LMFDB - Embedded newform 1089.2.e.p.727.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1089,2,Mod(364,1089)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1089, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1089.364"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1089 = 3^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1089.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [36,2,9,-12,1,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$8.69570878012$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			727.9
Character	$\chi$	$=$	1089.727
Dual form			1089.2.e.p.364.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.142574 + 0.246946i) q^{2} +(0.0364826 - 1.73167i) q^{3} +(0.959345 + 1.66163i) q^{4} +(-1.35437 - 2.34583i) q^{5} +(0.422426 + 0.255900i) q^{6} +(2.03667 - 3.52761i) q^{7} -1.11741 q^{8} +(-2.99734 - 0.126351i) q^{9} +0.772391 q^{10} +(2.91240 - 1.60065i) q^{12} +(-1.92548 - 3.33503i) q^{13} +(0.580752 + 1.00589i) q^{14} +(-4.11161 + 2.25973i) q^{15} +(-1.75938 + 3.04733i) q^{16} -4.32020 q^{17} +(0.458545 - 0.722165i) q^{18} -1.62229 q^{19} +(2.59861 - 4.50093i) q^{20} +(-6.03434 - 3.65553i) q^{21} +(0.932117 + 1.61447i) q^{23} +(-0.0407660 + 1.93498i) q^{24} +(-1.16862 + 2.02411i) q^{25} +1.09809 q^{26} +(-0.328149 + 5.18578i) q^{27} +7.81547 q^{28} +(-1.77667 + 3.07729i) q^{29} +(0.0281788 - 1.33752i) q^{30} +(2.43230 + 4.21286i) q^{31} +(-1.61909 - 2.80435i) q^{32} +(0.615950 - 1.06686i) q^{34} -11.0336 q^{35} +(-2.66553 - 5.10170i) q^{36} +7.74449 q^{37} +(0.231297 - 0.400619i) q^{38} +(-5.84540 + 3.21262i) q^{39} +(1.51338 + 2.62125i) q^{40} +(-3.43607 - 5.95145i) q^{41} +(1.76306 - 0.968972i) q^{42} +(-0.492496 + 0.853027i) q^{43} +(3.76310 + 7.20238i) q^{45} -0.531584 q^{46} +(-2.93317 + 5.08041i) q^{47} +(5.21277 + 3.15783i) q^{48} +(-4.79603 - 8.30697i) q^{49} +(-0.333230 - 0.577171i) q^{50} +(-0.157612 + 7.48115i) q^{51} +(3.69440 - 6.39888i) q^{52} -1.57183 q^{53} +(-1.23382 - 0.820393i) q^{54} +(-2.27579 + 3.94178i) q^{56} +(-0.0591855 + 2.80927i) q^{57} +(-0.506615 - 0.877483i) q^{58} +(-5.68125 - 9.84021i) q^{59} +(-7.69930 - 4.66413i) q^{60} +(4.30374 - 7.45430i) q^{61} -1.38713 q^{62} +(-6.55030 + 10.3161i) q^{63} -6.11414 q^{64} +(-5.21561 + 9.03370i) q^{65} +(0.870282 + 1.50737i) q^{67} +(-4.14457 - 7.17860i) q^{68} +(2.82974 - 1.55522i) q^{69} +(1.57310 - 2.72470i) q^{70} -5.74136 q^{71} +(3.34925 + 0.141186i) q^{72} -4.04662 q^{73} +(-1.10416 + 1.91247i) q^{74} +(3.46245 + 2.09750i) q^{75} +(-1.55634 - 2.69566i) q^{76} +(0.0400613 - 1.90153i) q^{78} +(2.14007 - 3.70672i) q^{79} +9.53137 q^{80} +(8.96807 + 0.757436i) q^{81} +1.95958 q^{82} +(3.25009 - 5.62933i) q^{83} +(0.285129 - 13.5338i) q^{84} +(5.85114 + 10.1345i) q^{85} +(-0.140434 - 0.243239i) q^{86} +(5.26402 + 3.18887i) q^{87} +9.26243 q^{89} +(-2.31512 - 0.0975927i) q^{90} -15.6862 q^{91} +(-1.78844 + 3.09768i) q^{92} +(7.38400 - 4.05823i) q^{93} +(-0.836390 - 1.44867i) q^{94} +(2.19718 + 3.80563i) q^{95} +(-4.91527 + 2.70142i) q^{96} +(3.70634 - 6.41957i) q^{97} +2.73516 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 2 q^{2} + 9 q^{3} - 12 q^{4} + q^{5} - q^{6} - q^{7} - 12 q^{8} - q^{9} - 4 q^{10} - 8 q^{12} - 3 q^{13} - 5 q^{15} + 8 q^{16} - 40 q^{17} + 17 q^{18} - 6 q^{19} + 5 q^{20} - 8 q^{21} + 10 q^{23}+ \cdots - 164 q^{98}+O(q^{100}) $ 36 * q + 2 * q^2 + 9 * q^3 - 12 * q^4 + q^5 - q^6 - q^7 - 12 * q^8 - q^9 - 4 * q^10 - 8 * q^12 - 3 * q^13 - 5 * q^15 + 8 * q^16 - 40 * q^17 + 17 * q^18 - 6 * q^19 + 5 * q^20 - 8 * q^21 + 10 * q^23 - 57 * q^24 - 7 * q^25 + 4 * q^26 - 9 * q^27 + 38 * q^28 + 21 * q^29 + 12 * q^30 - 6 * q^31 + 9 * q^32 + 4 * q^34 - 76 * q^35 - 65 * q^36 + 14 * q^37 - 13 * q^38 + 42 * q^39 + 20 * q^41 + 18 * q^42 - 4 * q^43 + 20 * q^45 + 16 * q^46 - 7 * q^47 + 10 * q^48 - 7 * q^49 + 25 * q^50 - 4 * q^51 + 19 * q^52 + 62 * q^53 + 17 * q^54 + 57 * q^56 - 18 * q^57 - 12 * q^58 + 12 * q^59 + 11 * q^60 + 16 * q^61 - 38 * q^62 + 5 * q^63 - 32 * q^64 + 42 * q^65 + 5 * q^67 + 51 * q^68 + 31 * q^69 - 8 * q^70 + 26 * q^71 + 51 * q^72 + 9 * q^74 - 16 * q^75 + 8 * q^76 - 32 * q^78 + 2 * q^79 + 92 * q^80 + 47 * q^81 - 68 * q^82 + 36 * q^83 + 60 * q^84 - 25 * q^85 - 26 * q^86 - 60 * q^87 - 28 * q^89 + 163 * q^90 - 30 * q^91 + 15 * q^92 - 39 * q^93 - 4 * q^94 + 64 * q^95 - 21 * q^96 + 16 * q^97 - 164 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times$.

$n$	$244$	$848$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.142574	+	0.246946i	−0.100815	+	0.174617i	−0.912021	−	0.410144i	$-0.865478\pi$
$2$	−0.142574	+	0.246946i	−0.100815	+	0.174617i	0.811206	+	0.584761i	$0.198812\pi$
$3$	0.0364826	−	1.73167i	0.0210632	−	0.999778i
$3$	0.0364826	−	1.73167i	0.0210632	−	0.999778i
$4$	0.959345	+	1.66163i	0.479673	+	0.830817i
$5$	−1.35437	−	2.34583i	−0.605691	−	1.04909i	−0.991942	−	0.126694i	$-0.959563\pi$
$5$	−1.35437	−	2.34583i	−0.605691	−	1.04909i	0.386251	−	0.922394i	$-0.373770\pi$
$6$	0.422426	+	0.255900i	0.172455	+	0.104471i
$7$	2.03667	−	3.52761i	0.769788	−	1.33331i	−0.167890	−	0.985806i	$-0.553695\pi$
$7$	2.03667	−	3.52761i	0.769788	−	1.33331i	0.937678	−	0.347506i	$-0.112971\pi$
$8$	−1.11741			−0.395063
$9$	−2.99734	−	0.126351i	−0.999113	−	0.0421171i
$10$	0.772391			0.244251
$11$		0			0
$11$		0			0
$12$	2.91240	−	1.60065i	0.840736	−	0.462066i
$13$	−1.92548	−	3.33503i	−0.534032	−	0.924970i	−0.999210	−	0.0397526i	$-0.987343\pi$
$13$	−1.92548	−	3.33503i	−0.534032	−	0.924970i	0.465178	−	0.885217i	$-0.345990\pi$
$14$	0.580752	+	1.00589i	0.155213	+	0.268836i
$15$	−4.11161	+	2.25973i	−1.06161	+	0.583460i
$16$	−1.75938	+	3.04733i	−0.439844	+	0.761833i
$17$	−4.32020			−1.04780			−0.523902	−	0.851779i	$-0.675524\pi$
$17$	−4.32020			−1.04780			−0.523902	+	0.851779i	$0.675524\pi$
$18$	0.458545	−	0.722165i	0.108080	−	0.170216i
$19$	−1.62229			−0.372180			−0.186090	−	0.982533i	$-0.559582\pi$
$19$	−1.62229			−0.372180			−0.186090	+	0.982533i	$0.559582\pi$
$20$	2.59861	−	4.50093i	0.581067	−	1.00644i
$21$	−6.03434	−	3.65553i	−1.31680	−	0.797701i
$22$		0			0
$23$	0.932117	+	1.61447i	0.194360	+	0.336641i	0.946691	−	0.322145i	$-0.104404\pi$
$23$	0.932117	+	1.61447i	0.194360	+	0.336641i	−0.752331	+	0.658786i	$0.771070\pi$
$24$	−0.0407660	+	1.93498i	−0.00832132	+	0.394976i
$25$	−1.16862	+	2.02411i	−0.233724	+	0.404822i
$26$	1.09809			0.215354
$27$	−0.328149	+	5.18578i	−0.0631523	+	0.998004i
$28$	7.81547			1.47698
$29$	−1.77667	+	3.07729i	−0.329920	+	0.571438i	−0.982496	−	0.186286i	$-0.940355\pi$
$29$	−1.77667	+	3.07729i	−0.329920	+	0.571438i	0.652576	+	0.757723i	$0.273688\pi$
$30$	0.0281788	−	1.33752i	0.00514473	−	0.244197i
$31$	2.43230	+	4.21286i	0.436853	+	0.756652i	0.997445	−	0.0714406i	$-0.0227596\pi$
$31$	2.43230	+	4.21286i	0.436853	+	0.756652i	−0.560592	+	0.828092i	$0.689426\pi$
$32$	−1.61909	−	2.80435i	−0.286218	−	0.495744i
$33$		0			0
$34$	0.615950	−	1.06686i	0.105634	−	0.182964i
$35$	−11.0336			−1.86502
$36$	−2.66553	−	5.10170i	−0.444255	−	0.850283i
$37$	7.74449			1.27319			0.636593	−	0.771200i	$-0.280343\pi$
$37$	7.74449			1.27319			0.636593	+	0.771200i	$0.280343\pi$
$38$	0.231297	−	0.400619i	0.0375214	−	0.0649889i
$39$	−5.84540	+	3.21262i	−0.936013	+	0.514430i
$40$	1.51338	+	2.62125i	0.239286	+	0.414456i
$41$	−3.43607	−	5.95145i	−0.536624	−	0.929461i	−0.999083	−	0.0428197i	$-0.986366\pi$
$41$	−3.43607	−	5.95145i	−0.536624	−	0.929461i	0.462458	−	0.886641i	$-0.346967\pi$
$42$	1.76306	−	0.968972i	0.272046	−	0.149516i
$43$	−0.492496	+	0.853027i	−0.0751049	+	0.130085i	−0.901132	−	0.433545i	$-0.857262\pi$
$43$	−0.492496	+	0.853027i	−0.0751049	+	0.130085i	0.826027	+	0.563631i	$0.190596\pi$
$44$		0			0
$45$	3.76310	+	7.20238i	0.560969	+	1.07367i
$46$	−0.531584			−0.0783777
$47$	−2.93317	+	5.08041i	−0.427847	+	0.741054i	−0.996682	−	0.0813987i	$-0.974061\pi$
$47$	−2.93317	+	5.08041i	−0.427847	+	0.741054i	0.568834	+	0.822452i	$0.307395\pi$
$48$	5.21277	+	3.15783i	0.752399	+	0.455793i
$49$	−4.79603	−	8.30697i	−0.685147	−	1.18671i
$50$	−0.333230	−	0.577171i	−0.0471258	−	0.0816243i
$51$	−0.157612	+	7.48115i	−0.0220701	+	1.04757i
$52$	3.69440	−	6.39888i	0.512321	−	0.887365i
$53$	−1.57183			−0.215907			−0.107953	−	0.994156i	$-0.534430\pi$
$53$	−1.57183			−0.215907			−0.107953	+	0.994156i	$0.534430\pi$
$54$	−1.23382	−	0.820393i	−0.167902	−	0.111641i
$55$		0			0
$56$	−2.27579	+	3.94178i	−0.304115	+	0.526743i
$57$	−0.0591855	+	2.80927i	−0.00783931	+	0.372097i
$58$	−0.506615	−	0.877483i	−0.0665218	−	0.115219i
$59$	−5.68125	−	9.84021i	−0.739635	−	1.28109i	−0.952660	−	0.304039i	$-0.901665\pi$
$59$	−5.68125	−	9.84021i	−0.739635	−	1.28109i	0.213024	−	0.977047i	$-0.431669\pi$
$60$	−7.69930	−	4.66413i	−0.993975	−	0.602137i
$61$	4.30374	−	7.45430i	0.551037	−	0.954425i	−0.447163	−	0.894453i	$-0.647566\pi$
$61$	4.30374	−	7.45430i	0.551037	−	0.954425i	0.998200	−	0.0599721i	$-0.0191012\pi$
$62$	−1.38713			−0.176166
$63$	−6.55030	+	10.3161i	−0.825260	+	1.29971i
$64$	−6.11414			−0.764268
$65$	−5.21561	+	9.03370i	−0.646916	+	1.12049i
$66$		0			0
$67$	0.870282	+	1.50737i	0.106322	+	0.184155i	0.914277	−	0.405088i	$-0.132759\pi$
$67$	0.870282	+	1.50737i	0.106322	+	0.184155i	−0.807956	+	0.589243i	$0.799426\pi$
$68$	−4.14457	−	7.17860i	−0.502603	−	0.870533i
$69$	2.82974	−	1.55522i	0.340660	−	0.187226i
$70$	1.57310	−	2.72470i	0.188022	−	0.325663i
$71$	−5.74136			−0.681374			−0.340687	−	0.940177i	$-0.610660\pi$
$71$	−5.74136			−0.681374			−0.340687	+	0.940177i	$0.610660\pi$
$72$	3.34925	+	0.141186i	0.394713	+	0.0166389i
$73$	−4.04662			−0.473622			−0.236811	−	0.971556i	$-0.576102\pi$
$73$	−4.04662			−0.473622			−0.236811	+	0.971556i	$0.576102\pi$
$74$	−1.10416	+	1.91247i	−0.128356	+	0.222320i
$75$	3.46245	+	2.09750i	0.399809	+	0.242199i
$76$	−1.55634	−	2.69566i	−0.178524	−	0.309213i
$77$		0			0
$78$	0.0400613	−	1.90153i	0.00453605	−	0.215306i
$79$	2.14007	−	3.70672i	0.240777	−	0.417038i	−0.720159	−	0.693809i	$-0.755931\pi$
$79$	2.14007	−	3.70672i	0.240777	−	0.417038i	0.960936	+	0.276771i	$0.0892644\pi$
$80$	9.53137			1.06564
$81$	8.96807	+	0.757436i	0.996452	+	0.0841595i
$82$	1.95958			0.216400
$83$	3.25009	−	5.62933i	0.356744	−	0.617899i	−0.630671	−	0.776050i	$-0.717220\pi$
$83$	3.25009	−	5.62933i	0.356744	−	0.617899i	0.987415	+	0.158152i	$0.0505535\pi$
$84$	0.285129	−	13.5338i	0.0311101	−	1.47666i
$85$	5.85114	+	10.1345i	0.634645	+	1.09924i
$86$	−0.140434	−	0.243239i	−0.0151434	−	0.0262292i
$87$	5.26402	+	3.18887i	0.564362	+	0.341883i
$88$		0			0
$89$	9.26243			0.981816			0.490908	−	0.871211i	$-0.336665\pi$
$89$	9.26243			0.981816			0.490908	+	0.871211i	$0.336665\pi$
$90$	−2.31512	−	0.0975927i	−0.244035	−	0.0102872i
$91$	−15.6862			−1.64436
$92$	−1.78844	+	3.09768i	−0.186458	+	0.322955i
$93$	7.38400	−	4.05823i	0.765685	−	0.420819i
$94$	−0.836390	−	1.44867i	−0.0862670	−	0.149419i
$95$	2.19718	+	3.80563i	0.225426	+	0.390449i
$96$	−4.91527	+	2.70142i	−0.501662	+	0.275712i
$97$	3.70634	−	6.41957i	0.376322	−	0.651809i	−0.614202	−	0.789149i	$-0.710522\pi$
$97$	3.70634	−	6.41957i	0.376322	−	0.651809i	0.990524	+	0.137340i	$0.0438553\pi$
$98$	2.73516			0.276293
$99$		0			0
$100$	−4.48444			−0.448444
$101$	6.85880	−	11.8798i	0.682476	−	1.18208i	−0.291747	−	0.956496i	$-0.594236\pi$
$101$	6.85880	−	11.8798i	0.682476	−	1.18208i	0.974223	−	0.225588i	$-0.0724303\pi$
$102$	−1.82497	−	1.10554i	−0.180699	−	0.109465i
$103$	−2.53762	−	4.39529i	−0.250039	−	0.433081i	0.713497	−	0.700658i	$-0.247110\pi$
$103$	−2.53762	−	4.39529i	−0.250039	−	0.433081i	−0.963536	+	0.267577i	$0.913777\pi$
$104$	2.15154	+	3.72659i	0.210976	+	0.365422i
$105$	−0.402534	+	19.1065i	−0.0392833	+	1.86460i
$106$	0.224102	−	0.388156i	0.0217667	−	0.0377010i
$107$	−2.77898			−0.268654			−0.134327	−	0.990937i	$-0.542887\pi$
$107$	−2.77898			−0.268654			−0.134327	+	0.990937i	$0.542887\pi$
$108$	−8.93168	+	4.42969i	−0.859451	+	0.426247i
$109$	−17.3573			−1.66253			−0.831263	−	0.555879i	$-0.812382\pi$
$109$	−17.3573			−1.66253			−0.831263	+	0.555879i	$0.812382\pi$
$110$		0			0
$111$	0.282539	−	13.4109i	0.0268174	−	1.27290i
$112$	7.16653	+	12.4128i	0.677174	+	1.17290i
$113$	−0.471827	−	0.817228i	−0.0443858	−	0.0768784i	0.842979	−	0.537946i	$-0.180800\pi$
$113$	−0.471827	−	0.817228i	−0.0443858	−	0.0768784i	−0.887365	+	0.461068i	$0.847466\pi$
$114$	−0.685300	−	0.415145i	−0.0641842	−	0.0388819i
$115$	2.52486	−	4.37318i	0.235444	−	0.407801i
$116$	−6.81777			−0.633014
$117$	5.34992	+	10.2395i	0.494601	+	0.946641i
$118$	3.24000			0.298266
$119$	−8.79882	+	15.2400i	−0.806587	+	1.39705i
$120$	4.59435	−	2.52504i	0.419405	−	0.230504i
$121$		0			0
$122$	1.22720	+	2.12558i	0.111106	+	0.192441i
$123$	−10.4313	+	5.73301i	−0.940558	+	0.516928i
$124$	−4.66682	+	8.08317i	−0.419093	+	0.725890i
$125$	−7.21271			−0.645125
$126$	−1.61362	−	3.08838i	−0.143752	−	0.275135i
$127$	2.45040			0.217438			0.108719	−	0.994073i	$-0.465325\pi$
$127$	2.45040			0.217438			0.108719	+	0.994073i	$0.465325\pi$
$128$	4.10990	−	7.11856i	0.363267	−	0.629198i
$129$	1.45919	+	0.883959i	0.128475	+	0.0778282i
$130$	−1.48722	−	2.57594i	−0.130438	−	0.225925i
$131$	−1.99869	−	3.46183i	−0.174626	−	0.302461i	0.765406	−	0.643548i	$-0.222538\pi$
$131$	−1.99869	−	3.46183i	−0.174626	−	0.302461i	−0.940032	+	0.341087i	$0.889205\pi$
$132$		0			0
$133$	−3.30407	+	5.72282i	−0.286500	+	0.496232i
$134$	−0.496319			−0.0428754
$135$	12.6094	−	6.25367i	1.08524	−	0.538230i
$136$	4.82743			0.413949
$137$	−0.544628	+	0.943324i	−0.0465307	+	0.0805936i	−0.888353	−	0.459162i	$-0.848150\pi$
$137$	−0.544628	+	0.943324i	−0.0465307	+	0.0805936i	0.841822	+	0.539755i	$0.181483\pi$
$138$	−0.0193935	+	0.920525i	−0.00165089	+	0.0783603i
$139$	−1.44246	−	2.49842i	−0.122348	−	0.211913i	0.798345	−	0.602200i	$-0.205709\pi$
$139$	−1.44246	−	2.49842i	−0.122348	−	0.211913i	−0.920693	+	0.390287i	$0.872376\pi$
$140$	−10.5850	−	18.3338i	−0.894597	−	1.54949i
$141$	8.69056	+	5.26463i	0.731877	+	0.443362i
$142$	0.818570	−	1.41780i	0.0686929	−	0.118980i
$143$		0			0
$144$	5.65848	−	8.91158i	0.471540	−	0.742632i
$145$	9.62506			0.799318
$146$	0.576944	−	0.999297i	0.0477482	−	0.0827024i
$147$	−14.5599	+	8.00206i	−1.20088	+	0.659999i
$148$	7.42964	+	12.8685i	0.610712	+	1.05778i
$149$	−10.0874	−	17.4719i	−0.826393	−	1.43135i	−0.900850	−	0.434130i	$-0.857056\pi$
$149$	−10.0874	−	17.4719i	−0.826393	−	1.43135i	0.0744578	−	0.997224i	$-0.476277\pi$
$150$	−1.01163	+	0.555986i	−0.0825988	+	0.0453961i
$151$	5.53918	−	9.59414i	0.450772	−	0.780760i	−0.547662	−	0.836700i	$-0.684482\pi$
$151$	5.53918	−	9.59414i	0.450772	−	0.780760i	0.998434	+	0.0559396i	$0.0178154\pi$
$152$	1.81276			0.147035
$153$	12.9491	+	0.545864i	1.04687	+	0.0441305i
$154$		0			0
$155$	6.58844	−	11.4115i	0.529196	−	0.916595i
$156$	−10.9459	−	6.63091i	−0.876377	−	0.530898i
$157$	−0.166392	−	0.288200i	−0.0132795	−	0.0230008i	0.859309	−	0.511456i	$-0.170894\pi$
$157$	−0.166392	−	0.288200i	−0.0132795	−	0.0230008i	−0.872589	+	0.488455i	$0.837560\pi$
$158$	0.610238	+	1.05696i	0.0485480	+	0.0840875i
$159$	−0.0573443	+	2.72188i	−0.00454770	+	0.215859i
$160$	−4.38569	+	7.59623i	−0.346719	+	0.600535i
$161$	7.59365			0.598464
$162$	−1.46566	+	2.10664i	−0.115153	+	0.165513i
$163$	13.3380			1.04472			0.522358	−	0.852726i	$-0.325053\pi$
$163$	13.3380			1.04472			0.522358	+	0.852726i	$0.325053\pi$
$164$	6.59276	−	11.4190i	0.514808	−	0.891674i
$165$		0			0
$166$	0.926759	+	1.60519i	0.0719304	+	0.124587i
$167$	9.45758	+	16.3810i	0.731849	+	1.26760i	0.956092	+	0.293067i	$0.0946758\pi$
$167$	9.45758	+	16.3810i	0.731849	+	1.26760i	−0.224243	+	0.974533i	$0.571991\pi$
$168$	6.74283	+	4.08471i	0.520220	+	0.315143i
$169$	−0.914932	+	1.58471i	−0.0703794	+	0.121901i
$170$	−3.33689			−0.255928
$171$	4.86256	+	0.204979i	0.371850	+	0.0156751i
$172$	−1.88989			−0.144103
$173$	0.757044	−	1.31124i	0.0575570	−	0.0996916i	−0.835811	−	0.549017i	$-0.815002\pi$
$173$	0.757044	−	1.31124i	0.0575570	−	0.0996916i	0.893368	+	0.449325i	$0.148336\pi$
$174$	−1.53799	+	0.845276i	−0.116595	+	0.0640802i
$175$	4.76018	+	8.24487i	0.359836	+	0.623254i
$176$		0			0
$177$	−17.2472	+	9.47903i	−1.29638	+	0.712487i
$178$	−1.32058	+	2.28732i	−0.0989819	+	0.171442i
$179$	13.1892			0.985810			0.492905	−	0.870083i	$-0.335935\pi$
$179$	13.1892			0.985810			0.492905	+	0.870083i	$0.335935\pi$
$180$	−8.35761	+	13.1625i	−0.622940	+	0.981072i
$181$	2.79883			0.208035			0.104018	−	0.994575i	$-0.466830\pi$
$181$	2.79883			0.208035			0.104018	+	0.994575i	$0.466830\pi$
$182$	2.23645	−	3.87365i	0.165777	−	0.287134i
$183$	−12.7513	−	7.72459i	−0.942606	−	0.571018i
$184$	−1.04156	−	1.80403i	−0.0767845	−	0.132995i
$185$	−10.4889	−	18.1673i	−0.771158	−	1.33568i
$186$	−0.0506061	+	2.40205i	−0.00371062	+	0.176127i
$187$		0			0
$188$	−11.2557			−0.820907
$189$	17.6251	+	11.7193i	1.28204	+	0.852453i
$190$	−1.25305			−0.0909055
$191$	8.37078	−	14.4986i	0.605688	−	1.04908i	−0.386254	−	0.922392i	$-0.626231\pi$
$191$	8.37078	−	14.4986i	0.605688	−	1.04908i	0.991942	−	0.126690i	$-0.0404354\pi$
$192$	−0.223060	+	10.5877i	−0.0160980	+	0.764099i
$193$	11.0197	+	19.0867i	0.793214	+	1.37389i	0.923967	+	0.382473i	$0.124927\pi$
$193$	11.0197	+	19.0867i	0.793214	+	1.37389i	−0.130752	+	0.991415i	$0.541739\pi$
$194$	1.05686	+	1.83053i	0.0758779	+	0.131424i
$195$	15.4531	+	9.36127i	1.10662	+	0.670374i
$196$	9.20210	−	15.9385i	0.657293	−	1.13846i
$197$	18.2247			1.29845			0.649227	−	0.760595i	$-0.275093\pi$
$197$	18.2247			1.29845			0.649227	+	0.760595i	$0.275093\pi$
$198$		0			0
$199$	−25.0958			−1.77899			−0.889497	−	0.456942i	$-0.848945\pi$
$199$	−25.0958			−1.77899			−0.889497	+	0.456942i	$0.848945\pi$
$200$	1.30582	−	2.26176i	0.0923358	−	0.159930i
$201$	2.64202	−	1.45204i	0.186353	−	0.102419i
$202$	1.95578	+	3.38750i	0.137608	+	0.238344i
$203$	7.23698	+	12.5348i	0.507937	+	0.879772i
$204$	−12.5821	+	6.91512i	−0.880927	+	0.484155i
$205$	−9.30741	+	16.1209i	−0.650057	+	1.12593i
$206$	1.44720			0.100831
$207$	−2.58988	−	4.95690i	−0.180009	−	0.344528i
$208$	13.5506			0.939563
$209$		0			0
$210$	−4.66087	−	2.82350i	−0.321631	−	0.194840i
$211$	−4.13501	−	7.16205i	−0.284666	−	0.493056i	0.687862	−	0.725841i	$-0.258549\pi$
$211$	−4.13501	−	7.16205i	−0.284666	−	0.493056i	−0.972528	+	0.232785i	$0.925216\pi$
$212$	−1.50792	−	2.61180i	−0.103565	−	0.179379i
$213$	−0.209460	+	9.94213i	−0.0143520	+	0.681223i
$214$	0.396210	−	0.686257i	0.0270844	−	0.0469115i
$215$	2.66808			0.181961
$216$	0.366677	−	5.79463i	0.0249492	−	0.394275i
$217$	19.8151			1.34514
$218$	2.47470	−	4.28631i	0.167608	−	0.290305i
$219$	−0.147631	+	7.00740i	−0.00997600	+	0.473516i
$220$		0			0
$221$	8.31846	+	14.4080i	0.559560	+	0.969187i
$222$	3.27147	+	1.98182i	0.219567	+	0.133011i
$223$	3.67604	−	6.36709i	0.246166	−	0.426372i	−0.716293	−	0.697800i	$-0.754163\pi$
$223$	3.67604	−	6.36709i	0.246166	−	0.426372i	0.962459	+	0.271428i	$0.0874959\pi$
$224$	−13.1902			−0.881308
$225$	3.75850	−	5.91928i	0.250566	−	0.394619i
$226$	0.269081			0.0178990
$227$	9.47060	−	16.4036i	0.628586	−	1.08874i	−0.359250	−	0.933241i	$-0.616968\pi$
$227$	9.47060	−	16.4036i	0.628586	−	1.08874i	0.987836	−	0.155501i	$-0.0496992\pi$
$228$	−4.72476	+	2.59672i	−0.312905	+	0.171972i
$229$	3.92972	+	6.80648i	0.259683	+	0.449785i	0.966157	−	0.257954i	$-0.0830485\pi$
$229$	3.92972	+	6.80648i	0.259683	+	0.449785i	−0.706474	+	0.707739i	$0.749715\pi$
$230$	0.719959	+	1.24701i	0.0474727	+	0.0822251i
$231$		0			0
$232$	1.98527	−	3.43859i	0.130339	−	0.225754i
$233$	−6.56942			−0.430377			−0.215188	−	0.976573i	$-0.569037\pi$
$233$	−6.56942			−0.430377			−0.215188	+	0.976573i	$0.569037\pi$
$234$	−3.29136	−	0.138746i	−0.215163	−	0.00907009i
$235$	15.8904			1.03657
$236$	10.9006	−	18.8803i	0.709566	−	1.22900i
$237$	−6.34072	−	3.84112i	−0.411874	−	0.249508i
$238$	−2.50897	−	4.34566i	−0.162632	−	0.281687i
$239$	12.7731	+	22.1237i	0.826226	+	1.43107i	0.900979	+	0.433863i	$0.142850\pi$
$239$	12.7731	+	22.1237i	0.826226	+	1.43107i	−0.0747530	+	0.997202i	$0.523817\pi$
$240$	0.347729	−	16.5051i	0.0224458	−	1.06540i
$241$	1.49099	−	2.58247i	0.0960432	−	0.166352i	−0.814000	−	0.580864i	$-0.802715\pi$
$241$	1.49099	−	2.58247i	0.0960432	−	0.166352i	0.910044	+	0.414513i	$0.136048\pi$
$242$		0			0
$243$	1.63880	−	15.5021i	0.105129	−	0.994459i
$244$	16.5151			1.05727
$245$	−12.9912	+	22.5014i	−0.829975	+	1.43756i
$246$	0.0714906	−	3.39334i	0.00455807	−	0.216352i
$247$	3.12369	+	5.41039i	0.198756	+	0.344255i
$248$	−2.71787	−	4.70748i	−0.172585	−	0.298925i
$249$	−9.62954	−	5.83345i	−0.610248	−	0.369680i
$250$	1.02835	−	1.78115i	0.0650383	−	0.112650i
$251$	11.6685			0.736510			0.368255	−	0.929725i	$-0.379955\pi$
$251$	11.6685			0.736510			0.368255	+	0.929725i	$0.379955\pi$
$252$	−23.4256	−	0.987495i	−1.47567	−	0.0622064i
$253$		0			0
$254$	−0.349364	+	0.605116i	−0.0219211	+	0.0379684i
$255$	17.7630	−	9.76250i	1.11236	−	0.611351i
$256$	−4.94221	−	8.56016i	−0.308888	−	0.535010i
$257$	−10.3622	−	17.9479i	−0.646378	−	1.11956i	−0.983981	−	0.178271i	$-0.942950\pi$
$257$	−10.3622	−	17.9479i	−0.646378	−	1.11956i	0.337604	−	0.941288i	$-0.390384\pi$
$258$	−0.426333	+	0.234311i	−0.0265423	+	0.0145876i
$259$	15.7729	−	27.3195i	0.980083	−	1.69755i
$260$	−20.0143			−1.24123
$261$	5.71411	−	8.99918i	0.353694	−	0.557035i
$262$	1.13984			0.0704198
$263$	−4.54273	+	7.86823i	−0.280117	+	0.485176i	−0.971413	−	0.237395i	$-0.923706\pi$
$263$	−4.54273	+	7.86823i	−0.280117	+	0.485176i	0.691297	+	0.722571i	$0.257040\pi$
$264$		0			0
$265$	2.12883	+	3.68724i	0.130773	+	0.226505i
$266$	−0.942151	−	1.63185i	−0.0577670	−	0.100055i
$267$	0.337918	−	16.0394i	0.0206802	−	0.981598i
$268$	−1.66980	+	2.89218i	−0.101999	+	0.176668i
$269$	7.94129			0.484189			0.242094	−	0.970253i	$-0.422166\pi$
$269$	7.94129			0.484189			0.242094	+	0.970253i	$0.422166\pi$
$270$	−0.253459	+	4.00545i	−0.0154251	+	0.243764i
$271$	3.72364			0.226195			0.113097	−	0.993584i	$-0.463923\pi$
$271$	3.72364			0.226195			0.113097	+	0.993584i	$0.463923\pi$
$272$	7.60087	−	13.1651i	0.460870	−	0.798251i
$273$	−0.572275	+	27.1633i	−0.0346356	+	1.64400i
$274$	−0.155300	−	0.268987i	−0.00938201	−	0.0162501i
$275$		0			0
$276$	5.29890	+	3.21000i	0.318956	+	0.193219i
$277$	1.95032	−	3.37805i	0.117183	−	0.202967i	−0.801467	−	0.598039i	$-0.795947\pi$
$277$	1.95032	−	3.37805i	0.117183	−	0.202967i	0.918650	+	0.395071i	$0.129280\pi$
$278$	0.822632			0.0493382
$279$	−6.75811	−	12.9347i	−0.404597	−	0.774379i
$280$	12.3290			0.736799
$281$	−0.0198115	+	0.0343146i	−0.00118186	+	0.00204704i	−0.866616	−	0.498976i	$-0.833710\pi$
$281$	−0.0198115	+	0.0343146i	−0.00118186	+	0.00204704i	0.865434	+	0.501023i	$0.167043\pi$
$282$	−2.53913	+	1.39550i	−0.151203	+	0.0831006i
$283$	−3.19694	−	5.53725i	−0.190038	−	0.329156i	0.755225	−	0.655466i	$-0.227528\pi$
$283$	−3.19694	−	5.53725i	−0.190038	−	0.329156i	−0.945263	+	0.326311i	$0.894194\pi$
$284$	−5.50795	−	9.54005i	−0.326837	−	0.566098i
$285$	6.67024	−	3.66595i	0.395111	−	0.217152i
$286$		0			0
$287$	−27.9925			−1.65235
$288$	4.49863	+	8.61016i	0.265084	+	0.507358i
$289$	1.66417			0.0978923
$290$	−1.37229	+	2.37687i	−0.0805834	+	0.139575i
$291$	−10.9813	−	6.65235i	−0.643738	−	0.389968i
$292$	−3.88211	−	6.72401i	−0.227183	−	0.393493i
$293$	11.7037	+	20.2714i	0.683738	+	1.18427i	0.973832	+	0.227271i	$0.0729802\pi$
$293$	11.7037	+	20.2714i	0.683738	+	1.18427i	−0.290094	+	0.956998i	$0.593686\pi$
$294$	0.0997857	−	4.73638i	0.00581962	−	0.276232i
$295$	−15.3890	+	26.6545i	−0.895981	+	1.55189i
$296$	−8.65375			−0.502989
$297$		0			0
$298$	5.75282			0.333252
$299$	3.58954	−	6.21727i	0.207589	−	0.359554i
$300$	−0.163604	+	7.76555i	−0.00944568	+	0.448344i
$301$	2.00610	+	3.47467i	0.115630	+	0.200276i
$302$	1.57949	+	2.73575i	0.0908893	+	0.157425i
$303$	−20.3216	−	12.3106i	−1.16745	−	0.707223i
$304$	2.85423	−	4.94367i	0.163701	−	0.283539i
$305$	−23.3154			−1.33503
$306$	−1.98101	+	3.11990i	−0.113247	+	0.178353i
$307$	29.1494			1.66365			0.831823	−	0.555042i	$-0.187298\pi$
$307$	29.1494			1.66365			0.831823	+	0.555042i	$0.187298\pi$
$308$		0			0
$309$	−7.70376	+	4.23397i	−0.438252	+	0.240862i
$310$	1.87868	+	3.25397i	0.106702	+	0.184813i
$311$	9.85287	+	17.0657i	0.558705	+	0.967705i	0.997605	+	0.0691692i	$0.0220348\pi$
$311$	9.85287	+	17.0657i	0.558705	+	0.967705i	−0.438900	+	0.898536i	$0.644632\pi$
$312$	6.53170	−	3.58980i	0.369785	−	0.203233i
$313$	−0.669188	+	1.15907i	−0.0378248	+	0.0655144i	−0.884318	−	0.466885i	$-0.845376\pi$
$313$	−0.669188	+	1.15907i	−0.0378248	+	0.0655144i	0.846493	+	0.532399i	$0.178710\pi$
$314$	0.0948929			0.00535511
$315$	33.0714	+	1.39411i	1.86336	+	0.0785491i
$316$	8.21228			0.461977
$317$	−2.00045	+	3.46487i	−0.112356	+	0.194607i	−0.916720	−	0.399531i	$-0.869173\pi$
$317$	−2.00045	+	3.46487i	−0.112356	+	0.194607i	0.804364	+	0.594137i	$0.202506\pi$
$318$	−0.663980	−	0.402230i	−0.0372342	−	0.0225560i
$319$		0			0
$320$	8.28080	+	14.3428i	0.462911	+	0.801785i
$321$	−0.101384	+	4.81226i	−0.00565872	+	0.268594i
$322$	−1.08266	+	1.87522i	−0.0603342	+	0.104502i
$323$	7.00864			0.389971
$324$	7.34489	+	15.6283i	0.408050	+	0.868239i
$325$	9.00060			0.499264
$326$	−1.90166	+	3.29377i	−0.105323	+	0.182425i
$327$	−0.633239	+	30.0570i	−0.0350182	+	1.66216i
$328$	3.83950	+	6.65020i	0.212001	+	0.367196i
$329$	11.9478	+	20.6942i	0.658704	+	1.14091i
$330$		0			0
$331$	−1.59017	+	2.75425i	−0.0874034	+	0.151387i	−0.906413	−	0.422393i	$-0.861190\pi$
$331$	−1.59017	+	2.75425i	−0.0874034	+	0.151387i	0.819009	+	0.573780i	$0.194524\pi$
$332$	12.4718			0.684481
$333$	−23.2128	−	0.978527i	−1.27206	−	0.0536229i
$334$	−5.39362			−0.295126
$335$	2.35736	−	4.08307i	0.128796	−	0.223082i
$336$	21.7563	−	11.9572i	1.18690	−	0.652318i
$337$	9.09890	+	15.7598i	0.495649	+	0.858489i	0.999987	−	0.00501702i	$-0.00159698\pi$
$337$	9.09890	+	15.7598i	0.495649	+	0.858489i	−0.504339	+	0.863506i	$0.668264\pi$
$338$	−0.260891	−	0.451877i	−0.0141906	−	0.0245789i
$339$	−1.43238	+	0.787232i	−0.0777962	+	0.0427566i
$340$	−11.2265	+	19.4449i	−0.608844	+	1.05455i
$341$		0			0
$342$	−0.743895	+	1.17156i	−0.0402252	+	0.0633510i
$343$	−10.5583			−0.570096
$344$	0.550319	−	0.953180i	0.0296712	−	0.0513920i
$345$	−7.48078	−	4.53176i	−0.402752	−	0.243982i
$346$	0.215870	+	0.373898i	0.0116052	+	0.0201009i
$347$	13.7071	+	23.7413i	0.735833	+	1.27450i	0.954357	+	0.298669i	$0.0965425\pi$
$347$	13.7071	+	23.7413i	0.735833	+	1.27450i	−0.218524	+	0.975832i	$0.570124\pi$
$348$	−0.248730	+	11.8061i	−0.0133333	+	0.632873i
$349$	−11.4528	+	19.8368i	−0.613052	+	1.06184i	0.377671	+	0.925940i	$0.376725\pi$
$349$	−11.4528	+	19.8368i	−0.613052	+	1.06184i	−0.990723	+	0.135898i	$0.956608\pi$
$350$	−2.71471			−0.145108
$351$	17.9266	−	8.89072i	0.956849	−	0.474552i
$352$		0			0
$353$	14.8524	−	25.7250i	0.790511	−	1.36921i	−0.135140	−	0.990827i	$-0.543148\pi$
$353$	14.8524	−	25.7250i	0.790511	−	1.36921i	0.925651	−	0.378379i	$-0.123518\pi$
$354$	0.118204	−	5.61059i	0.00628245	−	0.298200i
$355$	7.77591	+	13.4683i	0.412703	+	0.714822i
$356$	8.88587	+	15.3908i	0.470950	+	0.815710i
$357$	26.0696	+	15.7926i	1.37975	+	0.835834i
$358$	−1.88045	+	3.25703i	−0.0993846	+	0.172139i
$359$	−36.8574			−1.94526			−0.972631	−	0.232356i	$-0.925356\pi$
$359$	−36.8574			−1.94526			−0.972631	+	0.232356i	$0.925356\pi$
$360$	−4.20491	−	8.04800i	−0.221618	−	0.424167i
$361$	−16.3682			−0.861482
$362$	−0.399041	+	0.691159i	−0.0209731	+	0.0363265i
$363$		0			0
$364$	−15.0485	−	26.0648i	−0.788756	−	1.36617i
$365$	5.48061	+	9.49270i	0.286868	+	0.496871i
$366$	3.72557	−	2.04756i	0.194739	−	0.107028i
$367$	12.4303	−	21.5299i	0.648857	−	1.12385i	−0.334539	−	0.942382i	$-0.608581\pi$
$367$	12.4303	−	21.5299i	0.648857	−	1.12385i	0.983396	−	0.181472i	$-0.0580860\pi$
$368$	−6.55978			−0.341952
$369$	9.54710	+	18.2727i	0.497002	+	0.951237i
$370$	5.98177			0.310978
$371$	−3.20129	+	5.54479i	−0.166202	+	0.287871i
$372$	13.8271	+	8.37627i	0.716902	+	0.434290i
$373$	−9.13952	−	15.8301i	−0.473227	−	0.819653i	0.526304	−	0.850297i	$-0.323578\pi$
$373$	−9.13952	−	15.8301i	−0.473227	−	0.819653i	−0.999530	+	0.0306440i	$0.990244\pi$
$374$		0			0
$375$	−0.263138	+	12.4900i	−0.0135884	+	0.644981i
$376$	3.27755	−	5.67689i	0.169027	−	0.292763i
$377$	13.6838			0.704750
$378$	−5.40691	+	2.68157i	−0.278102	+	0.137925i
$379$	−31.4593			−1.61595			−0.807977	−	0.589213i	$-0.799438\pi$
$379$	−31.4593			−1.61595			−0.807977	+	0.589213i	$0.799438\pi$
$380$	−4.21571	+	7.30183i	−0.216261	+	0.374576i
$381$	0.0893970	−	4.24328i	0.00457995	−	0.217390i
$382$	2.38691	+	4.13425i	0.122125	+	0.211527i
$383$	6.21588	+	10.7662i	0.317617	+	0.550129i	0.979990	−	0.199045i	$-0.0637841\pi$
$383$	6.21588	+	10.7662i	0.317617	+	0.550129i	−0.662373	+	0.749174i	$0.730451\pi$
$384$	−12.1770	−	7.37668i	−0.621407	−	0.376440i
$385$		0			0
$386$	−6.28449			−0.319872
$387$	1.58396	−	2.49458i	0.0805170	−	0.126807i
$388$	14.2226			0.722045
$389$	−3.65984	+	6.33903i	−0.185561	+	0.321402i	−0.943766	−	0.330616i	$-0.892744\pi$
$389$	−3.65984	+	6.33903i	−0.185561	+	0.321402i	0.758204	+	0.652017i	$0.226077\pi$
$390$	−4.51493	+	2.48140i	−0.228623	+	0.125650i
$391$	−4.02694	−	6.97486i	−0.203651	−	0.352734i
$392$	5.35912	+	9.28227i	0.270677	+	0.468826i
$393$	−6.06765	+	3.33476i	−0.306072	+	0.168217i
$394$	−2.59837	+	4.50050i	−0.130904	+	0.226732i
$395$	−11.5938			−0.583346
$396$		0			0
$397$	34.2087			1.71688			0.858442	−	0.512911i	$-0.171433\pi$
$397$	34.2087			1.71688			0.858442	+	0.512911i	$0.171433\pi$
$398$	3.57801	−	6.19730i	0.179350	−	0.310642i
$399$	9.78948	+	5.93034i	0.490087	+	0.296888i
$400$	−4.11208	−	7.12234i	−0.205604	−	0.356117i
$401$	−3.73789	−	6.47421i	−0.186661	−	0.323307i	0.757474	−	0.652865i	$-0.226433\pi$
$401$	−3.73789	−	6.47421i	−0.186661	−	0.323307i	−0.944135	+	0.329559i	$0.893100\pi$
$402$	−0.0181070	+	0.859459i	−0.000903095	+	0.0428659i
$403$	9.36666	−	16.2235i	0.466587	−	0.808152i
$404$	26.3198			1.30946
$405$	−10.3692	−	22.0634i	−0.515252	−	1.09634i
$406$	−4.12723			−0.204831
$407$		0			0
$408$	0.176117	−	8.35950i	0.00871910	−	0.413857i
$409$	−1.20510	−	2.08729i	−0.0595883	−	0.103210i	0.834692	−	0.550717i	$-0.185645\pi$
$409$	−1.20510	−	2.08729i	−0.0595883	−	0.103210i	−0.894281	+	0.447507i	$0.852312\pi$
$410$	−2.65399	−	4.59685i	−0.131071	−	0.227022i
$411$	1.61365	+	0.977529i	0.0795956	+	0.0482180i
$412$	4.86891	−	8.43321i	0.239874	−	0.415474i
$413$	−46.2832			−2.27745
$414$	1.59334	+	0.0671663i	0.0783082	+	0.00330104i
$415$	−17.6073			−0.864307
$416$	−6.23505	+	10.7994i	−0.305699	+	0.529485i
$417$	−4.37905	+	2.40672i	−0.214443	+	0.117857i
$418$		0			0
$419$	5.60088	+	9.70101i	0.273621	+	0.473925i	0.969786	−	0.243956i	$-0.0784453\pi$
$419$	5.60088	+	9.70101i	0.273621	+	0.473925i	−0.696165	+	0.717881i	$0.745112\pi$
$420$	−32.1342	+	17.6608i	−1.56799	+	0.861761i
$421$	3.45243	−	5.97979i	0.168261	−	0.291437i	−0.769547	−	0.638590i	$-0.779518\pi$
$421$	3.45243	−	5.97979i	0.168261	−	0.291437i	0.937809	+	0.347153i	$0.112851\pi$
$422$	2.35818			0.114795
$423$	9.43363	−	14.8571i	0.458679	−	0.722376i
$424$	1.75637			0.0852969
$425$	5.04868	−	8.74456i	0.244897	−	0.424174i
$426$	−2.42530	−	1.46922i	−0.117506	−	0.0711837i
$427$	−17.5306	−	30.3638i	−0.848364	−	1.46941i
$428$	−2.66600	−	4.61765i	−0.128866	−	0.223202i
$429$		0			0
$430$	−0.380399	+	0.658871i	−0.0183445	+	0.0317736i
$431$	−29.1806			−1.40558			−0.702789	−	0.711398i	$-0.748062\pi$
$431$	−29.1806			−1.40558			−0.702789	+	0.711398i	$0.748062\pi$
$432$	−15.2254	−	10.1237i	−0.732535	−	0.487078i
$433$	−36.5360			−1.75581			−0.877903	−	0.478838i	$-0.841058\pi$
$433$	−36.5360			−1.75581			−0.877903	+	0.478838i	$0.841058\pi$
$434$	−2.82512	+	4.89326i	−0.135610	+	0.234884i
$435$	0.351147	−	16.6674i	0.0168362	−	0.799141i
$436$	−16.6516	−	28.8415i	−0.797468	−	1.38126i
$437$	−1.51217	−	2.61915i	−0.0723368	−	0.125291i
$438$	−1.70940	−	1.03553i	−0.0816783	−	0.0494796i
$439$	10.7487	−	18.6173i	0.513009	−	0.888557i	−0.486877	−	0.873470i	$-0.661864\pi$
$439$	10.7487	−	18.6173i	0.513009	−	0.888557i	0.999886	−	0.0150869i	$-0.00480250\pi$
$440$		0			0
$441$	13.3257	+	25.5048i	0.634558	+	1.21451i
$442$	−4.74399			−0.225649
$443$	16.7225	−	28.9642i	0.794510	−	1.37613i	−0.128640	−	0.991691i	$-0.541061\pi$
$443$	16.7225	−	28.9642i	0.794510	−	1.37613i	0.923150	−	0.384440i	$-0.125605\pi$
$444$	22.5550	−	12.3962i	1.07041	−	0.588297i
$445$	−12.5447	−	21.7281i	−0.594677	−	1.03001i
$446$	1.04822	+	1.81557i	0.0496345	+	0.0859695i
$447$	−30.6235	+	16.8306i	−1.44844	+	0.796060i
$448$	−12.4525	+	21.5683i	−0.588324	+	1.01901i
$449$	39.5333			1.86569			0.932846	−	0.360276i	$-0.117318\pi$
$449$	39.5333			1.86569			0.932846	+	0.360276i	$0.117318\pi$
$450$	0.925876	+	1.77208i	0.0436462	+	0.0835367i
$451$		0			0
$452$	0.905290	−	1.56801i	0.0425813	−	0.0737529i
$453$	−16.4118	−	9.94203i	−0.771092	−	0.467117i
$454$	2.70053	+	4.67745i	0.126742	+	0.219523i
$455$	21.2449	+	36.7973i	0.995977	+	1.72508i
$456$	0.0661344	−	3.13910i	0.00309703	−	0.147002i
$457$	−18.7562	+	32.4866i	−0.877376	+	1.51966i	−0.0231665	+	0.999732i	$0.507375\pi$
$457$	−18.7562	+	32.4866i	−0.877376	+	1.51966i	−0.854210	+	0.519929i	$0.825959\pi$
$458$	−2.24111			−0.104720
$459$	1.41767	−	22.4036i	0.0661712	−	1.04571i
$460$	9.68884			0.451745
$461$	−9.68265	+	16.7708i	−0.450966	+	0.781096i	−0.998446	−	0.0557228i	$-0.982254\pi$
$461$	−9.68265	+	16.7708i	−0.450966	+	0.781096i	0.547480	+	0.836818i	$0.315587\pi$
$462$		0			0
$463$	7.17464	+	12.4268i	0.333434	+	0.577524i	0.983183	−	0.182625i	$-0.0584594\pi$
$463$	7.17464	+	12.4268i	0.333434	+	0.577524i	−0.649749	+	0.760149i	$0.725126\pi$
$464$	−6.25167	−	10.8282i	−0.290227	−	0.502687i
$465$	−19.5206	−	11.8253i	−0.905245	−	0.548385i
$466$	0.936629	−	1.62229i	0.0433885	−	0.0751511i
$467$	−22.3209			−1.03289			−0.516445	−	0.856320i	$-0.672745\pi$
$467$	−22.3209			−1.03289			−0.516445	+	0.856320i	$0.672745\pi$
$468$	−11.8819	+	18.7128i	−0.549239	+	0.865000i
$469$	7.08990			0.327381
$470$	−2.26556	+	3.92406i	−0.104502	+	0.181003i
$471$	−0.505136	+	0.277621i	−0.0232754	+	0.0127921i
$472$	6.34827	+	10.9955i	0.292203	+	0.506110i
$473$		0			0
$474$	1.85257	−	1.01817i	0.0850915	−	0.0467660i
$475$	1.89584	−	3.28370i	0.0869873	−	0.150666i
$476$	−33.7644			−1.54759
$477$	4.71129	+	0.198602i	0.215715	+	0.00909338i
$478$	−7.28448			−0.333184
$479$	11.6308	−	20.1452i	0.531426	−	0.920456i	−0.467902	−	0.883781i	$-0.654990\pi$
$479$	11.6308	−	20.1452i	0.531426	−	0.920456i	0.999327	−	0.0366756i	$-0.0116768\pi$
$480$	12.9941	+	7.87168i	0.593099	+	0.359291i
$481$	−14.9118	−	25.8281i	−0.679921	−	1.17766i
$482$	0.425154	+	0.736388i	0.0193652	+	0.0335416i
$483$	0.277036	−	13.1497i	0.0126056	−	0.598331i
$484$		0			0
$485$	−20.0790			−0.911740
$486$	3.59452	+	2.61489i	0.163051	+	0.118614i
$487$	0.270802			0.0122712			0.00613559	−	0.999981i	$-0.498047\pi$
$487$	0.270802			0.0122712			0.00613559	+	0.999981i	$0.498047\pi$
$488$	−4.80903	+	8.32949i	−0.217695	+	0.377058i
$489$	0.486606	−	23.0970i	0.0220051	−	1.04448i
$490$	−3.70441	−	6.41623i	−0.167348	−	0.289856i
$491$	2.10328	+	3.64298i	0.0949196	+	0.164406i	0.909575	−	0.415540i	$-0.136407\pi$
$491$	2.10328	+	3.64298i	0.0949196	+	0.164406i	−0.814655	+	0.579945i	$0.803074\pi$
$492$	−19.5334	−	11.8331i	−0.880632	−	0.533475i
$493$	7.67559	−	13.2945i	0.345691	−	0.598755i
$494$	−1.78143			−0.0801504
$495$		0			0
$496$	−17.1173			−0.768589
$497$	−11.6932	+	20.2533i	−0.524514	+	0.908485i
$498$	2.81347	−	1.54628i	0.126075	−	0.0692903i
$499$	7.68212	+	13.3058i	0.343899	+	0.595650i	0.985153	−	0.171678i	$-0.0549189\pi$
$499$	7.68212	+	13.3058i	0.343899	+	0.595650i	−0.641254	+	0.767328i	$0.721586\pi$
$500$	−6.91948	−	11.9849i	−0.309449	−	0.535981i
$501$	28.7115	−	15.7797i	1.28273	−	0.704987i
$502$	−1.66363	+	2.88149i	−0.0742514	+	0.128607i
$503$	3.91570			0.174592			0.0872961	−	0.996182i	$-0.472177\pi$
$503$	3.91570			0.174592			0.0872961	+	0.996182i	$0.472177\pi$
$504$	7.31936	−	11.5273i	0.326030	−	0.513467i
$505$	−37.1573			−1.65348
$506$		0			0
$507$	2.71081	+	1.64217i	0.120391	+	0.0729314i
$508$	2.35078	+	4.07167i	0.104299	+	0.180651i
$509$	−14.2747	−	24.7245i	−0.632715	−	1.09589i	−0.986994	−	0.160754i	$-0.948607\pi$
$509$	−14.2747	−	24.7245i	−0.632715	−	1.09589i	0.354280	−	0.935139i	$-0.384726\pi$
$510$	−0.121738	+	5.77838i	−0.00539066	+	0.255871i
$511$	−8.24163	+	14.2749i	−0.364588	+	0.631485i
$512$	19.2581			0.851097
$513$	0.532354	−	8.41286i	0.0235040	−	0.371437i
$514$	5.90954			0.260659
$515$	−6.87375	+	11.9057i	−0.302893	+	0.524627i
$516$	−0.0689482	+	3.27266i	−0.00303528	+	0.144071i
$517$		0			0
$518$	4.49763	+	7.79012i	0.197615	+	0.342278i
$519$	−2.24301	−	1.35878i	−0.0984572	−	0.0596440i
$520$	5.82796	−	10.0943i	0.255573	−	0.442666i
$521$	−14.2748			−0.625388			−0.312694	−	0.949854i	$-0.601232\pi$
$521$	−14.2748			−0.625388			−0.312694	+	0.949854i	$0.601232\pi$
$522$	1.40763	+	2.69413i	0.0616101	+	0.117919i
$523$	−33.1573			−1.44987			−0.724934	−	0.688818i	$-0.758130\pi$
$523$	−33.1573			−1.44987			−0.724934	+	0.688818i	$0.758130\pi$
$524$	3.83486	−	6.64217i	0.167527	−	0.290165i
$525$	14.4510	−	7.94225i	0.630695	−	0.346628i
$526$	−1.29535	−	2.24361i	−0.0564800	−	0.0978262i
$527$	−10.5080	−	18.2004i	−0.457736	−	0.792822i
$528$		0			0
$529$	9.76231	−	16.9088i	0.424448	−	0.735166i
$530$	−1.21406			−0.0527356
$531$	15.7853	+	30.2123i	0.685023	+	1.31110i
$532$	−12.6790			−0.549704
$533$	−13.2322	+	22.9188i	−0.573149	+	0.992723i
$534$	3.91269	+	2.37026i	0.169319	+	0.102571i
$535$	3.76376	+	6.51902i	0.162721	+	0.281842i
$536$	−0.972460	−	1.68435i	−0.0420039	−	0.0727528i
$537$	0.481178	−	22.8394i	0.0207644	−	0.985591i
$538$	−1.13222	+	1.96107i	−0.0488136	+	0.0845476i
$539$		0			0
$540$	22.4881	+	14.9528i	0.967733	+	0.643466i
$541$	−28.4609			−1.22363			−0.611815	−	0.791001i	$-0.709560\pi$
$541$	−28.4609			−1.22363			−0.611815	+	0.791001i	$0.709560\pi$
$542$	−0.530894	+	0.919536i	−0.0228039	+	0.0394975i
$543$	0.102109	−	4.84664i	0.00438190	−	0.207989i
$544$	6.99481	+	12.1154i	0.299900	+	0.519442i
$545$	23.5081	+	40.7173i	1.00698	+	1.74414i
$546$	−6.62628	−	4.01411i	−0.283578	−	0.171788i
$547$	15.3733	−	26.6274i	0.657316	−	1.13850i	−0.323992	−	0.946060i	$-0.605025\pi$
$547$	15.3733	−	26.6274i	0.657316	−	1.13850i	0.981308	−	0.192444i	$-0.0616415\pi$
$548$	−2.08995			−0.0892781
$549$	−13.8416	+	21.7993i	−0.590746	+	0.930370i
$550$		0			0
$551$	2.88228	−	4.99226i	0.122789	−	0.212678i
$552$	−3.16197	+	1.73781i	−0.134582	+	0.0739662i
$553$	−8.71724	−	15.0987i	−0.370695	−	0.642062i
$554$	0.556130	+	0.963246i	0.0236277	+	0.0409244i
$555$	−31.8423	+	17.5004i	−1.35163	+	0.742853i
$556$	2.76764	−	4.79369i	0.117374	−	0.203298i
$557$	−7.29459			−0.309082			−0.154541	−	0.987986i	$-0.549390\pi$
$557$	−7.29459			−0.309082			−0.154541	+	0.987986i	$0.549390\pi$
$558$	4.15770	+	0.175266i	0.176009	+	0.00741959i
$559$	3.79316			0.160433
$560$	19.4122	−	33.6230i	0.820316	−	1.42083i
$561$		0			0
$562$	−0.00564923	−	0.00978475i	−0.000238298	−	0.000412745i
$563$	18.2867	+	31.6735i	0.770693	+	1.33488i	0.937183	+	0.348837i	$0.113423\pi$
$563$	18.2867	+	31.6735i	0.770693	+	1.33488i	−0.166490	+	0.986043i	$0.553243\pi$
$564$	−0.410637	+	19.4911i	−0.0172910	+	0.820725i
$565$	−1.27805	+	2.21365i	−0.0537681	+	0.0931291i
$566$	1.82320			0.0766349
$567$	20.9369	−	30.0932i	0.879268	−	1.26380i
$568$	6.41545			0.269186
$569$	−0.0757419	+	0.131189i	−0.00317527	+	0.00549972i	−0.867609	−	0.497248i	$-0.834344\pi$
$569$	−0.0757419	+	0.131189i	−0.00317527	+	0.00549972i	0.864433	+	0.502747i	$0.167677\pi$
$570$	−0.0457144	+	2.16986i	−0.00191476	+	0.0908853i
$571$	−21.6127	−	37.4343i	−0.904463	−	1.56658i	−0.821637	−	0.570012i	$-0.806939\pi$
$571$	−21.6127	−	37.4343i	−0.904463	−	1.56658i	−0.0828262	−	0.996564i	$-0.526395\pi$
$572$		0			0
$573$	−24.8014	−	15.0243i	−1.03609	−	0.627651i
$574$	3.99101	−	6.91264i	0.166582	−	0.288528i
$575$	−4.35716			−0.181706
$576$	18.3262	+	0.772531i	0.763590	+	0.0321888i
$577$	29.1251			1.21250			0.606248	−	0.795276i	$-0.292674\pi$
$577$	29.1251			1.21250			0.606248	+	0.795276i	$0.292674\pi$
$578$	−0.237268	+	0.410959i	−0.00986903	+	0.0170937i
$579$	33.4538	−	18.3861i	1.39029	−	0.764100i
$580$	9.23376	+	15.9933i	0.383411	+	0.664087i
$581$	−13.2387	−	22.9301i	−0.549235	−	0.951302i
$582$	3.20842	−	1.76334i	0.132993	−	0.0730929i
$583$		0			0
$584$	4.52173			0.187111
$585$	16.7744	−	26.4180i	0.693534	−	1.09225i
$586$	−6.67459			−0.275725
$587$	11.3474	−	19.6543i	0.468359	−	0.811221i	−0.530987	−	0.847380i	$-0.678179\pi$
$587$	11.3474	−	19.6543i	0.468359	−	0.811221i	0.999346	+	0.0361584i	$0.0115121\pi$
$588$	−27.2644	−	16.5164i	−1.12437	−	0.681126i
$589$	−3.94590	−	6.83450i	−0.162588	−	0.281610i
$590$	−4.38814	−	7.60049i	−0.180657	−	0.312907i
$591$	0.664883	−	31.5590i	0.0273496	−	1.29817i
$592$	−13.6255	+	23.6000i	−0.560003	+	0.969954i
$593$	−22.9308			−0.941656			−0.470828	−	0.882225i	$-0.656045\pi$
$593$	−22.9308			−0.941656			−0.470828	+	0.882225i	$0.656045\pi$
$594$		0			0
$595$	47.6673			1.95417
$596$	19.3546	−	33.5232i	0.792796	−	1.37316i
$597$	−0.915560	+	43.4575i	−0.0374714	+	1.77860i
$598$	1.02355	+	1.77284i	0.0418562	+	0.0724970i
$599$	6.25035	+	10.8259i	0.255382	+	0.442335i	0.964999	−	0.262253i	$-0.0844654\pi$
$599$	6.25035	+	10.8259i	0.255382	+	0.442335i	−0.709617	+	0.704588i	$0.751132\pi$
$600$	−3.86897	−	2.34377i	−0.157950	−	0.0956839i
$601$	−11.2394	+	19.4672i	−0.458465	+	0.794085i	−0.998880	−	0.0473137i	$-0.984934\pi$
$601$	−11.2394	+	19.4672i	−0.458465	+	0.794085i	0.540415	+	0.841399i	$0.318267\pi$
$602$	−1.14407			−0.0466289
$603$	−2.41807	−	4.62806i	−0.0984714	−	0.188469i
$604$	21.2559			0.864892
$605$		0			0
$606$	5.93738	−	3.26317i	0.241190	−	0.132557i
$607$	−13.3524	−	23.1270i	−0.541956	−	0.938695i	−0.998792	−	0.0491443i	$-0.984351\pi$
$607$	−13.3524	−	23.1270i	−0.541956	−	0.938695i	0.456836	−	0.889551i	$-0.348983\pi$
$608$	2.62664	+	4.54948i	0.106524	+	0.184506i
$609$	21.9702	−	12.0747i	0.890275	−	0.489293i
$610$	3.32417	−	5.75763i	0.134592	−	0.233120i
$611$	22.5911			0.913936
$612$	11.5156	+	22.0404i	0.465492	+	0.890929i
$613$	−43.4844			−1.75632			−0.878160	−	0.478367i	$-0.841229\pi$
$613$	−43.4844			−1.75632			−0.878160	+	0.478367i	$0.841229\pi$
$614$	−4.15595	+	7.19832i	−0.167721	+	0.290501i
$615$	27.5765	+	16.7055i	1.11199	+	0.673629i
$616$		0			0
$617$	−20.7128	−	35.8756i	−0.833864	−	1.44430i	−0.894952	−	0.446163i	$-0.852790\pi$
$617$	−20.7128	−	35.8756i	−0.833864	−	1.44430i	0.0610871	−	0.998132i	$-0.480543\pi$
$618$	0.0527976	−	2.50606i	0.00212383	−	0.100809i
$619$	−4.45588	+	7.71780i	−0.179097	+	0.310205i	−0.941571	−	0.336813i	$-0.890651\pi$
$619$	−4.45588	+	7.71780i	−0.179097	+	0.310205i	0.762475	+	0.647018i	$0.223984\pi$
$620$	25.2824			1.01536
$621$	−8.67818	+	4.30397i	−0.348244	+	0.172712i
$622$	−5.61906			−0.225304
$623$	18.8645	−	32.6743i	0.755790	−	1.30907i
$624$	0.494360	−	23.4651i	0.0197902	−	0.939354i
$625$	15.6118	+	27.0404i	0.624470	+	1.08161i
$626$	−0.190818	−	0.330506i	−0.00762662	−	0.0132097i
$627$		0			0
$628$	0.319255	−	0.552966i	0.0127397	−	0.0220657i
$629$	−33.4578			−1.33405
$630$	−5.05939	+	7.96807i	−0.201571	+	0.317456i
$631$	−5.67049			−0.225739			−0.112869	−	0.993610i	$-0.536004\pi$
$631$	−5.67049			−0.225739			−0.112869	+	0.993610i	$0.536004\pi$
$632$	−2.39134	+	4.14192i	−0.0951222	+	0.164757i
$633$	−12.5531	+	6.89917i	−0.498942	+	0.274217i
$634$	−0.570424	−	0.988003i	−0.0226544	−	0.0392386i
$635$	−3.31874	−	5.74823i	−0.131700	−	0.228112i
$636$	−4.57778	+	2.51594i	−0.181521	+	0.0997633i
$637$	−18.4693	+	31.9898i	−0.731780	+	1.26748i
$638$		0			0
$639$	17.2088	+	0.725429i	0.680770	+	0.0286975i
$640$	−22.2653			−0.880112
$641$	−13.4091	+	23.2252i	−0.529628	+	0.917342i	0.469775	+	0.882786i	$0.344335\pi$
$641$	−13.4091	+	23.2252i	−0.529628	+	0.917342i	−0.999403	+	0.0345558i	$0.988998\pi$
$642$	−1.17391	−	0.711141i	−0.0463306	−	0.0280665i
$643$	−7.06923	−	12.2443i	−0.278783	−	0.482866i	0.692299	−	0.721610i	$-0.256598\pi$
$643$	−7.06923	−	12.2443i	−0.278783	−	0.482866i	−0.971083	+	0.238744i	$0.923264\pi$
$644$	7.28493	+	12.6179i	0.287067	+	0.497214i
$645$	0.0973384	−	4.62022i	0.00383270	−	0.181921i
$646$	−0.999252	+	1.73075i	−0.0393150	+	0.0680956i
$647$	−1.27403			−0.0500875			−0.0250437	−	0.999686i	$-0.507973\pi$
$647$	−1.27403			−0.0500875			−0.0250437	+	0.999686i	$0.507973\pi$
$648$	−10.0210	−	0.846365i	−0.393662	−	0.0332484i
$649$		0			0
$650$	−1.28325	+	2.22266i	−0.0503334	+	0.0871799i
$651$	0.722907	−	34.3132i	0.0283329	−	1.34484i
$652$	12.7958	+	22.1629i	0.501121	+	0.867968i
$653$	2.41417	+	4.18146i	0.0944736	+	0.163633i	0.909389	−	0.415947i	$-0.136550\pi$
$653$	2.41417	+	4.18146i	0.0944736	+	0.163633i	−0.814915	+	0.579580i	$0.803217\pi$
$654$	−7.33217	−	4.44173i	−0.286711	−	0.173685i
$655$	−5.41391	+	9.37717i	−0.211539	+	0.366396i
$656$	24.1814			0.944124
$657$	12.1291	+	0.511297i	0.473201	+	0.0199476i
$658$	−6.81379			−0.265629
$659$	11.0889	−	19.2065i	0.431961	−	0.748178i	−0.565082	−	0.825035i	$-0.691155\pi$
$659$	11.0889	−	19.2065i	0.431961	−	0.748178i	0.997042	+	0.0768574i	$0.0244886\pi$
$660$		0			0
$661$	13.6987	+	23.7269i	0.532820	+	0.922871i	0.999265	+	0.0383209i	$0.0122009\pi$
$661$	13.6987	+	23.7269i	0.532820	+	0.922871i	−0.466446	+	0.884550i	$0.654466\pi$
$662$	−0.453433	−	0.785369i	−0.0176232	−	0.0305242i
$663$	25.2533	−	13.8792i	0.980758	−	0.539022i
$664$	−3.63168	+	6.29025i	−0.140937	+	0.244109i
$665$	17.8997			0.694121
$666$	3.55120	−	5.59280i	0.137606	−	0.216717i
$667$	−6.62427			−0.256493
$668$	−18.1462	+	31.4301i	−0.702096	+	1.21607i
$669$	−10.8916	−	6.59797i	−0.421092	−	0.255092i
$670$	0.672198	+	1.16428i	0.0259693	+	0.0449801i
$671$		0			0
$672$	−0.481213	+	22.8410i	−0.0185632	+	0.881112i
$673$	−17.6218	+	30.5218i	−0.679269	+	1.17653i	0.295932	+	0.955209i	$0.404370\pi$
$673$	−17.6218	+	30.5218i	−0.679269	+	1.17653i	−0.975201	+	0.221320i	$0.928963\pi$
$674$	−5.18907			−0.199876
$675$	−10.1131	−	6.72441i	−0.389253	−	0.258823i
$676$	−3.51094			−0.135036
$677$	22.0250	−	38.1484i	0.846489	−	1.46616i	−0.0378328	−	0.999284i	$-0.512045\pi$
$677$	22.0250	−	38.1484i	0.846489	−	1.46616i	0.884322	−	0.466878i	$-0.154621\pi$
$678$	0.00981679	−	0.465959i	0.000377012	−	0.0178951i
$679$	−15.0972	−	26.1491i	−0.579376	−	1.00351i
$680$	−6.53811	−	11.3243i	−0.250725	−	0.434269i
$681$	−28.0600	−	16.9984i	−1.07526	−	0.651379i
$682$		0			0
$683$	42.2845			1.61797			0.808985	−	0.587829i	$-0.200017\pi$
$683$	42.2845			1.61797			0.808985	+	0.587829i	$0.200017\pi$
$684$	4.32428	+	8.27645i	0.165343	+	0.316458i
$685$	2.95051			0.112733
$686$	1.50534	−	2.60733i	0.0574743	−	0.0995484i
$687$	11.9299	−	6.55665i	0.455155	−	0.250152i
$688$	−1.73297	−	3.00159i	−0.0660689	−	0.114435i
$689$	3.02652	+	5.24208i	0.115301	+	0.199707i
$690$	2.18566	−	1.20124i	0.0832068	−	0.0457302i
$691$	4.23344	−	7.33253i	0.161048	−	0.278943i	−0.774197	−	0.632945i	$-0.781846\pi$
$691$	4.23344	−	7.33253i	0.161048	−	0.278943i	0.935245	+	0.354002i	$0.115179\pi$
$692$	2.90507			0.110434
$693$		0			0
$694$	−7.81709			−0.296733
$695$	−3.90725	+	6.76755i	−0.148210	+	0.256708i
$696$	−5.88206	−	3.56327i	−0.222959	−	0.135065i
$697$	14.8445	+	25.7115i	0.562277	+	0.973892i
$698$	−3.26574	−	5.65642i	−0.123610	−	0.214099i
$699$	−0.239669	+	11.3760i	−0.00906513	+	0.430281i
$700$	−9.13331	+	15.8194i	−0.345207	+	0.597915i
$701$	43.5518			1.64493			0.822465	−	0.568816i	$-0.192599\pi$
$701$	43.5518			1.64493			0.822465	+	0.568816i	$0.192599\pi$
$702$	−0.360339	+	5.69447i	−0.0136001	+	0.214924i
$703$	−12.5638			−0.473854
$704$		0			0
$705$	0.579722	−	27.5168i	0.0218336	−	1.03634i
$706$	4.23512	+	7.33545i	0.159391	+	0.276073i
$707$	−27.9382	−	48.3904i	−1.05072	−	1.81991i
$708$	−32.2967	−	19.5649i	−1.21379	−	0.735295i
$709$	3.01364	−	5.21978i	0.113180	−	0.196033i	−0.803871	−	0.594804i	$-0.797230\pi$
$709$	3.01364	−	5.21978i	0.113180	−	0.196033i	0.917051	+	0.398771i	$0.130563\pi$
$710$	−4.43458			−0.166427
$711$	−6.88287	+	10.8399i	−0.258128	+	0.406527i
$712$	−10.3499			−0.387880
$713$	−4.53437	+	7.85376i	−0.169813	+	0.294126i
$714$	−7.61677	+	4.18616i	−0.285051	+	0.156663i
$715$		0			0
$716$	12.6530	+	21.9157i	0.472866	+	0.819028i
$717$	38.7769	−	21.3117i	1.44815	−	0.795900i
$718$	5.25492	−	9.10179i	0.196112	−	0.339676i
$719$	40.4066			1.50691			0.753457	−	0.657498i	$-0.228385\pi$
$719$	40.4066			1.50691			0.753457	+	0.657498i	$0.228385\pi$
$720$	−28.5687	−	1.20430i	−1.06469	−	0.0448817i
$721$	−20.6732			−0.769909
$722$	2.33368	−	4.04205i	0.0868505	−	0.150429i
$723$	−4.41759	−	2.67612i	−0.164292	−	0.0995258i
$724$	2.68504	+	4.65063i	0.0997889	+	0.172839i
$725$	−4.15251	−	7.19235i	−0.154220	−	0.267117i
$726$		0			0
$727$	−9.36031	+	16.2125i	−0.347155	+	0.601290i	−0.985743	−	0.168259i	$-0.946185\pi$
$727$	−9.36031	+	16.2125i	−0.347155	+	0.601290i	0.638588	+	0.769549i	$0.279519\pi$
$728$	17.5279			0.649628
$729$	−26.7846	−	3.40342i	−0.992024	−	0.126053i
$730$	−3.12558			−0.115683
$731$	2.12768	−	3.68525i	0.0786951	−	0.136304i
$732$	0.602513	−	28.5986i	0.0222695	−	1.05704i
$733$	−0.282096	−	0.488604i	−0.0104194	−	0.0180470i	0.860769	−	0.508996i	$-0.169983\pi$
$733$	−0.282096	−	0.488604i	−0.0104194	−	0.0180470i	−0.871188	+	0.490949i	$0.836650\pi$
$734$	3.54448	+	6.13923i	0.130829	+	0.226603i
$735$	38.4909	+	23.3173i	1.41976	+	0.860071i
$736$	3.01837	−	5.22796i	0.111258	−	0.192705i
$737$		0			0
$738$	−5.87353	−	0.247596i	−0.216208	−	0.00911413i
$739$	1.94812			0.0716629			0.0358315	−	0.999358i	$-0.488592\pi$
$739$	1.94812			0.0716629			0.0358315	+	0.999358i	$0.488592\pi$
$740$	20.1249	−	34.8574i	0.739806	−	1.28138i
$741$	9.48296	−	5.21181i	0.348365	−	0.191461i
$742$	−0.912842	−	1.58109i	−0.0335115	−	0.0580436i
$743$	13.6313	+	23.6102i	0.500086	+	0.866174i	1.00000		9.89898e-5i	$3.15094e-5\pi$
$743$	13.6313	+	23.6102i	0.500086	+	0.866174i	−0.499914	+	0.866075i	$0.666635\pi$
$744$	−8.25095	+	4.53470i	−0.302494	+	0.166250i
$745$	−27.3241	+	47.3267i	−1.00108	+	1.73392i
$746$	5.21224			0.190834
$747$	−10.4529	+	16.4623i	−0.382452	+	0.602325i
$748$		0			0
$749$	−5.65985	+	9.80315i	−0.206807	+	0.358199i
$750$	−3.04684	−	1.84573i	−0.111255	−	0.0673967i
$751$	−15.1531	−	26.2460i	−0.552946	−	0.957730i	−0.998060	−	0.0622562i	$-0.980170\pi$
$751$	−15.1531	−	26.2460i	−0.552946	−	0.957730i	0.445115	−	0.895474i	$-0.353163\pi$
$752$	−10.3211	−	17.8767i	−0.376372	−	0.651896i
$753$	0.425698	−	20.2060i	0.0155133	−	0.736347i
$754$	−1.95095	+	3.37915i	−0.0710495	+	0.123061i
$755$	−30.0083			−1.09211
$756$	−2.56464	+	40.5293i	−0.0932750	+	1.47404i
$757$	11.1070			0.403689			0.201845	−	0.979418i	$-0.435306\pi$
$757$	11.1070			0.403689			0.201845	+	0.979418i	$0.435306\pi$
$758$	4.48528	−	7.76874i	0.162913	−	0.282173i
$759$		0			0
$760$	−2.45515	−	4.25244i	−0.0890576	−	0.154252i
$761$	16.6705	+	28.8741i	0.604304	+	1.04669i	0.992161	+	0.124966i	$0.0398822\pi$
$761$	16.6705	+	28.8741i	0.604304	+	1.04669i	−0.387857	+	0.921720i	$0.626784\pi$
$762$	1.03511	+	0.627058i	0.0374982	+	0.0227159i
$763$	−35.3510	+	61.2298i	−1.27979	+	2.21667i
$764$	32.1219			1.16213
$765$	−16.2573	−	31.1157i	−0.587786	−	1.12499i
$766$	−3.54490			−0.128082
$767$	−21.8782	+	37.8942i	−0.789977	+	1.36828i
$768$	−15.0037	+	8.24597i	−0.541398	+	0.297551i
$769$	25.9701	+	44.9815i	0.936504	+	1.62207i	0.771929	+	0.635709i	$0.219292\pi$
$769$	25.9701	+	44.9815i	0.936504	+	1.62207i	0.164575	+	0.986364i	$0.447375\pi$
$770$		0			0
$771$	−31.4578	+	17.2891i	−1.13293	+	0.622653i
$772$	−21.1434	+	36.6214i	−0.760966	+	1.31803i
$773$	−7.72276			−0.277768			−0.138884	−	0.990309i	$-0.544352\pi$
$773$	−7.72276			−0.277768			−0.138884	+	0.990309i	$0.544352\pi$
$774$	0.390195	+	0.746815i	0.0140253	+	0.0268437i
$775$	−11.3697			−0.408412
$776$	−4.14150	+	7.17328i	−0.148671	+	0.257506i
$777$	−46.7329	−	28.3102i	−1.67653	−	1.01562i
$778$	−1.04360	−	1.80756i	−0.0374148	−	0.0648043i
$779$	5.57432	+	9.65501i	0.199721	+	0.345926i
$780$	−0.730173	+	34.6580i	−0.0261444	+	1.24096i
$781$		0			0
$782$	2.29655			0.0821244
$783$	−15.3751	−	10.2232i	−0.549462	−	0.365349i
$784$	33.7521			1.20543
$785$	−0.450712	+	0.780656i	−0.0160866	+	0.0278628i
$786$	0.0415845	−	1.97383i	0.00148327	−	0.0704042i
$787$	9.85316	+	17.0662i	0.351227	+	0.608343i	0.986465	−	0.163973i	$-0.0524311\pi$
$787$	9.85316	+	17.0662i	0.351227	+	0.608343i	−0.635238	+	0.772317i	$0.719098\pi$
$788$	17.4837	+	30.2827i	0.622833	+	1.07878i
$789$	13.4594	+	8.15354i	0.479168	+	0.290274i
$790$	1.65297	−	2.86303i	0.0588102	−	0.101862i
$791$	−3.84382			−0.136670
$792$		0			0
$793$	−33.1470			−1.17709
$794$	−4.87727	+	8.44768i	−0.173088	+	0.299797i
$795$	6.46273	−	3.55190i	0.229210	−	0.125973i
$796$	−24.0755	−	41.7000i	−0.853334	−	1.47802i
$797$	−7.01288	−	12.1467i	−0.248409	−	0.430257i	0.714676	−	0.699456i	$-0.246574\pi$
$797$	−7.01288	−	12.1467i	−0.248409	−	0.430257i	−0.963085	+	0.269199i	$0.913241\pi$
$798$	−2.86020	+	1.57196i	−0.101250	+	0.0556467i
$799$	12.6719	−	21.9484i	0.448300	−	0.776479i
$800$	7.56841			0.267584
$801$	−27.7626	−	1.17032i	−0.980945	−	0.0413513i
$802$	2.13170			0.0752731
$803$		0			0
$804$	4.94737	+	2.99705i	0.174480	+	0.105698i
$805$	−10.2846	−	17.8134i	−0.362484	−	0.627841i
$806$	2.67089	+	4.62611i	0.0940780	+	0.162948i
$807$	0.289719	−	13.7517i	0.0101986	−	0.484081i
$808$	−7.66408	+	13.2746i	−0.269621	+	0.466998i
$809$	−20.9298			−0.735854			−0.367927	−	0.929855i	$-0.619932\pi$
$809$	−20.9298			−0.735854			−0.367927	+	0.929855i	$0.619932\pi$
$810$	6.92686	+	0.585037i	0.243385	+	0.0205561i
$811$	1.94293			0.0682255			0.0341127	−	0.999418i	$-0.489139\pi$
$811$	1.94293			0.0682255			0.0341127	+	0.999418i	$0.489139\pi$
$812$	−13.8855	+	24.0504i	−0.487286	+	0.844005i
$813$	0.135848	−	6.44810i	0.00476440	−	0.226145i
$814$		0			0
$815$	−18.0646	−	31.2888i	−0.632775	−	1.09600i
$816$	−22.5202	−	13.6425i	−0.788366	−	0.477582i
$817$	0.798973	−	1.38386i	0.0279525	−	0.0484152i
$818$	0.687264			0.0240296
$819$	47.0169	+	1.98198i	1.64291	+	0.0692559i
$820$	−35.7161			−1.24726
$821$	−5.42088	+	9.38924i	−0.189190	+	0.327687i	−0.944980	−	0.327127i	$-0.893920\pi$
$821$	−5.42088	+	9.38924i	−0.189190	+	0.327687i	0.755790	+	0.654814i	$0.227253\pi$
$822$	−0.471462	+	0.259114i	−0.0164441	+	0.00903765i
$823$	−23.8339	−	41.2815i	−0.830798	−	1.43898i	−0.897407	−	0.441204i	$-0.854551\pi$
$823$	−23.8339	−	41.2815i	−0.830798	−	1.43898i	0.0666091	−	0.997779i	$-0.478782\pi$
$824$	2.83556	+	4.91134i	0.0987815	+	0.171094i
$825$		0			0
$826$	6.59880	−	11.4295i	0.229601	−	0.397681i
$827$	37.4150			1.30105			0.650524	−	0.759486i	$-0.274549\pi$
$827$	37.4150			1.30105			0.650524	+	0.759486i	$0.274549\pi$
$828$	5.75197	−	9.05881i	0.199895	−	0.314816i
$829$	10.7069			0.371866			0.185933	−	0.982562i	$-0.440469\pi$
$829$	10.7069			0.371866			0.185933	+	0.982562i	$0.440469\pi$
$830$	2.51034	−	4.34804i	0.0871353	−	0.150923i
$831$	−5.77850	−	3.50054i	−0.200454	−	0.121432i
$832$	11.7727	+	20.3908i	0.408143	+	0.706925i
$833$	20.7198	+	35.8878i	0.717900	+	1.24344i
$834$	0.0300117	−	1.42452i	0.00103922	−	0.0493272i
$835$	25.6181	−	44.3718i	0.886549	−	1.53555i
$836$		0			0
$837$	−22.6451	+	11.2309i	−0.782730	+	0.388197i
$838$	−3.19416			−0.110341
$839$	−7.68075	+	13.3035i	−0.265169	+	0.459286i	−0.967608	−	0.252458i	$-0.918761\pi$
$839$	−7.68075	+	13.3035i	−0.265169	+	0.459286i	0.702439	+	0.711744i	$0.252094\pi$
$840$	0.449794	−	21.3497i	0.0155194	−	0.736636i
$841$	8.18687	+	14.1801i	0.282306	+	0.488968i
$842$	0.984455	+	1.70513i	0.0339266	+	0.0587625i
$843$	0.0586987	+	0.0355589i	0.00202169	+	0.00122471i
$844$	7.93381	−	13.7418i	0.273093	−	0.473011i
$845$	4.95661			0.170513
$846$	2.32390	+	4.44783i	0.0798974	+	0.152920i
$847$		0			0
$848$	2.76543	−	4.78987i	0.0949654	−	0.164485i
$849$	−9.70531	+	5.33401i	−0.333085	+	0.183063i
$850$	1.43962	+	2.49350i	0.0493786	+	0.0855263i
$851$	7.21877	+	12.5033i	0.247456	+	0.428607i
$852$	−16.7211	+	9.18988i	−0.572856	+	0.314840i
$853$	−20.7321	+	35.9091i	−0.709854	+	1.22950i	0.255057	+	0.966926i	$0.417906\pi$
$853$	−20.7321	+	35.9091i	−0.709854	+	1.22950i	−0.964911	+	0.262578i	$0.915427\pi$
$854$	9.99763			0.342112
$855$	−6.10485	−	11.6844i	−0.208781	−	0.399597i
$856$	3.10525			0.106135
$857$	−9.20273	+	15.9396i	−0.314359	+	0.544486i	−0.979301	−	0.202409i	$-0.935123\pi$
$857$	−9.20273	+	15.9396i	−0.314359	+	0.544486i	0.664942	+	0.746895i	$0.268456\pi$
$858$		0			0
$859$	7.52426	+	13.0324i	0.256725	+	0.444660i	0.965363	−	0.260912i	$-0.0840233\pi$
$859$	7.52426	+	13.0324i	0.256725	+	0.444660i	−0.708638	+	0.705572i	$0.750690\pi$
$860$	2.55961	+	4.43337i	0.0872819	+	0.151177i
$861$	−1.02124	+	48.4738i	−0.0348038	+	1.65198i
$862$	4.16040	−	7.20602i	0.141704	−	0.245438i
$863$	−14.4298			−0.491196			−0.245598	−	0.969372i	$-0.578984\pi$
$863$	−14.4298			−0.491196			−0.245598	+	0.969372i	$0.578984\pi$
$864$	15.0740	−	7.47601i	0.512829	−	0.254339i
$865$	−4.10126			−0.139447
$866$	5.20909	−	9.02240i	0.177012	−	0.306594i
$867$	0.0607132	−	2.88179i	0.00206193	−	0.0978706i
$868$	19.0095	+	32.9255i	0.645225	+	1.11756i
$869$		0			0
$870$	4.06588	+	2.46306i	0.137846	+	0.0835054i
$871$	3.35142	−	5.80482i	0.113558	−	0.196689i
$872$	19.3952			0.656803
$873$	−11.9203	+	18.7733i	−0.403440	+	0.635381i
$874$	0.862385			0.0291706
$875$	−14.6899	+	25.4436i	−0.496609	+	0.860152i
$876$	−11.7854	+	6.47721i	−0.398191	+	0.218845i
$877$	12.0377	+	20.8499i	0.406484	+	0.704050i	0.994493	−	0.104804i	$-0.0334215\pi$
$877$	12.0377	+	20.8499i	0.406484	+	0.704050i	−0.588009	+	0.808854i	$0.700088\pi$
$878$	3.06498	+	5.30870i	0.103438	+	0.179160i
$879$	35.5303	−	19.5274i	1.19841	−	0.658642i
$880$		0			0
$881$	−10.0956			−0.340129			−0.170064	−	0.985433i	$-0.554398\pi$
$881$	−10.0956			−0.340129			−0.170064	+	0.985433i	$0.554398\pi$
$882$	−8.19820	−	0.345591i	−0.276048	−	0.0116367i
$883$	50.7198			1.70686			0.853429	−	0.521209i	$-0.174519\pi$
$883$	50.7198			1.70686			0.853429	+	0.521209i	$0.174519\pi$
$884$	−15.9605	+	27.6445i	−0.536811	+	0.929785i
$885$	45.5953	+	27.6210i	1.53267	+	0.928470i
$886$	4.76839	+	8.25910i	0.160197	+	0.277470i
$887$	1.28635	+	2.22803i	0.0431915	+	0.0748099i	0.886813	−	0.462128i	$-0.152914\pi$
$887$	1.28635	+	2.22803i	0.0431915	+	0.0748099i	−0.843621	+	0.536938i	$0.819581\pi$
$888$	−0.315711	+	14.9854i	−0.0105946	+	0.502878i
$889$	4.99065	−	8.64407i	0.167381	−	0.289913i
$890$	7.15422			0.239810
$891$		0			0
$892$	14.1064			0.472316
$893$	4.75847	−	8.24191i	0.159236	−	0.275805i
$894$	0.209878	−	9.96196i	0.00701936	−	0.333178i
$895$	−17.8631	−	30.9397i	−0.597097	−	1.03420i
$896$	−16.7410	−	28.9963i	−0.559278	−	0.968698i
$897$	−10.6353	−	6.44271i	−0.355102	−	0.215116i
$898$	−5.63643	+	9.76258i	−0.188090	+	0.325781i
$899$	−17.2856			−0.576506
$900$	13.4414	+	0.566615i	0.448046	+	0.0188872i
$901$	6.79061			0.226228
$902$		0			0
$903$	6.09015	−	3.34713i	0.202668	−	0.111386i
$904$	0.527223	+	0.913178i	0.0175352	+	0.0303718i
$905$	−3.79064	−	6.56559i	−0.126005	−	0.218247i
$906$	4.79504	−	2.63534i	0.159304	−	0.0875533i
$907$	−5.14743	+	8.91562i	−0.170918	+	0.296038i	−0.938741	−	0.344624i	$-0.888007\pi$
$907$	−5.14743	+	8.91562i	−0.170918	+	0.296038i	0.767823	+	0.640662i	$0.221340\pi$
$908$	36.3423			1.20606
$909$	−22.0592	+	34.7411i	−0.731657	+	1.15229i
$910$	−12.1159			−0.401638
$911$	7.80127	−	13.5122i	0.258468	−	0.447679i	−0.707364	−	0.706850i	$-0.750116\pi$
$911$	7.80127	−	13.5122i	0.258468	−	0.447679i	0.965832	+	0.259170i	$0.0834491\pi$
$912$	−8.45665	−	5.12293i	−0.280028	−	0.169637i
$913$		0			0
$914$	−5.34829	−	9.26351i	−0.176906	−	0.306410i
$915$	−0.850605	+	40.3744i	−0.0281201	+	1.33474i
$916$	−7.53992	+	13.0595i	−0.249126	+	0.431499i
$917$	−16.2826			−0.537700
$918$	5.33036	+	3.54427i	0.175928	+	0.116978i
$919$	11.2124			0.369864			0.184932	−	0.982751i	$-0.440794\pi$
$919$	11.2124			0.369864			0.184932	+	0.982751i	$0.440794\pi$
$920$	−2.82130	+	4.88663i	−0.0930154	+	0.161107i
$921$	1.06345	−	50.4771i	0.0350418	−	1.66328i
$922$	−2.76099	−	4.78218i	−0.0909284	−	0.157493i
$923$	11.0549	+	19.1476i	0.363875	+	0.630251i
$924$		0			0
$925$	−9.05036	+	15.6757i	−0.297574	+	0.515413i
$926$	−4.09167			−0.134461
$927$	7.05076	+	13.4948i	0.231577	+	0.443228i
$928$	11.5064			0.377715
$929$	−11.7638	+	20.3754i	−0.385956	+	0.668496i	−0.991901	−	0.127011i	$-0.959462\pi$
$929$	−11.7638	+	20.3754i	−0.385956	+	0.668496i	0.605945	+	0.795506i	$0.292795\pi$
$930$	5.70334	−	3.13454i	0.187020	−	0.102786i
$931$	7.78057	+	13.4763i	0.254998	+	0.441669i
$932$	−6.30234	−	10.9160i	−0.206440	−	0.357565i
$933$	29.9115	−	16.4393i	0.979258	−	0.538198i
$934$	3.18239	−	5.51206i	0.104131	−	0.180360i
$935$		0			0
$936$	−5.97805	−	11.4417i	−0.195399	−	0.373983i
$937$	18.6555			0.609448			0.304724	−	0.952441i	$-0.401436\pi$
$937$	18.6555			0.609448			0.304724	+	0.952441i	$0.401436\pi$
$938$	−1.01084	+	1.75082i	−0.0330050	+	0.0571663i
$939$	1.98271	+	1.20110i	0.0647032	+	0.0391963i
$940$	15.2444	+	26.4040i	0.497216	+	0.861204i
$941$	16.2463	+	28.1394i	0.529615	+	0.917320i	0.999403	+	0.0345407i	$0.0109968\pi$
$941$	16.2463	+	28.1394i	0.529615	+	0.917320i	−0.469789	+	0.882779i	$0.655670\pi$
$942$	0.00346194	−	0.164323i	0.000112796	−	0.00535393i
$943$	6.40565	−	11.0949i	0.208597	−	0.361300i
$944$	39.9818			1.30130
$945$	3.62066	−	57.2177i	0.117780	−	1.86129i
$946$		0			0
$947$	1.92137	−	3.32790i	0.0624360	−	0.108142i	−0.833118	−	0.553096i	$-0.813446\pi$
$947$	1.92137	−	3.32790i	0.0624360	−	0.108142i	0.895554	+	0.444953i	$0.146780\pi$
$948$	0.299605	−	14.2209i	0.00973073	−	0.461874i
$949$	7.79169	+	13.4956i	0.252929	+	0.438086i
$950$	0.540597	+	0.936341i	0.0175393	+	0.0303789i
$951$	5.92702	+	3.59051i	0.192197	+	0.116430i
$952$	9.83187	−	17.0293i	0.318653	−	0.551923i
$953$	19.0891			0.618358			0.309179	−	0.951004i	$-0.399946\pi$
$953$	19.0891			0.618358			0.309179	+	0.951004i	$0.399946\pi$
$954$	−0.720753	+	1.13512i	−0.0233352	+	0.0367508i
$955$	−45.3484			−1.46744
$956$	−24.5077	+	42.4486i	−0.792636	+	1.37289i
$957$		0			0
$958$	3.31651	+	5.74436i	0.107152	+	0.185592i
$959$	2.21845	+	3.84247i	0.0716376	+	0.124080i
$960$	25.1390	−	13.8163i	0.811357	−	0.445920i
$961$	3.66788	−	6.35296i	0.118319	−	0.204934i
$962$	8.50417			0.274186
$963$	8.32953	+	0.351128i	0.268416	+	0.0113149i
$964$	5.72150			0.184277
$965$	29.8494	−	51.7007i	0.960886	−	1.66430i
$966$	3.20776	+	1.94322i	0.103208	+	0.0625220i
$967$	−13.2813	−	23.0039i	−0.427099	−	0.739757i	0.569515	−	0.821981i	$-0.307131\pi$
$967$	−13.2813	−	23.0039i	−0.427099	−	0.739757i	−0.996614	+	0.0822239i	$0.973798\pi$
$968$		0			0
$969$	0.255693	−	12.1366i	0.00821406	−	0.389885i
$970$	2.86274	−	4.95842i	0.0919172	−	0.159205i
$971$	−51.1079			−1.64013			−0.820066	−	0.572269i	$-0.806063\pi$
$971$	−51.1079			−1.64013			−0.820066	+	0.572269i	$0.806063\pi$
$972$	27.3310	−	12.1487i	0.876641	−	0.389671i
$973$	−11.7513			−0.376728
$974$	−0.0386093	+	0.0668733i	−0.00123712	+	0.00214276i
$975$	0.328365	−	15.5860i	0.0105161	−	0.499153i
$976$	15.1438	+	26.2298i	0.484741	+	0.839596i
$977$	10.5873	+	18.3377i	0.338717	+	0.586676i	0.984192	−	0.177106i	$-0.0566736\pi$
$977$	10.5873	+	18.3377i	0.338717	+	0.586676i	−0.645474	+	0.763782i	$0.723340\pi$
$978$	5.63434	+	3.41321i	0.180166	+	0.109142i
$979$		0			0
$980$	−49.8521			−1.59247
$981$	52.0257	+	2.19312i	1.66105	+	0.0700208i
$982$	−1.19949			−0.0382774
$983$	−25.4177	+	44.0248i	−0.810699	+	1.40417i	0.101676	+	0.994818i	$0.467579\pi$
$983$	−25.4177	+	44.0248i	−0.810699	+	1.40417i	−0.912375	+	0.409355i	$0.865754\pi$
$984$	11.6560	−	6.40611i	0.371580	−	0.204219i
$985$	−24.6829	−	42.7520i	−0.786462	−	1.36219i
$986$	2.18868	+	3.79091i	0.0697018	+	0.120727i
$987$	36.2713	−	19.9346i	1.15453	−	0.634526i
$988$	−5.99340	+	10.3809i	−0.190675	+	0.330259i
$989$	−1.83625			−0.0583895
$990$		0			0
$991$	−13.1480			−0.417662			−0.208831	−	0.977952i	$-0.566966\pi$
$991$	−13.1480			−0.417662			−0.208831	+	0.977952i	$0.566966\pi$
$992$	7.87622	−	13.6420i	0.250070	−	0.433134i
$993$	4.71142	+	2.85412i	0.149513	+	0.0905727i
$994$	−3.33431	−	5.77519i	−0.105758	−	0.183178i
$995$	33.9889	+	58.8705i	1.07752	+	1.86632i
$996$	0.455005	−	21.5971i	0.0144174	−	0.684329i
$997$	18.6043	−	32.2237i	0.589205	−	1.02053i	−0.405132	−	0.914258i	$-0.632774\pi$
$997$	18.6043	−	32.2237i	0.589205	−	1.02053i	0.994337	−	0.106275i	$-0.0338924\pi$
$998$	−4.38109			−0.138681
$999$	−2.54135	+	40.1612i	−0.0804047	+	1.27064i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1089.2.e.p.727.9		36
9.2	odd	6		9801.2.a.cp.1.9		18
9.4	even	3	inner	1089.2.e.p.364.9		36
9.7	even	3		9801.2.a.cm.1.10		18
11.3	even	5		99.2.m.b.97.5	yes	72
11.4	even	5		99.2.m.b.16.5	✓	72
11.10	odd	2		1089.2.e.o.727.10		36
33.14	odd	10		297.2.n.b.262.5		72
33.26	odd	10		297.2.n.b.181.5		72
99.4	even	15		99.2.m.b.49.5	yes	72
99.14	odd	30		297.2.n.b.64.5		72
99.25	even	15		891.2.f.f.163.5		36
99.43	odd	6		9801.2.a.co.1.9		18
99.47	odd	30		891.2.f.e.163.5		36
99.58	even	15		99.2.m.b.31.5	yes	72
99.59	odd	30		297.2.n.b.280.5		72
99.65	even	6		9801.2.a.cn.1.10		18
99.70	even	15		891.2.f.f.82.5		36
99.76	odd	6		1089.2.e.o.364.10		36
99.92	odd	30		891.2.f.e.82.5		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.16.5	✓	72	11.4	even	5
99.2.m.b.31.5	yes	72	99.58	even	15
99.2.m.b.49.5	yes	72	99.4	even	15
99.2.m.b.97.5	yes	72	11.3	even	5
297.2.n.b.64.5		72	99.14	odd	30
297.2.n.b.181.5		72	33.26	odd	10
297.2.n.b.262.5		72	33.14	odd	10
297.2.n.b.280.5		72	99.59	odd	30
891.2.f.e.82.5		36	99.92	odd	30
891.2.f.e.163.5		36	99.47	odd	30
891.2.f.f.82.5		36	99.70	even	15
891.2.f.f.163.5		36	99.25	even	15
1089.2.e.o.364.10		36	99.76	odd	6
1089.2.e.o.727.10		36	11.10	odd	2
1089.2.e.p.364.9		36	9.4	even	3	inner
1089.2.e.p.727.9		36	1.1	even	1	trivial
9801.2.a.cm.1.10		18	9.7	even	3
9801.2.a.cn.1.10		18	99.65	even	6
9801.2.a.co.1.9		18	99.43	odd	6
9801.2.a.cp.1.9		18	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1089 = 3^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1089.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142574 + 0.246946i) q^{2} +(0.0364826 - 1.73167i) q^{3} +(0.959345 + 1.66163i) q^{4} +(-1.35437 - 2.34583i) q^{5} +(0.422426 + 0.255900i) q^{6} +(2.03667 - 3.52761i) q^{7} -1.11741 q^{8} +(-2.99734 - 0.126351i) q^{9} +0.772391 q^{10} +(2.91240 - 1.60065i) q^{12} +(-1.92548 - 3.33503i) q^{13} +(0.580752 + 1.00589i) q^{14} +(-4.11161 + 2.25973i) q^{15} +(-1.75938 + 3.04733i) q^{16} -4.32020 q^{17} +(0.458545 - 0.722165i) q^{18} -1.62229 q^{19} +(2.59861 - 4.50093i) q^{20} +(-6.03434 - 3.65553i) q^{21} +(0.932117 + 1.61447i) q^{23} +(-0.0407660 + 1.93498i) q^{24} +(-1.16862 + 2.02411i) q^{25} +1.09809 q^{26} +(-0.328149 + 5.18578i) q^{27} +7.81547 q^{28} +(-1.77667 + 3.07729i) q^{29} +(0.0281788 - 1.33752i) q^{30} +(2.43230 + 4.21286i) q^{31} +(-1.61909 - 2.80435i) q^{32} +(0.615950 - 1.06686i) q^{34} -11.0336 q^{35} +(-2.66553 - 5.10170i) q^{36} +7.74449 q^{37} +(0.231297 - 0.400619i) q^{38} +(-5.84540 + 3.21262i) q^{39} +(1.51338 + 2.62125i) q^{40} +(-3.43607 - 5.95145i) q^{41} +(1.76306 - 0.968972i) q^{42} +(-0.492496 + 0.853027i) q^{43} +(3.76310 + 7.20238i) q^{45} -0.531584 q^{46} +(-2.93317 + 5.08041i) q^{47} +(5.21277 + 3.15783i) q^{48} +(-4.79603 - 8.30697i) q^{49} +(-0.333230 - 0.577171i) q^{50} +(-0.157612 + 7.48115i) q^{51} +(3.69440 - 6.39888i) q^{52} -1.57183 q^{53} +(-1.23382 - 0.820393i) q^{54} +(-2.27579 + 3.94178i) q^{56} +(-0.0591855 + 2.80927i) q^{57} +(-0.506615 - 0.877483i) q^{58} +(-5.68125 - 9.84021i) q^{59} +(-7.69930 - 4.66413i) q^{60} +(4.30374 - 7.45430i) q^{61} -1.38713 q^{62} +(-6.55030 + 10.3161i) q^{63} -6.11414 q^{64} +(-5.21561 + 9.03370i) q^{65} +(0.870282 + 1.50737i) q^{67} +(-4.14457 - 7.17860i) q^{68} +(2.82974 - 1.55522i) q^{69} +(1.57310 - 2.72470i) q^{70} -5.74136 q^{71} +(3.34925 + 0.141186i) q^{72} -4.04662 q^{73} +(-1.10416 + 1.91247i) q^{74} +(3.46245 + 2.09750i) q^{75} +(-1.55634 - 2.69566i) q^{76} +(0.0400613 - 1.90153i) q^{78} +(2.14007 - 3.70672i) q^{79} +9.53137 q^{80} +(8.96807 + 0.757436i) q^{81} +1.95958 q^{82} +(3.25009 - 5.62933i) q^{83} +(0.285129 - 13.5338i) q^{84} +(5.85114 + 10.1345i) q^{85} +(-0.140434 - 0.243239i) q^{86} +(5.26402 + 3.18887i) q^{87} +9.26243 q^{89} +(-2.31512 - 0.0975927i) q^{90} -15.6862 q^{91} +(-1.78844 + 3.09768i) q^{92} +(7.38400 - 4.05823i) q^{93} +(-0.836390 - 1.44867i) q^{94} +(2.19718 + 3.80563i) q^{95} +(-4.91527 + 2.70142i) q^{96} +(3.70634 - 6.41957i) q^{97} +2.73516 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 2 q^{2} + 9 q^{3} - 12 q^{4} + q^{5} - q^{6} - q^{7} - 12 q^{8} - q^{9} - 4 q^{10} - 8 q^{12} - 3 q^{13} - 5 q^{15} + 8 q^{16} - 40 q^{17} + 17 q^{18} - 6 q^{19} + 5 q^{20} - 8 q^{21} + 10 q^{23}+ \cdots - 164 q^{98}+O(q^{100}) \) 36 * q + 2 * q^2 + 9 * q^3 - 12 * q^4 + q^5 - q^6 - q^7 - 12 * q^8 - q^9 - 4 * q^10 - 8 * q^12 - 3 * q^13 - 5 * q^15 + 8 * q^16 - 40 * q^17 + 17 * q^18 - 6 * q^19 + 5 * q^20 - 8 * q^21 + 10 * q^23 - 57 * q^24 - 7 * q^25 + 4 * q^26 - 9 * q^27 + 38 * q^28 + 21 * q^29 + 12 * q^30 - 6 * q^31 + 9 * q^32 + 4 * q^34 - 76 * q^35 - 65 * q^36 + 14 * q^37 - 13 * q^38 + 42 * q^39 + 20 * q^41 + 18 * q^42 - 4 * q^43 + 20 * q^45 + 16 * q^46 - 7 * q^47 + 10 * q^48 - 7 * q^49 + 25 * q^50 - 4 * q^51 + 19 * q^52 + 62 * q^53 + 17 * q^54 + 57 * q^56 - 18 * q^57 - 12 * q^58 + 12 * q^59 + 11 * q^60 + 16 * q^61 - 38 * q^62 + 5 * q^63 - 32 * q^64 + 42 * q^65 + 5 * q^67 + 51 * q^68 + 31 * q^69 - 8 * q^70 + 26 * q^71 + 51 * q^72 + 9 * q^74 - 16 * q^75 + 8 * q^76 - 32 * q^78 + 2 * q^79 + 92 * q^80 + 47 * q^81 - 68 * q^82 + 36 * q^83 + 60 * q^84 - 25 * q^85 - 26 * q^86 - 60 * q^87 - 28 * q^89 + 163 * q^90 - 30 * q^91 + 15 * q^92 - 39 * q^93 - 4 * q^94 + 64 * q^95 - 21 * q^96 + 16 * q^97 - 164 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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