	−6692.33	+	11591.5i	−0.253762	+	0.439529i
$887$	2347.21	−	4065.49i	0.0888520	−	0.153896i	−0.818174	−	0.574970i	$-0.805014\pi$
$887$	2347.21	−	4065.49i	0.0888520	−	0.153896i	0.907026	+	0.421074i	$0.138347\pi$
$888$	14210.5	+	24613.4i	0.537020	+	0.930147i
$889$	13077.9			0.493385
$890$	−1245.80	−	2157.79i	−0.0469206	−	0.0812688i
$891$	−12572.7	−	21776.5i	−0.472728	−	0.818790i
$892$	−6941.95			−0.260576
$893$	3000.57	+	5197.14i	0.112442	+	0.194754i
$894$	3162.95	−	5478.38i	0.118327	−	0.204949i
$895$	1203.09	−	2083.82i	0.0449330	−	0.0778262i
$896$	18042.7			0.672727
$897$	−45943.6	−	23001.3i	−1.71016	−	0.856179i
$898$	−6850.60			−0.254574
$899$	−18889.1	+	32716.8i	−0.700763	+	1.21376i
$900$	−28687.5	+	49688.2i	−1.06250	+	1.84031i
$901$	−3081.92	−	5338.05i	−0.113955	−	0.197376i
$902$	2133.78			0.0787661
$903$	−22016.7	−	38134.0i	−0.811373	−	1.40534i
$904$	−9091.65	−	15747.2i	−0.334495	−	0.579363i
$905$	−2859.17			−0.105019
$906$	12307.9	+	21318.0i	0.451329	+	0.781725i
$907$	5207.08	−	9018.93i	0.190627	−	0.330175i	−0.754832	−	0.655919i	$-0.772281\pi$
$907$	5207.08	−	9018.93i	0.190627	−	0.330175i	0.945458	+	0.325744i	$0.105615\pi$
$908$	14949.8	−	25893.9i	0.546396	−	0.946385i
$909$	−52345.1			−1.90999
$910$	−1208.31	+	796.898i	−0.0440165	+	0.0290296i
$911$	45611.2			1.65880			0.829400	−	0.558656i	$-0.188683\pi$
$911$	45611.2			1.65880			0.829400	+	0.558656i	$0.188683\pi$
$912$	−6222.00	+	10776.8i	−0.225911	+	0.391289i
$913$	−6775.44	+	11735.4i	−0.245602	+	0.425395i
$914$	−3468.77	−	6008.09i	−0.125533	−	0.217429i
$915$	13257.6			0.478997
$916$	−14016.0	−	24276.4i	−0.505569	−	0.875671i
$917$	13668.8	+	23675.1i	0.492241	+	0.852587i
$918$	−9610.22			−0.345517
$919$	3754.56	+	6503.10i	0.134768	+	0.233425i	0.925509	−	0.378726i	$-0.123638\pi$
$919$	3754.56	+	6503.10i	0.134768	+	0.233425i	−0.790741	+	0.612151i	$0.790304\pi$
$920$	2083.83	−	3609.31i	0.0746761	−	0.129343i
$921$	36614.1	−	63417.5i	1.30996	−	2.26892i
$922$	13559.8			0.484346
$923$	−36885.2	−	18466.3i	−1.31537	−	0.658533i
$924$	9104.56			0.324154
$925$	10852.6	−	18797.3i	0.385764	−	0.668163i
$926$	8870.91	−	15364.9i	0.314812	−	0.545271i
$927$	34853.0	+	60367.2i	1.23487	+	2.13885i
$928$	−35640.5			−1.26073
$929$	8592.97	+	14883.5i	0.303473	+	0.525630i	0.976920	−	0.213605i	$-0.0685205\pi$
$929$	8592.97	+	14883.5i	0.303473	+	0.525630i	−0.673447	+	0.739235i	$0.735187\pi$
$930$	−2204.43	−	3818.18i	−0.0777269	−	0.134627i
$931$	6429.12			0.226322
$932$	−11719.7	−	20299.1i	−0.411900	−	0.713432i
$933$	−21561.6	+	37345.7i	−0.756585	+	1.31044i
$934$	3179.98	−	5507.88i	0.111405	−	0.192959i
$935$	−550.514			−0.0192553
$936$	−46605.5	−	23332.7i	−1.62751	−	0.814801i
$937$	−11342.3			−0.395449			−0.197725	−	0.980258i	$-0.563355\pi$
$937$	−11342.3			−0.395449			−0.197725	+	0.980258i	$0.563355\pi$
$938$	7083.01	−	12268.1i	0.246555	−	0.427046i
$939$	53926.5	−	93403.5i	1.87415	−	3.24612i
$940$	1456.95	+	2523.52i	0.0505539	+	0.0875618i
$941$	−50673.1			−1.75547			−0.877734	−	0.479148i	$-0.840946\pi$
$941$	−50673.1			−1.75547			−0.877734	+	0.479148i	$0.840946\pi$
$942$	17408.4	+	30152.2i	0.602118	+	1.04290i
$943$	−10101.2	−	17495.8i	−0.348824	−	0.604181i
$944$	−13564.5			−0.467677
$945$	6127.75	+	10613.6i	0.210937	+	0.365354i
$946$	−2144.13	+	3713.74i	−0.0736909	+	0.127636i
$947$	−5197.90	+	9003.03i	−0.178362	+	0.308933i	−0.941320	−	0.337516i	$-0.890413\pi$
$947$	−5197.90	+	9003.03i	−0.178362	+	0.308933i	0.762957	+	0.646449i	$0.223747\pi$
$948$	−6285.37			−0.215337
$949$	27758.7	−	18307.3i	0.949511	−	0.626218i
$950$	−4252.44			−0.145229
$951$	7825.79	−	13554.7i	0.266844	−	0.462187i
$952$	2062.71	−	3572.73i	0.0702237	−	0.121631i
$953$	2493.71	+	4319.24i	0.0847632	+	0.146814i	0.905290	−	0.424793i	$-0.139653\pi$
$953$	2493.71	+	4319.24i	0.0847632	+	0.146814i	−0.820527	+	0.571608i	$0.806320\pi$
$954$	21745.7			0.737989
$955$	−370.965	−	642.531i	−0.0125698	−	0.0217715i
$956$	13376.3	+	23168.3i	0.452530	+	0.783805i
$957$	−23056.9			−0.778814
$958$	6823.49	+	11818.6i	0.230122	+	0.398583i
$959$	−3197.43	+	5538.11i	−0.107665	+	0.186481i
$960$	−1444.30	+	2501.60i	−0.0485568	+	0.0841029i
$961$	1732.25			0.0581469
$962$	8138.25	+	4074.36i	0.272752	+	0.136552i
$963$	70560.4			2.36114
$964$	19024.2	−	32950.8i	0.635609	−	1.10091i
$965$	−3982.94	+	6898.65i	−0.132866	+	0.230130i
$966$	7173.77	+	12425.3i	0.238936	+	0.413850i
$967$	−20072.0			−0.667498			−0.333749	−	0.942662i	$-0.608314\pi$
$967$	−20072.0			−0.667498			−0.333749	+	0.942662i	$0.608314\pi$
$968$	−960.450	−	1663.55i	−0.0318905	−	0.0552360i
$969$	3481.88	+	6030.79i	0.115433	+	0.199935i
$970$	272.648			0.00902494
$971$	440.354	+	762.716i	0.0145537	+	0.0252077i	0.873211	−	0.487343i	$-0.162034\pi$
$971$	440.354	+	762.716i	0.0145537	+	0.0252077i	−0.858657	+	0.512551i	$0.828701\pi$
$972$	−37962.5	+	65753.0i	−1.25273	+	2.16978i
$973$	−7792.40	+	13496.8i	−0.256745	+	0.444695i
$974$	4701.03			0.154652
$975$	3275.86	+	55050.1i	0.107601	+	1.80822i
$976$	−21622.7			−0.709145
$977$	6093.49	−	10554.2i	0.199537	−	0.345609i	−0.748841	−	0.662750i	$-0.769389\pi$
$977$	6093.49	−	10554.2i	0.199537	−	0.345609i	0.948379	+	0.317141i	$0.102723\pi$
$978$	−1525.95	+	2643.01i	−0.0498920	+	0.0864154i
$979$	5436.43	+	9416.18i	0.177476	+	0.307398i
$980$	3121.72			0.101755
$981$	−19565.1	−	33887.7i	−0.636763	−	1.10291i
$982$	−7585.34	−	13138.2i	−0.246495	−	0.426942i
$983$	26378.0			0.855877			0.427938	−	0.903808i	$-0.359240\pi$
$983$	26378.0			0.855877			0.427938	+	0.903808i	$0.359240\pi$
$984$	−14196.6	−	24589.2i	−0.459930	−	0.796622i
$985$	4067.10	−	7044.43i	0.131562	−	0.227872i
$986$	−2411.21	+	4176.33i	−0.0778788	+	0.134890i
$987$	−21732.4			−0.700861
$988$	636.366	+	10694.0i	0.0204914	+	0.344354i
$989$	40600.8			1.30539
$990$	971.088	−	1681.97i	0.0311750	−	0.0539966i
$991$	29179.7	−	50540.8i	0.935342	−	1.62006i	0.161320	−	0.986902i	$-0.448425\pi$
$991$	29179.7	−	50540.8i	0.935342	−	1.62006i	0.774022	−	0.633158i	$-0.218242\pi$
$992$	14869.8	+	25755.2i	0.475923	+	0.824324i
$993$	30364.1			0.970367
$994$	5759.37	+	9975.52i	0.183779	+	0.318314i
$995$	299.486	+	518.725i	0.00954205	+	0.0165273i
$996$	83231.0			2.64787
$997$	9418.62	+	16313.5i	0.299188	+	0.518209i	0.975950	−	0.217993i	$-0.0699508\pi$
$997$	9418.62	+	16313.5i	0.299188	+	0.518209i	−0.676762	+	0.736202i	$0.736618\pi$
$998$	−2127.54	+	3685.01i	−0.0674811	+	0.116881i
$999$	38530.2	−	66736.2i	1.22026	−	2.11355i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.e.b.100.11	✓	34
13.3	even	3	inner	143.4.e.b.133.11	yes	34
13.4	even	6		1859.4.a.h.1.11		17
13.9	even	3		1859.4.a.g.1.7		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.e.b.100.11	✓	34	1.1	even	1	trivial
143.4.e.b.133.11	yes	34	13.3	even	3	inner
1859.4.a.g.1.7		17	13.9	even	3
1859.4.a.h.1.11		17	13.4	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.534214 - 0.925286i) q^{2} +(4.92554 - 8.53128i) q^{3} +(3.42923 + 5.93960i) q^{4} +2.35929 q^{5} +(-5.26259 - 9.11507i) q^{6} +(-6.12528 - 10.6093i) q^{7} +15.8752 q^{8} +(-35.0219 - 60.6597i) q^{9} +O(q^{10})\)	\(q+(0.534214 - 0.925286i) q^{2} +(4.92554 - 8.53128i) q^{3} +(3.42923 + 5.93960i) q^{4} +2.35929 q^{5} +(-5.26259 - 9.11507i) q^{6} +(-6.12528 - 10.6093i) q^{7} +15.8752 q^{8} +(-35.0219 - 60.6597i) q^{9} +(1.26037 - 2.18302i) q^{10} +(-5.50000 + 9.52628i) q^{11} +67.5632 q^{12} +(39.1287 - 25.8060i) q^{13} -13.0888 q^{14} +(11.6208 - 20.1278i) q^{15} +(-18.9531 + 32.8277i) q^{16} +(10.6063 + 18.3707i) q^{17} -74.8367 q^{18} +(16.6623 + 28.8600i) q^{19} +(8.09055 + 14.0132i) q^{20} -120.681 q^{21} +(5.87636 + 10.1781i) q^{22} +(55.6369 - 96.3659i) q^{23} +(78.1939 - 135.436i) q^{24} -119.434 q^{25} +(-2.97481 - 49.9911i) q^{26} -424.027 q^{27} +(42.0100 - 72.7634i) q^{28} +(-106.389 + 184.270i) q^{29} +(-12.4160 - 21.5051i) q^{30} +177.548 q^{31} +(83.7508 + 145.061i) q^{32} +(54.1809 + 93.8441i) q^{33} +22.6641 q^{34} +(-14.4513 - 25.0304i) q^{35} +(240.196 - 416.032i) q^{36} +(-90.8672 + 157.387i) q^{37} +35.6050 q^{38} +(-27.4282 - 460.926i) q^{39} +37.4542 q^{40} +(90.7781 - 157.232i) q^{41} +(-64.4696 + 111.665i) q^{42} +(182.437 + 315.990i) q^{43} -75.4431 q^{44} +(-82.6267 - 143.114i) q^{45} +(-59.4440 - 102.960i) q^{46} +180.081 q^{47} +(186.708 + 323.388i) q^{48} +(96.4619 - 167.077i) q^{49} +(-63.8032 + 110.510i) q^{50} +208.967 q^{51} +(287.458 + 143.914i) q^{52} -290.575 q^{53} +(-226.521 + 392.346i) q^{54} +(-12.9761 + 22.4753i) q^{55} +(-97.2400 - 168.425i) q^{56} +328.284 q^{57} +(113.669 + 196.880i) q^{58} +(178.922 + 309.902i) q^{59} +159.401 q^{60} +(285.213 + 494.004i) q^{61} +(94.8486 - 164.283i) q^{62} +(-429.037 + 743.115i) q^{63} -124.286 q^{64} +(92.3159 - 60.8837i) q^{65} +115.777 q^{66} +(-541.149 + 937.297i) q^{67} +(-72.7429 + 125.994i) q^{68} +(-548.083 - 949.308i) q^{69} -30.8804 q^{70} +(-440.021 - 762.139i) q^{71} +(-555.979 - 962.984i) q^{72} +709.422 q^{73} +(97.0851 + 168.156i) q^{74} +(-588.276 + 1018.92i) q^{75} +(-114.278 + 197.935i) q^{76} +134.756 q^{77} +(-441.141 - 220.854i) q^{78} -93.0294 q^{79} +(-44.7158 + 77.4501i) q^{80} +(-1142.97 + 1979.69i) q^{81} +(-96.9899 - 167.991i) q^{82} +1231.90 q^{83} +(-413.844 - 716.798i) q^{84} +(25.0233 + 43.3417i) q^{85} +389.841 q^{86} +(1048.04 + 1815.26i) q^{87} +(-87.3136 + 151.232i) q^{88} +(494.221 - 856.016i) q^{89} -176.562 q^{90} +(-513.457 - 257.059i) q^{91} +763.167 q^{92} +(874.519 - 1514.71i) q^{93} +(96.2019 - 166.626i) q^{94} +(39.3113 + 68.0892i) q^{95} +1650.07 q^{96} +(54.0811 + 93.6712i) q^{97} +(-103.063 - 178.510i) q^{98} +770.481 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 6 q^{3} - 50 q^{4} - 48 q^{5} - 16 q^{6} + 62 q^{7} - 42 q^{8} - 135 q^{9}+O(q^{10}) \) 34 * q + 6 * q^3 - 50 * q^4 - 48 * q^5 - 16 * q^6 + 62 * q^7 - 42 * q^8 - 135 * q^9	\( 34 q + 6 q^{3} - 50 q^{4} - 48 q^{5} - 16 q^{6} + 62 q^{7} - 42 q^{8} - 135 q^{9} - 2 q^{10} - 187 q^{11} - 254 q^{12} + 76 q^{13} + 148 q^{15} - 126 q^{16} + 74 q^{17} + 180 q^{18} + 159 q^{19} + 222 q^{20} - 368 q^{21} + 215 q^{23} - 214 q^{24} + 190 q^{25} + 123 q^{26} - 384 q^{27} + 358 q^{28} + 157 q^{29} - 829 q^{30} - 788 q^{31} + 553 q^{32} + 66 q^{33} - 1404 q^{34} - 58 q^{35} + 700 q^{36} - 88 q^{37} - 2636 q^{38} + 798 q^{39} + 1466 q^{40} + 512 q^{41} - 337 q^{42} - 927 q^{43} + 1100 q^{44} + 1482 q^{45} + 1361 q^{46} - 286 q^{47} + 178 q^{48} - 1835 q^{49} + 583 q^{50} - 1136 q^{51} + 2306 q^{52} + 212 q^{53} + 67 q^{54} + 264 q^{55} - 2059 q^{56} + 2596 q^{57} + 1690 q^{58} + 266 q^{59} + 74 q^{60} + 624 q^{61} - 643 q^{62} + 2360 q^{63} - 3178 q^{64} + 470 q^{65} + 352 q^{66} + 676 q^{67} + 413 q^{68} - 764 q^{69} - 2122 q^{70} + 763 q^{71} + 1366 q^{72} - 4748 q^{73} + 1649 q^{74} - 2420 q^{75} + 2101 q^{76} - 1364 q^{77} - 5848 q^{78} + 4328 q^{79} + 1013 q^{80} - 537 q^{81} - 3152 q^{82} + 1554 q^{83} + 3381 q^{84} + 1690 q^{85} + 5788 q^{86} + 4200 q^{87} + 231 q^{88} + 1687 q^{89} - 10798 q^{90} - 3380 q^{91} + 11084 q^{92} + 4310 q^{93} - 1777 q^{94} - 1124 q^{95} - 6930 q^{96} + 2047 q^{97} - 1553 q^{98} + 2970 q^{99}+O(q^{100}) \) 34 * q + 6 * q^3 - 50 * q^4 - 48 * q^5 - 16 * q^6 + 62 * q^7 - 42 * q^8 - 135 * q^9 - 2 * q^10 - 187 * q^11 - 254 * q^12 + 76 * q^13 + 148 * q^15 - 126 * q^16 + 74 * q^17 + 180 * q^18 + 159 * q^19 + 222 * q^20 - 368 * q^21 + 215 * q^23 - 214 * q^24 + 190 * q^25 + 123 * q^26 - 384 * q^27 + 358 * q^28 + 157 * q^29 - 829 * q^30 - 788 * q^31 + 553 * q^32 + 66 * q^33 - 1404 * q^34 - 58 * q^35 + 700 * q^36 - 88 * q^37 - 2636 * q^38 + 798 * q^39 + 1466 * q^40 + 512 * q^41 - 337 * q^42 - 927 * q^43 + 1100 * q^44 + 1482 * q^45 + 1361 * q^46 - 286 * q^47 + 178 * q^48 - 1835 * q^49 + 583 * q^50 - 1136 * q^51 + 2306 * q^52 + 212 * q^53 + 67 * q^54 + 264 * q^55 - 2059 * q^56 + 2596 * q^57 + 1690 * q^58 + 266 * q^59 + 74 * q^60 + 624 * q^61 - 643 * q^62 + 2360 * q^63 - 3178 * q^64 + 470 * q^65 + 352 * q^66 + 676 * q^67 + 413 * q^68 - 764 * q^69 - 2122 * q^70 + 763 * q^71 + 1366 * q^72 - 4748 * q^73 + 1649 * q^74 - 2420 * q^75 + 2101 * q^76 - 1364 * q^77 - 5848 * q^78 + 4328 * q^79 + 1013 * q^80 - 537 * q^81 - 3152 * q^82 + 1554 * q^83 + 3381 * q^84 + 1690 * q^85 + 5788 * q^86 + 4200 * q^87 + 231 * q^88 + 1687 * q^89 - 10798 * q^90 - 3380 * q^91 + 11084 * q^92 + 4310 * q^93 - 1777 * q^94 - 1124 * q^95 - 6930 * q^96 + 2047 * q^97 - 1553 * q^98 + 2970 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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