LMFDB - Embedded newform 804.2.c.b.671.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(671,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("804.671");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.c (of order $2$, degree $1$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$128$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			671.19
Character	$\chi$	$=$	804.671
Dual form			804.2.c.b.671.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.27439 - 0.613127i) q^{2} +(-1.63926 - 0.559297i) q^{3} +(1.24815 + 1.56273i) q^{4} -0.350980i q^{5} +(1.74615 + 1.71784i) q^{6} +2.98214i q^{7} +(-0.632485 - 2.75680i) q^{8} +(2.37437 + 1.83367i) q^{9} +O(q^{10})$	\(q+(-1.27439 - 0.613127i) q^{2} +(-1.63926 - 0.559297i) q^{3} +(1.24815 + 1.56273i) q^{4} -0.350980i q^{5} +(1.74615 + 1.71784i) q^{6} +2.98214i q^{7} +(-0.632485 - 2.75680i) q^{8} +(2.37437 + 1.83367i) q^{9} +(-0.215195 + 0.447286i) q^{10} -1.69575 q^{11} +(-1.17202 - 3.25981i) q^{12} -4.42815 q^{13} +(1.82843 - 3.80041i) q^{14} +(-0.196302 + 0.575349i) q^{15} +(-0.884236 + 3.90104i) q^{16} +2.00327i q^{17} +(-1.90161 - 3.79261i) q^{18} -1.45165i q^{19} +(0.548486 - 0.438076i) q^{20} +(1.66790 - 4.88851i) q^{21} +(2.16105 + 1.03971i) q^{22} +3.48501 q^{23} +(-0.505063 + 4.87288i) q^{24} +4.87681 q^{25} +(5.64319 + 2.71501i) q^{26} +(-2.86666 - 4.33385i) q^{27} +(-4.66027 + 3.72216i) q^{28} -3.03917i q^{29} +(0.602928 - 0.612862i) q^{30} -10.5902i q^{31} +(3.51870 - 4.42931i) q^{32} +(2.77978 + 0.948428i) q^{33} +(1.22826 - 2.55295i) q^{34} +1.04667 q^{35} +(0.0980481 + 5.99920i) q^{36} -6.83128 q^{37} +(-0.890047 + 1.84997i) q^{38} +(7.25890 + 2.47665i) q^{39} +(-0.967583 + 0.221989i) q^{40} -0.934816i q^{41} +(-5.12284 + 5.20725i) q^{42} -2.28333i q^{43} +(-2.11655 - 2.65000i) q^{44} +(0.643582 - 0.833358i) q^{45} +(-4.44127 - 2.13675i) q^{46} -11.7382 q^{47} +(3.63134 - 5.90029i) q^{48} -1.89315 q^{49} +(-6.21497 - 2.99010i) q^{50} +(1.12042 - 3.28388i) q^{51} +(-5.52700 - 6.91999i) q^{52} +1.53931i q^{53} +(0.996046 + 7.28065i) q^{54} +0.595174i q^{55} +(8.22117 - 1.88616i) q^{56} +(-0.811905 + 2.37964i) q^{57} +(-1.86339 + 3.87309i) q^{58} -14.8437 q^{59} +(-1.14413 + 0.411356i) q^{60} -3.43726 q^{61} +(-6.49314 + 13.4961i) q^{62} +(-5.46826 + 7.08071i) q^{63} +(-7.19993 + 3.48727i) q^{64} +1.55419i q^{65} +(-2.96103 - 2.91303i) q^{66} +1.00000i q^{67} +(-3.13056 + 2.50038i) q^{68} +(-5.71286 - 1.94916i) q^{69} +(-1.33387 - 0.641742i) q^{70} +14.0214 q^{71} +(3.55332 - 7.70545i) q^{72} -5.28996 q^{73} +(8.70573 + 4.18844i) q^{74} +(-7.99438 - 2.72759i) q^{75} +(2.26854 - 1.81188i) q^{76} -5.05696i q^{77} +(-7.73219 - 7.60685i) q^{78} -16.7488i q^{79} +(1.36919 + 0.310349i) q^{80} +(2.27530 + 8.70764i) q^{81} +(-0.573160 + 1.19132i) q^{82} -6.63054 q^{83} +(9.72121 - 3.49513i) q^{84} +0.703107 q^{85} +(-1.39997 + 2.90986i) q^{86} +(-1.69980 + 4.98200i) q^{87} +(1.07254 + 4.67485i) q^{88} +5.60971i q^{89} +(-1.33113 + 0.667427i) q^{90} -13.2053i q^{91} +(4.34982 + 5.44613i) q^{92} +(-5.92307 + 17.3601i) q^{93} +(14.9591 + 7.19702i) q^{94} -0.509501 q^{95} +(-8.24537 + 5.29281i) q^{96} -9.69599 q^{97} +(2.41261 + 1.16074i) q^{98} +(-4.02634 - 3.10945i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 4 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) $ 128 * q + 4 * q^4 - 6 * q^6 - 4 * q^9	$ 128 q + 4 q^{4} - 6 q^{6} - 4 q^{9} - 4 q^{10} + 4 q^{12} - 8 q^{13} - 4 q^{16} + 18 q^{18} - 8 q^{21} - 8 q^{22} - 24 q^{24} - 136 q^{25} + 14 q^{30} - 32 q^{33} + 34 q^{36} - 48 q^{37} + 16 q^{40} - 28 q^{42} - 16 q^{45} - 28 q^{46} - 22 q^{48} - 152 q^{49} + 8 q^{52} - 16 q^{54} - 32 q^{57} - 20 q^{58} - 14 q^{60} + 8 q^{61} + 16 q^{64} + 14 q^{66} + 56 q^{69} - 4 q^{70} - 8 q^{72} - 48 q^{73} - 36 q^{76} + 40 q^{78} + 44 q^{81} + 60 q^{82} + 46 q^{84} + 64 q^{85} - 28 q^{88} - 14 q^{90} + 32 q^{93} - 8 q^{96} + 64 q^{97}+O(q^{100}) $ 128 * q + 4 * q^4 - 6 * q^6 - 4 * q^9 - 4 * q^10 + 4 * q^12 - 8 * q^13 - 4 * q^16 + 18 * q^18 - 8 * q^21 - 8 * q^22 - 24 * q^24 - 136 * q^25 + 14 * q^30 - 32 * q^33 + 34 * q^36 - 48 * q^37 + 16 * q^40 - 28 * q^42 - 16 * q^45 - 28 * q^46 - 22 * q^48 - 152 * q^49 + 8 * q^52 - 16 * q^54 - 32 * q^57 - 20 * q^58 - 14 * q^60 + 8 * q^61 + 16 * q^64 + 14 * q^66 + 56 * q^69 - 4 * q^70 - 8 * q^72 - 48 * q^73 - 36 * q^76 + 40 * q^78 + 44 * q^81 + 60 * q^82 + 46 * q^84 + 64 * q^85 - 28 * q^88 - 14 * q^90 + 32 * q^93 - 8 * q^96 + 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−1.27439	−	0.613127i	−0.901131	−	0.433546i
$2$	−1.27439	−	0.613127i	−0.901131	−	0.433546i
$3$	−1.63926	−	0.559297i	−0.946430	−	0.322910i
$3$	−1.63926	−	0.559297i	−0.946430	−	0.322910i
$4$	1.24815	+	1.56273i	0.624076	+	0.781364i
$5$		−	0.350980i		−	0.156963i	−0.996916	−	0.0784815i	$-0.974993\pi$
$5$		−	0.350980i		−	0.156963i	0.996916	−	0.0784815i	$-0.0250072\pi$
$6$	1.74615	+	1.71784i	0.712861	+	0.701305i
$7$			2.98214i			1.12714i	0.826068	+	0.563571i	$0.190573\pi$
$7$			2.98214i			1.12714i	−0.826068	+	0.563571i	$0.809427\pi$
$8$	−0.632485	−	2.75680i	−0.223617	−	0.974677i
$9$	2.37437	+	1.83367i	0.791458	+	0.611224i
$10$	−0.215195	+	0.447286i	−0.0680507	+	0.141444i
$11$	−1.69575			−0.511288			−0.255644	−	0.966771i	$-0.582287\pi$
$11$	−1.69575			−0.511288			−0.255644	+	0.966771i	$0.582287\pi$
$12$	−1.17202	−	3.25981i	−0.338333	−	0.941026i
$13$	−4.42815			−1.22815			−0.614073	−	0.789249i	$-0.710470\pi$
$13$	−4.42815			−1.22815			−0.614073	+	0.789249i	$0.710470\pi$
$14$	1.82843	−	3.80041i	0.488668	−	1.01570i
$15$	−0.196302	+	0.575349i	−0.0506850	+	0.148554i
$16$	−0.884236	+	3.90104i	−0.221059	+	0.975260i
$17$			2.00327i			0.485863i	0.970043	+	0.242932i	$0.0781091\pi$
$17$			2.00327i			0.485863i	−0.970043	+	0.242932i	$0.921891\pi$
$18$	−1.90161	−	3.79261i	−0.448214	−	0.893926i
$19$		−	1.45165i		−	0.333032i	−0.986039	−	0.166516i	$-0.946748\pi$
$19$		−	1.45165i		−	0.333032i	0.986039	−	0.166516i	$-0.0532517\pi$
$20$	0.548486	−	0.438076i	0.122645	−	0.0979568i
$21$	1.66790	−	4.88851i	0.363966	−	1.06676i
$22$	2.16105	+	1.03971i	0.460737	+	0.221667i
$23$	3.48501			0.726675			0.363338	−	0.931658i	$-0.381637\pi$
$23$	3.48501			0.726675			0.363338	+	0.931658i	$0.381637\pi$
$24$	−0.505063	+	4.87288i	−0.103096	+	0.994671i
$25$	4.87681			0.975363
$26$	5.64319	+	2.71501i	1.10672	+	0.532458i
$27$	−2.86666	−	4.33385i	−0.551689	−	0.834050i
$28$	−4.66027	+	3.72216i	−0.880708	+	0.703422i
$29$		−	3.03917i		−	0.564359i	−0.959362	−	0.282180i	$-0.908943\pi$
$29$		−	3.03917i		−	0.564359i	0.959362	−	0.282180i	$-0.0910574\pi$
$30$	0.602928	−	0.612862i	0.110079	−	0.111893i
$31$		−	10.5902i		−	1.90206i	−0.309104	−	0.951028i	$-0.600029\pi$
$31$		−	10.5902i		−	1.90206i	0.309104	−	0.951028i	$-0.399971\pi$
$32$	3.51870	−	4.42931i	0.622023	−	0.782999i
$33$	2.77978	+	0.948428i	0.483898	+	0.165100i
$34$	1.22826	−	2.55295i	0.210644	−	0.437827i
$35$	1.04667			0.176920
$36$	0.0980481	+	5.99920i	0.0163414	+	0.999866i
$37$	−6.83128			−1.12305			−0.561527	−	0.827458i	$-0.689786\pi$
$37$	−6.83128			−1.12305			−0.561527	+	0.827458i	$0.689786\pi$
$38$	−0.890047	+	1.84997i	−0.144385	+	0.300105i
$39$	7.25890	+	2.47665i	1.16235	+	0.396581i
$40$	−0.967583	+	0.221989i	−0.152988	+	0.0350996i
$41$		−	0.934816i		−	0.145994i	−0.997332	−	0.0729968i	$-0.976744\pi$
$41$		−	0.934816i		−	0.145994i	0.997332	−	0.0729968i	$-0.0232563\pi$
$42$	−5.12284	+	5.20725i	−0.790471	+	0.803496i
$43$		−	2.28333i		−	0.348205i	−0.984728	−	0.174103i	$-0.944298\pi$
$43$		−	2.28333i		−	0.348205i	0.984728	−	0.174103i	$-0.0557024\pi$
$44$	−2.11655	−	2.65000i	−0.319082	−	0.399502i
$45$	0.643582	−	0.833358i	0.0959396	−	0.124230i
$46$	−4.44127	−	2.13675i	−0.654830	−	0.315047i
$47$	−11.7382			−1.71220			−0.856099	−	0.516813i	$-0.827118\pi$
$47$	−11.7382			−1.71220			−0.856099	+	0.516813i	$0.827118\pi$
$48$	3.63134	−	5.90029i	0.524138	−	0.851633i
$49$	−1.89315			−0.270450
$50$	−6.21497	−	2.99010i	−0.878930	−	0.422865i
$51$	1.12042	−	3.28388i	0.156890	−	0.459836i
$52$	−5.52700	−	6.91999i	−0.766456	−	0.959629i
$53$			1.53931i			0.211441i	0.994396	+	0.105720i	$0.0337149\pi$
$53$			1.53931i			0.211441i	−0.994396	+	0.105720i	$0.966285\pi$
$54$	0.996046	+	7.28065i	0.135545	+	0.990771i
$55$			0.595174i			0.0802533i
$56$	8.22117	−	1.88616i	1.09860	−	0.252048i
$57$	−0.811905	+	2.37964i	−0.107539	+	0.315191i
$58$	−1.86339	+	3.87309i	−0.244676	+	0.508562i
$59$	−14.8437			−1.93248			−0.966241	−	0.257641i	$-0.917055\pi$
$59$	−14.8437			−1.93248			−0.966241	+	0.257641i	$0.917055\pi$
$60$	−1.14413	+	0.411356i	−0.147706	+	0.0531058i
$61$	−3.43726			−0.440096			−0.220048	−	0.975489i	$-0.570621\pi$
$61$	−3.43726			−0.440096			−0.220048	+	0.975489i	$0.570621\pi$
$62$	−6.49314	+	13.4961i	−0.824629	+	1.71400i
$63$	−5.46826	+	7.08071i	−0.688936	+	0.892086i
$64$	−7.19993	+	3.48727i	−0.899991	+	0.435909i
$65$			1.55419i			0.192774i
$66$	−2.96103	−	2.91303i	−0.364477	−	0.358569i
$67$			1.00000i			0.122169i
$67$			1.00000i			0.122169i
$68$	−3.13056	+	2.50038i	−0.379636	+	0.303216i
$69$	−5.71286	−	1.94916i	−0.687747	−	0.234651i
$70$	−1.33387	−	0.641742i	−0.159428	−	0.0767028i
$71$	14.0214			1.66403			0.832017	−	0.554750i	$-0.187186\pi$
$71$	14.0214			1.66403			0.832017	+	0.554750i	$0.187186\pi$
$72$	3.55332	−	7.70545i	0.418762	−	0.908096i
$73$	−5.28996			−0.619143			−0.309572	−	0.950876i	$-0.600186\pi$
$73$	−5.28996			−0.619143			−0.309572	+	0.950876i	$0.600186\pi$
$74$	8.70573	+	4.18844i	1.01202	+	0.486896i
$75$	−7.99438	−	2.72759i	−0.923112	−	0.314955i
$76$	2.26854	−	1.81188i	0.260219	−	0.207837i
$77$		−	5.05696i		−	0.576294i
$78$	−7.73219	−	7.60685i	−0.875498	−	0.861306i
$79$		−	16.7488i		−	1.88439i	−0.335062	−	0.942196i	$-0.608757\pi$
$79$		−	16.7488i		−	1.88439i	0.335062	−	0.942196i	$-0.391243\pi$
$80$	1.36919	+	0.310349i	0.153080	+	0.0346981i
$81$	2.27530	+	8.70764i	0.252811	+	0.967516i
$82$	−0.573160	+	1.19132i	−0.0632950	+	0.131559i
$83$	−6.63054			−0.727797			−0.363898	−	0.931439i	$-0.618554\pi$
$83$	−6.63054			−0.727797			−0.363898	+	0.931439i	$0.618554\pi$
$84$	9.72121	−	3.49513i	1.06067	−	0.381350i
$85$	0.703107			0.0762626
$86$	−1.39997	+	2.90986i	−0.150963	+	0.313779i
$87$	−1.69980	+	4.98200i	−0.182237	+	0.534126i
$88$	1.07254	+	4.67485i	0.114333	+	0.498340i
$89$			5.60971i			0.594628i	0.954780	+	0.297314i	$0.0960908\pi$
$89$			5.60971i			0.594628i	−0.954780	+	0.297314i	$0.903909\pi$
$90$	−1.33113	+	0.667427i	−0.140313	+	0.0703530i
$91$		−	13.2053i		−	1.38430i
$92$	4.34982	+	5.44613i	0.453500	+	0.567798i
$93$	−5.92307	+	17.3601i	−0.614194	+	1.80016i
$94$	14.9591	+	7.19702i	1.54291	+	0.742316i
$95$	−0.509501			−0.0522737
$96$	−8.24537	+	5.29281i	−0.841540	+	0.540195i
$97$	−9.69599			−0.984479			−0.492239	−	0.870460i	$-0.663822\pi$
$97$	−9.69599			−0.984479			−0.492239	+	0.870460i	$0.663822\pi$
$98$	2.41261	+	1.16074i	0.243711	+	0.117252i
$99$	−4.02634	−	3.10945i	−0.404663	−	0.312511i
$100$	6.08700	+	7.62113i	0.608700	+	0.762113i
$101$		−	12.5232i		−	1.24610i	−0.782180	−	0.623052i	$-0.785892\pi$
$101$		−	12.5232i		−	1.24610i	0.782180	−	0.623052i	$-0.214108\pi$
$102$	−3.44129	+	3.49799i	−0.340739	+	0.346353i
$103$		−	3.32384i		−	0.327508i	−0.986501	−	0.163754i	$-0.947640\pi$
$103$		−	3.32384i		−	0.327508i	0.986501	−	0.163754i	$-0.0523603\pi$
$104$	2.80073	+	12.2075i	0.274635	+	1.19705i
$105$	−1.71577	−	0.585400i	−0.167442	−	0.0571292i
$106$	0.943794	−	1.96169i	0.0916694	−	0.190536i
$107$	−0.522441			−0.0505063			−0.0252531	−	0.999681i	$-0.508039\pi$
$107$	−0.522441			−0.0505063			−0.0252531	+	0.999681i	$0.508039\pi$
$108$	3.19461	−	9.88911i	0.307401	−	0.951580i
$109$	−10.6357			−1.01872			−0.509358	−	0.860554i	$-0.670117\pi$
$109$	−10.6357			−1.01872			−0.509358	+	0.860554i	$0.670117\pi$
$110$	0.364917	−	0.758486i	0.0347935	−	0.0723188i
$111$	11.1983	+	3.82071i	1.06289	+	0.362646i
$112$	−11.6334	−	2.63691i	−1.09926	−	0.249165i
$113$		−	15.8801i		−	1.49387i	−0.664895	−	0.746937i	$-0.731524\pi$
$113$		−	15.8801i		−	1.49387i	0.664895	−	0.746937i	$-0.268476\pi$
$114$	2.49371	−	2.53480i	0.233557	−	0.237405i
$115$		−	1.22317i		−	0.114061i
$116$	4.74939	−	3.79334i	0.440970	−	0.352203i
$117$	−10.5141	−	8.11976i	−0.972026	−	0.750672i
$118$	18.9167	+	9.10105i	1.74142	+	0.837820i
$119$	−5.97402			−0.547637
$120$	1.71028	+	0.177267i	0.156127	+	0.0161822i
$121$	−8.12443			−0.738585
$122$	4.38041	+	2.10747i	0.396584	+	0.190802i
$123$	−0.522840	+	1.53241i	−0.0471429	+	0.138173i
$124$	16.5496	−	13.2182i	1.48620	−	1.18703i
$125$		−	3.46656i		−	0.310059i
$126$	11.3101	−	5.67086i	1.00758	−	0.505201i
$127$			5.42211i			0.481135i	0.970632	+	0.240567i	$0.0773335\pi$
$127$			5.42211i			0.481135i	−0.970632	+	0.240567i	$0.922666\pi$
$128$	11.3137	−	0.0296842i	0.999997	−	0.00262374i
$129$	−1.27706	+	3.74299i	−0.112439	+	0.329552i
$130$	0.952916	−	1.98065i	0.0835762	−	0.173714i
$131$	9.82550			0.858458			0.429229	−	0.903196i	$-0.358785\pi$
$131$	9.82550			0.858458			0.429229	+	0.903196i	$0.358785\pi$
$132$	1.98745	+	5.52782i	0.172986	+	0.481135i
$133$	4.32903			0.375374
$134$	0.613127	−	1.27439i	0.0529661	−	0.110091i
$135$	−1.52110	+	1.00614i	−0.130915	+	0.0865947i
$136$	5.52261	−	1.26704i	0.473560	−	0.108647i
$137$		−	0.602999i		−	0.0515177i	−0.999668	−	0.0257589i	$-0.991800\pi$
$137$		−	0.602999i		−	0.0515177i	0.999668	−	0.0257589i	$-0.00820021\pi$
$138$	6.08534	+	5.98670i	0.518018	+	0.509621i
$139$			16.3980i			1.39086i	0.718595	+	0.695429i	$0.244786\pi$
$139$			16.3980i			1.39086i	−0.718595	+	0.695429i	$0.755214\pi$
$140$	1.30640	+	1.63566i	0.110411	+	0.138239i
$141$	19.2421	+	6.56516i	1.62047	+	0.552886i
$142$	−17.8688	−	8.59690i	−1.49951	−	0.721436i
$143$	7.50903			0.627936
$144$	−9.25274	+	7.64113i	−0.771061	+	0.636761i
$145$	−1.06669			−0.0885836
$146$	6.74148	+	3.24342i	0.557929	+	0.268427i
$147$	3.10337	+	1.05883i	0.255962	+	0.0873311i
$148$	−8.52647	−	10.6754i	−0.700871	−	0.877515i
$149$			1.22296i			0.100189i	0.998744	+	0.0500945i	$0.0159523\pi$
$149$			1.22296i			0.100189i	−0.998744	+	0.0500945i	$0.984048\pi$
$150$	8.51562	+	8.37759i	0.695298	+	0.684027i
$151$		−	13.9947i		−	1.13887i	−0.822037	−	0.569435i	$-0.807162\pi$
$151$		−	13.9947i		−	1.13887i	0.822037	−	0.569435i	$-0.192838\pi$
$152$	−4.00192	+	0.918147i	−0.324598	+	0.0744716i
$153$	−3.67333	+	4.75650i	−0.296971	+	0.384540i
$154$	−3.10056	+	6.44455i	−0.249850	+	0.519317i
$155$	−3.71695			−0.298553
$156$	5.18988	+	14.4349i	0.415523	+	1.15572i
$157$	3.91727			0.312632			0.156316	−	0.987707i	$-0.450038\pi$
$157$	3.91727			0.312632			0.156316	+	0.987707i	$0.450038\pi$
$158$	−10.2692	+	21.3446i	−0.816971	+	1.69809i
$159$	0.860934	−	2.52334i	0.0682765	−	0.200114i
$160$	−1.55460	−	1.23499i	−0.122902	−	0.0976347i
$161$			10.3928i			0.819067i
$162$	2.43927	−	12.4920i	0.191647	−	0.981464i
$163$			1.06905i			0.0837345i	0.999123	+	0.0418673i	$0.0133307\pi$
$163$			1.06905i			0.0837345i	−0.999123	+	0.0418673i	$0.986669\pi$
$164$	1.46086	−	1.16679i	0.114074	−	0.0911111i
$165$	0.332879	−	0.975648i	0.0259146	−	0.0759541i
$166$	8.44991	+	4.06536i	0.655841	+	0.315533i
$167$	5.77658			0.447005			0.223503	−	0.974703i	$-0.428251\pi$
$167$	5.77658			0.447005			0.223503	+	0.974703i	$0.428251\pi$
$168$	−14.5316	−	1.50617i	−1.12114	−	0.116203i
$169$	6.60847			0.508344
$170$	−0.896034	−	0.431093i	−0.0687226	−	0.0330634i
$171$	2.66185	−	3.44676i	0.203557	−	0.263581i
$172$	3.56823	−	2.84995i	0.272075	−	0.217306i
$173$		−	11.3842i		−	0.865521i	−0.901509	−	0.432761i	$-0.857540\pi$
$173$		−	11.3842i		−	0.865521i	0.901509	−	0.432761i	$-0.142460\pi$
$174$	5.22080	−	5.30683i	0.395788	−	0.402310i
$175$			14.5433i			1.09937i
$176$	1.49944	−	6.61519i	0.113025	−	0.498639i
$177$	24.3327	+	8.30202i	1.82896	+	0.624018i
$178$	3.43946	−	7.14897i	0.257799	−	0.535838i
$179$	6.51691			0.487097			0.243548	−	0.969889i	$-0.421689\pi$
$179$	6.51691			0.487097			0.243548	+	0.969889i	$0.421689\pi$
$180$	2.10560	−	0.0344129i	0.156942	−	0.00256499i
$181$	16.6921			1.24071			0.620357	−	0.784320i	$-0.286988\pi$
$181$	16.6921			1.24071			0.620357	+	0.784320i	$0.286988\pi$
$182$	−8.09655	+	16.8288i	−0.600156	+	1.24743i
$183$	5.63457	+	1.92245i	0.416520	+	0.142111i
$184$	−2.20422	−	9.60749i	−0.162497	−	0.708274i
$185$			2.39764i			0.176278i
$186$	18.1923	−	18.4920i	1.33392	−	1.35590i
$187$		−	3.39704i		−	0.248416i
$188$	−14.6511	−	18.3437i	−1.06854	−	1.33785i
$189$	12.9241	−	8.54877i	0.940093	−	0.621831i
$190$	0.649304	+	0.312389i	0.0471055	+	0.0226631i
$191$	11.6575			0.843505			0.421752	−	0.906711i	$-0.361415\pi$
$191$	11.6575			0.843505			0.421752	+	0.906711i	$0.361415\pi$
$192$	13.7530	−	1.68966i	0.992537	−	0.121941i
$193$	−18.5012			−1.33174			−0.665872	−	0.746066i	$-0.731940\pi$
$193$	−18.5012			−1.33174			−0.665872	+	0.746066i	$0.731940\pi$
$194$	12.3565	+	5.94487i	0.887145	+	0.426817i
$195$	0.869254	−	2.54773i	0.0622486	−	0.182447i
$196$	−2.36294	−	2.95848i	−0.168781	−	0.211320i
$197$			7.06882i			0.503632i	0.967775	+	0.251816i	$0.0810278\pi$
$197$			7.06882i			0.503632i	−0.967775	+	0.251816i	$0.918972\pi$
$198$	3.22465	+	6.43131i	0.229166	+	0.457054i
$199$		−	13.5499i		−	0.960530i	−0.877124	−	0.480265i	$-0.840541\pi$
$199$		−	13.5499i		−	0.960530i	0.877124	−	0.480265i	$-0.159459\pi$
$200$	−3.08451	−	13.4444i	−0.218108	−	0.950664i
$201$	0.559297	−	1.63926i	0.0394498	−	0.115625i
$202$	−7.67830	+	15.9595i	−0.540243	+	1.12290i
$203$	9.06322			0.636113
$204$	6.53027	−	2.34787i	0.457210	−	0.164384i
$205$	−0.328102			−0.0229156
$206$	−2.03793	+	4.23588i	−0.141990	+	0.295127i
$207$	8.27472	+	6.39037i	0.575133	+	0.444161i
$208$	3.91553	−	17.2744i	0.271493	−	1.19776i
$209$			2.46164i			0.170275i
$210$	1.82764	+	1.79801i	0.126119	+	0.124075i
$211$		−	6.42279i		−	0.442163i	−0.975255	−	0.221082i	$-0.929041\pi$
$211$		−	6.42279i		−	0.442163i	0.975255	−	0.221082i	$-0.0709587\pi$
$212$	−2.40553	+	1.92130i	−0.165212	+	0.131955i
$213$	−22.9848	−	7.84213i	−1.57489	−	0.537334i
$214$	0.665794	+	0.320322i	0.0455128	+	0.0218968i
$215$	−0.801405			−0.0546553
$216$	−10.1345	+	10.6439i	−0.689563	+	0.724226i
$217$	31.5814			2.14389
$218$	13.5541	+	6.52104i	0.917998	+	0.441661i
$219$	8.67164	+	2.95866i	0.585975	+	0.199928i
$220$	−0.930095	+	0.742868i	−0.0627070	+	0.0500841i
$221$		−	8.87075i		−	0.596712i
$222$	−11.9284	−	11.7350i	−0.800582	−	0.787605i
$223$			28.1790i			1.88701i	0.331362	+	0.943504i	$0.392492\pi$
$223$			28.1790i			1.88701i	−0.331362	+	0.943504i	$0.607508\pi$
$224$	13.2088	+	10.4932i	0.882551	+	0.701109i
$225$	11.5794	+	8.94247i	0.771958	+	0.596165i
$226$	−9.73651	+	20.2375i	−0.647663	+	1.34618i
$227$	4.26297			0.282943			0.141472	−	0.989942i	$-0.454817\pi$
$227$	4.26297			0.282943			0.141472	+	0.989942i	$0.454817\pi$
$228$	−4.73211	+	1.70137i	−0.313392	+	0.112676i
$229$	18.4957			1.22223			0.611114	−	0.791543i	$-0.290722\pi$
$229$	18.4957			1.22223			0.611114	+	0.791543i	$0.290722\pi$
$230$	−0.749958	+	1.55880i	−0.0494508	+	0.102784i
$231$	−2.82834	+	8.28969i	−0.186091	+	0.545422i
$232$	−8.37839	+	1.92223i	−0.550068	+	0.126200i
$233$		−	23.5352i		−	1.54184i	−0.636932	−	0.770920i	$-0.719797\pi$
$233$		−	23.5352i		−	1.54184i	0.636932	−	0.770920i	$-0.280203\pi$
$234$	8.42061	+	16.7942i	0.550472	+	1.09787i
$235$			4.11989i			0.268752i
$236$	−18.5272	−	23.1966i	−1.20601	−	1.50997i
$237$	−9.36758	+	27.4558i	−0.608490	+	1.78344i
$238$	7.61324	+	3.66283i	0.493493	+	0.237426i
$239$	−9.29173			−0.601032			−0.300516	−	0.953777i	$-0.597159\pi$
$239$	−9.29173			−0.601032			−0.300516	+	0.953777i	$0.597159\pi$
$240$	−2.07088	−	1.27453i	−0.133675	−	0.0822704i
$241$	−17.3434			−1.11719			−0.558593	−	0.829442i	$-0.688659\pi$
$241$	−17.3434			−1.11719			−0.558593	+	0.829442i	$0.688659\pi$
$242$	10.3537	+	4.98131i	0.665562	+	0.320211i
$243$	1.14035	−	15.5467i	0.0731532	−	0.997321i
$244$	−4.29022	−	5.37150i	−0.274653	−	0.343875i
$245$			0.664458i			0.0424506i
$246$	1.60586	−	1.63232i	0.102386	−	0.104073i
$247$			6.42813i			0.409012i
$248$	−29.1951	+	6.69814i	−1.85389	+	0.425332i
$249$	10.8692	+	3.70844i	0.688808	+	0.235013i
$250$	−2.12544	+	4.41776i	−0.134425	+	0.279404i
$251$	−12.0936			−0.763344			−0.381672	−	0.924298i	$-0.624652\pi$
$251$	−12.0936			−0.763344			−0.381672	+	0.924298i	$0.624652\pi$
$252$	−17.8904	+	0.292393i	−1.12699	+	0.0184190i
$253$	−5.90971			−0.371540
$254$	3.32444	−	6.90990i	0.208594	−	0.433566i
$255$	−1.15258	−	0.393246i	−0.0721772	−	0.0246260i
$256$	−14.4363	−	6.89888i	−0.902266	−	0.431180i
$257$			3.87147i			0.241496i	0.992683	+	0.120748i	$0.0385293\pi$
$257$			3.87147i			0.241496i	−0.992683	+	0.120748i	$0.961471\pi$
$258$	3.92240	−	3.98703i	0.244198	−	0.248222i
$259$		−	20.3718i		−	1.26584i
$260$	−2.42878	+	1.93987i	−0.150626	+	0.120305i
$261$	5.57283	−	7.21612i	0.344950	−	0.446667i
$262$	−12.5215	−	6.02428i	−0.773584	−	0.372181i
$263$	−20.9768			−1.29349			−0.646743	−	0.762708i	$-0.723869\pi$
$263$	−20.9768			−1.29349			−0.646743	+	0.762708i	$0.723869\pi$
$264$	0.856460	−	8.26318i	0.0527115	−	0.508563i
$265$	0.540268			0.0331884
$266$	−5.51688	−	2.65424i	−0.338262	−	0.162742i
$267$	3.13749	−	9.19579i	0.192012	−	0.562773i
$268$	−1.56273	+	1.24815i	−0.0954588	+	0.0762430i
$269$			25.9623i			1.58295i	0.611203	+	0.791474i	$0.290686\pi$
$269$			25.9623i			1.58295i	−0.611203	+	0.791474i	$0.709314\pi$
$270$	2.55536	−	0.349592i	0.155514	−	0.0212755i
$271$			3.87398i			0.235328i	0.993053	+	0.117664i	$0.0375405\pi$
$271$			3.87398i			0.235328i	−0.993053	+	0.117664i	$0.962459\pi$
$272$	−7.81483	−	1.77136i	−0.473843	−	0.107404i
$273$	−7.38571	+	21.6470i	−0.447004	+	1.31014i
$274$	−0.369715	+	0.768458i	−0.0223353	+	0.0464242i
$275$	−8.26985			−0.498691
$276$	−4.08451	−	11.3605i	−0.245858	−	0.683821i
$277$	10.4518			0.627988			0.313994	−	0.949425i	$-0.398333\pi$
$277$	10.4518			0.627988			0.313994	+	0.949425i	$0.398333\pi$
$278$	10.0540	−	20.8974i	0.603001	−	1.25335i
$279$	19.4190	−	25.1451i	1.16258	−	1.50540i
$280$	−0.662003	−	2.88547i	−0.0395623	−	0.172440i
$281$			10.0426i			0.599093i	0.954082	+	0.299547i	$0.0968354\pi$
$281$			10.0426i			0.599093i	−0.954082	+	0.299547i	$0.903165\pi$
$282$	−20.4967	−	20.1644i	−1.22056	−	1.20077i
$283$		−	13.7073i		−	0.814814i	−0.913247	−	0.407407i	$-0.866433\pi$
$283$		−	13.7073i		−	0.814814i	0.913247	−	0.407407i	$-0.133567\pi$
$284$	17.5008	+	21.9116i	1.03848	+	1.30022i
$285$	0.835207	+	0.284962i	0.0494734	+	0.0168797i
$286$	−9.56944	−	4.60398i	−0.565853	−	0.272239i
$287$	2.78775			0.164556
$288$	16.4766	−	4.06470i	0.970893	−	0.239515i
$289$	12.9869			0.763937
$290$	1.35938	+	0.654014i	0.0798254	+	0.0384050i
$291$	15.8943	+	5.42294i	0.931740	+	0.317898i
$292$	−6.60267	−	8.26677i	−0.386392	−	0.483776i
$293$		−	27.3566i		−	1.59819i	−0.601207	−	0.799094i	$-0.705313\pi$
$293$		−	27.3566i		−	1.59819i	0.601207	−	0.799094i	$-0.294687\pi$
$294$	−3.30571	−	3.25213i	−0.192793	−	0.189668i
$295$			5.20983i			0.303328i
$296$	4.32068	+	18.8325i	0.251134	+	1.09462i
$297$	4.86113	+	7.34913i	0.282072	+	0.426440i
$298$	0.749832	−	1.55854i	0.0434366	−	0.0902835i
$299$	−15.4321			−0.892464
$300$	−5.71573	−	15.8975i	−0.329998	−	0.917842i
$301$	6.80922			0.392477
$302$	−8.58050	+	17.8347i	−0.493752	+	1.02627i
$303$	−7.00419	+	20.5288i	−0.402380	+	1.17935i
$304$	5.66296	+	1.28360i	0.324793	+	0.0736197i
$305$			1.20641i			0.0690788i
$306$	7.59761	−	3.80943i	0.434326	−	0.217771i
$307$			19.8275i			1.13161i	0.824538	+	0.565806i	$0.191435\pi$
$307$			19.8275i			1.13161i	−0.824538	+	0.565806i	$0.808565\pi$
$308$	7.90265	−	6.31185i	0.450295	−	0.359651i
$309$	−1.85901	+	5.44865i	−0.105756	+	0.309963i
$310$	4.73685	+	2.27896i	0.269035	+	0.129436i
$311$	−27.4539			−1.55677			−0.778383	−	0.627789i	$-0.783960\pi$
$311$	−27.4539			−1.55677			−0.778383	+	0.627789i	$0.783960\pi$
$312$	2.23649	−	21.5778i	0.126616	−	1.22160i
$313$	−8.09384			−0.457491			−0.228745	−	0.973486i	$-0.573462\pi$
$313$	−8.09384			−0.457491			−0.228745	+	0.973486i	$0.573462\pi$
$314$	−4.99214	−	2.40178i	−0.281723	−	0.135540i
$315$	2.48519	+	1.91925i	0.140024	+	0.108138i
$316$	26.1739	−	20.9051i	1.47240	−	1.17600i
$317$			0.987602i			0.0554692i	0.999615	+	0.0277346i	$0.00882934\pi$
$317$			0.987602i			0.0554692i	−0.999615	+	0.0277346i	$0.991171\pi$
$318$	−2.64429	+	2.68786i	−0.148285	+	0.150728i
$319$			5.15367i			0.288550i
$320$	1.22396	+	2.52703i	0.0684216	+	0.141265i
$321$	0.856418	+	0.292200i	0.0478006	+	0.0163090i
$322$	6.37210	−	13.2445i	0.355103	−	0.738087i
$323$	2.90805			0.161808
$324$	−10.7678	+	14.4241i	−0.598209	+	0.801340i
$325$	−21.5952			−1.19789
$326$	0.655463	−	1.36239i	0.0363028	−	0.0754558i
$327$	17.4347	+	5.94853i	0.964144	+	0.328954i
$328$	−2.57710	+	0.591256i	−0.142297	+	0.0326467i
$329$		−	35.0050i		−	1.92989i
$330$	−1.02241	+	1.03926i	−0.0562821	+	0.0572094i
$331$			12.4813i			0.686036i	0.939329	+	0.343018i	$0.111449\pi$
$331$			12.4813i			0.686036i	−0.939329	+	0.343018i	$0.888551\pi$
$332$	−8.27592	−	10.3617i	−0.454200	−	0.568674i
$333$	−16.2200	−	12.5263i	−0.888851	−	0.686438i
$334$	−7.36163	−	3.54177i	−0.402810	−	0.193797i
$335$	0.350980			0.0191761
$336$	17.5955	+	10.8292i	0.959912	+	0.590779i
$337$	−8.52881			−0.464594			−0.232297	−	0.972645i	$-0.574624\pi$
$337$	−8.52881			−0.464594			−0.232297	+	0.972645i	$0.574624\pi$
$338$	−8.42178	−	4.05183i	−0.458085	−	0.220390i
$339$	−8.88170	+	26.0317i	−0.482388	+	1.41385i
$340$	0.877583	+	1.09876i	0.0475936	+	0.0595889i
$341$			17.9583i			0.972498i
$342$	−5.50555	+	2.76048i	−0.297706	+	0.149269i
$343$			15.2293i			0.822307i
$344$	−6.29470	+	1.44417i	−0.339388	+	0.0778646i
$345$	−0.684116	+	2.00510i	−0.0368315	+	0.107951i
$346$	−6.97993	+	14.5079i	−0.375243	+	0.779948i
$347$	−16.6008			−0.891179			−0.445589	−	0.895237i	$-0.647006\pi$
$347$	−16.6008			−0.891179			−0.445589	+	0.895237i	$0.647006\pi$
$348$	−9.90711	+	3.56197i	−0.531077	+	0.190941i
$349$	2.10653			0.112760			0.0563799	−	0.998409i	$-0.482044\pi$
$349$	2.10653			0.112760			0.0563799	+	0.998409i	$0.482044\pi$
$350$	8.91690	−	18.5339i	0.476629	−	0.990679i
$351$	12.6940	+	19.1909i	0.677554	+	1.02434i
$352$	−5.96683	+	7.51100i	−0.318033	+	0.400338i
$353$			11.1806i			0.595081i	0.954709	+	0.297541i	$0.0961663\pi$
$353$			11.1806i			0.595081i	−0.954709	+	0.297541i	$0.903834\pi$
$354$	−25.9192	−	25.4991i	−1.37759	−	1.35526i
$355$		−	4.92123i		−	0.261192i
$356$	−8.76645	+	7.00177i	−0.464621	+	0.371093i
$357$	9.79299	+	3.34125i	0.518300	+	0.176838i
$358$	−8.30510	−	3.99569i	−0.438938	−	0.211179i
$359$	13.3649			0.705375			0.352688	−	0.935741i	$-0.385268\pi$
$359$	13.3649			0.705375			0.352688	+	0.935741i	$0.385268\pi$
$360$	−2.70446	−	1.24714i	−0.142538	−	0.0657302i
$361$	16.8927			0.889090
$362$	−21.2723	−	10.2344i	−1.11805	−	0.537907i
$363$	13.3181	+	4.54397i	0.699019	+	0.238497i
$364$	20.6364	−	16.4823i	1.08164	−	0.863905i
$365$			1.85667i			0.0971826i
$366$	−6.00195	−	5.90466i	−0.313727	−	0.308641i
$367$		−	15.4682i		−	0.807435i	−0.914884	−	0.403717i	$-0.867718\pi$
$367$		−	15.4682i		−	0.807435i	0.914884	−	0.403717i	$-0.132282\pi$
$368$	−3.08157	+	13.5952i	−0.160638	+	0.708698i
$369$	1.71414	−	2.21960i	0.0892348	−	0.115548i
$370$	1.47006	−	3.05554i	0.0764247	−	0.158850i
$371$	−4.59044			−0.238324
$372$	−34.5221	+	12.4119i	−1.78989	+	0.643529i
$373$	−3.08450			−0.159709			−0.0798546	−	0.996807i	$-0.525446\pi$
$373$	−3.08450			−0.159709			−0.0798546	+	0.996807i	$0.525446\pi$
$374$	−2.08281	+	4.32916i	−0.107700	+	0.223856i
$375$	−1.93884	+	5.68261i	−0.100121	+	0.293449i
$376$	7.42425	+	32.3600i	0.382876	+	1.66884i
$377$			13.4579i			0.693116i
$378$	−21.7119	+	2.97035i	−1.11674	+	0.152778i
$379$			26.8870i			1.38109i	0.723288	+	0.690547i	$0.242630\pi$
$379$			26.8870i			1.38109i	−0.723288	+	0.690547i	$0.757370\pi$
$380$	−0.635934	−	0.796211i	−0.0326227	−	0.0408448i
$381$	3.03257	−	8.88828i	0.155363	−	0.455360i
$382$	−14.8562	−	7.14750i	−0.760109	−	0.365698i
$383$	6.19252			0.316423			0.158211	−	0.987405i	$-0.449427\pi$
$383$	6.19252			0.316423			0.158211	+	0.987405i	$0.449427\pi$
$384$	−18.5627	−	6.27904i	−0.947274	−	0.320426i
$385$	−1.77489			−0.0904569
$386$	23.5778	+	11.3436i	1.20008	+	0.577372i
$387$	4.18688	−	5.42149i	0.212831	−	0.275590i
$388$	−12.1021	−	15.1522i	−0.614389	−	0.769236i
$389$		−	29.3150i		−	1.48633i	−0.669107	−	0.743166i	$-0.733323\pi$
$389$		−	29.3150i		−	1.48633i	0.669107	−	0.743166i	$-0.266677\pi$
$390$	−2.66985	+	2.71384i	−0.135193	+	0.137421i
$391$			6.98141i			0.353065i
$392$	1.19739	+	5.21904i	0.0604772	+	0.263601i
$393$	−16.1066	−	5.49538i	−0.812470	−	0.277205i
$394$	4.33408	−	9.00844i	0.218348	−	0.453839i
$395$	−5.87851			−0.295780
$396$	−0.166265	−	10.1731i	−0.00835513	−	0.511219i
$397$	27.2186			1.36606			0.683030	−	0.730390i	$-0.260662\pi$
$397$	27.2186			1.36606			0.683030	+	0.730390i	$0.260662\pi$
$398$	−8.30783	+	17.2679i	−0.416434	+	0.865563i
$399$	−7.09642	−	2.42121i	−0.355265	−	0.121212i
$400$	−4.31225	+	19.0247i	−0.215613	+	0.951233i
$401$			11.7112i			0.584827i	0.956292	+	0.292413i	$0.0944583\pi$
$401$			11.7112i			0.584827i	−0.956292	+	0.292413i	$0.905542\pi$
$402$	−1.71784	+	1.74615i	−0.0856781	+	0.0870898i
$403$			46.8950i			2.33600i
$404$	19.5703	−	15.6308i	0.973661	−	0.777663i
$405$	3.05621	−	0.798584i	0.151864	−	0.0396820i
$406$	−11.5501	−	5.55690i	−0.573222	−	0.275784i
$407$	11.5841			0.574204
$408$	−9.76167	−	1.01178i	−0.483275	−	0.0500904i
$409$	−32.9181			−1.62770			−0.813848	−	0.581078i	$-0.802631\pi$
$409$	−32.9181			−1.62770			−0.813848	+	0.581078i	$0.802631\pi$
$410$	0.418130	+	0.201168i	0.0206500	+	0.00993497i
$411$	−0.337256	+	0.988475i	−0.0166356	+	0.0487579i
$412$	5.19426	−	4.14866i	0.255903	−	0.204390i
$413$		−	44.2659i		−	2.17818i
$414$	−6.62714	−	13.2173i	−0.325706	−	0.649594i
$415$			2.32719i			0.114237i
$416$	−15.5813	+	19.6136i	−0.763936	+	0.961637i
$417$	9.17134	−	26.8806i	0.449122	−	1.31635i
$418$	1.50930	−	3.13709i	0.0738221	−	0.153440i
$419$	16.4243			0.802382			0.401191	−	0.915994i	$-0.368596\pi$
$419$	16.4243			0.802382			0.401191	+	0.915994i	$0.368596\pi$
$420$	−1.22672	−	3.41195i	−0.0598578	−	0.166486i
$421$	−16.4637			−0.802391			−0.401196	−	0.915992i	$-0.631405\pi$
$421$	−16.4637			−0.802391			−0.401196	+	0.915992i	$0.631405\pi$
$422$	−3.93798	+	8.18516i	−0.191698	+	0.398447i
$423$	−27.8709	−	21.5241i	−1.35513	−	1.04654i
$424$	4.24358	−	0.973592i	0.206087	−	0.0472818i
$425$			9.76956i			0.473893i
$426$	24.4834	+	24.0865i	1.18623	+	1.16700i
$427$		−	10.2504i		−	0.496050i
$428$	−0.652085	−	0.816433i	−0.0315197	−	0.0394638i
$429$	−12.3093	−	4.19978i	−0.594297	−	0.202767i
$430$	1.02130	+	0.491362i	0.0492516	+	0.0236956i
$431$	9.67349			0.465956			0.232978	−	0.972482i	$-0.425153\pi$
$431$	9.67349			0.465956			0.232978	+	0.972482i	$0.425153\pi$
$432$	19.4413	−	7.35080i	0.935372	−	0.353666i
$433$	10.5507			0.507034			0.253517	−	0.967331i	$-0.418413\pi$
$433$	10.5507			0.507034			0.253517	+	0.967331i	$0.418413\pi$
$434$	−40.2472	−	19.3634i	−1.93193	−	0.929474i
$435$	1.74858	+	0.596595i	0.0838381	+	0.0286045i
$436$	−13.2750	−	16.6207i	−0.635757	−	0.795989i
$437$		−	5.05903i		−	0.242006i
$438$	−9.23704	−	9.08731i	−0.441363	−	0.434208i
$439$			23.5551i			1.12422i	0.827061	+	0.562112i	$0.190011\pi$
$439$			23.5551i			1.12422i	−0.827061	+	0.562112i	$0.809989\pi$
$440$	1.64078	−	0.376439i	0.0782210	−	0.0179460i
$441$	−4.49504	−	3.47141i	−0.214050	−	0.165305i
$442$	−5.43890	+	11.3048i	−0.258702	+	0.537716i
$443$	2.64159			0.125506			0.0627530	−	0.998029i	$-0.480012\pi$
$443$	2.64159			0.125506			0.0627530	+	0.998029i	$0.480012\pi$
$444$	8.00640	+	22.2687i	0.379967	+	1.05682i
$445$	1.96890			0.0933346
$446$	17.2773	−	35.9111i	0.818105	−	1.70044i
$447$	0.684000	−	2.00476i	0.0323521	−	0.0948219i
$448$	−10.3995	−	21.4712i	−0.491331	−	1.01442i
$449$		−	23.9282i		−	1.12924i	−0.825350	−	0.564621i	$-0.809022\pi$
$449$		−	23.9282i		−	1.12924i	0.825350	−	0.564621i	$-0.190978\pi$
$450$	−9.27380	−	18.4958i	−0.437171	−	0.871902i
$451$			1.58521i			0.0746448i
$452$	24.8163	−	19.8208i	1.16726	−	0.932291i
$453$	−7.82717	+	22.9409i	−0.367753	+	1.07786i
$454$	−5.43269	−	2.61374i	−0.254969	−	0.122669i
$455$	−4.63481			−0.217283
$456$	7.07372	+	0.733176i	0.331257	+	0.0343341i
$457$	0.231675			0.0108373			0.00541864	−	0.999985i	$-0.498275\pi$
$457$	0.231675			0.0108373			0.00541864	+	0.999985i	$0.498275\pi$
$458$	−23.5707	−	11.3402i	−1.10139	−	0.529892i
$459$	8.68186	−	5.74268i	0.405235	−	0.268045i
$460$	1.91148	−	1.52670i	0.0891233	−	0.0711828i
$461$		−	23.3656i		−	1.08824i	−0.839007	−	0.544121i	$-0.816863\pi$
$461$		−	23.3656i		−	1.08824i	0.839007	−	0.544121i	$-0.183137\pi$
$462$	8.68705	−	8.83019i	0.404158	−	0.410818i
$463$		−	11.3756i		−	0.528667i	−0.964431	−	0.264334i	$-0.914848\pi$
$463$		−	11.3756i		−	0.528667i	0.964431	−	0.264334i	$-0.0851520\pi$
$464$	11.8559	+	2.68734i	0.550397	+	0.124757i
$465$	6.09306	+	2.07888i	0.282559	+	0.0964057i
$466$	−14.4300	+	29.9930i	−0.668458	+	1.38940i
$467$	18.8649			0.872962			0.436481	−	0.899713i	$-0.356225\pi$
$467$	18.8649			0.872962			0.436481	+	0.899713i	$0.356225\pi$
$468$	−0.434171	−	26.5653i	−0.0200696	−	1.22798i
$469$	−2.98214			−0.137702
$470$	2.52601	−	5.25035i	0.116516	−	0.242181i
$471$	−6.42144	−	2.19092i	−0.295884	−	0.100952i
$472$	9.38839	+	40.9211i	0.432136	+	1.88355i
$473$			3.87196i			0.178033i
$474$	28.7718	−	29.2459i	1.32153	−	1.34331i
$475$		−	7.07944i		−	0.324827i
$476$	−7.45648	−	9.33576i	−0.341767	−	0.427904i
$477$	−2.82259	+	3.65490i	−0.129238	+	0.167347i
$478$	11.8413	+	5.69701i	0.541609	+	0.260575i
$479$	−42.4876			−1.94131			−0.970655	−	0.240476i	$-0.922697\pi$
$479$	−42.4876			−1.94131			−0.970655	+	0.240476i	$0.922697\pi$
$480$	1.85767	+	2.89396i	0.0847907	+	0.132091i
$481$	30.2499			1.37928
$482$	22.1023	+	10.6337i	1.00673	+	0.484352i
$483$	5.81266	−	17.0365i	0.264485	−	0.775189i
$484$	−10.1405	−	12.6963i	−0.460933	−	0.577103i
$485$			3.40310i			0.154527i
$486$	−10.9853	+	19.1134i	−0.498305	+	0.867002i
$487$		−	2.38057i		−	0.107874i	−0.998544	−	0.0539369i	$-0.982823\pi$
$487$		−	2.38057i		−	0.107874i	0.998544	−	0.0539369i	$-0.0171770\pi$
$488$	2.17401	+	9.47584i	0.0984129	+	0.428951i
$489$	0.597917	−	1.75246i	0.0270387	−	0.0792488i
$490$	0.407397	−	0.846780i	0.0184043	−	0.0382536i
$491$	−4.74100			−0.213958			−0.106979	−	0.994261i	$-0.534118\pi$
$491$	−4.74100			−0.213958			−0.106979	+	0.994261i	$0.534118\pi$
$492$	−3.04732	+	1.09562i	−0.137384	+	0.0493945i
$493$	6.08826			0.274202
$494$	3.94126	−	8.19195i	0.177325	−	0.368573i
$495$	−1.09135	+	1.41317i	−0.0490527	+	0.0635171i
$496$	41.3128	+	9.36424i	1.85500	+	0.420467i
$497$			41.8138i			1.87560i
$498$	−11.5779	−	11.3902i	−0.518818	−	0.510408i
$499$			24.6933i			1.10542i	0.833373	+	0.552711i	$0.186407\pi$
$499$			24.6933i			1.10542i	−0.833373	+	0.552711i	$0.813593\pi$
$500$	5.41730	−	4.32680i	0.242269	−	0.193500i
$501$	−9.46934	−	3.23082i	−0.423059	−	0.144343i
$502$	15.4120	+	7.41494i	0.687873	+	0.330945i
$503$	−7.15017			−0.318810			−0.159405	−	0.987213i	$-0.550958\pi$
$503$	−7.15017			−0.318810			−0.159405	+	0.987213i	$0.550958\pi$
$504$	22.9787	+	10.5965i	1.02355	+	0.472005i
$505$	−4.39539			−0.195592
$506$	7.53129	+	3.62340i	0.334807	+	0.161080i
$507$	−10.8330	−	3.69610i	−0.481112	−	0.164150i
$508$	−8.47329	+	6.76762i	−0.375941	+	0.300265i
$509$		−	39.5239i		−	1.75187i	−0.482432	−	0.875934i	$-0.660246\pi$
$509$		−	39.5239i		−	1.75187i	0.482432	−	0.875934i	$-0.339754\pi$
$510$	1.22773	+	1.20782i	0.0543646	+	0.0534834i
$511$		−	15.7754i		−	0.697862i
$512$	14.1676	+	17.6431i	0.626124	+	0.779724i
$513$	−6.29125	+	4.16139i	−0.277765	+	0.183730i
$514$	2.37370	−	4.93378i	0.104700	−	0.217619i
$515$	−1.16660			−0.0514066
$516$	−7.44324	+	2.67611i	−0.327670	+	0.117809i
$517$	19.9051			0.875425
$518$	−12.4905	+	25.9617i	−0.548801	+	1.14069i
$519$	−6.36713	+	18.6616i	−0.279486	+	0.819155i
$520$	4.28460	−	0.983002i	0.187892	−	0.0431075i
$521$		−	0.206774i		−	0.00905892i	−0.999990	−	0.00452946i	$-0.998558\pi$
$521$		−	0.206774i		−	0.00905892i	0.999990	−	0.00452946i	$-0.00144178\pi$
$522$	−11.5264	+	5.77931i	−0.504496	+	0.252954i
$523$		−	26.7093i		−	1.16792i	−0.811784	−	0.583958i	$-0.801503\pi$
$523$		−	26.7093i		−	1.16792i	0.811784	−	0.583958i	$-0.198497\pi$
$524$	12.2637	+	15.3546i	0.535743	+	0.670768i
$525$	8.13404	−	23.8404i	0.354999	−	1.04048i
$526$	26.7327	+	12.8614i	1.16560	+	0.560786i
$527$	21.2150			0.924140
$528$	−6.15784	+	10.0054i	−0.267986	+	0.435430i
$529$	−10.8547			−0.471943
$530$	−0.688514	−	0.331253i	−0.0299071	−	0.0143887i
$531$	−35.2444	−	27.2184i	−1.52948	−	1.18118i
$532$	5.40328	+	6.76509i	0.234262	+	0.293304i
$533$			4.13950i			0.179302i
$534$	−9.63658	+	9.79537i	−0.417016	+	0.423887i
$535$			0.183366i			0.00792762i
$536$	2.75680	−	0.632485i	0.119076	−	0.0273192i
$537$	−10.6829	−	3.64489i	−0.461003	−	0.157289i
$538$	15.9182	−	33.0861i	0.686281	−	1.42644i
$539$	3.21031			0.138278
$540$	−3.47088	−	1.12124i	−0.149363	−	0.0482507i
$541$	−6.64574			−0.285723			−0.142861	−	0.989743i	$-0.545630\pi$
$541$	−6.64574			−0.285723			−0.142861	+	0.989743i	$0.545630\pi$
$542$	2.37524	−	4.93697i	0.102025	−	0.212061i
$543$	−27.3628	−	9.33584i	−1.17425	−	0.400639i
$544$	8.87309	+	7.04889i	0.380430	+	0.302218i
$545$			3.73292i			0.159901i
$546$	22.6847	−	23.0584i	0.970814	−	0.986810i
$547$		−	22.0801i		−	0.944077i	−0.881578	−	0.472038i	$-0.843518\pi$
$547$		−	22.0801i		−	0.944077i	0.881578	−	0.472038i	$-0.156482\pi$
$548$	0.942324	−	0.752634i	0.0402541	−	0.0321510i
$549$	−8.16133	−	6.30280i	−0.348317	−	0.268997i
$550$	10.5390	+	5.07047i	0.449386	+	0.216205i
$551$	−4.41181			−0.187950
$552$	−1.76015	+	16.9820i	−0.0749170	+	0.722803i
$553$	49.9474			2.12398
$554$	−13.3197	−	6.40828i	−0.565899	−	0.272262i
$555$	1.34099	−	3.93037i	0.0569220	−	0.166835i
$556$	−25.6256	+	20.4671i	−1.08677	+	0.868000i
$557$		−	40.4670i		−	1.71464i	−0.514783	−	0.857321i	$-0.672127\pi$
$557$		−	40.4670i		−	1.71464i	0.514783	−	0.857321i	$-0.327873\pi$
$558$	−40.1645	+	20.1384i	−1.70030	+	0.852528i
$559$			10.1109i			0.427647i
$560$	−0.925504	+	4.08311i	−0.0391097	+	0.172543i
$561$	−1.89995	+	5.56864i	−0.0802161	+	0.235108i
$562$	6.15740	−	12.7983i	0.259734	−	0.539862i
$563$	−16.7710			−0.706814			−0.353407	−	0.935470i	$-0.614977\pi$
$563$	−16.7710			−0.706814			−0.353407	+	0.935470i	$0.614977\pi$
$564$	13.7574	+	38.2644i	0.579293	+	1.61122i
$565$	−5.57360			−0.234483
$566$	−8.40430	+	17.4685i	−0.353259	+	0.734254i
$567$	−25.9674	+	6.78525i	−1.09053	+	0.284954i
$568$	−8.86832	−	38.6543i	−0.372107	−	1.62190i
$569$			29.1776i			1.22319i	0.791172	+	0.611594i	$0.209471\pi$
$569$			29.1776i			1.22319i	−0.791172	+	0.611594i	$0.790529\pi$
$570$	−0.889663	−	0.875241i	−0.0372639	−	0.0366598i
$571$			29.1656i			1.22054i	0.792193	+	0.610270i	$0.208939\pi$
$571$			29.1656i			1.22054i	−0.792193	+	0.610270i	$0.791061\pi$
$572$	9.37240	+	11.7346i	0.391880	+	0.490647i
$573$	−19.1097	−	6.51999i	−0.798318	−	0.272376i
$574$	−3.55269	−	1.70924i	−0.148286	−	0.0713424i
$575$	16.9958			0.708772
$576$	−23.4898	−	4.92222i	−0.978743	−	0.205092i
$577$	3.09196			0.128720			0.0643601	−	0.997927i	$-0.479499\pi$
$577$	3.09196			0.128720			0.0643601	+	0.997927i	$0.479499\pi$
$578$	−16.5504	−	7.96263i	−0.688407	−	0.331202i
$579$	30.3283	+	10.3477i	1.26040	+	0.430034i
$580$	−1.33139	−	1.66694i	−0.0552828	−	0.0692160i
$581$		−	19.7732i		−	0.820330i
$582$	−16.9306	−	16.6562i	−0.701796	−	0.690420i
$583$		−	2.61029i		−	0.108107i
$584$	3.34582	+	14.5834i	0.138451	+	0.603465i
$585$	−2.84988	+	3.69023i	−0.117828	+	0.152572i
$586$	−16.7730	+	34.8630i	−0.692888	+	1.44018i
$587$	−3.55145			−0.146584			−0.0732921	−	0.997311i	$-0.523351\pi$
$587$	−3.55145			−0.146584			−0.0732921	+	0.997311i	$0.523351\pi$
$588$	2.21881	+	6.17131i	0.0915022	+	0.254500i
$589$	−15.3733			−0.633445
$590$	3.19429	−	6.63937i	0.131507	−	0.273339i
$591$	3.95357	−	11.5877i	0.162628	−	0.476652i
$592$	6.04046	−	26.6491i	0.248261	−	1.09527i
$593$			36.4122i			1.49527i	0.664110	+	0.747635i	$0.268810\pi$
$593$			36.4122i			1.49527i	−0.664110	+	0.747635i	$0.731190\pi$
$594$	−1.68904	−	12.3462i	−0.0693023	−	0.506569i
$595$			2.09676i			0.0859588i
$596$	−1.91116	+	1.52644i	−0.0782841	+	0.0625256i
$597$	−7.57844	+	22.2119i	−0.310165	+	0.909074i
$598$	19.6666	+	9.46186i	0.804227	+	0.386924i
$599$	2.90754			0.118799			0.0593994	−	0.998234i	$-0.481081\pi$
$599$	2.90754			0.118799			0.0593994	+	0.998234i	$0.481081\pi$
$600$	−2.46310	+	23.7641i	−0.100556	+	0.970165i
$601$	0.0252815			0.00103125			0.000515627	−	1.00000i	$-0.499836\pi$
$601$	0.0252815			0.00103125			0.000515627		1.00000i	$0.499836\pi$
$602$	−8.67761	−	4.17491i	−0.353673	−	0.170157i
$603$	−1.83367	+	2.37437i	−0.0746729	+	0.0966920i
$604$	21.8698	−	17.4675i	0.889871	−	0.710741i
$605$			2.85151i			0.115931i
$606$	21.5128	−	21.8673i	0.873900	−	0.888299i
$607$			32.3617i			1.31352i	0.754099	+	0.656761i	$0.228074\pi$
$607$			32.3617i			1.31352i	−0.754099	+	0.656761i	$0.771926\pi$
$608$	−6.42982	−	5.10792i	−0.260763	−	0.207154i
$609$	−14.8570	−	5.06903i	−0.602036	−	0.205408i
$610$	0.739681	−	1.53744i	0.0299488	−	0.0622490i
$611$	51.9786			2.10283
$612$	−12.0180	+	0.196417i	−0.485799	+	0.00793967i
$613$	25.0972			1.01367			0.506834	−	0.862044i	$-0.330816\pi$
$613$	25.0972			1.01367			0.506834	+	0.862044i	$0.330816\pi$
$614$	12.1567	−	25.2680i	0.490606	−	1.01973i
$615$	0.537845	+	0.183506i	0.0216880	+	0.00739969i
$616$	−13.9410	+	3.19845i	−0.561701	+	0.128869i
$617$			36.3347i			1.46278i	0.681958	+	0.731391i	$0.261128\pi$
$617$			36.3347i			1.46278i	−0.681958	+	0.731391i	$0.738872\pi$
$618$	5.70983	−	5.80391i	0.229683	−	0.233467i
$619$		−	15.1003i		−	0.606934i	−0.952842	−	0.303467i	$-0.901856\pi$
$619$		−	15.1003i		−	0.606934i	0.952842	−	0.303467i	$-0.0981442\pi$
$620$	−4.63932	−	5.80858i	−0.186319	−	0.233278i
$621$	−9.99034	−	15.1035i	−0.400898	−	0.606084i
$622$	34.9870	+	16.8327i	1.40285	+	0.674930i
$623$	−16.7289			−0.670230
$624$	−16.0801	+	26.1273i	−0.643719	+	1.04593i
$625$	23.1674			0.926695
$626$	10.3147	+	4.96255i	0.412259	+	0.198343i
$627$	1.37679	−	4.03528i	0.0549836	−	0.161153i
$628$	4.88934	+	6.12162i	0.195106	+	0.244279i
$629$		−	13.6849i		−	0.545651i
$630$	−1.99036	−	3.96961i	−0.0792979	−	0.158153i
$631$		−	11.8772i		−	0.472822i	−0.971653	−	0.236411i	$-0.924029\pi$
$631$		−	11.8772i		−	0.472822i	0.971653	−	0.236411i	$-0.0759712\pi$
$632$	−46.1733	+	10.5934i	−1.83667	+	0.421382i
$633$	−3.59225	+	10.5287i	−0.142779	+	0.418476i
$634$	0.605525	−	1.25859i	0.0240485	−	0.0499851i
$635$	1.90305			0.0755204
$636$	5.01787	−	1.80411i	0.198971	−	0.0715375i
$637$	8.38314			0.332152
$638$	3.15985	−	6.56779i	0.125100	−	0.260021i
$639$	33.2921	+	25.7107i	1.31701	+	1.01710i
$640$	−0.0104186	−	3.97087i	−0.000411830	−	0.156963i
$641$			36.4801i			1.44088i	0.693520	+	0.720438i	$0.256059\pi$
$641$			36.4801i			1.44088i	−0.693520	+	0.720438i	$0.743941\pi$
$642$	−0.912258	−	0.897470i	−0.0360039	−	0.0354203i
$643$			32.3140i			1.27434i	0.770724	+	0.637170i	$0.219895\pi$
$643$			32.3140i			1.27434i	−0.770724	+	0.637170i	$0.780105\pi$
$644$	−16.2411	+	12.9718i	−0.639989	+	0.511160i
$645$	1.31371	+	0.448223i	0.0517274	+	0.0176488i
$646$	−3.70599	−	1.78300i	−0.145810	−	0.0701512i
$647$	−17.8380			−0.701285			−0.350642	−	0.936509i	$-0.614037\pi$
$647$	−17.8380			−0.701285			−0.350642	+	0.936509i	$0.614037\pi$
$648$	22.5662	−	11.7800i	0.886483	−	0.462762i
$649$	25.1712			0.988054
$650$	27.5208	+	13.2406i	1.07945	+	0.519340i
$651$	−51.7703	−	17.6634i	−2.02904	−	0.692284i
$652$	−1.67064	+	1.33434i	−0.0654271	+	0.0522567i
$653$			19.6414i			0.768627i	0.923203	+	0.384314i	$0.125562\pi$
$653$			19.6414i			0.768627i	−0.923203	+	0.384314i	$0.874438\pi$
$654$	−18.5715	−	18.2705i	−0.726203	−	0.714432i
$655$		−	3.44856i		−	0.134746i
$656$	3.64675	+	0.826598i	0.142382	+	0.0322732i
$657$	−12.5603	−	9.70005i	−0.490026	−	0.378435i
$658$	−21.4625	+	44.6101i	−0.836696	+	1.73908i
$659$	−12.1305			−0.472536			−0.236268	−	0.971688i	$-0.575924\pi$
$659$	−12.1305			−0.472536			−0.236268	+	0.971688i	$0.575924\pi$
$660$	1.94016	−	0.697557i	0.0755205	−	0.0271524i
$661$	−46.6603			−1.81488			−0.907439	−	0.420185i	$-0.861965\pi$
$661$	−46.6603			−1.81488			−0.907439	+	0.420185i	$0.861965\pi$
$662$	7.65263	−	15.9061i	0.297428	−	0.618208i
$663$	−4.96139	+	14.5415i	−0.192684	+	0.564745i
$664$	4.19372	+	18.2791i	0.162748	+	0.709367i
$665$		−	1.51940i		−	0.0589199i
$666$	12.9904	+	25.9084i	0.503369	+	1.00393i
$667$		−	10.5915i		−	0.410106i
$668$	7.21004	+	9.02722i	0.278965	+	0.349274i
$669$	15.7605	−	46.1929i	0.609334	−	1.78592i
$670$	−0.447286	−	0.215195i	−0.0172802	−	0.00831372i
$671$	5.82873			0.225016
$672$	−15.7839	−	24.5888i	−0.608877	−	0.948535i
$673$	−46.2504			−1.78282			−0.891411	−	0.453196i	$-0.850284\pi$
$673$	−46.2504			−1.78282			−0.891411	+	0.453196i	$0.850284\pi$
$674$	10.8690	+	5.22924i	0.418660	+	0.201423i
$675$	−13.9802	−	21.1354i	−0.538096	−	0.813501i
$676$	8.24837	+	10.3272i	0.317245	+	0.397202i
$677$			45.5607i			1.75104i	0.483183	+	0.875519i	$0.339481\pi$
$677$			45.5607i			1.75104i	−0.483183	+	0.875519i	$0.660519\pi$
$678$	27.2795	−	27.7290i	1.04766	−	1.06492i
$679$		−	28.9148i		−	1.10965i
$680$	−0.444704	−	1.93833i	−0.0170536	−	0.0743314i
$681$	−6.98813	−	2.38427i	−0.267786	−	0.0913653i
$682$	11.0107	−	22.8860i	0.421623	−	0.876349i
$683$	42.0262			1.60809			0.804043	−	0.594571i	$-0.202678\pi$
$683$	42.0262			1.60809			0.804043	+	0.594571i	$0.202678\pi$
$684$	8.70875	−	0.142332i	0.332987	−	0.00544219i
$685$	−0.211641			−0.00808638
$686$	9.33751	−	19.4081i	0.356508	−	0.741007i
$687$	−30.3193	−	10.3446i	−1.15675	−	0.394670i
$688$	8.90738	+	2.01901i	0.339591	+	0.0769739i
$689$		−	6.81630i		−	0.259680i
$690$	2.10121	−	2.13583i	0.0799917	−	0.0813098i
$691$		−	12.4465i		−	0.473489i	−0.971572	−	0.236744i	$-0.923920\pi$
$691$		−	12.4465i		−	0.473489i	0.971572	−	0.236744i	$-0.0760804\pi$
$692$	17.7903	−	14.2091i	0.676287	−	0.540151i
$693$	9.27280	−	12.0071i	0.352245	−	0.456112i
$694$	21.1560	+	10.1784i	0.803069	+	0.386367i
$695$	5.75536			0.218313
$696$	14.8095	+	1.53497i	0.561352	+	0.0581829i
$697$	1.87268			0.0709330
$698$	−2.68454	−	1.29157i	−0.101611	−	0.0488865i
$699$	−13.1631	+	38.5803i	−0.497876	+	1.45924i
$700$	−22.7273	+	18.1523i	−0.859010	+	0.686092i
$701$			38.1395i			1.44051i	0.693710	+	0.720255i	$0.255975\pi$
$701$			38.1395i			1.44051i	−0.693710	+	0.720255i	$0.744025\pi$
$702$	−4.41064	−	32.2398i	−0.166469	−	1.21681i
$703$			9.91664i			0.374013i
$704$	12.2093	−	5.91354i	0.460154	−	0.222875i
$705$	2.30424	−	6.75358i	0.0867827	−	0.254355i
$706$	6.85510	−	14.2484i	0.257995	−	0.536246i
$707$	37.3459			1.40454
$708$	17.3971	+	48.3876i	0.653823	+	1.81852i
$709$	33.0619			1.24166			0.620832	−	0.783943i	$-0.286795\pi$
$709$	33.0619			1.24166			0.620832	+	0.783943i	$0.286795\pi$
$710$	−3.01734	+	6.27158i	−0.113239	+	0.235368i
$711$	30.7119	−	39.7680i	1.15179	−	1.49142i
$712$	15.4649	−	3.54805i	0.579570	−	0.132969i
$713$		−	36.9070i		−	1.38218i
$714$	−10.4315	−	10.2624i	−0.390389	−	0.384061i
$715$		−	2.63552i		−	0.0985628i
$716$	8.13409	+	10.1842i	0.303985	+	0.380600i
$717$	15.2316	+	5.19684i	0.568835	+	0.194080i
$718$	−17.0322	−	8.19441i	−0.635636	−	0.305813i
$719$	2.64623			0.0986878			0.0493439	−	0.998782i	$-0.484287\pi$
$719$	2.64623			0.0986878			0.0493439	+	0.998782i	$0.484287\pi$
$720$	2.68188	+	3.24753i	0.0999479	+	0.121028i
$721$	9.91215			0.369148
$722$	−21.5279	−	10.3574i	−0.801187	−	0.385461i
$723$	28.4304	+	9.70011i	1.05734	+	0.360751i
$724$	20.8343	+	26.0852i	0.774299	+	0.969449i
$725$		−	14.8215i		−	0.550455i
$726$	−14.1864	−	13.9565i	−0.526508	−	0.517974i
$727$		−	48.0337i		−	1.78147i	−0.454522	−	0.890736i	$-0.650190\pi$
$727$		−	48.0337i		−	1.78147i	0.454522	−	0.890736i	$-0.349810\pi$
$728$	−36.4045	+	8.35217i	−1.34924	+	0.309552i
$729$	−10.5645	+	24.8473i	−0.391280	+	0.920272i
$730$	1.13837	−	2.36613i	0.0421331	−	0.0875743i
$731$	4.57413			0.169180
$732$	4.02854	+	11.2048i	0.148899	+	0.414142i
$733$	−26.9253			−0.994510			−0.497255	−	0.867605i	$-0.665659\pi$
$733$	−26.9253			−0.994510			−0.497255	+	0.867605i	$0.665659\pi$
$734$	−9.48398	+	19.7126i	−0.350060	+	0.727605i
$735$	0.371629	−	1.08922i	0.0137078	−	0.0401765i
$736$	12.2627	−	15.4362i	0.452009	−	0.568986i
$737$		−	1.69575i		−	0.0624637i
$738$	−3.54539	+	1.77765i	−0.130508	+	0.0654364i
$739$			35.8090i			1.31725i	0.752470	+	0.658627i	$0.228862\pi$
$739$			35.8090i			1.31725i	−0.752470	+	0.658627i	$0.771138\pi$
$740$	−3.74686	+	2.99262i	−0.137737	+	0.110011i
$741$	3.59523	−	10.5374i	0.132074	−	0.387101i
$742$	5.85003	+	2.81452i	0.214761	+	0.103324i
$743$	−22.9337			−0.841357			−0.420679	−	0.907210i	$-0.638208\pi$
$743$	−22.9337			−0.841357			−0.420679	+	0.907210i	$0.638208\pi$
$744$	51.6047	+	5.34872i	1.89192	+	0.196094i
$745$	0.429236			0.0157260
$746$	3.93086	+	1.89119i	0.143919	+	0.0692413i
$747$	−15.7434	−	12.1582i	−0.576020	−	0.444847i
$748$	5.30865	−	4.24002i	0.194103	−	0.155030i
$749$		−	1.55799i		−	0.0569277i
$750$	5.95500	−	6.05313i	0.217446	−	0.221029i
$751$		−	0.147527i		−	0.00538332i	−0.999996	−	0.00269166i	$-0.999143\pi$
$751$		−	0.147527i		−	0.00538332i	0.999996	−	0.00269166i	$-0.000856783\pi$
$752$	10.3794	−	45.7913i	0.378497	−	1.66984i
$753$	19.8247	+	6.76394i	0.722451	+	0.246492i
$754$	8.25138	−	17.1506i	0.300498	−	0.624588i
$755$	−4.91185			−0.178760
$756$	29.4907	+	9.52676i	1.07257	+	0.346485i
$757$	−30.6339			−1.11341			−0.556703	−	0.830711i	$-0.687934\pi$
$757$	−30.6339			−1.11341			−0.556703	+	0.830711i	$0.687934\pi$
$758$	16.4851	−	34.2646i	0.598767	−	1.24455i
$759$	9.68757	+	3.30528i	0.351637	+	0.119974i
$760$	0.322251	+	1.40459i	0.0116893	+	0.0509500i
$761$			19.4924i			0.706599i	0.935510	+	0.353299i	$0.114940\pi$
$761$			19.4924i			0.706599i	−0.935510	+	0.353299i	$0.885060\pi$
$762$	−9.31433	+	9.46780i	−0.337423	+	0.342982i
$763$		−	31.7172i		−	1.14824i
$764$	14.5503	+	18.2174i	0.526411	+	0.659084i
$765$	1.66944	+	1.28927i	0.0603586	+	0.0466135i
$766$	−7.89170	−	3.79680i	−0.285139	−	0.137184i
$767$	65.7299			2.37337
$768$	19.8063	+	19.3832i	0.714698	+	0.699433i
$769$	51.5761			1.85988			0.929940	−	0.367711i	$-0.119858\pi$
$769$	51.5761			1.85988			0.929940	+	0.367711i	$0.119858\pi$
$770$	2.26191	+	1.08823i	0.0815135	+	0.0392172i
$771$	2.16530	−	6.34637i	0.0779815	−	0.228559i
$772$	−23.0923	−	28.9123i	−0.831109	−	1.04058i
$773$			32.5670i			1.17135i	0.810544	+	0.585677i	$0.199171\pi$
$773$			32.5670i			1.17135i	−0.810544	+	0.585677i	$0.800829\pi$
$774$	−8.65979	+	4.34201i	−0.311270	+	0.156070i
$775$		−	51.6464i		−	1.85519i
$776$	6.13257	+	26.7299i	0.220146	+	0.959549i
$777$	−11.3939	+	33.3948i	−0.408754	+	1.19803i
$778$	−17.9738	+	37.3589i	−0.644393	+	1.33938i
$779$	−1.35703			−0.0486205
$780$	5.06637	−	1.82154i	0.181405	−	0.0652217i
$781$	−23.7768			−0.850801
$782$	4.28049	−	8.89705i	0.153070	−	0.318158i
$783$	−13.1713	+	8.71225i	−0.470704	+	0.311351i
$784$	1.67399	−	7.38525i	0.0597854	−	0.263759i
$785$		−	1.37488i		−	0.0490717i
$786$	17.1568	+	16.8786i	0.611961	+	0.602041i
$787$			28.3287i			1.00981i	0.863175	+	0.504904i	$0.168472\pi$
$787$			28.3287i			1.00981i	−0.863175	+	0.504904i	$0.831528\pi$
$788$	−11.0466	+	8.82295i	−0.393520	+	0.314305i
$789$	34.3866	+	11.7323i	1.22419	+	0.417680i
$790$	7.49153	+	3.60427i	0.266537	+	0.128234i
$791$	47.3567			1.68381
$792$	−6.02554	+	13.0665i	−0.214108	+	0.464298i
$793$	15.2207			0.540502
$794$	−34.6871	−	16.6884i	−1.23100	−	0.592250i
$795$	−0.885642	−	0.302171i	−0.0314105	−	0.0107169i
$796$	21.1749	−	16.9124i	0.750523	−	0.599443i
$797$		−	36.5770i		−	1.29562i	−0.761801	−	0.647811i	$-0.775685\pi$
$797$		−	36.5770i		−	1.29562i	0.761801	−	0.647811i	$-0.224315\pi$
$798$	7.55911	+	7.43658i	0.267590	+	0.263252i
$799$		−	23.5148i		−	0.831894i
$800$	17.1600	−	21.6009i	0.606698	−	0.763708i
$801$	−10.2864	+	13.3195i	−0.363451	+	0.470623i
$802$	7.18042	−	14.9246i	0.253549	−	0.527006i
$803$	8.97045			0.316560
$804$	3.25981	−	1.17202i	0.114965	−	0.0413340i
$805$	3.64766			0.128563
$806$	28.7525	−	59.7626i	1.01277	−	2.10505i
$807$	14.5206	−	42.5590i	0.511150	−	1.49815i
$808$	−34.5240	+	7.92072i	−1.21455	+	0.278650i
$809$			12.6520i			0.444822i	0.974953	+	0.222411i	$0.0713927\pi$
$809$			12.6520i			0.444822i	−0.974953	+	0.222411i	$0.928607\pi$
$810$	−4.38444	−	0.856134i	−0.154054	−	0.0300815i
$811$		−	33.9464i		−	1.19202i	−0.802977	−	0.596010i	$-0.796752\pi$
$811$		−	33.9464i		−	1.19202i	0.802977	−	0.596010i	$-0.203248\pi$
$812$	11.3123	+	14.1633i	0.396983	+	0.497036i
$813$	2.16671	−	6.35048i	0.0759897	−	0.222721i
$814$	−14.7627	−	7.10254i	−0.517434	−	0.248944i
$815$	0.375215			0.0131432
$816$	11.8198	+	7.27454i	0.413777	+	0.254660i
$817$	−3.31461			−0.115963
$818$	41.9506	+	20.1830i	1.46677	+	0.705681i
$819$	24.2143	−	31.3544i	0.846115	−	1.09561i
$820$	−0.409521	−	0.512734i	−0.0143011	−	0.0179054i
$821$			9.29308i			0.324331i	0.986764	+	0.162165i	$0.0518478\pi$
$821$			9.29308i			0.324331i	−0.986764	+	0.162165i	$0.948152\pi$
$822$	1.03586	−	1.05292i	0.0361296	−	0.0367250i
$823$			0.0285875i			0.000996496i	1.00000		0.000498248i	$0.000158597\pi$
$823$			0.0285875i			0.000996496i	−1.00000		0.000498248i	$0.999841\pi$
$824$	−9.16317	+	2.10228i	−0.319214	+	0.0732363i
$825$	13.5565	+	4.62531i	0.471976	+	0.161032i
$826$	−27.1406	+	56.4121i	−0.944342	+	1.96283i
$827$	34.0218			1.18306			0.591528	−	0.806285i	$-0.298525\pi$
$827$	34.0218			1.18306			0.591528	+	0.806285i	$0.298525\pi$
$828$	0.341699	+	20.9073i	0.0118749	+	0.726578i
$829$	−38.6899			−1.34376			−0.671878	−	0.740662i	$-0.734512\pi$
$829$	−38.6899			−1.34376			−0.671878	+	0.740662i	$0.734512\pi$
$830$	1.42686	−	2.96575i	0.0495271	−	0.102943i
$831$	−17.1333	−	5.84566i	−0.594346	−	0.202784i
$832$	31.8823	−	15.4421i	1.10532	−	0.535360i
$833$		−	3.79248i		−	0.131402i
$834$	−28.1691	+	28.6332i	−0.975416	+	0.991488i
$835$		−	2.02746i		−	0.0701633i
$836$	−3.84687	+	3.07250i	−0.133047	+	0.106265i
$837$	−45.8964	+	30.3585i	−1.58641	+	1.04934i
$838$	−20.9311	−	10.0702i	−0.723052	−	0.347869i
$839$	34.4929			1.19083			0.595414	−	0.803419i	$-0.296988\pi$
$839$	34.4929			1.19083			0.595414	+	0.803419i	$0.296988\pi$
$840$	−0.528635	+	5.10030i	−0.0182396	+	0.175977i
$841$	19.7635			0.681499
$842$	20.9812	+	10.0943i	0.723060	+	0.347874i
$843$	5.61682	−	16.4625i	0.193453	−	0.566999i
$844$	10.0371	−	8.01662i	0.345490	−	0.275943i
$845$		−	2.31944i		−	0.0797912i
$846$	22.3215	+	44.5185i	0.767430	+	1.53058i
$847$		−	24.2282i		−	0.832490i
$848$	−6.00492	−	1.36112i	−0.206210	−	0.0467409i
$849$	−7.66645	+	22.4699i	−0.263112	+	0.771164i
$850$	5.98997	−	12.4502i	0.205454	−	0.427040i
$851$	−23.8071			−0.816096
$852$	−16.4334	−	45.7071i	−0.562998	−	1.56590i
$853$	1.74939			0.0598981			0.0299490	−	0.999551i	$-0.490465\pi$
$853$	1.74939			0.0598981			0.0299490	+	0.999551i	$0.490465\pi$
$854$	−6.28478	+	13.0630i	−0.215061	+	0.447007i
$855$	−1.20975	−	0.934257i	−0.0413724	−	0.0319509i
$856$	0.330436	+	1.44027i	0.0112941	+	0.0492273i
$857$		−	8.72576i		−	0.298066i	−0.988832	−	0.149033i	$-0.952384\pi$
$857$		−	8.72576i		−	0.298066i	0.988832	−	0.149033i	$-0.0476161\pi$
$858$	13.1119	+	12.8993i	0.447631	+	0.440375i
$859$		−	21.0392i		−	0.717847i	−0.933367	−	0.358924i	$-0.883144\pi$
$859$		−	21.0392i		−	0.717847i	0.933367	−	0.358924i	$-0.116856\pi$
$860$	−1.00027	−	1.25238i	−0.0341091	−	0.0427057i
$861$	−4.56986	−	1.55918i	−0.155740	−	0.0531367i
$862$	−12.3278	−	5.93107i	−0.419887	−	0.202013i
$863$	−50.8751			−1.73181			−0.865904	−	0.500210i	$-0.833256\pi$
$863$	−50.8751			−1.73181			−0.865904	+	0.500210i	$0.833256\pi$
$864$	−29.2829	−	2.55220i	−0.996223	−	0.0868275i
$865$	−3.99561			−0.135855
$866$	−13.4457	−	6.46892i	−0.456905	−	0.219823i
$867$	−21.2890	−	7.26355i	−0.723012	−	0.246683i
$868$	39.4184	+	49.3532i	1.33795	+	1.67516i
$869$			28.4019i			0.963467i
$870$	−1.86259	−	1.83240i	−0.0631478	−	0.0621241i
$871$		−	4.42815i		−	0.150042i
$872$	6.72693	+	29.3206i	0.227802	+	0.992920i
$873$	−23.0219	−	17.7793i	−0.779173	−	0.601737i
$874$	−3.10182	+	6.44718i	−0.104921	+	0.218079i
$875$	10.3378			0.349481
$876$	6.19994	+	17.2443i	0.209477	+	0.582630i
$877$	25.6253			0.865306			0.432653	−	0.901561i	$-0.357578\pi$
$877$	25.6253			0.865306			0.432653	+	0.901561i	$0.357578\pi$
$878$	14.4423	−	30.0184i	0.487403	−	1.01307i
$879$	−15.3004	+	44.8446i	−0.516071	+	1.51257i
$880$	−2.32180	−	0.526275i	−0.0782679	−	0.0177407i
$881$			54.1226i			1.82344i	0.410816	+	0.911718i	$0.365244\pi$
$881$			54.1226i			1.82344i	−0.410816	+	0.911718i	$0.634756\pi$
$882$	3.60003	+	7.17997i	0.121219	+	0.241762i
$883$			24.3636i			0.819900i	0.912108	+	0.409950i	$0.134454\pi$
$883$			24.3636i			0.819900i	−0.912108	+	0.409950i	$0.865546\pi$
$884$	13.8626	−	11.0720i	0.466249	−	0.372393i
$885$	2.91385	−	8.54029i	0.0979478	−	0.287079i
$886$	−3.36643	−	1.61963i	−0.113097	−	0.0544126i
$887$	12.3265			0.413883			0.206941	−	0.978353i	$-0.433649\pi$
$887$	12.3265			0.413883			0.206941	+	0.978353i	$0.433649\pi$
$888$	3.45022	−	33.2880i	0.115782	−	1.11707i
$889$	−16.1695			−0.542307
$890$	−2.50915	−	1.20718i	−0.0841068	−	0.0404649i
$891$	−3.85833	−	14.7660i	−0.129259	−	0.494679i
$892$	−44.0362	+	35.1717i	−1.47444	+	1.17764i
$893$			17.0398i			0.570216i
$894$	−2.10086	+	2.13547i	−0.0702631	+	0.0714209i
$895$		−	2.28731i		−	0.0764562i
$896$	0.0885224	+	33.7389i	0.00295733	+	1.12714i
$897$	25.2974	+	8.63115i	0.844654	+	0.288186i
$898$	−14.6710	+	30.4939i	−0.489579	+	1.01760i
$899$	−32.1854			−1.07344
$900$	0.478162	+	29.2570i	0.0159387	+	0.975232i
$901$	−3.08365			−0.102731
$902$	0.971936	−	2.02018i	0.0323619	−	0.0672648i
$903$	−11.1621	−	3.80838i	−0.371452	−	0.126735i
$904$	−43.7783	+	10.0439i	−1.45605	+	0.334056i
$905$		−	5.85859i		−	0.194746i
$906$	24.0406	−	24.4367i	0.798695	−	0.811855i
$907$			36.8608i			1.22394i	0.790879	+	0.611972i	$0.209623\pi$
$907$			36.8608i			1.22394i	−0.790879	+	0.611972i	$0.790377\pi$
$908$	5.32083	+	6.66186i	0.176578	+	0.221082i
$909$	22.9634	−	29.7347i	0.761649	−	0.986239i
$910$	5.90657	+	2.84173i	0.195801	+	0.0942023i
$911$	−31.6676			−1.04920			−0.524598	−	0.851350i	$-0.675784\pi$
$911$	−31.6676			−1.04920			−0.524598	+	0.851350i	$0.675784\pi$
$912$	−8.56516	−	5.27144i	−0.283621	−	0.174555i
$913$	11.2437			0.372114
$914$	−0.295244	−	0.142046i	−0.00976582	−	0.00469846i
$915$	0.674741	−	1.97762i	0.0223062	−	0.0653782i
$916$	23.0854	+	28.9037i	0.762763	+	0.955005i
$917$			29.3010i			0.967604i
$918$	−14.5851	+	1.99535i	−0.481380	+	0.0658562i
$919$		−	19.4847i		−	0.642740i	−0.946954	−	0.321370i	$-0.895857\pi$
$919$		−	19.4847i		−	0.642740i	0.946954	−	0.321370i	$-0.104143\pi$
$920$	−3.37204	+	0.773636i	−0.111173	+	0.0255060i
$921$	11.0894	−	32.5024i	0.365409	−	1.07099i
$922$	−14.3260	+	29.7769i	−0.471803	+	0.980649i
$923$	−62.0888			−2.04368
$924$	−16.4847	+	5.92686i	−0.542308	+	0.194979i
$925$	−33.3149			−1.09539
$926$	−6.97466	+	14.4969i	−0.229202	+	0.476399i
$927$	6.09483	−	7.89204i	0.200181	−	0.259209i
$928$	−13.4614	−	10.6939i	−0.441892	−	0.351045i
$929$		−	10.1296i		−	0.332342i	−0.986097	−	0.166171i	$-0.946860\pi$
$929$		−	10.1296i		−	0.332342i	0.986097	−	0.166171i	$-0.0531404\pi$
$930$	−6.49034	−	6.38513i	−0.212826	−	0.209377i
$931$			2.74819i			0.0900684i
$932$	36.7790	−	29.3754i	1.20474	−	0.962225i
$933$	45.0042	+	15.3549i	1.47337	+	0.502696i
$934$	−24.0413	−	11.5666i	−0.786654	−	0.378469i
$935$	−1.19229			−0.0389921
$936$	−15.7346	+	34.1208i	−0.514302	+	1.11527i
$937$	−21.4503			−0.700749			−0.350375	−	0.936610i	$-0.613946\pi$
$937$	−21.4503			−0.700749			−0.350375	+	0.936610i	$0.613946\pi$
$938$	3.80041	+	1.82843i	0.124088	+	0.0597003i
$939$	13.2679	+	4.52686i	0.432983	+	0.147729i
$940$	−6.43826	+	5.14224i	−0.209993	+	0.167721i
$941$			15.1606i			0.494222i	0.968987	+	0.247111i	$0.0794812\pi$
$941$			15.1606i			0.494222i	−0.968987	+	0.247111i	$0.920519\pi$
$942$	6.84012	+	6.72924i	0.222863	+	0.219251i
$943$		−	3.25784i		−	0.106090i
$944$	13.1253	−	57.9058i	0.427192	−	1.88467i
$945$	−3.00045	−	4.53612i	−0.0976046	−	0.147560i
$946$	2.37400	−	4.93440i	0.0771855	−	0.160431i
$947$	2.73350			0.0888268			0.0444134	−	0.999013i	$-0.485858\pi$
$947$	2.73350			0.0888268			0.0444134	+	0.999013i	$0.485858\pi$
$948$	−54.5981	+	19.6300i	−1.77326	+	0.637553i
$949$	23.4247			0.760398
$950$	−4.34059	+	9.02198i	−0.140827	+	0.292712i
$951$	0.552363	−	1.61894i	0.0179116	−	0.0524977i
$952$	3.77847	+	16.4692i	0.122461	+	0.533770i
$953$		−	32.4065i		−	1.04975i	−0.851180	−	0.524874i	$-0.824112\pi$
$953$		−	32.4065i		−	1.04975i	0.851180	−	0.524874i	$-0.175888\pi$
$954$	5.83801	−	2.92717i	0.189013	−	0.0947707i
$955$		−	4.09154i		−	0.132399i
$956$	−11.5975	−	14.5205i	−0.375090	−	0.469625i
$957$	2.88243	−	8.44822i	0.0931758	−	0.273092i
$958$	54.1459	+	26.0503i	1.74938	+	0.841647i
$959$	1.79823			0.0580678
$960$	−0.593037	−	4.82703i	−0.0191402	−	0.155792i
$961$	−81.1524			−2.61782
$962$	−38.5502	−	18.5470i	−1.24291	−	0.597980i
$963$	−1.24047	−	0.957985i	−0.0399736	−	0.0308706i
$964$	−21.6472	−	27.1030i	−0.697209	−	0.872929i
$965$			6.49354i			0.209035i
$966$	−17.8532	+	18.1473i	−0.574416	+	0.583881i
$967$		−	28.4122i		−	0.913676i	−0.889550	−	0.456838i	$-0.848982\pi$
$967$		−	28.4122i		−	0.913676i	0.889550	−	0.456838i	$-0.151018\pi$
$968$	5.13858	+	22.3975i	0.165160	+	0.719882i
$969$	−4.76705	−	1.62646i	−0.153140	−	0.0522495i
$970$	2.08653	−	4.33688i	0.0669945	−	0.139249i
$971$	−24.4514			−0.784684			−0.392342	−	0.919819i	$-0.628335\pi$
$971$	−24.4514			−0.784684			−0.392342	+	0.919819i	$0.628335\pi$
$972$	25.7186	−	17.6226i	0.824924	−	0.565244i
$973$	−48.9010			−1.56769
$974$	−1.45959	+	3.03378i	−0.0467683	+	0.0972085i
$975$	35.4003	+	12.0782i	1.13372	+	0.386811i
$976$	3.03935	−	13.4089i	0.0972871	−	0.429208i
$977$		−	14.7929i		−	0.473267i	−0.971599	−	0.236633i	$-0.923956\pi$
$977$		−	14.7929i		−	0.473267i	0.971599	−	0.236633i	$-0.0760440\pi$
$978$	−1.83646	+	1.86672i	−0.0587235	+	0.0596911i
$979$		−	9.51266i		−	0.304026i
$980$	−1.03837	+	0.829344i	−0.0331694	+	0.0264924i
$981$	−25.2532	−	19.5024i	−0.806271	−	0.622664i
$982$	6.04189	+	2.90683i	0.192805	+	0.0927608i
$983$	−22.8355			−0.728340			−0.364170	−	0.931332i	$-0.618647\pi$
$983$	−22.8355			−0.728340			−0.364170	+	0.931332i	$0.618647\pi$
$984$	4.55524	+	0.472141i	0.145216	+	0.0150513i
$985$	2.48101			0.0790517
$986$	−7.75883	−	3.73288i	−0.247092	−	0.118879i
$987$	−19.5782	+	57.3825i	−0.623181	+	1.82650i
$988$	−10.0454	+	8.02327i	−0.319587	+	0.255254i
$989$		−	7.95745i		−	0.253032i
$990$	2.25726	−	1.13179i	0.0717405	−	0.0359706i
$991$			16.4157i			0.521462i	0.965411	+	0.260731i	$0.0839636\pi$
$991$			16.4157i			0.521462i	−0.965411	+	0.260731i	$0.916036\pi$
$992$	−46.9073	−	37.2637i	−1.48931	−	1.18312i
$993$	6.98077	−	20.4602i	0.221528	−	0.649284i
$994$	25.6371	−	53.2872i	0.813161	−	1.69017i
$995$	−4.75576			−0.150768
$996$	7.77113	+	21.6143i	0.246238	+	0.684876i
$997$	11.0803			0.350916			0.175458	−	0.984487i	$-0.443859\pi$
$997$	11.0803			0.350916			0.175458	+	0.984487i	$0.443859\pi$
$998$	15.1401	−	31.4689i	0.479251	−	0.996130i
$999$	19.5829	+	29.6057i	0.619577	+	0.936684i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.c.b.671.19	✓	128
3.2	odd	2	inner	804.2.c.b.671.110	yes	128
4.3	odd	2	inner	804.2.c.b.671.109	yes	128
12.11	even	2	inner	804.2.c.b.671.20	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.c.b.671.19	✓	128	1.1	even	1	trivial
804.2.c.b.671.20	yes	128	12.11	even	2	inner
804.2.c.b.671.109	yes	128	4.3	odd	2	inner
804.2.c.b.671.110	yes	128	3.2	odd	2	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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.27439 - 0.613127i) q^{2} +(-1.63926 - 0.559297i) q^{3} +(1.24815 + 1.56273i) q^{4} -0.350980i q^{5} +(1.74615 + 1.71784i) q^{6} +2.98214i q^{7} +(-0.632485 - 2.75680i) q^{8} +(2.37437 + 1.83367i) q^{9} +O(q^{10})\)	\(q+(-1.27439 - 0.613127i) q^{2} +(-1.63926 - 0.559297i) q^{3} +(1.24815 + 1.56273i) q^{4} -0.350980i q^{5} +(1.74615 + 1.71784i) q^{6} +2.98214i q^{7} +(-0.632485 - 2.75680i) q^{8} +(2.37437 + 1.83367i) q^{9} +(-0.215195 + 0.447286i) q^{10} -1.69575 q^{11} +(-1.17202 - 3.25981i) q^{12} -4.42815 q^{13} +(1.82843 - 3.80041i) q^{14} +(-0.196302 + 0.575349i) q^{15} +(-0.884236 + 3.90104i) q^{16} +2.00327i q^{17} +(-1.90161 - 3.79261i) q^{18} -1.45165i q^{19} +(0.548486 - 0.438076i) q^{20} +(1.66790 - 4.88851i) q^{21} +(2.16105 + 1.03971i) q^{22} +3.48501 q^{23} +(-0.505063 + 4.87288i) q^{24} +4.87681 q^{25} +(5.64319 + 2.71501i) q^{26} +(-2.86666 - 4.33385i) q^{27} +(-4.66027 + 3.72216i) q^{28} -3.03917i q^{29} +(0.602928 - 0.612862i) q^{30} -10.5902i q^{31} +(3.51870 - 4.42931i) q^{32} +(2.77978 + 0.948428i) q^{33} +(1.22826 - 2.55295i) q^{34} +1.04667 q^{35} +(0.0980481 + 5.99920i) q^{36} -6.83128 q^{37} +(-0.890047 + 1.84997i) q^{38} +(7.25890 + 2.47665i) q^{39} +(-0.967583 + 0.221989i) q^{40} -0.934816i q^{41} +(-5.12284 + 5.20725i) q^{42} -2.28333i q^{43} +(-2.11655 - 2.65000i) q^{44} +(0.643582 - 0.833358i) q^{45} +(-4.44127 - 2.13675i) q^{46} -11.7382 q^{47} +(3.63134 - 5.90029i) q^{48} -1.89315 q^{49} +(-6.21497 - 2.99010i) q^{50} +(1.12042 - 3.28388i) q^{51} +(-5.52700 - 6.91999i) q^{52} +1.53931i q^{53} +(0.996046 + 7.28065i) q^{54} +0.595174i q^{55} +(8.22117 - 1.88616i) q^{56} +(-0.811905 + 2.37964i) q^{57} +(-1.86339 + 3.87309i) q^{58} -14.8437 q^{59} +(-1.14413 + 0.411356i) q^{60} -3.43726 q^{61} +(-6.49314 + 13.4961i) q^{62} +(-5.46826 + 7.08071i) q^{63} +(-7.19993 + 3.48727i) q^{64} +1.55419i q^{65} +(-2.96103 - 2.91303i) q^{66} +1.00000i q^{67} +(-3.13056 + 2.50038i) q^{68} +(-5.71286 - 1.94916i) q^{69} +(-1.33387 - 0.641742i) q^{70} +14.0214 q^{71} +(3.55332 - 7.70545i) q^{72} -5.28996 q^{73} +(8.70573 + 4.18844i) q^{74} +(-7.99438 - 2.72759i) q^{75} +(2.26854 - 1.81188i) q^{76} -5.05696i q^{77} +(-7.73219 - 7.60685i) q^{78} -16.7488i q^{79} +(1.36919 + 0.310349i) q^{80} +(2.27530 + 8.70764i) q^{81} +(-0.573160 + 1.19132i) q^{82} -6.63054 q^{83} +(9.72121 - 3.49513i) q^{84} +0.703107 q^{85} +(-1.39997 + 2.90986i) q^{86} +(-1.69980 + 4.98200i) q^{87} +(1.07254 + 4.67485i) q^{88} +5.60971i q^{89} +(-1.33113 + 0.667427i) q^{90} -13.2053i q^{91} +(4.34982 + 5.44613i) q^{92} +(-5.92307 + 17.3601i) q^{93} +(14.9591 + 7.19702i) q^{94} -0.509501 q^{95} +(-8.24537 + 5.29281i) q^{96} -9.69599 q^{97} +(2.41261 + 1.16074i) q^{98} +(-4.02634 - 3.10945i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 4 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) \) 128 * q + 4 * q^4 - 6 * q^6 - 4 * q^9	\( 128 q + 4 q^{4} - 6 q^{6} - 4 q^{9} - 4 q^{10} + 4 q^{12} - 8 q^{13} - 4 q^{16} + 18 q^{18} - 8 q^{21} - 8 q^{22} - 24 q^{24} - 136 q^{25} + 14 q^{30} - 32 q^{33} + 34 q^{36} - 48 q^{37} + 16 q^{40} - 28 q^{42} - 16 q^{45} - 28 q^{46} - 22 q^{48} - 152 q^{49} + 8 q^{52} - 16 q^{54} - 32 q^{57} - 20 q^{58} - 14 q^{60} + 8 q^{61} + 16 q^{64} + 14 q^{66} + 56 q^{69} - 4 q^{70} - 8 q^{72} - 48 q^{73} - 36 q^{76} + 40 q^{78} + 44 q^{81} + 60 q^{82} + 46 q^{84} + 64 q^{85} - 28 q^{88} - 14 q^{90} + 32 q^{93} - 8 q^{96} + 64 q^{97}+O(q^{100}) \) 128 * q + 4 * q^4 - 6 * q^6 - 4 * q^9 - 4 * q^10 + 4 * q^12 - 8 * q^13 - 4 * q^16 + 18 * q^18 - 8 * q^21 - 8 * q^22 - 24 * q^24 - 136 * q^25 + 14 * q^30 - 32 * q^33 + 34 * q^36 - 48 * q^37 + 16 * q^40 - 28 * q^42 - 16 * q^45 - 28 * q^46 - 22 * q^48 - 152 * q^49 + 8 * q^52 - 16 * q^54 - 32 * q^57 - 20 * q^58 - 14 * q^60 + 8 * q^61 + 16 * q^64 + 14 * q^66 + 56 * q^69 - 4 * q^70 - 8 * q^72 - 48 * q^73 - 36 * q^76 + 40 * q^78 + 44 * q^81 + 60 * q^82 + 46 * q^84 + 64 * q^85 - 28 * q^88 - 14 * q^90 + 32 * q^93 - 8 * q^96 + 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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