LMFDB - Embedded newform 784.2.x.k.557.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(165,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("784.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.x (of order $12$, degree $4$, 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:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 4 x^{14} + 4 x^{13} - 13 x^{12} + 32 x^{11} - 4 x^{10} - 34 x^{9} + 121 x^{8} + \cdots + 256 $ x^16 - 2x^15 + 4x^14 + 4x^13 - 13x^12 + 32x^11 - 4x^10 - 34x^9 + 121x^8 - 68x^7 - 16x^6 + 256x^5 - 208x^4 + 128x^3 + 256x^2 - 256*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			557.2
Root			$0.772089 + 1.18485i$ of defining polynomial
Character	$\chi$	$=$	784.557
Dual form			784.2.x.k.373.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.146726 - 1.40658i) q^{2} +(0.977085 - 0.261809i) q^{3} +(-1.95694 + 0.412764i) q^{4} +(-1.18533 - 0.317608i) q^{5} +(-0.511620 - 1.33594i) q^{6} +(0.867721 + 2.69204i) q^{8} +(-1.71192 + 0.988380i) q^{9} +(-0.272823 + 1.71386i) q^{10} +(-1.08957 - 4.06633i) q^{11} +(-1.80403 + 0.915651i) q^{12} +(-2.02017 - 2.02017i) q^{13} -1.24132 q^{15} +(3.65925 - 1.61551i) q^{16} +(-0.132279 + 0.229115i) q^{17} +(1.64142 + 2.26294i) q^{18} +(-1.66161 + 6.20120i) q^{19} +(2.45072 + 0.132279i) q^{20} +(-5.55976 + 2.12921i) q^{22} +(-1.33906 + 0.773104i) q^{23} +(1.55264 + 2.40317i) q^{24} +(-3.02600 - 1.74706i) q^{25} +(-2.54512 + 3.13794i) q^{26} +(-3.55976 + 3.55976i) q^{27} +(-0.328129 - 0.328129i) q^{29} +(0.182134 + 1.74602i) q^{30} +(-3.02017 + 5.23108i) q^{31} +(-2.80926 - 4.91000i) q^{32} +(-2.12921 - 3.68789i) q^{33} +(0.341677 + 0.152445i) q^{34} +(2.94217 - 2.64082i) q^{36} +(-9.08220 - 2.43357i) q^{37} +(8.96629 + 1.42731i) q^{38} +(-2.50277 - 1.44498i) q^{39} +(-0.173522 - 3.46654i) q^{40} +11.0327i q^{41} +(3.38407 - 3.38407i) q^{43} +(3.81066 + 7.50784i) q^{44} +(2.34311 - 0.627835i) q^{45} +(1.28391 + 1.77006i) q^{46} +(-1.56283 - 2.70690i) q^{47} +(3.15244 - 2.53652i) q^{48} +(-2.01339 + 4.51265i) q^{50} +(-0.0692639 + 0.258496i) q^{51} +(4.78720 + 3.11950i) q^{52} +(0.157593 + 0.588145i) q^{53} +(5.52940 + 4.48478i) q^{54} +5.16599i q^{55} +6.49412i q^{57} +(-0.413395 + 0.509685i) q^{58} +(-1.69338 - 6.31978i) q^{59} +(2.42919 - 0.512372i) q^{60} +(1.78171 - 6.64943i) q^{61} +(7.80108 + 3.48057i) q^{62} +(-6.49412 + 4.67187i) q^{64} +(1.75294 + 3.03618i) q^{65} +(-4.87491 + 3.53601i) q^{66} +(-4.56764 + 1.22389i) q^{67} +(0.164293 - 0.502964i) q^{68} +(-1.10597 + 1.10597i) q^{69} -9.03885i q^{71} +(-4.14623 - 3.75093i) q^{72} +(12.8298 + 7.40731i) q^{73} +(-2.09042 + 13.1319i) q^{74} +(-3.41405 - 0.914793i) q^{75} +(0.692037 - 12.8212i) q^{76} +(-1.66525 + 3.73237i) q^{78} +(-6.29520 - 10.9036i) q^{79} +(-4.85051 + 0.752705i) q^{80} +(0.418932 - 0.725612i) q^{81} +(15.5184 - 1.61878i) q^{82} +(-0.715276 - 0.715276i) q^{83} +(0.229563 - 0.229563i) q^{85} +(-5.25651 - 4.26344i) q^{86} +(-0.406517 - 0.234703i) q^{87} +(10.0013 - 6.46160i) q^{88} +(9.51968 - 5.49619i) q^{89} +(-1.22690 - 3.20366i) q^{90} +(2.30135 - 2.06564i) q^{92} +(-1.58141 + 5.90192i) q^{93} +(-3.57817 + 2.59542i) q^{94} +(3.93910 - 6.82272i) q^{95} +(-4.03036 - 4.06200i) q^{96} -14.2452 q^{97} +(5.88434 + 5.88434i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} - 4 q^{4} + 4 q^{5} - 32 q^{6} - 8 q^{8} - 12 q^{10} + 12 q^{12} - 16 q^{15} - 8 q^{16} - 24 q^{17} - 6 q^{18} + 12 q^{19} - 16 q^{20} - 8 q^{22} - 8 q^{26} + 24 q^{27} - 32 q^{29} - 20 q^{30}+ \cdots + 96 q^{99}+O(q^{100}) $ 16 * q - 2 * q^2 - 4 * q^4 + 4 * q^5 - 32 * q^6 - 8 * q^8 - 12 * q^10 + 12 * q^12 - 16 * q^15 - 8 * q^16 - 24 * q^17 - 6 * q^18 + 12 * q^19 - 16 * q^20 - 8 * q^22 - 8 * q^26 + 24 * q^27 - 32 * q^29 - 20 * q^30 - 16 * q^31 + 28 * q^32 + 24 * q^33 - 24 * q^34 + 48 * q^36 - 16 * q^37 + 16 * q^38 - 28 * q^40 - 64 * q^43 + 32 * q^44 + 8 * q^45 - 20 * q^46 - 24 * q^47 + 40 * q^48 - 28 * q^50 - 8 * q^51 - 32 * q^52 + 8 * q^53 + 16 * q^54 - 12 * q^58 + 28 * q^59 + 28 * q^60 - 28 * q^61 + 40 * q^62 - 64 * q^64 + 48 * q^65 + 16 * q^66 - 28 * q^68 + 88 * q^69 - 44 * q^72 + 4 * q^74 - 28 * q^75 - 48 * q^76 + 24 * q^78 + 24 * q^79 + 12 * q^80 - 40 * q^81 - 4 * q^82 - 80 * q^85 + 40 * q^88 - 32 * q^90 + 72 * q^92 - 16 * q^93 - 28 * q^94 - 16 * q^95 - 8 * q^96 - 64 * q^97 + 96 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.146726	−	1.40658i	−0.103751	−	0.994603i
$2$	−0.146726	−	1.40658i	−0.103751	−	0.994603i
$3$	0.977085	−	0.261809i	0.564120	−	0.151156i	0.0345217	−	0.999404i	$-0.489009\pi$
$3$	0.977085	−	0.261809i	0.564120	−	0.151156i	0.529599	+	0.848248i	$0.322343\pi$
$4$	−1.95694	+	0.412764i	−0.978471	+	0.206382i
$5$	−1.18533	−	0.317608i	−0.530095	−	0.142039i	−0.0161629	−	0.999869i	$-0.505145\pi$
$5$	−1.18533	−	0.317608i	−0.530095	−	0.142039i	−0.513932	+	0.857831i	$0.671812\pi$
$6$	−0.511620	−	1.33594i	−0.208868	−	0.545393i
$7$		0			0
$7$		0			0
$8$	0.867721	+	2.69204i	0.306786	+	0.951779i
$9$	−1.71192	+	0.988380i	−0.570642	+	0.329460i
$10$	−0.272823	+	1.71386i	−0.0862741	+	0.541971i
$11$	−1.08957	−	4.06633i	−0.328518	−	1.22604i	−0.910728	−	0.413007i	$-0.864479\pi$
$11$	−1.08957	−	4.06633i	−0.328518	−	1.22604i	0.582210	−	0.813038i	$-0.302188\pi$
$12$	−1.80403	+	0.915651i	−0.520780	+	0.264326i
$13$	−2.02017	−	2.02017i	−0.560293	−	0.560293i	0.369098	−	0.929391i	$-0.379667\pi$
$13$	−2.02017	−	2.02017i	−0.560293	−	0.560293i	−0.929391	+	0.369098i	$0.879667\pi$
$14$		0			0
$15$	−1.24132			−0.320507
$16$	3.65925	−	1.61551i	0.914813	−	0.403878i
$17$	−0.132279	+	0.229115i	−0.0320825	+	0.0555685i	−0.881621	−	0.471958i	$-0.843547\pi$
$17$	−0.132279	+	0.229115i	−0.0320825	+	0.0555685i	0.849538	+	0.527527i	$0.176881\pi$
$18$	1.64142	+	2.26294i	0.386887	+	0.533380i
$19$	−1.66161	+	6.20120i	−0.381199	+	1.42265i	0.462874	+	0.886424i	$0.346818\pi$
$19$	−1.66161	+	6.20120i	−0.381199	+	1.42265i	−0.844073	+	0.536228i	$0.819849\pi$
$20$	2.45072	+	0.132279i	0.547997	+	0.0295786i
$21$		0			0
$22$	−5.55976	+	2.12921i	−1.18534	+	0.453948i
$23$	−1.33906	+	0.773104i	−0.279212	+	0.161203i	−0.633067	−	0.774097i	$-0.718204\pi$
$23$	−1.33906	+	0.773104i	−0.279212	+	0.161203i	0.353854	+	0.935301i	$0.384871\pi$
$24$	1.55264	+	2.40317i	0.316931	+	0.490545i
$25$	−3.02600	−	1.74706i	−0.605200	−	0.349412i
$26$	−2.54512	+	3.13794i	−0.499138	+	0.615400i
$27$	−3.55976	+	3.55976i	−0.685076	+	0.685076i
$28$		0			0
$29$	−0.328129	−	0.328129i	−0.0609320	−	0.0609320i	0.675984	−	0.736916i	$-0.263719\pi$
$29$	−0.328129	−	0.328129i	−0.0609320	−	0.0609320i	−0.736916	+	0.675984i	$0.763719\pi$
$30$	0.182134	+	1.74602i	0.0332529	+	0.318778i
$31$	−3.02017	+	5.23108i	−0.542438	+	0.939530i	0.456326	+	0.889813i	$0.349165\pi$
$31$	−3.02017	+	5.23108i	−0.542438	+	0.939530i	−0.998763	+	0.0497168i	$0.984168\pi$
$32$	−2.80926	−	4.91000i	−0.496611	−	0.867973i
$33$	−2.12921	−	3.68789i	−0.370647	−	0.641980i
$34$	0.341677	+	0.152445i	0.0585972	+	0.0261440i
$35$		0			0
$36$	2.94217	−	2.64082i	0.490362	−	0.440137i
$37$	−9.08220	−	2.43357i	−1.49310	−	0.400076i	−0.582320	−	0.812959i	$-0.697855\pi$
$37$	−9.08220	−	2.43357i	−1.49310	−	0.400076i	−0.910784	+	0.412883i	$0.864522\pi$
$38$	8.96629	+	1.42731i	1.45452	+	0.231540i
$39$	−2.50277	−	1.44498i	−0.400764	−	0.231381i
$40$	−0.173522	−	3.46654i	−0.0274363	−	0.548108i
$41$			11.0327i			1.72302i	0.507741	+	0.861510i	$0.330481\pi$
$41$			11.0327i			1.72302i	−0.507741	+	0.861510i	$0.669519\pi$
$42$		0			0
$43$	3.38407	−	3.38407i	0.516066	−	0.516066i	−0.400312	−	0.916379i	$-0.631098\pi$
$43$	3.38407	−	3.38407i	0.516066	−	0.516066i	0.916379	+	0.400312i	$0.131098\pi$
$44$	3.81066	+	7.50784i	0.574479	+	1.13185i
$45$	2.34311	−	0.627835i	0.349290	−	0.0935921i
$46$	1.28391	+	1.77006i	0.189302	+	0.260981i
$47$	−1.56283	−	2.70690i	−0.227962	−	0.394842i	0.729242	−	0.684256i	$-0.239873\pi$
$47$	−1.56283	−	2.70690i	−0.227962	−	0.394842i	−0.957204	+	0.289414i	$0.906540\pi$
$48$	3.15244	−	2.53652i	0.455016	−	0.366115i
$49$		0			0
$50$	−2.01339	+	4.51265i	−0.284736	+	0.638185i
$51$	−0.0692639	+	0.258496i	−0.00969889	+	0.0361967i
$52$	4.78720	+	3.11950i	0.663865	+	0.432596i
$53$	0.157593	+	0.588145i	0.0216471	+	0.0807879i	0.975904	−	0.218199i	$-0.0700181\pi$
$53$	0.157593	+	0.588145i	0.0216471	+	0.0807879i	−0.954257	+	0.298987i	$0.903351\pi$
$54$	5.52940	+	4.48478i	0.752456	+	0.610301i
$55$			5.16599i			0.696582i
$56$		0			0
$57$			6.49412i			0.860167i
$58$	−0.413395	+	0.509685i	−0.0542814	+	0.0669249i
$59$	−1.69338	−	6.31978i	−0.220459	−	0.822765i	−0.984173	−	0.177210i	$-0.943293\pi$
$59$	−1.69338	−	6.31978i	−0.220459	−	0.822765i	0.763714	−	0.645555i	$-0.223374\pi$
$60$	2.42919	−	0.512372i	0.313607	−	0.0661469i
$61$	1.78171	−	6.64943i	0.228125	−	0.851372i	−0.753004	−	0.658016i	$-0.771396\pi$
$61$	1.78171	−	6.64943i	0.228125	−	0.851372i	0.981129	−	0.193356i	$-0.0619374\pi$
$62$	7.80108	+	3.48057i	0.990738	+	0.442033i
$63$		0			0
$64$	−6.49412	+	4.67187i	−0.811765	+	0.583984i
$65$	1.75294	+	3.03618i	0.217425	+	0.376592i
$66$	−4.87491	+	3.53601i	−0.600060	+	0.435253i
$67$	−4.56764	+	1.22389i	−0.558026	+	0.149523i	−0.526799	−	0.849990i	$-0.676608\pi$
$67$	−4.56764	+	1.22389i	−0.558026	+	0.149523i	−0.0312266	+	0.999512i	$0.509941\pi$
$68$	0.164293	−	0.502964i	0.0199234	−	0.0609934i
$69$	−1.10597	+	1.10597i	−0.133143	+	0.133143i
$70$		0			0
$71$		−	9.03885i		−	1.07271i	−0.843991	−	0.536357i	$-0.819800\pi$
$71$		−	9.03885i		−	1.07271i	0.843991	−	0.536357i	$-0.180200\pi$
$72$	−4.14623	−	3.75093i	−0.488638	−	0.442051i
$73$	12.8298	+	7.40731i	1.50162	+	0.866960i	0.999998	+	0.00187294i	$0.000596176\pi$
$73$	12.8298	+	7.40731i	1.50162	+	0.866960i	0.501621	+	0.865087i	$0.332737\pi$
$74$	−2.09042	+	13.1319i	−0.243006	+	1.52655i
$75$	−3.41405	−	0.914793i	−0.394221	−	0.105631i
$76$	0.692037	−	12.8212i	0.0793820	−	1.47070i
$77$		0			0
$78$	−1.66525	+	3.73237i	−0.188553	+	0.422607i
$79$	−6.29520	−	10.9036i	−0.708265	−	1.22675i	−0.965500	−	0.260402i	$-0.916145\pi$
$79$	−6.29520	−	10.9036i	−0.708265	−	1.22675i	0.257235	−	0.966349i	$-0.417189\pi$
$80$	−4.85051	+	0.752705i	−0.542304	+	0.0841549i
$81$	0.418932	−	0.725612i	0.0465480	−	0.0806235i
$82$	15.5184	−	1.61878i	1.71372	−	0.178765i
$83$	−0.715276	−	0.715276i	−0.0785117	−	0.0785117i	0.666760	−	0.745272i	$-0.267680\pi$
$83$	−0.715276	−	0.715276i	−0.0785117	−	0.0785117i	−0.745272	+	0.666760i	$0.767680\pi$
$84$		0			0
$85$	0.229563	−	0.229563i	0.0248996	−	0.0248996i
$86$	−5.25651	−	4.26344i	−0.566824	−	0.459739i
$87$	−0.406517	−	0.234703i	−0.0435832	−	0.0251628i
$88$	10.0013	−	6.46160i	1.06614	−	0.688809i
$89$	9.51968	−	5.49619i	1.00908	−	0.582595i	0.0981604	−	0.995171i	$-0.468704\pi$
$89$	9.51968	−	5.49619i	1.00908	−	0.582595i	0.910923	+	0.412576i	$0.135371\pi$
$90$	−1.22690	−	3.20366i	−0.129326	−	0.337695i
$91$		0			0
$92$	2.30135	−	2.06564i	0.239932	−	0.215357i
$93$	−1.58141	+	5.90192i	−0.163985	+	0.612000i
$94$	−3.57817	+	2.59542i	−0.369060	+	0.267697i
$95$	3.93910	−	6.82272i	0.404143	−	0.699996i
$96$	−4.03036	−	4.06200i	−0.411347	−	0.414576i
$97$	−14.2452			−1.44638			−0.723189	−	0.690650i	$-0.757325\pi$
$97$	−14.2452			−1.44638			−0.723189	+	0.690650i	$0.757325\pi$
$98$		0			0
$99$	5.88434	+	5.88434i	0.591399	+	0.591399i
$100$	6.64283	+	2.16988i	0.664283	+	0.216988i
$101$	−3.85421	−	14.3841i	−0.383508	−	1.43127i	−0.840505	−	0.541804i	$-0.817741\pi$
$101$	−3.85421	−	14.3841i	−0.383508	−	1.43127i	0.456996	−	0.889469i	$-0.348925\pi$
$102$	0.373759	+	0.0594972i	0.0370077	+	0.00589110i
$103$	−11.2464	+	6.49311i	−1.10814	+	0.639785i	−0.938347	−	0.345694i	$-0.887643\pi$
$103$	−11.2464	+	6.49311i	−1.10814	+	0.639785i	−0.169794	+	0.985480i	$0.554310\pi$
$104$	3.68542	−	7.19130i	0.361385	−	0.705165i
$105$		0			0
$106$	0.804151	−	0.307963i	0.0781060	−	0.0299121i
$107$	1.69567	+	0.454354i	0.163927	+	0.0439241i	0.339849	−	0.940480i	$-0.389624\pi$
$107$	1.69567	+	0.454354i	0.163927	+	0.0439241i	−0.175922	+	0.984404i	$0.556291\pi$
$108$	5.49690	−	8.43558i	0.528940	−	0.811714i
$109$	14.9628	−	4.00927i	1.43318	−	0.384018i	0.543037	−	0.839709i	$-0.317274\pi$
$109$	14.9628	−	4.00927i	1.43318	−	0.384018i	0.890138	+	0.455691i	$0.150608\pi$
$110$	7.26639	−	0.757985i	0.692823	−	0.0722711i
$111$	−9.51121			−0.902764
$112$		0			0
$113$	7.63302			0.718054			0.359027	−	0.933327i	$-0.383109\pi$
$113$	7.63302			0.718054			0.359027	+	0.933327i	$0.383109\pi$
$114$	9.13451	−	0.952856i	0.855525	−	0.0892432i
$115$	1.83277	−	0.491088i	0.170906	−	0.0457942i
$116$	0.777569	+	0.506689i	0.0721955	+	0.0470449i
$117$	5.45506	+	1.46168i	0.504321	+	0.135132i
$118$	−8.64082	+	3.30915i	−0.795452	+	0.304632i
$119$		0			0
$120$	−1.07712	−	3.34168i	−0.0983270	−	0.305052i
$121$	−5.82160	+	3.36110i	−0.529237	+	0.305555i
$122$	−9.61439	−	1.53048i	−0.870446	−	0.138563i
$123$	2.88846	+	10.7799i	0.260444	+	0.971990i
$124$	3.75109	−	11.4835i	0.336858	−	1.03125i
$125$	7.37052	+	7.37052i	0.659240	+	0.659240i
$126$		0			0
$127$	−10.7393			−0.952959			−0.476479	−	0.879186i	$-0.658087\pi$
$127$	−10.7393			−0.952959			−0.476479	+	0.879186i	$0.658087\pi$
$128$	7.52422	+	8.44903i	0.665054	+	0.746796i
$129$	2.42055	−	4.19251i	0.213117	−	0.369130i
$130$	4.01343	−	2.91114i	0.352001	−	0.255324i
$131$	−4.71692	+	17.6038i	−0.412120	+	1.53805i	0.378416	+	0.925636i	$0.376469\pi$
$131$	−4.71692	+	17.6038i	−0.412120	+	1.53805i	−0.790536	+	0.612416i	$0.790198\pi$
$132$	5.68896	+	6.33813i	0.495161	+	0.551664i
$133$		0			0
$134$	2.39170	+	6.24518i	0.206611	+	0.539501i
$135$	5.35009	−	3.08887i	0.460462	−	0.265848i
$136$	−0.731566	−	0.157293i	−0.0627313	−	0.0134878i
$137$	6.35987	+	3.67187i	0.543360	+	0.313709i	0.746440	−	0.665453i	$-0.231762\pi$
$137$	6.35987	+	3.67187i	0.543360	+	0.313709i	−0.203079	+	0.979162i	$0.565095\pi$
$138$	1.71791	+	1.39336i	0.146238	+	0.118610i
$139$	8.36184	−	8.36184i	0.709242	−	0.709242i	−0.257134	−	0.966376i	$-0.582778\pi$
$139$	8.36184	−	8.36184i	0.709242	−	0.709242i	0.966376	+	0.257134i	$0.0827781\pi$
$140$		0			0
$141$	−2.23571	−	2.23571i	−0.188281	−	0.188281i
$142$	−12.7139	+	1.32623i	−1.06693	+	0.111295i
$143$	−6.01355	+	10.4158i	−0.502878	+	0.871011i
$144$	−4.66762	+	6.38237i	−0.388969	+	0.531864i
$145$	0.284724	+	0.493157i	0.0236450	+	0.0409544i
$146$	8.53652	−	19.1331i	0.706487	−	1.58346i
$147$		0			0
$148$	18.7778	+	1.01355i	1.54353	+	0.0833132i
$149$	17.5919	+	4.71375i	1.44119	+	0.386165i	0.892949	−	0.450157i	$-0.148632\pi$
$149$	17.5919	+	4.71375i	1.44119	+	0.386165i	0.548239	+	0.836322i	$0.315299\pi$
$150$	−0.785801	+	4.93637i	−0.0641604	+	0.403053i
$151$	−11.2731	−	6.50855i	−0.917394	−	0.529658i	−0.0345916	−	0.999402i	$-0.511013\pi$
$151$	−11.2731	−	6.50855i	−0.917394	−	0.529658i	−0.882803	+	0.469744i	$0.844346\pi$
$152$	−18.1357	+	0.907803i	−1.47100	+	0.0736326i
$153$		−	0.522969i		−	0.0422796i
$154$		0			0
$155$	5.24132	−	5.24132i	0.420993	−	0.420993i
$156$	5.49421	+	1.79468i	0.439889	+	0.143689i
$157$	−20.0219	+	5.36485i	−1.59792	+	0.428162i	−0.944414	−	0.328759i	$-0.893370\pi$
$157$	−20.0219	+	5.36485i	−1.59792	+	0.428162i	−0.653507	+	0.756921i	$0.726703\pi$
$158$	−14.4131	+	10.4546i	−1.14665	+	0.831719i
$159$	0.307963	+	0.533408i	0.0244231	+	0.0423020i
$160$	1.77044	+	6.71220i	0.139965	+	0.530646i
$161$		0			0
$162$	−1.08210	−	0.482796i	−0.0850178	−	0.0379321i
$163$	1.62795	−	6.07559i	0.127511	−	0.475877i	−0.872406	−	0.488782i	$-0.837441\pi$
$163$	1.62795	−	6.07559i	0.127511	−	0.475877i	0.999917	+	0.0129051i	$0.00410792\pi$
$164$	−4.55390	−	21.5904i	−0.355600	−	1.68593i
$165$	1.35250	+	5.04762i	0.105292	+	0.392956i
$166$	−0.901144	+	1.11104i	−0.0699424	+	0.0862337i
$167$		−	5.45765i		−	0.422326i	−0.977451	−	0.211163i	$-0.932275\pi$
$167$		−	5.45765i		−	0.422326i	0.977451	−	0.211163i	$-0.0677250\pi$
$168$		0			0
$169$		−	4.83786i		−	0.372143i
$170$	−0.356582	−	0.289216i	−0.0273486	−	0.0221819i
$171$	−3.28460	−	12.2583i	−0.251179	−	0.937414i
$172$	−5.22561	+	8.01926i	−0.398449	+	0.611463i
$173$	4.25406	−	15.8764i	0.323430	−	1.20706i	−0.592450	−	0.805607i	$-0.701839\pi$
$173$	4.25406	−	15.8764i	0.323430	−	1.20706i	0.915880	−	0.401452i	$-0.131494\pi$
$174$	−0.270482	+	0.606236i	−0.0205052	+	0.0459586i
$175$		0			0
$176$	−10.5562	−	13.1195i	−0.795705	−	0.988921i
$177$	−3.30915	−	5.73162i	−0.248731	−	0.430815i
$178$	−9.12762	−	12.5838i	−0.684144	−	0.943193i
$179$	−17.6788	+	4.73701i	−1.32137	+	0.354061i	−0.849492	−	0.527601i	$-0.823092\pi$
$179$	−17.6788	+	4.73701i	−1.32137	+	0.354061i	−0.471882	+	0.881662i	$0.656425\pi$
$180$	−4.32619	+	2.19579i	−0.322455	+	0.163664i
$181$	1.39069	−	1.39069i	0.103369	−	0.103369i	−0.653531	−	0.756900i	$-0.726713\pi$
$181$	1.39069	−	1.39069i	0.103369	−	0.103369i	0.756900	+	0.653531i	$0.226713\pi$
$182$		0			0
$183$		−	6.96353i		−	0.514759i
$184$	−3.24315	−	2.93395i	−0.239088	−	0.216294i
$185$	9.99247	+	5.76916i	0.734661	+	0.424157i
$186$	8.53356	+	1.35842i	0.625711	+	0.0996044i
$187$	1.07578	+	0.288255i	0.0786691	+	0.0210793i
$188$	4.17568	+	4.65217i	0.304543	+	0.339295i
$189$		0			0
$190$	−10.1747	−	4.53959i	−0.738149	−	0.329337i
$191$	1.73544	+	3.00587i	0.125572	+	0.217497i	0.921956	−	0.387294i	$-0.126590\pi$
$191$	1.73544	+	3.00587i	0.125572	+	0.217497i	−0.796384	+	0.604791i	$0.793257\pi$
$192$	−5.12217	+	6.26504i	−0.369661	+	0.452140i
$193$	3.79327	−	6.57014i	0.273046	−	0.472929i	−0.696595	−	0.717465i	$-0.745302\pi$
$193$	3.79327	−	6.57014i	0.273046	−	0.472929i	0.969640	+	0.244536i	$0.0786357\pi$
$194$	2.09014	+	20.0370i	0.150063	+	1.43857i
$195$	2.50767	+	2.50767i	0.179578	+	0.179578i
$196$		0			0
$197$	7.82786	−	7.82786i	0.557712	−	0.557712i	−0.370944	−	0.928655i	$-0.620966\pi$
$197$	7.82786	−	7.82786i	0.557712	−	0.557712i	0.928655	+	0.370944i	$0.120966\pi$
$198$	7.41342	−	9.14019i	0.526849	−	0.649565i
$199$	−17.0344	−	9.83479i	−1.20753	−	0.697170i	−0.245314	−	0.969444i	$-0.578891\pi$
$199$	−17.0344	−	9.83479i	−1.20753	−	0.697170i	−0.962220	+	0.272274i	$0.912224\pi$
$200$	2.07743	−	9.66206i	0.146897	−	0.683211i
$201$	−4.14254	+	2.39170i	−0.292192	+	0.168697i
$202$	−19.6669	+	7.53178i	−1.38376	+	0.529935i
$203$		0			0
$204$	0.0288475	−	0.534452i	0.00201973	−	0.0374192i
$205$	3.50407	−	13.0774i	0.244735	−	0.913364i
$206$	10.7832	+	14.8663i	0.751303	+	1.03578i
$207$	1.52824	−	2.64699i	0.106220	−	0.183979i
$208$	−10.6559	−	4.12869i	−0.738853	−	0.286273i
$209$	27.0266			1.86947
$210$		0			0
$211$	−1.13890	−	1.13890i	−0.0784048	−	0.0784048i	0.666817	−	0.745222i	$-0.267656\pi$
$211$	−1.13890	−	1.13890i	−0.0784048	−	0.0784048i	−0.745222	+	0.666817i	$0.767656\pi$
$212$	−0.551165	−	1.08592i	−0.0378542	−	0.0745811i
$213$	−2.36645	−	8.83173i	−0.162147	−	0.605140i
$214$	0.390287	−	2.45177i	0.0266795	−	0.167599i
$215$	−5.08605	+	2.93643i	−0.346865	+	0.200263i
$216$	−12.6719	−	6.49412i	−0.862212	−	0.441869i
$217$		0			0
$218$	−7.83479	−	20.4581i	−0.530639	−	1.38560i
$219$	14.4751	+	3.87860i	0.978140	+	0.262092i
$220$	−2.13234	−	10.1096i	−0.143762	−	0.681586i
$221$	0.730076	−	0.195623i	0.0491102	−	0.0131590i
$222$	1.39554	+	13.3783i	0.0936626	+	0.897892i
$223$	−8.02710			−0.537534			−0.268767	−	0.963205i	$-0.586616\pi$
$223$	−8.02710			−0.537534			−0.268767	+	0.963205i	$0.586616\pi$
$224$		0			0
$225$	6.90704			0.460469
$226$	−1.11996	−	10.7365i	−0.0744988	−	0.714179i
$227$	4.88260	−	1.30829i	0.324070	−	0.0868342i	−0.0931165	−	0.995655i	$-0.529683\pi$
$227$	4.88260	−	1.30829i	0.324070	−	0.0868342i	0.417186	+	0.908821i	$0.363016\pi$
$228$	−2.68054	−	12.7086i	−0.177523	−	0.841649i
$229$	−0.868918	−	0.232826i	−0.0574197	−	0.0153856i	0.229995	−	0.973192i	$-0.426129\pi$
$229$	−0.868918	−	0.232826i	−0.0574197	−	0.0153856i	−0.287415	+	0.957806i	$0.592796\pi$
$230$	−0.959669	−	2.50588i	−0.0632787	−	0.165233i
$231$		0			0
$232$	0.598610	−	1.16806i	0.0393007	−	0.0766868i
$233$	−21.2724	+	12.2816i	−1.39360	+	0.804598i	−0.993712	−	0.111965i	$-0.964286\pi$
$233$	−21.2724	+	12.2816i	−1.39360	+	0.804598i	−0.399892	+	0.916562i	$0.630952\pi$
$234$	1.25557	−	7.88746i	0.0820793	−	0.515619i
$235$	0.992735	+	3.70494i	0.0647589	+	0.241683i
$236$	5.92243	+	11.6685i	0.385517	+	0.759554i
$237$	−9.00561	−	9.00561i	−0.584977	−	0.584977i
$238$		0			0
$239$	−29.3026			−1.89543			−0.947714	−	0.319122i	$-0.896612\pi$
$239$	−29.3026			−1.89543			−0.947714	+	0.319122i	$0.896612\pi$
$240$	−4.54230	+	2.00537i	−0.293204	+	0.129446i
$241$	−3.97014	+	6.87649i	−0.255739	+	0.442954i	−0.965096	−	0.261896i	$-0.915652\pi$
$241$	−3.97014	+	6.87649i	−0.255739	+	0.442954i	0.709357	+	0.704850i	$0.248986\pi$
$242$	5.58185	+	7.69540i	0.358815	+	0.494679i
$243$	4.12825	−	15.4068i	0.264827	−	0.988348i
$244$	−0.742058	+	13.7480i	−0.0475054	+	0.880124i
$245$		0			0
$246$	14.7390	−	5.64455i	0.939723	−	0.359883i
$247$	15.8842	−	9.17073i	1.01069	−	0.583519i
$248$	−16.7029	−	3.59128i	−1.06064	−	0.228046i
$249$	−0.886151	−	0.511620i	−0.0561576	−	0.0324226i
$250$	9.28580	−	11.4487i	0.587285	−	0.724079i
$251$	6.93336	−	6.93336i	0.437630	−	0.437630i	−0.453584	−	0.891214i	$-0.649855\pi$
$251$	6.93336	−	6.93336i	0.437630	−	0.437630i	0.891214	+	0.453584i	$0.149855\pi$
$252$		0			0
$253$	4.60269	+	4.60269i	0.289369	+	0.289369i
$254$	1.57573	+	15.1057i	0.0988703	+	0.947816i
$255$	0.164201	−	0.284404i	0.0102827	−	0.0178101i
$256$	10.7802	−	11.8231i	0.673765	−	0.738945i
$257$	4.15244	+	7.19225i	0.259022	+	0.448640i	0.965980	−	0.258616i	$-0.0832663\pi$
$257$	4.15244	+	7.19225i	0.259022	+	0.448640i	−0.706958	+	0.707256i	$0.749933\pi$
$258$	−6.25226	−	2.78955i	−0.389249	−	0.173670i
$259$		0			0
$260$	−4.68363	−	5.21808i	−0.290466	−	0.323612i
$261$	0.886048	+	0.237416i	0.0548450	+	0.0146957i
$262$	25.4533	+	4.05180i	1.57251	+	0.250321i
$263$	11.9975	+	6.92674i	0.739795	+	0.427121i	0.821995	−	0.569495i	$-0.192861\pi$
$263$	11.9975	+	6.92674i	0.739795	+	0.427121i	−0.0821996	+	0.996616i	$0.526194\pi$
$264$	8.08038	−	8.93196i	0.497313	−	0.549724i
$265$		−	0.747198i		−	0.0459000i
$266$		0			0
$267$	7.86258	−	7.86258i	0.481182	−	0.481182i
$268$	8.43343	−	4.28045i	0.515153	−	0.261470i
$269$	−1.75698	+	0.470782i	−0.107125	+	0.0287041i	−0.311983	−	0.950088i	$-0.600993\pi$
$269$	−1.75698	+	0.470782i	−0.107125	+	0.0287041i	0.204858	+	0.978792i	$0.434327\pi$
$270$	−5.12975	−	7.07212i	−0.312187	−	0.430395i
$271$	8.18515	+	14.1771i	0.497212	+	0.861197i	0.999995	−	0.00321582i	$-0.00102363\pi$
$271$	8.18515	+	14.1771i	0.497212	+	0.861197i	−0.502782	+	0.864413i	$0.667690\pi$
$272$	−0.113906	+	1.05209i	−0.00690658	+	0.0637921i
$273$		0			0
$274$	4.23163	−	9.48443i	0.255642	−	0.572975i
$275$	−3.80709	+	14.2083i	−0.229576	+	0.856790i
$276$	1.70781	−	2.62082i	0.102798	−	0.157755i
$277$	3.02645	+	11.2949i	0.181842	+	0.678643i	0.995285	+	0.0969979i	$0.0309240\pi$
$277$	3.02645	+	11.2949i	0.181842	+	0.678643i	−0.813443	+	0.581645i	$0.802409\pi$
$278$	−12.9885	−	10.5347i	−0.778999	−	0.631830i
$279$		−	11.9403i		−	0.714846i
$280$		0			0
$281$			30.2126i			1.80233i	0.433476	+	0.901165i	$0.357287\pi$
$281$			30.2126i			1.80233i	−0.433476	+	0.901165i	$0.642713\pi$
$282$	−2.81667	+	3.47275i	−0.167730	+	0.206799i
$283$	−4.32192	−	16.1296i	−0.256911	−	0.958806i	−0.967017	−	0.254711i	$-0.918020\pi$
$283$	−4.32192	−	16.1296i	−0.256911	−	0.958806i	0.710106	−	0.704095i	$-0.248647\pi$
$284$	3.73091	+	17.6885i	0.221389	+	1.04962i
$285$	2.06258	−	7.69767i	0.122177	−	0.455970i
$286$	15.5330	+	6.93028i	0.918484	+	0.409796i
$287$		0			0
$288$	9.66218	+	5.62894i	0.569349	+	0.331688i
$289$	8.46500	+	14.6618i	0.497941	+	0.862460i
$290$	0.651888	−	0.472846i	0.0382802	−	0.0277665i
$291$	−13.9188	+	3.72952i	−0.815932	+	0.218628i
$292$	−28.1647	−	9.19999i	−1.64822	−	0.538389i
$293$	15.3849	−	15.3849i	0.898793	−	0.898793i	−0.0965365	−	0.995329i	$-0.530776\pi$
$293$	15.3849	−	15.3849i	0.898793	−	0.898793i	0.995329	+	0.0965365i	$0.0307765\pi$
$294$		0			0
$295$			8.02885i			0.467458i
$296$	−1.32956	−	26.5613i	−0.0772790	−	1.54384i
$297$	18.3538	+	10.5965i	1.06499	+	0.614874i
$298$	4.04907	−	25.4361i	0.234557	−	1.47348i
$299$	4.26691	+	1.14332i	0.246762	+	0.0661197i
$300$	7.05870	+	0.380999i	0.407534	+	0.0219970i
$301$		0			0
$302$	−7.50074	+	16.8116i	−0.431619	+	0.967396i
$303$	−7.53178	−	13.0454i	−0.432690	−	0.749441i
$304$	3.93787	+	25.3761i	0.225852	+	1.45542i
$305$	−4.22382	+	7.31587i	−0.241855	+	0.418906i
$306$	−0.735599	+	0.0767332i	−0.0420514	+	0.00438654i
$307$	−8.15291	−	8.15291i	−0.465311	−	0.465311i	0.435080	−	0.900392i	$-0.356720\pi$
$307$	−8.15291	−	8.15291i	−0.465311	−	0.465311i	−0.900392	+	0.435080i	$0.856720\pi$
$308$		0			0
$309$	−9.28874	+	9.28874i	−0.528418	+	0.528418i
$310$	−8.14138	−	6.60331i	−0.462399	−	0.375043i
$311$	26.9396	+	15.5536i	1.52761	+	0.881964i	0.999462	+	0.0328102i	$0.0104457\pi$
$311$	26.9396	+	15.5536i	1.52761	+	0.881964i	0.528145	+	0.849154i	$0.322888\pi$
$312$	1.71822	−	7.99139i	0.0972751	−	0.452423i
$313$	−2.75384	+	1.58993i	−0.155656	+	0.0898681i	−0.575805	−	0.817587i	$-0.695311\pi$
$313$	−2.75384	+	1.58993i	−0.155656	+	0.0898681i	0.420149	+	0.907455i	$0.361978\pi$
$314$	10.4838	+	27.3753i	0.591637	+	1.54488i
$315$		0			0
$316$	16.8200	+	18.7393i	0.946197	+	1.05417i
$317$	0.574458	−	2.14391i	0.0322648	−	0.120414i	−0.947915	−	0.318523i	$-0.896813\pi$
$317$	0.574458	−	2.14391i	0.0322648	−	0.120414i	0.980180	+	0.198109i	$0.0634800\pi$
$318$	0.705096	−	0.511440i	0.0395398	−	0.0286802i
$319$	−0.976761	+	1.69180i	−0.0546881	+	0.0947226i
$320$	9.18149	−	3.47512i	0.513261	−	0.194265i
$321$	1.77577			0.0991139
$322$		0			0
$323$	−1.20099	−	1.20099i	−0.0668248	−	0.0668248i
$324$	−0.520320	+	1.59290i	−0.0289067	+	0.0884945i
$325$	2.58366	+	9.64237i	0.143316	+	0.534862i
$326$	−8.78468	−	1.39840i	−0.486538	−	0.0774501i
$327$	13.5703	−	7.83479i	0.750437	−	0.433265i
$328$	−29.7004	+	9.57331i	−1.63993	+	0.528597i
$329$		0			0
$330$	6.90143	−	2.64302i	0.379911	−	0.145494i
$331$	−2.67696	−	0.717289i	−0.147139	−	0.0394258i	0.184498	−	0.982833i	$-0.440934\pi$
$331$	−2.67696	−	0.717289i	−0.147139	−	0.0394258i	−0.331637	+	0.943407i	$0.607601\pi$
$332$	1.69499	+	1.10451i	0.0930249	+	0.0606181i
$333$	17.9533	−	4.81058i	0.983837	−	0.263618i
$334$	−7.67663	+	0.800779i	−0.420046	+	0.0438167i
$335$	5.80287			0.317045
$336$		0			0
$337$	−28.7067			−1.56375			−0.781876	−	0.623434i	$-0.785737\pi$
$337$	−28.7067			−1.56375			−0.781876	+	0.623434i	$0.785737\pi$
$338$	−6.80485	+	0.709840i	−0.370135	+	0.0386102i
$339$	7.45811	−	1.99839i	0.405069	−	0.108538i
$340$	−0.354486	+	0.543997i	−0.0192247	+	0.0295024i
$341$	24.5620	+	6.58136i	1.33011	+	0.356401i
$342$	−16.7603	+	6.41866i	−0.906295	+	0.347082i
$343$		0			0
$344$	12.0465	+	6.17362i	0.649503	+	0.332859i
$345$	1.66220	−	0.959669i	0.0894896	−	0.0516669i
$346$	−22.9556	−	3.65421i	−1.23410	−	0.196452i
$347$	1.61739	+	6.03619i	0.0868261	+	0.324039i	0.995654	−	0.0931324i	$-0.0296880\pi$
$347$	1.61739	+	6.03619i	0.0868261	+	0.324039i	−0.908828	+	0.417172i	$0.863021\pi$
$348$	0.892407	+	0.291504i	0.0478380	+	0.0156263i
$349$	−7.46427	−	7.46427i	−0.399553	−	0.399553i	0.478522	−	0.878075i	$-0.341173\pi$
$349$	−7.46427	−	7.46427i	−0.399553	−	0.399553i	−0.878075	+	0.478522i	$0.841173\pi$
$350$		0			0
$351$	14.3826			0.767686
$352$	−16.9048	+	16.7731i	−0.901029	+	0.894012i
$353$	3.35343	−	5.80832i	0.178485	−	0.309146i	−0.762877	−	0.646544i	$-0.776214\pi$
$353$	3.35343	−	5.80832i	0.178485	−	0.309146i	0.941362	+	0.337399i	$0.109547\pi$
$354$	−7.57645	+	5.49557i	−0.402684	+	0.292086i
$355$	−2.87081	+	10.7140i	−0.152367	+	0.568641i
$356$	−16.3608	+	14.6851i	−0.867122	+	0.778309i
$357$		0			0
$358$	9.25693	+	24.1716i	0.489244	+	1.27751i
$359$	−10.1793	+	5.87700i	−0.537241	+	0.310176i	−0.743960	−	0.668224i	$-0.767055\pi$
$359$	−10.1793	+	5.87700i	−0.537241	+	0.310176i	0.206719	+	0.978400i	$0.433721\pi$
$360$	3.72332	+	5.76295i	0.196236	+	0.303734i
$361$	−19.2394	−	11.1079i	−1.01260	−	0.584626i
$362$	−2.16017	−	1.75207i	−0.113536	−	0.0920867i
$363$	−4.80823	+	4.80823i	−0.252367	+	0.252367i
$364$		0			0
$365$	−12.8550	−	12.8550i	−0.672859	−	0.672859i
$366$	−9.79477	+	1.02173i	−0.511981	+	0.0534067i
$367$	−17.2352	+	29.8522i	−0.899669	+	1.55827i	−0.0717506	+	0.997423i	$0.522859\pi$
$367$	−17.2352	+	29.8522i	−0.899669	+	1.55827i	−0.827918	+	0.560849i	$0.810475\pi$
$368$	−3.65098	+	4.99224i	−0.190321	+	0.260239i
$369$	−10.9045	−	18.8872i	−0.567666	−	0.983226i
$370$	6.64863	−	14.9017i	0.345646	−	0.774703i
$371$		0			0
$372$	0.658638	−	12.2025i	0.0341488	−	0.632668i
$373$	12.0177	+	3.22012i	0.622251	+	0.166732i	0.556151	−	0.831081i	$-0.312278\pi$
$373$	12.0177	+	3.22012i	0.622251	+	0.166732i	0.0660999	+	0.997813i	$0.478944\pi$
$374$	0.247609	−	1.55547i	0.0128036	−	0.0804315i
$375$	9.13130	+	5.27196i	0.471538	+	0.272243i
$376$	5.93098	−	6.55603i	0.305867	−	0.338102i
$377$			1.32575i			0.0682795i
$378$		0			0
$379$	−0.171601	+	0.171601i	−0.00881456	+	0.00881456i	−0.711500	−	0.702686i	$-0.751984\pi$
$379$	−0.171601	+	0.171601i	−0.00881456	+	0.00881456i	0.702686	+	0.711500i	$0.251984\pi$
$380$	−4.89242	+	14.9776i	−0.250976	+	0.768334i
$381$	−10.4932	+	2.81165i	−0.537583	+	0.144045i
$382$	3.97337	−	2.88208i	0.203295	−	0.147460i
$383$	−10.8580	−	18.8067i	−0.554819	−	0.960975i	−0.997918	−	0.0645023i	$-0.979454\pi$
$383$	−10.8580	−	18.8067i	−0.554819	−	0.960975i	0.443098	−	0.896473i	$-0.353879\pi$
$384$	9.56384	+	6.28551i	0.488053	+	0.320756i
$385$		0			0
$386$	−9.79800	−	4.37153i	−0.498705	−	0.222505i
$387$	−2.44853	+	9.13803i	−0.124466	+	0.464512i
$388$	27.8770	−	5.87990i	1.41524	−	0.298507i
$389$	4.14779	+	15.4798i	0.210302	+	0.784856i	0.987768	+	0.155931i	$0.0498379\pi$
$389$	4.14779	+	15.4798i	0.210302	+	0.784856i	−0.777466	+	0.628925i	$0.783495\pi$
$390$	3.15930	−	3.89518i	0.159977	−	0.197240i
$391$		−	0.409063i		−	0.0206872i
$392$		0			0
$393$			18.4353i			0.929940i
$394$	−12.1591	−	9.86197i	−0.612565	−	0.496839i
$395$	3.99881	+	14.9238i	0.201202	+	0.750896i
$396$	−13.9442	−	9.08648i	−0.700721	−	0.456613i
$397$	−5.39802	+	20.1457i	−0.270919	+	1.01108i	0.687608	+	0.726082i	$0.258661\pi$
$397$	−5.39802	+	20.1457i	−0.270919	+	1.01108i	−0.958527	+	0.285001i	$0.908006\pi$
$398$	−11.3341	+	25.4032i	−0.568125	+	1.27335i
$399$		0			0
$400$	−13.8953	−	1.50440i	−0.694764	−	0.0752200i
$401$	0.0734423	+	0.127206i	0.00366753	+	0.00635235i	0.867853	−	0.496820i	$-0.165499\pi$
$401$	0.0734423	+	0.127206i	0.00366753	+	0.00635235i	−0.864186	+	0.503173i	$0.832166\pi$
$402$	3.97194	+	5.47590i	0.198102	+	0.273113i
$403$	16.6689	−	4.46641i	0.830336	−	0.222488i
$404$	13.4797	+	26.5580i	0.670641	+	1.32131i
$405$	−0.727032	+	0.727032i	−0.0361265	+	0.0361265i
$406$		0			0
$407$			39.5828i			1.96205i
$408$	−0.755984	+	0.0378417i	−0.0374268	+	0.00187344i
$409$	1.96730	+	1.13582i	0.0972768	+	0.0561628i	0.547849	−	0.836577i	$-0.315447\pi$
$409$	1.96730	+	1.13582i	0.0972768	+	0.0561628i	−0.450572	+	0.892740i	$0.648780\pi$
$410$	−18.9085	−	3.00997i	−0.933826	−	0.148652i
$411$	7.17546	+	1.92266i	0.353939	+	0.0948378i
$412$	19.3284	−	17.3488i	0.952244	−	0.854712i
$413$		0			0
$414$	−3.94744	−	1.76121i	−0.194006	−	0.0865590i
$415$	0.620660	+	1.07501i	0.0304670	+	0.0527704i
$416$	−4.24385	+	15.5942i	−0.208072	+	0.764567i
$417$	5.98102	−	10.3594i	0.292892	−	0.507304i
$418$	−3.96550	−	38.0151i	−0.193959	−	1.85938i
$419$	19.3654	+	19.3654i	0.946061	+	0.946061i	0.998618	−	0.0525570i	$-0.0167371\pi$
$419$	19.3654	+	19.3654i	0.946061	+	0.946061i	−0.0525570	+	0.998618i	$0.516737\pi$
$420$		0			0
$421$	8.11005	−	8.11005i	0.395260	−	0.395260i	−0.481298	−	0.876557i	$-0.659834\pi$
$421$	8.11005	−	8.11005i	0.395260	−	0.395260i	0.876557	+	0.481298i	$0.159834\pi$
$422$	−1.43484	+	1.76906i	−0.0698471	+	0.0861163i
$423$	5.35090	+	3.08934i	0.260170	+	0.150209i
$424$	−1.44656	+	0.934591i	−0.0702512	+	0.0453878i
$425$	0.800554	−	0.462200i	0.0388326	−	0.0224200i
$426$	−12.0753	+	4.62446i	−0.585051	+	0.224056i
$427$		0			0
$428$	−3.50588	−	0.189233i	−0.169463	−	0.00914690i
$429$	−3.14880	+	11.7515i	−0.152026	+	0.567368i
$430$	4.87658	+	6.72309i	0.235170	+	0.324216i
$431$	5.38288	−	9.32343i	0.259284	−	0.449094i	−0.706766	−	0.707447i	$-0.749847\pi$
$431$	5.38288	−	9.32343i	0.259284	−	0.449094i	0.966050	+	0.258354i	$0.0831800\pi$
$432$	−7.27522	+	18.7769i	−0.350029	+	0.903403i
$433$	4.99439			0.240015			0.120008	−	0.992773i	$-0.461708\pi$
$433$	4.99439			0.240015			0.120008	+	0.992773i	$0.461708\pi$
$434$		0			0
$435$	0.407313	+	0.407313i	0.0195291	+	0.0195291i
$436$	−27.6264	+	14.0220i	−1.32307	+	0.671532i
$437$	−2.56919	−	9.58835i	−0.122901	−	0.458673i
$438$	3.33169	−	20.9296i	0.159194	−	1.00005i
$439$	1.47159	−	0.849621i	0.0702350	−	0.0405502i	−0.464471	−	0.885588i	$-0.653756\pi$
$439$	1.47159	−	0.849621i	0.0702350	−	0.0405502i	0.534706	+	0.845038i	$0.320422\pi$
$440$	−13.9070	+	4.48264i	−0.662992	+	0.213701i
$441$		0			0
$442$	−0.382281	−	0.998208i	−0.0181833	−	0.0474799i
$443$	10.7956	+	2.89267i	0.512913	+	0.137435i	0.505987	−	0.862541i	$-0.331128\pi$
$443$	10.7956	+	2.89267i	0.512913	+	0.137435i	0.00692670	+	0.999976i	$0.497795\pi$
$444$	18.6129	−	3.92589i	0.883329	−	0.186314i
$445$	−13.0296	+	3.49126i	−0.617661	+	0.165502i
$446$	1.17778	+	11.2908i	0.0557697	+	0.534633i
$447$	18.4229			0.871375
$448$		0			0
$449$	4.05419			0.191329			0.0956646	−	0.995414i	$-0.469502\pi$
$449$	4.05419			0.191329			0.0956646	+	0.995414i	$0.469502\pi$
$450$	−1.01344	−	9.71532i	−0.0477741	−	0.457984i
$451$	44.8626	−	12.0209i	2.11250	−	0.566042i
$452$	−14.9374	+	3.15064i	−0.702595	+	0.148193i
$453$	−12.7188	−	3.40799i	−0.597582	−	0.160122i
$454$	−2.55662	−	6.67582i	−0.119988	−	0.313312i
$455$		0			0
$456$	−17.4824	+	5.63508i	−0.818689	+	0.263887i
$457$	8.79002	−	5.07492i	0.411180	−	0.237395i	−0.280117	−	0.959966i	$-0.590373\pi$
$457$	8.79002	−	5.07492i	0.411180	−	0.237395i	0.691296	+	0.722571i	$0.257040\pi$
$458$	−0.199996	+	1.25637i	−0.00934519	+	0.0587061i
$459$	−0.344710	−	1.28647i	−0.0160897	−	0.0600475i
$460$	−3.38391	+	1.71753i	−0.157776	+	0.0800803i
$461$	1.02609	+	1.02609i	0.0477897	+	0.0477897i	0.730598	−	0.682808i	$-0.239241\pi$
$461$	1.02609	+	1.02609i	0.0477897	+	0.0477897i	−0.682808	+	0.730598i	$0.739241\pi$
$462$		0			0
$463$	10.5945			0.492369			0.246185	−	0.969223i	$-0.420823\pi$
$463$	10.5945			0.492369			0.246185	+	0.969223i	$0.420823\pi$
$464$	−1.73080	−	0.670610i	−0.0803504	−	0.0311323i
$465$	3.74899	−	6.49344i	0.173855	−	0.301126i
$466$	20.3964	+	28.1194i	0.944843	+	1.30261i
$467$	3.39211	−	12.6595i	0.156968	−	0.585812i	−0.841961	−	0.539539i	$-0.818599\pi$
$467$	3.39211	−	12.6595i	0.156968	−	0.585812i	0.998929	−	0.0462738i	$-0.0147347\pi$
$468$	−11.2786	−	0.608770i	−0.521352	−	0.0281404i
$469$		0			0
$470$	5.06564	−	1.93997i	0.233660	−	0.0894843i
$471$	−18.1585	+	10.4838i	−0.836701	+	0.483069i
$472$	15.5437	−	10.0424i	0.715457	−	0.462241i
$473$	−17.4479	−	10.0736i	−0.802257	−	0.463184i
$474$	−11.3458	+	13.9885i	−0.521128	+	0.642512i
$475$	15.8619	−	15.8619i	0.727793	−	0.727793i
$476$		0			0
$477$	−0.851098	−	0.851098i	−0.0389691	−	0.0389691i
$478$	4.29945	+	41.2165i	0.196652	+	1.88520i
$479$	−16.7383	+	28.9916i	−0.764792	+	1.32466i	0.175564	+	0.984468i	$0.443825\pi$
$479$	−16.7383	+	28.9916i	−0.764792	+	1.32466i	−0.940356	+	0.340191i	$0.889508\pi$
$480$	3.48718	+	6.09488i	0.159167	+	0.278192i
$481$	13.4313	+	23.2638i	0.612416	+	1.06074i
$482$	10.2549	+	4.57537i	0.467096	+	0.208402i
$483$		0			0
$484$	10.0052	−	8.98044i	0.454782	−	0.408202i
$485$	16.8852	+	4.52438i	0.766718	+	0.205441i
$486$	−22.2767	−	3.54613i	−1.01049	−	0.160856i
$487$	−19.9401	−	11.5124i	−0.903571	−	0.521677i	−0.0252137	−	0.999682i	$-0.508027\pi$
$487$	−19.9401	−	11.5124i	−0.903571	−	0.521677i	−0.878357	+	0.478005i	$0.841360\pi$
$488$	19.4465	−	0.973421i	0.880303	−	0.0440647i
$489$		−	6.36258i		−	0.287726i
$490$		0			0
$491$	−21.9341	+	21.9341i	−0.989874	+	0.989874i	−0.999949	−	0.0100754i	$-0.996793\pi$
$491$	−21.9341	+	21.9341i	−0.989874	+	0.989874i	0.0100754	+	0.999949i	$0.496793\pi$
$492$	−10.1021	−	19.9034i	−0.455438	−	0.897314i
$493$	0.118584	−	0.0317744i	0.00534074	−	0.00143105i
$494$	−15.2300	−	20.9968i	−0.685230	−	0.944690i
$495$	−5.10597	−	8.84379i	−0.229496	−	0.397499i
$496$	−2.60068	+	24.0209i	−0.116774	+	1.07857i
$497$		0			0
$498$	−0.589613	+	1.32151i	−0.0264212	+	0.0592184i
$499$	2.24074	−	8.36254i	0.100309	−	0.374359i	−0.897462	−	0.441092i	$-0.854591\pi$
$499$	2.24074	−	8.36254i	0.100309	−	0.374359i	0.997771	+	0.0667336i	$0.0212578\pi$
$500$	−17.4660	−	11.3814i	−0.781103	−	0.508992i
$501$	−1.42886	−	5.33259i	−0.0638369	−	0.238242i
$502$	−10.7696	−	8.73503i	−0.480672	−	0.389863i
$503$			11.5286i			0.514034i	0.966407	+	0.257017i	$0.0827396\pi$
$503$			11.5286i			0.514034i	−0.966407	+	0.257017i	$0.917260\pi$
$504$		0			0
$505$			18.2740i			0.813183i
$506$	5.79873	−	7.14940i	0.257785	−	0.317829i
$507$	−1.26660	−	4.72701i	−0.0562516	−	0.209934i
$508$	21.0162	−	4.43280i	0.932443	−	0.196674i
$509$	−6.56418	+	24.4978i	−0.290952	+	1.08585i	0.653427	+	0.756989i	$0.273331\pi$
$509$	−6.56418	+	24.4978i	−0.290952	+	1.08585i	−0.944379	+	0.328859i	$0.893336\pi$
$510$	−0.424131	−	0.189233i	−0.0187808	−	0.00837936i
$511$		0			0
$512$	−18.2119	−	13.4285i	−0.804861	−	0.593463i
$513$	−16.1598	−	27.9897i	−0.713475	−	1.23577i
$514$	9.50721	−	6.89604i	0.419345	−	0.304171i
$515$	15.3929	−	4.12453i	0.678294	−	0.181748i
$516$	−3.00635	+	9.20362i	−0.132347	+	0.405167i
$517$	−9.30435	+	9.30435i	−0.409205	+	0.409205i
$518$		0			0
$519$		−	16.6263i		−	0.729815i
$520$	−6.65244	+	7.35353i	−0.291729	+	0.322474i
$521$	0.249004	+	0.143762i	0.0109091	+	0.00629835i	0.505445	−	0.862859i	$-0.331328\pi$
$521$	0.249004	+	0.143762i	0.0109091	+	0.00629835i	−0.494536	+	0.869157i	$0.664662\pi$
$522$	0.203938	−	1.28113i	0.00892614	−	0.0560737i
$523$	5.24964	+	1.40664i	0.229551	+	0.0615079i	0.371761	−	0.928329i	$-0.378754\pi$
$523$	5.24964	+	1.40664i	0.229551	+	0.0615079i	−0.142210	+	0.989837i	$0.545421\pi$
$524$	1.96454	−	36.3966i	0.0858211	−	1.58999i
$525$		0			0
$526$	7.98268	−	17.8917i	0.348062	−	0.780117i
$527$	−0.799011	−	1.38393i	−0.0348055	−	0.0602848i
$528$	−13.7491	−	10.0552i	−0.598354	−	0.437595i
$529$	−10.3046	+	17.8481i	−0.448027	+	0.776005i
$530$	−1.05099	+	0.109633i	−0.0456523	+	0.00476217i
$531$	9.14529	+	9.14529i	0.396872	+	0.396872i
$532$		0			0
$533$	22.2879	−	22.2879i	0.965396	−	0.965396i
$534$	−12.2130	−	9.90572i	−0.528508	−	0.428662i
$535$	−1.86562	−	1.07712i	−0.0806580	−	0.0465679i
$536$	−7.25820	−	11.2342i	−0.313507	−	0.485246i
$537$	−16.0335	+	9.25693i	−0.691896	+	0.399466i
$538$	0.919989	+	2.40226i	0.0396635	+	0.103569i
$539$		0			0
$540$	−9.19484	+	8.25308i	−0.395683	+	0.355156i
$541$	9.64594	−	35.9992i	0.414712	−	1.54772i	−0.370701	−	0.928752i	$-0.620883\pi$
$541$	9.64594	−	35.9992i	0.414712	−	1.54772i	0.785413	−	0.618972i	$-0.212451\pi$
$542$	18.7403	−	13.5932i	0.804963	−	0.583879i
$543$	0.994727	−	1.72292i	0.0426878	−	0.0739375i
$544$	1.49656	+	0.00585000i	0.0641644	+	0.000250817i
$545$	−19.0092			−0.814264
$546$		0			0
$547$	10.4205	+	10.4205i	0.445550	+	0.445550i	0.893872	−	0.448322i	$-0.147978\pi$
$547$	10.4205	+	10.4205i	0.445550	+	0.445550i	−0.448322	+	0.893872i	$0.647978\pi$
$548$	−13.9615	−	4.56052i	−0.596406	−	0.194816i
$549$	3.52201	+	13.1443i	0.150316	+	0.560986i
$550$	20.5437	+	3.27026i	0.875985	+	0.139444i
$551$	2.58001	−	1.48957i	0.109912	−	0.0634578i
$552$	−3.93697	−	2.01763i	−0.167569	−	0.0858761i
$553$		0			0
$554$	15.4431	−	5.91420i	0.656114	−	0.251270i
$555$	11.2739	+	3.02084i	0.478551	+	0.128227i
$556$	−12.9122	+	19.8151i	−0.547598	+	0.840348i
$557$	−10.5829	+	2.83567i	−0.448411	+	0.120151i	−0.475956	−	0.879469i	$-0.657898\pi$
$557$	−10.5829	+	2.83567i	−0.448411	+	0.120151i	0.0275450	+	0.999621i	$0.491231\pi$
$558$	−16.7950	+	1.75195i	−0.710989	+	0.0741660i
$559$	−13.6728			−0.578297
$560$		0			0
$561$	1.12660			0.0475651
$562$	42.4964	−	4.43297i	1.79260	−	0.186993i
$563$	−19.2022	+	5.14520i	−0.809274	+	0.216844i	−0.639652	−	0.768665i	$-0.720921\pi$
$563$	−19.2022	+	5.14520i	−0.809274	+	0.216844i	−0.169622	+	0.985509i	$0.554255\pi$
$564$	5.29798	+	3.45234i	0.223085	+	0.145370i
$565$	−9.04763	−	2.42431i	−0.380637	−	0.101991i
$566$	−22.0535	+	8.44576i	−0.926977	+	0.355002i
$567$		0			0
$568$	24.3329	−	7.84320i	1.02099	−	0.329093i
$569$	23.3519	−	13.4822i	0.978963	−	0.565205i	0.0770061	−	0.997031i	$-0.475464\pi$
$569$	23.3519	−	13.4822i	0.978963	−	0.565205i	0.901957	+	0.431826i	$0.142131\pi$
$570$	−11.1300	−	1.77174i	−0.466186	−	0.0742102i
$571$	7.98417	+	29.7973i	0.334127	+	1.24698i	0.904813	+	0.425810i	$0.140011\pi$
$571$	7.98417	+	29.7973i	0.334127	+	1.24698i	−0.570686	+	0.821169i	$0.693322\pi$
$572$	7.46892	−	22.8652i	0.312291	−	0.956044i
$573$	2.48264	+	2.48264i	0.103714	+	0.103714i
$574$		0			0
$575$	5.40264			0.225306
$576$	6.49986	−	14.4166i	0.270828	−	0.600690i
$577$	−4.08125	+	7.06893i	−0.169905	+	0.294283i	−0.938386	−	0.345589i	$-0.887679\pi$
$577$	−4.08125	+	7.06893i	−0.169905	+	0.294283i	0.768482	+	0.639872i	$0.221013\pi$
$578$	19.3810	−	14.0580i	0.806144	−	0.584735i
$579$	1.98623	−	7.41269i	0.0825447	−	0.308061i
$580$	−0.760746	−	0.847555i	−0.0315883	−	0.0351928i
$581$		0			0
$582$	7.28811	+	19.0306i	0.302102	+	0.788845i
$583$	2.21988	−	1.28165i	0.0919382	−	0.0530805i
$584$	−8.80804	+	40.9659i	−0.364479	+	1.69518i
$585$	−6.00180	−	3.46514i	−0.248144	−	0.143266i
$586$	−23.8974	−	19.3827i	−0.987193	−	0.800692i
$587$	−0.0166226	+	0.0166226i	−0.000686087	+	0.000686087i	−0.707450	−	0.706764i	$-0.750154\pi$
$587$	−0.0166226	+	0.0166226i	−0.000686087	+	0.000686087i	0.706764	+	0.707450i	$0.250154\pi$
$588$		0			0
$589$	−27.4206	−	27.4206i	−1.12985	−	1.12985i
$590$	11.2932	−	1.17804i	0.464935	−	0.0484992i
$591$	5.59908	−	9.69789i	0.230315	−	0.398918i
$592$	−37.1655	+	5.76736i	−1.52749	+	0.237037i
$593$	−8.35729	−	14.4753i	−0.343193	−	0.594427i	0.641831	−	0.766846i	$-0.278175\pi$
$593$	−8.35729	−	14.4753i	−0.343193	−	0.594427i	−0.985024	+	0.172419i	$0.944842\pi$
$594$	12.2119	−	27.3708i	0.501062	−	1.12304i
$595$		0			0
$596$	−36.3721	−	1.96321i	−1.48986	−	0.0804163i
$597$	−19.2189	−	5.14968i	−0.786575	−	0.210762i
$598$	0.982100	−	6.16952i	0.0401611	−	0.252290i
$599$	15.2174	+	8.78578i	0.621767	+	0.358977i	0.777556	−	0.628813i	$-0.216459\pi$
$599$	15.2174	+	8.78578i	0.621767	+	0.358977i	−0.155790	+	0.987790i	$0.549792\pi$
$600$	−0.499789	−	9.98454i	−0.0204038	−	0.407617i
$601$			6.99237i			0.285225i	0.989779	+	0.142612i	$0.0455503\pi$
$601$			6.99237i			0.285225i	−0.989779	+	0.142612i	$0.954450\pi$
$602$		0			0
$603$	6.60978	−	6.60978i	0.269171	−	0.269171i
$604$	24.7474	+	8.08371i	1.00696	+	0.328921i
$605$	7.96802	−	2.13503i	0.323946	−	0.0868011i
$606$	−17.2444	+	12.5082i	−0.700504	+	0.508110i
$607$	3.12773	+	5.41738i	0.126951	+	0.219885i	0.922494	−	0.386012i	$-0.126148\pi$
$607$	3.12773	+	5.41738i	0.126951	+	0.219885i	−0.795543	+	0.605897i	$0.792814\pi$
$608$	35.1157	−	9.26227i	1.42413	−	0.375635i
$609$		0			0
$610$	10.9101	+	4.86772i	0.441738	+	0.197088i
$611$	−2.31121	+	8.62557i	−0.0935017	+	0.348953i
$612$	0.215863	+	1.02342i	0.00872574	+	0.0413693i
$613$	−2.08597	−	7.78494i	−0.0842514	−	0.314431i	0.910920	−	0.412583i	$-0.135373\pi$
$613$	−2.08597	−	7.78494i	−0.0842514	−	0.314431i	−0.995171	+	0.0981525i	$0.968707\pi$
$614$	−10.2715	+	12.6640i	−0.414524	+	0.511077i
$615$		−	13.6951i		−	0.552240i
$616$		0			0
$617$		−	44.4895i		−	1.79108i	−0.444980	−	0.895541i	$-0.646789\pi$
$617$		−	44.4895i		−	1.79108i	0.444980	−	0.895541i	$-0.353211\pi$
$618$	14.4283	+	11.7025i	0.580390	+	0.470742i
$619$	−5.07865	−	18.9538i	−0.204128	−	0.761816i	−0.989714	−	0.143063i	$-0.954305\pi$
$619$	−5.07865	−	18.9538i	−0.204128	−	0.761816i	0.785586	−	0.618753i	$-0.212362\pi$
$620$	−8.09353	+	12.4204i	−0.325044	+	0.498815i
$621$	2.01465	−	7.51878i	0.0808451	−	0.301718i
$622$	17.9247	−	40.1749i	0.718714	−	1.61087i
$623$		0			0
$624$	−11.4926	−	1.24427i	−0.460074	−	0.0498108i
$625$	2.33975	+	4.05256i	0.0935899	+	0.162103i
$626$	2.64042	+	3.64021i	0.105533	+	0.145492i
$627$	26.4072	−	7.07580i	1.05460	−	0.282580i
$628$	36.9673	−	18.7630i	1.47516	−	0.748726i
$629$	1.75895	−	1.75895i	0.0701341	−	0.0701341i
$630$		0			0
$631$		−	8.64101i		−	0.343993i	−0.985098	−	0.171997i	$-0.944978\pi$
$631$		−	8.64101i		−	0.343993i	0.985098	−	0.171997i	$-0.0550218\pi$
$632$	23.8904	−	26.4082i	0.950310	−	1.05046i
$633$	−1.41097	−	0.814625i	−0.0560811	−	0.0323784i
$634$	−3.09987	−	0.493455i	−0.123111	−	0.0195976i
$635$	12.7296	+	3.41088i	0.505159	+	0.135357i
$636$	−0.822839	−	0.916733i	−0.0326277	−	0.0363508i
$637$		0			0
$638$	2.52297	+	1.12566i	0.0998853	+	0.0445654i
$639$	8.93382	+	15.4738i	0.353417	+	0.612136i
$640$	−6.23520	−	12.4046i	−0.246468	−	0.490336i
$641$	−7.54432	+	13.0672i	−0.297983	+	0.516122i	−0.975674	−	0.219225i	$-0.929647\pi$
$641$	−7.54432	+	13.0672i	−0.297983	+	0.516122i	0.677691	+	0.735346i	$0.262981\pi$
$642$	−0.260552	−	2.49777i	−0.0102832	−	0.0985790i
$643$	−12.3557	−	12.3557i	−0.487261	−	0.487261i	0.420180	−	0.907441i	$-0.361967\pi$
$643$	−12.3557	−	12.3557i	−0.487261	−	0.487261i	−0.907441	+	0.420180i	$0.861967\pi$
$644$		0			0
$645$	−4.20072	+	4.20072i	−0.165403	+	0.165403i
$646$	−1.51307	+	1.86550i	−0.0595310	+	0.0733973i
$647$	−35.3412	−	20.4042i	−1.38941	−	0.802173i	−0.396157	−	0.918183i	$-0.629656\pi$
$647$	−35.3412	−	20.4042i	−1.38941	−	0.802173i	−0.993248	+	0.116009i	$0.962990\pi$
$648$	2.31689	+	0.498152i	0.0910160	+	0.0195693i
$649$	−23.8533	+	13.7717i	−0.936323	+	0.540586i
$650$	13.1837	−	5.04892i	0.517107	−	0.198035i
$651$		0			0
$652$	−0.678019	+	12.5615i	−0.0265533	+	0.491948i
$653$	−3.61772	+	13.5015i	−0.141572	+	0.528356i	0.858312	+	0.513129i	$0.171514\pi$
$653$	−3.61772	+	13.5015i	−0.141572	+	0.528356i	−0.999884	+	0.0152268i	$0.995153\pi$
$654$	−13.0114	−	17.9381i	−0.508785	−	0.701435i
$655$	11.1822	−	19.3682i	0.436925	−	0.756776i
$656$	17.8235	+	40.3714i	0.695889	+	1.57624i
$657$	−29.2850			−1.14252
$658$		0			0
$659$	−2.71835	−	2.71835i	−0.105892	−	0.105892i	0.652176	−	0.758068i	$-0.273856\pi$
$659$	−2.71835	−	2.71835i	−0.105892	−	0.105892i	−0.758068	+	0.652176i	$0.773856\pi$
$660$	−4.73025	−	9.31963i	−0.184125	−	0.362766i
$661$	−3.57716	−	13.3501i	−0.139135	−	0.519260i	−0.999947	−	0.0103356i	$-0.996710\pi$
$661$	−3.57716	−	13.3501i	−0.139135	−	0.519260i	0.860811	−	0.508924i	$-0.169957\pi$
$662$	−0.616146	+	3.87060i	−0.0239472	+	0.150435i
$663$	0.662130	−	0.382281i	0.0257150	−	0.0148466i
$664$	1.30489	−	2.54621i	0.0506395	−	0.0988121i
$665$		0			0
$666$	−9.40070	−	24.5470i	−0.364270	−	0.951177i
$667$	0.693060	+	0.185705i	0.0268354	+	0.00719053i
$668$	2.25272	+	10.6803i	0.0871604	+	0.413234i
$669$	−7.84316	+	2.10157i	−0.303234	+	0.0812513i
$670$	−0.851432	−	8.16221i	−0.0328937	−	0.315334i
$671$	−28.9801			−1.11876
$672$		0			0
$673$	−19.1036			−0.736391			−0.368195	−	0.929748i	$-0.620024\pi$
$673$	−19.1036			−0.736391			−0.368195	+	0.929748i	$0.620024\pi$
$674$	4.21202	+	40.3783i	0.162241	+	1.55531i
$675$	16.9909	−	4.55271i	0.653981	−	0.175234i
$676$	1.99690	+	9.46742i	0.0768037	+	0.364132i
$677$	−14.2373	−	3.81488i	−0.547186	−	0.146618i	−0.0253729	−	0.999678i	$-0.508077\pi$
$677$	−14.2373	−	3.81488i	−0.547186	−	0.146618i	−0.521813	+	0.853060i	$0.674744\pi$
$678$	−3.90520	−	10.1972i	−0.149978	−	0.391622i
$679$		0			0
$680$	0.817189	+	0.418796i	0.0313378	+	0.0160601i
$681$	4.42820	−	2.55662i	0.169689	−	0.0979699i
$682$	5.65334	−	35.5141i	0.216478	−	1.35990i
$683$	−12.8286	−	47.8769i	−0.490872	−	1.83196i	−0.552022	−	0.833830i	$-0.686143\pi$
$683$	−12.8286	−	47.8769i	−0.490872	−	1.83196i	0.0611498	−	0.998129i	$-0.480523\pi$
$684$	11.4875	+	22.6330i	0.439237	+	0.865394i
$685$	−6.37232	−	6.37232i	−0.243474	−	0.243474i
$686$		0			0
$687$	−0.909963			−0.0347172
$688$	6.91617	−	17.8502i	0.263676	−	0.680532i
$689$	0.869786	−	1.50651i	0.0331362	−	0.0573936i
$690$	−1.59374	−	2.19721i	−0.0606727	−	0.0836462i
$691$	1.46943	−	5.48399i	0.0558997	−	0.208621i	−0.932327	−	0.361616i	$-0.882225\pi$
$691$	1.46943	−	5.48399i	0.0558997	−	0.208621i	0.988227	+	0.152995i	$0.0488919\pi$
$692$	−1.77176	+	32.8251i	−0.0673522	+	1.24782i
$693$		0			0
$694$	8.25308	−	3.16066i	0.313282	−	0.119977i
$695$	−12.5673	+	7.25574i	−0.476705	+	0.275226i
$696$	0.279085	−	1.29801i	0.0105787	−	0.0492011i
$697$	−2.52775	−	1.45940i	−0.0957455	−	0.0552787i
$698$	−9.40390	+	11.5943i	−0.355943	+	0.438851i
$699$	−17.5695	+	17.5695i	−0.664541	+	0.664541i
$700$		0			0
$701$	6.91144	+	6.91144i	0.261041	+	0.261041i	0.825477	−	0.564436i	$-0.190906\pi$
$701$	6.91144	+	6.91144i	0.261041	+	0.261041i	−0.564436	+	0.825477i	$0.690906\pi$
$702$	−2.11030	−	20.2303i	−0.0796481	−	0.763543i
$703$	30.1821	−	52.2769i	1.13834	−	1.97166i
$704$	26.0732	+	21.3169i	0.982670	+	0.803411i
$705$	1.93997	+	3.36013i	0.0730636	+	0.126550i
$706$	−8.66191	−	3.86465i	−0.325995	−	0.145448i
$707$		0			0
$708$	8.84163	+	9.85056i	0.332289	+	0.370207i
$709$	−25.2840	−	6.77484i	−0.949562	−	0.254434i	−0.249385	−	0.968404i	$-0.580229\pi$
$709$	−25.2840	−	6.77484i	−0.949562	−	0.254434i	−0.700176	+	0.713970i	$0.746895\pi$
$710$	15.4913	+	2.46601i	0.581380	+	0.0925475i
$711$	21.5538	+	12.4441i	0.808331	+	0.466690i
$712$	23.0564	+	20.8582i	0.864073	+	0.781693i
$713$		−	9.33961i		−	0.349771i
$714$		0			0
$715$	10.4362	−	10.4362i	0.390290	−	0.390290i
$716$	32.6411	−	16.5672i	1.21985	−	0.619147i
$717$	−28.6311	+	7.67169i	−1.06925	+	0.286504i
$718$	9.76005	+	13.4557i	0.364242	+	0.502161i
$719$	−7.26709	−	12.5870i	−0.271017	−	0.469415i	0.698106	−	0.715995i	$-0.254027\pi$
$719$	−7.26709	−	12.5870i	−0.271017	−	0.469415i	−0.969122	+	0.246580i	$0.920693\pi$
$720$	7.55976	−	6.08273i	0.281736	−	0.226690i
$721$		0			0
$722$	−12.8012	+	28.6917i	−0.476413	+	1.06779i
$723$	−2.07884	+	7.75834i	−0.0773129	+	0.288536i
$724$	−2.14747	+	3.29553i	−0.0798102	+	0.122477i
$725$	0.419656	+	1.56618i	0.0155856	+	0.0581664i
$726$	7.46866	+	6.05768i	0.277188	+	0.224822i
$727$			35.2605i			1.30774i	0.756607	+	0.653870i	$0.226856\pi$
$727$			35.2605i			1.30774i	−0.756607	+	0.653870i	$0.773144\pi$
$728$		0			0
$729$		−	13.6210i		−	0.504481i
$730$	−16.1954	+	19.9677i	−0.599418	+	0.739038i
$731$	0.327697	+	1.22298i	0.0121203	+	0.0452337i
$732$	2.87429	+	13.6272i	0.106237	+	0.503677i
$733$	−1.71332	+	6.39419i	−0.0632828	+	0.236175i	−0.990322	−	0.138790i	$-0.955679\pi$
$733$	−1.71332	+	6.39419i	−0.0632828	+	0.236175i	0.927039	+	0.374965i	$0.122345\pi$
$734$	44.5184	+	19.8626i	1.64320	+	0.733141i
$735$		0			0
$736$	7.55769	+	4.40291i	0.278580	+	0.162294i
$737$	9.95352	+	17.2400i	0.366643	+	0.635044i
$738$	−24.9664	+	18.1093i	−0.919024	+	0.666613i
$739$	−15.1682	+	4.06431i	−0.557972	+	0.149508i	−0.526774	−	0.850005i	$-0.676599\pi$
$739$	−15.1682	+	4.06431i	−0.557972	+	0.149508i	−0.0311973	+	0.999513i	$0.509932\pi$
$740$	−21.9360	−	7.16538i	−0.806383	−	0.263404i
$741$	13.1192	−	13.1192i	0.481946	−	0.481946i
$742$		0			0
$743$			9.88941i			0.362807i	0.983409	+	0.181404i	$0.0580641\pi$
$743$			9.88941i			0.362807i	−0.983409	+	0.181404i	$0.941936\pi$
$744$	−17.2604	+	0.863991i	−0.632797	+	0.0316754i
$745$	−19.3551	−	11.1747i	−0.709116	−	0.409408i
$746$	2.76606	−	17.3763i	0.101273	−	0.636191i
$747$	1.93146	+	0.517534i	0.0706686	+	0.0189356i
$748$	−2.22423	−	0.120054i	−0.0813258	−	0.00438963i
$749$		0			0
$750$	6.07564	−	13.6175i	0.221851	−	0.497239i
$751$	1.95848	+	3.39219i	0.0714659	+	0.123783i	0.899544	−	0.436830i	$-0.143899\pi$
$751$	1.95848	+	3.39219i	0.0714659	+	0.123783i	−0.828078	+	0.560613i	$0.810566\pi$
$752$	−10.0918	−	7.38047i	−0.368011	−	0.269138i
$753$	4.95926	−	8.58970i	0.180726	−	0.313026i
$754$	1.86477	−	0.194522i	0.0679110	−	0.00708406i
$755$	11.2952	+	11.2952i	0.411074	+	0.411074i
$756$		0			0
$757$	30.8256	−	30.8256i	1.12037	−	1.12037i	0.128689	−	0.991685i	$-0.458923\pi$
$757$	30.8256	−	30.8256i	1.12037	−	1.12037i	0.991685	−	0.128689i	$-0.0410770\pi$
$758$	0.266550	+	0.216193i	0.00968151	+	0.00785248i
$759$	5.70225	+	3.29220i	0.206979	+	0.119499i
$760$	21.7850	+	4.68398i	0.790226	+	0.169906i
$761$	−26.7482	+	15.4431i	−0.969622	+	0.559812i	−0.899121	−	0.437700i	$-0.855793\pi$
$761$	−26.7482	+	15.4431i	−0.969622	+	0.559812i	−0.0705012	+	0.997512i	$0.522460\pi$
$762$	5.49444	+	14.3470i	0.199042	+	0.519737i
$763$		0			0
$764$	−4.63688	−	5.16599i	−0.167756	−	0.186899i
$765$	−0.166099	+	0.619890i	−0.00600533	+	0.0224122i
$766$	−24.8599	+	18.0321i	−0.898226	+	0.651527i
$767$	−9.34610	+	16.1879i	−0.337468	+	0.584512i
$768$	7.43781	−	14.3746i	0.268389	−	0.518698i
$769$	32.1016			1.15761			0.578807	−	0.815465i	$-0.303519\pi$
$769$	32.1016			1.15761			0.578807	+	0.815465i	$0.303519\pi$
$770$		0			0
$771$	5.94029	+	5.94029i	0.213934	+	0.213934i
$772$	−4.71130	+	14.4231i	−0.169563	+	0.519099i
$773$	−11.3371	−	42.3105i	−0.407766	−	1.52180i	−0.798896	−	0.601469i	$-0.794582\pi$
$773$	−11.3371	−	42.3105i	−0.407766	−	1.52180i	0.391130	−	0.920335i	$-0.372084\pi$
$774$	13.2126	+	2.10327i	0.474919	+	0.0756004i
$775$	18.2780	−	10.5528i	0.656566	−	0.379069i
$776$	−12.3608	−	38.3485i	−0.443728	−	1.37663i
$777$		0			0
$778$	21.1650	−	8.10550i	0.758801	−	0.290596i
$779$	−68.4160	−	18.3320i	−2.45126	−	0.656812i
$780$	−5.94244	−	3.87229i	−0.212774	−	0.138650i
$781$	−36.7550	+	9.84846i	−1.31520	+	0.352406i
$782$	−0.575381	+	0.0600202i	−0.0205756	+	0.00214632i
$783$	2.33612			0.0834860
$784$		0			0
$785$	25.4364			0.907865
$786$	25.9308	−	2.70494i	0.924922	−	0.0964822i
$787$	−33.4688	+	8.96793i	−1.19303	+	0.319672i	−0.800084	−	0.599888i	$-0.795212\pi$
$787$	−33.4688	+	8.96793i	−1.19303	+	0.319672i	−0.392949	+	0.919560i	$0.628545\pi$
$788$	−12.0876	+	18.5497i	−0.430603	+	0.660807i
$789$	13.5360	+	3.62697i	0.481895	+	0.129123i
$790$	20.4047	−	7.81435i	0.725968	−	0.278022i
$791$		0			0
$792$	−10.7349	+	20.9468i	−0.381448	+	0.744313i
$793$	−17.0323	+	9.83360i	−0.604835	+	0.349201i
$794$	29.1286	+	4.63686i	1.03373	+	0.164556i
$795$	−0.195623	−	0.730076i	−0.00693804	−	0.0258931i
$796$	37.3947	+	12.2150i	1.32542	+	0.432948i
$797$	−10.8522	−	10.8522i	−0.384403	−	0.384403i	0.488283	−	0.872686i	$-0.337624\pi$
$797$	−10.8522	−	10.8522i	−0.384403	−	0.384403i	−0.872686	+	0.488283i	$0.837624\pi$
$798$		0			0
$799$	0.826921			0.0292544
$800$	−0.0772631	+	19.7656i	−0.00273166	+	0.698819i
$801$	−10.8646	+	18.8181i	−0.383883	+	0.664906i
$802$	0.168149	−	0.121967i	0.00593756	−	0.00430680i
$803$	16.1416	−	60.2412i	0.569624	−	2.12586i
$804$	7.11951	−	6.39031i	0.251086	−	0.225369i
$805$		0			0
$806$	−8.72813	−	22.7908i	−0.307435	−	0.802772i
$807$	−1.59347	+	0.919989i	−0.0560927	+	0.0323851i
$808$	35.3782	−	22.8571i	1.24460	−	0.804109i
$809$	34.7775	+	20.0788i	1.22271	+	0.705932i	0.965495	−	0.260422i	$-0.0838616\pi$
$809$	34.7775	+	20.0788i	1.22271	+	0.705932i	0.257216	+	0.966354i	$0.417195\pi$
$810$	1.12930	+	0.915956i	0.0396797	+	0.0321834i
$811$	−15.7147	+	15.7147i	−0.551819	+	0.551819i	−0.926966	−	0.375147i	$-0.877592\pi$
$811$	−15.7147	+	15.7147i	−0.551819	+	0.551819i	0.375147	+	0.926966i	$0.377592\pi$
$812$		0			0
$813$	11.7093	+	11.7093i	0.410662	+	0.410662i
$814$	55.6764	−	5.80782i	1.95146	−	0.203564i
$815$	−3.85931	+	6.68452i	−0.135186	+	0.234149i
$816$	0.164150	+	1.05780i	0.00574639	+	0.0370304i
$817$	15.3623	+	26.6083i	0.537459	+	0.930907i
$818$	1.30897	−	2.93382i	0.0457671	−	0.102579i
$819$		0			0
$820$	−1.45940	+	27.0380i	−0.0509644	+	0.944209i
$821$	3.12519	+	0.837392i	0.109070	+	0.0292252i	0.312941	−	0.949773i	$-0.398686\pi$
$821$	3.12519	+	0.837392i	0.109070	+	0.0292252i	−0.203871	+	0.978998i	$0.565352\pi$
$822$	1.65155	−	10.3750i	0.0576044	−	0.361869i
$823$	−9.16184	−	5.28959i	−0.319362	−	0.184384i	0.331746	−	0.943369i	$-0.392362\pi$
$823$	−9.16184	−	5.28959i	−0.319362	−	0.184384i	−0.651108	+	0.758985i	$0.725696\pi$
$824$	−27.2384	−	24.6415i	−0.948896	−	0.858428i
$825$			14.8794i			0.518034i
$826$		0			0
$827$	16.8200	−	16.8200i	0.584887	−	0.584887i	−0.351355	−	0.936242i	$-0.614279\pi$
$827$	16.8200	−	16.8200i	0.584887	−	0.584887i	0.936242	+	0.351355i	$0.114279\pi$
$828$	−1.89810	+	5.81082i	−0.0659635	+	0.201940i
$829$	−7.46997	+	2.00157i	−0.259443	+	0.0695175i	−0.386196	−	0.922417i	$-0.626211\pi$
$829$	−7.46997	+	2.00157i	−0.259443	+	0.0695175i	0.126753	+	0.991934i	$0.459544\pi$
$830$	1.42103	−	1.03074i	0.0493246	−	0.0357775i
$831$	5.91420	+	10.2437i	0.205161	+	0.355350i
$832$	22.5572	+	3.68125i	0.782029	+	0.127624i
$833$		0			0
$834$	−15.4490	−	6.89280i	−0.534954	−	0.238678i
$835$	−1.73339	+	6.46911i	−0.0599865	+	0.223873i
$836$	−52.8894	+	11.1556i	−1.82922	+	0.385824i
$837$	−7.87032	−	29.3724i	−0.272038	−	1.01526i
$838$	24.3976	−	30.0804i	0.842801	−	1.03911i
$839$		−	6.99735i		−	0.241575i	−0.992678	−	0.120788i	$-0.961458\pi$
$839$		−	6.99735i		−	0.241575i	0.992678	−	0.120788i	$-0.0385420\pi$
$840$		0			0
$841$		−	28.7847i		−	0.992575i
$842$	−12.5974	−	10.2175i	−0.434135	−	0.352118i
$843$	7.90993	+	29.5202i	0.272432	+	1.01673i
$844$	2.69885	+	1.75866i	0.0928983	+	0.0605356i
$845$	−1.53654	+	5.73446i	−0.0528587	+	0.197271i
$846$	3.56030	−	7.97976i	0.122406	−	0.274350i
$847$		0			0
$848$	1.52683	+	1.89758i	0.0524315	+	0.0651631i
$849$	−8.44576	−	14.6285i	−0.289858	−	0.502048i
$850$	−0.767584	−	1.05823i	−0.0263279	−	0.0362969i
$851$	14.0430	−	3.76280i	0.481387	−	0.128987i
$852$	8.27644	+	16.3064i	0.283546	+	0.558648i
$853$	−32.6377	+	32.6377i	−1.11749	+	1.11749i	−0.125384	+	0.992108i	$0.540016\pi$
$853$	−32.6377	+	32.6377i	−1.11749	+	1.11749i	−0.992108	+	0.125384i	$0.959984\pi$
$854$		0			0
$855$			15.5733i			0.532596i
$856$	0.248232	+	4.95907i	0.00848441	+	0.169497i
$857$	−37.8047	−	21.8266i	−1.29139	−	0.745582i	−0.312486	−	0.949923i	$-0.601162\pi$
$857$	−37.8047	−	21.8266i	−1.29139	−	0.745582i	−0.978900	+	0.204341i	$0.934495\pi$
$858$	16.9915	+	2.70480i	0.580079	+	0.0923403i
$859$	−9.06433	−	2.42878i	−0.309271	−	0.0828689i	0.100845	−	0.994902i	$-0.467845\pi$
$859$	−9.06433	−	2.42878i	−0.309271	−	0.0828689i	−0.410116	+	0.912033i	$0.634512\pi$
$860$	8.74105	−	7.84576i	0.298067	−	0.267538i
$861$		0			0
$862$	−13.9040	−	6.20347i	−0.473571	−	0.211291i
$863$	4.05796	+	7.02860i	0.138135	+	0.239256i	0.926791	−	0.375579i	$-0.122556\pi$
$863$	4.05796	+	7.02860i	0.138135	+	0.239256i	−0.788656	+	0.614835i	$0.789223\pi$
$864$	27.4787	+	7.47813i	0.934843	+	0.254411i
$865$	−10.0849	+	17.4676i	−0.342898	+	0.593916i
$866$	−0.732807	−	7.02502i	−0.0249018	−	0.238720i
$867$	12.1096	+	12.1096i	0.411265	+	0.411265i
$868$		0			0
$869$	−37.4786	+	37.4786i	−1.27137	+	1.27137i
$870$	0.513155	−	0.632682i	0.0173976	−	0.0214499i
$871$	11.6999	+	6.75491i	0.396434	+	0.228881i
$872$	23.7766	+	36.8014i	0.805178	+	1.24625i
$873$	24.3867	−	14.0797i	0.825364	−	0.476524i
$874$	−13.1098	+	5.02063i	−0.443446	+	0.169825i
$875$		0			0
$876$	−29.9280	−	1.61539i	−1.01117	−	0.0545789i
$877$	8.49639	−	31.7089i	0.286903	−	1.07074i	−0.660535	−	0.750795i	$-0.729671\pi$
$877$	8.49639	−	31.7089i	0.286903	−	1.07074i	0.947438	−	0.319940i	$-0.103663\pi$
$878$	−1.41098	−	1.94524i	−0.0476183	−	0.0656488i
$879$	11.0044	−	19.0602i	0.371170	−	0.642885i
$880$	8.34572	+	18.9037i	0.281334	+	0.637243i
$881$	−12.2614			−0.413096			−0.206548	−	0.978436i	$-0.566223\pi$
$881$	−12.2614			−0.413096			−0.206548	+	0.978436i	$0.566223\pi$
$882$		0			0
$883$	4.12180	+	4.12180i	0.138710	+	0.138710i	0.773052	−	0.634342i	$-0.218729\pi$
$883$	4.12180	+	4.12180i	0.138710	+	0.138710i	−0.634342	+	0.773052i	$0.718729\pi$
$884$	−1.34797	+	0.684172i	−0.0453371	+	0.0230112i
$885$	2.10203	+	7.84487i	0.0706588	+	0.263702i
$886$	2.48478	−	15.6093i	0.0834778	−	0.524404i
$887$	20.6829	−	11.9413i	0.694465	−	0.400949i	−0.110818	−	0.993841i	$-0.535347\pi$
$887$	20.6829	−	11.9413i	0.694465	−	0.400949i	0.805283	+	0.592891i	$0.202014\pi$
$888$	−8.25308	−	25.6045i	−0.276955	−	0.859232i
$889$		0			0
$890$	6.82252	+	17.8149i	0.228692	+	0.597157i
$891$	−3.40703	−	0.912912i	−0.114140	−	0.0305837i
$892$	15.7086	−	3.31330i	0.525962	−	0.110937i
$893$	19.3829	−	5.19362i	0.648622	−	0.173798i
$894$	−2.70312	−	25.9133i	−0.0904059	−	0.866672i
$895$	22.4597			0.750744
$896$		0			0
$897$	4.46847			0.149198
$898$	−0.594856	−	5.70255i	−0.0198506	−	0.190297i
$899$	2.70747	−	0.725465i	0.0902992	−	0.0241956i
$900$	−13.5167	+	2.85098i	−0.450556	+	0.0950326i
$901$	−0.155599	−	0.0416926i	−0.00518375	−	0.00138898i
$902$	−23.4909	−	61.3392i	−0.782161	−	2.04237i
$903$		0			0
$904$	6.62333	+	20.5484i	0.220289	+	0.683428i
$905$	−2.09012	+	1.20673i	−0.0694779	+	0.0401131i
$906$	−2.92744	+	18.3901i	−0.0972577	+	0.610969i
$907$	12.3867	+	46.2279i	0.411295	+	1.53497i	0.792143	+	0.610335i	$0.208965\pi$
$907$	12.3867	+	46.2279i	0.411295	+	1.53497i	−0.380849	+	0.924637i	$0.624368\pi$
$908$	−9.01496	+	4.57561i	−0.299172	+	0.151847i
$909$	20.8151	+	20.8151i	0.690393	+	0.690393i
$910$		0			0
$911$	0.866439			0.0287064			0.0143532	−	0.999897i	$-0.495431\pi$
$911$	0.866439			0.0287064			0.0143532	+	0.999897i	$0.495431\pi$
$912$	10.4913	+	23.7636i	0.347403	+	0.786892i
$913$	−2.12921	+	3.68789i	−0.0704664	+	0.122051i
$914$	−8.42801	−	11.6193i	−0.278774	−	0.384331i
$915$	−2.21167	+	8.25407i	−0.0731156	+	0.272871i
$916$	1.79653	+	0.0969689i	0.0593589	+	0.00320394i
$917$		0			0
$918$	−1.75895	+	0.673622i	−0.0580541	+	0.0222328i
$919$	−28.1635	+	16.2602i	−0.929028	+	0.536375i	−0.886504	−	0.462721i	$-0.846873\pi$
$919$	−28.1635	+	16.2602i	−0.929028	+	0.536375i	−0.0425240	+	0.999095i	$0.513540\pi$
$920$	2.91235	+	4.50774i	0.0960175	+	0.148616i
$921$	−10.1006	−	5.83158i	−0.332826	−	0.192157i
$922$	1.29272	−	1.59383i	0.0425736	−	0.0524900i
$923$	−18.2600	+	18.2600i	−0.601034	+	0.601034i
$924$		0			0
$925$	23.2311	+	23.2311i	0.763835	+	0.763835i
$926$	−1.55449	−	14.9021i	−0.0510838	−	0.489712i
$927$	12.8353	−	22.2314i	0.421568	−	0.730176i
$928$	−0.689314	+	2.53291i	−0.0226278	+	0.0831468i
$929$	−5.10083	−	8.83489i	−0.167353	−	0.289863i	0.770136	−	0.637880i	$-0.220189\pi$
$929$	−5.10083	−	8.83489i	−0.167353	−	0.289863i	−0.937488	+	0.348017i	$0.886855\pi$
$930$	−9.68363	−	4.32050i	−0.317539	−	0.141675i
$931$		0			0
$932$	36.5595	−	32.8150i	1.19755	−	1.07489i
$933$	30.3944	+	8.14415i	0.995068	+	0.266628i
$934$	−18.3043	−	2.91379i	−0.598937	−	0.0953423i
$935$	−1.18360	−	0.683354i	−0.0387080	−	0.0223481i
$936$	0.798575	+	15.9536i	0.0261023	+	0.521458i
$937$		−	5.06532i		−	0.165477i	−0.996571	−	0.0827384i	$-0.973633\pi$
$937$		−	5.06532i		−	0.165477i	0.996571	−	0.0827384i	$-0.0263666\pi$
$938$		0			0
$939$	−2.27447	+	2.27447i	−0.0742247	+	0.0742247i
$940$	−3.47199	−	6.84058i	−0.113244	−	0.223115i
$941$	40.1915	−	10.7693i	1.31021	−	0.351069i	0.464906	−	0.885360i	$-0.346088\pi$
$941$	40.1915	−	10.7693i	1.31021	−	0.351069i	0.845300	+	0.534292i	$0.179422\pi$
$942$	17.4107	+	24.0032i	0.567271	+	0.782066i
$943$	−8.52943	−	14.7734i	−0.277757	−	0.481088i
$944$	−16.4062	−	20.3900i	−0.533976	−	0.663638i
$945$		0			0
$946$	−11.6092	+	26.0200i	−0.377449	+	0.845984i
$947$	6.95589	−	25.9598i	0.226036	−	0.843579i	−0.755951	−	0.654629i	$-0.772825\pi$
$947$	6.95589	−	25.9598i	0.226036	−	0.843579i	0.981987	−	0.188950i	$-0.0605084\pi$
$948$	21.3407	+	13.9063i	0.693112	+	0.451655i
$949$	−10.9544	−	40.8824i	−0.355595	−	1.32710i
$950$	−24.6384	−	19.9837i	−0.799375	−	0.648356i
$951$		−	2.24518i		−	0.0728049i
$952$		0			0
$953$		−	39.1113i		−	1.26694i	−0.773767	−	0.633470i	$-0.781630\pi$
$953$		−	39.1113i		−	1.26694i	0.773767	−	0.633470i	$-0.218370\pi$
$954$	−1.07226	+	1.32202i	−0.0347157	+	0.0428019i
$955$	−1.10238	−	4.11414i	−0.0356722	−	0.133130i
$956$	57.3435	−	12.0951i	1.85462	−	0.391182i
$957$	−0.511450	+	1.90876i	−0.0165328	+	0.0617013i
$958$	43.2349	+	19.2900i	1.39686	+	0.623230i
$959$		0			0
$960$	8.06128	−	5.79928i	0.260177	−	0.187171i
$961$	−2.74280	−	4.75066i	−0.0884773	−	0.153247i
$962$	30.7516	−	22.3057i	0.991473	−	0.719163i
$963$	−3.35194	+	0.898150i	−0.108015	+	0.0289425i
$964$	4.93098	−	15.0956i	0.158816	−	0.486198i
$965$	−6.58300	+	6.58300i	−0.211914	+	0.211914i
$966$		0			0
$967$		−	53.9124i		−	1.73371i	−0.498565	−	0.866853i	$-0.666139\pi$
$967$		−	53.9124i		−	1.73371i	0.498565	−	0.866853i	$-0.333861\pi$
$968$	−14.0997	−	12.7555i	−0.453183	−	0.409976i
$969$	−1.48790	−	0.859038i	−0.0477982	−	0.0275963i
$970$	3.88641	−	24.4143i	0.124785	−	0.783895i
$971$	−35.6676	−	9.55711i	−1.14463	−	0.306702i	−0.363818	−	0.931470i	$-0.618527\pi$
$971$	−35.6676	−	9.55711i	−1.14463	−	0.306702i	−0.780811	+	0.624768i	$0.785194\pi$
$972$	−1.71936	+	31.8543i	−0.0551485	+	1.02173i
$973$		0			0
$974$	−13.2674	+	29.7365i	−0.425115	+	0.952819i
$975$	5.04892	+	8.74499i	0.161695	+	0.280064i
$976$	−4.22251	−	27.2103i	−0.135159	−	0.870981i
$977$	28.5378	−	49.4289i	0.913004	−	1.58137i	0.103207	−	0.994660i	$-0.467090\pi$
$977$	28.5378	−	49.4289i	0.913004	−	1.58137i	0.809797	−	0.586710i	$-0.199577\pi$
$978$	−8.94949	+	0.933556i	−0.286173	+	0.0298518i
$979$	−32.7217	−	32.7217i	−1.04579	−	1.04579i
$980$		0			0
$981$	−21.6525	+	21.6525i	−0.691311	+	0.691311i
$982$	34.0705	+	27.6338i	1.08723	+	0.881831i
$983$	40.3197	+	23.2786i	1.28600	+	0.742471i	0.977938	−	0.208896i	$-0.0669869\pi$
$983$	40.3197	+	23.2786i	1.28600	+	0.742471i	0.308060	+	0.951367i	$0.400320\pi$
$984$	−26.5135	+	17.1298i	−0.845219	+	0.546078i
$985$	−11.7648	+	6.79239i	−0.374857	+	0.216424i
$986$	−0.0620926	−	0.162136i	−0.00197743	−	0.00516345i
$987$		0			0
$988$	−27.2991	+	24.5030i	−0.868499	+	0.779544i
$989$	−1.91522	+	7.14771i	−0.0609005	+	0.227284i
$990$	−11.6903	+	8.47957i	−0.371543	+	0.269498i
$991$	−26.4721	+	45.8511i	−0.840915	+	1.45651i	0.0482069	+	0.998837i	$0.484649\pi$
$991$	−26.4721	+	45.8511i	−0.840915	+	1.45651i	−0.889122	+	0.457670i	$0.848684\pi$
$992$	34.1690	+	0.133566i	1.08487	+	0.00424071i
$993$	−2.80341			−0.0889635
$994$		0			0
$995$	17.0677	+	17.0677i	0.541082	+	0.541082i
$996$	1.94533	+	0.635439i	0.0616400	+	0.0201347i
$997$	5.87285	+	21.9178i	0.185995	+	0.694143i	0.994415	+	0.105537i	$0.0336563\pi$
$997$	5.87285	+	21.9178i	0.185995	+	0.694143i	−0.808420	+	0.588606i	$0.799677\pi$
$998$	−12.0914	−	1.92478i	−0.382746	−	0.0609277i
$999$	40.9933	−	23.6675i	1.29697	−	0.748807i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.x.k.557.2		16
7.2	even	3	inner	784.2.x.k.765.2		16
7.3	odd	6		784.2.m.g.589.4		8
7.4	even	3		112.2.m.c.29.4	✓	8
7.5	odd	6		784.2.x.j.765.2		16
7.6	odd	2		784.2.x.j.557.2		16
16.5	even	4	inner	784.2.x.k.165.2		16
28.11	odd	6		448.2.m.c.337.3		8
56.11	odd	6		896.2.m.f.673.2		8
56.53	even	6		896.2.m.e.673.3		8
112.5	odd	12		784.2.x.j.373.2		16
112.11	odd	12		448.2.m.c.113.3		8
112.37	even	12	inner	784.2.x.k.373.2		16
112.53	even	12		112.2.m.c.85.4	yes	8
112.67	odd	12		896.2.m.f.225.2		8
112.69	odd	4		784.2.x.j.165.2		16
112.101	odd	12		784.2.m.g.197.4		8
112.109	even	12		896.2.m.e.225.3		8
224.11	odd	24		7168.2.a.bd.1.5		8
224.53	even	24		7168.2.a.bc.1.4		8
224.123	odd	24		7168.2.a.bd.1.4		8
224.165	even	24		7168.2.a.bc.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.m.c.29.4	✓	8	7.4	even	3
112.2.m.c.85.4	yes	8	112.53	even	12
448.2.m.c.113.3		8	112.11	odd	12
448.2.m.c.337.3		8	28.11	odd	6
784.2.m.g.197.4		8	112.101	odd	12
784.2.m.g.589.4		8	7.3	odd	6
784.2.x.j.165.2		16	112.69	odd	4
784.2.x.j.373.2		16	112.5	odd	12
784.2.x.j.557.2		16	7.6	odd	2
784.2.x.j.765.2		16	7.5	odd	6
784.2.x.k.165.2		16	16.5	even	4	inner
784.2.x.k.373.2		16	112.37	even	12	inner
784.2.x.k.557.2		16	1.1	even	1	trivial
784.2.x.k.765.2		16	7.2	even	3	inner
896.2.m.e.225.3		8	112.109	even	12
896.2.m.e.673.3		8	56.53	even	6
896.2.m.f.225.2		8	112.67	odd	12
896.2.m.f.673.2		8	56.11	odd	6
7168.2.a.bc.1.4		8	224.53	even	24
7168.2.a.bc.1.5		8	224.165	even	24
7168.2.a.bd.1.4		8	224.123	odd	24
7168.2.a.bd.1.5		8	224.11	odd	24

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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.146726 - 1.40658i) q^{2} +(0.977085 - 0.261809i) q^{3} +(-1.95694 + 0.412764i) q^{4} +(-1.18533 - 0.317608i) q^{5} +(-0.511620 - 1.33594i) q^{6} +(0.867721 + 2.69204i) q^{8} +(-1.71192 + 0.988380i) q^{9} +(-0.272823 + 1.71386i) q^{10} +(-1.08957 - 4.06633i) q^{11} +(-1.80403 + 0.915651i) q^{12} +(-2.02017 - 2.02017i) q^{13} -1.24132 q^{15} +(3.65925 - 1.61551i) q^{16} +(-0.132279 + 0.229115i) q^{17} +(1.64142 + 2.26294i) q^{18} +(-1.66161 + 6.20120i) q^{19} +(2.45072 + 0.132279i) q^{20} +(-5.55976 + 2.12921i) q^{22} +(-1.33906 + 0.773104i) q^{23} +(1.55264 + 2.40317i) q^{24} +(-3.02600 - 1.74706i) q^{25} +(-2.54512 + 3.13794i) q^{26} +(-3.55976 + 3.55976i) q^{27} +(-0.328129 - 0.328129i) q^{29} +(0.182134 + 1.74602i) q^{30} +(-3.02017 + 5.23108i) q^{31} +(-2.80926 - 4.91000i) q^{32} +(-2.12921 - 3.68789i) q^{33} +(0.341677 + 0.152445i) q^{34} +(2.94217 - 2.64082i) q^{36} +(-9.08220 - 2.43357i) q^{37} +(8.96629 + 1.42731i) q^{38} +(-2.50277 - 1.44498i) q^{39} +(-0.173522 - 3.46654i) q^{40} +11.0327i q^{41} +(3.38407 - 3.38407i) q^{43} +(3.81066 + 7.50784i) q^{44} +(2.34311 - 0.627835i) q^{45} +(1.28391 + 1.77006i) q^{46} +(-1.56283 - 2.70690i) q^{47} +(3.15244 - 2.53652i) q^{48} +(-2.01339 + 4.51265i) q^{50} +(-0.0692639 + 0.258496i) q^{51} +(4.78720 + 3.11950i) q^{52} +(0.157593 + 0.588145i) q^{53} +(5.52940 + 4.48478i) q^{54} +5.16599i q^{55} +6.49412i q^{57} +(-0.413395 + 0.509685i) q^{58} +(-1.69338 - 6.31978i) q^{59} +(2.42919 - 0.512372i) q^{60} +(1.78171 - 6.64943i) q^{61} +(7.80108 + 3.48057i) q^{62} +(-6.49412 + 4.67187i) q^{64} +(1.75294 + 3.03618i) q^{65} +(-4.87491 + 3.53601i) q^{66} +(-4.56764 + 1.22389i) q^{67} +(0.164293 - 0.502964i) q^{68} +(-1.10597 + 1.10597i) q^{69} -9.03885i q^{71} +(-4.14623 - 3.75093i) q^{72} +(12.8298 + 7.40731i) q^{73} +(-2.09042 + 13.1319i) q^{74} +(-3.41405 - 0.914793i) q^{75} +(0.692037 - 12.8212i) q^{76} +(-1.66525 + 3.73237i) q^{78} +(-6.29520 - 10.9036i) q^{79} +(-4.85051 + 0.752705i) q^{80} +(0.418932 - 0.725612i) q^{81} +(15.5184 - 1.61878i) q^{82} +(-0.715276 - 0.715276i) q^{83} +(0.229563 - 0.229563i) q^{85} +(-5.25651 - 4.26344i) q^{86} +(-0.406517 - 0.234703i) q^{87} +(10.0013 - 6.46160i) q^{88} +(9.51968 - 5.49619i) q^{89} +(-1.22690 - 3.20366i) q^{90} +(2.30135 - 2.06564i) q^{92} +(-1.58141 + 5.90192i) q^{93} +(-3.57817 + 2.59542i) q^{94} +(3.93910 - 6.82272i) q^{95} +(-4.03036 - 4.06200i) q^{96} -14.2452 q^{97} +(5.88434 + 5.88434i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 4 q^{4} + 4 q^{5} - 32 q^{6} - 8 q^{8} - 12 q^{10} + 12 q^{12} - 16 q^{15} - 8 q^{16} - 24 q^{17} - 6 q^{18} + 12 q^{19} - 16 q^{20} - 8 q^{22} - 8 q^{26} + 24 q^{27} - 32 q^{29} - 20 q^{30}+ \cdots + 96 q^{99}+O(q^{100}) \) 16 * q - 2 * q^2 - 4 * q^4 + 4 * q^5 - 32 * q^6 - 8 * q^8 - 12 * q^10 + 12 * q^12 - 16 * q^15 - 8 * q^16 - 24 * q^17 - 6 * q^18 + 12 * q^19 - 16 * q^20 - 8 * q^22 - 8 * q^26 + 24 * q^27 - 32 * q^29 - 20 * q^30 - 16 * q^31 + 28 * q^32 + 24 * q^33 - 24 * q^34 + 48 * q^36 - 16 * q^37 + 16 * q^38 - 28 * q^40 - 64 * q^43 + 32 * q^44 + 8 * q^45 - 20 * q^46 - 24 * q^47 + 40 * q^48 - 28 * q^50 - 8 * q^51 - 32 * q^52 + 8 * q^53 + 16 * q^54 - 12 * q^58 + 28 * q^59 + 28 * q^60 - 28 * q^61 + 40 * q^62 - 64 * q^64 + 48 * q^65 + 16 * q^66 - 28 * q^68 + 88 * q^69 - 44 * q^72 + 4 * q^74 - 28 * q^75 - 48 * q^76 + 24 * q^78 + 24 * q^79 + 12 * q^80 - 40 * q^81 - 4 * q^82 - 80 * q^85 + 40 * q^88 - 32 * q^90 + 72 * q^92 - 16 * q^93 - 28 * q^94 - 16 * q^95 - 8 * q^96 - 64 * q^97 + 96 * q^99

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