LMFDB - Embedded newform 1089.2.e.o.364.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1089,2,Mod(364,1089)]

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

lf = mfeigenbasis(mf)

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")

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

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

Self dual:	no
Analytic conductor:	$8.69570878012$
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			364.10
Character	$\chi$	$=$	1089.364
Dual form			1089.2.e.o.727.10

$q$-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 $\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times$.

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

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	$-0.134522\pi$
$2$	0.142574	+	0.246946i	0.100815	+	0.174617i	−0.811206	+	0.584761i	$0.801188\pi$
$3$	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	0.386251	+	0.922394i	$0.373770\pi$
$5$	−1.35437	+	2.34583i	−0.605691	+	1.04909i	−0.991942	+	0.126694i	$0.959563\pi$
$6$	−0.422426	+	0.255900i	−0.172455	+	0.104471i
$7$	−2.03667	−	3.52761i	−0.769788	−	1.33331i	−0.937678	−	0.347506i	$-0.887029\pi$
$7$	−2.03667	−	3.52761i	−0.769788	−	1.33331i	0.167890	−	0.985806i	$-0.446305\pi$
$8$	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	−0.465178	−	0.885217i	$-0.654010\pi$
$13$	1.92548	−	3.33503i	0.534032	−	0.924970i	0.999210	−	0.0397526i	$-0.0126570\pi$
$14$	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	$-0.324476\pi$
$17$	4.32020			1.04780			0.523902	+	0.851779i	$0.324476\pi$
$18$	−0.458545	−	0.722165i	−0.108080	−	0.170216i
$19$	1.62229			0.372180			0.186090	−	0.982533i	$-0.440418\pi$
$19$	1.62229			0.372180			0.186090	+	0.982533i	$0.440418\pi$
$20$	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	−0.752331	−	0.658786i	$-0.771070\pi$
$23$	0.932117	−	1.61447i	0.194360	−	0.336641i	0.946691	+	0.322145i	$0.104404\pi$
$24$	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	$-0.0596450\pi$
$29$	1.77667	+	3.07729i	0.329920	+	0.571438i	−0.652576	+	0.757723i	$0.726312\pi$
$30$	−0.0281788	−	1.33752i	−0.00514473	−	0.244197i
$31$	2.43230	−	4.21286i	0.436853	−	0.756652i	−0.560592	−	0.828092i	$-0.689426\pi$
$31$	2.43230	−	4.21286i	0.436853	−	0.756652i	0.997445	+	0.0714406i	$0.0227596\pi$
$32$	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	−0.462458	−	0.886641i	$-0.653033\pi$
$41$	3.43607	−	5.95145i	0.536624	−	0.929461i	0.999083	−	0.0428197i	$-0.0136341\pi$
$42$	1.76306	+	0.968972i	0.272046	+	0.149516i
$43$	0.492496	+	0.853027i	0.0751049	+	0.130085i	0.901132	−	0.433545i	$-0.142738\pi$
$43$	0.492496	+	0.853027i	0.0751049	+	0.130085i	−0.826027	+	0.563631i	$0.809404\pi$
$44$		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	0.568834	−	0.822452i	$-0.307395\pi$
$47$	−2.93317	−	5.08041i	−0.427847	−	0.741054i	−0.996682	+	0.0813987i	$0.974061\pi$
$48$	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	0.213024	+	0.977047i	$0.431669\pi$
$59$	−5.68125	+	9.84021i	−0.739635	+	1.28109i	−0.952660	+	0.304039i	$0.901665\pi$
$60$	−7.69930	+	4.66413i	−0.993975	+	0.602137i
$61$	−4.30374	−	7.45430i	−0.551037	−	0.954425i	−0.998200	−	0.0599721i	$-0.980899\pi$
$61$	−4.30374	−	7.45430i	−0.551037	−	0.954425i	0.447163	−	0.894453i	$-0.352434\pi$
$62$	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	−0.807956	−	0.589243i	$-0.799426\pi$
$67$	0.870282	−	1.50737i	0.106322	−	0.184155i	0.914277	+	0.405088i	$0.132759\pi$
$68$	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	$-0.423898\pi$
$73$	4.04662			0.473622			0.236811	+	0.971556i	$0.423898\pi$
$74$	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	$-0.244069\pi$
$79$	−2.14007	−	3.70672i	−0.240777	−	0.417038i	−0.960936	+	0.276771i	$0.910736\pi$
$80$	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	$-0.282780\pi$
$83$	−3.25009	−	5.62933i	−0.356744	−	0.617899i	−0.987415	+	0.158152i	$0.949446\pi$
$84$	−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	0.990524	−	0.137340i	$-0.0438553\pi$
$97$	3.70634	+	6.41957i	0.376322	+	0.651809i	−0.614202	+	0.789149i	$0.710522\pi$
$98$	−2.73516			−0.276293
$99$		0			0
$100$	−4.48444			−0.448444
$101$	−6.85880	−	11.8798i	−0.682476	−	1.18208i	−0.974223	−	0.225588i	$-0.927570\pi$
$101$	−6.85880	−	11.8798i	−0.682476	−	1.18208i	0.291747	−	0.956496i	$-0.405764\pi$
$102$	−1.82497	+	1.10554i	−0.180699	+	0.109465i
$103$	−2.53762	+	4.39529i	−0.250039	+	0.433081i	−0.963536	−	0.267577i	$-0.913777\pi$
$103$	−2.53762	+	4.39529i	−0.250039	+	0.433081i	0.713497	+	0.700658i	$0.247110\pi$
$104$	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	$-0.457113\pi$
$107$	2.77898			0.268654			0.134327	+	0.990937i	$0.457113\pi$
$108$	−8.93168	−	4.42969i	−0.859451	−	0.426247i
$109$	17.3573			1.66253			0.831263	−	0.555879i	$-0.187618\pi$
$109$	17.3573			1.66253			0.831263	+	0.555879i	$0.187618\pi$
$110$		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	−0.887365	−	0.461068i	$-0.847466\pi$
$113$	−0.471827	+	0.817228i	−0.0443858	+	0.0768784i	0.842979	+	0.537946i	$0.180800\pi$
$114$	−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	$-0.534675\pi$
$127$	−2.45040			−0.217438			−0.108719	+	0.994073i	$0.534675\pi$
$128$	−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	$-0.777462\pi$
$131$	1.99869	−	3.46183i	0.174626	−	0.302461i	0.940032	+	0.341087i	$0.110795\pi$
$132$		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	0.841822	−	0.539755i	$-0.181483\pi$
$137$	−0.544628	−	0.943324i	−0.0465307	−	0.0805936i	−0.888353	+	0.459162i	$0.848150\pi$
$138$	0.0193935	+	0.920525i	0.00165089	+	0.0783603i
$139$	1.44246	−	2.49842i	0.122348	−	0.211913i	−0.798345	−	0.602200i	$-0.794291\pi$
$139$	1.44246	−	2.49842i	0.122348	−	0.211913i	0.920693	+	0.390287i	$0.127624\pi$
$140$	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	−0.0744578	−	0.997224i	$-0.523723\pi$
$149$	10.0874	−	17.4719i	0.826393	−	1.43135i	0.900850	−	0.434130i	$-0.142944\pi$
$150$	1.01163	+	0.555986i	0.0825988	+	0.0453961i
$151$	−5.53918	−	9.59414i	−0.450772	−	0.780760i	0.547662	−	0.836700i	$-0.315518\pi$
$151$	−5.53918	−	9.59414i	−0.450772	−	0.780760i	−0.998434	+	0.0559396i	$0.982185\pi$
$152$	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	−0.872589	−	0.488455i	$-0.837560\pi$
$157$	−0.166392	+	0.288200i	−0.0132795	+	0.0230008i	0.859309	+	0.511456i	$0.170894\pi$
$158$	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	0.224243	+	0.974533i	$0.428009\pi$
$167$	−9.45758	+	16.3810i	−0.731849	+	1.26760i	−0.956092	+	0.293067i	$0.905324\pi$
$168$	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	$-0.184998\pi$
$173$	−0.757044	−	1.31124i	−0.0575570	−	0.0996916i	−0.893368	+	0.449325i	$0.851664\pi$
$174$	−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	0.991942	+	0.126690i	$0.0404354\pi$
$191$	8.37078	+	14.4986i	0.605688	+	1.04908i	−0.386254	+	0.922392i	$0.626231\pi$
$192$	−0.223060	−	10.5877i	−0.0160980	−	0.764099i
$193$	−11.0197	+	19.0867i	−0.793214	+	1.37389i	0.130752	+	0.991415i	$0.458261\pi$
$193$	−11.0197	+	19.0867i	−0.793214	+	1.37389i	−0.923967	+	0.382473i	$0.875073\pi$
$194$	−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	$-0.724907\pi$
$197$	−18.2247			−1.29845			−0.649227	+	0.760595i	$0.724907\pi$
$198$		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	$-0.741451\pi$
$211$	4.13501	−	7.16205i	0.284666	−	0.493056i	0.972528	+	0.232785i	$0.0747840\pi$
$212$	−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	0.962459	−	0.271428i	$-0.0874959\pi$
$223$	3.67604	+	6.36709i	0.246166	+	0.426372i	−0.716293	+	0.697800i	$0.754163\pi$
$224$	−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	−0.987836	−	0.155501i	$-0.950301\pi$
$227$	−9.47060	−	16.4036i	−0.628586	−	1.08874i	0.359250	−	0.933241i	$-0.383032\pi$
$228$	4.72476	+	2.59672i	0.312905	+	0.171972i
$229$	3.92972	−	6.80648i	0.259683	−	0.449785i	−0.706474	−	0.707739i	$-0.749715\pi$
$229$	3.92972	−	6.80648i	0.259683	−	0.449785i	0.966157	+	0.257954i	$0.0830485\pi$
$230$	−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	$-0.430963\pi$
$233$	6.56942			0.430377			0.215188	+	0.976573i	$0.430963\pi$
$234$	−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	0.0747530	+	0.997202i	$0.476183\pi$
$239$	−12.7731	+	22.1237i	−0.826226	+	1.43107i	−0.900979	+	0.433863i	$0.857150\pi$
$240$	0.347729	+	16.5051i	0.0224458	+	1.06540i
$241$	−1.49099	−	2.58247i	−0.0960432	−	0.166352i	0.814000	−	0.580864i	$-0.197285\pi$
$241$	−1.49099	−	2.58247i	−0.0960432	−	0.166352i	−0.910044	+	0.414513i	$0.863952\pi$
$242$		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	0.337604	+	0.941288i	$0.390384\pi$
$257$	−10.3622	+	17.9479i	−0.646378	+	1.11956i	−0.983981	+	0.178271i	$0.942950\pi$
$258$	−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	$-0.0762936\pi$
$263$	4.54273	+	7.86823i	0.280117	+	0.485176i	−0.691297	+	0.722571i	$0.742960\pi$
$264$		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	$-0.536077\pi$
$271$	−3.72364			−0.226195			−0.113097	+	0.993584i	$0.536077\pi$
$272$	−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	$-0.204053\pi$
$277$	−1.95032	−	3.37805i	−0.117183	−	0.202967i	−0.918650	+	0.395071i	$0.870720\pi$
$278$	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	$-0.166290\pi$
$281$	0.0198115	+	0.0343146i	0.00118186	+	0.00204704i	−0.865434	+	0.501023i	$0.832957\pi$
$282$	2.53913	+	1.39550i	0.151203	+	0.0831006i
$283$	3.19694	−	5.53725i	0.190038	−	0.329156i	−0.755225	−	0.655466i	$-0.772472\pi$
$283$	3.19694	−	5.53725i	0.190038	−	0.329156i	0.945263	+	0.326311i	$0.105806\pi$
$284$	−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	0.290094	+	0.956998i	$0.406314\pi$
$293$	−11.7037	+	20.2714i	−0.683738	+	1.18427i	−0.973832	+	0.227271i	$0.927020\pi$
$294$	−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	$-0.812702\pi$
$307$	−29.1494			−1.66365			−0.831823	+	0.555042i	$0.812702\pi$
$308$		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	−0.438900	−	0.898536i	$-0.644632\pi$
$311$	9.85287	−	17.0657i	0.558705	−	0.967705i	0.997605	−	0.0691692i	$-0.0220348\pi$
$312$	6.53170	+	3.58980i	0.369785	+	0.203233i
$313$	−0.669188	−	1.15907i	−0.0378248	−	0.0655144i	0.846493	−	0.532399i	$-0.178710\pi$
$313$	−0.669188	−	1.15907i	−0.0378248	−	0.0655144i	−0.884318	+	0.466885i	$0.845376\pi$
$314$	−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	0.804364	−	0.594137i	$-0.202506\pi$
$317$	−2.00045	−	3.46487i	−0.112356	−	0.194607i	−0.916720	+	0.399531i	$0.869173\pi$
$318$	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	0.819009	−	0.573780i	$-0.194524\pi$
$331$	−1.59017	−	2.75425i	−0.0874034	−	0.151387i	−0.906413	+	0.422393i	$0.861190\pi$
$332$	−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	$-0.998403\pi$
$337$	−9.09890	+	15.7598i	−0.495649	+	0.858489i	0.504339	+	0.863506i	$0.331736\pi$
$338$	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	0.218524	+	0.975832i	$0.429876\pi$
$347$	−13.7071	+	23.7413i	−0.735833	+	1.27450i	−0.954357	+	0.298669i	$0.903457\pi$
$348$	0.248730	+	11.8061i	0.0133333	+	0.632873i
$349$	11.4528	+	19.8368i	0.613052	+	1.06184i	0.990723	+	0.135898i	$0.0433919\pi$
$349$	11.4528	+	19.8368i	0.613052	+	1.06184i	−0.377671	+	0.925940i	$0.623275\pi$
$350$	−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	0.925651	+	0.378379i	$0.123518\pi$
$353$	14.8524	+	25.7250i	0.790511	+	1.36921i	−0.135140	+	0.990827i	$0.543148\pi$
$354$	−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	$-0.0746436\pi$
$359$	36.8574			1.94526			0.972631	+	0.232356i	$0.0746436\pi$
$360$	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	0.983396	+	0.181472i	$0.0580860\pi$
$367$	12.4303	+	21.5299i	0.648857	+	1.12385i	−0.334539	+	0.942382i	$0.608581\pi$
$368$	−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	$-0.676422\pi$
$373$	9.13952	−	15.8301i	0.473227	−	0.819653i	0.999530	+	0.0306440i	$0.00975583\pi$
$374$		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	−0.662373	−	0.749174i	$-0.730451\pi$
$383$	6.21588	−	10.7662i	0.317617	−	0.550129i	0.979990	+	0.199045i	$0.0637841\pi$
$384$	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	0.758204	−	0.652017i	$-0.226077\pi$
$389$	−3.65984	−	6.33903i	−0.185561	−	0.321402i	−0.943766	+	0.330616i	$0.892744\pi$
$390$	−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	−0.944135	−	0.329559i	$-0.893100\pi$
$401$	−3.73789	+	6.47421i	−0.186661	+	0.323307i	0.757474	+	0.652865i	$0.226433\pi$
$402$	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	$-0.814355\pi$
$409$	1.20510	−	2.08729i	0.0595883	−	0.103210i	0.894281	+	0.447507i	$0.147688\pi$
$410$	−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	−0.696165	−	0.717881i	$-0.745112\pi$
$419$	5.60088	−	9.70101i	0.273621	−	0.473925i	0.969786	+	0.243956i	$0.0784453\pi$
$420$	32.1342	+	17.6608i	1.56799	+	0.861761i
$421$	3.45243	+	5.97979i	0.168261	+	0.291437i	0.937809	−	0.347153i	$-0.112851\pi$
$421$	3.45243	+	5.97979i	0.168261	+	0.291437i	−0.769547	+	0.638590i	$0.779518\pi$
$422$	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	$-0.251938\pi$
$431$	29.1806			1.40558			0.702789	+	0.711398i	$0.251938\pi$
$432$	−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	−0.999886	−	0.0150869i	$-0.995197\pi$
$439$	−10.7487	−	18.6173i	−0.513009	−	0.888557i	0.486877	−	0.873470i	$-0.338136\pi$
$440$		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	0.923150	+	0.384440i	$0.125605\pi$
$443$	16.7225	+	28.9642i	0.794510	+	1.37613i	−0.128640	+	0.991691i	$0.541061\pi$
$444$	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	0.854210	+	0.519929i	$0.174041\pi$
$457$	18.7562	+	32.4866i	0.877376	+	1.51966i	0.0231665	+	0.999732i	$0.492625\pi$
$458$	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	$-0.0177463\pi$
$461$	9.68265	+	16.7708i	0.450966	+	0.781096i	−0.547480	+	0.836818i	$0.684413\pi$
$462$		0			0
$463$	7.17464	−	12.4268i	0.333434	−	0.577524i	−0.649749	−	0.760149i	$-0.725126\pi$
$463$	7.17464	−	12.4268i	0.333434	−	0.577524i	0.983183	+	0.182625i	$0.0584594\pi$
$464$	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	−0.999327	−	0.0366756i	$-0.988323\pi$
$479$	−11.6308	−	20.1452i	−0.531426	−	0.920456i	0.467902	−	0.883781i	$-0.345010\pi$
$480$	−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	$-0.863593\pi$
$491$	−2.10328	+	3.64298i	−0.0949196	+	0.164406i	0.814655	+	0.579945i	$0.196926\pi$
$492$	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	−0.641254	−	0.767328i	$-0.721586\pi$
$499$	7.68212	−	13.3058i	0.343899	−	0.595650i	0.985153	+	0.171678i	$0.0549189\pi$
$500$	−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	$-0.527823\pi$
$503$	−3.91570			−0.174592			−0.0872961	+	0.996182i	$0.527823\pi$
$504$	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	0.354280	+	0.935139i	$0.384726\pi$
$509$	−14.2747	+	24.7245i	−0.632715	+	1.09589i	−0.986994	+	0.160754i	$0.948607\pi$
$510$	−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	$-0.241870\pi$
$523$	33.1573			1.44987			0.724934	+	0.688818i	$0.241870\pi$
$524$	−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	$-0.290440\pi$
$541$	28.4609			1.22363			0.611815	+	0.791001i	$0.290440\pi$
$542$	−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	−0.981308	−	0.192444i	$-0.938359\pi$
$547$	−15.3733	−	26.6274i	−0.657316	−	1.13850i	0.323992	−	0.946060i	$-0.394975\pi$
$548$	−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	$-0.450610\pi$
$557$	7.29459			0.309082			0.154541	+	0.987986i	$0.450610\pi$
$558$	−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	0.166490	+	0.986043i	$0.446757\pi$
$563$	−18.2867	+	31.6735i	−0.770693	+	1.33488i	−0.937183	+	0.348837i	$0.886577\pi$
$564$	−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	$-0.165656\pi$
$569$	0.0757419	+	0.131189i	0.00317527	+	0.00549972i	−0.864433	+	0.502747i	$0.832323\pi$
$570$	−0.0457144	−	2.16986i	−0.00191476	−	0.0908853i
$571$	21.6127	−	37.4343i	0.904463	−	1.56658i	0.0828262	−	0.996564i	$-0.473605\pi$
$571$	21.6127	−	37.4343i	0.904463	−	1.56658i	0.821637	−	0.570012i	$-0.193061\pi$
$572$		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	0.999346	−	0.0361584i	$-0.0115121\pi$
$587$	11.3474	+	19.6543i	0.468359	+	0.811221i	−0.530987	+	0.847380i	$0.678179\pi$
$588$	−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	$-0.343955\pi$
$593$	22.9308			0.941656			0.470828	+	0.882225i	$0.343955\pi$
$594$		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	−0.709617	−	0.704588i	$-0.751132\pi$
$599$	6.25035	−	10.8259i	0.255382	−	0.442335i	0.964999	+	0.262253i	$0.0844654\pi$
$600$	3.86897	−	2.34377i	0.157950	−	0.0956839i
$601$	11.2394	+	19.4672i	0.458465	+	0.794085i	0.998880	−	0.0473137i	$-0.0150660\pi$
$601$	11.2394	+	19.4672i	0.458465	+	0.794085i	−0.540415	+	0.841399i	$0.681733\pi$
$602$	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	−0.456836	−	0.889551i	$-0.651017\pi$
$607$	13.3524	−	23.1270i	0.541956	−	0.938695i	0.998792	−	0.0491443i	$-0.0156494\pi$
$608$	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	$-0.158771\pi$
$613$	43.4844			1.75632			0.878160	+	0.478367i	$0.158771\pi$
$614$	−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	0.0610871	+	0.998132i	$0.480543\pi$
$617$	−20.7128	+	35.8756i	−0.833864	+	1.44430i	−0.894952	+	0.446163i	$0.852790\pi$
$618$	−0.0527976	−	2.50606i	−0.00212383	−	0.100809i
$619$	−4.45588	−	7.71780i	−0.179097	−	0.310205i	0.762475	−	0.647018i	$-0.223984\pi$
$619$	−4.45588	−	7.71780i	−0.179097	−	0.310205i	−0.941571	+	0.336813i	$0.890651\pi$
$620$	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	−0.999403	−	0.0345558i	$-0.988998\pi$
$641$	−13.4091	−	23.2252i	−0.529628	−	0.917342i	0.469775	−	0.882786i	$-0.344335\pi$
$642$	−1.17391	+	0.711141i	−0.0463306	+	0.0280665i
$643$	−7.06923	+	12.2443i	−0.278783	+	0.482866i	−0.971083	−	0.238744i	$-0.923264\pi$
$643$	−7.06923	+	12.2443i	−0.278783	+	0.482866i	0.692299	+	0.721610i	$0.256598\pi$
$644$	−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	−0.814915	−	0.579580i	$-0.803217\pi$
$653$	2.41417	−	4.18146i	0.0944736	−	0.163633i	0.909389	+	0.415947i	$0.136550\pi$
$654$	−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	$-0.308845\pi$
$659$	−11.0889	−	19.2065i	−0.431961	−	0.748178i	−0.997042	+	0.0768574i	$0.975511\pi$
$660$		0			0
$661$	13.6987	−	23.7269i	0.532820	−	0.922871i	−0.466446	−	0.884550i	$-0.654466\pi$
$661$	13.6987	−	23.7269i	0.532820	−	0.922871i	0.999265	−	0.0383209i	$-0.0122009\pi$
$662$	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	0.975201	+	0.221320i	$0.0710365\pi$
$673$	17.6218	+	30.5218i	0.679269	+	1.17653i	−0.295932	+	0.955209i	$0.595630\pi$
$674$	−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	−0.884322	−	0.466878i	$-0.845379\pi$
$677$	−22.0250	−	38.1484i	−0.846489	−	1.46616i	0.0378328	−	0.999284i	$-0.487955\pi$
$678$	−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	0.935245	−	0.354002i	$-0.115179\pi$
$691$	4.23344	+	7.33253i	0.161048	+	0.278943i	−0.774197	+	0.632945i	$0.781846\pi$
$692$	−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	$-0.807401\pi$
$701$	−43.5518			−1.64493			−0.822465	+	0.568816i	$0.807401\pi$
$702$	−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	0.917051	−	0.398771i	$-0.130563\pi$
$709$	3.01364	+	5.21978i	0.113180	+	0.196033i	−0.803871	+	0.594804i	$0.797230\pi$
$710$	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	0.638588	−	0.769549i	$-0.279519\pi$
$727$	−9.36031	−	16.2125i	−0.347155	−	0.601290i	−0.985743	+	0.168259i	$0.946185\pi$
$728$	−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	$-0.830017\pi$
$733$	0.282096	−	0.488604i	0.0104194	−	0.0180470i	0.871188	+	0.490949i	$0.163350\pi$
$734$	−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	$-0.511408\pi$
$739$	−1.94812			−0.0716629			−0.0358315	+	0.999358i	$0.511408\pi$
$740$	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	0.499914	+	0.866075i	$0.333365\pi$
$743$	−13.6313	+	23.6102i	−0.500086	+	0.866174i	−1.00000		9.89898e-5i	$0.999968\pi$
$744$	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	0.445115	+	0.895474i	$0.353163\pi$
$751$	−15.1531	+	26.2460i	−0.552946	+	0.957730i	−0.998060	+	0.0622562i	$0.980170\pi$
$752$	−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	0.387857	+	0.921720i	$0.373216\pi$
$761$	−16.6705	+	28.8741i	−0.604304	+	1.04669i	−0.992161	+	0.124966i	$0.960118\pi$
$762$	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	−0.164575	+	0.986364i	$0.552625\pi$
$769$	−25.9701	+	44.9815i	−0.936504	+	1.62207i	−0.771929	+	0.635709i	$0.780708\pi$
$770$		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	$-0.947569\pi$
$787$	−9.85316	+	17.0662i	−0.351227	+	0.608343i	0.635238	+	0.772317i	$0.280902\pi$
$788$	−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	−0.963085	−	0.269199i	$-0.913241\pi$
$797$	−7.01288	+	12.1467i	−0.248409	+	0.430257i	0.714676	+	0.699456i	$0.246574\pi$
$798$	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	$-0.380068\pi$
$809$	20.9298			0.735854			0.367927	+	0.929855i	$0.380068\pi$
$810$	−6.92686	+	0.585037i	−0.243385	+	0.0205561i
$811$	−1.94293			−0.0682255			−0.0341127	−	0.999418i	$-0.510861\pi$
$811$	−1.94293			−0.0682255			−0.0341127	+	0.999418i	$0.510861\pi$
$812$	−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	$-0.106080\pi$
$821$	5.42088	+	9.38924i	0.189190	+	0.327687i	−0.755790	+	0.654814i	$0.772747\pi$
$822$	0.471462	+	0.259114i	0.0164441	+	0.00903765i
$823$	−23.8339	+	41.2815i	−0.830798	+	1.43898i	0.0666091	+	0.997779i	$0.478782\pi$
$823$	−23.8339	+	41.2815i	−0.830798	+	1.43898i	−0.897407	+	0.441204i	$0.854551\pi$
$824$	−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	$-0.725451\pi$
$827$	−37.4150			−1.30105			−0.650524	+	0.759486i	$0.725451\pi$
$828$	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	0.702439	−	0.711744i	$-0.252094\pi$
$839$	−7.68075	−	13.3035i	−0.265169	−	0.459286i	−0.967608	+	0.252458i	$0.918761\pi$
$840$	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	0.964911	+	0.262578i	$0.0845726\pi$
$853$	20.7321	+	35.9091i	0.709854	+	1.22950i	−0.255057	+	0.966926i	$0.582094\pi$
$854$	−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	$-0.0648770\pi$
$857$	9.20273	+	15.9396i	0.314359	+	0.544486i	−0.664942	+	0.746895i	$0.731544\pi$
$858$		0			0
$859$	7.52426	−	13.0324i	0.256725	−	0.444660i	−0.708638	−	0.705572i	$-0.750690\pi$
$859$	7.52426	−	13.0324i	0.256725	−	0.444660i	0.965363	+	0.260912i	$0.0840233\pi$
$860$	−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	$-0.966579\pi$
$877$	−12.0377	+	20.8499i	−0.406484	+	0.704050i	0.588009	+	0.808854i	$0.299912\pi$
$878$	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	$-0.847086\pi$
$887$	−1.28635	+	2.22803i	−0.0431915	+	0.0748099i	0.843621	+	0.536938i	$0.180419\pi$
$888$	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	0.767823	−	0.640662i	$-0.221340\pi$
$907$	−5.14743	−	8.91562i	−0.170918	−	0.296038i	−0.938741	+	0.344624i	$0.888007\pi$
$908$	−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	0.965832	−	0.259170i	$-0.0834491\pi$
$911$	7.80127	+	13.5122i	0.258468	+	0.447679i	−0.707364	+	0.706850i	$0.750116\pi$
$912$	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	$-0.559206\pi$
$919$	−11.2124			−0.369864			−0.184932	+	0.982751i	$0.559206\pi$
$920$	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	0.605945	−	0.795506i	$-0.292795\pi$
$929$	−11.7638	−	20.3754i	−0.385956	−	0.668496i	−0.991901	+	0.127011i	$0.959462\pi$
$930$	−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	$-0.598564\pi$
$937$	−18.6555			−0.609448			−0.304724	+	0.952441i	$0.598564\pi$
$938$	−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	0.469789	+	0.882779i	$0.344330\pi$
$941$	−16.2463	+	28.1394i	−0.529615	+	0.917320i	−0.999403	+	0.0345407i	$0.989003\pi$
$942$	−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	0.895554	−	0.444953i	$-0.146780\pi$
$947$	1.92137	+	3.32790i	0.0624360	+	0.108142i	−0.833118	+	0.553096i	$0.813446\pi$
$948$	−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	$-0.600054\pi$
$953$	−19.0891			−0.618358			−0.309179	+	0.951004i	$0.600054\pi$
$954$	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	$-0.692869\pi$
$967$	13.2813	−	23.0039i	0.427099	−	0.739757i	0.996614	+	0.0822239i	$0.0262023\pi$
$968$		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	−0.645474	−	0.763782i	$-0.723340\pi$
$977$	10.5873	−	18.3377i	0.338717	−	0.586676i	0.984192	+	0.177106i	$0.0566736\pi$
$978$	−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	−0.912375	−	0.409355i	$-0.865754\pi$
$983$	−25.4177	−	44.0248i	−0.810699	−	1.40417i	0.101676	−	0.994818i	$-0.467579\pi$
$984$	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	−0.994337	−	0.106275i	$-0.966108\pi$
$997$	−18.6043	−	32.2237i	−0.589205	−	1.02053i	0.405132	−	0.914258i	$-0.367226\pi$
$998$	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.o.364.10		36
9.4	even	3		9801.2.a.co.1.9		18
9.5	odd	6		9801.2.a.cn.1.10		18
9.7	even	3	inner	1089.2.e.o.727.10		36
11.7	odd	10		99.2.m.b.49.5	yes	72
11.8	odd	10		99.2.m.b.31.5	yes	72
11.10	odd	2		1089.2.e.p.364.9		36
33.8	even	10		297.2.n.b.64.5		72
33.29	even	10		297.2.n.b.280.5		72
99.7	odd	30		99.2.m.b.16.5	✓	72
99.29	even	30		297.2.n.b.181.5		72
99.32	even	6		9801.2.a.cp.1.9		18
99.40	odd	30		891.2.f.f.82.5		36
99.41	even	30		891.2.f.e.163.5		36
99.43	odd	6		1089.2.e.p.727.9		36
99.52	odd	30		99.2.m.b.97.5	yes	72
99.74	even	30		297.2.n.b.262.5		72
99.76	odd	6		9801.2.a.cm.1.10		18
99.85	odd	30		891.2.f.f.163.5		36
99.95	even	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	99.7	odd	30
99.2.m.b.31.5	yes	72	11.8	odd	10
99.2.m.b.49.5	yes	72	11.7	odd	10
99.2.m.b.97.5	yes	72	99.52	odd	30
297.2.n.b.64.5		72	33.8	even	10
297.2.n.b.181.5		72	99.29	even	30
297.2.n.b.262.5		72	99.74	even	30
297.2.n.b.280.5		72	33.29	even	10
891.2.f.e.82.5		36	99.95	even	30
891.2.f.e.163.5		36	99.41	even	30
891.2.f.f.82.5		36	99.40	odd	30
891.2.f.f.163.5		36	99.85	odd	30
1089.2.e.o.364.10		36	1.1	even	1	trivial
1089.2.e.o.727.10		36	9.7	even	3	inner
1089.2.e.p.364.9		36	11.10	odd	2
1089.2.e.p.727.9		36	99.43	odd	6
9801.2.a.cm.1.10		18	99.76	odd	6
9801.2.a.cn.1.10		18	9.5	odd	6
9801.2.a.co.1.9		18	9.4	even	3
9801.2.a.cp.1.9		18	99.32	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1089 = 3^{2} \cdot 11^{2} \)
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

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Database

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