LMFDB - Embedded newform 800.2.ba.c.349.1

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			349.1
Root			$0.500000 + 0.0297061i$ of defining polynomial
Character	$\chi$	$=$	800.349
Dual form			800.2.ba.c.149.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.167452 + 1.40426i) q^{2} +(-0.529706 + 1.27882i) q^{3} +(-1.94392 - 0.470294i) q^{4} +(-1.70711 - 0.957989i) q^{6} +(2.74912 + 2.74912i) q^{7} +(0.985930 - 2.65103i) q^{8} +(0.766519 + 0.766519i) q^{9} +O(q^{10})$	\(q+(-0.167452 + 1.40426i) q^{2} +(-0.529706 + 1.27882i) q^{3} +(-1.94392 - 0.470294i) q^{4} +(-1.70711 - 0.957989i) q^{6} +(2.74912 + 2.74912i) q^{7} +(0.985930 - 2.65103i) q^{8} +(0.766519 + 0.766519i) q^{9} +(0.135390 - 0.0560803i) q^{11} +(1.63113 - 2.23681i) q^{12} +(2.85054 + 1.18073i) q^{13} +(-4.32083 + 3.40014i) q^{14} +(3.55765 + 1.82843i) q^{16} +6.44549 q^{17} +(-1.20475 + 0.948041i) q^{18} +(-0.805198 + 1.94392i) q^{19} +(-4.97186 + 2.05941i) q^{21} +(0.0560803 + 0.199514i) q^{22} +(-0.749118 + 0.749118i) q^{23} +(2.86794 + 2.66510i) q^{24} +(-2.13539 + 3.80520i) q^{26} +(-5.22274 + 2.16333i) q^{27} +(-4.05117 - 6.63696i) q^{28} +(-4.32417 - 1.79113i) q^{29} +1.17157 q^{31} +(-3.16333 + 4.68971i) q^{32} +0.202846i q^{33} +(-1.07931 + 9.05117i) q^{34} +(-1.12956 - 1.85054i) q^{36} +(4.18073 - 1.73172i) q^{37} +(-2.59495 - 1.45622i) q^{38} +(-3.01990 + 3.01990i) q^{39} +(-2.49824 - 2.49824i) q^{41} +(-2.05941 - 7.32666i) q^{42} +(-2.52971 - 6.10725i) q^{43} +(-0.289561 + 0.0453426i) q^{44} +(-0.926518 - 1.17740i) q^{46} -2.66981 q^{47} +(-4.22274 + 3.58107i) q^{48} +8.11529i q^{49} +(-3.41421 + 8.24264i) q^{51} +(-4.98593 - 3.63584i) q^{52} +(0.682497 + 1.64769i) q^{53} +(-2.16333 - 7.69637i) q^{54} +(9.99842 - 4.57754i) q^{56} +(-2.05941 - 2.05941i) q^{57} +(3.23931 - 5.77235i) q^{58} +(-1.43744 - 3.47029i) q^{59} +(-3.46760 - 1.43633i) q^{61} +(-0.196182 + 1.64520i) q^{62} +4.21450i q^{63} +(-6.05588 - 5.22746i) q^{64} +(-0.284849 - 0.0339670i) q^{66} +(-5.83176 + 14.0791i) q^{67} +(-12.5295 - 3.03127i) q^{68} +(-0.561177 - 1.35480i) q^{69} +(-3.40950 + 3.40950i) q^{71} +(2.78780 - 1.27633i) q^{72} +(0.442353 - 0.442353i) q^{73} +(1.73172 + 6.16084i) q^{74} +(2.47945 - 3.40014i) q^{76} +(0.526374 + 0.218031i) q^{77} +(-3.73505 - 4.74642i) q^{78} -7.07550i q^{79} -4.57283i q^{81} +(3.92652 - 3.08985i) q^{82} +(7.23931 + 2.99862i) q^{83} +(10.6334 - 1.66510i) q^{84} +(8.99980 - 2.52971i) q^{86} +(4.58107 - 4.58107i) q^{87} +(-0.0151854 - 0.414214i) q^{88} +(4.21803 - 4.21803i) q^{89} +(4.59050 + 11.0824i) q^{91} +(1.80853 - 1.10392i) q^{92} +(-0.620589 + 1.49824i) q^{93} +(0.447065 - 3.74912i) q^{94} +(-4.32167 - 6.52951i) q^{96} -10.3267i q^{97} +(-11.3960 - 1.35892i) q^{98} +(0.146766 + 0.0607923i) 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 $\left(\mathbb{Z}/800\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$577$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$1$	$-1$

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 $

$2$	−0.167452	+	1.40426i	−0.118406	+	0.992965i
$2$	−0.167452	+	1.40426i	−0.118406	+	0.992965i
$3$	−0.529706	+	1.27882i	−0.305826	+	0.738329i	0.694005	+	0.719970i	$0.255844\pi$
$3$	−0.529706	+	1.27882i	−0.305826	+	0.738329i	−0.999831	+	0.0183595i	$0.994156\pi$
$4$	−1.94392	−	0.470294i	−0.971960	−	0.235147i
$5$		0			0
$5$		0			0
$6$	−1.70711	−	0.957989i	−0.696923	−	0.391097i
$7$	2.74912	+	2.74912i	1.03907	+	1.03907i	0.999205	+	0.0398636i	$0.0126924\pi$
$7$	2.74912	+	2.74912i	1.03907	+	1.03907i	0.0398636	+	0.999205i	$0.487308\pi$
$8$	0.985930	−	2.65103i	0.348579	−	0.937279i
$9$	0.766519	+	0.766519i	0.255506	+	0.255506i
$10$		0			0
$11$	0.135390	−	0.0560803i	0.0408216	−	0.0169089i	−0.362179	−	0.932108i	$-0.617967\pi$
$11$	0.135390	−	0.0560803i	0.0408216	−	0.0169089i	0.403001	+	0.915200i	$0.367967\pi$
$12$	1.63113	−	2.23681i	0.470866	−	0.645712i
$13$	2.85054	+	1.18073i	0.790598	+	0.327476i	0.741184	−	0.671302i	$-0.234265\pi$
$13$	2.85054	+	1.18073i	0.790598	+	0.327476i	0.0494138	+	0.998778i	$0.484265\pi$
$14$	−4.32083	+	3.40014i	−1.15479	+	0.908727i
$15$		0			0
$16$	3.55765	+	1.82843i	0.889412	+	0.457107i
$17$	6.44549			1.56326			0.781630	−	0.623742i	$-0.214389\pi$
$17$	6.44549			1.56326			0.781630	+	0.623742i	$0.214389\pi$
$18$	−1.20475	+	0.948041i	−0.283962	+	0.223455i
$19$	−0.805198	+	1.94392i	−0.184725	+	0.445966i	−0.988929	−	0.148387i	$-0.952592\pi$
$19$	−0.805198	+	1.94392i	−0.184725	+	0.445966i	0.804204	+	0.594353i	$0.202592\pi$
$20$		0			0
$21$	−4.97186	+	2.05941i	−1.08495	+	0.449401i
$22$	0.0560803	+	0.199514i	0.0119564	+	0.0425365i
$23$	−0.749118	+	0.749118i	−0.156202	+	0.156202i	−0.780881	−	0.624679i	$-0.785230\pi$
$23$	−0.749118	+	0.749118i	−0.156202	+	0.156202i	0.624679	+	0.780881i	$0.285230\pi$
$24$	2.86794	+	2.66510i	0.585416	+	0.544010i
$25$		0			0
$26$	−2.13539	+	3.80520i	−0.418784	+	0.746261i
$27$	−5.22274	+	2.16333i	−1.00512	+	0.416333i
$28$	−4.05117	−	6.63696i	−0.765599	−	1.25427i
$29$	−4.32417	−	1.79113i	−0.802978	−	0.332604i	−0.0568292	−	0.998384i	$-0.518099\pi$
$29$	−4.32417	−	1.79113i	−0.802978	−	0.332604i	−0.746148	+	0.665780i	$0.768099\pi$
$30$		0			0
$31$	1.17157			0.210421			0.105210	−	0.994450i	$-0.466448\pi$
$31$	1.17157			0.210421			0.105210	+	0.994450i	$0.466448\pi$
$32$	−3.16333	+	4.68971i	−0.559203	+	0.829031i
$33$			0.202846i			0.0353109i
$34$	−1.07931	+	9.05117i	−0.185100	+	1.55226i
$35$		0			0
$36$	−1.12956	−	1.85054i	−0.188260	−	0.308423i
$37$	4.18073	−	1.73172i	0.687308	−	0.284692i	−0.0115700	−	0.999933i	$-0.503683\pi$
$37$	4.18073	−	1.73172i	0.687308	−	0.284692i	0.698878	+	0.715241i	$0.253683\pi$
$38$	−2.59495	−	1.45622i	−0.420956	−	0.236231i
$39$	−3.01990	+	3.01990i	−0.483571	+	0.483571i
$40$		0			0
$41$	−2.49824	−	2.49824i	−0.390159	−	0.390159i	0.484585	−	0.874744i	$-0.338971\pi$
$41$	−2.49824	−	2.49824i	−0.390159	−	0.390159i	−0.874744	+	0.484585i	$0.838971\pi$
$42$	−2.05941	−	7.32666i	−0.317774	−	1.13053i
$43$	−2.52971	−	6.10725i	−0.385777	−	0.931347i	−0.990824	−	0.135158i	$-0.956846\pi$
$43$	−2.52971	−	6.10725i	−0.385777	−	0.931347i	0.605048	−	0.796189i	$-0.293154\pi$
$44$	−0.289561	+	0.0453426i	−0.0436530	+	0.00683566i
$45$		0			0
$46$	−0.926518	−	1.17740i	−0.136608	−	0.173598i
$47$	−2.66981			−0.389432			−0.194716	−	0.980860i	$-0.562378\pi$
$47$	−2.66981			−0.389432			−0.194716	+	0.980860i	$0.562378\pi$
$48$	−4.22274	+	3.58107i	−0.609500	+	0.516884i
$49$			8.11529i			1.15933i
$50$		0			0
$51$	−3.41421	+	8.24264i	−0.478086	+	1.15420i
$52$	−4.98593	−	3.63584i	−0.691424	−	0.504200i
$53$	0.682497	+	1.64769i	0.0937482	+	0.226328i	0.963797	−	0.266638i	$-0.0859127\pi$
$53$	0.682497	+	1.64769i	0.0937482	+	0.226328i	−0.870049	+	0.492966i	$0.835913\pi$
$54$	−2.16333	−	7.69637i	−0.294392	−	1.04734i
$55$		0			0
$56$	9.99842	−	4.57754i	1.33610	−	0.611700i
$57$	−2.05941	−	2.05941i	−0.272776	−	0.272776i
$58$	3.23931	−	5.77235i	0.425342	−	0.757946i
$59$	−1.43744	−	3.47029i	−0.187139	−	0.451794i	0.802267	−	0.596965i	$-0.203627\pi$
$59$	−1.43744	−	3.47029i	−0.187139	−	0.451794i	−0.989407	+	0.145171i	$0.953627\pi$
$60$		0			0
$61$	−3.46760	−	1.43633i	−0.443981	−	0.183903i	0.149482	−	0.988764i	$-0.452239\pi$
$61$	−3.46760	−	1.43633i	−0.443981	−	0.183903i	−0.593462	+	0.804862i	$0.702239\pi$
$62$	−0.196182	+	1.64520i	−0.0249152	+	0.208940i
$63$			4.21450i			0.530977i
$64$	−6.05588	−	5.22746i	−0.756985	−	0.653432i
$65$		0			0
$66$	−0.284849	−	0.0339670i	−0.0350625	−	0.00418104i
$67$	−5.83176	+	14.0791i	−0.712463	+	1.72004i	−0.0187090	+	0.999825i	$0.505956\pi$
$67$	−5.83176	+	14.0791i	−0.712463	+	1.72004i	−0.693754	+	0.720212i	$0.744044\pi$
$68$	−12.5295	−	3.03127i	−1.51943	−	0.367596i
$69$	−0.561177	−	1.35480i	−0.0675578	−	0.163099i
$70$		0			0
$71$	−3.40950	+	3.40950i	−0.404633	+	0.404633i	−0.879862	−	0.475229i	$-0.842365\pi$
$71$	−3.40950	+	3.40950i	−0.404633	+	0.404633i	0.475229	+	0.879862i	$0.342365\pi$
$72$	2.78780	−	1.27633i	0.328545	−	0.150417i
$73$	0.442353	−	0.442353i	0.0517735	−	0.0517735i	−0.680746	−	0.732520i	$-0.738344\pi$
$73$	0.442353	−	0.442353i	0.0517735	−	0.0517735i	0.732520	+	0.680746i	$0.238344\pi$
$74$	1.73172	+	6.16084i	0.201308	+	0.716183i
$75$		0			0
$76$	2.47945	−	3.40014i	0.284413	−	0.390023i
$77$	0.526374	+	0.218031i	0.0599859	+	0.0248470i
$78$	−3.73505	−	4.74642i	−0.422911	−	0.537427i
$79$		−	7.07550i		−	0.796056i	−0.917373	−	0.398028i	$-0.869695\pi$
$79$		−	7.07550i		−	0.796056i	0.917373	−	0.398028i	$-0.130305\pi$
$80$		0			0
$81$		−	4.57283i		−	0.508093i
$82$	3.92652	−	3.08985i	0.433611	−	0.341217i
$83$	7.23931	+	2.99862i	0.794617	+	0.329141i	0.742798	−	0.669515i	$-0.233498\pi$
$83$	7.23931	+	2.99862i	0.794617	+	0.329141i	0.0518190	+	0.998656i	$0.483498\pi$
$84$	10.6334	−	1.66510i	1.16020	−	0.181677i
$85$		0			0
$86$	8.99980	−	2.52971i	0.970474	−	0.272785i
$87$	4.58107	−	4.58107i	0.491143	−	0.491143i
$88$	−0.0151854	−	0.414214i	−0.00161877	−	0.0441553i
$89$	4.21803	−	4.21803i	0.447110	−	0.447110i	−0.447282	−	0.894393i	$-0.647608\pi$
$89$	4.21803	−	4.21803i	0.447110	−	0.447110i	0.894393	+	0.447282i	$0.147608\pi$
$90$		0			0
$91$	4.59050	+	11.0824i	0.481215	+	1.16176i
$92$	1.80853	−	1.10392i	0.188552	−	0.115092i
$93$	−0.620589	+	1.49824i	−0.0643521	+	0.155360i
$94$	0.447065	−	3.74912i	0.0461112	−	0.386692i
$95$		0			0
$96$	−4.32167	−	6.52951i	−0.441079	−	0.666415i
$97$		−	10.3267i		−	1.04851i	−0.851560	−	0.524257i	$-0.824343\pi$
$97$		−	10.3267i		−	1.04851i	0.851560	−	0.524257i	$-0.175657\pi$
$98$	−11.3960	−	1.35892i	−1.15117	−	0.137272i
$99$	0.146766	+	0.0607923i	0.0147505	+	0.00610986i
$100$		0			0
$101$	−4.31750	−	10.4234i	−0.429608	−	1.03716i	−0.979412	−	0.201871i	$-0.935298\pi$
$101$	−4.31750	−	10.4234i	−0.429608	−	1.03716i	0.549805	−	0.835293i	$-0.314702\pi$
$102$	−11.0031	−	6.17471i	−1.08947	−	0.611387i
$103$	13.3134	+	13.3134i	1.31181	+	1.31181i	0.920080	+	0.391732i	$0.128124\pi$
$103$	13.3134	+	13.3134i	1.31181	+	1.31181i	0.391732	+	0.920080i	$0.371876\pi$
$104$	5.94059	−	6.39274i	0.582523	−	0.626860i
$105$		0			0
$106$	−2.42809	+	0.682497i	−0.235836	+	0.0662900i
$107$	−5.48861	−	13.2507i	−0.530604	−	1.28099i	−0.931124	−	0.364704i	$-0.881170\pi$
$107$	−5.48861	−	13.2507i	−0.530604	−	1.28099i	0.400519	−	0.916288i	$-0.368830\pi$
$108$	11.1700	−	1.74912i	1.07483	−	0.168309i
$109$	4.87515	−	11.7697i	0.466955	−	1.12733i	−0.498531	−	0.866872i	$-0.666127\pi$
$109$	4.87515	−	11.7697i	0.466955	−	1.12733i	0.965486	−	0.260456i	$-0.0838730\pi$
$110$		0			0
$111$			6.26372i			0.594526i
$112$	4.75383	+	14.8070i	0.449195	+	1.39913i
$113$	−5.88118			−0.553254			−0.276627	−	0.960977i	$-0.589217\pi$
$113$	−5.88118			−0.553254			−0.276627	+	0.960977i	$0.589217\pi$
$114$	3.23681	−	2.54711i	0.303155	−	0.238558i
$115$		0			0
$116$	7.56348	+	5.51544i	0.702251	+	0.512096i
$117$	1.27994	+	3.09005i	0.118330	+	0.285675i
$118$	5.11391	−	1.43744i	0.470774	−	0.132327i
$119$	17.7194	+	17.7194i	1.62433	+	1.62433i
$120$		0			0
$121$	−7.76299	+	7.76299i	−0.705726	+	0.705726i
$122$	2.59764	−	4.62891i	0.235179	−	0.419082i
$123$	4.51813	−	1.87147i	0.407386	−	0.168745i
$124$	−2.27744	−	0.550984i	−0.204520	−	0.0494798i
$125$		0			0
$126$	−5.91828	−	0.705727i	−0.527242	−	0.0628711i
$127$			15.4022i			1.36672i	0.730081	+	0.683360i	$0.239482\pi$
$127$			15.4022i			1.36672i	−0.730081	+	0.683360i	$0.760518\pi$
$128$	8.35480	−	7.62872i	0.738467	−	0.674290i
$129$	9.15010			0.805621
$130$		0			0
$131$	−2.96382	−	1.22765i	−0.258950	−	0.107261i	0.249432	−	0.968392i	$-0.419756\pi$
$131$	−2.96382	−	1.22765i	−0.258950	−	0.107261i	−0.508382	+	0.861132i	$0.669756\pi$
$132$	0.0953972	−	0.394316i	0.00830326	−	0.0343208i
$133$	−7.55765	+	3.13048i	−0.655331	+	0.271447i
$134$	−18.7943	−	10.5469i	−1.62358	−	0.911114i
$135$		0			0
$136$	6.35480	−	17.0872i	0.544920	−	1.46521i
$137$	10.7757	−	10.7757i	0.920628	−	0.920628i	−0.0764454	−	0.997074i	$-0.524357\pi$
$137$	10.7757	−	10.7757i	0.920628	−	0.920628i	0.997074	+	0.0764454i	$0.0243571\pi$
$138$	1.99647	−	0.561177i	0.169951	−	0.0477706i
$139$	−4.78372	+	1.98148i	−0.405750	+	0.168067i	−0.576218	−	0.817296i	$-0.695472\pi$
$139$	−4.78372	+	1.98148i	−0.405750	+	0.168067i	0.170468	+	0.985363i	$0.445472\pi$
$140$		0			0
$141$	1.41421	−	3.41421i	0.119098	−	0.287529i
$142$	−4.21692	−	5.35877i	−0.353876	−	0.449698i
$143$	0.452150			0.0378107
$144$	1.32548	+	4.12853i	0.110457	+	0.344044i
$145$		0			0
$146$	0.547108	+	0.695253i	0.0452789	+	0.0575396i
$147$	−10.3780	−	4.29872i	−0.855966	−	0.354553i
$148$	−8.94142	+	1.40014i	−0.734981	+	0.115091i
$149$	−4.32417	+	1.79113i	−0.354250	+	0.146735i	−0.552709	−	0.833374i	$-0.686406\pi$
$149$	−4.32417	+	1.79113i	−0.354250	+	0.146735i	0.198460	+	0.980109i	$0.436406\pi$
$150$		0			0
$151$	13.2344	+	13.2344i	1.07700	+	1.07700i	0.996777	+	0.0802232i	$0.0255633\pi$
$151$	13.2344	+	13.2344i	1.07700	+	1.07700i	0.0802232	+	0.996777i	$0.474437\pi$
$152$	4.35951	+	4.05117i	0.353603	+	0.328593i
$153$	4.94059	+	4.94059i	0.399423	+	0.399423i
$154$	−0.394316	+	0.702659i	−0.0317749	+	0.0566219i
$155$		0			0
$156$	7.29068	−	4.45020i	0.583721	−	0.356301i
$157$	−6.60790	+	15.9529i	−0.527368	+	1.27318i	0.405874	+	0.913929i	$0.366967\pi$
$157$	−6.60790	+	15.9529i	−0.527368	+	1.27318i	−0.933242	+	0.359249i	$0.883033\pi$
$158$	9.93588	+	1.18481i	0.790456	+	0.0942581i
$159$	−2.46863			−0.195775
$160$		0			0
$161$	−4.11882			−0.324609
$162$	6.42147	+	0.765730i	0.504518	+	0.0601614i
$163$	−4.41088	+	10.6488i	−0.345487	+	0.834079i	0.651654	+	0.758516i	$0.274075\pi$
$163$	−4.41088	+	10.6488i	−0.345487	+	0.834079i	−0.997141	+	0.0755629i	$0.975925\pi$
$164$	3.68146	+	6.03127i	0.287474	+	0.470963i
$165$		0			0
$166$	−5.42309	+	9.66378i	−0.420914	+	0.750055i
$167$	2.98677	+	2.98677i	0.231123	+	0.231123i	0.813161	−	0.582038i	$-0.197745\pi$
$167$	2.98677	+	2.98677i	0.231123	+	0.231123i	−0.582038	+	0.813161i	$0.697745\pi$
$168$	0.557647	+	15.2110i	0.0430234	+	1.17355i
$169$	−2.46094	−	2.46094i	−0.189303	−	0.189303i
$170$		0			0
$171$	−2.10725	+	0.872852i	−0.161145	+	0.0667486i
$172$	2.04534	+	13.0617i	0.155956	+	0.995946i
$173$	18.9529	+	7.85054i	1.44096	+	0.596866i	0.960031	−	0.279894i	$-0.0902992\pi$
$173$	18.9529	+	7.85054i	1.44096	+	0.596866i	0.480930	+	0.876759i	$0.340299\pi$
$174$	5.66593	+	7.20015i	0.429533	+	0.545842i
$175$		0			0
$176$	0.584208	+	0.0480365i	0.0440364	+	0.00362089i
$177$	5.19932			0.390805
$178$	5.21692	+	6.62955i	0.391024	+	0.496906i
$179$	9.60549	−	23.1897i	0.717948	−	1.73328i	0.0388344	−	0.999246i	$-0.487636\pi$
$179$	9.60549	−	23.1897i	0.717948	−	1.73328i	0.679113	−	0.734033i	$-0.262364\pi$
$180$		0			0
$181$	1.87868	−	0.778175i	0.139641	−	0.0578413i	−0.311768	−	0.950158i	$-0.600921\pi$
$181$	1.87868	−	0.778175i	0.139641	−	0.0578413i	0.451410	+	0.892317i	$0.350921\pi$
$182$	−16.3314	+	4.59050i	−1.21056	+	0.340270i
$183$	3.67362	−	3.67362i	0.271562	−	0.271562i
$184$	1.24735	+	2.72451i	0.0919561	+	0.200853i
$185$		0			0
$186$	−2.00000	−	1.12235i	−0.146647	−	0.0822950i
$187$	0.872654	−	0.361465i	0.0638148	−	0.0264329i
$188$	5.18989	+	1.25559i	0.378512	+	0.0915736i
$189$	−20.3052	−	8.41068i	−1.47699	−	0.611787i
$190$		0			0
$191$	9.05902			0.655487			0.327744	−	0.944767i	$-0.393712\pi$
$191$	9.05902			0.655487			0.327744	+	0.944767i	$0.393712\pi$
$192$	9.89283	−	4.97539i	0.713954	−	0.359068i
$193$			6.24707i			0.449674i	0.974396	+	0.224837i	$0.0721850\pi$
$193$			6.24707i			0.449674i	−0.974396	+	0.224837i	$0.927815\pi$
$194$	14.5014	+	1.72922i	1.04114	+	0.124151i
$195$		0			0
$196$	3.81657	−	15.7755i	0.272612	−	1.12682i
$197$	−4.37691	+	1.81298i	−0.311842	+	0.129169i	−0.533115	−	0.846043i	$-0.678979\pi$
$197$	−4.37691	+	1.81298i	−0.311842	+	0.129169i	0.221273	+	0.975212i	$0.428979\pi$
$198$	−0.109945	+	0.195918i	−0.00781343	+	0.0139233i
$199$	−6.14186	+	6.14186i	−0.435385	+	0.435385i	−0.890455	−	0.455071i	$-0.849614\pi$
$199$	−6.14186	+	6.14186i	−0.435385	+	0.435385i	0.455071	+	0.890455i	$0.349614\pi$
$200$		0			0
$201$	−14.9156	−	14.9156i	−1.05206	−	1.05206i
$202$	15.3602	−	4.31750i	1.08074	−	0.303778i
$203$	−6.96362	−	16.8117i	−0.488750	−	1.17995i
$204$	10.5134	−	14.4173i	0.736087	−	1.00942i
$205$		0			0
$206$	−20.9249	+	16.4662i	−1.45791	+	1.14726i
$207$	−1.14843			−0.0798211
$208$	7.98233	+	9.41264i	0.553475	+	0.652649i
$209$			0.308343i			0.0213285i
$210$		0			0
$211$	5.21588	−	12.5923i	0.359076	−	0.866886i	−0.636354	−	0.771397i	$-0.719558\pi$
$211$	5.21588	−	12.5923i	0.359076	−	0.866886i	0.995430	−	0.0954895i	$-0.0304416\pi$
$212$	−0.551819	−	3.52396i	−0.0378991	−	0.242027i
$213$	−2.55412	−	6.16619i	−0.175005	−	0.422500i
$214$	19.5265	−	5.48861i	1.33481	−	0.375194i
$215$		0			0
$216$	0.585786	+	15.9785i	0.0398577	+	1.08720i
$217$	3.22079	+	3.22079i	0.218642	+	0.218642i
$218$	15.7114	+	8.81685i	1.06411	+	0.597153i
$219$	0.331374	+	0.800008i	0.0223922	+	0.0540595i
$220$		0			0
$221$	18.3731	+	7.61040i	1.23591	+	0.511931i
$222$	−8.79592	−	1.04887i	−0.590344	−	0.0703957i
$223$		−	0.960579i		−	0.0643251i	−0.999483	−	0.0321626i	$-0.989761\pi$
$223$		−	0.960579i		−	0.0643251i	0.999483	−	0.0321626i	$-0.0102394\pi$
$224$	−21.5889	+	4.19618i	−1.44247	+	0.280369i
$225$		0			0
$226$	0.984815	−	8.25873i	0.0655089	−	0.549362i
$227$	5.86932	−	14.1698i	0.389561	−	0.940482i	−0.600472	−	0.799646i	$-0.705021\pi$
$227$	5.86932	−	14.1698i	0.389561	−	0.940482i	0.990033	−	0.140837i	$-0.0449793\pi$
$228$	3.03480	+	4.97186i	0.200985	+	0.329270i
$229$	−1.80408	−	4.35544i	−0.119217	−	0.287816i	0.852994	−	0.521920i	$-0.174784\pi$
$229$	−1.80408	−	4.35544i	−0.119217	−	0.287816i	−0.972211	+	0.234105i	$0.924784\pi$
$230$		0			0
$231$	−0.557647	+	0.557647i	−0.0366905	+	0.0366905i
$232$	−9.01166	+	9.69755i	−0.591644	+	0.636675i
$233$	16.7918	−	16.7918i	1.10007	−	1.10007i	0.105663	−	0.994402i	$-0.466303\pi$
$233$	16.7918	−	16.7918i	1.10007	−	1.10007i	0.994402	−	0.105663i	$-0.0336965\pi$
$234$	−4.55357	+	1.27994i	−0.297676	+	0.0836723i
$235$		0			0
$236$	1.16222	+	7.42199i	0.0756538	+	0.483131i
$237$	9.04832	+	3.74794i	0.587751	+	0.243455i
$238$	−27.8499	+	21.9156i	−1.80524	+	1.42058i
$239$			15.8414i			1.02469i	0.858779	+	0.512347i	$0.171224\pi$
$239$			15.8414i			1.02469i	−0.858779	+	0.512347i	$0.828776\pi$
$240$		0			0
$241$		−	0.313335i		−	0.0201837i	−0.999949	−	0.0100918i	$-0.996788\pi$
$241$		−	0.313335i		−	0.0201837i	0.999949	−	0.0100918i	$-0.00321239\pi$
$242$	−9.60136	−	12.2012i	−0.617199	−	0.784324i
$243$	−9.82038	−	4.06774i	−0.629978	−	0.260945i
$244$	6.06524	+	4.42290i	0.388287	+	0.283147i
$245$		0			0
$246$	1.87147	+	6.65804i	0.119321	+	0.424501i
$247$	−4.59050	+	4.59050i	−0.292086	+	0.292086i
$248$	1.15509	−	3.10587i	0.0733482	−	0.197223i
$249$	−7.66941	+	7.66941i	−0.486029	+	0.486029i
$250$		0			0
$251$	−3.55903	−	8.59225i	−0.224644	−	0.542338i	0.770866	−	0.636997i	$-0.219824\pi$
$251$	−3.55903	−	8.59225i	−0.224644	−	0.542338i	−0.995510	+	0.0946593i	$0.969824\pi$
$252$	1.98205	−	8.19265i	0.124858	−	0.516089i
$253$	−0.0594122	+	0.143434i	−0.00373521	+	0.00901760i
$254$	−21.6287	−	2.57912i	−1.35711	−	0.161829i
$255$		0			0
$256$	9.31371	+	13.0098i	0.582107	+	0.813112i
$257$		−	18.9043i		−	1.17922i	−0.807689	−	0.589609i	$-0.799282\pi$
$257$		−	18.9043i		−	1.17922i	0.807689	−	0.589609i	$-0.200718\pi$
$258$	−1.53220	+	12.8492i	−0.0953907	+	0.799954i
$259$	16.2540	+	6.73263i	1.00998	+	0.418346i
$260$		0			0
$261$	−1.94162	−	4.68749i	−0.120183	−	0.290148i
$262$	2.22025	−	3.95641i	0.137167	−	0.244428i
$263$	−16.6366	−	16.6366i	−1.02585	−	1.02585i	−0.999657	−	0.0261975i	$-0.991660\pi$
$263$	−16.6366	−	16.6366i	−1.02585	−	1.02585i	−0.0261975	−	0.999657i	$-0.508340\pi$
$264$	0.537750	+	0.199992i	0.0330962	+	0.0123087i
$265$		0			0
$266$	−3.13048	−	11.1371i	−0.191942	−	0.682862i
$267$	3.15980	+	7.62844i	0.193377	+	0.466853i
$268$	17.9578	−	24.6260i	1.09695	−	1.50427i
$269$	5.01046	−	12.0963i	0.305493	−	0.737525i	−0.694347	−	0.719640i	$-0.744307\pi$
$269$	5.01046	−	12.0963i	0.305493	−	0.737525i	0.999840	−	0.0178850i	$-0.00569329\pi$
$270$		0			0
$271$		−	28.2141i		−	1.71388i	−0.515412	−	0.856942i	$-0.672361\pi$
$271$		−	28.2141i		−	1.71388i	0.515412	−	0.856942i	$-0.327639\pi$
$272$	22.9308	+	11.7851i	1.39038	+	0.714577i
$273$	−16.6041			−1.00493
$274$	13.3275	+	16.9363i	0.805144	+	1.02316i
$275$		0			0
$276$	0.453728	+	2.89754i	0.0273112	+	0.174412i
$277$	9.04006	+	21.8246i	0.543165	+	1.31132i	0.922479	+	0.386047i	$0.126160\pi$
$277$	9.04006	+	21.8246i	0.543165	+	1.31132i	−0.379314	+	0.925268i	$0.623840\pi$
$278$	−1.98148	−	7.04942i	−0.118841	−	0.422796i
$279$	0.898033	+	0.898033i	0.0537638	+	0.0537638i
$280$		0			0
$281$	3.00666	−	3.00666i	0.179363	−	0.179363i	−0.611715	−	0.791078i	$-0.709520\pi$
$281$	3.00666	−	3.00666i	0.179363	−	0.179363i	0.791078	+	0.611715i	$0.209520\pi$
$282$	4.55765	+	2.55765i	0.271404	+	0.152306i
$283$	−1.71293	+	0.709521i	−0.101823	+	0.0421766i	−0.433014	−	0.901387i	$-0.642550\pi$
$283$	−1.71293	+	0.709521i	−0.101823	+	0.0421766i	0.331190	+	0.943564i	$0.392550\pi$
$284$	8.23127	−	5.02433i	0.488436	−	0.298139i
$285$		0			0
$286$	−0.0757135	+	0.634939i	−0.00447703	+	0.0375447i
$287$		−	13.7359i		−	0.810804i
$288$	−6.01950	+	1.16999i	−0.354703	+	0.0689426i
$289$	24.5443			1.44378
$290$		0			0
$291$	13.2060	+	5.47010i	0.774148	+	0.320663i
$292$	−1.06793	+	0.651862i	−0.0624961	+	0.0381474i
$293$	−25.3917	+	10.5176i	−1.48340	+	0.614444i	−0.969869	−	0.243627i	$-0.921663\pi$
$293$	−25.3917	+	10.5176i	−1.48340	+	0.614444i	−0.513530	+	0.858071i	$0.671663\pi$
$294$	7.77436	−	13.8537i	0.453410	−	0.807963i
$295$		0			0
$296$	−0.468914	−	12.7906i	−0.0272551	−	0.743438i
$297$	−0.585786	+	0.585786i	−0.0339908	+	0.0339908i
$298$	−1.79113	−	6.37220i	−0.103757	−	0.369132i
$299$	−3.01990	+	1.25088i	−0.174645	+	0.0723404i
$300$		0			0
$301$	9.83509	−	23.7440i	0.566885	−	1.36858i
$302$	−20.8007	+	16.3685i	−1.19695	+	0.941900i
$303$	15.6167			0.897154
$304$	−6.41893	+	5.44353i	−0.368151	+	0.312208i
$305$		0			0
$306$	−7.76521	+	6.11058i	−0.443907	+	0.349319i
$307$	−14.0065	−	5.80167i	−0.799391	−	0.331119i	−0.0546786	−	0.998504i	$-0.517413\pi$
$307$	−14.0065	−	5.80167i	−0.799391	−	0.331119i	−0.744713	+	0.667385i	$0.767413\pi$
$308$	−0.920690	−	0.671386i	−0.0524612	−	0.0382558i
$309$	−24.0777	+	9.97332i	−1.36973	+	0.567363i
$310$		0			0
$311$	7.15481	+	7.15481i	0.405712	+	0.405712i	0.880240	−	0.474528i	$-0.157381\pi$
$311$	7.15481	+	7.15481i	0.405712	+	0.405712i	−0.474528	+	0.880240i	$0.657381\pi$
$312$	5.02842	+	10.9832i	0.284678	+	0.621803i
$313$	−11.8512	−	11.8512i	−0.669868	−	0.669868i	0.287817	−	0.957685i	$-0.407070\pi$
$313$	−11.8512	−	11.8512i	−0.669868	−	0.669868i	−0.957685	+	0.287817i	$0.907070\pi$
$314$	−21.2956	−	11.9506i	−1.20178	−	0.674410i
$315$		0			0
$316$	−3.32756	+	13.7542i	−0.187190	+	0.773734i
$317$	7.84425	−	18.9377i	0.440577	−	1.06365i	−0.535170	−	0.844745i	$-0.679752\pi$
$317$	7.84425	−	18.9377i	0.440577	−	1.06365i	0.975747	−	0.218902i	$-0.0702476\pi$
$318$	0.413378	−	3.46662i	0.0231811	−	0.194398i
$319$	−0.685896			−0.0384028
$320$		0			0
$321$	19.8526			1.10807
$322$	0.689705	−	5.78392i	0.0384358	−	0.322325i
$323$	−5.18989	+	12.5295i	−0.288773	+	0.697160i
$324$	−2.15058	+	8.88922i	−0.119476	+	0.493846i
$325$		0			0
$326$	−14.2151	−	7.97721i	−0.787304	−	0.441817i
$327$	12.4689	+	12.4689i	0.689533	+	0.689533i
$328$	−9.08597	+	4.15980i	−0.501689	+	0.229687i
$329$	−7.33962	−	7.33962i	−0.404646	−	0.404646i
$330$		0			0
$331$	9.91107	−	4.10530i	0.544762	−	0.225648i	−0.0932931	−	0.995639i	$-0.529739\pi$
$331$	9.91107	−	4.10530i	0.544762	−	0.225648i	0.638055	+	0.769991i	$0.279739\pi$
$332$	−12.6624	−	9.23368i	−0.694940	−	0.506764i
$333$	4.53200	+	1.87722i	0.248352	+	0.102871i
$334$	−4.69435	+	3.69407i	−0.256863	+	0.202131i
$335$		0			0
$336$	−21.4536	−	1.76402i	−1.17039	−	0.0962353i
$337$	−3.23412			−0.176174			−0.0880868	−	0.996113i	$-0.528075\pi$
$337$	−3.23412			−0.176174			−0.0880868	+	0.996113i	$0.528075\pi$
$338$	3.86790	−	3.04372i	0.210386	−	0.165556i
$339$	3.11529	−	7.52099i	0.169200	−	0.408484i
$340$		0			0
$341$	0.158619	−	0.0657022i	0.00858971	−	0.00355797i
$342$	−0.872852	−	3.10530i	−0.0471984	−	0.167915i
$343$	−3.06608	+	3.06608i	−0.165553	+	0.165553i
$344$	−18.6846	+	0.684993i	−1.00741	+	0.0369324i
$345$		0			0
$346$	−14.1979	+	25.3003i	−0.763286	+	1.36015i
$347$	−23.7246	+	9.82705i	−1.27360	+	0.527544i	−0.914058	−	0.405584i	$-0.867068\pi$
$347$	−23.7246	+	9.82705i	−1.27360	+	0.527544i	−0.359545	+	0.933128i	$0.617068\pi$
$348$	−11.0597	+	6.75079i	−0.592862	+	0.361880i
$349$	12.5762	+	5.20925i	0.673190	+	0.278845i	0.692977	−	0.720960i	$-0.256299\pi$
$349$	12.5762	+	5.20925i	0.673190	+	0.278845i	−0.0197868	+	0.999804i	$0.506299\pi$
$350$		0			0
$351$	−17.4420			−0.930983
$352$	−0.165283	+	0.812340i	−0.00880961	+	0.0432978i
$353$		−	8.67371i		−	0.461655i	−0.972995	−	0.230828i	$-0.925857\pi$
$353$		−	8.67371i		−	0.461655i	0.972995	−	0.230828i	$-0.0741433\pi$
$354$	−0.870636	+	7.30122i	−0.0462738	+	0.388055i
$355$		0			0
$356$	−10.1832	+	6.21580i	−0.539710	+	0.329437i
$357$	−32.0461	+	13.2739i	−1.69606	+	0.702530i
$358$	30.9560	+	17.3718i	1.63608	+	0.918129i
$359$	−13.6307	+	13.6307i	−0.719399	+	0.719399i	−0.968482	−	0.249083i	$-0.919871\pi$
$359$	−13.6307	+	13.6307i	−0.719399	+	0.719399i	0.249083	+	0.968482i	$0.419871\pi$
$360$		0			0
$361$	10.3045	+	10.3045i	0.542345	+	0.542345i
$362$	0.778175	+	2.76847i	0.0408999	+	0.145508i
$363$	−5.81539	−	14.0396i	−0.305229	−	0.736888i
$364$	−3.71155	−	23.7023i	−0.194538	−	1.24234i
$365$		0			0
$366$	4.54358	+	5.77389i	0.237497	+	0.301806i
$367$	28.9800			1.51274			0.756371	−	0.654142i	$-0.226970\pi$
$367$	28.9800			1.51274			0.756371	+	0.654142i	$0.226970\pi$
$368$	−4.03480	+	1.29539i	−0.210329	+	0.0675268i
$369$		−	3.82989i		−	0.199376i
$370$		0			0
$371$	−2.65344	+	6.40597i	−0.137760	+	0.332581i
$372$	1.91099	−	2.62059i	0.0990800	−	0.135871i
$373$	−2.30455	−	5.56367i	−0.119325	−	0.288076i	0.852920	−	0.522042i	$-0.174830\pi$
$373$	−2.30455	−	5.56367i	−0.119325	−	0.288076i	−0.972245	+	0.233966i	$0.924830\pi$
$374$	0.361465	+	1.28597i	0.0186909	+	0.0664957i
$375$		0			0
$376$	−2.63224	+	7.07773i	−0.135748	+	0.365006i
$377$	−10.2114	−	10.2114i	−0.525912	−	0.525912i
$378$	15.2110	−	27.1055i	0.782368	−	1.39416i
$379$	−8.55274	−	20.6481i	−0.439325	−	1.06062i	−0.976183	−	0.216951i	$-0.930389\pi$
$379$	−8.55274	−	20.6481i	−0.439325	−	1.06062i	0.536858	−	0.843673i	$-0.319611\pi$
$380$		0			0
$381$	−19.6966	−	8.15862i	−1.00909	−	0.417979i
$382$	−1.51695	+	12.7213i	−0.0776139	+	0.650876i
$383$		−	30.5667i		−	1.56188i	−0.624603	−	0.780942i	$-0.714739\pi$
$383$		−	30.5667i		−	1.56188i	0.624603	−	0.780942i	$-0.285261\pi$
$384$	5.33019	+	14.7253i	0.272005	+	0.751447i
$385$		0			0
$386$	−8.77254	−	1.04608i	−0.446511	−	0.0532443i
$387$	2.74226	−	6.62039i	0.139397	−	0.336533i
$388$	−4.85657	+	20.0742i	−0.246555	+	1.01911i
$389$	7.06634	+	17.0597i	0.358278	+	0.864959i	0.995543	+	0.0943139i	$0.0300657\pi$
$389$	7.06634	+	17.0597i	0.358278	+	0.864959i	−0.637265	+	0.770645i	$0.719934\pi$
$390$		0			0
$391$	−4.82843	+	4.82843i	−0.244184	+	0.244184i
$392$	21.5139	+	8.00112i	1.08661	+	0.404117i
$393$	3.13990	−	3.13990i	0.158387	−	0.158387i
$394$	−1.81298	−	6.44993i	−0.0913365	−	0.324943i
$395$		0			0
$396$	−0.256710	−	0.187198i	−0.0129002	−	0.00940707i
$397$	−17.2799	−	7.15759i	−0.867255	−	0.359229i	−0.0957146	−	0.995409i	$-0.530514\pi$
$397$	−17.2799	−	7.15759i	−0.867255	−	0.359229i	−0.771541	+	0.636180i	$0.780514\pi$
$398$	−7.59633	−	9.65326i	−0.380769	−	0.483874i
$399$		−	11.3231i		−	0.566866i
$400$		0			0
$401$		−	11.0004i		−	0.549332i	−0.961540	−	0.274666i	$-0.911433\pi$
$401$		−	11.0004i		−	0.549332i	0.961540	−	0.274666i	$-0.0885674\pi$
$402$	23.4431	−	18.4478i	1.16923	−	0.920092i
$403$	3.33962	+	1.38331i	0.166358	+	0.0689078i
$404$	3.49083	+	22.2927i	0.173675	+	1.10910i
$405$		0			0
$406$	24.7741	−	6.96362i	1.22952	−	0.345599i
$407$	0.468914	−	0.468914i	0.0232432	−	0.0232432i
$408$	18.4853	+	17.1778i	0.915158	+	0.850430i
$409$	1.15862	−	1.15862i	0.0572900	−	0.0572900i	−0.677881	−	0.735171i	$-0.737102\pi$
$409$	1.15862	−	1.15862i	0.0572900	−	0.0572900i	0.735171	+	0.677881i	$0.237102\pi$
$410$		0			0
$411$	8.07225	+	19.4881i	0.398175	+	0.961279i
$412$	−19.6190	−	32.1415i	−0.966559	−	1.58350i
$413$	5.58855	−	13.4919i	0.274994	−	0.663895i
$414$	0.192306	−	1.61269i	0.00945133	−	0.0792596i
$415$		0			0
$416$	−14.5545	+	9.63315i	−0.713593	+	0.472304i
$417$		−	7.16714i		−	0.350976i
$418$	−0.432995	−	0.0516326i	−0.0211785	−	0.00252543i
$419$	32.0362	+	13.2698i	1.56507	+	0.648273i	0.985961	−	0.166978i	$-0.0534009\pi$
$419$	32.0362	+	13.2698i	1.56507	+	0.648273i	0.579108	+	0.815251i	$0.303401\pi$
$420$		0			0
$421$	9.34602	+	22.5633i	0.455497	+	1.09967i	0.970202	+	0.242299i	$0.0779016\pi$
$421$	9.34602	+	22.5633i	0.455497	+	1.09967i	−0.514705	+	0.857368i	$0.672098\pi$
$422$	16.8094	+	9.43308i	0.818271	+	0.459195i
$423$	−2.04646	−	2.04646i	−0.0995022	−	0.0995022i
$424$	5.04098	−	0.184807i	0.244811	−	0.00897500i
$425$		0			0
$426$	9.08665	−	2.55412i	0.440250	−	0.123747i
$427$	−5.58421	−	13.4815i	−0.270239	−	0.652414i
$428$	4.43771	+	28.3395i	0.214505	+	1.36984i
$429$	−0.239507	+	0.578221i	−0.0115635	+	0.0279168i
$430$		0			0
$431$		−	4.47586i		−	0.215594i	−0.994173	−	0.107797i	$-0.965620\pi$
$431$		−	4.47586i		−	0.215594i	0.994173	−	0.107797i	$-0.0343797\pi$
$432$	−22.5362	−	1.85304i	−1.08427	−	0.0891543i
$433$	1.44196			0.0692960			0.0346480	−	0.999400i	$-0.488969\pi$
$433$	1.44196			0.0692960			0.0346480	+	0.999400i	$0.488969\pi$
$434$	−5.06217	+	3.98352i	−0.242992	+	0.191215i
$435$		0			0
$436$	−15.0121	+	20.5865i	−0.718949	+	0.985915i
$437$	−0.853036	−	2.05941i	−0.0408063	−	0.0985150i
$438$	−1.17891	+	0.331374i	−0.0563306	+	0.0158337i
$439$	−0.854615	−	0.854615i	−0.0407885	−	0.0407885i	0.686418	−	0.727207i	$-0.259182\pi$
$439$	−0.854615	−	0.854615i	−0.0407885	−	0.0407885i	−0.727207	+	0.686418i	$0.759182\pi$
$440$		0			0
$441$	−6.22053	+	6.22053i	−0.296216	+	0.296216i
$442$	−13.7636	+	24.5264i	−0.654669	+	1.16660i
$443$	−11.3206	+	4.68913i	−0.537857	+	0.222787i	−0.635040	−	0.772479i	$-0.719017\pi$
$443$	−11.3206	+	4.68913i	−0.537857	+	0.222787i	0.0971838	+	0.995266i	$0.469017\pi$
$444$	2.94579	−	12.1762i	0.139801	−	0.577855i
$445$		0			0
$446$	1.34891	+	0.160851i	0.0638726	+	0.00761651i
$447$		−	6.47862i		−	0.306428i
$448$	−2.27744	−	31.0192i	−0.107599	−	1.46552i
$449$	24.5573			1.15893			0.579464	−	0.814998i	$-0.303262\pi$
$449$	24.5573			1.15893			0.579464	+	0.814998i	$0.303262\pi$
$450$		0			0
$451$	−0.478338	−	0.198134i	−0.0225240	−	0.00932976i
$452$	11.4325	+	2.76588i	0.537741	+	0.130096i
$453$	−23.9348	+	9.91412i	−1.12456	+	0.465806i
$454$	18.9153	+	10.6148i	0.887740	+	0.498179i
$455$		0			0
$456$	−7.48999	+	3.42912i	−0.350751	+	0.160583i
$457$	14.1684	−	14.1684i	0.662771	−	0.662771i	−0.293262	−	0.956032i	$-0.594741\pi$
$457$	14.1684	−	14.1684i	0.662771	−	0.662771i	0.956032	+	0.293262i	$0.0947407\pi$
$458$	6.41829	−	1.80408i	0.299907	−	0.0842992i
$459$	−33.6631	+	13.9437i	−1.57126	+	0.650837i
$460$		0			0
$461$	−11.7965	+	28.4793i	−0.549417	+	1.32641i	0.368496	+	0.929630i	$0.379873\pi$
$461$	−11.7965	+	28.4793i	−0.549417	+	1.32641i	−0.917913	+	0.396782i	$0.870127\pi$
$462$	−0.689705	−	0.876464i	−0.0320880	−	0.0407768i
$463$	14.8190			0.688697			0.344349	−	0.938842i	$-0.388100\pi$
$463$	14.8190			0.688697			0.344349	+	0.938842i	$0.388100\pi$
$464$	−12.1089	−	14.2786i	−0.562142	−	0.662869i
$465$		0			0
$466$	20.7683	+	26.3919i	0.962072	+	1.22258i
$467$	−13.1218	−	5.43521i	−0.607203	−	0.251512i	0.0578293	−	0.998326i	$-0.481582\pi$
$467$	−13.1218	−	5.43521i	−0.607203	−	0.251512i	−0.665032	+	0.746815i	$0.731582\pi$
$468$	−1.03487	−	6.60875i	−0.0478368	−	0.305490i
$469$	−54.7373	+	22.6729i	−2.52753	+	1.04694i
$470$		0			0
$471$	−16.9007	−	16.9007i	−0.778742	−	0.778742i
$472$	−10.6171	+	0.389231i	−0.488690	+	0.0179158i
$473$	−0.684993	−	0.684993i	−0.0314960	−	0.0314960i
$474$	−6.77825	+	12.0786i	−0.311335	+	0.554790i
$475$		0			0
$476$	−26.1118	−	42.7784i	−1.19683	−	1.96075i
$477$	−0.739842	+	1.78614i	−0.0338750	+	0.0817816i
$478$	−22.2455	−	2.65267i	−1.01749	−	0.121330i
$479$	−32.3727			−1.47915			−0.739574	−	0.673076i	$-0.764973\pi$
$479$	−32.3727			−1.47915			−0.739574	+	0.673076i	$0.764973\pi$
$480$		0			0
$481$	13.9620			0.636614
$482$	0.440005	+	0.0524685i	0.0200417	+	0.00238988i
$483$	2.18177	−	5.26725i	0.0992738	−	0.239668i
$484$	18.7415	−	11.4397i	0.851887	−	0.519988i
$485$		0			0
$486$	7.35662	−	13.1093i	0.333703	−	0.594649i
$487$	1.89478	+	1.89478i	0.0858608	+	0.0858608i	0.748733	−	0.662872i	$-0.230663\pi$
$487$	1.89478	+	1.89478i	0.0858608	+	0.0858608i	−0.662872	+	0.748733i	$0.730663\pi$
$488$	−7.22655	+	7.77658i	−0.327131	+	0.352029i
$489$	−11.2815	−	11.2815i	−0.510166	−	0.510166i
$490$		0			0
$491$	−18.2886	+	7.57539i	−0.825354	+	0.341873i	−0.755062	−	0.655654i	$-0.772393\pi$
$491$	−18.2886	+	7.57539i	−0.825354	+	0.341873i	−0.0702922	+	0.997526i	$0.522393\pi$
$492$	−9.66303	+	1.51314i	−0.435643	+	0.0682176i
$493$	−27.8714	−	11.5447i	−1.25526	−	0.519947i
$494$	−5.67759	−	7.21496i	−0.255447	−	0.324617i
$495$		0			0
$496$	4.16804	+	2.14214i	0.187151	+	0.0961847i
$497$	−18.7462			−0.840884
$498$	−9.48563	−	12.0541i	−0.425061	−	0.540159i
$499$	9.54921	−	23.0538i	0.427481	−	1.03203i	−0.552602	−	0.833445i	$-0.686365\pi$
$499$	9.54921	−	23.0538i	0.427481	−	1.03203i	0.980083	−	0.198586i	$-0.0636349\pi$
$500$		0			0
$501$	−5.40166	+	2.23744i	−0.241328	+	0.0999614i
$502$	12.6618	−	3.55903i	0.565122	−	0.158847i
$503$	−22.6436	+	22.6436i	−1.00963	+	1.00963i	−0.00967595	+	0.999953i	$0.503080\pi$
$503$	−22.6436	+	22.6436i	−1.00963	+	1.00963i	−0.999953	+	0.00967595i	$0.996920\pi$
$504$	11.1728	+	4.15521i	0.497674	+	0.185088i
$505$		0			0
$506$	−0.191470	−	0.107449i	−0.00851189	−	0.00477668i
$507$	4.45068	−	1.84353i	0.197661	−	0.0818741i
$508$	7.24354	−	29.9406i	0.321380	−	1.32840i
$509$	21.3715	+	8.85238i	0.947276	+	0.392375i	0.802206	−	0.597047i	$-0.203659\pi$
$509$	21.3715	+	8.85238i	0.947276	+	0.392375i	0.145070	+	0.989421i	$0.453659\pi$
$510$		0			0
$511$	2.43216			0.107592
$512$	−19.8288	+	10.9004i	−0.876317	+	0.481734i
$513$		−	11.8945i		−	0.525155i
$514$	26.5466	+	3.16556i	1.17092	+	0.139627i
$515$		0			0
$516$	−17.7871	−	4.30324i	−0.783031	−	0.189439i
$517$	−0.361465	+	0.149724i	−0.0158972	+	0.00658484i
$518$	−12.1762	+	21.6976i	−0.534990	+	0.953336i
$519$	−20.0789	+	20.0789i	−0.881366	+	0.881366i
$520$		0			0
$521$	−9.76588	−	9.76588i	−0.427851	−	0.427851i	0.460045	−	0.887896i	$-0.347833\pi$
$521$	−9.76588	−	9.76588i	−0.427851	−	0.427851i	−0.887896	+	0.460045i	$0.847833\pi$
$522$	6.90761	−	1.94162i	0.302338	−	0.0849825i
$523$	−7.01552	−	16.9370i	−0.306767	−	0.740601i	−0.999806	−	0.0197010i	$-0.993729\pi$
$523$	−7.01552	−	16.9370i	−0.306767	−	0.740601i	0.693039	−	0.720900i	$-0.256271\pi$
$524$	5.18406	+	3.78032i	0.226467	+	0.165144i
$525$		0			0
$526$	26.1480	−	20.5763i	1.14011	−	0.897170i
$527$	7.55136			0.328942
$528$	−0.370889	+	0.721654i	−0.0161409	+	0.0314060i
$529$			21.8776i			0.951202i
$530$		0			0
$531$	1.55822	−	3.76187i	0.0676209	−	0.163251i
$532$	16.1637	−	2.53109i	0.700785	−	0.109737i
$533$	−4.17157	−	10.0711i	−0.180691	−	0.436226i
$534$	−11.2415	+	3.15980i	−0.486465	+	0.136738i
$535$		0			0
$536$	31.5744	+	29.3412i	1.36381	+	1.26735i
$537$	24.5674	+	24.5674i	1.06016	+	1.06016i
$538$	16.1474	+	9.06156i	0.696165	+	0.390672i
$539$	0.455108	+	1.09873i	0.0196029	+	0.0473256i
$540$		0			0
$541$	14.2214	+	5.89071i	0.611427	+	0.253261i	0.666839	−	0.745202i	$-0.267647\pi$
$541$	14.2214	+	5.89071i	0.611427	+	0.253261i	−0.0554115	+	0.998464i	$0.517647\pi$
$542$	39.6201	+	4.72451i	1.70183	+	0.202935i
$543$			2.81470i			0.120791i
$544$	−20.3892	+	30.2274i	−0.874180	+	1.29599i
$545$		0			0
$546$	2.78039	−	23.3166i	0.118990	−	0.997857i
$547$	−4.00686	+	9.67342i	−0.171321	+	0.413606i	−0.986097	−	0.166170i	$-0.946860\pi$
$547$	−4.00686	+	9.67342i	−0.171321	+	0.413606i	0.814776	+	0.579776i	$0.196860\pi$
$548$	−26.0148	+	15.8793i	−1.11130	+	0.678331i
$549$	−1.55701	−	3.75895i	−0.0664515	−	0.160428i
$550$		0			0
$551$	6.96362	−	6.96362i	0.296660	−	0.296660i
$552$	−4.14490	+	0.151955i	−0.176418	+	0.00646765i
$553$	19.4514	−	19.4514i	0.827157	−	0.827157i
$554$	−32.1613	+	9.04006i	−1.36640	+	0.384075i
$555$		0			0
$556$	10.2311	−	1.60209i	0.433893	−	0.0679437i
$557$	7.45908	+	3.08965i	0.316051	+	0.130913i	0.535070	−	0.844808i	$-0.320285\pi$
$557$	7.45908	+	3.08965i	0.316051	+	0.130913i	−0.219018	+	0.975721i	$0.570285\pi$
$558$	−1.41145	+	1.11070i	−0.0597516	+	0.0470196i
$559$		−	20.3959i		−	0.862653i
$560$		0			0
$561$			1.30744i			0.0552002i
$562$	3.71868	+	4.72562i	0.156863	+	0.199338i
$563$	24.5802	+	10.1815i	1.03593	+	0.429097i	0.834850	−	0.550477i	$-0.185554\pi$
$563$	24.5802	+	10.1815i	1.03593	+	0.429097i	0.201082	+	0.979574i	$0.435554\pi$
$564$	−4.35480	+	5.97186i	−0.183370	+	0.251461i
$565$		0			0
$566$	−0.709521	−	2.52422i	−0.0298234	−	0.106101i
$567$	12.5713	−	12.5713i	0.527943	−	0.527943i
$568$	5.67715	+	12.4002i	0.238208	+	0.520301i
$569$	−8.12862	+	8.12862i	−0.340770	+	0.340770i	−0.856657	−	0.515887i	$-0.827462\pi$
$569$	−8.12862	+	8.12862i	−0.340770	+	0.340770i	0.515887	+	0.856657i	$0.327462\pi$
$570$		0			0
$571$	−7.40930	−	17.8876i	−0.310070	−	0.748574i	−0.999702	−	0.0244147i	$-0.992228\pi$
$571$	−7.40930	−	17.8876i	−0.310070	−	0.748574i	0.689632	−	0.724160i	$-0.257772\pi$
$572$	−0.878944	−	0.212644i	−0.0367505	−	0.00889107i
$573$	−4.79862	+	11.5849i	−0.200465	+	0.483965i
$574$	19.2888	+	2.30010i	0.805100	+	0.0960044i
$575$		0			0
$576$	−0.635005	−	8.64889i	−0.0264585	−	0.360371i
$577$			11.9134i			0.495959i	0.968765	+	0.247980i	$0.0797666\pi$
$577$			11.9134i			0.495959i	−0.968765	+	0.247980i	$0.920233\pi$
$578$	−4.10999	+	34.4667i	−0.170953	+	1.43363i
$579$	−7.98890	−	3.30911i	−0.332008	−	0.137522i
$580$		0			0
$581$	11.6582	+	28.1453i	0.483662	+	1.16766i
$582$	−9.89283	+	17.6287i	−0.410071	+	0.730734i
$583$	0.184807	+	0.184807i	0.00765391	+	0.00765391i
$584$	−0.736560	−	1.60882i	−0.0304791	−	0.0665734i
$585$		0			0
$586$	−10.5176	−	37.4179i	−0.434478	−	1.54572i
$587$	9.77588	+	23.6011i	0.403494	+	0.974120i	0.986811	+	0.161876i	$0.0517543\pi$
$587$	9.77588	+	23.6011i	0.403494	+	0.974120i	−0.583318	+	0.812244i	$0.698246\pi$
$588$	18.1524	+	13.2371i	0.748592	+	0.545889i
$589$	−0.943348	+	2.27744i	−0.0388700	+	0.0938404i
$590$		0			0
$591$		−	6.55765i		−	0.269746i
$592$	18.0399	+	1.48333i	0.741435	+	0.0609645i
$593$	12.5549			0.515567			0.257784	−	0.966203i	$-0.417008\pi$
$593$	12.5549			0.515567			0.257784	+	0.966203i	$0.417008\pi$
$594$	−0.724508	−	0.920690i	−0.0297269	−	0.0377764i
$595$		0			0
$596$	9.24819	−	1.44818i	0.378821	−	0.0593198i
$597$	−4.60097	−	11.1077i	−0.188305	−	0.454609i
$598$	−1.25088	−	4.45020i	−0.0511524	−	0.181982i
$599$	6.66010	+	6.66010i	0.272124	+	0.272124i	0.829955	−	0.557830i	$-0.188366\pi$
$599$	6.66010	+	6.66010i	0.272124	+	0.272124i	−0.557830	+	0.829955i	$0.688366\pi$
$600$		0			0
$601$	27.4318	−	27.4318i	1.11896	−	1.11896i	0.127071	−	0.991894i	$-0.459442\pi$
$601$	27.4318	−	27.4318i	1.11896	−	1.11896i	0.991894	−	0.127071i	$-0.0405577\pi$
$602$	31.6960	+	17.7871i	1.29183	+	0.724946i
$603$	−15.2621	+	6.32175i	−0.621519	+	0.257442i
$604$	−19.5026	−	31.9507i	−0.793548	−	1.30005i
$605$		0			0
$606$	−2.61504	+	21.9299i	−0.106229	+	0.890843i
$607$			20.3361i			0.825416i	0.910863	+	0.412708i	$0.135417\pi$
$607$			20.3361i			0.825416i	−0.910863	+	0.412708i	$0.864583\pi$
$608$	−6.56930	−	9.92540i	−0.266420	−	0.402528i
$609$	25.1878			1.02066
$610$		0			0
$611$	−7.61040	−	3.15233i	−0.307884	−	0.127530i
$612$	−7.28058	−	11.9276i	−0.294300	−	0.482146i
$613$	32.1759	−	13.3277i	1.29957	−	0.538301i	0.377748	−	0.925908i	$-0.376699\pi$
$613$	32.1759	−	13.3277i	1.29957	−	0.538301i	0.921824	+	0.387608i	$0.126699\pi$
$614$	10.4925	−	18.6973i	0.423442	−	0.754561i
$615$		0			0
$616$	1.09698	−	1.18047i	0.0441984	−	0.0475624i
$617$	−11.3168	+	11.3168i	−0.455599	+	0.455599i	−0.897208	−	0.441609i	$-0.854408\pi$
$617$	−11.3168	+	11.3168i	−0.455599	+	0.455599i	0.441609	+	0.897208i	$0.354408\pi$
$618$	−9.97332	−	35.4816i	−0.401186	−	1.42728i
$619$	0.224799	−	0.0931149i	0.00903545	−	0.00374260i	−0.378161	−	0.925740i	$-0.623443\pi$
$619$	0.224799	−	0.0931149i	0.00903545	−	0.00374260i	0.387197	+	0.921997i	$0.373443\pi$
$620$		0			0
$621$	2.29186	−	5.53304i	0.0919691	−	0.222033i
$622$	−11.2453	+	8.84916i	−0.450897	+	0.354819i
$623$	23.1917			0.929157
$624$	−16.2654	+	5.22207i	−0.651137	+	0.209050i
$625$		0			0
$626$	18.6267	−	14.6577i	0.744473	−	0.585839i
$627$	−0.394316	−	0.163331i	−0.0157475	−	0.00652282i
$628$	20.3478	−	27.9035i	0.811964	−	1.11347i
$629$	26.9469	−	11.1618i	1.07444	−	0.445048i
$630$		0			0
$631$	1.15481	+	1.15481i	0.0459722	+	0.0459722i	0.729719	−	0.683747i	$-0.239651\pi$
$631$	1.15481	+	1.15481i	0.0459722	+	0.0459722i	−0.683747	+	0.729719i	$0.739651\pi$
$632$	−18.7573	−	6.97595i	−0.746127	−	0.277488i
$633$	13.3404	+	13.3404i	0.530233	+	0.530233i
$634$	25.2800	+	14.1866i	1.00400	+	0.563420i
$635$		0			0
$636$	4.79883	+	1.16098i	0.190286	+	0.0460360i
$637$	−9.58199	+	23.1330i	−0.379652	+	0.916562i
$638$	0.114855	−	0.963179i	0.00454714	−	0.0381326i
$639$	−5.22690			−0.206773
$640$		0			0
$641$	−14.1953			−0.560679			−0.280339	−	0.959901i	$-0.590447\pi$
$641$	−14.1953			−0.560679			−0.280339	+	0.959901i	$0.590447\pi$
$642$	−3.32436	+	27.8784i	−0.131202	+	1.10027i
$643$	−14.0557	+	33.9334i	−0.554302	+	1.33820i	0.359917	+	0.932984i	$0.382805\pi$
$643$	−14.0557	+	33.9334i	−0.554302	+	1.33820i	−0.914219	+	0.405219i	$0.867195\pi$
$644$	8.00666	+	1.93706i	0.315507	+	0.0763308i
$645$		0			0
$646$	−16.7257	−	9.38607i	−0.658063	−	0.369290i
$647$	−8.73969	−	8.73969i	−0.343593	−	0.343593i	0.514123	−	0.857716i	$-0.328117\pi$
$647$	−8.73969	−	8.73969i	−0.343593	−	0.343593i	−0.857716	+	0.514123i	$0.828117\pi$
$648$	−12.1227	−	4.50849i	−0.476225	−	0.177110i
$649$	−0.389231	−	0.389231i	−0.0152786	−	0.0152786i
$650$		0			0
$651$	−5.82490	+	2.41275i	−0.228296	+	0.0945632i
$652$	13.5825	−	18.6260i	0.531931	−	0.729451i
$653$	38.9127	+	16.1182i	1.52277	+	0.630753i	0.978145	−	0.207926i	$-0.0666713\pi$
$653$	38.9127	+	16.1182i	1.52277	+	0.630753i	0.544627	+	0.838679i	$0.316671\pi$
$654$	−19.5976	+	15.4217i	−0.766327	+	0.603037i
$655$		0			0
$656$	−4.32000	−	13.4557i	−0.168668	−	0.525356i
$657$	0.678143			0.0264569
$658$	11.5358	−	9.07773i	0.449712	−	0.353887i
$659$	8.93958	−	21.5821i	0.348237	−	0.840718i	−0.648592	−	0.761136i	$-0.724642\pi$
$659$	8.93958	−	21.5821i	0.348237	−	0.840718i	0.996828	−	0.0795812i	$-0.0253583\pi$
$660$		0			0
$661$	−22.0088	+	9.11633i	−0.856042	+	0.354584i	−0.767158	−	0.641458i	$-0.778330\pi$
$661$	−22.0088	+	9.11633i	−0.856042	+	0.354584i	−0.0888835	+	0.996042i	$0.528330\pi$
$662$	4.10530	+	14.6052i	0.159557	+	0.567647i
$663$	−19.4647	+	19.4647i	−0.755947	+	0.755947i
$664$	15.0869	−	16.2352i	0.585484	−	0.630047i
$665$		0			0
$666$	−3.39500	+	6.04979i	−0.131554	+	0.234425i
$667$	4.58107	−	1.89754i	0.177380	−	0.0734732i
$668$	−4.40138	−	7.21069i	−0.170294	−	0.278990i
$669$	1.22841	+	0.508825i	0.0474931	+	0.0196723i
$670$		0			0
$671$	−0.550028			−0.0212336
$672$	6.06961	−	29.8312i	0.234140	−	1.15076i
$673$			45.0980i			1.73840i	0.494460	+	0.869200i	$0.335366\pi$
$673$			45.0980i			1.73840i	−0.494460	+	0.869200i	$0.664634\pi$
$674$	0.541560	−	4.54156i	0.0208601	−	0.174934i
$675$		0			0
$676$	3.62650	+	5.94123i	0.139481	+	0.228509i
$677$	32.8474	−	13.6058i	1.26243	−	0.522915i	0.351774	−	0.936085i	$-0.385579\pi$
$677$	32.8474	−	13.6058i	1.26243	−	0.522915i	0.910654	+	0.413170i	$0.135579\pi$
$678$	10.0398	+	5.63410i	0.385576	+	0.216376i
$679$	28.3892	−	28.3892i	1.08948	−	1.08948i
$680$		0			0
$681$	15.0117	+	15.0117i	0.575248	+	0.575248i
$682$	0.0657022	+	0.233745i	0.00251587	+	0.00895057i
$683$	7.79305	+	18.8141i	0.298193	+	0.719901i	0.999972	+	0.00750651i	$0.00238942\pi$
$683$	7.79305	+	18.8141i	0.298193	+	0.719901i	−0.701779	+	0.712395i	$0.747611\pi$
$684$	4.50682	−	0.705727i	0.172323	−	0.0269841i
$685$		0			0
$686$	−3.79216	−	4.81900i	−0.144785	−	0.183990i
$687$	6.52547			0.248962
$688$	2.16686	−	26.3528i	0.0826108	−	1.00469i
$689$			5.50267i			0.209635i
$690$		0			0
$691$	12.6322	−	30.4967i	0.480550	−	1.16015i	−0.478798	−	0.877925i	$-0.658927\pi$
$691$	12.6322	−	30.4967i	0.480550	−	1.16015i	0.959348	−	0.282226i	$-0.0910726\pi$
$692$	−33.1508	−	24.1742i	−1.26020	−	0.918967i
$693$	0.236351	+	0.570601i	0.00897822	+	0.0216753i
$694$	−9.82705	−	34.9612i	−0.373030	−	1.32711i
$695$		0			0
$696$	−7.62793	−	16.6612i	−0.289136	−	0.631540i
$697$	−16.1023	−	16.1023i	−0.609920	−	0.609920i
$698$	−9.42108	+	16.7881i	−0.356593	+	0.635437i
$699$	12.5790	+	30.3684i	0.475782	+	1.14864i
$700$		0			0
$701$	0.915341	+	0.379146i	0.0345719	+	0.0143202i	0.399902	−	0.916558i	$-0.369044\pi$
$701$	0.915341	+	0.379146i	0.0345719	+	0.0143202i	−0.365330	+	0.930878i	$0.619044\pi$
$702$	2.92069	−	24.4931i	0.110234	−	0.924434i
$703$			9.52138i			0.359106i
$704$	−1.11306	−	0.368129i	−0.0419501	−	0.0138744i
$705$		0			0
$706$	12.1802	+	1.45243i	0.458407	+	0.0546629i
$707$	16.7858	−	40.5244i	0.631293	−	1.52408i
$708$	−10.1071	−	2.44521i	−0.379846	−	0.0918965i
$709$	18.9677	+	45.7920i	0.712346	+	1.71975i	0.694055	+	0.719922i	$0.255823\pi$
$709$	18.9677	+	45.7920i	0.712346	+	1.71975i	0.0182911	+	0.999833i	$0.494177\pi$
$710$		0			0
$711$	5.42350	−	5.42350i	0.203397	−	0.203397i
$712$	−7.02343	−	15.3408i	−0.263214	−	0.574921i
$713$	−0.877646	+	0.877646i	−0.0328681	+	0.0328681i
$714$	−13.2739	−	47.2239i	−0.496764	−	1.76731i
$715$		0			0
$716$	−29.5783	+	40.5615i	−1.10539	+	1.51585i
$717$	−20.2583	−	8.39128i	−0.756561	−	0.313378i
$718$	−16.8586	−	21.4235i	−0.629157	−	0.799520i
$719$		−	12.7931i		−	0.477102i	−0.971130	−	0.238551i	$-0.923328\pi$
$719$		−	12.7931i		−	0.477102i	0.971130	−	0.238551i	$-0.0766724\pi$
$720$		0			0
$721$			73.2004i			2.72612i
$722$	−16.1958	+	12.7448i	−0.602746	+	0.474312i
$723$	0.400700	+	0.165975i	0.0149022	+	0.00617269i
$724$	−4.01797	+	0.629177i	−0.149327	+	0.0233832i
$725$		0			0
$726$	20.6891	−	5.81539i	0.767845	−	0.215829i
$727$	−0.466154	+	0.466154i	−0.0172887	+	0.0172887i	−0.715698	−	0.698410i	$-0.753891\pi$
$727$	−0.466154	+	0.466154i	−0.0172887	+	0.0172887i	0.698410	+	0.715698i	$0.253891\pi$
$728$	33.9058	−	1.24301i	1.25663	−	0.0460692i
$729$	20.1043	−	20.1043i	0.744603	−	0.744603i
$730$		0			0
$731$	−16.3052	−	39.3642i	−0.603069	−	1.45594i
$732$	−8.86890	+	5.41354i	−0.327804	+	0.200090i
$733$	−14.0945	+	34.0271i	−0.520591	+	1.25682i	0.416945	+	0.908932i	$0.363101\pi$
$733$	−14.0945	+	34.0271i	−0.520591	+	1.25682i	−0.937536	+	0.347887i	$0.886899\pi$
$734$	−4.85276	+	40.6956i	−0.179119	+	1.50210i
$735$		0			0
$736$	−1.14343	−	5.88285i	−0.0421475	−	0.216845i
$737$			2.23322i			0.0822616i
$738$	5.37818	+	0.641323i	0.197974	+	0.0236074i
$739$	−8.25825	−	3.42068i	−0.303785	−	0.125832i	0.225584	−	0.974224i	$-0.427571\pi$
$739$	−8.25825	−	3.42068i	−0.303785	−	0.125832i	−0.529368	+	0.848392i	$0.677571\pi$
$740$		0			0
$741$	−3.43882	−	8.30205i	−0.126328	−	0.304984i
$742$	−8.55136	−	4.79883i	−0.313930	−	0.176170i
$743$	−32.4060	−	32.4060i	−1.18886	−	1.18886i	−0.977383	−	0.211477i	$-0.932173\pi$
$743$	−32.4060	−	32.4060i	−1.18886	−	1.18886i	−0.211477	−	0.977383i	$-0.567827\pi$
$744$	3.36000	+	3.12235i	0.123184	+	0.114471i
$745$		0			0
$746$	8.19877	−	2.30455i	0.300178	−	0.0843755i
$747$	3.25057	+	7.84757i	0.118932	+	0.287127i
$748$	−1.86636	+	0.292255i	−0.0682410	+	0.0106859i
$749$	21.3388	−	51.5165i	0.779704	−	1.88237i
$750$		0			0
$751$		−	21.5108i		−	0.784939i	−0.919765	−	0.392470i	$-0.871621\pi$
$751$		−	21.5108i		−	0.784939i	0.919765	−	0.392470i	$-0.128379\pi$
$752$	−9.49824	−	4.88155i	−0.346365	−	0.178012i
$753$	12.8732			0.469126
$754$	16.0494	−	12.6296i	0.584484	−	0.459941i
$755$		0			0
$756$	35.5162	+	25.8991i	1.29171	+	0.941941i
$757$	7.19276	+	17.3649i	0.261425	+	0.631137i	0.999027	−	0.0440993i	$-0.0140418\pi$
$757$	7.19276	+	17.3649i	0.261425	+	0.631137i	−0.737602	+	0.675236i	$0.764042\pi$
$758$	30.4276	−	8.55274i	1.10518	−	0.310649i
$759$	−0.151955	−	0.151955i	−0.00551563	−	0.00551563i
$760$		0			0
$761$	−37.8574	+	37.8574i	−1.37233	+	1.37233i	−0.515354	+	0.856977i	$0.672340\pi$
$761$	−37.8574	+	37.8574i	−1.37233	+	1.37233i	−0.856977	+	0.515354i	$0.827660\pi$
$762$	14.7551	−	26.2931i	0.534521	−	0.952500i
$763$	45.7585	−	18.9538i	1.65657	−	0.686174i
$764$	−17.6100	−	4.26040i	−0.637107	−	0.154136i
$765$		0			0
$766$	42.9237	+	5.11845i	1.55090	+	0.184937i
$767$		−	11.5894i		−	0.418471i
$768$	−21.5708	+	5.01922i	−0.778368	+	0.181116i
$769$	−3.07370			−0.110840			−0.0554201	−	0.998463i	$-0.517650\pi$
$769$	−3.07370			−0.110840			−0.0554201	+	0.998463i	$0.517650\pi$
$770$		0			0
$771$	24.1753	+	10.0137i	0.870651	+	0.360635i
$772$	2.93796	−	12.1438i	0.105740	−	0.437065i
$773$	15.8332	−	6.55831i	0.569479	−	0.235886i	−0.0793155	−	0.996850i	$-0.525273\pi$
$773$	15.8332	−	6.55831i	0.569479	−	0.235886i	0.648795	+	0.760964i	$0.275273\pi$
$774$	8.83759	+	4.95945i	0.317660	+	0.178264i
$775$		0			0
$776$	−27.3763	−	10.1814i	−0.982750	−	0.365490i
$777$	−17.2197	+	17.2197i	−0.617753	+	0.617753i
$778$	−25.1395	+	7.06634i	−0.901296	+	0.253341i
$779$	6.86794	−	2.84479i	0.246070	−	0.101925i
$780$		0			0
$781$	−0.270406	+	0.652818i	−0.00967589	+	0.0233597i
$782$	−5.97186	−	7.58892i	−0.213553	−	0.271379i
$783$	26.4588			0.945561
$784$	−14.8382	+	28.8714i	−0.529937	+	1.03112i
$785$		0			0
$786$	3.88347	+	4.93504i	0.138519	+	0.176027i
$787$	16.3613	+	6.77706i	0.583216	+	0.241576i	0.654729	−	0.755864i	$-0.272783\pi$
$787$	16.3613	+	6.77706i	0.583216	+	0.241576i	−0.0715129	+	0.997440i	$0.522783\pi$
$788$	9.36100	−	1.46585i	0.333472	−	0.0522186i
$789$	30.0877	−	12.4627i	1.07115	−	0.443685i
$790$		0			0
$791$	−16.1680	−	16.1680i	−0.574869	−	0.574869i
$792$	0.305863	−	0.329142i	0.0108684	−	0.0116956i
$793$	−8.18862	−	8.18862i	−0.290786	−	0.290786i
$794$	12.9447	−	23.0671i	0.459390	−	0.818619i
$795$		0			0
$796$	14.8278	−	9.05080i	0.525556	−	0.320797i
$797$	−13.4402	+	32.4476i	−0.476077	+	1.14935i	0.485356	+	0.874316i	$0.338690\pi$
$797$	−13.4402	+	32.4476i	−0.476077	+	1.14935i	−0.961434	+	0.275036i	$0.911310\pi$
$798$	15.9007	+	1.89608i	0.562878	+	0.0671205i
$799$	−17.2082			−0.608783
$800$		0			0
$801$	6.46640			0.228479
$802$	15.4474	+	1.84203i	0.545468	+	0.0650445i
$803$	0.0350828	−	0.0846974i	0.00123805	−	0.00298891i
$804$	21.9800	+	36.0094i	0.775174	+	1.26995i
$805$		0			0
$806$	−2.50176	+	4.45807i	−0.0881209	+	0.157029i
$807$	12.8150	+	12.8150i	0.451109	+	0.451109i
$808$	−31.8894	+	1.16909i	−1.12187	+	0.0411285i
$809$	−11.2704	−	11.2704i	−0.396246	−	0.396246i	0.480661	−	0.876907i	$-0.340397\pi$
$809$	−11.2704	−	11.2704i	−0.396246	−	0.396246i	−0.876907	+	0.480661i	$0.840397\pi$
$810$		0			0
$811$	−16.3328	+	6.76529i	−0.573524	+	0.237561i	−0.650545	−	0.759468i	$-0.725459\pi$
$811$	−16.3328	+	6.76529i	−0.573524	+	0.237561i	0.0770206	+	0.997029i	$0.475459\pi$
$812$	5.63029	+	35.9555i	0.197585	+	1.26179i
$813$	36.0809	+	14.9452i	1.26541	+	0.524150i
$814$	0.579959	+	0.737000i	0.0203275	+	0.0258318i
$815$		0			0
$816$	−27.2176	+	23.0818i	−0.952808	+	0.808023i
$817$	13.9089			0.486611
$818$	1.43300	+	1.82102i	0.0501035	+	0.0636705i
$819$	−4.97620	+	12.0136i	−0.173882	+	0.419789i
$820$		0			0
$821$	29.5124	−	12.2244i	1.02999	−	0.426636i	0.197281	−	0.980347i	$-0.436789\pi$
$821$	29.5124	−	12.2244i	1.02999	−	0.426636i	0.832709	+	0.553711i	$0.186789\pi$
$822$	−28.7182	+	8.07225i	−1.00166	+	0.281552i
$823$	−1.00381	+	1.00381i	−0.0349906	+	0.0349906i	−0.724386	−	0.689395i	$-0.757876\pi$
$823$	−1.00381	+	1.00381i	−0.0349906	+	0.0349906i	0.689395	+	0.724386i	$0.257876\pi$
$824$	48.4204	−	22.1681i	1.68680	−	0.772264i
$825$		0			0
$826$	18.0105	+	10.1071i	0.626664	+	0.351669i
$827$	37.9176	−	15.7060i	1.31852	−	0.546151i	0.391165	−	0.920321i	$-0.372072\pi$
$827$	37.9176	−	15.7060i	1.31852	−	0.546151i	0.927360	+	0.374170i	$0.122072\pi$
$828$	2.23245	+	0.540098i	0.0775829	+	0.0187697i
$829$	−31.9806	−	13.2468i	−1.11073	−	0.460081i	−0.249543	−	0.968364i	$-0.580280\pi$
$829$	−31.9806	−	13.2468i	−1.11073	−	0.460081i	−0.861190	+	0.508283i	$0.830280\pi$
$830$		0			0
$831$	−32.6984			−1.13430
$832$	−11.0903	−	22.0515i	−0.384487	−	0.764496i
$833$			52.3070i			1.81233i
$834$	10.0646	+	1.20015i	0.348507	+	0.0415579i
$835$		0			0
$836$	0.145012	−	0.599394i	0.00501534	−	0.0207305i
$837$	−6.11882	+	2.53450i	−0.211498	+	0.0876051i
$838$	−23.9989	+	42.7652i	−0.829027	+	1.47730i
$839$	−3.42599	+	3.42599i	−0.118278	+	0.118278i	−0.763768	−	0.645490i	$-0.776653\pi$
$839$	−3.42599	+	3.42599i	−0.118278	+	0.118278i	0.645490	+	0.763768i	$0.276653\pi$
$840$		0			0
$841$	−5.01582	−	5.01582i	−0.172959	−	0.172959i
$842$	−33.2498	+	9.34602i	−1.14586	+	0.322085i
$843$	2.25234	+	5.43764i	0.0775749	+	0.187282i
$844$	−16.0613	+	22.0253i	−0.552853	+	0.758143i
$845$		0			0
$846$	3.21645	−	2.53109i	0.110584	−	0.0870205i
$847$	−42.6827			−1.46660
$848$	−0.584604	+	7.10981i	−0.0200754	+	0.244152i
$849$		−	2.56638i		−	0.0880779i
$850$		0			0
$851$	−1.83460	+	4.42912i	−0.0628893	+	0.151828i
$852$	2.06508	+	13.1878i	0.0707485	+	0.451805i
$853$	−13.8653	−	33.4739i	−0.474740	−	1.14612i	−0.962045	−	0.272892i	$-0.912020\pi$
$853$	−13.8653	−	33.4739i	−0.474740	−	1.14612i	0.487305	−	0.873232i	$-0.337980\pi$
$854$	19.8666	−	5.58421i	0.679823	−	0.191088i
$855$		0			0
$856$	−40.5393	+	1.48621i	−1.38560	+	0.0507975i
$857$	−19.6667	−	19.6667i	−0.671800	−	0.671800i	0.286331	−	0.958131i	$-0.407564\pi$
$857$	−19.6667	−	19.6667i	−0.671800	−	0.671800i	−0.958131	+	0.286331i	$0.907564\pi$
$858$	−0.771869	−	0.433155i	−0.0263512	−	0.0147877i
$859$	−15.0121	−	36.2424i	−0.512207	−	1.23658i	−0.942597	−	0.333933i	$-0.891624\pi$
$859$	−15.0121	−	36.2424i	−0.512207	−	1.23658i	0.430390	−	0.902643i	$-0.358376\pi$
$860$		0			0
$861$	17.5658	+	7.27598i	0.598640	+	0.247965i
$862$	6.28529	+	0.749491i	0.214078	+	0.0255278i
$863$			28.3727i			0.965819i	0.875670	+	0.482909i	$0.160420\pi$
$863$			28.3727i			0.965819i	−0.875670	+	0.482909i	$0.839580\pi$
$864$	6.37588	−	31.3365i	0.216912	−	1.06609i
$865$		0			0
$866$	−0.241459	+	2.02489i	−0.00820510	+	0.0688085i
$867$	−13.0013	+	31.3878i	−0.441546	+	1.06599i
$868$	−4.74624	−	7.77568i	−0.161098	−	0.263924i
$869$	−0.396796	−	0.957951i	−0.0134604	−	0.0324963i
$870$		0			0
$871$	−33.2473	+	33.2473i	−1.12654	+	1.12654i
$872$	−26.3951	−	24.5282i	−0.893851	−	0.830630i
$873$	7.91558	−	7.91558i	0.267902	−	0.267902i
$874$	3.03480	−	0.853036i	0.102654	−	0.0288544i
$875$		0			0
$876$	−0.267926	−	1.71099i	−0.00905238	−	0.0578092i
$877$	24.4793	+	10.1396i	0.826606	+	0.342391i	0.755558	−	0.655082i	$-0.227366\pi$
$877$	24.4793	+	10.1396i	0.826606	+	0.342391i	0.0710476	+	0.997473i	$0.477366\pi$
$878$	1.34321	−	1.05700i	0.0453312	−	0.0356720i
$879$		−	38.0427i		−	1.28315i
$880$		0			0
$881$		−	9.35846i		−	0.315295i	−0.987495	−	0.157647i	$-0.949609\pi$
$881$		−	9.35846i		−	0.315295i	0.987495	−	0.157647i	$-0.0503909\pi$
$882$	−7.69363	−	9.77691i	−0.259058	−	0.329206i
$883$	17.1218	+	7.09207i	0.576193	+	0.238667i	0.651698	−	0.758478i	$-0.274057\pi$
$883$	17.1218	+	7.09207i	0.576193	+	0.238667i	−0.0755050	+	0.997145i	$0.524057\pi$
$884$	−32.1367	−	23.4348i	−1.08088	−	0.788196i
$885$		0			0
$886$	−4.68913	−	16.6823i	−0.157535	−	0.560452i
$887$	30.8931	−	30.8931i	1.03729	−	1.03729i	0.0380100	−	0.999277i	$-0.487898\pi$
$887$	30.8931	−	30.8931i	1.03729	−	1.03729i	0.999277	−	0.0380100i	$-0.0121019\pi$
$888$	16.6053	+	6.17559i	0.557237	+	0.207239i
$889$	−42.3424	+	42.3424i	−1.42012	+	1.42012i
$890$		0			0
$891$	−0.256446	−	0.619115i	−0.00859126	−	0.0207411i
$892$	−0.451754	+	1.86729i	−0.0151259	+	0.0625214i
$893$	2.14972	−	5.18989i	0.0719378	−	0.173673i
$894$	9.09770	+	1.08486i	0.304272	+	0.0362831i
$895$		0			0
$896$	43.9406	+	1.99610i	1.46795	+	0.0666849i
$897$		−	4.52452i		−	0.151069i
$898$	−4.11216	+	34.4849i	−0.137225	+	1.15078i
$899$	−5.06608	−	2.09844i	−0.168963	−	0.0699868i
$900$		0			0
$901$	4.39903	+	10.6202i	0.146553	+	0.353810i
$902$	0.358331	−	0.638535i	0.0119311	−	0.0212609i
$903$	25.1547	+	25.1547i	0.837096	+	0.837096i
$904$	−5.79843	+	15.5912i	−0.192853	+	0.518554i
$905$		0			0
$906$	−9.91412	−	35.2709i	−0.329375	−	1.17180i
$907$	−5.23891	−	12.6479i	−0.173955	−	0.419965i	0.812723	−	0.582651i	$-0.197984\pi$
$907$	−5.23891	−	12.6479i	−0.173955	−	0.419965i	−0.986678	+	0.162686i	$0.947984\pi$
$908$	−18.0735	+	24.7846i	−0.599789	+	0.822507i
$909$	4.68027	−	11.2992i	0.155235	−	0.374770i
$910$		0			0
$911$			35.3498i			1.17119i	0.810604	+	0.585595i	$0.199139\pi$
$911$			35.3498i			1.17119i	−0.810604	+	0.585595i	$0.800861\pi$
$912$	−3.56118	−	11.0921i	−0.117922	−	0.367298i
$913$	1.14829			0.0380030
$914$	17.5237	+	22.2687i	0.579632	+	0.736584i
$915$		0			0
$916$	1.45865	+	9.31507i	0.0481953	+	0.307779i
$917$	−4.77292	−	11.5228i	−0.157616	−	0.380518i
$918$	−13.9437	−	49.6068i	−0.460211	−	1.63727i
$919$	30.0652	+	30.0652i	0.991759	+	0.991759i	0.999966	−	0.00820720i	$-0.00261246\pi$
$919$	30.0652	+	30.0652i	0.991759	+	0.991759i	−0.00820720	+	0.999966i	$0.502612\pi$
$920$		0			0
$921$	14.8386	−	14.8386i	0.488949	−	0.488949i
$922$	−38.0171	−	21.3343i	−1.25203	−	0.702608i
$923$	−13.7446	+	5.69321i	−0.452410	+	0.187394i
$924$	1.34628	−	0.821763i	0.0442893	−	0.0270340i
$925$		0			0
$926$	−2.48147	+	20.8098i	−0.0815462	+	0.683853i
$927$			20.4100i			0.670352i
$928$	22.0786	−	14.6131i	0.724767	−	0.479700i
$929$	−7.62858			−0.250286			−0.125143	−	0.992139i	$-0.539939\pi$
$929$	−7.62858			−0.250286			−0.125143	+	0.992139i	$0.539939\pi$
$930$		0			0
$931$	−15.7755	−	6.53442i	−0.517020	−	0.214157i
$932$	−40.5389	+	24.7448i	−1.32790	+	0.810542i
$933$	−12.9397	+	5.35979i	−0.423626	+	0.175472i
$934$	9.82974	−	17.5163i	0.321639	−	0.573151i
$935$		0			0
$936$	9.45373	−	0.346582i	0.309005	−	0.0113284i
$937$	−21.2074	+	21.2074i	−0.692817	+	0.692817i	−0.962851	−	0.270034i	$-0.912965\pi$
$937$	−21.2074	+	21.2074i	−0.692817	+	0.692817i	0.270034	+	0.962851i	$0.412965\pi$
$938$	−22.6729	−	80.6623i	−0.740298	−	2.63372i
$939$	21.4332	−	8.87793i	0.699446	−	0.289720i
$940$		0			0
$941$	13.0249	−	31.4448i	0.424599	−	1.02507i	−0.556375	−	0.830931i	$-0.687808\pi$
$941$	13.0249	−	31.4448i	0.424599	−	1.02507i	0.980974	−	0.194141i	$-0.0621918\pi$
$942$	26.5631	−	20.9030i	0.865472	−	0.681056i
$943$	3.74294			0.121887
$944$	1.23127	−	14.9743i	0.0400743	−	0.487373i
$945$		0			0
$946$	1.07662	−	0.847209i	0.0350038	−	0.0275451i
$947$	44.9596	+	18.6229i	1.46099	+	0.605162i	0.964784	−	0.263043i	$-0.0847260\pi$
$947$	44.9596	+	18.6229i	1.46099	+	0.605162i	0.496206	+	0.868205i	$0.334726\pi$
$948$	−15.8266	−	11.5411i	−0.514023	−	0.374836i
$949$	1.78324	−	0.738644i	0.0578866	−	0.0239774i
$950$		0			0
$951$	20.0628	+	20.0628i	0.650582	+	0.650582i
$952$	64.4447	−	29.5045i	2.08866	−	0.956246i
$953$	−33.7784	−	33.7784i	−1.09419	−	1.09419i	−0.995076	−	0.0991142i	$-0.968399\pi$
$953$	−33.7784	−	33.7784i	−1.09419	−	1.09419i	−0.0991142	−	0.995076i	$-0.531601\pi$
$954$	−2.38432	−	1.33803i	−0.0771952	−	0.0433202i
$955$		0			0
$956$	7.45010	−	30.7944i	0.240954	−	0.995961i
$957$	0.363323	−	0.877140i	0.0117446	−	0.0283539i
$958$	5.42088	−	45.4599i	0.175141	−	1.46874i
$959$	59.2472			1.91319
$960$		0			0
$961$	−29.6274			−0.955723
$962$	−2.33797	+	19.6064i	−0.0753792	+	0.632136i
$963$	5.94977	−	14.3640i	0.191729	−	0.462874i
$964$	−0.147359	+	0.609098i	−0.00474613	+	0.0196177i
$965$		0			0
$966$	7.03127	+	3.94579i	0.226228	+	0.126954i
$967$	−19.3234	−	19.3234i	−0.621399	−	0.621399i	0.324490	−	0.945889i	$-0.394807\pi$
$967$	−19.3234	−	19.3234i	−0.621399	−	0.621399i	−0.945889	+	0.324490i	$0.894807\pi$
$968$	12.9261	+	28.2337i	0.415461	+	0.907464i
$969$	−13.2739	−	13.2739i	−0.426420	−	0.426420i
$970$		0			0
$971$	−52.9160	+	21.9185i	−1.69816	+	0.703399i	−0.999922	−	0.0124699i	$-0.996031\pi$
$971$	−52.9160	+	21.9185i	−1.69816	+	0.703399i	−0.698234	+	0.715869i	$0.746031\pi$
$972$	17.1770	+	12.5258i	0.550953	+	0.401766i
$973$	−18.5983	−	7.70369i	−0.596236	−	0.246969i
$974$	−2.97806	+	2.34349i	−0.0954233	+	0.0750903i
$975$		0			0
$976$	−9.71028	−	11.4502i	−0.310818	−	0.366512i
$977$	−12.2792			−0.392848			−0.196424	−	0.980519i	$-0.562933\pi$
$977$	−12.2792			−0.392848			−0.196424	+	0.980519i	$0.562933\pi$
$978$	17.7313	−	13.9531i	0.566984	−	0.446170i
$979$	0.334530	−	0.807628i	0.0106916	−	0.0258119i
$980$		0			0
$981$	12.7586	−	5.28477i	0.407349	−	0.168730i
$982$	−7.57539	−	26.9506i	−0.241741	−	0.860028i
$983$	14.1052	−	14.1052i	0.449887	−	0.449887i	−0.445430	−	0.895317i	$-0.646949\pi$
$983$	14.1052	−	14.1052i	0.449887	−	0.449887i	0.895317	+	0.445430i	$0.146949\pi$
$984$	−0.506757	−	13.8228i	−0.0161548	−	0.440656i
$985$		0			0
$986$	20.8789	−	37.2056i	0.664920	−	1.18487i
$987$	13.2739	−	5.49824i	0.422513	−	0.175011i
$988$	11.0824	−	6.76468i	0.352579	−	0.215213i
$989$	6.47010	+	2.68000i	0.205737	+	0.0852191i
$990$		0			0
$991$	39.8015			1.26434			0.632169	−	0.774831i	$-0.282165\pi$
$991$	39.8015			1.26434			0.632169	+	0.774831i	$0.282165\pi$
$992$	−3.70607	+	5.49433i	−0.117668	+	0.174445i
$993$			14.8491i			0.471222i
$994$	3.13910	−	26.3247i	0.0995661	−	0.834968i
$995$		0			0
$996$	18.5156	−	11.3018i	0.586689	−	0.358113i
$997$	6.20720	−	2.57111i	0.196584	−	0.0814278i	−0.282219	−	0.959350i	$-0.591071\pi$
$997$	6.20720	−	2.57111i	0.196584	−	0.0814278i	0.478803	+	0.877922i	$0.341071\pi$
$998$	30.7746	+	17.2700i	0.974154	+	0.546673i
$999$	−18.0886	+	18.0886i	−0.572299	+	0.572299i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	800.2.ba.c.349.1		8
5.2	odd	4		32.2.g.b.29.1	yes	8
5.3	odd	4		800.2.y.b.701.2		8
5.4	even	2		800.2.ba.d.349.2		8
15.2	even	4		288.2.v.b.253.2		8
20.7	even	4		128.2.g.b.81.1		8
32.21	even	8		800.2.ba.d.149.2		8
40.27	even	4		256.2.g.c.161.2		8
40.37	odd	4		256.2.g.d.161.1		8
60.47	odd	4		1152.2.v.b.721.2		8
80.27	even	4		512.2.g.f.65.1		8
80.37	odd	4		512.2.g.h.65.2		8
80.67	even	4		512.2.g.g.65.2		8
80.77	odd	4		512.2.g.e.65.1		8
160.27	even	8		256.2.g.c.97.2		8
160.37	odd	8		256.2.g.d.97.1		8
160.53	odd	8		800.2.y.b.501.2		8
160.67	even	8		512.2.g.f.449.1		8
160.77	odd	8		512.2.g.e.449.1		8
160.107	even	8		128.2.g.b.49.1		8
160.117	odd	8		32.2.g.b.21.1	✓	8
160.147	even	8		512.2.g.g.449.2		8
160.149	even	8	inner	800.2.ba.c.149.1		8
160.157	odd	8		512.2.g.h.449.2		8
320.107	even	16		4096.2.a.q.1.6		8
320.117	odd	16		4096.2.a.k.1.6		8
320.267	even	16		4096.2.a.q.1.3		8
320.277	odd	16		4096.2.a.k.1.3		8
480.107	odd	8		1152.2.v.b.433.2		8
480.437	even	8		288.2.v.b.181.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.2.g.b.21.1	✓	8	160.117	odd	8
32.2.g.b.29.1	yes	8	5.2	odd	4
128.2.g.b.49.1		8	160.107	even	8
128.2.g.b.81.1		8	20.7	even	4
256.2.g.c.97.2		8	160.27	even	8
256.2.g.c.161.2		8	40.27	even	4
256.2.g.d.97.1		8	160.37	odd	8
256.2.g.d.161.1		8	40.37	odd	4
288.2.v.b.181.2		8	480.437	even	8
288.2.v.b.253.2		8	15.2	even	4
512.2.g.e.65.1		8	80.77	odd	4
512.2.g.e.449.1		8	160.77	odd	8
512.2.g.f.65.1		8	80.27	even	4
512.2.g.f.449.1		8	160.67	even	8
512.2.g.g.65.2		8	80.67	even	4
512.2.g.g.449.2		8	160.147	even	8
512.2.g.h.65.2		8	80.37	odd	4
512.2.g.h.449.2		8	160.157	odd	8
800.2.y.b.501.2		8	160.53	odd	8
800.2.y.b.701.2		8	5.3	odd	4
800.2.ba.c.149.1		8	160.149	even	8	inner
800.2.ba.c.349.1		8	1.1	even	1	trivial
800.2.ba.d.149.2		8	32.21	even	8
800.2.ba.d.349.2		8	5.4	even	2
1152.2.v.b.433.2		8	480.107	odd	8
1152.2.v.b.721.2		8	60.47	odd	4
4096.2.a.k.1.3		8	320.277	odd	16
4096.2.a.k.1.6		8	320.117	odd	16
4096.2.a.q.1.3		8	320.267	even	16
4096.2.a.q.1.6		8	320.107	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)

\(f(q)\)	\(=\)	\(q+(-0.167452 + 1.40426i) q^{2} +(-0.529706 + 1.27882i) q^{3} +(-1.94392 - 0.470294i) q^{4} +(-1.70711 - 0.957989i) q^{6} +(2.74912 + 2.74912i) q^{7} +(0.985930 - 2.65103i) q^{8} +(0.766519 + 0.766519i) q^{9} +O(q^{10})\)	\(q+(-0.167452 + 1.40426i) q^{2} +(-0.529706 + 1.27882i) q^{3} +(-1.94392 - 0.470294i) q^{4} +(-1.70711 - 0.957989i) q^{6} +(2.74912 + 2.74912i) q^{7} +(0.985930 - 2.65103i) q^{8} +(0.766519 + 0.766519i) q^{9} +(0.135390 - 0.0560803i) q^{11} +(1.63113 - 2.23681i) q^{12} +(2.85054 + 1.18073i) q^{13} +(-4.32083 + 3.40014i) q^{14} +(3.55765 + 1.82843i) q^{16} +6.44549 q^{17} +(-1.20475 + 0.948041i) q^{18} +(-0.805198 + 1.94392i) q^{19} +(-4.97186 + 2.05941i) q^{21} +(0.0560803 + 0.199514i) q^{22} +(-0.749118 + 0.749118i) q^{23} +(2.86794 + 2.66510i) q^{24} +(-2.13539 + 3.80520i) q^{26} +(-5.22274 + 2.16333i) q^{27} +(-4.05117 - 6.63696i) q^{28} +(-4.32417 - 1.79113i) q^{29} +1.17157 q^{31} +(-3.16333 + 4.68971i) q^{32} +0.202846i q^{33} +(-1.07931 + 9.05117i) q^{34} +(-1.12956 - 1.85054i) q^{36} +(4.18073 - 1.73172i) q^{37} +(-2.59495 - 1.45622i) q^{38} +(-3.01990 + 3.01990i) q^{39} +(-2.49824 - 2.49824i) q^{41} +(-2.05941 - 7.32666i) q^{42} +(-2.52971 - 6.10725i) q^{43} +(-0.289561 + 0.0453426i) q^{44} +(-0.926518 - 1.17740i) q^{46} -2.66981 q^{47} +(-4.22274 + 3.58107i) q^{48} +8.11529i q^{49} +(-3.41421 + 8.24264i) q^{51} +(-4.98593 - 3.63584i) q^{52} +(0.682497 + 1.64769i) q^{53} +(-2.16333 - 7.69637i) q^{54} +(9.99842 - 4.57754i) q^{56} +(-2.05941 - 2.05941i) q^{57} +(3.23931 - 5.77235i) q^{58} +(-1.43744 - 3.47029i) q^{59} +(-3.46760 - 1.43633i) q^{61} +(-0.196182 + 1.64520i) q^{62} +4.21450i q^{63} +(-6.05588 - 5.22746i) q^{64} +(-0.284849 - 0.0339670i) q^{66} +(-5.83176 + 14.0791i) q^{67} +(-12.5295 - 3.03127i) q^{68} +(-0.561177 - 1.35480i) q^{69} +(-3.40950 + 3.40950i) q^{71} +(2.78780 - 1.27633i) q^{72} +(0.442353 - 0.442353i) q^{73} +(1.73172 + 6.16084i) q^{74} +(2.47945 - 3.40014i) q^{76} +(0.526374 + 0.218031i) q^{77} +(-3.73505 - 4.74642i) q^{78} -7.07550i q^{79} -4.57283i q^{81} +(3.92652 - 3.08985i) q^{82} +(7.23931 + 2.99862i) q^{83} +(10.6334 - 1.66510i) q^{84} +(8.99980 - 2.52971i) q^{86} +(4.58107 - 4.58107i) q^{87} +(-0.0151854 - 0.414214i) q^{88} +(4.21803 - 4.21803i) q^{89} +(4.59050 + 11.0824i) q^{91} +(1.80853 - 1.10392i) q^{92} +(-0.620589 + 1.49824i) q^{93} +(0.447065 - 3.74912i) q^{94} +(-4.32167 - 6.52951i) q^{96} -10.3267i q^{97} +(-11.3960 - 1.35892i) q^{98} +(0.146766 + 0.0607923i) 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

L-functions

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Varieties

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