LMFDB - Embedded newform 850.2.v.c.193.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [850,2,Mod(107,850)]

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, 5]))

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

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

chi := DirichletCharacter("850.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 850 = 2 \cdot 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	850.v (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			193.1
Character	$\chi$	$=$	850.193
Dual form			850.2.v.c.207.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$477$	$751$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{15}{16}\right)$

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 $

$2$	0.923880	−	0.382683i	0.653281	−	0.270598i
$2$	0.923880	−	0.382683i	0.653281	−	0.270598i
$3$	−2.33925	−	1.56304i	−1.35057	−	0.902419i	−0.351141	−	0.936323i	$-0.614206\pi$
$3$	−2.33925	−	1.56304i	−1.35057	−	0.902419i	−0.999425	+	0.0339033i	$0.989206\pi$
$4$	0.707107	−	0.707107i	0.353553	−	0.353553i
$5$		0			0
$5$		0			0
$6$	−2.75933	−	0.548865i	−1.12649	−	0.224073i
$7$	1.27851	+	0.254312i	0.483232	+	0.0961208i	0.430694	−	0.902498i	$-0.358269\pi$
$7$	1.27851	+	0.254312i	0.483232	+	0.0961208i	0.0525381	+	0.998619i	$0.483269\pi$
$8$	0.382683	−	0.923880i	0.135299	−	0.326641i
$9$	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	$-0.280862\pi$
$12$	−2.75933	+	0.548865i	−0.796551	+	0.158444i
$13$	5.33794			1.48048			0.740239	−	0.672344i	$-0.234712\pi$
$13$	5.33794			1.48048			0.740239	+	0.672344i	$0.234712\pi$
$14$	1.27851	−	0.254312i	0.341696	−	0.0679677i
$15$		0			0
$16$		−	1.00000i		−	0.250000i
$17$	−3.93717	+	1.22423i	−0.954903	+	0.296919i
$17$	−3.93717	+	1.22423i	−0.954903	+	0.296919i
$18$	3.47555	+	3.47555i	0.819195	+	0.819195i
$19$	0.311731	−	0.752584i	0.0715159	−	0.172655i	−0.884080	−	0.467336i	$-0.845214\pi$
$19$	0.311731	−	0.752584i	0.0715159	−	0.172655i	0.955595	+	0.294682i	$0.0952137\pi$
$20$		0			0
$21$	−2.59326	−	2.59326i	−0.565895	−	0.565895i
$22$	−1.14054	−	5.73386i	−0.243163	−	1.22246i
$23$	−3.88994	−	5.82170i	−0.811108	−	1.21391i	−0.973839	−	0.227239i	$-0.927030\pi$
$23$	−3.88994	−	5.82170i	−0.811108	−	1.21391i	0.162731	−	0.986670i	$-0.447970\pi$
$24$	−2.33925	+	1.56304i	−0.477497	+	0.319053i
$25$		0			0
$26$	4.93161	−	2.04274i	0.967168	−	0.400614i
$27$	1.05117	−	5.28458i	0.202298	−	1.01702i
$28$	1.08387	−	0.724218i	0.204832	−	0.136864i
$29$	1.17050	−	1.75178i	0.217357	−	0.325298i	−0.706727	−	0.707486i	$-0.749829\pi$
$29$	1.17050	−	1.75178i	0.217357	−	0.325298i	0.924085	+	0.382188i	$0.124829\pi$
$30$		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	$0.893207\pi$
$32$	−0.382683	−	0.923880i	−0.0676495	−	0.163320i
$33$	−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
$37$	−3.87014	+	5.79208i	−0.636248	+	0.952212i	0.363539	+	0.931579i	$0.381568\pi$
$37$	−3.87014	+	5.79208i	−0.636248	+	0.952212i	−0.999787	+	0.0206333i	$0.993432\pi$
$38$		−	0.814591i		−	0.132144i
$39$	−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	$-0.399991\pi$
$42$	−3.38825	−	1.40346i	−0.522819	−	0.216559i
$43$	1.31384	+	0.544211i	0.200359	+	0.0829914i	0.480607	−	0.876936i	$-0.340417\pi$
$43$	1.31384	+	0.544211i	0.200359	+	0.0829914i	−0.280248	+	0.959928i	$0.590417\pi$
$44$	−3.24797	−	4.86093i	−0.489650	−	0.732813i
$45$		0			0
$46$	−5.82170	−	3.88994i	−0.858363	−	0.573540i
$47$		−	0.109944i		−	0.0160370i	−0.999968	−	0.00801850i	$-0.997448\pi$
$47$		−	0.109944i		−	0.0160370i	0.999968	−	0.00801850i	$-0.00255240\pi$
$48$	−1.56304	+	2.33925i	−0.225605	+	0.337642i
$49$	−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
$53$	−0.379151	−	0.915351i	−0.0520804	−	0.125733i	0.895698	−	0.444663i	$-0.146677\pi$
$53$	−0.379151	−	0.915351i	−0.0520804	−	0.125733i	−0.947778	+	0.318930i	$0.896677\pi$
$54$	−1.05117	−	5.28458i	−0.143046	−	0.719141i
$55$		0			0
$56$	0.724218	−	1.08387i	0.0967778	−	0.144838i
$57$	−1.90553	+	1.27324i	−0.252394	+	0.168644i
$58$	0.411026	−	2.06637i	0.0539704	−	0.271328i
$59$	5.08359	−	2.10569i	0.661827	−	0.274138i	−0.0263799	−	0.999652i	$-0.508398\pi$
$59$	5.08359	−	2.10569i	0.661827	−	0.274138i	0.688207	+	0.725514i	$0.258398\pi$
$60$		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	$0.433704\pi$
$62$	0.858089	+	1.28422i	0.108977	+	0.163096i
$63$	1.24998	+	6.28410i	0.157483	+	0.791722i
$64$	−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	$-0.365950\pi$
$67$	−4.12405	−	4.12405i	−0.503833	−	0.503833i	−0.912627	+	0.408794i	$0.865950\pi$
$68$	−1.91834	+	3.64966i	−0.232633	+	0.442586i
$69$			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	$0.543226\pi$
$72$	4.91517			0.579258
$73$	8.02579	−	1.59643i	0.939348	−	0.186848i	0.298407	−	0.954439i	$-0.403545\pi$
$73$	8.02579	−	1.59643i	0.939348	−	0.186848i	0.640940	+	0.767591i	$0.278545\pi$
$74$	−1.35901	+	6.83222i	−0.157982	+	0.794230i
$75$		0			0
$76$	−0.311731	−	0.752584i	−0.0357580	−	0.0863273i
$77$	2.91637	−	7.04075i	0.332352	−	0.802368i
$78$	−14.7291	−	2.92981i	−1.66775	−	0.331736i
$79$	5.01247	+	0.997043i	0.563947	+	0.112176i	0.468828	−	0.883290i	$-0.344677\pi$
$79$	5.01247	+	0.997043i	0.563947	+	0.112176i	0.0951198	+	0.995466i	$0.469677\pi$
$80$		0			0
$81$	−0.292298	+	0.292298i	−0.0324776	+	0.0324776i
$82$	−6.59188	−	4.40455i	−0.727952	−	0.486402i
$83$	2.38399	−	0.987480i	0.261677	−	0.108390i	−0.247988	−	0.968763i	$-0.579769\pi$
$83$	2.38399	−	0.987480i	0.261677	−	0.108390i	0.509665	+	0.860373i	$0.329769\pi$
$84$	−3.66742			−0.400148
$85$		0			0
$86$	1.42209			0.153348
$87$	−5.47620	+	2.26832i	−0.587110	+	0.243189i
$88$	−4.86093	−	3.24797i	−0.518177	−	0.346235i
$89$	−0.779290	+	0.779290i	−0.0826045	+	0.0826045i	−0.747202	−	0.664597i	$-0.768603\pi$
$89$	−0.779290	+	0.779290i	−0.0826045	+	0.0826045i	0.664597	+	0.747202i	$0.268603\pi$
$90$		0			0
$91$	6.82461	+	1.35750i	0.715414	+	0.142305i
$92$	−6.86717	−	1.36596i	−0.715952	−	0.142412i
$93$	1.66289	−	4.01457i	0.172434	−	0.416291i
$94$	−0.0420738	−	0.101575i	−0.00433958	−	0.0104767i
$95$		0			0
$96$	−0.548865	+	2.75933i	−0.0560183	+	0.281623i
$97$	14.7649	−	2.93692i	1.49915	−	0.298199i	0.623758	−	0.781617i	$-0.285605\pi$
$97$	14.7649	−	2.93692i	1.49915	−	0.298199i	0.875389	+	0.483418i	$0.160605\pi$
$98$	−5.30073			−0.535455
$99$	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	$0.890887\pi$
$102$	11.5359	−	1.21708i	1.14222	−	0.120508i
$103$	4.75400	+	4.75400i	0.468426	+	0.468426i	0.901404	−	0.432978i	$-0.142537\pi$
$103$	4.75400	+	4.75400i	0.468426	+	0.468426i	−0.432978	+	0.901404i	$0.642537\pi$
$104$	2.04274	−	4.93161i	0.200307	−	0.483584i
$105$		0			0
$106$	−0.700579	−	0.700579i	−0.0680463	−	0.0680463i
$107$	−3.26275	−	16.4030i	−0.315422	−	1.58573i	−0.735033	−	0.678031i	$-0.762834\pi$
$107$	−3.26275	−	16.4030i	−0.315422	−	1.58573i	0.419611	−	0.907704i	$-0.362166\pi$
$108$	−2.99348	−	4.48005i	−0.288047	−	0.431093i
$109$	2.02154	−	1.35075i	0.193628	−	0.129378i	−0.454977	−	0.890503i	$-0.650353\pi$
$109$	2.02154	−	1.35075i	0.193628	−	0.129378i	0.648605	+	0.761125i	$0.275353\pi$
$110$		0			0
$111$	18.1065	−	7.49994i	1.71859	−	0.711863i
$112$	0.254312	−	1.27851i	0.0240302	−	0.120808i
$113$	9.40688	−	6.28548i	0.884925	−	0.591288i	−0.0279127	−	0.999610i	$-0.508886\pi$
$113$	9.40688	−	6.28548i	0.884925	−	0.591288i	0.912838	+	0.408322i	$0.133886\pi$
$114$	−1.27324	+	1.90553i	−0.119249	+	0.178469i
$115$		0			0
$116$	−0.411026	−	2.06637i	−0.0381628	−	0.191858i
$117$	10.0404	+	24.2397i	0.928236	+	2.24096i
$118$	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
$122$	−3.22518	+	4.82682i	−0.291994	+	0.437000i
$123$			22.3045i			2.01113i
$124$	1.28422	+	0.858089i	0.115326	+	0.0770587i
$125$		0			0
$126$	3.55966	+	5.32740i	0.317119	+	0.474603i
$127$	3.29207	+	1.36362i	0.292124	+	0.121002i	0.523933	−	0.851760i	$-0.324464\pi$
$127$	3.29207	+	1.36362i	0.292124	+	0.121002i	−0.231809	+	0.972761i	$0.574464\pi$
$128$	−0.923880	−	0.382683i	−0.0816602	−	0.0338248i
$129$	−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	$0.515242\pi$
$132$			16.4476i			1.43158i
$133$	0.589942	−	0.882911i	0.0511545	−	0.0765581i
$134$	−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	−0.986060	−	0.166391i	$-0.946788\pi$
$137$	−9.59397	+	9.59397i	−0.819668	+	0.819668i	0.166391	+	0.986060i	$0.446788\pi$
$138$	7.53830	+	18.1991i	0.641703	+	1.54921i
$139$	−2.01112	−	10.1106i	−0.170581	−	0.857570i	−0.967381	−	0.253326i	$-0.918475\pi$
$139$	−2.01112	−	10.1106i	−0.170581	−	0.857570i	0.796800	−	0.604244i	$-0.206525\pi$
$140$		0			0
$141$	−0.171847	+	0.257187i	−0.0144721	+	0.0216590i
$142$	−4.56901	+	3.05292i	−0.383423	+	0.256195i
$143$	6.08810	−	30.6070i	0.509113	−	2.55948i
$144$	4.54102	−	1.88095i	0.378419	−	0.156746i
$145$		0			0
$146$	6.80394	−	4.54625i	0.563098	−	0.376250i
$147$	8.28524	+	12.3997i	0.683355	+	1.02271i
$148$	1.35901	+	6.83222i	0.111710	+	0.561605i
$149$	13.6274	+	13.6274i	1.11640	+	1.11640i	0.992265	+	0.124139i	$0.0396170\pi$
$149$	13.6274	+	13.6274i	1.11640	+	1.11640i	0.124139	+	0.992265i	$0.460383\pi$
$150$		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
$153$	−12.9649	−	15.5760i	−1.04815	−	1.25925i
$154$		−	7.62085i		−	0.614106i
$155$		0			0
$156$	−14.7291	+	2.92981i	−1.17928	+	0.234572i
$157$	0.880010			0.0702324			0.0351162	−	0.999383i	$-0.488820\pi$
$157$	0.880010			0.0702324			0.0351162	+	0.999383i	$0.488820\pi$
$158$	5.01247	−	0.997043i	0.398771	−	0.0793205i
$159$	−0.543799	+	2.73386i	−0.0431260	+	0.216809i
$160$		0			0
$161$	−3.49280	−	8.43237i	−0.275271	−	0.664564i
$162$	−0.158191	+	0.381906i	−0.0124286	+	0.0300054i
$163$	−6.68221	−	1.32917i	−0.523391	−	0.104109i	−0.0736779	−	0.997282i	$-0.523474\pi$
$163$	−6.68221	−	1.32917i	−0.523391	−	0.104109i	−0.449713	+	0.893173i	$0.648474\pi$
$164$	−7.77565	−	1.54667i	−0.607177	−	0.120775i
$165$		0			0
$166$	1.82463	−	1.82463i	0.141618	−	0.141618i
$167$	11.1600	+	7.45689i	0.863589	+	0.577032i	0.906575	−	0.422044i	$-0.138687\pi$
$167$	11.1600	+	7.45689i	0.863589	+	0.577032i	−0.0429863	+	0.999076i	$0.513687\pi$
$168$	−3.38825	+	1.40346i	−0.261409	+	0.108279i
$169$	15.4936			1.19181
$170$		0			0
$171$	4.00385			0.306182
$172$	1.31384	−	0.544211i	0.100180	−	0.0414957i
$173$	19.6568	+	13.1343i	1.49448	+	0.998580i	0.990895	+	0.134635i	$0.0429861\pi$
$173$	19.6568	+	13.1343i	1.49448	+	0.998580i	0.503585	+	0.863945i	$0.332014\pi$
$174$	−4.19130	+	4.19130i	−0.317742	+	0.317742i
$175$		0			0
$176$	−5.73386	−	1.14054i	−0.432206	−	0.0859711i
$177$	−15.1831	−	3.02010i	−1.14123	−	0.227005i
$178$	−0.421748	+	1.01819i	−0.0316114	+	0.0763166i
$179$	9.49226	+	22.9163i	0.709485	+	1.71285i	0.701284	+	0.712882i	$0.252610\pi$
$179$	9.49226	+	22.9163i	0.709485	+	1.71285i	0.00820077	+	0.999966i	$0.497390\pi$
$180$		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	$0.994852\pi$
$182$	6.82461	−	1.35750i	0.505874	−	0.100625i
$183$	16.3322			1.20731
$184$	−6.86717	+	1.36596i	−0.506254	+	0.100700i
$185$		0			0
$186$		−	4.34534i		−	0.318616i
$187$	2.52907	+	23.9714i	0.184944	+	1.75296i
$188$	−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	$0.753305\pi$
$192$	0.548865	+	2.75933i	0.0396109	+	0.199138i
$193$	−13.6206	−	20.3846i	−0.980429	−	1.46732i	−0.881479	−	0.472223i	$-0.843452\pi$
$193$	−13.6206	−	20.3846i	−0.980429	−	1.46732i	−0.0989501	−	0.995092i	$-0.531548\pi$
$194$	12.5171	−	8.36364i	0.898673	−	0.600474i
$195$		0			0
$196$	−4.89724	+	2.02850i	−0.349803	+	0.144893i
$197$	−0.490864	+	2.46774i	−0.0349726	+	0.175819i	−0.994324	−	0.106396i	$-0.966069\pi$
$197$	−0.490864	+	2.46774i	−0.0349726	+	0.175819i	0.959351	+	0.282215i	$0.0910690\pi$
$198$	23.8923	−	15.9643i	1.69795	−	1.13453i
$199$	−7.18214	+	10.7488i	−0.509128	+	0.761964i	−0.993614	−	0.112835i	$-0.964007\pi$
$199$	−7.18214	+	10.7488i	−0.509128	+	0.761964i	0.484485	+	0.874799i	$0.339007\pi$
$200$		0			0
$201$	3.20114	+	16.0932i	0.225791	+	1.13513i
$202$	2.58533	+	6.24155i	0.181904	+	0.439154i
$203$	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
$207$	19.1197	−	28.6146i	1.32891	−	1.98886i
$208$		−	5.33794i		−	0.370119i
$209$	−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	$0.649167\pi$
$212$	−0.915351	−	0.379151i	−0.0628666	−	0.0260402i
$213$	14.2831	+	5.91624i	0.978660	+	0.405374i
$214$	−9.29153	−	13.9058i	−0.635156	−	0.950578i
$215$		0			0
$216$	−4.48005	−	2.99348i	−0.304829	−	0.203680i
$217$			2.01337i			0.136677i
$218$	1.35075	−	2.02154i	0.0914842	−	0.136916i
$219$	−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
$223$	5.22346	+	12.6106i	0.349789	+	0.844465i	0.996644	+	0.0818526i	$0.0260837\pi$
$223$	5.22346	+	12.6106i	0.349789	+	0.844465i	−0.646856	+	0.762613i	$0.723916\pi$
$224$	−0.254312	−	1.27851i	−0.0169919	−	0.0854241i
$225$		0			0
$226$	6.28548	−	9.40688i	0.418104	−	0.625737i
$227$	6.55814	−	4.38201i	0.435279	−	0.290844i	−0.318561	−	0.947902i	$-0.603199\pi$
$227$	6.55814	−	4.38201i	0.435279	−	0.290844i	0.753840	+	0.657058i	$0.228199\pi$
$228$	−0.447101	+	2.24773i	−0.0296100	+	0.148859i
$229$	−9.79199	+	4.05598i	−0.647073	+	0.268026i	−0.681987	−	0.731364i	$-0.738884\pi$
$229$	−9.79199	+	4.05598i	−0.647073	+	0.268026i	0.0349144	+	0.999390i	$0.488884\pi$
$230$		0			0
$231$	−17.8271	+	11.9117i	−1.17294	+	0.783730i
$232$	−1.17050	−	1.75178i	−0.0768474	−	0.115010i
$233$	−0.465778	−	2.34162i	−0.0305141	−	0.153405i	0.962524	−	0.271195i	$-0.0874189\pi$
$233$	−0.465778	−	2.34162i	−0.0305141	−	0.153405i	−0.993038	+	0.117790i	$0.962419\pi$
$234$	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
$238$	−4.72237	+	2.56645i	−0.306106	+	0.166359i
$239$		−	10.4783i		−	0.677786i	−0.940825	−	0.338893i	$-0.889947\pi$
$239$		−	10.4783i		−	0.677786i	0.940825	−	0.338893i	$-0.110053\pi$
$240$		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	$0.370549\pi$
$242$	−23.1779			−1.48993
$243$	−14.7131	+	2.92662i	−0.943847	+	0.187743i
$244$	−1.13253	+	5.69362i	−0.0725029	+	0.364497i
$245$		0			0
$246$	8.53557	+	20.6067i	0.544208	+	1.31384i
$247$	1.66400	−	4.01725i	0.105878	−	0.255611i
$248$	1.51484	+	0.301321i	0.0961926	+	0.0191339i
$249$	−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	$0.00812236\pi$
$252$	5.32740	+	3.55966i	0.335595	+	0.224237i
$253$	−37.8174	+	15.6645i	−2.37756	+	0.984818i
$254$	3.56331			0.223582
$255$		0			0
$256$	−1.00000			−0.0625000
$257$	−8.96619	+	3.71392i	−0.559296	+	0.231668i	−0.644379	−	0.764706i	$-0.722884\pi$
$257$	−8.96619	+	3.71392i	−0.559296	+	0.231668i	0.0850837	+	0.996374i	$0.472884\pi$
$258$	−3.32663	−	2.22278i	−0.207107	−	0.138384i
$259$	−6.42102	+	6.42102i	−0.398983	+	0.398983i
$260$		0			0
$261$	10.1566	+	2.02026i	0.628675	+	0.125051i
$262$	11.5654	+	2.30050i	0.714512	+	0.142125i
$263$	6.13000	−	14.7991i	0.377992	−	0.912553i	−0.614350	−	0.789033i	$-0.710582\pi$
$263$	6.13000	−	14.7991i	0.377992	−	0.912553i	0.992342	−	0.123520i	$-0.0394182\pi$
$264$	6.29423	+	15.1956i	0.387383	+	0.935226i
$265$		0			0
$266$	0.207160	−	1.04146i	0.0127018	−	0.0638563i
$267$	3.04101	−	0.604895i	0.186107	−	0.0370189i
$268$	−5.83229			−0.356264
$269$	−16.1671	+	3.21583i	−0.985724	+	0.196073i	−0.661531	−	0.749918i	$-0.730093\pi$
$269$	−16.1671	+	3.21583i	−0.985724	+	0.196073i	−0.324194	+	0.945991i	$0.605093\pi$
$270$		0			0
$271$			5.17301i			0.314238i	0.987580	+	0.157119i	$0.0502206\pi$
$271$			5.17301i			0.314238i	−0.987580	+	0.157119i	$0.949779\pi$
$272$	1.22423	+	3.93717i	0.0742297	+	0.238726i
$273$	−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
$277$	4.03287	+	20.2746i	0.242312	+	1.21818i	0.889886	+	0.456182i	$0.150783\pi$
$277$	4.03287	+	20.2746i	0.242312	+	1.21818i	−0.647575	+	0.762002i	$0.724217\pi$
$278$	−5.72719	−	8.57135i	−0.343494	−	0.514076i
$279$	−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	$0.387419\pi$
$282$	−0.0603445	+	0.303372i	−0.00359347	+	0.0180656i
$283$	−3.79127	+	2.53325i	−0.225368	+	0.150586i	−0.663128	−	0.748506i	$-0.730772\pi$
$283$	−3.79127	+	2.53325i	−0.225368	+	0.150586i	0.437761	+	0.899091i	$0.355772\pi$
$284$	−3.05292	+	4.56901i	−0.181157	+	0.271121i
$285$		0			0
$286$	−6.08810	−	30.6070i	−0.359997	−	1.80983i
$287$	−3.95488	−	9.54792i	−0.233449	−	0.563596i
$288$	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
$292$	4.54625	−	6.80394i	0.266049	−	0.398170i
$293$			31.2813i			1.82747i	0.406310	+	0.913735i	$0.366815\pi$
$293$			31.2813i			1.82747i	−0.406310	+	0.913735i	$0.633185\pi$
$294$	12.3997	+	8.28524i	0.723167	+	0.483205i
$295$		0			0
$296$	3.87014	+	5.79208i	0.224948	+	0.336658i
$297$	−29.1022	−	12.0545i	−1.68868	−	0.699474i
$298$	17.8051	+	7.37512i	1.03142	+	0.427229i
$299$	−20.7642	−	31.0759i	−1.20083	−	1.79716i
$300$		0			0
$301$	1.54136	+	1.02991i	0.0888426	+	0.0593628i
$302$		−	8.52985i		−	0.490838i
$303$	10.5596	−	15.8035i	0.606631	−	0.907888i
$304$	−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	−0.271000	−	0.962579i	$-0.587354\pi$
$307$	12.1175	−	12.1175i	0.691579	−	0.691579i	0.962579	+	0.271000i	$0.0873543\pi$
$308$	−2.91637	−	7.04075i	−0.166176	−	0.401184i
$309$	−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	$0.237242\pi$
$312$	−12.4868	+	8.34339i	−0.706924	+	0.472351i
$313$	−1.25044	+	6.28639i	−0.0706791	+	0.355328i	−0.999899	−	0.0141989i	$-0.995480\pi$
$313$	−1.25044	+	6.28639i	−0.0706791	+	0.355328i	0.929220	+	0.369527i	$0.120480\pi$
$314$	0.813023	−	0.336765i	0.0458815	−	0.0190048i
$315$		0			0
$316$	4.24937	−	2.83934i	0.239046	−	0.159725i
$317$	−10.7218	−	16.0464i	−0.602199	−	0.901254i	0.397669	−	0.917529i	$-0.369819\pi$
$317$	−10.7218	−	16.0464i	−0.602199	−	0.901254i	−0.999868	+	0.0162752i	$0.994819\pi$
$318$	0.543799	+	2.73386i	0.0304947	+	0.153307i
$319$	−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
$323$	−0.306001	+	3.34468i	−0.0170263	+	0.186103i
$324$			0.413372i			0.0229651i
$325$		0			0
$326$	−6.68221	+	1.32917i	−0.370093	+	0.0736161i
$327$	−6.84014			−0.378261
$328$	−7.77565	+	1.54667i	−0.429339	+	0.0854008i
$329$	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	$-0.255110\pi$
$332$	0.987480	−	2.38399i	0.0541950	−	0.130838i
$333$	−33.5815	−	6.67978i	−1.84026	−	0.366050i
$334$	13.1642	+	2.61851i	0.720310	+	0.143279i
$335$		0			0
$336$	−2.59326	+	2.59326i	−0.141474	+	0.141474i
$337$	7.15312	+	4.77956i	0.389655	+	0.260359i	0.734931	−	0.678142i	$-0.237215\pi$
$337$	7.15312	+	4.77956i	0.389655	+	0.260359i	−0.345276	+	0.938501i	$0.612215\pi$
$338$	14.3142	−	5.92913i	0.778590	−	0.322502i
$339$	−31.8295			−1.72874
$340$		0			0
$341$	9.02956			0.488978
$342$	3.69908	−	1.53221i	0.200023	−	0.0828523i
$343$	−13.3324	−	8.90842i	−0.719881	−	0.481009i
$344$	1.00557	−	1.00557i	0.0542168	−	0.0542168i
$345$		0			0
$346$	23.1868	+	4.61214i	1.24653	+	0.247950i
$347$	−33.4249	−	6.64863i	−1.79434	−	0.356917i	−0.818350	−	0.574720i	$-0.805111\pi$
$347$	−33.4249	−	6.64863i	−1.79434	−	0.356917i	−0.975993	+	0.217802i	$0.930111\pi$
$348$	−2.26832	+	5.47620i	−0.121595	+	0.293555i
$349$	2.62113	+	6.32796i	0.140306	+	0.338728i	0.978376	−	0.206834i	$-0.0663161\pi$
$349$	2.62113	+	6.32796i	0.140306	+	0.338728i	−0.838070	+	0.545562i	$0.816316\pi$
$350$		0			0
$351$	5.61108	−	28.2088i	0.299497	−	1.50567i
$352$	−5.73386	+	1.14054i	−0.305616	+	0.0607907i
$353$	23.7210			1.26254			0.631270	−	0.775563i	$-0.282534\pi$
$353$	23.7210			1.26254			0.631270	+	0.775563i	$0.282534\pi$
$354$	−15.1831	+	3.02010i	−0.806971	+	0.160516i
$355$		0			0
$356$			1.10208i			0.0584102i
$357$	13.3848	+	7.03535i	0.708400	+	0.372350i
$358$	17.5394	+	17.5394i	0.926987	+	0.926987i
$359$	10.0001	−	24.1423i	0.527783	−	1.27418i	−0.405189	−	0.914233i	$-0.632794\pi$
$359$	10.0001	−	24.1423i	0.527783	−	1.27418i	0.932972	−	0.359948i	$-0.117206\pi$
$360$		0			0
$361$	12.9658	+	12.9658i	0.682412	+	0.682412i
$362$	1.10723	+	5.56640i	0.0581945	+	0.292564i
$363$	36.2280	+	54.2190i	1.90147	+	2.84576i
$364$	5.78563	−	3.86583i	0.303249	−	0.202625i
$365$		0			0
$366$	15.0890	−	6.25006i	0.788714	−	0.326696i
$367$	−2.97569	+	14.9598i	−0.155330	+	0.780894i	0.822052	+	0.569412i	$0.192829\pi$
$367$	−2.97569	+	14.9598i	−0.155330	+	0.780894i	−0.977382	+	0.211482i	$0.932171\pi$
$368$	−5.82170	+	3.88994i	−0.303477	+	0.202777i
$369$	21.6491	−	32.4002i	1.12701	−	1.68669i
$370$		0			0
$371$	−0.251964	−	1.26671i	−0.0130813	−	0.0657643i
$372$	−1.66289	−	4.01457i	−0.0862168	−	0.208146i
$373$	3.61554	−	3.61554i	0.187206	−	0.187206i	−0.607281	−	0.794487i	$-0.707740\pi$
$373$	3.61554	−	3.61554i	0.187206	−	0.187206i	0.794487	+	0.607281i	$0.207740\pi$
$374$	11.5100	+	21.1789i	0.595169	+	1.09513i
$375$		0			0
$376$	−0.101575	−	0.0420738i	−0.00523834	−	0.00216979i
$377$	6.24808	−	9.35091i	0.321792	−	0.481596i
$378$		−	7.02373i		−	0.361261i
$379$	20.5807	+	13.7516i	1.05716	+	0.706372i	0.957437	−	0.288643i	$-0.0932042\pi$
$379$	20.5807	+	13.7516i	1.05716	+	0.706372i	0.0997236	+	0.995015i	$0.468204\pi$
$380$		0			0
$381$	−5.56959	−	8.33548i	−0.285339	−	0.427039i
$382$	−0.265107	−	0.109811i	−0.0135641	−	0.00561842i
$383$	−15.5006	−	6.42058i	−0.792046	−	0.328076i	−0.0502803	−	0.998735i	$-0.516011\pi$
$383$	−15.5006	−	6.42058i	−0.792046	−	0.328076i	−0.741766	+	0.670659i	$0.766011\pi$
$384$	1.56304	+	2.33925i	0.0797634	+	0.119374i
$385$		0			0
$386$	−20.3846	−	13.6206i	−1.03755	−	0.693268i
$387$			6.98982i			0.355313i
$388$	8.36364	−	12.5171i	0.424599	−	0.635458i
$389$	10.3937	+	4.30522i	0.526983	+	0.218283i	0.630281	−	0.776367i	$-0.282940\pi$
$389$	10.3937	+	4.30522i	0.526983	+	0.218283i	−0.103298	+	0.994650i	$0.532940\pi$
$390$		0			0
$391$	22.4424	+	18.1588i	1.13496	+	0.918332i
$392$	−3.74819	+	3.74819i	−0.189312	+	0.189312i
$393$	−12.6957	−	30.6501i	−0.640413	−	1.54609i
$394$	0.490864	+	2.46774i	0.0247294	+	0.124323i
$395$		0			0
$396$	15.9643	−	23.8923i	0.802237	−	1.20063i
$397$	31.0249	−	20.7302i	1.55710	−	1.04042i	0.583508	−	0.812107i	$-0.301680\pi$
$397$	31.0249	−	20.7302i	1.55710	−	1.04042i	0.973588	−	0.228311i	$-0.0733204\pi$
$398$	−2.52203	+	12.6791i	−0.126418	+	0.635546i
$399$	−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	$0.344055\pi$
$402$	9.11608	+	13.6432i	0.454669	+	0.680460i
$403$	1.60843	+	8.08613i	0.0801217	+	0.402799i
$404$	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
$408$	7.29650	−	9.01770i	0.361230	−	0.446443i
$409$		−	0.304764i		−	0.0150696i	−0.999972	−	0.00753480i	$-0.997602\pi$
$409$		−	0.304764i		−	0.0150696i	0.999972	−	0.00753480i	$-0.00239842\pi$
$410$		0			0
$411$	37.4384	−	7.44696i	1.84670	−	0.367332i
$412$	6.72318			0.331227
$413$	7.03493	−	1.39933i	0.346166	−	0.0688568i
$414$	6.71394	−	33.7533i	0.329972	−	1.65888i
$415$		0			0
$416$	−2.04274	−	4.93161i	−0.100154	−	0.241792i
$417$	−11.0987	+	26.7947i	−0.543506	+	1.31214i
$418$	−4.67075	−	0.929070i	−0.228454	−	0.0454423i
$419$	35.8559	+	7.13218i	1.75168	+	0.348430i	0.963641	−	0.267201i	$-0.0860988\pi$
$419$	35.8559	+	7.13218i	1.75168	+	0.348430i	0.788035	+	0.615631i	$0.211099\pi$
$420$		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	$0.0677029\pi$
$422$	11.8580	+	7.92328i	0.577240	+	0.385699i
$423$	0.499259	−	0.206800i	0.0242748	−	0.0100550i
$424$	−0.990769			−0.0481160
$425$		0			0
$426$	15.4599			0.749034
$427$	−6.99134	+	2.89591i	−0.338335	+	0.140143i
$428$	−13.9058	−	9.29153i	−0.672160	−	0.449123i
$429$	−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	$0.888916\pi$
$432$	−5.28458	−	1.05117i	−0.254255	−	0.0505744i
$433$	1.80184	−	4.35002i	0.0865907	−	0.209048i	−0.874652	−	0.484751i	$-0.838910\pi$
$433$	1.80184	−	4.35002i	0.0865907	−	0.209048i	0.961243	+	0.275702i	$0.0889104\pi$
$434$	0.770484	+	1.86011i	0.0369844	+	0.0892883i
$435$		0			0
$436$	0.474319	−	2.38457i	0.0227158	−	0.114200i
$437$	−5.59393	+	1.11270i	−0.267594	+	0.0532278i
$438$	−23.0220			−1.10004
$439$	16.6816	−	3.31818i	0.796170	−	0.158368i	0.219787	−	0.975548i	$-0.429464\pi$
$439$	16.6816	−	3.31818i	0.796170	−	0.158368i	0.576383	+	0.817180i	$0.304464\pi$
$440$		0			0
$441$		−	26.0540i		−	1.24067i
$442$	−16.9158	+	14.0800i	−0.804602	+	0.669718i
$443$	−8.08098	−	8.08098i	−0.383939	−	0.383939i	0.488580	−	0.872519i	$-0.337515\pi$
$443$	−8.08098	−	8.08098i	−0.383939	−	0.383939i	−0.872519	+	0.488580i	$0.837515\pi$
$444$	7.49994	−	18.1065i	0.355931	−	0.859295i
$445$		0			0
$446$	9.65170	+	9.65170i	0.457021	+	0.457021i
$447$	−10.5778	−	53.1782i	−0.500313	−	2.51524i
$448$	−0.724218	−	1.08387i	−0.0342161	−	0.0512080i
$449$	−9.49028	+	6.34120i	−0.447874	+	0.299260i	−0.758978	−	0.651116i	$-0.774301\pi$
$449$	−9.49028	+	6.34120i	−0.447874	+	0.299260i	0.311104	+	0.950376i	$0.399301\pi$
$450$		0			0
$451$	−42.8205	+	17.7368i	−2.01634	+	0.835194i
$452$	2.20717	−	11.0962i	0.103816	−	0.521920i
$453$	−19.9534	+	13.3325i	−0.937494	+	0.626414i
$454$	4.38201	−	6.55814i	0.205658	−	0.307789i
$455$		0			0
$456$	0.447101	+	2.24773i	0.0209374	+	0.105260i
$457$	−3.07536	−	7.42458i	−0.143859	−	0.347307i	0.835483	−	0.549516i	$-0.185188\pi$
$457$	−3.07536	−	7.42458i	−0.143859	−	0.347307i	−0.979342	+	0.202209i	$0.935188\pi$
$458$	−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	$0.323194\pi$
$462$	−11.9117	+	17.8271i	−0.554181	+	0.829390i
$463$			39.0872i			1.81654i	0.418386	+	0.908269i	$0.362596\pi$
$463$			39.0872i			1.81654i	−0.418386	+	0.908269i	$0.637404\pi$
$464$	−1.75178	−	1.17050i	−0.0813245	−	0.0543393i
$465$		0			0
$466$	−1.32642	−	1.98513i	−0.0614454	−	0.0919595i
$467$	−15.5971	−	6.46053i	−0.721748	−	0.298958i	−0.00859198	−	0.999963i	$-0.502735\pi$
$467$	−15.5971	−	6.46053i	−0.721748	−	0.298958i	−0.713156	+	0.701005i	$0.752735\pi$
$468$	24.2397	+	10.0404i	1.12048	+	0.464118i
$469$	−4.22385	−	6.32144i	−0.195039	−	0.291897i
$470$		0			0
$471$	−2.05856	−	1.37549i	−0.0948535	−	0.0633791i
$472$		−	5.50244i		−	0.253270i
$473$	4.61891	−	6.91269i	0.212378	−	0.317846i
$474$	−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
$478$	−4.00988	−	9.68071i	−0.183408	−	0.442785i
$479$	1.23929	+	6.23034i	0.0566247	+	0.284672i	0.998714	−	0.0506892i	$-0.0161418\pi$
$479$	1.23929	+	6.23034i	0.0566247	+	0.284672i	−0.942090	+	0.335361i	$0.891142\pi$
$480$		0			0
$481$	−20.6586	+	30.9178i	−0.941950	+	1.40973i
$482$	5.38993	−	3.60143i	0.245504	−	0.164041i
$483$	−5.00957	+	25.1848i	−0.227943	+	1.14595i
$484$	−21.4136	+	8.86981i	−0.973346	+	0.403173i
$485$		0			0
$486$	−12.4732	+	8.33431i	−0.565795	+	0.378052i
$487$	15.0153	+	22.4720i	0.680407	+	1.01830i	0.997552	+	0.0699246i	$0.0222759\pi$
$487$	15.0153	+	22.4720i	0.680407	+	1.01830i	−0.317145	+	0.948377i	$0.602724\pi$
$488$	1.13253	+	5.69362i	0.0512673	+	0.257738i
$489$	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
$493$	−2.46389	+	8.33002i	−0.110968	+	0.375165i
$494$		−	4.34824i		−	0.195636i
$495$		0			0
$496$	1.51484	−	0.301321i	0.0680184	−	0.0135297i
$497$	−7.16319			−0.321313
$498$	−7.12021	+	1.41630i	−0.319064	+	0.0634658i
$499$	4.34370	−	21.8373i	0.194451	−	0.977570i	−0.753086	−	0.657923i	$-0.771435\pi$
$499$	4.34370	−	21.8373i	0.194451	−	0.977570i	0.947536	−	0.319648i	$-0.103565\pi$
$500$		0			0
$501$	−14.4507	−	34.8871i	−0.645609	−	1.55864i
$502$	8.35260	−	20.1650i	0.372795	−	0.900007i
$503$	−1.59744	−	0.317750i	−0.0712262	−	0.0141678i	0.159349	−	0.987222i	$-0.449061\pi$
$503$	−1.59744	−	0.317750i	−0.0712262	−	0.0141678i	−0.230575	+	0.973055i	$0.574061\pi$
$504$	6.28410	+	1.24998i	0.279916	+	0.0556787i
$505$		0			0
$506$	−28.9442	+	28.9442i	−1.28673	+	1.28673i
$507$	−36.2433	−	24.2170i	−1.60962	−	1.07552i
$508$	3.29207	−	1.36362i	0.146062	−	0.0605009i
$509$	35.1547			1.55820			0.779102	−	0.626897i	$-0.215675\pi$
$509$	35.1547			1.55820			0.779102	+	0.626897i	$0.215675\pi$
$510$		0			0
$511$	10.6671			0.471883
$512$	−0.923880	+	0.382683i	−0.0408301	+	0.0169124i
$513$	−3.64941	−	2.43846i	−0.161126	−	0.107661i
$514$	−6.86243	+	6.86243i	−0.302689	+	0.302689i
$515$		0			0
$516$	−3.92402	−	0.780537i	−0.172746	−	0.0343612i
$517$	−0.630404	−	0.125395i	−0.0277251	−	0.00551487i
$518$	−3.47503	+	8.38946i	−0.152684	+	0.368612i
$519$	−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	$-0.212853\pi$
$522$	10.1566	−	2.02026i	0.444540	−	0.0884246i
$523$	0.224643			0.00982294			0.00491147	−	0.999988i	$-0.498437\pi$
$523$	0.224643			0.00982294			0.00491147	+	0.999988i	$0.498437\pi$
$524$	11.5654	−	2.30050i	0.505237	−	0.100498i
$525$		0			0
$526$		−	16.0185i		−	0.698438i
$527$	−3.04086	−	5.59530i	−0.132462	−	0.243735i
$528$	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
$532$	−0.207160	−	1.04146i	−0.00898153	−	0.0451532i
$533$	−23.5112	−	35.1871i	−1.01838	−	1.52412i
$534$	2.57804	−	1.72259i	0.111563	−	0.0745439i
$535$		0			0
$536$	−5.38834	+	2.23192i	−0.232741	+	0.0964043i
$537$	13.6143	−	68.4438i	0.587501	−	2.95357i
$538$	−13.7058	+	9.15792i	−0.590899	+	0.394826i
$539$	−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	$0.696868\pi$
$542$	1.97962	+	4.77923i	0.0850321	+	0.205286i
$543$	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
$547$	3.82638	−	5.72658i	0.163604	−	0.244851i	−0.740605	−	0.671940i	$-0.765461\pi$
$547$	3.82638	−	5.72658i	0.163604	−	0.244851i	0.904209	+	0.427090i	$0.140461\pi$
$548$			13.5679i			0.579593i
$549$	−23.7246	−	15.8523i	−1.01254	−	0.676559i
$550$		0			0
$551$	−0.953483	−	1.42699i	−0.0406197	−	0.0607917i
$552$	18.1991	+	7.53830i	0.774604	+	0.320851i
$553$	6.15494	+	2.54946i	0.261735	+	0.108414i
$554$	11.4847	+	17.1880i	0.487936	+	0.730248i
$555$		0			0
$556$	−8.57135	−	5.72719i	−0.363506	−	0.242887i
$557$		−	33.2286i		−	1.40794i	−0.710228	−	0.703971i	$-0.751408\pi$
$557$		−	33.2286i		−	1.40794i	0.710228	−	0.703971i	$-0.248592\pi$
$558$	−4.21765	+	6.31216i	−0.178548	+	0.267215i
$559$	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
$563$	−8.49755	−	20.5149i	−0.358129	−	0.864600i	−0.995563	−	0.0940950i	$-0.970004\pi$
$563$	−8.49755	−	20.5149i	−0.358129	−	0.864600i	0.637434	−	0.770505i	$-0.279996\pi$
$564$	0.0603445	+	0.303372i	0.00254096	+	0.0127743i
$565$		0			0
$566$	−2.53325	+	3.79127i	−0.106480	+	0.159359i
$567$	−0.448041	+	0.299372i	−0.0188160	+	0.0125724i
$568$	−1.07204	+	5.38952i	−0.0449819	+	0.226139i
$569$	13.2905	−	5.50510i	0.557166	−	0.230786i	−0.0862883	−	0.996270i	$-0.527501\pi$
$569$	13.2905	−	5.50510i	0.557166	−	0.230786i	0.643454	+	0.765484i	$0.277501\pi$
$570$		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	$0.167825\pi$
$572$	−17.3375	−	25.9473i	−0.724915	−	1.08491i
$573$	0.157497	+	0.791791i	0.00657953	+	0.0330775i
$574$	−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	$-0.375302\pi$
$577$	−13.0297	−	13.0297i	−0.542435	−	0.542435i	−0.924242	+	0.381807i	$0.875302\pi$
$578$	9.24760	−	14.2647i	0.384650	−	0.593334i
$579$			68.9741i			2.86646i
$580$		0			0
$581$	3.29908	−	0.656228i	0.136869	−	0.0272249i
$582$	−42.3532			−1.75560
$583$	−5.68093	+	1.13001i	−0.235280	+	0.0468001i
$584$	1.59643	−	8.02579i	0.0660607	−	0.332110i
$585$		0			0
$586$	11.9708	+	28.9001i	0.494510	+	1.19385i
$587$	−8.94250	+	21.5891i	−0.369096	+	0.891077i	0.624803	+	0.780783i	$0.285179\pi$
$587$	−8.94250	+	21.5891i	−0.369096	+	0.891077i	−0.993899	+	0.110295i	$0.964821\pi$
$588$	14.6265	+	2.90939i	0.603186	+	0.119981i
$589$	1.23398	+	0.245453i	0.0508452	+	0.0101137i
$590$		0			0
$591$	5.00542	−	5.00542i	0.205895	−	0.205895i
$592$	5.79208	+	3.87014i	0.238053	+	0.159062i
$593$	25.7677	−	10.6733i	1.05815	−	0.438301i	0.215357	−	0.976535i	$-0.430908\pi$
$593$	25.7677	−	10.6733i	1.05815	−	0.438301i	0.842795	+	0.538234i	$0.180908\pi$
$594$	−31.4999			−1.29246
$595$		0			0
$596$	19.2721			0.789417
$597$	33.6016	−	13.9182i	1.37522	−	0.569636i
$598$	−31.0759	−	20.7642i	−1.27079	−	0.849113i
$599$	6.03820	−	6.03820i	0.246714	−	0.246714i	−0.572907	−	0.819621i	$-0.694184\pi$
$599$	6.03820	−	6.03820i	0.246714	−	0.246714i	0.819621	+	0.572907i	$0.194184\pi$
$600$		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	$0.570548\pi$
$602$	1.81816	+	0.361655i	0.0741027	+	0.0147399i
$603$	10.9703	−	26.4846i	0.446744	−	1.07854i
$604$	−3.26423	−	7.88055i	−0.132820	−	0.320655i
$605$		0			0
$606$	3.70803	−	18.6415i	0.150628	−	0.757260i
$607$	−35.7149	+	7.10414i	−1.44962	+	0.288348i	−0.856243	−	0.516574i	$-0.827207\pi$
$607$	−35.7149	+	7.10414i	−1.44962	+	0.288348i	−0.593381	+	0.804922i	$0.702207\pi$
$608$	−0.814591			−0.0330360
$609$	−7.57824	+	1.50741i	−0.307086	+	0.0610832i
$610$		0			0
$611$		−	0.586875i		−	0.0237424i
$612$	−20.1815	−	1.84638i	−0.815788	−	0.0746355i
$613$	1.67709	+	1.67709i	0.0677372	+	0.0677372i	0.740164	−	0.672427i	$-0.234748\pi$
$613$	1.67709	+	1.67709i	0.0677372	+	0.0677372i	−0.672427	+	0.740164i	$0.734748\pi$
$614$	6.55792	−	15.8322i	0.264656	−	0.638936i
$615$		0			0
$616$	−5.38876	−	5.38876i	−0.217119	−	0.217119i
$617$	1.85351	+	9.31821i	0.0746194	+	0.375137i	0.999992	−	0.00392093i	$-0.00124807\pi$
$617$	1.85351	+	9.31821i	0.0746194	+	0.375137i	−0.925373	+	0.379058i	$0.876248\pi$
$618$	−10.5086	−	15.7272i	−0.422717	−	0.632640i
$619$	−33.6978	+	22.5162i	−1.35443	+	0.905001i	−0.999553	−	0.0299118i	$-0.990477\pi$
$619$	−33.6978	+	22.5162i	−1.35443	+	0.905001i	−0.354877	+	0.934913i	$0.615477\pi$
$620$		0			0
$621$	−34.8543	+	14.4371i	−1.39865	+	0.579341i
$622$	−1.07090	+	5.38379i	−0.0429393	+	0.215870i
$623$	−1.19451	+	0.798148i	−0.0478571	+	0.0319771i
$624$	−8.34339	+	12.4868i	−0.334003	+	0.499871i
$625$		0			0
$626$	1.25044	+	6.28639i	0.0499777	+	0.251255i
$627$	5.12723	+	12.3782i	0.204762	+	0.494338i
$628$	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	$0.712800\pi$
$632$	2.83934	−	4.24937i	0.112943	−	0.169031i
$633$		−	40.1233i		−	1.59476i
$634$	−16.0464	−	10.7218i	−0.637283	−	0.425819i
$635$		0			0
$636$	1.54861	+	2.31766i	0.0614063	+	0.0919010i
$637$	−26.1412	−	10.8280i	−1.03575	−	0.429022i
$638$	−11.3795	−	4.71353i	−0.450518	−	0.186611i
$639$	−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	$0.922512\pi$
$642$			47.0520i			1.85700i
$643$	−6.38975	+	9.56293i	−0.251987	+	0.377125i	−0.935800	−	0.352532i	$-0.885321\pi$
$643$	−6.38975	+	9.56293i	−0.251987	+	0.377125i	0.683813	+	0.729658i	$0.260321\pi$
$644$	−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	−0.992136	−	0.125168i	$-0.960053\pi$
$647$	−22.0524	+	22.0524i	−0.866968	+	0.866968i	0.125168	+	0.992136i	$0.460053\pi$
$648$	0.158191	+	0.381906i	0.00621432	+	0.0150027i
$649$	−6.27573	−	31.5502i	−0.246344	−	1.23845i
$650$		0			0
$651$	3.14697	−	4.70978i	0.123340	−	0.184591i
$652$	−5.66490	+	3.78517i	−0.221855	+	0.148239i
$653$	−9.02163	+	45.3548i	−0.353044	+	1.77487i	0.241088	+	0.970503i	$0.422496\pi$
$653$	−9.02163	+	45.3548i	−0.353044	+	1.77487i	−0.594132	+	0.804368i	$0.702504\pi$
$654$	−6.31947	+	2.61761i	−0.247111	+	0.102357i
$655$		0			0
$656$	−6.59188	+	4.40455i	−0.257370	+	0.171969i
$657$	22.3456	+	33.4425i	0.871783	+	1.30472i
$658$	−0.0279601	−	0.140565i	−0.00109000	−	0.00547979i
$659$	−26.4734	−	26.4734i	−1.03126	−	1.03126i	−0.999495	−	0.0317611i	$-0.989888\pi$
$659$	−26.4734	−	26.4734i	−1.03126	−	1.03126i	−0.0317611	−	0.999495i	$-0.510112\pi$
$660$		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
$663$	59.3767	+	17.5627i	2.30600	+	0.682077i
$664$		−	2.58041i		−	0.100139i
$665$		0			0
$666$	−33.5815	+	6.67978i	−1.30126	+	0.258836i
$667$	−14.7516			−0.571182
$668$	13.1642	−	2.61851i	0.509336	−	0.101313i
$669$	7.49177	−	37.6637i	0.289649	−	1.45616i
$670$		0			0
$671$	12.9876	+	31.3547i	0.501379	+	1.21044i
$672$	−1.40346	+	3.38825i	−0.0541397	+	0.130705i
$673$	9.10724	+	1.81154i	0.351058	+	0.0698299i	0.367470	−	0.930035i	$-0.380224\pi$
$673$	9.10724	+	1.81154i	0.351058	+	0.0698299i	−0.0164114	+	0.999865i	$0.505224\pi$
$674$	8.43768	+	1.67836i	0.325007	+	0.0646480i
$675$		0			0
$676$	10.9556	−	10.9556i	0.421370	−	0.421370i
$677$	31.7217	+	21.1958i	1.21916	+	0.814619i	0.987414	−	0.158157i	$-0.0505551\pi$
$677$	31.7217	+	21.1958i	1.21916	+	0.814619i	0.231749	+	0.972776i	$0.425555\pi$
$678$	−29.4066	+	12.1806i	−1.12935	+	0.467794i
$679$	19.6240			0.753099
$680$		0			0
$681$	−22.1904			−0.850336
$682$	8.34222	−	3.45546i	0.319440	−	0.132316i
$683$	22.6804	+	15.1546i	0.867842	+	0.579874i	0.907836	−	0.419326i	$-0.137734\pi$
$683$	22.6804	+	15.1546i	0.867842	+	0.579874i	−0.0399935	+	0.999200i	$0.512734\pi$
$684$	2.83115	−	2.83115i	0.108252	−	0.108252i
$685$		0			0
$686$	−15.7266	−	3.12822i	−0.600445	−	0.119436i
$687$	29.2455	+	5.81730i	1.11579	+	0.221944i
$688$	0.544211	−	1.31384i	0.0207479	−	0.0500898i
$689$	−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	$0.881235\pi$
$692$	23.1868	−	4.61214i	0.881430	−	0.175327i
$693$	37.4578			1.42290
$694$	−33.4249	+	6.64863i	−1.26879	+	0.252378i
$695$		0			0
$696$			5.92740i			0.224677i
$697$	25.4114	+	20.5612i	0.962526	+	0.778809i
$698$	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	$0.775014\pi$
$702$	−5.61108	−	28.2088i	−0.211776	−	1.06467i
$703$	3.15259	+	4.71818i	0.118902	+	0.177949i
$704$	−4.86093	+	3.24797i	−0.183203	+	0.122412i
$705$		0			0
$706$	21.9153	−	9.07762i	0.824794	−	0.341641i
$707$	−1.71808	+	8.63737i	−0.0646151	+	0.324842i
$708$	−12.8716	+	8.60051i	−0.483744	+	0.323227i
$709$	−9.66796	+	14.4691i	−0.363088	+	0.543399i	−0.967369	−	0.253372i	$-0.918460\pi$
$709$	−9.66796	+	14.4691i	−0.363088	+	0.543399i	0.604281	+	0.796771i	$0.293460\pi$
$710$		0			0
$711$	4.90063	+	24.6371i	0.183788	+	0.923965i
$712$	0.421748	+	1.01819i	0.0158057	+	0.0381583i
$713$	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
$717$	−16.3780	+	24.5114i	−0.611647	+	0.915395i
$718$		−	26.1314i		−	0.975216i
$719$	−7.89793	−	5.27723i	−0.294543	−	0.196807i	0.399515	−	0.916727i	$-0.369179\pi$
$719$	−7.89793	−	5.27723i	−0.294543	−	0.196807i	−0.694058	+	0.719919i	$0.744179\pi$
$720$		0			0
$721$	4.86905	+	7.28705i	0.181333	+	0.271384i
$722$	16.9407	+	7.01705i	0.630466	+	0.261148i
$723$	−16.8493	−	6.97921i	−0.626632	−	0.259560i
$724$	3.15311	+	4.71897i	0.117185	+	0.175379i
$725$		0			0
$726$	54.2190	+	36.2280i	2.01225	+	1.34455i
$727$			11.5433i			0.428116i	0.976821	+	0.214058i	$0.0686681\pi$
$727$			11.5433i			0.428116i	−0.976821	+	0.214058i	$0.931332\pi$
$728$	3.86583	−	5.78563i	0.143277	−	0.214430i
$729$	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
$733$	−1.12997	−	2.72799i	−0.0417363	−	0.100760i	0.901637	−	0.432494i	$-0.142366\pi$
$733$	−1.12997	−	2.72799i	−0.0417363	−	0.100760i	−0.943373	+	0.331734i	$0.892366\pi$
$734$	2.97569	+	14.9598i	0.109835	+	0.552176i
$735$		0			0
$736$	−3.88994	+	5.82170i	−0.143385	+	0.214591i
$737$	−28.3504	+	18.9431i	−1.04430	+	0.697778i
$738$	7.60216	−	38.2186i	0.279839	−	1.40685i
$739$	9.10333	−	3.77072i	0.334871	−	0.138708i	−0.208911	−	0.977935i	$-0.566992\pi$
$739$	9.10333	−	3.77072i	0.334871	−	0.138708i	0.543782	+	0.839226i	$0.316992\pi$
$740$		0			0
$741$	−10.1716	+	6.79645i	−0.373663	+	0.249674i
$742$	−0.717533	−	1.07386i	−0.0263415	−	0.0394228i
$743$	−0.496966	−	2.49842i	−0.0182319	−	0.0916580i	0.970598	−	0.240706i	$-0.0773790\pi$
$743$	−0.496966	−	2.49842i	−0.0182319	−	0.0916580i	−0.988830	+	0.149048i	$0.952379\pi$
$744$	−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
$748$	18.7387	+	15.1620i	0.685154	+	0.554379i
$749$		−	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	$0.618235\pi$
$752$	−0.109944			−0.00400925
$753$	−60.2263	+	11.9798i	−2.19477	+	0.436567i
$754$	2.19403	−	11.0302i	0.0799020	−	0.401694i
$755$		0			0
$756$	−2.68786	−	6.48908i	−0.0977566	−	0.236005i
$757$	3.97997	−	9.60850i	0.144655	−	0.349227i	−0.834901	−	0.550400i	$-0.814475\pi$
$757$	3.97997	−	9.60850i	0.144655	−	0.349227i	0.979556	+	0.201173i	$0.0644753\pi$
$758$	24.2766	+	4.82892i	0.881766	+	0.175394i
$759$	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	$0.256878\pi$
$762$	−8.33548	−	5.56959i	−0.301962	−	0.201765i
$763$	2.92807	−	1.21285i	0.106003	−	0.0439080i
$764$	−0.286950			−0.0103815
$765$		0			0
$766$	−16.7778			−0.606206
$767$	27.1359	−	11.2401i	0.979820	−	0.405855i
$768$	2.33925	+	1.56304i	0.0844104	+	0.0564012i
$769$	−5.06321	+	5.06321i	−0.182584	+	0.182584i	−0.792481	−	0.609897i	$-0.791211\pi$
$769$	−5.06321	+	5.06321i	−0.182584	+	0.182584i	0.609897	+	0.792481i	$0.291211\pi$
$770$		0			0
$771$	26.7791	+	5.32670i	0.964427	+	0.191837i
$772$	−24.0453	−	4.78290i	−0.865408	−	0.172140i
$773$	0.443463	−	1.07061i	0.0159502	−	0.0385073i	−0.915704	−	0.401854i	$-0.868366\pi$
$773$	0.443463	−	1.07061i	0.0159502	−	0.0385073i	0.931654	+	0.363347i	$0.118366\pi$
$774$	2.67489	+	6.45775i	0.0961469	+	0.232119i
$775$		0			0
$776$	2.93692	−	14.7649i	0.105429	−	0.530029i
$777$	25.0566	−	4.98407i	0.898902	−	0.178803i
$778$	11.2501			0.403335
$779$	−6.33398	+	1.25991i	−0.226938	+	0.0451409i
$780$		0			0
$781$			32.1254i			1.14954i
$782$	27.6832	+	8.18824i	0.989948	+	0.292811i
$783$	−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
$787$	7.24294	+	36.4127i	0.258183	+	1.29797i	0.864453	+	0.502714i	$0.167665\pi$
$787$	7.24294	+	36.4127i	0.258183	+	1.29797i	−0.606270	+	0.795259i	$0.707335\pi$
$788$	1.39786	+	2.09205i	0.0497968	+	0.0745261i
$789$	−37.4712	+	25.0374i	−1.33401	+	0.891356i
$790$		0			0
$791$	13.6253	−	5.64377i	0.484459	−	0.200669i
$792$	5.60592	−	28.1829i	0.199198	−	1.00143i
$793$	−25.7653	+	17.2158i	−0.914951	+	0.611351i
$794$	20.7302	−	31.0249i	0.735687	−	1.10103i
$795$		0			0
$796$	2.52203	+	12.6791i	0.0893911	+	0.449399i
$797$	0.0157219	+	0.0379559i	0.000556897	+	0.00134447i	0.924158	−	0.382011i	$-0.124768\pi$
$797$	0.0157219	+	0.0379559i	0.000556897	+	0.00134447i	−0.923601	+	0.383356i	$0.874768\pi$
$798$	−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
$802$	−2.20217	+	3.29578i	−0.0777614	+	0.116378i
$803$		−	47.8395i		−	1.68822i
$804$	13.6432	+	9.11608i	0.481158	+	0.321500i
$805$		0			0
$806$	4.58043	+	6.85509i	0.161339	+	0.241460i
$807$	42.8453	+	17.7471i	1.50823	+	0.624727i
$808$	6.24155	+	2.58533i	0.219577	+	0.0909518i
$809$	21.2673	+	31.8287i	0.747717	+	1.11904i	0.988904	+	0.148559i	$0.0474635\pi$
$809$	21.2673	+	31.8287i	0.747717	+	1.11904i	−0.241186	+	0.970479i	$0.577537\pi$
$810$		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	$0.714025\pi$
$812$		−	2.74641i		−	0.0963799i
$813$	8.08560	−	12.1009i	0.283574	−	0.424399i
$814$	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
$818$	−0.116628	−	0.281565i	−0.00407780	−	0.00984469i
$819$	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	$-0.0860208\pi$
$822$	31.7388	−	21.2072i	1.10702	−	0.739685i
$823$	6.32657	−	31.8058i	0.220531	−	1.10868i	−0.698837	−	0.715281i	$-0.746299\pi$
$823$	6.32657	−	31.8058i	0.220531	−	1.10868i	0.919367	−	0.393401i	$-0.128701\pi$
$824$	6.21141	−	2.57285i	0.216385	−	0.0896294i
$825$		0			0
$826$	5.96393	−	3.98497i	0.207512	−	0.138655i
$827$	24.8130	+	37.1352i	0.862832	+	1.29132i	0.955311	+	0.295604i	$0.0955209\pi$
$827$	24.8130	+	37.1352i	0.862832	+	1.29132i	−0.0924789	+	0.995715i	$0.529479\pi$
$828$	−6.71394	−	33.7533i	−0.233326	−	1.17301i
$829$	24.9924	+	24.9924i	0.868024	+	0.868024i	0.992253	−	0.124230i	$-0.0396460\pi$
$829$	24.9924	+	24.9924i	0.868024	+	0.868024i	−0.124230	+	0.992253i	$0.539646\pi$
$830$		0			0
$831$	22.2561	−	53.7309i	0.772055	−	1.86390i
$832$	−3.77449	−	3.77449i	−0.130857	−	0.130857i
$833$	21.7646	+	1.99122i	0.754098	+	0.0689917i
$834$			29.0023i			1.00427i
$835$		0			0
$836$	−4.67075	+	0.929070i	−0.161541	+	0.0321326i
$837$	8.32205			0.287652
$838$	35.8559	−	7.13218i	1.23862	−	0.246377i
$839$	−9.26094	+	46.5579i	−0.319723	+	1.60736i	0.402314	+	0.915502i	$0.368206\pi$
$839$	−9.26094	+	46.5579i	−0.319723	+	1.60736i	−0.722037	+	0.691855i	$0.756794\pi$
$840$		0			0
$841$	9.39915	+	22.6916i	0.324109	+	0.782468i
$842$	8.51010	−	20.5452i	0.293277	−	0.708034i
$843$	3.60837	+	0.717749i	0.124279	+	0.0247206i
$844$	13.9875	+	2.78229i	0.481470	+	0.0957702i
$845$		0			0
$846$	0.382116	−	0.382116i	0.0131374	−	0.0131374i
$847$	−25.1219	−	16.7859i	−0.863197	−	0.576770i
$848$	−0.915351	+	0.379151i	−0.0314333	+	0.0130201i
$849$	12.8283			0.440265
$850$		0			0
$851$	48.7744			1.67196
$852$	14.2831	−	5.91624i	0.489330	−	0.202687i
$853$	16.1374	+	10.7826i	0.552533	+	0.369191i	0.800273	−	0.599636i	$-0.204688\pi$
$853$	16.1374	+	10.7826i	0.552533	+	0.369191i	−0.247740	+	0.968827i	$0.579688\pi$
$854$	−5.35094	+	5.35094i	−0.183106	+	0.183106i
$855$		0			0
$856$	−16.4030	−	3.26275i	−0.560642	−	0.111519i
$857$	−12.8130	−	2.54865i	−0.437682	−	0.0870604i	−0.0286691	−	0.999589i	$-0.509127\pi$
$857$	−12.8130	−	2.54865i	−0.437682	−	0.0870604i	−0.409013	+	0.912529i	$0.634127\pi$
$858$	−33.5982	+	81.1133i	−1.14702	+	2.76916i
$859$	−8.74774	−	21.1189i	−0.298469	−	0.720568i	−0.999969	−	0.00789846i	$-0.997486\pi$
$859$	−8.74774	−	21.1189i	−0.298469	−	0.720568i	0.701500	−	0.712670i	$-0.252514\pi$
$860$		0			0
$861$	−5.67230	+	28.5166i	−0.193312	+	0.971843i
$862$	−34.8166	+	6.92546i	−1.18586	+	0.235882i
$863$	−48.9670			−1.66686			−0.833429	−	0.552627i	$-0.813625\pi$
$863$	−48.9670			−1.66686			−0.833429	+	0.552627i	$0.813625\pi$
$864$	−5.28458	+	1.05117i	−0.179785	+	0.0357615i
$865$		0			0
$866$		−	4.70842i		−	0.159999i
$867$	−47.8230	+	0.663809i	−1.62416	+	0.0225441i
$868$	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
$872$	−0.474319	−	2.38457i	−0.0160625	−	0.0807516i
$873$	41.1087	+	61.5235i	1.39132	+	2.08226i
$874$	−4.74231	+	3.16871i	−0.160411	+	0.107183i
$875$		0			0
$876$	−21.2696	+	8.81016i	−0.718633	+	0.297668i
$877$	1.88944	−	9.49886i	0.0638019	−	0.320754i	−0.935683	−	0.352841i	$-0.885216\pi$
$877$	1.88944	−	9.49886i	0.0638019	−	0.320754i	0.999485	+	0.0320876i	$0.0102156\pi$
$878$	14.1420	−	9.44938i	0.477269	−	0.318901i
$879$	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	$-0.164596\pi$
$882$	−9.97043	−	24.0708i	−0.335722	−	0.810505i
$883$	19.9922	−	19.9922i	0.672793	−	0.672793i	−0.285566	−	0.958359i	$-0.592182\pi$
$883$	19.9922	−	19.9922i	0.672793	−	0.672793i	0.958359	+	0.285566i	$0.0921817\pi$
$884$	−10.2400	+	19.4816i	−0.344407	+	0.655238i
$885$		0			0
$886$	−10.5583	−	4.37340i	−0.354713	−	0.146927i
$887$	29.6178	−	44.3262i	0.994469	−	1.48833i	0.126341	−	0.991987i	$-0.459677\pi$
$887$	29.6178	−	44.3262i	0.994469	−	1.48833i	0.868128	−	0.496340i	$-0.165323\pi$
$888$		−	19.5983i		−	0.657676i
$889$	3.86217	+	2.58062i	0.129533	+	0.0865511i
$890$		0			0
$891$	1.34262	+	2.00937i	0.0449795	+	0.0673165i
$892$	12.6106	+	5.22346i	0.422233	+	0.174894i
$893$	−0.0827422	−	0.0342730i	−0.00276886	−	0.00114690i
$894$	−30.1230	−	45.0823i	−1.00746	−	1.50778i
$895$		0			0
$896$	−1.08387	−	0.724218i	−0.0362095	−	0.0241944i
$897$			105.150i			3.51084i
$898$	−6.34120	+	9.49028i	−0.211609	+	0.316695i
$899$	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
$903$	−1.99585	−	4.81841i	−0.0664178	−	0.160347i
$904$	−2.20717	−	11.0962i	−0.0734093	−	0.369053i
$905$		0			0
$906$	−13.3325	+	19.9534i	−0.442941	+	0.662909i
$907$	28.6777	−	19.1618i	0.952226	−	0.636257i	0.0206435	−	0.999787i	$-0.493428\pi$
$907$	28.6777	−	19.1618i	0.952226	−	0.636257i	0.931583	+	0.363530i	$0.118428\pi$
$908$	1.53876	−	7.73585i	0.0510654	−	0.256723i
$909$	−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	$0.418334\pi$
$912$	1.27324	+	1.90553i	0.0421610	+	0.0630985i
$913$	−2.94305	−	14.7957i	−0.0974007	−	0.489666i
$914$	−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
$918$	10.6082	+	19.5194i	0.350121	+	0.644237i
$919$			7.48557i			0.246926i	0.992349	+	0.123463i	$0.0394001\pi$
$919$			7.48557i			0.246926i	−0.992349	+	0.123463i	$0.960600\pi$
$920$		0			0
$921$	−47.2857	+	9.40572i	−1.55812	+	0.309929i
$922$	34.8833			1.14882
$923$	−28.7689	+	5.72249i	−0.946941	+	0.188358i
$924$	−4.18282	+	21.0285i	−0.137605	+	0.691786i
$925$		0			0
$926$	14.9580	+	36.1119i	0.491552	+	1.18671i
$927$	−12.6460	+	30.5301i	−0.415349	+	1.00274i
$928$	−2.06637	−	0.411026i	−0.0678319	−	0.0134926i
$929$	−23.3245	−	4.63954i	−0.765253	−	0.152218i	−0.202995	−	0.979180i	$-0.565067\pi$
$929$	−23.3245	−	4.63954i	−0.765253	−	0.152218i	−0.562258	+	0.826962i	$0.690067\pi$
$930$		0			0
$931$	−3.05324	+	3.05324i	−0.100066	+	0.100066i
$932$	−1.98513	−	1.32642i	−0.0650252	−	0.0434484i
$933$	14.2679	−	5.90995i	0.467110	−	0.193483i
$934$	−16.8822			−0.552402
$935$		0			0
$936$	26.2369			0.857579
$937$	27.2845	−	11.3016i	0.891345	−	0.369207i	0.110459	−	0.993881i	$-0.464768\pi$
$937$	27.2845	−	11.3016i	0.891345	−	0.369207i	0.780886	+	0.624674i	$0.214768\pi$
$938$	−6.32144	−	4.22385i	−0.206402	−	0.137914i
$939$	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	$0.555817\pi$
$942$	−2.42824	−	0.483007i	−0.0791163	−	0.0157372i
$943$	−21.2425	+	51.2840i	−0.691752	+	1.67004i
$944$	−2.10569	−	5.08359i	−0.0685345	−	0.165457i
$945$		0			0
$946$	1.62195	−	8.15407i	0.0527340	−	0.265112i
$947$	−36.8415	+	7.32823i	−1.19719	+	0.238136i	−0.753136	−	0.657865i	$-0.771460\pi$
$947$	−36.8415	+	7.32823i	−1.19719	+	0.238136i	−0.444052	+	0.896001i	$0.646460\pi$
$948$	−14.3783			−0.466986
$949$	42.8412	−	8.52164i	1.39068	−	0.276624i
$950$		0			0
$951$			54.2951i			1.76064i
$952$	−1.52447	+	5.15398i	−0.0494082	+	0.167041i
$953$	−25.9594	−	25.9594i	−0.840908	−	0.840908i	0.148069	−	0.988977i	$-0.452694\pi$
$953$	−25.9594	−	25.9594i	−0.840908	−	0.840908i	−0.988977	+	0.148069i	$0.952694\pi$
$954$	1.86359	−	4.49910i	0.0603360	−	0.145664i
$955$		0			0
$956$	−7.40929	−	7.40929i	−0.239634	−	0.239634i
$957$	6.76041	+	33.9869i	0.218533	+	1.09864i
$958$	3.52921	+	5.28183i	0.114023	+	0.170648i
$959$	−14.7059	+	9.82614i	−0.474877	+	0.317303i
$960$		0			0
$961$	26.4363	−	10.9503i	0.852784	−	0.353235i
$962$	−7.25433	+	36.4700i	−0.233889	+	1.17584i
$963$	68.3492	−	45.6695i	2.20252	−	1.47168i
$964$	3.60143	−	5.38993i	0.115994	−	0.173598i
$965$		0			0
$966$	5.00957	+	25.1848i	0.161180	+	0.810307i
$967$	−9.00902	−	21.7497i	−0.289711	−	0.699423i	0.710279	−	0.703920i	$-0.248569\pi$
$967$	−9.00902	−	21.7497i	−0.289711	−	0.699423i	−0.999990	+	0.00449664i	$0.998569\pi$
$968$	−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	$0.715253\pi$
$972$	−8.33431	+	12.4732i	−0.267323	+	0.400078i
$973$		−	13.4380i		−	0.430801i
$974$	22.4720	+	15.0153i	0.720048	+	0.481121i
$975$		0			0
$976$	3.22518	+	4.82682i	0.103235	+	0.154503i
$977$	11.9048	+	4.93111i	0.380867	+	0.157760i	0.564899	−	0.825160i	$-0.308915\pi$
$977$	11.9048	+	4.93111i	0.380867	+	0.157760i	−0.184032	+	0.982920i	$0.558915\pi$
$978$	17.7089	+	7.33526i	0.566268	+	0.234556i
$979$	3.57953	+	5.35714i	0.114402	+	0.171215i
$980$		0			0
$981$	9.93619	+	6.63915i	0.317238	+	0.211972i
$982$			0.205934i			0.00657160i
$983$	−18.1782	+	27.2056i	−0.579795	+	0.867724i	−0.999197	−	0.0400767i	$-0.987240\pi$
$983$	−18.1782	+	27.2056i	−0.579795	+	0.867724i	0.419402	+	0.907801i	$0.362240\pi$
$984$	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
$988$	−1.66400	−	4.01725i	−0.0529388	−	0.127806i
$989$	−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	$0.161466\pi$
$992$	1.28422	−	0.858089i	0.0407741	−	0.0272444i
$993$	−7.93796	+	39.9068i	−0.251903	+	1.26640i
$994$	−6.61793	+	2.74124i	−0.209908	+	0.0869467i
$995$		0			0
$996$	−6.03622	+	4.03327i	−0.191265	+	0.127799i
$997$	−28.9665	−	43.3514i	−0.917378	−	1.37295i	−0.927828	−	0.373007i	$-0.878327\pi$
$997$	−28.9665	−	43.3514i	−0.917378	−	1.37295i	0.0104506	−	0.999945i	$-0.496673\pi$
$998$	−4.34370	−	21.8373i	−0.137498	−	0.691247i
$999$	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.v.c.193.1		32
5.2	odd	4		850.2.s.c.57.1		32
5.3	odd	4		170.2.o.a.57.4	yes	32
5.4	even	2		170.2.r.a.23.4	yes	32
17.3	odd	16		850.2.s.c.343.1		32
85.3	even	16		170.2.r.a.37.4	yes	32
85.37	even	16	inner	850.2.v.c.207.1		32
85.54	odd	16		170.2.o.a.3.4	✓	32

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

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.v (of order \(16\), degree \(8\), minimal)

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

Introduction

L-functions

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