LMFDB - Embedded newform 87.2.k.a.8.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [87,2,Mod(2,87)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("87.2"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(87, base_ring=CyclotomicField(28)) chi = DirichletCharacter(H, H._module([14, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 87 = 3 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	87.k (of order $28$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$0.694698497585$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$8$ over $\Q(\zeta_{28})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			8.1
Character	$\chi$	$=$	87.8
Dual form			87.2.k.a.11.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.909159 + 2.59823i) q^{2} +(1.42570 + 0.983555i) q^{3} +(-4.36055 - 3.47743i) q^{4} +(-1.78469 + 0.859464i) q^{5} +(-3.85169 + 2.81008i) q^{6} +(0.785988 + 0.985597i) q^{7} +(8.33803 - 5.23913i) q^{8} +(1.06524 + 2.80451i) q^{9} +(-0.610511 - 5.41843i) q^{10} +(-0.431316 - 0.271014i) q^{11} +(-2.79660 - 9.24661i) q^{12} +(3.59753 - 0.821112i) q^{13} +(-3.27539 + 1.14611i) q^{14} +(-3.38977 - 0.530009i) q^{15} +(3.54970 + 15.5522i) q^{16} +(0.110605 - 0.110605i) q^{17} +(-8.25522 + 0.217987i) q^{18} +(0.668949 - 0.0753725i) q^{19} +(10.7710 + 2.45841i) q^{20} +(0.151193 + 2.17823i) q^{21} +(1.09629 - 0.874263i) q^{22} +(1.61952 - 3.36297i) q^{23} +(17.0405 + 0.731485i) q^{24} +(-0.670992 + 0.841397i) q^{25} +(-1.13729 + 10.0937i) q^{26} +(-1.23968 + 5.04611i) q^{27} -7.03096i q^{28} +(3.00250 - 4.47046i) q^{29} +(4.45892 - 8.32553i) q^{30} +(-2.07018 - 0.724387i) q^{31} +(-24.0646 - 2.71143i) q^{32} +(-0.348370 - 0.810608i) q^{33} +(0.186820 + 0.387935i) q^{34} +(-2.24983 - 1.08346i) q^{35} +(5.10744 - 15.9335i) q^{36} +(-2.40638 - 3.82973i) q^{37} +(-0.412346 + 1.80661i) q^{38} +(5.93660 + 2.36771i) q^{39} +(-10.3780 + 16.5165i) q^{40} +(-0.0648693 - 0.0648693i) q^{41} +(-5.79699 - 1.58752i) q^{42} +(0.322735 + 0.922323i) q^{43} +(0.938347 + 2.68164i) q^{44} +(-4.31150 - 4.08966i) q^{45} +(7.26537 + 7.26537i) q^{46} +(2.36268 - 3.76018i) q^{47} +(-10.2357 + 25.6642i) q^{48} +(1.20402 - 5.27516i) q^{49} +(-1.57610 - 2.50835i) q^{50} +(0.266476 - 0.0489034i) q^{51} +(-18.5426 - 8.92963i) q^{52} +(-4.31416 - 8.95845i) q^{53} +(-11.9839 - 7.80868i) q^{54} +(1.00269 + 0.112977i) q^{55} +(11.7173 + 4.10005i) q^{56} +(1.02785 + 0.550490i) q^{57} +(8.88552 + 11.8655i) q^{58} +7.58076i q^{59} +(12.9382 + 14.0988i) q^{60} +(1.34087 - 11.9006i) q^{61} +(3.76424 - 4.72021i) q^{62} +(-1.92685 + 3.25420i) q^{63} +(15.0806 - 31.3152i) q^{64} +(-5.71477 + 4.55738i) q^{65} +(2.42287 - 0.168173i) q^{66} +(10.6873 + 2.43930i) q^{67} +(-0.866921 + 0.0976785i) q^{68} +(5.61662 - 3.20170i) q^{69} +(4.86054 - 4.86054i) q^{70} +(2.52088 + 11.0447i) q^{71} +(23.5752 + 17.8031i) q^{72} +(-12.1719 + 4.25912i) q^{73} +(12.1383 - 2.77049i) q^{74} +(-1.78419 + 0.539622i) q^{75} +(-3.17909 - 1.99756i) q^{76} +(-0.0718986 - 0.638118i) q^{77} +(-11.5492 + 13.2720i) q^{78} +(-12.6934 + 7.97581i) q^{79} +(-19.7017 - 24.7052i) q^{80} +(-6.73054 + 5.97494i) q^{81} +(0.227522 - 0.109569i) q^{82} +(1.11672 + 0.890552i) q^{83} +(6.91534 - 10.0240i) q^{84} +(-0.102335 + 0.292458i) q^{85} -2.68982 q^{86} +(8.67760 - 3.42041i) q^{87} -5.01620 q^{88} +(-0.167005 + 0.477274i) q^{89} +(14.5457 - 7.48410i) q^{90} +(3.63690 + 2.90033i) q^{91} +(-18.7565 + 9.03266i) q^{92} +(-2.23898 - 3.06889i) q^{93} +(7.62176 + 9.55738i) q^{94} +(-1.12909 + 0.709454i) q^{95} +(-31.6420 - 27.5345i) q^{96} +(1.71405 + 15.2126i) q^{97} +(12.6114 + 7.92428i) q^{98} +(0.300606 - 1.49832i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 12 q^{3} - 28 q^{4} - 14 q^{6} - 20 q^{7} - 14 q^{9} - 4 q^{10} - 8 q^{12} - 28 q^{13} - 16 q^{15} - 48 q^{16} - 28 q^{18} - 20 q^{19} + 26 q^{21} - 28 q^{22} + 58 q^{24} - 20 q^{25} + 36 q^{27}+ \cdots + 82 q^{99}+O(q^{100}) $ 96 * q - 12 * q^3 - 28 * q^4 - 14 * q^6 - 20 * q^7 - 14 * q^9 - 4 * q^10 - 8 * q^12 - 28 * q^13 - 16 * q^15 - 48 * q^16 - 28 * q^18 - 20 * q^19 + 26 * q^21 - 28 * q^22 + 58 * q^24 - 20 * q^25 + 36 * q^27 + 96 * q^30 - 32 * q^31 + 28 * q^33 - 28 * q^34 + 22 * q^36 - 4 * q^37 - 40 * q^39 - 48 * q^40 - 14 * q^42 - 32 * q^43 + 42 * q^45 + 120 * q^46 - 20 * q^48 + 4 * q^49 - 14 * q^51 + 72 * q^52 - 30 * q^54 + 148 * q^55 + 112 * q^58 + 20 * q^60 + 12 * q^61 - 14 * q^63 + 224 * q^64 - 32 * q^66 + 28 * q^67 + 10 * q^69 + 52 * q^70 - 44 * q^72 + 16 * q^73 - 144 * q^75 - 100 * q^76 - 102 * q^78 - 60 * q^79 - 146 * q^81 - 108 * q^82 - 64 * q^84 - 104 * q^85 - 70 * q^87 - 312 * q^88 - 96 * q^90 - 112 * q^91 - 70 * q^93 + 56 * q^94 - 168 * q^96 + 32 * q^97 + 82 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/87\mathbb{Z}\right)^\times$.

$n$	$31$	$59$
$\chi(n)$	$e\left(\frac{3}{28}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.909159	+	2.59823i	−0.642873	+	1.83722i	−0.104486	+	0.994526i	$0.533320\pi$
$2$	−0.909159	+	2.59823i	−0.642873	+	1.83722i	−0.538386	+	0.842698i	$0.680966\pi$
$3$	1.42570	+	0.983555i	0.823128	+	0.567856i
$3$	1.42570	+	0.983555i	0.823128	+	0.567856i
$4$	−4.36055	−	3.47743i	−2.18028	−	1.73871i
$5$	−1.78469	+	0.859464i	−0.798140	+	0.384364i	−0.788070	−	0.615585i	$-0.788920\pi$
$5$	−1.78469	+	0.859464i	−0.798140	+	0.384364i	−0.0100696	+	0.999949i	$0.503205\pi$
$6$	−3.85169	+	2.81008i	−1.57245	+	1.14721i
$7$	0.785988	+	0.985597i	0.297075	+	0.372521i	0.907858	−	0.419277i	$-0.137717\pi$
$7$	0.785988	+	0.985597i	0.297075	+	0.372521i	−0.610783	+	0.791798i	$0.709145\pi$
$8$	8.33803	−	5.23913i	2.94794	−	1.85231i
$9$	1.06524	+	2.80451i	0.355079	+	0.934836i
$10$	−0.610511	−	5.41843i	−0.193060	−	1.71346i
$11$	−0.431316	−	0.271014i	−0.130047	−	0.0817138i	0.465438	−	0.885081i	$-0.345897\pi$
$11$	−0.431316	−	0.271014i	−0.130047	−	0.0817138i	−0.595484	+	0.803367i	$0.703040\pi$
$12$	−2.79660	−	9.24661i	−0.807309	−	2.66927i
$13$	3.59753	−	0.821112i	0.997774	−	0.227735i	0.307707	−	0.951481i	$-0.400438\pi$
$13$	3.59753	−	0.821112i	0.997774	−	0.227735i	0.690067	+	0.723746i	$0.257581\pi$
$14$	−3.27539	+	1.14611i	−0.875386	+	0.306311i
$15$	−3.38977	−	0.530009i	−0.875234	−	0.136848i
$16$	3.54970	+	15.5522i	0.887425	+	3.88806i
$17$	0.110605	−	0.110605i	0.0268257	−	0.0268257i	−0.693567	−	0.720392i	$-0.743962\pi$
$17$	0.110605	−	0.110605i	0.0268257	−	0.0268257i	0.720392	+	0.693567i	$0.243962\pi$
$18$	−8.25522	+	0.217987i	−1.94577	+	0.0513800i
$19$	0.668949	−	0.0753725i	0.153467	−	0.0172916i	−0.0348964	−	0.999391i	$-0.511110\pi$
$19$	0.668949	−	0.0753725i	0.153467	−	0.0172916i	0.188364	+	0.982099i	$0.439682\pi$
$20$	10.7710	+	2.45841i	2.40846	+	0.549716i
$21$	0.151193	+	2.17823i	0.0329930	+	0.475328i
$22$	1.09629	−	0.874263i	0.233730	−	0.186394i
$23$	1.61952	−	3.36297i	0.337694	−	0.701228i	−0.661102	−	0.750296i	$-0.729911\pi$
$23$	1.61952	−	3.36297i	0.337694	−	0.701228i	0.998795	+	0.0490679i	$0.0156251\pi$
$24$	17.0405	+	0.731485i	3.47838	+	0.149314i
$25$	−0.670992	+	0.841397i	−0.134198	+	0.168279i
$26$	−1.13729	+	10.0937i	−0.223041	+	1.97954i
$27$	−1.23968	+	5.04611i	−0.238576	+	0.971124i
$28$		−	7.03096i		−	1.32873i
$29$	3.00250	−	4.47046i	0.557550	−	0.830143i
$29$	3.00250	−	4.47046i	0.557550	−	0.830143i
$30$	4.45892	−	8.32553i	0.814084	−	1.52003i
$31$	−2.07018	−	0.724387i	−0.371815	−	0.130104i	0.137902	−	0.990446i	$-0.455964\pi$
$31$	−2.07018	−	0.724387i	−0.371815	−	0.130104i	−0.509717	+	0.860342i	$0.670250\pi$
$32$	−24.0646	−	2.71143i	−4.25406	−	0.479317i
$33$	−0.348370	−	0.810608i	−0.0606435	−	0.141109i
$34$	0.186820	+	0.387935i	0.0320393	+	0.0665303i
$35$	−2.24983	−	1.08346i	−0.380291	−	0.183139i
$36$	5.10744	−	15.9335i	0.851240	−	2.65558i
$37$	−2.40638	−	3.82973i	−0.395606	−	0.629604i	0.588226	−	0.808697i	$-0.299827\pi$
$37$	−2.40638	−	3.82973i	−0.395606	−	0.629604i	−0.983832	+	0.179093i	$0.942684\pi$
$38$	−0.412346	+	1.80661i	−0.0668914	+	0.293070i
$39$	5.93660	+	2.36771i	0.950617	+	0.379137i
$40$	−10.3780	+	16.5165i	−1.64090	+	2.61148i
$41$	−0.0648693	−	0.0648693i	−0.0101309	−	0.0101309i	0.702023	−	0.712154i	$-0.252280\pi$
$41$	−0.0648693	−	0.0648693i	−0.0101309	−	0.0101309i	−0.712154	+	0.702023i	$0.752280\pi$
$42$	−5.79699	−	1.58752i	−0.894495	−	0.244960i
$43$	0.322735	+	0.922323i	0.0492166	+	0.140653i	0.965868	−	0.259035i	$-0.0834044\pi$
$43$	0.322735	+	0.922323i	0.0492166	+	0.140653i	−0.916651	+	0.399688i	$0.869119\pi$
$44$	0.938347	+	2.68164i	0.141461	+	0.404273i
$45$	−4.31150	−	4.08966i	−0.642720	−	0.609650i
$46$	7.26537	+	7.26537i	1.07122	+	1.07122i
$47$	2.36268	−	3.76018i	0.344632	−	0.548479i	−0.628767	−	0.777593i	$-0.716440\pi$
$47$	2.36268	−	3.76018i	0.344632	−	0.548479i	0.973399	+	0.229115i	$0.0735831\pi$
$48$	−10.2357	+	25.6642i	−1.47739	+	3.70430i
$49$	1.20402	−	5.27516i	0.172003	−	0.753594i
$50$	−1.57610	−	2.50835i	−0.222895	−	0.354735i
$51$	0.266476	−	0.0489034i	0.0373141	−	0.00684785i
$52$	−18.5426	−	8.92963i	−2.57139	−	1.23832i
$53$	−4.31416	−	8.95845i	−0.592596	−	1.23054i	−0.954469	−	0.298310i	$-0.903577\pi$
$53$	−4.31416	−	8.95845i	−0.592596	−	1.23054i	0.361873	−	0.932227i	$-0.382137\pi$
$54$	−11.9839	−	7.80868i	−1.63080	−	1.06263i
$55$	1.00269	+	0.112977i	0.135203	+	0.0152338i
$56$	11.7173	+	4.10005i	1.56578	+	0.547892i
$57$	1.02785	+	0.550490i	0.136143	+	0.0729142i
$58$	8.88552	+	11.8655i	1.16673	+	1.55802i
$59$			7.58076i			0.986931i	0.869765	+	0.493466i	$0.164270\pi$
$59$			7.58076i			0.986931i	−0.869765	+	0.493466i	$0.835730\pi$
$60$	12.9382	+	14.0988i	1.67031	+	1.82015i
$61$	1.34087	−	11.9006i	0.171681	−	1.52371i	−0.552156	−	0.833741i	$-0.686195\pi$
$61$	1.34087	−	11.9006i	0.171681	−	1.52371i	0.723837	−	0.689971i	$-0.242377\pi$
$62$	3.76424	−	4.72021i	0.478060	−	0.599468i
$63$	−1.92685	+	3.25420i	−0.242761	+	0.409991i
$64$	15.0806	−	31.3152i	1.88508	−	3.91441i
$65$	−5.71477	+	4.55738i	−0.708830	+	0.565273i
$66$	2.42287	−	0.168173i	0.298234	−	0.0207007i
$67$	10.6873	+	2.43930i	1.30566	+	0.298008i	0.818096	−	0.575081i	$-0.195029\pi$
$67$	10.6873	+	2.43930i	1.30566	+	0.298008i	0.487561	+	0.873089i	$0.337887\pi$
$68$	−0.866921	+	0.0976785i	−0.105130	+	0.0118453i
$69$	5.61662	−	3.20170i	0.676162	−	0.385439i
$70$	4.86054	−	4.86054i	0.580945	−	0.580945i
$71$	2.52088	+	11.0447i	0.299173	+	1.31076i	0.871362	+	0.490641i	$0.163237\pi$
$71$	2.52088	+	11.0447i	0.299173	+	1.31076i	−0.572189	+	0.820122i	$0.693906\pi$
$72$	23.5752	+	17.8031i	2.77836	+	2.09812i
$73$	−12.1719	+	4.25912i	−1.42461	+	0.498492i	−0.929009	−	0.370058i	$-0.879338\pi$
$73$	−12.1719	+	4.25912i	−1.42461	+	0.498492i	−0.495601	+	0.868551i	$0.665052\pi$
$74$	12.1383	−	2.77049i	1.41105	−	0.322062i
$75$	−1.78419	+	0.539622i	−0.206021	+	0.0623102i
$76$	−3.17909	−	1.99756i	−0.364667	−	0.229135i
$77$	−0.0718986	−	0.638118i	−0.00819361	−	0.0727203i
$78$	−11.5492	+	13.2720i	−1.30768	+	1.50276i
$79$	−12.6934	+	7.97581i	−1.42812	+	0.897348i	−0.999980	−	0.00636306i	$-0.997975\pi$
$79$	−12.6934	+	7.97581i	−1.42812	+	0.897348i	−0.428142	+	0.903711i	$0.640832\pi$
$80$	−19.7017	−	24.7052i	−2.20272	−	2.76212i
$81$	−6.73054	+	5.97494i	−0.747837	+	0.663882i
$82$	0.227522	−	0.109569i	0.0251256	−	0.0120998i
$83$	1.11672	+	0.890552i	0.122576	+	0.0977508i	0.682859	−	0.730550i	$-0.260736\pi$
$83$	1.11672	+	0.890552i	0.122576	+	0.0977508i	−0.560283	+	0.828301i	$0.689308\pi$
$84$	6.91534	−	10.0240i	0.754526	−	1.09371i
$85$	−0.102335	+	0.292458i	−0.0110998	+	0.0317215i
$86$	−2.68982			−0.290051
$87$	8.67760	−	3.42041i	0.930337	−	0.366706i
$88$	−5.01620			−0.534729
$89$	−0.167005	+	0.477274i	−0.0177025	+	0.0505909i	−0.952396	−	0.304865i	$-0.901389\pi$
$89$	−0.167005	+	0.477274i	−0.0177025	+	0.0505909i	0.934693	+	0.355456i	$0.115674\pi$
$90$	14.5457	−	7.48410i	1.53325	−	0.788894i
$91$	3.63690	+	2.90033i	0.381250	+	0.304037i
$92$	−18.7565	+	9.03266i	−1.95550	+	0.941720i
$93$	−2.23898	−	3.06889i	−0.232171	−	0.318229i
$94$	7.62176	+	9.55738i	0.786124	+	0.985769i
$95$	−1.12909	+	0.709454i	−0.115842	+	0.0727885i
$96$	−31.6420	−	27.5345i	−3.22945	−	2.81023i
$97$	1.71405	+	15.2126i	0.174035	+	1.54461i	0.712328	+	0.701847i	$0.247641\pi$
$97$	1.71405	+	15.2126i	0.174035	+	1.54461i	−0.538292	+	0.842758i	$0.680930\pi$
$98$	12.6114	+	7.92428i	1.27395	+	0.800473i
$99$	0.300606	−	1.49832i	0.0302121	−	0.150587i
$100$	5.85179	−	1.33563i	0.585179	−	0.133563i
$101$	−9.80137	+	3.42965i	−0.975272	+	0.341263i	−0.770425	−	0.637531i	$-0.779956\pi$
$101$	−9.80137	+	3.42965i	−0.975272	+	0.341263i	−0.204848	+	0.978794i	$0.565670\pi$
$102$	−0.115207	+	0.736826i	−0.0114072	+	0.0729567i
$103$	−2.45982	−	10.7772i	−0.242373	−	1.06191i	−0.938850	−	0.344326i	$-0.888107\pi$
$103$	−2.45982	−	10.7772i	−0.242373	−	1.06191i	0.696477	−	0.717579i	$-0.254750\pi$
$104$	25.6944	−	25.6944i	2.51954	−	2.51954i
$105$	−2.14194	−	3.75753i	−0.209032	−	0.366697i
$106$	27.1983	−	3.06452i	2.64174	−	0.297652i
$107$	−5.74264	−	1.31072i	−0.555162	−	0.126712i	−0.0642700	−	0.997933i	$-0.520472\pi$
$107$	−5.74264	−	1.31072i	−0.555162	−	0.126712i	−0.490892	+	0.871220i	$0.663329\pi$
$108$	22.9531	−	17.6929i	2.20867	−	1.70250i
$109$	−3.19616	+	2.54885i	−0.306137	+	0.244136i	−0.764492	−	0.644633i	$-0.777010\pi$
$109$	−3.19616	+	2.54885i	−0.306137	+	0.244136i	0.458355	+	0.888769i	$0.348439\pi$
$110$	−1.20515	+	2.50251i	−0.114906	+	0.238605i
$111$	0.335978	−	7.82685i	0.0318896	−	0.742892i
$112$	−12.5382	+	15.7224i	−1.18475	+	1.48563i
$113$	1.33336	−	11.8339i	0.125432	−	1.11324i	−0.760471	−	0.649372i	$-0.775032\pi$
$113$	1.33336	−	11.8339i	0.125432	−	1.11324i	0.885903	−	0.463870i	$-0.153540\pi$
$114$	−2.36478	+	2.17011i	−0.221482	+	0.203250i
$115$			7.39380i			0.689476i
$116$	−28.6382	+	9.05272i	−2.65899	+	0.840523i
$117$	6.13504	+	9.21461i	0.567184	+	0.851891i
$118$	−19.6965	−	6.89212i	−1.81321	−	0.634471i
$119$	0.195946	+	0.0220779i	0.0179624	+	0.00202387i
$120$	−31.0408	+	13.3402i	−2.83362	+	1.21779i
$121$	−4.66014	−	9.67687i	−0.423649	−	0.879716i
$122$	29.7013	+	14.3034i	2.68903	+	1.29497i
$123$	−0.0286816	−	0.156287i	−0.00258613	−	0.0140919i
$124$	6.50813	+	10.3576i	0.584447	+	0.930142i
$125$	2.67828	−	11.7343i	0.239553	−	1.04955i
$126$	−6.70335	−	7.96499i	−0.597182	−	0.709578i
$127$	−2.67325	+	4.25445i	−0.237212	+	0.377521i	−0.944022	−	0.329882i	$-0.892991\pi$
$127$	−2.67325	+	4.25445i	−0.237212	+	0.377521i	0.706810	+	0.707404i	$0.250134\pi$
$128$	33.4057	+	33.4057i	2.95267	+	2.95267i
$129$	−0.447033	+	1.63238i	−0.0393590	+	0.143723i
$130$	−6.64547	−	18.9917i	−0.582846	−	1.66568i
$131$	4.26077	+	12.1766i	0.372265	+	1.06387i	0.965850	+	0.259101i	$0.0834262\pi$
$131$	4.26077	+	12.1766i	0.372265	+	1.06387i	−0.593585	+	0.804771i	$0.702288\pi$
$132$	−1.29974	+	4.74613i	−0.113128	+	0.413098i
$133$	0.600073	+	0.600073i	0.0520329	+	0.0520329i
$134$	−16.0543	+	25.5502i	−1.38688	+	2.20720i
$135$	−2.12450	−	10.0712i	−0.182848	−	0.866793i
$136$	0.342754	−	1.50170i	0.0293909	−	0.128770i
$137$	2.02352	+	3.22041i	0.172881	+	0.275138i	0.921914	−	0.387394i	$-0.126625\pi$
$137$	2.02352	+	3.22041i	0.172881	+	0.275138i	−0.749034	+	0.662532i	$0.769482\pi$
$138$	3.21234	+	17.5041i	0.273453	+	1.49005i
$139$	10.7513	+	5.17754i	0.911912	+	0.439154i	0.830177	−	0.557501i	$-0.188240\pi$
$139$	10.7513	+	5.17754i	0.911912	+	0.439154i	0.0817352	+	0.996654i	$0.473954\pi$
$140$	6.04286	+	12.5481i	0.510715	+	1.06051i
$141$	7.06682	−	3.03706i	0.595133	−	0.255767i
$142$	−30.9885	−	3.49156i	−2.60049	−	0.293005i
$143$	−1.77420	−	0.620821i	−0.148366	−	0.0519157i
$144$	−39.8351	+	26.5220i	−3.31959	+	2.21017i
$145$	−1.51634	+	10.5589i	−0.125926	+	0.876872i
$146$		−	35.4975i		−	2.93779i
$147$	6.90498	−	6.33657i	0.569513	−	0.522632i
$148$	−2.82446	+	25.0677i	−0.232169	+	2.06056i
$149$	4.07702	−	5.11243i	0.334003	−	0.418826i	−0.586263	−	0.810121i	$-0.699401\pi$
$149$	4.07702	−	5.11243i	0.334003	−	0.418826i	0.920265	+	0.391295i	$0.127973\pi$
$150$	0.220055	−	5.12634i	0.0179674	−	0.418564i
$151$	−5.40904	+	11.2320i	−0.440181	+	0.914046i	0.556359	+	0.830942i	$0.312198\pi$
$151$	−5.40904	+	11.2320i	−0.440181	+	0.914046i	−0.996541	+	0.0831045i	$0.973516\pi$
$152$	5.18283	−	4.13317i	0.420383	−	0.335244i
$153$	0.428014	+	0.192372i	0.0346029	+	0.0155524i
$154$	1.72334	+	0.393342i	0.138871	+	0.0316964i
$155$	4.31722	−	0.486434i	0.346768	−	0.0390713i
$156$	−17.6533	−	30.9686i	−1.41340	−	2.47947i
$157$	13.1194	−	13.1194i	1.04704	−	1.04704i	0.0482045	−	0.998837i	$-0.484650\pi$
$157$	13.1194	−	13.1194i	1.04704	−	1.04704i	0.998837	−	0.0482045i	$-0.0153499\pi$
$158$	−9.18262	−	40.2317i	−0.730530	−	3.20066i
$159$	2.66043	−	17.0153i	0.210986	−	1.34940i
$160$	45.2783	−	15.8436i	3.57956	−	1.25254i
$161$	4.58746	−	1.04706i	0.361543	−	0.0825198i
$162$	−9.40512	−	22.9196i	−0.738936	−	1.80074i
$163$	−10.1931	−	6.40474i	−0.798384	−	0.501658i	0.0700021	−	0.997547i	$-0.477699\pi$
$163$	−10.1931	−	6.40474i	−0.798384	−	0.501658i	−0.868386	+	0.495889i	$0.834842\pi$
$164$	0.0572879	+	0.508444i	0.00447343	+	0.0397028i
$165$	1.31842	+	1.14728i	0.102639	+	0.0893153i
$166$	−3.32913	+	2.09183i	−0.258391	+	0.162358i
$167$	1.34260	+	1.68357i	0.103893	+	0.130278i	0.831060	−	0.556183i	$-0.187735\pi$
$167$	1.34260	+	1.68357i	0.103893	+	0.130278i	−0.727166	+	0.686461i	$0.759163\pi$
$168$	12.6727	+	17.3700i	0.977717	+	1.34012i
$169$	0.555375	−	0.267455i	0.0427212	−	0.0205734i
$170$	−0.666832	−	0.531781i	−0.0511437	−	0.0407857i
$171$	0.923973	+	1.79578i	0.0706580	+	0.137327i
$172$	1.80001	−	5.14413i	0.137249	−	0.392236i
$173$	3.00042			0.228118			0.114059	−	0.993474i	$-0.463615\pi$
$173$	3.00042			0.228118			0.114059	+	0.993474i	$0.463615\pi$
$174$	0.997679	+	25.6561i	0.0756338	+	1.94498i
$175$	−1.35667			−0.102555
$176$	2.68383	−	7.66996i	0.202302	−	0.578145i
$177$	−7.45610	+	10.8079i	−0.560435	+	0.812371i
$178$	−1.08823	−	0.867835i	−0.0815664	−	0.0650470i
$179$	10.7443	−	5.17416i	0.803064	−	0.386735i	0.0131197	−	0.999914i	$-0.495824\pi$
$179$	10.7443	−	5.17416i	0.803064	−	0.386735i	0.789944	+	0.613179i	$0.210109\pi$
$180$	4.57904	+	32.8261i	0.341301	+	2.44671i
$181$	2.03612	+	2.55321i	0.151344	+	0.189779i	0.851724	−	0.523991i	$-0.175558\pi$
$181$	2.03612	+	2.55321i	0.151344	+	0.189779i	−0.700380	+	0.713770i	$0.746986\pi$
$182$	−10.8422	+	6.81263i	−0.803680	+	0.504985i
$183$	13.6166	−	15.6478i	1.00656	−	1.15672i
$184$	−4.11543	−	36.5254i	−0.303393	−	2.69269i
$185$	7.58616	+	4.76670i	0.557746	+	0.350455i
$186$	10.0093	−	3.02726i	0.733915	−	0.221970i
$187$	−0.0776814	+	0.0177303i	−0.00568062	+	0.00129657i
$188$	−23.3783	+	8.18043i	−1.70504	+	0.596620i
$189$	−5.94780	+	2.74435i	−0.432639	+	0.199622i
$190$	−0.816801	−	3.57864i	−0.0592570	−	0.259622i
$191$	−10.7449	+	10.7449i	−0.777477	+	0.777477i	−0.979401	−	0.201925i	$-0.935280\pi$
$191$	−10.7449	+	10.7449i	−0.777477	+	0.777477i	0.201925	+	0.979401i	$0.435280\pi$
$192$	52.3007	−	29.8135i	3.77448	−	2.15160i
$193$	−1.88780	+	0.212704i	−0.135887	+	0.0153107i	−0.179646	−	0.983731i	$-0.557495\pi$
$193$	−1.88780	+	0.212704i	−0.135887	+	0.0153107i	0.0437592	+	0.999042i	$0.486067\pi$
$194$	−41.0841	−	9.37718i	−2.94967	−	0.673243i
$195$	−12.6300	+	0.876658i	−0.904451	+	0.0627788i
$196$	−23.5942	+	18.8157i	−1.68530	+	1.34398i
$197$	1.04404	−	2.16798i	0.0743849	−	0.154462i	−0.860460	−	0.509518i	$-0.829824\pi$
$197$	1.04404	−	2.16798i	0.0743849	−	0.154462i	0.934845	+	0.355056i	$0.115538\pi$
$198$	3.61969	+	2.14326i	0.257240	+	0.152315i
$199$	5.71243	−	7.16316i	0.404943	−	0.507783i	−0.536987	−	0.843590i	$-0.680438\pi$
$199$	5.71243	−	7.16316i	0.404943	−	0.507783i	0.941931	+	0.335808i	$0.109009\pi$
$200$	−1.18656	+	10.5310i	−0.0839024	+	0.744655i
$201$	12.8376	+	13.9892i	0.905498	+	0.986724i
$202$		−	28.5843i		−	2.01118i
$203$	6.76600	−	0.554472i	0.474880	−	0.0389163i
$204$	−1.33204	−	0.713404i	−0.0932615	−	0.0499483i
$205$	0.171525	+	0.0600191i	0.0119798	+	0.00419192i
$206$	30.2379	+	3.40699i	2.10677	+	0.237376i
$207$	11.1567	+	0.959597i	0.775442	+	0.0666966i
$208$	25.5403	+	53.0349i	1.77090	+	3.67731i
$209$	−0.308956	−	0.148785i	−0.0213709	−	0.0102917i
$210$	11.7103	−	2.14906i	0.808086	−	0.148299i
$211$	−5.64694	−	8.98706i	−0.388751	−	0.618694i	0.593816	−	0.804601i	$-0.297621\pi$
$211$	−5.64694	−	8.98706i	−0.388751	−	0.618694i	−0.982567	+	0.185906i	$0.940478\pi$
$212$	−12.3402	+	54.0660i	−0.847529	+	3.71327i
$213$	−7.26904	+	18.2258i	−0.498067	+	1.24881i
$214$	8.62652	−	13.7290i	0.589697	−	0.938497i
$215$	−1.36869	−	1.36869i	−0.0933436	−	0.0933436i
$216$	16.1007	+	48.5694i	1.09552	+	3.30473i
$217$	−0.913181	−	2.60972i	−0.0619908	−	0.177159i
$218$	−3.71668	−	10.6217i	−0.251725	−	0.719390i
$219$	−21.5425	−	5.89948i	−1.45571	−	0.398650i
$220$	−3.97944	−	3.97944i	−0.268293	−	0.268293i
$221$	0.307086	−	0.488724i	0.0206568	−	0.0328751i
$222$	20.0305	+	7.98880i	1.34436	+	0.536173i
$223$	2.49050	−	10.9116i	0.166776	−	0.730694i	−0.820496	−	0.571653i	$-0.806303\pi$
$223$	2.49050	−	10.9116i	0.166776	−	0.730694i	0.987272	−	0.159041i	$-0.0508403\pi$
$224$	−16.2421	−	25.8491i	−1.08522	−	1.72712i
$225$	−3.07447	−	0.985514i	−0.204965	−	0.0657009i
$226$	29.5350	+	14.2233i	1.96464	+	0.946120i
$227$	0.915740	+	1.90155i	0.0607798	+	0.126211i	0.929146	−	0.369713i	$-0.120544\pi$
$227$	0.915740	+	1.90155i	0.0607798	+	0.126211i	−0.868366	+	0.495923i	$0.834830\pi$
$228$	−2.56772	−	5.97473i	−0.170052	−	0.395686i
$229$	18.2038	+	2.05108i	1.20294	+	0.135539i	0.690596	−	0.723241i	$-0.257348\pi$
$229$	18.2038	+	2.05108i	1.20294	+	0.135539i	0.512345	+	0.858780i	$0.328777\pi$
$230$	−19.2108	−	6.72214i	−1.26672	−	0.443245i
$231$	0.525118	−	0.980481i	0.0345502	−	0.0645109i
$232$	1.61359	−	53.0053i	0.105938	−	3.47997i
$233$		−	14.5174i		−	0.951069i	−0.879697	−	0.475535i	$-0.842255\pi$
$233$		−	14.5174i		−	0.951069i	0.879697	−	0.475535i	$-0.157745\pi$
$234$	−29.5194	+	7.56267i	−1.92974	+	0.494388i
$235$	−0.984921	+	8.74141i	−0.0642491	+	0.570227i
$236$	26.3615	−	33.0563i	1.71599	−	2.15178i
$237$	−25.9417	−	1.11358i	−1.68509	−	0.0723348i
$238$	−0.235510	+	0.489041i	−0.0152658	+	0.0316998i
$239$	−15.8855	+	12.6683i	−1.02755	+	0.819444i	−0.983740	−	0.179596i	$-0.942521\pi$
$239$	−15.8855	+	12.6683i	−1.02755	+	0.819444i	−0.0438097	+	0.999040i	$0.513950\pi$
$240$	−3.78983	−	54.5999i	−0.244632	−	3.52441i
$241$	3.29409	+	0.751854i	0.212191	+	0.0484312i	0.327295	−	0.944922i	$-0.393863\pi$
$241$	3.29409	+	0.751854i	0.212191	+	0.0484312i	−0.115104	+	0.993353i	$0.536720\pi$
$242$	29.3795	−	3.31028i	1.88859	−	0.212793i
$243$	−15.4724	+	1.89861i	−0.992555	+	0.121796i
$244$	−47.2303	+	47.2303i	−3.02361	+	3.02361i
$245$	2.38500	+	10.4494i	0.152372	+	0.667585i
$246$	0.432145	+	0.0675682i	0.0275525	+	0.00430799i
$247$	2.34467	−	0.820437i	0.149188	−	0.0522031i
$248$	−21.0564	+	4.80598i	−1.33708	+	0.305180i
$249$	0.716195	+	2.36801i	0.0453870	+	0.150067i
$250$	28.0534	+	17.6271i	1.77426	+	1.11484i
$251$	−0.436959	−	3.87812i	−0.0275806	−	0.244785i	−0.999936	−	0.0112803i	$-0.996409\pi$
$251$	−0.436959	−	3.87812i	−0.0275806	−	0.244785i	0.972356	−	0.233504i	$-0.0750193\pi$
$252$	19.7184	−	7.48965i	1.24214	−	0.471804i
$253$	−1.60994	+	1.01159i	−0.101216	+	0.0635982i
$254$	−8.62362	−	10.8137i	−0.541094	−	0.678511i
$255$	−0.433548	+	0.316304i	−0.0271498	+	0.0198077i
$256$	−54.5361	+	26.2632i	−3.40850	+	1.64145i
$257$	8.88689	+	7.08705i	0.554349	+	0.442078i	0.860168	−	0.510011i	$-0.170359\pi$
$257$	8.88689	+	7.08705i	0.554349	+	0.442078i	−0.305819	+	0.952090i	$0.598930\pi$
$258$	−3.83488	−	2.64559i	−0.238749	−	0.164707i
$259$	1.88319	−	5.38184i	0.117016	−	0.334411i
$260$	40.7675			2.52829
$261$	15.7358	+	3.65843i	0.974023	+	0.226451i
$262$	−35.5112			−2.19389
$263$	−6.45686	+	18.4526i	−0.398147	+	1.13784i	0.554084	+	0.832460i	$0.313068\pi$
$263$	−6.45686	+	18.4526i	−0.398147	+	1.13784i	−0.952231	+	0.305378i	$0.901217\pi$
$264$	−7.15160	−	4.93371i	−0.440150	−	0.303649i
$265$	15.3989	+	12.2802i	0.945948	+	0.754368i
$266$	−2.10469	+	1.01356i	−0.129047	+	0.0621456i
$267$	−0.707524	+	0.516190i	−0.0432998	+	0.0315903i
$268$	−38.1199	−	47.8009i	−2.32854	−	2.91990i
$269$	−2.15492	+	1.35403i	−0.131388	+	0.0825564i	−0.596122	−	0.802894i	$-0.703293\pi$
$269$	−2.15492	+	1.35403i	−0.131388	+	0.0825564i	0.464734	+	0.885450i	$0.346150\pi$
$270$	28.0988	+	3.63642i	1.71004	+	0.221305i
$271$	0.762174	+	6.76448i	0.0462988	+	0.410913i	0.995390	+	0.0959113i	$0.0305765\pi$
$271$	0.762174	+	6.76448i	0.0462988	+	0.410913i	−0.949091	+	0.315002i	$0.897995\pi$
$272$	2.11277	+	1.32754i	0.128106	+	0.0804942i
$273$	2.33249	+	7.71209i	0.141169	+	0.466757i
$274$	−10.2071	+	2.32969i	−0.616631	+	0.140742i
$275$	0.517440	−	0.181060i	0.0312028	−	0.0109183i
$276$	−35.6253	−	5.57020i	−2.14439	−	0.335287i
$277$	−1.55153	−	6.79769i	−0.0932224	−	0.408434i	0.906688	−	0.421801i	$-0.138602\pi$
$277$	−1.55153	−	6.79769i	−0.0932224	−	0.408434i	−0.999911	+	0.0133675i	$0.995745\pi$
$278$	−23.2271	+	23.2271i	−1.39307	+	1.39307i
$279$	−0.173684	−	6.57748i	−0.0103982	−	0.393783i
$280$	−24.4356	+	2.75323i	−1.46030	+	0.164537i
$281$	25.4409	+	5.80671i	1.51768	+	0.346400i	0.898542	−	0.438887i	$-0.144627\pi$
$281$	25.4409	+	5.80671i	1.51768	+	0.346400i	0.619133	+	0.785286i	$0.287484\pi$
$282$	1.46612	+	21.1224i	0.0873064	+	1.25782i
$283$	13.8996	−	11.0846i	0.826246	−	0.658910i	−0.116215	−	0.993224i	$-0.537076\pi$
$283$	13.8996	−	11.0846i	0.826246	−	0.658910i	0.942462	+	0.334315i	$0.108505\pi$
$284$	27.4146	−	56.9271i	1.62676	−	3.37800i
$285$	−2.30753	−	0.0990538i	−0.136686	−	0.00586744i
$286$	3.22607	−	4.04536i	0.190761	−	0.239207i
$287$	0.0129485	−	0.114922i	0.000764328	−	0.00678360i
$288$	−18.0303	−	70.3776i	−1.06244	−	4.14704i
$289$			16.9755i			0.998561i
$290$	−26.0559	−	13.5396i	−1.53006	−	0.795071i
$291$	−12.5187	+	23.3745i	−0.733860	+	1.37023i
$292$	67.8868	+	23.7546i	3.97278	+	1.39013i
$293$	−32.8396	−	3.70013i	−1.91851	−	0.216164i	−0.930025	−	0.367496i	$-0.880215\pi$
$293$	−32.8396	−	3.70013i	−1.91851	−	0.216164i	−0.988483	+	0.151332i	$0.951644\pi$
$294$	10.1861	+	23.7017i	0.594067	+	1.38231i
$295$	−6.51539	−	13.5293i	−0.379341	−	0.787709i
$296$	−40.1289	−	19.3251i	−2.33244	−	1.12325i
$297$	1.90226	−	1.84050i	0.110380	−	0.106797i
$298$	9.57658	+	15.2410i	0.554757	+	0.882890i
$299$	3.06490	−	13.4282i	0.177248	−	0.776573i
$300$	9.65657	+	3.85135i	0.557522	+	0.222358i
$301$	−0.655374	+	1.04302i	−0.0377751	+	0.0601187i
$302$	−24.2656	−	24.2656i	−1.39633	−	1.39633i
$303$	−17.3471	−	4.75054i	−0.996562	−	0.272911i
$304$	3.54678	+	10.1361i	0.203422	+	0.581346i
$305$	7.83506	+	22.3913i	0.448634	+	1.28212i
$306$	−0.888960	+	0.937181i	−0.0508185	+	0.0535751i
$307$	−9.00476	−	9.00476i	−0.513929	−	0.513929i	0.401799	−	0.915728i	$-0.368385\pi$
$307$	−9.00476	−	9.00476i	−0.513929	−	0.513929i	−0.915728	+	0.401799i	$0.868385\pi$
$308$	−1.90549	+	3.03257i	−0.108575	+	0.172797i
$309$	7.09298	−	17.7844i	0.403505	−	1.01172i
$310$	−2.66118	+	11.6594i	−0.151145	+	0.662208i
$311$	11.2780	+	17.9489i	0.639519	+	1.01779i	0.996493	+	0.0836747i	$0.0266657\pi$
$311$	11.2780	+	17.9489i	0.639519	+	1.01779i	−0.356974	+	0.934114i	$0.616191\pi$
$312$	61.9042	−	11.3606i	3.50464	−	0.643168i
$313$	−23.5716	−	11.3515i	−1.33234	−	0.641623i	−0.374051	−	0.927408i	$-0.622031\pi$
$313$	−23.5716	−	11.3515i	−1.33234	−	0.641623i	−0.958294	+	0.285785i	$0.907746\pi$
$314$	22.1596	+	46.0148i	1.25054	+	2.59677i
$315$	0.641972	−	7.46382i	0.0361710	−	0.420539i
$316$	83.0856	+	9.36150i	4.67393	+	0.526626i
$317$	−3.67441	−	1.28573i	−0.206376	−	0.0722140i	0.225112	−	0.974333i	$-0.427725\pi$
$317$	−3.67441	−	1.28573i	−0.206376	−	0.0722140i	−0.431487	+	0.902119i	$0.642011\pi$
$318$	41.7908	+	22.3820i	2.34351	+	1.25512i
$319$	−2.50658	+	1.11446i	−0.140342	+	0.0623979i
$320$			68.8494i			3.84880i
$321$	−6.89811	−	7.51690i	−0.385015	−	0.419552i
$322$	−1.45024	+	12.8712i	−0.0808186	+	0.717285i
$323$	0.0656527	−	0.0823258i	0.00365301	−	0.00458073i
$324$	50.1263	−	2.64911i	2.78479	−	0.147173i
$325$	−1.72303	+	3.57791i	−0.0955765	+	0.198467i
$326$	25.9081	−	20.6610i	1.43492	−	1.14431i
$327$	−7.06370	+	0.490298i	−0.390624	+	0.0271135i
$328$	−0.880741	−	0.201023i	−0.0486308	−	0.0110997i
$329$	5.56306	−	0.626807i	0.306702	−	0.0345570i
$330$	−4.17954	+	2.38250i	−0.230076	+	0.131153i
$331$	6.84625	−	6.84625i	0.376304	−	0.376304i	−0.493463	−	0.869767i	$-0.664269\pi$
$331$	6.84625	−	6.84625i	0.376304	−	0.376304i	0.869767	+	0.493463i	$0.164269\pi$
$332$	−1.77268	−	7.76660i	−0.0972882	−	0.426247i
$333$	8.17714	−	10.8283i	0.448105	−	0.593386i
$334$	−5.59493	+	1.95775i	−0.306141	+	0.107123i
$335$	−21.1700	+	4.83191i	−1.15664	+	0.263996i
$336$	−33.3396	+	10.0834i	−1.81883	+	0.550097i
$337$	−1.56912	−	0.985943i	−0.0854754	−	0.0537078i	0.488616	−	0.872499i	$-0.337502\pi$
$337$	−1.56912	−	0.985943i	−0.0854754	−	0.0537078i	−0.574092	+	0.818791i	$0.694645\pi$
$338$	0.189984	+	1.68615i	0.0103337	+	0.0917145i
$339$	13.5403	−	15.5602i	0.735408	−	0.845113i
$340$	1.46324	−	0.919413i	0.0793552	−	0.0498622i
$341$	0.696583	+	0.873487i	0.0377221	+	0.0473020i
$342$	−5.50589	+	0.768039i	−0.297725	+	0.0415308i
$343$	14.0960	−	6.78829i	0.761114	−	0.366533i
$344$	7.52314	+	5.99950i	0.405620	+	0.323472i
$345$	−7.27221	+	10.5413i	−0.391523	+	0.567527i
$346$	−2.72786	+	7.79577i	−0.146651	+	0.419103i
$347$	−23.4170			−1.25709			−0.628545	−	0.777773i	$-0.716349\pi$
$347$	−23.4170			−1.25709			−0.628545	+	0.777773i	$0.716349\pi$
$348$	−49.7334	−	15.2608i	−2.66599	−	0.818067i
$349$	14.0403			0.751559			0.375779	−	0.926709i	$-0.377375\pi$
$349$	14.0403			0.751559			0.375779	+	0.926709i	$0.377375\pi$
$350$	1.23343	−	3.52494i	0.0659296	−	0.188416i
$351$	−0.316361	+	19.1714i	−0.0168861	+	1.02329i
$352$	9.64461	+	7.69132i	0.514059	+	0.409949i
$353$	8.86952	−	4.27134i	0.472077	−	0.227340i	−0.182691	−	0.983170i	$-0.558481\pi$
$353$	8.86952	−	4.27134i	0.472077	−	0.227340i	0.654768	+	0.755830i	$0.272766\pi$
$354$	−21.3026	−	29.1987i	−1.13222	−	1.55190i
$355$	−13.9915	−	17.5448i	−0.742591	−	0.931180i
$356$	2.38792	−	1.50043i	0.126559	−	0.0795226i
$357$	0.257646	+	0.224201i	0.0136361	+	0.0118660i
$358$	3.67541	+	32.6202i	0.194252	+	1.72403i
$359$	−27.9743	−	17.5774i	−1.47643	−	0.927702i	−0.998792	−	0.0491445i	$-0.984351\pi$
$359$	−27.9743	−	17.5774i	−1.47643	−	0.927702i	−0.477637	−	0.878557i	$-0.658507\pi$
$360$	−57.3756	−	11.5112i	−3.02396	−	0.606692i
$361$	−18.0818	+	4.12706i	−0.951675	+	0.217214i
$362$	−8.48499	+	2.96903i	−0.445961	+	0.156049i
$363$	2.87378	−	18.3798i	0.150835	−	0.964690i
$364$	−5.77321	−	25.2941i	−0.302598	−	1.32577i
$365$	18.0625	−	18.0625i	0.945435	−	0.945435i
$366$	28.2770	+	49.6053i	1.47806	+	2.59291i
$367$	11.6270	−	1.31005i	0.606926	−	0.0683841i	0.196847	−	0.980434i	$-0.436930\pi$
$367$	11.6270	−	1.31005i	0.606926	−	0.0683841i	0.410079	+	0.912050i	$0.365501\pi$
$368$	58.0506	+	13.2497i	3.02610	+	0.690687i
$369$	0.112825	−	0.251028i	0.00587345	−	0.0130680i
$370$	−19.2820	+	15.3769i	−1.00242	+	0.799406i
$371$	5.43855	−	11.2933i	0.282355	−	0.586317i
$372$	−0.908662	+	21.1680i	−0.0471119	+	1.09751i
$373$	4.13496	−	5.18507i	0.214100	−	0.268473i	−0.663171	−	0.748468i	$-0.730790\pi$
$373$	4.13496	−	5.18507i	0.214100	−	0.268473i	0.877271	+	0.479995i	$0.159361\pi$
$374$	0.0245575	−	0.217953i	0.00126984	−	0.0112701i
$375$	15.3598	−	14.0954i	0.793175	−	0.727882i
$376$		−	43.7309i		−	2.25525i
$377$	7.13082	−	18.5480i	0.367256	−	0.955270i
$378$	−1.72296	−	17.9488i	−0.0886192	−	0.923187i
$379$	−24.9237	−	8.72119i	−1.28025	−	0.447977i	−0.397402	−	0.917645i	$-0.630088\pi$
$379$	−24.9237	−	8.72119i	−1.28025	−	0.447977i	−0.882843	+	0.469667i	$0.844374\pi$
$380$	7.39053	+	0.832713i	0.379126	+	0.0427173i
$381$	−7.99574	+	3.43628i	−0.409634	+	0.176046i
$382$	−18.1489	−	37.6867i	−0.928581	−	1.92822i
$383$	25.7378	+	12.3947i	1.31514	+	0.633339i	0.954178	−	0.299240i	$-0.0967332\pi$
$383$	25.7378	+	12.3947i	1.31514	+	0.633339i	0.360965	+	0.932579i	$0.382447\pi$
$384$	14.7701	+	80.4827i	0.753735	+	4.10712i
$385$	0.676756	+	1.07705i	0.0344907	+	0.0548916i
$386$	1.16365	−	5.09831i	0.0592285	−	0.259497i
$387$	−2.24287	+	1.88761i	−0.114012	+	0.0959524i
$388$	45.4265	−	72.2958i	2.30618	−	3.67026i
$389$	−0.240188	−	0.240188i	−0.0121780	−	0.0121780i	0.700992	−	0.713170i	$-0.252741\pi$
$389$	−0.240188	−	0.240188i	−0.0121780	−	0.0121780i	−0.713170	+	0.700992i	$0.752741\pi$
$390$	9.20490	−	33.6126i	0.466108	−	1.70204i
$391$	−0.192835	−	0.551090i	−0.00975207	−	0.0278698i
$392$	−17.5981	−	50.2924i	−0.888838	−	2.54015i
$393$	−5.90176	+	21.5508i	−0.297704	+	1.08710i
$394$	4.68369	+	4.68369i	0.235961	+	0.235961i
$395$	15.7990	−	25.1439i	0.794932	−	1.26513i
$396$	−6.52112	+	5.48819i	−0.327699	+	0.275792i
$397$	1.90881	−	8.36304i	0.0958004	−	0.419729i	−0.904172	−	0.427169i	$-0.859511\pi$
$397$	1.90881	−	8.36304i	0.0958004	−	0.419729i	0.999972	+	0.00743970i	$0.00236815\pi$
$398$	13.4180	+	21.3546i	0.672584	+	1.07041i
$399$	0.265319	+	1.44573i	0.0132825	+	0.0723769i
$400$	−15.4674	−	7.44873i	−0.773372	−	0.372436i
$401$	−7.13490	−	14.8158i	−0.356300	−	0.739865i	0.643370	−	0.765555i	$-0.277536\pi$
$401$	−7.13490	−	14.8158i	−0.356300	−	0.739865i	−0.999670	+	0.0256909i	$0.991821\pi$
$402$	−48.0187	+	20.6367i	−2.39495	+	1.02926i
$403$	−8.04233	−	0.906153i	−0.400617	−	0.0451387i
$404$	54.6657	+	19.1284i	2.71972	+	0.951672i
$405$	6.87671	−	16.4481i	0.341706	−	0.817312i
$406$	−4.71073	+	18.0837i	−0.233789	+	0.897479i
$407$			2.30399i			0.114204i
$408$	1.96567	−	1.80386i	0.0973153	−	0.0893044i
$409$	−2.05387	+	18.2286i	−0.101557	+	0.901346i	0.834861	+	0.550461i	$0.185548\pi$
$409$	−2.05387	+	18.2286i	−0.101557	+	0.901346i	−0.936418	+	0.350885i	$0.885881\pi$
$410$	−0.311887	+	0.391093i	−0.0154030	+	0.0193147i
$411$	−0.282523	+	6.58157i	−0.0139358	+	0.324645i
$412$	−26.7506	+	55.5482i	−1.31791	+	2.73667i
$413$	−7.47158	+	5.95839i	−0.367652	+	0.293193i
$414$	−12.6364	+	28.1151i	−0.621047	+	1.38178i
$415$	−2.75839	−	0.629586i	−0.135404	−	0.0309051i
$416$	−88.7993	+	10.0053i	−4.35374	+	0.490549i
$417$	10.2357	+	17.9561i	0.501244	+	0.879314i
$418$	0.667468	−	0.667468i	0.0326469	−	0.0326469i
$419$	4.74876	+	20.8057i	0.231992	+	1.01642i	0.947984	+	0.318316i	$0.103117\pi$
$419$	4.74876	+	20.8057i	0.231992	+	1.01642i	−0.715992	+	0.698108i	$0.754025\pi$
$420$	−3.72647	+	23.8333i	−0.181833	+	1.16295i
$421$	−13.6372	+	4.77186i	−0.664636	+	0.232566i	−0.641450	−	0.767165i	$-0.721667\pi$
$421$	−13.6372	+	4.77186i	−0.664636	+	0.232566i	−0.0231862	+	0.999731i	$0.507381\pi$
$422$	28.4844	−	6.50137i	1.38660	−	0.316482i
$423$	13.0623	+	2.62066i	0.635110	+	0.127421i
$424$	−82.9060	−	52.0933i	−4.02627	−	2.52988i
$425$	0.0188477	+	0.167278i	0.000914248	+	0.00811418i
$426$	−40.7461	−	35.4568i	−1.97416	−	1.71789i
$427$	12.7831	−	8.03214i	0.618617	−	0.388703i
$428$	20.4832	+	25.6851i	0.990091	+	1.24153i
$429$	−1.91887	−	2.63013i	−0.0926440	−	0.126984i
$430$	4.80051	−	2.31180i	0.231501	−	0.111485i
$431$	−5.35855	−	4.27330i	−0.258112	−	0.205838i	0.485881	−	0.874025i	$-0.338499\pi$
$431$	−5.35855	−	4.27330i	−0.258112	−	0.205838i	−0.743993	+	0.668187i	$0.767070\pi$
$432$	−82.8788	−	1.36764i	−3.98751	−	0.0658006i
$433$	−10.5612	+	30.1822i	−0.507540	+	1.45047i	0.350343	+	0.936621i	$0.386065\pi$
$433$	−10.5612	+	30.1822i	−0.507540	+	1.45047i	−0.857883	+	0.513845i	$0.828221\pi$
$434$	7.61088			0.365334
$435$	−12.5472	+	13.5625i	−0.601590	+	0.650271i
$436$	22.8005			1.09194
$437$	0.829903	−	2.37173i	0.0396996	−	0.113455i
$438$	34.9137	−	50.6088i	1.66824	−	2.41818i
$439$	21.2873	+	16.9761i	1.01599	+	0.810225i	0.981939	−	0.189196i	$-0.0605880\pi$
$439$	21.2873	+	16.9761i	1.01599	+	0.810225i	0.0340500	+	0.999420i	$0.489159\pi$
$440$	8.95239	−	4.31124i	0.426788	−	0.205530i
$441$	16.0768	−	2.24262i	0.765562	−	0.106791i
$442$	0.990627	+	1.24221i	0.0471193	+	0.0590858i
$443$	27.9272	−	17.5478i	1.32686	−	0.833722i	0.332847	−	0.942981i	$-0.391991\pi$
$443$	27.9272	−	17.5478i	1.32686	−	0.833722i	0.994013	+	0.109259i	$0.0348479\pi$
$444$	−28.6823	+	32.9611i	−1.36120	+	1.56426i
$445$	−0.112146	−	0.995322i	−0.00531623	−	0.0471828i
$446$	26.0865	+	16.3913i	1.23523	+	0.776148i
$447$	10.8410	−	3.27881i	0.512760	−	0.155082i
$448$	42.7174	−	9.74997i	2.01821	−	0.460643i
$449$	−33.0691	+	11.5714i	−1.56063	+	0.546087i	−0.966140	−	0.258018i	$-0.916931\pi$
$449$	−33.0691	+	11.5714i	−1.56063	+	0.546087i	−0.594487	+	0.804105i	$0.702645\pi$
$450$	5.35577	−	7.09219i	0.252474	−	0.334329i
$451$	0.0103987	+	0.0455597i	0.000489656	+	0.00214532i
$452$	−46.9658	+	46.9658i	−2.20909	+	2.20909i
$453$	−18.7589	+	10.6934i	−0.881372	+	0.502417i
$454$	−5.77322	+	0.650486i	−0.270951	+	0.0305288i
$455$	−8.98348	−	2.05042i	−0.421152	−	0.0961252i
$456$	11.4544	−	0.795057i	0.536399	−	0.0372320i
$457$	−11.2484	+	8.97029i	−0.526177	+	0.419612i	−0.850218	−	0.526431i	$-0.823530\pi$
$457$	−11.2484	+	8.97029i	−0.526177	+	0.419612i	0.324041	+	0.946043i	$0.394959\pi$
$458$	−21.8793	+	45.4328i	−1.02235	+	2.12294i
$459$	0.421011	+	0.695240i	0.0196511	+	0.0324510i
$460$	25.7114	−	32.2411i	1.19880	−	1.50325i
$461$	−1.54032	+	13.6707i	−0.0717399	+	0.636709i	0.905467	+	0.424418i	$0.139521\pi$
$461$	−1.54032	+	13.6707i	−0.0717399	+	0.636709i	−0.977206	+	0.212291i	$0.931907\pi$
$462$	2.07010	+	2.25579i	0.0963096	+	0.104949i
$463$			20.1745i			0.937587i	0.883308	+	0.468793i	$0.155311\pi$
$463$			20.1745i			0.937587i	−0.883308	+	0.468793i	$0.844689\pi$
$464$	80.1836	+	30.8268i	3.72243	+	1.43110i
$465$	6.63350	+	3.55272i	0.307621	+	0.164753i
$466$	37.7196	+	13.1987i	1.74733	+	0.611416i
$467$	7.32310	+	0.825115i	0.338873	+	0.0381818i	0.279761	−	0.960070i	$-0.409745\pi$
$467$	7.32310	+	0.825115i	0.338873	+	0.0381818i	0.0591114	+	0.998251i	$0.481173\pi$
$468$	5.29097	−	61.5150i	0.244575	−	2.84353i
$469$	5.99589	+	12.4506i	0.276865	+	0.574915i
$470$	−21.8167	−	10.5064i	−1.00633	−	0.484623i
$471$	31.6080	−	5.80067i	1.45642	−	0.267281i
$472$	39.7166	+	63.2086i	1.82810	+	2.90941i
$473$	0.110762	−	0.485279i	0.00509283	−	0.0223131i
$474$	26.4784	−	66.3899i	1.21619	−	3.04939i
$475$	−0.385441	+	0.613426i	−0.0176853	+	0.0281459i
$476$	−0.777661	−	0.777661i	−0.0356440	−	0.0356440i
$477$	20.5284	−	21.6420i	0.939932	−	0.990918i
$478$	−18.4726	−	52.7917i	−0.844918	−	2.41464i
$479$	6.25321	+	17.8707i	0.285717	+	0.816531i	0.993878	+	0.110481i	$0.0352391\pi$
$479$	6.25321	+	17.8707i	0.285717	+	0.816531i	−0.708162	+	0.706050i	$0.750475\pi$
$480$	80.1362	+	21.9455i	3.65770	+	1.00167i
$481$	−11.8016	−	11.8016i	−0.538109	−	0.538109i
$482$	−4.94834	+	7.87523i	−0.225391	+	0.358707i
$483$	7.57018	+	3.01923i	0.344455	+	0.137380i
$484$	−13.3298	+	58.4018i	−0.605901	+	2.65463i
$485$	−16.1337	−	25.6767i	−0.732595	−	1.16592i
$486$	9.13384	−	41.9270i	0.414320	−	1.90185i
$487$	14.0280	+	6.75552i	0.635669	+	0.306122i	0.723824	−	0.689985i	$-0.242383\pi$
$487$	14.0280	+	6.75552i	0.635669	+	0.306122i	−0.0881552	+	0.996107i	$0.528097\pi$
$488$	−51.1684	−	106.252i	−2.31628	−	4.80981i
$489$	−8.23286	−	19.1567i	−0.372303	−	0.866295i
$490$	−29.3182	−	3.30336i	−1.32446	−	0.149231i
$491$	−36.1067	−	12.6343i	−1.62947	−	0.570177i	−0.647977	−	0.761660i	$-0.724385\pi$
$491$	−36.1067	−	12.6343i	−1.62947	−	0.570177i	−0.981496	+	0.191483i	$0.938670\pi$
$492$	−0.418408	+	0.781235i	−0.0188633	+	0.0352208i
$493$	−0.162364	−	0.826548i	−0.00731251	−	0.0372258i
$494$			6.83790i			0.307652i
$495$	0.751265	+	2.93241i	0.0337668	+	0.131802i
$496$	3.91733	−	34.7673i	0.175893	−	1.56110i
$497$	−8.90423	+	11.1656i	−0.399409	+	0.500843i
$498$	−6.80377	−	0.292061i	−0.304884	−	0.0130876i
$499$	−9.16424	+	19.0297i	−0.410248	+	0.851888i	0.588801	+	0.808278i	$0.299600\pi$
$499$	−9.16424	+	19.0297i	−0.410248	+	0.851888i	−0.999049	+	0.0436100i	$0.986114\pi$
$500$	−52.4840	+	41.8546i	−2.34716	+	1.87179i
$501$	0.258263	+	3.72078i	0.0115383	+	0.166232i
$502$	10.4735	+	2.39051i	0.467455	+	0.106694i
$503$	−21.2274	+	2.39175i	−0.946482	+	0.106643i	−0.571694	−	0.820467i	$-0.693713\pi$
$503$	−21.2274	+	2.39175i	−0.946482	+	0.106643i	−0.374789	+	0.927110i	$0.622285\pi$
$504$	0.983057	+	37.2287i	0.0437889	+	1.65830i
$505$	14.5448	−	14.5448i	0.647235	−	0.647235i
$506$	−1.16465	−	5.10269i	−0.0517752	−	0.226842i
$507$	1.05485	+	0.164932i	0.0468477	+	0.00732490i
$508$	26.4514	−	9.25574i	1.17359	−	0.410657i
$509$	30.2601	−	6.90666i	1.34125	−	0.306132i	0.509114	−	0.860699i	$-0.329973\pi$
$509$	30.2601	−	6.90666i	1.34125	−	0.306132i	0.832140	+	0.554566i	$0.187116\pi$
$510$	−0.427666	−	1.41403i	−0.0189374	−	0.0626141i
$511$	−13.7647	−	8.64894i	−0.608915	−	0.382607i
$512$	−8.07676	−	71.6832i	−0.356946	−	3.16798i
$513$	−0.448945	+	3.46903i	−0.0198214	+	0.153161i
$514$	−26.4934	+	16.6469i	−1.16857	+	0.734263i
$515$	13.6526	+	17.1198i	0.601606	+	0.754390i
$516$	7.62580	−	5.56357i	0.335707	−	0.244923i
$517$	−2.03812	+	0.981509i	−0.0896366	+	0.0431667i
$518$	12.2711	+	9.78590i	0.539163	+	0.429968i
$519$	4.27769	+	2.95108i	0.187770	+	0.129538i
$520$	−23.7732	+	67.9399i	−1.04252	+	2.97936i
$521$	−26.5342			−1.16248			−0.581242	−	0.813731i	$-0.697433\pi$
$521$	−26.5342			−1.16248			−0.581242	+	0.813731i	$0.697433\pi$
$522$	−23.8118	+	37.5591i	−1.04221	+	1.64392i
$523$	27.3276			1.19495			0.597476	−	0.801887i	$-0.296170\pi$
$523$	27.3276			1.19495			0.597476	+	0.801887i	$0.296170\pi$
$524$	23.7638	−	67.9131i	1.03813	−	2.96680i
$525$	−1.93420	−	1.33436i	−0.0844156	−	0.0582363i
$526$	−42.0738	−	33.5528i	−1.83451	−	1.46297i
$527$	−0.309093	+	0.148852i	−0.0134643	+	0.00648408i
$528$	11.3702	−	8.29535i	0.494823	−	0.361009i
$529$	5.65353	+	7.08930i	0.245806	+	0.308230i
$530$	−45.9069	+	28.8452i	−1.99407	+	1.25296i
$531$	−21.2603	+	8.07532i	−0.922619	+	0.350439i
$532$	−0.529941	−	4.70336i	−0.0229759	−	0.203916i
$533$	−0.286634	−	0.180104i	−0.0124155	−	0.00780117i
$534$	−0.697927	−	2.30761i	−0.0302022	−	0.0998600i
$535$	11.3754	−	2.59636i	0.491800	−	0.112250i
$536$	101.891	−	35.6530i	4.40100	−	1.53998i
$537$	20.4072	+	3.19077i	0.880634	+	0.137692i
$538$	−1.55890	−	6.83000i	−0.0672090	−	0.294462i
$539$	−1.94896	+	1.94896i	−0.0839475	+	0.0839475i
$540$	−25.7579	+	51.3039i	−1.10844	+	2.20777i
$541$	−7.76350	+	0.874736i	−0.333779	+	0.0376078i	−0.277264	−	0.960794i	$-0.589428\pi$
$541$	−7.76350	+	0.874736i	−0.333779	+	0.0376078i	−0.0565152	+	0.998402i	$0.517999\pi$
$542$	−18.2686	−	4.16969i	−0.784704	−	0.179104i
$543$	0.391669	+	5.64275i	0.0168081	+	0.242154i
$544$	−2.96156	+	2.36177i	−0.126976	+	0.101260i
$545$	3.51352	−	7.29591i	0.150503	−	0.312522i
$546$	−22.1584	−	0.951177i	−0.948290	−	0.0407066i
$547$	−19.1628	+	24.0294i	−0.819343	+	1.02742i	0.179701	+	0.983721i	$0.442487\pi$
$547$	−19.1628	+	24.0294i	−0.819343	+	1.02742i	−0.999045	+	0.0437029i	$0.986085\pi$
$548$	2.37508	−	21.0794i	0.101458	−	0.900467i
$549$	34.8036	−	8.91646i	1.48538	−	0.380545i
$550$			1.50904i			0.0643457i
$551$	1.67157	−	3.21682i	0.0712112	−	0.137041i
$552$	30.0574	−	56.1221i	1.27933	−	2.38871i
$553$	−17.8378	−	6.24172i	−0.758541	−	0.265425i
$554$	19.0725	+	2.14896i	0.810315	+	0.0913005i
$555$	6.12728	+	14.2573i	0.260088	+	0.605189i
$556$	−28.8770	−	59.9637i	−1.22466	−	2.54303i
$557$	9.50842	+	4.57902i	0.402885	+	0.194019i	0.624342	−	0.781151i	$-0.285367\pi$
$557$	9.50842	+	4.57902i	0.402885	+	0.194019i	−0.221457	+	0.975170i	$0.571081\pi$
$558$	17.2477	+	5.52870i	0.730153	+	0.234049i
$559$	1.91838	+	3.05308i	0.0811387	+	0.129132i
$560$	8.86405	−	38.8359i	0.374574	−	1.64112i
$561$	−0.128189	−	0.0511259i	−0.00541214	−	0.00215854i
$562$	−38.2170	+	60.8220i	−1.61209	+	2.56562i
$563$	6.14604	+	6.14604i	0.259025	+	0.259025i	0.824657	−	0.565633i	$-0.191368\pi$
$563$	6.14604	+	6.14604i	0.259025	+	0.259025i	−0.565633	+	0.824657i	$0.691368\pi$
$564$	−41.3764	−	11.3310i	−1.74226	−	0.477123i
$565$	7.79118	+	22.2659i	0.327778	+	0.936734i
$566$	16.1633	+	46.1920i	0.679393	+	1.94159i
$567$	−11.1790	−	1.93737i	−0.469474	−	0.0813619i
$568$	78.8836	+	78.8836i	3.30988	+	3.30988i
$569$	5.16363	−	8.21788i	0.216471	−	0.344511i	−0.720782	−	0.693162i	$-0.756217\pi$
$569$	5.16363	−	8.21788i	0.216471	−	0.344511i	0.937253	+	0.348650i	$0.113360\pi$
$570$	2.35528	−	5.90543i	0.0986517	−	0.247351i
$571$	−2.10283	+	9.21311i	−0.0880008	+	0.385557i	−0.999679	−	0.0253490i	$-0.991930\pi$
$571$	−2.10283	+	9.21311i	−0.0880008	+	0.385557i	0.911678	+	0.410906i	$0.134787\pi$
$572$	5.57766	+	8.87679i	0.233213	+	0.371157i
$573$	−25.8873	+	4.75081i	−1.08146	+	0.198468i
$574$	0.286820	+	0.138125i	0.0119716	+	0.00576523i
$575$	1.74291	+	3.61919i	0.0726844	+	0.150931i
$576$	103.888	+	8.93555i	4.32868	+	0.372315i
$577$	15.4297	+	1.73851i	0.642346	+	0.0723750i	0.427128	−	0.904191i	$-0.359525\pi$
$577$	15.4297	+	1.73851i	0.642346	+	0.0723750i	0.215218	+	0.976566i	$0.430954\pi$
$578$	−44.1063	−	15.4335i	−1.83458	−	0.641947i
$579$	−2.90064	−	1.55350i	−0.120546	−	0.0645613i
$580$	43.3300	−	40.7699i	1.79918	−	1.69288i
$581$			1.80060i			0.0747013i
$582$	−49.3506	−	53.7776i	−2.04565	−	2.22915i
$583$	−0.567097	+	5.03312i	−0.0234867	+	0.208451i
$584$	−79.1752	+	99.2826i	−3.27629	+	4.10834i
$585$	−18.8688	−	11.1724i	−0.780129	−	0.461923i
$586$	39.4702	−	81.9607i	1.63050	−	3.38576i
$587$	17.1985	−	13.7154i	0.709859	−	0.566093i	−0.200610	−	0.979671i	$-0.564292\pi$
$587$	17.1985	−	13.7154i	0.709859	−	0.566093i	0.910469	+	0.413578i	$0.135721\pi$
$588$	−52.1445	+	3.61940i	−2.15040	+	0.149261i
$589$	−1.43944	−	0.328544i	−0.0593112	−	0.0135374i
$590$	41.0758	−	4.62814i	1.69107	−	0.190537i
$591$	3.62081	−	2.06401i	0.148940	−	0.0849020i
$592$	51.0190	−	51.0190i	2.09687	−	2.09687i
$593$	2.57934	+	11.3008i	0.105921	+	0.464070i	0.999873	+	0.0159082i	$0.00506395\pi$
$593$	2.57934	+	11.3008i	0.105921	+	0.464070i	−0.893953	+	0.448162i	$0.852079\pi$
$594$	3.05258	+	6.61581i	0.125249	+	0.271450i
$595$	−0.368680	+	0.129007i	−0.0151144	+	0.00528876i
$596$	−35.5562	+	8.11546i	−1.45644	+	0.332422i
$597$	15.1896	−	4.59402i	0.621667	−	0.188021i
$598$	32.1030	+	20.1717i	1.31279	+	0.824881i
$599$	0.489069	+	4.34061i	0.0199828	+	0.177353i	0.999739	−	0.0228415i	$-0.00727131\pi$
$599$	0.489069	+	4.34061i	0.0199828	+	0.177353i	−0.979756	+	0.200194i	$0.935843\pi$
$600$	−12.0495	+	13.8470i	−0.491919	+	0.565302i
$601$	30.1277	−	18.9305i	1.22894	−	0.772192i	0.248424	−	0.968651i	$-0.420087\pi$
$601$	30.1277	−	18.9305i	1.22894	−	0.772192i	0.980512	+	0.196460i	$0.0629445\pi$
$602$	−2.11417	−	2.65108i	−0.0861670	−	0.108050i
$603$	4.54345	+	32.5710i	0.185024	+	1.32639i
$604$	62.6448	−	30.1682i	2.54898	−	1.22752i
$605$	16.6338	+	13.2650i	0.676262	+	0.539301i
$606$	28.1142	−	40.7526i	1.14206	−	1.65546i
$607$	−1.38281	+	3.95186i	−0.0561267	+	0.160401i	−0.968533	−	0.248884i	$-0.919936\pi$
$607$	−1.38281	+	3.95186i	−0.0561267	+	0.160401i	0.912407	+	0.409285i	$0.134222\pi$
$608$	−16.3023			−0.661147
$609$	10.1916	+	5.86422i	0.412986	+	0.237630i
$610$	−65.3011			−2.64396
$611$	5.41227	−	15.4674i	0.218957	−	0.625743i
$612$	−1.19742	−	2.32724i	−0.0484027	−	0.0940730i
$613$	−21.0947	−	16.8224i	−0.852006	−	0.679452i	0.0968025	−	0.995304i	$-0.469138\pi$
$613$	−21.0947	−	16.8224i	−0.852006	−	0.679452i	−0.948809	+	0.315851i	$0.897710\pi$
$614$	31.5832	−	15.2097i	1.27459	−	0.613812i
$615$	0.185511	+	0.254273i	0.00748051	+	0.0102533i
$616$	−3.94267	−	4.94396i	−0.158855	−	0.199198i
$617$	12.8597	−	8.08026i	0.517710	−	0.325299i	−0.247705	−	0.968835i	$-0.579676\pi$
$617$	12.8597	−	8.08026i	0.517710	−	0.325299i	0.765415	+	0.643536i	$0.222534\pi$
$618$	39.7592	+	34.5980i	1.59935	+	1.39174i
$619$	−1.08812	−	9.65736i	−0.0437354	−	0.388162i	−0.996443	−	0.0842729i	$-0.973143\pi$
$619$	−1.08812	−	9.65736i	−0.0437354	−	0.388162i	0.952707	−	0.303889i	$-0.0982853\pi$
$620$	−20.5170	−	12.8917i	−0.823983	−	0.517743i
$621$	14.9622	+	12.3413i	0.600414	+	0.495239i
$622$	−56.8889	+	12.9845i	−2.28104	+	0.520632i
$623$	−0.601664	+	0.210531i	−0.0241051	+	0.00843475i
$624$	−15.7500	+	100.732i	−0.630505	+	4.03251i
$625$	4.10793	+	17.9980i	0.164317	+	0.719921i
$626$	50.9240	−	50.9240i	2.03533	−	2.03533i
$627$	−0.294139	−	0.515998i	−0.0117468	−	0.0206070i
$628$	−102.830	+	11.5861i	−4.10335	+	0.462336i
$629$	−0.689746	−	0.157430i	−0.0275020	−	0.00627714i
$630$	18.8091	+	8.45379i	0.749371	+	0.336807i
$631$	5.54004	−	4.41803i	0.220545	−	0.175879i	−0.506984	−	0.861955i	$-0.669240\pi$
$631$	5.54004	−	4.41803i	0.220545	−	0.175879i	0.727530	+	0.686076i	$0.240668\pi$
$632$	−64.0518	+	133.005i	−2.54784	+	5.29065i
$633$	0.788424	−	18.3669i	0.0313370	−	0.730019i
$634$	6.68125	−	8.37803i	0.265347	−	0.332734i
$635$	1.11439	−	9.89045i	0.0442231	−	0.392491i
$636$	−70.7703	+	64.9446i	−2.80622	+	2.57522i
$637$		−	19.9662i		−	0.791088i
$638$	−0.616745	−	7.52590i	−0.0244172	−	0.297953i
$639$	−28.2896	+	18.8350i	−1.11912	+	0.745102i
$640$	−88.3298	−	30.9079i	−3.49154	−	1.22174i
$641$	−13.4647	−	1.51711i	−0.531824	−	0.0599221i	−0.158031	−	0.987434i	$-0.550514\pi$
$641$	−13.4647	−	1.51711i	−0.531824	−	0.0599221i	−0.373793	+	0.927512i	$0.621943\pi$
$642$	25.8021	−	11.0888i	1.01833	−	0.437641i
$643$	16.1936	+	33.6263i	0.638612	+	1.32609i	0.929319	+	0.369279i	$0.120395\pi$
$643$	16.1936	+	33.6263i	0.638612	+	1.32609i	−0.290707	+	0.956812i	$0.593890\pi$
$644$	−23.6449	−	11.3868i	−0.931741	−	0.448703i
$645$	−0.605157	−	3.29751i	−0.0238280	−	0.129839i
$646$	0.154213	+	0.245428i	0.00606741	+	0.00965623i
$647$	9.38920	−	41.1368i	0.369127	−	1.61725i	−0.360053	−	0.932932i	$-0.617241\pi$
$647$	9.38920	−	41.1368i	0.369127	−	1.61725i	0.729181	−	0.684321i	$-0.239901\pi$
$648$	−24.8159	+	85.0813i	−0.974861	+	3.34231i
$649$	2.05449	−	3.26971i	0.0806459	−	0.128347i
$650$	−7.72971	−	7.72971i	−0.303184	−	0.303184i
$651$	1.26488	−	4.61884i	0.0495747	−	0.181027i
$652$	22.1755	+	63.3739i	0.868459	+	2.48191i
$653$	4.53130	+	12.9497i	0.177323	+	0.506761i	0.997900	−	0.0647757i	$-0.0206332\pi$
$653$	4.53130	+	12.9497i	0.177323	+	0.506761i	−0.820577	+	0.571537i	$0.806347\pi$
$654$	5.14812	−	18.7989i	0.201308	−	0.735094i
$655$	−18.0695	−	18.0695i	−0.706033	−	0.706033i
$656$	0.778597	−	1.23913i	0.0303991	−	0.0483799i
$657$	−24.9107	−	29.5991i	−0.971858	−	1.15477i
$658$	−3.42912	+	15.0240i	−0.133681	+	0.585695i
$659$	−3.73456	−	5.94352i	−0.145478	−	0.231527i	0.766034	−	0.642800i	$-0.222227\pi$
$659$	−3.73456	−	5.94352i	−0.145478	−	0.231527i	−0.911512	+	0.411273i	$0.865084\pi$
$660$	−1.75948	−	9.58747i	−0.0684878	−	0.373192i
$661$	−14.7924	−	7.12366i	−0.575359	−	0.277078i	0.123492	−	0.992346i	$-0.460591\pi$
$661$	−14.7924	−	7.12366i	−0.575359	−	0.277078i	−0.698851	+	0.715267i	$0.746305\pi$
$662$	11.5638	+	24.0125i	0.449440	+	0.933271i
$663$	0.918499	−	0.394738i	0.0356716	−	0.0153304i
$664$	13.9769	+	1.57482i	0.542410	+	0.0611149i
$665$	−1.58669	−	0.555206i	−0.0615291	−	0.0215300i
$666$	20.7000	+	31.0907i	0.802110	+	1.20474i
$667$	−10.1714	−	17.3373i	−0.393839	−	0.671304i
$668$		−	12.0101i		−	0.464684i
$669$	14.2829	−	13.1071i	0.552207	−	0.506750i
$670$	6.69249	−	59.3975i	0.258553	−	2.29472i
$671$	−3.80356	+	4.76952i	−0.146835	+	0.184125i
$672$	2.26771	−	52.8281i	0.0874790	−	2.03789i
$673$	17.5406	−	36.4234i	0.676139	−	1.40402i	−0.226668	−	0.973972i	$-0.572783\pi$
$673$	17.5406	−	36.4234i	0.676139	−	1.40402i	0.902807	−	0.430046i	$-0.141502\pi$
$674$	3.98828	−	3.18055i	0.153623	−	0.122510i
$675$	−3.41397	−	4.42896i	−0.131404	−	0.170471i
$676$	−3.35180	−	0.765026i	−0.128915	−	0.0294241i
$677$	−8.16278	+	0.919724i	−0.313721	+	0.0353479i	−0.267421	−	0.963580i	$-0.586172\pi$
$677$	−8.16278	+	0.919724i	−0.313721	+	0.0353479i	−0.0462998	+	0.998928i	$0.514743\pi$
$678$	28.1186	+	49.3275i	1.07989	+	1.89441i
$679$	−13.6463	+	13.6463i	−0.523696	+	0.523696i
$680$	0.678948	+	2.97467i	0.0260365	+	0.114073i
$681$	−0.564713	+	3.61173i	−0.0216399	+	0.138402i
$682$	−2.90282	+	1.01574i	−0.111155	+	0.0388948i
$683$	29.8869	−	6.82150i	1.14359	−	0.261017i	0.391565	−	0.920150i	$-0.371934\pi$
$683$	29.8869	−	6.82150i	1.14359	−	0.261017i	0.752027	+	0.659133i	$0.229077\pi$
$684$	2.21567	−	11.0437i	0.0847183	−	0.422265i
$685$	−6.37918	−	4.00831i	−0.243736	−	0.153149i
$686$	4.82199	+	42.7963i	0.184104	+	1.63397i
$687$	23.9358	+	20.8287i	0.913208	+	0.794663i
$688$	−13.1986	+	8.29322i	−0.503191	+	0.316176i
$689$	−22.8762	−	28.6858i	−0.871514	−	1.09284i
$690$	−20.7772	−	28.4786i	−0.790974	−	1.08416i
$691$	−33.6401	+	16.2002i	−1.27973	+	0.616286i	−0.945321	−	0.326142i	$-0.894251\pi$
$691$	−33.6401	+	16.2002i	−1.27973	+	0.616286i	−0.334409	+	0.942428i	$0.608537\pi$
$692$	−13.0835	−	10.4337i	−0.497359	−	0.396631i
$693$	1.71302	−	0.881388i	0.0650722	−	0.0334812i
$694$	21.2898	−	60.8426i	0.808148	−	2.30956i
$695$	−23.6377			−0.896628
$696$	54.4341	−	73.9825i	2.06332	−	2.80430i
$697$	−0.0143498			−0.000543536
$698$	−12.7648	+	36.4798i	−0.483156	+	1.38078i
$699$	14.2787	−	20.6975i	0.540070	−	0.782852i
$700$	5.91583	+	4.71772i	0.223598	+	0.178313i
$701$	−13.2440	+	6.37795i	−0.500217	+	0.240892i	−0.666939	−	0.745112i	$-0.732396\pi$
$701$	−13.2440	+	6.37795i	−0.500217	+	0.240892i	0.166722	+	0.986004i	$0.446682\pi$
$702$	−49.5241	−	18.2518i	−1.86917	−	0.688872i
$703$	−1.89840	−	2.38052i	−0.0715996	−	0.0897830i
$704$	−14.9914	+	9.41971i	−0.565009	+	0.355019i
$705$	−10.0019	+	11.4939i	−0.376692	+	0.432885i
$706$	3.03410	+	26.9284i	0.114190	+	1.01346i
$707$	−11.0840	−	6.96454i	−0.416857	−	0.261929i
$708$	70.0963	−	21.2004i	2.63438	−	0.796758i
$709$	22.2893	−	5.08740i	0.837094	−	0.191061i	0.217575	−	0.976043i	$-0.430185\pi$
$709$	22.2893	−	5.08740i	0.837094	−	0.191061i	0.619518	+	0.784982i	$0.287328\pi$
$710$	58.3058	−	20.4021i	2.18818	−	0.765677i
$711$	−35.8897	−	27.1027i	−1.34597	−	1.01643i
$712$	1.10800	+	4.85448i	0.0415242	+	0.181929i
$713$	−5.78880	+	5.78880i	−0.216792	+	0.216792i
$714$	−0.816765	+	0.465589i	−0.0305667	+	0.0174242i
$715$	3.69999	−	0.416888i	0.138372	−	0.0155907i
$716$	−64.8437	−	14.8002i	−2.42332	−	0.553108i
$717$	−35.1080	+	2.43688i	−1.31113	+	0.0910068i
$718$	71.1033	−	56.7030i	2.65355	−	2.11614i
$719$	5.06393	−	10.5154i	0.188853	−	0.392157i	−0.784947	−	0.619562i	$-0.787310\pi$
$719$	5.06393	−	10.5154i	0.188853	−	0.392157i	0.973800	+	0.227406i	$0.0730244\pi$
$720$	48.2988	−	81.5705i	1.79999	−	3.03995i
$721$	8.68856	−	10.8951i	0.323579	−	0.405755i
$722$	5.71622	−	50.7328i	0.212736	−	1.88808i
$723$	3.95689	+	4.31183i	0.147158	+	0.160359i
$724$		−	18.2139i		−	0.676914i
$725$	1.74678	+	5.52594i	0.0648738	+	0.205228i
$726$	45.1422	+	24.1769i	1.67538	+	0.897290i
$727$	27.9560	+	9.78224i	1.03683	+	0.362803i	0.794419	−	0.607370i	$-0.207775\pi$
$727$	27.9560	+	9.78224i	1.03683	+	0.362803i	0.242413	+	0.970173i	$0.422061\pi$
$728$	45.5197	+	5.12884i	1.68707	+	0.190088i
$729$	−23.9264	−	12.5111i	−0.886163	−	0.463374i
$730$	30.5088	+	63.3522i	1.12918	+	2.34477i
$731$	0.137710	+	0.0663176i	0.00509338	+	0.00245284i
$732$	−113.790	+	20.8826i	−4.20579	+	0.771843i
$733$	−15.7762	−	25.1077i	−0.582708	−	0.927375i	−0.999828	−	0.0185236i	$-0.994103\pi$
$733$	−15.7762	−	25.1077i	−0.582708	−	0.927375i	0.417120	−	0.908851i	$-0.363039\pi$
$734$	−7.16700	+	31.4007i	−0.264539	+	1.15902i
$735$	−6.87723	+	17.2434i	−0.253671	+	0.636033i
$736$	−48.0916	+	76.5373i	−1.77268	+	2.82120i
$737$	−3.94851	−	3.94851i	−0.145445	−	0.145445i
$738$	0.549651	+	0.521370i	0.0202329	+	0.0191919i
$739$	5.32548	+	15.2194i	0.195901	+	0.559853i	0.999370	−	0.0354939i	$-0.0113004\pi$
$739$	5.32548	+	15.2194i	0.195901	+	0.559853i	−0.803469	+	0.595347i	$0.797015\pi$
$740$	−16.5040	−	47.1658i	−0.606700	−	1.73385i
$741$	4.14974	+	1.13642i	0.152445	+	0.0417474i
$742$	24.3979	+	24.3979i	0.895677	+	0.895677i
$743$	9.77350	−	15.5544i	0.358555	−	0.570637i	−0.617927	−	0.786235i	$-0.712027\pi$
$743$	9.77350	−	15.5544i	0.358555	−	0.570637i	0.976482	+	0.215598i	$0.0691702\pi$
$744$	−34.7470	−	13.8582i	−1.27389	−	0.508067i
$745$	−2.88230	+	12.6282i	−0.105599	+	0.462660i
$746$	9.71267	+	15.4576i	0.355606	+	0.565944i
$747$	−1.30799	+	4.08049i	−0.0478569	+	0.149297i
$748$	0.400389	+	0.192817i	0.0146397	+	0.00705010i
$749$	−3.22180	−	6.69014i	−0.117722	−	0.244452i
$750$	22.6585	+	52.7231i	0.827372	+	1.92518i
$751$	−41.8475	−	4.71508i	−1.52704	−	0.172056i	−0.691858	−	0.722033i	$-0.743208\pi$
$751$	−41.8475	−	4.71508i	−1.52704	−	0.172056i	−0.835179	+	0.549978i	$0.814636\pi$
$752$	66.8661	+	23.3975i	2.43835	+	0.853217i
$753$	3.19137	−	5.95880i	0.116300	−	0.217151i
$754$	41.7088	+	35.3906i	1.51895	+	1.28885i
$755$		−	24.6945i		−	0.898726i
$756$	35.4790	+	8.71614i	1.29036	+	0.317003i
$757$	4.40632	−	39.1072i	0.160151	−	1.42138i	−0.614465	−	0.788944i	$-0.710628\pi$
$757$	4.40632	−	39.1072i	0.160151	−	1.42138i	0.774616	−	0.632432i	$-0.217943\pi$
$758$	45.3192	−	56.8285i	1.64607	−	2.06411i
$759$	−3.29025	−	0.141238i	−0.119428	−	0.00512662i
$760$	−5.69746	+	11.8309i	−0.206669	+	0.429152i
$761$	−31.8267	+	25.3810i	−1.15372	+	0.920059i	−0.997706	−	0.0676958i	$-0.978435\pi$
$761$	−31.8267	+	25.3810i	−1.15372	+	0.920059i	−0.156012	+	0.987755i	$0.549864\pi$
$762$	−1.65884	−	23.8989i	−0.0600935	−	0.865765i
$763$	−5.02428	−	1.14676i	−0.181891	−	0.0415155i
$764$	84.2186	−	9.48916i	3.04692	−	0.343306i
$765$	−0.929211	+	0.0245367i	−0.0335957	+	0.000887126i
$766$	−55.6040	+	55.6040i	−2.00906	+	2.00906i
$767$	6.22465	+	27.2720i	0.224759	+	0.984734i
$768$	−103.583	−	16.1958i	−3.73774	−	0.584417i
$769$	31.8427	−	11.1423i	1.14828	−	0.401800i	0.311987	−	0.950086i	$-0.399005\pi$
$769$	31.8427	−	11.1423i	1.14828	−	0.401800i	0.836291	+	0.548286i	$0.184720\pi$
$770$	−3.41370	+	0.779155i	−0.123021	+	0.0280788i
$771$	5.69952	+	18.8448i	0.205263	+	0.678677i
$772$	8.97150	+	5.63717i	0.322891	+	0.202886i
$773$	3.56569	+	31.6463i	0.128249	+	1.13824i	0.878720	+	0.477337i	$0.158398\pi$
$773$	3.56569	+	31.6463i	0.128249	+	1.13824i	−0.750471	+	0.660903i	$0.770174\pi$
$774$	−2.86530	−	7.54363i	−0.102991	−	0.271150i
$775$	1.99857	−	1.25579i	0.0717908	−	0.0451091i
$776$	93.9925	+	117.863i	3.37413	+	4.23103i
$777$	7.97820	−	5.82067i	0.286216	−	0.208815i
$778$	0.842433	−	0.405694i	0.0302027	−	0.0145448i
$779$	−0.0482836	−	0.0385049i	−0.00172994	−	0.00137958i
$780$	58.1222	+	40.0971i	2.08111	+	1.43571i
$781$	1.90597	−	5.44694i	0.0682009	−	0.194907i
$782$	1.60717			0.0574724
$783$	18.8363	+	20.6929i	0.673154	+	0.739503i
$784$	86.3145			3.08266
$785$	−12.1385	+	34.6898i	−0.433241	+	1.23813i
$786$	−50.6283	−	34.9272i	−1.80585	−	1.24581i
$787$	−21.4059	−	17.0706i	−0.763038	−	0.608503i	0.162697	−	0.986676i	$-0.447981\pi$
$787$	−21.4059	−	17.0706i	−0.763038	−	0.608503i	−0.925735	+	0.378174i	$0.876552\pi$
$788$	−12.0916	+	5.82300i	−0.430745	+	0.207436i
$789$	−27.3547	+	19.9572i	−0.973854	+	0.710497i
$790$	50.9658	+	63.9091i	1.81328	+	2.27379i
$791$	12.7115	−	7.98716i	0.451969	−	0.283991i
$792$	−5.34345	−	14.0680i	−0.189871	−	0.499884i
$793$	−4.94788	−	43.9136i	−0.175704	−	1.55942i
$794$	19.9937	+	12.5629i	0.709549	+	0.445839i
$795$	9.87595	+	32.6536i	0.350264	+	1.15810i
$796$	−49.8187	+	11.3708i	−1.76578	+	0.403027i
$797$	−14.7691	+	5.16792i	−0.523147	+	0.183057i	−0.578917	−	0.815386i	$-0.696524\pi$
$797$	−14.7691	+	5.16792i	−0.523147	+	0.183057i	0.0557696	+	0.998444i	$0.482239\pi$
$798$	−3.99755	−	0.625038i	−0.141512	−	0.0221261i
$799$	−0.154571	−	0.677220i	−0.00546833	−	0.0239583i
$800$	18.4285	−	18.4285i	0.651547	−	0.651547i
$801$	−1.51642	+	0.0400424i	−0.0535800	+	0.00141483i
$802$	44.9815	−	5.06820i	1.58835	−	0.178964i
$803$	6.40420	+	1.46172i	0.225999	+	0.0515829i
$804$	−7.33276	−	105.643i	−0.258606	−	3.72573i
$805$	−7.28731	+	5.81144i	−0.256844	+	0.204826i
$806$	9.66615	−	20.0720i	0.340475	−	0.707005i
$807$	−4.40403	−	0.189049i	−0.155029	−	0.00665483i
$808$	−63.7557	+	79.9471i	−2.24292	+	2.81253i
$809$	−4.02264	+	35.7019i	−0.141429	+	1.25521i	0.699723	+	0.714414i	$0.253307\pi$
$809$	−4.02264	+	35.7019i	−0.141429	+	1.25521i	−0.841152	+	0.540799i	$0.818122\pi$
$810$	36.4839	+	32.8212i	1.28191	+	1.15322i
$811$			19.2084i			0.674497i	0.941416	+	0.337249i	$0.109496\pi$
$811$			19.2084i			0.674497i	−0.941416	+	0.337249i	$0.890504\pi$
$812$	−31.4316	−	21.1105i	−1.10303	−	0.740832i
$813$	−5.56661	+	10.3938i	−0.195230	+	0.364525i
$814$	−5.98628	−	2.09469i	−0.209819	−	0.0734189i
$815$	23.6962	+	2.66992i	0.830041	+	0.0935231i
$816$	1.70647	+	3.97071i	0.0597383	+	0.139003i
$817$	0.285411	+	0.592662i	0.00998526	+	0.0207346i
$818$	−45.4947	−	21.9091i	−1.59069	−	0.766034i
$819$	−4.25983	+	13.2892i	−0.148851	+	0.464364i
$820$	−0.539231	−	0.858181i	−0.0188308	−	0.0299690i
$821$	−10.1067	+	44.2805i	−0.352727	+	1.54540i	0.418127	+	0.908389i	$0.362687\pi$
$821$	−10.1067	+	44.2805i	−0.352727	+	1.54540i	−0.770855	+	0.637011i	$0.780170\pi$
$822$	−16.8436	−	6.71776i	−0.587487	−	0.234309i
$823$	8.17897	−	13.0168i	0.285101	−	0.453736i	−0.673215	−	0.739447i	$-0.735087\pi$
$823$	8.17897	−	13.0168i	0.285101	−	0.453736i	0.958316	+	0.285711i	$0.0922298\pi$
$824$	−76.9730	−	76.9730i	−2.68148	−	2.68148i
$825$	0.915797	+	0.250794i	0.0318840	+	0.00873151i
$826$	−8.68839	−	24.8300i	−0.302308	−	0.863946i
$827$	−15.9611	−	45.6142i	−0.555022	−	1.58616i	−0.789310	−	0.613995i	$-0.789561\pi$
$827$	−15.9611	−	45.6142i	−0.555022	−	1.58616i	0.234287	−	0.972167i	$-0.424724\pi$
$828$	−45.3123	−	42.9808i	−1.57471	−	1.49369i
$829$	26.3314	+	26.3314i	0.914527	+	0.914527i	0.996624	−	0.0820970i	$-0.0261617\pi$
$829$	26.3314	+	26.3314i	0.914527	+	0.914527i	−0.0820970	+	0.996624i	$0.526162\pi$
$830$	4.14363	−	6.59454i	0.143827	−	0.228900i
$831$	4.47389	−	11.2175i	0.155198	−	0.389130i
$832$	28.5396	−	125.040i	0.989434	−	4.33499i
$833$	−0.450289	−	0.716631i	−0.0156016	−	0.0248298i
$834$	−55.9599	+	10.2697i	−1.93773	+	0.355611i
$835$	−3.84309	−	1.85074i	−0.132996	−	0.0640474i
$836$	0.829828	+	1.72316i	0.0287002	+	0.0595966i
$837$	6.22169	−	9.54834i	0.215053	−	0.330039i
$838$	−58.3753	−	6.57732i	−2.01654	−	0.227210i
$839$	−1.64193	−	0.574538i	−0.0566859	−	0.0198352i	0.301787	−	0.953375i	$-0.402417\pi$
$839$	−1.64193	−	0.574538i	−0.0566859	−	0.0198352i	−0.358473	+	0.933540i	$0.616703\pi$
$840$	−37.5457	−	20.1085i	−1.29545	−	0.693808i
$841$	−10.9700	−	26.8451i	−0.378276	−	0.925693i
$842$		−	39.7709i		−	1.37060i
$843$	30.5598	+	33.3011i	1.05254	+	1.14695i
$844$	−6.62803	+	58.8254i	−0.228146	+	2.02485i
$845$	−0.761308	+	0.954650i	−0.0261898	+	0.0328410i
$846$	−18.6848	+	31.5562i	−0.642396	+	1.08492i
$847$	5.87469	−	12.1989i	0.201857	−	0.419160i
$848$	124.010	−	98.8947i	4.25852	−	3.39606i
$849$	30.7190	−	2.13223i	1.05427	−	0.0731780i
$850$	−0.451762	−	0.103112i	−0.0154953	−	0.00353670i
$851$	−16.7765	+	1.89025i	−0.575090	+	0.0647971i
$852$	95.0760	−	54.1971i	3.25725	−	1.85676i
$853$	3.82522	−	3.82522i	0.130973	−	0.130973i	−0.638581	−	0.769554i	$-0.720478\pi$
$853$	3.82522	−	3.82522i	0.130973	−	0.130973i	0.769554	+	0.638581i	$0.220478\pi$
$854$	9.24748	+	40.5159i	0.316442	+	1.38642i
$855$	−3.19242	−	2.41080i	−0.109178	−	0.0824478i
$856$	−54.7493	+	19.1576i	−1.87129	+	0.654794i
$857$	36.8075	−	8.40108i	1.25732	−	0.286975i	0.458582	−	0.888652i	$-0.348358\pi$
$857$	36.8075	−	8.40108i	1.25732	−	0.286975i	0.798740	+	0.601677i	$0.205501\pi$
$858$	8.57824	−	2.59445i	0.292856	−	0.0885732i
$859$	15.6829	+	9.85420i	0.535092	+	0.336221i	0.772320	−	0.635233i	$-0.219096\pi$
$859$	15.6829	+	9.85420i	0.535092	+	0.336221i	−0.237228	+	0.971454i	$0.576239\pi$
$860$	1.20873	+	10.7277i	0.0412172	+	0.365813i
$861$	0.131492	−	0.151108i	0.00448125	−	0.00514974i
$862$	15.9748	−	10.0376i	0.544103	−	0.341883i
$863$	21.0557	+	26.4030i	0.716745	+	0.898770i	0.998149	−	0.0608195i	$-0.0193714\pi$
$863$	21.0557	+	26.4030i	0.716745	+	0.898770i	−0.281404	+	0.959589i	$0.590800\pi$
$864$	43.5145	−	118.071i	1.48039	−	4.01686i
$865$	−5.35483	+	2.57875i	−0.182070	+	0.0876801i
$866$	−68.8185	−	54.8809i	−2.33855	−	1.86493i
$867$	−16.6964	+	24.2020i	−0.567039	+	0.821943i
$868$	−5.09314	+	14.5554i	−0.172872	+	0.494041i
$869$	7.63644			0.259048
$870$	−23.8310	−	44.9308i	−0.807947	−	1.52330i
$871$	40.4507			1.37062
$872$	−13.2959	+	37.9975i	−0.450256	+	1.28676i
$873$	−40.8380	+	21.0121i	−1.38216	+	0.711152i
$874$	5.40777	+	4.31255i	0.182921	+	0.145874i
$875$	13.6704	−	6.58332i	0.462144	−	0.222557i
$876$	73.4222	+	100.637i	2.48071	+	3.40022i
$877$	18.3684	+	23.0332i	0.620256	+	0.777777i	0.988381	−	0.152000i	$-0.0485713\pi$
$877$	18.3684	+	23.0332i	0.620256	+	0.777777i	−0.368124	+	0.929777i	$0.620000\pi$
$878$	−63.4613	+	39.8754i	−2.14172	+	1.34573i
$879$	−43.1801	−	37.5748i	−1.45643	−	1.26737i
$880$	1.80222	+	15.9952i	0.0607530	+	0.539198i
$881$	10.1576	+	6.38246i	0.342219	+	0.215030i	0.692165	−	0.721740i	$-0.256657\pi$
$881$	10.1576	+	6.38246i	0.342219	+	0.215030i	−0.349946	+	0.936770i	$0.613800\pi$
$882$	−8.78955	+	43.8101i	−0.295959	+	1.47516i
$883$	31.0147	−	7.07889i	1.04373	−	0.238224i	0.333906	−	0.942606i	$-0.391633\pi$
$883$	31.0147	−	7.07889i	1.04373	−	0.238224i	0.709821	+	0.704383i	$0.248776\pi$
$884$	−3.03857	+	1.06324i	−0.102198	+	0.0357606i
$885$	4.01787	−	25.6970i	0.135059	−	0.863796i
$886$	20.2030	+	88.5149i	0.678731	+	2.97372i
$887$	−35.5758	+	35.5758i	−1.19452	+	1.19452i	−0.218733	+	0.975785i	$0.570193\pi$
$887$	−35.5758	+	35.5758i	−1.19452	+	1.19452i	−0.975785	+	0.218733i	$0.929807\pi$
$888$	−38.2045	−	67.0207i	−1.28206	−	2.24907i
$889$	−6.29431	+	0.709199i	−0.211105	+	0.0237858i
$890$	2.68803	+	0.613526i	0.0901031	+	0.0205654i
$891$	4.52228	−	0.753019i	0.151502	−	0.0252271i
$892$	−48.8042	+	38.9200i	−1.63409	+	1.30314i
$893$	1.29710	−	2.69345i	0.0434057	−	0.0901329i
$894$	−1.33708	+	31.1482i	−0.0447186	+	1.04175i
$895$	−14.7282	+	18.4686i	−0.492310	+	0.617337i
$896$	−6.66809	+	59.1810i	−0.222765	+	1.97710i
$897$	17.5770	−	16.1301i	0.586879	−	0.538567i
$898$		−	96.4413i		−	3.21829i
$899$	−9.45405	+	7.07968i	−0.315310	+	0.236121i
$900$	9.97935	+	14.9886i	0.332645	+	0.499621i
$901$	−1.46802	−	0.513682i	−0.0489068	−	0.0171132i
$902$	−0.127828	−	0.0144028i	−0.00425622	−	0.000479561i
$903$	−1.96023	+	0.842438i	−0.0652325	+	0.0280346i
$904$	−50.8818	−	105.657i	−1.69231	−	3.51411i
$905$	−5.82825	−	2.80674i	−0.193738	−	0.0932991i
$906$	−10.7289	−	58.4620i	−0.356443	−	1.94227i
$907$	17.4994	+	27.8502i	0.581060	+	0.924751i	0.999861	+	0.0166732i	$0.00530749\pi$
$907$	17.4994	+	27.8502i	0.581060	+	0.924751i	−0.418801	+	0.908078i	$0.637550\pi$
$908$	2.61938	−	11.4762i	0.0869271	−	0.380853i
$909$	−20.0593	−	23.8346i	−0.665324	−	0.790545i
$910$	13.4949	−	21.4770i	0.447351	−	0.711954i
$911$	−29.7696	−	29.7696i	−0.986310	−	0.986310i	0.0135971	−	0.999908i	$-0.495672\pi$
$911$	−29.7696	−	29.7696i	−0.986310	−	0.986310i	−0.999908	+	0.0135971i	$0.995672\pi$
$912$	−4.91279	+	17.9395i	−0.162679	+	0.594036i
$913$	−0.240306	−	0.686755i	−0.00795297	−	0.0227283i
$914$	−13.0803	−	37.3813i	−0.432657	−	1.23646i
$915$	−10.8527	+	39.6295i	−0.358778	+	1.31011i
$916$	−72.2462	−	72.2462i	−2.38708	−	2.38708i
$917$	−8.65228	+	13.7700i	−0.285724	+	0.454726i
$918$	−2.18916	+	0.461797i	−0.0722530	+	0.0152416i
$919$	4.79993	−	21.0299i	0.158335	−	0.693712i	−0.831972	−	0.554817i	$-0.812788\pi$
$919$	4.79993	−	21.0299i	0.158335	−	0.693712i	0.990307	−	0.138894i	$-0.0443548\pi$
$920$	38.7371	+	61.6497i	1.27712	+	2.03253i
$921$	−3.98140	−	21.6948i	−0.131192	−	0.714867i
$922$	−34.1193	−	16.4310i	−1.12366	−	0.541125i
$923$	18.1378	+	37.6636i	0.597014	+	1.23971i
$924$	−5.69935	+	2.44938i	−0.187495	+	0.0805786i
$925$	4.83699	+	0.544997i	0.159039	+	0.0179194i
$926$	−52.4179	−	18.3418i	−1.72256	−	0.602749i
$927$	27.6044	−	18.3788i	0.906646	−	0.603640i
$928$	−84.3751	+	99.4386i	−2.76975	+	3.26423i
$929$		−	38.1303i		−	1.25102i	−0.780218	−	0.625508i	$-0.784892\pi$
$929$		−	38.1303i		−	1.25102i	0.780218	−	0.625508i	$-0.215108\pi$
$930$	−15.2617	+	14.0053i	−0.500450	+	0.459253i
$931$	0.407827	−	3.61956i	0.0133660	−	0.118626i
$932$	−50.4833	+	63.3041i	−1.65364	+	2.07359i
$933$	−1.57464	+	36.6823i	−0.0515513	+	1.20093i
$934$	−8.80170	+	18.2769i	−0.288000	+	0.598039i
$935$	0.123399	−	0.0984074i	0.00403558	−	0.00321827i
$936$	99.4306	+	44.6894i	3.24999	+	1.46072i
$937$	14.3342	+	3.27168i	0.468277	+	0.106881i	0.450147	−	0.892954i	$-0.351372\pi$
$937$	14.3342	+	3.27168i	0.468277	+	0.106881i	0.0181302	+	0.999836i	$0.494229\pi$
$938$	−37.8007	+	4.25912i	−1.23424	+	0.139065i
$939$	−22.4412	−	39.3677i	−0.732340	−	1.28472i
$940$	34.6924	−	34.6924i	1.13154	−	1.13154i
$941$	−9.62425	−	42.1666i	−0.313742	−	1.37459i	−0.848325	−	0.529476i	$-0.822389\pi$
$941$	−9.62425	−	42.1666i	−0.313742	−	1.37459i	0.534583	−	0.845116i	$-0.320469\pi$
$942$	−13.6652	+	87.3984i	−0.445237	+	2.84759i
$943$	−0.323211	+	0.113096i	−0.0105252	+	0.00368293i
$944$	−117.898	+	26.9094i	−3.83725	+	0.875827i
$945$	8.25634	−	10.0098i	0.268579	−	0.325617i
$946$	1.16016	+	0.728979i	0.0377202	+	0.0237012i
$947$	2.21240	+	19.6356i	0.0718934	+	0.638071i	0.977053	+	0.212998i	$0.0683229\pi$
$947$	2.21240	+	19.6356i	0.0718934	+	0.638071i	−0.905159	+	0.425073i	$0.860248\pi$
$948$	109.248	+	95.0660i	3.54820	+	3.08760i
$949$	−40.2914	+	25.3168i	−1.30791	+	0.821817i
$950$	−1.24339	−	1.55917i	−0.0403410	−	0.0505860i
$951$	−3.97402	−	5.44706i	−0.128866	−	0.176633i
$952$	1.74948	−	0.842503i	0.0567008	−	0.0273057i
$953$	40.6330	+	32.4038i	1.31623	+	1.04966i	0.994706	+	0.102760i	$0.0327673\pi$
$953$	40.6330	+	32.4038i	1.31623	+	1.04966i	0.321526	+	0.946901i	$0.395804\pi$
$954$	37.5672	+	73.0136i	1.21628	+	2.36390i
$955$	9.94155	−	28.4113i	0.321701	−	0.919369i
$956$	113.323			3.66512
$957$	−4.66977	−	0.876474i	−0.150952	−	0.0283324i
$958$	−52.1172			−1.68383
$959$	−1.58357	+	4.52557i	−0.0511360	+	0.146138i
$960$	−67.7172	+	98.1586i	−2.18556	+	3.16805i
$961$	−20.4759	−	16.3290i	−0.660512	−	0.526741i
$962$	41.3929	−	19.9338i	1.33456	−	0.642691i
$963$	−2.44135	−	17.5015i	−0.0786715	−	0.563978i
$964$	−11.7495	−	14.7334i	−0.378427	−	0.474532i
$965$	3.18633	−	2.00210i	0.102572	−	0.0644500i
$966$	−14.7272	+	16.9241i	−0.473838	+	0.544524i
$967$	−1.17102	−	10.3931i	−0.0376575	−	0.334220i	−0.998389	−	0.0567399i	$-0.981929\pi$
$967$	−1.17102	−	10.3931i	−0.0376575	−	0.334220i	0.960731	−	0.277480i	$-0.0894991\pi$
$968$	−89.5547	−	56.2710i	−2.87840	−	1.80862i
$969$	0.174573	−	0.0527989i	0.00560809	−	0.00169614i
$970$	81.3820	−	18.5749i	2.61302	−	0.596404i
$971$	46.2628	−	16.1880i	1.48464	−	0.519499i	0.538325	−	0.842737i	$-0.319057\pi$
$971$	46.2628	−	16.1880i	1.48464	−	0.519499i	0.946318	+	0.323238i	$0.104772\pi$
$972$	74.0705	+	45.5251i	2.37581	+	1.46022i
$973$	3.34740	+	14.6659i	0.107313	+	0.470168i
$974$	−30.3060	+	30.3060i	−0.971068	+	0.971068i
$975$	−5.97559	+	3.40633i	−0.191372	+	0.109090i
$976$	189.840	−	21.3899i	6.07664	−	0.684673i
$977$	23.1071	+	5.27405i	0.739263	+	0.168732i	0.575539	−	0.817774i	$-0.304792\pi$
$977$	23.1071	+	5.27405i	0.739263	+	0.168732i	0.163724	+	0.986506i	$0.447649\pi$
$978$	57.2584	−	3.97436i	1.83092	−	0.127086i
$979$	0.201380	−	0.160595i	0.00643613	−	0.00513264i
$980$	25.9370	−	53.8587i	0.828526	−	1.72045i
$981$	−10.5529	−	6.24852i	−0.336930	−	0.199500i
$982$	65.6535	−	82.3269i	2.09509	−	2.62716i
$983$	5.07702	−	45.0598i	0.161932	−	1.43718i	−0.605394	−	0.795926i	$-0.706984\pi$
$983$	5.07702	−	45.0598i	0.161932	−	1.43718i	0.767326	−	0.641258i	$-0.221587\pi$
$984$	−1.05795	−	1.15286i	−0.0337263	−	0.0367517i
$985$			4.76649i			0.151873i
$986$	2.29517	+	0.329604i	0.0730932	+	0.0104967i
$987$	8.54775	+	4.57794i	0.272078	+	0.145717i
$988$	−13.0771	−	4.57587i	−0.416037	−	0.145578i
$989$	3.62442	+	0.408375i	0.115250	+	0.0129856i
$990$	−8.30209	−	0.714072i	−0.263858	−	0.0226947i
$991$	10.4938	+	21.7906i	0.333346	+	0.692201i	0.998514	−	0.0544931i	$-0.0173543\pi$
$991$	10.4938	+	21.7906i	0.333346	+	0.692201i	−0.665168	+	0.746694i	$0.731640\pi$
$992$	47.8539	+	23.0452i	1.51936	+	0.731686i
$993$	16.4944	−	3.02703i	0.523433	−	0.0960600i
$994$	−20.9153	−	33.2865i	−0.663393	−	1.05578i
$995$	−4.03846	+	17.6937i	−0.128028	+	0.560927i
$996$	5.11158	−	12.8164i	0.161966	−	0.406102i
$997$	−9.92290	+	15.7922i	−0.314261	+	0.500144i	−0.966084	−	0.258227i	$-0.916862\pi$
$997$	−9.92290	+	15.7922i	−0.314261	+	0.500144i	0.651823	+	0.758371i	$0.274005\pi$
$998$	−41.1118	−	41.1118i	−1.30137	−	1.30137i
$999$	22.3084	−	7.39521i	0.705805	−	0.233974i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	87.2.k.a.8.1	✓	96
3.2	odd	2	inner	87.2.k.a.8.8	yes	96
29.11	odd	28	inner	87.2.k.a.11.8	yes	96
87.11	even	28	inner	87.2.k.a.11.1	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.2.k.a.8.1	✓	96	1.1	even	1	trivial
87.2.k.a.8.8	yes	96	3.2	odd	2	inner
87.2.k.a.11.1	yes	96	87.11	even	28	inner
87.2.k.a.11.8	yes	96	29.11	odd	28	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 87 = 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	87.k (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.909159 + 2.59823i) q^{2} +(1.42570 + 0.983555i) q^{3} +(-4.36055 - 3.47743i) q^{4} +(-1.78469 + 0.859464i) q^{5} +(-3.85169 + 2.81008i) q^{6} +(0.785988 + 0.985597i) q^{7} +(8.33803 - 5.23913i) q^{8} +(1.06524 + 2.80451i) q^{9} +(-0.610511 - 5.41843i) q^{10} +(-0.431316 - 0.271014i) q^{11} +(-2.79660 - 9.24661i) q^{12} +(3.59753 - 0.821112i) q^{13} +(-3.27539 + 1.14611i) q^{14} +(-3.38977 - 0.530009i) q^{15} +(3.54970 + 15.5522i) q^{16} +(0.110605 - 0.110605i) q^{17} +(-8.25522 + 0.217987i) q^{18} +(0.668949 - 0.0753725i) q^{19} +(10.7710 + 2.45841i) q^{20} +(0.151193 + 2.17823i) q^{21} +(1.09629 - 0.874263i) q^{22} +(1.61952 - 3.36297i) q^{23} +(17.0405 + 0.731485i) q^{24} +(-0.670992 + 0.841397i) q^{25} +(-1.13729 + 10.0937i) q^{26} +(-1.23968 + 5.04611i) q^{27} -7.03096i q^{28} +(3.00250 - 4.47046i) q^{29} +(4.45892 - 8.32553i) q^{30} +(-2.07018 - 0.724387i) q^{31} +(-24.0646 - 2.71143i) q^{32} +(-0.348370 - 0.810608i) q^{33} +(0.186820 + 0.387935i) q^{34} +(-2.24983 - 1.08346i) q^{35} +(5.10744 - 15.9335i) q^{36} +(-2.40638 - 3.82973i) q^{37} +(-0.412346 + 1.80661i) q^{38} +(5.93660 + 2.36771i) q^{39} +(-10.3780 + 16.5165i) q^{40} +(-0.0648693 - 0.0648693i) q^{41} +(-5.79699 - 1.58752i) q^{42} +(0.322735 + 0.922323i) q^{43} +(0.938347 + 2.68164i) q^{44} +(-4.31150 - 4.08966i) q^{45} +(7.26537 + 7.26537i) q^{46} +(2.36268 - 3.76018i) q^{47} +(-10.2357 + 25.6642i) q^{48} +(1.20402 - 5.27516i) q^{49} +(-1.57610 - 2.50835i) q^{50} +(0.266476 - 0.0489034i) q^{51} +(-18.5426 - 8.92963i) q^{52} +(-4.31416 - 8.95845i) q^{53} +(-11.9839 - 7.80868i) q^{54} +(1.00269 + 0.112977i) q^{55} +(11.7173 + 4.10005i) q^{56} +(1.02785 + 0.550490i) q^{57} +(8.88552 + 11.8655i) q^{58} +7.58076i q^{59} +(12.9382 + 14.0988i) q^{60} +(1.34087 - 11.9006i) q^{61} +(3.76424 - 4.72021i) q^{62} +(-1.92685 + 3.25420i) q^{63} +(15.0806 - 31.3152i) q^{64} +(-5.71477 + 4.55738i) q^{65} +(2.42287 - 0.168173i) q^{66} +(10.6873 + 2.43930i) q^{67} +(-0.866921 + 0.0976785i) q^{68} +(5.61662 - 3.20170i) q^{69} +(4.86054 - 4.86054i) q^{70} +(2.52088 + 11.0447i) q^{71} +(23.5752 + 17.8031i) q^{72} +(-12.1719 + 4.25912i) q^{73} +(12.1383 - 2.77049i) q^{74} +(-1.78419 + 0.539622i) q^{75} +(-3.17909 - 1.99756i) q^{76} +(-0.0718986 - 0.638118i) q^{77} +(-11.5492 + 13.2720i) q^{78} +(-12.6934 + 7.97581i) q^{79} +(-19.7017 - 24.7052i) q^{80} +(-6.73054 + 5.97494i) q^{81} +(0.227522 - 0.109569i) q^{82} +(1.11672 + 0.890552i) q^{83} +(6.91534 - 10.0240i) q^{84} +(-0.102335 + 0.292458i) q^{85} -2.68982 q^{86} +(8.67760 - 3.42041i) q^{87} -5.01620 q^{88} +(-0.167005 + 0.477274i) q^{89} +(14.5457 - 7.48410i) q^{90} +(3.63690 + 2.90033i) q^{91} +(-18.7565 + 9.03266i) q^{92} +(-2.23898 - 3.06889i) q^{93} +(7.62176 + 9.55738i) q^{94} +(-1.12909 + 0.709454i) q^{95} +(-31.6420 - 27.5345i) q^{96} +(1.71405 + 15.2126i) q^{97} +(12.6114 + 7.92428i) q^{98} +(0.300606 - 1.49832i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 12 q^{3} - 28 q^{4} - 14 q^{6} - 20 q^{7} - 14 q^{9} - 4 q^{10} - 8 q^{12} - 28 q^{13} - 16 q^{15} - 48 q^{16} - 28 q^{18} - 20 q^{19} + 26 q^{21} - 28 q^{22} + 58 q^{24} - 20 q^{25} + 36 q^{27}+ \cdots + 82 q^{99}+O(q^{100}) \) 96 * q - 12 * q^3 - 28 * q^4 - 14 * q^6 - 20 * q^7 - 14 * q^9 - 4 * q^10 - 8 * q^12 - 28 * q^13 - 16 * q^15 - 48 * q^16 - 28 * q^18 - 20 * q^19 + 26 * q^21 - 28 * q^22 + 58 * q^24 - 20 * q^25 + 36 * q^27 + 96 * q^30 - 32 * q^31 + 28 * q^33 - 28 * q^34 + 22 * q^36 - 4 * q^37 - 40 * q^39 - 48 * q^40 - 14 * q^42 - 32 * q^43 + 42 * q^45 + 120 * q^46 - 20 * q^48 + 4 * q^49 - 14 * q^51 + 72 * q^52 - 30 * q^54 + 148 * q^55 + 112 * q^58 + 20 * q^60 + 12 * q^61 - 14 * q^63 + 224 * q^64 - 32 * q^66 + 28 * q^67 + 10 * q^69 + 52 * q^70 - 44 * q^72 + 16 * q^73 - 144 * q^75 - 100 * q^76 - 102 * q^78 - 60 * q^79 - 146 * q^81 - 108 * q^82 - 64 * q^84 - 104 * q^85 - 70 * q^87 - 312 * q^88 - 96 * q^90 - 112 * q^91 - 70 * q^93 + 56 * q^94 - 168 * q^96 + 32 * q^97 + 82 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more