LMFDB - Embedded newform 735.2.p.f.509.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(374,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("735.374");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.p (of order $6$, degree $2$, 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:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			509.3
Character	$\chi$	$=$	735.509
Dual form			735.2.p.f.374.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.757344 + 1.31176i) q^{2} +(-0.419611 - 1.68045i) q^{3} +(-0.147140 - 0.254854i) q^{4} +(-2.20411 - 0.376714i) q^{5} +(2.52214 + 0.722254i) q^{6} -2.58363 q^{8} +(-2.64785 + 1.41027i) q^{9} +(2.16343 - 2.60595i) q^{10} +(1.86048 - 1.07415i) q^{11} +(-0.366529 + 0.354202i) q^{12} +3.48097 q^{13} +(0.291817 + 3.86197i) q^{15} +(2.25098 - 3.89881i) q^{16} +(-3.09793 + 1.78859i) q^{17} +(0.155396 - 4.54141i) q^{18} +(1.05858 + 0.611171i) q^{19} +(0.228305 + 0.617156i) q^{20} +3.25401i q^{22} +(0.757344 - 1.31176i) q^{23} +(1.08412 + 4.34168i) q^{24} +(4.71617 + 1.66064i) q^{25} +(-2.63629 + 4.56619i) q^{26} +(3.48097 + 3.85783i) q^{27} +5.95645i q^{29} +(-5.28698 - 2.54205i) q^{30} +(-2.75098 + 1.58828i) q^{31} +(0.825899 + 1.43050i) q^{32} +(-2.58574 - 2.67573i) q^{33} -5.41832i q^{34} +(0.749020 + 0.467309i) q^{36} +(6.75803 + 3.90175i) q^{37} +(-1.60342 + 0.925734i) q^{38} +(-1.46065 - 5.84961i) q^{39} +(5.69460 + 0.973292i) q^{40} +11.8685 q^{41} -2.99294i q^{43} +(-0.547504 - 0.316101i) q^{44} +(6.36742 - 2.11091i) q^{45} +(1.14714 + 1.98691i) q^{46} +(5.28420 + 3.05084i) q^{47} +(-7.49631 - 2.14668i) q^{48} +(-5.75012 + 4.92881i) q^{50} +(4.30557 + 4.45542i) q^{51} +(-0.512191 - 0.887140i) q^{52} +(5.61301 + 9.72202i) q^{53} +(-7.69683 + 1.64449i) q^{54} +(-4.50535 + 1.66667i) q^{55} +(0.582853 - 2.03535i) q^{57} +(-7.81342 - 4.51108i) q^{58} +(1.08467 + 1.87871i) q^{59} +(0.941303 - 0.642622i) q^{60} +(2.94338 + 1.69936i) q^{61} -4.81149i q^{62} +6.50196 q^{64} +(-7.67243 - 1.31133i) q^{65} +(5.46821 - 1.36542i) q^{66} +(-8.93534 + 5.15882i) q^{67} +(0.911660 + 0.526347i) q^{68} +(-2.52214 - 0.722254i) q^{69} -10.3968i q^{71} +(6.84108 - 3.64363i) q^{72} +(3.42779 + 5.93710i) q^{73} +(-10.2363 + 5.90993i) q^{74} +(0.811666 - 8.62213i) q^{75} -0.359711i q^{76} +(8.77950 + 2.51414i) q^{78} +(0.941421 - 1.63059i) q^{79} +(-6.43014 + 7.74542i) q^{80} +(5.02225 - 7.46840i) q^{81} +(-8.98853 + 15.5686i) q^{82} +9.10486i q^{83} +(7.50196 - 2.77521i) q^{85} +(3.92601 + 2.26668i) q^{86} +(10.0095 - 2.49939i) q^{87} +(-4.80681 + 2.77521i) q^{88} +(-0.889962 + 1.54146i) q^{89} +(-2.05332 + 9.95121i) q^{90} -0.445743 q^{92} +(3.82337 + 3.95644i) q^{93} +(-8.00392 + 4.62107i) q^{94} +(-2.10299 - 1.74587i) q^{95} +(2.05733 - 1.98814i) q^{96} -1.32584 q^{97} +(-3.41144 + 5.46799i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{4} - 6 q^{9} - 24 q^{15} - 12 q^{16} - 18 q^{24} - 12 q^{25} + 18 q^{30} + 84 q^{36} - 12 q^{39} + 72 q^{40} + 18 q^{45} + 36 q^{46} - 12 q^{51} + 36 q^{54} + 12 q^{60} - 36 q^{61} + 24 q^{64}+ \cdots - 48 q^{99}+O(q^{100}) $ 24 * q - 12 * q^4 - 6 * q^9 - 24 * q^15 - 12 * q^16 - 18 * q^24 - 12 * q^25 + 18 * q^30 + 84 * q^36 - 12 * q^39 + 72 * q^40 + 18 * q^45 + 36 * q^46 - 12 * q^51 + 36 * q^54 + 12 * q^60 - 36 * q^61 + 24 * q^64 + 72 * q^66 - 72 * q^75 + 48 * q^79 - 6 * q^81 + 48 * q^85 + 72 * q^94 + 90 * q^96 - 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$

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 $

$2$	−0.757344	+	1.31176i	−0.535523	+	0.927553i	0.463615	+	0.886037i	$0.346552\pi$
$2$	−0.757344	+	1.31176i	−0.535523	+	0.927553i	−0.999138	+	0.0415164i	$0.986781\pi$
$3$	−0.419611	−	1.68045i	−0.242263	−	0.970211i
$3$	−0.419611	−	1.68045i	−0.242263	−	0.970211i
$4$	−0.147140	−	0.254854i	−0.0735701	−	0.127427i
$5$	−2.20411	−	0.376714i	−0.985706	−	0.168472i
$5$	−2.20411	−	0.376714i	−0.985706	−	0.168472i
$6$	2.52214	+	0.722254i	1.02966	+	0.294859i
$7$		0			0
$7$		0			0
$8$	−2.58363			−0.913452
$9$	−2.64785	+	1.41027i	−0.882618	+	0.470092i
$10$	2.16343	−	2.60595i	0.684135	−	0.824075i
$11$	1.86048	−	1.07415i	0.560957	−	0.323869i	−0.192573	−	0.981283i	$-0.561683\pi$
$11$	1.86048	−	1.07415i	0.560957	−	0.323869i	0.753529	+	0.657414i	$0.228350\pi$
$12$	−0.366529	+	0.354202i	−0.105808	+	0.102249i
$13$	3.48097			0.965448			0.482724	−	0.875773i	$-0.339647\pi$
$13$	3.48097			0.965448			0.482724	+	0.875773i	$0.339647\pi$
$14$		0			0
$15$	0.291817	+	3.86197i	0.0753468	+	0.997157i
$16$	2.25098	−	3.89881i	0.562745	−	0.974703i
$17$	−3.09793	+	1.78859i	−0.751359	+	0.433797i	−0.826185	−	0.563399i	$-0.809493\pi$
$17$	−3.09793	+	1.78859i	−0.751359	+	0.433797i	0.0748259	+	0.997197i	$0.476160\pi$
$18$	0.155396	−	4.54141i	0.0366272	−	1.07042i
$19$	1.05858	+	0.611171i	0.242855	+	0.140212i	0.616488	−	0.787364i	$-0.288555\pi$
$19$	1.05858	+	0.611171i	0.242855	+	0.140212i	−0.373633	+	0.927576i	$0.621888\pi$
$20$	0.228305	+	0.617156i	0.0510506	+	0.138000i
$21$		0			0
$22$			3.25401i			0.693757i
$23$	0.757344	−	1.31176i	0.157917	−	0.273521i	−0.776200	−	0.630486i	$-0.782855\pi$
$23$	0.757344	−	1.31176i	0.157917	−	0.273521i	0.934117	+	0.356966i	$0.116189\pi$
$24$	1.08412	+	4.34168i	0.221295	+	0.886241i
$25$	4.71617	+	1.66064i	0.943235	+	0.332127i
$26$	−2.63629	+	4.56619i	−0.517020	+	0.895504i
$27$	3.48097	+	3.85783i	0.669913	+	0.742439i
$28$		0			0
$29$			5.95645i			1.10608i	0.833153	+	0.553042i	$0.186533\pi$
$29$			5.95645i			1.10608i	−0.833153	+	0.553042i	$0.813467\pi$
$30$	−5.28698	−	2.54205i	−0.965267	−	0.464113i
$31$	−2.75098	+	1.58828i	−0.494091	+	0.285263i	−0.726270	−	0.687410i	$-0.758748\pi$
$31$	−2.75098	+	1.58828i	−0.494091	+	0.285263i	0.232179	+	0.972673i	$0.425414\pi$
$32$	0.825899	+	1.43050i	0.146000	+	0.252879i
$33$	−2.58574	−	2.67573i	−0.450120	−	0.465785i
$34$		−	5.41832i		−	0.929234i
$35$		0			0
$36$	0.749020	+	0.467309i	0.124837	+	0.0778848i
$37$	6.75803	+	3.90175i	1.11101	+	0.641444i	0.939092	−	0.343667i	$-0.111669\pi$
$37$	6.75803	+	3.90175i	1.11101	+	0.641444i	0.171921	+	0.985111i	$0.445002\pi$
$38$	−1.60342	+	0.925734i	−0.260109	+	0.150174i
$39$	−1.46065	−	5.84961i	−0.233892	−	0.936688i
$40$	5.69460	+	0.973292i	0.900396	+	0.153891i
$41$	11.8685			1.85355			0.926773	−	0.375622i	$-0.122571\pi$
$41$	11.8685			1.85355			0.926773	+	0.375622i	$0.122571\pi$
$42$		0			0
$43$		−	2.99294i		−	0.456419i	−0.973612	−	0.228209i	$-0.926713\pi$
$43$		−	2.99294i		−	0.456419i	0.973612	−	0.228209i	$-0.0732871\pi$
$44$	−0.547504	−	0.316101i	−0.0825393	−	0.0476541i
$45$	6.36742	−	2.11091i	0.949199	−	0.314676i
$46$	1.14714	+	1.98691i	0.169137	+	0.292953i
$47$	5.28420	+	3.05084i	0.770780	+	0.445010i	0.833153	−	0.553043i	$-0.186533\pi$
$47$	5.28420	+	3.05084i	0.770780	+	0.445010i	−0.0623727	+	0.998053i	$0.519867\pi$
$48$	−7.49631	−	2.14668i	−1.08200	−	0.309847i
$49$		0			0
$50$	−5.75012	+	4.92881i	−0.813190	+	0.697038i
$51$	4.30557	+	4.45542i	0.602901	+	0.623883i
$52$	−0.512191	−	0.887140i	−0.0710281	−	0.123024i
$53$	5.61301	+	9.72202i	0.771006	+	1.33542i	0.937012	+	0.349297i	$0.113580\pi$
$53$	5.61301	+	9.72202i	0.771006	+	1.33542i	−0.166006	+	0.986125i	$0.553087\pi$
$54$	−7.69683	+	1.64449i	−1.04741	+	0.223787i
$55$	−4.50535	+	1.66667i	−0.607502	+	0.224734i
$56$		0			0
$57$	0.582853	−	2.03535i	0.0772008	−	0.269589i
$58$	−7.81342	−	4.51108i	−1.02595	−	0.592334i
$59$	1.08467	+	1.87871i	0.141213	+	0.244587i	0.927954	−	0.372696i	$-0.121567\pi$
$59$	1.08467	+	1.87871i	0.141213	+	0.244587i	−0.786741	+	0.617283i	$0.788233\pi$
$60$	0.941303	−	0.642622i	0.121522	−	0.0829622i
$61$	2.94338	+	1.69936i	0.376861	+	0.217581i	0.676452	−	0.736487i	$-0.263517\pi$
$61$	2.94338	+	1.69936i	0.376861	+	0.217581i	−0.299591	+	0.954068i	$0.596850\pi$
$62$		−	4.81149i		−	0.611060i
$63$		0			0
$64$	6.50196			0.812745
$65$	−7.67243	−	1.31133i	−0.951648	−	0.162651i
$66$	5.46821	−	1.36542i	0.673090	−	0.168071i
$67$	−8.93534	+	5.15882i	−1.09163	+	0.630250i	−0.934009	−	0.357250i	$-0.883714\pi$
$67$	−8.93534	+	5.15882i	−1.09163	+	0.630250i	−0.157617	+	0.987500i	$0.550381\pi$
$68$	0.911660	+	0.526347i	0.110555	+	0.0638290i
$69$	−2.52214	−	0.722254i	−0.303630	−	0.0869491i
$70$		0			0
$71$		−	10.3968i		−	1.23387i	−0.787013	−	0.616936i	$-0.788374\pi$
$71$		−	10.3968i		−	1.23387i	0.787013	−	0.616936i	$-0.211626\pi$
$72$	6.84108	−	3.64363i	0.806229	−	0.429406i
$73$	3.42779	+	5.93710i	0.401192	+	0.694885i	0.993870	−	0.110555i	$-0.0352627\pi$
$73$	3.42779	+	5.93710i	0.401192	+	0.694885i	−0.592678	+	0.805439i	$0.701929\pi$
$74$	−10.2363	+	5.90993i	−1.18995	+	0.687016i
$75$	0.811666	−	8.62213i	0.0937231	−	0.995598i
$76$		−	0.359711i		−	0.0412617i
$77$		0			0
$78$	8.77950	+	2.51414i	0.994082	+	0.284671i
$79$	0.941421	−	1.63059i	0.105918	−	0.183456i	−0.808195	−	0.588915i	$-0.799555\pi$
$79$	0.941421	−	1.63059i	0.105918	−	0.183456i	0.914113	+	0.405460i	$0.132889\pi$
$80$	−6.43014	+	7.74542i	−0.718911	+	0.865964i
$81$	5.02225	−	7.46840i	0.558028	−	0.829822i
$82$	−8.98853	+	15.5686i	−0.992617	+	1.71926i
$83$			9.10486i			0.999388i	0.866202	+	0.499694i	$0.166554\pi$
$83$			9.10486i			0.999388i	−0.866202	+	0.499694i	$0.833446\pi$
$84$		0			0
$85$	7.50196	−	2.77521i	0.813702	−	0.301014i
$86$	3.92601	+	2.26668i	0.423353	+	0.244423i
$87$	10.0095	−	2.49939i	1.07313	−	0.267963i
$88$	−4.80681	+	2.77521i	−0.512407	+	0.295839i
$89$	−0.889962	+	1.54146i	−0.0943358	+	0.163394i	−0.909331	−	0.416073i	$-0.863406\pi$
$89$	−0.889962	+	1.54146i	−0.0943358	+	0.163394i	0.814995	+	0.579467i	$0.196739\pi$
$90$	−2.05332	+	9.95121i	−0.216439	+	1.04895i
$91$		0			0
$92$	−0.445743			−0.0464719
$93$	3.82337	+	3.95644i	0.396465	+	0.410263i
$94$	−8.00392	+	4.62107i	−0.825541	+	0.476626i
$95$	−2.10299	−	1.74587i	−0.215762	−	0.179122i
$96$	2.05733	−	1.98814i	0.209976	−	0.202914i
$97$	−1.32584			−0.134618			−0.0673092	−	0.997732i	$-0.521441\pi$
$97$	−1.32584			−0.134618			−0.0673092	+	0.997732i	$0.521441\pi$
$98$		0			0
$99$	−3.41144	+	5.46799i	−0.342863	+	0.549553i
$100$	−0.270718	−	1.44628i	−0.0270718	−	0.144628i
$101$	−6.71005	−	11.6221i	−0.667675	−	1.15645i	−0.978553	−	0.205997i	$-0.933956\pi$
$101$	−6.71005	−	11.6221i	−0.667675	−	1.15645i	0.310878	−	0.950450i	$-0.399377\pi$
$102$	−9.10523	+	2.27359i	−0.901553	+	0.225119i
$103$	2.89342	−	5.01154i	0.285097	−	0.493802i	−0.687536	−	0.726150i	$-0.741308\pi$
$103$	2.89342	−	5.01154i	0.285097	−	0.493802i	0.972633	+	0.232348i	$0.0746409\pi$
$104$	−8.99355			−0.881890
$105$		0			0
$106$	−17.0039			−1.65157
$107$	1.94323	−	3.36576i	0.187859	−	0.325381i	−0.756677	−	0.653788i	$-0.773179\pi$
$107$	1.94323	−	3.36576i	0.187859	−	0.325381i	0.944536	+	0.328408i	$0.106512\pi$
$108$	0.470993	−	1.45478i	0.0453214	−	0.139986i
$109$	−2.60384	−	4.50998i	−0.249403	−	0.431978i	0.713958	−	0.700189i	$-0.246901\pi$
$109$	−2.60384	−	4.50998i	−0.249403	−	0.431978i	−0.963360	+	0.268211i	$0.913568\pi$
$110$	1.22583	−	7.17218i	0.116878	−	0.683840i
$111$	3.72097	−	12.9938i	0.353179	−	1.23331i
$112$		0			0
$113$	−9.36235			−0.880736			−0.440368	−	0.897817i	$-0.645152\pi$
$113$	−9.36235			−0.880736			−0.440368	+	0.897817i	$0.645152\pi$
$114$	2.22847	+	2.30602i	0.208715	+	0.215979i
$115$	−2.16343	+	2.60595i	−0.201740	+	0.243006i
$116$	1.51803	−	0.876432i	0.140945	−	0.0813747i
$117$	−9.21710	+	4.90913i	−0.852121	+	0.453849i
$118$	−3.28589			−0.302490
$119$		0			0
$120$	−0.753947	−	9.97793i	−0.0688257	−	0.910856i
$121$	−3.19240	+	5.52940i	−0.290218	+	0.502673i
$122$	−4.45830	+	2.57400i	−0.403636	+	0.233039i
$123$	−4.98015	−	19.9444i	−0.449045	−	1.79833i
$124$	0.809559	+	0.467399i	0.0727006	+	0.0419737i
$125$	−9.76936	−	5.43687i	−0.873798	−	0.486289i
$126$		0			0
$127$			9.57778i			0.849891i	0.905219	+	0.424945i	$0.139707\pi$
$127$			9.57778i			0.849891i	−0.905219	+	0.424945i	$0.860293\pi$
$128$	−6.57602	+	11.3900i	−0.581243	+	1.00674i
$129$	−5.02950	+	1.25587i	−0.442823	+	0.110573i
$130$	7.53082	−	9.07125i	0.660497	−	0.795601i
$131$	4.72508	−	8.18408i	0.412832	−	0.715047i	−0.582366	−	0.812927i	$-0.697873\pi$
$131$	4.72508	−	8.18408i	0.412832	−	0.715047i	0.995198	+	0.0978802i	$0.0312062\pi$
$132$	−0.301455	+	1.05269i	−0.0262383	+	0.0916253i
$133$		0			0
$134$		−	15.6280i		−	1.35005i
$135$	−6.21913	−	9.81440i	−0.535258	−	0.844689i
$136$	8.00392	−	4.62107i	0.686330	−	0.396253i
$137$	5.35276	+	9.27125i	0.457317	+	0.792096i	0.998818	−	0.0486038i	$-0.0154772\pi$
$137$	5.35276	+	9.27125i	0.457317	+	0.792096i	−0.541501	+	0.840700i	$0.682144\pi$
$138$	2.85755	−	2.76144i	0.243251	−	0.235070i
$139$			4.11136i			0.348721i	0.984682	+	0.174360i	$0.0557858\pi$
$139$			4.11136i			0.348721i	−0.984682	+	0.174360i	$0.944214\pi$
$140$		0			0
$141$	2.90948	−	10.1600i	0.245022	−	0.855629i
$142$	13.6381	+	7.87395i	1.14448	+	0.660767i
$143$	6.47629	−	3.73909i	0.541575	−	0.312678i
$144$	−0.461868	+	13.4980i	−0.0384890	+	1.12483i
$145$	2.24388	−	13.1286i	0.186344	−	1.09027i
$146$	−10.3841			−0.859390
$147$		0			0
$148$		−	2.29642i		−	0.188764i
$149$	−2.20294	−	1.27187i	−0.180472	−	0.104196i	0.407042	−	0.913409i	$-0.366560\pi$
$149$	−2.20294	−	1.27187i	−0.180472	−	0.104196i	−0.587514	+	0.809214i	$0.699893\pi$
$150$	10.6954	+	7.59463i	0.873280	+	0.620099i
$151$	2.80956	+	4.86630i	0.228639	+	0.396014i	0.957405	−	0.288749i	$-0.0932392\pi$
$151$	2.80956	+	4.86630i	0.228639	+	0.396014i	−0.728766	+	0.684763i	$0.759906\pi$
$152$	−2.73498	−	1.57904i	−0.221836	−	0.128077i
$153$	5.68046	−	9.10486i	0.459238	−	0.736084i
$154$		0			0
$155$	6.66178	−	2.46440i	0.535087	−	0.197946i
$156$	−1.27588	+	1.23297i	−0.102152	+	0.0987164i
$157$	−6.96194	−	12.0584i	−0.555623	−	0.962368i	−0.997855	−	0.0654670i	$-0.979146\pi$
$157$	−6.96194	−	12.0584i	−0.555623	−	0.962368i	0.442231	−	0.896901i	$-0.354187\pi$
$158$	1.42596	+	2.46983i	0.113443	+	0.196489i
$159$	13.9821	−	13.5119i	1.10885	−	1.07156i
$160$	−1.28148	−	3.46410i	−0.101310	−	0.273861i
$161$		0			0
$162$	5.99317	+	12.2441i	0.470868	+	0.961990i
$163$	−3.52533	−	2.03535i	−0.276125	−	0.159421i	0.355543	−	0.934660i	$-0.384296\pi$
$163$	−3.52533	−	2.03535i	−0.276125	−	0.159421i	−0.631668	+	0.775239i	$0.717629\pi$
$164$	−1.74633	−	3.02473i	−0.136366	−	0.236192i
$165$	4.69126	+	6.87168i	0.365214	+	0.534960i
$166$	−11.9434	−	6.89551i	−0.926986	−	0.535196i
$167$		−	13.9722i		−	1.08120i	−0.841279	−	0.540602i	$-0.818197\pi$
$167$		−	13.9722i		−	1.08120i	0.841279	−	0.540602i	$-0.181803\pi$
$168$		0			0
$169$	−0.882841			−0.0679109
$170$	−2.04116	+	11.9425i	−0.156550	+	0.915952i
$171$	−3.66488	−	0.125403i	−0.280261	−	0.00958983i
$172$	−0.762763	+	0.440382i	−0.0581602	+	0.0335788i
$173$	8.66256	+	5.00133i	0.658602	+	0.380244i	0.791744	−	0.610853i	$-0.209173\pi$
$173$	8.66256	+	5.00133i	0.658602	+	0.380244i	−0.133142	+	0.991097i	$0.542507\pi$
$174$	−4.30206	+	15.0230i	−0.326139	+	1.13889i
$175$		0			0
$176$		−	9.67157i		−	0.729022i
$177$	2.70195	−	2.61107i	0.203091	−	0.196260i
$178$	−1.34801	−	2.33483i	−0.101038	−	0.175003i
$179$	14.0378	−	8.10475i	1.04924	−	0.605777i	0.126801	−	0.991928i	$-0.459529\pi$
$179$	14.0378	−	8.10475i	1.04924	−	0.605777i	0.922436	+	0.386151i	$0.126196\pi$
$180$	−1.47488	−	1.31216i	−0.109931	−	0.0978030i
$181$			19.4123i			1.44290i	0.692465	+	0.721451i	$0.256525\pi$
$181$			19.4123i			1.44290i	−0.692465	+	0.721451i	$0.743475\pi$
$182$		0			0
$183$	1.62062	−	5.65929i	0.119800	−	0.418347i
$184$	−1.95670	+	3.38910i	−0.144250	+	0.249848i
$185$	−13.4256	−	11.1457i	−0.987068	−	0.819450i
$186$	−8.08550	+	2.01896i	−0.592857	+	0.148037i
$187$	−3.84243	+	6.65529i	−0.280987	+	0.486683i
$188$		−	1.79560i		−	0.130958i
$189$		0			0
$190$	3.88284	−	1.43639i	0.281691	−	0.104206i
$191$	11.0018	+	6.35188i	0.796061	+	0.459606i	0.842092	−	0.539334i	$-0.181324\pi$
$191$	11.0018	+	6.35188i	0.796061	+	0.459606i	−0.0460309	+	0.998940i	$0.514657\pi$
$192$	−2.72830	−	10.9262i	−0.196898	−	0.788534i
$193$	18.0302	−	10.4098i	1.29785	−	0.749311i	0.317813	−	0.948153i	$-0.397051\pi$
$193$	18.0302	−	10.4098i	1.29785	−	0.749311i	0.980032	+	0.198842i	$0.0637181\pi$
$194$	1.00411	−	1.73918i	0.0720912	−	0.124866i
$195$	1.01581	+	13.4434i	0.0727433	+	0.962703i
$196$		0			0
$197$	2.23465			0.159212			0.0796062	−	0.996826i	$-0.474634\pi$
$197$	2.23465			0.159212			0.0796062	+	0.996826i	$0.474634\pi$
$198$	−4.58904	−	8.61613i	−0.326129	−	0.612322i
$199$	21.5831	−	12.4610i	1.52998	−	0.883337i	0.530622	−	0.847608i	$-0.321958\pi$
$199$	21.5831	−	12.4610i	1.52998	−	0.883337i	0.999362	−	0.0357284i	$-0.0113751\pi$
$200$	−12.1849	−	4.29048i	−0.861600	−	0.303383i
$201$	12.4185	+	12.8507i	0.875936	+	0.906421i
$202$	20.3273			1.43022
$203$		0			0
$204$	0.501960	−	1.75286i	0.0351442	−	0.122725i
$205$	−26.1594	−	4.47103i	−1.82705	−	0.312270i
$206$	4.38262	+	7.59093i	0.305352	+	0.528885i
$207$	−0.155396	+	4.54141i	−0.0108008	+	0.315650i
$208$	7.83560	−	13.5716i	0.543301	−	0.941025i
$209$	2.62596			0.181641
$210$		0			0
$211$	−6.61520			−0.455409			−0.227705	−	0.973730i	$-0.573122\pi$
$211$	−6.61520			−0.455409			−0.227705	+	0.973730i	$0.573122\pi$
$212$	1.65180	−	2.86100i	0.113446	−	0.196494i
$213$	−17.4713	+	4.36261i	−1.19712	+	0.298921i
$214$	2.94338	+	5.09808i	0.201205	+	0.348498i
$215$	−1.12748	+	6.59676i	−0.0768937	+	0.449895i
$216$	−8.99355	−	9.96721i	−0.611934	−	0.678183i
$217$		0			0
$218$	7.88801			0.534243
$219$	8.53868	−	8.25151i	0.576991	−	0.557585i
$220$	1.08768	+	0.902974i	0.0733312	+	0.0608785i
$221$	−10.7838	+	6.22604i	−0.725398	+	0.418808i
$222$	14.2266	+	14.7218i	0.954830	+	0.988060i
$223$	4.31027			0.288637			0.144318	−	0.989531i	$-0.453901\pi$
$223$	4.31027			0.288637			0.144318	+	0.989531i	$0.453901\pi$
$224$		0			0
$225$	−14.8297	+	2.25398i	−0.988646	+	0.150265i
$226$	7.09052	−	12.2811i	0.471654	−	0.816929i
$227$	−9.62260	+	5.55561i	−0.638675	+	0.368739i	−0.784104	−	0.620630i	$-0.786877\pi$
$227$	−9.62260	+	5.55561i	−0.638675	+	0.368739i	0.145429	+	0.989369i	$0.453544\pi$
$228$	−0.604478	+	0.150939i	−0.0400326	+	0.00999617i
$229$	−8.63774	−	4.98700i	−0.570798	−	0.329550i	0.186670	−	0.982423i	$-0.440230\pi$
$229$	−8.63774	−	4.98700i	−0.570798	−	0.329550i	−0.757468	+	0.652872i	$0.773564\pi$
$230$	−1.77992	−	4.81149i	−0.117365	−	0.317261i
$231$		0			0
$232$		−	15.3893i		−	1.01036i
$233$	10.3144	−	17.8650i	0.675716	−	1.17037i	−0.300543	−	0.953768i	$-0.597168\pi$
$233$	10.3144	−	17.8650i	0.675716	−	1.17037i	0.976259	−	0.216606i	$-0.0694988\pi$
$234$	0.540929	−	15.8085i	0.0353616	−	1.03343i
$235$	−10.4977	−	8.71500i	−0.684791	−	0.568504i
$236$	0.319198	−	0.552868i	0.0207780	−	0.0359886i
$237$	−3.13516	−	0.897801i	−0.203650	−	0.0583184i
$238$		0			0
$239$			2.87353i			0.185873i	0.995672	+	0.0929365i	$0.0296254\pi$
$239$			2.87353i			0.185873i	−0.995672	+	0.0929365i	$0.970375\pi$
$240$	15.7140	+	7.55549i	1.01433	+	0.487705i
$241$	−22.5792	+	13.0361i	−1.45445	+	0.839728i	−0.998729	−	0.0503940i	$-0.983952\pi$
$241$	−22.5792	+	13.0361i	−1.45445	+	0.839728i	−0.455722	+	0.890122i	$0.650619\pi$
$242$	−4.83549	−	8.37532i	−0.310837	−	0.538386i
$243$	−14.6577	−	5.30584i	−0.940292	−	0.340370i
$244$		−	1.00018i		−	0.0640298i
$245$		0			0
$246$	29.9340	+	8.57206i	1.90852	+	0.546534i
$247$	3.68488	+	2.12747i	0.234464	+	0.135368i
$248$	7.10752	−	4.10353i	0.451328	−	0.260574i
$249$	15.3003	−	3.82050i	0.969617	−	0.242114i
$250$	14.5306	−	8.69746i	0.918998	−	0.550076i
$251$	−0.161120			−0.0101698			−0.00508489	−	0.999987i	$-0.501619\pi$
$251$	−0.161120			−0.0101698			−0.00508489	+	0.999987i	$0.501619\pi$
$252$		0			0
$253$		−	3.25401i		−	0.204578i
$254$	−12.5637	−	7.25368i	−0.788319	−	0.455136i
$255$	−7.81152	−	11.4422i	−0.489177	−	0.716538i
$256$	−3.45866	−	5.99057i	−0.216166	−	0.374411i
$257$	11.3712	+	6.56514i	0.709314	+	0.409522i	0.810807	−	0.585314i	$-0.199029\pi$
$257$	11.3712	+	6.56514i	0.709314	+	0.409522i	−0.101493	+	0.994836i	$0.532362\pi$
$258$	2.16166	−	7.54861i	0.134579	−	0.469956i
$259$		0			0
$260$	0.794725	+	2.14830i	0.0492867	+	0.133232i
$261$	−8.40022	−	15.7718i	−0.519961	−	0.976249i
$262$	7.15703	+	12.3963i	0.442163	+	0.765848i
$263$	8.86526	+	15.3551i	0.546655	+	0.946835i	0.998501	+	0.0547384i	$0.0174325\pi$
$263$	8.86526	+	15.3551i	0.546655	+	0.946835i	−0.451846	+	0.892096i	$0.649234\pi$
$264$	6.68061	+	6.91311i	0.411163	+	0.425473i
$265$	−8.70925	−	23.5429i	−0.535005	−	1.44623i
$266$		0			0
$267$	2.96379	+	0.848727i	0.181381	+	0.0519412i
$268$	2.62950	+	1.51814i	0.160622	+	0.0927352i
$269$	−2.20294	−	3.81561i	−0.134316	−	0.232642i	0.791020	−	0.611790i	$-0.209550\pi$
$269$	−2.20294	−	3.81561i	−0.134316	−	0.232642i	−0.925336	+	0.379148i	$0.876217\pi$
$270$	17.5841	−	0.725124i	1.07014	−	0.0441296i
$271$	−20.4287	−	11.7945i	−1.24095	−	0.716465i	−0.271665	−	0.962392i	$-0.587574\pi$
$271$	−20.4287	−	11.7945i	−1.24095	−	0.716465i	−0.969288	+	0.245927i	$0.920908\pi$
$272$			16.1043i			0.976469i
$273$		0			0
$274$	−16.2155			−0.979615
$275$	10.5581	−	1.97629i	0.636680	−	0.119175i
$276$	0.187039	+	0.749051i	0.0112584	+	0.0450876i
$277$	−11.1127	+	6.41589i	−0.667695	+	0.385494i	−0.795203	−	0.606344i	$-0.792636\pi$
$277$	−11.1127	+	6.41589i	−0.667695	+	0.385494i	0.127508	+	0.991838i	$0.459302\pi$
$278$	−5.39311	−	3.11371i	−0.323457	−	0.186748i
$279$	5.04428	−	8.08517i	0.301993	−	0.484046i
$280$		0			0
$281$			21.2397i			1.26706i	0.773719	+	0.633528i	$0.218394\pi$
$281$			21.2397i			1.26706i	−0.773719	+	0.633528i	$0.781606\pi$
$282$	11.1240	+	11.5112i	0.662426	+	0.685480i
$283$	−3.27706	−	5.67603i	−0.194801	−	0.337405i	0.752034	−	0.659124i	$-0.229073\pi$
$283$	−3.27706	−	5.67603i	−0.194801	−	0.337405i	−0.946835	+	0.321719i	$0.895739\pi$
$284$	−2.64967	+	1.52979i	−0.157229	+	0.0907761i
$285$	−2.05142	+	4.26656i	−0.121515	+	0.252729i
$286$			11.3271i			0.669786i
$287$		0			0
$288$	−4.20426	−	2.62301i	−0.247738	−	0.154562i
$289$	−2.10188	+	3.64056i	−0.123640	+	0.214151i
$290$	15.5222	+	12.8863i	0.911496	+	0.756711i
$291$	0.556336	+	2.22801i	0.0326130	+	0.130608i
$292$	1.00873	−	1.74717i	0.0590315	−	0.102245i
$293$			3.71937i			0.217288i	0.994081	+	0.108644i	$0.0346509\pi$
$293$			3.71937i			0.217288i	−0.994081	+	0.108644i	$0.965349\pi$
$294$		0			0
$295$	−1.68300	−	4.54949i	−0.0979881	−	0.264882i
$296$	−17.4603	−	10.0807i	−1.01486	−	0.585928i
$297$	10.6202	+	3.43834i	0.616245	+	0.199513i
$298$	3.33677	−	1.92648i	0.193294	−	0.111598i
$299$	2.63629	−	4.56619i	0.152461	−	0.264070i
$300$	−2.31682	+	1.06181i	−0.133761	+	0.0613034i
$301$		0			0
$302$	−8.51121			−0.489765
$303$	−16.7149	+	16.1527i	−0.960245	+	0.927949i
$304$	4.76568	−	2.75147i	0.273331	−	0.157808i
$305$	−5.84735	−	4.85439i	−0.334818	−	0.277961i
$306$	7.64132	+	14.3469i	0.436825	+	0.820158i
$307$	−11.2102			−0.639800			−0.319900	−	0.947451i	$-0.603649\pi$
$307$	−11.2102			−0.639800			−0.319900	+	0.947451i	$0.603649\pi$
$308$		0			0
$309$	−9.63578	−	2.75935i	−0.548160	−	0.156974i
$310$	−1.81256	+	10.6050i	−0.102946	+	0.602326i
$311$	9.46050	+	16.3861i	0.536456	+	0.929168i	0.999091	+	0.0426199i	$0.0135704\pi$
$311$	9.46050	+	16.3861i	0.536456	+	0.929168i	−0.462636	+	0.886548i	$0.653096\pi$
$312$	3.77380	+	15.1133i	0.213649	+	0.855620i
$313$	−8.19024	+	14.1859i	−0.462940	+	0.801835i	−0.999106	−	0.0422775i	$-0.986539\pi$
$313$	−8.19024	+	14.1859i	−0.462940	+	0.801835i	0.536166	+	0.844112i	$0.319872\pi$
$314$	21.0903			1.19020
$315$		0			0
$316$	−0.554083			−0.0311696
$317$	−5.05836	+	8.76134i	−0.284106	+	0.492086i	−0.972392	−	0.233353i	$-0.925030\pi$
$317$	−5.05836	+	8.76134i	−0.284106	+	0.492086i	0.688286	+	0.725439i	$0.258363\pi$
$318$	7.13503	+	28.5743i	0.400113	+	1.60237i
$319$	6.39812	+	11.0819i	0.358226	+	0.620466i
$320$	−14.3310	−	2.44938i	−0.801128	−	0.136925i
$321$	−6.47141	−	1.85319i	−0.361199	−	0.103435i
$322$		0			0
$323$	−4.37254			−0.243295
$324$	−2.64233	−	0.181040i	−0.146796	−	0.0100578i
$325$	16.4169	+	5.78063i	0.910644	+	0.320652i
$326$	5.33977	−	3.08292i	0.295743	−	0.170747i
$327$	−6.48622	+	6.26807i	−0.358689	+	0.346625i
$328$	−30.6638			−1.69313
$329$		0			0
$330$	−12.5669	+	0.949574i	−0.691785	+	0.0522723i
$331$	−9.63774	+	16.6931i	−0.529738	+	0.917533i	0.469660	+	0.882847i	$0.344376\pi$
$331$	−9.63774	+	16.6931i	−0.529738	+	0.917533i	−0.999398	+	0.0346861i	$0.988957\pi$
$332$	2.32041	−	1.33969i	0.127349	−	0.0735251i
$333$	−23.3968	−	0.800582i	−1.28214	−	0.0438716i
$334$	18.3282	+	10.5818i	1.00287	+	0.579009i
$335$	21.6378	−	8.00452i	1.18220	−	0.437334i
$336$		0			0
$337$			23.6381i			1.28765i	0.765174	+	0.643824i	$0.222653\pi$
$337$			23.6381i			1.28765i	−0.765174	+	0.643824i	$0.777347\pi$
$338$	0.668614	−	1.15807i	0.0363678	−	0.0629909i
$339$	3.92855	+	15.7330i	0.213369	+	0.854499i
$340$	−1.81111	−	1.50356i	−0.0982215	−	0.0815421i
$341$	−3.41210	+	5.90993i	−0.184776	+	0.320041i
$342$	2.94008	−	4.71247i	0.158981	−	0.254821i
$343$		0			0
$344$			7.73266i			0.416917i
$345$	5.28698	+	2.54205i	0.284642	+	0.136859i
$346$	−13.1211	+	7.57546i	−0.705394	+	0.407259i
$347$	−7.95360	−	13.7760i	−0.426971	−	0.739536i	0.569631	−	0.821901i	$-0.307086\pi$
$347$	−7.95360	−	13.7760i	−0.426971	−	0.739536i	−0.996602	+	0.0823644i	$0.973753\pi$
$348$	−2.10979	−	2.18321i	−0.113096	−	0.117032i
$349$			0.0192397i			0.00102988i	1.00000		0.000514938i	$0.000163910\pi$
$349$			0.0192397i			0.00102988i	−1.00000		0.000514938i	$0.999836\pi$
$350$		0			0
$351$	12.1172	+	13.4290i	0.646766	+	0.716786i
$352$	3.07314	+	1.77428i	0.163799	+	0.0945695i
$353$	22.0143	−	12.7100i	1.17170	−	0.676484i	0.217624	−	0.976033i	$-0.430170\pi$
$353$	22.0143	−	12.7100i	1.17170	−	0.676484i	0.954081	+	0.299549i	$0.0968362\pi$
$354$	1.37880	+	5.52178i	0.0732821	+	0.293479i
$355$	−3.91662	+	22.9156i	−0.207873	+	1.21624i
$356$	0.523797			0.0277612
$357$		0			0
$358$			24.5523i			1.29763i
$359$	20.9396	+	12.0895i	1.10515	+	0.638057i	0.937568	−	0.347801i	$-0.113072\pi$
$359$	20.9396	+	12.0895i	1.10515	+	0.638057i	0.167579	+	0.985859i	$0.446405\pi$
$360$	−16.4511	+	5.45382i	−0.867048	+	0.287442i
$361$	−8.75294	−	15.1605i	−0.460681	−	0.797923i
$362$	−25.4642	−	14.7018i	−1.33837	−	0.772708i
$363$	10.6315	+	3.04448i	0.558007	+	0.159794i
$364$		0			0
$365$	−5.31861	−	14.3773i	−0.278389	−	0.752542i
$366$	6.19625	+	6.41189i	0.323883	+	0.335155i
$367$	4.53636	+	7.85721i	0.236796	+	0.410143i	0.959793	−	0.280708i	$-0.0905693\pi$
$367$	4.53636	+	7.85721i	0.236796	+	0.410143i	−0.722997	+	0.690851i	$0.757236\pi$
$368$	−3.40953	−	5.90548i	−0.177734	−	0.307845i
$369$	−31.4260	+	16.7378i	−1.63597	+	0.871336i
$370$	24.7883	−	9.16996i	1.28868	−	0.476724i
$371$		0			0
$372$	0.445743	−	1.55655i	0.0231107	−	0.0807035i
$373$	13.4785	+	7.78183i	0.697891	+	0.402928i	0.806562	−	0.591150i	$-0.201326\pi$
$373$	13.4785	+	7.78183i	0.697891	+	0.402928i	−0.108670	+	0.994078i	$0.534659\pi$
$374$	−5.82009	−	10.0807i	−0.300950	−	0.521260i
$375$	−5.03708	+	18.6983i	−0.260114	+	0.965578i
$376$	−13.6524	−	7.88224i	−0.704071	−	0.406496i
$377$			20.7342i			1.06787i
$378$		0			0
$379$	34.0984			1.75152			0.875758	−	0.482751i	$-0.160362\pi$
$379$	34.0984			1.75152			0.875758	+	0.482751i	$0.160362\pi$
$380$	−0.135508	+	0.792842i	−0.00695143	+	0.0406719i
$381$	16.0950	−	4.01894i	0.824573	−	0.205897i
$382$	−16.6643	+	9.62112i	−0.852618	+	0.492259i
$383$	9.15965	+	5.28833i	0.468036	+	0.270221i	0.715417	−	0.698697i	$-0.246237\pi$
$383$	9.15965	+	5.28833i	0.468036	+	0.270221i	−0.247381	+	0.968918i	$0.579570\pi$
$384$	21.8997	+	6.27133i	1.11757	+	0.320032i
$385$		0			0
$386$			31.5351i			1.60509i
$387$	4.22087	+	7.92486i	0.214559	+	0.402843i
$388$	0.195084	+	0.337895i	0.00990388	+	0.0171540i
$389$	14.6659	−	8.46736i	0.743590	−	0.429312i	−0.0797828	−	0.996812i	$-0.525423\pi$
$389$	14.6659	−	8.46736i	0.743590	−	0.429312i	0.823373	+	0.567500i	$0.192089\pi$
$390$	−18.4038	−	8.84880i	−0.931914	−	0.448077i
$391$			5.41832i			0.274016i
$392$		0			0
$393$	−15.7357	−	4.50615i	−0.793760	−	0.227305i
$394$	−1.69240	+	2.93132i	−0.0852619	+	0.147678i
$395$	−2.68926	+	3.23934i	−0.135311	+	0.162989i
$396$	1.89550	+	0.0648594i	0.0952524	+	0.00325931i
$397$	−0.203913	+	0.353188i	−0.0102341	+	0.0177260i	−0.871097	−	0.491111i	$-0.836591\pi$
$397$	−0.203913	+	0.353188i	−0.0102341	+	0.0177260i	0.860863	+	0.508837i	$0.169924\pi$
$398$			37.7491i			1.89219i
$399$		0			0
$400$	17.0905	−	14.6494i	0.854526	−	0.732470i
$401$	−24.2302	−	13.9893i	−1.21000	−	0.698593i	−0.247240	−	0.968954i	$-0.579524\pi$
$401$	−24.2302	−	13.9893i	−1.21000	−	0.698593i	−0.962759	+	0.270361i	$0.912857\pi$
$402$	−26.2622	+	6.55769i	−1.30984	+	0.327068i
$403$	−9.57608	+	5.52875i	−0.477019	+	0.275407i
$404$	−1.97464	+	3.42017i	−0.0982418	+	0.170160i
$405$	−13.8830	+	14.5692i	−0.689853	+	0.723949i
$406$		0			0
$407$	16.7643			0.830974
$408$	−11.1240	−	11.5112i	−0.550721	−	0.569888i
$409$	−2.26960	+	1.31036i	−0.112225	+	0.0647929i	−0.555062	−	0.831809i	$-0.687305\pi$
$409$	−2.26960	+	1.31036i	−0.112225	+	0.0647929i	0.442837	+	0.896602i	$0.353972\pi$
$410$	25.6766	−	30.9287i	1.26808	−	1.52746i
$411$	13.3338	−	12.8854i	0.657709	−	0.635589i
$412$	−1.70295			−0.0838984
$413$		0			0
$414$	−5.83954	−	3.64325i	−0.286998	−	0.179056i
$415$	3.42993	−	20.0681i	0.168369	−	0.985104i
$416$	2.87493	+	4.97953i	0.140955	+	0.244141i
$417$	6.90895	−	1.72517i	0.338333	−	0.0844820i
$418$	−1.98876	+	3.44462i	−0.0972732	+	0.168482i
$419$	8.39649			0.410195			0.205098	−	0.978742i	$-0.434249\pi$
$419$	8.39649			0.410195			0.205098	+	0.978742i	$0.434249\pi$
$420$		0			0
$421$	−7.84952			−0.382562			−0.191281	−	0.981535i	$-0.561264\pi$
$421$	−7.84952			−0.382562			−0.191281	+	0.981535i	$0.561264\pi$
$422$	5.00998	−	8.67754i	0.243882	−	0.422416i
$423$	−18.2943	−	0.625987i	−0.889500	−	0.0304365i
$424$	−14.5020	−	25.1181i	−0.704277	−	1.21984i
$425$	−17.5806	+	3.29077i	−0.852783	+	0.159626i
$426$	7.50912	−	26.2222i	0.363818	−	1.27047i
$427$		0			0
$428$	−1.14371			−0.0552831
$429$	−9.00089	−	9.31415i	−0.434567	−	0.449691i
$430$	−7.79946	−	6.47500i	−0.376123	−	0.312252i
$431$	−10.6154	+	6.12880i	−0.511326	+	0.295214i	−0.733378	−	0.679821i	$-0.762058\pi$
$431$	−10.6154	+	6.12880i	−0.511326	+	0.295214i	0.222053	+	0.975035i	$0.428724\pi$
$432$	22.8765	−	4.88776i	1.10065	−	0.235162i
$433$	5.13957			0.246992			0.123496	−	0.992345i	$-0.460589\pi$
$433$	5.13957			0.246992			0.123496	+	0.992345i	$0.460589\pi$
$434$		0			0
$435$	−23.0036	+	1.73819i	−1.10294	+	0.0833398i
$436$	−0.766259	+	1.32720i	−0.0366971	+	0.0635613i
$437$	1.60342	−	0.925734i	0.0767019	−	0.0442838i
$438$	4.35726	+	17.4499i	0.208198	+	0.833790i
$439$	14.4620	+	8.34964i	0.690234	+	0.398507i	0.803700	−	0.595035i	$-0.202862\pi$
$439$	14.4620	+	8.34964i	0.690234	+	0.398507i	−0.113466	+	0.993542i	$0.536195\pi$
$440$	11.6402	−	4.30607i	0.554924	−	0.205284i
$441$		0			0
$442$		−	18.8610i		−	0.897127i
$443$	−0.126110	+	0.218429i	−0.00599167	+	0.0103779i	−0.869006	−	0.494802i	$-0.835241\pi$
$443$	−0.126110	+	0.218429i	−0.00599167	+	0.0103779i	0.863014	+	0.505180i	$0.168574\pi$
$444$	−3.85902	+	0.963602i	−0.183141	+	0.0457305i
$445$	2.54226	−	3.06228i	0.120515	−	0.145166i
$446$	−3.26436	+	5.65403i	−0.154572	+	0.267726i
$447$	−1.21294	+	4.23563i	−0.0573700	+	0.200339i
$448$		0			0
$449$			28.8710i			1.36250i	0.732049	+	0.681252i	$0.238564\pi$
$449$			28.8710i			1.36250i	−0.732049	+	0.681252i	$0.761436\pi$
$450$	8.27450	−	21.1600i	0.390064	−	0.997492i
$451$	22.0811	−	12.7485i	1.03976	−	0.600305i
$452$	1.37758	+	2.38603i	0.0647958	+	0.112230i
$453$	6.99867	−	6.76329i	0.328826	−	0.317767i
$454$		−	16.8300i		−	0.789873i
$455$		0			0
$456$	−1.50588	+	5.25859i	−0.0705193	+	0.246256i
$457$	−20.8483	−	12.0368i	−0.975242	−	0.563056i	−0.0744117	−	0.997228i	$-0.523708\pi$
$457$	−20.8483	−	12.0368i	−0.975242	−	0.563056i	−0.900830	+	0.434171i	$0.857041\pi$
$458$	13.0835	−	7.55375i	0.611351	−	0.352964i
$459$	−17.6839	−	5.72525i	−0.825413	−	0.267232i
$460$	0.982465	+	0.167918i	0.0458077	+	0.00782921i
$461$	−39.8709			−1.85697			−0.928486	−	0.371367i	$-0.878889\pi$
$461$	−39.8709			−1.85697			−0.928486	+	0.371367i	$0.878889\pi$
$462$		0			0
$463$		−	29.8417i		−	1.38686i	−0.720524	−	0.693430i	$-0.756099\pi$
$463$		−	29.8417i		−	1.38686i	0.720524	−	0.693430i	$-0.243901\pi$
$464$	23.2231	+	13.4078i	1.07810	+	0.622443i
$465$	−6.93667	−	10.1607i	−0.321681	−	0.471192i
$466$	15.6230	+	27.0599i	0.723723	+	1.25353i
$467$	3.62140	+	2.09082i	0.167579	+	0.0967515i	0.581444	−	0.813587i	$-0.302488\pi$
$467$	3.62140	+	2.09082i	0.167579	+	0.0967515i	−0.413865	+	0.910338i	$0.635821\pi$
$468$	2.60732	+	1.62669i	0.120523	+	0.0751937i
$469$		0			0
$470$	19.3823	−	7.17013i	0.894039	−	0.330733i
$471$	−17.3423	+	16.7591i	−0.799093	+	0.772218i
$472$	−2.80240	−	4.85390i	−0.128991	−	0.223419i
$473$	−3.21487	−	5.56831i	−0.147820	−	0.256031i
$474$	3.55209	−	3.43263i	0.163153	−	0.157666i
$475$	3.97751	+	4.64030i	0.182501	+	0.212912i
$476$		0			0
$477$	−28.5731	−	17.8266i	−1.30827	−	0.816223i
$478$	−3.76937	−	2.17625i	−0.172407	−	0.0995393i
$479$	13.9676	+	24.1926i	0.638196	+	1.10539i	0.985828	+	0.167757i	$0.0536525\pi$
$479$	13.9676	+	24.1926i	0.638196	+	1.10539i	−0.347632	+	0.937631i	$0.613014\pi$
$480$	−5.28354	+	3.60705i	−0.241160	+	0.164638i
$481$	23.5245	+	13.5819i	1.07262	+	0.619280i
$482$		−	39.4912i		−	1.79878i
$483$		0			0
$484$	1.87892			0.0854055
$485$	2.92229	+	0.499462i	0.132694	+	0.0226794i
$486$	18.0609	−	15.2090i	0.819259	−	0.689895i
$487$	32.2536	−	18.6216i	1.46155	−	0.843826i	0.462466	−	0.886637i	$-0.346965\pi$
$487$	32.2536	−	18.6216i	1.46155	−	0.843826i	0.999083	+	0.0428116i	$0.0136315\pi$
$488$	−7.60462	−	4.39053i	−0.344245	−	0.198750i
$489$	−1.94104	+	6.77821i	−0.0877770	+	0.306521i
$490$		0			0
$491$			5.90572i			0.266522i	0.991081	+	0.133261i	$0.0425448\pi$
$491$			5.90572i			0.266522i	−0.991081	+	0.133261i	$0.957455\pi$
$492$	−4.35015	+	4.20384i	−0.196120	+	0.189524i
$493$	−10.6536	−	18.4527i	−0.479816	−	0.831066i
$494$	−5.58145	+	3.22245i	−0.251121	+	0.144985i
$495$	9.57904	−	10.7669i	0.430546	−	0.483936i
$496$			14.3007i			0.642122i
$497$		0			0
$498$	−6.57602	+	22.9637i	−0.294678	+	1.02903i
$499$	9.37010	−	16.2295i	0.419463	−	0.726532i	−0.576422	−	0.817152i	$-0.695552\pi$
$499$	9.37010	−	16.2295i	0.419463	−	0.726532i	0.995886	+	0.0906204i	$0.0288850\pi$
$500$	0.0518560	+	3.28975i	0.00231907	+	0.147122i
$501$	−23.4797	+	5.86290i	−1.04899	+	0.261935i
$502$	0.122023	−	0.211350i	0.00544615	−	0.00943301i
$503$		−	32.0398i		−	1.42858i	−0.699849	−	0.714291i	$-0.746749\pi$
$503$		−	32.0398i		−	1.42858i	0.699849	−	0.714291i	$-0.253251\pi$
$504$		0			0
$505$	10.4114	+	28.1442i	0.463303	+	1.25240i
$506$	4.26847	+	2.46440i	0.189757	+	0.109556i
$507$	0.370450	+	1.48357i	0.0164523	+	0.0658878i
$508$	2.44094	−	1.40928i	0.108299	−	0.0625265i
$509$	−9.57465	+	16.5838i	−0.424389	+	0.735063i	−0.996363	−	0.0852085i	$-0.972844\pi$
$509$	−9.57465	+	16.5838i	−0.424389	+	0.735063i	0.571974	+	0.820272i	$0.306178\pi$
$510$	20.9254	−	1.58116i	0.926592	−	0.0700147i
$511$		0			0
$512$	−15.8265			−0.699439
$513$	1.32709	+	6.21129i	0.0585925	+	0.274235i
$514$	−17.2238	+	9.94415i	−0.759708	+	0.438617i
$515$	−8.26532	+	9.95599i	−0.364213	+	0.438713i
$516$	1.06011	+	1.09700i	0.0466685	+	0.0482927i
$517$	13.1082			0.576499
$518$		0			0
$519$	4.76960	−	16.6557i	0.209362	−	0.731102i
$520$	19.8228	+	3.38800i	0.869285	+	0.148574i
$521$	−1.94104	−	3.36199i	−0.0850387	−	0.147291i	0.820369	−	0.571834i	$-0.193768\pi$
$521$	−1.94104	−	3.36199i	−0.0850387	−	0.147291i	−0.905408	+	0.424543i	$0.860435\pi$
$522$	27.0506	+	0.925607i	1.18397	+	0.0405127i
$523$	1.06192	−	1.83929i	0.0464343	−	0.0804266i	−0.841874	−	0.539674i	$-0.818548\pi$
$523$	1.06192	−	1.83929i	0.0464343	−	0.0804266i	0.888308	+	0.459247i	$0.151881\pi$
$524$	−2.78100			−0.121488
$525$		0			0
$526$	−26.8562			−1.17099
$527$	5.68157	−	9.84076i	0.247493	−	0.428670i
$528$	−16.2526	+	4.05830i	−0.707305	+	0.176615i
$529$	10.3529	+	17.9317i	0.450124	+	0.779638i
$530$	37.4785	+	6.40562i	1.62796	+	0.278242i
$531$	−5.52156	−	3.44486i	−0.239615	−	0.149494i
$532$		0			0
$533$	41.3138			1.78950
$534$	−3.35793	+	3.24500i	−0.145312	+	0.140425i
$535$	−5.55101	+	6.68646i	−0.239991	+	0.289081i
$536$	23.0856	−	13.3285i	0.997148	−	0.575704i
$537$	−19.5101	−	20.1891i	−0.841922	−	0.871224i
$538$	6.67354			0.287717
$539$		0			0
$540$	−1.58616	+	3.02906i	−0.0682573	+	0.130350i
$541$	7.59052	−	13.1472i	0.326342	−	0.565241i	−0.655441	−	0.755246i	$-0.727517\pi$
$541$	7.59052	−	13.1472i	0.326342	−	0.565241i	0.981783	+	0.190005i	$0.0608506\pi$
$542$	30.9431	−	17.8650i	1.32912	−	0.767367i
$543$	32.6214	−	8.14561i	1.39992	−	0.349561i
$544$	−5.11716	−	2.95439i	−0.219396	−	0.126669i
$545$	4.04017	+	10.9214i	0.173062	+	0.467821i
$546$		0			0
$547$			11.7540i			0.502566i	0.967914	+	0.251283i	$0.0808525\pi$
$547$			11.7540i			0.502566i	−0.967914	+	0.251283i	$0.919148\pi$
$548$	1.57521	−	2.72835i	0.0672897	−	0.116549i
$549$	−10.1902	−	0.348684i	−0.434907	−	0.0148815i
$550$	−5.40372	+	15.3465i	−0.230416	+	0.654375i
$551$	−3.64041	+	6.30537i	−0.155087	+	0.268618i
$552$	6.51629	+	1.86604i	0.277352	+	0.0794239i
$553$		0			0
$554$		−	19.4362i		−	0.825763i
$555$	−13.0963	+	27.2379i	−0.555909	+	1.15619i
$556$	1.04780	−	0.604946i	0.0444365	−	0.0256554i
$557$	−4.70135	−	8.14298i	−0.199203	−	0.345029i	0.749068	−	0.662494i	$-0.230502\pi$
$557$	−4.70135	−	8.14298i	−0.199203	−	0.345029i	−0.948270	+	0.317465i	$0.897169\pi$
$558$	6.78553	+	12.7401i	0.287254	+	0.539333i
$559$		−	10.4183i		−	0.440649i
$560$		0			0
$561$	12.7962	+	3.66440i	0.540258	+	0.154711i
$562$	−27.8614	−	16.0858i	−1.17526	−	0.678538i
$563$	−16.9106	+	9.76331i	−0.712695	+	0.411475i	−0.812058	−	0.583577i	$-0.801653\pi$
$563$	−16.9106	+	9.76331i	−0.712695	+	0.411475i	0.0993632	+	0.995051i	$0.468319\pi$
$564$	−3.01743	+	0.753455i	−0.127057	+	0.0317262i
$565$	20.6356	+	3.52693i	0.868147	+	0.148379i
$566$	9.92744			0.417281
$567$		0			0
$568$			26.8615i			1.12708i
$569$	−11.1702	−	6.44911i	−0.468279	−	0.270361i	0.247240	−	0.968954i	$-0.420476\pi$
$569$	−11.1702	−	6.44911i	−0.468279	−	0.270361i	−0.715519	+	0.698593i	$0.753810\pi$
$570$	−4.04306	−	5.92221i	−0.169345	−	0.248054i
$571$	20.8321	+	36.0823i	0.871796	+	1.51000i	0.860137	+	0.510063i	$0.170378\pi$
$571$	20.8321	+	36.0823i	0.871796	+	1.51000i	0.0116595	+	0.999932i	$0.496289\pi$
$572$	−1.90584	−	1.10034i	−0.0796874	−	0.0460075i
$573$	6.05758	−	21.1533i	0.253059	−	0.883692i
$574$		0			0
$575$	5.75012	−	4.92881i	0.239797	−	0.205545i
$576$	−17.2162	+	9.16955i	−0.717343	+	0.382065i
$577$	−3.74489	−	6.48634i	−0.155902	−	0.270030i	0.777485	−	0.628901i	$-0.216495\pi$
$577$	−3.74489	−	6.48634i	−0.155902	−	0.270030i	−0.933387	+	0.358871i	$0.883162\pi$
$578$	−3.18369	−	5.51432i	−0.132424	−	0.229365i
$579$	−25.0588	−	25.9309i	−1.04141	−	1.07765i
$580$	−3.67605	+	1.35989i	−0.152640	+	0.0564663i
$581$		0			0
$582$	−3.34395	−	0.957590i	−0.138611	−	0.0396934i
$583$	20.8858	+	12.0584i	0.865003	+	0.499409i
$584$	−8.85614	−	15.3393i	−0.366470	−	0.634744i
$585$	22.1648	−	7.34802i	0.916402	−	0.303803i
$586$	−4.87892	−	2.81685i	−0.201546	−	0.116363i
$587$			22.1920i			0.915961i	0.888962	+	0.457981i	$0.151427\pi$
$587$			22.1920i			0.915961i	−0.888962	+	0.457981i	$0.848573\pi$
$588$		0			0
$589$	−3.88284			−0.159990
$590$	7.24245	+	1.23784i	0.298167	+	0.0509611i
$591$	−0.937685	−	3.75523i	−0.0385712	−	0.154470i
$592$	30.4244	−	17.5655i	1.25043	−	0.721938i
$593$	−5.46787	−	3.15687i	−0.224538	−	0.129637i	0.383512	−	0.923536i	$-0.374715\pi$
$593$	−5.46787	−	3.15687i	−0.224538	−	0.129637i	−0.608050	+	0.793899i	$0.708048\pi$
$594$	−12.5534	+	11.3271i	−0.515072	+	0.464757i
$595$		0			0
$596$			0.748572i			0.0306627i
$597$	−29.9966	−	31.0406i	−1.22768	−	1.27041i
$598$	3.99316	+	6.91636i	0.163293	+	0.282831i
$599$	−17.8962	+	10.3324i	−0.731219	+	0.422170i	−0.818868	−	0.573982i	$-0.805398\pi$
$599$	−17.8962	+	10.3324i	−0.731219	+	0.422170i	0.0876487	+	0.996151i	$0.472065\pi$
$600$	−2.09705	+	22.2764i	−0.0856116	+	0.909432i
$601$			12.5956i			0.513785i	0.966440	+	0.256892i	$0.0826986\pi$
$601$			12.5956i			0.513785i	−0.966440	+	0.256892i	$0.917301\pi$
$602$		0			0
$603$	16.3841	−	26.2611i	0.667213	−	1.06943i
$604$	0.826798	−	1.43206i	0.0336419	−	0.0582695i
$605$	9.11940	−	10.9848i	0.370756	−	0.446594i
$606$	−8.52955	−	34.1590i	−0.346489	−	1.38762i
$607$	21.3383	−	36.9590i	0.866095	−	1.50012i	0.000139312	−	1.00000i	$-0.499956\pi$
$607$	21.3383	−	36.9590i	0.866095	−	1.50012i	0.865956	−	0.500121i	$-0.166711\pi$
$608$			2.01906i			0.0818838i
$609$		0			0
$610$	10.7962	−	3.99387i	0.437127	−	0.161707i
$611$	18.3942	+	10.6199i	0.744148	+	0.429634i
$612$	−3.15624	−	0.107999i	−0.127583	−	0.00436559i
$613$	4.60972	−	2.66142i	0.186185	−	0.107494i	−0.404011	−	0.914754i	$-0.632384\pi$
$613$	4.60972	−	2.66142i	0.186185	−	0.107494i	0.590195	+	0.807261i	$0.299051\pi$
$614$	8.48998	−	14.7051i	0.342628	−	0.593448i
$615$	3.46342	+	45.8358i	0.139659	+	1.84828i
$616$		0			0
$617$	30.1002			1.21179			0.605895	−	0.795545i	$-0.292815\pi$
$617$	30.1002			1.21179			0.605895	+	0.795545i	$0.292815\pi$
$618$	10.9172	−	10.5500i	0.439154	−	0.424385i
$619$	−11.0265	+	6.36613i	−0.443191	+	0.255876i	−0.704950	−	0.709257i	$-0.749031\pi$
$619$	−11.0265	+	6.36613i	−0.443191	+	0.255876i	0.261759	+	0.965133i	$0.415697\pi$
$620$	−1.60828	−	1.33517i	−0.0645900	−	0.0536217i
$621$	7.69683	−	1.64449i	0.308863	−	0.0659911i
$622$	−28.6594			−1.14914
$623$		0			0
$624$	−26.0944	−	7.47254i	−1.04461	−	0.299141i
$625$	19.4846	+	15.6637i	0.779383	+	0.626548i
$626$	−12.4057	−	21.4872i	−0.495830	−	0.858802i
$627$	−1.10188	−	4.41281i	−0.0440049	−	0.176230i
$628$	−2.04876	+	3.54856i	−0.0817545	+	0.141603i
$629$	−27.9145			−1.11303
$630$		0			0
$631$	−17.4114			−0.693138			−0.346569	−	0.938024i	$-0.612653\pi$
$631$	−17.4114			−0.693138			−0.346569	+	0.938024i	$0.612653\pi$
$632$	−2.43229	+	4.21284i	−0.0967511	+	0.167578i
$633$	2.77581	+	11.1165i	0.110329	+	0.441843i
$634$	−7.66184	−	13.2707i	−0.304291	−	0.527047i
$635$	3.60809	−	21.1104i	0.143183	−	0.837743i
$636$	−5.50089	−	1.57526i	−0.218125	−	0.0624633i
$637$		0			0
$638$	−19.3823			−0.767353
$639$	14.6623	+	27.5292i	0.580033	+	1.08904i
$640$	18.7850	−	22.6275i	0.742543	−	0.894430i
$641$	−1.13893	+	0.657564i	−0.0449852	+	0.0259722i	−0.522324	−	0.852747i	$-0.674935\pi$
$641$	−1.13893	+	0.657564i	−0.0449852	+	0.0259722i	0.477339	+	0.878719i	$0.341601\pi$
$642$	7.33202	−	7.08543i	0.289372	−	0.279640i
$643$	39.2223			1.54678			0.773389	−	0.633932i	$-0.218560\pi$
$643$	39.2223			1.54678			0.773389	+	0.633932i	$0.218560\pi$
$644$		0			0
$645$	11.5587	−	0.873390i	0.455121	−	0.0343897i
$646$	3.31152	−	5.73572i	0.130290	−	0.225669i
$647$	−5.39634	+	3.11558i	−0.212152	+	0.122486i	−0.602311	−	0.798261i	$-0.705753\pi$
$647$	−5.39634	+	3.11558i	−0.212152	+	0.122486i	0.390159	+	0.920747i	$0.372420\pi$
$648$	−12.9757	+	19.2956i	−0.509732	+	0.758003i
$649$	4.03604	+	2.33021i	0.158428	+	0.0914687i
$650$	−20.0160	+	17.1570i	−0.785092	+	0.672954i
$651$		0			0
$652$			1.19793i			0.0469144i
$653$	9.43091	−	16.3348i	0.369060	−	0.639230i	−0.620359	−	0.784318i	$-0.713013\pi$
$653$	9.43091	−	16.3348i	0.369060	−	0.639230i	0.989419	+	0.145088i	$0.0463464\pi$
$654$	−3.30990	−	13.2554i	−0.129427	−	0.518329i
$655$	−13.4976	+	16.2586i	−0.527397	+	0.635275i
$656$	26.7157	−	46.2730i	1.04307	−	1.80666i
$657$	−17.4492	−	10.8864i	−0.680759	−	0.424721i
$658$		0			0
$659$		−	41.6170i		−	1.62117i	−0.585622	−	0.810584i	$-0.699150\pi$
$659$		−	41.6170i		−	1.62117i	0.585622	−	0.810584i	$-0.300850\pi$
$660$	1.06100	−	2.20669i	0.0412996	−	0.0858953i
$661$	−3.27232	+	1.88927i	−0.127278	+	0.0734842i	−0.562287	−	0.826942i	$-0.690079\pi$
$661$	−3.27232	+	1.88927i	−0.127278	+	0.0734842i	0.435009	+	0.900426i	$0.356745\pi$
$662$	−14.5982	−	25.2848i	−0.567374	−	0.982721i
$663$	14.9876	+	15.5092i	0.582069	+	0.602327i
$664$		−	23.5236i		−	0.912894i
$665$		0			0
$666$	18.7696	−	30.0846i	0.727307	−	1.16576i
$667$	7.81342	+	4.51108i	0.302537	+	0.174670i
$668$	−3.56088	+	2.05588i	−0.137775	+	0.0795442i
$669$	−1.80864	−	7.24321i	−0.0699259	−	0.280039i
$670$	−5.88730	+	34.4458i	−0.227446	+	1.33076i
$671$	7.30148			0.281871
$672$		0			0
$673$		−	31.2573i		−	1.20488i	−0.798163	−	0.602441i	$-0.794195\pi$
$673$		−	31.2573i		−	1.20488i	0.798163	−	0.602441i	$-0.205805\pi$
$674$	−31.0075	−	17.9022i	−1.19436	−	0.689565i
$675$	10.0104	+	23.9748i	0.385301	+	0.922791i
$676$	0.129901	+	0.224996i	0.00499621	+	0.00865369i
$677$	−7.56724	−	4.36895i	−0.290832	−	0.167912i	0.347485	−	0.937686i	$-0.387036\pi$
$677$	−7.56724	−	4.36895i	−0.290832	−	0.167912i	−0.638317	+	0.769773i	$0.720369\pi$
$678$	−23.6132	−	6.76199i	−0.906858	−	0.259693i
$679$		0			0
$680$	−19.3823	+	7.17013i	−0.743278	+	0.274962i
$681$	13.3737	+	13.8391i	0.512481	+	0.530317i
$682$	−5.16827	−	8.95171i	−0.197903	−	0.342779i
$683$	−10.9346	−	18.9393i	−0.418401	−	0.724691i	0.577378	−	0.816477i	$-0.304076\pi$
$683$	−10.9346	−	18.9393i	−0.418401	−	0.724691i	−0.995779	+	0.0917858i	$0.970743\pi$
$684$	0.507292	+	0.952463i	0.0193968	+	0.0364183i
$685$	−8.30544	−	22.4513i	−0.317334	−	0.857819i
$686$		0			0
$687$	−4.75594	+	16.6079i	−0.181450	+	0.633632i
$688$	−11.6689	−	6.73705i	−0.444873	−	0.256847i
$689$	19.5387	+	33.8421i	0.744366	+	1.28928i
$690$	−7.33862	+	5.01004i	−0.279377	+	0.190729i
$691$	−19.5167	−	11.2680i	−0.742449	−	0.428653i	0.0805102	−	0.996754i	$-0.474345\pi$
$691$	−19.5167	−	11.2680i	−0.742449	−	0.428653i	−0.822959	+	0.568101i	$0.807678\pi$
$692$		−	2.94359i		−	0.111898i
$693$		0			0
$694$	24.0944			0.914612
$695$	1.54881	−	9.06187i	0.0587496	−	0.343736i
$696$	−25.8610	+	6.45751i	−0.980257	+	0.244771i
$697$	−36.7678	+	21.2279i	−1.39268	+	0.804063i
$698$	−0.0252378	−	0.0145711i	−0.000955266	−	0.000551523i
$699$	−34.3493	−	9.83646i	−1.29921	−	0.372049i
$700$		0			0
$701$		−	35.5019i		−	1.34089i	−0.741960	−	0.670444i	$-0.766104\pi$
$701$		−	35.5019i		−	1.34089i	0.741960	−	0.670444i	$-0.233896\pi$
$702$	−26.7924	+	5.72442i	−1.01122	+	0.216054i
$703$	4.76927	+	8.26062i	0.179877	+	0.311555i
$704$	12.0968	−	6.98408i	0.455915	−	0.263223i
$705$	−10.2402	+	21.2977i	−0.385669	+	0.802119i
$706$			38.5033i			1.44909i
$707$		0			0
$708$	−1.06301	−	0.304409i	−0.0399503	−	0.0114404i
$709$	−2.03390	+	3.52282i	−0.0763847	+	0.132302i	−0.901688	−	0.432388i	$-0.857671\pi$
$709$	−2.03390	+	3.52282i	−0.0763847	+	0.132302i	0.825303	+	0.564690i	$0.191004\pi$
$710$	−27.0936	−	22.4927i	−1.01680	−	0.844135i
$711$	−0.193166	+	5.64522i	−0.00724428	+	0.211712i
$712$	2.29934	−	3.98257i	0.0861712	−	0.149253i
$713$			4.81149i			0.180192i
$714$		0			0
$715$	−15.6830	+	5.80164i	−0.586511	+	0.216969i
$716$	−4.13106	−	2.38507i	−0.154385	−	0.0891342i
$717$	4.82883	−	1.20576i	0.180336	−	0.0450301i
$718$	−31.7169	+	18.3118i	−1.18366	+	0.683389i
$719$	15.2703	−	26.4489i	0.569484	−	0.986376i	−0.427133	−	0.904189i	$-0.640476\pi$
$719$	15.2703	−	26.4489i	0.569484	−	0.986376i	0.996617	−	0.0821868i	$-0.0261904\pi$
$720$	6.10289	−	29.5770i	0.227441	−	1.10227i
$721$		0			0
$722$	26.5159			0.986821
$723$	31.3810	+	32.4732i	1.16707	+	1.20769i
$724$	4.94730	−	2.85632i	0.183865	−	0.106154i
$725$	−9.89149	+	28.0916i	−0.367361	+	1.04330i
$726$	−12.0453	+	11.6402i	−0.447043	+	0.432008i
$727$	−23.4181			−0.868528			−0.434264	−	0.900786i	$-0.642992\pi$
$727$	−23.4181			−0.868528			−0.434264	+	0.900786i	$0.642992\pi$
$728$		0			0
$729$	−2.76568	+	26.8580i	−0.102433	+	0.994740i
$730$	22.8876	+	3.91182i	0.847107	+	0.144783i
$731$	5.35315	+	9.27192i	0.197993	+	0.342934i
$732$	−1.68075	+	0.419686i	−0.0621224	+	0.0155120i
$733$	−8.44533	+	14.6277i	−0.311935	+	0.540288i	−0.978781	−	0.204908i	$-0.934311\pi$
$733$	−8.44533	+	14.6277i	−0.311935	+	0.540288i	0.666846	+	0.745196i	$0.267644\pi$
$734$	−13.7423			−0.507239
$735$		0			0
$736$	2.50196			0.0922235
$737$	−11.0827	+	19.1958i	−0.408237	+	0.707087i
$738$	1.84431	−	53.8996i	0.0678901	−	1.98407i
$739$	−13.8321	−	23.9579i	−0.508822	−	0.881306i	−0.999948	−	0.0102170i	$-0.996748\pi$
$739$	−13.8321	−	23.9579i	−0.508822	−	0.881306i	0.491126	−	0.871089i	$-0.336586\pi$
$740$	−0.865093	+	5.06155i	−0.0318014	+	0.186066i
$741$	2.02890	−	7.08499i	0.0745333	−	0.260274i
$742$		0			0
$743$	−40.1701			−1.47370			−0.736850	−	0.676056i	$-0.763688\pi$
$743$	−40.1701			−1.47370			−0.736850	+	0.676056i	$0.763688\pi$
$744$	−9.87819	−	10.2220i	−0.362152	−	0.374756i
$745$	4.37639	+	3.63321i	0.160338	+	0.133111i
$746$	−20.4158	+	11.7870i	−0.747474	+	0.431554i
$747$	−12.8404	−	24.1083i	−0.469804	−	0.882078i
$748$	2.26151			0.0826888
$749$		0			0
$750$	−20.7129	−	20.7685i	−0.756328	−	0.758359i
$751$	24.8188	−	42.9874i	0.905650	−	1.56863i	0.0856082	−	0.996329i	$-0.472717\pi$
$751$	24.8188	−	42.9874i	0.905650	−	1.56863i	0.820042	−	0.572303i	$-0.193950\pi$
$752$	23.7893	−	13.7347i	0.867505	−	0.500854i
$753$	0.0676076	+	0.270754i	0.00246376	+	0.00986683i
$754$	−27.1983	−	15.7029i	−0.990503	−	0.571867i
$755$	−4.35936	−	11.7842i	−0.158654	−	0.428873i
$756$		0			0
$757$		−	47.7116i		−	1.73411i	−0.498214	−	0.867054i	$-0.666011\pi$
$757$		−	47.7116i		−	1.73411i	0.498214	−	0.867054i	$-0.333989\pi$
$758$	−25.8242	+	44.7288i	−0.937977	+	1.62462i
$759$	−5.46821	+	1.36542i	−0.198483	+	0.0495615i
$760$	5.43334	+	4.51068i	0.197088	+	0.163620i
$761$	−9.91711	+	17.1769i	−0.359495	+	0.622663i	−0.987876	−	0.155242i	$-0.950384\pi$
$761$	−9.91711	+	17.1769i	−0.359495	+	0.622663i	0.628382	+	0.777905i	$0.283718\pi$
$762$	−6.91759	+	24.1565i	−0.250598	+	0.875098i
$763$		0			0
$764$		−	3.73847i		−	0.135253i
$765$	−15.9503	+	17.9282i	−0.576683	+	0.648195i
$766$	−13.8740	+	8.01017i	−0.501289	+	0.289419i
$767$	3.77572	+	6.53974i	0.136333	+	0.236136i
$768$	−8.61559	+	8.32583i	−0.310888	+	0.300433i
$769$			10.6337i			0.383461i	0.981448	+	0.191731i	$0.0614100\pi$
$769$			10.6337i			0.383461i	−0.981448	+	0.191731i	$0.938590\pi$
$770$		0			0
$771$	6.26096	−	21.8635i	0.225483	−	0.787396i
$772$	−5.30595	−	3.06339i	−0.190965	−	0.110254i
$773$	12.4039	−	7.16138i	0.446136	−	0.257577i	−0.260061	−	0.965592i	$-0.583743\pi$
$773$	12.4039	−	7.16138i	0.446136	−	0.257577i	0.706197	+	0.708015i	$0.250409\pi$
$774$	−13.5922	−	0.465090i	−0.488560	−	0.0167173i
$775$	−15.6117	+	2.92222i	−0.560787	+	0.104969i
$776$	3.42548			0.122967
$777$		0			0
$778$			25.6508i			0.919626i
$779$	12.5637	+	7.25368i	0.450142	+	0.259890i
$780$	3.27665	−	2.23695i	0.117323	−	0.0800956i
$781$	−11.1677	−	19.3431i	−0.399613	−	0.692149i
$782$	−7.10752	−	4.10353i	−0.254165	−	0.146742i
$783$	−22.9789	+	20.7342i	−0.821200	+	0.740980i
$784$		0			0
$785$	10.8023	+	29.2007i	0.385550	+	1.04222i
$786$	17.8283	−	17.2287i	0.635914	−	0.614527i
$787$	18.4671	+	31.9859i	0.658280	+	1.14017i	0.981061	+	0.193700i	$0.0620490\pi$
$787$	18.4671	+	31.9859i	0.658280	+	1.14017i	−0.322781	+	0.946474i	$0.604618\pi$
$788$	−0.328807	−	0.569511i	−0.0117133	−	0.0202880i
$789$	22.0835	−	21.3408i	0.786195	−	0.759753i
$790$	−2.21254	−	5.98095i	−0.0787188	−	0.212793i
$791$		0			0
$792$	8.81391	−	14.1273i	0.313189	−	0.501991i
$793$	10.2458	+	5.91543i	0.363840	+	0.210063i
$794$	−0.308865	−	0.534970i	−0.0109612	−	0.0189854i
$795$	−35.9082	+	24.5143i	−1.27353	+	0.869434i
$796$	−6.35148	−	3.66703i	−0.225122	−	0.129974i
$797$		−	37.4862i		−	1.32783i	−0.747809	−	0.663914i	$-0.768894\pi$
$797$		−	37.4862i		−	1.32783i	0.747809	−	0.663914i	$-0.231106\pi$
$798$		0			0
$799$	−21.8268			−0.772177
$800$	1.51954	+	8.11800i	0.0537240	+	0.287015i
$801$	0.182607	−	5.33665i	0.00645210	−	0.188561i
$802$	36.7012	−	21.1895i	1.29597	−	0.748226i
$803$	12.7547	+	7.36392i	0.450103	+	0.259867i
$804$	1.44780	−	5.05578i	0.0510599	−	0.178303i
$805$		0			0
$806$		−	16.7487i		−	0.589947i
$807$	−5.48757	+	5.30301i	−0.193172	+	0.186675i
$808$	17.3363	+	30.0274i	0.609889	+	1.05636i
$809$	−22.1518	+	12.7893i	−0.778814	+	0.449649i	−0.836010	−	0.548714i	$-0.815117\pi$
$809$	−22.1518	+	12.7893i	−0.778814	+	0.449649i	0.0571956	+	0.998363i	$0.481784\pi$
$810$	−8.59704	−	29.2451i	−0.302069	−	1.02757i
$811$		−	7.28791i		−	0.255913i	−0.991780	−	0.127957i	$-0.959158\pi$
$811$		−	7.28791i		−	0.255913i	0.991780	−	0.127957i	$-0.0408418\pi$
$812$		0			0
$813$	−11.2480	+	39.2786i	−0.394485	+	1.37756i
$814$	−12.6963	+	21.9907i	−0.445006	+	0.770773i
$815$	7.00345	+	5.81417i	0.245320	+	0.203661i
$816$	27.0626	−	6.75756i	0.947380	−	0.236562i
$817$	1.82920	−	3.16826i	0.0639955	−	0.110844i
$818$		−	3.96956i		−	0.138792i
$819$		0			0
$820$	2.70964	+	7.32470i	0.0946247	+	0.255790i
$821$	−0.00729231	−	0.00421022i	−0.000254504	−	0.000146938i	0.499873	−	0.866099i	$-0.333380\pi$
$821$	−0.00729231	−	0.00421022i	−0.000254504	−	0.000146938i	−0.500127	+	0.865952i	$0.666713\pi$
$822$	6.80421	+	27.2494i	0.237324	+	0.950433i
$823$	−27.0406	+	15.6119i	−0.942578	+	0.544198i	−0.890767	−	0.454459i	$-0.849832\pi$
$823$	−27.0406	+	15.6119i	−0.942578	+	0.544198i	−0.0518103	+	0.998657i	$0.516499\pi$
$824$	−7.47553	+	12.9480i	−0.260422	+	0.451065i
$825$	−7.75138	−	16.9132i	−0.269868	−	0.588842i
$826$		0			0
$827$	−38.3189			−1.33248			−0.666239	−	0.745738i	$-0.732097\pi$
$827$	−38.3189			−1.33248			−0.666239	+	0.745738i	$0.732097\pi$
$828$	1.18026	−	0.628620i	0.0410169	−	0.0218461i
$829$	1.94142	−	1.12088i	0.0674283	−	0.0389298i	−0.465907	−	0.884834i	$-0.654272\pi$
$829$	1.94142	−	1.12088i	0.0674283	−	0.0389298i	0.533335	+	0.845904i	$0.320938\pi$
$830$	23.7268	+	19.6977i	0.823571	+	0.683717i
$831$	15.4446	+	15.9821i	0.535768	+	0.554414i
$832$	22.6331			0.784663
$833$		0			0
$834$	−2.96944	+	10.3694i	−0.102823	+	0.359064i
$835$	−5.26354	+	30.7963i	−0.182152	+	1.06575i
$836$	−0.386384	−	0.669237i	−0.0133634	−	0.0231460i
$837$	−15.7034	−	5.08406i	−0.542789	−	0.175731i
$838$	−6.35903	+	11.0142i	−0.219669	+	0.380478i
$839$	−20.6544			−0.713069			−0.356535	−	0.934282i	$-0.616042\pi$
$839$	−20.6544			−0.713069			−0.356535	+	0.934282i	$0.616042\pi$
$840$		0			0
$841$	−6.47924			−0.223422
$842$	5.94479	−	10.2967i	0.204871	−	0.354847i
$843$	35.6924	−	8.91243i	1.22931	−	0.306961i
$844$	0.973362	+	1.68591i	0.0335045	+	0.0580315i
$845$	1.94588	+	0.332579i	0.0669402	+	0.0114411i
$846$	14.6762	−	23.5236i	0.504579	−	0.808759i
$847$		0			0
$848$	50.5391			1.73552
$849$	−8.16322	+	7.88867i	−0.280161	+	0.270738i
$850$	8.99786	−	25.5537i	0.308624	−	0.876485i
$851$	10.2363	−	5.90993i	0.350896	−	0.202590i
$852$	3.68257	+	3.81073i	0.126163	+	0.130553i
$853$	−7.06831			−0.242014			−0.121007	−	0.992652i	$-0.538612\pi$
$853$	−7.06831			−0.242014			−0.121007	+	0.992652i	$0.538612\pi$
$854$		0			0
$855$	8.03055	+	1.65702i	0.274639	+	0.0566687i
$856$	−5.02058	+	8.69590i	−0.171600	+	0.297220i
$857$	−14.5780	+	8.41661i	−0.497975	+	0.287506i	−0.727877	−	0.685708i	$-0.759493\pi$
$857$	−14.5780	+	8.41661i	−0.497975	+	0.287506i	0.229902	+	0.973214i	$0.426159\pi$
$858$	19.0347	−	4.75298i	0.649833	−	0.162264i
$859$	30.4698	+	17.5918i	1.03962	+	0.600223i	0.919725	−	0.392563i	$-0.128412\pi$
$859$	30.4698	+	17.5918i	1.03962	+	0.600223i	0.119893	+	0.992787i	$0.461745\pi$
$860$	1.84711	−	0.683304i	0.0629859	−	0.0233005i
$861$		0			0
$862$		−	18.5665i		−	0.632376i
$863$	18.9879	−	32.8880i	0.646356	−	1.11952i	−0.337630	−	0.941279i	$-0.609625\pi$
$863$	18.9879	−	32.8880i	0.646356	−	1.11952i	0.983986	−	0.178243i	$-0.0570414\pi$
$864$	−2.64369	+	8.16571i	−0.0899402	+	0.277803i
$865$	−17.2091	−	14.2868i	−0.585128	−	0.485765i
$866$	−3.89242	+	6.74187i	−0.132270	+	0.229098i
$867$	6.99977	+	2.00449i	0.237725	+	0.0680761i
$868$		0			0
$869$		−	4.04491i		−	0.137214i
$870$	15.1416	−	31.4916i	0.513348	−	1.06767i
$871$	−31.1037	+	17.9577i	−1.05391	+	0.608474i
$872$	6.72737	+	11.6521i	0.227817	+	0.394591i
$873$	3.51062	−	1.86979i	0.118817	−	0.0632829i
$874$			2.80440i			0.0948601i
$875$		0			0
$876$	−3.35932	−	0.961992i	−0.113501	−	0.0325027i
$877$	−9.91566	−	5.72481i	−0.334828	−	0.193313i	0.323155	−	0.946346i	$-0.395257\pi$
$877$	−9.91566	−	5.72481i	−0.334828	−	0.193313i	−0.657983	+	0.753033i	$0.728590\pi$
$878$	−21.9054	+	12.6471i	−0.739272	+	0.426819i
$879$	6.25024	−	1.56069i	0.210815	−	0.0526408i
$880$	−3.64342	+	21.3172i	−0.122820	+	0.718601i
$881$	23.6698			0.797455			0.398728	−	0.917069i	$-0.369452\pi$
$881$	23.6698			0.797455			0.398728	+	0.917069i	$0.369452\pi$
$882$		0			0
$883$			16.8355i			0.566560i	0.959037	+	0.283280i	$0.0914226\pi$
$883$			16.8355i			0.566560i	−0.959037	+	0.283280i	$0.908577\pi$
$884$	3.17346	+	1.83220i	0.106735	+	0.0616236i
$885$	−6.93901	+	4.73722i	−0.233252	+	0.159240i
$886$	−0.191017	−	0.330852i	−0.00641735	−	0.0111152i
$887$	45.5385	+	26.2917i	1.52903	+	0.882789i	0.999403	+	0.0345613i	$0.0110034\pi$
$887$	45.5385	+	26.2917i	1.52903	+	0.882789i	0.529632	+	0.848227i	$0.322330\pi$
$888$	−9.61362	+	33.5712i	−0.322612	+	1.12657i
$889$		0			0
$890$	2.09160	+	5.65403i	0.0701107	+	0.189524i
$891$	1.32163	−	19.2895i	0.0442761	−	0.646222i
$892$	−0.634214	−	1.09849i	−0.0212350	−	0.0367802i
$893$	3.72917	+	6.45910i	0.124792	+	0.216146i
$894$	−4.63752	−	4.79891i	−0.155102	−	0.160500i
$895$	−33.9941	+	12.5755i	−1.13630	+	0.420352i
$896$		0			0
$897$	−8.77950	−	2.51414i	−0.293139	−	0.0839448i
$898$	−37.8717	−	21.8652i	−1.26380	−	0.729653i
$899$	−9.46050	−	16.3861i	−0.315525	−	0.546506i
$900$	2.75648	+	3.44776i	0.0918826	+	0.114925i
$901$	−34.7774	−	20.0788i	−1.15860	−	0.668921i
$902$			38.6201i			1.28591i
$903$		0			0
$904$	24.1889			0.804510
$905$	7.31288	−	42.7867i	0.243088	−	1.42228i
$906$	3.57140	+	14.3027i	0.118652	+	0.475176i
$907$	43.9694	−	25.3858i	1.45998	−	0.842920i	0.460971	−	0.887415i	$-0.347501\pi$
$907$	43.9694	−	25.3858i	1.45998	−	0.842920i	0.999010	+	0.0444946i	$0.0141678\pi$
$908$	2.83174	+	1.63491i	0.0939747	+	0.0542563i
$909$	34.1577	+	21.3107i	1.13294	+	0.706832i
$910$		0			0
$911$		−	16.1165i		−	0.533963i	−0.963702	−	0.266981i	$-0.913974\pi$
$911$		−	16.1165i		−	0.533963i	0.963702	−	0.266981i	$-0.0860262\pi$
$912$	−6.62345	−	6.85396i	−0.219324	−	0.226957i
$913$	9.77999	+	16.9394i	0.323671	+	0.560614i
$914$	31.5787	−	18.2319i	1.04453	−	0.603059i
$915$	−5.70396	+	11.8632i	−0.188567	+	0.392184i
$916$			2.93515i			0.0969802i
$917$		0			0
$918$	20.9029	−	18.8610i	0.689900	−	0.622506i
$919$	−19.8721	+	34.4194i	−0.655519	+	1.13539i	0.326245	+	0.945285i	$0.394217\pi$
$919$	−19.8721	+	34.4194i	−0.655519	+	1.13539i	−0.981763	+	0.190106i	$0.939117\pi$
$920$	5.58950	−	6.73283i	0.184280	−	0.221975i
$921$	4.70392	+	18.8382i	0.155000	+	0.620740i
$922$	30.1960	−	52.3010i	0.994452	−	1.72244i
$923$		−	36.1909i		−	1.19124i
$924$		0			0
$925$	25.3926	+	29.6240i	0.834905	+	0.974030i
$926$	39.1451	+	22.6004i	1.28639	+	0.742696i
$927$	−0.593686	+	17.3503i	−0.0194992	+	0.569860i
$928$	−8.52069	+	4.91942i	−0.279705	+	0.161488i
$929$	−18.2593	+	31.6261i	−0.599069	+	1.03762i	0.393889	+	0.919158i	$0.371129\pi$
$929$	−18.2593	+	31.6261i	−0.599069	+	1.03762i	−0.992959	+	0.118461i	$0.962204\pi$
$930$	18.5819	−	1.40407i	0.609323	−	0.0460414i
$931$		0			0
$932$	−6.07063			−0.198850
$933$	23.5663	−	22.7737i	0.771526	−	0.745578i
$934$	−5.48530	+	3.16694i	−0.179484	+	0.103625i
$935$	10.9763	−	13.2215i	0.358963	−	0.432388i
$936$	23.8136	−	12.6834i	0.778372	−	0.414569i
$937$	−7.60980			−0.248601			−0.124301	−	0.992245i	$-0.539669\pi$
$937$	−7.60980			−0.248601			−0.124301	+	0.992245i	$0.539669\pi$
$938$		0			0
$939$	27.2755	+	7.81075i	0.890102	+	0.254894i
$940$	−0.676429	+	3.95770i	−0.0220627	+	0.129086i
$941$	−11.0121	−	19.0735i	−0.358985	−	0.621780i	0.628807	−	0.777562i	$-0.283544\pi$
$941$	−11.0121	−	19.0735i	−0.358985	−	0.621780i	−0.987791	+	0.155782i	$0.950210\pi$
$942$	−8.84974	−	35.4414i	−0.288340	−	1.15474i
$943$	8.98853	−	15.5686i	0.292707	−	0.506983i
$944$	9.76632			0.317867
$945$		0			0
$946$	9.73904			0.316644
$947$	−24.6291	+	42.6589i	−0.800339	+	1.38623i	0.119053	+	0.992888i	$0.462014\pi$
$947$	−24.6291	+	42.6589i	−0.800339	+	1.38623i	−0.919393	+	0.393341i	$0.871319\pi$
$948$	0.232499	+	0.931111i	0.00755123	+	0.0302411i
$949$	11.9320	+	20.6669i	0.387330	+	0.670875i
$950$	−9.09930	+	1.70323i	−0.295220	+	0.0552599i
$951$	16.8456	+	4.82399i	0.546255	+	0.156429i
$952$		0			0
$953$	10.2538			0.332154			0.166077	−	0.986113i	$-0.446890\pi$
$953$	10.2538			0.332154			0.166077	+	0.986113i	$0.446890\pi$
$954$	45.0239	−	23.9802i	1.45770	−	0.776388i
$955$	−21.8563	−	18.1448i	−0.707252	−	0.587150i
$956$	0.732331	−	0.422811i	0.0236853	−	0.0136747i
$957$	15.9379	−	15.4018i	0.515198	−	0.497870i
$958$	−42.3131			−1.36708
$959$		0			0
$960$	1.89738	+	25.1104i	0.0612377	+	0.810435i
$961$	−10.4547	+	18.1081i	−0.337250	+	0.584134i
$962$	−35.6323	+	20.5723i	−1.14883	+	0.663278i
$963$	−0.398721	+	11.6525i	−0.0128486	+	0.375498i
$964$	6.64460	+	3.83626i	0.214008	+	0.123558i
$965$	−43.6621	+	16.1520i	−1.40553	+	0.519951i
$966$		0			0
$967$		−	4.62632i		−	0.148772i	−0.997230	−	0.0743862i	$-0.976300\pi$
$967$		−	4.62632i		−	0.148772i	0.997230	−	0.0743862i	$-0.0236998\pi$
$968$	8.24799	−	14.2859i	0.265101	−	0.459168i
$969$	1.83477	+	7.34786i	0.0589412	+	0.236047i
$970$	−2.86835	+	3.45507i	−0.0920971	+	0.110936i
$971$	−12.6443	+	21.9006i	−0.405775	+	0.702822i	−0.994411	−	0.105575i	$-0.966332\pi$
$971$	−12.6443	+	21.9006i	−0.405775	+	0.702822i	0.588637	+	0.808398i	$0.299665\pi$
$972$	0.804521	+	4.51628i	0.0258050	+	0.144860i
$973$		0			0
$974$			56.4119i			1.80755i
$975$	2.82538	−	30.0134i	0.0904847	−	0.961198i
$976$	13.2510	−	7.65046i	0.424154	−	0.244885i
$977$	12.0549	+	20.8797i	0.385670	+	0.668000i	0.991862	−	0.127318i	$-0.0406370\pi$
$977$	12.0549	+	20.8797i	0.385670	+	0.668000i	−0.606192	+	0.795318i	$0.707304\pi$
$978$	−7.42133	−	7.67961i	−0.237308	−	0.245567i
$979$			3.82381i			0.122210i
$980$		0			0
$981$	13.2549	+	8.26964i	0.423196	+	0.264029i
$982$	−7.74688	−	4.47267i	−0.247213	−	0.142728i
$983$	−41.6456	+	24.0441i	−1.32829	+	0.766888i	−0.985035	−	0.172354i	$-0.944863\pi$
$983$	−41.6456	+	24.0441i	−1.32829	+	0.766888i	−0.343254	+	0.939243i	$0.611529\pi$
$984$	12.8669	+	51.5291i	0.410181	+	1.64269i
$985$	−4.92541	−	0.841825i	−0.156937	−	0.0268228i
$986$	32.2739			1.02781
$987$		0			0
$988$		−	1.25214i		−	0.0398360i
$989$	−3.92601	−	2.26668i	−0.124840	−	0.0720764i
$990$	6.86892	+	20.7196i	0.218309	+	0.658513i
$991$	−14.8587	−	25.7361i	−0.472003	−	0.817534i	0.527483	−	0.849565i	$-0.323136\pi$
$991$	−14.8587	−	25.7361i	−0.472003	−	0.817534i	−0.999487	+	0.0320314i	$0.989802\pi$
$992$	−4.54406	−	2.62352i	−0.144274	−	0.0832967i
$993$	32.0960	+	9.19119i	1.01854	+	0.291674i
$994$		0			0
$995$	−52.2656	+	19.3347i	−1.65693	+	0.612952i
$996$	−3.22496	−	3.33720i	−0.102187	−	0.105743i
$997$	−13.3742	−	23.1647i	−0.423564	−	0.733634i	0.572721	−	0.819750i	$-0.305888\pi$
$997$	−13.3742	−	23.1647i	−0.423564	−	0.733634i	−0.996285	+	0.0861161i	$0.972554\pi$
$998$	14.1928	+	24.5826i	0.449265	+	0.778149i
$999$	8.47222	+	39.6532i	0.268049	+	1.25457i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.p.f.509.3		24
3.2	odd	2	inner	735.2.p.f.509.9		24
5.4	even	2	inner	735.2.p.f.509.10		24
7.2	even	3		735.2.g.b.734.20		24
7.3	odd	6	inner	735.2.p.f.374.4		24
7.4	even	3		105.2.p.a.59.3	✓	24
7.5	odd	6		735.2.g.b.734.17		24
7.6	odd	2		105.2.p.a.89.4	yes	24
15.14	odd	2	inner	735.2.p.f.509.4		24
21.2	odd	6		735.2.g.b.734.7		24
21.5	even	6		735.2.g.b.734.6		24
21.11	odd	6		105.2.p.a.59.9	yes	24
21.17	even	6	inner	735.2.p.f.374.10		24
21.20	even	2		105.2.p.a.89.10	yes	24
35.4	even	6		105.2.p.a.59.10	yes	24
35.9	even	6		735.2.g.b.734.5		24
35.13	even	4		525.2.t.j.26.9		24
35.18	odd	12		525.2.t.j.101.3		24
35.19	odd	6		735.2.g.b.734.8		24
35.24	odd	6	inner	735.2.p.f.374.9		24
35.27	even	4		525.2.t.j.26.4		24
35.32	odd	12		525.2.t.j.101.10		24
35.34	odd	2		105.2.p.a.89.9	yes	24
105.32	even	12		525.2.t.j.101.4		24
105.44	odd	6		735.2.g.b.734.18		24
105.53	even	12		525.2.t.j.101.9		24
105.59	even	6	inner	735.2.p.f.374.3		24
105.62	odd	4		525.2.t.j.26.10		24
105.74	odd	6		105.2.p.a.59.4	yes	24
105.83	odd	4		525.2.t.j.26.3		24
105.89	even	6		735.2.g.b.734.19		24
105.104	even	2		105.2.p.a.89.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.p.a.59.3	✓	24	7.4	even	3
105.2.p.a.59.4	yes	24	105.74	odd	6
105.2.p.a.59.9	yes	24	21.11	odd	6
105.2.p.a.59.10	yes	24	35.4	even	6
105.2.p.a.89.3	yes	24	105.104	even	2
105.2.p.a.89.4	yes	24	7.6	odd	2
105.2.p.a.89.9	yes	24	35.34	odd	2
105.2.p.a.89.10	yes	24	21.20	even	2
525.2.t.j.26.3		24	105.83	odd	4
525.2.t.j.26.4		24	35.27	even	4
525.2.t.j.26.9		24	35.13	even	4
525.2.t.j.26.10		24	105.62	odd	4
525.2.t.j.101.3		24	35.18	odd	12
525.2.t.j.101.4		24	105.32	even	12
525.2.t.j.101.9		24	105.53	even	12
525.2.t.j.101.10		24	35.32	odd	12
735.2.g.b.734.5		24	35.9	even	6
735.2.g.b.734.6		24	21.5	even	6
735.2.g.b.734.7		24	21.2	odd	6
735.2.g.b.734.8		24	35.19	odd	6
735.2.g.b.734.17		24	7.5	odd	6
735.2.g.b.734.18		24	105.44	odd	6
735.2.g.b.734.19		24	105.89	even	6
735.2.g.b.734.20		24	7.2	even	3
735.2.p.f.374.3		24	105.59	even	6	inner
735.2.p.f.374.4		24	7.3	odd	6	inner
735.2.p.f.374.9		24	35.24	odd	6	inner
735.2.p.f.374.10		24	21.17	even	6	inner
735.2.p.f.509.3		24	1.1	even	1	trivial
735.2.p.f.509.4		24	15.14	odd	2	inner
735.2.p.f.509.9		24	3.2	odd	2	inner
735.2.p.f.509.10		24	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.757344 + 1.31176i) q^{2} +(-0.419611 - 1.68045i) q^{3} +(-0.147140 - 0.254854i) q^{4} +(-2.20411 - 0.376714i) q^{5} +(2.52214 + 0.722254i) q^{6} -2.58363 q^{8} +(-2.64785 + 1.41027i) q^{9} +(2.16343 - 2.60595i) q^{10} +(1.86048 - 1.07415i) q^{11} +(-0.366529 + 0.354202i) q^{12} +3.48097 q^{13} +(0.291817 + 3.86197i) q^{15} +(2.25098 - 3.89881i) q^{16} +(-3.09793 + 1.78859i) q^{17} +(0.155396 - 4.54141i) q^{18} +(1.05858 + 0.611171i) q^{19} +(0.228305 + 0.617156i) q^{20} +3.25401i q^{22} +(0.757344 - 1.31176i) q^{23} +(1.08412 + 4.34168i) q^{24} +(4.71617 + 1.66064i) q^{25} +(-2.63629 + 4.56619i) q^{26} +(3.48097 + 3.85783i) q^{27} +5.95645i q^{29} +(-5.28698 - 2.54205i) q^{30} +(-2.75098 + 1.58828i) q^{31} +(0.825899 + 1.43050i) q^{32} +(-2.58574 - 2.67573i) q^{33} -5.41832i q^{34} +(0.749020 + 0.467309i) q^{36} +(6.75803 + 3.90175i) q^{37} +(-1.60342 + 0.925734i) q^{38} +(-1.46065 - 5.84961i) q^{39} +(5.69460 + 0.973292i) q^{40} +11.8685 q^{41} -2.99294i q^{43} +(-0.547504 - 0.316101i) q^{44} +(6.36742 - 2.11091i) q^{45} +(1.14714 + 1.98691i) q^{46} +(5.28420 + 3.05084i) q^{47} +(-7.49631 - 2.14668i) q^{48} +(-5.75012 + 4.92881i) q^{50} +(4.30557 + 4.45542i) q^{51} +(-0.512191 - 0.887140i) q^{52} +(5.61301 + 9.72202i) q^{53} +(-7.69683 + 1.64449i) q^{54} +(-4.50535 + 1.66667i) q^{55} +(0.582853 - 2.03535i) q^{57} +(-7.81342 - 4.51108i) q^{58} +(1.08467 + 1.87871i) q^{59} +(0.941303 - 0.642622i) q^{60} +(2.94338 + 1.69936i) q^{61} -4.81149i q^{62} +6.50196 q^{64} +(-7.67243 - 1.31133i) q^{65} +(5.46821 - 1.36542i) q^{66} +(-8.93534 + 5.15882i) q^{67} +(0.911660 + 0.526347i) q^{68} +(-2.52214 - 0.722254i) q^{69} -10.3968i q^{71} +(6.84108 - 3.64363i) q^{72} +(3.42779 + 5.93710i) q^{73} +(-10.2363 + 5.90993i) q^{74} +(0.811666 - 8.62213i) q^{75} -0.359711i q^{76} +(8.77950 + 2.51414i) q^{78} +(0.941421 - 1.63059i) q^{79} +(-6.43014 + 7.74542i) q^{80} +(5.02225 - 7.46840i) q^{81} +(-8.98853 + 15.5686i) q^{82} +9.10486i q^{83} +(7.50196 - 2.77521i) q^{85} +(3.92601 + 2.26668i) q^{86} +(10.0095 - 2.49939i) q^{87} +(-4.80681 + 2.77521i) q^{88} +(-0.889962 + 1.54146i) q^{89} +(-2.05332 + 9.95121i) q^{90} -0.445743 q^{92} +(3.82337 + 3.95644i) q^{93} +(-8.00392 + 4.62107i) q^{94} +(-2.10299 - 1.74587i) q^{95} +(2.05733 - 1.98814i) q^{96} -1.32584 q^{97} +(-3.41144 + 5.46799i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{4} - 6 q^{9} - 24 q^{15} - 12 q^{16} - 18 q^{24} - 12 q^{25} + 18 q^{30} + 84 q^{36} - 12 q^{39} + 72 q^{40} + 18 q^{45} + 36 q^{46} - 12 q^{51} + 36 q^{54} + 12 q^{60} - 36 q^{61} + 24 q^{64}+ \cdots - 48 q^{99}+O(q^{100}) \) 24 * q - 12 * q^4 - 6 * q^9 - 24 * q^15 - 12 * q^16 - 18 * q^24 - 12 * q^25 + 18 * q^30 + 84 * q^36 - 12 * q^39 + 72 * q^40 + 18 * q^45 + 36 * q^46 - 12 * q^51 + 36 * q^54 + 12 * q^60 - 36 * q^61 + 24 * q^64 + 72 * q^66 - 72 * q^75 + 48 * q^79 - 6 * q^81 + 48 * q^85 + 72 * q^94 + 90 * q^96 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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