LMFDB - Embedded newform 43.3.d.a.37.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,3,Mod(7,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("43.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	43.d (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:	$1.17166513675$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 37x^{10} + 483x^{8} + 2718x^{6} + 6923x^{4} + 7253x^{2} + 1849 $ x^12 + 37x^10 + 483x^8 + 2718x^6 + 6923x^4 + 7253*x^2 + 1849
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			37.3
Root			$-1.51156i$ of defining polynomial
Character	$\chi$	$=$	43.37
Dual form			43.3.d.a.7.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.51156i q^{2} +(-3.66976 - 2.11873i) q^{3} +1.71518 q^{4} +(-4.51092 - 2.60438i) q^{5} +(-3.20260 + 5.54707i) q^{6} +(1.23619 - 0.713712i) q^{7} -8.63885i q^{8} +(4.47807 + 7.75625i) q^{9} +O(q^{10})$	\(q-1.51156i q^{2} +(-3.66976 - 2.11873i) q^{3} +1.71518 q^{4} +(-4.51092 - 2.60438i) q^{5} +(-3.20260 + 5.54707i) q^{6} +(1.23619 - 0.713712i) q^{7} -8.63885i q^{8} +(4.47807 + 7.75625i) q^{9} +(-3.93669 + 6.81854i) q^{10} +19.5852 q^{11} +(-6.29427 - 3.63400i) q^{12} +(4.99698 + 8.65502i) q^{13} +(-1.07882 - 1.86857i) q^{14} +(11.0360 + 19.1149i) q^{15} -6.19747 q^{16} +(-12.5438 - 21.7264i) q^{17} +(11.7241 - 6.76889i) q^{18} +(9.29850 + 5.36849i) q^{19} +(-7.73701 - 4.46697i) q^{20} -6.04866 q^{21} -29.6043i q^{22} +(-16.7391 + 28.9930i) q^{23} +(-18.3034 + 31.7025i) q^{24} +(1.06559 + 1.84565i) q^{25} +(13.0826 - 7.55325i) q^{26} +0.185841i q^{27} +(2.12027 - 1.22414i) q^{28} +(13.9164 - 8.03462i) q^{29} +(28.8934 - 16.6816i) q^{30} +(3.71424 - 6.43325i) q^{31} -25.1875i q^{32} +(-71.8730 - 41.4959i) q^{33} +(-32.8409 + 18.9607i) q^{34} -7.43511 q^{35} +(7.68068 + 13.3033i) q^{36} +(18.9142 + 10.9201i) q^{37} +(8.11482 - 14.0553i) q^{38} -42.3491i q^{39} +(-22.4989 + 38.9692i) q^{40} -22.3015 q^{41} +9.14294i q^{42} +(35.8442 + 23.7528i) q^{43} +33.5921 q^{44} -46.6504i q^{45} +(43.8248 + 25.3022i) q^{46} +78.3686 q^{47} +(22.7432 + 13.1308i) q^{48} +(-23.4812 + 40.6707i) q^{49} +(2.78982 - 1.61070i) q^{50} +106.308i q^{51} +(8.57070 + 14.8449i) q^{52} +(-13.1640 + 22.8006i) q^{53} +0.280911 q^{54} +(-88.3474 - 51.0074i) q^{55} +(-6.16565 - 10.6792i) q^{56} +(-22.7488 - 39.4021i) q^{57} +(-12.1448 - 21.0355i) q^{58} +39.1712 q^{59} +(18.9286 + 32.7854i) q^{60} +(-27.5478 + 15.9047i) q^{61} +(-9.72426 - 5.61430i) q^{62} +(11.0715 + 6.39211i) q^{63} -62.8625 q^{64} -52.0561i q^{65} +(-62.7237 + 108.641i) q^{66} +(61.2076 - 106.015i) q^{67} +(-21.5147 - 37.2646i) q^{68} +(122.857 - 70.9315i) q^{69} +11.2386i q^{70} +(-110.307 + 63.6857i) q^{71} +(67.0051 - 38.6854i) q^{72} +(14.9276 - 8.61845i) q^{73} +(16.5064 - 28.5900i) q^{74} -9.03079i q^{75} +(15.9486 + 9.20790i) q^{76} +(24.2110 - 13.9782i) q^{77} -64.0134 q^{78} +(-18.2494 - 31.6090i) q^{79} +(27.9563 + 16.1406i) q^{80} +(40.6964 - 70.4882i) q^{81} +33.7102i q^{82} +(-42.8675 + 74.2487i) q^{83} -10.3745 q^{84} +130.675i q^{85} +(35.9038 - 54.1808i) q^{86} -68.0929 q^{87} -169.194i q^{88} +(-11.1803 - 6.45493i) q^{89} -70.5150 q^{90} +(12.3544 + 7.13281i) q^{91} +(-28.7105 + 49.7281i) q^{92} +(-27.2607 + 15.7390i) q^{93} -118.459i q^{94} +(-27.9632 - 48.4336i) q^{95} +(-53.3657 + 92.4321i) q^{96} -113.142 q^{97} +(61.4763 + 35.4934i) q^{98} +(87.7041 + 151.908i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 26 q^{4} - 3 q^{5} - 9 q^{6} + 9 q^{7} - 12 q^{9}+O(q^{10}) $ 12 * q - 26 * q^4 - 3 * q^5 - 9 * q^6 + 9 * q^7 - 12 * q^9	$ 12 q - 26 q^{4} - 3 q^{5} - 9 q^{6} + 9 q^{7} - 12 q^{9} - q^{10} + 28 q^{11} - 6 q^{12} + 24 q^{13} - 18 q^{14} - 13 q^{15} + 110 q^{16} - 7 q^{17} + 33 q^{18} + 66 q^{19} - 99 q^{20} - 80 q^{21} - 16 q^{23} - 2 q^{24} - 21 q^{25} + 9 q^{26} - 192 q^{28} - 111 q^{29} + 99 q^{30} - 29 q^{31} - 114 q^{33} + 213 q^{34} + 38 q^{35} + 152 q^{36} + 120 q^{37} + 172 q^{38} - 29 q^{40} + 94 q^{41} + 5 q^{43} - 174 q^{44} + 156 q^{46} - 18 q^{47} - 213 q^{48} - 99 q^{49} - 198 q^{50} - 234 q^{52} - 58 q^{53} + 128 q^{54} - 258 q^{55} + 315 q^{56} + 51 q^{57} - 196 q^{58} + 336 q^{59} - 5 q^{60} + 204 q^{61} + 261 q^{62} - 153 q^{63} - 604 q^{64} - 201 q^{66} + 115 q^{67} - 106 q^{68} + 423 q^{69} - 66 q^{71} + 294 q^{72} + 249 q^{73} - 214 q^{74} - 438 q^{76} + 117 q^{77} + 136 q^{78} + 236 q^{79} + 681 q^{80} + 110 q^{81} - 4 q^{83} + 248 q^{84} + 102 q^{86} - 408 q^{87} - 45 q^{89} - 44 q^{90} - 156 q^{91} - 483 q^{92} - 567 q^{93} - 389 q^{95} - 278 q^{96} - 370 q^{97} - 879 q^{98} + 157 q^{99}+O(q^{100}) $ 12 * q - 26 * q^4 - 3 * q^5 - 9 * q^6 + 9 * q^7 - 12 * q^9 - q^10 + 28 * q^11 - 6 * q^12 + 24 * q^13 - 18 * q^14 - 13 * q^15 + 110 * q^16 - 7 * q^17 + 33 * q^18 + 66 * q^19 - 99 * q^20 - 80 * q^21 - 16 * q^23 - 2 * q^24 - 21 * q^25 + 9 * q^26 - 192 * q^28 - 111 * q^29 + 99 * q^30 - 29 * q^31 - 114 * q^33 + 213 * q^34 + 38 * q^35 + 152 * q^36 + 120 * q^37 + 172 * q^38 - 29 * q^40 + 94 * q^41 + 5 * q^43 - 174 * q^44 + 156 * q^46 - 18 * q^47 - 213 * q^48 - 99 * q^49 - 198 * q^50 - 234 * q^52 - 58 * q^53 + 128 * q^54 - 258 * q^55 + 315 * q^56 + 51 * q^57 - 196 * q^58 + 336 * q^59 - 5 * q^60 + 204 * q^61 + 261 * q^62 - 153 * q^63 - 604 * q^64 - 201 * q^66 + 115 * q^67 - 106 * q^68 + 423 * q^69 - 66 * q^71 + 294 * q^72 + 249 * q^73 - 214 * q^74 - 438 * q^76 + 117 * q^77 + 136 * q^78 + 236 * q^79 + 681 * q^80 + 110 * q^81 - 4 * q^83 + 248 * q^84 + 102 * q^86 - 408 * q^87 - 45 * q^89 - 44 * q^90 - 156 * q^91 - 483 * q^92 - 567 * q^93 - 389 * q^95 - 278 * q^96 - 370 * q^97 - 879 * q^98 + 157 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		−	1.51156i		−	0.755782i	−0.925850	−	0.377891i	$-0.876649\pi$
$2$		−	1.51156i		−	0.755782i	0.925850	−	0.377891i	$-0.123351\pi$
$3$	−3.66976	−	2.11873i	−1.22325	−	0.706245i	−0.257642	−	0.966240i	$-0.582946\pi$
$3$	−3.66976	−	2.11873i	−1.22325	−	0.706245i	−0.965610	+	0.259996i	$0.916279\pi$
$4$	1.71518			0.428794
$5$	−4.51092	−	2.60438i	−0.902184	−	0.520876i	−0.0242756	−	0.999705i	$-0.507728\pi$
$5$	−4.51092	−	2.60438i	−0.902184	−	0.520876i	−0.877908	+	0.478829i	$0.841061\pi$
$6$	−3.20260	+	5.54707i	−0.533767	+	0.924512i
$7$	1.23619	−	0.713712i	0.176598	−	0.101959i	−0.409095	−	0.912492i	$-0.634156\pi$
$7$	1.23619	−	0.713712i	0.176598	−	0.101959i	0.585693	+	0.810533i	$0.300822\pi$
$8$		−	8.63885i		−	1.07986i
$9$	4.47807	+	7.75625i	0.497564	+	0.861805i
$10$	−3.93669	+	6.81854i	−0.393669	+	0.681854i
$11$	19.5852			1.78048			0.890238	−	0.455496i	$-0.150538\pi$
$11$	19.5852			1.78048			0.890238	+	0.455496i	$0.150538\pi$
$12$	−6.29427	−	3.63400i	−0.524523	−	0.302833i
$13$	4.99698	+	8.65502i	0.384383	+	0.665771i	0.991683	−	0.128701i	$-0.0410808\pi$
$13$	4.99698	+	8.65502i	0.384383	+	0.665771i	−0.607300	+	0.794472i	$0.707748\pi$
$14$	−1.07882	−	1.86857i	−0.0770587	−	0.133469i
$15$	11.0360	+	19.1149i	0.735732	+	1.27433i
$16$	−6.19747			−0.387342
$17$	−12.5438	−	21.7264i	−0.737868	−	1.27802i	−0.953454	−	0.301540i	$-0.902499\pi$
$17$	−12.5438	−	21.7264i	−0.737868	−	1.27802i	0.215586	−	0.976485i	$-0.430834\pi$
$18$	11.7241	−	6.76889i	0.651337	−	0.376049i
$19$	9.29850	+	5.36849i	0.489395	+	0.282552i	0.724323	−	0.689460i	$-0.242152\pi$
$19$	9.29850	+	5.36849i	0.489395	+	0.282552i	−0.234929	+	0.972013i	$0.575486\pi$
$20$	−7.73701	−	4.46697i	−0.386851	−	0.223348i
$21$	−6.04866			−0.288032
$22$		−	29.6043i		−	1.34565i
$23$	−16.7391	+	28.9930i	−0.727788	+	1.26057i	0.230029	+	0.973184i	$0.426118\pi$
$23$	−16.7391	+	28.9930i	−0.727788	+	1.26057i	−0.957816	+	0.287381i	$0.907215\pi$
$24$	−18.3034	+	31.7025i	−0.762643	+	1.32094i
$25$	1.06559	+	1.84565i	0.0426235	+	0.0738261i
$26$	13.0826	−	7.55325i	0.503178	−	0.290510i
$27$			0.185841i			0.00688300i
$28$	2.12027	−	1.22414i	0.0757241	−	0.0437193i
$29$	13.9164	−	8.03462i	0.479875	−	0.277056i	−0.240490	−	0.970652i	$-0.577308\pi$
$29$	13.9164	−	8.03462i	0.479875	−	0.277056i	0.720364	+	0.693596i	$0.243975\pi$
$30$	28.8934	−	16.6816i	0.963112	−	0.556053i
$31$	3.71424	−	6.43325i	0.119814	−	0.207524i	−0.799880	−	0.600160i	$-0.795103\pi$
$31$	3.71424	−	6.43325i	0.119814	−	0.207524i	0.919694	+	0.392636i	$0.128437\pi$
$32$		−	25.1875i		−	0.787110i
$33$	−71.8730	−	41.4959i	−2.17797	−	1.25745i
$34$	−32.8409	+	18.9607i	−0.965908	+	0.557667i
$35$	−7.43511			−0.212432
$36$	7.68068	+	13.3033i	0.213352	+	0.369537i
$37$	18.9142	+	10.9201i	0.511194	+	0.295138i	0.733324	−	0.679879i	$-0.237968\pi$
$37$	18.9142	+	10.9201i	0.511194	+	0.295138i	−0.222130	+	0.975017i	$0.571301\pi$
$38$	8.11482	−	14.0553i	0.213548	−	0.369876i
$39$		−	42.3491i		−	1.08587i
$40$	−22.4989	+	38.9692i	−0.562471	+	0.974229i
$41$	−22.3015			−0.543940			−0.271970	−	0.962306i	$-0.587675\pi$
$41$	−22.3015			−0.543940			−0.271970	+	0.962306i	$0.587675\pi$
$42$			9.14294i			0.217689i
$43$	35.8442	+	23.7528i	0.833586	+	0.552390i
$43$	35.8442	+	23.7528i	0.833586	+	0.552390i
$44$	33.5921			0.763457
$45$		−	46.6504i		−	1.03668i
$46$	43.8248	+	25.3022i	0.952712	+	0.550049i
$47$	78.3686			1.66742			0.833709	−	0.552204i	$-0.186213\pi$
$47$	78.3686			1.66742			0.833709	+	0.552204i	$0.186213\pi$
$48$	22.7432	+	13.1308i	0.473817	+	0.273558i
$49$	−23.4812	+	40.6707i	−0.479209	+	0.830014i
$50$	2.78982	−	1.61070i	0.0557964	−	0.0322141i
$51$			106.308i			2.08446i
$52$	8.57070	+	14.8449i	0.164821	+	0.285478i
$53$	−13.1640	+	22.8006i	−0.248376	+	0.430201i	−0.963076	−	0.269231i	$-0.913230\pi$
$53$	−13.1640	+	22.8006i	−0.248376	+	0.430201i	0.714699	+	0.699432i	$0.246564\pi$
$54$	0.280911			0.00520205
$55$	−88.3474	−	51.0074i	−1.60632	−	0.927407i
$56$	−6.16565	−	10.6792i	−0.110101	−	0.190700i
$57$	−22.7488	−	39.4021i	−0.399102	−	0.691265i
$58$	−12.1448	−	21.0355i	−0.209394	−	0.362680i
$59$	39.1712			0.663919			0.331959	−	0.943294i	$-0.392290\pi$
$59$	39.1712			0.663919			0.331959	+	0.943294i	$0.392290\pi$
$60$	18.9286	+	32.7854i	0.315477	+	0.546423i
$61$	−27.5478	+	15.9047i	−0.451603	+	0.260733i	−0.708507	−	0.705704i	$-0.750631\pi$
$61$	−27.5478	+	15.9047i	−0.451603	+	0.260733i	0.256904	+	0.966437i	$0.417298\pi$
$62$	−9.72426	−	5.61430i	−0.156843	−	0.0905533i
$63$	11.0715	+	6.39211i	0.175737	+	0.101462i
$64$	−62.8625			−0.982226
$65$		−	52.0561i		−	0.800864i
$66$	−62.7237	+	108.641i	−0.950359	+	1.64607i
$67$	61.2076	−	106.015i	0.913546	−	1.58231i	0.104530	−	0.994522i	$-0.466666\pi$
$67$	61.2076	−	106.015i	0.913546	−	1.58231i	0.809016	−	0.587787i	$-0.200001\pi$
$68$	−21.5147	−	37.2646i	−0.316393	−	0.548009i
$69$	122.857	−	70.9315i	1.78054	−	1.02799i
$70$			11.2386i			0.160552i
$71$	−110.307	+	63.6857i	−1.55362	+	0.896982i	−0.555776	+	0.831332i	$0.687579\pi$
$71$	−110.307	+	63.6857i	−1.55362	+	0.896982i	−0.997843	+	0.0656495i	$0.979088\pi$
$72$	67.0051	−	38.6854i	0.930626	−	0.537297i
$73$	14.9276	−	8.61845i	0.204488	−	0.118061i	−0.394259	−	0.918999i	$-0.628999\pi$
$73$	14.9276	−	8.61845i	0.204488	−	0.118061i	0.598747	+	0.800938i	$0.295666\pi$
$74$	16.5064	−	28.5900i	0.223060	−	0.386351i
$75$		−	9.03079i		−	0.120411i
$76$	15.9486	+	9.20790i	0.209849	+	0.121157i
$77$	24.2110	−	13.9782i	0.314428	−	0.181535i
$78$	−64.0134			−0.820684
$79$	−18.2494	−	31.6090i	−0.231006	−	0.400113i	0.727099	−	0.686533i	$-0.240868\pi$
$79$	−18.2494	−	31.6090i	−0.231006	−	0.400113i	−0.958104	+	0.286419i	$0.907535\pi$
$80$	27.9563	+	16.1406i	0.349454	+	0.201757i
$81$	40.6964	−	70.4882i	0.502425	−	0.870225i
$82$			33.7102i			0.411100i
$83$	−42.8675	+	74.2487i	−0.516476	+	0.894562i	0.483341	+	0.875432i	$0.339423\pi$
$83$	−42.8675	+	74.2487i	−0.516476	+	0.894562i	−0.999817	+	0.0191303i	$0.993910\pi$
$84$	−10.3745			−0.123506
$85$			130.675i			1.53735i
$86$	35.9038	−	54.1808i	0.417487	−	0.630009i
$87$	−68.0929			−0.782677
$88$		−	169.194i		−	1.92266i
$89$	−11.1803	−	6.45493i	−0.125621	−	0.0725273i	0.435873	−	0.900008i	$-0.356440\pi$
$89$	−11.1803	−	6.45493i	−0.125621	−	0.0725273i	−0.561494	+	0.827481i	$0.689773\pi$
$90$	−70.5150			−0.783501
$91$	12.3544	+	7.13281i	0.135763	+	0.0783825i
$92$	−28.7105	+	49.7281i	−0.312071	+	0.540523i
$93$	−27.2607	+	15.7390i	−0.293126	+	0.169236i
$94$		−	118.459i		−	1.26020i
$95$	−27.9632	−	48.4336i	−0.294349	−	0.509828i
$96$	−53.3657	+	92.4321i	−0.555893	+	0.962834i
$97$	−113.142			−1.16642			−0.583208	−	0.812323i	$-0.698203\pi$
$97$	−113.142			−1.16642			−0.583208	+	0.812323i	$0.698203\pi$
$98$	61.4763	+	35.4934i	0.627310	+	0.362177i
$99$	87.7041	+	151.908i	0.885900	+	1.53442i
$100$	1.82767	+	3.16562i	0.0182767	+	0.0316562i
$101$	34.0992	+	59.0615i	0.337616	+	0.584768i	0.983984	−	0.178258i	$-0.0570462\pi$
$101$	34.0992	+	59.0615i	0.337616	+	0.584768i	−0.646368	+	0.763026i	$0.723713\pi$
$102$	160.691			1.57540
$103$	31.5613	+	54.6657i	0.306420	+	0.530735i	0.977576	−	0.210581i	$-0.0675355\pi$
$103$	31.5613	+	54.6657i	0.306420	+	0.530735i	−0.671156	+	0.741316i	$0.734202\pi$
$104$	74.7695	−	43.1682i	0.718937	−	0.415079i
$105$	27.2850	+	15.7530i	0.259857	+	0.150029i
$106$	34.4646	+	19.8982i	0.325138	+	0.187718i
$107$	−109.460			−1.02299			−0.511497	−	0.859285i	$-0.670909\pi$
$107$	−109.460			−1.02299			−0.511497	+	0.859285i	$0.670909\pi$
$108$			0.318750i			0.00295139i
$109$	17.3755	−	30.0953i	0.159408	−	0.276103i	−0.775247	−	0.631658i	$-0.782375\pi$
$109$	17.3755	−	30.0953i	0.159408	−	0.276103i	0.934655	+	0.355555i	$0.115708\pi$
$110$	−77.1009	+	133.543i	−0.700918	+	1.21402i
$111$	−46.2736	−	80.1483i	−0.416879	−	0.722056i
$112$	−7.66123	+	4.42321i	−0.0684038	+	0.0394930i
$113$			25.0080i			0.221310i	0.993859	+	0.110655i	$0.0352949\pi$
$113$			25.0080i			0.221310i	−0.993859	+	0.110655i	$0.964705\pi$
$114$	−59.5588	+	34.3863i	−0.522445	+	0.301634i
$115$	151.018	−	87.1900i	1.31320	−	0.758174i
$116$	23.8690	−	13.7808i	0.205767	−	0.118800i
$117$	−44.7537	+	77.5156i	−0.382510	+	0.662527i
$118$		−	59.2098i		−	0.501778i
$119$	−31.0128	−	17.9053i	−0.260612	−	0.150464i
$120$	165.131	−	95.3382i	1.37609	−	0.794485i
$121$	262.582			2.17010
$122$	24.0410	+	41.6402i	0.197057	+	0.341313i
$123$	81.8412	+	47.2510i	0.665375	+	0.384155i
$124$	6.37056	−	11.0341i	0.0513755	−	0.0889850i
$125$			119.118i			0.952946i
$126$	9.66208	−	16.7352i	0.0766831	−	0.132819i
$127$	−27.5460			−0.216897			−0.108449	−	0.994102i	$-0.534588\pi$
$127$	−27.5460			−0.216897			−0.108449	+	0.994102i	$0.534588\pi$
$128$		−	5.72951i		−	0.0447618i
$129$	−81.2135	−	163.111i	−0.629562	−	1.26443i
$130$	−78.6862			−0.605278
$131$			30.8157i			0.235234i	0.993059	+	0.117617i	$0.0375256\pi$
$131$			30.8157i			0.235234i	−0.993059	+	0.117617i	$0.962474\pi$
$132$	−123.275	−	71.1728i	−0.933900	−	0.539188i
$133$	15.3262			0.115235
$134$	−160.248	−	92.5192i	−1.19588	−	0.690442i
$135$	0.484001	−	0.838314i	0.00358519	−	0.00620973i
$136$	−187.691	+	108.364i	−1.38008	+	0.796792i
$137$			171.866i			1.25450i	0.778819	+	0.627249i	$0.215819\pi$
$137$			171.866i			1.25450i	−0.778819	+	0.627249i	$0.784181\pi$
$138$	−107.217	−	185.706i	−0.776938	−	1.34570i
$139$	30.8690	−	53.4666i	0.222079	−	0.384652i	−0.733360	−	0.679840i	$-0.762049\pi$
$139$	30.8690	−	53.4666i	0.222079	−	0.384652i	0.955439	+	0.295188i	$0.0953824\pi$
$140$	−12.7525			−0.0910894
$141$	−287.594	−	166.042i	−2.03967	−	1.17761i
$142$	96.2650	+	166.736i	0.677923	+	1.17420i
$143$	97.8671	+	169.511i	0.684385	+	1.18539i
$144$	−27.7527	−	48.0691i	−0.192727	−	0.333814i
$145$	−83.7008			−0.577247
$146$	−13.0273	−	22.5640i	−0.0892283	−	0.154548i
$147$	172.341	−	99.5010i	1.17239	−	0.676877i
$148$	32.4411	+	18.7299i	0.219197	+	0.126553i
$149$	−180.832	−	104.403i	−1.21364	−	0.700694i	−0.250088	−	0.968223i	$-0.580459\pi$
$149$	−180.832	−	104.403i	−1.21364	−	0.700694i	−0.963550	+	0.267529i	$0.913793\pi$
$150$	−13.6506			−0.0910041
$151$			154.264i			1.02162i	0.859694	+	0.510810i	$0.170654\pi$
$151$			154.264i			1.02162i	−0.859694	+	0.510810i	$0.829346\pi$
$152$	46.3776	−	80.3283i	0.305116	−	0.528476i
$153$	112.344	−	194.585i	0.734272	−	1.27180i
$154$	−21.1290	−	36.5964i	−0.137201	−	0.237639i
$155$	−33.5092	+	19.3466i	−0.216189	+	0.124817i
$156$		−	72.6361i		−	0.465616i
$157$	137.667	−	79.4818i	0.876857	−	0.506254i	0.00723635	−	0.999974i	$-0.497697\pi$
$157$	137.667	−	79.4818i	0.876857	−	0.506254i	0.869621	+	0.493720i	$0.164363\pi$
$158$	−47.7790	+	27.5852i	−0.302399	+	0.174590i
$159$	96.6170	−	55.7818i	0.607654	−	0.350829i
$160$	−65.5979	+	113.619i	−0.409987	+	0.710118i
$161$			47.7876i			0.296818i
$162$	−106.547	−	61.5152i	−0.657700	−	0.379723i
$163$	−34.1370	+	19.7090i	−0.209429	+	0.120914i	−0.601046	−	0.799214i	$-0.705249\pi$
$163$	−34.1370	+	19.7090i	−0.209429	+	0.120914i	0.391617	+	0.920128i	$0.371916\pi$
$164$	−38.2510			−0.233238
$165$	216.142	+	374.369i	1.30995	+	2.26891i
$166$	112.232	+	64.7969i	0.676094	+	0.390343i
$167$	99.7184	−	172.717i	0.597116	−	1.03424i	−0.396128	−	0.918195i	$-0.629646\pi$
$167$	99.7184	−	172.717i	0.597116	−	1.03424i	0.993244	−	0.116041i	$-0.0370203\pi$
$168$			52.2535i			0.311033i
$169$	34.5604	−	59.8603i	0.204499	−	0.354203i
$170$	197.523			1.16190
$171$			96.1619i			0.562351i
$172$	61.4790	+	40.7402i	0.357436	+	0.236862i
$173$	−86.0652			−0.497487			−0.248743	−	0.968569i	$-0.580018\pi$
$173$	−86.0652			−0.497487			−0.248743	+	0.968569i	$0.580018\pi$
$174$			102.927i			0.591533i
$175$	2.63453	+	1.52105i	0.0150545	+	0.00869169i
$176$	−121.379			−0.689653
$177$	−143.749	−	82.9934i	−0.812140	−	0.468889i
$178$	−9.75704	+	16.8997i	−0.0548148	+	0.0949421i
$179$	−70.6225	+	40.7739i	−0.394539	+	0.227787i	−0.684125	−	0.729365i	$-0.739816\pi$
$179$	−70.6225	+	40.7739i	−0.394539	+	0.227787i	0.289586	+	0.957152i	$0.406482\pi$
$180$		−	80.0136i		−	0.444520i
$181$	−84.7687	−	146.824i	−0.468335	−	0.811181i	0.531010	−	0.847366i	$-0.321813\pi$
$181$	−84.7687	−	146.824i	−0.468335	−	0.811181i	−0.999345	+	0.0361849i	$0.988479\pi$
$182$	10.7817	−	18.6744i	0.0592401	−	0.102607i
$183$	134.791			0.736566
$184$	250.466	+	144.607i	1.36123	+	0.785906i
$185$	−56.8802	−	98.5194i	−0.307461	−	0.532537i
$186$	23.7904	+	41.2063i	0.127906	+	0.221539i
$187$	−245.672	−	425.517i	−1.31376	−	2.27549i
$188$	134.416			0.714978
$189$	0.132637	+	0.229734i	0.000701783	+	0.00121552i
$190$	−73.2105	+	42.2681i	−0.385319	+	0.222464i
$191$	85.6498	+	49.4499i	0.448428	+	0.258900i	0.707166	−	0.707047i	$-0.249973\pi$
$191$	85.6498	+	49.4499i	0.448428	+	0.258900i	−0.258738	+	0.965948i	$0.583307\pi$
$192$	230.690	+	133.189i	1.20151	+	0.693692i
$193$	−243.765			−1.26303			−0.631515	−	0.775363i	$-0.717567\pi$
$193$	−243.765			−1.26303			−0.631515	+	0.775363i	$0.717567\pi$
$194$			171.022i			0.881556i
$195$	−110.293	+	191.033i	−0.565606	+	0.979658i
$196$	−40.2744	+	69.7573i	−0.205482	+	0.355905i
$197$	160.733	+	278.398i	0.815903	+	1.41319i	0.908678	+	0.417498i	$0.137093\pi$
$197$	160.733	+	278.398i	0.815903	+	1.41319i	−0.0927748	+	0.995687i	$0.529574\pi$
$198$	229.619	−	132.570i	1.15969	−	0.669547i
$199$		−	39.2071i		−	0.197021i	−0.995136	−	0.0985103i	$-0.968592\pi$
$199$		−	39.2071i		−	0.197021i	0.995136	−	0.0985103i	$-0.0314077\pi$
$200$	15.9443	−	9.20546i	0.0797216	−	0.0460273i
$201$	−449.234	+	259.365i	−2.23499	+	1.29037i
$202$	89.2753	−	51.5431i	0.441957	−	0.255164i
$203$	11.4688	−	19.8645i	0.0564966	−	0.0978549i
$204$			182.336i			0.893804i
$205$	100.600	+	58.0817i	0.490734	+	0.283325i
$206$	82.6307	−	47.7069i	0.401120	−	0.231587i
$207$	−299.836			−1.44848
$208$	−30.9687	−	53.6393i	−0.148888	−	0.257881i
$209$	182.113	+	105.143i	0.871355	+	0.503077i
$210$	23.8117	−	41.2431i	0.113389	−	0.196396i
$211$		−	378.026i		−	1.79159i	−0.444466	−	0.895796i	$-0.646606\pi$
$211$		−	378.026i		−	1.79159i	0.444466	−	0.895796i	$-0.353394\pi$
$212$	−22.5785	+	39.1071i	−0.106502	+	0.184467i
$213$	539.732			2.53396
$214$			165.456i			0.773161i
$215$	−99.8289	−	200.499i	−0.464320	−	0.932552i
$216$	1.60545			0.00743266
$217$		−	10.6036i		−	0.0488644i
$218$	−45.4909	−	26.2642i	−0.208674	−	0.120478i
$219$	−73.0408			−0.333520
$220$	−151.531	−	87.4866i	−0.688778	−	0.397666i
$221$	125.362	−	217.133i	0.567248	−	0.982502i
$222$	−121.149	+	69.9455i	−0.545717	+	0.315070i
$223$			222.482i			0.997678i	0.866695	+	0.498839i	$0.166240\pi$
$223$			222.482i			0.997678i	−0.866695	+	0.498839i	$0.833760\pi$
$224$	−17.9766	−	31.1365i	−0.0802529	−	0.139002i
$225$	−9.54356	+	16.5299i	−0.0424158	+	0.0734664i
$226$	37.8012			0.167262
$227$	−175.306	−	101.213i	−0.772271	−	0.445871i	0.0614129	−	0.998112i	$-0.480439\pi$
$227$	−175.306	−	101.213i	−0.772271	−	0.445871i	−0.833684	+	0.552241i	$0.813773\pi$
$228$	−39.0182	−	67.5815i	−0.171132	−	0.296410i
$229$	70.4417	+	122.009i	0.307606	+	0.532789i	0.977838	−	0.209363i	$-0.0671389\pi$
$229$	70.4417	+	122.009i	0.307606	+	0.532789i	−0.670232	+	0.742151i	$0.733806\pi$
$230$	−131.793	−	228.273i	−0.573014	−	0.992490i
$231$	−118.465			−0.512833
$232$	−69.4098	−	120.221i	−0.299180	−	0.518196i
$233$	43.7817	−	25.2774i	0.187904	−	0.108487i	−0.403097	−	0.915157i	$-0.632066\pi$
$233$	43.7817	−	25.2774i	0.187904	−	0.108487i	0.591001	+	0.806671i	$0.298733\pi$
$234$	117.170	+	67.6480i	0.500726	+	0.289094i
$235$	−353.515	−	204.102i	−1.50432	−	0.868518i
$236$	67.1855			0.284684
$237$			154.663i			0.652586i
$238$	−27.0649	+	46.8778i	−0.113718	+	0.196966i
$239$	−5.88438	+	10.1920i	−0.0246208	+	0.0426445i	−0.878073	−	0.478526i	$-0.841171\pi$
$239$	−5.88438	+	10.1920i	−0.0246208	+	0.0426445i	0.853452	+	0.521171i	$0.174505\pi$
$240$	−68.3952	−	118.464i	−0.284980	−	0.493600i
$241$	131.634	−	75.9987i	0.546198	−	0.315348i	−0.201389	−	0.979511i	$-0.564546\pi$
$241$	131.634	−	75.9987i	0.546198	−	0.315348i	0.747587	+	0.664164i	$0.231212\pi$
$242$		−	396.909i		−	1.64012i
$243$	−297.243	+	171.613i	−1.22322	+	0.706228i
$244$	−47.2493	+	27.2794i	−0.193645	+	0.111801i
$245$	211.844	−	122.308i	0.864669	−	0.499217i
$246$	71.4229	−	123.708i	0.290337	−	0.502879i
$247$			107.305i			0.434433i
$248$	−55.5759	−	32.0867i	−0.224096	−	0.129382i
$249$	314.626	−	181.650i	1.26356	−	0.729517i
$250$	180.055			0.720219
$251$	−21.4395	−	37.1344i	−0.0854165	−	0.147946i	0.820152	−	0.572146i	$-0.193889\pi$
$251$	−21.4395	−	37.1344i	−0.0854165	−	0.147946i	−0.905569	+	0.424200i	$0.860555\pi$
$252$	18.9895	+	10.9636i	0.0753551	+	0.0435063i
$253$	−327.840	+	567.835i	−1.29581	+	2.24441i
$254$			41.6375i			0.163927i
$255$	276.865	−	479.545i	1.08575	−	1.88057i
$256$	−260.110			−1.01606
$257$		−	169.737i		−	0.660455i	−0.943901	−	0.330227i	$-0.892875\pi$
$257$		−	169.737i		−	0.660455i	0.943901	−	0.330227i	$-0.107125\pi$
$258$	−246.553	+	122.759i	−0.955632	+	0.475812i
$259$	31.1752			0.120368
$260$		−	89.2854i		−	0.343405i
$261$	124.637	+	71.9592i	0.477536	+	0.275706i
$262$	46.5799			0.177786
$263$	241.781	+	139.592i	0.919319	+	0.530769i	0.883418	−	0.468586i	$-0.155237\pi$
$263$	241.781	+	139.592i	0.919319	+	0.530769i	0.0359012	+	0.999355i	$0.488570\pi$
$264$	−358.477	+	620.901i	−1.35787	+	2.35190i
$265$	118.763	−	68.5679i	0.448162	−	0.258747i
$266$		−	23.1666i		−	0.0870923i
$267$	27.3526	+	47.3760i	0.102444	+	0.177438i
$268$	104.982	−	181.834i	0.391723	−	0.678484i
$269$	−112.264			−0.417337			−0.208668	−	0.977986i	$-0.566913\pi$
$269$	−112.264			−0.417337			−0.208668	+	0.977986i	$0.566913\pi$
$270$	−1.26717	−	0.731598i	−0.00469320	−	0.00270962i
$271$	−16.6159	−	28.7796i	−0.0613133	−	0.106198i	0.833739	−	0.552158i	$-0.186196\pi$
$271$	−16.6159	−	28.7796i	−0.0613133	−	0.106198i	−0.895053	+	0.445960i	$0.852862\pi$
$272$	77.7396	+	134.649i	0.285807	+	0.495033i
$273$	−30.2251	−	52.3513i	−0.110715	−	0.191763i
$274$	259.787			0.948127
$275$	20.8698	+	36.1476i	0.0758902	+	0.131446i
$276$	210.721	−	121.660i	0.763482	−	0.440797i
$277$	81.5518	+	47.0839i	0.294411	+	0.169978i	0.639929	−	0.768434i	$-0.278964\pi$
$277$	81.5518	+	47.0839i	0.294411	+	0.169978i	−0.345519	+	0.938412i	$0.612297\pi$
$278$	−80.8182	−	46.6604i	−0.290713	−	0.167843i
$279$	66.5305			0.238460
$280$			64.2308i			0.229396i
$281$	−38.5912	+	66.8420i	−0.137335	+	0.237872i	−0.926487	−	0.376326i	$-0.877187\pi$
$281$	−38.5912	+	66.8420i	−0.137335	+	0.237872i	0.789152	+	0.614198i	$0.210520\pi$
$282$	−250.984	+	434.716i	−0.890013	+	1.54155i
$283$	82.1091	+	142.217i	0.290138	+	0.502534i	0.973842	−	0.227225i	$-0.0729654\pi$
$283$	82.1091	+	142.217i	0.290138	+	0.502534i	−0.683704	+	0.729759i	$0.739632\pi$
$284$	−189.196	+	109.232i	−0.666182	+	0.384620i
$285$			236.986i			0.831530i
$286$	256.226	−	147.932i	0.895896	−	0.517246i
$287$	−27.5688	+	15.9169i	−0.0960586	+	0.0554595i
$288$	195.361	−	112.792i	0.678336	−	0.391637i
$289$	−170.192	+	294.781i	−0.588898	+	1.02000i
$290$			126.519i			0.436273i
$291$	415.205	+	239.719i	1.42682	+	0.823775i
$292$	25.6034	−	14.7822i	0.0876830	−	0.0506238i
$293$	177.674			0.606394			0.303197	−	0.952928i	$-0.401946\pi$
$293$	177.674			0.606394			0.303197	+	0.952928i	$0.401946\pi$
$294$	−150.402	−	260.504i	−0.511572	−	0.886068i
$295$	−176.698	−	102.017i	−0.598977	−	0.345819i
$296$	94.3372	−	163.397i	0.318707	−	0.552016i
$297$			3.63974i			0.0122550i
$298$	−157.812	+	273.339i	−0.529572	+	0.917245i
$299$	−334.580			−1.11900
$300$		−	15.4894i		−	0.0516313i
$301$	61.2627	+	3.78043i	0.203531	+	0.0125596i
$302$	233.181			0.772121
$303$		−	288.989i		−	0.953757i
$304$	−57.6272	−	33.2711i	−0.189563	−	0.109444i
$305$	165.688			0.543238
$306$	−294.128	−	169.815i	−0.961201	−	0.554950i
$307$	−120.549	+	208.796i	−0.392666	+	0.680118i	−0.992800	−	0.119781i	$-0.961781\pi$
$307$	−120.549	+	208.796i	−0.392666	+	0.680118i	0.600134	+	0.799900i	$0.295114\pi$
$308$	41.5261	−	23.9751i	0.134825	−	0.0778412i
$309$		−	267.480i		−	0.865630i
$310$	29.2436	+	50.6513i	0.0943341	+	0.163391i
$311$	23.5430	−	40.7777i	0.0757009	−	0.131118i	−0.825690	−	0.564124i	$-0.809214\pi$
$311$	23.5430	−	40.7777i	0.0757009	−	0.131118i	0.901391	+	0.433006i	$0.142547\pi$
$312$	−365.848			−1.17259
$313$	3.18599	+	1.83943i	0.0101789	+	0.00587678i	0.505081	−	0.863072i	$-0.331463\pi$
$313$	3.18599	+	1.83943i	0.0101789	+	0.00587678i	−0.494902	+	0.868949i	$0.664796\pi$
$314$	−120.142	−	208.092i	−0.382617	−	0.662713i
$315$	−33.2949	−	57.6685i	−0.105698	−	0.183075i
$316$	−31.3010	−	54.2149i	−0.0990538	−	0.171566i
$317$	−78.3317			−0.247103			−0.123552	−	0.992338i	$-0.539428\pi$
$317$	−78.3317			−0.247103			−0.123552	+	0.992338i	$0.539428\pi$
$318$	−84.3178	−	146.043i	−0.265150	−	0.459254i
$319$	272.555	−	157.360i	0.854405	−	0.493291i
$320$	283.567	+	163.718i	0.886148	+	0.511618i
$321$	401.693	+	231.918i	1.25138	+	0.722484i
$322$	72.2341			0.224329
$323$		−	269.364i		−	0.833945i
$324$	69.8014	−	120.900i	0.215437	−	0.373147i
$325$	−10.6494	+	18.4454i	−0.0327675	+	0.0567550i
$326$	29.7914	+	51.6002i	0.0913847	+	0.158283i
$327$	−127.528	+	73.6282i	−0.389993	+	0.225163i
$328$			192.660i			0.587377i
$329$	96.8782	−	55.9326i	0.294463	−	0.170008i
$330$	565.883	−	326.713i	1.71480	−	0.990039i
$331$	−65.0459	+	37.5543i	−0.196513	+	0.113457i	−0.595028	−	0.803705i	$-0.702859\pi$
$331$	−65.0459	+	37.5543i	−0.196513	+	0.113457i	0.398515	+	0.917162i	$0.369526\pi$
$332$	−73.5253	+	127.349i	−0.221462	+	0.383583i
$333$			195.604i			0.587400i
$334$	−261.073	−	150.731i	−0.781657	−	0.451290i
$335$	−552.205	+	318.816i	−1.64837	+	0.951688i
$336$	37.4864			0.111567
$337$	−131.845	−	228.363i	−0.391232	−	0.677634i	0.601380	−	0.798963i	$-0.294618\pi$
$337$	−131.845	−	228.363i	−0.391232	−	0.677634i	−0.992612	+	0.121329i	$0.961284\pi$
$338$	−90.4827	−	52.2402i	−0.267700	−	0.154557i
$339$	52.9854	−	91.7734i	0.156299	−	0.270718i
$340$			224.130i			0.659206i
$341$	72.7442	−	125.997i	0.213326	−	0.369492i
$342$	145.355			0.425014
$343$			136.979i			0.399356i
$344$	205.197	−	309.653i	0.596502	−	0.900153i
$345$	−738.930			−2.14183
$346$			130.093i			0.375991i
$347$	508.938	+	293.836i	1.46668	+	0.846789i	0.999305	−	0.0372699i	$-0.0118661\pi$
$347$	508.938	+	293.836i	1.46668	+	0.846789i	0.467376	+	0.884059i	$0.345199\pi$
$348$	−116.791			−0.335607
$349$	384.482	+	221.981i	1.10167	+	0.636048i	0.936659	−	0.350244i	$-0.113901\pi$
$349$	384.482	+	221.981i	1.10167	+	0.636048i	0.165009	+	0.986292i	$0.447235\pi$
$350$	2.29916	−	3.98226i	0.00656902	−	0.0113779i
$351$	−1.60846	+	0.928644i	−0.00458250	+	0.00264571i
$352$		−	493.304i		−	1.40143i
$353$	−298.730	−	517.416i	−0.846262	−	1.46577i	−0.884521	−	0.466501i	$-0.845515\pi$
$353$	−298.730	−	517.416i	−0.846262	−	1.46577i	0.0382591	−	0.999268i	$-0.487819\pi$
$354$	−125.450	+	217.285i	−0.354378	+	0.613801i
$355$	663.447			1.86887
$356$	−19.1761	−	11.0713i	−0.0538655	−	0.0310993i
$357$	75.8730	+	131.416i	0.212529	+	0.368112i
$358$	61.6324	+	106.750i	0.172158	+	0.298186i
$359$	127.194	+	220.307i	0.354302	+	0.613668i	0.986998	−	0.160731i	$-0.0513853\pi$
$359$	127.194	+	220.307i	0.354302	+	0.613668i	−0.632697	+	0.774400i	$0.718052\pi$
$360$	−403.006			−1.11946
$361$	−122.859	−	212.797i	−0.340329	−	0.589466i
$362$	−221.933	+	128.133i	−0.613076	+	0.353959i
$363$	−963.610	−	556.341i	−2.65457	−	1.53262i
$364$	21.1899	+	12.2340i	0.0582141	+	0.0336099i
$365$	−89.7829			−0.245980
$366$		−	203.746i		−	0.556683i
$367$	−142.193	+	246.286i	−0.387447	+	0.671078i	−0.992105	−	0.125407i	$-0.959976\pi$
$367$	−142.193	+	246.286i	−0.387447	+	0.671078i	0.604658	+	0.796485i	$0.293310\pi$
$368$	103.740	−	179.683i	0.281903	−	0.488270i
$369$	−99.8679	−	172.976i	−0.270645	−	0.468770i
$370$	−148.918	+	85.9781i	−0.402482	+	0.232373i
$371$			37.5811i			0.101297i
$372$	−46.7568	+	26.9951i	−0.125690	+	0.0725674i
$373$	−229.260	+	132.363i	−0.614637	+	0.354861i	−0.774778	−	0.632233i	$-0.782138\pi$
$373$	−229.260	+	132.363i	−0.614637	+	0.354861i	0.160141	+	0.987094i	$0.448805\pi$
$374$	−643.196	+	371.350i	−1.71978	+	0.992913i
$375$	252.380	−	437.135i	0.673013	−	1.16569i
$376$		−	677.015i		−	1.80057i
$377$	139.080	+	80.2976i	0.368911	+	0.212991i
$378$	0.347258	−	0.200489i	0.000918671	−	0.000530395i
$379$	−98.0731			−0.258768			−0.129384	−	0.991595i	$-0.541300\pi$
$379$	−98.0731			−0.258768			−0.129384	+	0.991595i	$0.541300\pi$
$380$	−47.9617	−	83.0722i	−0.126215	−	0.218611i
$381$	101.087	+	58.3626i	0.265320	+	0.153183i
$382$	74.7467	−	129.465i	0.195672	−	0.338914i
$383$			439.727i			1.14811i	0.818816	+	0.574056i	$0.194631\pi$
$383$			439.727i			1.14811i	−0.818816	+	0.574056i	$0.805369\pi$
$384$	−12.1393	+	21.0259i	−0.0316128	+	0.0547550i
$385$	−145.618			−0.378230
$386$			368.466i			0.954576i
$387$	−23.7197	+	384.383i	−0.0612911	+	0.993238i
$388$	−194.059			−0.500152
$389$		−	279.833i		−	0.719366i	−0.933075	−	0.359683i	$-0.882885\pi$
$389$		−	279.833i		−	0.719366i	0.933075	−	0.359683i	$-0.117115\pi$
$390$	288.759	+	166.715i	0.740408	+	0.427475i
$391$	839.886			2.14804
$392$	351.348	+	202.851i	0.896296	+	0.517477i
$393$	65.2903	−	113.086i	0.166133	−	0.287751i
$394$	420.816	−	242.958i	1.06806	−	0.616645i
$395$			190.114i			0.481301i
$396$	150.428	+	260.549i	0.379868	+	0.657951i
$397$	−108.633	+	188.157i	−0.273634	+	0.473948i	−0.969790	−	0.243943i	$-0.921559\pi$
$397$	−108.633	+	188.157i	−0.273634	+	0.473948i	0.696156	+	0.717891i	$0.254892\pi$
$398$	−59.2640			−0.148905
$399$	−56.2435	−	32.4722i	−0.140961	−	0.0813840i
$400$	−6.60396	−	11.4384i	−0.0165099	−	0.0285960i
$401$	−203.564	−	352.583i	−0.507641	−	0.879260i	−0.999961	−	0.00884561i	$-0.997184\pi$
$401$	−203.564	−	352.583i	−0.507641	−	0.879260i	0.492320	−	0.870414i	$-0.336149\pi$
$402$	392.047	+	679.046i	0.975242	+	1.68917i
$403$	74.2399			0.184218
$404$	58.4861	+	101.301i	0.144768	+	0.250745i
$405$	−367.156	+	211.978i	−0.906559	+	0.523402i
$406$	−30.0265	−	17.3358i	−0.0739570	−	0.0426991i
$407$	370.439	+	213.873i	0.910169	+	0.525486i
$408$	918.375			2.25092
$409$			63.1215i			0.154331i	0.997018	+	0.0771656i	$0.0245870\pi$
$409$			63.1215i			0.154331i	−0.997018	+	0.0771656i	$0.975413\pi$
$410$	87.7941	−	152.064i	0.214132	−	0.370888i
$411$	364.139	−	630.707i	0.885983	−	1.53457i
$412$	54.1331	+	93.7613i	0.131391	+	0.227576i
$413$	48.4229	−	27.9570i	0.117247	−	0.0676924i
$414$			453.221i			1.09474i
$415$	386.743	−	223.286i	0.931912	−	0.538040i
$416$	217.999	−	125.862i	0.524035	−	0.302552i
$417$	−226.563	+	130.806i	−0.543317	+	0.313684i
$418$	158.931	−	275.276i	0.380217	−	0.658555i
$419$			182.446i			0.435432i	0.976012	+	0.217716i	$0.0698606\pi$
$419$			182.446i			0.435432i	−0.976012	+	0.217716i	$0.930139\pi$
$420$	46.7986	+	27.0192i	0.111425	+	0.0643314i
$421$	−310.193	+	179.090i	−0.736800	+	0.425392i	−0.820905	−	0.571065i	$-0.806530\pi$
$421$	−310.193	+	179.090i	−0.736800	+	0.425392i	0.0841044	+	0.996457i	$0.473197\pi$
$422$	−571.410			−1.35405
$423$	350.940	+	607.847i	0.829646	+	1.43699i
$424$	196.971	+	113.721i	0.464555	+	0.268211i
$425$	26.7330	−	46.3028i	0.0629011	−	0.108948i
$426$		−	815.840i		−	1.91512i
$427$	−22.7028	+	39.3224i	−0.0531681	+	0.0920898i
$428$	−187.744			−0.438654
$429$		−	829.417i		−	1.93337i
$430$	−303.067	+	150.898i	−0.704806	+	0.350925i
$431$	−201.977			−0.468624			−0.234312	−	0.972161i	$-0.575284\pi$
$431$	−201.977			−0.468624			−0.234312	+	0.972161i	$0.575284\pi$
$432$		−	1.15175i		−	0.00266608i
$433$	−404.038	−	233.272i	−0.933114	−	0.538734i	−0.0453190	−	0.998973i	$-0.514430\pi$
$433$	−404.038	−	233.272i	−0.933114	−	0.538734i	−0.887795	+	0.460239i	$0.847764\pi$
$434$	−16.0280			−0.0369308
$435$	307.161	+	177.340i	0.706118	+	0.407677i
$436$	29.8020	−	51.6187i	0.0683533	−	0.118391i
$437$	−311.297	+	179.728i	−0.712351	+	0.411276i
$438$			110.406i			0.252068i
$439$	319.089	+	552.679i	0.726855	+	1.25895i	0.958206	+	0.286079i	$0.0923520\pi$
$439$	319.089	+	552.679i	0.726855	+	1.25895i	−0.231351	+	0.972870i	$0.574315\pi$
$440$	−440.645	+	763.220i	−1.00147	+	1.73459i
$441$	−420.603			−0.953747
$442$	−328.210	−	189.492i	−0.742557	−	0.428716i
$443$	−181.021	−	313.538i	−0.408626	−	0.707761i	0.586110	−	0.810231i	$-0.300659\pi$
$443$	−181.021	−	313.538i	−0.408626	−	0.707761i	−0.994736	+	0.102470i	$0.967325\pi$
$444$	−79.3674	−	137.468i	−0.178755	−	0.309613i
$445$	33.6222	+	58.2353i	0.0755555	+	0.130866i
$446$	336.296			0.754027
$447$	442.406	+	766.270i	0.989723	+	1.71425i
$448$	−77.7096	+	44.8657i	−0.173459	+	0.100147i
$449$	−613.878	−	354.423i	−1.36721	−	0.789360i	−0.376640	−	0.926360i	$-0.622921\pi$
$449$	−613.878	−	354.423i	−1.36721	−	0.789360i	−0.990571	+	0.137000i	$0.956254\pi$
$450$	24.9860	+	14.4257i	0.0555245	+	0.0320571i
$451$	−436.781			−0.968472
$452$			42.8932i			0.0948964i
$453$	326.845	−	566.113i	0.721513	−	1.24970i
$454$	−152.990	+	264.986i	−0.336981	+	0.583669i
$455$	−37.1531	−	64.3510i	−0.0816551	−	0.141431i
$456$	−340.389	+	196.524i	−0.746467	+	0.430973i
$457$		−	444.549i		−	0.972755i	−0.873749	−	0.486378i	$-0.838318\pi$
$457$		−	444.549i		−	0.972755i	0.873749	−	0.486378i	$-0.161682\pi$
$458$	184.424	−	106.477i	0.402672	−	0.232483i
$459$	4.03766	−	2.33115i	0.00879665	−	0.00507875i
$460$	259.022	−	149.546i	0.563090	−	0.325100i
$461$	250.340	−	433.602i	0.543038	−	0.940569i	−0.455690	−	0.890139i	$-0.650607\pi$
$461$	250.340	−	433.602i	0.543038	−	0.940569i	0.998728	−	0.0504301i	$-0.0160592\pi$
$462$			179.067i			0.387590i
$463$	−756.342	−	436.674i	−1.63357	−	0.943141i	−0.982980	−	0.183710i	$-0.941189\pi$
$463$	−756.342	−	436.674i	−1.63357	−	0.943141i	−0.650588	−	0.759431i	$-0.725478\pi$
$464$	−86.2463	+	49.7943i	−0.185876	+	0.107315i
$465$	163.961			0.352604
$466$	−38.2084	−	66.1788i	−0.0819922	−	0.142015i
$467$	−19.1619	−	11.0631i	−0.0410320	−	0.0236898i	0.479344	−	0.877627i	$-0.340875\pi$
$467$	−19.1619	−	11.0631i	−0.0410320	−	0.0236898i	−0.520376	+	0.853937i	$0.674208\pi$
$468$	−76.7604	+	132.953i	−0.164018	+	0.284087i
$469$		−	174.738i		−	0.372576i
$470$	−308.513	+	534.360i	−0.656410	+	1.13694i
$471$	−673.604			−1.43016
$472$		−	338.394i		−	0.716937i
$473$	702.017	+	465.204i	1.48418	+	0.983518i
$474$	233.783			0.493213
$475$			22.8824i			0.0481735i
$476$	−53.1924	−	30.7107i	−0.111749	−	0.0645182i
$477$	−235.797			−0.494332
$478$	15.4059	+	8.89461i	0.0322300	+	0.0186080i
$479$	366.668	−	635.088i	0.765487	−	1.32586i	−0.174502	−	0.984657i	$-0.555832\pi$
$479$	366.668	−	635.088i	0.765487	−	1.32586i	0.939989	−	0.341205i	$-0.110835\pi$
$480$	481.456	−	277.969i	1.00303	−	0.579102i
$481$			218.270i			0.453784i
$482$	−114.877	−	198.973i	−0.238334	−	0.412806i
$483$	101.249	−	175.369i	0.209626	−	0.363083i
$484$	450.373			0.930523
$485$	510.376	+	294.666i	1.05232	+	0.607558i
$486$	259.405	+	449.302i	0.533754	+	0.924490i
$487$	−237.862	−	411.988i	−0.488422	−	0.845972i	0.511489	−	0.859290i	$-0.329094\pi$
$487$	−237.862	−	411.988i	−0.488422	−	0.845972i	−0.999911	+	0.0133179i	$0.995761\pi$
$488$	137.398	+	237.981i	0.281554	+	0.487666i
$489$	167.033			0.341580
$490$	−184.876	−	320.215i	−0.377299	−	0.653501i
$491$	40.6876	−	23.4910i	0.0828669	−	0.0478432i	−0.457994	−	0.888955i	$-0.651432\pi$
$491$	40.6876	−	23.4910i	0.0828669	−	0.0478432i	0.540861	+	0.841112i	$0.318099\pi$
$492$	140.372	+	81.0438i	0.285309	+	0.164723i
$493$	−349.127	−	201.569i	−0.708168	−	0.408861i
$494$	162.198			0.328337
$495$		−	913.659i		−	1.84578i
$496$	−23.0189	+	39.8699i	−0.0464090	+	0.0803828i
$497$	−90.9065	+	157.455i	−0.182910	+	0.316810i
$498$	−274.575	−	475.578i	−0.551356	−	0.954976i
$499$	−476.488	+	275.101i	−0.954886	+	0.551304i	−0.894595	−	0.446877i	$-0.852536\pi$
$499$	−476.488	+	275.101i	−0.954886	+	0.551304i	−0.0602909	+	0.998181i	$0.519203\pi$
$500$			204.309i			0.408617i
$501$	−731.885	+	422.554i	−1.46085	+	0.843421i
$502$	−56.1310	+	32.4072i	−0.111815	+	0.0645563i
$503$	−515.731	+	297.757i	−1.02531	+	0.591963i	−0.915638	−	0.402005i	$-0.868313\pi$
$503$	−515.731	+	297.757i	−1.02531	+	0.591963i	−0.109672	+	0.993968i	$0.534980\pi$
$504$	55.2205	−	95.6446i	0.109564	−	0.189771i
$505$		−	355.229i		−	0.703424i
$506$	858.319	+	495.550i	1.69628	+	0.979349i
$507$	−253.656	+	146.449i	−0.500308	+	0.288853i
$508$	−47.2462			−0.0930043
$509$	−2.32623	−	4.02916i	−0.00457021	−	0.00791583i	0.863731	−	0.503953i	$-0.168121\pi$
$509$	−2.32623	−	4.02916i	−0.00457021	−	0.00791583i	−0.868301	+	0.496037i	$0.834788\pi$
$510$	−724.862	−	418.499i	−1.42130	−	0.820587i
$511$	12.3022	−	21.3080i	0.0240747	−	0.0416986i
$512$			370.255i			0.723155i
$513$	−0.997686	+	1.72804i	−0.00194481	+	0.00336851i
$514$	−256.568			−0.499160
$515$		−	328.790i		−	0.638427i
$516$	−139.295	−	279.764i	−0.269952	−	0.542179i
$517$	1534.87			2.96880
$518$		−	47.1234i		−	0.0909718i
$519$	315.838	+	182.349i	0.608552	+	0.351347i
$520$	−449.705			−0.864818
$521$	428.671	+	247.493i	0.822785	+	0.475035i	0.851376	−	0.524556i	$-0.175769\pi$
$521$	428.671	+	247.493i	0.822785	+	0.475035i	−0.0285906	+	0.999591i	$0.509102\pi$
$522$	108.771	−	188.397i	0.208373	−	0.360913i
$523$	531.027	−	306.589i	1.01535	−	0.586212i	0.102596	−	0.994723i	$-0.467285\pi$
$523$	531.027	−	306.589i	1.01535	−	0.586212i	0.912753	+	0.408511i	$0.133952\pi$
$524$			52.8543i			0.100867i
$525$	−6.44539	−	11.1637i	−0.0122769	−	0.0212643i
$526$	211.003	−	365.467i	0.401146	−	0.694805i
$527$	−186.362			−0.353628
$528$	445.431	+	257.170i	0.843620	+	0.487064i
$529$	−295.896	−	512.507i	−0.559350	−	0.968822i
$530$	−103.645	−	179.518i	−0.195556	−	0.338713i
$531$	175.412	+	303.822i	0.330342	+	0.572169i
$532$	26.2872			0.0494119
$533$	−111.440	−	193.020i	−0.209081	−	0.362139i
$534$	71.6119	−	41.3452i	0.134105	−	0.0774254i
$535$	493.767	+	285.076i	0.922929	+	0.532853i
$536$	−915.845	−	528.763i	−1.70867	−	0.986499i
$537$	345.557			0.643495
$538$			169.693i			0.315415i
$539$	−459.885	+	796.545i	−0.853220	+	1.47782i
$540$	0.830146	−	1.43786i	0.00153731	−	0.00266269i
$541$	392.586	+	679.979i	0.725668	+	1.25689i	0.958699	+	0.284424i	$0.0918024\pi$
$541$	392.586	+	679.979i	0.725668	+	1.25689i	−0.233031	+	0.972469i	$0.574864\pi$
$542$	−43.5022	+	25.1160i	−0.0802623	+	0.0463394i
$543$			718.410i			1.32304i
$544$	−547.235	+	315.946i	−1.00595	+	0.580783i
$545$	−156.759	+	90.5049i	−0.287631	+	0.166064i
$546$	−79.1324	+	45.6871i	−0.144931	+	0.0836760i
$547$	81.3090	−	140.831i	0.148645	−	0.257461i	−0.782082	−	0.623176i	$-0.785842\pi$
$547$	81.3090	−	140.831i	0.148645	−	0.257461i	0.930727	+	0.365715i	$0.119175\pi$
$548$			294.781i			0.537921i
$549$	−246.722	−	142.445i	−0.449402	−	0.259463i
$550$	54.6393	−	31.5460i	0.0993442	−	0.0573564i
$551$	172.535			0.313131
$552$	−612.767	−	1061.34i	−1.11008	−	1.92272i
$553$	−45.1194	−	26.0497i	−0.0815902	−	0.0471061i
$554$	71.1704	−	123.271i	0.128466	−	0.222510i
$555$			482.056i			0.868570i
$556$	52.9457	−	91.7046i	0.0952260	−	0.164936i
$557$	46.2986			0.0831213			0.0415607	−	0.999136i	$-0.486767\pi$
$557$	46.2986			0.0831213			0.0415607	+	0.999136i	$0.486767\pi$
$558$		−	100.565i		−	0.180224i
$559$	−26.4683	+	428.924i	−0.0473493	+	0.767307i
$560$	46.0789			0.0822837
$561$			2082.06i			3.71133i
$562$	101.036	+	58.3331i	0.179779	+	0.103796i
$563$	−246.469			−0.437778			−0.218889	−	0.975750i	$-0.570243\pi$
$563$	−246.469			−0.437778			−0.218889	+	0.975750i	$0.570243\pi$
$564$	−493.274	−	284.792i	−0.874599	−	0.504950i
$565$	65.1304	−	112.809i	0.115275	−	0.199662i
$566$	214.970	−	124.113i	0.379806	−	0.219281i
$567$		−	116.182i		−	0.204907i
$568$	550.171	+	952.925i	0.968612	+	1.67768i
$569$	424.894	−	735.938i	0.746738	−	1.29339i	−0.202640	−	0.979253i	$-0.564952\pi$
$569$	424.894	−	735.938i	0.746738	−	1.29339i	0.949378	−	0.314135i	$-0.101715\pi$
$570$	358.220			0.628456
$571$	175.177	+	101.138i	0.306790	+	0.177125i	0.645489	−	0.763770i	$-0.276654\pi$
$571$	175.177	+	101.138i	0.306790	+	0.177125i	−0.338699	+	0.940895i	$0.609987\pi$
$572$	167.859	+	290.741i	0.293460	+	0.508288i
$573$	−209.542	−	362.938i	−0.365694	−	0.633400i
$574$	24.0594	+	41.6720i	0.0419153	+	0.0725994i
$575$	−71.3480			−0.124084
$576$	−281.503	−	487.577i	−0.488720	−	0.846487i
$577$	−634.982	+	366.607i	−1.10049	+	0.635368i	−0.936349	−	0.351069i	$-0.885818\pi$
$577$	−634.982	+	366.607i	−1.10049	+	0.635368i	−0.164140	+	0.986437i	$0.552485\pi$
$578$	445.580	+	257.256i	0.770899	+	0.445079i
$579$	894.558	+	516.473i	1.54500	+	0.892009i
$580$	−143.561			−0.247520
$581$			122.380i			0.210637i
$582$	362.350	−	627.608i	0.622594	−	1.07836i
$583$	−257.819	+	446.556i	−0.442228	+	0.765962i
$584$	−74.4535	−	128.957i	−0.127489	−	0.220817i
$585$	403.760	−	233.111i	0.690189	−	0.398481i
$586$		−	268.565i		−	0.458302i
$587$	549.572	−	317.295i	0.936238	−	0.540537i	0.0474590	−	0.998873i	$-0.484888\pi$
$587$	549.572	−	317.295i	0.936238	−	0.540537i	0.888779	+	0.458336i	$0.151554\pi$
$588$	295.595	−	170.662i	0.502712	−	0.290241i
$589$	69.0736	−	39.8797i	0.117273	−	0.0677074i
$590$	−154.205	+	267.091i	−0.261364	+	0.452696i
$591$		−	1362.20i		−	2.30491i
$592$	−117.220	−	67.6771i	−0.198007	−	0.114319i
$593$	577.047	−	333.158i	0.973098	−	0.561818i	0.0729186	−	0.997338i	$-0.476769\pi$
$593$	577.047	−	333.158i	0.973098	−	0.561818i	0.900179	+	0.435520i	$0.143435\pi$
$594$	5.50170			0.00926213
$595$	93.2642	+	161.538i	0.156747	+	0.271493i
$596$	−310.158	−	179.070i	−0.520400	−	0.300453i
$597$	−83.0694	+	143.881i	−0.139145	+	0.241006i
$598$			505.739i			0.845718i
$599$	−354.761	+	614.463i	−0.592255	+	1.02582i	0.401673	+	0.915783i	$0.368429\pi$
$599$	−354.761	+	614.463i	−0.592255	+	1.02582i	−0.993928	+	0.110032i	$0.964905\pi$
$600$	−78.0157			−0.130026
$601$			389.979i			0.648884i	0.945906	+	0.324442i	$0.105176\pi$
$601$			389.979i			0.648884i	−0.945906	+	0.324442i	$0.894824\pi$
$602$	5.71435	−	92.6025i	0.00949228	−	0.153825i
$603$	1096.37			1.81819
$604$			264.591i			0.438064i
$605$	−1184.48	−	683.862i	−1.95782	−	1.13035i
$606$	−436.825			−0.720833
$607$	−818.471	−	472.545i	−1.34839	−	0.778492i	−0.360366	−	0.932811i	$-0.617348\pi$
$607$	−818.471	−	472.545i	−1.34839	−	0.778492i	−0.988021	+	0.154319i	$0.950682\pi$
$608$	135.219	−	234.206i	0.222400	−	0.385208i
$609$	−84.1754	+	48.5987i	−0.138219	+	0.0798008i
$610$		−	250.448i		−	0.410570i
$611$	391.607	+	678.283i	0.640927	+	1.11012i
$612$	192.689	−	333.747i	0.314851	−	0.545339i
$613$	−89.2278			−0.145559			−0.0727796	−	0.997348i	$-0.523187\pi$
$613$	−89.2278			−0.145559			−0.0727796	+	0.997348i	$0.523187\pi$
$614$	315.609	+	182.217i	0.514021	+	0.296770i
$615$	−246.119	−	426.291i	−0.400194	−	0.693156i
$616$	−120.756	−	209.155i	−0.196032	−	0.339537i
$617$	−46.9205	−	81.2687i	−0.0760462	−	0.131716i	0.825495	−	0.564410i	$-0.190896\pi$
$617$	−46.9205	−	81.2687i	−0.0760462	−	0.131716i	−0.901541	+	0.432694i	$0.857563\pi$
$618$	−404.313			−0.654228
$619$	113.587	+	196.739i	0.183501	+	0.317834i	0.943071	−	0.332593i	$-0.107923\pi$
$619$	113.587	+	196.739i	0.183501	+	0.317834i	−0.759569	+	0.650427i	$0.774590\pi$
$620$	−57.4742	+	33.1827i	−0.0927003	+	0.0535206i
$621$	−5.38809	−	3.11082i	−0.00867648	−	0.00500937i
$622$	−61.6380	−	35.5867i	−0.0990965	−	0.0572134i
$623$	−18.4278			−0.0295792
$624$			262.457i			0.420605i
$625$	336.869	−	583.474i	0.538990	−	0.933558i
$626$	2.78042	−	4.81582i	0.00444156	−	0.00769301i
$627$	−445.541	−	771.699i	−0.710591	−	1.23078i
$628$	236.122	−	136.325i	0.375991	−	0.217078i
$629$		−	547.917i		−	0.871092i
$630$	−87.1697	+	50.3274i	−0.138365	+	0.0798848i
$631$	−405.265	+	233.980i	−0.642259	+	0.370808i	−0.785484	−	0.618882i	$-0.787586\pi$
$631$	−405.265	+	233.980i	−0.642259	+	0.370808i	0.143225	+	0.989690i	$0.454253\pi$
$632$	−273.065	+	157.654i	−0.432065	+	0.249453i
$633$	−800.936	+	1387.26i	−1.26530	+	2.19157i
$634$			118.403i			0.186756i
$635$	124.258	+	71.7402i	0.195681	+	0.112977i
$636$	165.715	−	95.6756i	0.260558	−	0.150433i
$637$	−469.341			−0.736799
$638$	−237.859	−	411.985i	−0.372820	−	0.645744i
$639$	−987.924	−	570.378i	−1.54605	−	0.892611i
$640$	−14.9218	+	25.8454i	−0.0233153	+	0.0403834i
$641$		−	1181.26i		−	1.84283i	−0.388577	−	0.921416i	$-0.627033\pi$
$641$		−	1181.26i		−	1.84283i	0.388577	−	0.921416i	$-0.372967\pi$
$642$	350.558	−	607.184i	0.546041	−	0.945770i
$643$	1130.33			1.75790			0.878948	−	0.476917i	$-0.158246\pi$
$643$	1130.33			1.75790			0.878948	+	0.476917i	$0.158246\pi$
$644$			81.9642i			0.127274i
$645$	−58.4559	+	947.292i	−0.0906293	+	1.46867i
$646$	−407.161			−0.630280
$647$		−	1275.13i		−	1.97084i	−0.170149	−	0.985418i	$-0.554425\pi$
$647$		−	1275.13i		−	1.97084i	0.170149	−	0.985418i	$-0.445575\pi$
$648$	−608.937	−	351.570i	−0.939718	−	0.542546i
$649$	767.178			1.18209
$650$	27.8814	+	16.0973i	0.0428944	+	0.0247651i
$651$	−22.4662	+	38.9125i	−0.0345102	+	0.0597735i
$652$	−58.5509	+	33.8044i	−0.0898020	+	0.0518472i
$653$		−	185.383i		−	0.283894i	−0.989874	−	0.141947i	$-0.954664\pi$
$653$		−	185.383i		−	0.283894i	0.989874	−	0.141947i	$-0.0453363\pi$
$654$	111.294	+	192.766i	0.170174	+	0.294750i
$655$	80.2558	−	139.007i	0.122528	−	0.212225i
$656$	138.213			0.210691
$657$	133.694	+	77.1881i	0.203491	+	0.117486i
$658$	−84.5458	−	146.438i	−0.128489	−	0.222549i
$659$	119.493	+	206.969i	0.181325	+	0.314065i	0.942332	−	0.334679i	$-0.108628\pi$
$659$	119.493	+	206.969i	0.181325	+	0.314065i	−0.761007	+	0.648744i	$0.775295\pi$
$660$	370.722	+	642.109i	0.561700	+	0.972892i
$661$	−1149.01			−1.73829			−0.869144	−	0.494559i	$-0.835330\pi$
$661$	−1149.01			−1.73829			−0.869144	+	0.494559i	$0.835330\pi$
$662$	56.7657	+	98.3211i	0.0857488	+	0.148521i
$663$	−920.094	+	531.217i	−1.38777	+	0.801232i
$664$	641.423	+	370.326i	0.965999	+	0.557720i
$665$	−69.1353	−	39.9153i	−0.103963	−	0.0600230i
$666$	295.668			0.443946
$667$			537.969i			0.806551i
$668$	171.035	−	296.241i	0.256040	−	0.443474i
$669$	471.381	−	816.455i	0.704605	−	1.22041i
$670$	481.910	+	834.693i	0.719269	+	1.24581i
$671$	−539.530	+	311.498i	−0.804068	+	0.464229i
$672$			152.351i			0.226713i
$673$	106.943	−	61.7437i	0.158905	−	0.0917440i	−0.418439	−	0.908245i	$-0.637423\pi$
$673$	106.943	−	61.7437i	0.158905	−	0.0917440i	0.577344	+	0.816501i	$0.304089\pi$
$674$	−345.185	+	199.292i	−0.512143	+	0.295686i
$675$	−0.342998	+	0.198030i	−0.000508145	+	0.000293378i
$676$	59.2771	−	102.671i	0.0876880	−	0.151880i
$677$			444.331i			0.656323i	0.944622	+	0.328162i	$0.106429\pi$
$677$			444.331i			0.656323i	−0.944622	+	0.328162i	$0.893571\pi$
$678$	−138.721	−	80.0908i	−0.204604	−	0.118128i
$679$	−139.865	+	80.7510i	−0.205987	+	0.118926i
$680$	1128.88			1.66012
$681$	428.886	+	742.852i	0.629788	+	1.09083i
$682$	−190.452	−	109.957i	−0.279255	−	0.161228i
$683$	162.804	−	281.985i	0.238366	−	0.412863i	−0.721879	−	0.692019i	$-0.756721\pi$
$683$	162.804	−	281.985i	0.238366	−	0.412863i	0.960246	+	0.279156i	$0.0900547\pi$
$684$			164.935i			0.241132i
$685$	447.605	−	775.274i	0.653438	−	1.13179i
$686$	207.053			0.301826
$687$		−	596.989i		−	0.868980i
$688$	−222.143	−	147.207i	−0.322883	−	0.213964i
$689$	−263.120			−0.381887
$690$			1116.94i			1.61875i
$691$	6.60671	+	3.81439i	0.00956109	+	0.00552010i	0.504773	−	0.863252i	$-0.331576\pi$
$691$	6.60671	+	3.81439i	0.00956109	+	0.00552010i	−0.495212	+	0.868772i	$0.664910\pi$
$692$	−147.617			−0.213319
$693$	216.837	+	125.191i	0.312896	+	0.180651i
$694$	444.151	−	769.293i	0.639988	−	1.10849i
$695$	−278.495	+	160.789i	−0.400712	+	0.231351i
$696$			588.244i			0.845178i
$697$	279.745	+	484.533i	0.401356	+	0.695169i
$698$	335.538	−	581.169i	0.480714	−	0.832620i
$699$	−214.224			−0.306472
$700$	4.51868	+	2.60886i	0.00645526	+	0.00372694i
$701$	154.353	+	267.347i	0.220189	+	0.381379i	0.954865	−	0.297039i	$-0.0959991\pi$
$701$	154.353	+	267.347i	0.220189	+	0.381379i	−0.734676	+	0.678418i	$0.762666\pi$
$702$	1.40371	+	2.43129i	0.00199958	+	0.00346337i
$703$	117.249	+	203.081i	0.166784	+	0.288878i
$704$	−1231.18			−1.74883
$705$	864.875	+	1498.01i	1.22677	+	2.12483i
$706$	−782.108	+	451.550i	−1.10780	+	0.639589i
$707$	84.3058	+	48.6740i	0.119244	+	0.0688458i
$708$	−246.554	−	142.348i	−0.348241	−	0.201057i
$709$	−85.3563			−0.120390			−0.0601949	−	0.998187i	$-0.519172\pi$
$709$	−85.3563			−0.120390			−0.0601949	+	0.998187i	$0.519172\pi$
$710$		−	1002.84i		−	1.41245i
$711$	163.445	−	283.094i	0.229880	−	0.398164i
$712$	−55.7632	+	96.5847i	−0.0783191	+	0.135653i
$713$	124.346	+	215.374i	0.174398	+	0.302067i
$714$	198.643	−	114.687i	0.278212	−	0.160626i
$715$		−	1019.53i		−	1.42592i
$716$	−121.130	+	69.9345i	−0.169176	+	0.0976738i
$717$	43.1885	−	24.9349i	0.0602349	−	0.0347767i
$718$	333.008	−	192.262i	0.463800	−	0.267775i
$719$	−253.076	+	438.341i	−0.351984	+	0.609654i	−0.986597	−	0.163176i	$-0.947826\pi$
$719$	−253.076	+	438.341i	−0.351984	+	0.609654i	0.634613	+	0.772830i	$0.281159\pi$
$720$			289.115i			0.401548i
$721$	78.0311	+	45.0513i	0.108226	+	0.0624845i
$722$	−321.657	+	185.709i	−0.445508	+	0.257214i
$723$	−644.085			−0.890850
$724$	−145.393	−	251.828i	−0.200819	−	0.347829i
$725$	29.6582	+	17.1232i	0.0409079	+	0.0236182i
$726$	−840.944	+	1456.56i	−1.15833	+	2.00628i
$727$		−	230.282i		−	0.316757i	−0.987379	−	0.158378i	$-0.949373\pi$
$727$		−	230.282i		−	0.316757i	0.987379	−	0.158378i	$-0.0506265\pi$
$728$	61.6193	−	106.728i	0.0846419	−	0.146604i
$729$	721.878			0.990230
$730$			135.713i			0.185908i
$731$	66.4424	−	1076.71i	0.0908925	−	1.47293i
$732$	231.191			0.315835
$733$		−	500.013i		−	0.682147i	−0.940037	−	0.341073i	$-0.889210\pi$
$733$		−	500.013i		−	0.682147i	0.940037	−	0.341073i	$-0.110790\pi$
$734$	372.277	+	214.934i	0.507189	+	0.292826i
$735$	−1036.55			−1.41028
$736$	730.262	+	421.617i	0.992204	+	0.572849i
$737$	1198.77	−	2076.32i	1.62655	−	2.81726i
$738$	−261.465	+	150.957i	−0.354288	+	0.204548i
$739$			865.575i			1.17128i	0.810572	+	0.585639i	$0.199157\pi$
$739$			865.575i			1.17128i	−0.810572	+	0.585639i	$0.800843\pi$
$740$	−97.5595	−	168.978i	−0.131837	−	0.228349i
$741$	227.351	−	393.783i	0.306816	−	0.531421i
$742$	56.8062			0.0765582
$743$	1045.99	+	603.905i	1.40780	+	0.812793i	0.995176	−	0.0981096i	$-0.0312796\pi$
$743$	1045.99	+	603.905i	1.40780	+	0.812793i	0.412622	+	0.910902i	$0.364613\pi$
$744$	135.967	+	235.501i	0.182751	+	0.316534i
$745$	543.812	+	941.910i	0.729949	+	1.26431i
$746$	200.075	+	346.540i	0.268197	+	0.464531i
$747$	−767.855			−1.02792
$748$	−421.371	−	729.836i	−0.563331	−	0.975717i
$749$	−135.313	+	78.1232i	−0.180659	+	0.104303i
$750$	−660.757	−	381.488i	−0.881009	−	0.508651i
$751$	405.939	+	234.369i	0.540532	+	0.312076i	0.745294	−	0.666735i	$-0.232309\pi$
$751$	405.939	+	234.369i	0.540532	+	0.312076i	−0.204763	+	0.978812i	$0.565642\pi$
$752$	−485.688			−0.645861
$753$			181.699i			0.241300i
$754$	121.375	−	210.228i	0.160975	−	0.278817i
$755$	401.763	−	695.874i	0.532137	−	0.921688i
$756$	0.227496	+	0.394034i	0.000300920	+	0.000521209i
$757$	591.471	−	341.486i	0.781336	−	0.451104i	−0.0555678	−	0.998455i	$-0.517697\pi$
$757$	591.471	−	341.486i	0.781336	−	0.451104i	0.836903	+	0.547351i	$0.184364\pi$
$758$			148.244i			0.195572i
$759$	2406.18	−	1389.21i	3.17020	−	1.83032i
$760$	−418.411	+	241.570i	−0.550541	+	0.317855i
$761$	−284.325	+	164.155i	−0.373620	+	0.215710i	−0.675039	−	0.737782i	$-0.735873\pi$
$761$	−284.325	+	164.155i	−0.373620	+	0.215710i	0.301419	+	0.953492i	$0.402540\pi$
$762$	88.2188	−	152.799i	0.115773	−	0.200524i
$763$		−	49.6044i		−	0.0650124i
$764$	146.904	+	84.8153i	0.192283	+	0.111015i
$765$	−1013.55	+	585.171i	−1.32490	+	0.764930i
$766$	664.675			0.867723
$767$	195.738	+	339.028i	0.255199	+	0.442018i
$768$	954.541	+	551.105i	1.24289	+	0.717584i
$769$	−278.216	+	481.884i	−0.361789	+	0.626637i	−0.988255	−	0.152811i	$-0.951167\pi$
$769$	−278.216	+	481.884i	−0.361789	+	0.626637i	0.626466	+	0.779449i	$0.284501\pi$
$770$			220.111i			0.285859i
$771$	−359.627	+	622.893i	−0.466443	+	0.807903i
$772$	−418.100			−0.541580
$773$			440.683i			0.570095i	0.958513	+	0.285047i	$0.0920093\pi$
$773$			440.683i			0.570095i	−0.958513	+	0.285047i	$0.907991\pi$
$774$	581.019	+	35.8538i	0.750671	+	0.0463227i
$775$	15.8314			0.0204276
$776$			977.420i			1.25956i
$777$	−114.406	−	66.0521i	−0.147240	−	0.0850091i
$778$	−422.986			−0.543683
$779$	−207.371	−	119.726i	−0.266201	−	0.153691i
$780$	−189.172	+	327.656i	−0.242528	+	0.420071i
$781$	−2160.39	+	1247.30i	−2.76618	+	1.59705i
$782$		−	1269.54i		−	1.62345i
$783$	1.49316	+	2.58623i	0.00190698	+	0.00330298i
$784$	145.524	−	252.056i	0.185618	−	0.321499i
$785$	−828.004			−1.05478
$786$	−170.937	−	98.6904i	−0.217477	−	0.125560i
$787$	81.7718	+	141.633i	0.103903	+	0.179966i	0.913290	−	0.407311i	$-0.133533\pi$
$787$	81.7718	+	141.633i	0.103903	+	0.179966i	−0.809386	+	0.587277i	$0.800200\pi$
$788$	275.685	+	477.500i	0.349854	+	0.605965i
$789$	−591.518	−	1024.54i	−0.749706	−	1.29853i
$790$	287.369			0.363759
$791$	17.8485	+	30.9146i	0.0225645	+	0.0390829i
$792$	1312.31	−	757.663i	1.65696	−	0.956645i
$793$	−275.311	−	158.951i	−0.347177	−	0.200443i
$794$	284.412	+	164.205i	0.358201	+	0.206807i
$795$	−581.108			−0.730954
$796$		−	67.2471i		−	0.0844812i
$797$	527.628	−	913.878i	0.662017	−	1.14665i	−0.318068	−	0.948068i	$-0.603034\pi$
$797$	527.628	−	913.878i	0.662017	−	1.14665i	0.980085	−	0.198579i	$-0.0636327\pi$
$798$	−49.0838	+	85.0156i	−0.0615085	+	0.106536i
$799$	−983.037	−	1702.67i	−1.23033	−	2.13100i
$800$	46.4874	−	26.8395i	0.0581093	−	0.0335494i
$801$		−	115.623i		−	0.144348i
$802$	−532.952	+	307.700i	−0.664529	+	0.383666i
$803$	292.360	−	168.794i	0.364085	−	0.210205i
$804$	−770.515	+	444.857i	−0.958352	+	0.553305i
$805$	124.457	−	215.566i	0.154605	−	0.267784i
$806$		−	112.218i		−	0.139229i
$807$	411.980	+	237.857i	0.510508	+	0.294742i
$808$	510.224	−	294.578i	0.631465	−	0.364577i
$809$	−1278.56			−1.58042			−0.790209	−	0.612837i	$-0.790028\pi$
$809$	−1278.56			−1.58042			−0.790209	+	0.612837i	$0.790028\pi$
$810$	320.418	+	554.980i	0.395578	+	0.685160i
$811$	−1346.24	−	777.252i	−1.65998	−	0.958387i	−0.972723	−	0.231968i	$-0.925484\pi$
$811$	−1346.24	−	777.252i	−1.65998	−	0.958387i	−0.687252	−	0.726419i	$-0.741183\pi$
$812$	19.6710	−	34.0712i	0.0242254	−	0.0419596i
$813$			140.819i			0.173209i
$814$	323.283	−	559.942i	0.397153	−	0.687889i
$815$	205.319			0.251925
$816$		−	658.838i		−	0.807400i
$817$	205.780	+	413.294i	0.251873	+	0.505868i
$818$	95.4121			0.116641
$819$			127.765i			0.156001i
$820$	172.547	+	99.6202i	0.210423	+	0.121488i
$821$	−271.907			−0.331189			−0.165595	−	0.986194i	$-0.552954\pi$
$821$	−271.907			−0.331189			−0.165595	+	0.986194i	$0.552954\pi$
$822$	−953.354	−	550.419i	−1.15980	−	0.669610i
$823$	−311.057	+	538.766i	−0.377955	+	0.654637i	−0.990765	−	0.135594i	$-0.956706\pi$
$823$	−311.057	+	538.766i	−0.377955	+	0.654637i	0.612810	+	0.790230i	$0.290039\pi$
$824$	472.249	−	272.653i	0.573118	−	0.330890i
$825$		−	176.870i		−	0.214388i
$826$	−42.2587	−	73.1943i	−0.0511607	−	0.0886129i
$827$	−529.310	+	916.791i	−0.640036	+	1.10857i	0.345388	+	0.938460i	$0.387747\pi$
$827$	−529.310	+	916.791i	−0.640036	+	1.10857i	−0.985424	+	0.170115i	$0.945586\pi$
$828$	−514.271			−0.621100
$829$	269.501	+	155.597i	0.325092	+	0.187692i	0.653660	−	0.756788i	$-0.273233\pi$
$829$	269.501	+	155.597i	0.325092	+	0.187692i	−0.328568	+	0.944480i	$0.606566\pi$
$830$	−337.512	−	584.587i	−0.406641	−	0.704322i
$831$	−199.517	−	345.573i	−0.240092	−	0.415852i
$832$	−314.122	−	544.076i	−0.377551	−	0.653938i
$833$	1178.17			1.41437
$834$	197.722	+	342.465i	0.237077	+	0.410629i
$835$	−899.643	+	519.409i	−1.07742	+	0.622047i
$836$	312.356	+	180.339i	0.373632	+	0.215716i
$837$	1.19556	+	0.690258i	0.00142839	+	0.000824681i
$838$	275.779			0.329091
$839$			827.992i			0.986879i	0.869780	+	0.493440i	$0.164261\pi$
$839$			827.992i			0.986879i	−0.869780	+	0.493440i	$0.835739\pi$
$840$	136.088	−	235.711i	0.162010	−	0.280609i
$841$	−291.390	+	504.702i	−0.346480	+	0.600121i
$842$	270.706	+	468.876i	0.321504	+	0.556860i
$843$	283.241	−	163.529i	0.335991	−	0.193985i
$844$		−	648.380i		−	0.768223i
$845$	−311.798	+	180.017i	−0.368992	+	0.213037i
$846$	918.799	−	530.469i	1.08605	−	0.627032i
$847$	324.599	−	187.408i	0.383234	−	0.221260i
$848$	81.5833	−	141.306i	0.0962067	−	0.166635i
$849$		−	695.869i		−	0.819634i
$850$	−69.9897	−	40.4086i	−0.0823408	−	0.0475395i
$851$	−633.213	+	365.586i	−0.744082	+	0.429596i
$852$	925.736			1.08654
$853$	−764.869	−	1324.79i	−0.896682	−	1.55310i	−0.831709	−	0.555211i	$-0.812637\pi$
$853$	−764.869	−	1324.79i	−0.896682	−	1.55310i	−0.0649722	−	0.997887i	$-0.520696\pi$
$854$	59.4382	+	34.3167i	0.0695998	+	0.0401835i
$855$	250.442	−	433.779i	0.292915	−	0.507343i
$856$			945.612i			1.10469i
$857$	−622.430	+	1078.08i	−0.726289	+	1.25797i	0.232152	+	0.972679i	$0.425423\pi$
$857$	−622.430	+	1078.08i	−0.726289	+	1.25797i	−0.958441	+	0.285290i	$0.907910\pi$
$858$	−1253.72			−1.46121
$859$			158.942i			0.185032i	0.995711	+	0.0925159i	$0.0294909\pi$
$859$			158.942i			0.185032i	−0.995711	+	0.0925159i	$0.970509\pi$
$860$	−171.224	−	343.890i	−0.199098	−	0.399873i
$861$	134.894			0.156672
$862$			305.301i			0.354177i
$863$	−320.063	−	184.788i	−0.370872	−	0.214123i	0.302967	−	0.953001i	$-0.402023\pi$
$863$	−320.063	−	184.788i	−0.370872	−	0.214123i	−0.673839	+	0.738878i	$0.735356\pi$
$864$	4.68088			0.00541768
$865$	388.233	+	224.146i	0.448824	+	0.259129i
$866$	−352.605	+	610.730i	−0.407165	+	0.705231i
$867$	1249.12	−	721.182i	1.44074	−	0.831813i
$868$		−	18.1870i		−	0.0209528i
$869$	−357.420	−	619.069i	−0.411300	−	0.712393i
$870$	268.060	−	464.294i	0.308115	−	0.533671i
$871$	1223.41			1.40461
$872$	−259.989	−	150.104i	−0.298152	−	0.172138i
$873$	−506.659	−	877.560i	−0.580366	−	1.00522i
$874$	271.670	+	470.546i	0.310835	+	0.538382i
$875$	85.0161	+	147.252i	0.0971612	+	0.168288i
$876$	−125.278			−0.143011
$877$	411.371	+	712.516i	0.469067	+	0.812447i	0.999375	−	0.0353577i	$-0.0112571\pi$
$877$	411.371	+	712.516i	0.469067	+	0.812447i	−0.530308	+	0.847805i	$0.677924\pi$
$878$	835.409	−	482.324i	0.951491	−	0.549344i
$879$	−652.018	−	376.443i	−0.741773	−	0.428263i
$880$	547.531	+	316.117i	0.622194	+	0.359224i
$881$	1688.29			1.91634			0.958169	−	0.286205i	$-0.0923937\pi$
$881$	1688.29			1.91634			0.958169	+	0.286205i	$0.0923937\pi$
$882$			635.768i			0.720825i
$883$	299.386	−	518.552i	0.339055	−	0.587261i	−0.645200	−	0.764014i	$-0.723226\pi$
$883$	299.386	−	518.552i	0.339055	−	0.587261i	0.984255	+	0.176753i	$0.0565592\pi$
$884$	215.017	−	372.421i	0.243232	−	0.421291i
$885$	432.293	+	748.753i	0.488466	+	0.846048i
$886$	−473.933	+	273.625i	−0.534913	+	0.308832i
$887$			1583.51i			1.78524i	0.450810	+	0.892620i	$0.351135\pi$
$887$			1583.51i			1.78524i	−0.450810	+	0.892620i	$0.648865\pi$
$888$	−692.389	+	399.751i	−0.779717	+	0.450170i
$889$	−34.0519	+	19.6599i	−0.0383036	+	0.0221146i
$890$	88.0264	−	50.8221i	0.0989061	−	0.0571035i
$891$	797.049	−	1380.53i	0.894555	−	1.54941i
$892$			381.596i			0.427798i
$893$	728.711	+	420.721i	0.816025	+	0.471133i
$894$	1158.27	−	668.725i	1.29560	−	0.748015i
$895$	424.763			0.474596
$896$	−4.08922	−	7.08274i	−0.00456386	−	0.00790484i
$897$	1227.83	+	708.887i	1.36882	+	0.790286i
$898$	−535.732	+	927.915i	−0.596584	+	1.03331i
$899$		−	119.370i		−	0.132781i
$900$	−16.3689	+	28.3517i	−0.0181876	+	0.0315019i
$901$	660.502			0.733076
$902$			660.222i			0.731953i
$903$	−216.809	−	143.673i	−0.240099	−	0.159106i
$904$	216.041			0.238983
$905$			883.080i			0.975779i
$906$	−855.716	−	494.048i	−0.944499	−	0.545307i
$907$	1250.79			1.37904			0.689518	−	0.724269i	$-0.257822\pi$
$907$	1250.79			1.37904			0.689518	+	0.724269i	$0.257822\pi$
$908$	−300.680	−	173.598i	−0.331145	−	0.191187i
$909$	−305.397	+	528.964i	−0.335971	+	0.581918i
$910$	−97.2707	+	56.1593i	−0.106891	+	0.0617135i
$911$			170.898i			0.187594i	0.995591	+	0.0937970i	$0.0299005\pi$
$911$			170.898i			0.187594i	−0.995591	+	0.0937970i	$0.970100\pi$
$912$	140.985	+	244.193i	0.154589	+	0.267756i
$913$	−839.570	+	1454.18i	−0.919573	+	1.59275i
$914$	−671.964			−0.735191
$915$	−608.033	−	351.048i	−0.664517	−	0.383659i
$916$	120.820	+	209.266i	0.131899	+	0.228457i
$917$	21.9935	+	38.0939i	0.0239842	+	0.0415419i
$918$	−3.52367	−	6.10318i	−0.00383843	−	0.00664835i
$919$	−169.349			−0.184275			−0.0921377	−	0.995746i	$-0.529370\pi$
$919$	−169.349			−0.184275			−0.0921377	+	0.995746i	$0.529370\pi$
$920$	−753.222	−	1304.62i	−0.818719	−	1.41806i
$921$	884.768	−	510.821i	0.960660	−	0.554637i
$922$	−655.417	−	378.405i	−0.710865	−	0.410418i
$923$	−1102.40	−	636.473i	−1.19437	−	0.689569i
$924$	−203.187			−0.219900
$925$			46.5454i			0.0503193i
$926$	−660.061	+	1143.26i	−0.712809	+	1.23462i
$927$	−282.667	+	489.594i	−0.304927	+	0.528149i
$928$	−202.372	−	350.519i	−0.218073	−	0.377714i
$929$	−850.652	+	491.124i	−0.915665	+	0.528659i	−0.882249	−	0.470782i	$-0.843972\pi$
$929$	−850.652	+	491.124i	−0.915665	+	0.528659i	−0.0334152	+	0.999442i	$0.510638\pi$
$930$		−	247.837i		−	0.266492i
$931$	−436.680	+	252.118i	−0.469044	+	0.270803i
$932$	75.0933	−	43.3551i	0.0805722	−	0.0465184i
$933$	−172.794	+	99.7627i	−0.185203	+	0.106927i
$934$	−16.7227	+	28.9645i	−0.0179043	+	0.0310112i
$935$			2559.30i			2.73722i
$936$	669.646	+	386.620i	0.715434	+	0.413056i
$937$	999.637	−	577.141i	1.06685	−	0.615945i	0.139530	−	0.990218i	$-0.455441\pi$
$937$	999.637	−	577.141i	1.06685	−	0.615945i	0.927319	+	0.374273i	$0.122108\pi$
$938$	−264.128			−0.281587
$939$	−7.79453	−	13.5005i	−0.00830089	−	0.0143776i
$940$	−606.339	−	350.070i	−0.645042	−	0.372415i
$941$	832.384	−	1441.73i	0.884574	−	1.53213i	0.0383733	−	0.999263i	$-0.487782\pi$
$941$	832.384	−	1441.73i	0.884574	−	1.53213i	0.846201	−	0.532864i	$-0.178884\pi$
$942$			1018.19i			1.08089i
$943$	373.308	−	646.588i	0.395873	−	0.685672i
$944$	−242.763			−0.257164
$945$		−	1.38175i		−	0.00146217i
$946$	703.185	−	1061.14i	0.743325	−	1.12172i
$947$	−451.815			−0.477101			−0.238551	−	0.971130i	$-0.576672\pi$
$947$	−451.815			−0.477101			−0.238551	+	0.971130i	$0.576672\pi$
$948$			265.274i			0.279825i
$949$	149.186	+	86.1325i	0.157203	+	0.0907613i
$950$	34.5882			0.0364086
$951$	287.458	+	165.964i	0.302270	+	0.174515i
$952$	−154.681	+	267.915i	−0.162480	+	0.281423i
$953$	538.083	−	310.662i	0.564620	−	0.325984i	−0.190378	−	0.981711i	$-0.560971\pi$
$953$	538.083	−	310.662i	0.564620	−	0.325984i	0.754998	+	0.655727i	$0.227638\pi$
$954$			356.421i			0.373607i
$955$	−257.573	−	446.129i	−0.269710	−	0.467151i
$956$	−10.0927	+	17.4811i	−0.0105573	+	0.0182857i
$957$	−1333.61			−1.39354
$958$	−959.976	−	554.242i	−1.00206	−	0.578541i
$959$	122.663	+	212.459i	0.127907	+	0.221542i
$960$	−693.749	−	1201.61i	−0.722655	−	1.25167i
$961$	452.909	+	784.461i	0.471289	+	0.816297i
$962$	329.929			0.342962
$963$	−490.171	−	849.002i	−0.509005	−	0.881622i
$964$	225.775	−	130.351i	0.234206	−	0.135219i
$965$	1099.60	+	634.856i	1.13949	+	0.657882i
$966$	−265.081	−	153.045i	−0.274411	−	0.158431i
$967$	19.2812			0.0199392			0.00996961	−	0.999950i	$-0.496827\pi$
$967$	19.2812			0.0199392			0.00996961	+	0.999950i	$0.496827\pi$
$968$		−	2268.40i		−	2.34339i
$969$	−570.711	+	988.501i	−0.588969	+	1.02012i
$970$	445.406	−	771.465i	0.459181	−	0.795325i
$971$	454.351	+	786.958i	0.467920	+	0.810462i	0.999328	−	0.0366546i	$-0.0116701\pi$
$971$	454.351	+	786.958i	0.467920	+	0.810462i	−0.531408	+	0.847116i	$0.678337\pi$
$972$	−509.824	+	294.347i	−0.524510	+	0.302826i
$973$		−	88.1262i		−	0.0905716i
$974$	−622.746	+	359.543i	−0.639370	+	0.369140i
$975$	78.1617	−	45.1267i	0.0801659	−	0.0462838i
$976$	170.727	−	98.5691i	0.174925	−	0.100993i
$977$	−464.004	+	803.679i	−0.474928	+	0.822599i	−0.999588	−	0.0287130i	$-0.990859\pi$
$977$	−464.004	+	803.679i	−0.474928	+	0.822599i	0.524660	+	0.851312i	$0.324192\pi$
$978$		−	252.480i		−	0.258160i
$979$	−218.968	−	126.421i	−0.223665	−	0.129133i
$980$	363.349	−	209.780i	0.370765	−	0.214061i
$981$	311.235			0.317263
$982$	−35.5082	−	61.5019i	−0.0361590	−	0.0626293i
$983$	895.385	+	516.951i	0.910869	+	0.525891i	0.880711	−	0.473654i	$-0.157065\pi$
$983$	895.385	+	516.951i	0.910869	+	0.525891i	0.0301586	+	0.999545i	$0.490399\pi$
$984$	408.195	−	707.014i	0.414832	−	0.718510i
$985$		−	1674.44i		−	1.69994i
$986$	−304.684	+	527.728i	−0.309010	+	0.535221i
$987$	−474.026			−0.480269
$988$			184.047i			0.186282i
$989$	−1288.66	+	641.630i	−1.30300	+	0.648766i
$990$	−1381.05			−1.39500
$991$		−	1837.99i		−	1.85469i	−0.374212	−	0.927343i	$-0.622087\pi$
$991$		−	1837.99i		−	1.85469i	0.374212	−	0.927343i	$-0.377913\pi$
$992$	−162.038	−	93.5524i	−0.163344	−	0.0943069i
$993$	318.270			0.320514
$994$	238.003	+	137.411i	0.239439	+	0.138240i
$995$	−102.110	+	176.860i	−0.102623	+	0.177749i
$996$	539.639	−	311.561i	0.541807	−	0.312812i
$997$		−	1108.28i		−	1.11161i	−0.831312	−	0.555806i	$-0.812410\pi$
$997$		−	1108.28i		−	1.11161i	0.831312	−	0.555806i	$-0.187590\pi$
$998$	415.832	+	720.242i	0.416666	+	0.721686i
$999$	−2.02940	+	3.51503i	−0.00203144	+	0.00351855i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.3.d.a.37.3	yes	12
3.2	odd	2		387.3.j.c.37.4		12
4.3	odd	2		688.3.t.c.209.6		12
43.7	odd	6	inner	43.3.d.a.7.4	✓	12
129.50	even	6		387.3.j.c.136.3		12
172.7	even	6		688.3.t.c.609.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.3.d.a.7.4	✓	12	43.7	odd	6	inner
43.3.d.a.37.3	yes	12	1.1	even	1	trivial
387.3.j.c.37.4		12	3.2	odd	2
387.3.j.c.136.3		12	129.50	even	6
688.3.t.c.209.6		12	4.3	odd	2
688.3.t.c.609.6		12	172.7	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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	43.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.51156i q^{2} +(-3.66976 - 2.11873i) q^{3} +1.71518 q^{4} +(-4.51092 - 2.60438i) q^{5} +(-3.20260 + 5.54707i) q^{6} +(1.23619 - 0.713712i) q^{7} -8.63885i q^{8} +(4.47807 + 7.75625i) q^{9} +O(q^{10})\)	\(q-1.51156i q^{2} +(-3.66976 - 2.11873i) q^{3} +1.71518 q^{4} +(-4.51092 - 2.60438i) q^{5} +(-3.20260 + 5.54707i) q^{6} +(1.23619 - 0.713712i) q^{7} -8.63885i q^{8} +(4.47807 + 7.75625i) q^{9} +(-3.93669 + 6.81854i) q^{10} +19.5852 q^{11} +(-6.29427 - 3.63400i) q^{12} +(4.99698 + 8.65502i) q^{13} +(-1.07882 - 1.86857i) q^{14} +(11.0360 + 19.1149i) q^{15} -6.19747 q^{16} +(-12.5438 - 21.7264i) q^{17} +(11.7241 - 6.76889i) q^{18} +(9.29850 + 5.36849i) q^{19} +(-7.73701 - 4.46697i) q^{20} -6.04866 q^{21} -29.6043i q^{22} +(-16.7391 + 28.9930i) q^{23} +(-18.3034 + 31.7025i) q^{24} +(1.06559 + 1.84565i) q^{25} +(13.0826 - 7.55325i) q^{26} +0.185841i q^{27} +(2.12027 - 1.22414i) q^{28} +(13.9164 - 8.03462i) q^{29} +(28.8934 - 16.6816i) q^{30} +(3.71424 - 6.43325i) q^{31} -25.1875i q^{32} +(-71.8730 - 41.4959i) q^{33} +(-32.8409 + 18.9607i) q^{34} -7.43511 q^{35} +(7.68068 + 13.3033i) q^{36} +(18.9142 + 10.9201i) q^{37} +(8.11482 - 14.0553i) q^{38} -42.3491i q^{39} +(-22.4989 + 38.9692i) q^{40} -22.3015 q^{41} +9.14294i q^{42} +(35.8442 + 23.7528i) q^{43} +33.5921 q^{44} -46.6504i q^{45} +(43.8248 + 25.3022i) q^{46} +78.3686 q^{47} +(22.7432 + 13.1308i) q^{48} +(-23.4812 + 40.6707i) q^{49} +(2.78982 - 1.61070i) q^{50} +106.308i q^{51} +(8.57070 + 14.8449i) q^{52} +(-13.1640 + 22.8006i) q^{53} +0.280911 q^{54} +(-88.3474 - 51.0074i) q^{55} +(-6.16565 - 10.6792i) q^{56} +(-22.7488 - 39.4021i) q^{57} +(-12.1448 - 21.0355i) q^{58} +39.1712 q^{59} +(18.9286 + 32.7854i) q^{60} +(-27.5478 + 15.9047i) q^{61} +(-9.72426 - 5.61430i) q^{62} +(11.0715 + 6.39211i) q^{63} -62.8625 q^{64} -52.0561i q^{65} +(-62.7237 + 108.641i) q^{66} +(61.2076 - 106.015i) q^{67} +(-21.5147 - 37.2646i) q^{68} +(122.857 - 70.9315i) q^{69} +11.2386i q^{70} +(-110.307 + 63.6857i) q^{71} +(67.0051 - 38.6854i) q^{72} +(14.9276 - 8.61845i) q^{73} +(16.5064 - 28.5900i) q^{74} -9.03079i q^{75} +(15.9486 + 9.20790i) q^{76} +(24.2110 - 13.9782i) q^{77} -64.0134 q^{78} +(-18.2494 - 31.6090i) q^{79} +(27.9563 + 16.1406i) q^{80} +(40.6964 - 70.4882i) q^{81} +33.7102i q^{82} +(-42.8675 + 74.2487i) q^{83} -10.3745 q^{84} +130.675i q^{85} +(35.9038 - 54.1808i) q^{86} -68.0929 q^{87} -169.194i q^{88} +(-11.1803 - 6.45493i) q^{89} -70.5150 q^{90} +(12.3544 + 7.13281i) q^{91} +(-28.7105 + 49.7281i) q^{92} +(-27.2607 + 15.7390i) q^{93} -118.459i q^{94} +(-27.9632 - 48.4336i) q^{95} +(-53.3657 + 92.4321i) q^{96} -113.142 q^{97} +(61.4763 + 35.4934i) q^{98} +(87.7041 + 151.908i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 26 q^{4} - 3 q^{5} - 9 q^{6} + 9 q^{7} - 12 q^{9}+O(q^{10}) \) 12 * q - 26 * q^4 - 3 * q^5 - 9 * q^6 + 9 * q^7 - 12 * q^9	\( 12 q - 26 q^{4} - 3 q^{5} - 9 q^{6} + 9 q^{7} - 12 q^{9} - q^{10} + 28 q^{11} - 6 q^{12} + 24 q^{13} - 18 q^{14} - 13 q^{15} + 110 q^{16} - 7 q^{17} + 33 q^{18} + 66 q^{19} - 99 q^{20} - 80 q^{21} - 16 q^{23} - 2 q^{24} - 21 q^{25} + 9 q^{26} - 192 q^{28} - 111 q^{29} + 99 q^{30} - 29 q^{31} - 114 q^{33} + 213 q^{34} + 38 q^{35} + 152 q^{36} + 120 q^{37} + 172 q^{38} - 29 q^{40} + 94 q^{41} + 5 q^{43} - 174 q^{44} + 156 q^{46} - 18 q^{47} - 213 q^{48} - 99 q^{49} - 198 q^{50} - 234 q^{52} - 58 q^{53} + 128 q^{54} - 258 q^{55} + 315 q^{56} + 51 q^{57} - 196 q^{58} + 336 q^{59} - 5 q^{60} + 204 q^{61} + 261 q^{62} - 153 q^{63} - 604 q^{64} - 201 q^{66} + 115 q^{67} - 106 q^{68} + 423 q^{69} - 66 q^{71} + 294 q^{72} + 249 q^{73} - 214 q^{74} - 438 q^{76} + 117 q^{77} + 136 q^{78} + 236 q^{79} + 681 q^{80} + 110 q^{81} - 4 q^{83} + 248 q^{84} + 102 q^{86} - 408 q^{87} - 45 q^{89} - 44 q^{90} - 156 q^{91} - 483 q^{92} - 567 q^{93} - 389 q^{95} - 278 q^{96} - 370 q^{97} - 879 q^{98} + 157 q^{99}+O(q^{100}) \) 12 * q - 26 * q^4 - 3 * q^5 - 9 * q^6 + 9 * q^7 - 12 * q^9 - q^10 + 28 * q^11 - 6 * q^12 + 24 * q^13 - 18 * q^14 - 13 * q^15 + 110 * q^16 - 7 * q^17 + 33 * q^18 + 66 * q^19 - 99 * q^20 - 80 * q^21 - 16 * q^23 - 2 * q^24 - 21 * q^25 + 9 * q^26 - 192 * q^28 - 111 * q^29 + 99 * q^30 - 29 * q^31 - 114 * q^33 + 213 * q^34 + 38 * q^35 + 152 * q^36 + 120 * q^37 + 172 * q^38 - 29 * q^40 + 94 * q^41 + 5 * q^43 - 174 * q^44 + 156 * q^46 - 18 * q^47 - 213 * q^48 - 99 * q^49 - 198 * q^50 - 234 * q^52 - 58 * q^53 + 128 * q^54 - 258 * q^55 + 315 * q^56 + 51 * q^57 - 196 * q^58 + 336 * q^59 - 5 * q^60 + 204 * q^61 + 261 * q^62 - 153 * q^63 - 604 * q^64 - 201 * q^66 + 115 * q^67 - 106 * q^68 + 423 * q^69 - 66 * q^71 + 294 * q^72 + 249 * q^73 - 214 * q^74 - 438 * q^76 + 117 * q^77 + 136 * q^78 + 236 * q^79 + 681 * q^80 + 110 * q^81 - 4 * q^83 + 248 * q^84 + 102 * q^86 - 408 * q^87 - 45 * q^89 - 44 * q^90 - 156 * q^91 - 483 * q^92 - 567 * q^93 - 389 * q^95 - 278 * q^96 - 370 * q^97 - 879 * q^98 + 157 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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