LMFDB - Embedded newform 416.2.bf.a.53.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [416,2,Mod(53,416)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(416, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("416.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 416 = 2^{5} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	416.bf (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:	$3.32177672409$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			53.20
Character	$\chi$	$=$	416.53
Dual form			416.2.bf.a.157.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.493432 + 1.32534i) q^{2} +(1.01315 - 0.419661i) q^{3} +(-1.51305 - 1.30793i) q^{4} +(-1.26766 + 3.06041i) q^{5} +(0.0562725 + 1.54984i) q^{6} +(-0.757044 - 0.757044i) q^{7} +(2.48004 - 1.35993i) q^{8} +(-1.27096 + 1.27096i) q^{9} +O(q^{10})$	\(q+(-0.493432 + 1.32534i) q^{2} +(1.01315 - 0.419661i) q^{3} +(-1.51305 - 1.30793i) q^{4} +(-1.26766 + 3.06041i) q^{5} +(0.0562725 + 1.54984i) q^{6} +(-0.757044 - 0.757044i) q^{7} +(2.48004 - 1.35993i) q^{8} +(-1.27096 + 1.27096i) q^{9} +(-3.43058 - 3.19019i) q^{10} +(-5.35270 - 2.21716i) q^{11} +(-2.08183 - 0.690161i) q^{12} +(0.382683 + 0.923880i) q^{13} +(1.37689 - 0.629791i) q^{14} +3.63264i q^{15} +(0.578644 + 3.95793i) q^{16} +4.42274i q^{17} +(-1.05732 - 2.31159i) q^{18} +(-1.84901 - 4.46390i) q^{19} +(5.92084 - 2.97254i) q^{20} +(-1.08470 - 0.449298i) q^{21} +(5.57968 - 6.00013i) q^{22} +(-2.30995 + 2.30995i) q^{23} +(1.94194 - 2.41859i) q^{24} +(-4.22360 - 4.22360i) q^{25} +(-1.41328 + 0.0513142i) q^{26} +(-2.01328 + 4.86050i) q^{27} +(0.155286 + 2.13560i) q^{28} +(4.83456 - 2.00254i) q^{29} +(-4.81449 - 1.79246i) q^{30} -2.03351 q^{31} +(-5.53112 - 1.18606i) q^{32} -6.35355 q^{33} +(-5.86163 - 2.18232i) q^{34} +(3.27654 - 1.35719i) q^{35} +(3.58536 - 0.260702i) q^{36} +(-1.25821 + 3.03760i) q^{37} +(6.82854 - 0.247935i) q^{38} +(0.775432 + 0.775432i) q^{39} +(1.01810 + 9.31386i) q^{40} +(-7.20822 + 7.20822i) q^{41} +(1.13070 - 1.21590i) q^{42} +(-2.37002 - 0.981695i) q^{43} +(5.19902 + 10.3556i) q^{44} +(-2.27851 - 5.50081i) q^{45} +(-1.92166 - 4.20126i) q^{46} +3.59073i q^{47} +(2.24724 + 3.76714i) q^{48} -5.85377i q^{49} +(7.68176 - 3.51365i) q^{50} +(1.85605 + 4.48090i) q^{51} +(0.629349 - 1.89840i) q^{52} +(9.03605 + 3.74285i) q^{53} +(-5.44839 - 5.06661i) q^{54} +(13.5708 - 13.5708i) q^{55} +(-2.90702 - 0.847968i) q^{56} +(-3.74665 - 3.74665i) q^{57} +(0.268522 + 7.39555i) q^{58} +(1.81249 - 4.37573i) q^{59} +(4.75124 - 5.49637i) q^{60} +(4.32920 - 1.79321i) q^{61} +(1.00340 - 2.69509i) q^{62} +1.92435 q^{63} +(4.30117 - 6.74537i) q^{64} -3.31256 q^{65} +(3.13504 - 8.42061i) q^{66} +(6.15037 - 2.54757i) q^{67} +(5.78463 - 6.69183i) q^{68} +(-1.37093 + 3.30972i) q^{69} +(0.181986 + 5.01221i) q^{70} +(5.53830 + 5.53830i) q^{71} +(-1.42361 + 4.88045i) q^{72} +(-8.59523 + 8.59523i) q^{73} +(-3.40500 - 3.16641i) q^{74} +(-6.05162 - 2.50666i) q^{75} +(-3.04082 + 9.17248i) q^{76} +(2.37374 + 5.73071i) q^{77} +(-1.41033 + 0.645088i) q^{78} +7.19156i q^{79} +(-12.8464 - 3.24643i) q^{80} +0.377083i q^{81} +(-5.99658 - 13.1101i) q^{82} +(3.96324 + 9.56811i) q^{83} +(1.05356 + 2.09852i) q^{84} +(-13.5354 - 5.60654i) q^{85} +(2.47052 - 2.65668i) q^{86} +(4.05775 - 4.05775i) q^{87} +(-16.2901 + 1.78067i) q^{88} +(2.57613 + 2.57613i) q^{89} +(8.41473 - 0.305527i) q^{90} +(0.409709 - 0.989125i) q^{91} +(6.51631 - 0.473820i) q^{92} +(-2.06025 + 0.853384i) q^{93} +(-4.75894 - 1.77178i) q^{94} +16.0053 q^{95} +(-6.10160 + 1.11953i) q^{96} -4.78872 q^{97} +(7.75823 + 2.88843i) q^{98} +(9.62100 - 3.98515i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q+O(q^{10}) $ 192 * q	$ 192 q - 16 q^{10} - 16 q^{12} - 40 q^{16} - 40 q^{18} - 8 q^{22} - 16 q^{23} + 24 q^{24} + 80 q^{30} - 48 q^{31} - 48 q^{35} + 80 q^{36} - 56 q^{38} - 64 q^{40} - 16 q^{43} - 80 q^{44} + 24 q^{50} + 32 q^{51} - 32 q^{53} - 24 q^{54} + 32 q^{55} + 16 q^{56} - 64 q^{58} - 56 q^{60} - 64 q^{61} + 24 q^{62} + 80 q^{63} + 72 q^{64} + 96 q^{66} + 80 q^{67} - 32 q^{68} - 64 q^{69} - 120 q^{72} - 32 q^{74} + 32 q^{75} + 64 q^{76} - 32 q^{77} - 56 q^{80} - 80 q^{82} - 80 q^{83} + 112 q^{84} - 112 q^{87} - 88 q^{88} - 120 q^{90} + 144 q^{92} + 40 q^{94} + 136 q^{96} + 56 q^{98}+O(q^{100}) $ 192 * q - 16 * q^10 - 16 * q^12 - 40 * q^16 - 40 * q^18 - 8 * q^22 - 16 * q^23 + 24 * q^24 + 80 * q^30 - 48 * q^31 - 48 * q^35 + 80 * q^36 - 56 * q^38 - 64 * q^40 - 16 * q^43 - 80 * q^44 + 24 * q^50 + 32 * q^51 - 32 * q^53 - 24 * q^54 + 32 * q^55 + 16 * q^56 - 64 * q^58 - 56 * q^60 - 64 * q^61 + 24 * q^62 + 80 * q^63 + 72 * q^64 + 96 * q^66 + 80 * q^67 - 32 * q^68 - 64 * q^69 - 120 * q^72 - 32 * q^74 + 32 * q^75 + 64 * q^76 - 32 * q^77 - 56 * q^80 - 80 * q^82 - 80 * q^83 + 112 * q^84 - 112 * q^87 - 88 * q^88 - 120 * q^90 + 144 * q^92 + 40 * q^94 + 136 * q^96 + 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.493432	+	1.32534i	−0.348909	+	0.937157i
$2$	−0.493432	+	1.32534i	−0.348909	+	0.937157i
$3$	1.01315	−	0.419661i	0.584943	−	0.242291i	−0.0705305	−	0.997510i	$-0.522469\pi$
$3$	1.01315	−	0.419661i	0.584943	−	0.242291i	0.655473	+	0.755218i	$0.272469\pi$
$4$	−1.51305	−	1.30793i	−0.756525	−	0.653964i
$5$	−1.26766	+	3.06041i	−0.566916	+	1.36866i	0.337226	+	0.941424i	$0.390511\pi$
$5$	−1.26766	+	3.06041i	−0.566916	+	1.36866i	−0.904142	+	0.427233i	$0.859489\pi$
$6$	0.0562725	+	1.54984i	0.0229732	+	0.632721i
$7$	−0.757044	−	0.757044i	−0.286136	−	0.286136i	0.549414	−	0.835550i	$-0.314851\pi$
$7$	−0.757044	−	0.757044i	−0.286136	−	0.286136i	−0.835550	+	0.549414i	$0.814851\pi$
$8$	2.48004	−	1.35993i	0.876825	−	0.480809i
$9$	−1.27096	+	1.27096i	−0.423654	+	0.423654i
$10$	−3.43058	−	3.19019i	−1.08484	−	1.00883i
$11$	−5.35270	−	2.21716i	−1.61390	−	0.668499i	−0.620606	−	0.784122i	$-0.713113\pi$
$11$	−5.35270	−	2.21716i	−1.61390	−	0.668499i	−0.993293	+	0.115623i	$0.963113\pi$
$12$	−2.08183	−	0.690161i	−0.600974	−	0.199232i
$13$	0.382683	+	0.923880i	0.106137	+	0.256238i
$13$	0.382683	+	0.923880i	0.106137	+	0.256238i
$14$	1.37689	−	0.629791i	0.367989	−	0.168319i
$15$			3.63264i			0.937945i
$16$	0.578644	+	3.95793i	0.144661	+	0.989481i
$17$			4.42274i			1.07267i	0.844005	+	0.536336i	$0.180192\pi$
$17$			4.42274i			1.07267i	−0.844005	+	0.536336i	$0.819808\pi$
$18$	−1.05732	−	2.31159i	−0.249213	−	0.544846i
$19$	−1.84901	−	4.46390i	−0.424192	−	1.02409i	−0.981098	−	0.193514i	$-0.938012\pi$
$19$	−1.84901	−	4.46390i	−0.424192	−	1.02409i	0.556906	−	0.830576i	$-0.311988\pi$
$20$	5.92084	−	2.97254i	1.32394	−	0.664680i
$21$	−1.08470	−	0.449298i	−0.236701	−	0.0980448i
$22$	5.57968	−	6.00013i	1.18959	−	1.27923i
$23$	−2.30995	+	2.30995i	−0.481657	+	0.481657i	−0.905660	−	0.424004i	$-0.860624\pi$
$23$	−2.30995	+	2.30995i	−0.481657	+	0.481657i	0.424004	+	0.905660i	$0.360624\pi$
$24$	1.94194	−	2.41859i	0.396397	−	0.493693i
$25$	−4.22360	−	4.22360i	−0.844720	−	0.844720i
$26$	−1.41328	+	0.0513142i	−0.277167	+	0.0100635i
$27$	−2.01328	+	4.86050i	−0.387457	+	0.935404i
$28$	0.155286	+	2.13560i	0.0293463	+	0.403591i
$29$	4.83456	−	2.00254i	0.897755	−	0.371862i	0.114399	−	0.993435i	$-0.463506\pi$
$29$	4.83456	−	2.00254i	0.897755	−	0.371862i	0.783357	+	0.621573i	$0.213506\pi$
$30$	−4.81449	−	1.79246i	−0.879001	−	0.327257i
$31$	−2.03351			−0.365229			−0.182615	−	0.983185i	$-0.558456\pi$
$31$	−2.03351			−0.365229			−0.182615	+	0.983185i	$0.558456\pi$
$32$	−5.53112	−	1.18606i	−0.977773	−	0.209669i
$33$	−6.35355			−1.10601
$34$	−5.86163	−	2.18232i	−1.00526	−	0.374265i
$35$	3.27654	−	1.35719i	0.553836	−	0.229407i
$36$	3.58536	−	0.260702i	0.597559	−	0.0434503i
$37$	−1.25821	+	3.03760i	−0.206849	+	0.499378i	−0.992924	−	0.118754i	$-0.962110\pi$
$37$	−1.25821	+	3.03760i	−0.206849	+	0.499378i	0.786075	+	0.618132i	$0.212110\pi$
$38$	6.82854	−	0.247935i	1.10774	−	0.0402203i
$39$	0.775432	+	0.775432i	0.124168	+	0.124168i
$40$	1.01810	+	9.31386i	0.160976	+	1.47265i
$41$	−7.20822	+	7.20822i	−1.12573	+	1.12573i	−0.134872	+	0.990863i	$0.543062\pi$
$41$	−7.20822	+	7.20822i	−1.12573	+	1.12573i	−0.990863	+	0.134872i	$0.956938\pi$
$42$	1.13070	−	1.21590i	0.174470	−	0.187617i
$43$	−2.37002	−	0.981695i	−0.361425	−	0.149707i	0.194579	−	0.980887i	$-0.437666\pi$
$43$	−2.37002	−	0.981695i	−0.361425	−	0.149707i	−0.556004	+	0.831180i	$0.687666\pi$
$44$	5.19902	+	10.3556i	0.783781	+	1.56117i
$45$	−2.27851	−	5.50081i	−0.339660	−	0.820013i
$46$	−1.92166	−	4.20126i	−0.283334	−	0.619442i
$47$			3.59073i			0.523762i	0.965100	+	0.261881i	$0.0843428\pi$
$47$			3.59073i			0.523762i	−0.965100	+	0.261881i	$0.915657\pi$
$48$	2.24724	+	3.76714i	0.324361	+	0.543740i
$49$		−	5.85377i		−	0.836253i
$50$	7.68176	−	3.51365i	1.08637	−	0.496905i
$51$	1.85605	+	4.48090i	0.259899	+	0.627452i
$52$	0.629349	−	1.89840i	0.0872750	−	0.263261i
$53$	9.03605	+	3.74285i	1.24120	+	0.514121i	0.904089	−	0.427345i	$-0.140551\pi$
$53$	9.03605	+	3.74285i	1.24120	+	0.514121i	0.337108	+	0.941466i	$0.390551\pi$
$54$	−5.44839	−	5.06661i	−0.741433	−	0.689478i
$55$	13.5708	−	13.5708i	1.82989	−	1.82989i
$56$	−2.90702	−	0.847968i	−0.388468	−	0.113314i
$57$	−3.74665	−	3.74665i	−0.496256	−	0.496256i
$58$	0.268522	+	7.39555i	0.0352586	+	0.971083i
$59$	1.81249	−	4.37573i	0.235966	−	0.569672i	−0.760893	−	0.648878i	$-0.775239\pi$
$59$	1.81249	−	4.37573i	0.235966	−	0.569672i	0.996858	+	0.0792063i	$0.0252386\pi$
$60$	4.75124	−	5.49637i	0.613382	−	0.709579i
$61$	4.32920	−	1.79321i	0.554297	−	0.229597i	−0.0879103	−	0.996128i	$-0.528019\pi$
$61$	4.32920	−	1.79321i	0.554297	−	0.229597i	0.642207	+	0.766531i	$0.278019\pi$
$62$	1.00340	−	2.69509i	0.127432	−	0.342277i
$63$	1.92435			0.242445
$64$	4.30117	−	6.74537i	0.537646	−	0.843171i
$65$	−3.31256			−0.410873
$66$	3.13504	−	8.42061i	0.385897	−	1.03650i
$67$	6.15037	−	2.54757i	0.751387	−	0.311235i	0.0260796	−	0.999660i	$-0.491698\pi$
$67$	6.15037	−	2.54757i	0.751387	−	0.311235i	0.725307	+	0.688425i	$0.241698\pi$
$68$	5.78463	−	6.69183i	0.701489	−	0.811503i
$69$	−1.37093	+	3.30972i	−0.165040	+	0.398443i
$70$	0.181986	+	5.01221i	0.0217515	+	0.599073i
$71$	5.53830	+	5.53830i	0.657275	+	0.657275i	0.954735	−	0.297459i	$-0.0961392\pi$
$71$	5.53830	+	5.53830i	0.657275	+	0.657275i	−0.297459	+	0.954735i	$0.596139\pi$
$72$	−1.42361	+	4.88045i	−0.167774	+	0.575167i
$73$	−8.59523	+	8.59523i	−1.00600	+	1.00600i	−0.00601359	+	0.999982i	$0.501914\pi$
$73$	−8.59523	+	8.59523i	−1.00600	+	1.00600i	−0.999982	+	0.00601359i	$0.998086\pi$
$74$	−3.40500	−	3.16641i	−0.395824	−	0.368087i
$75$	−6.05162	−	2.50666i	−0.698781	−	0.289445i
$76$	−3.04082	+	9.17248i	−0.348806	+	1.05216i
$77$	2.37374	+	5.73071i	0.270513	+	0.653076i
$78$	−1.41033	+	0.645088i	−0.159689	+	0.0730418i
$79$			7.19156i			0.809113i	0.914513	+	0.404557i	$0.132574\pi$
$79$			7.19156i			0.809113i	−0.914513	+	0.404557i	$0.867426\pi$
$80$	−12.8464	−	3.24643i	−1.43627	−	0.362962i
$81$			0.377083i			0.0418981i
$82$	−5.99658	−	13.1101i	−0.662211	−	1.44777i
$83$	3.96324	+	9.56811i	0.435022	+	1.05024i	0.977645	+	0.210260i	$0.0674311\pi$
$83$	3.96324	+	9.56811i	0.435022	+	1.05024i	−0.542623	+	0.839976i	$0.682569\pi$
$84$	1.05356	+	2.09852i	0.114953	+	0.228968i
$85$	−13.5354	−	5.60654i	−1.46812	−	0.608115i
$86$	2.47052	−	2.65668i	0.266403	−	0.286478i
$87$	4.05775	−	4.05775i	0.435036	−	0.435036i
$88$	−16.2901	+	1.78067i	−1.73653	+	0.189820i
$89$	2.57613	+	2.57613i	0.273069	+	0.273069i	0.830334	−	0.557265i	$-0.188149\pi$
$89$	2.57613	+	2.57613i	0.273069	+	0.273069i	−0.557265	+	0.830334i	$0.688149\pi$
$90$	8.41473	−	0.305527i	0.886991	−	0.0322054i
$91$	0.409709	−	0.989125i	0.0429492	−	0.103689i
$92$	6.51631	−	0.473820i	0.679372	−	0.0493991i
$93$	−2.06025	+	0.853384i	−0.213638	+	0.0884918i
$94$	−4.75894	−	1.77178i	−0.490847	−	0.182745i
$95$	16.0053			1.64211
$96$	−6.10160	+	1.11953i	−0.622742	+	0.114262i
$97$	−4.78872			−0.486221			−0.243111	−	0.969999i	$-0.578168\pi$
$97$	−4.78872			−0.486221			−0.243111	+	0.969999i	$0.578168\pi$
$98$	7.75823	+	2.88843i	0.783700	+	0.291776i
$99$	9.62100	−	3.98515i	0.966947	−	0.400522i
$100$	0.866352	+	11.9147i	0.0866352	+	1.19147i
$101$	1.33974	−	3.23443i	0.133309	−	0.321837i	−0.843103	−	0.537753i	$-0.819273\pi$
$101$	1.33974	−	3.23443i	0.133309	−	0.321837i	0.976412	+	0.215915i	$0.0692735\pi$
$102$	−6.85455	+	0.248879i	−0.678702	+	0.0246427i
$103$	11.8356	+	11.8356i	1.16620	+	1.16620i	0.983093	+	0.183107i	$0.0586155\pi$
$103$	11.8356	+	11.8356i	1.16620	+	1.16620i	0.183107	+	0.983093i	$0.441385\pi$
$104$	2.20548	+	1.77083i	0.216265	+	0.173644i
$105$	2.75007	−	2.75007i	0.268379	−	0.268379i
$106$	−9.41923	+	10.1290i	−0.914876	+	0.983815i
$107$	−8.77157	−	3.63330i	−0.847980	−	0.351245i	−0.0839851	−	0.996467i	$-0.526765\pi$
$107$	−8.77157	−	3.63330i	−0.847980	−	0.351245i	−0.763995	+	0.645222i	$0.776765\pi$
$108$	9.40339	−	4.72095i	0.904842	−	0.454273i
$109$	−2.01178	−	4.85687i	−0.192694	−	0.465203i	0.797773	−	0.602958i	$-0.206011\pi$
$109$	−2.01178	−	4.85687i	−0.192694	−	0.465203i	−0.990466	+	0.137755i	$0.956011\pi$
$110$	11.2897	+	24.6822i	1.07643	+	2.35336i
$111$			3.60557i			0.342225i
$112$	2.55826	−	3.43438i	0.241733	−	0.324519i
$113$			13.1503i			1.23708i	0.785755	+	0.618538i	$0.212275\pi$
$113$			13.1503i			1.23708i	−0.785755	+	0.618538i	$0.787725\pi$
$114$	6.81429	−	3.11687i	0.638217	−	0.291921i
$115$	−4.14115	−	9.99761i	−0.386164	−	0.932282i
$116$	−9.93411	−	3.29332i	−0.922359	−	0.305777i
$117$	−1.66059	−	0.687839i	−0.153522	−	0.0635908i
$118$	4.90499	+	4.56128i	0.451541	+	0.419900i
$119$	3.34821	−	3.34821i	0.306930	−	0.306930i
$120$	4.94015	+	9.00909i	0.450972	+	0.822414i
$121$	15.9574	+	15.9574i	1.45067	+	1.45067i
$122$	0.240453	+	6.62248i	0.0217696	+	0.599571i
$123$	−4.27801	+	10.3280i	−0.385735	+	0.931246i
$124$	3.07680	+	2.65969i	0.276305	+	0.238847i
$125$	2.97800	−	1.23353i	0.266361	−	0.110330i
$126$	−0.949533	+	2.55041i	−0.0845912	+	0.227209i
$127$	9.39372			0.833558			0.416779	−	0.909008i	$-0.363159\pi$
$127$	9.39372			0.833558			0.416779	+	0.909008i	$0.363159\pi$
$128$	6.81757	+	9.02888i	0.602594	+	0.798048i
$129$	−2.81317			−0.247686
$130$	1.63452	−	4.39027i	0.143357	−	0.385052i
$131$	−2.76958	+	1.14720i	−0.241979	+	0.100231i	−0.500377	−	0.865807i	$-0.666805\pi$
$131$	−2.76958	+	1.14720i	−0.241979	+	0.100231i	0.258398	+	0.966039i	$0.416805\pi$
$132$	9.61324	+	8.30999i	0.836725	+	0.723291i
$133$	−1.97959	+	4.77915i	−0.171652	+	0.414405i
$134$	0.341604	+	9.40837i	0.0295101	+	0.812760i
$135$	−12.3230	−	12.3230i	−1.06059	−	1.06059i
$136$	6.01463	+	10.9686i	0.515750	+	0.940546i
$137$	16.0912	−	16.0912i	1.37476	−	1.37476i	0.521533	−	0.853231i	$-0.325360\pi$
$137$	16.0912	−	16.0912i	1.37476	−	1.37476i	0.853231	−	0.521533i	$-0.174640\pi$
$138$	−3.71004	−	3.45006i	−0.315819	−	0.293689i
$139$	−13.7848	−	5.70987i	−1.16921	−	0.484305i	−0.288282	−	0.957546i	$-0.593084\pi$
$139$	−13.7848	−	5.70987i	−1.16921	−	0.484305i	−0.880933	+	0.473241i	$0.843084\pi$
$140$	−6.73267	−	2.23199i	−0.569015	−	0.188637i
$141$	1.50689	+	3.63795i	0.126903	+	0.306371i
$142$	−10.0729	+	4.60736i	−0.845299	+	0.386641i
$143$		−	5.79372i		−	0.484495i
$144$	−5.76580	−	4.29494i	−0.480484	−	0.357911i
$145$			17.3343i			1.43953i
$146$	−7.15044	−	15.6328i	−0.591775	−	1.29378i
$147$	−2.45660	−	5.93075i	−0.202617	−	0.489160i
$148$	5.87670	−	2.95038i	0.483062	−	0.242520i
$149$	−8.05770	−	3.33761i	−0.660113	−	0.273428i	0.0273733	−	0.999625i	$-0.491286\pi$
$149$	−8.05770	−	3.33761i	−0.660113	−	0.273428i	−0.687486	+	0.726198i	$0.741286\pi$
$150$	6.30824	−	6.78359i	0.515066	−	0.553878i
$151$	−9.53466	+	9.53466i	−0.775920	+	0.775920i	−0.979134	−	0.203214i	$-0.934861\pi$
$151$	−9.53466	+	9.53466i	−0.775920	+	0.775920i	0.203214	+	0.979134i	$0.434861\pi$
$152$	−10.6562	−	8.55611i	−0.864333	−	0.693992i
$153$	−5.62113	−	5.62113i	−0.454442	−	0.454442i
$154$	−8.76642	+	0.318296i	−0.706418	+	0.0256490i
$155$	2.57780	−	6.22337i	0.207054	−	0.499873i
$156$	−0.159058	−	2.18748i	−0.0127348	−	0.175138i
$157$	−14.2743	+	5.91261i	−1.13921	+	0.471878i	−0.870903	−	0.491455i	$-0.836465\pi$
$157$	−14.2743	+	5.91261i	−1.13921	+	0.471878i	−0.268311	+	0.963332i	$0.586465\pi$
$158$	−9.53125	−	3.54854i	−0.758266	−	0.282307i
$159$	10.7256			0.850596
$160$	10.6414	−	15.4239i	0.841279	−	1.21937i
$161$	3.49746			0.275638
$162$	−0.499763	−	0.186064i	−0.0392651	−	0.0146186i
$163$	11.5754	−	4.79470i	0.906658	−	0.375550i	0.119881	−	0.992788i	$-0.461749\pi$
$163$	11.5754	−	4.79470i	0.906658	−	0.375550i	0.786776	+	0.617238i	$0.211749\pi$
$164$	20.3342	−	1.47856i	1.58784	−	0.115456i
$165$	8.05415	−	19.4444i	0.627015	−	1.51375i
$166$	−14.6366	+	0.531433i	−1.13602	+	0.0412472i
$167$	−12.8544	−	12.8544i	−0.994704	−	0.994704i	0.00528239	−	0.999986i	$-0.498319\pi$
$167$	−12.8544	−	12.8544i	−0.994704	−	0.994704i	−0.999986	+	0.00528239i	$0.998319\pi$
$168$	−3.30111	+	0.360845i	−0.254686	+	0.0278398i
$169$	−0.707107	+	0.707107i	−0.0543928	+	0.0543928i
$170$	14.1094	−	15.1725i	1.08214	−	1.16368i
$171$	8.02346	+	3.32343i	0.613570	+	0.254149i
$172$	2.30198	+	4.58517i	0.175524	+	0.349616i
$173$	−6.94880	−	16.7759i	−0.528308	−	1.27545i	−0.932631	−	0.360831i	$-0.882493\pi$
$173$	−6.94880	−	16.7759i	−0.528308	−	1.27545i	0.404323	−	0.914616i	$-0.367507\pi$
$174$	3.37567	+	7.38012i	0.255909	+	0.559485i
$175$			6.39490i			0.483409i
$176$	5.67805	−	22.4685i	0.427999	−	1.69363i
$177$		−	5.19390i		−	0.390398i
$178$	−4.68539	+	2.14310i	−0.351185	+	0.160632i
$179$	8.15746	+	19.6939i	0.609717	+	1.47199i	0.863308	+	0.504677i	$0.168388\pi$
$179$	8.15746	+	19.6939i	0.609717	+	1.47199i	−0.253591	+	0.967312i	$0.581612\pi$
$180$	−3.74717	+	11.3031i	−0.279297	+	0.842486i
$181$	15.1966	+	6.29465i	1.12956	+	0.467877i	0.867630	−	0.497211i	$-0.165642\pi$
$181$	15.1966	+	6.29465i	1.12956	+	0.467877i	0.261926	+	0.965088i	$0.415642\pi$
$182$	1.10876	+	1.03107i	0.0821870	+	0.0764279i
$183$	3.63359	−	3.63359i	0.268603	−	0.268603i
$184$	−2.58738	+	8.87012i	−0.190744	+	0.653914i
$185$	−7.70130	−	7.70130i	−0.566211	−	0.566211i
$186$	−0.114431	−	3.15162i	−0.00839047	−	0.231088i
$187$	9.80592	−	23.6736i	0.717080	−	1.73118i
$188$	4.69642	−	5.43296i	0.342522	−	0.396239i
$189$	5.20376	−	2.15547i	0.378518	−	0.156787i
$190$	−7.89751	+	21.2124i	−0.572946	+	1.53891i
$191$	−25.8065			−1.86730			−0.933648	−	0.358191i	$-0.883394\pi$
$191$	−25.8065			−1.86730			−0.933648	+	0.358191i	$0.883394\pi$
$192$	1.52696	−	8.63910i	0.110199	−	0.623474i
$193$	−17.3084			−1.24588			−0.622942	−	0.782268i	$-0.714063\pi$
$193$	−17.3084			−1.24588			−0.622942	+	0.782268i	$0.714063\pi$
$194$	2.36291	−	6.34669i	0.169647	−	0.455665i
$195$	−3.35613	+	1.39015i	−0.240337	+	0.0995509i
$196$	−7.65631	+	8.85705i	−0.546880	+	0.632646i
$197$	5.07851	−	12.2606i	0.361829	−	0.873532i	−0.633204	−	0.773985i	$-0.718261\pi$
$197$	5.07851	−	12.2606i	0.361829	−	0.873532i	0.995033	−	0.0995472i	$-0.0317394\pi$
$198$	0.534371	+	14.7175i	0.0379761	+	1.04593i
$199$	−3.02689	−	3.02689i	−0.214571	−	0.214571i	0.591635	−	0.806206i	$-0.298483\pi$
$199$	−3.02689	−	3.02689i	−0.214571	−	0.214571i	−0.806206	+	0.591635i	$0.798483\pi$
$200$	−16.2185	−	4.73087i	−1.14682	−	0.334523i
$201$	5.16213	−	5.16213i	0.364109	−	0.364109i
$202$	3.62564	+	3.37158i	0.255099	+	0.237224i
$203$	−5.17598	−	2.14396i	−0.363283	−	0.150477i
$204$	3.05240	−	9.20741i	0.213711	−	0.644648i
$205$	−12.9225	−	31.1977i	−0.902547	−	2.17894i
$206$	−21.5263	+	9.84616i	−1.49981	+	0.686015i
$207$		−	5.87170i		−	0.408111i
$208$	−3.43521	+	2.04923i	−0.238189	+	0.142089i
$209$			27.9935i			1.93635i
$210$	2.28781	+	5.00175i	0.157874	+	0.345153i
$211$	−7.63088	−	18.4226i	−0.525331	−	1.26826i	−0.934552	−	0.355827i	$-0.884199\pi$
$211$	−7.63088	−	18.4226i	−0.525331	−	1.26826i	0.409220	−	0.912436i	$-0.365801\pi$
$212$	−8.77661	−	17.4816i	−0.602780	−	1.20064i
$213$	7.93534	+	3.28693i	0.543721	+	0.225216i
$214$	9.14353	−	9.83253i	0.625039	−	0.672138i
$215$	6.00878	−	6.00878i	0.409795	−	0.409795i
$216$	1.61693	+	14.7922i	0.110018	+	1.00648i
$217$	1.53946	+	1.53946i	0.104505	+	0.104505i
$218$	7.42967	−	0.269761i	0.503201	−	0.0182705i
$219$	−5.10118	+	12.3153i	−0.344706	+	0.832194i
$220$	−38.2831	+	2.78367i	−2.58104	+	0.187675i
$221$	−4.08608	+	1.69251i	−0.274859	+	0.113850i
$222$	−4.77860	−	1.77910i	−0.320719	−	0.119405i
$223$	12.4665			0.834818			0.417409	−	0.908719i	$-0.362938\pi$
$223$	12.4665			0.834818			0.417409	+	0.908719i	$0.362938\pi$
$224$	3.28939	+	5.08520i	0.219782	+	0.339769i
$225$	10.7361			0.715738
$226$	−17.4286	−	6.48877i	−1.15933	−	0.431627i
$227$	−16.8253	+	6.96925i	−1.11673	+	0.462565i	−0.863251	−	0.504775i	$-0.831575\pi$
$227$	−16.8253	+	6.96925i	−1.11673	+	0.462565i	−0.253481	+	0.967340i	$0.581575\pi$
$228$	0.768519	+	10.5692i	0.0508964	+	0.699963i
$229$	−6.19266	+	14.9504i	−0.409222	+	0.987950i	0.576120	+	0.817365i	$0.304566\pi$
$229$	−6.19266	+	14.9504i	−0.409222	+	0.987950i	−0.985343	+	0.170586i	$0.945434\pi$
$230$	15.2936	−	0.555288i	1.00843	−	0.0366146i
$231$	4.80991	+	4.80991i	0.316469	+	0.316469i
$232$	9.26657	−	11.5410i	0.608380	−	0.757707i
$233$	15.4887	−	15.4887i	1.01470	−	1.01470i	0.0148065	−	0.999890i	$-0.495287\pi$
$233$	15.4887	−	15.4887i	1.01470	−	1.01470i	0.999890	−	0.0148065i	$-0.00471322\pi$
$234$	1.73101	−	1.86145i	0.113160	−	0.121686i
$235$	−10.9891	−	4.55184i	−0.716850	−	0.296929i
$236$	−8.46553	+	4.25010i	−0.551059	+	0.276658i
$237$	3.01801	+	7.28613i	0.196041	+	0.473285i
$238$	2.78540	+	6.08962i	0.180551	+	0.394732i
$239$			3.54698i			0.229435i	0.993398	+	0.114718i	$0.0365963\pi$
$239$			3.54698i			0.229435i	−0.993398	+	0.114718i	$0.963404\pi$
$240$	−14.3777	+	2.10201i	−0.928079	+	0.135684i
$241$		−	13.0662i		−	0.841666i	−0.907138	−	0.420833i	$-0.861738\pi$
$241$		−	13.0662i		−	0.841666i	0.907138	−	0.420833i	$-0.138262\pi$
$242$	−29.0229	+	13.2751i	−1.86566	+	0.853356i
$243$	−5.88161	−	14.1995i	−0.377305	−	0.910896i
$244$	−8.89569	−	2.94906i	−0.569488	−	0.188794i
$245$	17.9149	+	7.42061i	1.14454	+	0.474085i
$246$	−11.5772	−	10.7660i	−0.738137	−	0.686414i
$247$	3.41652	−	3.41652i	0.217388	−	0.217388i
$248$	−5.04318	+	2.76544i	−0.320242	+	0.175605i
$249$	8.03072	+	8.03072i	0.508926	+	0.508926i
$250$	0.165405	+	4.55553i	0.0104611	+	0.288117i
$251$	3.31521	−	8.00362i	0.209254	−	0.505184i	−0.784052	−	0.620695i	$-0.786851\pi$
$251$	3.31521	−	8.00362i	0.209254	−	0.505184i	0.993306	+	0.115511i	$0.0368506\pi$
$252$	−2.91163	−	2.51691i	−0.183416	−	0.158550i
$253$	17.4860	−	7.24292i	1.09933	−	0.455359i
$254$	−4.63516	+	12.4499i	−0.290836	+	0.781174i
$255$	−16.0662			−1.00611
$256$	−15.3303	+	4.58046i	−0.958146	+	0.286279i
$257$	−6.96033			−0.434174			−0.217087	−	0.976152i	$-0.569655\pi$
$257$	−6.96033			−0.434174			−0.217087	+	0.976152i	$0.569655\pi$
$258$	1.38811	−	3.72840i	0.0864197	−	0.232120i
$259$	3.25212	−	1.34707i	0.202077	−	0.0837029i
$260$	5.01208	+	4.33260i	0.310836	+	0.268696i
$261$	−3.59939	+	8.68969i	−0.222796	+	0.537878i
$262$	−0.153828	−	4.23670i	−0.00950355	−	0.261744i
$263$	15.2113	+	15.2113i	0.937968	+	0.937968i	0.998185	−	0.0602174i	$-0.0191794\pi$
$263$	15.2113	+	15.2113i	0.937968	+	0.937968i	−0.0602174	+	0.998185i	$0.519179\pi$
$264$	−15.7570	+	8.64039i	−0.969778	+	0.531780i
$265$	−22.9093	+	22.9093i	−1.40731	+	1.40731i
$266$	−5.35720	−	4.98181i	−0.328471	−	0.305454i
$267$	3.69111	+	1.52891i	0.225892	+	0.0935675i
$268$	−12.6379	−	4.18965i	−0.771980	−	0.255923i
$269$	−10.3363	−	24.9541i	−0.630216	−	1.52148i	−0.839351	−	0.543590i	$-0.817065\pi$
$269$	−10.3363	−	24.9541i	−0.630216	−	1.52148i	0.209135	−	0.977887i	$-0.432935\pi$
$270$	22.4126	−	10.2516i	1.36399	−	0.623890i
$271$			0.561795i			0.0341266i	0.999854	+	0.0170633i	$0.00543168\pi$
$271$			0.561795i			0.0341266i	−0.999854	+	0.0170633i	$0.994568\pi$
$272$	−17.5049	+	2.55919i	−1.06139	+	0.155174i
$273$		−	1.17407i		−	0.0710581i
$274$	13.3864	+	29.2662i	0.808702	+	1.76804i
$275$	13.2433	+	31.9721i	0.798599	+	1.92799i
$276$	6.40316	−	3.21469i	0.385425	−	0.193502i
$277$	21.0765	+	8.73017i	1.26636	+	0.524545i	0.911857	−	0.410509i	$-0.134649\pi$
$277$	21.0765	+	8.73017i	1.26636	+	0.524545i	0.354507	+	0.935054i	$0.384649\pi$
$278$	14.3694	−	15.4522i	0.861818	−	0.926759i
$279$	2.58451	−	2.58451i	0.154731	−	0.154731i
$280$	6.28026	−	7.82175i	0.375317	−	0.467439i
$281$	10.6371	+	10.6371i	0.634557	+	0.634557i	0.949207	−	0.314651i	$-0.101887\pi$
$281$	10.6371	+	10.6371i	0.634557	+	0.634557i	−0.314651	+	0.949207i	$0.601887\pi$
$282$	−5.56507	+	0.202060i	−0.331395	+	0.0120325i
$283$	−5.95342	+	14.3728i	−0.353894	+	0.854376i	0.642238	+	0.766505i	$0.278006\pi$
$283$	−5.95342	+	14.3728i	−0.353894	+	0.854376i	−0.996132	+	0.0878703i	$0.971994\pi$
$284$	−1.13603	−	15.6234i	−0.0674107	−	0.927080i
$285$	16.2158	−	6.71679i	0.960539	−	0.397868i
$286$	7.67865	+	2.85880i	0.454048	+	0.169045i
$287$	10.9139			0.644226
$288$	8.53728	−	5.52239i	0.503064	−	0.325410i
$289$	−2.56063			−0.150625
$290$	−22.9738	−	8.55328i	−1.34907	−	0.502266i
$291$	−4.85170	+	2.00964i	−0.284412	+	0.117807i
$292$	24.2470	−	1.76307i	1.41895	−	0.103176i
$293$	1.01155	−	2.44210i	0.0590953	−	0.142669i	−0.891574	−	0.452875i	$-0.850398\pi$
$293$	1.01155	−	2.44210i	0.0590953	−	0.142669i	0.950669	+	0.310207i	$0.100398\pi$
$294$	9.07242	−	0.329406i	0.529114	−	0.0192114i
$295$	11.0939	+	11.0939i	0.645912	+	0.645912i
$296$	1.01051	+	9.24444i	0.0587347	+	0.537322i
$297$	21.5530	−	21.5530i	1.25063	−	1.25063i
$298$	8.39939	−	9.03231i	0.486564	−	0.523228i
$299$	−3.01809	−	1.25013i	−0.174541	−	0.0722971i
$300$	5.87787	+	11.7078i	0.339359	+	0.675950i
$301$	1.05102	+	2.53740i	0.0605800	+	0.146253i
$302$	−7.93196	−	17.3414i	−0.456433	−	0.997884i
$303$		−	3.83920i		−	0.220556i
$304$	16.5979	−	9.90125i	0.951953	−	0.567875i
$305$			15.5223i			0.888804i
$306$	10.2236	−	4.67626i	0.584442	−	0.267324i
$307$	−7.85856	−	18.9722i	−0.448512	−	1.08280i	−0.972880	−	0.231311i	$-0.925698\pi$
$307$	−7.85856	−	18.9722i	−0.448512	−	1.08280i	0.524368	−	0.851492i	$-0.324302\pi$
$308$	3.90378	−	11.7755i	0.222438	−	0.670974i
$309$	16.9582	+	7.02433i	0.964720	+	0.399600i
$310$	6.97611	+	6.48727i	0.396216	+	0.368452i
$311$	−20.1824	+	20.1824i	−1.14444	+	1.14444i	−0.156812	+	0.987628i	$0.550122\pi$
$311$	−20.1824	+	20.1824i	−1.14444	+	1.14444i	−0.987628	+	0.156812i	$0.949878\pi$
$312$	2.97763	+	0.868565i	0.168575	+	0.0491728i
$313$	−16.1542	−	16.1542i	−0.913087	−	0.913087i	0.0834267	−	0.996514i	$-0.473414\pi$
$313$	−16.1542	−	16.1542i	−0.913087	−	0.913087i	−0.996514	+	0.0834267i	$0.973414\pi$
$314$	−0.792825	−	21.8358i	−0.0447417	−	1.23226i
$315$	−2.43942	+	5.88929i	−0.137446	+	0.331824i
$316$	9.40604	−	10.8812i	0.529131	−	0.612115i
$317$	1.18816	−	0.492153i	0.0667338	−	0.0276421i	−0.349067	−	0.937098i	$-0.613501\pi$
$317$	1.18816	−	0.492153i	0.0667338	−	0.0276421i	0.415801	+	0.909456i	$0.363501\pi$
$318$	−5.29235	+	14.2151i	−0.296780	+	0.797142i
$319$	−30.3179			−1.69748
$320$	15.1912	+	21.7142i	0.849211	+	1.21386i
$321$	−10.4117			−0.581123
$322$	−1.72576	+	4.63532i	−0.0961727	+	0.258316i
$323$	19.7427	−	8.17768i	1.09851	−	0.455018i
$324$	0.493197	−	0.570545i	0.0273999	−	0.0316970i
$325$	2.28580	−	5.51840i	0.126793	−	0.306106i
$326$	0.642924	+	17.7072i	0.0356083	+	0.980713i
$327$	−4.07647	−	4.07647i	−0.225429	−	0.225429i
$328$	−8.07396	+	27.6793i	−0.445810	+	1.52834i
$329$	2.71834	−	2.71834i	0.149867	−	0.149867i
$330$	21.7963	+	20.2690i	1.19985	+	1.11577i
$331$	−10.8868	−	4.50946i	−0.598392	−	0.247862i	0.0628642	−	0.998022i	$-0.479977\pi$
$331$	−10.8868	−	4.50946i	−0.598392	−	0.247862i	−0.661256	+	0.750160i	$0.729977\pi$
$332$	6.51782	−	19.6607i	0.357712	−	1.07902i
$333$	−2.26153	−	5.45981i	−0.123931	−	0.299196i
$334$	23.3792	−	10.6937i	1.27925	−	0.585132i
$335$			22.0521i			1.20483i
$336$	1.15063	−	4.55315i	0.0627721	−	0.248395i
$337$		−	21.0302i		−	1.14559i	−0.819699	−	0.572795i	$-0.805859\pi$
$337$		−	21.0302i		−	1.14559i	0.819699	−	0.572795i	$-0.194141\pi$
$338$	−0.588248	−	1.28607i	−0.0319965	−	0.0699527i
$339$	5.51866	+	13.3232i	0.299733	+	0.723618i
$340$	13.1468	+	26.1863i	0.712984	+	1.42015i
$341$	10.8848	+	4.50862i	0.589443	+	0.244155i
$342$	−8.36370	+	8.99393i	−0.452257	+	0.486336i
$343$	−9.73087	+	9.73087i	−0.525417	+	0.525417i
$344$	−7.21278	+	0.788430i	−0.388887	+	0.0425093i
$345$	−8.39121	−	8.39121i	−0.451767	−	0.451767i
$346$	25.6625	−	0.931769i	1.37963	−	0.0500922i
$347$	−8.60862	+	20.7830i	−0.462135	+	1.11569i	0.505384	+	0.862894i	$0.331351\pi$
$347$	−8.60862	+	20.7830i	−0.462135	+	1.11569i	−0.967519	+	0.252798i	$0.918649\pi$
$348$	−11.4468	+	0.832333i	−0.613614	+	0.0446177i
$349$	−16.2518	+	6.73171i	−0.869938	+	0.360340i	−0.772586	−	0.634910i	$-0.781037\pi$
$349$	−16.2518	+	6.73171i	−0.869938	+	0.360340i	−0.0973518	+	0.995250i	$0.531037\pi$
$350$	−8.47542	−	3.15545i	−0.453030	−	0.168666i
$351$	−5.26097			−0.280810
$352$	26.9767	+	18.6120i	1.43786	+	0.992024i
$353$	2.29778			0.122299			0.0611493	−	0.998129i	$-0.480523\pi$
$353$	2.29778			0.122299			0.0611493	+	0.998129i	$0.480523\pi$
$354$	6.88369	+	2.56284i	0.365864	+	0.136213i
$355$	−23.9702	+	9.92877i	−1.27220	+	0.526964i
$356$	−0.528420	−	7.26720i	−0.0280062	−	0.385161i
$357$	1.98713	−	4.79735i	0.105170	−	0.253903i
$358$	−30.1262	+	1.09384i	−1.59222	+	0.0578112i
$359$	7.76395	+	7.76395i	0.409765	+	0.409765i	0.881657	−	0.471891i	$-0.156429\pi$
$359$	7.76395	+	7.76395i	0.409765	+	0.409765i	−0.471891	+	0.881657i	$0.656429\pi$
$360$	−13.1315	−	10.5436i	−0.692092	−	0.555696i
$361$	−3.07255	+	3.07255i	−0.161713	+	0.161713i
$362$	−15.8410	+	17.0347i	−0.832586	+	0.895324i
$363$	22.8640	+	9.47056i	1.20005	+	0.497076i
$364$	−1.91362	+	0.960726i	−0.100301	+	0.0503557i
$365$	−15.4091	−	37.2008i	−0.806547	−	1.94718i
$366$	3.02281	+	6.60866i	0.158005	+	0.345440i
$367$			24.7472i			1.29179i	0.763425	+	0.645896i	$0.223516\pi$
$367$			24.7472i			1.29179i	−0.763425	+	0.645896i	$0.776484\pi$
$368$	−10.4792	−	7.80595i	−0.546267	−	0.406913i
$369$		−	18.3227i		−	0.953844i
$370$	14.0069	−	6.40677i	0.728184	−	0.333072i
$371$	−4.00718	−	9.67419i	−0.208042	−	0.502259i
$372$	4.23343	+	1.40345i	0.219493	+	0.0727654i
$373$	8.01888	+	3.32153i	0.415202	+	0.171982i	0.580498	−	0.814262i	$-0.302858\pi$
$373$	8.01888	+	3.32153i	0.415202	+	0.171982i	−0.165296	+	0.986244i	$0.552858\pi$
$374$	26.5370	+	24.6775i	1.37220	+	1.27604i
$375$	2.49950	−	2.49950i	0.129074	−	0.129074i
$376$	4.88315	+	8.90515i	0.251829	+	0.459248i
$377$	3.70021	+	3.70021i	0.190571	+	0.190571i
$378$	0.289028	+	7.96032i	0.0148660	+	0.409435i
$379$	5.35093	−	12.9183i	0.274859	−	0.663568i	−0.724819	−	0.688939i	$-0.758077\pi$
$379$	5.35093	−	12.9183i	0.274859	−	0.663568i	0.999678	+	0.0253712i	$0.00807677\pi$
$380$	−24.2168	−	20.9338i	−1.24230	−	1.07388i
$381$	9.51725	−	3.94217i	0.487583	−	0.201964i
$382$	12.7338	−	34.2024i	0.651516	−	1.74995i
$383$	−4.33354			−0.221433			−0.110717	−	0.993852i	$-0.535315\pi$
$383$	−4.33354			−0.221433			−0.110717	+	0.993852i	$0.535315\pi$
$384$	10.6963	+	6.28655i	0.545843	+	0.320809i
$385$	−20.5474			−1.04719
$386$	8.54050	−	22.9395i	0.434700	−	1.16759i
$387$	4.25990	−	1.76451i	0.216543	−	0.0896950i
$388$	7.24558	+	6.26331i	0.367839	+	0.317971i
$389$	−12.0353	+	29.0557i	−0.610212	+	1.47318i	0.252556	+	0.967582i	$0.418729\pi$
$389$	−12.0353	+	29.0557i	−0.610212	+	1.47318i	−0.862768	+	0.505600i	$0.831271\pi$
$390$	−0.186406	−	5.13395i	−0.00943905	−	0.259968i
$391$	−10.2163	−	10.2163i	−0.516660	−	0.516660i
$392$	−7.96073	−	14.5176i	−0.402078	−	0.733248i
$393$	−2.32457	+	2.32457i	−0.117259	+	0.117259i
$394$	13.7436	+	12.7805i	0.692391	+	0.643873i
$395$	−22.0091	−	9.11647i	−1.10740	−	0.458699i
$396$	−19.7693	−	6.55385i	−0.993447	−	0.329343i
$397$	10.3887	+	25.0806i	0.521395	+	1.25876i	0.937037	+	0.349231i	$0.113557\pi$
$397$	10.3887	+	25.0806i	0.521395	+	1.25876i	−0.415641	+	0.909529i	$0.636443\pi$
$398$	5.50523	−	2.51810i	0.275952	−	0.126221i
$399$			5.67275i			0.283993i
$400$	14.2727	−	19.1607i	0.713637	−	0.958033i
$401$			31.0882i			1.55247i	0.630445	+	0.776234i	$0.282873\pi$
$401$			31.0882i			1.55247i	−0.630445	+	0.776234i	$0.717127\pi$
$402$	4.29442	+	9.38874i	0.214186	+	0.468268i
$403$	−0.778190	−	1.87872i	−0.0387644	−	0.0935856i
$404$	−6.25750	+	3.14156i	−0.311322	+	0.156299i
$405$	−1.15403	−	0.478014i	−0.0573441	−	0.0237527i
$406$	5.39547	−	5.80204i	0.267773	−	0.287950i
$407$	13.4697	−	13.4697i	0.667667	−	0.667667i
$408$	10.6968	+	8.58870i	0.529570	+	0.425204i
$409$	12.6091	+	12.6091i	0.623478	+	0.623478i	0.946419	−	0.322941i	$-0.104671\pi$
$409$	12.6091	+	12.6091i	0.623478	+	0.623478i	−0.322941	+	0.946419i	$0.604671\pi$
$410$	47.7239	−	1.73279i	2.35692	−	0.0855762i
$411$	9.54997	−	23.0557i	0.471065	−	1.13725i
$412$	−2.42775	−	33.3881i	−0.119606	−	1.64491i
$413$	−4.68475	+	1.94049i	−0.230522	+	0.0954851i
$414$	7.78200	+	2.89728i	0.382464	+	0.142394i
$415$	−34.3064			−1.68403
$416$	−1.02089	−	5.56397i	−0.0500530	−	0.272796i
$417$	−16.3623			−0.801266
$418$	−37.1009	−	13.8129i	−1.81466	−	0.675609i
$419$	−11.5522	+	4.78507i	−0.564361	+	0.233766i	−0.646577	−	0.762849i	$-0.723800\pi$
$419$	−11.5522	+	4.78507i	−0.564361	+	0.233766i	0.0822162	+	0.996615i	$0.473800\pi$
$420$	−7.75789	+	0.564099i	−0.378546	+	0.0275252i
$421$	−3.61625	+	8.73041i	−0.176245	+	0.425494i	−0.987173	−	0.159652i	$-0.948963\pi$
$421$	−3.61625	+	8.73041i	−0.176245	+	0.425494i	0.810928	+	0.585146i	$0.198963\pi$
$422$	28.1815	−	1.02323i	1.37185	−	0.0498100i
$423$	−4.56368	−	4.56368i	−0.221894	−	0.221894i
$424$	27.4998	−	3.00600i	1.33551	−	0.145984i
$425$	18.6799	−	18.6799i	0.906108	−	0.906108i
$426$	−8.27184	+	8.89515i	−0.400772	+	0.430971i
$427$	−4.63493	−	1.91985i	−0.224300	−	0.0929081i
$428$	8.51973	+	16.9700i	0.411817	+	0.820274i
$429$	−2.43140	−	5.86991i	−0.117389	−	0.283402i
$430$	4.99875	+	10.9286i	0.241061	+	0.527023i
$431$			28.0471i			1.35098i	0.737368	+	0.675491i	$0.236068\pi$
$431$			28.0471i			1.35098i	−0.737368	+	0.675491i	$0.763932\pi$
$432$	−20.4025	−	5.15593i	−0.981614	−	0.248065i
$433$			15.6197i			0.750636i	0.926896	+	0.375318i	$0.122467\pi$
$433$			15.6197i			0.750636i	−0.926896	+	0.375318i	$0.877533\pi$
$434$	−2.79992	+	1.28069i	−0.134400	+	0.0614749i
$435$	7.27452	+	17.5622i	0.348786	+	0.842045i
$436$	−3.30851	+	9.97995i	−0.158449	+	0.477953i
$437$	14.5825	+	6.04026i	0.697574	+	0.288945i
$438$	−13.8049	−	12.8376i	−0.659625	−	0.613403i
$439$	4.31984	−	4.31984i	0.206175	−	0.206175i	−0.596465	−	0.802639i	$-0.703428\pi$
$439$	4.31984	−	4.31984i	0.206175	−	0.206175i	0.802639	+	0.596465i	$0.203428\pi$
$440$	15.2008	−	52.1116i	0.724667	−	2.48432i
$441$	7.43991	+	7.43991i	0.354282	+	0.354282i
$442$	−0.226949	−	6.25058i	−0.0107949	−	0.297310i
$443$	6.93031	−	16.7313i	0.329269	−	0.794926i	−0.669378	−	0.742922i	$-0.733439\pi$
$443$	6.93031	−	16.7313i	0.329269	−	0.794926i	0.998647	−	0.0520039i	$-0.0165608\pi$
$444$	4.71582	−	5.45540i	0.223803	−	0.258902i
$445$	−11.1497	+	4.61834i	−0.528545	+	0.218930i
$446$	−6.15136	+	16.5223i	−0.291275	+	0.782355i
$447$	−9.56433			−0.452377
$448$	−8.36271	+	1.85037i	−0.395101	+	0.0874216i
$449$	−19.6940			−0.929417			−0.464708	−	0.885464i	$-0.653841\pi$
$449$	−19.6940			−0.929417			−0.464708	+	0.885464i	$0.653841\pi$
$450$	−5.29751	+	14.2289i	−0.249727	+	0.670758i
$451$	54.5652	−	22.6017i	2.56938	−	1.06427i
$452$	17.1996	−	19.8971i	0.809003	−	0.935879i
$453$	−5.65873	+	13.6614i	−0.265870	+	0.641867i
$454$	−0.934511	−	25.7380i	−0.0438588	−	1.20795i
$455$	2.50776	+	2.50776i	0.117565	+	0.117565i
$456$	−14.3870	−	4.19664i	−0.673734	−	0.196525i
$457$	17.8585	−	17.8585i	0.835384	−	0.835384i	−0.152863	−	0.988247i	$-0.548849\pi$
$457$	17.8585	−	17.8585i	0.835384	−	0.835384i	0.988247	+	0.152863i	$0.0488494\pi$
$458$	−16.7587	−	15.5844i	−0.783083	−	0.728210i
$459$	−21.4967	−	8.90423i	−1.00338	−	0.415614i
$460$	−6.81040	+	20.5432i	−0.317536	+	0.957832i
$461$	12.3286	+	29.7639i	0.574201	+	1.38624i	0.897949	+	0.440100i	$0.145057\pi$
$461$	12.3286	+	29.7639i	0.574201	+	1.38624i	−0.323748	+	0.946143i	$0.604943\pi$
$462$	−8.74813	+	4.00140i	−0.407000	+	0.186162i
$463$		−	20.3212i		−	0.944407i	−0.881490	−	0.472203i	$-0.843459\pi$
$463$		−	20.3212i		−	0.944407i	0.881490	−	0.472203i	$-0.156541\pi$
$464$	10.7234	+	17.9761i	0.497821	+	0.834518i
$465$		−	7.38701i		−	0.342565i
$466$	12.8852	+	28.1704i	0.596893	+	1.30497i
$467$	−1.59366	−	3.84743i	−0.0737456	−	0.178038i	0.882708	−	0.469922i	$-0.155718\pi$
$467$	−1.59366	−	3.84743i	−0.0737456	−	0.178038i	−0.956454	+	0.291884i	$0.905718\pi$
$468$	1.61291	+	3.21267i	0.0745569	+	0.148506i
$469$	−6.58472	−	2.72748i	−0.304054	−	0.125943i
$470$	11.4551	−	12.3183i	0.528384	−	0.568200i
$471$	−11.9807	+	11.9807i	−0.552043	+	0.552043i
$472$	−1.45566	−	13.3168i	−0.0670024	−	0.612957i
$473$	10.5094	+	10.5094i	0.483224	+	0.483224i
$474$	−11.1458	+	0.404687i	−0.511943	+	0.0185879i
$475$	−11.0443	+	26.6632i	−0.506745	+	1.22339i
$476$	−9.44522	+	0.686790i	−0.432921	+	0.0314790i
$477$	−16.2415	+	6.72745i	−0.743647	+	0.308029i
$478$	−4.70095	−	1.75019i	−0.215017	−	0.0800519i
$479$	1.94204			0.0887343			0.0443671	−	0.999015i	$-0.485873\pi$
$479$	1.94204			0.0887343			0.0443671	+	0.999015i	$0.485873\pi$
$480$	4.30855	−	20.0926i	0.196658	−	0.917096i
$481$	−3.28787			−0.149914
$482$	17.3171	+	6.44726i	0.788773	+	0.293665i
$483$	3.54345	−	1.46775i	0.161233	−	0.0667848i
$484$	−3.27321	−	45.0155i	−0.148782	−	2.04616i
$485$	6.07049	−	14.6555i	0.275647	−	0.665470i
$486$	21.7213	−	0.788668i	0.985297	−	0.0357747i
$487$	−4.64745	−	4.64745i	−0.210596	−	0.210596i	0.593925	−	0.804521i	$-0.297578\pi$
$487$	−4.64745	−	4.64745i	−0.210596	−	0.210596i	−0.804521	+	0.593925i	$0.797578\pi$
$488$	8.29792	−	10.3346i	0.375629	−	0.467828i
$489$	9.71551	−	9.71551i	0.439350	−	0.439350i
$490$	−18.6746	+	20.0818i	−0.843633	+	0.907204i
$491$	8.20870	+	3.40016i	0.370453	+	0.153447i	0.560140	−	0.828398i	$-0.310747\pi$
$491$	8.20870	+	3.40016i	0.370453	+	0.153447i	−0.189687	+	0.981845i	$0.560747\pi$
$492$	19.9812	−	10.0315i	0.900820	−	0.452254i
$493$	8.85671	+	21.3820i	0.398886	+	0.962997i
$494$	2.84223	+	6.21387i	0.127878	+	0.279575i
$495$			34.4960i			1.55048i
$496$	−1.17668	−	8.04848i	−0.0528344	−	0.361387i
$497$		−	8.38547i		−	0.376140i
$498$	−14.6060	+	6.68082i	−0.654512	+	0.299375i
$499$	1.46533	+	3.53762i	0.0655972	+	0.158366i	0.953279	−	0.302092i	$-0.0976851\pi$
$499$	1.46533	+	3.53762i	0.0655972	+	0.158366i	−0.887681	+	0.460458i	$0.847685\pi$
$500$	−6.11924	−	2.02862i	−0.273661	−	0.0907228i
$501$	−18.4179	−	7.62896i	−0.822853	−	0.340837i
$502$	8.97168	+	8.34301i	0.400426	+	0.372367i
$503$	15.3259	−	15.3259i	0.683349	−	0.683349i	−0.277404	−	0.960753i	$-0.589474\pi$
$503$	15.3259	−	15.3259i	0.683349	−	0.683349i	0.960753	+	0.277404i	$0.0894741\pi$
$504$	4.77245	−	2.61698i	0.212582	−	0.116570i
$505$	8.20032	+	8.20032i	0.364910	+	0.364910i
$506$	0.971207	+	26.7487i	0.0431754	+	1.18913i
$507$	−0.419661	+	1.01315i	−0.0186378	+	0.0449956i
$508$	−14.2132	−	12.2863i	−0.630607	−	0.545117i
$509$	−11.3314	+	4.69360i	−0.502253	+	0.208040i	−0.619402	−	0.785074i	$-0.712625\pi$
$509$	−11.3314	+	4.69360i	−0.502253	+	0.208040i	0.117148	+	0.993114i	$0.462625\pi$
$510$	7.92759	−	21.2932i	0.351040	−	0.942880i
$511$	13.0139			0.575702
$512$	1.49381	−	22.5781i	0.0660176	−	0.997818i
$513$	25.4194			1.12229
$514$	3.43445	−	9.22481i	0.151487	−	0.406889i
$515$	−51.2255	+	21.2183i	−2.25726	+	0.934990i
$516$	4.25647	+	3.67942i	0.187380	+	0.161978i
$517$	7.96123	−	19.2201i	0.350134	−	0.845299i
$518$	0.180629	+	4.97485i	0.00793640	+	0.218582i
$519$	−14.0804	−	14.0804i	−0.618059	−	0.618059i
$520$	−8.21528	+	4.50486i	−0.360264	+	0.197551i
$521$	12.4631	−	12.4631i	0.546018	−	0.546018i	−0.379269	−	0.925287i	$-0.623824\pi$
$521$	12.4631	−	12.4631i	0.546018	−	0.546018i	0.925287	+	0.379269i	$0.123824\pi$
$522$	−9.74074	−	9.05818i	−0.426341	−	0.396466i
$523$	9.55699	+	3.95864i	0.417898	+	0.173099i	0.581717	−	0.813391i	$-0.302381\pi$
$523$	9.55699	+	3.95864i	0.417898	+	0.173099i	−0.163819	+	0.986490i	$0.552381\pi$
$524$	5.69097	+	1.88665i	0.248611	+	0.0824185i
$525$	2.68369	+	6.47900i	0.117126	+	0.282767i
$526$	−27.6658	+	12.6544i	−1.20629	+	0.551758i
$527$		−	8.99368i		−	0.391771i
$528$	−3.67644	−	25.1469i	−0.159997	−	1.09438i
$529$			12.3283i			0.536013i
$530$	−19.0585	−	41.6668i	−0.827847	−	1.80989i
$531$	3.25778	+	7.86498i	0.141376	+	0.341311i
$532$	9.24600	−	4.64193i	0.400865	−	0.201253i
$533$	−9.41799	−	3.90106i	−0.407939	−	0.168974i
$534$	−3.84763	+	4.13756i	−0.166503	+	0.179050i
$535$	22.2388	−	22.2388i	0.961467	−	0.961467i
$536$	11.7886	−	14.6821i	0.509191	−	0.634172i
$537$	16.5295	+	16.5295i	0.713300	+	0.713300i
$538$	38.1729	−	1.38600i	1.64575	−	0.0597548i
$539$	−12.9787	+	31.3335i	−0.559034	+	1.34963i
$540$	2.52771	+	34.7628i	0.108775	+	1.49595i
$541$	40.4549	−	16.7570i	1.73929	−	0.720438i	0.740460	−	0.672101i	$-0.234608\pi$
$541$	40.4549	−	16.7570i	1.73929	−	0.720438i	0.998831	−	0.0483374i	$-0.0153923\pi$
$542$	−0.744569	−	0.277207i	−0.0319820	−	0.0119071i
$543$	18.0381			0.774088
$544$	5.24566	−	24.4627i	0.224906	−	1.04883i
$545$	17.4143			0.745945
$546$	1.55604	+	0.579324i	0.0665925	+	0.0247928i
$547$	−14.3090	+	5.92698i	−0.611809	+	0.253420i	−0.667002	−	0.745056i	$-0.732423\pi$
$547$	−14.3090	+	5.92698i	−0.611809	+	0.253420i	0.0551928	+	0.998476i	$0.482423\pi$
$548$	−45.3930	+	3.30066i	−1.93909	+	0.140997i
$549$	−3.22314	+	7.78134i	−0.137560	+	0.332100i
$550$	−48.9085	+	1.77580i	−2.08546	+	0.0757202i
$551$	−17.8783	−	17.8783i	−0.761640	−	0.761640i
$552$	1.10104	+	10.0726i	0.0468632	+	0.428718i
$553$	5.44432	−	5.44432i	0.231516	−	0.231516i
$554$	−21.9702	+	23.6258i	−0.933426	+	1.00376i
$555$	−11.0345	−	4.57064i	−0.468389	−	0.194013i
$556$	13.3891	+	26.6689i	0.567822	+	1.13101i
$557$	−0.725757	−	1.75213i	−0.0307513	−	0.0742403i	0.907758	−	0.419495i	$-0.137793\pi$
$557$	−0.725757	−	1.75213i	−0.0307513	−	0.0742403i	−0.938509	+	0.345254i	$0.887793\pi$
$558$	2.15008	+	4.70064i	0.0910200	+	0.198994i
$559$		−	2.56529i		−	0.108500i
$560$	7.26760	+	12.1830i	0.307112	+	0.514824i
$561$		−	28.1001i		−	1.18639i
$562$	−19.3465	+	8.84910i	−0.816081	+	0.373277i
$563$	7.50977	+	18.1302i	0.316499	+	0.764096i	0.999435	+	0.0336179i	$0.0107029\pi$
$563$	7.50977	+	18.1302i	0.316499	+	0.764096i	−0.682936	+	0.730479i	$0.739297\pi$
$564$	2.47818	−	7.47531i	0.104350	−	0.314767i
$565$	−40.2453	−	16.6701i	−1.69313	−	0.701318i
$566$	−16.1113	−	14.9823i	−0.677207	−	0.629753i
$567$	0.285468	−	0.285468i	0.0119885	−	0.0119885i
$568$	21.2669	+	6.20347i	0.892340	+	0.260292i
$569$	−28.4862	−	28.4862i	−1.19420	−	1.19420i	−0.975875	−	0.218329i	$-0.929939\pi$
$569$	−28.4862	−	28.4862i	−1.19420	−	1.19420i	−0.218329	−	0.975875i	$-0.570061\pi$
$570$	0.900658	+	24.8057i	0.0377244	+	1.03900i
$571$	13.9367	−	33.6461i	0.583232	−	1.40805i	−0.306636	−	0.951827i	$-0.599203\pi$
$571$	13.9367	−	33.6461i	0.583232	−	1.40805i	0.889868	−	0.456219i	$-0.150797\pi$
$572$	−7.57777	+	8.76619i	−0.316843	+	0.366533i
$573$	−26.1459	+	10.8300i	−1.09226	+	0.452430i
$574$	−5.38525	+	14.4646i	−0.224776	+	0.603740i
$575$	19.5126			0.813730
$576$	3.10648	+	14.0397i	0.129437	+	0.584988i
$577$	16.0082			0.666430			0.333215	−	0.942851i	$-0.391867\pi$
$577$	16.0082			0.666430			0.333215	+	0.942851i	$0.391867\pi$
$578$	1.26349	−	3.39370i	0.0525544	−	0.141159i
$579$	−17.5360	+	7.26365i	−0.728771	+	0.301867i
$580$	22.6720	−	26.2276i	0.941404	−	1.08904i
$581$	4.24313	−	10.2438i	0.176035	−	0.424985i
$582$	−0.269474	−	7.42177i	−0.0111700	−	0.307642i
$583$	−40.0688	−	40.0688i	−1.65948	−	1.65948i
$584$	−9.62755	+	33.0054i	−0.398391	+	1.36577i
$585$	4.21014	−	4.21014i	0.174068	−	0.174068i
$586$	2.73748	+	2.54565i	0.113084	+	0.105160i
$587$	35.5810	+	14.7381i	1.46858	+	0.608307i	0.966536	−	0.256533i	$-0.0825801\pi$
$587$	35.5810	+	14.7381i	1.46858	+	0.608307i	0.502048	+	0.864840i	$0.332580\pi$
$588$	−4.04004	+	12.1866i	−0.166609	+	0.502566i
$589$	3.75998	+	9.07738i	0.154927	+	0.374027i
$590$	−20.1773	+	9.22911i	−0.830685	+	0.379956i
$591$		−	14.5531i		−	0.598634i
$592$	−12.7506	−	3.22223i	−0.524048	−	0.132433i
$593$		−	6.87316i		−	0.282247i	−0.989992	−	0.141123i	$-0.954929\pi$
$593$		−	6.87316i		−	0.282247i	0.989992	−	0.141123i	$-0.0450715\pi$
$594$	17.9301	+	39.2000i	0.735682	+	1.60840i
$595$	6.00249	+	14.4913i	0.246078	+	0.594085i
$596$	7.82635	+	15.5889i	0.320580	+	0.638545i
$597$	−4.33697	−	1.79643i	−0.177500	−	0.0735230i
$598$	3.14607	−	3.38314i	0.128652	−	0.138347i
$599$	−10.9328	+	10.9328i	−0.446700	+	0.446700i	−0.894256	−	0.447556i	$-0.852295\pi$
$599$	−10.9328	+	10.9328i	−0.446700	+	0.446700i	0.447556	+	0.894256i	$0.352295\pi$
$600$	−18.4171	+	2.01318i	−0.751877	+	0.0821877i
$601$	21.8811	+	21.8811i	0.892547	+	0.892547i	0.994762	−	0.102215i	$-0.0325931\pi$
$601$	21.8811	+	21.8811i	0.892547	+	0.892547i	−0.102215	+	0.994762i	$0.532593\pi$
$602$	−3.88152	+	0.140932i	−0.158199	+	0.00574397i
$603$	−4.57902	+	11.0547i	−0.186472	+	0.450184i
$604$	26.8971	−	1.95577i	1.09443	−	0.0795790i
$605$	−69.0648	+	28.6076i	−2.80788	+	1.16306i
$606$	5.08824	+	1.89438i	0.206696	+	0.0769540i
$607$	38.8750			1.57789			0.788943	−	0.614466i	$-0.210629\pi$
$607$	38.8750			1.57789			0.788943	+	0.614466i	$0.210629\pi$
$608$	4.93260	+	26.8834i	0.200044	+	1.09027i
$609$	−6.14379			−0.248959
$610$	−20.5723	−	7.65919i	−0.832949	−	0.310112i
$611$	−3.31740	+	1.37411i	−0.134208	+	0.0555907i
$612$	1.15302	+	15.8571i	0.0466079	+	0.640985i
$613$	−3.61729	+	8.73292i	−0.146101	+	0.352719i	−0.979941	−	0.199287i	$-0.936137\pi$
$613$	−3.61729	+	8.73292i	−0.146101	+	0.352719i	0.833840	+	0.552006i	$0.186137\pi$
$614$	29.0223	−	1.05376i	1.17125	−	0.0425262i
$615$	−26.1849	−	26.1849i	−1.05588	−	1.05588i
$616$	13.6803	+	10.9843i	0.551197	+	0.442568i
$617$	−23.8027	+	23.8027i	−0.958261	+	0.958261i	−0.999163	−	0.0409019i	$-0.986977\pi$
$617$	−23.8027	+	23.8027i	−0.958261	+	0.958261i	0.0409019	+	0.999163i	$0.486977\pi$
$618$	−17.6774	+	19.0094i	−0.711087	+	0.764670i
$619$	24.8180	+	10.2800i	0.997520	+	0.413186i	0.820887	−	0.571091i	$-0.193480\pi$
$619$	24.8180	+	10.2800i	0.997520	+	0.413186i	0.176633	+	0.984277i	$0.443480\pi$
$620$	−12.0401	+	6.04469i	−0.483541	+	0.242761i
$621$	−6.57691	−	15.8781i	−0.263922	−	0.637165i
$622$	−16.7899	−	36.7072i	−0.673215	−	1.47183i
$623$		−	3.90048i		−	0.156270i
$624$	−2.62040	+	3.51780i	−0.104900	+	0.140825i
$625$		−	19.1878i		−	0.767511i
$626$	29.3807	−	13.4388i	1.17429	−	0.537122i
$627$	11.7478	+	28.3616i	0.469160	+	1.13265i
$628$	29.3310	+	9.72370i	1.17044	+	0.388018i
$629$	−13.4345	−	5.56475i	−0.535669	−	0.221881i
$630$	−6.60162	−	6.13902i	−0.263015	−	0.244585i
$631$	2.35179	−	2.35179i	0.0936234	−	0.0936234i	−0.658744	−	0.752367i	$-0.728912\pi$
$631$	2.35179	−	2.35179i	0.0936234	−	0.0936234i	0.752367	+	0.658744i	$0.228912\pi$
$632$	9.78003	+	17.8353i	0.389029	+	0.709451i
$633$	−15.4625	−	15.4625i	−0.614578	−	0.614578i
$634$	0.0659931	+	1.81756i	0.00262092	+	0.0721846i
$635$	−11.9081	+	28.7486i	−0.472557	+	1.14085i
$636$	−16.2284	−	14.0283i	−0.643498	−	0.556260i
$637$	5.40818	−	2.24014i	0.214280	−	0.0887576i
$638$	14.9598	−	40.1815i	0.592264	−	1.59080i
$639$	−14.0779			−0.556914
$640$	−36.2745	+	9.41898i	−1.43387	+	0.372318i
$641$	32.0137			1.26446			0.632232	−	0.774779i	$-0.282139\pi$
$641$	32.0137			1.26446			0.632232	+	0.774779i	$0.282139\pi$
$642$	5.13745	−	13.7990i	0.202759	−	0.544604i
$643$	−1.07509	+	0.445315i	−0.0423972	+	0.0175615i	−0.403781	−	0.914856i	$-0.632304\pi$
$643$	−1.07509	+	0.445315i	−0.0423972	+	0.0175615i	0.361384	+	0.932417i	$0.382304\pi$
$644$	−5.29183	−	4.57443i	−0.208527	−	0.180258i
$645$	3.56615	−	8.60944i	0.140417	−	0.338997i
$646$	1.09655	+	30.2009i	0.0431432	+	1.18824i
$647$	−10.7821	−	10.7821i	−0.423888	−	0.423888i	0.462652	−	0.886540i	$-0.346898\pi$
$647$	−10.7821	−	10.7821i	−0.423888	−	0.423888i	−0.886540	+	0.462652i	$0.846898\pi$
$648$	0.512807	+	0.935179i	0.0201450	+	0.0367373i
$649$	−19.4034	+	19.4034i	−0.761650	+	0.761650i
$650$	6.18587	+	5.75241i	0.242630	+	0.225628i
$651$	2.20575	+	0.913651i	0.0864501	+	0.0358088i
$652$	−23.7853	−	7.88522i	−0.931506	−	0.308809i
$653$	−3.91148	−	9.44315i	−0.153068	−	0.369539i	0.828681	−	0.559722i	$-0.189092\pi$
$653$	−3.91148	−	9.44315i	−0.153068	−	0.369539i	−0.981749	+	0.190183i	$0.939092\pi$
$654$	7.41417	−	3.39125i	0.289917	−	0.132608i
$655$		−	9.93031i		−	0.388009i
$656$	−32.7006	−	24.3586i	−1.27674	−	0.951043i
$657$		−	21.8484i		−	0.852388i
$658$	2.26141	+	4.94404i	0.0881589	+	0.192739i
$659$	−5.97229	−	14.4184i	−0.232647	−	0.561661i	0.763840	−	0.645406i	$-0.223312\pi$
$659$	−5.97229	−	14.4184i	−0.232647	−	0.561661i	−0.996487	+	0.0837453i	$0.973312\pi$
$660$	−37.6183	+	18.8862i	−1.46429	+	0.735143i
$661$	37.0616	+	15.3514i	1.44153	+	0.597101i	0.960168	−	0.279422i	$-0.0901429\pi$
$661$	37.0616	+	15.3514i	1.44153	+	0.597101i	0.481360	+	0.876523i	$0.340143\pi$
$662$	11.3485	−	12.2036i	0.441070	−	0.474306i
$663$	−3.42953	+	3.42953i	−0.133192	+	0.133192i
$664$	22.8410	+	18.3395i	0.886401	+	0.711711i
$665$	−12.1167	−	12.1167i	−0.469865	−	0.469865i
$666$	8.35201	−	0.303249i	0.323634	−	0.0117507i
$667$	−6.54181	+	15.7933i	−0.253300	+	0.611520i
$668$	2.63672	+	36.2620i	0.102018	+	1.40302i
$669$	12.6304	−	5.23169i	0.488320	−	0.202269i
$670$	−29.2265	−	10.8812i	−1.12912	−	0.420377i
$671$	−27.1487			−1.04806
$672$	5.46671	+	3.77164i	0.210883	+	0.145494i
$673$	−11.5931			−0.446883			−0.223442	−	0.974717i	$-0.571729\pi$
$673$	−11.5931			−0.446883			−0.223442	+	0.974717i	$0.571729\pi$
$674$	27.8722	+	10.3770i	1.07360	+	0.399707i
$675$	29.0321	−	12.0255i	1.11745	−	0.462862i
$676$	1.99473	−	0.145043i	0.0767205	−	0.00557858i
$677$	−10.6400	+	25.6872i	−0.408928	+	0.987241i	0.576492	+	0.817103i	$0.304421\pi$
$677$	−10.6400	+	25.6872i	−0.408928	+	0.987241i	−0.985420	+	0.170138i	$0.945579\pi$
$678$	−20.3809	+	0.740000i	−0.782723	+	0.0284195i
$679$	3.62527	+	3.62527i	0.139125	+	0.139125i
$680$	−41.1928	+	4.50279i	−1.57967	+	0.172674i
$681$	−14.1218	+	14.1218i	−0.541149	+	0.541149i
$682$	−11.3463	+	12.2013i	−0.434474	+	0.467213i
$683$	−34.8193	−	14.4226i	−1.33232	−	0.551866i	−0.401006	−	0.916076i	$-0.631339\pi$
$683$	−34.8193	−	14.4226i	−1.33232	−	0.551866i	−0.931317	+	0.364209i	$0.881339\pi$
$684$	−7.79310	−	15.5226i	−0.297977	−	0.593523i
$685$	28.8474	+	69.6439i	1.10220	+	2.66096i
$686$	−8.09519	−	17.6982i	−0.309076	−	0.675721i
$687$			17.7458i			0.677045i
$688$	2.51408	−	9.94842i	0.0958483	−	0.379280i
$689$			9.78055i			0.372609i
$690$	15.2617	−	6.98071i	0.581002	−	0.265751i
$691$	12.7094	+	30.6833i	0.483489	+	1.16725i	0.957941	+	0.286965i	$0.0926462\pi$
$691$	12.7094	+	30.6833i	0.483489	+	1.16725i	−0.474452	+	0.880281i	$0.657354\pi$
$692$	−11.4278	+	34.4713i	−0.434419	+	1.31040i
$693$	−10.3004	−	4.26659i	−0.391282	−	0.162074i
$694$	−23.2968	−	21.6643i	−0.884335	−	0.822367i
$695$	34.9491	−	34.9491i	1.32569	−	1.32569i
$696$	4.54510	−	15.5816i	0.172282	−	0.590620i
$697$	−31.8801	−	31.8801i	−1.20754	−	1.20754i
$698$	−0.902659	−	24.8608i	−0.0341661	−	0.940994i
$699$	9.19237	−	22.1923i	0.347687	−	0.839392i
$700$	8.36407	−	9.67581i	0.316132	−	0.365711i
$701$	8.98073	−	3.71994i	0.339197	−	0.140500i	−0.206581	−	0.978429i	$-0.566234\pi$
$701$	8.98073	−	3.71994i	0.339197	−	0.140500i	0.545779	+	0.837929i	$0.316234\pi$
$702$	2.59593	−	6.97257i	0.0979770	−	0.263163i
$703$	15.8860			0.599151
$704$	−37.9784	+	26.5695i	−1.43137	+	1.00138i
$705$	−13.0438			−0.491260
$706$	−1.13380	+	3.04534i	−0.0426710	+	0.114613i
$707$	−3.46285	+	1.43436i	−0.130234	+	0.0539446i
$708$	−6.79326	+	7.85864i	−0.255306	+	0.295346i
$709$	−4.16733	+	10.0608i	−0.156507	+	0.377842i	−0.982611	−	0.185676i	$-0.940552\pi$
$709$	−4.16733	+	10.0608i	−0.156507	+	0.377842i	0.826104	+	0.563518i	$0.190552\pi$
$710$	−1.33135	−	36.6678i	−0.0499648	−	1.37612i
$711$	−9.14019	−	9.14019i	−0.342784	−	0.342784i
$712$	9.89225	+	2.88553i	0.370728	+	0.108140i
$713$	4.69729	−	4.69729i	0.175915	−	0.175915i
$714$	5.37761	+	5.00078i	0.201252	+	0.187150i
$715$	17.7312	+	7.34448i	0.663108	+	0.274668i
$716$	13.4155	−	40.4672i	0.501361	−	1.51233i
$717$	1.48853	+	3.59363i	0.0555901	+	0.134206i
$718$	−14.1208	+	6.45889i	−0.526985	+	0.241044i
$719$		−	35.6873i		−	1.33091i	−0.746438	−	0.665455i	$-0.768238\pi$
$719$		−	35.6873i		−	1.33091i	0.746438	−	0.665455i	$-0.231762\pi$
$720$	20.4534	−	12.2012i	0.762252	−	0.454711i
$721$		−	17.9202i		−	0.667383i
$722$	−2.55608	−	5.58826i	−0.0951274	−	0.207974i
$723$	−5.48336	−	13.2380i	−0.203928	−	0.492326i
$724$	−14.7603	−	29.4002i	−0.548562	−	1.09265i
$725$	−28.8772	−	11.9613i	−1.07247	−	0.444232i
$726$	−23.8335	+	25.6294i	−0.884545	+	0.951198i
$727$	14.1375	−	14.1375i	0.524331	−	0.524331i	−0.394546	−	0.918876i	$-0.629098\pi$
$727$	14.1375	−	14.1375i	0.524331	−	0.524331i	0.918876	+	0.394546i	$0.129098\pi$
$728$	−0.329050	−	3.01024i	−0.0121954	−	0.111567i
$729$	−12.7178	−	12.7178i	−0.471030	−	0.471030i
$730$	56.9070	−	2.06621i	2.10622	−	0.0764739i
$731$	4.34178	−	10.4820i	0.160587	−	0.387690i
$732$	−10.2503	+	0.745328i	−0.378861	+	0.0275481i
$733$	12.6579	−	5.24308i	0.467531	−	0.193658i	−0.136465	−	0.990645i	$-0.543574\pi$
$733$	12.6579	−	5.24308i	0.467531	−	0.193658i	0.603996	+	0.796987i	$0.293574\pi$
$734$	−32.7984	−	12.2110i	−1.21061	−	0.450718i
$735$	21.2647			0.784359
$736$	15.5163	−	10.0368i	0.571939	−	0.369962i
$737$	−38.5694			−1.42072
$738$	24.2839	+	9.04102i	0.893901	+	0.332804i
$739$	41.7532	−	17.2947i	1.53591	−	0.636197i	0.555213	−	0.831708i	$-0.312637\pi$
$739$	41.7532	−	17.2947i	1.53591	−	0.636197i	0.980701	+	0.195511i	$0.0626366\pi$
$740$	1.57970	+	21.7252i	0.0580711	+	0.798634i
$741$	2.02767	−	4.89523i	0.0744884	−	0.179831i
$742$	14.7989	−	0.537325i	0.543283	−	0.0197258i
$743$	26.9932	+	26.9932i	0.990286	+	0.990286i	0.999953	−	0.00966771i	$-0.00307738\pi$
$743$	26.9932	+	26.9932i	0.990286	+	0.990286i	−0.00966771	+	0.999953i	$0.503077\pi$
$744$	−3.94895	+	4.91823i	−0.144776	+	0.180311i
$745$	20.4289	−	20.4289i	0.748457	−	0.748457i
$746$	−8.35892	+	8.98879i	−0.306042	+	0.329103i
$747$	−17.1978	−	7.12357i	−0.629235	−	0.260638i
$748$	−45.8002	+	22.9939i	−1.67462	+	0.840740i
$749$	3.88989	+	9.39104i	0.142134	+	0.343141i
$750$	2.07936	+	4.54602i	0.0759273	+	0.165997i
$751$		−	42.3097i		−	1.54390i	−0.635681	−	0.771952i	$-0.719280\pi$
$751$		−	42.3097i		−	1.54390i	0.635681	−	0.771952i	$-0.280720\pi$
$752$	−14.2118	+	2.07776i	−0.518253	+	0.0757680i
$753$		−	9.50013i		−	0.346204i
$754$	−6.72984	+	3.07824i	−0.245086	+	0.112103i
$755$	−17.0932	−	41.2667i	−0.622086	−	1.50185i
$756$	−10.6927	−	3.54481i	−0.388891	−	0.128924i
$757$	−37.1760	−	15.3988i	−1.35119	−	0.559679i	−0.414563	−	0.910021i	$-0.636066\pi$
$757$	−37.1760	−	15.3988i	−1.35119	−	0.559679i	−0.936622	+	0.350341i	$0.886066\pi$
$758$	14.4808	+	13.4661i	0.525966	+	0.489110i
$759$	14.6763	−	14.6763i	0.532717	−	0.532717i
$760$	39.6937	−	21.7661i	1.43984	−	0.789540i
$761$	9.71750	+	9.71750i	0.352259	+	0.352259i	0.860950	−	0.508690i	$-0.169870\pi$
$761$	9.71750	+	9.71750i	0.352259	+	0.352259i	−0.508690	+	0.860950i	$0.669870\pi$
$762$	0.528608	+	14.5588i	0.0191495	+	0.527409i
$763$	−2.15386	+	5.19987i	−0.0779748	+	0.188248i
$764$	39.0466	+	33.7531i	1.41266	+	1.22115i
$765$	24.3287	−	10.0773i	0.879605	−	0.364344i
$766$	2.13830	−	5.74341i	0.0772601	−	0.207518i
$767$	4.73626			0.171016
$768$	−13.6097	+	11.0742i	−0.491098	+	0.399607i
$769$	33.7249			1.21615			0.608075	−	0.793880i	$-0.291942\pi$
$769$	33.7249			1.21615			0.608075	+	0.793880i	$0.291942\pi$
$770$	10.1388

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:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	416.bf (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.493432 + 1.32534i) q^{2} +(1.01315 - 0.419661i) q^{3} +(-1.51305 - 1.30793i) q^{4} +(-1.26766 + 3.06041i) q^{5} +(0.0562725 + 1.54984i) q^{6} +(-0.757044 - 0.757044i) q^{7} +(2.48004 - 1.35993i) q^{8} +(-1.27096 + 1.27096i) q^{9} +O(q^{10})\)	\(q+(-0.493432 + 1.32534i) q^{2} +(1.01315 - 0.419661i) q^{3} +(-1.51305 - 1.30793i) q^{4} +(-1.26766 + 3.06041i) q^{5} +(0.0562725 + 1.54984i) q^{6} +(-0.757044 - 0.757044i) q^{7} +(2.48004 - 1.35993i) q^{8} +(-1.27096 + 1.27096i) q^{9} +(-3.43058 - 3.19019i) q^{10} +(-5.35270 - 2.21716i) q^{11} +(-2.08183 - 0.690161i) q^{12} +(0.382683 + 0.923880i) q^{13} +(1.37689 - 0.629791i) q^{14} +3.63264i q^{15} +(0.578644 + 3.95793i) q^{16} +4.42274i q^{17} +(-1.05732 - 2.31159i) q^{18} +(-1.84901 - 4.46390i) q^{19} +(5.92084 - 2.97254i) q^{20} +(-1.08470 - 0.449298i) q^{21} +(5.57968 - 6.00013i) q^{22} +(-2.30995 + 2.30995i) q^{23} +(1.94194 - 2.41859i) q^{24} +(-4.22360 - 4.22360i) q^{25} +(-1.41328 + 0.0513142i) q^{26} +(-2.01328 + 4.86050i) q^{27} +(0.155286 + 2.13560i) q^{28} +(4.83456 - 2.00254i) q^{29} +(-4.81449 - 1.79246i) q^{30} -2.03351 q^{31} +(-5.53112 - 1.18606i) q^{32} -6.35355 q^{33} +(-5.86163 - 2.18232i) q^{34} +(3.27654 - 1.35719i) q^{35} +(3.58536 - 0.260702i) q^{36} +(-1.25821 + 3.03760i) q^{37} +(6.82854 - 0.247935i) q^{38} +(0.775432 + 0.775432i) q^{39} +(1.01810 + 9.31386i) q^{40} +(-7.20822 + 7.20822i) q^{41} +(1.13070 - 1.21590i) q^{42} +(-2.37002 - 0.981695i) q^{43} +(5.19902 + 10.3556i) q^{44} +(-2.27851 - 5.50081i) q^{45} +(-1.92166 - 4.20126i) q^{46} +3.59073i q^{47} +(2.24724 + 3.76714i) q^{48} -5.85377i q^{49} +(7.68176 - 3.51365i) q^{50} +(1.85605 + 4.48090i) q^{51} +(0.629349 - 1.89840i) q^{52} +(9.03605 + 3.74285i) q^{53} +(-5.44839 - 5.06661i) q^{54} +(13.5708 - 13.5708i) q^{55} +(-2.90702 - 0.847968i) q^{56} +(-3.74665 - 3.74665i) q^{57} +(0.268522 + 7.39555i) q^{58} +(1.81249 - 4.37573i) q^{59} +(4.75124 - 5.49637i) q^{60} +(4.32920 - 1.79321i) q^{61} +(1.00340 - 2.69509i) q^{62} +1.92435 q^{63} +(4.30117 - 6.74537i) q^{64} -3.31256 q^{65} +(3.13504 - 8.42061i) q^{66} +(6.15037 - 2.54757i) q^{67} +(5.78463 - 6.69183i) q^{68} +(-1.37093 + 3.30972i) q^{69} +(0.181986 + 5.01221i) q^{70} +(5.53830 + 5.53830i) q^{71} +(-1.42361 + 4.88045i) q^{72} +(-8.59523 + 8.59523i) q^{73} +(-3.40500 - 3.16641i) q^{74} +(-6.05162 - 2.50666i) q^{75} +(-3.04082 + 9.17248i) q^{76} +(2.37374 + 5.73071i) q^{77} +(-1.41033 + 0.645088i) q^{78} +7.19156i q^{79} +(-12.8464 - 3.24643i) q^{80} +0.377083i q^{81} +(-5.99658 - 13.1101i) q^{82} +(3.96324 + 9.56811i) q^{83} +(1.05356 + 2.09852i) q^{84} +(-13.5354 - 5.60654i) q^{85} +(2.47052 - 2.65668i) q^{86} +(4.05775 - 4.05775i) q^{87} +(-16.2901 + 1.78067i) q^{88} +(2.57613 + 2.57613i) q^{89} +(8.41473 - 0.305527i) q^{90} +(0.409709 - 0.989125i) q^{91} +(6.51631 - 0.473820i) q^{92} +(-2.06025 + 0.853384i) q^{93} +(-4.75894 - 1.77178i) q^{94} +16.0053 q^{95} +(-6.10160 + 1.11953i) q^{96} -4.78872 q^{97} +(7.75823 + 2.88843i) q^{98} +(9.62100 - 3.98515i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q+O(q^{10}) \) 192 * q	\( 192 q - 16 q^{10} - 16 q^{12} - 40 q^{16} - 40 q^{18} - 8 q^{22} - 16 q^{23} + 24 q^{24} + 80 q^{30} - 48 q^{31} - 48 q^{35} + 80 q^{36} - 56 q^{38} - 64 q^{40} - 16 q^{43} - 80 q^{44} + 24 q^{50} + 32 q^{51} - 32 q^{53} - 24 q^{54} + 32 q^{55} + 16 q^{56} - 64 q^{58} - 56 q^{60} - 64 q^{61} + 24 q^{62} + 80 q^{63} + 72 q^{64} + 96 q^{66} + 80 q^{67} - 32 q^{68} - 64 q^{69} - 120 q^{72} - 32 q^{74} + 32 q^{75} + 64 q^{76} - 32 q^{77} - 56 q^{80} - 80 q^{82} - 80 q^{83} + 112 q^{84} - 112 q^{87} - 88 q^{88} - 120 q^{90} + 144 q^{92} + 40 q^{94} + 136 q^{96} + 56 q^{98}+O(q^{100}) \) 192 * q - 16 * q^10 - 16 * q^12 - 40 * q^16 - 40 * q^18 - 8 * q^22 - 16 * q^23 + 24 * q^24 + 80 * q^30 - 48 * q^31 - 48 * q^35 + 80 * q^36 - 56 * q^38 - 64 * q^40 - 16 * q^43 - 80 * q^44 + 24 * q^50 + 32 * q^51 - 32 * q^53 - 24 * q^54 + 32 * q^55 + 16 * q^56 - 64 * q^58 - 56 * q^60 - 64 * q^61 + 24 * q^62 + 80 * q^63 + 72 * q^64 + 96 * q^66 + 80 * q^67 - 32 * q^68 - 64 * q^69 - 120 * q^72 - 32 * q^74 + 32 * q^75 + 64 * q^76 - 32 * q^77 - 56 * q^80 - 80 * q^82 - 80 * q^83 + 112 * q^84 - 112 * q^87 - 88 * q^88 - 120 * q^90 + 144 * q^92 + 40 * q^94 + 136 * q^96 + 56 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more