LMFDB - Embedded newform 686.2.g.h.569.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [686,2,Mod(67,686)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(686, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([16]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("686.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 686 = 2 \cdot 7^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	686.g (of order $21$, degree $12$, not 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:	$5.47773757866$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$3$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 98)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			569.1
Character	$\chi$	$=$	686.569
Dual form			686.2.g.h.557.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.365341 - 0.930874i) q^{2} +(-0.160278 - 2.13877i) q^{3} +(-0.733052 + 0.680173i) q^{4} +(-1.11395 + 0.759477i) q^{5} +(-1.93237 + 0.930578i) q^{6} +(0.900969 + 0.433884i) q^{8} +(-1.58214 + 0.238470i) q^{9} +O(q^{10})$	\(q+(-0.365341 - 0.930874i) q^{2} +(-0.160278 - 2.13877i) q^{3} +(-0.733052 + 0.680173i) q^{4} +(-1.11395 + 0.759477i) q^{5} +(-1.93237 + 0.930578i) q^{6} +(0.900969 + 0.433884i) q^{8} +(-1.58214 + 0.238470i) q^{9} +(1.11395 + 0.759477i) q^{10} +(-1.33316 - 0.200941i) q^{11} +(1.57222 + 1.45881i) q^{12} +(-3.94258 + 4.94384i) q^{13} +(1.80289 + 2.26075i) q^{15} +(0.0747301 - 0.997204i) q^{16} +(-4.24343 + 1.30892i) q^{17} +(0.800006 + 1.38565i) q^{18} +(-0.695872 + 1.20529i) q^{19} +(0.300006 - 1.31441i) q^{20} +(0.300006 + 1.31441i) q^{22} +(5.36586 + 1.65515i) q^{23} +(0.783570 - 1.99650i) q^{24} +(-1.16263 + 2.96233i) q^{25} +(6.04248 + 1.86386i) q^{26} +(-0.668151 - 2.92736i) q^{27} +(-1.36054 + 5.96092i) q^{29} +(1.44580 - 2.50420i) q^{30} +(-2.44432 - 4.23369i) q^{31} +(-0.955573 + 0.294755i) q^{32} +(-0.216090 + 2.88352i) q^{33} +(2.76874 + 3.47189i) q^{34} +(0.997592 - 1.25094i) q^{36} +(-1.05016 - 0.974406i) q^{37} +(1.37620 + 0.207429i) q^{38} +(11.2056 + 7.63987i) q^{39} +(-1.33316 + 0.200941i) q^{40} +(5.29397 + 2.54944i) q^{41} +(-7.44405 + 3.58487i) q^{43} +(1.11395 - 0.759477i) q^{44} +(1.58131 - 1.46724i) q^{45} +(-0.419634 - 5.59963i) q^{46} +(1.40886 + 3.58972i) q^{47} -2.14476 q^{48} +3.18231 q^{50} +(3.47962 + 8.86592i) q^{51} +(-0.472549 - 6.30573i) q^{52} +(9.79429 - 9.08777i) q^{53} +(-2.48090 + 1.69145i) q^{54} +(1.63768 - 0.788665i) q^{55} +(2.68936 + 1.29513i) q^{57} +(6.04593 - 0.911277i) q^{58} +(-5.57024 - 3.79772i) q^{59} +(-2.85931 - 0.430972i) q^{60} +(-7.60489 - 7.05630i) q^{61} +(-3.04802 + 3.82210i) q^{62} +(0.623490 + 0.781831i) q^{64} +(0.637098 - 8.50148i) q^{65} +(2.76314 - 0.852316i) q^{66} +(5.19393 + 8.99615i) q^{67} +(2.22036 - 3.84578i) q^{68} +(2.67995 - 11.7416i) q^{69} +(-1.29530 - 5.67509i) q^{71} +(-1.52893 - 0.471612i) q^{72} +(-2.80716 + 7.15253i) q^{73} +(-0.523383 + 1.33356i) q^{74} +(6.52208 + 2.01180i) q^{75} +(-0.309692 - 1.35685i) q^{76} +(3.01788 - 13.2222i) q^{78} +(2.89060 - 5.00666i) q^{79} +(0.674108 + 1.16759i) q^{80} +(-10.7406 + 3.31305i) q^{81} +(0.439103 - 5.85943i) q^{82} +(4.84202 + 6.07170i) q^{83} +(3.73287 - 4.68086i) q^{85} +(6.05668 + 5.61978i) q^{86} +(12.9671 + 1.95447i) q^{87} +(-1.11395 - 0.759477i) q^{88} +(-10.2854 + 1.55027i) q^{89} +(-1.94354 - 0.935958i) q^{90} +(-5.05924 + 2.43640i) q^{92} +(-8.66311 + 5.90641i) q^{93} +(2.82686 - 2.62294i) q^{94} +(-0.140221 - 1.87112i) q^{95} +(0.783570 + 1.99650i) q^{96} +3.70350 q^{97} +2.15716 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 3 q^{2} + 5 q^{3} + 3 q^{4} + 10 q^{6} + 6 q^{8} + 10 q^{9}+O(q^{10}) $ 36 * q - 3 * q^2 + 5 * q^3 + 3 * q^4 + 10 * q^6 + 6 * q^8 + 10 * q^9	$ 36 q - 3 q^{2} + 5 q^{3} + 3 q^{4} + 10 q^{6} + 6 q^{8} + 10 q^{9} - 7 q^{11} - 2 q^{12} - 20 q^{13} + 14 q^{15} + 3 q^{16} - q^{17} + 32 q^{18} + 44 q^{19} + 14 q^{20} + 14 q^{22} - 21 q^{23} + 2 q^{24} - q^{25} - 3 q^{26} + 20 q^{27} + 22 q^{29} + 24 q^{31} - 3 q^{32} + 14 q^{33} - 2 q^{34} - 20 q^{36} + 13 q^{37} + 19 q^{38} + 3 q^{39} - 7 q^{40} + 16 q^{41} - 48 q^{43} - 98 q^{45} - 21 q^{46} - 40 q^{47} + 4 q^{48} - 100 q^{50} - 36 q^{51} - 18 q^{52} - 10 q^{53} - 4 q^{54} + 98 q^{55} + 38 q^{57} - 24 q^{58} - 13 q^{59} - 7 q^{60} - 27 q^{61} - 22 q^{62} - 6 q^{64} + 21 q^{66} + 86 q^{67} + 34 q^{68} - 182 q^{69} - 3 q^{72} - 5 q^{73} - 13 q^{74} + 3 q^{75} - 4 q^{76} + 76 q^{78} + 66 q^{79} + 2 q^{81} + 8 q^{82} + 110 q^{83} - 98 q^{85} + 18 q^{86} + 110 q^{87} - 62 q^{89} + 42 q^{90} - 42 q^{92} - 46 q^{93} - 23 q^{94} + 7 q^{95} + 2 q^{96} - 64 q^{97} + 28 q^{99}+O(q^{100}) $ 36 * q - 3 * q^2 + 5 * q^3 + 3 * q^4 + 10 * q^6 + 6 * q^8 + 10 * q^9 - 7 * q^11 - 2 * q^12 - 20 * q^13 + 14 * q^15 + 3 * q^16 - q^17 + 32 * q^18 + 44 * q^19 + 14 * q^20 + 14 * q^22 - 21 * q^23 + 2 * q^24 - q^25 - 3 * q^26 + 20 * q^27 + 22 * q^29 + 24 * q^31 - 3 * q^32 + 14 * q^33 - 2 * q^34 - 20 * q^36 + 13 * q^37 + 19 * q^38 + 3 * q^39 - 7 * q^40 + 16 * q^41 - 48 * q^43 - 98 * q^45 - 21 * q^46 - 40 * q^47 + 4 * q^48 - 100 * q^50 - 36 * q^51 - 18 * q^52 - 10 * q^53 - 4 * q^54 + 98 * q^55 + 38 * q^57 - 24 * q^58 - 13 * q^59 - 7 * q^60 - 27 * q^61 - 22 * q^62 - 6 * q^64 + 21 * q^66 + 86 * q^67 + 34 * q^68 - 182 * q^69 - 3 * q^72 - 5 * q^73 - 13 * q^74 + 3 * q^75 - 4 * q^76 + 76 * q^78 + 66 * q^79 + 2 * q^81 + 8 * q^82 + 110 * q^83 - 98 * q^85 + 18 * q^86 + 110 * q^87 - 62 * q^89 + 42 * q^90 - 42 * q^92 - 46 * q^93 - 23 * q^94 + 7 * q^95 + 2 * q^96 - 64 * q^97 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/686\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{10}{21}\right)$

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 $

$2$	−0.365341	−	0.930874i	−0.258335	−	0.658227i
$2$	−0.365341	−	0.930874i	−0.258335	−	0.658227i
$3$	−0.160278	−	2.13877i	−0.0925368	−	1.23482i	−0.829353	−	0.558725i	$-0.811291\pi$
$3$	−0.160278	−	2.13877i	−0.0925368	−	1.23482i	0.736816	−	0.676093i	$-0.236328\pi$
$4$	−0.733052	+	0.680173i	−0.366526	+	0.340086i
$5$	−1.11395	+	0.759477i	−0.498173	+	0.339649i	−0.786198	−	0.617974i	$-0.787954\pi$
$5$	−1.11395	+	0.759477i	−0.498173	+	0.339649i	0.288025	+	0.957623i	$0.407001\pi$
$6$	−1.93237	+	0.930578i	−0.788885	+	0.379907i
$7$		0			0
$7$		0			0
$8$	0.900969	+	0.433884i	0.318541	+	0.153401i
$9$	−1.58214	+	0.238470i	−0.527381	+	0.0794898i
$10$	1.11395	+	0.759477i	0.352262	+	0.240168i
$11$	−1.33316	−	0.200941i	−0.401962	−	0.0605861i	−0.0550499	−	0.998484i	$-0.517532\pi$
$11$	−1.33316	−	0.200941i	−0.401962	−	0.0605861i	−0.346912	+	0.937898i	$0.612770\pi$
$12$	1.57222	+	1.45881i	0.453862	+	0.421122i
$13$	−3.94258	+	4.94384i	−1.09347	+	1.37117i	−0.170931	+	0.985283i	$0.554677\pi$
$13$	−3.94258	+	4.94384i	−1.09347	+	1.37117i	−0.922544	+	0.385891i	$0.873894\pi$
$14$		0			0
$15$	1.80289	+	2.26075i	0.465503	+	0.583723i
$16$	0.0747301	−	0.997204i	0.0186825	−	0.249301i
$17$	−4.24343	+	1.30892i	−1.02918	+	0.317461i	−0.762957	−	0.646450i	$-0.776253\pi$
$17$	−4.24343	+	1.30892i	−1.02918	+	0.317461i	−0.266226	+	0.963911i	$0.585777\pi$
$18$	0.800006	+	1.38565i	0.188563	+	0.326601i
$19$	−0.695872	+	1.20529i	−0.159644	+	0.276511i	−0.934740	−	0.355332i	$-0.884368\pi$
$19$	−0.695872	+	1.20529i	−0.159644	+	0.276511i	0.775096	+	0.631843i	$0.217701\pi$
$20$	0.300006	−	1.31441i	0.0670835	−	0.293912i
$21$		0			0
$22$	0.300006	+	1.31441i	0.0639616	+	0.280234i
$23$	5.36586	+	1.65515i	1.11886	+	0.345122i	0.798392	−	0.602137i	$-0.205684\pi$
$23$	5.36586	+	1.65515i	1.11886	+	0.345122i	0.320467	+	0.947260i	$0.396160\pi$
$24$	0.783570	−	1.99650i	0.159946	−	0.407535i
$25$	−1.16263	+	2.96233i	−0.232526	+	0.592466i
$26$	6.04248	+	1.86386i	1.18503	+	0.365532i
$27$	−0.668151	−	2.92736i	−0.128586	−	0.563371i
$28$		0			0
$29$	−1.36054	+	5.96092i	−0.252646	+	1.10692i	0.676278	+	0.736646i	$0.263592\pi$
$29$	−1.36054	+	5.96092i	−0.252646	+	1.10692i	−0.928925	+	0.370269i	$0.879265\pi$
$30$	1.44580	−	2.50420i	0.263966	−	0.457203i
$31$	−2.44432	−	4.23369i	−0.439013	−	0.760393i	0.558600	−	0.829437i	$-0.311339\pi$
$31$	−2.44432	−	4.23369i	−0.439013	−	0.760393i	−0.997614	+	0.0690436i	$0.978005\pi$
$32$	−0.955573	+	0.294755i	−0.168923	+	0.0521058i
$33$	−0.216090	+	2.88352i	−0.0376164	+	0.501957i
$34$	2.76874	+	3.47189i	0.474836	+	0.595425i
$35$		0			0
$36$	0.997592	−	1.25094i	0.166265	−	0.208490i
$37$	−1.05016	−	0.974406i	−0.172645	−	0.160191i	0.589118	−	0.808047i	$-0.299475\pi$
$37$	−1.05016	−	0.974406i	−0.172645	−	0.160191i	−0.761763	+	0.647856i	$0.775666\pi$
$38$	1.37620	+	0.207429i	0.223249	+	0.0336494i
$39$	11.2056	+	7.63987i	1.79434	+	1.22336i
$40$	−1.33316	+	0.200941i	−0.210791	+	0.0317716i
$41$	5.29397	+	2.54944i	0.826779	+	0.398156i	0.798906	−	0.601456i	$-0.205412\pi$
$41$	5.29397	+	2.54944i	0.826779	+	0.398156i	0.0278726	+	0.999611i	$0.491127\pi$
$42$		0			0
$43$	−7.44405	+	3.58487i	−1.13521	+	0.546687i	−0.904558	−	0.426350i	$-0.859799\pi$
$43$	−7.44405	+	3.58487i	−1.13521	+	0.546687i	−0.230649	+	0.973037i	$0.574085\pi$
$44$	1.11395	−	0.759477i	0.167934	−	0.114496i
$45$	1.58131	−	1.46724i	0.235728	−	0.218724i
$46$	−0.419634	−	5.59963i	−0.0618717	−	0.825621i
$47$	1.40886	+	3.58972i	0.205503	+	0.523614i	0.996051	−	0.0887870i	$-0.0282990\pi$
$47$	1.40886	+	3.58972i	0.205503	+	0.523614i	−0.790547	+	0.612401i	$0.790204\pi$
$48$	−2.14476			−0.309570
$49$		0			0
$50$	3.18231			0.450047
$51$	3.47962	+	8.86592i	0.487244	+	1.24148i
$52$	−0.472549	−	6.30573i	−0.0655307	−	0.874447i
$53$	9.79429	−	9.08777i	1.34535	−	1.24830i	0.402359	−	0.915482i	$-0.368190\pi$
$53$	9.79429	−	9.08777i	1.34535	−	1.24830i	0.942990	−	0.332820i	$-0.108000\pi$
$54$	−2.48090	+	1.69145i	−0.337608	+	0.230177i
$55$	1.63768	−	0.788665i	0.220825	−	0.106344i
$56$		0			0
$57$	2.68936	+	1.29513i	0.356214	+	0.171544i
$58$	6.04593	−	0.911277i	0.793869	−	0.119657i
$59$	−5.57024	−	3.79772i	−0.725183	−	0.494422i	0.143586	−	0.989638i	$-0.454136\pi$
$59$	−5.57024	−	3.79772i	−0.725183	−	0.494422i	−0.868770	+	0.495216i	$0.835089\pi$
$60$	−2.85931	−	0.430972i	−0.369135	−	0.0556382i
$61$	−7.60489	−	7.05630i	−0.973706	−	0.903467i	0.0216465	−	0.999766i	$-0.493109\pi$
$61$	−7.60489	−	7.05630i	−0.973706	−	0.903467i	−0.995352	+	0.0962985i	$0.969300\pi$
$62$	−3.04802	+	3.82210i	−0.387099	+	0.485407i
$63$		0			0
$64$	0.623490	+	0.781831i	0.0779362	+	0.0977289i
$65$	0.637098	−	8.50148i	0.0790223	−	1.05448i
$66$	2.76314	−	0.852316i	0.340119	−	0.104913i
$67$	5.19393	+	8.99615i	0.634539	+	1.09905i	0.986613	+	0.163082i	$0.0521435\pi$
$67$	5.19393	+	8.99615i	0.634539	+	1.09905i	−0.352073	+	0.935972i	$0.614523\pi$
$68$	2.22036	−	3.84578i	0.269258	−	0.466369i
$69$	2.67995	−	11.7416i	0.322628	−	1.41352i
$70$		0			0
$71$	−1.29530	−	5.67509i	−0.153724	−	0.673509i	−0.991783	−	0.127930i	$-0.959167\pi$
$71$	−1.29530	−	5.67509i	−0.153724	−	0.673509i	0.838059	−	0.545579i	$-0.183690\pi$
$72$	−1.52893	−	0.471612i	−0.180186	−	0.0555800i
$73$	−2.80716	+	7.15253i	−0.328553	+	0.837140i	0.667183	+	0.744894i	$0.267500\pi$
$73$	−2.80716	+	7.15253i	−0.328553	+	0.837140i	−0.995736	+	0.0922461i	$0.970595\pi$
$74$	−0.523383	+	1.33356i	−0.0608420	+	0.155023i
$75$	6.52208	+	2.01180i	0.753105	+	0.232302i
$76$	−0.309692	−	1.35685i	−0.0355241	−	0.155641i
$77$		0			0
$78$	3.01788	−	13.2222i	0.341707	−	1.49712i
$79$	2.89060	−	5.00666i	0.325218	−	0.563294i	−0.656339	−	0.754466i	$-0.727896\pi$
$79$	2.89060	−	5.00666i	0.325218	−	0.563294i	0.981556	+	0.191173i	$0.0612290\pi$
$80$	0.674108	+	1.16759i	0.0753676	+	0.130540i
$81$	−10.7406	+	3.31305i	−1.19340	+	0.368116i
$82$	0.439103	−	5.85943i	0.0484909	−	0.647066i
$83$	4.84202	+	6.07170i	0.531480	+	0.666455i	0.973002	−	0.230795i	$-0.0741327\pi$
$83$	4.84202	+	6.07170i	0.531480	+	0.666455i	−0.441522	+	0.897250i	$0.645561\pi$
$84$		0			0
$85$	3.73287	−	4.68086i	0.404886	−	0.507711i
$86$	6.05668	+	5.61978i	0.653108	+	0.605996i
$87$	12.9671	+	1.95447i	1.39022	+	0.209542i
$88$	−1.11395	−	0.759477i	−0.118747	−	0.0809606i
$89$	−10.2854	+	1.55027i	−1.09025	+	0.164328i	−0.669472	−	0.742837i	$-0.733480\pi$
$89$	−10.2854	+	1.55027i	−1.09025	+	0.164328i	−0.420774	+	0.907165i	$0.638242\pi$
$90$	−1.94354	−	0.935958i	−0.204867	−	0.0986587i
$91$		0			0
$92$	−5.05924	+	2.43640i	−0.527462	+	0.254012i
$93$	−8.66311	+	5.90641i	−0.898322	+	0.612466i
$94$	2.82686	−	2.62294i	0.291568	−	0.270536i
$95$	−0.140221	−	1.87112i	−0.0143864	−	0.191973i
$96$	0.783570	+	1.99650i	0.0799728	+	0.203767i
$97$	3.70350			0.376033			0.188017	−	0.982166i	$-0.439794\pi$
$97$	3.70350			0.376033			0.188017	+	0.982166i	$0.439794\pi$
$98$		0			0
$99$	2.15716			0.216803
$100$	−1.16263	−	2.96233i	−0.116263	−	0.296233i
$101$	1.07577	+	14.3552i	0.107043	+	1.42839i	0.749466	+	0.662043i	$0.230310\pi$
$101$	1.07577	+	14.3552i	0.107043	+	1.42839i	−0.642423	+	0.766351i	$0.722071\pi$
$102$	6.98180	−	6.47817i	0.691301	−	0.641434i
$103$	1.38390	−	0.943529i	0.136360	−	0.0929687i	−0.493219	−	0.869905i	$-0.664180\pi$
$103$	1.38390	−	0.943529i	0.136360	−	0.0929687i	0.629579	+	0.776937i	$0.283227\pi$
$104$	−5.69719	+	2.74362i	−0.558656	+	0.269034i
$105$		0			0
$106$	−12.0378	−	5.79711i	−1.16922	−	0.563065i
$107$	−14.2890	+	2.15372i	−1.38137	+	0.208208i	−0.797342	−	0.603528i	$-0.793761\pi$
$107$	−14.2890	+	2.15372i	−1.38137	+	0.208208i	−0.584025	+	0.811735i	$0.698523\pi$
$108$	2.48090	+	1.69145i	0.238725	+	0.162760i
$109$	−18.3456	−	2.76515i	−1.75719	−	0.264854i	−0.810208	−	0.586143i	$-0.800646\pi$
$109$	−18.3456	−	2.76515i	−1.75719	−	0.264854i	−0.946981	+	0.321289i	$0.895884\pi$
$110$	−1.33246	−	1.23634i	−0.127045	−	0.117881i
$111$	−1.91571	+	2.40222i	−0.181831	+	0.228009i
$112$		0			0
$113$	−0.715156	−	0.896778i	−0.0672763	−	0.0843618i	0.747055	−	0.664763i	$-0.231467\pi$
$113$	−0.715156	−	0.896778i	−0.0672763	−	0.0843618i	−0.814331	+	0.580401i	$0.802896\pi$
$114$	0.223066	−	2.97662i	0.0208921	−	0.278786i
$115$	−7.23434	+	2.23150i	−0.674606	+	0.208088i
$116$	−3.05711	−	5.29507i	−0.283845	−	0.491635i
$117$	5.05877	−	8.76204i	0.467683	−	0.810051i
$118$	−1.50017	+	6.57265i	−0.138101	+	0.605062i
$119$		0			0
$120$	0.643443	+	2.81911i	0.0587380	+	0.257348i
$121$	−8.77437	−	2.70653i	−0.797670	−	0.246049i
$122$	−3.79015	+	9.65715i	−0.343144	+	0.874317i
$123$	4.60415	−	11.7312i	0.415142	−	1.05776i
$124$	4.67146	+	1.44095i	0.419509	+	0.129401i
$125$	−2.45475	−	10.7549i	−0.219559	−	0.961952i
$126$		0			0
$127$	−2.98988	+	13.0995i	−0.265309	+	1.16240i	0.650093	+	0.759855i	$0.274730\pi$
$127$	−2.98988	+	13.0995i	−0.265309	+	1.16240i	−0.915402	+	0.402541i	$0.868127\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	8.86032	+	15.3465i	0.780107	+	1.35119i
$130$	−8.14657	+	2.51288i	−0.714501	+	0.220394i
$131$	−1.14473	+	15.2754i	−0.100015	+	1.33461i	0.691017	+	0.722839i	$0.257163\pi$
$131$	−1.14473	+	15.2754i	−0.100015	+	1.33461i	−0.791032	+	0.611775i	$0.790456\pi$
$132$	−1.80289	−	2.26075i	−0.156921	−	0.196773i
$133$		0			0
$134$	6.47672	−	8.12155i	0.559504	−	0.701595i
$135$	2.96755	+	2.75348i	0.255406	+	0.236982i
$136$	−4.39112	−	0.661855i	−0.376535	−	0.0567536i
$137$	1.44531	+	0.985399i	0.123482	+	0.0841883i	0.623486	−	0.781835i	$-0.285716\pi$
$137$	1.44531	+	0.985399i	0.123482	+	0.0841883i	−0.500004	+	0.866023i	$0.666668\pi$
$138$	−11.9090	+	1.79500i	−1.01377	+	0.152801i
$139$	1.54942	+	0.746161i	0.131420	+	0.0632885i	0.498438	−	0.866925i	$-0.333907\pi$
$139$	1.54942	+	0.746161i	0.131420	+	0.0632885i	−0.367018	+	0.930214i	$0.619621\pi$
$140$		0			0
$141$	7.45176	−	3.58858i	0.627551	−	0.302213i
$142$	−4.80956	+	3.27911i	−0.403610	+	0.275176i
$143$	6.24950	−	5.79869i	0.522610	−	0.484911i
$144$	0.119569	+	1.59554i	0.00996409	+	0.132962i
$145$	−3.01161	−	7.67346i	−0.250101	−	0.637246i
$146$	7.68367			0.635905
$147$		0			0
$148$	1.43259			0.117758
$149$	−2.08287	−	5.30707i	−0.170635	−	0.434772i	0.819817	−	0.572625i	$-0.194075\pi$
$149$	−2.08287	−	5.30707i	−0.170635	−	0.434772i	−0.990453	+	0.137853i	$0.955980\pi$
$150$	−0.510056	−	6.80622i	−0.0416459	−	0.555726i
$151$	−14.0347	+	13.0223i	−1.14213	+	1.05974i	−0.144601	+	0.989490i	$0.546190\pi$
$151$	−14.0347	+	13.0223i	−1.14213	+	1.05974i	−0.997529	+	0.0702517i	$0.977620\pi$
$152$	−1.14991	+	0.783997i	−0.0932702	+	0.0635906i
$153$	6.40157	−	3.08283i	0.517536	−	0.249232i
$154$		0			0
$155$	5.93824	+	2.85971i	0.476971	+	0.229697i
$156$	−13.4107	+	2.02134i	−1.07372	+	0.161837i
$157$	−7.78113	−	5.30508i	−0.621002	−	0.423392i	0.211528	−	0.977372i	$-0.432156\pi$
$157$	−7.78113	−	5.30508i	−0.621002	−	0.423392i	−0.832530	+	0.553980i	$0.813108\pi$
$158$	−5.71663	−	0.861643i	−0.454790	−	0.0685486i
$159$	−21.0064	−	19.4911i	−1.66592	−	1.54575i
$160$	0.840599	−	1.05408i	0.0664552	−	0.0833322i
$161$		0			0
$162$	7.00802	+	8.78778i	0.550602	+	0.690434i
$163$	−0.479907	+	6.40391i	−0.0375892	+	0.501593i	0.946356	+	0.323125i	$0.104733\pi$
$163$	−0.479907	+	6.40391i	−0.0375892	+	0.501593i	−0.983946	+	0.178469i	$0.942886\pi$
$164$	−5.61481	+	1.73194i	−0.438443	+	0.135242i
$165$	−1.94926	−	3.37621i	−0.151749	−	0.262838i
$166$	3.88300	−	6.72555i	0.301379	−	0.522004i
$167$	2.52705	−	11.0717i	0.195549	−	0.856755i	−0.777998	−	0.628267i	$-0.783765\pi$
$167$	2.52705	−	11.0717i	0.195549	−	0.856755i	0.973547	−	0.228488i	$-0.0733782\pi$
$168$		0			0
$169$	−6.00483	−	26.3089i	−0.461910	−	2.02376i
$170$	−5.72106	−	1.76471i	−0.438785	−	0.135347i
$171$	0.813544	−	2.07288i	0.0622133	−	0.158517i
$172$	3.01855	−	7.69114i	0.230162	−	0.586444i
$173$	14.9022	+	4.59673i	1.13300	+	0.349483i	0.803871	−	0.594803i	$-0.202770\pi$
$173$	14.9022	+	4.59673i	1.13300	+	0.349483i	0.329125	+	0.944286i	$0.393246\pi$
$174$	−2.91804	−	12.7848i	−0.221216	−	0.969211i
$175$		0			0
$176$	−0.300006	+	1.31441i	−0.0226138	+	0.0990777i
$177$	−7.22966	+	12.5221i	−0.543414	+	0.941221i
$178$	5.20077	+	9.00800i	0.389814	+	0.675178i
$179$	5.41339	−	1.66981i	0.404616	−	0.124807i	−0.0857657	−	0.996315i	$-0.527334\pi$
$179$	5.41339	−	1.66981i	0.404616	−	0.124807i	0.490382	+	0.871508i	$0.336857\pi$
$180$	−0.161205	+	2.15113i	−0.0120155	+	0.160336i
$181$	−3.98556	−	4.99774i	−0.296245	−	0.371479i	0.611326	−	0.791379i	$-0.290637\pi$
$181$	−3.98556	−	4.99774i	−0.296245	−	0.371479i	−0.907570	+	0.419900i	$0.862065\pi$
$182$		0			0
$183$	−13.8729	+	17.3961i	−1.02551	+	1.28595i
$184$	4.11633	+	3.81940i	0.303460	+	0.281570i
$185$	1.90986	+	0.287866i	0.140416	+	0.0211643i
$186$	8.66311	+	5.90641i	0.635210	+	0.433079i
$187$	5.92018	−	0.892324i	0.432926	−	0.0652532i
$188$	−3.47440	−	1.67318i	−0.253396	−	0.122029i
$189$		0			0
$190$	−1.69055	+	0.814127i	−0.122646	+	0.0590630i
$191$	11.9599	−	8.15411i	0.865386	−	0.590010i	−0.0472041	−	0.998885i	$-0.515031\pi$
$191$	11.9599	−	8.15411i	0.865386	−	0.590010i	0.912590	+	0.408875i	$0.134079\pi$
$192$	1.57222	−	1.45881i	0.113465	−	0.105281i
$193$	−0.293087	−	3.91098i	−0.0210969	−	0.281519i	−0.997768	−	0.0667774i	$-0.978728\pi$
$193$	−0.293087	−	3.91098i	−0.0210969	−	0.281519i	0.976671	−	0.214741i	$-0.0688908\pi$
$194$	−1.35304	−	3.44749i	−0.0971426	−	0.247515i
$195$	−18.2848			−1.30940
$196$		0			0
$197$	−9.22994			−0.657606			−0.328803	−	0.944399i	$-0.606645\pi$
$197$	−9.22994			−0.657606			−0.328803	+	0.944399i	$0.606645\pi$
$198$	−0.788100	−	2.00805i	−0.0560079	−	0.142706i
$199$	−1.22235	−	16.3112i	−0.0866503	−	1.15627i	−0.855838	−	0.517245i	$-0.826958\pi$
$199$	−1.22235	−	16.3112i	−0.0866503	−	1.15627i	0.769187	−	0.639023i	$-0.220661\pi$
$200$	−2.33280	+	2.16452i	−0.164954	+	0.153055i
$201$	18.4082	−	12.5505i	1.29841	−	0.885243i
$202$	12.9698	−	6.24594i	0.912554	−	0.439463i
$203$		0			0
$204$	−8.58109	−	4.13244i	−0.600797	−	0.289328i
$205$	−7.83345	+	1.18070i	−0.547112	+	0.0824638i
$206$	−1.38390	−	0.943529i	−0.0964211	−	0.0657388i
$207$	−8.88426	−	1.33909i	−0.617498	−	0.0930729i
$208$	4.63539	+	4.30101i	0.321406	+	0.298221i
$209$	1.16990	−	1.46701i	0.0809236	−	0.101475i
$210$		0			0
$211$	−14.2940	−	17.9241i	−0.984040	−	1.23395i	−0.972233	−	0.234017i	$-0.924813\pi$
$211$	−14.2940	−	17.9241i	−0.984040	−	1.23395i	−0.0118073	−	0.999930i	$-0.503758\pi$
$212$	−0.998467	+	13.3236i	−0.0685750	+	0.915070i
$213$	−11.9301	+	3.67994i	−0.817436	+	0.252146i
$214$	7.22519	+	12.5144i	0.493904	+	0.855466i
$215$	5.56967	−	9.64695i	0.379848	−	0.657917i
$216$	0.668151	−	2.92736i	0.0454619	−	0.199182i
$217$		0			0
$218$	4.12839	+	18.0877i	0.279610	+	1.22505i
$219$	15.7475	+	4.85746i	1.06412	+	0.328237i
$220$	−0.664076	+	1.69204i	−0.0447720	+	0.114077i
$221$	10.2589	−	26.1394i	0.690092	−	1.75832i
$222$	2.93605	+	0.905653i	0.197055	+	0.0607834i
$223$	3.82009	+	16.7369i	0.255812	+	1.12079i	0.925680	+	0.378306i	$0.123493\pi$
$223$	3.82009	+	16.7369i	0.255812	+	1.12079i	−0.669868	+	0.742480i	$0.733649\pi$
$224$		0			0
$225$	1.13302	−	4.96408i	0.0755346	−	0.330939i
$226$	−0.573511	+	0.993350i	−0.0381494	+	0.0660767i
$227$	2.31866	+	4.01603i	0.153895	+	0.266553i	0.932656	−	0.360767i	$-0.117485\pi$
$227$	2.31866	+	4.01603i	0.153895	+	0.266553i	−0.778761	+	0.627320i	$0.784152\pi$
$228$	−2.85235	+	0.879833i	−0.188901	+	0.0582684i
$229$	−0.379305	+	5.06148i	−0.0250652	+	0.334472i	0.970548	+	0.240908i	$0.0774451\pi$
$229$	−0.379305	+	5.06148i	−0.0250652	+	0.334472i	−0.995613	+	0.0935642i	$0.970174\pi$
$230$	4.72025	+	5.91900i	0.311244	+	0.390287i
$231$		0			0
$232$	−3.81215	+	4.78029i	−0.250280	+	0.313841i
$233$	7.89264	+	7.32330i	0.517064	+	0.479765i	0.895000	−	0.446066i	$-0.147175\pi$
$233$	7.89264	+	7.32330i	0.517064	+	0.479765i	−0.377936	+	0.925832i	$0.623366\pi$
$234$	−10.0045	−	1.50794i	−0.654016	−	0.0985771i
$235$	−4.29571	−	2.92876i	−0.280221	−	0.191051i
$236$	6.66638	−	1.00480i	0.433945	−	0.0654066i
$237$	−11.1714	−	5.37986i	−0.725660	−	0.349459i
$238$		0			0
$239$	23.8771	−	11.4986i	1.54448	−	0.743784i	0.548743	−	0.835991i	$-0.315107\pi$
$239$	23.8771	−	11.4986i	1.54448	−	0.743784i	0.995740	+	0.0922073i	$0.0293922\pi$
$240$	2.38916	−	1.62890i	0.154219	−	0.105145i
$241$	7.43589	−	6.89949i	0.478988	−	0.444436i	−0.403355	−	0.915044i	$-0.632156\pi$
$241$	7.43589	−	6.89949i	0.478988	−	0.444436i	0.882342	+	0.470608i	$0.155965\pi$
$242$	0.686195	+	9.15664i	0.0441103	+	0.588611i
$243$	5.51636	+	14.0555i	0.353875	+	0.901658i
$244$	10.3743			0.664145
$245$		0			0
$246$	−12.6023			−0.803495
$247$	−3.21521	−	8.19221i	−0.204579	−	0.521258i
$248$	−0.365329	−	4.87498i	−0.0231984	−	0.309561i
$249$	12.2099	−	11.3291i	0.773769	−	0.717953i
$250$	−9.11468	+	6.21428i	−0.576463	+	0.393026i
$251$	−5.07195	+	2.44252i	−0.320138	+	0.154171i	−0.587050	−	0.809550i	$-0.699711\pi$
$251$	−5.07195	+	2.44252i	−0.320138	+	0.154171i	0.266912	+	0.963721i	$0.413997\pi$
$252$		0			0
$253$	−6.82095	−	3.28480i	−0.428830	−	0.206513i
$254$	13.2863	−	2.00259i	0.833659	−	0.125654i
$255$	−10.6096	−	7.23349i	−0.664397	−	0.452978i
$256$	−0.988831	−	0.149042i	−0.0618019	−	0.00931514i
$257$	−3.06928	−	2.84787i	−0.191456	−	0.177645i	0.578620	−	0.815597i	$-0.303591\pi$
$257$	−3.06928	−	2.84787i	−0.191456	−	0.177645i	−0.770076	+	0.637952i	$0.779782\pi$
$258$	11.0486	−	13.8546i	0.687858	−	0.862547i
$259$		0			0
$260$	5.31545	+	6.66536i	0.329650	+	0.413368i
$261$	0.731072	−	9.75547i	0.0452522	−	0.603849i
$262$	14.6376	−	4.51511i	0.904316	−	0.278945i
$263$	10.5009	+	18.1882i	0.647516	+	1.12153i	0.983714	+	0.179739i	$0.0575253\pi$
$263$	10.5009	+	18.1882i	0.647516	+	1.12153i	−0.336199	+	0.941791i	$0.609141\pi$
$264$	−1.44580	+	2.50420i	−0.0889830	+	0.154123i
$265$	−4.00838	+	17.5619i	−0.246233	+	1.07882i
$266$		0			0
$267$	4.96419	+	21.7495i	0.303803	+	1.33105i
$268$	−9.92635	−	3.06187i	−0.606349	−	0.187034i
$269$	4.11287	−	10.4794i	0.250766	−	0.638942i	−0.748953	−	0.662623i	$-0.769443\pi$
$269$	4.11287	−	10.4794i	0.250766	−	0.638942i	0.999720	+	0.0236807i	$0.00753851\pi$
$270$	1.47898	−	3.76837i	0.0900077	−	0.229336i
$271$	6.27044	+	1.93417i	0.380902	+	0.117493i	0.479293	−	0.877655i	$-0.340893\pi$
$271$	6.27044	+	1.93417i	0.380902	+	0.117493i	−0.0983906	+	0.995148i	$0.531369\pi$
$272$	0.988153	+	4.32938i	0.0599156	+	0.262507i
$273$		0			0
$274$	0.389249	−	1.70541i	0.0235154	−	0.103028i
$275$	2.14522	−	3.71564i	0.129362	−	0.224061i
$276$	6.02178	+	10.4300i	0.362469	+	0.627814i
$277$	−23.4196	+	7.22399i	−1.40715	+	0.434047i	−0.903026	−	0.429586i	$-0.858660\pi$
$277$	−23.4196	+	7.22399i	−1.40715	+	0.434047i	−0.504121	+	0.863633i	$0.668183\pi$
$278$	0.128515	−	1.71492i	0.00770783	−	0.102854i
$279$	4.87687	+	6.11540i	0.291971	+	0.366120i
$280$		0			0
$281$	2.25301	−	2.82518i	0.134403	−	0.168536i	−0.710075	−	0.704126i	$-0.751339\pi$
$281$	2.25301	−	2.82518i	0.134403	−	0.168536i	0.844478	+	0.535589i	$0.179911\pi$
$282$	−6.06295	−	5.62559i	−0.361043	−	0.334999i
$283$	14.1119	+	2.12703i	0.838866	+	0.126439i	0.554403	−	0.832248i	$-0.312947\pi$
$283$	14.1119	+	2.12703i	0.838866	+	0.126439i	0.284463	+	0.958687i	$0.408185\pi$
$284$	4.80956	+	3.27911i	0.285395	+	0.194579i
$285$	−3.97943	+	0.599802i	−0.235721	+	0.0355292i
$286$	−7.68105	−	3.69900i	−0.454190	−	0.218726i
$287$		0			0
$288$	1.44156	−	0.694220i	0.0849448	−	0.0409073i
$289$	2.24736	−	1.53222i	0.132198	−	0.0901308i
$290$	−6.04276	+	5.60686i	−0.354843	+	0.329246i
$291$	−0.593591	−	7.92092i	−0.0347969	−	0.464333i
$292$	−2.80716	−	7.15253i	−0.164277	−	0.418570i
$293$	12.5071			0.730675			0.365338	−	0.930875i	$-0.380954\pi$
$293$	12.5071			0.730675			0.365338	+	0.930875i	$0.380954\pi$
$294$		0			0
$295$	9.08925			0.529196
$296$	−0.523383	−	1.33356i	−0.0304210	−	0.0775114i
$297$	0.302523	+	4.03689i	0.0175542	+	0.234244i
$298$	−4.17925	+	3.87778i	−0.242098	+	0.224634i
$299$	−29.3381	+	20.0024i	−1.69667	+	1.15677i
$300$	−6.14939	+	2.96139i	−0.355035	+	0.170976i
$301$		0			0
$302$	17.2496	+	8.30697i	0.992603	+	0.478012i
$303$	30.5300	−	4.60165i	1.75390	−	0.264358i
$304$	1.14991	+	0.783997i	0.0659520	+	0.0449653i
$305$	13.8306	+	2.08462i	0.791935	+	0.119365i
$306$	−5.20849	−	4.83277i	−0.297749	−	0.276271i
$307$	−13.5861	+	17.0364i	−0.775400	+	0.972321i	−0.999998	−	0.00213071i	$-0.999322\pi$
$307$	−13.5861	+	17.0364i	−0.775400	+	0.972321i	0.224598	+	0.974452i	$0.427893\pi$
$308$		0			0
$309$	−2.23980	−	2.80862i	−0.127418	−	0.159777i
$310$	0.492542	−	6.57252i	0.0279745	−	0.373294i
$311$	6.14038	−	1.89406i	0.348189	−	0.107402i	−0.115727	−	0.993281i	$-0.536920\pi$
$311$	6.14038	−	1.89406i	0.348189	−	0.107402i	0.463917	+	0.885879i	$0.346444\pi$
$312$	6.78111	+	11.7452i	0.383905	+	0.664942i
$313$	8.81309	−	15.2647i	0.498145	−	0.862813i	−0.501852	−	0.864953i	$-0.667348\pi$
$313$	8.81309	−	15.2647i	0.498145	−	0.862813i	0.999998	+	0.00214037i	$0.000681302\pi$
$314$	−2.09560	+	9.18142i	−0.118261	+	0.518137i
$315$		0			0
$316$	1.28644	+	5.63625i	0.0723678	+	0.317064i
$317$	−2.06604	−	0.637289i	−0.116040	−	0.0357937i	0.236191	−	0.971707i	$-0.424101\pi$
$317$	−2.06604	−	0.637289i	−0.116040	−	0.0357937i	−0.352232	+	0.935913i	$0.614577\pi$
$318$	−10.4693	+	26.6753i	−0.587087	+	1.49587i
$319$	3.01161	−	7.67346i	0.168618	−	0.429631i
$320$	−1.28832	−	0.397394i	−0.0720192	−	0.0222150i
$321$	6.89651	+	30.2156i	0.384926	+	1.68647i
$322$		0			0
$323$	1.37526	−	6.02539i	0.0765213	−	0.335262i
$324$	5.62000	−	9.73412i	0.312222	−	0.540785i
$325$	−10.0615	−	17.4271i	−0.558113	−	0.966680i
$326$	6.13656	−	1.89288i	0.339873	−	0.104837i
$327$	−2.97361	+	39.6801i	−0.164441	+	2.19432i
$328$	3.66354	+	4.59393i	0.202285	+	0.253657i
$329$		0			0
$330$	−2.43068	+	3.04798i	−0.133805	+	0.167786i
$331$	−13.7841	−	12.7897i	−0.757640	−	0.702987i	0.203492	−	0.979077i	$-0.434771\pi$
$331$	−13.7841	−	12.7897i	−0.757640	−	0.702987i	−0.961132	+	0.276089i	$0.910961\pi$
$332$	−7.67925	−	1.15746i	−0.421454	−	0.0635239i
$333$	1.89387	+	1.29122i	0.103783	+	0.0707583i
$334$	−11.2296	+	1.69259i	−0.614456	+	0.0926144i
$335$	−12.6181	−	6.07658i	−0.689403	−	0.331999i
$336$		0			0
$337$	6.56597	−	3.16200i	0.357671	−	0.172245i	−0.246415	−	0.969164i	$-0.579253\pi$
$337$	6.56597	−	3.16200i	0.357671	−	0.172245i	0.604086	+	0.796919i	$0.293538\pi$
$338$	−22.2964	+	15.2015i	−1.21277	+	0.826850i
$339$	−1.80337	+	1.67329i	−0.0979458	+	0.0908805i
$340$	0.447413	+	5.97031i	0.0242644	+	0.323786i
$341$	2.40795	+	6.13534i	0.130398	+	0.332248i
$342$	−2.22681			−0.120412
$343$		0			0
$344$	−8.26228			−0.445472
$345$	5.93216	+	15.1149i	0.319377	+	0.813759i
$346$	−1.16542	−	15.5515i	−0.0626535	−	0.836053i
$347$	−10.9382	+	10.1491i	−0.587192	+	0.544835i	−0.916833	−	0.399272i	$-0.869263\pi$
$347$	−10.9382	+	10.1491i	−0.587192	+	0.544835i	0.329640	+	0.944107i	$0.393072\pi$
$348$	−10.8349	+	7.38713i	−0.580813	+	0.395992i
$349$	22.6289	−	10.8975i	1.21130	−	0.583329i	0.284420	−	0.958700i	$-0.408199\pi$
$349$	22.6289	−	10.8975i	1.21130	−	0.583329i	0.926875	+	0.375371i	$0.122485\pi$
$350$		0			0
$351$	17.1066	+	8.23812i	0.913084	+	0.439718i
$352$	1.33316	−	0.200941i	0.0710576	−	0.0107102i
$353$	6.11995	+	4.17251i	0.325732	+	0.222080i	0.715134	−	0.698988i	$-0.246366\pi$
$353$	6.11995	+	4.17251i	0.325732	+	0.222080i	−0.389402	+	0.921068i	$0.627318\pi$
$354$	14.2978	+	2.15505i	0.759920	+	0.114540i
$355$	5.75300	+	5.33800i	0.305338	+	0.283312i
$356$	6.48525	−	8.13225i	0.343718	−	0.431008i
$357$		0			0
$358$	−3.53212	−	4.42913i	−0.186678	−	0.234087i
$359$	1.04217	−	13.9069i	0.0550039	−	0.733976i	−0.899717	−	0.436473i	$-0.856227\pi$
$359$	1.04217	−	13.9069i	0.0550039	−	0.733976i	0.954721	−	0.297502i	$-0.0961536\pi$
$360$	2.06133	−	0.635835i	0.108641	−	0.0335115i
$361$	8.53152	+	14.7770i	0.449028	+	0.777739i
$362$	−3.19617	+	5.53594i	−0.167987	+	0.290962i
$363$	−4.38230	+	19.2001i	−0.230011	+	1.00775i
$364$		0			0
$365$	−2.30515	−	10.0995i	−0.120657	−	0.528633i
$366$	21.2619	+	6.55842i	1.11138	+	0.342814i
$367$	−0.251857	+	0.641720i	−0.0131468	+	0.0334975i	−0.937296	−	0.348533i	$-0.886680\pi$
$367$	−0.251857	+	0.641720i	−0.0131468	+	0.0334975i	0.924150	+	0.382031i	$0.124775\pi$
$368$	2.05151	−	5.22717i	0.106942	−	0.272485i
$369$	−8.98377	−	2.77113i	−0.467676	−	0.144259i
$370$	−0.429785	−	1.88301i	−0.0223435	−	0.0978931i
$371$		0			0
$372$	2.33313	−	10.2221i	0.120967	−	0.529992i
$373$	12.1132	−	20.9807i	0.627197	−	1.08634i	−0.360914	−	0.932599i	$-0.617535\pi$
$373$	12.1132	−	20.9807i	0.627197	−	1.08634i	0.988112	−	0.153739i	$-0.0491314\pi$
$374$	−2.99353	−	5.18494i	−0.154792	−	0.268107i
$375$	−22.6089	+	6.97391i	−1.16752	+	0.360131i
$376$	−0.288181	+	3.84551i	−0.0148618	+	0.198317i
$377$	−24.1058	−	30.2277i	−1.24151	−	1.55681i
$378$		0			0
$379$	−2.46956	+	3.09673i	−0.126853	+	0.159069i	−0.841202	−	0.540721i	$-0.818151\pi$
$379$	−2.46956	+	3.09673i	−0.126853	+	0.159069i	0.714349	+	0.699790i	$0.246723\pi$
$380$	1.37548	+	1.27626i	0.0705605	+	0.0654706i
$381$	28.4961	+	4.29509i	1.45990	+	0.220044i
$382$	−11.9599	−	8.15411i	−0.611921	−	0.417200i
$383$	1.07640	−	0.162241i	0.0550014	−	0.00829013i	−0.121484	−	0.992593i	$-0.538765\pi$
$383$	1.07640	−	0.162241i	0.0550014	−	0.00829013i	0.176485	+	0.984303i	$0.443527\pi$
$384$	−1.93237	−	0.930578i	−0.0986106	−	0.0474884i
$385$		0			0
$386$	−3.53355	+	1.70167i	−0.179853	+	0.0866127i
$387$	10.9227	−	7.44695i	0.555230	−	0.378550i
$388$	−2.71486	+	2.51902i	−0.137826	+	0.127884i
$389$	1.26864	+	16.9288i	0.0643225	+	0.858324i	0.932292	+	0.361707i	$0.117806\pi$
$389$	1.26864	+	16.9288i	0.0643225	+	0.858324i	−0.867969	+	0.496618i	$0.834575\pi$
$390$	6.68019	+	17.0208i	0.338265	+	0.861884i
$391$	−24.9361			−1.26107
$392$		0			0
$393$	32.8539			1.65726
$394$	3.37208	+	8.59191i	0.169883	+	0.432854i
$395$	0.582469	+	7.77251i	0.0293072	+	0.391078i
$396$	−1.58131	+	1.46724i	−0.0794640	+	0.0737318i
$397$	7.89198	−	5.38066i	0.396087	−	0.270048i	−0.348855	−	0.937177i	$-0.613429\pi$
$397$	7.89198	−	5.38066i	0.396087	−	0.270048i	0.744942	+	0.667129i	$0.232477\pi$
$398$	−14.7371	+	7.09699i	−0.738702	+	0.355740i
$399$		0			0
$400$	2.86716	+	1.38075i	0.143358	+	0.0690377i
$401$	17.0744	−	2.57355i	0.852655	−	0.128517i	0.291849	−	0.956464i	$-0.405730\pi$
$401$	17.0744	−	2.57355i	0.852655	−	0.128517i	0.560806	+	0.827947i	$0.310491\pi$
$402$	−18.4082	−	12.5505i	−0.918117	−	0.625962i
$403$	30.5676	+	4.60733i	1.52268	+	0.229507i
$404$	−10.5526	−	9.79138i	−0.525011	−	0.487139i
$405$	9.44833	−	11.8478i	0.469491	−	0.588724i
$406$		0			0
$407$	1.20423	+	1.51006i	0.0596915	+	0.0748508i
$408$	−0.711751	+	9.49766i	−0.0352369	+	0.470204i
$409$	−4.22390	+	1.30290i	−0.208858	+	0.0644243i	−0.397419	−	0.917637i	$-0.630094\pi$
$409$	−4.22390	+	1.30290i	−0.208858	+	0.0644243i	0.188561	+	0.982062i	$0.439618\pi$
$410$	3.96096	+	6.86059i	0.195618	+	0.338821i
$411$	1.87589	−	3.24913i	0.0925306	−	0.160268i
$412$	−0.372710	+	1.63295i	−0.0183621	+	0.0804496i
$413$		0			0
$414$	1.99926	+	8.75934i	0.0982584	+	0.430498i
$415$	−10.0051	−	3.08616i	−0.491130	−	0.151493i
$416$	2.31020	−	5.88629i	0.113267	−	0.288599i
$417$	1.34753	−	3.43344i	0.0659886	−	0.168136i
$418$	−1.79301	−	0.553070i	−0.0876990	−	0.0270516i
$419$	1.06671	+	4.67354i	0.0521120	+	0.228317i	0.994277	−	0.106831i	$-0.0340705\pi$
$419$	1.06671	+	4.67354i	0.0521120	+	0.228317i	−0.942165	+	0.335149i	$0.891213\pi$
$420$		0			0
$421$	−6.49465	+	28.4549i	−0.316530	+	1.38681i	0.527064	+	0.849826i	$0.323293\pi$
$421$	−6.49465	+	28.4549i	−0.316530	+	1.38681i	−0.843593	+	0.536982i	$0.819564\pi$
$422$	−11.4629	+	19.8543i	−0.558005	+	0.966494i
$423$	−3.08505	−	5.34347i	−0.150001	−	0.259808i
$424$	12.7674	−	3.93822i	0.620039	−	0.191257i
$425$	1.05607	−	14.0922i	0.0512268	−	0.683574i
$426$	7.78411	+	9.76097i	0.377141	+	0.472920i
$427$		0			0
$428$	9.00966	−	11.2978i	0.435498	−	0.546098i
$429$	−13.4037	−	12.4368i	−0.647137	−	0.600456i
$430$	−11.0149	−	1.66023i	−0.531187	−	0.0800635i
$431$	−15.1279	−	10.3140i	−0.728684	−	0.496808i	0.141252	−	0.989974i	$-0.454887\pi$
$431$	−15.1279	−	10.3140i	−0.728684	−	0.496808i	−0.869935	+	0.493166i	$0.835840\pi$
$432$	−2.96911	+	0.447521i	−0.142851	+	0.0215313i
$433$	23.2031	+	11.1740i	1.11507	+	0.536989i	0.898366	−	0.439248i	$-0.144755\pi$
$433$	23.2031	+	11.1740i	1.11507	+	0.536989i	0.216704	+	0.976237i	$0.430469\pi$
$434$		0			0
$435$	−15.9290	+	7.67103i	−0.763739	+	0.367798i
$436$	15.3290	−	10.4512i	0.734128	−	0.500520i
$437$	−5.72888	+	5.31562i	−0.274049	+	0.254281i
$438$	−1.23153	−	16.4336i	−0.0588446	−	0.785227i
$439$	−6.84359	−	17.4372i	−0.326627	−	0.832231i	−0.996004	−	0.0893085i	$-0.971534\pi$
$439$	−6.84359	−	17.4372i	−0.326627	−	0.832231i	0.669377	−	0.742923i	$-0.266561\pi$
$440$	1.81769			0.0866549
$441$		0			0
$442$	−28.0805			−1.33565
$443$	−0.826477	−	2.10583i	−0.0392671	−	0.100051i	0.909895	−	0.414839i	$-0.136162\pi$
$443$	−0.826477	−	2.10583i	−0.0392671	−	0.100051i	−0.949162	+	0.314788i	$0.898067\pi$
$444$	−0.229613	−	3.06397i	−0.0108969	−	0.145409i
$445$	10.2800	−	9.53842i	0.487317	−	0.452165i
$446$	14.1843	−	9.67070i	0.671647	−	0.457921i
$447$	−11.0167	+	5.30538i	−0.521074	+	0.250936i
$448$		0			0
$449$	−0.220557	−	0.106215i	−0.0104087	−	0.00501258i	0.428672	−	0.903460i	$-0.358982\pi$
$449$	−0.220557	−	0.106215i	−0.0104087	−	0.00501258i	−0.439081	+	0.898448i	$0.644696\pi$
$450$	−5.03487	+	0.758885i	−0.237346	+	0.0357742i
$451$	−6.54541	−	4.46258i	−0.308211	−	0.210135i
$452$	1.13421	+	0.170955i	0.0533488	+	0.00804103i
$453$	30.1012	+	27.9298i	1.41428	+	1.31226i
$454$	2.89132	−	3.62560i	0.135696	−	0.170158i
$455$		0			0
$456$	1.86109	+	2.33374i	0.0871537	+	0.109287i
$457$	−2.25692	+	30.1165i	−0.105574	+	1.40879i	0.653077	+	0.757292i	$0.273478\pi$
$457$	−2.25692	+	30.1165i	−0.105574	+	1.40879i	−0.758651	+	0.651497i	$0.774141\pi$
$458$	4.85017	−	1.49608i	0.226634	−	0.0699072i
$459$	6.66695	+	11.5475i	0.311186	+	0.538991i
$460$	3.78534	−	6.55641i	0.176493	−	0.305694i
$461$	−5.36722	+	23.5153i	−0.249977	+	1.09522i	0.681615	+	0.731711i	$0.261278\pi$
$461$	−5.36722	+	23.5153i	−0.249977	+	1.09522i	−0.931591	+	0.363508i	$0.881579\pi$
$462$		0			0
$463$	4.43486	+	19.4304i	0.206105	+	0.903006i	0.967130	+	0.254283i	$0.0818395\pi$
$463$	4.43486	+	19.4304i	0.206105	+	0.903006i	−0.761024	+	0.648723i	$0.775303\pi$
$464$	5.84258	+	1.80220i	0.271235	+	0.0836649i
$465$	5.16447	−	13.1589i	0.239497	−	0.610228i
$466$	3.93356	−	10.0226i	0.182219	−	0.464286i
$467$	35.3986	+	10.9190i	1.63805	+	0.505272i	0.970867	−	0.239620i	$-0.0770230\pi$
$467$	35.3986	+	10.9190i	1.63805	+	0.505272i	0.667185	+	0.744892i	$0.267499\pi$
$468$	2.25136	+	9.86386i	0.104069	+	0.455957i
$469$		0			0
$470$	−1.15691	+	5.06876i	−0.0533643	+	0.233804i
$471$	−10.0992	+	17.4923i	−0.465346	+	0.806003i
$472$	−3.37084	−	5.83847i	−0.155156	−	0.268737i
$473$	10.6444	−	3.28338i	0.489432	−	0.150970i
$474$	−0.926601	+	12.3646i	−0.0425602	+	0.567927i
$475$	−2.76141	−	3.46270i	−0.126702	−	0.158880i
$476$		0			0
$477$	−13.3288	+	16.7138i	−0.610284	+	0.765272i
$478$	−19.4271	−	18.0257i	−0.888573	−	0.824475i
$479$	15.9964	+	2.41107i	0.730894	+	0.110165i	0.503937	−	0.863740i	$-0.331884\pi$
$479$	15.9964	+	2.41107i	0.730894	+	0.110165i	0.226957	+	0.973905i	$0.427122\pi$
$480$	−2.38916	−	1.62890i	−0.109050	−	0.0743488i
$481$	8.95765	−	1.35015i	0.408434	−	0.0615614i
$482$	−9.13919	−	4.40120i	−0.416279	−	0.200469i
$483$		0			0
$484$	8.27298	−	3.98406i	0.376044	−	0.181093i
$485$	−4.12551	+	2.81272i	−0.187330	+	0.127719i
$486$	11.0685	−	10.2701i	0.502078	−	0.465860i
$487$	−0.0803853	−	1.07267i	−0.00364261	−	0.0486072i	0.995086	−	0.0990115i	$-0.0315681\pi$
$487$	−0.0803853	−	1.07267i	−0.00364261	−	0.0486072i	−0.998729	+	0.0504043i	$0.983949\pi$
$488$	−3.79015	−	9.65715i	−0.171572	−	0.437159i
$489$	13.7734			0.622854
$490$		0			0
$491$	−2.32348			−0.104857			−0.0524286	−	0.998625i	$-0.516696\pi$
$491$	−2.32348			−0.104857			−0.0524286	+	0.998625i	$0.516696\pi$
$492$	4.60415	+	11.7312i	0.207571	+	0.528882i
$493$	−2.02904	−	27.0756i	−0.0913832	−	1.21942i
$494$	−6.45127	+	5.98590i	−0.290256	+	0.269318i
$495$	−2.40297	+	1.63832i	−0.108005	+	0.0736369i
$496$	−4.40452	+	2.12110i	−0.197769	+	0.0952404i
$497$		0			0
$498$	−15.0067	−	7.22686i	−0.672468	−	0.323843i
$499$	−1.32819	+	0.200192i	−0.0594579	+	0.00896183i	−0.178704	−	0.983903i	$-0.557190\pi$
$499$	−1.32819	+	0.200192i	−0.0594579	+	0.00896183i	0.119246	+	0.992865i	$0.461952\pi$
$500$	9.11468	+	6.21428i	0.407621	+	0.277911i
$501$	−24.0848	−	3.63021i	−1.07603	−	0.162186i
$502$	4.12667	+	3.82899i	0.184182	+	0.170896i
$503$	20.9686	−	26.2938i	0.934943	−	1.17238i	−0.0498682	−	0.998756i	$-0.515880\pi$
$503$	20.9686	−	26.2938i	0.934943	−	1.17238i	0.984812	−	0.173626i	$-0.0555484\pi$
$504$		0			0
$505$	−12.1008	−	15.1739i	−0.538478	−	0.675230i
$506$	−0.565758	+	7.54952i	−0.0251510	+	0.335617i
$507$	−55.3061	+	17.0597i	−2.45623	+	0.757647i
$508$	−6.71821	−	11.6363i	−0.298072	−	0.516276i
$509$	−6.35261	+	11.0030i	−0.281574	+	0.487701i	−0.971773	−	0.235919i	$-0.924190\pi$
$509$	−6.35261	+	11.0030i	−0.281574	+	0.487701i	0.690198	+	0.723620i	$0.257523\pi$
$510$	−2.85735	+	12.5189i	−0.126526	+	0.554345i
$511$		0			0
$512$	0.222521	+	0.974928i	0.00983413	+	0.0430861i
$513$	3.99325	+	1.23175i	0.176306	+	0.0543833i
$514$	−1.52968	+	3.89755i	−0.0674712	+	0.171914i
$515$	−0.825008	+	2.10209i	−0.0363542	+	0.0926290i
$516$	−16.9334	−	5.22325i	−0.745449	−	0.229941i
$517$	−1.15691	−	5.06876i	−0.0508809	−	0.222924i
$518$		0			0
$519$	7.44283	−	32.6092i	0.326704	−	1.43138i
$520$	4.26266	−	7.38315i	0.186930	−	0.323772i
$521$	0.948342	+	1.64258i	0.0415476	+	0.0719626i	0.886051	−	0.463587i	$-0.153438\pi$
$521$	0.948342	+	1.64258i	0.0415476	+	0.0719626i	−0.844504	+	0.535550i	$0.820105\pi$
$522$	−9.34820	+	2.88354i	−0.409160	+	0.126209i
$523$	2.72167	−	36.3182i	0.119010	−	1.58808i	−0.543746	−	0.839250i	$-0.682995\pi$
$523$	2.72167	−	36.3182i	0.119010	−	1.58808i	0.662757	−	0.748835i	$-0.269386\pi$
$524$	−9.55073	−	11.9762i	−0.417226	−	0.523184i
$525$		0			0
$526$	13.0945	−	16.4199i	0.570946	−	0.715943i
$527$	15.9139	+	14.7659i	0.693220	+	0.643214i
$528$	2.85931	+	0.430972i	0.124435	+	0.0187556i
$529$	7.04945	+	4.80623i	0.306498	+	0.208967i
$530$	17.8123	−	2.68477i	0.773717	−	0.116619i
$531$	9.71855	+	4.68021i	0.421749	+	0.203104i
$532$		0			0
$533$	−33.4759	+	16.1211i	−1.45000	+	0.698284i
$534$	18.4324	−	12.5670i	0.797649	−	0.543828i
$535$	14.2815	−	13.2513i	0.617443	−	0.572903i
$536$	0.776285	+	10.3588i	0.0335304	+	0.447432i
$537$	−4.43898	−	11.3103i	−0.191556	−	0.488077i
$538$	−11.2576			−0.485351
$539$		0			0
$540$	−4.04821			−0.174207
$541$	−9.36210	−	23.8542i	−0.402508	−	1.02557i	−0.978155	−	0.207876i	$-0.933345\pi$
$541$	−9.36210	−	23.8542i	−0.402508	−	1.02557i	0.575647	−	0.817698i	$-0.304750\pi$
$542$	−0.490377	−	6.54362i	−0.0210635	−	0.281073i
$543$	−10.0502	+	9.32522i	−0.431295	+	0.400184i
$544$	3.66909	−	2.50155i	0.157311	−	0.107253i
$545$	22.5361	−	10.8528i	0.965341	−	0.464884i
$546$		0			0
$547$	15.0226	+	7.23448i	0.642318	+	0.309324i	0.726541	−	0.687123i	$-0.241127\pi$
$547$	15.0226	+	7.23448i	0.642318	+	0.309324i	−0.0842232	+	0.996447i	$0.526841\pi$
$548$	−1.72973	+	0.260715i	−0.0738905	+	0.0111372i
$549$	13.7147	+	9.35054i	0.585330	+	0.399071i
$550$	−4.24253	−	0.639458i	−0.180902	−	0.0272666i
$551$	−6.23785	−	5.78788i	−0.265741	−	0.246572i
$552$	7.50904	−	9.41604i	0.319606	−	0.400773i
$553$		0			0
$554$	15.2808	+	19.1615i	0.649217	+	0.814093i
$555$	0.309568	−	4.13089i	0.0131404	−	0.175347i
$556$	−1.64332	+	0.506898i	−0.0696924	+	0.0214973i
$557$	−16.6945	−	28.9157i	−0.707367	−	1.22520i	−0.965830	−	0.259175i	$-0.916549\pi$
$557$	−16.6945	−	28.9157i	−0.707367	−	1.22520i	0.258463	−	0.966021i	$-0.416784\pi$
$558$	3.91095	−	6.77396i	0.165564	−	0.286765i
$559$	11.6258	−	50.9358i	0.491718	−	2.15436i
$560$		0			0
$561$	−2.85735	−	12.5189i	−0.120637	−	0.528547i
$562$	−3.45301	−	1.06511i	−0.145656	−	0.0449290i
$563$	6.71266	−	17.1036i	0.282905	−	0.720830i	−0.716817	−	0.697261i	$-0.754402\pi$
$563$	6.71266	−	17.1036i	0.282905	−	0.720830i	0.999722	−	0.0235688i	$-0.00750287\pi$
$564$	−3.02167	+	7.69910i	−0.127235	+	0.324190i
$565$	1.47773	+	0.455819i	0.0621686	+	0.0191765i
$566$	−3.17566	−	13.9135i	−0.133483	−	0.584828i
$567$		0			0
$568$	1.29530	−	5.67509i	0.0543497	−	0.238121i
$569$	−2.92800	+	5.07144i	−0.122748	+	0.212606i	−0.920850	−	0.389916i	$-0.872504\pi$
$569$	−2.92800	+	5.07144i	−0.122748	+	0.212606i	0.798102	+	0.602522i	$0.205837\pi$
$570$	2.01219	+	3.48521i	0.0842812	+	0.145979i
$571$	3.18702	−	0.983065i	0.133373	−	0.0411400i	−0.227350	−	0.973813i	$-0.573006\pi$
$571$	3.18702	−	0.983065i	0.133373	−	0.0411400i	0.360723	+	0.932673i	$0.382530\pi$
$572$	−0.637098	+	8.50148i	−0.0266384	+	0.355465i
$573$	−19.3566	−	24.2725i	−0.808635	−	1.01400i
$574$		0			0
$575$	−11.1416	+	13.9711i	−0.464637	+	0.582636i
$576$	−1.17289	−	1.08829i	−0.0488705	−	0.0453452i
$577$	−28.6915	−	4.32454i	−1.19444	−	0.180033i	−0.478433	−	0.878124i	$-0.658795\pi$
$577$	−28.6915	−	4.32454i	−1.19444	−	0.180033i	−0.716009	+	0.698091i	$0.754033\pi$
$578$	−2.24736	−	1.53222i	−0.0934778	−	0.0637321i
$579$	−8.31770	+	1.25369i	−0.345672	+	0.0521016i
$580$	7.42695	+	3.57663i	0.308387	+	0.148511i
$581$		0			0
$582$	−7.15651	+	3.44640i	−0.296647	+	0.142858i
$583$	−14.8834	+	10.1474i	−0.616409	+	0.420261i
$584$	−5.63253	+	5.22622i	−0.233076	+	0.216263i
$585$	1.01937	+	13.6025i	0.0421456	+	0.562393i
$586$	−4.56937	−	11.6426i	−0.188759	−	0.480950i
$587$	−22.5431			−0.930453			−0.465226	−	0.885192i	$-0.654027\pi$
$587$	−22.5431			−0.930453			−0.465226	+	0.885192i	$0.654027\pi$
$588$		0			0
$589$	6.80374			0.280343
$590$	−3.32067	−	8.46094i	−0.136710	−	0.348331i
$591$	1.47936	+	19.7407i	0.0608527	+	0.812023i
$592$	−1.05016	+	0.974406i	−0.0431613	+	0.0400478i
$593$	−34.7262	+	23.6760i	−1.42604	+	0.972255i	−0.428396	+	0.903591i	$0.640921\pi$
$593$	−34.7262	+	23.6760i	−1.42604	+	0.972255i	−0.997640	+	0.0686637i	$0.978126\pi$
$594$	3.64731	−	1.75645i	0.149651	−	0.0720681i
$595$		0			0
$596$	5.13657	+	2.47364i	0.210402	+	0.101324i
$597$	−34.6899	+	5.22866i	−1.41976	+	0.213995i
$598$	29.3381	+	20.0024i	1.19972	+	0.817959i
$599$	−5.09339	−	0.767705i	−0.208110	−	0.0313676i	0.0441597	−	0.999024i	$-0.485939\pi$
$599$	−5.09339	−	0.767705i	−0.208110	−	0.0313676i	−0.252270	+	0.967657i	$0.581177\pi$
$600$	5.00331	+	4.64239i	0.204259	+	0.189525i
$601$	−13.1096	+	16.4389i	−0.534753	+	0.670559i	−0.973668	−	0.227970i	$-0.926791\pi$
$601$	−13.1096	+	16.4389i	−0.534753	+	0.670559i	0.438916	+	0.898528i	$0.355363\pi$
$602$		0			0
$603$	−10.3628	−	12.9946i	−0.422007	−	0.529181i
$604$	1.43075	−	19.0921i	0.0582165	−	0.776846i
$605$	11.8297	−	3.64899i	0.480948	−	0.148353i
$606$	−15.4374	−	26.7384i	−0.627101	−	1.08617i
$607$	2.52716	−	4.37716i	0.102574	−	0.177664i	−0.810170	−	0.586194i	$-0.800625\pi$
$607$	2.52716	−	4.37716i	0.102574	−	0.177664i	0.912744	+	0.408531i	$0.133959\pi$
$608$	0.309692	−	1.35685i	0.0125597	−	0.0550275i
$609$		0			0
$610$	−3.11235	−	13.6361i	−0.126015	−	0.552110i
$611$	−23.3015	−	7.18757i	−0.942679	−	0.290778i
$612$	−2.59582	+	6.61405i	−0.104930	+	0.267357i
$613$	−7.68917	+	19.5917i	−0.310563	+	0.791300i	0.687326	+	0.726349i	$0.258784\pi$
$613$	−7.68917	+	19.5917i	−0.310563	+	0.791300i	−0.997888	+	0.0649513i	$0.979311\pi$
$614$	20.8223	+	6.42284i	0.840321	+	0.259205i
$615$	3.78078	+	16.5647i	0.152456	+	0.667952i
$616$		0			0
$617$	1.12264	−	4.91861i	0.0451958	−	0.198016i	−0.947290	−	0.320378i	$-0.896190\pi$
$617$	1.12264	−	4.91861i	0.0451958	−	0.198016i	0.992485	+	0.122363i	$0.0390471\pi$
$618$	−1.79618	+	3.11107i	−0.0722529	+	0.125146i
$619$	18.4383	+	31.9361i	0.741098	+	1.28362i	0.951996	+	0.306111i	$0.0990280\pi$
$619$	18.4383	+	31.9361i	0.741098	+	1.28362i	−0.210898	+	0.977508i	$0.567639\pi$
$620$	−6.29813	+	1.94272i	−0.252939	+	0.0780214i
$621$	1.26001	−	16.8137i	0.0505625	−	0.674710i
$622$	−4.00646	−	5.02394i	−0.160645	−	0.201442i
$623$		0			0
$624$	8.45590	−	10.6034i	0.338507	−	0.424474i
$625$	−0.761402	−	0.706478i	−0.0304561	−	0.0282591i
$626$	−17.4293	−	2.62705i	−0.696615	−	0.104998i
$627$	−3.32509	−	2.26701i	−0.132791	−	0.0905357i
$628$	9.31235	−	1.40361i	0.371603	−	0.0560102i
$629$	5.73171	+	2.76024i	0.228538	+	0.110058i
$630$		0			0
$631$	24.6596	−	11.8754i	0.981682	−	0.472753i	0.126999	−	0.991903i	$-0.459466\pi$
$631$	24.6596	−	11.8754i	0.981682	−	0.472753i	0.854683	+	0.519149i	$0.173751\pi$
$632$	4.77665	−	3.25667i	0.190005	−	0.129543i
$633$	−36.0445	+	33.4444i	−1.43264	+	1.32930i
$634$	0.161574	+	2.15605i	0.00641691	+	0.0856277i
$635$	−6.61823	−	16.8630i	−0.262636	−	0.669186i
$636$	28.6561			1.13629
$637$		0			0
$638$	−8.24329			−0.326355
$639$	3.40269	+	8.66991i	0.134608	+	0.342976i
$640$	0.100752	+	1.34445i	0.00398259	+	0.0531439i
$641$	15.9921	−	14.8385i	0.631650	−	0.586086i	−0.297983	−	0.954571i	$-0.596314\pi$
$641$	15.9921	−	14.8385i	0.631650	−	0.586086i	0.929634	+	0.368485i	$0.120123\pi$
$642$	25.6073	−	17.4588i	1.01064	−	0.689043i
$643$	−22.0770	+	10.6317i	−0.870634	+	0.419275i	−0.815195	−	0.579187i	$-0.803370\pi$
$643$	−22.0770	+	10.6317i	−0.870634	+	0.419275i	−0.0554389	+	0.998462i	$0.517656\pi$
$644$		0			0
$645$	−21.5253	−	10.3660i	−0.847557	−	0.408162i
$646$	−6.11131	+	0.921132i	−0.240446	+	0.0362415i
$647$	−8.36425	−	5.70265i	−0.328832	−	0.224194i	0.387638	−	0.921812i	$-0.373291\pi$
$647$	−8.36425	−	5.70265i	−0.328832	−	0.224194i	−0.716470	+	0.697618i	$0.754243\pi$
$648$	−11.1145	−	1.67523i	−0.436617	−	0.0658094i
$649$	6.66289	+	6.18226i	0.261541	+	0.242675i
$650$	−12.5465	+	15.7328i	−0.492115	+	0.617093i
$651$		0			0
$652$	−4.00397	−	5.02082i	−0.156808	−	0.196630i
$653$	−3.39353	+	45.2836i	−0.132799	+	1.77208i	0.391144	+	0.920330i	$0.372079\pi$
$653$	−3.39353	+	45.2836i	−0.132799	+	1.77208i	−0.523943	+	0.851753i	$0.675540\pi$
$654$	38.0236	−	11.7287i	1.48684	−	0.458629i
$655$	−10.3261	−	17.8854i	−0.403475	−	0.698839i
$656$	2.93793	−	5.08864i	0.114707	−	0.198678i
$657$	2.73567	−	11.9857i	0.106728	−	0.467608i
$658$		0			0
$659$	−4.55935	−	19.9758i	−0.177607	−	0.778148i	−0.982731	−	0.185041i	$-0.940758\pi$
$659$	−4.55935	−	19.9758i	−0.177607	−	0.778148i	0.805124	−	0.593107i	$-0.202099\pi$
$660$	3.72531	+	1.14911i	0.145008	+	0.0447289i
$661$	−7.47424	+	19.0441i	−0.290714	+	0.740728i	0.708666	+	0.705544i	$0.249297\pi$
$661$	−7.47424	+	19.0441i	−0.290714	+	0.740728i	−0.999381	+	0.0351846i	$0.988798\pi$
$662$	−6.86975	+	17.5038i	−0.267000	+	0.680306i
$663$	−57.5503	−	17.7519i	−2.23507	−	0.689428i
$664$	1.72810	+	7.57128i	0.0670631	+	0.293823i
$665$		0			0
$666$	0.510053	−	2.23469i	0.0197641	−	0.0865924i
$667$	−17.1667	+	29.7336i	−0.664697	+	1.15129i
$668$	5.67822	+	9.83497i	0.219697	+	0.380526i
$669$	35.1841	−	10.8528i	1.36029	−	0.419595i
$670$	−1.04660	+	13.9659i	−0.0404337	+	0.539550i
$671$	8.72061	+	10.9353i	0.336656	+	0.422153i
$672$		0			0
$673$	6.76513	−	8.48320i	0.260776	−	0.327003i	−0.634156	−	0.773205i	$-0.718652\pi$
$673$	6.76513	−	8.48320i	0.260776	−	0.327003i	0.894932	+	0.446202i	$0.147224\pi$
$674$	−5.34224	−	4.95688i	−0.205775	−	0.190932i
$675$	9.44862	+	1.42415i	0.363678	+	0.0548156i
$676$	22.2964	+	15.2015i	0.857556	+	0.584672i
$677$	−17.2603	+	2.60157i	−0.663366	+	0.0999863i	−0.472091	−	0.881550i	$-0.656500\pi$
$677$	−17.2603	+	2.60157i	−0.663366	+	0.0999863i	−0.191275	+	0.981536i	$0.561262\pi$
$678$	2.21647	+	1.06739i	0.0851228	+	0.0409930i
$679$		0			0
$680$	5.39415	−	2.59768i	0.206856	−	0.0996166i
$681$	8.21772	−	5.60275i	0.314904	−	0.214698i
$682$	4.83151	−	4.48299i	0.185008	−	0.171662i
$683$	−2.36645	−	31.5780i	−0.0905495	−	1.20830i	−0.838634	−	0.544696i	$-0.816645\pi$
$683$	−2.36645	−	31.5780i	−0.0905495	−	1.20830i	0.748084	−	0.663604i	$-0.230974\pi$
$684$	0.813544	+	2.07288i	0.0311066	+	0.0792584i
$685$	−2.35839			−0.0901096
$686$		0			0
$687$	10.8861			0.415331
$688$	3.01855	+	7.69114i	0.115081	+	0.293222i
$689$	6.31371	+	84.2507i	0.240533	+	3.20969i
$690$	11.9028	−	11.0442i	0.453132	−	0.420445i
$691$	−19.2027	+	13.0922i	−0.730504	+	0.498049i	−0.870540	−	0.492097i	$-0.836230\pi$
$691$	−19.2027	+	13.0922i	−0.730504	+	0.498049i	0.140036	+	0.990146i	$0.455278\pi$
$692$	−14.0507	+	6.76645i	−0.534127	+	0.257222i
$693$		0			0
$694$	13.4437	+	6.47416i	0.510317	+	0.245756i
$695$	−2.29267	+	0.345564i	−0.0869658	+	0.0131080i
$696$	10.8349	+	7.38713i	0.410697	+	0.280008i
$697$	−25.8016	−	3.88897i	−0.977305	−	0.147305i
$698$	−18.4114	−	17.0833i	−0.696883	−	0.646613i
$699$	14.3978	−	18.0543i	0.544575	−	0.682876i
$700$		0			0
$701$	1.95508	+	2.45159i	0.0738424	+	0.0925954i	0.817381	−	0.576098i	$-0.195425\pi$
$701$	1.95508	+	2.45159i	0.0738424	+	0.0925954i	−0.743538	+	0.668693i	$0.766854\pi$
$702$	1.41890	−	18.9338i	0.0535527	−	0.714612i
$703$	1.90521	−	0.587681i	0.0718565	−	0.0221648i
$704$	−0.674108	−	1.16759i	−0.0254064	−	0.0440052i
$705$	−5.57543	+	9.65693i	−0.209983	+	0.363701i
$706$	1.64821	−	7.22129i	0.0620313	−	0.271777i
$707$		0			0
$708$	−3.21750	−	14.0968i	−0.120921	−	0.529790i
$709$	2.07637	+	0.640475i	0.0779797	+	0.0240536i	0.333500	−	0.942750i	$-0.391770\pi$
$709$	2.07637	+	0.640475i	0.0779797	+	0.0240536i	−0.255520	+	0.966804i	$0.582247\pi$
$710$	2.86720	−	7.30551i	0.107604	−	0.274171i
$711$	−3.37940	+	8.61057i	−0.126737	+	0.322922i
$712$	−9.93943	−	3.06591i	−0.372496	−	0.114900i
$713$	−6.10851	−	26.7631i	−0.228765	−	1.00229i
$714$		0			0
$715$	−2.55765	+	11.2058i	−0.0956507	+	0.419073i
$716$	−2.83254	+	4.90610i	−0.105857	+	0.183350i
$717$	−28.4199	−	49.2246i	−1.06136	−	1.83833i
$718$	−13.3263	+	4.11061i	−0.497332	+	0.153407i
$719$	1.21153	−	16.1668i	0.0451825	−	0.602918i	−0.927955	−	0.372693i	$-0.878435\pi$
$719$	1.21153	−	16.1668i	0.0451825	−	0.602918i	0.973137	−	0.230226i	$-0.0739464\pi$
$720$	−1.34497	−	1.68654i	−0.0501241	−	0.0628536i
$721$		0			0
$722$	10.6386	−	13.3404i	0.395929	−	0.496479i
$723$	−15.9482	−	14.7978i	−0.593121	−	0.550336i
$724$	6.32095	+	0.952730i	0.234916	+	0.0354079i
$725$	−16.0764	−	10.9607i	−0.597063	−	0.407071i
$726$	19.4739	−	2.93522i	0.722745	−	0.108936i
$727$	46.2682	+	22.2816i	1.71599	+	0.826379i	0.990396	+	0.138260i	$0.0441510\pi$
$727$	46.2682	+	22.2816i	1.71599	+	0.826379i	0.725598	+	0.688119i	$0.241563\pi$
$728$		0			0
$729$	−1.20346	+	0.579555i	−0.0445725	+	0.0214650i
$730$	−8.55921	+	5.83557i	−0.316791	+	0.215984i
$731$	26.8960	−	24.9558i	0.994785	−	0.923025i
$732$	−1.66277	−	22.1882i	−0.0614579	−	0.820098i
$733$	−6.39053	−	16.2828i	−0.236039	−	0.601419i	0.762946	−	0.646463i	$-0.223752\pi$
$733$	−6.39053	−	16.2828i	−0.236039	−	0.601419i	−0.998985	+	0.0450440i	$0.985657\pi$
$734$	0.689374			0.0254453
$735$		0			0
$736$	−5.61533			−0.206984
$737$	−5.11663	−	13.0370i	−0.188473	−	0.480223i
$738$	0.702571	+	9.37516i	0.0258620	+	0.345104i
$739$	−6.16161	+	5.71714i	−0.226658	+	0.210308i	−0.785324	−	0.619084i	$-0.787504\pi$
$739$	−6.16161	+	5.71714i	−0.226658	+	0.210308i	0.558666	+	0.829393i	$0.311313\pi$
$740$	−1.59583	+	1.08802i	−0.0586638	+	0.0399963i
$741$	−17.0059	+	8.18961i	−0.624727	+	0.300853i
$742$		0			0
$743$	−21.3935	−	10.3026i	−0.784851	−	0.377964i	−0.00186062	−	0.999998i	$-0.500592\pi$
$743$	−21.3935	−	10.3026i	−0.784851	−	0.377964i	−0.782990	+	0.622034i	$0.786307\pi$
$744$	−10.3679	+	1.56271i	−0.380105	+	0.0572916i
$745$	6.35081	+	4.32991i	0.232676	+	0.158636i
$746$	−23.9558	−	3.61075i	−0.877084	−	0.132199i
$747$	−9.10867	−	8.45161i	−0.333269	−	0.309228i
$748$	−3.73287	+	4.68086i	−0.136487	+	0.171149i
$749$		0			0
$750$	14.7518	+	18.4982i	0.538659	+	0.675457i
$751$	−0.827274	+	11.0392i	−0.0301877	+	0.402826i	0.961558	+	0.274603i	$0.0885465\pi$
$751$	−0.827274	+	11.0392i	−0.0301877	+	0.402826i	−0.991745	+	0.128223i	$0.959073\pi$
$752$	3.68496	−	1.13666i	0.134377	−	0.0414498i
$753$	6.03691	+	10.4562i	0.219997	+	0.381046i
$754$	−19.3313	+	33.4829i	−0.704006	+	1.21937i
$755$	5.74381	−	25.1653i	0.209039	−	0.915858i
$756$		0			0
$757$	0.100651	+	0.440980i	0.00365821	+	0.0160277i	0.976724	−	0.214500i	$-0.0688121\pi$
$757$	0.100651	+	0.440980i	0.00365821	+	0.0160277i	−0.973066	+	0.230527i	$0.925955\pi$
$758$	3.78490	+	1.16749i	0.137474	+	0.0424050i
$759$	−5.93216	+	15.1149i	−0.215324	+	0.548636i
$760$	0.685516	−	1.74667i	0.0248663	−	0.0633582i
$761$	−47.9122	−	14.7790i	−1.73682	−	0.535737i	−0.745415	−	0.666600i	$-0.767749\pi$
$761$	−47.9122	−	14.7790i	−1.73682	−	0.535737i	−0.991400	+	0.130864i	$0.958225\pi$
$762$	−6.41260	−	28.0954i	−0.232304	−	1.01779i
$763$		0			0
$764$	−3.22101	+	14.1122i	−0.116532	+	0.510560i
$765$	−4.78968	+	8.29597i	−0.173171	+	0.299941i
$766$	−0.544279	−	0.942718i	−0.0196656	−	0.0340618i
$767$	40.7364	−	12.5655i	1.47091	−	0.453715i
$768$	−0.160278	+	2.13877i	−0.00578355	+	0.0771761i
$769$	19.6850	+	24.6842i	0.709860	+	0.890136i	0.997717	−	0.0675370i	$-0.0215141\pi$
$769$	19.6850	+	24.6842i	0.709860	+	0.890136i	−0.287857	+	0.957674i	$0.592943\pi$
$770$		0			0
$771$	−5.59900	+	7.02092i	−0.201643	+	0.252852i
$772$	2.87499	+	2.66760i	0.103473	+	0.0960091i
$773$	18.8516	+	2.84143i	0.678046	+	0.102199i	0.479032	−	0.877798i	$-0.340988\pi$
$773$	18.8516	+	2.84143i	0.678046	+	0.102199i	0.199014	+	0.979997i	$0.436226\pi$
$774$	−10.9227	−	7.44695i	−0.392607	−	0.267675i
$775$	15.3834	−	2.31868i	0.552589	−	0.0832894i
$776$	3.33674	+	1.60689i	0.119782	+	0.0576839i
$777$		0			0
$778$	15.2951	−	7.36573i	0.548356	−	0.264074i
$779$	−6.75672	+	4.60666i	−0.242085	+	0.165051i
$780$	13.4037	−	12.4368i	0.479930	−	0.445310i
$781$	0.586483	+	7.82607i	0.0209860	+	0.280039i
$782$	9.11019	+	23.2124i	0.325780	+	0.830073i
$783$	18.3588			0.656090
$784$		0			0
$785$	12.6969			0.453171
$786$	−12.0029	−	30.5828i	−0.428128	−	1.09085i
$787$	1.51817	+	20.2586i	0.0541171	+	0.722142i	0.956598	+	0.291412i	$0.0941249\pi$
$787$	1.51817	+	20.2586i	0.0541171	+	0.722142i	−0.902481	+	0.430730i	$0.858256\pi$
$788$	6.76602	−	6.27795i	0.241030	−	0.223643i
$789$	37.2172	−	25.3742i	1.32497	−	0.903347i
$790$	7.02243	−	3.38182i	0.249847	−	0.120320i
$791$		0			0
$792$	1.94354	+	0.935958i	0.0690606	+	0.0332578i
$793$	64.8681	−	9.77729i	2.30353	−	0.347202i
$794$	−7.89198	−	5.38066i	−0.280076	−	0.190953i
$795$	38.2032	+	5.75820i	1.35493	+	0.204222i
$796$	11.9905	+	11.1255i	0.424991	+	0.394334i
$797$	−18.1712	+	22.7860i	−0.643658	+	0.807122i	−0.991455	−	0.130448i	$-0.958358\pi$
$797$	−18.1712	+	22.7860i	−0.643658	+	0.807122i	0.347797	+	0.937570i	$0.386930\pi$
$798$		0			0
$799$	−10.6771	−	13.3886i	−0.377728	−	0.473655i
$800$	0.237815	−	3.17341i	0.00840801	−	0.112197i
$801$	15.9032	−	4.90549i	0.561912	−	0.173327i
$802$	−8.63363	−	14.9539i	−0.304864	−	0.528040i
$803$	5.17963	−	8.97137i	0.182785	−	0.316593i
$804$	−4.95766	+	21.7209i	−0.174843	+	0.766037i
$805$		0			0
$806$	−6.87877	−	30.1378i	−0.242294	−	1.06156i
$807$	−23.0723	−	7.11685i	−0.812182	−	0.250525i
$808$	−5.25924	+	13.4003i	−0.185019	+	0.471422i
$809$	−14.5308	+	37.0239i	−0.510877	+	1.30169i	0.410088	+	0.912046i	$0.365498\pi$
$809$	−14.5308	+	37.0239i	−0.510877	+	1.30169i	−0.920964	+	0.389647i	$0.872597\pi$
$810$	−14.4807	−	4.46671i	−0.508800	−	0.156944i
$811$	−4.53521	−	19.8701i	−0.159253	−	0.697732i	−0.989998	−	0.141080i	$-0.954943\pi$
$811$	−4.53521	−	19.8701i	−0.159253	−	0.697732i	0.830745	−	0.556652i	$-0.187914\pi$
$812$		0			0
$813$	3.13173	−	13.7210i	0.109835	−	0.481217i
$814$	0.965718	−	1.67267i	0.0338484	−	0.0586272i
$815$	−4.32904	−	7.49811i	−0.151639	−	0.262647i
$816$	9.10116	−	2.80734i	0.318604	−	0.0982764i
$817$	0.859319	−	11.4668i	0.0300638	−	0.401173i
$818$	2.75600	+	3.45591i	0.0963613	+	0.120833i
$819$		0			0
$820$	4.93924	−	6.19361i	0.172486	−	0.216290i
$821$	8.77636	+	8.14327i	0.306297	+	0.284202i	0.818312	−	0.574775i	$-0.194910\pi$
$821$	8.77636	+	8.14327i	0.306297	+	0.284202i	−0.512015	+	0.858977i	$0.671101\pi$
$822$	−3.70987	−	0.559172i	−0.129396	−	0.0195034i
$823$	23.5972	+	16.0883i	0.822546	+	0.560802i	0.899847	−	0.436205i	$-0.143678\pi$
$823$	23.5972	+	16.0883i	0.822546	+	0.560802i	−0.0773011	+	0.997008i	$0.524630\pi$
$824$	1.65624	−	0.249637i	0.0576977	−	0.00869653i
$825$	−8.29071	−	3.99260i	−0.288645	−	0.139004i
$826$		0			0
$827$	−45.3777	+	21.8527i	−1.57794	+	0.759895i	−0.998480	−	0.0551083i	$-0.982450\pi$
$827$	−45.3777	+	21.8527i	−1.57794	+	0.759895i	−0.579457	+	0.815003i	$0.696735\pi$
$828$	7.42343	−	5.06121i	0.257982	−	0.175889i
$829$	−11.5503	+	10.7171i	−0.401157	+	0.372220i	−0.854794	−	0.518967i	$-0.826317\pi$
$829$	−11.5503	+	10.7171i	−0.401157	+	0.372220i	0.453637	+	0.891187i	$0.350126\pi$
$830$	0.782442	+	10.4410i	0.0271590	+	0.362411i
$831$	19.2041	+	48.9312i	0.666182	+	1.69740i
$832$	−6.32341			−0.219225
$833$		0			0
$834$	−3.68841			−0.127719
$835$	5.59372	+	14.2526i	0.193578	+	0.493230i
$836$	0.140221	+	1.87112i	0.00484966	+	0.0647142i
$837$	−10.7604	+	9.98416i	−0.371932	+	0.345103i
$838$	3.96076	−	2.70040i	0.136822	−	0.0932839i
$839$	11.6905	−	5.62986i	0.403602	−	0.194365i	−0.221059	−	0.975260i	$-0.570951\pi$
$839$	11.6905	−	5.62986i	0.403602	−	0.194365i	0.624661	+	0.780896i	$0.285237\pi$
$840$		0			0
$841$	−7.55341	−	3.63753i	−0.260463	−	0.125432i
$842$	28.8607	−	4.35005i	0.994606	−	0.149913i
$843$	−6.40352	−	4.36584i	−0.220549	−	0.150368i
$844$	22.6697	+	3.41691i	0.780325	+	0.117615i
$845$	26.6701	+	24.7462i	0.917479	+	0.851296i
$846$	−3.84700	+	4.82399i	−0.132263	+	0.165852i
$847$		0			0
$848$	−8.33043	−	10.4460i	−0.286068	−	0.358718i
$849$	2.28738	−	30.5230i	0.0785027	−	1.04755i
$850$	−13.5039	+	4.16541i	−0.463181	+	0.142872i
$851$	−4.02223	−	6.96670i	−0.137880	−	0.238815i
$852$	6.24237	−	10.8121i	0.213860	−	0.370417i
$853$	6.72523	−	29.4652i	0.230268	−	1.00887i	−0.719151	−	0.694854i	$-0.755469\pi$
$853$	6.72523	−	29.4652i	0.230268	−	1.00887i	0.949418	−	0.314014i	$-0.101674\pi$
$854$		0			0
$855$	0.668056	+	2.92695i	0.0228471	+	0.100099i
$856$	−13.8084	−	4.25932i	−0.471961	−	0.145581i
$857$	16.1938	−	41.2612i	0.553171	−	1.40946i	−0.331595	−	0.943422i	$-0.607587\pi$
$857$	16.1938	−	41.2612i	0.553171	−	1.40946i	0.884766	−	0.466035i	$-0.154318\pi$
$858$	−6.68019	+	17.0208i	−0.228058	+	0.581082i
$859$	19.4393	+	5.99624i	0.663262	+	0.204589i	0.608066	−	0.793886i	$-0.291946\pi$
$859$	19.4393	+	5.99624i	0.663262	+	0.204589i	0.0551957	+	0.998476i	$0.482422\pi$
$860$	2.47874	+	10.8601i	0.0845242	+	0.370325i
$861$		0			0
$862$	−4.07421	+	17.8503i	−0.138768	+	0.607982i
$863$	21.6007	−	37.4135i	0.735295	−	1.27357i	−0.219298	−	0.975658i	$-0.570377\pi$
$863$	21.6007	−	37.4135i	0.735295	−	1.27357i	0.954594	−	0.297911i	$-0.0962898\pi$
$864$	1.50132	+	2.60036i	0.0510760	+	0.0884662i
$865$	−20.0914	+	6.19739i	−0.683130	+	0.210718i
$866$	1.92456	−	25.6815i	0.0653992	−	0.872692i
$867$	−3.63727	−	4.56100i	−0.123528	−	0.154900i
$868$		0			0
$869$	−4.85967	+	6.09383i	−0.164853	+	0.206719i
$870$	12.9603	+	12.0254i	0.439395	+	0.407699i
$871$	−64.9530	−	9.79009i	−2.20085	−	0.331724i
$872$	−15.3290	−	10.4512i	−0.519107	−	0.353921i
$873$	−5.85946	+	0.883172i	−0.198313	+	0.0298908i
$874$	7.04117	+	3.39085i	0.238171	+	0.114697i
$875$		0			0
$876$	−14.8477	+	7.15026i	−0.501656	+	0.241585i
$877$	−1.71208	+	1.16728i	−0.0578129	+	0.0394162i	−0.591882	−	0.806025i	$-0.701615\pi$
$877$	−1.71208	+	1.16728i	−0.0578129	+	0.0394162i	0.534069	+	0.845441i	$0.320662\pi$
$878$	−13.7316	+	12.7410i	−0.463418	+	0.429989i
$879$	−2.00463	−	26.7499i	−0.0676144	−	0.902251i
$880$	−0.664076	−	1.69204i	−0.0223860	−	0.0570386i
$881$	16.2998			0.549154			0.274577	−	0.961565i	$-0.411462\pi$
$881$	16.2998			0.549154			0.274577	+	0.961565i	$0.411462\pi$
$882$		0			0
$883$	27.6453			0.930337			0.465168	−	0.885222i	$-0.345994\pi$
$883$	27.6453			0.930337			0.465168	+	0.885222i	$0.345994\pi$
$884$	10.2589	+	26.1394i	0.345046	+	0.879162i
$885$	−1.45681	−	19.4398i	−0.0489701	−	0.653461i
$886$	−1.65832	+	1.53869i	−0.0557122	+	0.0516934i
$887$	12.7073	−	8.66372i	0.426671	−	0.290899i	−0.330883	−	0.943672i	$-0.607347\pi$
$887$	12.7073	−	8.66372i	0.426671	−	0.290899i	0.757554	+	0.652772i	$0.226394\pi$
$888$	−2.76828	+	1.33313i	−0.0928974	+	0.0447370i
$889$		0			0
$890$	−12.6348	−	6.08458i	−0.423518	−	0.203956i
$891$	14.9847	−	2.25858i	0.502006	−	0.0756652i
$892$	−14.1843	−	9.67070i	−0.474926	−	0.323799i
$893$	−5.30702	−	0.799905i	−0.177593	−	0.0267678i
$894$	8.96351	+	8.31692i	0.299785	+	0.278159i
$895$	−4.76206	+	5.97143i	−0.159178	+	0.199603i
$896$		0			0
$897$	47.4827	+	59.5414i	1.58540	+	1.98803i
$898$	−0.0182939	+	0.244115i	−0.000610476	+	0.00814624i
$899$	28.5623	−	8.81030i	0.952606	−	0.293840i
$900$	2.54587	+	4.40958i	0.0848623	+	0.146986i
$901$	−29.6662	+	51.3833i	−0.988324	+	1.71183i
$902$	−1.76280	+	7.72331i	−0.0586947	+	0.257158i
$903$		0			0
$904$	−0.255236	−	1.11826i	−0.00848903	−	0.0371929i
$905$	8.23539	+	2.54028i	0.273753	+	0.0844418i
$906$	15.0019	−	38.2243i	0.498406	−	1.26992i
$907$	−11.1254	+	28.3469i	−0.369411	+	0.941245i	0.618439	+	0.785833i	$0.287766\pi$
$907$	−11.1254	+	28.3469i	−0.369411	+	0.941245i	−0.987850	+	0.155411i	$0.950330\pi$
$908$	−4.43129	−	1.36687i	−0.147057	−	0.0453612i
$909$	−5.12530	−	22.4554i	−0.169995	−	0.744798i
$910$		0			0
$911$	0.600845	−	2.63247i	0.0199069	−	0.0872178i	−0.963999	−	0.265907i	$-0.914329\pi$
$911$	0.600845	−	2.63247i	0.0199069	−	0.0872178i	0.983906	+	0.178689i	$0.0571857\pi$
$912$	1.49248	−	2.58505i	0.0494210	−	0.0855996i
$913$	−5.23512	−	9.06749i	−0.173257	−	0.300090i
$914$	28.8592	−	8.90188i	0.954577	−	0.294448i
$915$	2.24178	−	29.9145i	0.0741109	−	0.988941i
$916$	−3.16463	−	3.96832i	−0.104562	−	0.131117i
$917$		0			0
$918$	8.31355	−	10.4249i	0.274388	−	0.344072i
$919$	32.0926	+	29.7776i	1.05864	+	0.982273i	0.999872	−	0.0159990i	$-0.00509284\pi$
$919$	32.0926	+	29.7776i	1.05864	+	0.982273i	0.0587663	+	0.998272i	$0.481283\pi$
$920$	−7.48613	−	1.12835i	−0.246810	−	0.0372007i
$921$	38.6145	+	26.3269i	1.27239	+	0.867502i
$922$	23.8507	−	3.59491i	0.785481	−	0.118392i
$923$	33.1636	+	15.9707i	1.09159	+	0.525683i
$924$		0			0
$925$	4.10746	−	1.97805i	0.135052	−	0.0650378i
$926$	16.4670	−	11.2270i	0.541139	−	0.368942i
$927$	−1.96453	+	1.82282i	−0.0645236	+	0.0598691i
$928$	−0.456916	−	6.09712i	−0.0149990	−	0.200148i
$929$	−7.79963	−	19.8731i	−0.255898	−	0.652017i	0.743971	−	0.668212i	$-0.232940\pi$
$929$	−7.79963	−	19.8731i	−0.255898	−	0.652017i	−0.999869	+	0.0161951i	$0.994845\pi$
$930$	−14.1360			−0.463539
$931$		0			0
$932$	−10.7668			−0.352679
$933$	−5.03512	−	12.8293i	−0.164842	−	0.420012i
$934$	−2.76833	−	36.9408i	−0.0905825	−	1.20874i
$935$	−5.91708	+	5.49025i	−0.193509	+	0.179550i
$936$	8.35950	−	5.69941i	0.273239	−	0.186291i
$937$	−29.6876	+	14.2968i	−0.969851	+	0.467056i	−0.850603	−	0.525809i	$-0.823763\pi$
$937$	−29.6876	+	14.2968i	−0.969851	+	0.467056i	−0.119248	+	0.992864i	$0.538048\pi$
$938$		0			0
$939$	−34.0602	−	16.4025i	−1.11151	−	0.535277i
$940$	5.14104	−	0.774887i	0.167682	−	0.0252740i
$941$	−10.9225	−	7.44681i	−0.356062	−	0.242759i	0.372057	−	0.928210i	$-0.378653\pi$
$941$	−10.9225	−	7.44681i	−0.356062	−	0.242759i	−0.728119	+	0.685451i	$0.759605\pi$
$942$	19.9728	+	3.01041i	0.650749	+	0.0980846i
$943$	24.1870	+	22.4422i	0.787636	+	0.730820i
$944$	−4.20337	+	5.27086i	−0.136808	+	0.171552i
$945$		0			0
$946$	−6.94526	−	8.70909i	−0.225810	−	0.283157i
$947$	−0.148792	+	1.98549i	−0.00483508	+	0.0645197i	−0.999099	−	0.0424311i	$-0.986490\pi$
$947$	−0.148792	+	1.98549i	−0.00483508	+	0.0645197i	0.994264	+	0.106951i	$0.0341087\pi$
$948$	11.8484	−	3.65476i	0.384819	−	0.118701i
$949$	−24.2935	−	42.0776i	−0.788600	−	1.36590i
$950$	−2.21448	+	3.83559i	−0.0718473	+	0.124443i
$951$	−1.03187	+	4.52092i	−0.0334607	+	0.146601i
$952$		0			0
$953$	5.19823	+	22.7749i	0.168387	+	0.737752i	0.986643	+	0.162898i	$0.0520841\pi$
$953$	5.19823	+	22.7749i	0.168387	+	0.737752i	−0.818256	+	0.574854i	$0.805059\pi$
$954$	20.4280	+	6.30120i	0.661380	+	0.204009i
$955$	−7.12983	+	18.1665i	−0.230716	+	0.587855i
$956$	−9.68213	+	24.6697i	−0.313142	+	0.797874i
$957$	−16.8944	−	5.21124i	−0.546120	−	0.168456i
$958$	−3.59974	−	15.7715i	−0.116302	−	0.509554i
$959$		0			0
$960$	−0.643443	+	2.81911i	−0.0207670	+	0.0909863i
$961$	3.55057	−	6.14978i	0.114535	−	0.198380i
$962$	−4.52941	−	7.84517i	−0.146034	−	0.252939i
$963$	22.0936	−	6.81497i	0.711956	−	0.219609i
$964$	−0.758043	+	10.1154i	−0.0244149	+	0.325794i
$965$	3.29679	+	4.13404i	0.106127	+	0.133079i
$966$		0			0
$967$	−12.2152	+	15.3173i	−0.392813	+	0.492572i	−0.938433	−	0.345461i	$-0.887723\pi$
$967$	−12.2152	+	15.3173i	−0.392813	+	0.492572i	0.545620	+	0.838033i	$0.316294\pi$
$968$	−6.73111	−	6.24556i	−0.216346	−	0.200740i
$969$	−13.1073	−	1.97561i	−0.421068	−	0.0634658i
$970$	4.12551	+	2.81272i	0.132462	+	0.0903111i
$971$	15.2617	−	2.30033i	0.489772	−	0.0738212i	0.100486	−	0.994938i	$-0.467960\pi$
$971$	15.2617	−	2.30033i	0.489772	−	0.0738212i	0.389285	+	0.921117i	$0.372722\pi$
$972$	−13.6039	−	6.55130i	−0.436346	−	0.210133i
$973$		0			0
$974$	−0.969150	+	0.466718i	−0.0310536	+	0.0149546i
$975$	−35.6598	+	24.3124i	−1.14203	+	0.778621i
$976$	−7.60489	+	7.05630i	−0.243427	+	0.225867i
$977$	4.56920	+	60.9717i	0.146182	+	1.95066i	0.280812	+	0.959763i	$0.409396\pi$
$977$	4.56920	+	60.9717i	0.146182	+	1.95066i	−0.134630	+	0.990896i	$0.542985\pi$
$978$	−5.03199	−	12.8213i	−0.160905	−	0.409980i
$979$	14.0235			0.448194
$980$		0			0
$981$	29.6847			0.947760
$982$	0.848862	+	2.16287i	0.0270883	+	0.0690198i
$983$	−1.61690	−	21.5760i	−0.0515711	−	0.688169i	−0.961746	−	0.273944i	$-0.911672\pi$
$983$	−1.61690	−	21.5760i	−0.0515711	−	0.688169i	0.910175	−	0.414225i	$-0.135947\pi$
$984$	9.23816	−	8.57176i	0.294502	−	0.273258i
$985$	10.2817	−	7.00993i	0.327602	−	0.223355i
$986$	−24.4627	+	11.7806i	−0.779050	+	0.375171i
$987$		0			0
$988$	7.92903	+	3.81842i	0.252256	+	0.121480i
$989$	−45.8772	+	6.91488i	−1.45881	+	0.219880i
$990$	2.40297	+	1.63832i	0.0763714	+	0.0520691i
$991$	33.9294	+	5.11404i	1.07780	+	0.162453i	0.663865	−	0.747852i	$-0.268915\pi$
$991$	33.9294	+	5.11404i	1.07780	+	0.162453i	0.413938	+	0.910305i	$0.364153\pi$
$992$	3.58363	+	3.32512i	0.113780	+	0.105573i
$993$	−25.1450	+	31.5308i	−0.797952	+	1.00060i
$994$		0			0
$995$	13.7496	+	17.2415i	0.435892	+	0.546591i
$996$	−1.24472	+	16.6096i	−0.0394405	+	0.526297i
$997$	30.0434	−	9.26718i	0.951486	−	0.293494i	0.220114	−	0.975474i	$-0.429357\pi$
$997$	30.0434	−	9.26718i	0.951486	−	0.293494i	0.731371	+	0.681980i	$0.238881\pi$
$998$	0.671595	+	1.16324i	0.0212590	+	0.0368216i
$999$	−2.15077	+	3.72525i	−0.0680474	+	0.117862i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	686.2.g.h.569.1		36
7.2	even	3		98.2.e.b.43.3	✓	18
7.3	odd	6		686.2.g.g.165.3		36
7.4	even	3	inner	686.2.g.h.165.1		36
7.5	odd	6		686.2.e.b.295.1		18
7.6	odd	2		686.2.g.g.569.3		36
21.2	odd	6		882.2.u.g.631.2		18
28.23	odd	6		784.2.u.d.337.1		18
49.3	odd	42		686.2.g.g.557.3		36
49.5	odd	42		686.2.e.b.393.1		18
49.8	even	7	inner	686.2.g.h.79.1		36
49.12	odd	42		4802.2.a.c.1.7		9
49.37	even	21		4802.2.a.d.1.3		9
49.41	odd	14		686.2.g.g.79.3		36
49.44	even	21		98.2.e.b.57.3	yes	18
49.46	even	21	inner	686.2.g.h.557.1		36
147.44	odd	42		882.2.u.g.253.2		18
196.191	odd	42		784.2.u.d.449.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.2.e.b.43.3	✓	18	7.2	even	3
98.2.e.b.57.3	yes	18	49.44	even	21
686.2.e.b.295.1		18	7.5	odd	6
686.2.e.b.393.1		18	49.5	odd	42
686.2.g.g.79.3		36	49.41	odd	14
686.2.g.g.165.3		36	7.3	odd	6
686.2.g.g.557.3		36	49.3	odd	42
686.2.g.g.569.3		36	7.6	odd	2
686.2.g.h.79.1		36	49.8	even	7	inner
686.2.g.h.165.1		36	7.4	even	3	inner
686.2.g.h.557.1		36	49.46	even	21	inner
686.2.g.h.569.1		36	1.1	even	1	trivial
784.2.u.d.337.1		18	28.23	odd	6
784.2.u.d.449.1		18	196.191	odd	42
882.2.u.g.253.2		18	147.44	odd	42
882.2.u.g.631.2		18	21.2	odd	6
4802.2.a.c.1.7		9	49.12	odd	42
4802.2.a.d.1.3		9	49.37	even	21

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:	\( N \)	\(=\)	\( 686 = 2 \cdot 7^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	686.g (of order \(21\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.365341 - 0.930874i) q^{2} +(-0.160278 - 2.13877i) q^{3} +(-0.733052 + 0.680173i) q^{4} +(-1.11395 + 0.759477i) q^{5} +(-1.93237 + 0.930578i) q^{6} +(0.900969 + 0.433884i) q^{8} +(-1.58214 + 0.238470i) q^{9} +O(q^{10})\)	\(q+(-0.365341 - 0.930874i) q^{2} +(-0.160278 - 2.13877i) q^{3} +(-0.733052 + 0.680173i) q^{4} +(-1.11395 + 0.759477i) q^{5} +(-1.93237 + 0.930578i) q^{6} +(0.900969 + 0.433884i) q^{8} +(-1.58214 + 0.238470i) q^{9} +(1.11395 + 0.759477i) q^{10} +(-1.33316 - 0.200941i) q^{11} +(1.57222 + 1.45881i) q^{12} +(-3.94258 + 4.94384i) q^{13} +(1.80289 + 2.26075i) q^{15} +(0.0747301 - 0.997204i) q^{16} +(-4.24343 + 1.30892i) q^{17} +(0.800006 + 1.38565i) q^{18} +(-0.695872 + 1.20529i) q^{19} +(0.300006 - 1.31441i) q^{20} +(0.300006 + 1.31441i) q^{22} +(5.36586 + 1.65515i) q^{23} +(0.783570 - 1.99650i) q^{24} +(-1.16263 + 2.96233i) q^{25} +(6.04248 + 1.86386i) q^{26} +(-0.668151 - 2.92736i) q^{27} +(-1.36054 + 5.96092i) q^{29} +(1.44580 - 2.50420i) q^{30} +(-2.44432 - 4.23369i) q^{31} +(-0.955573 + 0.294755i) q^{32} +(-0.216090 + 2.88352i) q^{33} +(2.76874 + 3.47189i) q^{34} +(0.997592 - 1.25094i) q^{36} +(-1.05016 - 0.974406i) q^{37} +(1.37620 + 0.207429i) q^{38} +(11.2056 + 7.63987i) q^{39} +(-1.33316 + 0.200941i) q^{40} +(5.29397 + 2.54944i) q^{41} +(-7.44405 + 3.58487i) q^{43} +(1.11395 - 0.759477i) q^{44} +(1.58131 - 1.46724i) q^{45} +(-0.419634 - 5.59963i) q^{46} +(1.40886 + 3.58972i) q^{47} -2.14476 q^{48} +3.18231 q^{50} +(3.47962 + 8.86592i) q^{51} +(-0.472549 - 6.30573i) q^{52} +(9.79429 - 9.08777i) q^{53} +(-2.48090 + 1.69145i) q^{54} +(1.63768 - 0.788665i) q^{55} +(2.68936 + 1.29513i) q^{57} +(6.04593 - 0.911277i) q^{58} +(-5.57024 - 3.79772i) q^{59} +(-2.85931 - 0.430972i) q^{60} +(-7.60489 - 7.05630i) q^{61} +(-3.04802 + 3.82210i) q^{62} +(0.623490 + 0.781831i) q^{64} +(0.637098 - 8.50148i) q^{65} +(2.76314 - 0.852316i) q^{66} +(5.19393 + 8.99615i) q^{67} +(2.22036 - 3.84578i) q^{68} +(2.67995 - 11.7416i) q^{69} +(-1.29530 - 5.67509i) q^{71} +(-1.52893 - 0.471612i) q^{72} +(-2.80716 + 7.15253i) q^{73} +(-0.523383 + 1.33356i) q^{74} +(6.52208 + 2.01180i) q^{75} +(-0.309692 - 1.35685i) q^{76} +(3.01788 - 13.2222i) q^{78} +(2.89060 - 5.00666i) q^{79} +(0.674108 + 1.16759i) q^{80} +(-10.7406 + 3.31305i) q^{81} +(0.439103 - 5.85943i) q^{82} +(4.84202 + 6.07170i) q^{83} +(3.73287 - 4.68086i) q^{85} +(6.05668 + 5.61978i) q^{86} +(12.9671 + 1.95447i) q^{87} +(-1.11395 - 0.759477i) q^{88} +(-10.2854 + 1.55027i) q^{89} +(-1.94354 - 0.935958i) q^{90} +(-5.05924 + 2.43640i) q^{92} +(-8.66311 + 5.90641i) q^{93} +(2.82686 - 2.62294i) q^{94} +(-0.140221 - 1.87112i) q^{95} +(0.783570 + 1.99650i) q^{96} +3.70350 q^{97} +2.15716 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 3 q^{2} + 5 q^{3} + 3 q^{4} + 10 q^{6} + 6 q^{8} + 10 q^{9}+O(q^{10}) \) 36 * q - 3 * q^2 + 5 * q^3 + 3 * q^4 + 10 * q^6 + 6 * q^8 + 10 * q^9	\( 36 q - 3 q^{2} + 5 q^{3} + 3 q^{4} + 10 q^{6} + 6 q^{8} + 10 q^{9} - 7 q^{11} - 2 q^{12} - 20 q^{13} + 14 q^{15} + 3 q^{16} - q^{17} + 32 q^{18} + 44 q^{19} + 14 q^{20} + 14 q^{22} - 21 q^{23} + 2 q^{24} - q^{25} - 3 q^{26} + 20 q^{27} + 22 q^{29} + 24 q^{31} - 3 q^{32} + 14 q^{33} - 2 q^{34} - 20 q^{36} + 13 q^{37} + 19 q^{38} + 3 q^{39} - 7 q^{40} + 16 q^{41} - 48 q^{43} - 98 q^{45} - 21 q^{46} - 40 q^{47} + 4 q^{48} - 100 q^{50} - 36 q^{51} - 18 q^{52} - 10 q^{53} - 4 q^{54} + 98 q^{55} + 38 q^{57} - 24 q^{58} - 13 q^{59} - 7 q^{60} - 27 q^{61} - 22 q^{62} - 6 q^{64} + 21 q^{66} + 86 q^{67} + 34 q^{68} - 182 q^{69} - 3 q^{72} - 5 q^{73} - 13 q^{74} + 3 q^{75} - 4 q^{76} + 76 q^{78} + 66 q^{79} + 2 q^{81} + 8 q^{82} + 110 q^{83} - 98 q^{85} + 18 q^{86} + 110 q^{87} - 62 q^{89} + 42 q^{90} - 42 q^{92} - 46 q^{93} - 23 q^{94} + 7 q^{95} + 2 q^{96} - 64 q^{97} + 28 q^{99}+O(q^{100}) \) 36 * q - 3 * q^2 + 5 * q^3 + 3 * q^4 + 10 * q^6 + 6 * q^8 + 10 * q^9 - 7 * q^11 - 2 * q^12 - 20 * q^13 + 14 * q^15 + 3 * q^16 - q^17 + 32 * q^18 + 44 * q^19 + 14 * q^20 + 14 * q^22 - 21 * q^23 + 2 * q^24 - q^25 - 3 * q^26 + 20 * q^27 + 22 * q^29 + 24 * q^31 - 3 * q^32 + 14 * q^33 - 2 * q^34 - 20 * q^36 + 13 * q^37 + 19 * q^38 + 3 * q^39 - 7 * q^40 + 16 * q^41 - 48 * q^43 - 98 * q^45 - 21 * q^46 - 40 * q^47 + 4 * q^48 - 100 * q^50 - 36 * q^51 - 18 * q^52 - 10 * q^53 - 4 * q^54 + 98 * q^55 + 38 * q^57 - 24 * q^58 - 13 * q^59 - 7 * q^60 - 27 * q^61 - 22 * q^62 - 6 * q^64 + 21 * q^66 + 86 * q^67 + 34 * q^68 - 182 * q^69 - 3 * q^72 - 5 * q^73 - 13 * q^74 + 3 * q^75 - 4 * q^76 + 76 * q^78 + 66 * q^79 + 2 * q^81 + 8 * q^82 + 110 * q^83 - 98 * q^85 + 18 * q^86 + 110 * q^87 - 62 * q^89 + 42 * q^90 - 42 * q^92 - 46 * q^93 - 23 * q^94 + 7 * q^95 + 2 * q^96 - 64 * q^97 + 28 * q^99

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