LMFDB - Embedded newform 800.2.y.f.101.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [800,2,Mod(101,800)]

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, 1, 0]))

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

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

chi := DirichletCharacter("800.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 800 = 2^{5} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	800.y (of order $8$, degree $4$, 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:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 160)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			101.1
Character	$\chi$	$=$	800.101
Dual form			800.2.y.f.301.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40863 - 0.125510i) q^{2} +(-0.772505 - 1.86499i) q^{3} +(1.96849 + 0.353596i) q^{4} +(0.854100 + 2.72405i) q^{6} +(0.798508 + 0.798508i) q^{7} +(-2.72851 - 0.745154i) q^{8} +(-0.760109 + 0.760109i) q^{9} +O(q^{10})$	\(q+(-1.40863 - 0.125510i) q^{2} +(-0.772505 - 1.86499i) q^{3} +(1.96849 + 0.353596i) q^{4} +(0.854100 + 2.72405i) q^{6} +(0.798508 + 0.798508i) q^{7} +(-2.72851 - 0.745154i) q^{8} +(-0.760109 + 0.760109i) q^{9} +(-1.21174 + 2.92539i) q^{11} +(-0.861217 - 3.94438i) q^{12} +(0.424491 - 0.175830i) q^{13} +(-1.02458 - 1.22503i) q^{14} +(3.74994 + 1.39210i) q^{16} -3.66556i q^{17} +(1.16612 - 0.975313i) q^{18} +(5.39199 - 2.23343i) q^{19} +(0.872360 - 2.10606i) q^{21} +(2.07406 - 3.96871i) q^{22} +(3.04392 - 3.04392i) q^{23} +(0.718078 + 5.66428i) q^{24} +(-0.620020 + 0.194402i) q^{26} +(-3.59019 - 1.48711i) q^{27} +(1.28951 + 1.85421i) q^{28} +(-0.995872 - 2.40425i) q^{29} -2.13401 q^{31} +(-5.10756 - 2.43162i) q^{32} +6.39190 q^{33} +(-0.460066 + 5.16343i) q^{34} +(-1.76504 + 1.22750i) q^{36} +(10.4643 + 4.33444i) q^{37} +(-7.87565 + 2.46934i) q^{38} +(-0.655842 - 0.655842i) q^{39} +(6.79854 - 6.79854i) q^{41} +(-1.49317 + 2.85718i) q^{42} +(-3.80728 + 9.19158i) q^{43} +(-3.41970 + 5.33015i) q^{44} +(-4.66981 + 3.90572i) q^{46} -2.81155i q^{47} +(-0.300582 - 8.06901i) q^{48} -5.72477i q^{49} +(-6.83623 + 2.83166i) q^{51} +(0.897781 - 0.196022i) q^{52} +(0.144134 - 0.347970i) q^{53} +(4.87061 + 2.54539i) q^{54} +(-1.58372 - 2.77375i) q^{56} +(-8.33067 - 8.33067i) q^{57} +(1.10106 + 3.51170i) q^{58} +(-10.0632 - 4.16829i) q^{59} +(-5.16229 - 12.4629i) q^{61} +(3.00603 + 0.267840i) q^{62} -1.21391 q^{63} +(6.88949 + 4.06632i) q^{64} +(-9.00384 - 0.802250i) q^{66} +(-3.30530 - 7.97969i) q^{67} +(1.29613 - 7.21563i) q^{68} +(-8.02832 - 3.32544i) q^{69} +(5.88607 + 5.88607i) q^{71} +(2.64036 - 1.50756i) q^{72} +(4.50108 - 4.50108i) q^{73} +(-14.1963 - 7.41901i) q^{74} +(11.4038 - 2.48992i) q^{76} +(-3.30353 + 1.36837i) q^{77} +(0.841526 + 1.00616i) q^{78} -5.05155i q^{79} +11.0693i q^{81} +(-10.4299 + 8.72336i) q^{82} +(-6.80560 + 2.81897i) q^{83} +(2.46193 - 3.83731i) q^{84} +(6.51669 - 12.4697i) q^{86} +(-3.71459 + 3.71459i) q^{87} +(5.48609 - 7.07901i) q^{88} +(-7.44423 - 7.44423i) q^{89} +(0.479361 + 0.198558i) q^{91} +(7.06825 - 4.91562i) q^{92} +(1.64853 + 3.97991i) q^{93} +(-0.352879 + 3.96044i) q^{94} +(-0.589336 + 11.4040i) q^{96} +1.85143 q^{97} +(-0.718518 + 8.06410i) q^{98} +(-1.30256 - 3.14467i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 8 q^{4} - 8 q^{6} + 8 q^{9}+O(q^{10}) $ 88 * q + 8 * q^4 - 8 * q^6 + 8 * q^9	$ 88 q + 8 q^{4} - 8 q^{6} + 8 q^{9} - 8 q^{11} + 24 q^{14} - 8 q^{16} + 8 q^{19} - 8 q^{21} + 16 q^{24} + 32 q^{26} + 8 q^{29} - 64 q^{31} + 24 q^{34} + 72 q^{36} + 8 q^{39} - 8 q^{41} + 8 q^{44} - 8 q^{46} - 48 q^{51} - 24 q^{54} - 56 q^{56} - 24 q^{59} + 24 q^{61} - 64 q^{64} - 8 q^{66} + 40 q^{69} - 40 q^{71} - 128 q^{74} - 8 q^{76} - 200 q^{84} + 24 q^{86} + 8 q^{89} - 8 q^{91} - 120 q^{94} - 56 q^{96} + 48 q^{99}+O(q^{100}) $ 88 * q + 8 * q^4 - 8 * q^6 + 8 * q^9 - 8 * q^11 + 24 * q^14 - 8 * q^16 + 8 * q^19 - 8 * q^21 + 16 * q^24 + 32 * q^26 + 8 * q^29 - 64 * q^31 + 24 * q^34 + 72 * q^36 + 8 * q^39 - 8 * q^41 + 8 * q^44 - 8 * q^46 - 48 * q^51 - 24 * q^54 - 56 * q^56 - 24 * q^59 + 24 * q^61 - 64 * q^64 - 8 * q^66 + 40 * q^69 - 40 * q^71 - 128 * q^74 - 8 * q^76 - 200 * q^84 + 24 * q^86 + 8 * q^89 - 8 * q^91 - 120 * q^94 - 56 * q^96 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.40863	−	0.125510i	−0.996054	−	0.0887493i
$2$	−1.40863	−	0.125510i	−0.996054	−	0.0887493i
$3$	−0.772505	−	1.86499i	−0.446006	−	1.07675i	−0.973805	−	0.227384i	$-0.926983\pi$
$3$	−0.772505	−	1.86499i	−0.446006	−	1.07675i	0.527799	−	0.849369i	$-0.323017\pi$
$4$	1.96849	+	0.353596i	0.984247	+	0.176798i
$5$		0			0
$5$		0			0
$6$	0.854100	+	2.72405i	0.348685	+	1.11209i
$7$	0.798508	+	0.798508i	0.301808	+	0.301808i	0.841721	−	0.539913i	$-0.181543\pi$
$7$	0.798508	+	0.798508i	0.301808	+	0.301808i	−0.539913	+	0.841721i	$0.681543\pi$
$8$	−2.72851	−	0.745154i	−0.964673	−	0.263452i
$9$	−0.760109	+	0.760109i	−0.253370	+	0.253370i
$10$		0			0
$11$	−1.21174	+	2.92539i	−0.365352	+	0.882038i	0.629146	+	0.777287i	$0.283405\pi$
$11$	−1.21174	+	2.92539i	−0.365352	+	0.882038i	−0.994498	+	0.104751i	$0.966595\pi$
$12$	−0.861217	−	3.94438i	−0.248612	−	1.13864i
$13$	0.424491	−	0.175830i	0.117733	−	0.0487664i	−0.323040	−	0.946385i	$-0.604705\pi$
$13$	0.424491	−	0.175830i	0.117733	−	0.0487664i	0.440772	+	0.897619i	$0.354705\pi$
$14$	−1.02458	−	1.22503i	−0.273832	−	0.327402i
$15$		0			0
$16$	3.74994	+	1.39210i	0.937485	+	0.348026i
$17$		−	3.66556i		−	0.889028i	−0.895772	−	0.444514i	$-0.853376\pi$
$17$		−	3.66556i		−	0.889028i	0.895772	−	0.444514i	$-0.146624\pi$
$18$	1.16612	−	0.975313i	0.274856	−	0.229884i
$19$	5.39199	−	2.23343i	1.23701	−	0.512385i	0.334229	−	0.942492i	$-0.391524\pi$
$19$	5.39199	−	2.23343i	1.23701	−	0.512385i	0.902778	+	0.430107i	$0.141524\pi$
$20$		0			0
$21$	0.872360	−	2.10606i	0.190364	−	0.459581i
$22$	2.07406	−	3.96871i	0.442191	−	0.846133i
$23$	3.04392	−	3.04392i	0.634701	−	0.634701i	−0.314543	−	0.949243i	$-0.601851\pi$
$23$	3.04392	−	3.04392i	0.634701	−	0.634701i	0.949243	+	0.314543i	$0.101851\pi$
$24$	0.718078	+	5.66428i	0.146577	+	1.15622i
$25$		0			0
$26$	−0.620020	+	0.194402i	−0.121596	+	0.0381253i
$27$	−3.59019	−	1.48711i	−0.690932	−	0.286194i
$28$	1.28951	+	1.85421i	0.243694	+	0.350413i
$29$	−0.995872	−	2.40425i	−0.184929	−	0.446458i	0.804041	−	0.594574i	$-0.202679\pi$
$29$	−0.995872	−	2.40425i	−0.184929	−	0.446458i	−0.988970	+	0.148116i	$0.952679\pi$
$30$		0			0
$31$	−2.13401			−0.383279			−0.191640	−	0.981465i	$-0.561380\pi$
$31$	−2.13401			−0.383279			−0.191640	+	0.981465i	$0.561380\pi$
$32$	−5.10756	−	2.43162i	−0.902898	−	0.429854i
$33$	6.39190			1.11269
$34$	−0.460066	+	5.16343i	−0.0789007	+	0.885520i
$35$		0			0
$36$	−1.76504	+	1.22750i	−0.294174	+	0.204583i
$37$	10.4643	+	4.33444i	1.72032	+	0.712578i	0.999817	+	0.0191211i	$0.00608682\pi$
$37$	10.4643	+	4.33444i	1.72032	+	0.712578i	0.720498	+	0.693457i	$0.243913\pi$
$38$	−7.87565	+	2.46934i	−1.27760	+	0.400580i
$39$	−0.655842	−	0.655842i	−0.105019	−	0.105019i
$40$		0			0
$41$	6.79854	−	6.79854i	1.06175	−	1.06175i	0.0637899	−	0.997963i	$-0.479681\pi$
$41$	6.79854	−	6.79854i	1.06175	−	1.06175i	0.997963	−	0.0637899i	$-0.0203187\pi$
$42$	−1.49317	+	2.85718i	−0.230401	+	0.440872i
$43$	−3.80728	+	9.19158i	−0.580604	+	1.40170i	0.311662	+	0.950193i	$0.399114\pi$
$43$	−3.80728	+	9.19158i	−0.580604	+	1.40170i	−0.892266	+	0.451509i	$0.850886\pi$
$44$	−3.41970	+	5.33015i	−0.515540	+	0.803550i
$45$		0			0
$46$	−4.66981	+	3.90572i	−0.688525	+	0.575867i
$47$		−	2.81155i		−	0.410106i	−0.978751	−	0.205053i	$-0.934263\pi$
$47$		−	2.81155i		−	0.410106i	0.978751	−	0.205053i	$-0.0657367\pi$
$48$	−0.300582	−	8.06901i	−0.0433853	−	1.16466i
$49$		−	5.72477i		−	0.817824i
$50$		0			0
$51$	−6.83623	+	2.83166i	−0.957264	+	0.396512i
$52$	0.897781	−	0.196022i	0.124500	−	0.0271833i
$53$	0.144134	−	0.347970i	0.0197983	−	0.0477974i	−0.913671	−	0.406454i	$-0.866765\pi$
$53$	0.144134	−	0.347970i	0.0197983	−	0.0477974i	0.933470	+	0.358657i	$0.116765\pi$
$54$	4.87061	+	2.54539i	0.662806	+	0.346384i
$55$		0			0
$56$	−1.58372	−	2.77375i	−0.211634	−	0.370657i
$57$	−8.33067	−	8.33067i	−1.10342	−	1.10342i
$58$	1.10106	+	3.51170i	0.144576	+	0.461108i
$59$	−10.0632	−	4.16829i	−1.31011	−	0.542666i	−0.385194	−	0.922836i	$-0.625865\pi$
$59$	−10.0632	−	4.16829i	−1.31011	−	0.542666i	−0.924917	+	0.380170i	$0.875865\pi$
$60$		0			0
$61$	−5.16229	−	12.4629i	−0.660964	−	1.59571i	−0.796296	−	0.604908i	$-0.793210\pi$
$61$	−5.16229	−	12.4629i	−0.660964	−	1.59571i	0.135332	−	0.990800i	$-0.456790\pi$
$62$	3.00603	+	0.267840i	0.381767	+	0.0340157i
$63$	−1.21391			−0.152938
$64$	6.88949	+	4.06632i	0.861186	+	0.508289i
$65$		0			0
$66$	−9.00384	−	0.802250i	−1.10830	−	0.0987502i
$67$	−3.30530	−	7.97969i	−0.403806	−	0.974874i	−0.986733	−	0.162350i	$-0.948093\pi$
$67$	−3.30530	−	7.97969i	−0.403806	−	0.974874i	0.582927	−	0.812524i	$-0.301907\pi$
$68$	1.29613	−	7.21563i	0.157179	−	0.875024i
$69$	−8.02832	−	3.32544i	−0.966496	−	0.400336i
$70$		0			0
$71$	5.88607	+	5.88607i	0.698548	+	0.698548i	0.964097	−	0.265549i	$-0.0855532\pi$
$71$	5.88607	+	5.88607i	0.698548	+	0.698548i	−0.265549	+	0.964097i	$0.585553\pi$
$72$	2.64036	−	1.50756i	0.311170	−	0.177668i
$73$	4.50108	−	4.50108i	0.526812	−	0.526812i	−0.392808	−	0.919620i	$-0.628496\pi$
$73$	4.50108	−	4.50108i	0.526812	−	0.526812i	0.919620	+	0.392808i	$0.128496\pi$
$74$	−14.1963	−	7.41901i	−1.65029	−	0.862443i
$75$		0			0
$76$	11.4038	−	2.48992i	1.30811	−	0.285613i
$77$	−3.30353	+	1.36837i	−0.376472	+	0.155940i
$78$	0.841526	+	1.00616i	0.0952841	+	0.113925i
$79$		−	5.05155i		−	0.568344i	−0.958773	−	0.284172i	$-0.908281\pi$
$79$		−	5.05155i		−	0.568344i	0.958773	−	0.284172i	$-0.0917187\pi$
$80$		0			0
$81$			11.0693i			1.22993i
$82$	−10.4299	+	8.72336i	−1.15179	+	0.963334i
$83$	−6.80560	+	2.81897i	−0.747012	+	0.309422i	−0.723522	−	0.690302i	$-0.757478\pi$
$83$	−6.80560	+	2.81897i	−0.747012	+	0.309422i	−0.0234902	+	0.999724i	$0.507478\pi$
$84$	2.46193	−	3.83731i	0.268619	−	0.418685i
$85$		0			0
$86$	6.51669	−	12.4697i	0.702713	−	1.34464i
$87$	−3.71459	+	3.71459i	−0.398245	+	0.398245i
$88$	5.48609	−	7.07901i	0.584820	−	0.754625i
$89$	−7.44423	−	7.44423i	−0.789087	−	0.789087i	0.192257	−	0.981345i	$-0.438419\pi$
$89$	−7.44423	−	7.44423i	−0.789087	−	0.789087i	−0.981345	+	0.192257i	$0.938419\pi$
$90$		0			0
$91$	0.479361	+	0.198558i	0.0502507	+	0.0208145i
$92$	7.06825	−	4.91562i	0.736916	−	0.512488i
$93$	1.64853	+	3.97991i	0.170945	+	0.412697i
$94$	−0.352879	+	3.96044i	−0.0363966	+	0.408488i
$95$		0			0
$96$	−0.589336	+	11.4040i	−0.0601488	+	1.16392i
$97$	1.85143			0.187984			0.0939920	−	0.995573i	$-0.470037\pi$
$97$	1.85143			0.187984			0.0939920	+	0.995573i	$0.470037\pi$
$98$	−0.718518	+	8.06410i	−0.0725813	+	0.814597i
$99$	−1.30256	−	3.14467i	−0.130913	−	0.316051i
$100$		0			0
$101$	−5.38144	−	2.22907i	−0.535474	−	0.221800i	0.0985250	−	0.995135i	$-0.468588\pi$
$101$	−5.38144	−	2.22907i	−0.535474	−	0.221800i	−0.633999	+	0.773334i	$0.718588\pi$
$102$	9.98515	−	3.13075i	0.988677	−	0.309991i
$103$	−9.17653	−	9.17653i	−0.904190	−	0.904190i	0.0916051	−	0.995795i	$-0.470800\pi$
$103$	−9.17653	−	9.17653i	−0.904190	−	0.904190i	−0.995795	+	0.0916051i	$0.970800\pi$
$104$	−1.28925	+	0.163442i	−0.126421	+	0.0160268i
$105$		0			0
$106$	−0.246706	+	0.472072i	−0.0239622	+	0.0458517i
$107$	−4.02227	+	9.71062i	−0.388848	+	0.938761i	0.601337	+	0.798996i	$0.294635\pi$
$107$	−4.02227	+	9.71062i	−0.388848	+	0.938761i	−0.990185	+	0.139766i	$0.955365\pi$
$108$	−6.54143	−	4.19684i	−0.629450	−	0.403841i
$109$	18.0950	−	7.49520i	1.73319	−	0.717910i	0.733936	−	0.679219i	$-0.237681\pi$
$109$	18.0950	−	7.49520i	1.73319	−	0.717910i	0.999251	−	0.0386910i	$-0.0123188\pi$
$110$		0			0
$111$		−	22.8642i		−	2.17017i
$112$	1.88275	+	4.10596i	0.177903	+	0.387977i
$113$		−	1.66682i		−	0.156801i	−0.996922	−	0.0784004i	$-0.975019\pi$
$113$		−	1.66682i		−	0.156801i	0.996922	−	0.0784004i	$-0.0249813\pi$
$114$	10.6893	+	12.7804i	1.00114	+	1.19700i
$115$		0			0
$116$	−1.11024	−	5.08489i	−0.103083	−	0.472120i
$117$	−0.189010	+	0.456309i	−0.0174739	+	0.0421858i
$118$	13.6521	+	7.13463i	1.25678	+	0.656796i
$119$	2.92698	−	2.92698i	0.268316	−	0.268316i
$120$		0			0
$121$	0.688576	+	0.688576i	0.0625978	+	0.0625978i
$122$	5.70755	+	18.2035i	0.516738	+	1.64807i
$123$	−17.9311	−	7.42731i	−1.61679	−	0.669698i
$124$	−4.20078	−	0.754577i	−0.377241	−	0.0677630i
$125$		0			0
$126$	1.70995	+	0.152358i	0.152334	+	0.0135731i
$127$	11.9791			1.06297			0.531487	−	0.847066i	$-0.321633\pi$
$127$	11.9791			1.06297			0.531487	+	0.847066i	$0.321633\pi$
$128$	−9.19440	−	6.59265i	−0.812678	−	0.582713i
$129$	20.0834			1.76824
$130$		0			0
$131$	1.07279	+	2.58995i	0.0937303	+	0.226285i	0.963791	−	0.266660i	$-0.0859202\pi$
$131$	1.07279	+	2.58995i	0.0937303	+	0.226285i	−0.870060	+	0.492945i	$0.835920\pi$
$132$	12.5824	+	2.26015i	1.09516	+	0.196721i
$133$	6.08896	+	2.52213i	0.527980	+	0.218697i
$134$	3.65441	+	11.6553i	0.315693	+	1.00686i
$135$		0			0
$136$	−2.73141	+	10.0015i	−0.234216	+	0.857621i
$137$	7.11033	−	7.11033i	0.607476	−	0.607476i	−0.334810	−	0.942286i	$-0.608672\pi$
$137$	7.11033	−	7.11033i	0.607476	−	0.607476i	0.942286	+	0.334810i	$0.108672\pi$
$138$	10.8916	+	5.69196i	0.927153	+	0.484532i
$139$	−7.78228	+	18.7881i	−0.660084	+	1.59358i	0.137585	+	0.990490i	$0.456066\pi$
$139$	−7.78228	+	18.7881i	−0.660084	+	1.59358i	−0.797669	+	0.603095i	$0.793934\pi$
$140$		0			0
$141$	−5.24351	+	2.17193i	−0.441583	+	0.182910i
$142$	−7.55255	−	9.03008i	−0.633796	−	0.757788i
$143$			1.45486i			0.121662i
$144$	−3.90851	+	1.79221i	−0.325710	+	0.149351i
$145$		0			0
$146$	−6.90531	+	5.77544i	−0.571487	+	0.477979i
$147$	−10.6766	+	4.42241i	−0.880595	+	0.364754i
$148$	19.0662	+	12.2325i	1.56723	+	1.00550i
$149$	−1.78543	+	4.31042i	−0.146268	+	0.353123i	−0.979986	−	0.199068i	$-0.936208\pi$
$149$	−1.78543	+	4.31042i	−0.146268	+	0.353123i	0.833717	+	0.552192i	$0.186208\pi$
$150$		0			0
$151$	8.74596	−	8.74596i	0.711736	−	0.711736i	−0.255162	−	0.966898i	$-0.582129\pi$
$151$	8.74596	−	8.74596i	0.711736	−	0.711736i	0.966898	+	0.255162i	$0.0821288\pi$
$152$	−16.3763	+	2.07608i	−1.32830	+	0.168392i
$153$	2.78622	+	2.78622i	0.225253	+	0.225253i
$154$	4.82520	−	1.51290i	0.388826	−	0.121913i
$155$		0			0
$156$	−1.05912	−	1.52293i	−0.0847973	−	0.121932i
$157$	6.63117	+	16.0091i	0.529225	+	1.27766i	0.932032	+	0.362377i	$0.118035\pi$
$157$	6.63117	+	16.0091i	0.529225	+	1.27766i	−0.402806	+	0.915285i	$0.631965\pi$
$158$	−0.634023	+	7.11579i	−0.0504402	+	0.566102i
$159$	−0.760305			−0.0602961
$160$		0			0
$161$	4.86119			0.383115
$162$	1.38932	−	15.5926i	0.109155	−	1.22507i
$163$	0.947748	+	2.28807i	0.0742334	+	0.179215i	0.956640	−	0.291272i	$-0.0940783\pi$
$163$	0.947748	+	2.28807i	0.0742334	+	0.179215i	−0.882407	+	0.470487i	$0.844078\pi$
$164$	15.7868	−	10.9789i	1.23274	−	0.857311i
$165$		0			0
$166$	9.94041	−	3.11672i	0.771525	−	0.241905i
$167$	−2.97405	−	2.97405i	−0.230139	−	0.230139i	0.582612	−	0.812750i	$-0.302031\pi$
$167$	−2.97405	−	2.97405i	−0.230139	−	0.230139i	−0.812750	+	0.582612i	$0.802031\pi$
$168$	−3.94958	+	5.09636i	−0.304717	+	0.393193i
$169$	−9.04311	+	9.04311i	−0.695624	+	0.695624i
$170$		0			0
$171$	−2.40085	+	5.79615i	−0.183597	+	0.443243i
$172$	−10.7447	+	16.7473i	−0.819276	+	1.27697i
$173$	8.98865	−	3.72322i	0.683394	−	0.283071i	−0.0138508	−	0.999904i	$-0.504409\pi$
$173$	8.98865	−	3.72322i	0.683394	−	0.283071i	0.697245	+	0.716833i	$0.254409\pi$
$174$	5.69871	−	4.76627i	0.432018	−	0.361330i
$175$		0			0
$176$	−8.61638	+	9.28317i	−0.649484	+	0.699745i
$177$			21.9877i			1.65270i
$178$	9.55186	+	11.4205i	0.715942	+	0.856004i
$179$	12.4973	−	5.17653i	0.934089	−	0.386912i	0.136861	−	0.990590i	$-0.456299\pi$
$179$	12.4973	−	5.17653i	0.934089	−	0.386912i	0.797228	+	0.603678i	$0.206299\pi$
$180$		0			0
$181$	−2.52860	+	6.10459i	−0.187950	+	0.453751i	−0.989565	−	0.144090i	$-0.953975\pi$
$181$	−2.52860	+	6.10459i	−0.187950	+	0.453751i	0.801615	+	0.597841i	$0.203975\pi$
$182$	−0.650323	−	0.339860i	−0.0482051	−	0.0251921i
$183$	−19.2553	+	19.2553i	−1.42339	+	1.42339i
$184$	−10.5735	+	6.03716i	−0.779491	+	0.445065i
$185$		0			0
$186$	−1.82266	−	5.81313i	−0.133644	−	0.426240i
$187$	10.7232	+	4.44169i	0.784157	+	0.324808i
$188$	0.994153	−	5.53451i	0.0725060	−	0.403646i
$189$	−1.67933	−	4.05426i	−0.122153	−	0.294904i
$190$		0			0
$191$	15.4267			1.11624			0.558120	−	0.829760i	$-0.311523\pi$
$191$	15.4267			1.11624			0.558120	+	0.829760i	$0.311523\pi$
$192$	2.26148	−	15.9901i	0.163208	−	1.15399i
$193$	7.08523			0.510006			0.255003	−	0.966940i	$-0.417923\pi$
$193$	7.08523			0.510006			0.255003	+	0.966940i	$0.417923\pi$
$194$	−2.60798	−	0.232373i	−0.187242	−	0.0166834i
$195$		0			0
$196$	2.02426	−	11.2692i	0.144590	−	0.804941i
$197$	0.832884	+	0.344992i	0.0593405	+	0.0245797i	0.412156	−	0.911113i	$-0.364776\pi$
$197$	0.832884	+	0.344992i	0.0593405	+	0.0245797i	−0.352816	+	0.935693i	$0.614776\pi$
$198$	1.44015	+	4.59317i	0.102347	+	0.326422i
$199$	2.91076	+	2.91076i	0.206338	+	0.206338i	0.802709	−	0.596371i	$-0.203391\pi$
$199$	2.91076	+	2.91076i	0.206338	+	0.206338i	−0.596371	+	0.802709i	$0.703391\pi$
$200$		0			0
$201$	−12.3287	+	12.3287i	−0.869599	+	0.869599i
$202$	7.30071	+	3.81536i	0.513676	+	0.268448i
$203$	1.12460	−	2.71502i	0.0789314	−	0.190557i
$204$	−14.4584	+	3.15684i	−1.01229	+	0.221023i
$205$		0			0
$206$	11.7746	+	14.0781i	0.820376	+	0.980869i
$207$			4.62742i			0.321628i
$208$	1.83659	−	0.0684155i	0.127345	−	0.00474376i
$209$			18.4800i			1.27829i
$210$		0			0
$211$	−7.92698	+	3.28346i	−0.545716	+	0.226043i	−0.638471	−	0.769646i	$-0.720433\pi$
$211$	−7.92698	+	3.28346i	−0.545716	+	0.226043i	0.0927548	+	0.995689i	$0.470433\pi$
$212$	0.406768	−	0.634012i	0.0279369	−	0.0435441i
$213$	6.43046	−	15.5245i	0.440608	−	1.06372i
$214$	6.88469	−	13.1739i	0.470628	−	0.900547i
$215$		0			0
$216$	8.68773	+	6.73282i	0.591125	+	0.458110i
$217$	−1.70402	−	1.70402i	−0.115677	−	0.115677i
$218$	−26.4299	+	8.28687i	−1.79006	+	0.561258i
$219$	−11.8716	−	4.91737i	−0.802208	−	0.332285i
$220$		0			0
$221$	−0.644515	−	1.55600i	−0.0433547	−	0.104668i
$222$	−2.86969	+	32.2072i	−0.192601	+	2.16161i
$223$	5.77501			0.386723			0.193362	−	0.981128i	$-0.438061\pi$
$223$	5.77501			0.386723			0.193362	+	0.981128i	$0.438061\pi$
$224$	−2.13676	−	6.02010i	−0.142768	−	0.402235i
$225$		0			0
$226$	−0.209203	+	2.34793i	−0.0139160	+	0.156182i
$227$	−1.22561	−	2.95889i	−0.0813469	−	0.196389i	0.877973	−	0.478710i	$-0.158896\pi$
$227$	−1.22561	−	2.95889i	−0.0813469	−	0.196389i	−0.959320	+	0.282321i	$0.908896\pi$
$228$	−13.4532	−	19.3446i	−0.890959	−	1.28113i
$229$	−15.2062	−	6.29862i	−1.00485	−	0.416224i	−0.181279	−	0.983432i	$-0.558024\pi$
$229$	−15.2062	−	6.29862i	−1.00485	−	0.416224i	−0.823575	+	0.567207i	$0.808024\pi$
$230$		0			0
$231$	5.10398	+	5.10398i	0.335817	+	0.335817i
$232$	0.925708	+	7.30208i	0.0607757	+	0.479405i
$233$	−5.63270	+	5.63270i	−0.369010	+	0.369010i	−0.867116	−	0.498106i	$-0.834029\pi$
$233$	−5.63270	+	5.63270i	−0.369010	+	0.369010i	0.498106	+	0.867116i	$0.334029\pi$
$234$	0.323517	−	0.619050i	0.0211489	−	0.0404685i
$235$		0			0
$236$	−18.3354	−	11.7636i	−1.19353	−	0.765742i
$237$	−9.42111	+	3.90235i	−0.611967	+	0.253485i
$238$	−4.49041	+	3.75567i	−0.291070	+	0.243444i
$239$		−	9.70011i		−	0.627448i	−0.949514	−	0.313724i	$-0.898423\pi$
$239$		−	9.70011i		−	0.627448i	0.949514	−	0.313724i	$-0.101577\pi$
$240$		0			0
$241$			16.7088i			1.07631i	0.842847	+	0.538154i	$0.180878\pi$
$241$			16.7088i			1.07631i	−0.842847	+	0.538154i	$0.819122\pi$
$242$	−0.883527	−	1.05637i	−0.0567953	−	0.0679063i
$243$	9.87365	−	4.08980i	0.633395	−	0.262361i
$244$	−5.75512	−	26.3585i	−0.368433	−	1.68743i
$245$		0			0
$246$	24.3262	+	12.7129i	1.55098	+	0.810545i
$247$	1.89615	−	1.89615i	0.120649	−	0.120649i
$248$	5.82265	+	1.59016i	0.369739	+	0.100976i
$249$	10.5147	+	10.5147i	0.666343	+	0.666343i
$250$		0			0
$251$	−6.61061	−	2.73821i	−0.417258	−	0.172834i	0.164169	−	0.986432i	$-0.447506\pi$
$251$	−6.61061	−	2.73821i	−0.417258	−	0.172834i	−0.581428	+	0.813598i	$0.697506\pi$
$252$	−2.38957	−	0.429233i	−0.150529	−	0.0270391i
$253$	5.21622	+	12.5931i	0.327941	+	0.791719i
$254$	−16.8742	−	1.50350i	−1.05878	−	0.0943383i
$255$		0			0
$256$	12.1241	+	10.4406i	0.757755	+	0.652539i
$257$	10.2334			0.638344			0.319172	−	0.947697i	$-0.396595\pi$
$257$	10.2334			0.638344			0.319172	+	0.947697i	$0.396595\pi$
$258$	−28.2901	−	2.52067i	−1.76126	−	0.156930i
$259$	4.89472	+	11.8169i	0.304143	+	0.734266i
$260$		0			0
$261$	2.58446	+	1.07052i	0.159974	+	0.0662635i
$262$	−1.18610	−	3.78294i	−0.0732778	−	0.233711i
$263$	1.31205	+	1.31205i	0.0809045	+	0.0809045i	0.746401	−	0.665496i	$-0.231780\pi$
$263$	1.31205	+	1.31205i	0.0809045	+	0.0809045i	−0.665496	+	0.746401i	$0.731780\pi$
$264$	−17.4403	−	4.76295i	−1.07338	−	0.293139i
$265$		0			0
$266$	−8.26056	−	4.31699i	−0.506488	−	0.264691i
$267$	−8.13273	+	19.6341i	−0.497715	+	1.20159i
$268$	−3.68487	−	16.8767i	−0.225089	−	1.03091i
$269$	−16.4601	+	6.81801i	−1.00359	+	0.415701i	−0.823113	−	0.567878i	$-0.807765\pi$
$269$	−16.4601	+	6.81801i	−1.00359	+	0.415701i	−0.180479	+	0.983579i	$0.557765\pi$
$270$		0			0
$271$		−	9.45666i		−	0.574451i	−0.957863	−	0.287226i	$-0.907267\pi$
$271$		−	9.45666i		−	0.574451i	0.957863	−	0.287226i	$-0.0927329\pi$
$272$	5.10284	−	13.7456i	0.309405	−	0.833451i
$273$		−	1.04739i		−	0.0633910i
$274$	−10.9083	+	9.12342i	−0.658992	+	0.551166i
$275$		0			0
$276$	−14.6278	−	9.38489i	−0.880492	−	0.564904i
$277$	10.8805	−	26.2678i	0.653743	−	1.57828i	−0.153560	−	0.988139i	$-0.549074\pi$
$277$	10.8805	−	26.2678i	0.653743	−	1.57828i	0.807303	−	0.590137i	$-0.200926\pi$
$278$	13.3205	−	25.4888i	0.798909	−	1.52871i
$279$	1.62208	−	1.62208i	0.0971113	−	0.0971113i
$280$		0			0
$281$	13.8016	+	13.8016i	0.823332	+	0.823332i	0.986584	−	0.163253i	$-0.0521985\pi$
$281$	13.8016	+	13.8016i	0.823332	+	0.823332i	−0.163253	+	0.986584i	$0.552199\pi$
$282$	7.65878	−	2.40134i	0.456074	−	0.142998i
$283$	22.0556	+	9.13571i	1.31107	+	0.543062i	0.925196	−	0.379491i	$-0.123901\pi$
$283$	22.0556	+	9.13571i	1.31107	+	0.543062i	0.385872	+	0.922553i	$0.373901\pi$
$284$	9.50541	+	13.6680i	0.564042	+	0.811046i
$285$		0			0
$286$	0.182600	−	2.04936i	0.0107974	−	0.121181i
$287$	10.8574			0.640891
$288$	5.73060	−	2.03401i	0.337679	−	0.119855i
$289$	3.56368			0.209628
$290$		0			0
$291$	−1.43024	−	3.45290i	−0.0838419	−	0.202412i
$292$	10.4519	−	7.26879i	0.611653	−	0.425374i
$293$	17.3991	+	7.20694i	1.01647	+	0.421034i	0.827809	−	0.561009i	$-0.189587\pi$
$293$	17.3991	+	7.20694i	1.01647	+	0.421034i	0.188656	+	0.982043i	$0.439587\pi$
$294$	15.5945	−	4.88952i	0.909492	−	0.285163i
$295$		0			0
$296$	−25.3220	−	19.6240i	−1.47181	−	1.14062i
$297$	8.70072	−	8.70072i	0.504867	−	0.504867i
$298$	3.05602	−	5.84771i	0.177031	−	0.338749i
$299$	0.756903	−	1.82733i	0.0437729	−	0.105677i
$300$		0			0
$301$	−10.3797	+	4.29941i	−0.598276	+	0.247814i
$302$	−13.4176	+	11.2221i	−0.772094	+	0.645762i
$303$			11.7583i			0.675497i
$304$	23.3288	−	0.869031i	1.33800	−	0.0498423i
$305$		0			0
$306$	−3.57507	−	4.27447i	−0.204373	−	0.244355i
$307$	10.8037	−	4.47505i	0.616601	−	0.255404i	−0.0524470	−	0.998624i	$-0.516702\pi$
$307$	10.8037	−	4.47505i	0.616601	−	0.255404i	0.669048	+	0.743219i	$0.266702\pi$
$308$	−6.98683	+	1.52551i	−0.398111	+	0.0869238i
$309$	−10.0252	+	24.2031i	−0.570316	+	1.37686i
$310$		0			0
$311$	−5.50620	+	5.50620i	−0.312228	+	0.312228i	−0.845772	−	0.533544i	$-0.820860\pi$
$311$	−5.50620	+	5.50620i	−0.312228	+	0.312228i	0.533544	+	0.845772i	$0.320860\pi$
$312$	1.30077	+	2.27817i	0.0736414	+	0.128976i
$313$	−5.15295	−	5.15295i	−0.291262	−	0.291262i	0.546317	−	0.837579i	$-0.316029\pi$
$313$	−5.15295	−	5.15295i	−0.291262	−	0.291262i	−0.837579	+	0.546317i	$0.816029\pi$
$314$	−7.33158	−	23.3832i	−0.413745	−	1.31959i
$315$		0			0
$316$	1.78621	−	9.94396i	0.100482	−	0.559391i
$317$	−7.67876	−	18.5382i	−0.431282	−	1.04121i	−0.978874	−	0.204462i	$-0.934455\pi$
$317$	−7.67876	−	18.5382i	−0.431282	−	1.04121i	0.547592	−	0.836745i	$-0.315545\pi$
$318$	1.07099	+	0.0954263i	0.0600582	+	0.00535124i
$319$	8.24010			0.461357
$320$		0			0
$321$	21.2175			1.18424
$322$	−6.84763	−	0.610130i	−0.381603	−	0.0340012i
$323$	−8.18679	−	19.7646i	−0.455525	−	1.09973i
$324$	−3.91408	+	21.7899i	−0.217449	+	1.21055i
$325$		0			0
$326$	−1.04785	−	3.34200i	−0.0580352	−	0.185096i
$327$	−27.9570	−	27.9570i	−1.54602	−	1.54602i
$328$	−23.6158	+	13.4839i	−1.30396	+	0.744523i
$329$	2.24504	−	2.24504i	0.123773	−	0.123773i
$330$		0			0
$331$	−1.58035	+	3.81529i	−0.0868637	+	0.209708i	−0.961342	−	0.275357i	$-0.911204\pi$
$331$	−1.58035	+	3.81529i	−0.0868637	+	0.209708i	0.874478	+	0.485065i	$0.161204\pi$
$332$	−14.3936	+	3.14270i	−0.789950	+	0.172478i
$333$	−11.2486	+	4.65934i	−0.616422	+	0.255330i
$334$	3.81607	+	4.56261i	0.208806	+	0.249655i
$335$		0			0
$336$	6.20316	−	6.68319i	0.338410	−	0.364598i
$337$			7.45730i			0.406225i	0.979155	+	0.203112i	$0.0651057\pi$
$337$			7.45730i			0.406225i	−0.979155	+	0.203112i	$0.934894\pi$
$338$	13.8734	−	11.6034i	0.754615	−	0.631143i
$339$	−3.10860	+	1.28762i	−0.168836	+	0.0699341i
$340$		0			0
$341$	2.58585	−	6.24280i	0.140032	−	0.338067i
$342$	4.10939	−	7.86332i	0.222210	−	0.425200i
$343$	10.1608	−	10.1608i	0.548633	−	0.548633i
$344$	17.2373	−	22.2423i	0.929374	−	1.19922i
$345$		0			0
$346$	−13.1290	+	4.11648i	−0.705820	+	0.221303i
$347$	−7.19799	−	2.98151i	−0.386409	−	0.160056i	0.181018	−	0.983480i	$-0.442061\pi$
$347$	−7.19799	−	2.98151i	−0.386409	−	0.160056i	−0.567426	+	0.823424i	$0.692061\pi$
$348$	−8.62561	+	5.99868i	−0.462381	+	0.321563i
$349$	−4.45368	−	10.7521i	−0.238400	−	0.575548i	0.758718	−	0.651419i	$-0.225826\pi$
$349$	−4.45368	−	10.7521i	−0.238400	−	0.575548i	−0.997118	+	0.0758714i	$0.975826\pi$
$350$		0			0
$351$	−1.78548			−0.0953019
$352$	13.3025	−	11.9951i	0.709023	−	0.639343i
$353$	0.146505			0.00779766			0.00389883	−	0.999992i	$-0.498759\pi$
$353$	0.146505			0.00779766			0.00389883	+	0.999992i	$0.498759\pi$
$354$	2.75969	−	30.9726i	0.146676	−	1.64618i
$355$		0			0
$356$	−12.0217	−	17.2862i	−0.637148	−	0.916166i
$357$	−7.71990	−	3.19769i	−0.408580	−	0.169239i
$358$	−18.2538	+	5.72330i	−0.964741	+	0.302486i
$359$	20.8531	+	20.8531i	1.10058	+	1.10058i	0.994340	+	0.106242i	$0.0338817\pi$
$359$	20.8531	+	20.8531i	1.10058	+	1.10058i	0.106242	+	0.994340i	$0.466118\pi$
$360$		0			0
$361$	10.6503	−	10.6503i	0.560541	−	0.560541i
$362$	4.32807	−	8.28176i	0.227478	−	0.435280i
$363$	0.752260	−	1.81612i	0.0394834	−	0.0953214i
$364$	0.873410	+	0.560360i	0.0457791	+	0.0293709i
$365$		0			0
$366$	29.5403	−	24.7069i	1.54410	−	1.29145i
$367$		−	5.98845i		−	0.312594i	−0.987710	−	0.156297i	$-0.950044\pi$
$367$		−	5.98845i		−	0.312594i	0.987710	−	0.156297i	$-0.0499558\pi$
$368$	15.6520	−	7.17705i	0.815915	−	0.374130i
$369$			10.3353i			0.538032i
$370$		0			0
$371$	0.392949	−	0.162765i	0.0204009	−	0.00845033i
$372$	1.83784	+	8.41734i	0.0952877	+	0.436419i
$373$	−2.74847	+	6.63539i	−0.142310	+	0.343568i	−0.978924	−	0.204226i	$-0.934532\pi$
$373$	−2.74847	+	6.63539i	−0.142310	+	0.343568i	0.836613	+	0.547794i	$0.184532\pi$
$374$	−14.5476	−	7.60258i	−0.752236	−	0.393120i
$375$		0			0
$376$	−2.09504	+	7.67132i	−0.108043	+	0.395618i
$377$	−0.845477	−	0.845477i	−0.0435443	−	0.0435443i
$378$	1.85671	+	5.92174i	0.0954987	+	0.304581i
$379$	9.53326	+	3.94881i	0.489691	+	0.202837i	0.613845	−	0.789426i	$-0.289622\pi$
$379$	9.53326	+	3.94881i	0.489691	+	0.202837i	−0.124154	+	0.992263i	$0.539622\pi$
$380$		0			0
$381$	−9.25393	−	22.3410i	−0.474093	−	1.14456i
$382$	−21.7306	−	1.93622i	−1.11184	−	0.0990655i
$383$	−12.9567			−0.662057			−0.331028	−	0.943621i	$-0.607396\pi$
$383$	−12.9567			−0.662057			−0.331028	+	0.943621i	$0.607396\pi$
$384$	−5.19252	+	22.2403i	−0.264980	+	1.13495i
$385$		0			0
$386$	−9.98049	−	0.889271i	−0.507994	−	0.0452627i
$387$	−4.09266	−	9.88055i	−0.208041	−	0.502256i
$388$	3.64452	+	0.654658i	0.185023	+	0.0332352i
$389$	25.6596	+	10.6286i	1.30099	+	0.538889i	0.922244	−	0.386609i	$-0.126354\pi$
$389$	25.6596	+	10.6286i	1.30099	+	0.538889i	0.378751	+	0.925499i	$0.376354\pi$
$390$		0			0
$391$	−11.1577	−	11.1577i	−0.564267	−	0.564267i
$392$	−4.26584	+	15.6201i	−0.215457	+	0.788933i
$393$	4.00150	−	4.00150i	0.201849	−	0.201849i
$394$	−1.12993	−	0.590503i	−0.0569250	−	0.0297491i
$395$		0			0
$396$	−1.45215	−	6.65084i	−0.0729731	−	0.334217i
$397$	−32.5215	+	13.4708i	−1.63221	+	0.676082i	−0.995477	−	0.0950060i	$-0.969713\pi$
$397$	−32.5215	+	13.4708i	−1.63221	+	0.676082i	−0.636729	+	0.771088i	$0.719713\pi$
$398$	−3.73486	−	4.46552i	−0.187211	−	0.223836i
$399$		−	13.3042i		−	0.666044i
$400$		0			0
$401$		−	2.52062i		−	0.125874i	−0.998018	−	0.0629368i	$-0.979953\pi$
$401$		−	2.52062i		−	0.125874i	0.998018	−	0.0629368i	$-0.0200466\pi$
$402$	18.9140	−	15.8192i	0.943344	−	0.788991i
$403$	−0.905867	+	0.375222i	−0.0451244	+	0.0186912i
$404$	−9.80515	−	6.29076i	−0.487824	−	0.312977i
$405$		0			0
$406$	−1.92491	+	3.68332i	−0.0955318	+	0.182800i
$407$	−25.3599	+	25.3599i	−1.25704	+	1.25704i
$408$	20.7627	−	2.63216i	1.02791	−	0.130311i
$409$	−5.83443	−	5.83443i	−0.288494	−	0.288494i	0.547991	−	0.836484i	$-0.315393\pi$
$409$	−5.83443	−	5.83443i	−0.288494	−	0.288494i	−0.836484	+	0.547991i	$0.815393\pi$
$410$		0			0
$411$	−18.7535	−	7.76794i	−0.925040	−	0.383164i
$412$	−14.8192	−	21.3087i	−0.730087	−	1.04981i
$413$	−4.70709	−	11.3639i	−0.231621	−	0.559182i
$414$	0.580789	−	6.51834i	0.0285442	−	0.320359i
$415$		0			0
$416$	−2.59567	−	0.134139i	−0.127263	−	0.00657669i
$417$	41.0515			2.01030
$418$	2.31943	−	26.0315i	0.113447	−	1.27324i
$419$	5.75322	+	13.8895i	0.281063	+	0.678546i	0.999861	−	0.0166728i	$-0.00530736\pi$
$419$	5.75322	+	13.8895i	0.281063	+	0.678546i	−0.718798	+	0.695219i	$0.755307\pi$
$420$		0			0
$421$	−27.5675	−	11.4188i	−1.34356	−	0.556520i	−0.409066	−	0.912505i	$-0.634145\pi$
$421$	−27.5675	−	11.4188i	−1.34356	−	0.556520i	−0.934492	+	0.355985i	$0.884145\pi$
$422$	11.5783	−	3.63028i	0.563624	−	0.176719i
$423$	2.13708	+	2.13708i	0.103909	+	0.103909i
$424$	−0.652561	+	0.842036i	−0.0316912	+	0.0408929i
$425$		0			0
$426$	−11.0066	+	21.0612i	−0.533274	+	1.02042i
$427$	5.82958	−	14.0738i	0.282113	−	0.681081i
$428$	−11.3515	+	17.6930i	−0.548694	+	0.855226i
$429$	2.71330	−	1.12389i	0.130999	−	0.0542618i
$430$		0			0
$431$			34.5185i			1.66270i	0.555750	+	0.831349i	$0.312431\pi$
$431$			34.5185i			1.66270i	−0.555750	+	0.831349i	$0.687569\pi$
$432$	−11.3928	−	10.5745i	−0.548136	−	0.508765i
$433$			16.9110i			0.812690i	0.913720	+	0.406345i	$0.133197\pi$
$433$			16.9110i			0.812690i	−0.913720	+	0.406345i	$0.866803\pi$
$434$	2.18647	+	2.61422i	0.104954	+	0.125486i
$435$		0			0
$436$	38.2702	−	8.35592i	1.83281	−	0.400176i
$437$	9.61438	−	23.2112i	0.459918	−	1.11034i
$438$	16.1055	+	8.41678i	0.769552	+	0.402170i
$439$	−7.67146	+	7.67146i	−0.366139	+	0.366139i	−0.866067	−	0.499928i	$-0.833360\pi$
$439$	−7.67146	+	7.67146i	−0.366139	+	0.366139i	0.499928	+	0.866067i	$0.333360\pi$
$440$		0			0
$441$	4.35145	+	4.35145i	0.207212	+	0.207212i
$442$	0.712591	+	2.27272i	0.0338945	+	0.108102i
$443$	3.78465	+	1.56765i	0.179814	+	0.0744815i	0.470774	−	0.882254i	$-0.343975\pi$
$443$	3.78465	+	1.56765i	0.179814	+	0.0744815i	−0.290960	+	0.956735i	$0.593975\pi$
$444$	8.08468	−	45.0080i	0.383682	−	2.13598i
$445$		0			0
$446$	−8.13487	−	0.724824i	−0.385197	−	0.0343214i
$447$	9.41815			0.445463
$448$	2.25433	+	8.74830i	0.106507	+	0.413318i
$449$	−3.12042			−0.147262			−0.0736309	−	0.997286i	$-0.523459\pi$
$449$	−3.12042			−0.147262			−0.0736309	+	0.997286i	$0.523459\pi$
$450$		0			0
$451$	11.6503	+	28.1264i	0.548593	+	1.32442i
$452$	0.589380	−	3.28112i	0.0277221	−	0.154331i
$453$	−23.0674	−	9.55485i	−1.08380	−	0.448926i
$454$	1.35507	+	4.32182i	0.0635965	+	0.202833i
$455$		0			0
$456$	16.5227	+	28.9379i	0.773744	+	1.35514i
$457$	−28.7210	+	28.7210i	−1.34351	+	1.34351i	−0.450978	+	0.892535i	$0.648925\pi$
$457$	−28.7210	+	28.7210i	−1.34351	+	1.34351i	−0.892535	+	0.450978i	$0.851075\pi$
$458$	20.6294	+	10.7810i	0.963950	+	0.503762i
$459$	−5.45107	+	13.1600i	−0.254434	+	0.614258i
$460$		0			0
$461$	33.4225	−	13.8441i	1.55664	−	0.644782i	0.572139	−	0.820157i	$-0.306114\pi$
$461$	33.4225	−	13.8441i	1.55664	−	0.644782i	0.984502	+	0.175375i	$0.0561138\pi$
$462$	−6.54904	−	7.83024i	−0.304689	−	0.364296i
$463$		−	13.9489i		−	0.648259i	−0.946013	−	0.324130i	$-0.894929\pi$
$463$		−	13.9489i		−	0.648259i	0.946013	−	0.324130i	$-0.105071\pi$
$464$	−0.387495	−	10.4021i	−0.0179890	−	0.482907i
$465$		0			0
$466$	8.64136	−	7.22744i	0.400303	−	0.334805i
$467$	34.9426	−	14.4737i	1.61695	−	0.669763i	0.623271	−	0.782006i	$-0.285803\pi$
$467$	34.9426	−	14.4737i	1.61695	−	0.669763i	0.993681	+	0.112243i	$0.0358034\pi$
$468$	−0.533413	+	0.831409i	−0.0246570	+	0.0384319i
$469$	3.73254	−	9.01115i	0.172353	−	0.416096i
$470$		0			0
$471$	24.7342	−	24.7342i	1.13969	−	1.13969i
$472$	24.3513	+	18.8718i	1.12086	+	0.868646i
$473$	−22.2755	−	22.2755i	−1.02423	−	1.02423i
$474$	13.7607	−	4.31453i	0.632048	−	0.198173i
$475$		0			0
$476$	6.79671	−	4.72677i	0.311527	−	0.216651i
$477$	0.154938	+	0.374053i	0.00709411	+	0.0171267i
$478$	−1.21747	+	13.6639i	−0.0556856	+	0.624972i
$479$	1.27470			0.0582424			0.0291212	−	0.999576i	$-0.490729\pi$
$479$	1.27470			0.0582424			0.0291212	+	0.999576i	$0.490729\pi$
$480$		0			0
$481$	5.20411			0.237287
$482$	2.09713	−	23.5365i	0.0955215	−	1.07206i
$483$	−3.75529	−	9.06607i	−0.170872	−	0.412521i
$484$	1.11198	+	1.59894i	0.0505445	+	0.0726789i
$485$		0			0
$486$	−14.4217	+	4.52178i	−0.654180	+	0.205112i
$487$	5.87473	+	5.87473i	0.266209	+	0.266209i	0.827571	−	0.561361i	$-0.189722\pi$
$487$	5.87473	+	5.87473i	0.266209	+	0.266209i	−0.561361	+	0.827571i	$0.689722\pi$
$488$	4.79858	+	37.8517i	0.217222	+	1.71347i
$489$	3.53508	−	3.53508i	0.159862	−	0.159862i
$490$		0			0
$491$	−14.2233	+	34.3381i	−0.641889	+	1.54966i	0.182240	+	0.983254i	$0.441665\pi$
$491$	−14.2233	+	34.3381i	−0.641889	+	1.54966i	−0.824129	+	0.566403i	$0.808335\pi$
$492$	−32.6710	−	20.9610i	−1.47292	−	0.944995i
$493$	−8.81291	+	3.65043i	−0.396914	+	0.164407i
$494$	−2.90896	+	2.43299i	−0.130880	+	0.109465i
$495$		0			0
$496$	−8.00240	−	2.97076i	−0.359318	−	0.133391i
$497$			9.40016i			0.421655i
$498$	−13.4917	−	16.1311i	−0.604576	−	0.722851i
$499$	−33.8195	+	14.0085i	−1.51397	+	0.627107i	−0.976372	−	0.216095i	$-0.930668\pi$
$499$	−33.8195	+	14.0085i	−1.51397	+	0.627107i	−0.537597	+	0.843202i	$0.680668\pi$
$500$		0			0
$501$	−3.24911	+	7.84403i	−0.145159	+	0.350446i
$502$	8.96825	+	4.68683i	0.400273	+	0.209183i
$503$	0.844993	−	0.844993i	0.0376764	−	0.0376764i	−0.688018	−	0.725694i	$-0.741519\pi$
$503$	0.844993	−	0.844993i	0.0376764	−	0.0376764i	0.725694	+	0.688018i	$0.241519\pi$
$504$	3.31215	+	0.904548i	0.147535	+	0.0402918i
$505$		0			0
$506$	−5.76718	−	18.3937i	−0.256382	−	0.817700i
$507$	23.8512	+	9.87948i	1.05927	+	0.438763i
$508$	23.5808	+	4.23577i	1.04623	+	0.187932i
$509$	−0.698779	−	1.68700i	−0.0309728	−	0.0747750i	0.907636	−	0.419757i	$-0.137885\pi$
$509$	−0.698779	−	1.68700i	−0.0309728	−	0.0747750i	−0.938609	+	0.344982i	$0.887885\pi$
$510$		0			0
$511$	7.18831			0.317992
$512$	−15.7680	−	16.2287i	−0.696853	−	0.717214i
$513$	−22.6796			−1.00133
$514$	−14.4152	−	1.28440i	−0.635825	−	0.0566526i
$515$		0			0
$516$	39.5340	+	7.10140i	1.74039	+	0.312622i
$517$	8.22487	+	3.40685i	0.361729	+	0.149833i
$518$	−5.41172	−	17.2600i	−0.237777	−	0.758361i
$519$	−13.8875	−	13.8875i	−0.609596	−	0.609596i
$520$		0			0
$521$	−19.8057	+	19.8057i	−0.867706	+	0.867706i	−0.992218	−	0.124513i	$-0.960263\pi$
$521$	−19.8057	+	19.8057i	−0.867706	+	0.867706i	0.124513	+	0.992218i	$0.460263\pi$
$522$	−3.50620	−	1.83235i	−0.153462	−	0.0801996i
$523$	−0.999058	+	2.41194i	−0.0436858	+	0.105467i	−0.944216	−	0.329326i	$-0.893178\pi$
$523$	−0.999058	+	2.41194i	−0.0436858	+	0.105467i	0.900530	+	0.434793i	$0.143178\pi$
$524$	1.19599	+	5.47764i	0.0522470	+	0.239292i
$525$		0			0
$526$	−1.68352	−	2.01287i	−0.0734050	−	0.0877654i
$527$			7.82233i			0.340746i
$528$	23.9692	+	8.89819i	1.04313	+	0.387244i
$529$			4.46914i			0.194310i
$530$		0			0
$531$	10.8175	−	4.48074i	0.469437	−	0.194447i
$532$	11.0943	+	7.11784i	0.480998	+	0.308597i
$533$	1.69053	−	4.08130i	0.0732250	−	0.176781i
$534$	13.9203	−	26.6366i	0.602391	−	1.15268i
$535$		0			0
$536$	3.07242	+	24.2356i	0.132708	+	1.04682i
$537$	−19.3084	−	19.3084i	−0.833218	−	0.833218i
$538$	24.0420	−	7.53815i	1.03652	−	0.324993i
$539$	16.7472	+	6.93691i	0.721352	+	0.298794i
$540$		0			0
$541$	5.84464	+	14.1102i	0.251281	+	0.606645i	0.998308	−	0.0581482i	$-0.0185196\pi$
$541$	5.84464	+	14.1102i	0.251281	+	0.606645i	−0.747027	+	0.664793i	$0.768520\pi$
$542$	−1.18691	+	13.3210i	−0.0509821	+	0.572184i
$543$	13.3384			0.572404
$544$	−8.91325	+	18.7221i	−0.382152	+	0.802702i
$545$		0			0
$546$	−0.131459	+	1.47539i	−0.00562591	+	0.0631409i
$547$	−13.7675	−	33.2376i	−0.588655	−	1.42114i	−0.884789	−	0.465992i	$-0.845698\pi$
$547$	−13.7675	−	33.2376i	−0.588655	−	1.42114i	0.296134	−	0.955146i	$-0.404302\pi$
$548$	16.5108	−	11.4825i	0.705307	−	0.490506i
$549$	13.3971	+	5.54924i	0.571772	+	0.236836i
$550$		0			0
$551$	−10.7395	−	10.7395i	−0.457517	−	0.457517i
$552$	19.4274	+	15.0558i	0.826883	+	0.640818i
$553$	4.03371	−	4.03371i	0.171531	−	0.171531i
$554$	−18.6235	+	35.6360i	−0.791235	+	1.51403i
$555$		0			0
$556$	−21.9628	+	34.2325i	−0.931429	+	1.45178i
$557$	2.78566	−	1.15386i	0.118032	−	0.0488905i	−0.322886	−	0.946438i	$-0.604653\pi$
$557$	2.78566	−	1.15386i	0.118032	−	0.0488905i	0.440918	+	0.897547i	$0.354653\pi$
$558$	−2.48850	+	2.08133i	−0.105347	+	0.0881096i
$559$			4.57117i			0.193340i
$560$		0			0
$561$		−	23.4299i		−	0.989210i
$562$	−17.7091	−	21.1736i	−0.747013	−	0.893153i
$563$	0.817314	−	0.338542i	0.0344457	−	0.0142679i	−0.365394	−	0.930853i	$-0.619066\pi$
$563$	0.817314	−	0.338542i	0.0344457	−	0.0142679i	0.399840	+	0.916585i	$0.369066\pi$
$564$	−11.0898	+	2.42135i	−0.466965	+	0.101957i
$565$		0			0
$566$	−29.9216	−	15.6371i	−1.25770	−	0.657275i
$567$	−8.83896	+	8.83896i	−0.371201	+	0.371201i
$568$	−11.6742	−	20.4462i	−0.489837	−	0.857904i
$569$	1.30773	+	1.30773i	0.0548229	+	0.0548229i	0.733987	−	0.679164i	$-0.237657\pi$
$569$	1.30773	+	1.30773i	0.0548229	+	0.0548229i	−0.679164	+	0.733987i	$0.737657\pi$
$570$		0			0
$571$	−3.63704	−	1.50651i	−0.152206	−	0.0630456i	0.305280	−	0.952263i	$-0.401250\pi$
$571$	−3.63704	−	1.50651i	−0.152206	−	0.0630456i	−0.457486	+	0.889217i	$0.651250\pi$
$572$	−0.514433	+	2.86388i	−0.0215095	+	0.119745i
$573$	−11.9172	−	28.7708i	−0.497850	−	1.20192i
$574$	−15.2941	−	1.36271i	−0.638362	−	0.0568786i
$575$		0			0
$576$	−8.32761	+	2.14592i	−0.346984	+	0.0894134i
$577$	−33.9400			−1.41294			−0.706470	−	0.707743i	$-0.749714\pi$
$577$	−33.9400			−1.41294			−0.706470	+	0.707743i	$0.749714\pi$
$578$	−5.01992	−	0.447280i	−0.208801	−	0.0186044i
$579$	−5.47338	−	13.2139i	−0.227466	−	0.549151i
$580$		0			0
$581$	−7.68530	−	3.18336i	−0.318840	−	0.132068i
$582$	1.58130	+	5.04337i	0.0655471	+	0.209055i
$583$	0.843295	+	0.843295i	0.0349257	+	0.0349257i
$584$	−15.6352	+	8.92723i	−0.646991	+	0.369412i
$585$		0			0
$586$	−23.6044	−	12.3357i	−0.975088	−	0.509583i
$587$	−17.6954	+	42.7204i	−0.730367	+	1.76326i	−0.0889930	+	0.996032i	$0.528365\pi$
$587$	−17.6954	+	42.7204i	−0.730367	+	1.76326i	−0.641374	+	0.767229i	$0.721635\pi$
$588$	−22.5807	+	4.93027i	−0.931211	+	0.203321i
$589$	−11.5065	+	4.76617i	−0.474119	+	0.196386i
$590$		0			0
$591$		−	1.81983i		−	0.0748578i
$592$	33.2064	+	30.8213i	1.36477	+	1.26675i
$593$			24.2307i			0.995036i	0.867454	+	0.497518i	$0.165755\pi$
$593$			24.2307i			0.995036i	−0.867454	+	0.497518i	$0.834245\pi$
$594$	−13.3482	+	11.1641i	−0.547682	+	0.458068i
$595$		0			0
$596$	−5.03877	+	7.85371i	−0.206396	+	0.321701i
$597$	3.17996	−	7.67711i	0.130147	−	0.314203i
$598$	−1.29555	+	2.47903i	−0.0529789	+	0.101375i
$599$	−13.7452	+	13.7452i	−0.561614	+	0.561614i	−0.929766	−	0.368152i	$-0.879991\pi$
$599$	−13.7452	+	13.7452i	−0.561614	+	0.561614i	0.368152	+	0.929766i	$0.379991\pi$
$600$		0			0
$601$	−7.85659	−	7.85659i	−0.320477	−	0.320477i	0.528473	−	0.848950i	$-0.322765\pi$
$601$	−7.85659	−	7.85659i	−0.320477	−	0.320477i	−0.848950	+	0.528473i	$0.822765\pi$
$602$	15.1608	−	4.75353i	0.617908	−	0.193739i
$603$	8.57782	+	3.55305i	0.349316	+	0.144691i
$604$	20.3089	−	14.1238i	0.826358	−	0.574691i
$605$		0			0
$606$	1.47579	−	16.5631i	0.0599499	−	0.672832i
$607$	28.6943			1.16467			0.582333	−	0.812950i	$-0.302140\pi$
$607$	28.6943			1.16467			0.582333	+	0.812950i	$0.302140\pi$
$608$	−32.9708	−	1.70386i	−1.33714	−	0.0691008i
$609$	−5.93226			−0.240387
$610$		0			0
$611$	−0.494354	−	1.19348i	−0.0199994	−	0.0482829i
$612$	4.49947	+	6.46987i	0.181880	+	0.261529i
$613$	−17.0046	−	7.04353i	−0.686808	−	0.284485i	0.0118614	−	0.999930i	$-0.496224\pi$
$613$	−17.0046	−	7.04353i	−0.686808	−	0.284485i	−0.698670	+	0.715444i	$0.746224\pi$
$614$	−15.7801	+	4.94772i	−0.636835	+	0.199674i
$615$		0			0
$616$	10.0333	−	1.27196i	0.404255	−	0.0512486i
$617$	−5.61180	+	5.61180i	−0.225922	+	0.225922i	−0.810987	−	0.585064i	$-0.801069\pi$
$617$	−5.61180	+	5.61180i	−0.225922	+	0.225922i	0.585064	+	0.810987i	$0.301069\pi$
$618$	17.1596	−	32.8350i	0.690261	−	1.32082i
$619$	10.2233	−	24.6813i	0.410911	−	0.992027i	−0.573983	−	0.818867i	$-0.694602\pi$
$619$	10.2233	−	24.6813i	0.410911	−	0.992027i	0.984894	−	0.173160i	$-0.0553976\pi$
$620$		0			0
$621$	−15.4549	+	6.40161i	−0.620182	+	0.256888i
$622$	8.44730	−	7.06513i	0.338706	−	0.283286i
$623$		−	11.8886i		−	0.476305i
$624$	−1.54637	−	3.37237i	−0.0619043	−	0.135003i
$625$		0			0
$626$	6.61186	+	7.90536i	0.264263	+	0.315962i
$627$	34.4650	−	14.2759i	1.37640	−	0.570124i
$628$	7.39268	+	33.8585i	0.295000	+	1.35110i
$629$	15.8882	−	38.3574i	0.633502	−	1.52941i
$630$		0			0
$631$	−3.09520	+	3.09520i	−0.123218	+	0.123218i	−0.766027	−	0.642809i	$-0.777769\pi$
$631$	−3.09520	+	3.09520i	−0.123218	+	0.123218i	0.642809	+	0.766027i	$0.277769\pi$
$632$	−3.76419	+	13.7832i	−0.149731	+	0.548266i
$633$	12.2473	+	12.2473i	0.486785	+	0.486785i
$634$	8.48982	+	27.0772i	0.337174	+	1.07537i
$635$		0			0
$636$	−1.49666	−	0.268841i	−0.0593463	−	0.0106602i
$637$	−1.00659	−	2.43011i	−0.0398824	−	0.0962845i
$638$	−11.6073	−	1.03422i	−0.459536	−	0.0409451i
$639$	−8.94812			−0.353982
$640$		0			0
$641$	−7.87672			−0.311112			−0.155556	−	0.987827i	$-0.549717\pi$
$641$	−7.87672			−0.311112			−0.155556	+	0.987827i	$0.549717\pi$
$642$	−29.8876	−	2.66301i	−1.17957	−	0.105101i
$643$	8.21644	+	19.8362i	0.324025	+	0.782265i	0.999012	+	0.0444357i	$0.0141490\pi$
$643$	8.21644	+	19.8362i	0.324025	+	0.782265i	−0.674988	+	0.737829i	$0.735851\pi$
$644$	9.56922	+	1.71890i	0.377080	+	0.0677341i
$645$		0			0
$646$	9.05151	+	28.8687i	0.356127	+	1.13582i
$647$	−23.8640	−	23.8640i	−0.938192	−	0.938192i	0.0600057	−	0.998198i	$-0.480888\pi$
$647$	−23.8640	−	23.8640i	−0.938192	−	0.938192i	−0.998198	+	0.0600057i	$0.980888\pi$
$648$	8.24836	−	30.2028i	0.324026	−	1.18648i
$649$	24.3878	−	24.3878i	0.957303	−	0.957303i
$650$		0			0
$651$	−1.86162	+	4.49435i	−0.0729627	+	0.176148i
$652$	1.05658	+	4.83917i	0.0413791	+	0.189516i
$653$	−36.1824	+	14.9873i	−1.41593	+	0.586497i	−0.953834	−	0.300334i	$-0.902902\pi$
$653$	−36.1824	+	14.9873i	−1.41593	+	0.586497i	−0.462095	+	0.886831i	$0.652902\pi$
$654$	35.8722	+	42.8900i	1.40271	+	1.67713i
$655$		0			0
$656$	34.9584	−	16.0298i	1.36490	−	0.625860i
$657$			6.84263i			0.266956i
$658$	−3.44422	+	2.88067i	−0.134270	+	0.112300i
$659$	−20.8508	+	8.63670i	−0.812233	+	0.336438i	−0.749845	−	0.661614i	$-0.769872\pi$
$659$	−20.8508	+	8.63670i	−0.812233	+	0.336438i	−0.0623886	+	0.998052i	$0.519872\pi$
$660$		0			0
$661$	12.8313	−	30.9774i	0.499078	−	1.20488i	−0.450902	−	0.892573i	$-0.648898\pi$
$661$	12.8313	−	30.9774i	0.499078	−	1.20488i	0.949981	−	0.312308i	$-0.101102\pi$
$662$	2.70499	−	5.17600i	0.105132	−	0.201171i
$663$	−2.40403	+	2.40403i	−0.0933647	+	0.0933647i
$664$	20.6697	−	2.62036i	0.802140	−	0.101690i
$665$		0			0
$666$	16.4300	−	5.15148i	0.636650	−	0.199616i
$667$	−10.3497	−	4.28698i	−0.400741	−	0.165993i
$668$	−4.80278	−	6.90600i	−0.185825	−	0.267201i
$669$	−4.46122	−	10.7703i	−0.172481	−	0.416405i
$670$		0			0
$671$	42.7141			1.64896
$672$	−9.57678	+	8.63560i	−0.369432	+	0.333126i
$673$	31.7494			1.22385			0.611925	−	0.790916i	$-0.290395\pi$
$673$	31.7494			1.22385			0.611925	+	0.790916i	$0.290395\pi$
$674$	0.935969	−	10.5046i	0.0360522	−	0.404622i
$675$		0			0
$676$	−20.9989	+	14.6037i	−0.807651	+	0.561681i
$677$	8.71700	+	3.61070i	0.335022	+	0.138770i	0.543851	−	0.839182i	$-0.316965\pi$
$677$	8.71700	+	3.61070i	0.335022	+	0.138770i	−0.208830	+	0.977952i	$0.566965\pi$
$678$	4.54048	−	1.42363i	0.174376	−	0.0546740i
$679$	1.47838	+	1.47838i	0.0567350	+	0.0567350i
$680$		0			0
$681$	−4.57152	+	4.57152i	−0.175181	+	0.175181i
$682$	−4.42606	+	8.46927i	−0.169482	+	0.324305i
$683$	−12.2934	+	29.6789i	−0.470394	+	1.13563i	0.493595	+	0.869692i	$0.335683\pi$
$683$	−12.2934	+	29.6789i	−0.470394	+	1.13563i	−0.963989	+	0.265941i	$0.914317\pi$
$684$	−6.77555	+	10.5608i	−0.259070	+	0.403801i
$685$		0			0
$686$	−15.5882	+	13.0376i	−0.595159	+	0.497778i
$687$			33.2252i			1.26762i
$688$	−27.0727	+	29.1677i	−1.03214	+	1.11201i
$689$		−	0.173053i		−	0.00659280i
$690$		0			0
$691$	−36.7401	+	15.2182i	−1.39766	+	0.578929i	−0.949143	−	0.314846i	$-0.898047\pi$
$691$	−36.7401	+	15.2182i	−1.39766	+	0.578929i	−0.448516	+	0.893775i	$0.648047\pi$
$692$	19.0106	−	4.15078i	0.722675	−	0.157789i
$693$	1.47093	−	3.55115i	0.0558762	−	0.134897i
$694$	9.76512	+	5.10327i	0.370679	+	0.193718i
$695$		0			0
$696$	12.9032	−	7.36733i	0.489095	−	0.279258i
$697$	−24.9204	−	24.9204i	−0.943929	−	0.943929i
$698$	4.92409	+	15.7048i	0.186380	+	0.594435i
$699$	14.8562	+	6.15365i	0.561914	+	0.232752i
$700$		0			0
$701$	10.8619	+	26.2229i	0.410248	+	0.990427i	0.985071	+	0.172149i	$0.0550709\pi$
$701$	10.8619	+	26.2229i	0.410248	+	0.990427i	−0.574823	+	0.818278i	$0.694929\pi$
$702$	2.51509	+	0.224096i	0.0949258	+	0.00845797i
$703$	66.1039			2.49316
$704$	−20.2438	+	15.2271i	−0.762967	+	0.573894i
$705$		0			0
$706$	−0.206371	−	0.0183879i	−0.00776689	−	0.000692037i
$707$	−2.51720	−	6.07706i	−0.0946690	−	0.228551i
$708$	−7.77478	+	43.2827i	−0.292194	+	1.62666i
$709$	−11.9035	−	4.93060i	−0.447046	−	0.185172i	0.147791	−	0.989019i	$-0.452784\pi$
$709$	−11.9035	−	4.93060i	−0.447046	−	0.185172i	−0.594837	+	0.803846i	$0.702784\pi$
$710$		0			0
$711$	3.83973	+	3.83973i	0.144001	+	0.144001i
$712$	14.7645	+	25.8587i	0.553324	+	0.969097i
$713$	−6.49574	+	6.49574i	−0.243267	+	0.243267i
$714$	10.4732	+	5.47329i	0.391948	+	0.204833i
$715$		0			0
$716$	26.4312	−	5.77099i	0.987779	−	0.215672i
$717$	−18.0906	+	7.49338i	−0.675607	+	0.279845i
$718$	−26.7570	−	31.9916i	−0.998563	−	1.19391i
$719$			29.8520i			1.11329i	0.830750	+	0.556645i	$0.187912\pi$
$719$			29.8520i			1.11329i	−0.830750	+	0.556645i	$0.812088\pi$
$720$		0			0
$721$		−	14.6551i		−	0.545783i
$722$	−16.3391	+	13.6656i	−0.608077	+	0.508582i
$723$	31.1617	−	12.9076i	1.15892	−	0.480039i
$724$	−7.13611	+	11.1227i	−0.265211	+	0.413374i
$725$		0			0
$726$	−1.28760	+	2.46382i	−0.0477873	+	0.0914411i
$727$	−5.31546	+	5.31546i	−0.197139	+	0.197139i	−0.798773	−	0.601633i	$-0.794517\pi$
$727$	−5.31546	+	5.31546i	−0.197139	+	0.197139i	0.601633	+	0.798773i	$0.294517\pi$
$728$	−1.15998	−	0.898964i	−0.0429918	−	0.0333178i
$729$	8.22672	+	8.22672i	0.304693	+	0.304693i
$730$		0			0
$731$	33.6923	+	13.9558i	1.24615	+	0.516174i
$732$	−44.7125	+	31.0953i	−1.65262	+	1.14931i
$733$	8.72796	+	21.0712i	0.322375	+	0.778281i	0.999115	+	0.0420595i	$0.0133919\pi$
$733$	8.72796	+	21.0712i	0.322375	+	0.778281i	−0.676740	+	0.736222i	$0.736608\pi$
$734$	−0.751613	+	8.43552i	−0.0277425	+	0.311361i
$735$		0			0
$736$	−22.9487	+	8.14535i	−0.845899	+	0.300242i
$737$	27.3488			1.00741
$738$	1.29718	−	14.5586i	0.0477500	−	0.535909i
$739$	−12.8599	−	31.0465i	−0.473059	−	1.14207i	−0.962804	−	0.270200i	$-0.912910\pi$
$739$	−12.8599	−	31.0465i	−0.473059	−	1.14207i	0.489745	−	0.871866i	$-0.337090\pi$
$740$		0			0
$741$	−5.00108	−	2.07151i	−0.183719	−	0.0760990i
$742$	−0.573950	+	0.179957i	−0.0210704	+	0.00660642i
$743$	−5.20989	−	5.20989i	−0.191133	−	0.191133i	0.605053	−	0.796185i	$-0.293152\pi$
$743$	−5.20989	−	5.20989i	−0.191133	−	0.191133i	−0.796185	+	0.605053i	$0.793152\pi$
$744$	−1.53238	−	12.0876i	−0.0561799	−	0.443153i
$745$		0			0
$746$	4.70440	−	9.00187i	0.172240	−	0.329582i
$747$	3.03027	−	7.31573i	0.110872	−	0.267669i
$748$	19.5380	+	12.5351i	0.714379	+	0.458329i
$749$	−10.9658	+	4.54220i	−0.400683	+	0.165968i
$750$		0			0
$751$		−	13.7728i		−	0.502575i	−0.967913	−	0.251287i	$-0.919146\pi$
$751$		−	13.7728i		−	0.502575i	0.967913	−	0.251287i	$-0.0808539\pi$
$752$	3.91397	−	10.5431i	0.142728	−	0.384468i
$753$			14.4440i			0.526369i
$754$	1.08485	+	1.29708i	0.0395079	+	0.0472370i
$755$		0			0
$756$	−1.87218	−	8.57460i	−0.0680905	−	0.311855i
$757$	−5.46900	+	13.2033i	−0.198774	+	0.479883i	−0.991565	−	0.129611i	$-0.958627\pi$
$757$	−5.46900	+	13.2033i	−0.198774	+	0.479883i	0.792791	+	0.609494i	$0.208627\pi$
$758$	−12.9333	−	6.75895i	−0.469757	−	0.245496i
$759$	19.4564	−	19.4564i	0.706223	−	0.706223i
$760$		0			0
$761$	23.8131	+	23.8131i	0.863225	+	0.863225i	0.991711	−	0.128487i	$-0.0410119\pi$
$761$	23.8131	+	23.8131i	0.863225	+	0.863225i	−0.128487	+	0.991711i	$0.541012\pi$
$762$	10.2314	+	32.6317i	0.370643	+	1.18212i
$763$	20.4340	+	8.46404i	0.739760	+	0.306419i
$764$	30.3675	+	5.45484i	1.09866	+	0.197349i
$765$		0			0
$766$	18.2512	+	1.62620i	0.659444	+	0.0587571i
$767$	−5.00463			−0.180707
$768$	10.1057	−	30.6767i	0.364660	−	1.10695i
$769$	−43.8494			−1.58125			−0.790626	−	0.612300i	$-0.790244\pi$
$769$	−43.8494			−1.58125			−0.790626	+	0.612300i	$0.790244\pi$
$770$		0			0
$771$	−7.90538	−	19.0853i	−0.284705	−	0.687339i
$772$	13.9472	+	2.50531i	0.501972	+	0.0901682i
$773$	21.1489	+	8.76014i	0.760672	+	0.315080i	0.729087	−	0.684421i	$-0.239945\pi$
$773$	21.1489	+	8.76014i	0.760672	+	0.315080i	0.0315842	+	0.999501i	$0.489945\pi$
$774$	4.52494	+	14.4317i	0.162646	+	0.518738i
$775$		0			0
$776$	−5.05163	−	1.37960i	−0.181343	−	0.0495247i
$777$	18.2572	−	18.2572i	0.654974	−	0.654974i
$778$	−34.8110	−	18.1923i	−1.24803	−	0.652225i
$779$	21.4735	−	51.8417i	0.769370	−	1.85742i
$780$		0			0
$781$	−24.3514	+	10.0867i	−0.871363	+	0.360930i
$782$	14.3166	+	17.1174i	0.511962	+	0.612119i
$783$			10.1127i			0.361397i
$784$	7.96948	−	21.4675i	0.284624	−	0.766698i
$785$		0			0
$786$	−6.13887	+	5.13441i	−0.218966	+	0.183138i
$787$	16.0504	−	6.64829i	0.572134	−	0.236986i	−0.0778092	−	0.996968i	$-0.524792\pi$
$787$	16.0504	−	6.64829i	0.572134	−	0.236986i	0.649944	+	0.759982i	$0.274792\pi$
$788$	1.51754	+	0.973619i	0.0540601	+	0.0346838i
$789$	1.43340	−	3.46053i	0.0510303	−	0.123198i
$790$		0			0
$791$	1.33097	−	1.33097i	0.0473237	−	0.0473237i
$792$	1.21079	+	9.55085i	0.0430236	+	0.339375i
$793$	−4.38269	−	4.38269i	−0.155634	−	0.155634i
$794$	47.5015	−	14.8937i	1.68577	−	0.528557i
$795$		0			0
$796$	4.70057	+	6.75904i	0.166607	+	0.239568i
$797$	19.9501	+	48.1639i	0.706670	+	1.70605i	0.708159	+	0.706053i	$0.249526\pi$
$797$	19.9501	+	48.1639i	0.706670	+	1.70605i	−0.00148846	+	0.999999i	$0.500474\pi$
$798$	−1.66982	+	18.7408i	−0.0591110	+	0.663416i
$799$	−10.3059			−0.364596
$800$		0			0
$801$	11.3169			0.399862
$802$	−0.316364	+	3.55062i	−0.0111712	+	0.125377i
$803$	7.71330	+	18.6215i	0.272196	+	0.657140i
$804$	−28.6283	+	19.9096i	−1.00964	+	0.702157i
$805$		0			0
$806$	1.32313	−	0.414855i	0.0466052	−	0.0146126i
$807$	25.4311	+	25.4311i	0.895216	+	0.895216i
$808$	13.0223	+	10.0920i	0.458123	+	0.355036i
$809$	11.9277	−	11.9277i	0.419355	−	0.419355i	−0.465626	−	0.884981i	$-0.654171\pi$
$809$	11.9277	−	11.9277i	0.419355	−	0.419355i	0.884981	+	0.465626i	$0.154171\pi$
$810$		0			0
$811$	13.7044	−	33.0853i	0.481225	−	1.16178i	−0.477802	−	0.878468i	$-0.658566\pi$
$811$	13.7044	−	33.0853i	0.481225	−	1.16178i	0.959027	−	0.283313i	$-0.0914337\pi$
$812$	3.17379	−	4.94686i	0.111378	−	0.173601i
$813$	−17.6366	+	7.30531i	−0.618542	+	0.256209i
$814$	38.9057	−	32.5398i	1.36364	−	1.14052i
$815$		0			0
$816$	−29.5774	+	1.10180i	−1.03542	+	0.0385708i
$817$			58.0642i			2.03141i
$818$	7.48628	+	8.95085i	0.261752	+	0.312959i
$819$	−0.515292	+	0.213441i	−0.0180058	+	0.00745824i
$820$		0			0
$821$	3.61317	−	8.72295i	0.126100	−	0.304433i	−0.848204	−	0.529670i	$-0.822316\pi$
$821$	3.61317	−	8.72295i	0.126100	−	0.304433i	0.974304	+	0.225237i	$0.0723157\pi$
$822$	25.4418	+	13.2959i	0.887384	+	0.463749i
$823$	−9.66407	+	9.66407i	−0.336868	+	0.336868i	−0.855187	−	0.518319i	$-0.826558\pi$
$823$	−9.66407	+	9.66407i	−0.336868	+	0.336868i	0.518319	+	0.855187i	$0.326558\pi$
$824$	18.2003	+	31.8761i	0.634037	+	1.11046i
$825$		0			0
$826$	5.20427	+	16.5984i	0.181080	+	0.577532i
$827$	29.6154	+	12.2671i	1.02983	+	0.426569i	0.832651	−	0.553798i	$-0.186822\pi$
$827$	29.6154	+	12.2671i	1.02983	+	0.426569i	0.197178	+	0.980368i	$0.436822\pi$
$828$	−1.63624	+	9.10905i	−0.0568632	+	0.316561i
$829$	3.93773	+	9.50653i	0.136763	+	0.330175i	0.977392	−	0.211437i	$-0.0678142\pi$
$829$	3.93773	+	9.50653i	0.136763	+	0.330175i	−0.840629	+	0.541612i	$0.817814\pi$
$830$		0			0
$831$	−57.3943			−1.99099
$832$	3.63951	+	0.514736i	0.126177	+	0.0178452i
$833$	−20.9845			−0.727069
$834$	−57.8265	−	5.15239i	−2.00237	−	0.178413i
$835$		0			0
$836$	−6.53446	+	36.3778i	−0.225999	+	1.25815i
$837$	7.66149	+	3.17349i	0.264820	+	0.109692i
$838$	−6.36090	−	20.2873i	−0.219733	−	0.700813i
$839$	−2.71963	−	2.71963i	−0.0938921	−	0.0938921i	0.658601	−	0.752493i	$-0.271149\pi$
$839$	−2.71963	−	2.71963i	−0.0938921	−	0.0938921i	−0.752493	+	0.658601i	$0.771149\pi$
$840$		0			0
$841$	15.7174	−	15.7174i	0.541981	−	0.541981i
$842$	37.3993	+	19.5450i	1.28887	+	0.673564i
$843$	15.0780	−	36.4015i	0.519314	−	1.25374i
$844$	−16.7652	+	3.66053i	−0.577083	+	0.126001i
$845$		0			0
$846$	−2.74214	−	3.27859i	−0.0942767	−	0.112720i
$847$			1.09967i			0.0377850i
$848$	1.02490	−	1.10422i	0.0351953	−	0.0379190i
$849$		−	48.1908i		−	1.65390i
$850$		0			0
$851$	45.0461	−	18.6587i	1.54416	−	0.639612i
$852$	18.1477	−	28.2861i	0.621731	−	0.969066i
$853$	−0.203359	+	0.490953i	−0.00696289	+	0.0168099i	−0.927323	−	0.374263i	$-0.877896\pi$
$853$	−0.203359	+	0.490953i	−0.00696289	+	0.0168099i	0.920360	+	0.391073i	$0.127896\pi$
$854$	−9.97815	+	19.0932i	−0.341445	+	0.653356i
$855$		0			0
$856$	18.2107	−	23.4983i	0.622429	−	0.803155i
$857$	−9.02822	−	9.02822i	−0.308398	−	0.308398i	0.535890	−	0.844288i	$-0.319976\pi$
$857$	−9.02822	−	9.02822i	−0.308398	−	0.308398i	−0.844288	+	0.535890i	$0.819976\pi$
$858$	−3.96311	+	1.24260i	−0.135298	+	0.0424215i
$859$	−9.49187	−	3.93166i	−0.323858	−	0.134147i	0.214830	−	0.976651i	$-0.431080\pi$
$859$	−9.49187	−	3.93166i	−0.323858	−	0.134147i	−0.538689	+	0.842505i	$0.681080\pi$
$860$		0			0
$861$	−8.38738	−	20.2489i	−0.285841	−	0.690081i
$862$	4.33243	−	48.6239i	0.147563	−	1.65614i
$863$	−2.75061			−0.0936320			−0.0468160	−	0.998904i	$-0.514907\pi$
$863$	−2.75061			−0.0936320			−0.0468160	+	0.998904i	$0.514907\pi$
$864$	14.7210	+	16.3255i	0.500820	+	0.555404i
$865$		0			0
$866$	2.12251	−	23.8214i	0.0721257	−	0.809483i
$867$	−2.75296	−	6.64624i	−0.0934955	−	0.225718i
$868$	−2.75182	−	3.95690i	−0.0934029	−	0.134306i
$869$	14.7778	+	6.12115i	0.501301	+	0.207646i
$870$		0			0
$871$	−2.80614	−	2.80614i	−0.0950823	−	0.0950823i
$872$	−54.9574	+	6.96712i	−1.86109	+	0.235936i
$873$	−1.40729	+	1.40729i	−0.0476294	+	0.0476294i
$874$	−16.4564	+	31.4893i	−0.556645	+	1.06514i
$875$		0			0
$876$	−21.6304	−	13.8776i	−0.730823	−	0.468880i
$877$	15.3614	−	6.36290i	0.518718	−	0.214860i	−0.107936	−	0.994158i	$-0.534424\pi$
$877$	15.3614	−	6.36290i	0.518718	−	0.214860i	0.626654	+	0.779298i	$0.284424\pi$
$878$	11.7691	−	9.84342i	0.397189	−	0.332199i
$879$		−	38.0165i		−	1.28227i
$880$		0			0
$881$		−	10.9358i		−	0.368435i	−0.982885	−	0.184218i	$-0.941025\pi$
$881$		−	10.9358i		−	0.368435i	0.982885	−	0.184218i	$-0.0589752\pi$
$882$	−5.58344	−	6.67575i	−0.188004	−	0.224784i
$883$	1.99995	−	0.828407i	0.0673037	−	0.0278781i	−0.348778	−	0.937206i	$-0.613403\pi$
$883$	1.99995	−	0.828407i	0.0673037	−	0.0278781i	0.416081	+	0.909327i	$0.363403\pi$
$884$	−0.718529	−	3.29087i	−0.0241667	−	0.110684i
$885$		0			0
$886$	−5.13443	−	2.68326i	−0.172495	−	0.0901460i
$887$	26.2532	−	26.2532i	0.881497	−	0.881497i	−0.112189	−	0.993687i	$-0.535786\pi$
$887$	26.2532	−	26.2532i	0.881497	−	0.881497i	0.993687	+	0.112189i	$0.0357863\pi$
$888$	−17.0373	+	62.3850i	−0.571735	+	2.09350i
$889$	9.56543	+	9.56543i	0.320814	+	0.320814i
$890$		0			0
$891$	−32.3821	−	13.4131i	−1.08484	−	0.449356i
$892$	11.3681	+	2.04202i	0.380631	+	0.0683720i
$893$	−6.27941	−	15.1598i	−0.210132	−	0.507304i
$894$	−13.2667	−	1.18208i	−0.443706	−	0.0395346i
$895$		0			0
$896$	−2.07752	−	12.6061i	−0.0694050	−	0.421140i
$897$	−3.99266			−0.133311
$898$	4.39553	+	0.391646i	0.146681	+	0.0130694i
$899$	2.12520	+	5.13068i	0.0708793	+	0.171118i
$900$		0			0
$901$	−1.27550	−	0.528331i	−0.0424932	−	0.0176013i
$902$	−12.8809	−	41.0820i	−0.428887	−	1.36788i
$903$	16.0367	+	16.0367i	0.533669	+	0.533669i
$904$	−1.24203	+	4.54792i	−0.0413094	+	0.151261i
$905$		0			0
$906$	31.2943	+	16.3545i	1.03968	+	0.543341i
$907$	−10.7461	+	25.9433i	−0.356817	+	0.861432i	0.638927	+	0.769268i	$0.279379\pi$
$907$	−10.7461	+	25.9433i	−0.356817	+	0.861432i	−0.995744	+	0.0921648i	$0.970621\pi$
$908$	−1.36636	−	6.25794i	−0.0453443	−	0.207677i
$909$	5.78482	−	2.39615i	0.191870	−	0.0794753i
$910$		0			0
$911$			23.8049i			0.788691i	0.918962	+	0.394345i	$0.129029\pi$
$911$			23.8049i			0.788691i	−0.918962	+	0.394345i	$0.870971\pi$
$912$	−19.6423	−	42.8367i	−0.650423	−	1.41846i
$913$		−	23.3249i		−	0.771941i
$914$	44.0622	−	36.8526i	1.45745	−	1.21898i
$915$		0			0
$916$	−27.7062	−	17.7757i	−0.915437	−	0.587324i
$917$	−1.21146	+	2.92473i	−0.0400060	+	0.0965831i
$918$	9.33028	−	17.8535i	0.307945	−	0.589254i
$919$	28.3643	−	28.3643i	0.935652	−	0.935652i	−0.0623993	−	0.998051i	$-0.519875\pi$
$919$	28.3643	−	28.3643i	0.935652	−	0.935652i	0.998051	+	0.0623993i	$0.0198752\pi$
$920$		0			0
$921$	−16.6919	−	16.6919i	−0.550015	−	0.550015i
$922$	−48.8176	+	15.3063i	−1.60772	+	0.504087i
$923$	3.53353	+	1.46364i	0.116308	+	0.0481762i
$924$	8.24241	+	11.8519i	0.271155	+	0.389899i
$925$		0			0
$926$	−1.75073	+	19.6489i	−0.0575326	+	0.645701i
$927$	13.9503			0.458189
$928$	−0.759740	+	14.7014i	−0.0249397	+	0.482598i
$929$	−24.6748			−0.809553			−0.404777	−	0.914416i	$-0.632651\pi$
$929$	−24.6748			−0.809553			−0.404777	+	0.914416i	$0.632651\pi$
$930$		0			0
$931$	−12.7859	−	30.8679i	−0.419041	−	1.01165i
$932$	−13.0796	+	9.09623i	−0.428438	+	0.297957i
$933$	14.5226	+	6.01545i	0.475448	+	0.196937i
$934$	−51.0379	+	16.0025i	−1.67001	+	0.523617i
$935$		0			0
$936$	0.855734	−	1.10420i	0.0279706	−	0.0360920i
$937$	−6.68724	+	6.68724i	−0.218463	+	0.218463i	−0.807850	−	0.589388i	$-0.799369\pi$
$937$	−6.68724	+	6.68724i	−0.218463	+	0.218463i	0.589388	+	0.807850i	$0.299369\pi$
$938$	−6.38878	+	12.2249i	−0.208601	+	0.399158i
$939$	−5.62953	+	13.5909i	−0.183713	+	0.443522i
$940$		0			0
$941$	27.0354	−	11.1984i	0.881327	−	0.365058i	0.104316	−	0.994544i	$-0.466735\pi$
$941$	27.0354	−	11.1984i	0.881327	−	0.365058i	0.777011	+	0.629486i	$0.216735\pi$
$942$	−37.9457	+	31.7370i	−1.23634	+	1.03405i
$943$		−	41.3884i		−	1.34779i
$944$	−31.9335	−	29.6398i	−1.03935	−	0.964694i
$945$		0			0
$946$	28.5822	+	34.1739i	0.929289	+	1.11109i
$947$	−50.6915	+	20.9971i	−1.64725	+	0.682314i	−0.997000	−	0.0774050i	$-0.975337\pi$
$947$	−50.6915	+	20.9971i	−1.64725	+	0.682314i	−0.650252	+	0.759719i	$0.725337\pi$
$948$	−19.9252	+	4.35048i	−0.647142	+	0.141297i
$949$	1.11924	−	2.70209i	0.0363322	−	0.0877137i
$950$		0			0
$951$	−28.6417	+	28.6417i	−0.928769	+	0.928769i
$952$	−10.1673	+	5.80523i	−0.329525	+	0.188149i
$953$	−16.5754	−	16.5754i	−0.536931	−	0.536931i	0.385695	−	0.922626i	$-0.373962\pi$
$953$	−16.5754	−	16.5754i	−0.536931	−	0.536931i	−0.922626	+	0.385695i	$0.873962\pi$
$954$	−0.171303	−	0.546349i	−0.00554613	−	0.0176887i
$955$		0			0
$956$	3.42992	−	19.0946i	0.110932	−	0.617564i
$957$	−6.36551	−	15.3677i	−0.205768	−	0.496767i
$958$	−1.79558	−	0.159988i	−0.0580126	−	0.00516897i
$959$	11.3553			0.366682
$960$		0			0
$961$	−26.4460			−0.853097
$962$	−7.33068	−	0.653170i	−0.236351	−	0.0210591i
$963$	−4.32377	−	10.4385i	−0.139331	−	0.336376i
$964$	−5.90816	+	32.8911i	−0.190289	+	1.05935i
$965$		0			0
$966$	4.15194	+	13.2421i	0.133586	+	0.426057i
$967$	−14.6698	−	14.6698i	−0.471749	−	0.471749i	0.430731	−	0.902480i	$-0.358256\pi$
$967$	−14.6698	−	14.6698i	−0.471749	−	0.471749i	−0.902480	+	0.430731i	$0.858256\pi$
$968$	−1.36569	−	2.39188i	−0.0438949	−	0.0768779i
$969$	−30.5366	+	30.5366i	−0.980976	+	0.980976i
$970$		0			0
$971$	17.8403	−	43.0702i	0.572521	−	1.38219i	−0.326881	−	0.945065i	$-0.605998\pi$
$971$	17.8403	−	43.0702i	0.572521	−	1.38219i	0.899402	−	0.437122i	$-0.144002\pi$
$972$	20.8824	−	4.55946i	0.669802	−	0.146245i
$973$	−21.2167	+	8.78823i	−0.680175	+	0.281738i
$974$	−7.53800	−	9.01268i	−0.241533	−	0.288785i
$975$		0			0
$976$	−2.00865	−	53.9215i	−0.0642954	−	1.72598i
$977$		−	43.7977i		−	1.40121i	−0.713548	−	0.700607i	$-0.752913\pi$
$977$		−	43.7977i		−	1.40121i	0.713548	−	0.700607i	$-0.247087\pi$
$978$	−5.42333	+	4.53595i	−0.173419	+	0.145044i
$979$	30.7977	−	12.7568i	0.984300	−	0.407710i
$980$		0			0
$981$	−8.05701	+	19.4513i	−0.257241	+	0.621034i
$982$	24.3452	−	46.5846i	0.776887	−	1.48657i
$983$	34.5849	−	34.5849i	1.10309	−	1.10309i	0.109050	−	0.994036i	$-0.465219\pi$
$983$	34.5849	−	34.5849i	1.10309	−	1.10309i	0.994036	−	0.109050i	$-0.0347808\pi$
$984$	43.3907	+	33.6269i	1.38324	+	1.07199i
$985$		0			0
$986$	12.8723	−	4.03600i	0.409938	−	0.128532i
$987$	−5.92129	−	2.45268i	−0.188477	−	0.0780697i
$988$	4.40302	−	3.06208i	0.140079	−	0.0974178i
$989$	16.3894	+	39.5674i	0.521152	+	1.25817i
$990$		0			0
$991$	−27.5480			−0.875090			−0.437545	−	0.899196i	$-0.644152\pi$
$991$	−27.5480			−0.875090			−0.437545	+	0.899196i	$0.644152\pi$
$992$	10.8996	+	5.18910i	0.346062	+	0.164754i
$993$	8.33632			0.264545
$994$	1.17982	−	13.2414i	0.0374216	−	0.419991i
$995$		0			0
$996$	16.9802	+	24.4161i	0.538038	+	0.773655i
$997$	5.62550	+	2.33016i	0.178161	+	0.0737968i	0.469981	−	0.882677i	$-0.344261\pi$
$997$	5.62550	+	2.33016i	0.178161	+	0.0737968i	−0.291820	+	0.956473i	$0.594261\pi$
$998$	49.3975	−	15.4881i	1.56365	−	0.490268i
$999$	−31.1229	−	31.1229i	−0.984686	−	0.984686i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	800.2.y.f.101.1		88
5.2	odd	4		160.2.z.a.69.12	yes	88
5.3	odd	4		160.2.z.a.69.11	✓	88
5.4	even	2	inner	800.2.y.f.101.22		88
20.3	even	4		640.2.z.a.369.5		88
20.7	even	4		640.2.z.a.369.18		88
32.13	even	8	inner	800.2.y.f.301.1		88
160.13	odd	8		160.2.z.a.109.12	yes	88
160.77	odd	8		160.2.z.a.109.11	yes	88
160.83	even	8		640.2.z.a.529.18		88
160.109	even	8	inner	800.2.y.f.301.22		88
160.147	even	8		640.2.z.a.529.5		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.2.z.a.69.11	✓	88	5.3	odd	4
160.2.z.a.69.12	yes	88	5.2	odd	4
160.2.z.a.109.11	yes	88	160.77	odd	8
160.2.z.a.109.12	yes	88	160.13	odd	8
640.2.z.a.369.5		88	20.3	even	4
640.2.z.a.369.18		88	20.7	even	4
640.2.z.a.529.5		88	160.147	even	8
640.2.z.a.529.18		88	160.83	even	8
800.2.y.f.101.1		88	1.1	even	1	trivial
800.2.y.f.101.22		88	5.4	even	2	inner
800.2.y.f.301.1		88	32.13	even	8	inner
800.2.y.f.301.22		88	160.109	even	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 800 = 2^{5} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	800.y (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40863 - 0.125510i) q^{2} +(-0.772505 - 1.86499i) q^{3} +(1.96849 + 0.353596i) q^{4} +(0.854100 + 2.72405i) q^{6} +(0.798508 + 0.798508i) q^{7} +(-2.72851 - 0.745154i) q^{8} +(-0.760109 + 0.760109i) q^{9} +O(q^{10})\)	\(q+(-1.40863 - 0.125510i) q^{2} +(-0.772505 - 1.86499i) q^{3} +(1.96849 + 0.353596i) q^{4} +(0.854100 + 2.72405i) q^{6} +(0.798508 + 0.798508i) q^{7} +(-2.72851 - 0.745154i) q^{8} +(-0.760109 + 0.760109i) q^{9} +(-1.21174 + 2.92539i) q^{11} +(-0.861217 - 3.94438i) q^{12} +(0.424491 - 0.175830i) q^{13} +(-1.02458 - 1.22503i) q^{14} +(3.74994 + 1.39210i) q^{16} -3.66556i q^{17} +(1.16612 - 0.975313i) q^{18} +(5.39199 - 2.23343i) q^{19} +(0.872360 - 2.10606i) q^{21} +(2.07406 - 3.96871i) q^{22} +(3.04392 - 3.04392i) q^{23} +(0.718078 + 5.66428i) q^{24} +(-0.620020 + 0.194402i) q^{26} +(-3.59019 - 1.48711i) q^{27} +(1.28951 + 1.85421i) q^{28} +(-0.995872 - 2.40425i) q^{29} -2.13401 q^{31} +(-5.10756 - 2.43162i) q^{32} +6.39190 q^{33} +(-0.460066 + 5.16343i) q^{34} +(-1.76504 + 1.22750i) q^{36} +(10.4643 + 4.33444i) q^{37} +(-7.87565 + 2.46934i) q^{38} +(-0.655842 - 0.655842i) q^{39} +(6.79854 - 6.79854i) q^{41} +(-1.49317 + 2.85718i) q^{42} +(-3.80728 + 9.19158i) q^{43} +(-3.41970 + 5.33015i) q^{44} +(-4.66981 + 3.90572i) q^{46} -2.81155i q^{47} +(-0.300582 - 8.06901i) q^{48} -5.72477i q^{49} +(-6.83623 + 2.83166i) q^{51} +(0.897781 - 0.196022i) q^{52} +(0.144134 - 0.347970i) q^{53} +(4.87061 + 2.54539i) q^{54} +(-1.58372 - 2.77375i) q^{56} +(-8.33067 - 8.33067i) q^{57} +(1.10106 + 3.51170i) q^{58} +(-10.0632 - 4.16829i) q^{59} +(-5.16229 - 12.4629i) q^{61} +(3.00603 + 0.267840i) q^{62} -1.21391 q^{63} +(6.88949 + 4.06632i) q^{64} +(-9.00384 - 0.802250i) q^{66} +(-3.30530 - 7.97969i) q^{67} +(1.29613 - 7.21563i) q^{68} +(-8.02832 - 3.32544i) q^{69} +(5.88607 + 5.88607i) q^{71} +(2.64036 - 1.50756i) q^{72} +(4.50108 - 4.50108i) q^{73} +(-14.1963 - 7.41901i) q^{74} +(11.4038 - 2.48992i) q^{76} +(-3.30353 + 1.36837i) q^{77} +(0.841526 + 1.00616i) q^{78} -5.05155i q^{79} +11.0693i q^{81} +(-10.4299 + 8.72336i) q^{82} +(-6.80560 + 2.81897i) q^{83} +(2.46193 - 3.83731i) q^{84} +(6.51669 - 12.4697i) q^{86} +(-3.71459 + 3.71459i) q^{87} +(5.48609 - 7.07901i) q^{88} +(-7.44423 - 7.44423i) q^{89} +(0.479361 + 0.198558i) q^{91} +(7.06825 - 4.91562i) q^{92} +(1.64853 + 3.97991i) q^{93} +(-0.352879 + 3.96044i) q^{94} +(-0.589336 + 11.4040i) q^{96} +1.85143 q^{97} +(-0.718518 + 8.06410i) q^{98} +(-1.30256 - 3.14467i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 8 q^{4} - 8 q^{6} + 8 q^{9}+O(q^{10}) \) 88 * q + 8 * q^4 - 8 * q^6 + 8 * q^9	\( 88 q + 8 q^{4} - 8 q^{6} + 8 q^{9} - 8 q^{11} + 24 q^{14} - 8 q^{16} + 8 q^{19} - 8 q^{21} + 16 q^{24} + 32 q^{26} + 8 q^{29} - 64 q^{31} + 24 q^{34} + 72 q^{36} + 8 q^{39} - 8 q^{41} + 8 q^{44} - 8 q^{46} - 48 q^{51} - 24 q^{54} - 56 q^{56} - 24 q^{59} + 24 q^{61} - 64 q^{64} - 8 q^{66} + 40 q^{69} - 40 q^{71} - 128 q^{74} - 8 q^{76} - 200 q^{84} + 24 q^{86} + 8 q^{89} - 8 q^{91} - 120 q^{94} - 56 q^{96} + 48 q^{99}+O(q^{100}) \) 88 * q + 8 * q^4 - 8 * q^6 + 8 * q^9 - 8 * q^11 + 24 * q^14 - 8 * q^16 + 8 * q^19 - 8 * q^21 + 16 * q^24 + 32 * q^26 + 8 * q^29 - 64 * q^31 + 24 * q^34 + 72 * q^36 + 8 * q^39 - 8 * q^41 + 8 * q^44 - 8 * q^46 - 48 * q^51 - 24 * q^54 - 56 * q^56 - 24 * q^59 + 24 * q^61 - 64 * q^64 - 8 * q^66 + 40 * q^69 - 40 * q^71 - 128 * q^74 - 8 * q^76 - 200 * q^84 + 24 * q^86 + 8 * q^89 - 8 * q^91 - 120 * q^94 - 56 * q^96 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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