LMFDB - Embedded newform 800.2.ba.d.749.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [800,2,Mod(149,800)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(800, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 5, 4]))

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

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

chi := DirichletCharacter("800.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 800 = 2^{5} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	800.ba (of order $8$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.38803216170$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{8})$
Coefficient field:	8.0.18939904.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 $ x^8 - 4x^7 + 14x^6 - 28x^5 + 43x^4 - 44x^3 + 30x^2 - 12*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			749.1
Root			$0.500000 + 0.691860i$ of defining polynomial
Character	$\chi$	$=$	800.749
Dual form			800.2.ba.d.549.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.635665 - 1.26330i) q^{2} +(2.60607 + 1.07947i) q^{3} +(-1.19186 + 1.60607i) q^{4} +(-0.292893 - 3.97844i) q^{6} +(1.68554 + 1.68554i) q^{7} +(2.78658 + 0.484753i) q^{8} +(3.50504 + 3.50504i) q^{9} +O(q^{10})$	\(q+(-0.635665 - 1.26330i) q^{2} +(2.60607 + 1.07947i) q^{3} +(-1.19186 + 1.60607i) q^{4} +(-0.292893 - 3.97844i) q^{6} +(1.68554 + 1.68554i) q^{7} +(2.78658 + 0.484753i) q^{8} +(3.50504 + 3.50504i) q^{9} +(-0.334743 - 0.808140i) q^{11} +(-4.83978 + 2.89897i) q^{12} +(0.451835 - 1.09083i) q^{13} +(1.05791 - 3.20079i) q^{14} +(-1.15894 - 3.82843i) q^{16} -0.224777 q^{17} +(2.19989 - 6.65595i) q^{18} +(2.87740 + 1.19186i) q^{19} +(2.57316 + 6.21215i) q^{21} +(-0.808140 + 0.936588i) q^{22} +(-3.68554 + 3.68554i) q^{23} +(6.73875 + 4.27133i) q^{24} +(-1.66526 + 0.122597i) q^{26} +(2.11239 + 5.09976i) q^{27} +(-4.71604 + 0.698175i) q^{28} +(-2.34610 + 5.66398i) q^{29} +6.82843 q^{31} +(-4.09976 + 3.89769i) q^{32} -2.46742i q^{33} +(0.142883 + 0.283962i) q^{34} +(-9.80686 + 1.45183i) q^{36} +(-4.09083 - 9.87613i) q^{37} +(-0.323388 - 4.39265i) q^{38} +(2.35503 - 2.35503i) q^{39} +(6.37109 + 6.37109i) q^{41} +(6.21215 - 7.19951i) q^{42} +(4.60607 - 1.90790i) q^{43} +(1.69690 + 0.425569i) q^{44} +(6.99872 + 2.31318i) q^{46} -0.542661 q^{47} +(1.11239 - 11.2282i) q^{48} -1.31788i q^{49} +(-0.585786 - 0.242641i) q^{51} +(1.21342 + 2.02579i) q^{52} +(-9.46191 + 3.91925i) q^{53} +(5.09976 - 5.91032i) q^{54} +(3.87983 + 5.51397i) q^{56} +(6.21215 + 6.21215i) q^{57} +(8.64665 - 0.636568i) q^{58} +(3.36524 - 1.39393i) q^{59} +(0.398630 - 0.962379i) q^{61} +(-4.34059 - 8.62636i) q^{62} +11.8158i q^{63} +(7.53003 + 2.70160i) q^{64} +(-3.11709 + 1.56845i) q^{66} +(3.57558 + 1.48105i) q^{67} +(0.267903 - 0.361009i) q^{68} +(-13.5832 + 5.62636i) q^{69} +(-5.39978 + 5.39978i) q^{71} +(8.06799 + 11.4661i) q^{72} +(-5.15894 + 5.15894i) q^{73} +(-9.87613 + 11.4459i) q^{74} +(-5.34367 + 3.20079i) q^{76} +(0.797933 - 1.92638i) q^{77} +(-4.47212 - 1.47810i) q^{78} -8.39218i q^{79} +0.699980i q^{81} +(3.99872 - 12.0985i) q^{82} +(4.64665 - 11.2180i) q^{83} +(-13.0440 - 3.27133i) q^{84} +(-5.33817 - 4.60607i) q^{86} +(-12.2282 + 12.2282i) q^{87} +(-0.541038 - 2.41421i) q^{88} +(5.92638 - 5.92638i) q^{89} +(2.60022 - 1.07705i) q^{91} +(-1.52660 - 10.3119i) q^{92} +(17.7954 + 7.37109i) q^{93} +(0.344951 + 0.685544i) q^{94} +(-14.8917 + 5.73210i) q^{96} -4.19951i q^{97} +(-1.66488 + 0.837733i) q^{98} +(1.65928 - 4.00585i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} - 4 q^{4} - 8 q^{6} - 8 q^{7} + 12 q^{8}+O(q^{10}) $ 8 * q + 4 * q^3 - 4 * q^4 - 8 * q^6 - 8 * q^7 + 12 * q^8	$ 8 q + 4 q^{3} - 4 q^{4} - 8 q^{6} - 8 q^{7} + 12 q^{8} + 4 q^{11} - 4 q^{12} - 12 q^{14} + 8 q^{18} - 4 q^{19} - 12 q^{22} - 8 q^{23} + 8 q^{24} - 20 q^{26} + 16 q^{27} - 16 q^{28} + 32 q^{31} - 40 q^{36} - 16 q^{37} - 8 q^{38} - 16 q^{39} + 8 q^{41} + 16 q^{42} + 20 q^{43} - 20 q^{44} + 12 q^{46} + 16 q^{47} + 8 q^{48} - 16 q^{51} + 20 q^{52} - 16 q^{53} + 8 q^{54} + 8 q^{56} + 16 q^{57} - 4 q^{58} + 20 q^{59} + 24 q^{61} + 8 q^{62} + 8 q^{64} - 28 q^{66} + 12 q^{67} + 32 q^{68} - 32 q^{69} - 24 q^{71} - 12 q^{72} - 32 q^{73} - 8 q^{74} - 20 q^{76} - 16 q^{77} - 4 q^{78} - 12 q^{82} - 36 q^{83} - 8 q^{84} + 4 q^{86} - 56 q^{87} + 16 q^{89} + 40 q^{91} + 32 q^{93} + 24 q^{94} - 16 q^{96} + 36 q^{98} - 28 q^{99}+O(q^{100}) $ 8 * q + 4 * q^3 - 4 * q^4 - 8 * q^6 - 8 * q^7 + 12 * q^8 + 4 * q^11 - 4 * q^12 - 12 * q^14 + 8 * q^18 - 4 * q^19 - 12 * q^22 - 8 * q^23 + 8 * q^24 - 20 * q^26 + 16 * q^27 - 16 * q^28 + 32 * q^31 - 40 * q^36 - 16 * q^37 - 8 * q^38 - 16 * q^39 + 8 * q^41 + 16 * q^42 + 20 * q^43 - 20 * q^44 + 12 * q^46 + 16 * q^47 + 8 * q^48 - 16 * q^51 + 20 * q^52 - 16 * q^53 + 8 * q^54 + 8 * q^56 + 16 * q^57 - 4 * q^58 + 20 * q^59 + 24 * q^61 + 8 * q^62 + 8 * q^64 - 28 * q^66 + 12 * q^67 + 32 * q^68 - 32 * q^69 - 24 * q^71 - 12 * q^72 - 32 * q^73 - 8 * q^74 - 20 * q^76 - 16 * q^77 - 4 * q^78 - 12 * q^82 - 36 * q^83 - 8 * q^84 + 4 * q^86 - 56 * q^87 + 16 * q^89 + 40 * q^91 + 32 * q^93 + 24 * q^94 - 16 * q^96 + 36 * q^98 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/800\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$577$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$-1$

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 $

$2$	−0.635665	−	1.26330i	−0.449483	−	0.893289i
$2$	−0.635665	−	1.26330i	−0.449483	−	0.893289i
$3$	2.60607	+	1.07947i	1.50462	+	0.623233i	0.974439	−	0.224653i	$-0.0721250\pi$
$3$	2.60607	+	1.07947i	1.50462	+	0.623233i	0.530178	+	0.847886i	$0.322125\pi$
$4$	−1.19186	+	1.60607i	−0.595930	+	0.803037i
$5$		0			0
$5$		0			0
$6$	−0.292893	−	3.97844i	−0.119573	−	1.62419i
$7$	1.68554	+	1.68554i	0.637076	+	0.637076i	0.949833	−	0.312757i	$-0.101253\pi$
$7$	1.68554	+	1.68554i	0.637076	+	0.637076i	−0.312757	+	0.949833i	$0.601253\pi$
$8$	2.78658	+	0.484753i	0.985204	+	0.171386i
$9$	3.50504	+	3.50504i	1.16835	+	1.16835i
$10$		0			0
$11$	−0.334743	−	0.808140i	−0.100929	−	0.243664i	0.865347	−	0.501173i	$-0.167098\pi$
$11$	−0.334743	−	0.808140i	−0.100929	−	0.243664i	−0.966276	+	0.257510i	$0.917098\pi$
$12$	−4.83978	+	2.89897i	−1.39712	+	0.836859i
$13$	0.451835	−	1.09083i	0.125316	−	0.302541i	−0.848753	−	0.528789i	$-0.822646\pi$
$13$	0.451835	−	1.09083i	0.125316	−	0.302541i	0.974070	+	0.226249i	$0.0726462\pi$
$14$	1.05791	−	3.20079i	0.282738	−	0.855447i
$15$		0			0
$16$	−1.15894	−	3.82843i	−0.289735	−	0.957107i
$17$	−0.224777			−0.0545165			−0.0272583	−	0.999628i	$-0.508678\pi$
$17$	−0.224777			−0.0545165			−0.0272583	+	0.999628i	$0.508678\pi$
$18$	2.19989	−	6.65595i	0.518519	−	1.56882i
$19$	2.87740	+	1.19186i	0.660122	+	0.273431i	0.687490	−	0.726194i	$-0.258713\pi$
$19$	2.87740	+	1.19186i	0.660122	+	0.273431i	−0.0273681	+	0.999625i	$0.508713\pi$
$20$		0			0
$21$	2.57316	+	6.21215i	0.561509	+	1.35560i
$22$	−0.808140	+	0.936588i	−0.172296	+	0.199681i
$23$	−3.68554	+	3.68554i	−0.768489	+	0.768489i	−0.977840	−	0.209351i	$-0.932865\pi$
$23$	−3.68554	+	3.68554i	−0.768489	+	0.768489i	0.209351	+	0.977840i	$0.432865\pi$
$24$	6.73875	+	4.27133i	1.37554	+	0.871882i
$25$		0			0
$26$	−1.66526	+	0.122597i	−0.326584	+	0.0240432i
$27$	2.11239	+	5.09976i	0.406529	+	0.981449i
$28$	−4.71604	+	0.698175i	−0.891247	+	0.131943i
$29$	−2.34610	+	5.66398i	−0.435659	+	1.05177i	0.541773	+	0.840525i	$0.317753\pi$
$29$	−2.34610	+	5.66398i	−0.435659	+	1.05177i	−0.977432	+	0.211250i	$0.932247\pi$
$30$		0			0
$31$	6.82843			1.22642			0.613211	−	0.789919i	$-0.289878\pi$
$31$	6.82843			1.22642			0.613211	+	0.789919i	$0.289878\pi$
$32$	−4.09976	+	3.89769i	−0.724742	+	0.689021i
$33$		−	2.46742i		−	0.429522i
$34$	0.142883	+	0.283962i	0.0245043	+	0.0486990i
$35$		0			0
$36$	−9.80686	+	1.45183i	−1.63448	+	0.241972i
$37$	−4.09083	−	9.87613i	−0.672528	−	1.62363i	−0.777301	−	0.629129i	$-0.783412\pi$
$37$	−4.09083	−	9.87613i	−0.672528	−	1.62363i	0.104773	−	0.994496i	$-0.466588\pi$
$38$	−0.323388	−	4.39265i	−0.0524604	−	0.712582i
$39$	2.35503	−	2.35503i	0.377107	−	0.377107i
$40$		0			0
$41$	6.37109	+	6.37109i	0.994997	+	0.994997i	0.999988	−	0.00499079i	$-0.00158862\pi$
$41$	6.37109	+	6.37109i	0.994997	+	0.994997i	−0.00499079	+	0.999988i	$0.501589\pi$
$42$	6.21215	−	7.19951i	0.958555	−	1.11091i
$43$	4.60607	−	1.90790i	0.702420	−	0.290952i	−0.00274415	−	0.999996i	$-0.500873\pi$
$43$	4.60607	−	1.90790i	0.702420	−	0.290952i	0.705164	+	0.709045i	$0.250873\pi$
$44$	1.69690	+	0.425569i	0.255817	+	0.0641569i
$45$		0			0
$46$	6.99872	+	2.31318i	1.03191	+	0.341060i
$47$	−0.542661			−0.0791552			−0.0395776	−	0.999216i	$-0.512601\pi$
$47$	−0.542661			−0.0791552			−0.0395776	+	0.999216i	$0.512601\pi$
$48$	1.11239	−	11.2282i	0.160559	−	1.62065i
$49$		−	1.31788i		−	0.188269i
$50$		0			0
$51$	−0.585786	−	0.242641i	−0.0820265	−	0.0339765i
$52$	1.21342	+	2.02579i	0.168271	+	0.280927i
$53$	−9.46191	+	3.91925i	−1.29969	+	0.538351i	−0.921860	−	0.387523i	$-0.873331\pi$
$53$	−9.46191	+	3.91925i	−1.29969	+	0.538351i	−0.377834	+	0.925873i	$0.623331\pi$
$54$	5.09976	−	5.91032i	0.693989	−	0.804293i
$55$		0			0
$56$	3.87983	+	5.51397i	0.518464	+	0.736835i
$57$	6.21215	+	6.21215i	0.822819	+	0.822819i
$58$	8.64665	−	0.636568i	1.13536	−	0.0835854i
$59$	3.36524	−	1.39393i	0.438117	−	0.181474i	−0.152712	−	0.988271i	$-0.548801\pi$
$59$	3.36524	−	1.39393i	0.438117	−	0.181474i	0.590829	+	0.806797i	$0.298801\pi$
$60$		0			0
$61$	0.398630	−	0.962379i	0.0510394	−	0.123220i	−0.896303	−	0.443442i	$-0.853757\pi$
$61$	0.398630	−	0.962379i	0.0510394	−	0.123220i	0.947343	+	0.320222i	$0.103757\pi$
$62$	−4.34059	−	8.62636i	−0.551256	−	1.09555i
$63$			11.8158i			1.48865i
$64$	7.53003	+	2.70160i	0.941254	+	0.337700i
$65$		0			0
$66$	−3.11709	+	1.56845i	−0.383688	+	0.193063i
$67$	3.57558	+	1.48105i	0.436826	+	0.180939i	0.590249	−	0.807221i	$-0.299030\pi$
$67$	3.57558	+	1.48105i	0.436826	+	0.180939i	−0.153423	+	0.988161i	$0.549030\pi$
$68$	0.267903	−	0.361009i	0.0324880	−	0.0437788i
$69$	−13.5832	+	5.62636i	−1.63523	+	0.677334i
$70$		0			0
$71$	−5.39978	+	5.39978i	−0.640836	+	0.640836i	−0.950761	−	0.309925i	$-0.899696\pi$
$71$	−5.39978	+	5.39978i	−0.640836	+	0.640836i	0.309925	+	0.950761i	$0.399696\pi$
$72$	8.06799	+	11.4661i	0.950821	+	1.35130i
$73$	−5.15894	+	5.15894i	−0.603808	+	0.603808i	−0.941321	−	0.337513i	$-0.890414\pi$
$73$	−5.15894	+	5.15894i	−0.603808	+	0.603808i	0.337513	+	0.941321i	$0.390414\pi$
$74$	−9.87613	+	11.4459i	−1.14808	+	1.33055i
$75$		0			0
$76$	−5.34367	+	3.20079i	−0.612961	+	0.367156i
$77$	0.797933	−	1.92638i	0.0909329	−	0.219531i
$78$	−4.47212	−	1.47810i	−0.506368	−	0.167362i
$79$		−	8.39218i		−	0.944194i	−0.881547	−	0.472097i	$-0.843497\pi$
$79$		−	8.39218i		−	0.944194i	0.881547	−	0.472097i	$-0.156503\pi$
$80$		0			0
$81$			0.699980i			0.0777755i
$82$	3.99872	−	12.0985i	0.441585	−	1.33605i
$83$	4.64665	−	11.2180i	0.510036	−	1.23134i	−0.433827	−	0.900996i	$-0.642837\pi$
$83$	4.64665	−	11.2180i	0.510036	−	1.23134i	0.943862	−	0.330339i	$-0.107163\pi$
$84$	−13.0440	−	3.27133i	−1.42322	−	0.356931i
$85$		0			0
$86$	−5.33817	−	4.60607i	−0.575630	−	0.496686i
$87$	−12.2282	+	12.2282i	−1.31100	+	1.31100i
$88$	−0.541038	−	2.41421i	−0.0576749	−	0.257356i
$89$	5.92638	−	5.92638i	0.628195	−	0.628195i	−0.319419	−	0.947614i	$-0.603488\pi$
$89$	5.92638	−	5.92638i	0.628195	−	0.628195i	0.947614	+	0.319419i	$0.103488\pi$
$90$		0			0
$91$	2.60022	−	1.07705i	0.272577	−	0.112905i
$92$	−1.52660	−	10.3119i	−0.159159	−	1.07509i
$93$	17.7954	+	7.37109i	1.84529	+	0.764346i
$94$	0.344951	+	0.685544i	0.0355789	+	0.0707085i
$95$		0			0
$96$	−14.8917	+	5.73210i	−1.51988	+	0.585030i
$97$		−	4.19951i		−	0.426396i	−0.977009	−	0.213198i	$-0.931612\pi$
$97$		−	4.19951i		−	0.426396i	0.977009	−	0.213198i	$-0.0683880\pi$
$98$	−1.66488	+	0.837733i	−0.168179	+	0.0846238i
$99$	1.65928	−	4.00585i	0.166764	−	0.402603i
$100$		0			0
$101$	4.46191	−	1.84819i	0.443977	−	0.183901i	−0.149484	−	0.988764i	$-0.547761\pi$
$101$	4.46191	−	1.84819i	0.443977	−	0.183901i	0.593461	+	0.804863i	$0.297761\pi$
$102$	0.0658358	+	0.894263i	0.00651871	+	0.0885452i
$103$	−10.9635	−	10.9635i	−1.08027	−	1.08027i	−0.996484	−	0.0837844i	$-0.973299\pi$
$103$	−10.9635	−	10.9635i	−1.08027	−	1.08027i	−0.0837844	−	0.996484i	$-0.526701\pi$
$104$	1.78785	−	2.82064i	0.175313	−	0.276587i
$105$		0			0
$106$	10.9658	+	9.46191i	1.06509	+	0.919022i
$107$	−8.08128	+	3.34737i	−0.781246	+	0.323603i	−0.737418	−	0.675436i	$-0.763955\pi$
$107$	−8.08128	+	3.34737i	−0.781246	+	0.323603i	−0.0438280	+	0.999039i	$0.513955\pi$
$108$	−10.7083	−	2.68554i	−1.03040	−	0.258417i
$109$	−8.62086	−	3.57088i	−0.825728	−	0.342028i	−0.0705180	−	0.997511i	$-0.522465\pi$
$109$	−8.62086	−	3.57088i	−0.825728	−	0.342028i	−0.755210	+	0.655483i	$0.772465\pi$
$110$		0			0
$111$		−	30.1538i		−	2.86208i
$112$	4.49954	−	8.40643i	0.425166	−	0.794333i
$113$	−2.42429			−0.228058			−0.114029	−	0.993477i	$-0.536376\pi$
$113$	−2.42429			−0.228058			−0.114029	+	0.993477i	$0.536376\pi$
$114$	3.89897	−	11.7967i	0.365172	−	1.10486i
$115$		0			0
$116$	−6.30055	−	10.5187i	−0.584991	−	0.976634i
$117$	5.40709	−	2.23969i	0.499885	−	0.207059i
$118$	−3.90011	−	3.36524i	−0.359035	−	0.309795i
$119$	−0.378872	−	0.378872i	−0.0347312	−	0.0347312i
$120$		0			0
$121$	7.23714	−	7.23714i	0.657921	−	0.657921i
$122$	−1.46917	+	0.108161i	−0.133012	+	0.00979239i
$123$	9.72612	+	23.4809i	0.876974	+	2.11720i
$124$	−8.13853	+	10.9670i	−0.730861	+	0.984861i
$125$		0			0
$126$	14.9269	−	7.51089i	1.32979	−	0.669123i
$127$		−	2.19266i		−	0.194567i	−0.995257	−	0.0972836i	$-0.968985\pi$
$127$		−	2.19266i		−	0.194567i	0.995257	−	0.0972836i	$-0.0310154\pi$
$128$	−1.37364	−	11.2300i	−0.121414	−	0.992602i
$129$	14.0633			1.23820
$130$		0			0
$131$	3.16317	−	7.63657i	0.276367	−	0.667210i	−0.723362	−	0.690469i	$-0.757404\pi$
$131$	3.16317	−	7.63657i	0.276367	−	0.667210i	0.999729	+	0.0232589i	$0.00740422\pi$
$132$	3.96285	+	2.94082i	0.344922	+	0.255965i
$133$	2.84106	+	6.85892i	0.246351	+	0.594744i
$134$	−0.401855	−	5.45849i	−0.0347150	−	0.471541i
$135$		0			0
$136$	−0.626360	−	0.108961i	−0.0537099	−	0.00934337i
$137$	−7.76744	+	7.76744i	−0.663617	+	0.663617i	−0.956231	−	0.292614i	$-0.905475\pi$
$137$	−7.76744	+	7.76744i	−0.663617	+	0.663617i	0.292614	+	0.956231i	$0.405475\pi$
$138$	15.7422	+	13.5832i	1.34006	+	1.15628i
$139$	−0.357453	−	0.862967i	−0.0303188	−	0.0731959i	0.907995	−	0.418981i	$-0.137613\pi$
$139$	−0.357453	−	0.862967i	−0.0303188	−	0.0731959i	−0.938314	+	0.345785i	$0.887613\pi$
$140$		0			0
$141$	−1.41421	−	0.585786i	−0.119098	−	0.0493321i
$142$	10.2540	+	3.38909i	0.860496	+	0.284406i
$143$	−1.03279			−0.0863662
$144$	9.35665	−	17.4809i	0.779721	−	1.45674i
$145$		0			0
$146$	9.79666	+	3.23794i	0.810777	+	0.267974i
$147$	1.42262	−	3.43450i	0.117335	−	0.283273i
$148$	20.7375	+	5.20079i	1.70461	+	0.427502i
$149$	−2.34610	−	5.66398i	−0.192200	−	0.464011i	0.798175	−	0.602426i	$-0.205799\pi$
$149$	−2.34610	−	5.66398i	−0.192200	−	0.464011i	−0.990374	+	0.138415i	$0.955799\pi$
$150$		0			0
$151$	−8.17083	−	8.17083i	−0.664932	−	0.664932i	0.291606	−	0.956538i	$-0.405810\pi$
$151$	−8.17083	−	8.17083i	−0.664932	−	0.664932i	−0.956538	+	0.291606i	$0.905810\pi$
$152$	7.44035	+	4.71604i	0.603492	+	0.382521i
$153$	−0.787854	−	0.787854i	−0.0636942	−	0.0636942i
$154$	−2.94082	+	0.216503i	−0.236978	+	0.0174463i
$155$		0			0
$156$	0.975485	+	6.58921i	0.0781013	+	0.527559i
$157$	11.7908	+	4.88391i	0.941009	+	0.389779i	0.799844	−	0.600208i	$-0.204915\pi$
$157$	11.7908	+	4.88391i	0.941009	+	0.389779i	0.141164	+	0.989986i	$0.454915\pi$
$158$	−10.6018	+	5.33461i	−0.843437	+	0.424399i
$159$	−28.8892			−2.29106
$160$		0			0
$161$	−12.4243			−0.979171
$162$	0.884285	−	0.444953i	0.0694760	−	0.0349588i
$163$	−1.81822	−	0.753131i	−0.142414	−	0.0589898i	0.310338	−	0.950626i	$-0.399558\pi$
$163$	−1.81822	−	0.753131i	−0.142414	−	0.0589898i	−0.452752	+	0.891636i	$0.649558\pi$
$164$	−17.8259	+	2.63899i	−1.39197	+	0.206071i
$165$		0			0
$166$	−17.1254	+	1.26078i	−1.32919	+	0.0978552i
$167$	−15.1630	−	15.1630i	−1.17335	−	1.17335i	−0.981406	−	0.191946i	$-0.938520\pi$
$167$	−15.1630	−	15.1630i	−1.17335	−	1.17335i	−0.191946	−	0.981406i	$-0.561480\pi$
$168$	4.15894	+	18.5580i	0.320869	+	1.43178i
$169$	8.20664	+	8.20664i	0.631280	+	0.631280i
$170$		0			0
$171$	5.90790	+	14.2629i	0.451788	+	1.09071i
$172$	−2.42557	+	9.67164i	−0.184948	+	0.737455i
$173$	1.88391	−	4.54817i	0.143231	−	0.345791i	−0.835942	−	0.548818i	$-0.815078\pi$
$173$	1.88391	−	4.54817i	0.143231	−	0.345791i	0.979173	+	0.203027i	$0.0650780\pi$
$174$	23.2209	+	7.67486i	1.76038	+	0.581830i
$175$		0			0
$176$	−2.70596	+	2.21813i	−0.203969	+	0.167198i
$177$	10.2748			0.772298
$178$	−11.2540	−	3.71961i	−0.843523	−	0.278796i
$179$	−7.27899	−	3.01505i	−0.544057	−	0.225356i	0.0936904	−	0.995601i	$-0.470134\pi$
$179$	−7.27899	−	3.01505i	−0.544057	−	0.225356i	−0.637747	+	0.770246i	$0.720134\pi$
$180$		0			0
$181$	6.12132	+	14.7782i	0.454994	+	1.09845i	0.970399	+	0.241506i	$0.0776415\pi$
$181$	6.12132	+	14.7782i	0.454994	+	1.09845i	−0.515405	+	0.856947i	$0.672359\pi$
$182$	−3.01351	−	2.60022i	−0.223376	−	0.192741i
$183$	2.07772	−	2.07772i	0.153589	−	0.153589i
$184$	−12.0566	+	8.48348i	−0.888827	+	0.625410i
$185$		0			0
$186$	−2.00000	−	27.1665i	−0.146647	−	1.99194i
$187$	0.0752426	+	0.181652i	0.00550228	+	0.0132837i
$188$	0.646775	−	0.871553i	0.0471709	−	0.0635645i
$189$	−5.03534	+	12.1564i	−0.366267	+	0.884247i
$190$		0			0
$191$	−15.4642			−1.11895			−0.559475	−	0.828847i	$-0.688997\pi$
$191$	−15.4642			−1.11895			−0.559475	+	0.828847i	$0.688997\pi$
$192$	16.7075	+	15.1690i	1.20576	+	1.09473i
$193$		−	13.2206i		−	0.951640i	−0.879543	−	0.475820i	$-0.842151\pi$
$193$		−	13.2206i		−	0.951640i	0.879543	−	0.475820i	$-0.157849\pi$
$194$	−5.30525	+	2.66949i	−0.380895	+	0.191658i
$195$		0			0
$196$	2.11662	+	1.57073i	0.151187	+	0.112195i
$197$	−0.249768	−	0.602992i	−0.0177952	−	0.0429614i	0.914732	−	0.404061i	$-0.132402\pi$
$197$	−0.249768	−	0.602992i	−0.0177952	−	0.0429614i	−0.932527	+	0.361099i	$0.882402\pi$
$198$	−6.11534	+	0.450212i	−0.434598	+	0.0319952i
$199$	1.86490	−	1.86490i	0.132199	−	0.132199i	−0.637911	−	0.770110i	$-0.720201\pi$
$199$	1.86490	−	1.86490i	0.132199	−	0.132199i	0.770110	+	0.637911i	$0.220201\pi$
$200$		0			0
$201$	7.71947	+	7.71947i	0.544489	+	0.544489i
$202$	−5.17110	−	4.46191i	−0.363837	−	0.313939i
$203$	−13.5013	+	5.59244i	−0.947608	+	0.392512i
$204$	1.08787	−	0.651622i	0.0761664	−	0.0456227i
$205$		0			0
$206$	−6.88110	+	20.8194i	−0.479429	+	1.45055i
$207$	−25.8360			−1.79572
$208$	−4.69980	−	0.465613i	−0.325872	−	0.0322845i
$209$		−	2.72431i		−	0.188445i
$210$		0			0
$211$	−19.0338	−	7.88406i	−1.31034	−	0.542761i	−0.385357	−	0.922768i	$-0.625922\pi$
$211$	−19.0338	−	7.88406i	−1.31034	−	0.542761i	−0.924984	+	0.380007i	$0.875922\pi$
$212$	4.98267	−	19.8677i	0.342211	−	1.36452i
$213$	−19.9011	+	8.24331i	−1.36360	+	0.564822i
$214$	9.36573	+	8.08128i	0.640228	+	0.552425i
$215$		0			0
$216$	3.41421	+	15.2349i	0.232308	+	1.03660i
$217$	11.5096	+	11.5096i	0.781324	+	0.781324i
$218$	0.968887	+	13.1606i	0.0656213	+	0.891349i
$219$	−19.0135	+	7.87565i	−1.28481	+	0.532187i
$220$		0			0
$221$	−0.101562	+	0.245193i	−0.00683182	+	0.0164935i
$222$	−38.0934	+	19.1677i	−2.55666	+	1.28645i
$223$			17.2119i			1.15259i	0.817241	+	0.576297i	$0.195503\pi$
$223$			17.2119i			1.15259i	−0.817241	+	0.576297i	$0.804497\pi$
$224$	−13.4800	−	0.340593i	−0.900674	−	0.0227569i
$225$		0			0
$226$	1.54104	+	3.06261i	0.102508	+	0.203722i
$227$	−1.52075	−	0.629916i	−0.100936	−	0.0418090i	0.331644	−	0.943405i	$-0.392397\pi$
$227$	−1.52075	−	0.629916i	−0.100936	−	0.0418090i	−0.432580	+	0.901596i	$0.642397\pi$
$228$	−17.3812	+	2.57316i	−1.15110	+	0.170411i
$229$	−2.45021	+	1.01491i	−0.161915	+	0.0670672i	−0.462169	−	0.886792i	$-0.652929\pi$
$229$	−2.45021	+	1.01491i	−0.161915	+	0.0670672i	0.300254	+	0.953859i	$0.402929\pi$
$230$		0			0
$231$	4.15894	−	4.15894i	0.273638	−	0.273638i
$232$	−9.28321	+	14.6458i	−0.609473	+	0.961547i
$233$	−10.9475	+	10.9475i	−0.717192	+	0.717192i	−0.968029	−	0.250837i	$-0.919294\pi$
$233$	−10.9475	+	10.9475i	−0.717192	+	0.717192i	0.250837	+	0.968029i	$0.419294\pi$
$234$	−6.26650	−	5.40709i	−0.409654	−	0.353472i
$235$		0			0
$236$	−1.77214	+	7.06618i	−0.115357	+	0.459969i
$237$	9.05911	−	21.8706i	0.588452	−	1.42065i
$238$	−0.237794	+	0.719466i	−0.0154139	+	0.0466360i
$239$			18.2858i			1.18281i	0.806375	+	0.591404i	$0.201426\pi$
$239$			18.2858i			1.18281i	−0.806375	+	0.591404i	$0.798574\pi$
$240$		0			0
$241$			27.8155i			1.79176i	0.444300	+	0.895878i	$0.353452\pi$
$241$			27.8155i			1.79176i	−0.444300	+	0.895878i	$0.646548\pi$
$242$	−13.7431	−	4.54229i	−0.883439	−	0.291989i
$243$	5.58156	−	13.4751i	0.358057	−	0.864426i
$244$	1.07054	+	1.78725i	0.0685342	+	0.114417i
$245$		0			0
$246$	23.4809	−	27.2130i	1.49709	−	1.73504i
$247$	2.60022	−	2.60022i	0.165448	−	0.165448i
$248$	19.0279	+	3.31010i	1.20828	+	0.210191i
$249$	24.2190	−	24.2190i	1.53482	−	1.53482i
$250$		0			0
$251$	9.37694	−	3.88406i	0.591867	−	0.245159i	−0.0665866	−	0.997781i	$-0.521211\pi$
$251$	9.37694	−	3.88406i	0.591867	−	0.245159i	0.658454	+	0.752621i	$0.271211\pi$
$252$	−18.9770	−	14.0828i	−1.19544	−	0.887131i
$253$	4.21215	+	1.74473i	0.264815	+	0.109690i
$254$	−2.76999	+	1.39380i	−0.173805	+	0.0874547i
$255$		0			0
$256$	−13.3137	+	8.87385i	−0.832107	+	0.554615i
$257$			20.0656i			1.25166i	0.779961	+	0.625828i	$0.215239\pi$
$257$			20.0656i			1.25166i	−0.779961	+	0.625828i	$0.784761\pi$
$258$	−8.93954	−	17.7662i	−0.556551	−	1.10607i
$259$	9.75138	−	23.5419i	0.605921	−	1.46282i
$260$		0			0
$261$	−28.0756	+	11.6293i	−1.73784	+	0.719836i
$262$	−11.6580	+	0.858264i	−0.720234	+	0.0530237i
$263$	−17.9782	−	17.9782i	−1.10858	−	1.10858i	−0.993337	−	0.115244i	$-0.963235\pi$
$263$	−17.9782	−	17.9782i	−1.10858	−	1.10858i	−0.115244	−	0.993337i	$-0.536765\pi$
$264$	1.19609	−	6.87565i	0.0736141	−	0.423167i
$265$		0			0
$266$	6.85892	−	7.94909i	0.420547	−	0.487390i
$267$	21.8419	−	9.04722i	1.33670	−	0.553681i
$268$	−6.64027	+	3.97743i	−0.405619	+	0.242960i
$269$	25.6598	+	10.6286i	1.56451	+	0.648040i	0.985865	−	0.167543i	$-0.0535832\pi$
$269$	25.6598	+	10.6286i	1.56451	+	0.648040i	0.578641	+	0.815582i	$0.303583\pi$
$270$		0			0
$271$			16.4921i			1.00183i	0.865498	+	0.500913i	$0.167002\pi$
$271$			16.4921i			1.00183i	−0.865498	+	0.500913i	$0.832998\pi$
$272$	0.260504	+	0.860544i	0.0157954	+	0.0521781i
$273$	7.93901			0.480491
$274$	14.7501	+	4.87512i	0.891086	+	0.294517i
$275$		0			0
$276$	7.15296	−	28.5215i	0.430558	−	1.71679i
$277$	5.60044	−	2.31978i	0.336498	−	0.139382i	−0.208035	−	0.978121i	$-0.566707\pi$
$277$	5.60044	−	2.31978i	0.336498	−	0.139382i	0.544533	+	0.838739i	$0.316707\pi$
$278$	−0.862967	+	1.00013i	−0.0517573	+	0.0599837i
$279$	23.9339	+	23.9339i	1.43289	+	1.43289i
$280$		0			0
$281$	9.80801	−	9.80801i	0.585097	−	0.585097i	−0.351203	−	0.936299i	$-0.614227\pi$
$281$	9.80801	−	9.80801i	0.585097	−	0.585097i	0.936299	+	0.351203i	$0.114227\pi$
$282$	0.158942	+	2.15894i	0.00946484	+	0.128563i
$283$	−8.84871	−	21.3627i	−0.526001	−	1.26988i	−0.934123	−	0.356952i	$-0.883816\pi$
$283$	−8.84871	−	21.3627i	−0.526001	−	1.26988i	0.408121	−	0.912928i	$-0.366184\pi$
$284$	−2.23666	−	15.1082i	−0.132721	−	0.896508i
$285$		0			0
$286$	0.656508	+	1.30472i	0.0388201	+	0.0771499i
$287$			21.4775i			1.26778i
$288$	−28.0314	−	0.708254i	−1.65176	−	0.0417343i
$289$	−16.9495			−0.997028
$290$		0			0
$291$	4.53325	−	10.9442i	0.265744	−	0.641563i
$292$	−2.13690	−	14.4344i	−0.125053	−	0.844708i
$293$	−8.46715	−	20.4415i	−0.494656	−	1.19421i	−0.952326	−	0.305083i	$-0.901316\pi$
$293$	−8.46715	−	20.4415i	−0.494656	−	1.19421i	0.457670	−	0.889122i	$-0.348684\pi$
$294$	−5.24312	+	0.385999i	−0.305785	+	0.0225119i
$295$		0			0
$296$	−6.61192	−	29.5036i	−0.384310	−	1.71486i
$297$	3.41421	−	3.41421i	0.198113	−	0.198113i
$298$	−5.66398	+	6.56422i	−0.328106	+	0.380255i
$299$	2.35503	+	5.68554i	0.136195	+	0.328803i
$300$		0			0
$301$	10.9796	+	4.54789i	0.632853	+	0.262136i
$302$	−5.12830	+	15.5161i	−0.295101	+	0.892852i
$303$	13.6231			0.782629
$304$	1.22820	−	12.3972i	0.0704424	−	0.711030i
$305$		0			0
$306$	−0.494485	+	1.49611i	−0.0282678	+	0.0855268i
$307$	6.46984	−	15.6196i	0.369253	−	0.891456i	−0.624620	−	0.780929i	$-0.714746\pi$
$307$	6.46984	−	15.6196i	0.369253	−	0.891456i	0.993873	−	0.110527i	$-0.0352540\pi$
$308$	2.14288	+	3.57751i	0.122102	+	0.203848i
$309$	−16.7369	−	40.4066i	−0.952131	−	2.29865i
$310$		0			0
$311$	7.24929	+	7.24929i	0.411070	+	0.411070i	0.882111	−	0.471041i	$-0.156122\pi$
$311$	7.24929	+	7.24929i	0.411070	+	0.411070i	−0.471041	+	0.882111i	$0.656122\pi$
$312$	7.70408	−	5.42087i	0.436158	−	0.306896i
$313$	10.1596	+	10.1596i	0.574255	+	0.574255i	0.933315	−	0.359059i	$-0.116902\pi$
$313$	10.1596	+	10.1596i	0.574255	+	0.574255i	−0.359059	+	0.933315i	$0.616902\pi$
$314$	−1.32515	−	17.9999i	−0.0747827	−	1.01579i
$315$		0			0
$316$	13.4784	+	10.0023i	0.758222	+	0.562673i
$317$	−3.24198	−	1.34287i	−0.182088	−	0.0754233i	0.289777	−	0.957094i	$-0.406419\pi$
$317$	−3.24198	−	1.34287i	−0.182088	−	0.0754233i	−0.471865	+	0.881671i	$0.656419\pi$
$318$	18.3638	+	36.4957i	1.02979	+	2.04658i
$319$	5.36263			0.300250
$320$		0			0
$321$	−24.6738			−1.37716
$322$	7.89769	+	15.6956i	0.440121	+	0.874683i
$323$	−0.646775	−	0.267903i	−0.0359875	−	0.0149065i
$324$	−1.12422	−	0.834278i	−0.0624566	−	0.0463488i
$325$		0			0
$326$	0.204347	+	2.77570i	0.0113178	+	0.153732i
$327$	−18.6119	−	18.6119i	−1.02924	−	1.02924i
$328$	14.6651	+	20.8419i	0.809746	+	1.15080i
$329$	−0.914679	−	0.914679i	−0.0504279	−	0.0504279i
$330$		0			0
$331$	6.43270	+	15.5299i	0.353573	+	0.853601i	0.996173	+	0.0873991i	$0.0278555\pi$
$331$	6.43270	+	15.5299i	0.353573	+	0.853601i	−0.642600	+	0.766201i	$0.722144\pi$
$332$	12.4788	+	20.8331i	0.684862	+	1.14337i
$333$	20.2777	−	48.9547i	1.11121	−	2.68270i
$334$	−9.51687	+	28.7941i	−0.520740	+	1.57554i
$335$		0			0
$336$	20.8006	−	17.0507i	1.13477	−	0.930189i
$337$	2.10641			0.114743			0.0573717	−	0.998353i	$-0.481728\pi$
$337$	2.10641			0.114743			0.0573717	+	0.998353i	$0.481728\pi$
$338$	5.15078	−	15.5841i	0.280166	−	0.847665i
$339$	−6.31788	−	2.61695i	−0.343140	−	0.142133i
$340$		0			0
$341$	−2.28577	−	5.51833i	−0.123781	−	0.298834i
$342$	14.2629	−	16.5299i	0.771251	−	0.893835i
$343$	14.0202	−	14.0202i	0.757017	−	0.757017i
$344$	13.7600	−	3.08370i	0.741892	−	0.166262i
$345$		0			0
$346$	−6.94324	+	0.511162i	−0.373271	+	0.0274803i
$347$	−5.13193	−	12.3896i	−0.275496	−	0.665107i	0.724204	−	0.689586i	$-0.242207\pi$
$347$	−5.13193	−	12.3896i	−0.275496	−	0.665107i	−0.999700	+	0.0244788i	$0.992207\pi$
$348$	−5.06509	−	34.2137i	−0.271517	−	1.83405i
$349$	−7.52453	+	18.1658i	−0.402779	+	0.972394i	0.584210	+	0.811603i	$0.301404\pi$
$349$	−7.52453	+	18.1658i	−0.402779	+	0.972394i	−0.986988	+	0.160791i	$0.948596\pi$
$350$		0			0
$351$	6.51740			0.347873
$352$	4.52225	+	2.00846i	0.241036	+	0.107051i
$353$			28.7013i			1.52762i	0.645442	+	0.763809i	$0.276673\pi$
$353$			28.7013i			1.52762i	−0.645442	+	0.763809i	$0.723327\pi$
$354$	−6.53131	−	12.9801i	−0.347135	−	0.689885i
$355$		0			0
$356$	2.45479	+	16.5816i	0.130103	+	0.878824i
$357$	−0.578387	−	1.39635i	−0.0306115	−	0.0739027i
$358$	0.818076	+	11.1121i	0.0432367	+	0.587294i
$359$	−6.39199	+	6.39199i	−0.337356	+	0.337356i	−0.855372	−	0.518015i	$-0.826671\pi$
$359$	−6.39199	+	6.39199i	−0.337356	+	0.337356i	0.518015	+	0.855372i	$0.326671\pi$
$360$		0			0
$361$	−6.57611	−	6.57611i	−0.346111	−	0.346111i
$362$	14.7782	−	17.1270i	0.776724	−	0.900177i
$363$	26.6728	−	11.0482i	1.39996	−	0.579882i
$364$	−1.36928	+	5.45984i	−0.0717699	+	0.286173i
$365$		0			0
$366$	−3.94552	−	1.30405i	−0.206236	−	0.0681639i
$367$	14.5985			0.762038			0.381019	−	0.924567i	$-0.375573\pi$
$367$	14.5985			0.762038			0.381019	+	0.924567i	$0.375573\pi$
$368$	18.3812	+	9.83851i	0.958185	+	0.512868i
$369$			44.6618i			2.32500i
$370$		0			0
$371$	−22.5545	−	9.34240i	−1.17097	−	0.485033i
$372$	−33.0481	+	19.7954i	−1.71346	+	1.02634i
$373$	−14.5761	+	6.03762i	−0.754722	+	0.312616i	−0.726667	−	0.686990i	$-0.758932\pi$
$373$	−14.5761	+	6.03762i	−0.754722	+	0.312616i	−0.0280555	+	0.999606i	$0.508932\pi$
$374$	0.181652	−	0.210524i	0.00939299	−	0.0108859i
$375$		0			0
$376$	−1.51217	−	0.263056i	−0.0779840	−	0.0135661i
$377$	5.11837	+	5.11837i	0.263609	+	0.263609i
$378$	18.5580	−	1.36624i	0.954519	−	0.0702719i
$379$	5.68312	−	2.35403i	0.291922	−	0.120918i	−0.231916	−	0.972736i	$-0.574500\pi$
$379$	5.68312	−	2.35403i	0.291922	−	0.120918i	0.523839	+	0.851818i	$0.324500\pi$
$380$		0			0
$381$	2.36691	−	5.71423i	0.121261	−	0.292749i
$382$	9.83005	+	19.5359i	0.502949	+	0.999545i
$383$		−	12.4633i		−	0.636843i	−0.947949	−	0.318422i	$-0.896847\pi$
$383$		−	12.4633i		−	0.636843i	0.947949	−	0.318422i	$-0.103153\pi$
$384$	8.54266	−	30.7490i	0.435941	−	1.56915i
$385$		0			0
$386$	−16.7016	+	8.40388i	−0.850089	+	0.427746i
$387$	22.8317	+	9.45721i	1.16060	+	0.480737i
$388$	6.74473	+	5.00523i	0.342412	+	0.254102i
$389$	14.1298	−	5.85275i	0.716408	−	0.296746i	0.00545476	−	0.999985i	$-0.498264\pi$
$389$	14.1298	−	5.85275i	0.716408	−	0.296746i	0.710953	+	0.703239i	$0.248264\pi$
$390$		0			0
$391$	0.828427	−	0.828427i	0.0418954	−	0.0418954i
$392$	0.638848	−	3.67238i	0.0322667	−	0.185483i
$393$	16.4869	−	16.4869i	0.831654	−	0.831654i
$394$	−0.602992	+	0.698833i	−0.0303783	+	0.0352067i
$395$		0			0
$396$	4.45606	+	7.43933i	0.223926	+	0.373841i
$397$	10.5929	−	25.5736i	0.531643	−	1.28350i	−0.398791	−	0.917042i	$-0.630570\pi$
$397$	10.5929	−	25.5736i	0.531643	−	1.28350i	0.930434	−	0.366458i	$-0.119430\pi$
$398$	−3.54138	−	1.17048i	−0.177514	−	0.0586708i
$399$			20.9417i			1.04840i
$400$		0			0
$401$		−	16.5018i		−	0.824062i	−0.911170	−	0.412031i	$-0.864820\pi$
$401$		−	16.5018i		−	0.824062i	0.911170	−	0.412031i	$-0.135180\pi$
$402$	4.84501	−	14.6590i	0.241647	−	0.731125i
$403$	3.08532	−	7.44862i	0.153691	−	0.371042i
$404$	−2.34965	+	9.36894i	−0.116900	+	0.466122i
$405$		0			0
$406$	15.6473	+	13.5013i	0.776561	+	0.670060i
$407$	−6.61192	+	6.61192i	−0.327741	+	0.327741i
$408$	−1.51472	−	0.960099i	−0.0749897	−	0.0475320i
$409$	−1.28577	+	1.28577i	−0.0635771	+	0.0635771i	−0.738180	−	0.674603i	$-0.764315\pi$
$409$	−1.28577	+	1.28577i	−0.0635771	+	0.0635771i	0.674603	+	0.738180i	$0.264315\pi$
$410$		0			0
$411$	−28.6272	+	11.8578i	−1.41208	+	0.584902i
$412$	30.6752	−	4.54124i	1.51126	−	0.223731i
$413$	8.02178	+	3.32273i	0.394726	+	0.163501i
$414$	16.4230	+	32.6386i	0.807147	+	1.60410i
$415$		0			0
$416$	2.39929	+	6.23323i	0.117635	+	0.305609i
$417$		−	2.63482i		−	0.129028i
$418$	−3.44163	+	1.73175i	−0.168335	+	0.0847027i
$419$	14.9887	−	36.1858i	0.732244	−	1.76779i	0.0972723	−	0.995258i	$-0.468988\pi$
$419$	14.9887	−	36.1858i	0.732244	−	1.76779i	0.634972	−	0.772535i	$-0.281012\pi$
$420$		0			0
$421$	13.6131	−	5.63872i	0.663460	−	0.274814i	−0.0254334	−	0.999677i	$-0.508097\pi$
$421$	13.6131	−	5.63872i	0.663460	−	0.274814i	0.688894	+	0.724862i	$0.258097\pi$
$422$	2.13918	+	29.0570i	0.104134	+	1.41447i
$423$	−1.90205	−	1.90205i	−0.0924807	−	0.0924807i
$424$	−28.2662	+	6.33461i	−1.37273	+	0.307636i
$425$		0			0
$426$	23.0642	+	19.9011i	1.11747	+	0.964212i
$427$	2.29404	−	0.950223i	0.111016	−	0.0459845i
$428$	4.25562	−	16.9687i	0.205703	−	0.820214i
$429$	−2.69152	−	1.11487i	−0.129948	−	0.0538262i
$430$		0			0
$431$			2.85730i			0.137631i	0.997629	+	0.0688156i	$0.0219220\pi$
$431$			2.85730i			0.137631i	−0.997629	+	0.0688156i	$0.978078\pi$
$432$	17.0759	−	13.9974i	0.821565	−	0.673453i
$433$	22.5174			1.08212			0.541059	−	0.840985i	$-0.318024\pi$
$433$	22.5174			1.08212			0.541059	+	0.840985i	$0.318024\pi$
$434$	7.22385	−	21.8564i	0.346756	−	1.04914i
$435$		0			0
$436$	16.0099	−	9.58974i	0.766737	−	0.459265i
$437$	−14.9974	+	6.21215i	−0.717425	+	0.297167i
$438$	22.0355	+	19.0135i	1.05290	+	0.908500i
$439$	8.87727	+	8.87727i	0.423689	+	0.423689i	0.886472	−	0.462783i	$-0.153149\pi$
$439$	8.87727	+	8.87727i	0.423689	+	0.423689i	−0.462783	+	0.886472i	$0.653149\pi$
$440$		0			0
$441$	4.61923	−	4.61923i	0.219963	−	0.219963i
$442$	0.374312	−	0.0275569i	0.0178042	−	0.00131075i
$443$	9.83247	+	23.7377i	0.467155	+	1.12781i	0.965400	+	0.260775i	$0.0839781\pi$
$443$	9.83247	+	23.7377i	0.467155	+	1.12781i	−0.498245	+	0.867036i	$0.666022\pi$
$444$	48.4293	+	35.9391i	2.29835	+	1.70560i
$445$		0			0
$446$	21.7438	−	10.9410i	1.02960	−	0.518071i
$447$		−	17.2933i		−	0.817945i
$448$	8.13853	+	17.2459i	0.384509	+	0.814791i
$449$	−8.83528			−0.416963			−0.208481	−	0.978026i	$-0.566852\pi$
$449$	−8.83528			−0.416963			−0.208481	+	0.978026i	$0.566852\pi$
$450$		0			0
$451$	3.01606	−	7.28141i	0.142021	−	0.342868i
$452$	2.88942	−	3.89359i	0.135907	−	0.183139i
$453$	−12.4736	−	30.1139i	−0.586061	−	1.41488i
$454$	0.170915	+	2.32158i	0.00802145	+	0.108957i
$455$		0			0
$456$	14.2993	+	20.3220i	0.669625	+	0.951664i
$457$	−7.58808	+	7.58808i	−0.354955	+	0.354955i	−0.861950	−	0.506994i	$-0.830757\pi$
$457$	−7.58808	+	7.58808i	−0.354955	+	0.354955i	0.506994	+	0.861950i	$0.330757\pi$
$458$	2.83965	+	2.45021i	0.132688	+	0.114491i
$459$	−0.474817	−	1.14631i	−0.0221626	−	0.0535052i
$460$		0			0
$461$	15.2534	+	6.31816i	0.710421	+	0.294266i	0.708479	−	0.705732i	$-0.249382\pi$
$461$	15.2534	+	6.31816i	0.710421	+	0.294266i	0.00194197	+	0.999998i	$0.499382\pi$
$462$	−7.89769	−	2.61030i	−0.367434	−	0.121442i
$463$	−18.7996			−0.873689			−0.436845	−	0.899537i	$-0.643904\pi$
$463$	−18.7996			−0.873689			−0.436845	+	0.899537i	$0.643904\pi$
$464$	24.4031	+	2.41764i	1.13289	+	0.112236i
$465$		0			0
$466$	20.7889	+	6.87102i	0.963026	+	0.318294i
$467$	−3.84804	+	9.28999i	−0.178066	+	0.429890i	−0.987561	−	0.157238i	$-0.949741\pi$
$467$	−3.84804	+	9.28999i	−0.178066	+	0.429890i	0.809495	+	0.587127i	$0.199741\pi$
$468$	−2.84738	+	11.3536i	−0.131620	+	0.524819i
$469$	3.53041	+	8.52318i	0.163019	+	0.393564i
$470$		0			0
$471$	25.4557	+	25.4557i	1.17293	+	1.17293i
$472$	10.0532	−	2.25298i	0.462736	−	0.103702i
$473$	−3.08370	−	3.08370i	−0.141789	−	0.141789i
$474$	−33.3877	+	2.45801i	−1.53355	+	0.112900i
$475$		0			0
$476$	1.06006	−	0.156934i	0.0485877	−	0.00719306i
$477$	−46.9015	−	19.4272i	−2.14747	−	0.889512i
$478$	23.1004	−	11.6236i	1.05659	−	0.531652i
$479$	14.7779			0.675220			0.337610	−	0.941286i	$-0.390382\pi$
$479$	14.7779			0.675220			0.337610	+	0.941286i	$0.390382\pi$
$480$		0			0
$481$	−12.6215			−0.575491
$482$	35.1394	−	17.6814i	1.60056	−	0.805364i
$483$	−32.3786	−	13.4117i	−1.47328	−	0.610252i
$484$	2.99772	+	20.2490i	0.136260	+	0.920410i
$485$		0			0
$486$	−20.5711	+	1.51445i	−0.933123	+	0.0686967i
$487$	13.0855	+	13.0855i	0.592961	+	0.592961i	0.938430	−	0.345469i	$-0.112280\pi$
$487$	13.0855	+	13.0855i	0.592961	+	0.592961i	−0.345469	+	0.938430i	$0.612280\pi$
$488$	1.57733	−	2.48851i	0.0714024	−	0.112649i
$489$	−3.92543	−	3.92543i	−0.177514	−	0.177514i
$490$		0			0
$491$	−11.7944	−	28.4741i	−0.532273	−	1.28502i	−0.930015	−	0.367523i	$-0.880206\pi$
$491$	−11.7944	−	28.4741i	−0.532273	−	1.28502i	0.397742	−	0.917497i	$-0.369794\pi$
$492$	−49.3042	−	12.3651i	−2.22281	−	0.557462i
$493$	0.527350	−	1.27314i	0.0237506	−	0.0573391i
$494$	−4.93773	−	1.63199i	−0.222159	−	0.0734268i
$495$		0			0
$496$	−7.91375	−	26.1421i	−0.355338	−	1.17382i
$497$	−18.2031			−0.816522
$498$	−45.9911	−	15.2007i	−2.06091	−	0.681160i
$499$	−22.4253	−	9.28886i	−1.00389	−	0.415827i	−0.180670	−	0.983544i	$-0.557827\pi$
$499$	−22.4253	−	9.28886i	−1.00389	−	0.415827i	−0.823224	+	0.567717i	$0.807827\pi$
$500$		0			0
$501$	−23.1479	−	55.8841i	−1.03417	−	2.49672i
$502$	−10.8673	−	9.37694i	−0.485032	−	0.418513i
$503$	23.5062	−	23.5062i	1.04809	−	1.04809i	0.0493053	−	0.998784i	$-0.484299\pi$
$503$	23.5062	−	23.5062i	1.04809	−	1.04809i	0.998784	−	0.0493053i	$-0.0157007\pi$
$504$	−5.72774	+	32.9256i	−0.255134	+	1.46662i
$505$		0			0
$506$	−0.473398	−	6.43027i	−0.0210451	−	0.285860i
$507$	12.5283	+	30.2459i	0.556400	+	1.34327i
$508$	3.52157	+	2.61334i	0.156245	+	0.115948i
$509$	13.1651	−	31.7834i	0.583534	−	1.40877i	−0.306056	−	0.952014i	$-0.599009\pi$
$509$	13.1651	−	31.7834i	0.583534	−	1.40877i	0.889589	−	0.456761i	$-0.150991\pi$
$510$		0			0
$511$	−17.3912			−0.769343
$512$	19.6734	+	11.1784i	0.869450	+	0.494021i
$513$			17.1917i			0.759033i
$514$	25.3489	−	12.7550i	1.11809	−	0.562598i
$515$		0			0
$516$	−16.7615	+	22.5867i	−0.737882	+	0.994322i
$517$	0.181652	+	0.438546i	0.00798903	+	0.0192872i
$518$	−35.9391	+	2.64585i	−1.57908	+	0.116252i
$519$	9.81922	−	9.81922i	0.431016	−	0.431016i
$520$		0			0
$521$	−10.8936	−	10.8936i	−0.477257	−	0.477257i	0.426996	−	0.904253i	$-0.359572\pi$
$521$	−10.8936	−	10.8936i	−0.477257	−	0.477257i	−0.904253	+	0.426996i	$0.859572\pi$
$522$	32.5380	+	28.0756i	1.42415	+	1.22884i
$523$	−15.6600	+	6.48657i	−0.684763	+	0.283638i	−0.697816	−	0.716277i	$-0.745845\pi$
$523$	−15.6600	+	6.48657i	−0.684763	+	0.283638i	0.0130536	+	0.999915i	$0.495845\pi$
$524$	8.49483	+	14.1820i	0.371098	+	0.619543i
$525$		0			0
$526$	−11.2837	+	34.1399i	−0.491995	+	1.48857i
$527$	−1.53488			−0.0668603
$528$	−9.44633	+	2.85959i	−0.411099	+	0.124448i
$529$		−	4.16647i		−	0.181151i
$530$		0			0
$531$	16.6811	+	6.90952i	0.723896	+	0.299848i
$532$	−14.4021	−	3.61192i	−0.624409	−	0.156597i
$533$	9.82843	−	4.07107i	0.425716	−	0.176338i
$534$	−25.3135	−	21.8419i	−1.09542	−	0.945193i
$535$		0			0
$536$	9.24568	+	5.86034i	0.399353	+	0.253128i
$537$	−15.7149	−	15.7149i	−0.678148	−	0.678148i
$538$	−2.88387	−	39.1723i	−0.124333	−	1.68884i
$539$	−1.06503	+	0.441152i	−0.0458743	+	0.0190018i
$540$		0			0
$541$	1.10183	−	2.66006i	0.0473716	−	0.114365i	−0.898422	−	0.439132i	$-0.855286\pi$
$541$	1.10183	−	2.66006i	0.0473716	−	0.114365i	0.945794	+	0.324767i	$0.105286\pi$
$542$	20.8345	−	10.4835i	0.894920	−	0.450304i
$543$			45.1208i			1.93632i
$544$	0.921533	−	0.876113i	0.0395104	−	0.0375630i
$545$		0			0
$546$	−5.04655	−	10.0294i	−0.215973	−	0.429217i
$547$	25.1462	+	10.4159i	1.07517	+	0.445351i	0.848813	−	0.528693i	$-0.177318\pi$
$547$	25.1462	+	10.4159i	1.07517	+	0.445351i	0.226360	+	0.974044i	$0.427318\pi$
$548$	−3.21738	−	21.7328i	−0.137440	−	0.928378i
$549$	4.77039	−	1.97596i	0.203595	−	0.0843319i
$550$		0			0
$551$	−13.5013	+	13.5013i	−0.575176	+	0.575176i
$552$	−40.5781	+	9.09378i	−1.72712	+	0.387057i
$553$	14.1454	−	14.1454i	0.601523	−	0.601523i
$554$	−6.49058	−	5.60044i	−0.275758	−	0.237940i
$555$		0			0
$556$	1.81202	+	0.454441i	0.0768469	+	0.0192726i
$557$	−10.9504	+	26.4367i	−0.463984	+	1.12016i	0.502763	+	0.864424i	$0.332317\pi$
$557$	−10.9504	+	26.4367i	−0.463984	+	1.12016i	−0.966748	+	0.255733i	$0.917683\pi$
$558$	15.0218	−	45.4497i	0.635923	−	1.92404i
$559$		−	5.88648i		−	0.248972i
$560$		0			0
$561$			0.554620i			0.0234161i
$562$	−18.6251	−	6.15586i	−0.785652	−	0.259669i
$563$	−9.49093	+	22.9131i	−0.399995	+	0.965673i	0.587671	+	0.809100i	$0.300045\pi$
$563$	−9.49093	+	22.9131i	−0.399995	+	0.965673i	−0.987666	+	0.156574i	$0.949955\pi$
$564$	2.62636	−	1.57316i	0.110590	−	0.0662418i
$565$		0			0
$566$	−21.3627	+	24.7581i	−0.897941	+	1.04066i
$567$	−1.17985	+	1.17985i	−0.0495489	+	0.0495489i
$568$	−17.6645	+	12.4293i	−0.741184	+	0.521524i
$569$	−12.2981	+	12.2981i	−0.515565	+	0.515565i	−0.916226	−	0.400661i	$-0.868780\pi$
$569$	−12.2981	+	12.2981i	−0.515565	+	0.515565i	0.400661	+	0.916226i	$0.368780\pi$
$570$		0			0
$571$	4.93839	−	2.04555i	0.206665	−	0.0856036i	−0.276950	−	0.960884i	$-0.589324\pi$
$571$	4.93839	−	2.04555i	0.206665	−	0.0856036i	0.483615	+	0.875281i	$0.339324\pi$
$572$	1.23094	−	1.65873i	0.0514682	−	0.0693552i
$573$	−40.3008	−	16.6931i	−1.68359	−	0.697366i
$574$	27.1325	−	13.6525i	1.13249	−	0.569844i
$575$		0			0
$576$	16.9238	+	35.8623i	0.705159	+	1.49426i
$577$			2.06423i			0.0859352i	0.999076	+	0.0429676i	$0.0136812\pi$
$577$			2.06423i			0.0859352i	−0.999076	+	0.0429676i	$0.986319\pi$
$578$	10.7742	+	21.4123i	0.448147	+	0.890634i
$579$	14.2713	−	34.4539i	0.593093	−	1.43185i
$580$		0			0
$581$	26.7406	−	11.0763i	1.10939	−	0.459522i
$582$	−16.7075	+	1.23001i	−0.692548	+	0.0509855i
$583$	6.33461	+	6.33461i	0.262353	+	0.262353i
$584$	−16.8766	+	11.8750i	−0.698359	+	0.491390i
$585$		0			0
$586$	−20.4415	+	23.6905i	−0.844431	+	0.978646i
$587$	−21.1056	+	8.74223i	−0.871122	+	0.360830i	−0.773047	−	0.634349i	$-0.781268\pi$
$587$	−21.1056	+	8.74223i	−0.871122	+	0.360830i	−0.0980746	+	0.995179i	$0.531268\pi$
$588$	3.82050	+	6.37827i	0.157555	+	0.263035i
$589$	19.6481	+	8.13853i	0.809588	+	0.335342i
$590$		0			0
$591$		−	1.84106i		−	0.0757310i
$592$	−33.0690	+	27.1073i	−1.35913	+	1.11410i
$593$	−24.2771			−0.996939			−0.498470	−	0.866907i	$-0.666104\pi$
$593$	−24.2771			−0.996939			−0.498470	+	0.866907i	$0.666104\pi$
$594$	−6.48348	−	2.14288i	−0.266020	−	0.0879236i
$595$		0			0
$596$	11.8930	+	2.98267i	0.487156	+	0.122175i
$597$	6.87318	−	2.84696i	0.281300	−	0.116518i
$598$	5.68554	−	6.58921i	0.232499	−	0.269453i
$599$	33.3626	+	33.3626i	1.36316	+	1.36316i	0.869862	+	0.493295i	$0.164208\pi$
$599$	33.3626	+	33.3626i	1.36316	+	1.36316i	0.493295	+	0.869862i	$0.335792\pi$
$600$		0			0
$601$	−21.0676	+	21.0676i	−0.859365	+	0.859365i	−0.991263	−	0.131898i	$-0.957893\pi$
$601$	−21.0676	+	21.0676i	−0.859365	+	0.859365i	0.131898	+	0.991263i	$0.457893\pi$
$602$	−1.23398	−	16.7615i	−0.0502933	−	0.683146i
$603$	7.34139	+	17.7237i	0.298965	+	0.721765i
$604$	22.8614	−	3.38447i	0.930218	−	0.137712i
$605$		0			0
$606$	−8.65975	−	17.2101i	−0.351778	−	0.699113i
$607$			3.82750i			0.155353i	0.996979	+	0.0776767i	$0.0247502\pi$
$607$			3.82750i			0.155353i	−0.996979	+	0.0776767i	$0.975250\pi$
$608$	−16.4422	+	6.32889i	−0.666817	+	0.256670i
$609$	−41.2224			−1.67041
$610$		0			0
$611$	−0.245193	+	0.591948i	−0.00991945	+	0.0239477i
$612$	2.20436	−	0.326340i	0.0891060	−	0.0131915i
$613$	12.0488	+	29.0883i	0.486645	+	1.17486i	0.956398	+	0.292067i	$0.0943429\pi$
$613$	12.0488	+	29.0883i	0.486645	+	1.17486i	−0.469753	+	0.882798i	$0.655657\pi$
$614$	−23.8449	+	1.75546i	−0.962301	+	0.0708448i
$615$		0			0
$616$	3.15732	−	4.98121i	0.127212	−	0.200699i
$617$	−22.2479	+	22.2479i	−0.895666	+	0.895666i	−0.995049	−	0.0993836i	$-0.968313\pi$
$617$	−22.2479	+	22.2479i	−0.895666	+	0.895666i	0.0993836	+	0.995049i	$0.468313\pi$
$618$	−40.4066	+	46.8288i	−1.62539	+	1.88373i
$619$	−2.70650	−	6.53408i	−0.108784	−	0.262627i	0.860108	−	0.510112i	$-0.170396\pi$
$619$	−2.70650	−	6.53408i	−0.108784	−	0.262627i	−0.968892	+	0.247485i	$0.920396\pi$
$620$		0			0
$621$	−26.5807	−	11.0101i	−1.06665	−	0.441819i
$622$	4.54992	−	13.7662i	0.182435	−	0.551973i
$623$	19.9783			0.800416
$624$	−11.7454	−	6.28672i	−0.470192	−	0.251670i
$625$		0			0
$626$	6.37654	−	19.2928i	0.254858	−	0.771094i
$627$	2.94082	−	7.09976i	0.117445	−	0.283537i
$628$	−21.8969	+	13.1160i	−0.873782	+	0.523384i
$629$	0.919525	+	2.21993i	0.0366639	+	0.0885144i
$630$		0			0
$631$	1.24929	+	1.24929i	0.0497335	+	0.0497335i	0.731536	−	0.681803i	$-0.238804\pi$
$631$	1.24929	+	1.24929i	0.0497335	+	0.0497335i	−0.681803	+	0.731536i	$0.738804\pi$
$632$	4.06813	−	23.3854i	0.161822	−	0.930223i
$633$	−41.0928	−	41.0928i	−1.63329	−	1.63329i
$634$	0.364362	+	4.94922i	0.0144707	+	0.196559i
$635$		0			0
$636$	34.4318	−	46.3981i	1.36531	−	1.83980i
$637$	−1.43758	−	0.595466i	−0.0569590	−	0.0235932i
$638$	−3.40884	−	6.77462i	−0.134957	−	0.268210i
$639$	−37.8529			−1.49744
$640$		0			0
$641$	11.2362			0.443802			0.221901	−	0.975069i	$-0.428774\pi$
$641$	11.2362			0.443802			0.221901	+	0.975069i	$0.428774\pi$
$642$	15.6843	+	31.1704i	0.619009	+	1.23020i
$643$	−13.8682	−	5.74440i	−0.546908	−	0.226537i	0.0920822	−	0.995751i	$-0.470648\pi$
$643$	−13.8682	−	5.74440i	−0.546908	−	0.226537i	−0.638991	+	0.769215i	$0.720648\pi$
$644$	14.8080	−	19.9543i	0.583517	−	0.786310i
$645$		0			0
$646$	0.0726903	+	0.987369i	0.00285996	+	0.0388475i
$647$	13.9424	+	13.9424i	0.548134	+	0.548134i	0.925901	−	0.377767i	$-0.123308\pi$
$647$	13.9424	+	13.9424i	0.548134	+	0.548134i	−0.377767	+	0.925901i	$0.623308\pi$
$648$	−0.339317	+	1.95055i	−0.0133296	+	0.0766248i
$649$	−2.25298	−	2.25298i	−0.0884371	−	0.0884371i
$650$		0			0
$651$	17.5706	+	42.4192i	0.688646	+	1.66254i
$652$	3.37665	−	2.02257i	0.132240	−	0.0792098i
$653$	−0.149807	+	0.361667i	−0.00586241	+	0.0141531i	−0.926784	−	0.375596i	$-0.877438\pi$
$653$	−0.149807	+	0.361667i	−0.00586241	+	0.0141531i	0.920921	+	0.389749i	$0.127438\pi$
$654$	−11.6815	+	35.3434i	−0.456783	+	1.38204i
$655$		0			0
$656$	17.0075	−	31.7750i	0.664032	−	1.24060i
$657$	−36.1646			−1.41091
$658$	−0.574085	+	1.73694i	−0.0223802	+	0.0677131i
$659$	18.5077	+	7.66613i	0.720957	+	0.298630i	0.712830	−	0.701337i	$-0.247413\pi$
$659$	18.5077	+	7.66613i	0.720957	+	0.298630i	0.00812687	+	0.999967i	$0.497413\pi$
$660$		0			0
$661$	12.4139	+	29.9699i	0.482846	+	1.16569i	0.958251	+	0.285927i	$0.0923015\pi$
$661$	12.4139	+	29.9699i	0.482846	+	1.16569i	−0.475405	+	0.879767i	$0.657698\pi$
$662$	15.5299	−	17.9982i	0.603587	−	0.699522i
$663$	−0.529357	+	0.529357i	−0.0205585	+	0.0205585i
$664$	18.3862	−	29.0073i	0.713523	−	1.12570i
$665$		0			0
$666$	−74.7344	+	5.50196i	−2.89590	+	0.213197i
$667$	−12.2282	−	29.5215i	−0.473478	−	1.14308i
$668$	42.4252	−	6.28074i	1.64148	−	0.243009i
$669$	−18.5797	+	44.8554i	−0.718334	+	1.73421i
$670$		0			0
$671$	−0.911176			−0.0351755
$672$	−34.7623	−	15.4389i	−1.34099	−	0.595570i
$673$			47.5269i			1.83203i	0.401146	+	0.916014i	$0.368612\pi$
$673$			47.5269i			1.83203i	−0.401146	+	0.916014i	$0.631388\pi$
$674$	−1.33897	−	2.66103i	−0.0515752	−	0.102499i
$675$		0			0
$676$	−22.9616	+	3.39930i	−0.883140	+	0.130742i
$677$	−17.3078	−	41.7848i	−0.665194	−	1.60592i	−0.789553	−	0.613682i	$-0.789688\pi$
$677$	−17.3078	−	41.7848i	−0.665194	−	1.60592i	0.124360	−	0.992237i	$-0.460312\pi$
$678$	0.710059	+	9.64490i	0.0272696	+	0.370410i
$679$	7.07847	−	7.07847i	0.271647	−	0.271647i
$680$		0			0
$681$	−3.28321	−	3.28321i	−0.125813	−	0.125813i
$682$	−5.51833	+	6.39542i	−0.211308	+	0.244893i
$683$	32.0496	−	13.2754i	1.22634	−	0.507968i	0.326922	−	0.945051i	$-0.393988\pi$
$683$	32.0496	−	13.2754i	1.22634	−	0.507968i	0.899421	+	0.437083i	$0.143988\pi$
$684$	−29.9487	−	7.51089i	−1.14512	−	0.287186i
$685$		0			0
$686$	−26.6238	−	8.79956i	−1.01650	−	0.335969i
$687$	−7.48100			−0.285418
$688$	−12.6424	−	15.4229i	−0.481988	−	0.587992i
$689$			12.0922i			0.460674i
$690$		0			0
$691$	46.1276	+	19.1067i	1.75478	+	0.726852i	0.997255	+	0.0740401i	$0.0235893\pi$
$691$	46.1276	+	19.1067i	1.75478	+	0.726852i	0.757520	+	0.652812i	$0.226411\pi$
$692$	5.05933	+	8.44647i	0.192327	+	0.321087i
$693$	9.54882	−	3.95525i	0.362730	−	0.150248i
$694$	−12.3896	+	14.3588i	−0.470302	+	0.545052i
$695$		0			0
$696$	−40.0025	+	28.1472i	−1.51629	+	1.06692i
$697$	−1.43208	−	1.43208i	−0.0542438	−	0.0542438i
$698$	27.7320	−	2.04163i	1.04967	−	0.0772769i
$699$	−40.3474	+	16.7124i	−1.52608	+	0.632122i
$700$		0			0
$701$	5.34543	−	12.9050i	0.201894	−	0.487415i	−0.790210	−	0.612837i	$-0.790028\pi$
$701$	5.34543	−	12.9050i	0.201894	−	0.487415i	0.992104	+	0.125422i	$0.0400283\pi$
$702$	−4.14288	−	8.23344i	−0.156363	−	0.310751i
$703$		−	33.2933i		−	1.25568i
$704$	−0.337349	−	6.98966i	−0.0127143	−	0.263433i
$705$		0			0
$706$	36.2584	−	18.2444i	1.36460	−	0.686639i
$707$	10.6359	+	4.40555i	0.400006	+	0.165688i
$708$	−12.2461	+	16.5020i	−0.460235	+	0.620184i
$709$	−31.1013	+	12.8826i	−1.16803	+	0.483815i	−0.880542	−	0.473968i	$-0.842821\pi$
$709$	−31.1013	+	12.8826i	−1.16803	+	0.483815i	−0.287491	+	0.957783i	$0.592821\pi$
$710$		0			0
$711$	29.4149	−	29.4149i	1.10315	−	1.10315i
$712$	19.3871	−	13.6415i	0.726564	−	0.511236i
$713$	−25.1665	+	25.1665i	−0.942492	+	0.942492i
$714$	−1.39635	+	1.61829i	−0.0522571	+	0.0605629i
$715$		0			0
$716$	13.5179	−	8.09706i	0.505189	−	0.302601i
$717$	−19.7390	+	47.6540i	−0.737165	+	1.77967i
$718$	12.1382	+	4.01184i	0.452993	+	0.149721i
$719$		−	0.571168i		−	0.0213010i	−0.999943	−	0.0106505i	$-0.996610\pi$
$719$		−	0.571168i		−	0.0213010i	0.999943	−	0.0106505i	$-0.00339022\pi$
$720$		0			0
$721$		−	36.9590i		−	1.37643i
$722$	−4.12740	+	12.4878i	−0.153606	+	0.464748i
$723$	−30.0261	+	72.4893i	−1.11668	+	2.69591i
$724$	−31.0306	−	7.78222i	−1.15324	−	0.289224i
$725$		0			0
$726$	−30.9122	−	26.6728i	−1.14726	−	0.989920i
$727$	23.0479	−	23.0479i	0.854800	−	0.854800i	−0.135920	−	0.990720i	$-0.543399\pi$
$727$	23.0479	−	23.0479i	0.854800	−	0.854800i	0.990720	+	0.135920i	$0.0433990\pi$
$728$	7.76782	−	1.74081i	0.287895	−	0.0645188i
$729$	30.5768	−	30.5768i	1.13247	−	1.13247i
$730$		0			0
$731$	−1.03534	+	0.428852i	−0.0382935	+	0.0158617i
$732$	0.860620	+	5.81332i	0.0318094	+	0.214866i
$733$	28.7029	+	11.8891i	1.06017	+	0.439136i	0.843511	−	0.537112i	$-0.180485\pi$
$733$	28.7029	+	11.8891i	1.06017	+	0.439136i	0.216656	+	0.976248i	$0.430485\pi$
$734$	−9.27979	−	18.4424i	−0.342523	−	0.680720i
$735$		0			0
$736$	0.744728	−	29.4749i	0.0274510	−	1.08646i
$737$		−	3.38534i		−	0.124701i
$738$	56.4213	−	28.3900i	2.07690	−	1.04505i
$739$	−2.87645	+	6.94437i	−0.105812	+	0.255453i	−0.967914	−	0.251282i	$-0.919148\pi$
$739$	−2.87645	+	6.94437i	−0.105812	+	0.255453i	0.862102	+	0.506735i	$0.169148\pi$
$740$		0			0
$741$	9.58323	−	3.96951i	0.352049	−	0.145823i
$742$	2.53488	+	34.4318i	0.0930582	+	1.26403i
$743$	16.6576	+	16.6576i	0.611108	+	0.611108i	0.943235	−	0.332127i	$-0.107766\pi$
$743$	16.6576	+	16.6576i	0.611108	+	0.611108i	−0.332127	+	0.943235i	$0.607766\pi$
$744$	46.0151	+	29.1665i	1.68699	+	1.06929i
$745$		0			0
$746$	16.8929	+	14.5761i	0.618491	+	0.533669i
$747$	55.6062	−	23.0328i	2.03452	−	0.842728i
$748$	−0.381425	−	0.0956582i	−0.0139463	−	0.00349761i
$749$	−19.2635	−	7.97920i	−0.703873	−	0.291554i
$750$		0			0
$751$			31.1077i			1.13514i	0.823326	+	0.567569i	$0.192116\pi$
$751$			31.1077i			1.13514i	−0.823326	+	0.567569i	$0.807884\pi$
$752$	0.628912	+	2.07754i	0.0229341	+	0.0757600i
$753$	28.6297			1.04332
$754$	3.21247	−	9.71961i	0.116991	−	0.353967i
$755$		0			0
$756$	−13.5226	−	22.5758i	−0.491813	−	0.821075i
$757$	5.69056	−	2.35711i	0.206827	−	0.0856705i	−0.276865	−	0.960909i	$-0.589296\pi$
$757$	5.69056	−	2.35711i	0.206827	−	0.0856705i	0.483692	+	0.875238i	$0.339296\pi$
$758$	−6.58641	−	5.68312i	−0.239229	−	0.206420i
$759$	9.09378	+	9.09378i	0.330083	+	0.330083i
$760$		0			0
$761$	−14.2913	+	14.2913i	−0.518059	+	0.518059i	−0.916984	−	0.398925i	$-0.869383\pi$
$761$	−14.2913	+	14.2913i	−0.518059	+	0.518059i	0.398925	+	0.916984i	$0.369383\pi$
$762$	−8.72336	+	0.642215i	−0.316014	+	0.0232650i
$763$	−8.51196	−	20.5497i	−0.308154	−	0.743949i
$764$	18.4311	−	24.8366i	0.666815	−	0.898558i
$765$		0			0
$766$	−15.7449	+	7.92246i	−0.568885	+	0.286250i
$767$		−	4.30071i		−	0.155290i
$768$	−44.2756	+	8.75413i	−1.59766	+	0.315888i
$769$	−8.95004			−0.322747			−0.161373	−	0.986893i	$-0.551592\pi$
$769$	−8.95004			−0.322747			−0.161373	+	0.986893i	$0.551592\pi$
$770$		0			0
$771$	−21.6602	+	52.2924i	−0.780073	+	1.88326i
$772$	21.2333	+	15.7571i	0.764202	+	0.567110i
$773$	11.0293	+	26.6270i	0.396695	+	0.957707i	0.988444	+	0.151585i	$0.0484377\pi$
$773$	11.0293	+	26.6270i	0.396695	+	0.957707i	−0.591749	+	0.806122i	$0.701562\pi$
$774$	−2.56603	−	34.8550i	−0.0922340	−	1.25284i
$775$		0			0
$776$	2.03573	−	11.7023i	0.0730783	−	0.420087i
$777$	50.8256	−	50.8256i	1.82336	−	1.82336i
$778$	−16.3756	−	14.1298i	−0.587093	−	0.506577i
$779$	10.7387	+	25.9256i	0.384756	+	0.928882i
$780$		0			0
$781$	6.17132	+	2.55624i	0.220827	+	0.0914695i
$782$	−1.57316	−	0.519951i	−0.0562559	−	0.0185934i
$783$	−33.8408			−1.20937
$784$	−5.04542	+	1.52735i	−0.180194	+	0.0545482i
$785$		0			0
$786$	−31.3081	−	10.3478i	−1.11672	−	0.369093i
$787$	−1.84348	+	4.45056i	−0.0657130	+	0.158645i	−0.953324	−	0.301948i	$-0.902363\pi$
$787$	−1.84348	+	4.45056i	−0.0657130	+	0.158645i	0.887611	+	0.460593i	$0.152363\pi$
$788$	1.26614	+	0.317537i	0.0451043	+	0.0113118i
$789$	−27.4455	−	66.2593i	−0.977086	−	2.35889i
$790$		0			0
$791$	−4.08625	−	4.08625i	−0.145290	−	0.145290i
$792$	6.56555	−	10.3583i	0.233297	−	0.368065i
$793$	−0.869673	−	0.869673i	−0.0308830	−	0.0308830i
$794$	−39.0406	+	2.87418i	−1.38550	+	0.102001i
$795$		0			0
$796$	0.772467	+	5.21787i	0.0273794	+	0.184942i
$797$	36.2064	+	14.9972i	1.28250	+	0.531227i	0.916740	−	0.399484i	$-0.130811\pi$
$797$	36.2064	+	14.9972i	1.28250	+	0.531227i	0.365756	+	0.930711i	$0.380811\pi$
$798$	26.4557	−	13.3119i	0.936520	−	0.471236i
$799$	0.121978			0.00431527
$800$		0			0
$801$	41.5444			1.46790
$802$	−20.8468	+	10.4896i	−0.736125	+	0.370402i
$803$	5.89607	+	2.44223i	0.208068	+	0.0861845i
$804$	−21.5985	+	3.19751i	−0.761722	+	0.112767i
$805$		0			0
$806$	−11.3711	+	0.837141i	−0.400529	+	0.0294870i
$807$	55.3980	+	55.3980i	1.95010	+	1.95010i
$808$	13.3294	−	2.98719i	0.468926	−	0.105089i
$809$	18.3458	+	18.3458i	0.645005	+	0.645005i	0.951782	−	0.306777i	$-0.0992505\pi$
$809$	18.3458	+	18.3458i	0.645005	+	0.645005i	−0.306777	+	0.951782i	$0.599250\pi$
$810$		0			0
$811$	−14.5476	−	35.1209i	−0.510834	−	1.23326i	−0.943399	−	0.331660i	$-0.892391\pi$
$811$	−14.5476	−	35.1209i	−0.510834	−	1.23326i	0.432565	−	0.901603i	$-0.357609\pi$
$812$	7.10984	−	28.3495i	0.249506	−	0.994874i
$813$	−17.8028	+	42.9797i	−0.624371	+	1.50736i
$814$	12.5558	+	4.14988i	0.440081	+	0.145453i
$815$		0			0
$816$	−0.250040	+	2.52385i	−0.00875315	+	0.0883523i
$817$	15.5275			0.543238
$818$	2.44163	+	0.806993i	0.0853695	+	0.0282159i
$819$	12.8890	+	5.33879i	0.450377	+	0.186552i
$820$		0			0
$821$	−10.1999	−	24.6248i	−0.355979	−	0.859410i	−0.995857	−	0.0909335i	$-0.971015\pi$
$821$	−10.1999	−	24.6248i	−0.355979	−	0.859410i	0.639877	−	0.768477i	$-0.278985\pi$
$822$	33.1773	+	28.6272i	1.15719	+	0.998489i
$823$	−1.53506	+	1.53506i	−0.0535088	+	0.0535088i	−0.733355	−	0.679846i	$-0.762047\pi$
$823$	−1.53506	+	1.53506i	−0.0535088	+	0.0535088i	0.679846	+	0.733355i	$0.262047\pi$
$824$	−25.2361	−	35.8653i	−0.879142	−	1.24943i
$825$		0			0
$826$	−0.901558	−	12.2461i	−0.0313692	−	0.426095i
$827$	7.71287	+	18.6205i	0.268203	+	0.647499i	0.999399	−	0.0346687i	$-0.0110376\pi$
$827$	7.71287	+	18.6205i	0.268203	+	0.647499i	−0.731196	+	0.682167i	$0.761038\pi$
$828$	30.7928	−	41.4944i	1.07012	−	1.44203i
$829$	9.98710	−	24.1110i	0.346866	−	0.837409i	−0.650120	−	0.759831i	$-0.725281\pi$
$829$	9.98710	−	24.1110i	0.346866	−	0.837409i	0.996986	−	0.0775776i	$-0.0247186\pi$
$830$		0			0
$831$	17.0993			0.593168
$832$	6.34931	−	6.99327i	0.220123	−	0.242448i
$833$			0.296230i			0.0102638i
$834$	−3.32857	+	1.67486i	−0.115259	+	0.0579957i
$835$		0			0
$836$	4.37545	+	3.24700i	0.151328	+	0.112300i
$837$	14.4243	+	34.8233i	0.498576	+	1.20367i
$838$	−55.2414	+	4.06688i	−1.90828	+	0.140488i
$839$	−31.2561	+	31.2561i	−1.07908	+	1.07908i	−0.0824901	+	0.996592i	$0.526287\pi$
$839$	−31.2561	+	31.2561i	−1.07908	+	1.07908i	−0.996592	+	0.0824901i	$0.973713\pi$
$840$		0			0
$841$	−6.07041	−	6.07041i	−0.209324	−	0.209324i
$842$	−15.7768	−	13.6131i	−0.543703	−	0.469137i
$843$	36.1479	−	14.9729i	1.24500	−	0.515695i
$844$	35.3480	−	21.1730i	1.21673	−	0.728804i
$845$		0			0
$846$	−1.19379	+	3.61192i	−0.0410435	+	0.124180i
$847$	24.3970			0.838292
$848$	25.9704	+	31.6821i	0.891827	+	1.08797i
$849$		−	65.2246i		−	2.23850i
$850$		0			0
$851$	51.4758	+	21.3220i	1.76457	+	0.730908i
$852$	10.4800	−	41.7875i	0.359038	−	1.43162i
$853$	−18.6692	+	7.73304i	−0.639222	+	0.264774i	−0.678666	−	0.734447i	$-0.737441\pi$
$853$	−18.6692	+	7.73304i	−0.639222	+	0.264774i	0.0394438	+	0.999222i	$0.487441\pi$
$854$	−2.65866	−	2.29404i	−0.0909774	−	0.0785004i
$855$		0			0
$856$	−24.1418	+	5.41030i	−0.825148	+	0.184920i
$857$	4.21699	+	4.21699i	0.144050	+	0.144050i	0.775454	−	0.631404i	$-0.217521\pi$
$857$	4.21699	+	4.21699i	0.144050	+	0.144050i	−0.631404	+	0.775454i	$0.717521\pi$
$858$	0.302497	+	4.10889i	0.0103271	+	0.140275i
$859$	32.3968	−	13.4192i	1.10536	−	0.457857i	0.246025	−	0.969263i	$-0.420875\pi$
$859$	32.3968	−	13.4192i	1.10536	−	0.457857i	0.859339	+	0.511407i	$0.170875\pi$
$860$		0			0
$861$	−23.1843	+	55.9719i	−0.790120	+	1.90752i
$862$	3.60963	−	1.81629i	0.122944	−	0.0618629i
$863$			18.7779i			0.639207i	0.947551	+	0.319604i	$0.103550\pi$
$863$			18.7779i			0.639207i	−0.947551	+	0.319604i	$0.896450\pi$
$864$	−28.5376	−	12.6743i	−0.970867	−	0.431190i
$865$		0			0
$866$	−14.3135	−	28.4463i	−0.486393	−	0.966643i
$867$	−44.1716	−	18.2965i	−1.50015	−	0.621380i
$868$	−32.2031	+	4.76744i	−1.09305	+	0.161817i
$869$	−6.78206	+	2.80922i	−0.230066	+	0.0952963i
$870$		0			0
$871$	3.23114	−	3.23114i	0.109483	−	0.109483i
$872$	−22.2917	−	14.1295i	−0.754892	−	0.478485i
$873$	14.7195	−	14.7195i	0.498178	−	0.498178i
$874$	17.3812	+	14.9974i	0.587927	+	0.507296i
$875$		0			0
$876$	10.0126	−	39.9238i	0.338293	−	1.34890i
$877$	−2.31816	+	5.59652i	−0.0782786	+	0.188981i	−0.958174	−	0.286186i	$-0.907612\pi$
$877$	−2.31816	+	5.59652i	−0.0782786	+	0.188981i	0.879895	+	0.475167i	$0.157612\pi$
$878$	5.57170	−	16.8576i	0.188036	−	0.568918i
$879$		−	62.4121i		−	2.10511i
$880$		0			0
$881$			16.3413i			0.550552i	0.961365	+	0.275276i	$0.0887692\pi$
$881$			16.3413i			0.550552i	−0.961365	+	0.275276i	$0.911231\pi$
$882$	−8.77177	−	2.89920i	−0.295361	−	0.0976210i
$883$	−0.151958	+	0.366860i	−0.00511380	+	0.0123458i	−0.926416	−	0.376502i	$-0.877127\pi$
$883$	−0.151958	+	0.366860i	−0.00511380	+	0.0123458i	0.921302	+	0.388848i	$0.127127\pi$
$884$	−0.272750	−	0.455352i	−0.00917357	−	0.0153151i
$885$		0			0
$886$	23.7377	−	27.5106i	0.797483	−	0.924237i
$887$	6.38554	−	6.38554i	0.214406	−	0.214406i	−0.591730	−	0.806136i	$-0.701555\pi$
$887$	6.38554	−	6.38554i	0.214406	−	0.214406i	0.806136	+	0.591730i	$0.201555\pi$
$888$	14.6172	−	84.0260i	0.490520	−	2.81973i
$889$	3.69583	−	3.69583i	0.123954	−	0.123954i
$890$		0			0
$891$	0.565682	−	0.234313i	0.0189511	−	0.00784979i
$892$	−27.6436	−	20.5142i	−0.925575	−	0.686865i
$893$	−1.56145	−	0.646775i	−0.0522521	−	0.0216435i
$894$	−21.8466	+	10.9927i	−0.730661	+	0.367652i
$895$		0			0
$896$	16.6133	−	21.2440i	0.555013	−	0.709712i
$897$			17.3591i			0.579604i
$898$	5.61628	+	11.1616i	0.187418	+	0.372468i
$899$	−16.0202	+	38.6761i	−0.534302	+	1.28992i
$900$		0			0
$901$	2.12682	−	0.880960i	0.0708548	−	0.0293490i
$902$	−11.1158	+	0.818348i	−0.370116	+	0.0272480i
$903$	23.7043	+	23.7043i	0.788829	+	0.788829i
$904$	−6.75548	−	1.17518i	−0.224684	−	0.0390860i
$905$		0			0
$906$	−30.1139	+	34.9003i	−1.00047	+	1.15948i
$907$	−35.3230	+	14.6313i	−1.17288	+	0.485823i	−0.882144	−	0.470980i	$-0.843900\pi$
$907$	−35.3230	+	14.6313i	−1.17288	+	0.485823i	−0.290737	+	0.956803i	$0.593900\pi$
$908$	2.82421	−	1.69167i	0.0937248	−	0.0561399i
$909$	22.1171	+	9.16122i	0.733579	+	0.303859i
$910$		0			0
$911$			30.2904i			1.00356i	0.864994	+	0.501782i	$0.167322\pi$
$911$			30.2904i			1.00356i	−0.864994	+	0.501782i	$0.832678\pi$
$912$	16.5832	−	30.9823i	0.549126	−	1.02593i
$913$	−10.6211			−0.351509
$914$	14.4095	+	4.76255i	0.476624	+	0.157531i
$915$		0			0
$916$	1.29029	−	5.14485i	0.0426323	−	0.169991i
$917$	18.2034	−	7.54011i	0.601130	−	0.248996i
$918$	−1.14631	+	1.32851i	−0.0378339	+	0.0438473i
$919$	−42.1116	−	42.1116i	−1.38913	−	1.38913i	−0.827146	−	0.561987i	$-0.810037\pi$
$919$	−42.1116	−	42.1116i	−1.38913	−	1.38913i	−0.561987	−	0.827146i	$-0.689963\pi$
$920$		0			0
$921$	33.7218	−	33.7218i	1.11117	−	1.11117i
$922$	−1.71431	−	23.2858i	−0.0564577	−	0.766878i
$923$	3.45041	+	8.33002i	0.113572	+	0.274186i
$924$	1.72269	+	11.6364i	0.0566723	+	0.382811i
$925$		0			0
$926$	11.9502	+	23.7495i	0.392709	+	0.780457i
$927$		−	76.8552i		−	2.52426i
$928$	−12.4580	−	32.3653i	−0.408954	−	1.06244i
$929$	−25.2271			−0.827674			−0.413837	−	0.910351i	$-0.635812\pi$
$929$	−25.2271			−0.827674			−0.413837	+	0.910351i	$0.635812\pi$
$930$		0			0
$931$	1.57073	−	3.79208i	0.0514787	−	0.124280i
$932$	−4.53459	−	30.6303i	−0.148535	−	1.00333i
$933$	11.0668	+	26.7176i	0.362310	+	0.874694i
$934$	14.1821	−	1.04409i	0.464053	−	0.0341637i
$935$		0			0
$936$	16.1530	−	3.61997i	0.527976	−	0.118322i
$937$	−30.3001	+	30.3001i	−0.989863	+	0.989863i	−0.999949	−	0.0100865i	$-0.996789\pi$
$937$	−30.3001	+	30.3001i	−0.989863	+	0.989863i	0.0100865	+	0.999949i	$0.496789\pi$
$938$	8.52318	−	9.87786i	0.278292	−	0.322524i
$939$	15.5097	+	37.4437i	0.506140	+	1.22193i
$940$		0			0
$941$	−1.05940	−	0.438818i	−0.0345355	−	0.0143051i	0.365349	−	0.930871i	$-0.380950\pi$
$941$	−1.05940	−	0.438818i	−0.0345355	−	0.0143051i	−0.399884	+	0.916566i	$0.630950\pi$
$942$	15.9769	−	48.3394i	0.520555	−	1.57498i
$943$	−46.9618			−1.52929
$944$	−9.23666	−	11.2681i	−0.300628	−	0.366745i
$945$		0			0
$946$	−1.93544	+	5.85584i	−0.0629266	+	0.190390i
$947$	10.4790	−	25.2985i	0.340520	−	0.822089i	−0.657143	−	0.753766i	$-0.728235\pi$
$947$	10.4790	−	25.2985i	0.340520	−	0.822089i	0.997663	−	0.0683231i	$-0.0217649\pi$
$948$	24.3286	+	40.6163i	0.790157	+	1.31916i
$949$	3.29652	+	7.95850i	0.107009	+	0.258344i
$950$		0			0
$951$	−6.99925	−	6.99925i	−0.226966	−	0.226966i
$952$	−0.872098	−	1.23942i	−0.0282648	−	0.0401697i
$953$	−8.84307	−	8.84307i	−0.286455	−	0.286455i	0.549222	−	0.835677i	$-0.314924\pi$
$953$	−8.84307	−	8.84307i	−0.286455	−	0.286455i	−0.835677	+	0.549222i	$0.814924\pi$
$954$	5.27120	+	71.6000i	0.170661	+	2.31813i
$955$		0			0
$956$	−29.3683	−	21.7941i	−0.949838	−	0.704870i
$957$	13.9754	+	5.78880i	0.451761	+	0.187125i
$958$	−9.39380	−	18.6689i	−0.303500	−	0.603166i
$959$	−26.1847			−0.845549
$960$		0			0
$961$	15.6274			0.504110
$962$	8.02306	+	15.9448i	0.258674	+	0.514080i
$963$	−40.0579	−	16.5925i	−1.29085	−	0.534686i
$964$	−44.6738	−	33.1522i	−1.43885	−	1.06776i
$965$		0			0
$966$	3.63899	+	49.4293i	0.117083	+	1.59036i
$967$	−33.2189	−	33.2189i	−1.06825	−	1.06825i	−0.997494	−	0.0707549i	$-0.977459\pi$
$967$	−33.2189	−	33.2189i	−1.06825	−	1.06825i	−0.0707549	−	0.997494i	$-0.522541\pi$
$968$	23.6751	−	16.6586i	0.760945	−	0.535428i
$969$	−1.39635	−	1.39635i	−0.0448572	−	0.0448572i
$970$		0			0
$971$	−1.16696	−	2.81729i	−0.0374495	−	0.0904111i	0.904048	−	0.427431i	$-0.140581\pi$
$971$	−1.16696	−	2.81729i	−0.0374495	−	0.0904111i	−0.941498	+	0.337019i	$0.890581\pi$
$972$	14.9895	+	25.0248i	0.480789	+	0.802670i
$973$	0.852067	−	2.05707i	0.0273160	−	0.0659467i
$974$	8.21293	−	24.8489i	0.263159	−	0.796211i
$975$		0			0
$976$	−4.14639	−	0.410786i	−0.132723	−	0.0131489i
$977$	13.5807			0.434484			0.217242	−	0.976118i	$-0.430294\pi$
$977$	13.5807			0.434484			0.217242	+	0.976118i	$0.430294\pi$
$978$	−2.46374	+	7.45426i	−0.0787817	+	0.238361i
$979$	−6.77316	−	2.80553i	−0.216471	−	0.0896653i
$980$		0			0
$981$	−17.7004	−	42.7325i	−0.565130	−	1.36434i
$982$	−28.4741	+	32.9999i	−0.908646	+	1.05307i
$983$	−29.0855	+	29.0855i	−0.927684	+	0.927684i	−0.997556	−	0.0698724i	$-0.977741\pi$
$983$	−29.0855	+	29.0855i	−0.927684	+	0.927684i	0.0698724	+	0.997556i	$0.477741\pi$
$984$	15.7201	+	70.1462i	0.501140	+	2.23618i
$985$		0			0
$986$	−1.94357	+	0.143086i	−0.0618959	+	0.00455679i
$987$	−1.39635	−	3.37109i	−0.0444463	−	0.107303i
$988$	1.07705	+	7.27525i	0.0342654	+	0.231456i
$989$	−9.94424	+	24.0075i	−0.316209	+	0.763395i
$990$		0			0
$991$	6.64680			0.211143			0.105571	−	0.994412i	$-0.466333\pi$
$991$	6.64680			0.211143			0.105571	+	0.994412i	$0.466333\pi$
$992$	−27.9949	+	26.6151i	−0.888839	+	0.845030i
$993$			47.4160i			1.50470i
$994$	11.5711	+	22.9960i	0.367013	+	0.729390i
$995$		0			0
$996$	10.0318	+	67.7631i	0.317871	+	2.14716i
$997$	18.2353	+	44.0238i	0.577516	+	1.39425i	0.895035	+	0.445996i	$0.147150\pi$
$997$	18.2353	+	44.0238i	0.577516	+	1.39425i	−0.317519	+	0.948252i	$0.602850\pi$
$998$	2.52035	+	34.2345i	0.0797803	+	1.08367i
$999$	41.7244	−	41.7244i	1.32010	−	1.32010i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	800.2.ba.d.749.1		8
5.2	odd	4		800.2.y.b.301.2		8
5.3	odd	4		32.2.g.b.13.1	yes	8
5.4	even	2		800.2.ba.c.749.2		8
15.8	even	4		288.2.v.b.109.2		8
20.3	even	4		128.2.g.b.17.2		8
32.5	even	8		800.2.ba.c.549.2		8
40.3	even	4		256.2.g.c.33.1		8
40.13	odd	4		256.2.g.d.33.2		8
60.23	odd	4		1152.2.v.b.145.1		8
80.3	even	4		512.2.g.g.321.2		8
80.13	odd	4		512.2.g.e.321.1		8
80.43	even	4		512.2.g.f.321.1		8
80.53	odd	4		512.2.g.h.321.2		8
160.3	even	8		512.2.g.g.193.2		8
160.13	odd	8		512.2.g.h.193.2		8
160.37	odd	8		800.2.y.b.101.2		8
160.43	even	8		256.2.g.c.225.1		8
160.53	odd	8		256.2.g.d.225.2		8
160.69	even	8	inner	800.2.ba.d.549.1		8
160.83	even	8		512.2.g.f.193.1		8
160.93	odd	8		512.2.g.e.193.1		8
160.123	even	8		128.2.g.b.113.2		8
160.133	odd	8		32.2.g.b.5.1	✓	8
320.123	even	16		4096.2.a.q.1.8		8
320.133	odd	16		4096.2.a.k.1.1		8
320.283	even	16		4096.2.a.q.1.1		8
320.293	odd	16		4096.2.a.k.1.8		8
480.293	even	8		288.2.v.b.37.2		8
480.443	odd	8		1152.2.v.b.1009.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.2.g.b.5.1	✓	8	160.133	odd	8
32.2.g.b.13.1	yes	8	5.3	odd	4
128.2.g.b.17.2		8	20.3	even	4
128.2.g.b.113.2		8	160.123	even	8
256.2.g.c.33.1		8	40.3	even	4
256.2.g.c.225.1		8	160.43	even	8
256.2.g.d.33.2		8	40.13	odd	4
256.2.g.d.225.2		8	160.53	odd	8
288.2.v.b.37.2		8	480.293	even	8
288.2.v.b.109.2		8	15.8	even	4
512.2.g.e.193.1		8	160.93	odd	8
512.2.g.e.321.1		8	80.13	odd	4
512.2.g.f.193.1		8	160.83	even	8
512.2.g.f.321.1		8	80.43	even	4
512.2.g.g.193.2		8	160.3	even	8
512.2.g.g.321.2		8	80.3	even	4
512.2.g.h.193.2		8	160.13	odd	8
512.2.g.h.321.2		8	80.53	odd	4
800.2.y.b.101.2		8	160.37	odd	8
800.2.y.b.301.2		8	5.2	odd	4
800.2.ba.c.549.2		8	32.5	even	8
800.2.ba.c.749.2		8	5.4	even	2
800.2.ba.d.549.1		8	160.69	even	8	inner
800.2.ba.d.749.1		8	1.1	even	1	trivial
1152.2.v.b.145.1		8	60.23	odd	4
1152.2.v.b.1009.1		8	480.443	odd	8
4096.2.a.k.1.1		8	320.133	odd	16
4096.2.a.k.1.8		8	320.293	odd	16
4096.2.a.q.1.1		8	320.283	even	16
4096.2.a.q.1.8		8	320.123	even	16

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 800 = 2^{5} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	800.ba (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.635665 - 1.26330i) q^{2} +(2.60607 + 1.07947i) q^{3} +(-1.19186 + 1.60607i) q^{4} +(-0.292893 - 3.97844i) q^{6} +(1.68554 + 1.68554i) q^{7} +(2.78658 + 0.484753i) q^{8} +(3.50504 + 3.50504i) q^{9} +O(q^{10})\)	\(q+(-0.635665 - 1.26330i) q^{2} +(2.60607 + 1.07947i) q^{3} +(-1.19186 + 1.60607i) q^{4} +(-0.292893 - 3.97844i) q^{6} +(1.68554 + 1.68554i) q^{7} +(2.78658 + 0.484753i) q^{8} +(3.50504 + 3.50504i) q^{9} +(-0.334743 - 0.808140i) q^{11} +(-4.83978 + 2.89897i) q^{12} +(0.451835 - 1.09083i) q^{13} +(1.05791 - 3.20079i) q^{14} +(-1.15894 - 3.82843i) q^{16} -0.224777 q^{17} +(2.19989 - 6.65595i) q^{18} +(2.87740 + 1.19186i) q^{19} +(2.57316 + 6.21215i) q^{21} +(-0.808140 + 0.936588i) q^{22} +(-3.68554 + 3.68554i) q^{23} +(6.73875 + 4.27133i) q^{24} +(-1.66526 + 0.122597i) q^{26} +(2.11239 + 5.09976i) q^{27} +(-4.71604 + 0.698175i) q^{28} +(-2.34610 + 5.66398i) q^{29} +6.82843 q^{31} +(-4.09976 + 3.89769i) q^{32} -2.46742i q^{33} +(0.142883 + 0.283962i) q^{34} +(-9.80686 + 1.45183i) q^{36} +(-4.09083 - 9.87613i) q^{37} +(-0.323388 - 4.39265i) q^{38} +(2.35503 - 2.35503i) q^{39} +(6.37109 + 6.37109i) q^{41} +(6.21215 - 7.19951i) q^{42} +(4.60607 - 1.90790i) q^{43} +(1.69690 + 0.425569i) q^{44} +(6.99872 + 2.31318i) q^{46} -0.542661 q^{47} +(1.11239 - 11.2282i) q^{48} -1.31788i q^{49} +(-0.585786 - 0.242641i) q^{51} +(1.21342 + 2.02579i) q^{52} +(-9.46191 + 3.91925i) q^{53} +(5.09976 - 5.91032i) q^{54} +(3.87983 + 5.51397i) q^{56} +(6.21215 + 6.21215i) q^{57} +(8.64665 - 0.636568i) q^{58} +(3.36524 - 1.39393i) q^{59} +(0.398630 - 0.962379i) q^{61} +(-4.34059 - 8.62636i) q^{62} +11.8158i q^{63} +(7.53003 + 2.70160i) q^{64} +(-3.11709 + 1.56845i) q^{66} +(3.57558 + 1.48105i) q^{67} +(0.267903 - 0.361009i) q^{68} +(-13.5832 + 5.62636i) q^{69} +(-5.39978 + 5.39978i) q^{71} +(8.06799 + 11.4661i) q^{72} +(-5.15894 + 5.15894i) q^{73} +(-9.87613 + 11.4459i) q^{74} +(-5.34367 + 3.20079i) q^{76} +(0.797933 - 1.92638i) q^{77} +(-4.47212 - 1.47810i) q^{78} -8.39218i q^{79} +0.699980i q^{81} +(3.99872 - 12.0985i) q^{82} +(4.64665 - 11.2180i) q^{83} +(-13.0440 - 3.27133i) q^{84} +(-5.33817 - 4.60607i) q^{86} +(-12.2282 + 12.2282i) q^{87} +(-0.541038 - 2.41421i) q^{88} +(5.92638 - 5.92638i) q^{89} +(2.60022 - 1.07705i) q^{91} +(-1.52660 - 10.3119i) q^{92} +(17.7954 + 7.37109i) q^{93} +(0.344951 + 0.685544i) q^{94} +(-14.8917 + 5.73210i) q^{96} -4.19951i q^{97} +(-1.66488 + 0.837733i) q^{98} +(1.65928 - 4.00585i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} - 4 q^{4} - 8 q^{6} - 8 q^{7} + 12 q^{8}+O(q^{10}) \) 8 * q + 4 * q^3 - 4 * q^4 - 8 * q^6 - 8 * q^7 + 12 * q^8	\( 8 q + 4 q^{3} - 4 q^{4} - 8 q^{6} - 8 q^{7} + 12 q^{8} + 4 q^{11} - 4 q^{12} - 12 q^{14} + 8 q^{18} - 4 q^{19} - 12 q^{22} - 8 q^{23} + 8 q^{24} - 20 q^{26} + 16 q^{27} - 16 q^{28} + 32 q^{31} - 40 q^{36} - 16 q^{37} - 8 q^{38} - 16 q^{39} + 8 q^{41} + 16 q^{42} + 20 q^{43} - 20 q^{44} + 12 q^{46} + 16 q^{47} + 8 q^{48} - 16 q^{51} + 20 q^{52} - 16 q^{53} + 8 q^{54} + 8 q^{56} + 16 q^{57} - 4 q^{58} + 20 q^{59} + 24 q^{61} + 8 q^{62} + 8 q^{64} - 28 q^{66} + 12 q^{67} + 32 q^{68} - 32 q^{69} - 24 q^{71} - 12 q^{72} - 32 q^{73} - 8 q^{74} - 20 q^{76} - 16 q^{77} - 4 q^{78} - 12 q^{82} - 36 q^{83} - 8 q^{84} + 4 q^{86} - 56 q^{87} + 16 q^{89} + 40 q^{91} + 32 q^{93} + 24 q^{94} - 16 q^{96} + 36 q^{98} - 28 q^{99}+O(q^{100}) \) 8 * q + 4 * q^3 - 4 * q^4 - 8 * q^6 - 8 * q^7 + 12 * q^8 + 4 * q^11 - 4 * q^12 - 12 * q^14 + 8 * q^18 - 4 * q^19 - 12 * q^22 - 8 * q^23 + 8 * q^24 - 20 * q^26 + 16 * q^27 - 16 * q^28 + 32 * q^31 - 40 * q^36 - 16 * q^37 - 8 * q^38 - 16 * q^39 + 8 * q^41 + 16 * q^42 + 20 * q^43 - 20 * q^44 + 12 * q^46 + 16 * q^47 + 8 * q^48 - 16 * q^51 + 20 * q^52 - 16 * q^53 + 8 * q^54 + 8 * q^56 + 16 * q^57 - 4 * q^58 + 20 * q^59 + 24 * q^61 + 8 * q^62 + 8 * q^64 - 28 * q^66 + 12 * q^67 + 32 * q^68 - 32 * q^69 - 24 * q^71 - 12 * q^72 - 32 * q^73 - 8 * q^74 - 20 * q^76 - 16 * q^77 - 4 * q^78 - 12 * q^82 - 36 * q^83 - 8 * q^84 + 4 * q^86 - 56 * q^87 + 16 * q^89 + 40 * q^91 + 32 * q^93 + 24 * q^94 - 16 * q^96 + 36 * q^98 - 28 * q^99

Introduction

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Database

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