LMFDB - Embedded newform 143.4.j.a.23.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,4,Mod(23,143)]

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, 5]))

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

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

chi := DirichletCharacter("143.23");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	143.j (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$8.43727313082$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			23.6
Character	$\chi$	$=$	143.23
Dual form			143.4.j.a.56.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.65232 + 2.10867i) q^{2} +(4.62634 + 8.01306i) q^{3} +(4.89294 - 8.47483i) q^{4} +13.5656i q^{5} +(-33.7937 - 19.5108i) q^{6} +(13.5120 + 7.80115i) q^{7} +7.53168i q^{8} +(-29.3061 + 50.7597i) q^{9} +O(q^{10})$	\(q+(-3.65232 + 2.10867i) q^{2} +(4.62634 + 8.01306i) q^{3} +(4.89294 - 8.47483i) q^{4} +13.5656i q^{5} +(-33.7937 - 19.5108i) q^{6} +(13.5120 + 7.80115i) q^{7} +7.53168i q^{8} +(-29.3061 + 50.7597i) q^{9} +(-28.6052 - 49.5457i) q^{10} +(-9.52628 + 5.50000i) q^{11} +90.5458 q^{12} +(1.06674 + 46.8600i) q^{13} -65.8001 q^{14} +(-108.702 + 62.7590i) q^{15} +(23.2618 + 40.2905i) q^{16} +(44.0174 - 76.2403i) q^{17} -247.187i q^{18} +(133.517 + 77.0861i) q^{19} +(114.966 + 66.3756i) q^{20} +144.363i q^{21} +(23.1953 - 40.1755i) q^{22} +(-62.2862 - 107.883i) q^{23} +(-60.3518 + 34.8441i) q^{24} -59.0246 q^{25} +(-102.708 - 168.898i) q^{26} -292.498 q^{27} +(132.227 - 76.3412i) q^{28} +(-87.7628 - 152.010i) q^{29} +(264.675 - 458.431i) q^{30} -115.011i q^{31} +(-222.100 - 128.229i) q^{32} +(-88.1437 - 50.8898i) q^{33} +371.272i q^{34} +(-105.827 + 183.298i) q^{35} +(286.786 + 496.729i) q^{36} +(179.091 - 103.398i) q^{37} -650.196 q^{38} +(-370.557 + 225.339i) q^{39} -102.171 q^{40} +(371.800 - 214.659i) q^{41} +(-304.414 - 527.260i) q^{42} +(54.3773 - 94.1843i) q^{43} +107.645i q^{44} +(-688.584 - 397.554i) q^{45} +(454.978 + 262.681i) q^{46} +280.611i q^{47} +(-215.234 + 372.796i) q^{48} +(-49.7842 - 86.2287i) q^{49} +(215.577 - 124.463i) q^{50} +814.558 q^{51} +(402.350 + 220.243i) q^{52} +212.661 q^{53} +(1068.30 - 616.781i) q^{54} +(-74.6106 - 129.229i) q^{55} +(-58.7557 + 101.768i) q^{56} +1426.51i q^{57} +(641.075 + 370.125i) q^{58} +(91.5914 + 52.8803i) q^{59} +1228.30i q^{60} +(-66.6457 + 115.434i) q^{61} +(242.519 + 420.055i) q^{62} +(-791.968 + 457.243i) q^{63} +709.383 q^{64} +(-635.683 + 14.4710i) q^{65} +429.238 q^{66} +(-467.307 + 269.800i) q^{67} +(-430.749 - 746.079i) q^{68} +(576.314 - 998.206i) q^{69} -892.615i q^{70} +(296.102 + 170.955i) q^{71} +(-382.306 - 220.724i) q^{72} -317.790i q^{73} +(-436.065 + 755.287i) q^{74} +(-273.068 - 472.968i) q^{75} +(1306.58 - 754.356i) q^{76} -171.625 q^{77} +(878.229 - 1604.39i) q^{78} -209.400 q^{79} +(-546.564 + 315.559i) q^{80} +(-561.933 - 973.296i) q^{81} +(-905.288 + 1568.01i) q^{82} +664.488i q^{83} +(1223.45 + 706.361i) q^{84} +(1034.24 + 597.121i) q^{85} +458.654i q^{86} +(812.042 - 1406.50i) q^{87} +(-41.4242 - 71.7489i) q^{88} +(-623.905 + 360.212i) q^{89} +3353.24 q^{90} +(-351.148 + 641.494i) q^{91} -1219.05 q^{92} +(921.587 - 532.078i) q^{93} +(-591.715 - 1024.88i) q^{94} +(-1045.72 + 1811.24i) q^{95} -2372.93i q^{96} +(-593.899 - 342.888i) q^{97} +(363.655 + 209.956i) q^{98} -644.735i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 12 q^{3} + 152 q^{4} + 90 q^{6} - 36 q^{7} - 360 q^{9}+O(q^{10}) $ 72 * q - 12 * q^3 + 152 * q^4 + 90 * q^6 - 36 * q^7 - 360 * q^9	\( 72 q - 12 q^{3} + 152 q^{4} + 90 q^{6} - 36 q^{7} - 360 q^{9} - 56 q^{10} - 132 q^{12} - 46 q^{13} + 328 q^{14} - 644 q^{16} + 138 q^{17} + 492 q^{19} + 540 q^{20} - 44 q^{22} + 46 q^{23} + 720 q^{24} - 1636 q^{25} - 902 q^{26} + 48 q^{27} - 714 q^{28} - 262 q^{29} + 104 q^{30} + 144 q^{32} - 68 q^{35} + 1960 q^{36} + 630 q^{37} - 448 q^{38} - 1612 q^{39} + 216 q^{40} + 126 q^{41} - 82 q^{42} + 436 q^{43} - 570 q^{45} - 1590 q^{46} + 1944 q^{48} + 1192 q^{49} + 1290 q^{50} - 1424 q^{51} + 590 q^{52} + 292 q^{53} - 528 q^{54} - 440 q^{55} - 102 q^{56} - 1128 q^{58} + 504 q^{59} + 590 q^{61} + 1776 q^{62} + 1884 q^{63} - 5028 q^{64} + 994 q^{65} + 2156 q^{66} + 3396 q^{67} + 1530 q^{68} + 12 q^{69} - 1014 q^{71} - 1062 q^{72} - 1568 q^{74} + 4688 q^{75} + 7872 q^{76} - 1232 q^{77} - 4964 q^{78} - 2928 q^{79} - 558 q^{80} - 3780 q^{81} - 4072 q^{82} + 696 q^{84} + 4662 q^{85} + 1832 q^{87} + 924 q^{88} + 1014 q^{89} + 6844 q^{90} + 2900 q^{91} - 1336 q^{92} - 4092 q^{93} + 4166 q^{94} - 256 q^{95} - 5070 q^{97} - 8550 q^{98}+O(q^{100}) \) 72 * q - 12 * q^3 + 152 * q^4 + 90 * q^6 - 36 * q^7 - 360 * q^9 - 56 * q^10 - 132 * q^12 - 46 * q^13 + 328 * q^14 - 644 * q^16 + 138 * q^17 + 492 * q^19 + 540 * q^20 - 44 * q^22 + 46 * q^23 + 720 * q^24 - 1636 * q^25 - 902 * q^26 + 48 * q^27 - 714 * q^28 - 262 * q^29 + 104 * q^30 + 144 * q^32 - 68 * q^35 + 1960 * q^36 + 630 * q^37 - 448 * q^38 - 1612 * q^39 + 216 * q^40 + 126 * q^41 - 82 * q^42 + 436 * q^43 - 570 * q^45 - 1590 * q^46 + 1944 * q^48 + 1192 * q^49 + 1290 * q^50 - 1424 * q^51 + 590 * q^52 + 292 * q^53 - 528 * q^54 - 440 * q^55 - 102 * q^56 - 1128 * q^58 + 504 * q^59 + 590 * q^61 + 1776 * q^62 + 1884 * q^63 - 5028 * q^64 + 994 * q^65 + 2156 * q^66 + 3396 * q^67 + 1530 * q^68 + 12 * q^69 - 1014 * q^71 - 1062 * q^72 - 1568 * q^74 + 4688 * q^75 + 7872 * q^76 - 1232 * q^77 - 4964 * q^78 - 2928 * q^79 - 558 * q^80 - 3780 * q^81 - 4072 * q^82 + 696 * q^84 + 4662 * q^85 + 1832 * q^87 + 924 * q^88 + 1014 * q^89 + 6844 * q^90 + 2900 * q^91 - 1336 * q^92 - 4092 * q^93 + 4166 * q^94 - 256 * q^95 - 5070 * q^97 - 8550 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$67$	$79$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−3.65232	+	2.10867i	−1.29129	+	0.745526i	−0.978883	−	0.204423i	$-0.934468\pi$
$2$	−3.65232	+	2.10867i	−1.29129	+	0.745526i	−0.312406	+	0.949949i	$0.601135\pi$
$3$	4.62634	+	8.01306i	0.890340	+	1.54211i	0.839468	+	0.543410i	$0.182867\pi$
$3$	4.62634	+	8.01306i	0.890340	+	1.54211i	0.0508728	+	0.998705i	$0.483800\pi$
$4$	4.89294	−	8.47483i	0.611618	−	1.05935i
$5$			13.5656i			1.21334i	0.794953	+	0.606671i	$0.207495\pi$
$5$			13.5656i			1.21334i	−0.794953	+	0.606671i	$0.792505\pi$
$6$	−33.7937	−	19.5108i	−2.29937	−	1.32754i
$7$	13.5120	+	7.80115i	0.729579	+	0.421222i	0.818268	−	0.574837i	$-0.194935\pi$
$7$	13.5120	+	7.80115i	0.729579	+	0.421222i	−0.0886894	+	0.996059i	$0.528268\pi$
$8$			7.53168i			0.332856i
$9$	−29.3061	+	50.7597i	−1.08541	+	1.87999i
$10$	−28.6052	−	49.5457i	−0.904577	−	1.56677i
$11$	−9.52628	+	5.50000i	−0.261116	+	0.150756i
$11$	−9.52628	+	5.50000i	−0.261116	+	0.150756i
$12$	90.5458			2.17819
$13$	1.06674	+	46.8600i	0.0227586	+	0.999741i
$13$	1.06674	+	46.8600i	0.0227586	+	0.999741i
$14$	−65.8001			−1.25613
$15$	−108.702	+	62.7590i	−1.87111	+	1.08029i
$16$	23.2618	+	40.2905i	0.363465	+	0.629540i
$17$	44.0174	−	76.2403i	0.627987	−	1.08771i	−0.359968	−	0.932965i	$-0.617212\pi$
$17$	44.0174	−	76.2403i	0.627987	−	1.08771i	0.987955	−	0.154741i	$-0.0494542\pi$
$18$		−	247.187i		−	3.23681i
$19$	133.517	+	77.0861i	1.61215	+	0.930778i	0.988870	+	0.148782i	$0.0475353\pi$
$19$	133.517	+	77.0861i	1.61215	+	0.930778i	0.623284	+	0.781996i	$0.285798\pi$
$20$	114.966	+	66.3756i	1.28536	+	0.742101i
$21$			144.363i			1.50013i
$22$	23.1953	−	40.1755i	0.224785	−	0.389338i
$23$	−62.2862	−	107.883i	−0.564677	−	0.978049i	−0.997080	−	0.0763681i	$-0.975668\pi$
$23$	−62.2862	−	107.883i	−0.564677	−	0.978049i	0.432403	−	0.901680i	$-0.357666\pi$
$24$	−60.3518	+	34.8441i	−0.513303	+	0.296355i
$25$	−59.0246			−0.472197
$26$	−102.708	−	168.898i	−0.774721	−	1.27399i
$27$	−292.498			−2.08486
$28$	132.227	−	76.3412i	0.892447	−	0.515254i
$29$	−87.7628	−	152.010i	−0.561971	−	0.973362i	−0.997324	−	0.0731023i	$-0.976710\pi$
$29$	−87.7628	−	152.010i	−0.561971	−	0.973362i	0.435354	−	0.900259i	$-0.356623\pi$
$30$	264.675	−	458.431i	1.61076	−	2.78992i
$31$		−	115.011i		−	0.666339i	−0.942867	−	0.333169i	$-0.891882\pi$
$31$		−	115.011i		−	0.666339i	0.942867	−	0.333169i	$-0.108118\pi$
$32$	−222.100	−	128.229i	−1.22694	−	0.708373i
$33$	−88.1437	−	50.8898i	−0.464965	−	0.268448i
$34$			371.272i			1.87272i
$35$	−105.827	+	183.298i	−0.511087	+	0.885228i
$36$	286.786	+	496.729i	1.32772	+	2.29967i
$37$	179.091	−	103.398i	0.795741	−	0.459421i	−0.0462391	−	0.998930i	$-0.514724\pi$
$37$	179.091	−	103.398i	0.795741	−	0.459421i	0.841980	+	0.539509i	$0.181390\pi$
$38$	−650.196			−2.77568
$39$	−370.557	+	225.339i	−1.52145	+	0.925206i
$40$	−102.171			−0.403868
$41$	371.800	−	214.659i	1.41623	−	0.817661i	0.420265	−	0.907401i	$-0.361937\pi$
$41$	371.800	−	214.659i	1.41623	−	0.817661i	0.995965	+	0.0897401i	$0.0286036\pi$
$42$	−304.414	−	527.260i	−1.11838	−	1.93710i
$43$	54.3773	−	94.1843i	0.192848	−	0.334022i	−0.753345	−	0.657626i	$-0.771561\pi$
$43$	54.3773	−	94.1843i	0.192848	−	0.334022i	0.946193	+	0.323603i	$0.104894\pi$
$44$			107.645i			0.368819i
$45$	−688.584	−	397.554i	−2.28107	−	1.31698i
$46$	454.978	+	262.681i	1.45832	+	0.841962i
$47$			280.611i			0.870879i	0.900218	+	0.435439i	$0.143407\pi$
$47$			280.611i			0.870879i	−0.900218	+	0.435439i	$0.856593\pi$
$48$	−215.234	+	372.796i	−0.647215	+	1.12101i
$49$	−49.7842	−	86.2287i	−0.145143	−	0.251396i
$50$	215.577	−	124.463i	0.609743	−	0.352035i
$51$	814.558			2.23649
$52$	402.350	+	220.243i	1.07300	+	0.587350i
$53$	212.661			0.551156			0.275578	−	0.961279i	$-0.411131\pi$
$53$	212.661			0.551156			0.275578	+	0.961279i	$0.411131\pi$
$54$	1068.30	−	616.781i	2.69216	−	1.55432i
$55$	−74.6106	−	129.229i	−0.182918	−	0.316823i
$56$	−58.7557	+	101.768i	−0.140207	+	0.242845i
$57$			1426.51i			3.31484i
$58$	641.075	+	370.125i	1.45133	+	0.837927i
$59$	91.5914	+	52.8803i	0.202105	+	0.116685i	0.597637	−	0.801767i	$-0.296106\pi$
$59$	91.5914	+	52.8803i	0.202105	+	0.116685i	−0.395532	+	0.918452i	$0.629440\pi$
$60$			1228.30i			2.64289i
$61$	−66.6457	+	115.434i	−0.139887	+	0.242291i	−0.927454	−	0.373938i	$-0.878007\pi$
$61$	−66.6457	+	115.434i	−0.139887	+	0.242291i	0.787567	+	0.616229i	$0.211341\pi$
$62$	242.519	+	420.055i	0.496773	+	0.860436i
$63$	−791.968	+	457.243i	−1.58379	+	0.914400i
$64$	709.383			1.38551
$65$	−635.683	+	14.4710i	−1.21303	+	0.0276139i
$66$	429.238			0.800539
$67$	−467.307	+	269.800i	−0.852099	+	0.491960i	−0.861359	−	0.507997i	$-0.830386\pi$
$67$	−467.307	+	269.800i	−0.852099	+	0.491960i	0.00925937	+	0.999957i	$0.497053\pi$
$68$	−430.749	−	746.079i	−0.768176	−	1.33052i
$69$	576.314	−	998.206i	1.00551	−	1.74159i
$70$		−	892.615i		−	1.52411i
$71$	296.102	+	170.955i	0.494942	+	0.285755i	0.726622	−	0.687037i	$-0.241089\pi$
$71$	296.102	+	170.955i	0.494942	+	0.285755i	−0.231680	+	0.972792i	$0.574422\pi$
$72$	−382.306	−	220.724i	−0.625766	−	0.361286i
$73$		−	317.790i		−	0.509514i	−0.967005	−	0.254757i	$-0.918004\pi$
$73$		−	317.790i		−	0.509514i	0.967005	−	0.254757i	$-0.0819955\pi$
$74$	−436.065	+	755.287i	−0.685021	+	1.18649i
$75$	−273.068	−	472.968i	−0.420416	−	0.728182i
$76$	1306.58	−	754.356i	1.97204	−	1.13856i
$77$	−171.625			−0.254007
$78$	878.229	−	1604.39i	1.27487	−	2.32899i
$79$	−209.400			−0.298220			−0.149110	−	0.988821i	$-0.547641\pi$
$79$	−209.400			−0.298220			−0.149110	+	0.988821i	$0.547641\pi$
$80$	−546.564	+	315.559i	−0.763847	+	0.441007i
$81$	−561.933	−	973.296i	−0.770827	−	1.33511i
$82$	−905.288	+	1568.01i	−1.21918	+	2.11167i
$83$			664.488i			0.878760i	0.898301	+	0.439380i	$0.144802\pi$
$83$			664.488i			0.878760i	−0.898301	+	0.439380i	$0.855198\pi$
$84$	1223.45	+	706.361i	1.58916	+	0.917504i
$85$	1034.24	+	597.121i	1.31976	+	0.761963i
$86$			458.654i			0.575093i
$87$	812.042	−	1406.50i	1.00069	−	1.73325i
$88$	−41.4242	−	71.7489i	−0.0501800	−	0.0869143i
$89$	−623.905	+	360.212i	−0.743077	+	0.429016i	−0.823187	−	0.567770i	$-0.807806\pi$
$89$	−623.905	+	360.212i	−0.743077	+	0.429016i	0.0801102	+	0.996786i	$0.474473\pi$
$90$	3353.24			3.92736
$91$	−351.148	+	641.494i	−0.404509	+	0.738976i
$92$	−1219.05			−1.38147
$93$	921.587	−	532.078i	1.02757	−	0.593268i
$94$	−591.715	−	1024.88i	−0.649263	−	1.12456i
$95$	−1045.72	+	1811.24i	−1.12935	+	1.95609i
$96$		−	2372.93i		−	2.52277i
$97$	−593.899	−	342.888i	−0.621663	−	0.358917i	0.155853	−	0.987780i	$-0.450187\pi$
$97$	−593.899	−	342.888i	−0.621663	−	0.358917i	−0.777516	+	0.628863i	$0.783521\pi$
$98$	363.655	+	209.956i	0.374844	+	0.216416i
$99$		−	644.735i		−	0.654528i
$100$	−288.804	+	500.223i	−0.288804	+	0.500223i
$101$	−684.957	−	1186.38i	−0.674809	−	1.16880i	−0.976525	−	0.215406i	$-0.930893\pi$
$101$	−684.957	−	1186.38i	−0.674809	−	1.16880i	0.301715	−	0.953398i	$-0.402441\pi$
$102$	−2975.02	+	1717.63i	−2.88795	+	1.66736i
$103$	98.7397			0.0944574			0.0472287	−	0.998884i	$-0.484961\pi$
$103$	98.7397			0.0944574			0.0472287	+	0.998884i	$0.484961\pi$
$104$	−352.935	+	8.03437i	−0.332770	+	0.00757533i
$105$	−1958.37			−1.82016
$106$	−776.706	+	448.432i	−0.711702	+	0.410901i
$107$	−486.053	−	841.869i	−0.439145	−	0.760622i	0.558479	−	0.829519i	$-0.311385\pi$
$107$	−486.053	−	841.869i	−0.439145	−	0.760622i	−0.997624	+	0.0688971i	$0.978052\pi$
$108$	−1431.18	+	2478.87i	−1.27514	+	2.20861i
$109$			2119.81i			1.86276i	0.364042	+	0.931382i	$0.381396\pi$
$109$			2119.81i			1.86276i	−0.364042	+	0.931382i	$0.618604\pi$
$110$	545.003	+	314.658i	0.472400	+	0.272740i
$111$	1657.07	+	956.712i	1.41696	+	0.818082i
$112$			725.874i			0.612398i
$113$	−657.337	+	1138.54i	−0.547231	+	0.947832i	0.451232	+	0.892407i	$0.350985\pi$
$113$	−657.337	+	1138.54i	−0.547231	+	0.947832i	−0.998463	+	0.0554252i	$0.982349\pi$
$114$	−3008.03	−	5210.06i	−2.47130	−	4.28041i
$115$	1463.49	−	844.947i	1.18671	−	0.685145i
$116$	−1717.67			−1.37485
$117$	−2409.86	−	1319.14i	−1.90420	−	1.04235i
$118$	−446.028			−0.347968
$119$	1189.52	−	686.772i	0.916332	−	0.529044i
$120$	−472.681	−	818.707i	−0.359580	−	0.622811i
$121$	60.5000	−	104.789i	0.0454545	−	0.0787296i
$122$		−	562.134i		−	0.417157i
$123$	3440.15	+	1986.17i	2.52185	+	1.45599i
$124$	−974.695	−	562.740i	−0.705888	−	0.407545i
$125$			894.993i			0.640405i
$126$	1928.35	−	3339.99i	1.36342	−	2.36151i
$127$	−491.886	−	851.972i	−0.343684	−	0.595278i	0.641430	−	0.767182i	$-0.278342\pi$
$127$	−491.886	−	851.972i	−0.343684	−	0.595278i	−0.985114	+	0.171904i	$0.945008\pi$
$128$	−814.093	+	470.017i	−0.562159	+	0.324562i
$129$	1006.27			0.686801
$130$	2291.20	−	1393.30i	1.54578	−	0.940001i
$131$	1574.05			1.04981			0.524905	−	0.851161i	$-0.324101\pi$
$131$	1574.05			1.04981			0.524905	+	0.851161i	$0.324101\pi$
$132$	−862.564	+	498.002i	−0.568762	+	0.328375i
$133$	1202.72	+	2083.17i	0.784129	+	1.35815i
$134$	1137.84	−	1970.79i	0.733537	−	1.27052i
$135$		−	3967.91i		−	2.52965i
$136$	574.218	+	331.525i	0.362050	+	0.209029i
$137$	−1809.49	−	1044.71i	−1.12843	−	0.651499i	−0.184890	−	0.982759i	$-0.559193\pi$
$137$	−1809.49	−	1044.71i	−1.12843	−	0.651499i	−0.943539	+	0.331260i	$0.892526\pi$
$138$			4861.02i			2.99853i
$139$	804.324	−	1393.13i	0.490805	−	0.850099i	−0.509139	−	0.860684i	$-0.670036\pi$
$139$	804.324	−	1393.13i	0.490805	−	0.850099i	0.999944	+	0.0105854i	$0.00336951\pi$
$140$	1035.61	+	1793.73i	0.625179	+	1.08284i
$141$	−2248.55	+	1298.20i	−1.34300	+	0.775379i
$142$	−1441.95			−0.852151
$143$	−267.892	−	440.535i	−0.156659	−	0.257618i
$144$	−2726.85			−1.57804
$145$	2062.10	−	1190.55i	1.18102	−	0.681862i
$146$	670.113	+	1160.67i	0.379856	+	0.657930i
$147$	460.637	−	797.847i	0.258454	−	0.447655i
$148$		−	2023.69i		−	1.12396i
$149$	410.734	+	237.137i	0.225830	+	0.130383i	0.608647	−	0.793441i	$-0.291713\pi$
$149$	410.734	+	237.137i	0.225830	+	0.130383i	−0.382817	+	0.923824i	$0.625046\pi$
$150$	1994.66	+	1151.62i	1.08576	+	0.626862i
$151$		−	2062.26i		−	1.11142i	−0.831376	−	0.555711i	$-0.812446\pi$
$151$		−	2062.26i		−	1.11142i	0.831376	−	0.555711i	$-0.187554\pi$
$152$	−580.588	+	1005.61i	−0.309815	+	0.536616i
$153$	2579.96	+	4468.62i	1.36325	+	2.36122i
$154$	626.830	−	361.900i	0.327996	−	0.189369i
$155$	1560.18			0.808496
$156$	96.5891	+	4242.98i	0.0495725	+	2.17763i
$157$	83.4582			0.0424248			0.0212124	−	0.999775i	$-0.493247\pi$
$157$	83.4582			0.0424248			0.0212124	+	0.999775i	$0.493247\pi$
$158$	764.796	−	441.555i	0.385088	−	0.222331i
$159$	983.844	+	1704.07i	0.490717	+	0.849946i
$160$	1739.50	−	3012.91i	0.859498	−	1.48870i
$161$		−	1943.61i		−	0.951418i
$162$	4104.71	+	2369.86i	1.99072	+	1.14934i
$163$	1558.51	+	899.805i	0.748907	+	0.432382i	0.825299	−	0.564696i	$-0.191007\pi$
$163$	1558.51	+	899.805i	0.748907	+	0.432382i	−0.0763920	+	0.997078i	$0.524340\pi$
$164$		−	4201.26i		−	2.00038i
$165$	690.349	−	1195.72i	0.325719	−	0.564161i
$166$	−1401.18	−	2426.92i	−0.655138	−	1.13473i
$167$	−441.604	+	254.960i	−0.204625	+	0.118140i	−0.598811	−	0.800890i	$-0.704360\pi$
$167$	−441.604	+	254.960i	−0.204625	+	0.118140i	0.394186	+	0.919031i	$0.371027\pi$
$168$	−1087.30			−0.499326
$169$	−2194.72	+	99.9752i	−0.998964	+	0.0455053i
$170$	−5036.51			−2.27225
$171$	−7825.74	+	4518.19i	−3.49970	+	2.02055i
$172$	−532.130	−	921.677i	−0.235899	−	0.408588i
$173$	−1267.69	+	2195.70i	−0.557113	+	0.964948i	0.440623	+	0.897692i	$0.354758\pi$
$173$	−1267.69	+	2195.70i	−0.557113	+	0.964948i	−0.997736	+	0.0672559i	$0.978576\pi$
$174$			6849.30i			2.98416i
$175$	−797.540	−	460.460i	−0.344505	−	0.198900i
$176$	−443.196	−	255.879i	−0.189813	−	0.109589i
$177$			978.570i			0.415558i
$178$	1519.13	−	2631.22i	0.639684	−	1.10797i
$179$	1854.09	+	3211.38i	0.774197	+	1.34095i	0.935245	+	0.354001i	$0.115179\pi$
$179$	1854.09	+	3211.38i	0.774197	+	1.34095i	−0.161048	+	0.986947i	$0.551487\pi$
$180$	−6738.41	+	3890.42i	−2.79028	+	1.61097i
$181$	−403.323			−0.165628			−0.0828142	−	0.996565i	$-0.526391\pi$
$181$	−403.323			−0.165628			−0.0828142	+	0.996565i	$0.526391\pi$
$182$	−70.1918	−	3083.39i	−0.0285877	−	1.25580i
$183$	−1233.30			−0.498188
$184$	812.538	−	469.119i	0.325550	−	0.187956i
$185$	1402.66	+	2429.47i	0.557434	+	0.965505i
$186$	−2243.95	+	3886.64i	−0.884594	+	1.53216i
$187$			968.382i			0.378690i
$188$	2378.13	+	1373.01i	0.922569	+	0.532645i
$189$	−3952.23	−	2281.82i	−1.52107	−	0.878192i
$190$		−	8820.27i		−	3.36784i
$191$	−903.482	+	1564.88i	−0.342270	+	0.592830i	−0.984854	−	0.173386i	$-0.944529\pi$
$191$	−903.482	+	1564.88i	−0.342270	+	0.592830i	0.642584	+	0.766216i	$0.277863\pi$
$192$	3281.85	+	5684.33i	1.23358	+	2.13662i
$193$	3418.25	−	1973.53i	1.27487	−	0.736049i	0.298973	−	0.954262i	$-0.403356\pi$
$193$	3418.25	−	1973.53i	1.27487	−	0.736049i	0.975901	+	0.218212i	$0.0700226\pi$
$194$	2892.14			1.07033
$195$	−3056.84	−	5026.82i	−1.12259	−	1.84604i
$196$	−974.365			−0.355089
$197$	55.5235	−	32.0565i	0.0200806	−	0.0115936i	−0.489926	−	0.871764i	$-0.662976\pi$
$197$	55.5235	−	32.0565i	0.0200806	−	0.0115936i	0.510007	+	0.860170i	$0.329643\pi$
$198$	1359.53	+	2354.78i	0.487968	+	0.845185i
$199$	−78.2942	+	135.610i	−0.0278901	+	0.0483071i	−0.879634	−	0.475652i	$-0.842212\pi$
$199$	−78.2942	+	135.610i	−0.0278901	+	0.0483071i	0.851743	+	0.523959i	$0.175546\pi$
$200$		−	444.554i		−	0.157174i
$201$	−4323.85	−	2496.37i	−1.51732	−	0.876023i
$202$	5003.36	+	2888.69i	1.74275	+	1.00618i
$203$		−	2738.60i		−	0.946859i
$204$	3985.59	−	6903.24i	1.36788	−	2.36923i
$205$	2911.97	+	5043.68i	0.992102	+	1.71837i
$206$	−360.628	+	208.209i	−0.121972	+	0.0704204i
$207$	7301.46			2.45163
$208$	−1863.20	+	1133.03i	−0.621105	+	0.377698i
$209$	−1695.90			−0.561280
$210$	7152.58	−	4129.55i	2.35036	−	1.35698i
$211$	−838.715	−	1452.70i	−0.273647	−	0.473971i	0.696146	−	0.717900i	$-0.254897\pi$
$211$	−838.715	−	1452.70i	−0.273647	−	0.473971i	−0.969793	+	0.243930i	$0.921563\pi$
$212$	1040.54	−	1802.27i	0.337097	−	0.583869i
$213$			3163.58i			1.01768i
$214$	3550.44	+	2049.85i	1.13413	+	0.654788i
$215$	1277.66	+	737.659i	0.405283	+	0.233990i
$216$		−	2203.00i		−	0.693960i
$217$	897.214	−	1554.02i	0.280677	−	0.486147i
$218$	−4469.98	−	7742.23i	−1.38874	−	2.40537i
$219$	2546.47	−	1470.21i	0.785729	−	0.453641i
$220$	−1460.26			−0.447504
$221$	3619.58	+	1981.33i	1.10172	+	0.603070i
$222$	−8069.55			−2.43961
$223$	−1636.16	+	944.636i	−0.491324	+	0.283666i	−0.725124	−	0.688619i	$-0.758217\pi$
$223$	−1636.16	+	944.636i	−0.491324	+	0.283666i	0.233800	+	0.972285i	$0.424884\pi$
$224$	−2000.67	−	3465.26i	−0.596765	−	1.03363i
$225$	1729.78	−	2996.07i	0.512528	−	0.887725i
$226$		−	5544.42i		−	1.63190i
$227$	−4378.20	−	2527.75i	−1.28014	−	0.739088i	−0.303264	−	0.952907i	$-0.598076\pi$
$227$	−4378.20	−	2527.75i	−1.28014	−	0.739088i	−0.976873	+	0.213819i	$0.931410\pi$
$228$	12089.4	+	6979.82i	3.51158	+	2.02741i
$229$		−	5531.10i		−	1.59609i	−0.602596	−	0.798047i	$-0.705867\pi$
$229$		−	5531.10i		−	1.59609i	0.602596	−	0.798047i	$-0.294133\pi$
$230$	−3563.42	+	6172.03i	−1.02159	+	1.76944i
$231$	−793.998	−	1375.24i	−0.226152	−	0.391707i
$232$	1144.89	−	661.001i	0.323990	−	0.187055i
$233$	2981.35			0.838260			0.419130	−	0.907926i	$-0.362335\pi$
$233$	2981.35			0.838260			0.419130	+	0.907926i	$0.362335\pi$
$234$	11583.2	−	263.685i	3.23597	−	0.0736652i
$235$	−3806.65			−1.05667
$236$	896.303	−	517.481i	0.247222	−	0.142734i
$237$	−968.758	−	1677.94i	−0.265517	−	0.459889i
$238$	−2896.35	+	5016.62i	−0.788833	+	1.36630i
$239$		−	688.362i		−	0.186303i	−0.995652	−	0.0931515i	$-0.970306\pi$
$239$		−	688.362i		−	0.186303i	0.995652	−	0.0931515i	$-0.0296941\pi$
$240$	−5057.19	−	2919.77i	−1.36017	−	0.785293i
$241$	4935.40	+	2849.45i	1.31916	+	0.761616i	0.983593	−	0.180401i	$-0.0577396\pi$
$241$	4935.40	+	2849.45i	1.31916	+	0.761616i	0.335564	+	0.942017i	$0.391073\pi$
$242$			510.297i			0.135550i
$243$	1250.66	−	2166.21i	0.330165	−	0.571862i
$244$	652.187	+	1129.62i	0.171115	+	0.296379i
$245$	1169.74	−	675.351i	0.305029	−	0.176108i
$246$	−16752.7			−4.34192
$247$	−3469.83	+	6338.85i	−0.893846	+	1.63292i
$248$	866.222			0.221795
$249$	−5324.59	+	3074.15i	−1.35515	+	0.782396i
$250$	−1887.24	−	3268.80i	−0.477439	−	0.826948i
$251$	2523.05	−	4370.04i	0.634475	−	1.09894i	−0.352151	−	0.935943i	$-0.614550\pi$
$251$	2523.05	−	4370.04i	0.634475	−	1.09894i	0.986626	−	0.163000i	$-0.0521170\pi$
$252$			8949.06i			2.23705i
$253$	1186.71	+	685.148i	0.294893	+	0.170256i
$254$	3593.05	+	2074.45i	0.887590	+	0.512451i
$255$			11049.9i			2.71362i
$256$	−855.314	+	1481.45i	−0.208817	+	0.361681i
$257$	−621.878	−	1077.12i	−0.150940	−	0.261437i	0.780633	−	0.624990i	$-0.214897\pi$
$257$	−621.878	−	1077.12i	−0.150940	−	0.261437i	−0.931573	+	0.363553i	$0.881564\pi$
$258$	−3675.23	+	2121.89i	−0.886859	+	0.512028i
$259$	3226.50			0.774074
$260$	−2987.72	+	5458.11i	−0.712656	+	1.30191i
$261$	10288.0			2.43988
$262$	−5748.92	+	3319.14i	−1.35561	+	0.782661i
$263$	−1973.88	−	3418.86i	−0.462793	−	0.801580i	0.536306	−	0.844024i	$-0.319819\pi$
$263$	−1973.88	−	3418.86i	−0.462793	−	0.801580i	−0.999099	+	0.0424430i	$0.986486\pi$
$264$	383.286	−	663.870i	0.0893545	−	0.154767i
$265$			2884.87i			0.668740i
$266$	−8785.43	−	5072.27i	−2.02507	−	1.16918i
$267$	−5772.80	−	3332.93i	−1.32318	−	0.763940i
$268$			5280.46i			1.20357i
$269$	4116.12	−	7129.33i	0.932953	−	1.61592i	0.154710	−	0.987960i	$-0.450556\pi$
$269$	4116.12	−	7129.33i	0.932953	−	1.61592i	0.778243	−	0.627963i	$-0.216111\pi$
$270$	8366.99	+	14492.1i	1.88592	+	3.26651i
$271$	2771.06	−	1599.87i	0.621144	−	0.358618i	−0.156170	−	0.987730i	$-0.549915\pi$
$271$	2771.06	−	1599.87i	0.621144	−	0.358618i	0.777314	+	0.629113i	$0.216582\pi$
$272$	4095.68			0.913005
$273$	−6764.86	+	153.998i	−1.49974	+	0.0341407i
$274$	8811.76			1.94284
$275$	562.285	−	324.635i	0.123298	−	0.0711864i
$276$	−5639.75	−	9768.33i	−1.22997	−	2.13038i
$277$	−2124.63	+	3679.96i	−0.460853	+	0.798221i	−0.999004	−	0.0446275i	$-0.985790\pi$
$277$	−2124.63	+	3679.96i	−0.460853	+	0.798221i	0.538150	+	0.842849i	$0.319123\pi$
$278$			6784.20i			1.46363i
$279$	5837.90	+	3370.51i	1.25271	+	0.723252i
$280$	−1380.54	−	797.055i	−0.294654	−	0.170118i
$281$		−	3379.10i		−	0.717366i	−0.933459	−	0.358683i	$-0.883226\pi$
$281$		−	3379.10i		−	0.717366i	0.933459	−	0.358683i	$-0.116774\pi$
$282$	5474.95	−	9482.90i	1.15613	−	2.00248i
$283$	1063.32	+	1841.72i	0.223348	+	0.386851i	0.955823	−	0.293944i	$-0.0949679\pi$
$283$	1063.32	+	1841.72i	0.223348	+	0.386851i	−0.732474	+	0.680795i	$0.761635\pi$
$284$	2897.63	−	1672.94i	0.605431	−	0.349546i
$285$	−19351.4			−4.02203
$286$	1907.37	+	1044.08i	0.394353	+	0.215866i
$287$	6698.35			1.37767
$288$	13017.8	−	7515.81i	2.66347	−	1.53775i
$289$	−1418.56	−	2457.01i	−0.288735	−	0.500104i
$290$	−5020.96	+	8696.55i	−1.01669	+	1.76096i
$291$		−	6345.27i		−	1.27823i
$292$	−2693.22	−	1554.93i	−0.539755	−	0.311628i
$293$	1769.14	+	1021.42i	0.352745	+	0.203658i	0.665894	−	0.746047i	$-0.268050\pi$
$293$	1769.14	+	1021.42i	0.352745	+	0.203658i	−0.313148	+	0.949704i	$0.601384\pi$
$294$			3885.32i			0.770737i
$295$	−717.351	+	1242.49i	−0.141579	+	0.245222i
$296$	778.763	+	1348.86i	0.152921	+	0.264867i
$297$	2786.42	−	1608.74i	0.544393	−	0.314305i
$298$	−2000.17			−0.388815
$299$	4988.95	−	3033.81i	0.964944	−	0.586789i
$300$	−5344.43			−1.02854
$301$	1469.49	−	848.411i	0.281395	−	0.162464i
$302$	4348.63	+	7532.04i	0.828594	+	1.43517i
$303$	6337.69	−	10977.2i	1.20162	−	2.08127i
$304$			7172.64i			1.35322i
$305$	−1565.92	−	904.086i	−0.293982	−	0.169731i
$306$	−18845.6	−	10880.5i	−3.52070	−	2.03268i
$307$		−	8839.19i		−	1.64325i	−0.570025	−	0.821627i	$-0.693067\pi$
$307$		−	8839.19i		−	1.64325i	0.570025	−	0.821627i	$-0.306933\pi$
$308$	−839.753	+	1454.49i	−0.155355	+	0.269083i
$309$	456.804	+	791.207i	0.0840992	+	0.145664i
$310$	−5698.28	+	3289.91i	−1.04400	+	0.602755i
$311$	−8714.80			−1.58897			−0.794487	−	0.607281i	$-0.792260\pi$
$311$	−8714.80			−1.58897			−0.794487	+	0.607281i	$0.792260\pi$
$312$	−1697.18	−	2790.92i	−0.307961	−	0.506425i
$313$	−1842.77			−0.332778			−0.166389	−	0.986060i	$-0.553211\pi$
$313$	−1842.77			−0.332778			−0.166389	+	0.986060i	$0.553211\pi$
$314$	−304.816	+	175.985i	−0.0547826	+	0.0316288i
$315$	−6202.76	−	10743.5i	−1.10948	−	1.92167i
$316$	−1024.58	+	1774.63i	−0.182397	+	0.315920i
$317$			7477.04i			1.32477i	0.749163	+	0.662385i	$0.230456\pi$
$317$			7477.04i			1.32477i	−0.749163	+	0.662385i	$0.769544\pi$
$318$	−7186.62	−	4149.20i	−1.26731	−	0.731684i
$319$	1672.11	+	965.391i	0.293480	+	0.169441i
$320$			9623.18i			1.68110i
$321$	4497.30	−	7789.55i	0.781978	−	1.35442i
$322$	4098.43	+	7098.69i	0.709307	+	1.22856i
$323$	11754.1	−	6786.26i	2.02482	−	1.16903i
$324$	−10998.0			−1.88581
$325$	−62.9641	−	2765.90i	−0.0107465	−	0.472075i
$326$	−7589.55			−1.28941
$327$	−16986.2	+	9806.99i	−2.87260	+	1.65849i
$328$	1616.74	+	2800.28i	0.272164	+	0.471401i
$329$	−2189.09	+	3791.61i	−0.366834	+	0.635375i
$330$			5822.86i			0.971327i
$331$	2063.48	+	1191.35i	0.342655	+	0.197832i	0.661446	−	0.749993i	$-0.269943\pi$
$331$	2063.48	+	1191.35i	0.342655	+	0.197832i	−0.318790	+	0.947825i	$0.603277\pi$
$332$	5631.42	+	3251.30i	0.930917	+	0.537465i
$333$			12120.8i			1.99464i
$334$	1075.25	−	1862.39i	0.176153	−	0.305106i
$335$	−3659.99	−	6339.29i	−0.596915	−	1.03389i
$336$	−5816.47	+	3358.14i	−0.944389	+	0.545243i
$337$	−1393.84			−0.225303			−0.112652	−	0.993635i	$-0.535934\pi$
$337$	−1393.84			−0.225303			−0.112652	+	0.993635i	$0.535934\pi$
$338$	7805.01	−	4993.08i	1.25603	−	0.803514i
$339$	−12164.3			−1.94889
$340$	10121.0	−	5843.35i	1.61438	−	0.932060i
$341$	632.558	+	1095.62i	0.100454	+	0.173992i
$342$	19054.7	−	33003.7i	3.01275	−	5.21824i
$343$		−	6905.08i		−	1.08700i
$344$	709.366	+	409.552i	0.111181	+	0.0641907i
$345$	13541.2	+	7818.03i	2.11315	+	1.22003i
$346$		−	10692.5i		−	1.66137i
$347$	−83.8013	+	145.148i	−0.0129645	+	0.0224552i	−0.872435	−	0.488730i	$-0.837460\pi$
$347$	−83.8013	+	145.148i	−0.0129645	+	0.0224552i	0.859470	+	0.511186i	$0.170794\pi$
$348$	−7946.55	−	13763.8i	−1.22408	−	2.12017i
$349$	−5209.19	+	3007.53i	−0.798973	+	0.461287i	−0.843112	−	0.537738i	$-0.819279\pi$
$349$	−5209.19	+	3007.53i	−0.798973	+	0.461287i	0.0441388	+	0.999025i	$0.485946\pi$
$350$	3883.82			0.593140
$351$	−312.021	−	13706.5i	−0.0474485	−	2.08432i
$352$	2821.04			0.427165
$353$	−10623.4	+	6133.45i	−1.60178	+	0.924789i	−0.610651	+	0.791900i	$0.709092\pi$
$353$	−10623.4	+	6133.45i	−1.60178	+	0.924789i	−0.991131	+	0.132889i	$0.957575\pi$
$354$	−2063.48	−	3574.05i	−0.309810	−	0.536606i
$355$	−2319.10	+	4016.80i	−0.346718	+	0.600534i
$356$			7049.99i			1.04957i
$357$	11006.3	+	6354.49i	1.63169	+	0.942059i
$358$	−13543.4	−	7819.31i	−1.99942	−	1.15437i
$359$		−	4060.42i		−	0.596939i	−0.954419	−	0.298469i	$-0.903524\pi$
$359$		−	4060.42i		−	0.596939i	0.954419	−	0.298469i	$-0.0964761\pi$
$360$	2994.25	−	5186.19i	0.438364	−	0.759268i
$361$	8455.05	+	14644.6i	1.23269	+	2.13509i
$362$	1473.06	−	850.473i	0.213874	−	0.123480i
$363$	1119.58			0.161880
$364$	3718.40	+	6114.71i	0.535432	+	0.880489i
$365$	4311.00			0.618214
$366$	4504.41	−	2600.62i	0.643304	−	0.371412i
$367$	462.027	+	800.255i	0.0657156	+	0.113823i	0.897011	−	0.442008i	$-0.145734\pi$
$367$	462.027	+	800.255i	0.0657156	+	0.113823i	−0.831296	+	0.555831i	$0.812400\pi$
$368$	2897.77	−	5019.09i	0.410480	−	0.710973i
$369$			25163.3i			3.55000i
$370$	−10245.9	−	5915.47i	−1.43962	−	0.831164i
$371$	2873.48	+	1659.00i	0.402112	+	0.232159i
$372$		−	10413.7i		−	1.45141i
$373$	117.872	−	204.160i	0.0163624	−	0.0283405i	−0.857728	−	0.514103i	$-0.828125\pi$
$373$	117.872	−	204.160i	0.0163624	−	0.0283405i	0.874091	+	0.485763i	$0.161458\pi$
$374$	−2041.99	−	3536.84i	−0.282324	−	0.488999i
$375$	−7171.64	+	4140.55i	−0.987578	+	0.570179i
$376$	−2113.47			−0.289878
$377$	7029.56	−	4274.72i	0.960320	−	0.583977i
$378$	19246.4			2.61886
$379$	8180.73	−	4723.14i	1.10875	−	0.640136i	0.170243	−	0.985402i	$-0.445545\pi$
$379$	8180.73	−	4723.14i	1.10875	−	0.640136i	0.938505	+	0.345266i	$0.112211\pi$
$380$	10233.3	+	17724.5i	1.38146	+	2.39276i
$381$	4551.27	−	7883.03i	0.611991	−	1.06000i
$382$		−	7620.56i		−	1.02069i
$383$	5025.90	+	2901.70i	0.670526	+	0.387128i	0.796276	−	0.604934i	$-0.206800\pi$
$383$	5025.90	+	2901.70i	0.670526	+	0.387128i	−0.125750	+	0.992062i	$0.540134\pi$
$384$	−7532.55	−	4348.92i	−1.00103	−	0.577942i
$385$		−	2328.19i		−	0.308197i
$386$	−8323.01	+	14415.9i	−1.09749	+	1.90090i
$387$	3187.18	+	5520.35i	0.418639	+	0.725104i
$388$	−5811.83	+	3355.46i	−0.760440	+	0.439041i
$389$	2931.38			0.382074			0.191037	−	0.981583i	$-0.438815\pi$
$389$	2931.38			0.382074			0.191037	+	0.981583i	$0.438815\pi$
$390$	21764.4	+	11913.7i	2.82586	+	1.54685i
$391$	−10966.7			−1.41844
$392$	649.447	−	374.958i	0.0836786	−	0.0483119i
$393$	7282.09	+	12612.9i	0.934689	+	1.61893i
$394$	−135.193	+	234.161i	−0.0172866	+	0.0299413i
$395$		−	2840.63i		−	0.361843i
$396$	−5464.02	−	3154.65i	−0.693377	−	0.400321i
$397$	−5816.73	−	3358.29i	−0.735348	−	0.424554i	0.0850272	−	0.996379i	$-0.472902\pi$
$397$	−5816.73	−	3358.29i	−0.735348	−	0.424554i	−0.820376	+	0.571825i	$0.806236\pi$
$398$		−	660.385i		−	0.0831711i
$399$	−11128.4	+	19275.0i	−1.39628	+	2.41843i
$400$	−1373.02	−	2378.13i	−0.171627	−	0.297267i
$401$	−7890.66	+	4555.67i	−0.982645	+	0.567330i	−0.903068	−	0.429498i	$-0.858690\pi$
$401$	−7890.66	+	4555.67i	−0.982645	+	0.567330i	−0.0795773	+	0.996829i	$0.525357\pi$
$402$	21056.1			2.61239
$403$	5389.40	−	122.687i	0.666166	−	0.0151649i
$404$	−13405.8			−1.65090
$405$	13203.3	−	7622.94i	1.61995	−	0.935276i
$406$	5774.80	+	10002.2i	0.705908	+	1.22267i
$407$	−1137.38	+	1970.00i	−0.138521	+	0.239925i
$408$			6134.99i			0.744429i
$409$	−683.942	−	394.874i	−0.0826865	−	0.0477391i	0.458087	−	0.888908i	$-0.348535\pi$
$409$	−683.942	−	394.874i	−0.0826865	−	0.0477391i	−0.540773	+	0.841168i	$0.681868\pi$
$410$	−21270.9	−	12280.7i	−2.56218	−	1.47928i
$411$		−	19332.7i		−	2.32022i
$412$	483.128	−	836.801i	0.0577718	−	0.100064i
$413$	825.054	+	1429.04i	0.0983009	+	0.170262i
$414$	−26667.3	+	15396.3i	−3.16576	+	1.82775i
$415$	−9014.16			−1.06624
$416$	5771.90	−	10544.4i	0.680266	−	1.24274i
$417$	14884.3			1.74793
$418$	6193.95	−	3576.08i	0.724775	−	0.418449i
$419$	6867.83	+	11895.4i	0.800753	+	1.38694i	0.919121	+	0.393975i	$0.128900\pi$
$419$	6867.83	+	11895.4i	0.800753	+	1.38694i	−0.118369	+	0.992970i	$0.537766\pi$
$420$	−9582.19	+	16596.8i	−1.11324	+	1.92820i
$421$		−	8608.86i		−	0.996604i	−0.867004	−	0.498302i	$-0.833957\pi$
$421$		−	8608.86i		−	0.996604i	0.867004	−	0.498302i	$-0.166043\pi$
$422$	6126.51	+	3537.14i	0.706715	+	0.408022i
$423$	−14243.7	−	8223.62i	−1.63724	−	0.945263i
$424$			1601.70i			0.183456i
$425$	−2598.11	+	4500.06i	−0.296534	+	0.513611i
$426$	−6670.94	−	11554.4i	−0.758705	−	1.31411i
$427$	−1801.03	+	1039.83i	−0.204117	+	0.117847i
$428$	−9512.92			−1.07436
$429$	2290.67	−	4184.70i	0.257796	−	0.470954i
$430$	−6221.91			−0.697784
$431$	−4230.85	+	2442.68i	−0.472838	+	0.272993i	−0.717427	−	0.696634i	$-0.754680\pi$
$431$	−4230.85	+	2442.68i	−0.472838	+	0.272993i	0.244589	+	0.969627i	$0.421347\pi$
$432$	−6804.03	−	11784.9i	−0.757775	−	1.31251i
$433$	−3577.60	+	6196.58i	−0.397063	+	0.687733i	−0.993362	−	0.115029i	$-0.963304\pi$
$433$	−3577.60	+	6196.58i	−0.397063	+	0.687733i	0.596299	+	0.802762i	$0.296637\pi$
$434$			7567.70i			0.837008i
$435$	19080.0	+	11015.8i	2.10302	+	1.21418i
$436$	17965.1	+	10372.1i	1.97333	+	1.13930i
$437$		−	19205.6i		−	2.10235i
$438$	−6200.35	+	10739.3i	−0.676402	+	1.17156i
$439$	−6165.69	−	10679.3i	−0.670324	−	1.16104i	−0.977812	−	0.209483i	$-0.932822\pi$
$439$	−6165.69	−	10679.3i	−0.670324	−	1.16104i	0.307488	−	0.951552i	$-0.400512\pi$
$440$	973.314	−	561.943i	0.105457	−	0.0608854i
$441$	5835.93			0.630161
$442$	−17397.8	+	396.052i	−1.87224	+	0.0426205i
$443$	15229.5			1.63335			0.816677	−	0.577095i	$-0.195814\pi$
$443$	15229.5			1.63335			0.816677	+	0.577095i	$0.195814\pi$
$444$	16215.9	−	9362.28i	1.73328	−	1.00071i
$445$	−4886.48	−	8463.63i	−0.520542	−	0.901606i
$446$	3983.84	−	6900.22i	0.422961	−	0.732589i
$447$			4388.32i			0.464341i
$448$	9585.17	+	5534.00i	1.01084	+	0.583609i
$449$	11231.4	+	6484.46i	1.18050	+	0.681560i	0.956129	−	0.292945i	$-0.0946351\pi$
$449$	11231.4	+	6484.46i	1.18050	+	0.681560i	0.224367	+	0.974505i	$0.427968\pi$
$450$			14590.1i			1.52841i
$451$	−2361.25	+	4089.80i	−0.246534	+	0.427010i
$452$	6432.63	+	11141.6i	0.669393	+	1.15942i
$453$	16525.1	−	9540.74i	1.71394	−	0.989544i
$454$	21320.7			2.20404
$455$	−8702.23	−	4763.52i	−0.896630	−	0.490808i
$456$	−10744.0			−1.10336
$457$	−8480.54	+	4896.24i	−0.868059	+	0.501174i	−0.866703	−	0.498825i	$-0.833765\pi$
$457$	−8480.54	+	4896.24i	−0.868059	+	0.501174i	−0.00135606	+	0.999999i	$0.500432\pi$
$458$	11663.2	+	20201.3i	1.18993	+	2.06102i
$459$	−12875.0	+	22300.2i	−1.30927	+	2.26772i
$460$		−	16537.1i		−	1.67619i
$461$	−5792.88	−	3344.52i	−0.585253	−	0.337896i	0.177965	−	0.984037i	$-0.443048\pi$
$461$	−5792.88	−	3344.52i	−0.585253	−	0.337896i	−0.763218	+	0.646141i	$0.776382\pi$
$462$	5799.86	+	3348.55i	0.584056	+	0.337205i
$463$			1840.73i			0.184764i	0.995724	+	0.0923821i	$0.0294481\pi$
$463$			1840.73i			0.184764i	−0.995724	+	0.0923821i	$0.970552\pi$
$464$	4083.04	−	7072.02i	0.408513	−	0.707566i
$465$	7217.95	+	12501.8i	0.719837	+	1.24679i
$466$	−10888.8	+	6286.67i	−1.08244	+	0.624945i
$467$	14833.8			1.46987			0.734933	−	0.678140i	$-0.237214\pi$
$467$	14833.8			1.46987			0.734933	+	0.678140i	$0.237214\pi$
$468$	−22970.8	+	13968.7i	−2.26886	+	1.37971i
$469$	−8419.00			−0.828898
$470$	13903.1	−	8026.95i	1.36447	−	0.787777i
$471$	386.106	+	668.756i	0.0377725	+	0.0654239i
$472$	−398.278	+	689.837i	−0.0388394	+	0.0672719i
$473$			1196.30i			0.116292i
$474$	7076.42	+	4085.57i	0.685719	+	0.395900i
$475$	−7880.80	−	4549.98i	−0.761254	−	0.439510i
$476$		−	13441.3i		−	1.29429i
$477$	−6232.28	+	10794.6i	−0.598232	+	1.03617i
$478$	1451.53	+	2514.12i	0.138894	+	0.240571i
$479$	−6367.00	+	3675.99i	−0.607340	+	0.350648i	−0.771924	−	0.635715i	$-0.780705\pi$
$479$	−6367.00	+	3675.99i	−0.607340	+	0.350648i	0.164584	+	0.986363i	$0.447372\pi$
$480$	32190.2			3.06098
$481$	5036.29	+	8281.92i	0.477412	+	0.785079i
$482$	−24034.2			−2.27122
$483$	15574.3	−	8991.83i	1.46720	−	0.847086i
$484$	−592.046	−	1025.45i	−0.0556016	−	0.0963049i
$485$	4651.47	−	8056.58i	0.435489	−	0.754289i
$486$			10548.9i			0.984585i
$487$	−2696.79	−	1556.99i	−0.250931	−	0.144875i	0.369259	−	0.929326i	$-0.379611\pi$
$487$	−2696.79	−	1556.99i	−0.250931	−	0.144875i	−0.620190	+	0.784451i	$0.712945\pi$
$488$	−869.409	−	501.954i	−0.0806482	−	0.0465622i
$489$			16651.2i			1.53987i
$490$	−2848.18	+	4933.19i	−0.262587	+	0.454814i
$491$	−3555.26	−	6157.89i	−0.326775	−	0.565992i	0.655095	−	0.755547i	$-0.272629\pi$
$491$	−3555.26	−	6157.89i	−0.326775	−	0.565992i	−0.981870	+	0.189555i	$0.939295\pi$
$492$	33664.9	−	19436.5i	3.08482	−	1.78102i
$493$	−15452.4			−1.41164
$494$	−693.592	−	30468.2i	−0.0631704	−	2.77496i
$495$	8746.19			0.794166
$496$	4633.84	−	2675.35i	0.419487	−	0.242191i
$497$	2667.29	+	4619.88i	0.240733	+	0.416961i
$498$	12964.7	−	22455.6i	1.16659	−	2.02060i
$499$		−	1126.51i		−	0.101061i	−0.998723	−	0.0505304i	$-0.983909\pi$
$499$		−	1126.51i		−	0.101061i	0.998723	−	0.0505304i	$-0.0160912\pi$
$500$	7584.91	+	4379.15i	0.678415	+	0.391683i
$501$	−4086.03	−	2359.07i	−0.364372	−	0.210370i
$502$			21281.0i			1.89207i
$503$	4345.51	−	7526.64i	0.385202	−	0.667189i	−0.606595	−	0.795011i	$-0.707465\pi$
$503$	4345.51	−	7526.64i	0.385202	−	0.667189i	0.991797	+	0.127821i	$0.0407984\pi$
$504$	−3443.81	−	5964.85i	−0.304364	−	0.527173i
$505$	16093.9	−	9291.83i	1.41816	−	0.818774i
$506$	−5778.99			−0.507722
$507$	−10954.7	−	17123.9i	−0.959593	−	1.50000i
$508$	−9627.09			−0.840813
$509$	−3937.96	+	2273.58i	−0.342922	+	0.197986i	−0.661563	−	0.749889i	$-0.730107\pi$
$509$	−3937.96	+	2273.58i	−0.342922	+	0.197986i	0.318642	+	0.947875i	$0.396773\pi$
$510$	−23300.6	−	40357.9i	−2.02308	−	3.50407i
$511$	2479.13	−	4293.98i	0.214619	−	0.371731i
$512$		−	14734.6i		−	1.27184i
$513$	−39053.5	−	22547.6i	−3.36112	−	1.94055i
$514$	4542.59	+	2622.67i	0.389816	+	0.225060i
$515$			1339.46i			0.114609i
$516$	4923.64	−	8527.99i	0.420060	−	0.727565i
$517$	−1543.36	−	2673.18i	−0.131290	−	0.227401i
$518$	−11784.2	+	6803.61i	−0.999553	+	0.577092i
$519$	−23459.1			−1.98408
$520$	−108.991	−	4787.76i	−0.00919146	−	0.403764i
$521$	16348.6			1.37475			0.687374	−	0.726304i	$-0.258763\pi$
$521$	16348.6			1.37475			0.687374	+	0.726304i	$0.258763\pi$
$522$	−37574.9	+	21693.9i	−3.15059	+	1.81899i
$523$	591.137	+	1023.88i	0.0494237	+	0.0856044i	0.889679	−	0.456587i	$-0.150928\pi$
$523$	591.137	+	1023.88i	0.0494237	+	0.0856044i	−0.840255	+	0.542191i	$0.817595\pi$
$524$	7701.73	−	13339.8i	0.642083	−	1.11212i
$525$		−	8520.98i		−	0.708355i
$526$	14418.4	+	8324.50i	1.19520	+	0.690048i
$527$	−8768.44	−	5062.46i	−0.724780	−	0.418452i
$528$		−	4735.14i		−	0.390285i
$529$	−1675.63	+	2902.28i	−0.137719	+	0.238537i
$530$	−6083.23	−	10536.5i	−0.498563	−	0.863537i
$531$	−5368.38	+	3099.43i	−0.438734	+	0.253303i
$532$	23539.4			1.91835
$533$	10455.5	+	17193.6i	0.849681	+	1.39726i
$534$	28112.1			2.27815
$535$	11420.4	−	6593.59i	0.922894	−	0.532833i
$536$	−2032.05	−	3519.61i	−0.163752	−	0.283627i
$537$	−17155.3	+	29713.9i	−1.37860	+	2.38780i
$538$			34718.1i			2.78216i
$539$	948.516	+	547.626i	0.0757986	+	0.0437624i
$540$	−33627.3	−	19414.7i	−2.67980	−	1.54718i
$541$			1844.72i			0.146600i	0.997310	+	0.0733002i	$0.0233531\pi$
$541$			1844.72i			0.146600i	−0.997310	+	0.0733002i	$0.976647\pi$
$542$	−6747.20	+	11686.5i	−0.534718	+	0.926158i
$543$	−1865.91	−	3231.85i	−0.147466	−	0.255418i
$544$	−19552.5	+	11288.6i	−1.54100	+	0.889698i
$545$	−28756.5			−2.26017
$546$	24382.7	−	14827.3i	1.91114	−	1.16218i
$547$	1629.03			0.127335			0.0636675	−	0.997971i	$-0.479720\pi$
$547$	1629.03			0.127335			0.0636675	+	0.997971i	$0.479720\pi$
$548$	−17707.4	+	10223.4i	−1.38034	+	0.796937i
$549$	−3906.25	−	6765.83i	−0.303670	−	0.525972i
$550$	−1369.10	+	2371.34i	−0.106143	+	0.183844i
$551$		−	27061.2i		−	2.09228i
$552$	7518.17	+	4340.62i	0.579700	+	0.334690i
$553$	−2829.41	−	1633.56i	−0.217575	−	0.125617i
$554$		−	17920.5i		−	1.37431i
$555$	−12978.3	+	22479.2i	−0.992613	+	1.71926i
$556$	−7871.02	−	13633.0i	−0.600370	−	1.03987i
$557$	−12394.3	+	7155.87i	−0.942844	+	0.544351i	−0.890851	−	0.454296i	$-0.849891\pi$
$557$	−12394.3	+	7155.87i	−0.942844	+	0.544351i	−0.0519936	+	0.998647i	$0.516558\pi$
$558$	−28429.2			−2.15681
$559$	4471.48	+	2447.65i	0.338325	+	0.185196i
$560$	−9846.89			−0.743048
$561$	−7759.71	+	4480.07i	−0.583984	+	0.337163i
$562$	7125.38	+	12341.5i	0.534815	+	0.926327i
$563$	3773.32	−	6535.57i	0.282462	−	0.489239i	−0.689528	−	0.724259i	$-0.742182\pi$
$563$	3773.32	−	6535.57i	0.282462	−	0.489239i	0.971991	+	0.235020i	$0.0755155\pi$
$564$			25408.1i			1.89694i
$565$	−15445.0	−	8917.16i	−1.15004	−	0.663978i
$566$	−7767.13	−	4484.36i	−0.576814	−	0.333024i
$567$		−	17534.9i		−	1.29876i
$568$	−1287.58	+	2230.15i	−0.0951154	+	0.164745i
$569$	−3412.55	−	5910.71i	−0.251426	−	0.435483i	0.712492	−	0.701680i	$-0.247566\pi$
$569$	−3412.55	−	5910.71i	−0.251426	−	0.435483i	−0.963919	+	0.266197i	$0.914233\pi$
$570$	70677.4	−	40805.6i	5.19360	−	2.99853i
$571$	20460.3			1.49954			0.749770	−	0.661699i	$-0.230164\pi$
$571$	20460.3			1.49954			0.749770	+	0.661699i	$0.230164\pi$
$572$	−5044.24	+	114.829i	−0.368724	+	0.00839380i
$573$	−16719.3			−1.21895
$574$	−24464.5	+	14124.6i	−1.77897	+	1.02709i
$575$	3676.42	+	6367.74i	0.266639	+	0.461832i
$576$	−20789.3	+	36008.0i	−1.50385	+	2.60475i
$577$		−	22770.7i		−	1.64291i	−0.570276	−	0.821453i	$-0.693164\pi$
$577$		−	22770.7i		−	1.64291i	0.570276	−	0.821453i	$-0.306836\pi$
$578$	10362.0	+	5982.53i	0.745682	+	0.430520i
$579$	31628.0	+	18260.4i	2.27014	+	1.31067i
$580$		−	23301.2i		−	1.66816i
$581$	−5183.77	+	8978.56i	−0.370153	+	0.641125i
$582$	13380.1	+	23174.9i	0.952957	+	1.65057i
$583$	−2025.87	+	1169.64i	−0.143916	+	0.0830899i
$584$	2393.49			0.169595
$585$	17894.9	−	32691.2i	1.26472	−	2.31045i
$586$	−8615.29			−0.607328
$587$	2497.30	−	1441.82i	0.175596	−	0.101380i	−0.409626	−	0.912254i	$-0.634341\pi$
$587$	2497.30	−	1441.82i	0.175596	−	0.101380i	0.585222	+	0.810873i	$0.301007\pi$
$588$	−4507.75	−	7807.65i	−0.316150	−	0.547588i
$589$	8865.72	−	15355.9i	0.620213	−	1.07424i
$590$		−	6050.62i		−	0.422203i
$591$	513.742	+	296.609i	0.0357572	+	0.0206444i
$592$	8331.95	+	4810.45i	0.578448	+	0.333967i
$593$			15329.1i			1.06154i	0.847517	+	0.530768i	$0.178096\pi$
$593$			15329.1i			1.06154i	−0.847517	+	0.530768i	$0.821904\pi$
$594$	−6784.60	+	11751.3i	−0.468645	+	0.811717i
$595$	9316.45	+	16136.6i	0.641911	+	1.11182i
$596$	4019.40	−	2320.60i	0.276243	−	0.159489i
$597$	−1448.86			−0.0993267
$598$	−11823.9	+	21600.5i	−0.808555	+	1.47711i
$599$	−16105.9			−1.09861			−0.549307	−	0.835621i	$-0.685108\pi$
$599$	−16105.9			−1.09861			−0.549307	+	0.835621i	$0.685108\pi$
$600$	3562.24	−	2056.66i	0.242380	−	0.139938i
$601$	−4813.52	−	8337.27i	−0.326702	−	0.565864i	0.655154	−	0.755496i	$-0.272604\pi$
$601$	−4813.52	−	8337.27i	−0.326702	−	0.565864i	−0.981855	+	0.189632i	$0.939271\pi$
$602$	−3578.03	+	6197.33i	−0.242242	+	0.419575i
$603$		−	31627.2i		−	2.13592i
$604$	−17477.3	−	10090.5i	−1.17739	−	0.679765i
$605$	1421.52	+	820.717i	0.0955259	+	0.0551519i
$606$			53456.3i			3.58336i
$607$	−7794.63	+	13500.7i	−0.521210	+	0.902762i	0.478486	+	0.878095i	$0.341186\pi$
$607$	−7794.63	+	13500.7i	−0.521210	+	0.902762i	−0.999696	+	0.0246664i	$0.992148\pi$
$608$	−19769.4	−	34241.6i	−1.31868	−	2.28401i
$609$	21944.6	−	12669.7i	1.46016	−	0.843027i
$610$	7625.66			0.506154
$611$	−13149.4	+	299.340i	−0.870653	+	0.0198200i
$612$	50494.3			3.33515
$613$	−6305.30	+	3640.37i	−0.415447	+	0.239858i	−0.693127	−	0.720815i	$-0.743768\pi$
$613$	−6305.30	+	3640.37i	−0.415447	+	0.239858i	0.277681	+	0.960673i	$0.410434\pi$
$614$	18638.9	+	32283.5i	1.22509	+	2.12192i
$615$	−26943.6	+	46667.6i	−1.76662	+	3.05987i
$616$		−	1292.63i		−	0.0845477i
$617$	13635.8	+	7872.62i	0.889718	+	0.513679i	0.873850	−	0.486195i	$-0.161616\pi$
$617$	13635.8	+	7872.62i	0.889718	+	0.513679i	0.0158677	+	0.999874i	$0.494949\pi$
$618$	−3336.78	−	1926.49i	−0.217193	−	0.125396i
$619$		−	17858.0i		−	1.15957i	−0.814770	−	0.579785i	$-0.803137\pi$
$619$		−	17858.0i		−	1.15957i	0.814770	−	0.579785i	$-0.196863\pi$
$620$	7633.89	−	13222.3i	0.494491	−	0.856483i
$621$	18218.6	+	31555.5i	1.17727	+	2.03910i
$622$	31829.2	−	18376.6i	2.05182	−	1.18462i
$623$	−11240.3			−0.722844
$624$	−17698.8	−	9688.18i	−1.13545	−	0.621535i
$625$	−19519.2			−1.24923
$626$	6730.38	−	3885.79i	0.429713	−	0.248095i
$627$	−7845.80	−	13589.3i	−0.499730	−	0.865558i
$628$	408.356	−	707.294i	0.0259478	−	0.0449428i
$629$		−	18205.3i		−	1.15404i
$630$	45308.9	+	26159.1i	2.86532	+	1.65429i
$631$	8172.24	+	4718.24i	0.515581	+	0.297671i	0.735125	−	0.677932i	$-0.237124\pi$
$631$	8172.24	+	4718.24i	0.515581	+	0.297671i	−0.219544	+	0.975603i	$0.570457\pi$
$632$		−	1577.14i		−	0.0992644i
$633$	7760.37	−	13441.4i	0.487278	−	0.843991i
$634$	−15766.6	−	27308.5i	−0.987651	−	1.71066i
$635$	11557.5	−	6672.72i	0.722275	−	0.417006i
$636$	19255.6			1.20052
$637$	3987.57	−	2424.87i	0.248027	−	0.150827i
$638$	−8142.75			−0.505289
$639$	−17355.2	+	10020.0i	−1.07443	+	0.620324i
$640$	−6376.04	−	11043.6i	−0.393805	−	0.682090i
$641$	−3371.82	+	5840.17i	−0.207768	+	0.359864i	−0.951011	−	0.309157i	$-0.899953\pi$
$641$	−3371.82	+	5840.17i	−0.207768	+	0.359864i	0.743243	+	0.669021i	$0.233286\pi$
$642$			37933.2i			2.33194i
$643$	−10340.7	−	5970.23i	−0.634213	−	0.366163i	0.148169	−	0.988962i	$-0.452662\pi$
$643$	−10340.7	−	5970.23i	−0.634213	−	0.366163i	−0.782382	+	0.622799i	$0.785995\pi$
$644$	−16471.8	−	9509.99i	−1.00789	−	0.581904i
$645$			13650.7i			0.833324i
$646$	−28619.9	+	49571.1i	−1.74309	+	3.01912i
$647$	10946.8	+	18960.4i	0.665167	+	1.15210i	0.979240	+	0.202704i	$0.0649730\pi$
$647$	10946.8	+	18960.4i	0.665167	+	1.15210i	−0.314073	+	0.949399i	$0.601694\pi$
$648$	7330.55	−	4232.30i	0.444400	−	0.256575i
$649$	−1163.37			−0.0703639
$650$	6062.31	+	9969.16i	0.365821	+	0.601573i
$651$	16603.3			0.999592
$652$	15251.4	−	8805.39i	0.916090	−	0.528905i
$653$	136.012	+	235.579i	0.00815093	+	0.0141178i	0.870072	−	0.492924i	$-0.164072\pi$
$653$	136.012	+	235.579i	0.00815093	+	0.0141178i	−0.861921	+	0.507042i	$0.830739\pi$
$654$	41359.3	−	71636.5i	2.47290	−	4.28319i
$655$			21352.9i			1.27378i
$656$	17297.5	+	9986.69i	1.02950	+	0.594382i
$657$	16130.9	+	9313.20i	0.957881	+	0.553033i
$658$		−	18464.2i		−	1.09394i
$659$	−2206.62	+	3821.98i	−0.130436	+	0.225923i	−0.923845	−	0.382767i	$-0.874971\pi$
$659$	−2206.62	+	3821.98i	−0.130436	+	0.225923i	0.793408	+	0.608690i	$0.208305\pi$
$660$	−6755.68	−	11701.2i	−0.398431	−	0.690102i
$661$	−25094.1	+	14488.1i	−1.47662	+	0.852528i	−0.999652	−	0.0263923i	$-0.991598\pi$
$661$	−25094.1	+	14488.1i	−1.47662	+	0.852528i	−0.476969	+	0.878920i	$0.658265\pi$
$662$	−10048.6			−0.589956
$663$	868.924	+	38170.2i	0.0508993	+	2.23591i
$664$	−5004.71			−0.292501
$665$	−28259.4	+	16315.6i	−1.64790	+	0.951416i
$666$	−25558.8	−	44269.1i	−1.48706	−	2.57566i
$667$	−10932.8	+	18936.2i	−0.634663	+	1.09927i
$668$			4990.03i			0.289027i
$669$	−15138.9	−	8740.42i	−0.874891	−	0.505119i
$670$	26734.9	+	15435.4i	1.54158	+	0.890031i
$671$		−	1466.20i		−	0.0843550i
$672$	18511.6	−	32063.0i	1.06265	−	1.84056i
$673$	13802.6	+	23906.9i	0.790568	+	1.36930i	0.925616	+	0.378465i	$0.123548\pi$
$673$	13802.6	+	23906.9i	0.790568	+	1.36930i	−0.135048	+	0.990839i	$0.543119\pi$
$674$	5090.74	−	2939.14i	0.290932	−	0.167969i
$675$	17264.6			0.984467
$676$	−9891.39	+	19089.1i	−0.562778	+	1.08609i
$677$	−24147.8			−1.37087			−0.685433	−	0.728135i	$-0.740387\pi$
$677$	−24147.8			−1.37087			−0.685433	+	0.728135i	$0.740387\pi$
$678$	44427.8	−	25650.4i	2.51658	−	1.45295i
$679$	−5349.84	−	9266.19i	−0.302368	−	0.523717i
$680$	−4497.32	+	7789.59i	−0.253624	+	0.439290i
$681$		−	46777.0i		−	2.63216i
$682$	−4620.60	−	2667.71i	−0.259431	−	0.149783i
$683$	−13590.6	−	7846.51i	−0.761388	−	0.439588i	0.0684059	−	0.997658i	$-0.478209\pi$
$683$	−13590.6	−	7846.51i	−0.761388	−	0.439588i	−0.829794	+	0.558070i	$0.811542\pi$
$684$			88429.0i			4.94323i
$685$	14172.0	−	24546.7i	0.790491	−	1.36917i
$686$	14560.5	+	25219.5i	0.810383	+	1.40363i
$687$	44321.1	−	25588.8i	2.46136	−	1.42107i
$688$	5059.65			0.280374
$689$	226.855	+	9965.31i	0.0125435	+	0.551013i
$690$	−65942.5			−3.63824
$691$	17643.5	−	10186.5i	0.971331	−	0.560799i	0.0716896	−	0.997427i	$-0.477161\pi$
$691$	17643.5	−	10186.5i	0.971331	−	0.560799i	0.899642	+	0.436628i	$0.143828\pi$
$692$	12405.5	+	21486.9i	0.681481	+	1.18036i
$693$	5029.67	−	8711.65i	0.275702	−	0.477530i
$694$		−	706.835i		−	0.0386615i
$695$	18898.6	+	10911.1i	1.03146	+	0.595514i
$696$	10593.3	+	6116.04i	0.576922	+	0.333086i
$697$		−	37794.9i		−	2.05392i
$698$	12683.7	−	21968.9i	0.687803	−	1.19131i
$699$	13792.7	+	23889.7i	0.746337	+	1.29269i
$700$	−7804.64	+	4506.01i	−0.421411	+	0.243302i
$701$	−14583.4			−0.785746			−0.392873	−	0.919593i	$-0.628519\pi$
$701$	−14583.4			−0.785746			−0.392873	+	0.919593i	$0.628519\pi$
$702$	30042.0	+	49402.5i	1.61519	+	2.65609i
$703$	31882.3			1.71048
$704$	−6757.78	+	3901.60i	−0.361780	+	0.208874i
$705$	−17610.9	−	30502.9i	−0.940799	−	1.62951i
$706$	25866.8	−	44802.6i	1.37891	−	2.38834i
$707$		−	21373.8i		−	1.13698i
$708$	8293.21	+	4788.09i	0.440223	+	0.254163i
$709$	20144.3	+	11630.3i	1.06705	+	0.616059i	0.927373	−	0.374139i	$-0.122062\pi$
$709$	20144.3	+	11630.3i	1.06705	+	0.616059i	0.139673	+	0.990198i	$0.455395\pi$
$710$		−	19560.8i		−	1.03395i
$711$	6136.71	−	10629.1i	0.323692	−	0.560650i
$712$	−2713.00	−	4699.05i	−0.142801	−	0.247338i
$713$	−12407.7	+	7163.57i	−0.651712	+	0.376266i
$714$	−53598.0			−2.80932
$715$	5976.10	−	3634.11i	0.312578	−	0.190081i
$716$	36287.8			1.89405
$717$	5515.89	−	3184.60i	0.287301	−	0.165873i
$718$	8562.08	+	14830.0i	0.445033	+	0.770820i
$719$	12852.8	−	22261.7i	0.666661	−	1.15469i	−0.312171	−	0.950026i	$-0.601056\pi$
$719$	12852.8	−	22261.7i	0.666661	−	1.15469i	0.978832	−	0.204665i	$-0.0656106\pi$
$720$		−	36991.2i		−	1.91470i
$721$	1334.17	+	770.283i	0.0689141	+	0.0397876i
$722$	−61761.0	−	35657.7i	−3.18353	−	1.83801i
$723$			52730.2i			2.71239i
$724$	−1973.43	+	3418.09i	−0.101301	+	0.175459i
$725$	5180.17	+	8972.32i	0.265361	+	0.459619i
$726$	−4089.04	+	2360.81i	−0.209034	+	0.120686i
$727$	6611.90			0.337306			0.168653	−	0.985675i	$-0.446058\pi$
$727$	6611.90			0.337306			0.168653	+	0.985675i	$0.446058\pi$
$728$	−4831.52	−	2644.74i	−0.245973	−	0.134643i
$729$	−7200.40			−0.365818
$730$	−15745.2	+	9090.47i	−0.798293	+	0.460895i
$731$	−4787.09	−	8291.49i	−0.242212	−	0.419524i
$732$	−6034.48	+	10452.0i	−0.304701	+	0.527757i
$733$			29018.2i			1.46222i	0.682257	+	0.731112i	$0.260998\pi$
$733$			29018.2i			1.46222i	−0.682257	+	0.731112i	$0.739002\pi$
$734$	−3374.94	−	1948.52i	−0.169716	−	0.0979854i
$735$	10823.3	+	6248.81i	0.543159	+	0.313593i
$736$			31947.6i			1.60001i
$737$	2967.80	−	5140.38i	0.148331	−	0.256918i
$738$	−53061.0	−	91904.3i	−2.64662	−	4.58407i
$739$	−7350.45	+	4243.78i	−0.365887	+	0.211245i	−0.671660	−	0.740859i	$-0.734418\pi$
$739$	−7350.45	+	4243.78i	−0.365887	+	0.211245i	0.305773	+	0.952104i	$0.401085\pi$
$740$	27452.5			1.36375
$741$	−66846.2	+	1521.72i	−3.31398	+	0.0754409i
$742$	−13993.1			−0.692323
$743$	29427.1	−	16989.7i	1.45299	−	0.838887i	0.454344	−	0.890826i	$-0.349874\pi$
$743$	29427.1	−	16989.7i	1.45299	−	0.838887i	0.998650	+	0.0519397i	$0.0165404\pi$
$744$	4007.44	+	6941.10i	0.197473	+	0.342034i
$745$	−3216.90	+	5571.84i	−0.158199	+	0.274009i
$746$			994.208i			0.0487943i
$747$	−33729.2	−	19473.6i	−1.65206	−	0.953817i
$748$	8206.87	+	4738.24i	0.401167	+	0.231614i
$749$		−	15167.1i		−	0.739911i
$750$	17462.1	−	30245.2i	0.850166	−	1.47253i
$751$	−1815.37	−	3144.30i	−0.0882072	−	0.152779i	0.818546	−	0.574441i	$-0.194780\pi$
$751$	−1815.37	−	3144.30i	−0.0882072	−	0.152779i	−0.906753	+	0.421661i	$0.861447\pi$
$752$	−11306.0	+	6527.50i	−0.548253	+	0.316534i
$753$	46689.9			2.25959
$754$	−16660.2	+	30435.6i	−0.804680	+	1.47003i
$755$	27975.8			1.34853
$756$	−38676.1	+	22329.7i	−1.86063	+	1.07424i
$757$	−16239.8	−	28128.1i	−0.779715	−	1.35051i	−0.932106	−	0.362186i	$-0.882030\pi$
$757$	−16239.8	−	28128.1i	−0.779715	−	1.35051i	0.152390	−	0.988320i	$-0.451303\pi$
$758$	−19919.1	+	34500.8i	−0.954476	+	1.65320i
$759$			12678.9i			0.606345i
$760$	−13641.6	−	7876.01i	−0.651098	−	0.375912i
$761$	22317.5	+	12885.0i	1.06309	+	0.613774i	0.926285	−	0.376825i	$-0.122984\pi$
$761$	22317.5	+	12885.0i	1.06309	+	0.613774i	0.136803	+	0.990598i	$0.456317\pi$
$762$			38388.4i			1.82502i
$763$	−16537.0	+	28642.9i	−0.784638	+	1.35903i
$764$	8841.37	+	15313.7i	0.418677	+	0.725170i
$765$	−60619.3	+	34998.6i	−2.86496	+	1.65409i
$766$	−24474.9			−1.15446
$767$	−2380.27	+	4348.38i	−0.112055	+	0.204708i
$768$	−15827.9			−0.743672
$769$	27639.7	−	15957.8i	1.29612	−	0.748313i	0.316385	−	0.948631i	$-0.397531\pi$
$769$	27639.7	−	15957.8i	1.29612	−	0.748313i	0.979731	+	0.200318i	$0.0641974\pi$
$770$	4909.38	+	8503.30i	0.229769	+	0.397971i
$771$	5754.05	−	9966.30i	0.268777	−	0.465535i
$772$		−	38625.4i		−	1.80072i
$773$	−17403.5	−	10047.9i	−0.809782	−	0.467528i	0.0370984	−	0.999312i	$-0.488189\pi$
$773$	−17403.5	−	10047.9i	−0.809782	−	0.467528i	−0.846880	+	0.531784i	$0.821522\pi$
$774$	−23281.2	−	13441.4i	−1.08117	−	0.624213i
$775$			6788.45i			0.314643i
$776$	2582.52	−	4473.06i	0.119468	−	0.206924i
$777$	14926.9	+	25854.2i	0.689189	+	1.19371i
$778$	−10706.3	+	6181.29i	−0.493368	+	0.284846i
$779$	66188.9			3.04424
$780$	−57558.4	+	1310.29i	−2.64221	+	0.0601484i
$781$	−3761.01			−0.172317
$782$	40053.8	−	23125.1i	1.83161	−	1.05748i
$783$	25670.5	+	44462.6i	1.17163	+	2.02933i
$784$	2316.13	−	4011.66i	0.105509	−	0.182747i
$785$			1132.16i			0.0514757i
$786$	−53193.0	−	30711.0i	−2.41391	−	1.39367i
$787$	−9711.04	−	5606.67i	−0.439849	−	0.253947i	0.263685	−	0.964609i	$-0.415062\pi$
$787$	−9711.04	−	5606.67i	−0.439849	−	0.253947i	−0.703534	+	0.710662i	$0.748396\pi$
$788$		−	627.403i		−	0.0283633i
$789$	18263.7	−	31633.6i	0.824086	−	1.42736i
$790$	5989.95	+	10374.9i	0.269763	+	0.467243i
$791$	−17763.9	+	10256.0i	−0.798496	+	0.461012i
$792$	4855.94			0.217864
$793$	−5480.32	−	2999.88i	−0.245412	−	0.134336i
$794$	28326.1			1.26606
$795$	−23116.7	+	13346.4i	−1.03127	+	0.595407i
$796$	766.178	+	1327.06i	0.0341162	+	0.0590909i
$797$	1396.68	−	2419.12i	0.0620739	−	0.107515i	−0.833318	−	0.552793i	$-0.813562\pi$
$797$	1396.68	−	2419.12i	0.0620739	−	0.107515i	0.895392	+	0.445278i	$0.146895\pi$
$798$		−	93864.3i		−	4.16386i
$799$	21393.9	+	12351.8i	0.947260	+	0.546901i
$800$	13109.3	+	7568.68i	0.579357	+	0.334492i
$801$		−	42225.7i		−	1.86263i
$802$	19212.8	−	33277.5i	0.845919	−	1.46517i
$803$	1747.85	+	3027.36i	0.0768121	+	0.133043i
$804$	−42312.7	+	24429.2i	−1.85604	+	1.07158i
$805$	26366.2			1.15439
$806$	−19425.1	+	11812.5i	−0.848907	+	0.516227i
$807$	76170.4			3.32258
$808$	8935.43	−	5158.87i	0.389044	−	0.224615i
$809$	−10231.0	−	17720.7i	−0.444628	−	0.770119i	0.553398	−	0.832917i	$-0.313331\pi$
$809$	−10231.0	−	17720.7i	−0.444628	−	0.770119i	−0.998026	+	0.0627980i	$0.979998\pi$
$810$	−32148.5	+	55682.8i	−1.39455	+	2.41542i
$811$			26215.5i			1.13508i	0.823345	+	0.567541i	$0.192105\pi$
$811$			26215.5i			1.13508i	−0.823345	+	0.567541i	$0.807895\pi$
$812$	−23209.2	−	13399.8i	−1.00306	−	0.579116i
$813$	25639.8	+	14803.1i	1.10606	+	0.638584i
$814$		−	9593.43i		−	0.413083i
$815$	−12206.4	+	21142.1i	−0.524626	+	0.908679i
$816$	18948.0	+	32819.0i	0.812885	+	1.40796i
$817$	14520.6	−	8383.47i	0.621801	−	0.358997i
$818$	3330.63			0.142363
$819$	−22271.2	−	36623.9i	−0.950208	−	1.56257i
$820$	56992.4			2.42715
$821$	−5815.14	+	3357.37i	−0.247198	+	0.142720i	−0.618481	−	0.785800i	$-0.712251\pi$
$821$	−5815.14	+	3357.37i	−0.247198	+	0.142720i	0.371283	+	0.928520i	$0.378918\pi$
$822$	40766.2	+	70609.2i	1.72979	+	2.99608i
$823$	−150.268	+	260.271i	−0.00636453	+	0.0110237i	−0.869190	−	0.494478i	$-0.835359\pi$
$823$	−150.268	+	260.271i	−0.00636453	+	0.0110237i	0.862826	+	0.505502i	$0.168693\pi$
$824$			743.675i			0.0314407i
$825$	5202.65	+	3003.75i	0.219555	+	0.126760i
$826$	−6026.72	−	3479.53i	−0.253870	−	0.146572i
$827$			5572.63i			0.234316i	0.993113	+	0.117158i	$0.0373784\pi$
$827$			5572.63i			0.234316i	−0.993113	+	0.117158i	$0.962622\pi$
$828$	35725.7	−	61878.6i	1.49946	−	2.59714i
$829$	−9219.67	−	15968.9i	−0.386264	−	0.669028i	0.605680	−	0.795708i	$-0.292901\pi$
$829$	−9219.67	−	15968.9i	−0.386264	−	0.669028i	−0.991944	+	0.126680i	$0.959568\pi$
$830$	32922.6	−	19007.9i	1.37682	−	0.794906i
$831$	−39317.0			−1.64127
$832$	756.729	+	33241.7i	0.0315323	+	1.38515i
$833$	−8765.47			−0.364593
$834$	−54362.2	+	31386.1i	−2.25709	+	1.30313i
$835$	−3458.68	−	5990.61i	−0.143344	−	0.248280i
$836$	−8297.92	+	14372.4i	−0.343289	+	0.594594i
$837$			33640.4i			1.38923i
$838$	−50167.0	−	28963.9i	−2.06801	−	1.19396i
$839$	3931.71	+	2269.98i	0.161785	+	0.0934067i	0.578707	−	0.815536i	$-0.303558\pi$
$839$	3931.71	+	2269.98i	0.161785	+	0.0934067i	−0.416921	+	0.908943i	$0.636891\pi$
$840$		−	14749.8i		−	0.605853i
$841$	−3210.13	+	5560.11i	−0.131622	+	0.227976i
$842$	18153.2	+	31442.3i	0.742994	+	1.28690i
$843$	27076.9	−	15632.9i	1.10626	−	0.638700i
$844$	−16415.1			−0.669470
$845$	−1356.22	−	29772.7i	−0.0552135	−	1.21208i
$846$	69363.5			2.81887
$847$	1634.95	−	943.939i	0.0663253	−	0.0382929i
$848$	4946.87	+	8568.24i	0.200326	+	0.346975i
$849$	−9838.53	+	17040.8i	−0.397712	+	0.688858i
$850$		−	21914.2i		−	0.884294i
$851$	−22309.8	−	12880.6i	−0.898672	−	0.518849i
$852$	26810.8	+	15479.2i	1.07808	+	0.622429i
$853$			8043.37i			0.322860i	0.986884	+	0.161430i	$0.0516106\pi$
$853$			8043.37i			0.322860i	−0.986884	+	0.161430i	$0.948389\pi$
$854$	4385.29	−	7595.54i	0.175716	−	0.304349i
$855$	−61291.8	−	106161.i	−2.45162	−	4.24633i
$856$	6340.69	−	3660.80i	0.253178	−	0.146172i
$857$	−23162.7			−0.923249			−0.461624	−	0.887075i	$-0.652733\pi$
$857$	−23162.7			−0.923249			−0.461624	+	0.887075i	$0.652733\pi$
$858$	457.887	+	20114.1i	0.0182191	+	0.800332i
$859$	13609.3			0.540562			0.270281	−	0.962781i	$-0.412883\pi$
$859$	13609.3			0.540562			0.270281	+	0.962781i	$0.412883\pi$
$860$	12503.1	−	7218.65i	0.495757	−	0.286225i
$861$	30988.9	+	53674.3i	1.22659	+	2.12452i
$862$	10301.6	−	17842.9i	0.407047	−	0.705026i
$863$			14662.7i			0.578359i	0.957275	+	0.289179i	$0.0933824\pi$
$863$			14662.7i			0.578359i	−0.957275	+	0.289179i	$0.906618\pi$
$864$	64963.8	+	37506.9i	2.55800	+	1.47686i
$865$	−29785.9	−	17196.9i	−1.17081	−	0.675968i
$866$		−	30175.8i		−	1.18408i
$867$	13125.5	−	22734.0i	0.514146	−	0.890526i
$868$	−8780.04	−	15207.5i	−0.343334	−	0.594672i
$869$	1994.81	−	1151.70i	0.0778702	−	0.0449584i
$870$	−92914.7			−3.62081
$871$	−13141.3	−	21610.2i	−0.511225	−	0.840682i
$872$	−15965.8			−0.620033
$873$	34809.8	−	20097.4i	1.34952	−	0.779146i
$874$	40498.2	+	70144.9i	1.56736	+	2.71475i
$875$	−6981.98	+	12093.1i	−0.269753	+	0.467226i
$876$		−	28774.6i		−	1.10982i
$877$	−9169.42	−	5293.97i	−0.353055	−	0.203836i	0.312975	−	0.949761i	$-0.398674\pi$
$877$	−9169.42	−	5293.97i	−0.353055	−	0.203836i	−0.666030	+	0.745925i	$0.732008\pi$
$878$	45038.1	+	26002.7i	1.73116	+	0.999488i
$879$			18901.7i			0.725299i
$880$	3471.15	−	6012.20i	0.132969	−	0.230308i
$881$	−18123.6	−	31391.0i	−0.693076	−	1.20044i	−0.970825	−	0.239789i	$-0.922922\pi$
$881$	−18123.6	−	31391.0i	−0.693076	−	1.20044i	0.277749	−	0.960654i	$-0.410412\pi$
$882$	−21314.6	+	12306.0i	−0.813720	+	0.469802i
$883$	13400.7			0.510724			0.255362	−	0.966846i	$-0.417805\pi$
$883$	13400.7			0.510724			0.255362	+	0.966846i	$0.417805\pi$
$884$	34501.8	−	20980.8i	1.31269	−	0.798258i
$885$	−13274.9			−0.504214
$886$	−55623.0	+	32113.9i	−2.10913	+	1.21771i
$887$	13067.0	+	22632.7i	0.494642	+	0.856744i	0.999981	−	0.00617642i	$-0.00196603\pi$
$887$	13067.0	+	22632.7i	0.494642	+	0.856744i	−0.505339	+	0.862921i	$0.668633\pi$
$888$	−7205.65	+	12480.6i	−0.272304	+	0.471644i
$889$		−	15349.1i		−	0.579069i
$890$	35693.9	+	20607.9i	1.34434	+	0.776156i
$891$	10706.3	+	6181.26i	0.402551	+	0.232413i
$892$			18488.2i			0.693981i
$893$	−21631.2	+	37466.4i	−0.810595	+	1.40399i
$894$	−9253.49	−	16027.5i	−0.346178	−	0.599598i
$895$	−43564.2	+	25151.8i	−1.62703	+	0.939365i
$896$	−14666.7			−0.546852
$897$	47390.7	+	25941.3i	1.76403	+	0.965612i
$898$	−54694.2			−2.03248
$899$	−17482.7	+	10093.7i	−0.648589	+	0.374463i
$900$	−16927.5	−	29319.2i	−0.626943	−	1.08590i
$901$	9360.79	−	16213.4i	0.346119	−	0.599495i
$902$		−	19916.3i		−	0.735190i
$903$	13596.7	+	7850.08i	0.501076	+	0.289296i
$904$	−8575.13	−	4950.85i	−0.315492	−	0.182149i
$905$		−	5471.30i		−	0.200964i
$906$	−40236.5	+	69691.6i	−1.47546	+	2.55557i
$907$	−11519.2	−	19951.9i	−0.421709	−	0.730422i	0.574398	−	0.818576i	$-0.305236\pi$
$907$	−11519.2	−	19951.9i	−0.421709	−	0.730422i	−0.996107	+	0.0881547i	$0.971903\pi$
$908$	−42844.5	+	24736.3i	−1.56591	+	0.904078i
$909$	80293.7			2.92978
$910$	41828.0	−	952.191i	1.52372	−	0.0346866i
$911$	32677.0			1.18841			0.594203	−	0.804315i	$-0.297468\pi$
$911$	32677.0			1.18841			0.594203	+	0.804315i	$0.297468\pi$
$912$	−57474.8	+	33183.1i	−2.08682	+	1.20483i
$913$	−3654.69	−	6330.10i	−0.132478	−	0.229459i
$914$	20649.1	−	35765.2i	0.747276	−	1.29432i
$915$		−	16730.5i		−	0.604472i
$916$	−46875.1	−	27063.4i	−1.69083	−	0.976199i
$917$	21268.5	+	12279.4i	0.765919	+	0.442204i
$918$		−	108596.i		−	3.90437i
$919$	19217.3	−	33285.4i	0.689795	−	1.19476i	−0.282109	−	0.959382i	$-0.591034\pi$
$919$	19217.3	−	33285.4i	0.689795	−	1.19476i	0.971904	−	0.235377i	$-0.0756326\pi$
$920$	6363.87	+	11022.5i	0.228055	+	0.395003i
$921$	70829.0	−	40893.1i	2.53409	−	1.46306i
$922$	28209.9			1.00764
$923$	−7695.08	+	14057.7i	−0.274417	+	0.501317i
$924$	−15539.9			−0.553275
$925$	−10570.8	+	6103.05i	−0.375746	+	0.216937i
$926$	−3881.48	−	6722.92i	−0.137747	−	0.238584i
$927$	−2893.68	+	5012.00i	−0.102525	+	0.177579i
$928$			45015.1i			1.59234i
$929$	46901.2	+	27078.4i	1.65638	+	0.956312i	0.974364	+	0.224975i	$0.0722301\pi$
$929$	46901.2	+	27078.4i	1.65638	+	0.956312i	0.682016	+	0.731337i	$0.261103\pi$
$930$	−52724.4	−	30440.5i	−1.85904	−	1.07331i
$931$		−	15350.7i		−	0.540385i
$932$	14587.6	−	25266.4i	0.512695	−	0.888014i
$933$	−40317.7	−	69832.2i	−1.41473	−	2.45038i
$934$	−54177.8	+	31279.6i	−1.89802	+	1.09582i
$935$	−13136.7			−0.459481
$936$	9935.33	−	18150.3i	0.346951	−	0.633826i
$937$	−46687.3			−1.62775			−0.813877	−	0.581037i	$-0.802647\pi$
$937$	−46687.3			−1.62775			−0.813877	+	0.581037i	$0.802647\pi$
$938$	30748.8	−	17752.8i	1.07035	−	0.617965i
$939$	−8525.30	−	14766.2i	−0.296286	−	0.513182i
$940$	−18625.7	+	32260.7i	−0.646280	+	1.11939i
$941$			46603.0i			1.61447i	0.590230	+	0.807235i	$0.299037\pi$
$941$			46603.0i			1.61447i	−0.590230	+	0.807235i	$0.700963\pi$
$942$	−2820.37	−	1628.34i	−0.0975504	−	0.0563207i
$943$	−46316.0	−	26740.6i	−1.59942	−	0.923428i
$944$			4920.36i			0.169644i
$945$	30954.2	−	53614.3i	1.06555	−	1.84558i
$946$	−2522.60	−	4369.27i	−0.0866985	−	0.150166i
$947$	−46323.5	+	26744.9i	−1.58956	+	0.917733i	−0.596180	+	0.802850i	$0.703316\pi$
$947$	−46323.5	+	26744.9i	−1.58956	+	0.917733i	−0.993379	+	0.114882i	$0.963351\pi$
$948$	−18960.3			−0.649581
$949$	14891.7	−	339.001i	0.509382	−	0.0115958i
$950$	38377.6			1.31067
$951$	−59914.0	+	34591.4i	−2.04295	+	1.17950i
$952$	5172.55	+	8959.11i	0.176096	+	0.305007i
$953$	−2579.35	+	4467.56i	−0.0876739	+	0.151856i	−0.906528	−	0.422147i	$-0.861277\pi$
$953$	−2579.35	+	4467.56i	−0.0876739	+	0.151856i	0.818854	+	0.574002i	$0.194610\pi$
$954$		−	52567.2i		−	1.78399i
$955$	−21228.4	−	12256.2i	−0.719305	−	0.415291i
$956$	−5833.75	−	3368.12i	−0.197361	−	0.113946i
$957$			17864.9i			0.603439i
$958$	15502.9	−	26851.8i	0.522834	−	0.905575i
$959$	−16299.8	−	28232.1i	−0.548852	−	0.950640i
$960$	−77111.1	+	44520.1i	−2.59245	+	1.49675i
$961$	16563.6			0.555993
$962$	−35857.9	−	19628.3i	−1.20177	−	0.657840i
$963$	56977.4			1.90661
$964$	48297.3	−	27884.4i	1.61364	−	0.931636i
$965$	26772.0	+	46370.5i	0.893079	+	1.54686i
$966$	−37921.5	+	65682.0i	−1.26305	+	2.18766i
$967$			39239.5i			1.30492i	0.757824	+	0.652459i	$0.226263\pi$
$967$			39239.5i			1.30492i	−0.757824	+	0.652459i	$0.773737\pi$
$968$	789.238	+	455.667i	0.0262056	+	0.0151298i
$969$	108757.	+	62791.1i	3.60556	+	2.08167i
$970$			39233.6i			1.29867i
$971$	−2317.01	+	4013.18i	−0.0765771	+	0.132635i	−0.901771	−	0.432214i	$-0.857732\pi$
$971$	−2317.01	+	4013.18i	−0.0765771	+	0.132635i	0.825194	+	0.564850i	$0.191066\pi$
$972$	−12238.8	−	21198.3i	−0.403869	−	0.699522i
$973$	21736.0	−	12549.3i	0.716161	−	0.413476i
$974$	13132.7			0.432033
$975$	21872.0	−	13300.5i	0.718425	−	0.436880i
$976$	−6201.18			−0.203376
$977$	−3969.56	+	2291.83i	−0.129987	+	0.0750481i	−0.563584	−	0.826059i	$-0.690578\pi$
$977$	−3969.56	+	2291.83i	−0.129987	+	0.0750481i	0.433596	+	0.901107i	$0.357244\pi$
$978$	−35111.9	−	60815.6i	−1.14801	−	1.98841i
$979$	3962.33	−	6862.96i	0.129353	−	0.224046i
$980$		−	13217.8i		−	0.430844i
$981$	−107601.	−	62123.5i	−3.50198	−	2.02187i
$982$	25969.9	+	14993.7i	0.843923	+	0.487239i
$983$		−	6067.88i		−	0.196882i	−0.995143	−	0.0984412i	$-0.968614\pi$
$983$		−	6067.88i		−	0.196882i	0.995143	−	0.0984412i	$-0.0313856\pi$
$984$	−14959.2	+	25910.1i	−0.484637	+	0.839415i
$985$	434.865	+	753.208i	0.0140670	+	0.0243647i
$986$	56436.9	−	32583.9i	1.82284	−	1.05242i
$987$	−40509.9			−1.30643
$988$	36742.9	+	60421.8i	1.18315	+	1.94562i
$989$	−13547.8			−0.435587
$990$	−31943.9	+	18442.8i	−1.02550	+	0.592071i
$991$	−10456.5	−	18111.2i	−0.335179	−	0.580546i	0.648340	−	0.761351i	$-0.275463\pi$
$991$	−10456.5	−	18111.2i	−0.335179	−	0.580546i	−0.983519	+	0.180804i	$0.942130\pi$
$992$	−14747.7	+	25543.8i	−0.472017	+	0.817557i
$993$			22046.4i			0.704552i
$994$	−19483.6	−	11248.8i	−0.621711	−	0.358945i
$995$	−1839.62	−	1062.11i	−0.0586129	−	0.0338402i
$996$			60166.6i			1.91411i
$997$	−11532.3	+	19974.5i	−0.366330	+	0.634503i	−0.988989	−	0.147991i	$-0.952719\pi$
$997$	−11532.3	+	19974.5i	−0.366330	+	0.634503i	0.622658	+	0.782494i	$0.286053\pi$
$998$	2375.43	+	4114.36i	0.0753435	+	0.130499i
$999$	−52383.9	+	30243.8i	−1.65901	+	0.957831i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.j.a.23.6	✓	72
13.2	odd	12		1859.4.a.m.1.6		36
13.4	even	6	inner	143.4.j.a.56.6	yes	72
13.11	odd	12		1859.4.a.l.1.31		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.j.a.23.6	✓	72	1.1	even	1	trivial
143.4.j.a.56.6	yes	72	13.4	even	6	inner
1859.4.a.l.1.31		36	13.11	odd	12
1859.4.a.m.1.6		36	13.2	odd	12

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.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.65232 + 2.10867i) q^{2} +(4.62634 + 8.01306i) q^{3} +(4.89294 - 8.47483i) q^{4} +13.5656i q^{5} +(-33.7937 - 19.5108i) q^{6} +(13.5120 + 7.80115i) q^{7} +7.53168i q^{8} +(-29.3061 + 50.7597i) q^{9} +O(q^{10})\)	\(q+(-3.65232 + 2.10867i) q^{2} +(4.62634 + 8.01306i) q^{3} +(4.89294 - 8.47483i) q^{4} +13.5656i q^{5} +(-33.7937 - 19.5108i) q^{6} +(13.5120 + 7.80115i) q^{7} +7.53168i q^{8} +(-29.3061 + 50.7597i) q^{9} +(-28.6052 - 49.5457i) q^{10} +(-9.52628 + 5.50000i) q^{11} +90.5458 q^{12} +(1.06674 + 46.8600i) q^{13} -65.8001 q^{14} +(-108.702 + 62.7590i) q^{15} +(23.2618 + 40.2905i) q^{16} +(44.0174 - 76.2403i) q^{17} -247.187i q^{18} +(133.517 + 77.0861i) q^{19} +(114.966 + 66.3756i) q^{20} +144.363i q^{21} +(23.1953 - 40.1755i) q^{22} +(-62.2862 - 107.883i) q^{23} +(-60.3518 + 34.8441i) q^{24} -59.0246 q^{25} +(-102.708 - 168.898i) q^{26} -292.498 q^{27} +(132.227 - 76.3412i) q^{28} +(-87.7628 - 152.010i) q^{29} +(264.675 - 458.431i) q^{30} -115.011i q^{31} +(-222.100 - 128.229i) q^{32} +(-88.1437 - 50.8898i) q^{33} +371.272i q^{34} +(-105.827 + 183.298i) q^{35} +(286.786 + 496.729i) q^{36} +(179.091 - 103.398i) q^{37} -650.196 q^{38} +(-370.557 + 225.339i) q^{39} -102.171 q^{40} +(371.800 - 214.659i) q^{41} +(-304.414 - 527.260i) q^{42} +(54.3773 - 94.1843i) q^{43} +107.645i q^{44} +(-688.584 - 397.554i) q^{45} +(454.978 + 262.681i) q^{46} +280.611i q^{47} +(-215.234 + 372.796i) q^{48} +(-49.7842 - 86.2287i) q^{49} +(215.577 - 124.463i) q^{50} +814.558 q^{51} +(402.350 + 220.243i) q^{52} +212.661 q^{53} +(1068.30 - 616.781i) q^{54} +(-74.6106 - 129.229i) q^{55} +(-58.7557 + 101.768i) q^{56} +1426.51i q^{57} +(641.075 + 370.125i) q^{58} +(91.5914 + 52.8803i) q^{59} +1228.30i q^{60} +(-66.6457 + 115.434i) q^{61} +(242.519 + 420.055i) q^{62} +(-791.968 + 457.243i) q^{63} +709.383 q^{64} +(-635.683 + 14.4710i) q^{65} +429.238 q^{66} +(-467.307 + 269.800i) q^{67} +(-430.749 - 746.079i) q^{68} +(576.314 - 998.206i) q^{69} -892.615i q^{70} +(296.102 + 170.955i) q^{71} +(-382.306 - 220.724i) q^{72} -317.790i q^{73} +(-436.065 + 755.287i) q^{74} +(-273.068 - 472.968i) q^{75} +(1306.58 - 754.356i) q^{76} -171.625 q^{77} +(878.229 - 1604.39i) q^{78} -209.400 q^{79} +(-546.564 + 315.559i) q^{80} +(-561.933 - 973.296i) q^{81} +(-905.288 + 1568.01i) q^{82} +664.488i q^{83} +(1223.45 + 706.361i) q^{84} +(1034.24 + 597.121i) q^{85} +458.654i q^{86} +(812.042 - 1406.50i) q^{87} +(-41.4242 - 71.7489i) q^{88} +(-623.905 + 360.212i) q^{89} +3353.24 q^{90} +(-351.148 + 641.494i) q^{91} -1219.05 q^{92} +(921.587 - 532.078i) q^{93} +(-591.715 - 1024.88i) q^{94} +(-1045.72 + 1811.24i) q^{95} -2372.93i q^{96} +(-593.899 - 342.888i) q^{97} +(363.655 + 209.956i) q^{98} -644.735i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 12 q^{3} + 152 q^{4} + 90 q^{6} - 36 q^{7} - 360 q^{9}+O(q^{10}) \) 72 * q - 12 * q^3 + 152 * q^4 + 90 * q^6 - 36 * q^7 - 360 * q^9	\( 72 q - 12 q^{3} + 152 q^{4} + 90 q^{6} - 36 q^{7} - 360 q^{9} - 56 q^{10} - 132 q^{12} - 46 q^{13} + 328 q^{14} - 644 q^{16} + 138 q^{17} + 492 q^{19} + 540 q^{20} - 44 q^{22} + 46 q^{23} + 720 q^{24} - 1636 q^{25} - 902 q^{26} + 48 q^{27} - 714 q^{28} - 262 q^{29} + 104 q^{30} + 144 q^{32} - 68 q^{35} + 1960 q^{36} + 630 q^{37} - 448 q^{38} - 1612 q^{39} + 216 q^{40} + 126 q^{41} - 82 q^{42} + 436 q^{43} - 570 q^{45} - 1590 q^{46} + 1944 q^{48} + 1192 q^{49} + 1290 q^{50} - 1424 q^{51} + 590 q^{52} + 292 q^{53} - 528 q^{54} - 440 q^{55} - 102 q^{56} - 1128 q^{58} + 504 q^{59} + 590 q^{61} + 1776 q^{62} + 1884 q^{63} - 5028 q^{64} + 994 q^{65} + 2156 q^{66} + 3396 q^{67} + 1530 q^{68} + 12 q^{69} - 1014 q^{71} - 1062 q^{72} - 1568 q^{74} + 4688 q^{75} + 7872 q^{76} - 1232 q^{77} - 4964 q^{78} - 2928 q^{79} - 558 q^{80} - 3780 q^{81} - 4072 q^{82} + 696 q^{84} + 4662 q^{85} + 1832 q^{87} + 924 q^{88} + 1014 q^{89} + 6844 q^{90} + 2900 q^{91} - 1336 q^{92} - 4092 q^{93} + 4166 q^{94} - 256 q^{95} - 5070 q^{97} - 8550 q^{98}+O(q^{100}) \) 72 * q - 12 * q^3 + 152 * q^4 + 90 * q^6 - 36 * q^7 - 360 * q^9 - 56 * q^10 - 132 * q^12 - 46 * q^13 + 328 * q^14 - 644 * q^16 + 138 * q^17 + 492 * q^19 + 540 * q^20 - 44 * q^22 + 46 * q^23 + 720 * q^24 - 1636 * q^25 - 902 * q^26 + 48 * q^27 - 714 * q^28 - 262 * q^29 + 104 * q^30 + 144 * q^32 - 68 * q^35 + 1960 * q^36 + 630 * q^37 - 448 * q^38 - 1612 * q^39 + 216 * q^40 + 126 * q^41 - 82 * q^42 + 436 * q^43 - 570 * q^45 - 1590 * q^46 + 1944 * q^48 + 1192 * q^49 + 1290 * q^50 - 1424 * q^51 + 590 * q^52 + 292 * q^53 - 528 * q^54 - 440 * q^55 - 102 * q^56 - 1128 * q^58 + 504 * q^59 + 590 * q^61 + 1776 * q^62 + 1884 * q^63 - 5028 * q^64 + 994 * q^65 + 2156 * q^66 + 3396 * q^67 + 1530 * q^68 + 12 * q^69 - 1014 * q^71 - 1062 * q^72 - 1568 * q^74 + 4688 * q^75 + 7872 * q^76 - 1232 * q^77 - 4964 * q^78 - 2928 * q^79 - 558 * q^80 - 3780 * q^81 - 4072 * q^82 + 696 * q^84 + 4662 * q^85 + 1832 * q^87 + 924 * q^88 + 1014 * q^89 + 6844 * q^90 + 2900 * q^91 - 1336 * q^92 - 4092 * q^93 + 4166 * q^94 - 256 * q^95 - 5070 * q^97 - 8550 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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