LMFDB - Embedded newform 850.2.s.c.57.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [850,2,Mod(7,850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(850, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([4, 11]))

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

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

chi := DirichletCharacter("850.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 850 = 2 \cdot 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	850.s (of order $16$, degree $8$, 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:	$6.78728417181$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 170)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			57.1
Character	$\chi$	$=$	850.57
Dual form			850.2.s.c.343.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.382683 + 0.923880i) q^{2} +(-1.56304 + 2.33925i) q^{3} +(-0.707107 + 0.707107i) q^{4} +(-2.75933 - 0.548865i) q^{6} +(-0.254312 + 1.27851i) q^{7} +(-0.923880 - 0.382683i) q^{8} +(-1.88095 - 4.54102i) q^{9} +O(q^{10})$	\(q+(0.382683 + 0.923880i) q^{2} +(-1.56304 + 2.33925i) q^{3} +(-0.707107 + 0.707107i) q^{4} +(-2.75933 - 0.548865i) q^{6} +(-0.254312 + 1.27851i) q^{7} +(-0.923880 - 0.382683i) q^{8} +(-1.88095 - 4.54102i) q^{9} +(1.14054 - 5.73386i) q^{11} +(-0.548865 - 2.75933i) q^{12} -5.33794i q^{13} +(-1.27851 + 0.254312i) q^{14} -1.00000i q^{16} +(-1.22423 - 3.93717i) q^{17} +(3.47555 - 3.47555i) q^{18} +(-0.311731 + 0.752584i) q^{19} +(-2.59326 - 2.59326i) q^{21} +(5.73386 - 1.14054i) q^{22} +(-5.82170 + 3.88994i) q^{23} +(2.33925 - 1.56304i) q^{24} +(4.93161 - 2.04274i) q^{26} +(5.28458 + 1.05117i) q^{27} +(-0.724218 - 1.08387i) q^{28} +(-1.17050 + 1.75178i) q^{29} +(0.301321 + 1.51484i) q^{31} +(0.923880 - 0.382683i) q^{32} +(11.6302 + 11.6302i) q^{33} +(3.16897 - 2.63773i) q^{34} +(4.54102 + 1.88095i) q^{36} +(-5.79208 - 3.87014i) q^{37} -0.814591 q^{38} +(12.4868 + 8.34339i) q^{39} +(-4.40455 - 6.59188i) q^{41} +(1.40346 - 3.38825i) q^{42} +(0.544211 - 1.31384i) q^{43} +(3.24797 + 4.86093i) q^{44} +(-5.82170 - 3.88994i) q^{46} +0.109944 q^{47} +(2.33925 + 1.56304i) q^{48} +(4.89724 + 2.02850i) q^{49} +(11.1235 + 3.29016i) q^{51} +(3.77449 + 3.77449i) q^{52} +(-0.915351 + 0.379151i) q^{53} +(1.05117 + 5.28458i) q^{54} +(0.724218 - 1.08387i) q^{56} +(-1.27324 - 1.90553i) q^{57} +(-2.06637 - 0.411026i) q^{58} +(-5.08359 + 2.10569i) q^{59} +(-4.82682 + 3.22518i) q^{61} +(-1.28422 + 0.858089i) q^{62} +(6.28410 - 1.24998i) q^{63} +(0.707107 + 0.707107i) q^{64} +(-6.29423 + 15.1956i) q^{66} +(4.12405 - 4.12405i) q^{67} +(3.64966 + 1.91834i) q^{68} -19.6985i q^{69} +(-5.38952 + 1.07204i) q^{71} +4.91517i q^{72} +(-1.59643 - 8.02579i) q^{73} +(1.35901 - 6.83222i) q^{74} +(-0.311731 - 0.752584i) q^{76} +(7.04075 + 2.91637i) q^{77} +(-2.92981 + 14.7291i) q^{78} +(-5.01247 - 0.997043i) q^{79} +(-0.292298 + 0.292298i) q^{81} +(4.40455 - 6.59188i) q^{82} +(-0.987480 - 2.38399i) q^{83} +3.66742 q^{84} +1.42209 q^{86} +(-2.26832 - 5.47620i) q^{87} +(-3.24797 + 4.86093i) q^{88} +(0.779290 - 0.779290i) q^{89} +(6.82461 + 1.35750i) q^{91} +(1.36596 - 6.86717i) q^{92} +(-4.01457 - 1.66289i) q^{93} +(0.0420738 + 0.101575i) q^{94} +(-0.548865 + 2.75933i) q^{96} +(2.93692 + 14.7649i) q^{97} +5.30073i q^{98} +(-28.1829 + 5.60592i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 16 q^{18} + 8 q^{26} + 72 q^{27} - 8 q^{28} + 8 q^{29} - 16 q^{31} + 64 q^{33} - 24 q^{34} - 16 q^{37} + 32 q^{39} + 16 q^{41} + 40 q^{42} - 48 q^{43} + 16 q^{44} + 64 q^{47} + 16 q^{49} + 32 q^{51} + 16 q^{52} - 24 q^{54} + 8 q^{56} + 8 q^{57} + 16 q^{58} + 64 q^{59} - 24 q^{61} + 24 q^{62} + 24 q^{63} + 16 q^{67} + 16 q^{68} + 8 q^{71} - 16 q^{73} - 8 q^{74} - 40 q^{77} - 48 q^{78} - 72 q^{79} + 48 q^{81} - 16 q^{82} - 16 q^{83} - 64 q^{86} - 24 q^{87} - 16 q^{88} - 16 q^{89} + 48 q^{91} - 8 q^{92} - 8 q^{93} - 8 q^{94} - 16 q^{97} + 64 q^{99}+O(q^{100}) $ 32 * q - 16 * q^18 + 8 * q^26 + 72 * q^27 - 8 * q^28 + 8 * q^29 - 16 * q^31 + 64 * q^33 - 24 * q^34 - 16 * q^37 + 32 * q^39 + 16 * q^41 + 40 * q^42 - 48 * q^43 + 16 * q^44 + 64 * q^47 + 16 * q^49 + 32 * q^51 + 16 * q^52 - 24 * q^54 + 8 * q^56 + 8 * q^57 + 16 * q^58 + 64 * q^59 - 24 * q^61 + 24 * q^62 + 24 * q^63 + 16 * q^67 + 16 * q^68 + 8 * q^71 - 16 * q^73 - 8 * q^74 - 40 * q^77 - 48 * q^78 - 72 * q^79 + 48 * q^81 - 16 * q^82 - 16 * q^83 - 64 * q^86 - 24 * q^87 - 16 * q^88 - 16 * q^89 + 48 * q^91 - 8 * q^92 - 8 * q^93 - 8 * q^94 - 16 * q^97 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/850\mathbb{Z}\right)^\times$.

$n$	$477$	$751$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{15}{16}\right)$

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 $

$2$	0.382683	+	0.923880i	0.270598	+	0.653281i
$2$	0.382683	+	0.923880i	0.270598	+	0.653281i
$3$	−1.56304	+	2.33925i	−0.902419	+	1.35057i	0.0339033	+	0.999425i	$0.489206\pi$
$3$	−1.56304	+	2.33925i	−0.902419	+	1.35057i	−0.936323	+	0.351141i	$0.885794\pi$
$4$	−0.707107	+	0.707107i	−0.353553	+	0.353553i
$5$		0			0
$5$		0			0
$6$	−2.75933	−	0.548865i	−1.12649	−	0.224073i
$7$	−0.254312	+	1.27851i	−0.0961208	+	0.483232i	0.902498	+	0.430694i	$0.141731\pi$
$7$	−0.254312	+	1.27851i	−0.0961208	+	0.483232i	−0.998619	+	0.0525381i	$0.983269\pi$
$8$	−0.923880	−	0.382683i	−0.326641	−	0.135299i
$9$	−1.88095	−	4.54102i	−0.626984	−	1.51367i
$10$		0			0
$11$	1.14054	−	5.73386i	0.343884	−	1.72882i	−0.291450	−	0.956586i	$-0.594138\pi$
$11$	1.14054	−	5.73386i	0.343884	−	1.72882i	0.635335	−	0.772237i	$-0.280862\pi$
$12$	−0.548865	−	2.75933i	−0.158444	−	0.796551i
$13$		−	5.33794i		−	1.48048i	−0.672344	−	0.740239i	$-0.734712\pi$
$13$		−	5.33794i		−	1.48048i	0.672344	−	0.740239i	$-0.265288\pi$
$14$	−1.27851	+	0.254312i	−0.341696	+	0.0679677i
$15$		0			0
$16$		−	1.00000i		−	0.250000i
$17$	−1.22423	−	3.93717i	−0.296919	−	0.954903i
$17$	−1.22423	−	3.93717i	−0.296919	−	0.954903i
$18$	3.47555	−	3.47555i	0.819195	−	0.819195i
$19$	−0.311731	+	0.752584i	−0.0715159	+	0.172655i	−0.955595	−	0.294682i	$-0.904786\pi$
$19$	−0.311731	+	0.752584i	−0.0715159	+	0.172655i	0.884080	+	0.467336i	$0.154786\pi$
$20$		0			0
$21$	−2.59326	−	2.59326i	−0.565895	−	0.565895i
$22$	5.73386	−	1.14054i	1.22246	−	0.243163i
$23$	−5.82170	+	3.88994i	−1.21391	+	0.811108i	−0.986670	−	0.162731i	$-0.947970\pi$
$23$	−5.82170	+	3.88994i	−1.21391	+	0.811108i	−0.227239	+	0.973839i	$0.572970\pi$
$24$	2.33925	−	1.56304i	0.477497	−	0.319053i
$25$		0			0
$26$	4.93161	−	2.04274i	0.967168	−	0.400614i
$27$	5.28458	+	1.05117i	1.01702	+	0.202298i
$28$	−0.724218	−	1.08387i	−0.136864	−	0.204832i
$29$	−1.17050	+	1.75178i	−0.217357	+	0.325298i	−0.924085	−	0.382188i	$-0.875171\pi$
$29$	−1.17050	+	1.75178i	−0.217357	+	0.325298i	0.706727	+	0.707486i	$0.250171\pi$
$30$		0			0
$31$	0.301321	+	1.51484i	0.0541188	+	0.272074i	0.998365	−	0.0571677i	$-0.0182070\pi$
$31$	0.301321	+	1.51484i	0.0541188	+	0.272074i	−0.944246	+	0.329241i	$0.893207\pi$
$32$	0.923880	−	0.382683i	0.163320	−	0.0676495i
$33$	11.6302	+	11.6302i	2.02456	+	2.02456i
$34$	3.16897	−	2.63773i	0.543475	−	0.452366i
$35$		0			0
$36$	4.54102	+	1.88095i	0.756837	+	0.313492i
$37$	−5.79208	−	3.87014i	−0.952212	−	0.636248i	−0.0206333	−	0.999787i	$-0.506568\pi$
$37$	−5.79208	−	3.87014i	−0.952212	−	0.636248i	−0.931579	+	0.363539i	$0.881568\pi$
$38$	−0.814591			−0.132144
$39$	12.4868	+	8.34339i	1.99948	+	1.33601i
$40$		0			0
$41$	−4.40455	−	6.59188i	−0.687876	−	1.02948i	−0.996920	−	0.0784311i	$-0.975009\pi$
$41$	−4.40455	−	6.59188i	−0.687876	−	1.02948i	0.309044	−	0.951048i	$-0.399991\pi$
$42$	1.40346	−	3.38825i	0.216559	−	0.522819i
$43$	0.544211	−	1.31384i	0.0829914	−	0.200359i	−0.876936	−	0.480607i	$-0.840417\pi$
$43$	0.544211	−	1.31384i	0.0829914	−	0.200359i	0.959928	+	0.280248i	$0.0904165\pi$
$44$	3.24797	+	4.86093i	0.489650	+	0.732813i
$45$		0			0
$46$	−5.82170	−	3.88994i	−0.858363	−	0.573540i
$47$	0.109944			0.0160370			0.00801850	−	0.999968i	$-0.497448\pi$
$47$	0.109944			0.0160370			0.00801850	+	0.999968i	$0.497448\pi$
$48$	2.33925	+	1.56304i	0.337642	+	0.225605i
$49$	4.89724	+	2.02850i	0.699606	+	0.289786i
$50$		0			0
$51$	11.1235	+	3.29016i	1.55760	+	0.460715i
$52$	3.77449	+	3.77449i	0.523428	+	0.523428i
$53$	−0.915351	+	0.379151i	−0.125733	+	0.0520804i	−0.444663	−	0.895698i	$-0.646677\pi$
$53$	−0.915351	+	0.379151i	−0.125733	+	0.0520804i	0.318930	+	0.947778i	$0.396677\pi$
$54$	1.05117	+	5.28458i	0.143046	+	0.719141i
$55$		0			0
$56$	0.724218	−	1.08387i	0.0967778	−	0.144838i
$57$	−1.27324	−	1.90553i	−0.168644	−	0.252394i
$58$	−2.06637	−	0.411026i	−0.271328	−	0.0539704i
$59$	−5.08359	+	2.10569i	−0.661827	+	0.274138i	−0.688207	−	0.725514i	$-0.741602\pi$
$59$	−5.08359	+	2.10569i	−0.661827	+	0.274138i	0.0263799	+	0.999652i	$0.491602\pi$
$60$		0			0
$61$	−4.82682	+	3.22518i	−0.618011	+	0.412942i	−0.824785	−	0.565447i	$-0.808704\pi$
$61$	−4.82682	+	3.22518i	−0.618011	+	0.412942i	0.206774	+	0.978389i	$0.433704\pi$
$62$	−1.28422	+	0.858089i	−0.163096	+	0.108977i
$63$	6.28410	−	1.24998i	0.791722	−	0.157483i
$64$	0.707107	+	0.707107i	0.0883883	+	0.0883883i
$65$		0			0
$66$	−6.29423	+	15.1956i	−0.774766	+	1.87045i
$67$	4.12405	−	4.12405i	0.503833	−	0.503833i	−0.408794	−	0.912627i	$-0.634050\pi$
$67$	4.12405	−	4.12405i	0.503833	−	0.503833i	0.912627	+	0.408794i	$0.134050\pi$
$68$	3.64966	+	1.91834i	0.442586	+	0.232633i
$69$		−	19.6985i		−	2.37142i
$70$		0			0
$71$	−5.38952	+	1.07204i	−0.639618	+	0.127228i	−0.504237	−	0.863566i	$-0.668226\pi$
$71$	−5.38952	+	1.07204i	−0.639618	+	0.127228i	−0.135382	+	0.990794i	$0.543226\pi$
$72$			4.91517i			0.579258i
$73$	−1.59643	−	8.02579i	−0.186848	−	0.939348i	−0.954439	−	0.298407i	$-0.903545\pi$
$73$	−1.59643	−	8.02579i	−0.186848	−	0.939348i	0.767591	−	0.640940i	$-0.221455\pi$
$74$	1.35901	−	6.83222i	0.157982	−	0.794230i
$75$		0			0
$76$	−0.311731	−	0.752584i	−0.0357580	−	0.0863273i
$77$	7.04075	+	2.91637i	0.802368	+	0.332352i
$78$	−2.92981	+	14.7291i	−0.331736	+	1.66775i
$79$	−5.01247	−	0.997043i	−0.563947	−	0.112176i	−0.0951198	−	0.995466i	$-0.530323\pi$
$79$	−5.01247	−	0.997043i	−0.563947	−	0.112176i	−0.468828	+	0.883290i	$0.655323\pi$
$80$		0			0
$81$	−0.292298	+	0.292298i	−0.0324776	+	0.0324776i
$82$	4.40455	−	6.59188i	0.486402	−	0.727952i
$83$	−0.987480	−	2.38399i	−0.108390	−	0.261677i	0.860373	−	0.509665i	$-0.170231\pi$
$83$	−0.987480	−	2.38399i	−0.108390	−	0.261677i	−0.968763	+	0.247988i	$0.920231\pi$
$84$	3.66742			0.400148
$85$		0			0
$86$	1.42209			0.153348
$87$	−2.26832	−	5.47620i	−0.243189	−	0.587110i
$88$	−3.24797	+	4.86093i	−0.346235	+	0.518177i
$89$	0.779290	−	0.779290i	0.0826045	−	0.0826045i	−0.664597	−	0.747202i	$-0.731397\pi$
$89$	0.779290	−	0.779290i	0.0826045	−	0.0826045i	0.747202	+	0.664597i	$0.231397\pi$
$90$		0			0
$91$	6.82461	+	1.35750i	0.715414	+	0.142305i
$92$	1.36596	−	6.86717i	0.142412	−	0.715952i
$93$	−4.01457	−	1.66289i	−0.416291	−	0.172434i
$94$	0.0420738	+	0.101575i	0.00433958	+	0.0104767i
$95$		0			0
$96$	−0.548865	+	2.75933i	−0.0560183	+	0.281623i
$97$	2.93692	+	14.7649i	0.298199	+	1.49915i	0.781617	+	0.623758i	$0.214395\pi$
$97$	2.93692	+	14.7649i	0.298199	+	1.49915i	−0.483418	+	0.875389i	$0.660605\pi$
$98$			5.30073i			0.535455i
$99$	−28.1829	+	5.60592i	−2.83249	+	0.563416i
$100$		0			0
$101$			6.75581i			0.672228i	0.941821	+	0.336114i	$0.109113\pi$
$101$			6.75581i			0.672228i	−0.941821	+	0.336114i	$0.890887\pi$
$102$	1.21708	+	11.5359i	0.120508	+	1.14222i
$103$	4.75400	−	4.75400i	0.468426	−	0.468426i	−0.432978	−	0.901404i	$-0.642537\pi$
$103$	4.75400	−	4.75400i	0.468426	−	0.468426i	0.901404	+	0.432978i	$0.142537\pi$
$104$	−2.04274	+	4.93161i	−0.200307	+	0.483584i
$105$		0			0
$106$	−0.700579	−	0.700579i	−0.0680463	−	0.0680463i
$107$	16.4030	−	3.26275i	1.58573	−	0.315422i	0.678031	−	0.735033i	$-0.262834\pi$
$107$	16.4030	−	3.26275i	1.58573	−	0.315422i	0.907704	+	0.419611i	$0.137834\pi$
$108$	−4.48005	+	2.99348i	−0.431093	+	0.288047i
$109$	−2.02154	+	1.35075i	−0.193628	+	0.129378i	−0.648605	−	0.761125i	$-0.724647\pi$
$109$	−2.02154	+	1.35075i	−0.193628	+	0.129378i	0.454977	+	0.890503i	$0.349647\pi$
$110$		0			0
$111$	18.1065	−	7.49994i	1.71859	−	0.711863i
$112$	1.27851	+	0.254312i	0.120808	+	0.0240302i
$113$	−6.28548	−	9.40688i	−0.591288	−	0.884925i	0.408322	−	0.912838i	$-0.366114\pi$
$113$	−6.28548	−	9.40688i	−0.591288	−	0.884925i	−0.999610	+	0.0279127i	$0.991114\pi$
$114$	1.27324	−	1.90553i	0.119249	−	0.178469i
$115$		0			0
$116$	−0.411026	−	2.06637i	−0.0381628	−	0.191858i
$117$	−24.2397	+	10.0404i	−2.24096	+	0.928236i
$118$	−3.89081	−	3.89081i	−0.358178	−	0.358178i
$119$	5.34504	−	0.563921i	0.489979	−	0.0516945i
$120$		0			0
$121$	−21.4136	−	8.86981i	−1.94669	−	0.806347i
$122$	−4.82682	−	3.22518i	−0.437000	−	0.291994i
$123$	22.3045			2.01113
$124$	−1.28422	−	0.858089i	−0.115326	−	0.0770587i
$125$		0			0
$126$	3.55966	+	5.32740i	0.317119	+	0.474603i
$127$	−1.36362	+	3.29207i	−0.121002	+	0.292124i	−0.972761	−	0.231809i	$-0.925536\pi$
$127$	−1.36362	+	3.29207i	−0.121002	+	0.292124i	0.851760	+	0.523933i	$0.175536\pi$
$128$	−0.382683	+	0.923880i	−0.0338248	+	0.0816602i
$129$	2.22278	+	3.32663i	0.195705	+	0.292893i
$130$		0			0
$131$	9.80467	+	6.55127i	0.856638	+	0.572387i	0.904503	−	0.426467i	$-0.140242\pi$
$131$	9.80467	+	6.55127i	0.856638	+	0.572387i	−0.0478655	+	0.998854i	$0.515242\pi$
$132$	−16.4476			−1.43158
$133$	−0.882911	−	0.589942i	−0.0765581	−	0.0511545i
$134$	5.38834	+	2.23192i	0.465481	+	0.192809i
$135$		0			0
$136$	−0.375650	+	4.10596i	−0.0322117	+	0.352083i
$137$	−9.59397	−	9.59397i	−0.819668	−	0.819668i	0.166391	−	0.986060i	$-0.446788\pi$
$137$	−9.59397	−	9.59397i	−0.819668	−	0.819668i	−0.986060	+	0.166391i	$0.946788\pi$
$138$	18.1991	−	7.53830i	1.54921	−	0.641703i
$139$	2.01112	+	10.1106i	0.170581	+	0.857570i	0.967381	+	0.253326i	$0.0815246\pi$
$139$	2.01112	+	10.1106i	0.170581	+	0.857570i	−0.796800	+	0.604244i	$0.793475\pi$
$140$		0			0
$141$	−0.171847	+	0.257187i	−0.0144721	+	0.0216590i
$142$	−3.05292	−	4.56901i	−0.256195	−	0.383423i
$143$	−30.6070	−	6.08810i	−2.55948	−	0.509113i
$144$	−4.54102	+	1.88095i	−0.378419	+	0.156746i
$145$		0			0
$146$	6.80394	−	4.54625i	0.563098	−	0.376250i
$147$	−12.3997	+	8.28524i	−1.02271	+	0.683355i
$148$	6.83222	−	1.35901i	0.561605	−	0.111710i
$149$	−13.6274	−	13.6274i	−1.11640	−	1.11640i	−0.992265	−	0.124139i	$-0.960383\pi$
$149$	−13.6274	−	13.6274i	−1.11640	−	1.11640i	−0.124139	−	0.992265i	$-0.539617\pi$
$150$		0			0
$151$	3.26423	−	7.88055i	0.265639	−	0.641310i	−0.733629	−	0.679550i	$-0.762175\pi$
$151$	3.26423	−	7.88055i	0.265639	−	0.641310i	0.999269	+	0.0382398i	$0.0121751\pi$
$152$	0.576003	−	0.576003i	0.0467200	−	0.0467200i
$153$	−15.5760	+	12.9649i	−1.25925	+	1.04815i
$154$			7.62085i			0.614106i
$155$		0			0
$156$	−14.7291	+	2.92981i	−1.17928	+	0.234572i
$157$			0.880010i			0.0702324i	0.999383	+	0.0351162i	$0.0111801\pi$
$157$			0.880010i			0.0702324i	−0.999383	+	0.0351162i	$0.988820\pi$
$158$	−0.997043	−	5.01247i	−0.0793205	−	0.398771i
$159$	0.543799	−	2.73386i	0.0431260	−	0.216809i
$160$		0			0
$161$	−3.49280	−	8.43237i	−0.275271	−	0.664564i
$162$	−0.381906	−	0.158191i	−0.0300054	−	0.0124286i
$163$	−1.32917	+	6.68221i	−0.104109	+	0.523391i	0.893173	+	0.449713i	$0.148474\pi$
$163$	−1.32917	+	6.68221i	−0.104109	+	0.523391i	−0.997282	+	0.0736779i	$0.976526\pi$
$164$	7.77565	+	1.54667i	0.607177	+	0.120775i
$165$		0			0
$166$	1.82463	−	1.82463i	0.141618	−	0.141618i
$167$	−7.45689	+	11.1600i	−0.577032	+	0.863589i	−0.999076	−	0.0429863i	$-0.986313\pi$
$167$	−7.45689	+	11.1600i	−0.577032	+	0.863589i	0.422044	+	0.906575i	$0.361313\pi$
$168$	1.40346	+	3.38825i	0.108279	+	0.261409i
$169$	−15.4936			−1.19181
$170$		0			0
$171$	4.00385			0.306182
$172$	0.544211	+	1.31384i	0.0414957	+	0.100180i
$173$	13.1343	−	19.6568i	0.998580	−	1.49448i	0.134635	−	0.990895i	$-0.457014\pi$
$173$	13.1343	−	19.6568i	0.998580	−	1.49448i	0.863945	−	0.503585i	$-0.167986\pi$
$174$	4.19130	−	4.19130i	0.317742	−	0.317742i
$175$		0			0
$176$	−5.73386	−	1.14054i	−0.432206	−	0.0859711i
$177$	3.02010	−	15.1831i	0.227005	−	1.14123i
$178$	1.01819	+	0.421748i	0.0763166	+	0.0316114i
$179$	−9.49226	−	22.9163i	−0.709485	−	1.71285i	−0.701284	−	0.712882i	$-0.747390\pi$
$179$	−9.49226	−	22.9163i	−0.709485	−	1.71285i	−0.00820077	−	0.999966i	$-0.502610\pi$
$180$		0			0
$181$	−1.10723	+	5.56640i	−0.0822995	+	0.413747i	0.917570	+	0.397575i	$0.130148\pi$
$181$	−1.10723	+	5.56640i	−0.0822995	+	0.413747i	−0.999869	+	0.0161726i	$0.994852\pi$
$182$	1.35750	+	6.82461i	0.100625	+	0.505874i
$183$		−	16.3322i		−	1.20731i
$184$	6.86717	−	1.36596i	0.506254	−	0.100700i
$185$		0			0
$186$		−	4.34534i		−	0.318616i
$187$	−23.9714	+	2.52907i	−1.75296	+	0.184944i
$188$	−0.0777423	+	0.0777423i	−0.00566994	+	0.00566994i
$189$	−2.68786	+	6.48908i	−0.195513	+	0.472011i
$190$		0			0
$191$	−0.202904	−	0.202904i	−0.0146816	−	0.0146816i	0.699728	−	0.714409i	$-0.253305\pi$
$191$	−0.202904	−	0.202904i	−0.0146816	−	0.0146816i	−0.714409	+	0.699728i	$0.753305\pi$
$192$	−2.75933	+	0.548865i	−0.199138	+	0.0396109i
$193$	−20.3846	+	13.6206i	−1.46732	+	0.980429i	−0.472223	+	0.881479i	$0.656548\pi$
$193$	−20.3846	+	13.6206i	−1.46732	+	0.980429i	−0.995092	+	0.0989501i	$0.968452\pi$
$194$	−12.5171	+	8.36364i	−0.898673	+	0.600474i
$195$		0			0
$196$	−4.89724	+	2.02850i	−0.349803	+	0.144893i
$197$	−2.46774	−	0.490864i	−0.175819	−	0.0349726i	0.106396	−	0.994324i	$-0.466069\pi$
$197$	−2.46774	−	0.490864i	−0.175819	−	0.0349726i	−0.282215	+	0.959351i	$0.591069\pi$
$198$	−15.9643	−	23.8923i	−1.13453	−	1.69795i
$199$	7.18214	−	10.7488i	0.509128	−	0.761964i	−0.484485	−	0.874799i	$-0.660993\pi$
$199$	7.18214	−	10.7488i	0.509128	−	0.761964i	0.993614	+	0.112835i	$0.0359931\pi$
$200$		0			0
$201$	3.20114	+	16.0932i	0.225791	+	1.13513i
$202$	−6.24155	+	2.58533i	−0.439154	+	0.181904i
$203$	−1.94200	−	1.94200i	−0.136302	−	0.136302i
$204$	−10.1920	+	5.53902i	−0.713584	+	0.387809i
$205$		0			0
$206$	6.21141	+	2.57285i	0.432769	+	0.179259i
$207$	28.6146	+	19.1197i	1.98886	+	1.32891i
$208$	−5.33794			−0.370119
$209$	3.95967	+	2.64577i	0.273896	+	0.183012i
$210$		0			0
$211$	7.92328	+	11.8580i	0.545461	+	0.816340i	0.997119	−	0.0758509i	$-0.0241673\pi$
$211$	7.92328	+	11.8580i	0.545461	+	0.816340i	−0.451658	+	0.892191i	$0.649167\pi$
$212$	0.379151	−	0.915351i	0.0260402	−	0.0628666i
$213$	5.91624	−	14.2831i	0.405374	−	0.978660i
$214$	9.29153	+	13.9058i	0.635156	+	0.950578i
$215$		0			0
$216$	−4.48005	−	2.99348i	−0.304829	−	0.203680i
$217$	−2.01337			−0.136677
$218$	−2.02154	−	1.35075i	−0.136916	−	0.0914842i
$219$	21.2696	+	8.81016i	1.43727	+	0.595335i
$220$		0			0
$221$	−21.0163	+	6.53485i	−1.41371	+	0.439581i
$222$	13.8581	+	13.8581i	0.930094	+	0.930094i
$223$	12.6106	−	5.22346i	0.844465	−	0.349789i	0.0818526	−	0.996644i	$-0.473916\pi$
$223$	12.6106	−	5.22346i	0.844465	−	0.349789i	0.762613	+	0.646856i	$0.223916\pi$
$224$	0.254312	+	1.27851i	0.0169919	+	0.0854241i
$225$		0			0
$226$	6.28548	−	9.40688i	0.418104	−	0.625737i
$227$	4.38201	+	6.55814i	0.290844	+	0.435279i	0.947902	−	0.318561i	$-0.103199\pi$
$227$	4.38201	+	6.55814i	0.290844	+	0.435279i	−0.657058	+	0.753840i	$0.728199\pi$
$228$	2.24773	+	0.447101i	0.148859	+	0.0296100i
$229$	9.79199	−	4.05598i	0.647073	−	0.268026i	−0.0349144	−	0.999390i	$-0.511116\pi$
$229$	9.79199	−	4.05598i	0.647073	−	0.268026i	0.681987	+	0.731364i	$0.261116\pi$
$230$		0			0
$231$	−17.8271	+	11.9117i	−1.17294	+	0.783730i
$232$	1.75178	−	1.17050i	0.115010	−	0.0768474i
$233$	−2.34162	+	0.465778i	−0.153405	+	0.0305141i	−0.271195	−	0.962524i	$-0.587419\pi$
$233$	−2.34162	+	0.465778i	−0.153405	+	0.0305141i	0.117790	+	0.993038i	$0.462419\pi$
$234$	−18.5523	−	18.5523i	−1.21280	−	1.21280i
$235$		0			0
$236$	2.10569	−	5.08359i	0.137069	−	0.330914i
$237$	10.1670	−	10.1670i	0.660418	−	0.660418i
$238$	2.56645	+	4.72237i	0.166359	+	0.306106i
$239$			10.4783i			0.677786i	0.940825	+	0.338893i	$0.110053\pi$
$239$			10.4783i			0.677786i	−0.940825	+	0.338893i	$0.889947\pi$
$240$		0			0
$241$	6.35785	−	1.26466i	0.409545	−	0.0814636i	0.0139818	−	0.999902i	$-0.495549\pi$
$241$	6.35785	−	1.26466i	0.409545	−	0.0814636i	0.395564	+	0.918439i	$0.370549\pi$
$242$		−	23.1779i		−	1.48993i
$243$	2.92662	+	14.7131i	0.187743	+	0.943847i
$244$	1.13253	−	5.69362i	0.0725029	−	0.364497i
$245$		0			0
$246$	8.53557	+	20.6067i	0.544208	+	1.31384i
$247$	4.01725	+	1.66400i	0.255611	+	0.105878i
$248$	0.301321	−	1.51484i	0.0191339	−	0.0961926i
$249$	7.12021	+	1.41630i	0.451225	+	0.0897542i
$250$		0			0
$251$	15.4336	−	15.4336i	0.974160	−	0.974160i	−0.0255144	−	0.999674i	$-0.508122\pi$
$251$	15.4336	−	15.4336i	0.974160	−	0.974160i	0.999674	+	0.0255144i	$0.00812236\pi$
$252$	−3.55966	+	5.32740i	−0.224237	+	0.335595i
$253$	15.6645	+	37.8174i	0.984818	+	2.37756i
$254$	−3.56331			−0.223582
$255$		0			0
$256$	−1.00000			−0.0625000
$257$	−3.71392	−	8.96619i	−0.231668	−	0.559296i	0.764706	−	0.644379i	$-0.222884\pi$
$257$	−3.71392	−	8.96619i	−0.231668	−	0.559296i	−0.996374	+	0.0850837i	$0.972884\pi$
$258$	−2.22278	+	3.32663i	−0.138384	+	0.207107i
$259$	6.42102	−	6.42102i	0.398983	−	0.398983i
$260$		0			0
$261$	10.1566	+	2.02026i	0.628675	+	0.125051i
$262$	−2.30050	+	11.5654i	−0.142125	+	0.714512i
$263$	−14.7991	−	6.13000i	−0.912553	−	0.377992i	−0.123520	−	0.992342i	$-0.539418\pi$
$263$	−14.7991	−	6.13000i	−0.912553	−	0.377992i	−0.789033	+	0.614350i	$0.789418\pi$
$264$	−6.29423	−	15.1956i	−0.387383	−	0.935226i
$265$		0			0
$266$	0.207160	−	1.04146i	0.0127018	−	0.0638563i
$267$	0.604895	+	3.04101i	0.0370189	+	0.186107i
$268$			5.83229i			0.356264i
$269$	16.1671	−	3.21583i	0.985724	−	0.196073i	0.324194	−	0.945991i	$-0.394907\pi$
$269$	16.1671	−	3.21583i	0.985724	−	0.196073i	0.661531	+	0.749918i	$0.269907\pi$
$270$		0			0
$271$			5.17301i			0.314238i	0.987580	+	0.157119i	$0.0502206\pi$
$271$			5.17301i			0.314238i	−0.987580	+	0.157119i	$0.949779\pi$
$272$	−3.93717	+	1.22423i	−0.238726	+	0.0742297i
$273$	−13.8426	+	13.8426i	−0.837795	+	0.837795i
$274$	5.19222	−	12.5351i	0.313673	−	0.757275i
$275$		0			0
$276$	13.9290	+	13.9290i	0.838425	+	0.838425i
$277$	−20.2746	+	4.03287i	−1.21818	+	0.242312i	−0.762002	−	0.647575i	$-0.775783\pi$
$277$	−20.2746	+	4.03287i	−1.21818	+	0.242312i	−0.456182	+	0.889886i	$0.650783\pi$
$278$	−8.57135	+	5.72719i	−0.514076	+	0.343494i
$279$	6.31216	−	4.21765i	0.377899	−	0.252504i
$280$		0			0
$281$	−1.20815	+	0.500433i	−0.0720724	+	0.0298534i	−0.418428	−	0.908250i	$-0.637419\pi$
$281$	−1.20815	+	0.500433i	−0.0720724	+	0.0298534i	0.346356	+	0.938103i	$0.387419\pi$
$282$	−0.303372	−	0.0603445i	−0.0180656	−	0.00359347i
$283$	2.53325	+	3.79127i	0.150586	+	0.225368i	0.899091	−	0.437761i	$-0.144228\pi$
$283$	2.53325	+	3.79127i	0.150586	+	0.225368i	−0.748506	+	0.663128i	$0.769228\pi$
$284$	3.05292	−	4.56901i	0.181157	−	0.271121i
$285$		0			0
$286$	−6.08810	−	30.6070i	−0.359997	−	1.80983i
$287$	9.54792	−	3.95488i	0.563596	−	0.233449i
$288$	−3.47555	−	3.47555i	−0.204799	−	0.204799i
$289$	−14.0025	+	9.63997i	−0.823679	+	0.567057i
$290$		0			0
$291$	−39.1293	−	16.2079i	−2.29380	−	0.950122i
$292$	6.80394	+	4.54625i	0.398170	+	0.266049i
$293$	31.2813			1.82747			0.913735	−	0.406310i	$-0.133185\pi$
$293$	31.2813			1.82747			0.913735	+	0.406310i	$0.133185\pi$
$294$	−12.3997	−	8.28524i	−0.723167	−	0.483205i
$295$		0			0
$296$	3.87014	+	5.79208i	0.224948	+	0.336658i
$297$	12.0545	−	29.1022i	0.699474	−	1.68868i
$298$	7.37512	−	17.8051i	0.427229	−	1.03142i
$299$	20.7642	+	31.0759i	1.20083	+	1.79716i
$300$		0			0
$301$	1.54136	+	1.02991i	0.0888426	+	0.0593628i
$302$	8.52985			0.490838
$303$	−15.8035	−	10.5596i	−0.907888	−	0.606631i
$304$	0.752584	+	0.311731i	0.0431637	+	0.0178790i
$305$		0			0
$306$	−17.9387	−	9.42895i	−1.02549	−	0.539017i
$307$	12.1175	+	12.1175i	0.691579	+	0.691579i	0.962579	−	0.271000i	$-0.0873543\pi$
$307$	12.1175	+	12.1175i	0.691579	+	0.691579i	−0.271000	+	0.962579i	$0.587354\pi$
$308$	−7.04075	+	2.91637i	−0.401184	+	0.166176i
$309$	3.69012	+	18.5515i	0.209924	+	1.05536i
$310$		0			0
$311$	−3.04967	+	4.56416i	−0.172931	+	0.258810i	−0.907804	−	0.419396i	$-0.862242\pi$
$311$	−3.04967	+	4.56416i	−0.172931	+	0.258810i	0.734872	+	0.678205i	$0.237242\pi$
$312$	−8.34339	−	12.4868i	−0.472351	−	0.706924i
$313$	6.28639	+	1.25044i	0.355328	+	0.0706791i	0.369527	−	0.929220i	$-0.379520\pi$
$313$	6.28639	+	1.25044i	0.355328	+	0.0706791i	−0.0141989	+	0.999899i	$0.504520\pi$
$314$	−0.813023	+	0.336765i	−0.0458815	+	0.0190048i
$315$		0			0
$316$	4.24937	−	2.83934i	0.239046	−	0.159725i
$317$	16.0464	−	10.7218i	0.901254	−	0.602199i	−0.0162752	−	0.999868i	$-0.505181\pi$
$317$	16.0464	−	10.7218i	0.901254	−	0.602199i	0.917529	+	0.397669i	$0.130181\pi$
$318$	2.73386	−	0.543799i	0.153307	−	0.0304947i
$319$	8.70947	+	8.70947i	0.487637	+	0.487637i
$320$		0			0
$321$	−18.0060	+	43.4704i	−1.00500	+	2.42628i
$322$	6.45386	−	6.45386i	0.359659	−	0.359659i
$323$	3.34468	+	0.306001i	0.186103	+	0.0170263i
$324$		−	0.413372i		−	0.0229651i
$325$		0			0
$326$	−6.68221	+	1.32917i	−0.370093	+	0.0736161i
$327$		−	6.84014i		−	0.378261i
$328$	1.54667	+	7.77565i	0.0854008	+	0.429339i
$329$	−0.0279601	+	0.140565i	−0.00154149	+	0.00774959i
$330$		0			0
$331$	−5.53455	−	13.3616i	−0.304207	−	0.734420i	−0.999871	−	0.0160529i	$-0.994890\pi$
$331$	−5.53455	−	13.3616i	−0.304207	−	0.734420i	0.695665	−	0.718367i	$-0.255110\pi$
$332$	2.38399	+	0.987480i	0.130838	+	0.0541950i
$333$	−6.67978	+	33.5815i	−0.366050	+	1.84026i
$334$	−13.1642	−	2.61851i	−0.720310	−	0.143279i
$335$		0			0
$336$	−2.59326	+	2.59326i	−0.141474	+	0.141474i
$337$	−4.77956	+	7.15312i	−0.260359	+	0.389655i	−0.938501	−	0.345276i	$-0.887785\pi$
$337$	−4.77956	+	7.15312i	−0.260359	+	0.389655i	0.678142	+	0.734931i	$0.262785\pi$
$338$	−5.92913	−	14.3142i	−0.322502	−	0.778590i
$339$	31.8295			1.72874
$340$		0			0
$341$	9.02956			0.488978
$342$	1.53221	+	3.69908i	0.0828523	+	0.200023i
$343$	−8.90842	+	13.3324i	−0.481009	+	0.719881i
$344$	−1.00557	+	1.00557i	−0.0542168	+	0.0542168i
$345$		0			0
$346$	23.1868	+	4.61214i	1.24653	+	0.247950i
$347$	6.64863	−	33.4249i	0.356917	−	1.79434i	−0.217802	−	0.975993i	$-0.569889\pi$
$347$	6.64863	−	33.4249i	0.356917	−	1.79434i	0.574720	−	0.818350i	$-0.305111\pi$
$348$	5.47620	+	2.26832i	0.293555	+	0.121595i
$349$	−2.62113	−	6.32796i	−0.140306	−	0.338728i	0.838070	−	0.545562i	$-0.183684\pi$
$349$	−2.62113	−	6.32796i	−0.140306	−	0.338728i	−0.978376	+	0.206834i	$0.933684\pi$
$350$		0			0
$351$	5.61108	−	28.2088i	0.299497	−	1.50567i
$352$	−1.14054	−	5.73386i	−0.0607907	−	0.305616i
$353$		−	23.7210i		−	1.26254i	−0.775563	−	0.631270i	$-0.782534\pi$
$353$		−	23.7210i		−	1.26254i	0.775563	−	0.631270i	$-0.217466\pi$
$354$	15.1831	−	3.02010i	0.806971	−	0.160516i
$355$		0			0
$356$			1.10208i			0.0584102i
$357$	−7.03535	+	13.3848i	−0.372350	+	0.708400i
$358$	17.5394	−	17.5394i	0.926987	−	0.926987i
$359$	−10.0001	+	24.1423i	−0.527783	+	1.27418i	0.405189	+	0.914233i	$0.367206\pi$
$359$	−10.0001	+	24.1423i	−0.527783	+	1.27418i	−0.932972	+	0.359948i	$0.882794\pi$
$360$		0			0
$361$	12.9658	+	12.9658i	0.682412	+	0.682412i
$362$	−5.56640	+	1.10723i	−0.292564	+	0.0581945i
$363$	54.2190	−	36.2280i	2.84576	−	1.90147i
$364$	−5.78563	+	3.86583i	−0.303249	+	0.202625i
$365$		0			0
$366$	15.0890	−	6.25006i	0.788714	−	0.326696i
$367$	−14.9598	−	2.97569i	−0.780894	−	0.155330i	−0.211482	−	0.977382i	$-0.567829\pi$
$367$	−14.9598	−	2.97569i	−0.780894	−	0.155330i	−0.569412	+	0.822052i	$0.692829\pi$
$368$	3.88994	+	5.82170i	0.202777	+	0.303477i
$369$	−21.6491	+	32.4002i	−1.12701	+	1.68669i
$370$		0			0
$371$	−0.251964	−	1.26671i	−0.0130813	−	0.0657643i
$372$	4.01457	−	1.66289i	0.208146	−	0.0862168i
$373$	−3.61554	−	3.61554i	−0.187206	−	0.187206i	0.607281	−	0.794487i	$-0.292260\pi$
$373$	−3.61554	−	3.61554i	−0.187206	−	0.187206i	−0.794487	+	0.607281i	$0.792260\pi$
$374$	−11.5100	−	21.1789i	−0.595169	−	1.09513i
$375$		0			0
$376$	−0.101575	−	0.0420738i	−0.00523834	−	0.00216979i
$377$	9.35091	+	6.24808i	0.481596	+	0.321792i
$378$	−7.02373			−0.361261
$379$	−20.5807	−	13.7516i	−1.05716	−	0.706372i	−0.0997236	−	0.995015i	$-0.531796\pi$
$379$	−20.5807	−	13.7516i	−1.05716	−	0.706372i	−0.957437	+	0.288643i	$0.906796\pi$
$380$		0			0
$381$	−5.56959	−	8.33548i	−0.285339	−	0.427039i
$382$	0.109811	−	0.265107i	0.00561842	−	0.0135641i
$383$	−6.42058	+	15.5006i	−0.328076	+	0.792046i	0.670659	+	0.741766i	$0.266011\pi$
$383$	−6.42058	+	15.5006i	−0.328076	+	0.792046i	−0.998735	+	0.0502803i	$0.983989\pi$
$384$	−1.56304	−	2.33925i	−0.0797634	−	0.119374i
$385$		0			0
$386$	−20.3846	−	13.6206i	−1.03755	−	0.693268i
$387$	−6.98982			−0.355313
$388$	−12.5171	−	8.36364i	−0.635458	−	0.424599i
$389$	−10.3937	−	4.30522i	−0.526983	−	0.218283i	0.103298	−	0.994650i	$-0.467060\pi$
$389$	−10.3937	−	4.30522i	−0.526983	−	0.218283i	−0.630281	+	0.776367i	$0.717060\pi$
$390$		0			0
$391$	22.4424	+	18.1588i	1.13496	+	0.918332i
$392$	−3.74819	−	3.74819i	−0.189312	−	0.189312i
$393$	−30.6501	+	12.6957i	−1.54609	+	0.640413i
$394$	−0.490864	−	2.46774i	−0.0247294	−	0.124323i
$395$		0			0
$396$	15.9643	−	23.8923i	0.802237	−	1.20063i
$397$	20.7302	+	31.0249i	1.04042	+	1.55710i	0.812107	+	0.583508i	$0.198320\pi$
$397$	20.7302	+	31.0249i	1.04042	+	1.55710i	0.228311	+	0.973588i	$0.426680\pi$
$398$	12.6791	+	2.52203i	0.635546	+	0.126418i
$399$	2.76004	−	1.14325i	0.138175	−	0.0572339i
$400$		0			0
$401$	−3.29578	+	2.20217i	−0.164583	+	0.109971i	−0.635134	−	0.772402i	$-0.719055\pi$
$401$	−3.29578	+	2.20217i	−0.164583	+	0.109971i	0.470551	+	0.882373i	$0.344055\pi$
$402$	−13.6432	+	9.11608i	−0.680460	+	0.454669i
$403$	8.08613	−	1.60843i	0.402799	−	0.0801217i
$404$	−4.77708	−	4.77708i	−0.237668	−	0.237668i
$405$		0			0
$406$	1.05100	−	2.53735i	0.0521604	−	0.125926i
$407$	−28.7969	+	28.7969i	−1.42741	+	1.42741i
$408$	−9.01770	−	7.29650i	−0.446443	−	0.361230i
$409$			0.304764i			0.0150696i	0.999972	+	0.00753480i	$0.00239842\pi$
$409$			0.304764i			0.0150696i	−0.999972	+	0.00753480i	$0.997602\pi$
$410$		0			0
$411$	37.4384	−	7.44696i	1.84670	−	0.367332i
$412$			6.72318i			0.331227i
$413$	−1.39933	−	7.03493i	−0.0688568	−	0.346166i
$414$	−6.71394	+	33.7533i	−0.329972	+	1.65888i
$415$		0			0
$416$	−2.04274	−	4.93161i	−0.100154	−	0.241792i
$417$	−26.7947	−	11.0987i	−1.31214	−	0.543506i
$418$	−0.929070	+	4.67075i	−0.0454423	+	0.228454i
$419$	−35.8559	−	7.13218i	−1.75168	−	0.348430i	−0.788035	−	0.615631i	$-0.788901\pi$
$419$	−35.8559	−	7.13218i	−1.75168	−	0.348430i	−0.963641	+	0.267201i	$0.913901\pi$
$420$		0			0
$421$	15.7246	−	15.7246i	0.766371	−	0.766371i	−0.211095	−	0.977466i	$-0.567703\pi$
$421$	15.7246	−	15.7246i	0.766371	−	0.766371i	0.977466	+	0.211095i	$0.0677029\pi$
$422$	−7.92328	+	11.8580i	−0.385699	+	0.577240i
$423$	−0.206800	−	0.499259i	−0.0100550	−	0.0242748i
$424$	0.990769			0.0481160
$425$		0			0
$426$	15.4599			0.749034
$427$	−2.89591	−	6.99134i	−0.140143	−	0.338335i
$428$	−9.29153	+	13.9058i	−0.449123	+	0.672160i
$429$	62.0814	−	62.0814i	2.99732	−	2.99732i
$430$		0			0
$431$	−34.8166	−	6.92546i	−1.67706	−	0.333588i	−0.737336	−	0.675526i	$-0.763916\pi$
$431$	−34.8166	−	6.92546i	−1.67706	−	0.333588i	−0.939722	+	0.341939i	$0.888916\pi$
$432$	1.05117	−	5.28458i	0.0505744	−	0.254255i
$433$	−4.35002	−	1.80184i	−0.209048	−	0.0865907i	0.275702	−	0.961243i	$-0.411090\pi$
$433$	−4.35002	−	1.80184i	−0.209048	−	0.0865907i	−0.484751	+	0.874652i	$0.661090\pi$
$434$	−0.770484	−	1.86011i	−0.0369844	−	0.0892883i
$435$		0			0
$436$	0.474319	−	2.38457i	0.0227158	−	0.114200i
$437$	−1.11270	−	5.59393i	−0.0532278	−	0.267594i
$438$			23.0220i			1.10004i
$439$	−16.6816	+	3.31818i	−0.796170	+	0.158368i	−0.576383	−	0.817180i	$-0.695536\pi$
$439$	−16.6816	+	3.31818i	−0.796170	+	0.158368i	−0.219787	+	0.975548i	$0.570536\pi$
$440$		0			0
$441$		−	26.0540i		−	1.24067i
$442$	−14.0800	−	16.9158i	−0.669718	−	0.804602i
$443$	−8.08098	+	8.08098i	−0.383939	+	0.383939i	−0.872519	−	0.488580i	$-0.837515\pi$
$443$	−8.08098	+	8.08098i	−0.383939	+	0.383939i	0.488580	+	0.872519i	$0.337515\pi$
$444$	−7.49994	+	18.1065i	−0.355931	+	0.859295i
$445$		0			0
$446$	9.65170	+	9.65170i	0.457021	+	0.457021i
$447$	53.1782	−	10.5778i	2.51524	−	0.500313i
$448$	−1.08387	+	0.724218i	−0.0512080	+	0.0342161i
$449$	9.49028	−	6.34120i	0.447874	−	0.299260i	−0.311104	−	0.950376i	$-0.600699\pi$
$449$	9.49028	−	6.34120i	0.447874	−	0.299260i	0.758978	+	0.651116i	$0.225699\pi$
$450$		0			0
$451$	−42.8205	+	17.7368i	−2.01634	+	0.835194i
$452$	11.0962	+	2.20717i	0.521920	+	0.103816i
$453$	13.3325	+	19.9534i	0.626414	+	0.937494i
$454$	−4.38201	+	6.55814i	−0.205658	+	0.307789i
$455$		0			0
$456$	0.447101	+	2.24773i	0.0209374	+	0.105260i
$457$	7.42458	−	3.07536i	0.347307	−	0.143859i	−0.202209	−	0.979342i	$-0.564812\pi$
$457$	7.42458	−	3.07536i	0.347307	−	0.143859i	0.549516	+	0.835483i	$0.314812\pi$
$458$	7.49447	+	7.49447i	0.350193	+	0.350193i
$459$	−2.33090	−	22.0932i	−0.108797	−	1.03122i
$460$		0			0
$461$	32.2280	+	13.3493i	1.50101	+	0.621737i	0.973679	−	0.227924i	$-0.0731939\pi$
$461$	32.2280	+	13.3493i	1.50101	+	0.621737i	0.527328	+	0.849662i	$0.323194\pi$
$462$	−17.8271	−	11.9117i	−0.829390	−	0.554181i
$463$	39.0872			1.81654			0.908269	−	0.418386i	$-0.137404\pi$
$463$	39.0872			1.81654			0.908269	+	0.418386i	$0.137404\pi$
$464$	1.75178	+	1.17050i	0.0813245	+	0.0543393i
$465$		0			0
$466$	−1.32642	−	1.98513i	−0.0614454	−	0.0919595i
$467$	6.46053	−	15.5971i	0.298958	−	0.721748i	−0.701005	−	0.713156i	$-0.747265\pi$
$467$	6.46053	−	15.5971i	0.298958	−	0.721748i	0.999963	−	0.00859198i	$-0.00273495\pi$
$468$	10.0404	−	24.2397i	0.464118	−	1.12048i
$469$	4.22385	+	6.32144i	0.195039	+	0.291897i
$470$		0			0
$471$	−2.05856	−	1.37549i	−0.0948535	−	0.0633791i
$472$	5.50244			0.253270
$473$	−6.91269	−	4.61891i	−0.317846	−	0.212378i
$474$	13.2838	+	5.50235i	0.610147	+	0.252731i
$475$		0			0
$476$	−3.38077	+	4.17827i	−0.154957	+	0.191511i
$477$	3.44347	+	3.44347i	0.157665	+	0.157665i
$478$	−9.68071	+	4.00988i	−0.442785	+	0.183408i
$479$	−1.23929	−	6.23034i	−0.0566247	−	0.284672i	0.942090	−	0.335361i	$-0.108858\pi$
$479$	−1.23929	−	6.23034i	−0.0566247	−	0.284672i	−0.998714	+	0.0506892i	$0.983858\pi$
$480$		0			0
$481$	−20.6586	+	30.9178i	−0.941950	+	1.40973i
$482$	3.60143	+	5.38993i	0.164041	+	0.245504i
$483$	25.1848	+	5.00957i	1.14595	+	0.227943i
$484$	21.4136	−	8.86981i	0.973346	−	0.403173i
$485$		0			0
$486$	−12.4732	+	8.33431i	−0.565795	+	0.378052i
$487$	−22.4720	+	15.0153i	−1.01830	+	0.680407i	−0.948377	−	0.317145i	$-0.897276\pi$
$487$	−22.4720	+	15.0153i	−1.01830	+	0.680407i	−0.0699246	+	0.997552i	$0.522276\pi$
$488$	5.69362	−	1.13253i	0.257738	−	0.0512673i
$489$	−13.5538	−	13.5538i	−0.612924	−	0.612924i
$490$		0			0
$491$	−0.0788074	+	0.190258i	−0.00355653	+	0.00858621i	−0.925648	−	0.378386i	$-0.876479\pi$
$491$	−0.0788074	+	0.190258i	−0.00355653	+	0.00858621i	0.922091	+	0.386972i	$0.126479\pi$
$492$	−15.7717	+	15.7717i	−0.711042	+	0.711042i
$493$	8.33002	+	2.46389i	0.375165	+	0.110968i
$494$			4.34824i			0.195636i
$495$		0			0
$496$	1.51484	−	0.301321i	0.0680184	−	0.0135297i
$497$		−	7.16319i		−	0.321313i
$498$	1.41630	+	7.12021i	0.0634658	+	0.319064i
$499$	−4.34370	+	21.8373i	−0.194451	+	0.977570i	0.753086	+	0.657923i	$0.228565\pi$
$499$	−4.34370	+	21.8373i	−0.194451	+	0.977570i	−0.947536	+	0.319648i	$0.896435\pi$
$500$		0			0
$501$	−14.4507	−	34.8871i	−0.645609	−	1.55864i
$502$	20.1650	+	8.35260i	0.900007	+	0.372795i
$503$	−0.317750	+	1.59744i	−0.0141678	+	0.0712262i	−0.987222	−	0.159349i	$-0.949061\pi$
$503$	−0.317750	+	1.59744i	−0.0141678	+	0.0712262i	0.973055	+	0.230575i	$0.0740606\pi$
$504$	−6.28410	−	1.24998i	−0.279916	−	0.0556787i
$505$		0			0
$506$	−28.9442	+	28.9442i	−1.28673	+	1.28673i
$507$	24.2170	−	36.2433i	1.07552	−	1.60962i
$508$	−1.36362	−	3.29207i	−0.0605009	−	0.146062i
$509$	−35.1547			−1.55820			−0.779102	−	0.626897i	$-0.784325\pi$
$509$	−35.1547			−1.55820			−0.779102	+	0.626897i	$0.784325\pi$
$510$		0			0
$511$	10.6671			0.471883
$512$	−0.382683	−	0.923880i	−0.0169124	−	0.0408301i
$513$	−2.43846	+	3.64941i	−0.107661	+	0.161126i
$514$	6.86243	−	6.86243i	0.302689	−	0.302689i
$515$		0			0
$516$	−3.92402	−	0.780537i	−0.172746	−	0.0343612i
$517$	0.125395	−	0.630404i	0.00551487	−	0.0277251i
$518$	8.38946	+	3.47503i	0.368612	+	0.152684i
$519$	25.4529	+	61.4487i	1.11726	+	2.69730i
$520$		0			0
$521$	6.77862	−	34.0784i	0.296977	−	1.49300i	−0.487653	−	0.873038i	$-0.662147\pi$
$521$	6.77862	−	34.0784i	0.296977	−	1.49300i	0.784629	−	0.619965i	$-0.212853\pi$
$522$	2.02026	+	10.1566i	0.0884246	+	0.444540i
$523$		−	0.224643i		−	0.00982294i	−0.999988	−	0.00491147i	$-0.998437\pi$
$523$		−	0.224643i		−	0.00982294i	0.999988	−	0.00491147i	$-0.00156338\pi$
$524$	−11.5654	+	2.30050i	−0.505237	+	0.100498i
$525$		0			0
$526$		−	16.0185i		−	0.698438i
$527$	5.59530	−	3.04086i	0.243735	−	0.132462i
$528$	11.6302	−	11.6302i	0.506140	−	0.506140i
$529$	9.95889	−	24.0429i	0.432995	−	1.04534i
$530$		0			0
$531$	19.1240	+	19.1240i	0.829911	+	0.829911i
$532$	1.04146	−	0.207160i	0.0451532	−	0.00898153i
$533$	−35.1871	+	23.5112i	−1.52412	+	1.01838i
$534$	−2.57804	+	1.72259i	−0.111563	+	0.0745439i
$535$		0			0
$536$	−5.38834	+	2.23192i	−0.232741	+	0.0964043i
$537$	68.4438	+	13.6143i	2.95357	+	0.587501i
$538$	9.15792	+	13.7058i	0.394826	+	0.590899i
$539$	17.2166	−	25.7665i	0.741572	−	1.10984i
$540$		0			0
$541$	6.22565	+	31.2985i	0.267662	+	1.34563i	0.847457	+	0.530864i	$0.178132\pi$
$541$	6.22565	+	31.2985i	0.267662	+	1.34563i	−0.579796	+	0.814762i	$0.696868\pi$
$542$	−4.77923	+	1.97962i	−0.205286	+	0.0850321i
$543$	−11.2906	−	11.2906i	−0.484525	−	0.484525i
$544$	−2.63773	−	3.16897i	−0.113092	−	0.135869i
$545$		0			0
$546$	−18.0863	−	7.49159i	−0.774022	−	0.320610i
$547$	5.72658	+	3.82638i	0.244851	+	0.163604i	0.671940	−	0.740605i	$-0.265461\pi$
$547$	5.72658	+	3.82638i	0.244851	+	0.163604i	−0.427090	+	0.904209i	$0.640461\pi$
$548$	13.5679			0.579593
$549$	23.7246	+	15.8523i	1.01254	+	0.676559i
$550$		0			0
$551$	−0.953483	−	1.42699i	−0.0406197	−	0.0607917i
$552$	−7.53830	+	18.1991i	−0.320851	+	0.774604i
$553$	2.54946	−	6.15494i	0.108414	−	0.261735i
$554$	−11.4847	−	17.1880i	−0.487936	−	0.730248i
$555$		0			0
$556$	−8.57135	−	5.72719i	−0.363506	−	0.242887i
$557$	33.2286			1.40794			0.703971	−	0.710228i	$-0.251408\pi$
$557$	33.2286			1.40794			0.703971	+	0.710228i	$0.251408\pi$
$558$	6.31216	+	4.21765i	0.267215	+	0.178548i
$559$	−7.01321	−	2.90496i	−0.296627	−	0.122867i
$560$		0			0
$561$	31.5521	−	60.0281i	1.33213	−	2.53439i
$562$	−0.924680	−	0.924680i	−0.0390053	−	0.0390053i
$563$	−20.5149	+	8.49755i	−0.864600	+	0.358129i	−0.770505	−	0.637434i	$-0.779996\pi$
$563$	−20.5149	+	8.49755i	−0.864600	+	0.358129i	−0.0940950	+	0.995563i	$0.529996\pi$
$564$	−0.0603445	−	0.303372i	−0.00254096	−	0.0127743i
$565$		0			0
$566$	−2.53325	+	3.79127i	−0.106480	+	0.159359i
$567$	−0.299372	−	0.448041i	−0.0125724	−	0.0188160i
$568$	5.38952	+	1.07204i	0.226139	+	0.0449819i
$569$	−13.2905	+	5.50510i	−0.557166	+	0.230786i	−0.643454	−	0.765484i	$-0.722499\pi$
$569$	−13.2905	+	5.50510i	−0.557166	+	0.230786i	0.0862883	+	0.996270i	$0.472499\pi$
$570$		0			0
$571$	17.4454	−	11.6566i	0.730068	−	0.487816i	−0.134133	−	0.990963i	$-0.542825\pi$
$571$	17.4454	−	11.6566i	0.730068	−	0.487816i	0.864200	+	0.503148i	$0.167825\pi$
$572$	25.9473	−	17.3375i	1.08491	−	0.724915i
$573$	0.791791	−	0.157497i	0.0330775	−	0.00657953i
$574$	7.30766	+	7.30766i	0.305016	+	0.305016i
$575$		0			0
$576$	1.88095	−	4.54102i	0.0783731	−	0.189209i
$577$	13.0297	−	13.0297i	0.542435	−	0.542435i	−0.381807	−	0.924242i	$-0.624698\pi$
$577$	13.0297	−	13.0297i	0.542435	−	0.542435i	0.924242	+	0.381807i	$0.124698\pi$
$578$	−14.2647	−	9.24760i	−0.593334	−	0.384650i
$579$		−	68.9741i		−	2.86646i
$580$		0			0
$581$	3.29908	−	0.656228i	0.136869	−	0.0272249i
$582$		−	42.3532i		−	1.75560i
$583$	1.13001	+	5.68093i	0.0468001	+	0.235280i
$584$	−1.59643	+	8.02579i	−0.0660607	+	0.332110i
$585$		0			0
$586$	11.9708	+	28.9001i	0.494510	+	1.19385i
$587$	−21.5891	−	8.94250i	−0.891077	−	0.369096i	−0.110295	−	0.993899i	$-0.535179\pi$
$587$	−21.5891	−	8.94250i	−0.891077	−	0.369096i	−0.780783	+	0.624803i	$0.785179\pi$
$588$	2.90939	−	14.6265i	0.119981	−	0.603186i
$589$	−1.23398	−	0.245453i	−0.0508452	−	0.0101137i
$590$		0			0
$591$	5.00542	−	5.00542i	0.205895	−	0.205895i
$592$	−3.87014	+	5.79208i	−0.159062	+	0.238053i
$593$	−10.6733	−	25.7677i	−0.438301	−	1.05815i	−0.976535	−	0.215357i	$-0.930908\pi$
$593$	−10.6733	−	25.7677i	−0.438301	−	1.05815i	0.538234	−	0.842795i	$-0.319092\pi$
$594$	31.4999			1.29246
$595$		0			0
$596$	19.2721			0.789417
$597$	13.9182	+	33.6016i	0.569636	+	1.37522i
$598$	−20.7642	+	31.0759i	−0.849113	+	1.27079i
$599$	−6.03820	+	6.03820i	−0.246714	+	0.246714i	−0.819621	−	0.572907i	$-0.805816\pi$
$599$	−6.03820	+	6.03820i	−0.246714	+	0.246714i	0.572907	+	0.819621i	$0.305816\pi$
$600$		0			0
$601$	−1.21570	−	0.241819i	−0.0495896	−	0.00986398i	0.170233	−	0.985404i	$-0.445548\pi$
$601$	−1.21570	−	0.241819i	−0.0495896	−	0.00986398i	−0.219823	+	0.975540i	$0.570548\pi$
$602$	−0.361655	+	1.81816i	−0.0147399	+	0.0741027i
$603$	−26.4846	−	10.9703i	−1.07854	−	0.446744i
$604$	3.26423	+	7.88055i	0.132820	+	0.320655i
$605$		0			0
$606$	3.70803	−	18.6415i	0.150628	−	0.757260i
$607$	−7.10414	−	35.7149i	−0.288348	−	1.44962i	−0.804922	−	0.593381i	$-0.797793\pi$
$607$	−7.10414	−	35.7149i	−0.288348	−	1.44962i	0.516574	−	0.856243i	$-0.327207\pi$
$608$			0.814591i			0.0330360i
$609$	7.57824	−	1.50741i	0.307086	−	0.0610832i
$610$		0			0
$611$		−	0.586875i		−	0.0237424i
$612$	1.84638	−	20.1815i	0.0746355	−	0.815788i
$613$	1.67709	−	1.67709i	0.0677372	−	0.0677372i	−0.672427	−	0.740164i	$-0.734748\pi$
$613$	1.67709	−	1.67709i	0.0677372	−	0.0677372i	0.740164	+	0.672427i	$0.234748\pi$
$614$	−6.55792	+	15.8322i	−0.264656	+	0.638936i
$615$		0			0
$616$	−5.38876	−	5.38876i	−0.217119	−	0.217119i
$617$	−9.31821	+	1.85351i	−0.375137	+	0.0746194i	−0.379058	−	0.925373i	$-0.623752\pi$
$617$	−9.31821	+	1.85351i	−0.375137	+	0.0746194i	0.00392093	+	0.999992i	$0.498752\pi$
$618$	−15.7272	+	10.5086i	−0.632640	+	0.422717i
$619$	33.6978	−	22.5162i	1.35443	−	0.905001i	0.354877	−	0.934913i	$-0.384523\pi$
$619$	33.6978	−	22.5162i	1.35443	−	0.905001i	0.999553	+	0.0299118i	$0.00952263\pi$
$620$		0			0
$621$	−34.8543	+	14.4371i	−1.39865	+	0.579341i
$622$	−5.38379	−	1.07090i	−0.215870	−	0.0429393i
$623$	0.798148	+	1.19451i	0.0319771	+	0.0478571i
$624$	8.34339	−	12.4868i	0.334003	−	0.499871i
$625$		0			0
$626$	1.25044	+	6.28639i	0.0499777	+	0.251255i
$627$	−12.3782	+	5.12723i	−0.494338	+	0.204762i
$628$	−0.622261	−	0.622261i	−0.0248309	−	0.0248309i
$629$	−8.14658	+	27.5423i	−0.324825	+	1.09818i
$630$		0			0
$631$	−12.6410	−	5.23609i	−0.503232	−	0.208446i	0.116602	−	0.993179i	$-0.462800\pi$
$631$	−12.6410	−	5.23609i	−0.503232	−	0.208446i	−0.619834	+	0.784733i	$0.712800\pi$
$632$	4.24937	+	2.83934i	0.169031	+	0.112943i
$633$	−40.1233			−1.59476
$634$	16.0464	+	10.7218i	0.637283	+	0.425819i
$635$		0			0
$636$	1.54861	+	2.31766i	0.0614063	+	0.0919010i
$637$	10.8280	−	26.1412i	0.429022	−	1.03575i
$638$	−4.71353	+	11.3795i	−0.186611	+	0.450518i
$639$	15.0056	+	22.4575i	0.593613	+	0.888404i
$640$		0			0
$641$	−28.3365	−	18.9339i	−1.11923	−	0.747843i	−0.148711	−	0.988881i	$-0.547512\pi$
$641$	−28.3365	−	18.9339i	−1.11923	−	0.747843i	−0.970516	+	0.241038i	$0.922512\pi$
$642$	−47.0520			−1.85700
$643$	9.56293	+	6.38975i	0.377125	+	0.251987i	0.729658	−	0.683813i	$-0.239679\pi$
$643$	9.56293	+	6.38975i	0.377125	+	0.251987i	−0.352532	+	0.935800i	$0.614679\pi$
$644$	8.43237	+	3.49280i	0.332282	+	0.137636i
$645$		0			0
$646$	0.997245	+	3.20718i	0.0392361	+	0.126185i
$647$	−22.0524	−	22.0524i	−0.866968	−	0.866968i	0.125168	−	0.992136i	$-0.460053\pi$
$647$	−22.0524	−	22.0524i	−0.866968	−	0.866968i	−0.992136	+	0.125168i	$0.960053\pi$
$648$	0.381906	−	0.158191i	0.0150027	−	0.00621432i
$649$	6.27573	+	31.5502i	0.246344	+	1.23845i
$650$		0			0
$651$	3.14697	−	4.70978i	0.123340	−	0.184591i
$652$	−3.78517	−	5.66490i	−0.148239	−	0.221855i
$653$	45.3548	+	9.02163i	1.77487	+	0.353044i	0.970503	−	0.241088i	$-0.0775043\pi$
$653$	45.3548	+	9.02163i	1.77487	+	0.353044i	0.804368	+	0.594132i	$0.202504\pi$
$654$	6.31947	−	2.61761i	0.247111	−	0.102357i
$655$		0			0
$656$	−6.59188	+	4.40455i	−0.257370	+	0.171969i
$657$	−33.4425	+	22.3456i	−1.30472	+	0.871783i
$658$	−0.140565	+	0.0279601i	−0.00547979	+	0.00109000i
$659$	26.4734	+	26.4734i	1.03126	+	1.03126i	0.999495	+	0.0317611i	$0.0101116\pi$
$659$	26.4734	+	26.4734i	1.03126	+	1.03126i	0.0317611	+	0.999495i	$0.489888\pi$
$660$		0			0
$661$	−3.99375	+	9.64176i	−0.155339	+	0.375021i	−0.982320	−	0.187208i	$-0.940056\pi$
$661$	−3.99375	+	9.64176i	−0.155339	+	0.375021i	0.826981	+	0.562229i	$0.190056\pi$
$662$	10.2265	−	10.2265i	0.397465	−	0.397465i
$663$	17.5627	−	59.3767i	0.682077	−	2.30600i
$664$			2.58041i			0.100139i
$665$		0			0
$666$	−33.5815	+	6.67978i	−1.30126	+	0.258836i
$667$		−	14.7516i		−	0.571182i
$668$	−2.61851	−	13.1642i	−0.101313	−	0.509336i
$669$	−7.49177	+	37.6637i	−0.289649	+	1.45616i
$670$		0			0
$671$	12.9876	+	31.3547i	0.501379	+	1.21044i
$672$	−3.38825	−	1.40346i	−0.130705	−	0.0541397i
$673$	1.81154	−	9.10724i	0.0698299	−	0.351058i	−0.930035	−	0.367470i	$-0.880224\pi$
$673$	1.81154	−	9.10724i	0.0698299	−	0.351058i	0.999865	+	0.0164114i	$0.00522414\pi$
$674$	−8.43768	−	1.67836i	−0.325007	−	0.0646480i
$675$		0			0
$676$	10.9556	−	10.9556i	0.421370	−	0.421370i
$677$	−21.1958	+	31.7217i	−0.814619	+	1.21916i	0.158157	+	0.987414i	$0.449445\pi$
$677$	−21.1958	+	31.7217i	−0.814619	+	1.21916i	−0.972776	+	0.231749i	$0.925555\pi$
$678$	12.1806	+	29.4066i	0.467794	+	1.12935i
$679$	−19.6240			−0.753099
$680$		0			0
$681$	−22.1904			−0.850336
$682$	3.45546	+	8.34222i	0.132316	+	0.319440i
$683$	15.1546	−	22.6804i	0.579874	−	0.867842i	−0.419326	−	0.907836i	$-0.637734\pi$
$683$	15.1546	−	22.6804i	0.579874	−	0.867842i	0.999200	+	0.0399935i	$0.0127337\pi$
$684$	−2.83115	+	2.83115i	−0.108252	+	0.108252i
$685$		0			0
$686$	−15.7266	−	3.12822i	−0.600445	−	0.119436i
$687$	−5.81730	+	29.2455i	−0.221944	+	1.11579i
$688$	−1.31384	−	0.544211i	−0.0500898	−	0.0207479i
$689$	2.02388	+	4.88609i	0.0771038	+	0.186145i
$690$		0			0
$691$	−5.53015	+	27.8020i	−0.210377	+	1.05764i	0.720821	+	0.693122i	$0.243765\pi$
$691$	−5.53015	+	27.8020i	−0.210377	+	1.05764i	−0.931198	+	0.364515i	$0.881235\pi$
$692$	4.61214	+	23.1868i	0.175327	+	0.881430i
$693$		−	37.4578i		−	1.42290i
$694$	33.4249	−	6.64863i	1.26879	−	0.252378i
$695$		0			0
$696$			5.92740i			0.224677i
$697$	−20.5612	+	25.4114i	−0.778809	+	0.962526i
$698$	4.84321	−	4.84321i	0.183318	−	0.183318i
$699$	2.57047	−	6.20567i	0.0972242	−	0.234720i
$700$		0			0
$701$	−2.93942	−	2.93942i	−0.111020	−	0.111020i	0.649414	−	0.760435i	$-0.275014\pi$
$701$	−2.93942	−	2.93942i	−0.111020	−	0.111020i	−0.760435	+	0.649414i	$0.775014\pi$
$702$	28.2088	−	5.61108i	1.06467	−	0.211776i
$703$	4.71818	−	3.15259i	0.177949	−	0.118902i
$704$	4.86093	−	3.24797i	0.183203	−	0.122412i
$705$		0			0
$706$	21.9153	−	9.07762i	0.824794	−	0.341641i
$707$	−8.63737	−	1.71808i	−0.324842	−	0.0646151i
$708$	8.60051	+	12.8716i	0.323227	+	0.483744i
$709$	9.66796	−	14.4691i	0.363088	−	0.543399i	−0.604281	−	0.796771i	$-0.706540\pi$
$709$	9.66796	−	14.4691i	0.363088	−	0.543399i	0.967369	+	0.253372i	$0.0815396\pi$
$710$		0			0
$711$	4.90063	+	24.6371i	0.183788	+	0.923965i
$712$	−1.01819	+	0.421748i	−0.0381583	+	0.0158057i
$713$	−7.64684	−	7.64684i	−0.286377	−	0.286377i
$714$	−15.0583	−	1.37767i	−0.563542	−	0.0515578i
$715$		0			0
$716$	22.9163	+	9.49226i	0.856424	+	0.354742i
$717$	−24.5114	−	16.3780i	−0.915395	−	0.611647i
$718$	−26.1314			−0.975216
$719$	7.89793	+	5.27723i	0.294543	+	0.196807i	0.694058	−	0.719919i	$-0.255821\pi$
$719$	7.89793	+	5.27723i	0.294543	+	0.196807i	−0.399515	+	0.916727i	$0.630821\pi$
$720$		0			0
$721$	4.86905	+	7.28705i	0.181333	+	0.271384i
$722$	−7.01705	+	16.9407i	−0.261148	+	0.630466i
$723$	−6.97921	+	16.8493i	−0.259560	+	0.626632i
$724$	−3.15311	−	4.71897i	−0.117185	−	0.175379i
$725$		0			0
$726$	54.2190	+	36.2280i	2.01225	+	1.34455i
$727$	−11.5433			−0.428116			−0.214058	−	0.976821i	$-0.568668\pi$
$727$	−11.5433			−0.428116			−0.214058	+	0.976821i	$0.568668\pi$
$728$	−5.78563	−	3.86583i	−0.214430	−	0.143277i
$729$	−40.1378	−	16.6256i	−1.48658	−	0.615764i
$730$		0			0
$731$	−5.83905	−	0.534208i	−0.215965	−	0.0197584i
$732$	11.5486	+	11.5486i	0.426849	+	0.426849i
$733$	−2.72799	+	1.12997i	−0.100760	+	0.0417363i	−0.432494	−	0.901637i	$-0.642366\pi$
$733$	−2.72799	+	1.12997i	−0.100760	+	0.0417363i	0.331734	+	0.943373i	$0.392366\pi$
$734$	−2.97569	−	14.9598i	−0.109835	−	0.552176i
$735$		0			0
$736$	−3.88994	+	5.82170i	−0.143385	+	0.214591i
$737$	−18.9431	−	28.3504i	−0.697778	−	1.04430i
$738$	−38.2186	−	7.60216i	−1.40685	−	0.279839i
$739$	−9.10333	+	3.77072i	−0.334871	+	0.138708i	−0.543782	−	0.839226i	$-0.683008\pi$
$739$	−9.10333	+	3.77072i	−0.334871	+	0.138708i	0.208911	+	0.977935i	$0.433008\pi$
$740$		0			0
$741$	−10.1716	+	6.79645i	−0.373663	+	0.249674i
$742$	1.07386	−	0.717533i	0.0394228	−	0.0263415i
$743$	−2.49842	+	0.496966i	−0.0916580	+	0.0182319i	−0.240706	−	0.970598i	$-0.577379\pi$
$743$	−2.49842	+	0.496966i	−0.0916580	+	0.0182319i	0.149048	+	0.988830i	$0.452379\pi$
$744$	3.07262	+	3.07262i	0.112648	+	0.112648i
$745$		0			0
$746$	1.95672	−	4.72394i	0.0716406	−	0.172956i
$747$	−8.96834	+	8.96834i	−0.328134	+	0.328134i
$748$	15.1620	−	18.7387i	0.554379	−	0.685154i
$749$			21.8011i			0.796596i
$750$		0			0
$751$	−28.9085	+	5.75025i	−1.05489	+	0.209830i	−0.691921	−	0.721973i	$-0.743235\pi$
$751$	−28.9085	+	5.75025i	−1.05489	+	0.209830i	−0.362964	+	0.931803i	$0.618235\pi$
$752$		−	0.109944i		−	0.00400925i
$753$	11.9798	+	60.2263i	0.436567	+	2.19477i
$754$	−2.19403	+	11.0302i	−0.0799020	+	0.401694i
$755$		0			0
$756$	−2.68786	−	6.48908i	−0.0977566	−	0.236005i
$757$	9.60850	+	3.97997i	0.349227	+	0.144655i	0.550400	−	0.834901i	$-0.314475\pi$
$757$	9.60850	+	3.97997i	0.349227	+	0.144655i	−0.201173	+	0.979556i	$0.564475\pi$
$758$	4.82892	−	24.2766i	0.175394	−	0.881766i
$759$	−112.949	−	22.4669i	−4.09977	−	0.815495i
$760$		0			0
$761$	−0.842952	+	0.842952i	−0.0305570	+	0.0305570i	−0.722220	−	0.691663i	$-0.756878\pi$
$761$	−0.842952	+	0.842952i	−0.0305570	+	0.0305570i	0.691663	+	0.722220i	$0.256878\pi$
$762$	5.56959	−	8.33548i	0.201765	−	0.301962i
$763$	−1.21285	−	2.92807i	−0.0439080	−	0.106003i
$764$	0.286950			0.0103815
$765$		0			0
$766$	−16.7778			−0.606206
$767$	11.2401	+	27.1359i	0.405855	+	0.979820i
$768$	1.56304	−	2.33925i	0.0564012	−	0.0844104i
$769$	5.06321	−	5.06321i	0.182584	−	0.182584i	−0.609897	−	0.792481i	$-0.708789\pi$
$769$	5.06321	−	5.06321i	0.182584	−	0.182584i	0.792481	+	0.609897i	$0.208789\pi$
$770$		0			0
$771$	26.7791	+	5.32670i	0.964427	+	0.191837i
$772$	4.78290	−	24.0453i	0.172140	−	0.865408i
$773$	−1.07061	−	0.443463i	−0.0385073	−	0.0159502i	0.363347	−	0.931654i	$-0.381634\pi$
$773$	−1.07061	−	0.443463i	−0.0385073	−	0.0159502i	−0.401854	+	0.915704i	$0.631634\pi$
$774$	−2.67489	−	6.45775i	−0.0961469	−	0.232119i
$775$		0			0
$776$	2.93692	−	14.7649i	0.105429	−	0.530029i
$777$	4.98407	+	25.0566i	0.178803	+	0.898902i
$778$		−	11.2501i		−	0.403335i
$779$	6.33398	−	1.25991i	0.226938	−	0.0451409i
$780$		0			0
$781$			32.1254i			1.14954i
$782$	−8.18824	+	27.6832i	−0.292811	+	0.989948i
$783$	−8.02705	+	8.02705i	−0.286863	+	0.286863i
$784$	2.02850	−	4.89724i	0.0724465	−	0.174901i
$785$		0			0
$786$	−23.4586	−	23.4586i	−0.836740	−	0.836740i
$787$	−36.4127	+	7.24294i	−1.29797	+	0.258183i	−0.795259	−	0.606270i	$-0.792665\pi$
$787$	−36.4127	+	7.24294i	−1.29797	+	0.258183i	−0.502714	+	0.864453i	$0.667665\pi$
$788$	2.09205	−	1.39786i	0.0745261	−	0.0497968i
$789$	37.4712	−	25.0374i	1.33401	−	0.891356i
$790$		0			0
$791$	13.6253	−	5.64377i	0.484459	−	0.200669i
$792$	28.1829	+	5.60592i	1.00143	+	0.199198i
$793$	17.2158	+	25.7653i	0.611351	+	0.914951i
$794$	−20.7302	+	31.0249i	−0.735687	+	1.10103i
$795$		0			0
$796$	2.52203	+	12.6791i	0.0893911	+	0.449399i
$797$	−0.0379559	+	0.0157219i	−0.00134447	+	0.000556897i	−0.383356	−	0.923601i	$-0.625232\pi$
$797$	−0.0379559	+	0.0157219i	−0.00134447	+	0.000556897i	0.382011	+	0.924158i	$0.375232\pi$
$798$	2.11245	+	2.11245i	0.0747797	+	0.0747797i
$799$	−0.134597	−	0.432868i	−0.00476169	−	0.0153138i
$800$		0			0
$801$	−5.00458	−	2.07296i	−0.176828	−	0.0732446i
$802$	−3.29578	−	2.20217i	−0.116378	−	0.0777614i
$803$	−47.8395			−1.68822
$804$	−13.6432	−	9.11608i	−0.481158	−	0.321500i
$805$		0			0
$806$	4.58043	+	6.85509i	0.161339	+	0.241460i
$807$	−17.7471	+	42.8453i	−0.624727	+	1.50823i
$808$	2.58533	−	6.24155i	0.0909518	−	0.219577i
$809$	−21.2673	−	31.8287i	−0.747717	−	1.11904i	−0.988904	−	0.148559i	$-0.952537\pi$
$809$	−21.2673	−	31.8287i	−0.747717	−	1.11904i	0.241186	−	0.970479i	$-0.422463\pi$
$810$		0			0
$811$	−3.94173	−	2.63378i	−0.138413	−	0.0924845i	0.484436	−	0.874827i	$-0.339025\pi$
$811$	−3.94173	−	2.63378i	−0.138413	−	0.0924845i	−0.622849	+	0.782342i	$0.714025\pi$
$812$	2.74641			0.0963799
$813$	−12.1009	−	8.08560i	−0.424399	−	0.283574i
$814$	−37.6250	−	15.5848i	−1.31876	−	0.546246i
$815$		0			0
$816$	3.29016	−	11.1235i	0.115179	−	0.389401i
$817$	0.819129	+	0.819129i	0.0286577	+	0.0286577i
$818$	−0.281565	+	0.116628i	−0.00984469	+	0.00407780i
$819$	−6.67234	−	33.5441i	−0.233150	−	1.17213i
$820$		0			0
$821$	24.1132	−	36.0879i	0.841555	−	1.25948i	−0.122151	−	0.992512i	$-0.538979\pi$
$821$	24.1132	−	36.0879i	0.841555	−	1.25948i	0.963706	−	0.266965i	$-0.0860208\pi$
$822$	21.2072	+	31.7388i	0.739685	+	1.10702i
$823$	−31.8058	−	6.32657i	−1.10868	−	0.220531i	−0.393401	−	0.919367i	$-0.628701\pi$
$823$	−31.8058	−	6.32657i	−1.10868	−	0.220531i	−0.715281	+	0.698837i	$0.753701\pi$
$824$	−6.21141	+	2.57285i	−0.216385	+	0.0896294i
$825$		0			0
$826$	5.96393	−	3.98497i	0.207512	−	0.138655i
$827$	−37.1352	+	24.8130i	−1.29132	+	0.862832i	−0.995715	−	0.0924789i	$-0.970521\pi$
$827$	−37.1352	+	24.8130i	−1.29132	+	0.862832i	−0.295604	+	0.955311i	$0.595521\pi$
$828$	−33.7533	+	6.71394i	−1.17301	+	0.233326i
$829$	−24.9924	−	24.9924i	−0.868024	−	0.868024i	0.124230	−	0.992253i	$-0.460354\pi$
$829$	−24.9924	−	24.9924i	−0.868024	−	0.868024i	−0.992253	+	0.124230i	$0.960354\pi$
$830$		0			0
$831$	22.2561	−	53.7309i	0.772055	−	1.86390i
$832$	3.77449	−	3.77449i	0.130857	−	0.130857i
$833$	1.99122	−	21.7646i	0.0689917	−	0.754098i
$834$		−	29.0023i		−	1.00427i
$835$		0			0
$836$	−4.67075	+	0.929070i	−0.161541	+	0.0321326i
$837$			8.32205i			0.287652i
$838$	−7.13218	−	35.8559i	−0.246377	−	1.23862i
$839$	9.26094	−	46.5579i	0.319723	−	1.60736i	−0.402314	−	0.915502i	$-0.631794\pi$
$839$	9.26094	−	46.5579i	0.319723	−	1.60736i	0.722037	−	0.691855i	$-0.243206\pi$
$840$		0			0
$841$	9.39915	+	22.6916i	0.324109	+	0.782468i
$842$	20.5452	+	8.51010i	0.708034	+	0.293277i
$843$	0.717749	−	3.60837i	0.0247206	−	0.124279i
$844$	−13.9875	−	2.78229i	−0.481470	−	0.0957702i
$845$		0			0
$846$	0.382116	−	0.382116i	0.0131374	−	0.0131374i
$847$	16.7859	−	25.1219i	0.576770	−	0.863197i
$848$	0.379151	+	0.915351i	0.0130201	+	0.0314333i
$849$	−12.8283			−0.440265
$850$		0			0
$851$	48.7744			1.67196
$852$	5.91624	+	14.2831i	0.202687	+	0.489330i
$853$	10.7826	−	16.1374i	0.369191	−	0.552533i	−0.599636	−	0.800273i	$-0.704688\pi$
$853$	10.7826	−	16.1374i	0.369191	−	0.552533i	0.968827	+	0.247740i	$0.0796878\pi$
$854$	5.35094	−	5.35094i	0.183106	−	0.183106i
$855$		0			0
$856$	−16.4030	−	3.26275i	−0.560642	−	0.111519i
$857$	2.54865	−	12.8130i	0.0870604	−	0.437682i	−0.912529	−	0.409013i	$-0.865873\pi$
$857$	2.54865	−	12.8130i	0.0870604	−	0.437682i	0.999589	−	0.0286691i	$-0.00912691\pi$
$858$	81.1133	+	33.5982i	2.76916	+	1.14702i
$859$	8.74774	+	21.1189i	0.298469	+	0.720568i	0.999969	+	0.00789846i	$0.00251418\pi$
$859$	8.74774	+	21.1189i	0.298469	+	0.720568i	−0.701500	+	0.712670i	$0.747486\pi$
$860$		0			0
$861$	−5.67230	+	28.5166i	−0.193312	+	0.971843i
$862$	−6.92546	−	34.8166i	−0.235882	−	1.18586i
$863$			48.9670i			1.66686i	0.552627	+	0.833429i	$0.313625\pi$
$863$			48.9670i			1.66686i	−0.552627	+	0.833429i	$0.686375\pi$
$864$	5.28458	−	1.05117i	0.179785	−	0.0357615i
$865$		0			0
$866$		−	4.70842i		−	0.159999i
$867$	−0.663809	−	47.8230i	−0.0225441	−	1.62416i
$868$	1.42367	−	1.42367i	0.0483225	−	0.0483225i
$869$	−11.4338	+	27.6036i	−0.387865	+	0.936390i
$870$		0			0
$871$	−22.0139	−	22.0139i	−0.745914	−	0.745914i
$872$	2.38457	−	0.474319i	0.0807516	−	0.0160625i
$873$	61.5235	−	41.1087i	2.08226	−	1.39132i
$874$	4.74231	−	3.16871i	0.160411	−	0.107183i
$875$		0			0
$876$	−21.2696	+	8.81016i	−0.718633	+	0.297668i
$877$	9.49886	+	1.88944i	0.320754	+	0.0638019i	0.352841	−	0.935683i	$-0.385216\pi$
$877$	9.49886	+	1.88944i	0.320754	+	0.0638019i	−0.0320876	+	0.999485i	$0.510216\pi$
$878$	−9.44938	−	14.1420i	−0.318901	−	0.477269i
$879$	−48.8937	+	73.1747i	−1.64915	+	2.46812i
$880$		0			0
$881$	−3.65125	−	18.3561i	−0.123014	−	0.618431i	−0.992273	−	0.124075i	$-0.960404\pi$
$881$	−3.65125	−	18.3561i	−0.123014	−	0.618431i	0.869259	−	0.494356i	$-0.164596\pi$
$882$	24.0708	−	9.97043i	0.810505	−	0.335722i
$883$	−19.9922	−	19.9922i	−0.672793	−	0.672793i	0.285566	−	0.958359i	$-0.407818\pi$
$883$	−19.9922	−	19.9922i	−0.672793	−	0.672793i	−0.958359	+	0.285566i	$0.907818\pi$
$884$	10.2400	−	19.4816i	0.344407	−	0.655238i
$885$		0			0
$886$	−10.5583	−	4.37340i	−0.354713	−	0.146927i
$887$	44.3262	+	29.6178i	1.48833	+	0.994469i	0.991987	+	0.126341i	$0.0403232\pi$
$887$	44.3262	+	29.6178i	1.48833	+	0.994469i	0.496340	+	0.868128i	$0.334677\pi$
$888$	−19.5983			−0.657676
$889$	−3.86217	−	2.58062i	−0.129533	−	0.0865511i
$890$		0			0
$891$	1.34262	+	2.00937i	0.0449795	+	0.0673165i
$892$	−5.22346	+	12.6106i	−0.174894	+	0.422233i
$893$	−0.0342730	+	0.0827422i	−0.00114690	+	0.00276886i
$894$	30.1230	+	45.0823i	1.00746	+	1.50778i
$895$		0			0
$896$	−1.08387	−	0.724218i	−0.0362095	−	0.0241944i
$897$	−105.150			−3.51084
$898$	9.49028	+	6.34120i	0.316695	+	0.211609i
$899$	−3.00637	−	1.24528i	−0.100268	−	0.0415324i
$900$		0			0
$901$	2.61338	+	3.13972i	0.0870642	+	0.104599i
$902$	−32.7734	−	32.7734i	−1.09123	−	1.09123i
$903$	−4.81841	+	1.99585i	−0.160347	+	0.0664178i
$904$	2.20717	+	11.0962i	0.0734093	+	0.369053i
$905$		0			0
$906$	−13.3325	+	19.9534i	−0.442941	+	0.662909i
$907$	19.1618	+	28.6777i	0.636257	+	0.952226i	0.999787	+	0.0206435i	$0.00657151\pi$
$907$	19.1618	+	28.6777i	0.636257	+	0.952226i	−0.363530	+	0.931583i	$0.618428\pi$
$908$	−7.73585	−	1.53876i	−0.256723	−	0.0510654i
$909$	30.6783	−	12.7074i	1.01753	−	0.421476i
$910$		0			0
$911$	−16.3825	+	10.9464i	−0.542777	+	0.362672i	−0.796532	−	0.604597i	$-0.793334\pi$
$911$	−16.3825	+	10.9464i	−0.542777	+	0.362672i	0.253755	+	0.967269i	$0.418334\pi$
$912$	−1.90553	+	1.27324i	−0.0630985	+	0.0421610i
$913$	−14.7957	+	2.94305i	−0.489666	+	0.0974007i
$914$	5.68253	+	5.68253i	0.187961	+	0.187961i
$915$		0			0
$916$	−4.05598	+	9.79199i	−0.134013	+	0.323537i
$917$	−10.8693	+	10.8693i	−0.358936	+	0.358936i
$918$	19.5194	−	10.6082i	0.644237	−	0.350121i
$919$		−	7.48557i		−	0.246926i	−0.992349	−	0.123463i	$-0.960600\pi$
$919$		−	7.48557i		−	0.246926i	0.992349	−	0.123463i	$-0.0394001\pi$
$920$		0			0
$921$	−47.2857	+	9.40572i	−1.55812	+	0.309929i
$922$			34.8833i			1.14882i
$923$	5.72249	+	28.7689i	0.188358	+	0.946941i
$924$	4.18282	−	21.0285i	0.137605	−	0.691786i
$925$		0			0
$926$	14.9580	+	36.1119i	0.491552	+	1.18671i
$927$	−30.5301	−	12.6460i	−1.00274	−	0.415349i
$928$	−0.411026	+	2.06637i	−0.0134926	+	0.0678319i
$929$	23.3245	+	4.63954i	0.765253	+	0.152218i	0.562258	−	0.826962i	$-0.309933\pi$
$929$	23.3245	+	4.63954i	0.765253	+	0.152218i	0.202995	+	0.979180i	$0.434933\pi$
$930$		0			0
$931$	−3.05324	+	3.05324i	−0.100066	+	0.100066i
$932$	1.32642	−	1.98513i	0.0434484	−	0.0650252i
$933$	−5.90995	−	14.2679i	−0.193483	−	0.467110i
$934$	16.8822			0.552402
$935$		0			0
$936$	26.2369			0.857579
$937$	11.3016	+	27.2845i	0.369207	+	0.891345i	0.993881	+	0.110459i	$0.0352320\pi$
$937$	11.3016	+	27.2845i	0.369207	+	0.891345i	−0.624674	+	0.780886i	$0.714768\pi$
$938$	−4.22385	+	6.32144i	−0.137914	+	0.206402i
$939$	−12.7510	+	12.7510i	−0.416112	+	0.416112i
$940$		0			0
$941$	1.26326	+	0.251277i	0.0411810	+	0.00819140i	0.215638	−	0.976473i	$-0.430817\pi$
$941$	1.26326	+	0.251277i	0.0411810	+	0.00819140i	−0.174457	+	0.984665i	$0.555817\pi$
$942$	0.483007	−	2.42824i	0.0157372	−	0.0791163i
$943$	51.2840	+	21.2425i	1.67004	+	0.691752i
$944$	2.10569	+	5.08359i	0.0685345	+	0.165457i
$945$		0			0
$946$	1.62195	−	8.15407i	0.0527340	−	0.265112i
$947$	−7.32823	−	36.8415i	−0.238136	−	1.19719i	−0.896001	−	0.444052i	$-0.853540\pi$
$947$	−7.32823	−	36.8415i	−0.238136	−	1.19719i	0.657865	−	0.753136i	$-0.271460\pi$
$948$			14.3783i			0.466986i
$949$	−42.8412	+	8.52164i	−1.39068	+	0.276624i
$950$		0			0
$951$			54.2951i			1.76064i
$952$	−5.15398	−	1.52447i	−0.167041	−	0.0494082i
$953$	−25.9594	+	25.9594i	−0.840908	+	0.840908i	−0.988977	−	0.148069i	$-0.952694\pi$
$953$	−25.9594	+	25.9594i	−0.840908	+	0.840908i	0.148069	+	0.988977i	$0.452694\pi$
$954$	−1.86359	+	4.49910i	−0.0603360	+	0.145664i
$955$		0			0
$956$	−7.40929	−	7.40929i	−0.239634	−	0.239634i
$957$	−33.9869	+	6.76041i	−1.09864	+	0.218533i
$958$	5.28183	−	3.52921i	0.170648	−	0.114023i
$959$	14.7059	−	9.82614i	0.474877	−	0.317303i
$960$		0			0
$961$	26.4363	−	10.9503i	0.852784	−	0.353235i
$962$	−36.4700	−	7.25433i	−1.17584	−	0.233889i
$963$	−45.6695	−	68.3492i	−1.47168	−	2.20252i
$964$	−3.60143	+	5.38993i	−0.115994	+	0.173598i
$965$		0			0
$966$	5.00957	+	25.1848i	0.161180	+	0.810307i
$967$	21.7497	−	9.00902i	0.699423	−	0.289711i	−0.00449664	−	0.999990i	$-0.501431\pi$
$967$	21.7497	−	9.00902i	0.699423	−	0.289711i	0.703920	+	0.710279i	$0.251431\pi$
$968$	16.3893	+	16.3893i	0.526771	+	0.526771i
$969$	−5.94366	+	7.34574i	−0.190938	+	0.235979i
$970$		0			0
$971$	−16.1076	−	6.67199i	−0.516918	−	0.214114i	0.108945	−	0.994048i	$-0.465253\pi$
$971$	−16.1076	−	6.67199i	−0.516918	−	0.214114i	−0.625862	+	0.779933i	$0.715253\pi$
$972$	−12.4732	−	8.33431i	−0.400078	−	0.267323i
$973$	−13.4380			−0.430801
$974$	−22.4720	−	15.0153i	−0.720048	−	0.481121i
$975$		0			0
$976$	3.22518	+	4.82682i	0.103235	+	0.154503i
$977$	−4.93111	+	11.9048i	−0.157760	+	0.380867i	−0.982920	−	0.184032i	$-0.941085\pi$
$977$	−4.93111	+	11.9048i	−0.157760	+	0.380867i	0.825160	+	0.564899i	$0.191085\pi$
$978$	7.33526	−	17.7089i	0.234556	−	0.566268i
$979$	−3.57953	−	5.35714i	−0.114402	−	0.171215i
$980$		0			0
$981$	9.93619	+	6.63915i	0.317238	+	0.211972i
$982$	−0.205934			−0.00657160
$983$	27.2056	+	18.1782i	0.867724	+	0.579795i	0.907801	−	0.419402i	$-0.137760\pi$
$983$	27.2056	+	18.1782i	0.867724	+	0.579795i	−0.0400767	+	0.999197i	$0.512760\pi$
$984$	−20.6067	−	8.53557i	−0.656918	−	0.272104i
$985$		0			0
$986$	0.911426	+	8.63883i	0.0290257	+	0.275116i
$987$	−0.285114	−	0.285114i	−0.00907526	−	0.00907526i
$988$	−4.01725	+	1.66400i	−0.127806	+	0.0529388i
$989$	1.94253	+	9.76574i	0.0617688	+	0.310533i
$990$		0			0
$991$	2.85767	−	4.27680i	0.0907767	−	0.135857i	−0.783302	−	0.621642i	$-0.786466\pi$
$991$	2.85767	−	4.27680i	0.0907767	−	0.135857i	0.874079	+	0.485785i	$0.161466\pi$
$992$	0.858089	+	1.28422i	0.0272444	+	0.0407741i
$993$	39.9068	+	7.93796i	1.26640	+	0.251903i
$994$	6.61793	−	2.74124i	0.209908	−	0.0869467i
$995$		0			0
$996$	−6.03622	+	4.03327i	−0.191265	+	0.127799i
$997$	43.3514	−	28.9665i	1.37295	−	0.917378i	0.373007	−	0.927828i	$-0.378327\pi$
$997$	43.3514	−	28.9665i	1.37295	−	0.917378i	0.999945	+	0.0104506i	$0.00332658\pi$
$998$	−21.8373	+	4.34370i	−0.691247	+	0.137498i
$999$	−26.5406	−	26.5406i	−0.839706	−	0.839706i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	850.2.s.c.57.1		32
5.2	odd	4		170.2.r.a.23.4	yes	32
5.3	odd	4		850.2.v.c.193.1		32
5.4	even	2		170.2.o.a.57.4	yes	32
17.3	odd	16		850.2.v.c.207.1		32
85.3	even	16	inner	850.2.s.c.343.1		32
85.37	even	16		170.2.o.a.3.4	✓	32
85.54	odd	16		170.2.r.a.37.4	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.o.a.3.4	✓	32	85.37	even	16
170.2.o.a.57.4	yes	32	5.4	even	2
170.2.r.a.23.4	yes	32	5.2	odd	4
170.2.r.a.37.4	yes	32	85.54	odd	16
850.2.s.c.57.1		32	1.1	even	1	trivial
850.2.s.c.343.1		32	85.3	even	16	inner
850.2.v.c.193.1		32	5.3	odd	4
850.2.v.c.207.1		32	17.3	odd	16

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:	\( N \)	\(=\)	\( 850 = 2 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	850.s (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.382683 + 0.923880i) q^{2} +(-1.56304 + 2.33925i) q^{3} +(-0.707107 + 0.707107i) q^{4} +(-2.75933 - 0.548865i) q^{6} +(-0.254312 + 1.27851i) q^{7} +(-0.923880 - 0.382683i) q^{8} +(-1.88095 - 4.54102i) q^{9} +O(q^{10})\)	\(q+(0.382683 + 0.923880i) q^{2} +(-1.56304 + 2.33925i) q^{3} +(-0.707107 + 0.707107i) q^{4} +(-2.75933 - 0.548865i) q^{6} +(-0.254312 + 1.27851i) q^{7} +(-0.923880 - 0.382683i) q^{8} +(-1.88095 - 4.54102i) q^{9} +(1.14054 - 5.73386i) q^{11} +(-0.548865 - 2.75933i) q^{12} -5.33794i q^{13} +(-1.27851 + 0.254312i) q^{14} -1.00000i q^{16} +(-1.22423 - 3.93717i) q^{17} +(3.47555 - 3.47555i) q^{18} +(-0.311731 + 0.752584i) q^{19} +(-2.59326 - 2.59326i) q^{21} +(5.73386 - 1.14054i) q^{22} +(-5.82170 + 3.88994i) q^{23} +(2.33925 - 1.56304i) q^{24} +(4.93161 - 2.04274i) q^{26} +(5.28458 + 1.05117i) q^{27} +(-0.724218 - 1.08387i) q^{28} +(-1.17050 + 1.75178i) q^{29} +(0.301321 + 1.51484i) q^{31} +(0.923880 - 0.382683i) q^{32} +(11.6302 + 11.6302i) q^{33} +(3.16897 - 2.63773i) q^{34} +(4.54102 + 1.88095i) q^{36} +(-5.79208 - 3.87014i) q^{37} -0.814591 q^{38} +(12.4868 + 8.34339i) q^{39} +(-4.40455 - 6.59188i) q^{41} +(1.40346 - 3.38825i) q^{42} +(0.544211 - 1.31384i) q^{43} +(3.24797 + 4.86093i) q^{44} +(-5.82170 - 3.88994i) q^{46} +0.109944 q^{47} +(2.33925 + 1.56304i) q^{48} +(4.89724 + 2.02850i) q^{49} +(11.1235 + 3.29016i) q^{51} +(3.77449 + 3.77449i) q^{52} +(-0.915351 + 0.379151i) q^{53} +(1.05117 + 5.28458i) q^{54} +(0.724218 - 1.08387i) q^{56} +(-1.27324 - 1.90553i) q^{57} +(-2.06637 - 0.411026i) q^{58} +(-5.08359 + 2.10569i) q^{59} +(-4.82682 + 3.22518i) q^{61} +(-1.28422 + 0.858089i) q^{62} +(6.28410 - 1.24998i) q^{63} +(0.707107 + 0.707107i) q^{64} +(-6.29423 + 15.1956i) q^{66} +(4.12405 - 4.12405i) q^{67} +(3.64966 + 1.91834i) q^{68} -19.6985i q^{69} +(-5.38952 + 1.07204i) q^{71} +4.91517i q^{72} +(-1.59643 - 8.02579i) q^{73} +(1.35901 - 6.83222i) q^{74} +(-0.311731 - 0.752584i) q^{76} +(7.04075 + 2.91637i) q^{77} +(-2.92981 + 14.7291i) q^{78} +(-5.01247 - 0.997043i) q^{79} +(-0.292298 + 0.292298i) q^{81} +(4.40455 - 6.59188i) q^{82} +(-0.987480 - 2.38399i) q^{83} +3.66742 q^{84} +1.42209 q^{86} +(-2.26832 - 5.47620i) q^{87} +(-3.24797 + 4.86093i) q^{88} +(0.779290 - 0.779290i) q^{89} +(6.82461 + 1.35750i) q^{91} +(1.36596 - 6.86717i) q^{92} +(-4.01457 - 1.66289i) q^{93} +(0.0420738 + 0.101575i) q^{94} +(-0.548865 + 2.75933i) q^{96} +(2.93692 + 14.7649i) q^{97} +5.30073i q^{98} +(-28.1829 + 5.60592i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 16 q^{18} + 8 q^{26} + 72 q^{27} - 8 q^{28} + 8 q^{29} - 16 q^{31} + 64 q^{33} - 24 q^{34} - 16 q^{37} + 32 q^{39} + 16 q^{41} + 40 q^{42} - 48 q^{43} + 16 q^{44} + 64 q^{47} + 16 q^{49} + 32 q^{51} + 16 q^{52} - 24 q^{54} + 8 q^{56} + 8 q^{57} + 16 q^{58} + 64 q^{59} - 24 q^{61} + 24 q^{62} + 24 q^{63} + 16 q^{67} + 16 q^{68} + 8 q^{71} - 16 q^{73} - 8 q^{74} - 40 q^{77} - 48 q^{78} - 72 q^{79} + 48 q^{81} - 16 q^{82} - 16 q^{83} - 64 q^{86} - 24 q^{87} - 16 q^{88} - 16 q^{89} + 48 q^{91} - 8 q^{92} - 8 q^{93} - 8 q^{94} - 16 q^{97} + 64 q^{99}+O(q^{100}) \) 32 * q - 16 * q^18 + 8 * q^26 + 72 * q^27 - 8 * q^28 + 8 * q^29 - 16 * q^31 + 64 * q^33 - 24 * q^34 - 16 * q^37 + 32 * q^39 + 16 * q^41 + 40 * q^42 - 48 * q^43 + 16 * q^44 + 64 * q^47 + 16 * q^49 + 32 * q^51 + 16 * q^52 - 24 * q^54 + 8 * q^56 + 8 * q^57 + 16 * q^58 + 64 * q^59 - 24 * q^61 + 24 * q^62 + 24 * q^63 + 16 * q^67 + 16 * q^68 + 8 * q^71 - 16 * q^73 - 8 * q^74 - 40 * q^77 - 48 * q^78 - 72 * q^79 + 48 * q^81 - 16 * q^82 - 16 * q^83 - 64 * q^86 - 24 * q^87 - 16 * q^88 - 16 * q^89 + 48 * q^91 - 8 * q^92 - 8 * q^93 - 8 * q^94 - 16 * q^97 + 64 * q^99

Introduction

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