LMFDB - Embedded newform 416.2.bf.a.157.20

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			157.20
Character	$\chi$	$=$	416.157
Dual form			416.2.bf.a.53.20

$q$-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 $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.493432	−	1.32534i	−0.348909	−	0.937157i
$2$	−0.493432	−	1.32534i	−0.348909	−	0.937157i
$3$	1.01315	+	0.419661i	0.584943	+	0.242291i	0.655473	−	0.755218i	$-0.272469\pi$
$3$	1.01315	+	0.419661i	0.584943	+	0.242291i	−0.0705305	+	0.997510i	$0.522469\pi$
$4$	−1.51305	+	1.30793i	−0.756525	+	0.653964i
$5$	−1.26766	−	3.06041i	−0.566916	−	1.36866i	−0.904142	−	0.427233i	$-0.859489\pi$
$5$	−1.26766	−	3.06041i	−0.566916	−	1.36866i	0.337226	−	0.941424i	$-0.390511\pi$
$6$	0.0562725	−	1.54984i	0.0229732	−	0.632721i
$7$	−0.757044	+	0.757044i	−0.286136	+	0.286136i	−0.835550	−	0.549414i	$-0.814851\pi$
$7$	−0.757044	+	0.757044i	−0.286136	+	0.286136i	0.549414	+	0.835550i	$0.314851\pi$
$8$	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	−0.993293	−	0.115623i	$-0.963113\pi$
$11$	−5.35270	+	2.21716i	−1.61390	+	0.668499i	−0.620606	+	0.784122i	$0.713113\pi$
$12$	−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	$-0.819808\pi$
$17$		−	4.42274i		−	1.07267i	0.844005	−	0.536336i	$-0.180192\pi$
$18$	−1.05732	+	2.31159i	−0.249213	+	0.544846i
$19$	−1.84901	+	4.46390i	−0.424192	+	1.02409i	0.556906	+	0.830576i	$0.311988\pi$
$19$	−1.84901	+	4.46390i	−0.424192	+	1.02409i	−0.981098	+	0.193514i	$0.938012\pi$
$20$	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	0.424004	−	0.905660i	$-0.360624\pi$
$23$	−2.30995	−	2.30995i	−0.481657	−	0.481657i	−0.905660	+	0.424004i	$0.860624\pi$
$24$	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	0.783357	−	0.621573i	$-0.213506\pi$
$29$	4.83456	+	2.00254i	0.897755	+	0.371862i	0.114399	+	0.993435i	$0.463506\pi$
$30$	−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	0.786075	−	0.618132i	$-0.212110\pi$
$37$	−1.25821	−	3.03760i	−0.206849	−	0.499378i	−0.992924	+	0.118754i	$0.962110\pi$
$38$	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	−0.990863	−	0.134872i	$-0.956938\pi$
$41$	−7.20822	−	7.20822i	−1.12573	−	1.12573i	−0.134872	−	0.990863i	$-0.543062\pi$
$42$	1.13070	+	1.21590i	0.174470	+	0.187617i
$43$	−2.37002	+	0.981695i	−0.361425	+	0.149707i	−0.556004	−	0.831180i	$-0.687666\pi$
$43$	−2.37002	+	0.981695i	−0.361425	+	0.149707i	0.194579	+	0.980887i	$0.437666\pi$
$44$	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	$-0.915657\pi$
$47$		−	3.59073i		−	0.523762i	0.965100	−	0.261881i	$-0.0843428\pi$
$48$	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	0.337108	−	0.941466i	$-0.390551\pi$
$53$	9.03605	−	3.74285i	1.24120	−	0.514121i	0.904089	+	0.427345i	$0.140551\pi$
$54$	−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	0.996858	−	0.0792063i	$-0.0252386\pi$
$59$	1.81249	+	4.37573i	0.235966	+	0.569672i	−0.760893	+	0.648878i	$0.775239\pi$
$60$	4.75124	+	5.49637i	0.613382	+	0.709579i
$61$	4.32920	+	1.79321i	0.554297	+	0.229597i	0.642207	−	0.766531i	$-0.278019\pi$
$61$	4.32920	+	1.79321i	0.554297	+	0.229597i	−0.0879103	+	0.996128i	$0.528019\pi$
$62$	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	0.725307	−	0.688425i	$-0.241698\pi$
$67$	6.15037	+	2.54757i	0.751387	+	0.311235i	0.0260796	+	0.999660i	$0.491698\pi$
$68$	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	−0.297459	−	0.954735i	$-0.596139\pi$
$71$	5.53830	−	5.53830i	0.657275	−	0.657275i	0.954735	+	0.297459i	$0.0961392\pi$
$72$	−1.42361	−	4.88045i	−0.167774	−	0.575167i
$73$	−8.59523	−	8.59523i	−1.00600	−	1.00600i	−0.999982	−	0.00601359i	$-0.998086\pi$
$73$	−8.59523	−	8.59523i	−1.00600	−	1.00600i	−0.00601359	−	0.999982i	$-0.501914\pi$
$74$	−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	$-0.867426\pi$
$79$		−	7.19156i		−	0.809113i	0.914513	−	0.404557i	$-0.132574\pi$
$80$	−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	−0.542623	−	0.839976i	$-0.682569\pi$
$83$	3.96324	−	9.56811i	0.435022	−	1.05024i	0.977645	−	0.210260i	$-0.0674311\pi$
$84$	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	−0.557265	−	0.830334i	$-0.688149\pi$
$89$	2.57613	−	2.57613i	0.273069	−	0.273069i	0.830334	+	0.557265i	$0.188149\pi$
$90$	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	0.976412	−	0.215915i	$-0.0692735\pi$
$101$	1.33974	+	3.23443i	0.133309	+	0.321837i	−0.843103	+	0.537753i	$0.819273\pi$
$102$	−6.85455	−	0.248879i	−0.678702	−	0.0246427i
$103$	11.8356	−	11.8356i	1.16620	−	1.16620i	0.183107	−	0.983093i	$-0.441385\pi$
$103$	11.8356	−	11.8356i	1.16620	−	1.16620i	0.983093	−	0.183107i	$-0.0586155\pi$
$104$	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	−0.763995	−	0.645222i	$-0.776765\pi$
$107$	−8.77157	+	3.63330i	−0.847980	+	0.351245i	−0.0839851	+	0.996467i	$0.526765\pi$
$108$	9.40339	+	4.72095i	0.904842	+	0.454273i
$109$	−2.01178	+	4.85687i	−0.192694	+	0.465203i	−0.990466	−	0.137755i	$-0.956011\pi$
$109$	−2.01178	+	4.85687i	−0.192694	+	0.465203i	0.797773	+	0.602958i	$0.206011\pi$
$110$	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	$-0.787725\pi$
$113$		−	13.1503i		−	1.23708i	0.785755	−	0.618538i	$-0.212275\pi$
$114$	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	0.258398	−	0.966039i	$-0.416805\pi$
$131$	−2.76958	−	1.14720i	−0.241979	−	0.100231i	−0.500377	+	0.865807i	$0.666805\pi$
$132$	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	0.853231	+	0.521533i	$0.174640\pi$
$137$	16.0912	+	16.0912i	1.37476	+	1.37476i	0.521533	+	0.853231i	$0.325360\pi$
$138$	−3.71004	+	3.45006i	−0.315819	+	0.293689i
$139$	−13.7848	+	5.70987i	−1.16921	+	0.484305i	−0.880933	−	0.473241i	$-0.843084\pi$
$139$	−13.7848	+	5.70987i	−1.16921	+	0.484305i	−0.288282	+	0.957546i	$0.593084\pi$
$140$	−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	−0.687486	−	0.726198i	$-0.741286\pi$
$149$	−8.05770	+	3.33761i	−0.660113	+	0.273428i	0.0273733	+	0.999625i	$0.491286\pi$
$150$	6.30824	+	6.78359i	0.515066	+	0.553878i
$151$	−9.53466	−	9.53466i	−0.775920	−	0.775920i	0.203214	−	0.979134i	$-0.434861\pi$
$151$	−9.53466	−	9.53466i	−0.775920	−	0.775920i	−0.979134	+	0.203214i	$0.934861\pi$
$152$	−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	−0.268311	−	0.963332i	$-0.586465\pi$
$157$	−14.2743	−	5.91261i	−1.13921	−	0.471878i	−0.870903	+	0.491455i	$0.836465\pi$
$158$	−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	0.786776	−	0.617238i	$-0.211749\pi$
$163$	11.5754	+	4.79470i	0.906658	+	0.375550i	0.119881	+	0.992788i	$0.461749\pi$
$164$	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	−0.999986	−	0.00528239i	$-0.998319\pi$
$167$	−12.8544	+	12.8544i	−0.994704	+	0.994704i	0.00528239	+	0.999986i	$0.498319\pi$
$168$	−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	0.404323	+	0.914616i	$0.367507\pi$
$173$	−6.94880	+	16.7759i	−0.528308	+	1.27545i	−0.932631	+	0.360831i	$0.882493\pi$
$174$	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	−0.253591	−	0.967312i	$-0.581612\pi$
$179$	8.15746	−	19.6939i	0.609717	−	1.47199i	0.863308	−	0.504677i	$-0.168388\pi$
$180$	−3.74717	−	11.3031i	−0.279297	−	0.842486i
$181$	15.1966	−	6.29465i	1.12956	−	0.467877i	0.261926	−	0.965088i	$-0.415642\pi$
$181$	15.1966	−	6.29465i	1.12956	−	0.467877i	0.867630	+	0.497211i	$0.165642\pi$
$182$	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	0.995033	+	0.0995472i	$0.0317394\pi$
$197$	5.07851	+	12.2606i	0.361829	+	0.873532i	−0.633204	+	0.773985i	$0.718261\pi$
$198$	0.534371	−	14.7175i	0.0379761	−	1.04593i
$199$	−3.02689	+	3.02689i	−0.214571	+	0.214571i	−0.806206	−	0.591635i	$-0.798483\pi$
$199$	−3.02689	+	3.02689i	−0.214571	+	0.214571i	0.591635	+	0.806206i	$0.298483\pi$
$200$	−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	0.409220	+	0.912436i	$0.365801\pi$
$211$	−7.63088	+	18.4226i	−0.525331	+	1.26826i	−0.934552	+	0.355827i	$0.884199\pi$
$212$	−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	−0.253481	−	0.967340i	$-0.581575\pi$
$227$	−16.8253	−	6.96925i	−1.11673	−	0.462565i	−0.863251	+	0.504775i	$0.831575\pi$
$228$	0.768519	−	10.5692i	0.0508964	−	0.699963i
$229$	−6.19266	−	14.9504i	−0.409222	−	0.987950i	−0.985343	−	0.170586i	$-0.945434\pi$
$229$	−6.19266	−	14.9504i	−0.409222	−	0.987950i	0.576120	−	0.817365i	$-0.304566\pi$
$230$	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	0.999890	+	0.0148065i	$0.00471322\pi$
$233$	15.4887	+	15.4887i	1.01470	+	1.01470i	0.0148065	+	0.999890i	$0.495287\pi$
$234$	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	$-0.963404\pi$
$239$		−	3.54698i		−	0.229435i	0.993398	−	0.114718i	$-0.0365963\pi$
$240$	−14.3777	−	2.10201i	−0.928079	−	0.135684i
$241$			13.0662i			0.841666i	0.907138	+	0.420833i	$0.138262\pi$
$241$			13.0662i			0.841666i	−0.907138	+	0.420833i	$0.861738\pi$
$242$	−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	0.993306	−	0.115511i	$-0.0368506\pi$
$251$	3.31521	+	8.00362i	0.209254	+	0.505184i	−0.784052	+	0.620695i	$0.786851\pi$
$252$	−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	−0.0602174	−	0.998185i	$-0.519179\pi$
$263$	15.2113	−	15.2113i	0.937968	−	0.937968i	0.998185	+	0.0602174i	$0.0191794\pi$
$264$	−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	0.209135	+	0.977887i	$0.432935\pi$
$269$	−10.3363	+	24.9541i	−0.630216	+	1.52148i	−0.839351	+	0.543590i	$0.817065\pi$
$270$	22.4126	+	10.2516i	1.36399	+	0.623890i
$271$		−	0.561795i		−	0.0341266i	−0.999854	−	0.0170633i	$-0.994568\pi$
$271$		−	0.561795i		−	0.0341266i	0.999854	−	0.0170633i	$-0.00543168\pi$
$272$	−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	0.354507	−	0.935054i	$-0.384649\pi$
$277$	21.0765	−	8.73017i	1.26636	−	0.524545i	0.911857	+	0.410509i	$0.134649\pi$
$278$	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	−0.314651	−	0.949207i	$-0.601887\pi$
$281$	10.6371	−	10.6371i	0.634557	−	0.634557i	0.949207	+	0.314651i	$0.101887\pi$
$282$	−5.56507	−	0.202060i	−0.331395	−	0.0120325i
$283$	−5.95342	−	14.3728i	−0.353894	−	0.854376i	−0.996132	−	0.0878703i	$-0.971994\pi$
$283$	−5.95342	−	14.3728i	−0.353894	−	0.854376i	0.642238	−	0.766505i	$-0.278006\pi$
$284$	−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	0.950669	−	0.310207i	$-0.100398\pi$
$293$	1.01155	+	2.44210i	0.0590953	+	0.142669i	−0.891574	+	0.452875i	$0.850398\pi$
$294$	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	0.524368	+	0.851492i	$0.324302\pi$
$307$	−7.85856	+	18.9722i	−0.448512	+	1.08280i	−0.972880	+	0.231311i	$0.925698\pi$
$308$	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	−0.987628	−	0.156812i	$-0.949878\pi$
$311$	−20.1824	−	20.1824i	−1.14444	−	1.14444i	−0.156812	−	0.987628i	$-0.550122\pi$
$312$	2.97763	−	0.868565i	0.168575	−	0.0491728i
$313$	−16.1542	+	16.1542i	−0.913087	+	0.913087i	−0.996514	−	0.0834267i	$-0.973414\pi$
$313$	−16.1542	+	16.1542i	−0.913087	+	0.913087i	0.0834267	+	0.996514i	$0.473414\pi$
$314$	−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	0.415801	−	0.909456i	$-0.363501\pi$
$317$	1.18816	+	0.492153i	0.0667338	+	0.0276421i	−0.349067	+	0.937098i	$0.613501\pi$
$318$	−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	−0.661256	−	0.750160i	$-0.729977\pi$
$331$	−10.8868	+	4.50946i	−0.598392	+	0.247862i	0.0628642	+	0.998022i	$0.479977\pi$
$332$	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	$0.194141\pi$
$337$			21.0302i			1.14559i	−0.819699	+	0.572795i	$0.805859\pi$
$338$	−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	−0.967519	−	0.252798i	$-0.918649\pi$
$347$	−8.60862	−	20.7830i	−0.462135	−	1.11569i	0.505384	−	0.862894i	$-0.331351\pi$
$348$	−11.4468	−	0.832333i	−0.613614	−	0.0446177i
$349$	−16.2518	−	6.73171i	−0.869938	−	0.360340i	−0.0973518	−	0.995250i	$-0.531037\pi$
$349$	−16.2518	−	6.73171i	−0.869938	−	0.360340i	−0.772586	+	0.634910i	$0.781037\pi$
$350$	−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	−0.471891	−	0.881657i	$-0.656429\pi$
$359$	7.76395	−	7.76395i	0.409765	−	0.409765i	0.881657	+	0.471891i	$0.156429\pi$
$360$	−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	$-0.776484\pi$
$367$		−	24.7472i		−	1.29179i	0.763425	−	0.645896i	$-0.223516\pi$
$368$	−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	−0.165296	−	0.986244i	$-0.552858\pi$
$373$	8.01888	−	3.32153i	0.415202	−	0.171982i	0.580498	+	0.814262i	$0.302858\pi$
$374$	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	0.999678	−	0.0253712i	$-0.00807677\pi$
$379$	5.35093	+	12.9183i	0.274859	+	0.663568i	−0.724819	+	0.688939i	$0.758077\pi$
$380$	−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	−0.862768	−	0.505600i	$-0.831271\pi$
$389$	−12.0353	−	29.0557i	−0.610212	−	1.47318i	0.252556	−	0.967582i	$-0.418729\pi$
$390$	−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	−0.415641	−	0.909529i	$-0.636443\pi$
$397$	10.3887	−	25.0806i	0.521395	−	1.25876i	0.937037	−	0.349231i	$-0.113557\pi$
$398$	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	$-0.717127\pi$
$401$		−	31.0882i		−	1.55247i	0.630445	−	0.776234i	$-0.282873\pi$
$402$	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	−0.322941	−	0.946419i	$-0.604671\pi$
$409$	12.6091	−	12.6091i	0.623478	−	0.623478i	0.946419	+	0.322941i	$0.104671\pi$
$410$	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	0.0822162	−	0.996615i	$-0.473800\pi$
$419$	−11.5522	−	4.78507i	−0.564361	−	0.233766i	−0.646577	+	0.762849i	$0.723800\pi$
$420$	−7.75789	−	0.564099i	−0.378546	−	0.0275252i
$421$	−3.61625	−	8.73041i	−0.176245	−	0.425494i	0.810928	−	0.585146i	$-0.198963\pi$
$421$	−3.61625	−	8.73041i	−0.176245	−	0.425494i	−0.987173	+	0.159652i	$0.948963\pi$
$422$	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	$-0.763932\pi$
$431$		−	28.0471i		−	1.35098i	0.737368	−	0.675491i	$-0.236068\pi$
$432$	−20.4025	+	5.15593i	−0.981614	+	0.248065i
$433$		−	15.6197i		−	0.750636i	−0.926896	−	0.375318i	$-0.877533\pi$
$433$		−	15.6197i		−	0.750636i	0.926896	−	0.375318i	$-0.122467\pi$
$434$	−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	0.802639	−	0.596465i	$-0.203428\pi$
$439$	4.31984	+	4.31984i	0.206175	+	0.206175i	−0.596465	+	0.802639i	$0.703428\pi$
$440$	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	0.998647	+	0.0520039i	$0.0165608\pi$
$443$	6.93031	+	16.7313i	0.329269	+	0.794926i	−0.669378	+	0.742922i	$0.733439\pi$
$444$	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	0.988247	−	0.152863i	$-0.0488494\pi$
$457$	17.8585	+	17.8585i	0.835384	+	0.835384i	−0.152863	+	0.988247i	$0.548849\pi$
$458$	−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	−0.323748	−	0.946143i	$-0.604943\pi$
$461$	12.3286	−	29.7639i	0.574201	−	1.38624i	0.897949	−	0.440100i	$-0.145057\pi$
$462$	−8.74813	−	4.00140i	−0.407000	−	0.186162i
$463$			20.3212i			0.944407i	0.881490	+	0.472203i	$0.156541\pi$
$463$			20.3212i			0.944407i	−0.881490	+	0.472203i	$0.843459\pi$
$464$	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	−0.956454	−	0.291884i	$-0.905718\pi$
$467$	−1.59366	+	3.84743i	−0.0737456	+	0.178038i	0.882708	+	0.469922i	$0.155718\pi$
$468$	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	−0.804521	−	0.593925i	$-0.797578\pi$
$487$	−4.64745	+	4.64745i	−0.210596	+	0.210596i	0.593925	+	0.804521i	$0.297578\pi$
$488$	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	−0.189687	−	0.981845i	$-0.560747\pi$
$491$	8.20870	−	3.40016i	0.370453	−	0.153447i	0.560140	+	0.828398i	$0.310747\pi$
$492$	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	−0.887681	−	0.460458i	$-0.847685\pi$
$499$	1.46533	−	3.53762i	0.0655972	−	0.158366i	0.953279	+	0.302092i	$0.0976851\pi$
$500$	−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	0.960753	−	0.277404i	$-0.0894741\pi$
$503$	15.3259	+	15.3259i	0.683349	+	0.683349i	−0.277404	+	0.960753i	$0.589474\pi$
$504$	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	0.117148	−	0.993114i	$-0.462625\pi$
$509$	−11.3314	−	4.69360i	−0.502253	−	0.208040i	−0.619402	+	0.785074i	$0.712625\pi$
$510$	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	0.925287	−	0.379269i	$-0.123824\pi$
$521$	12.4631	+	12.4631i	0.546018	+	0.546018i	−0.379269	+	0.925287i	$0.623824\pi$
$522$	−9.74074	+	9.05818i	−0.426341	+	0.396466i
$523$	9.55699	−	3.95864i	0.417898	−	0.173099i	−0.163819	−	0.986490i	$-0.552381\pi$
$523$	9.55699	−	3.95864i	0.417898	−	0.173099i	0.581717	+	0.813391i	$0.302381\pi$
$524$	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	0.998831	+	0.0483374i	$0.0153923\pi$
$541$	40.4549	+	16.7570i	1.73929	+	0.720438i	0.740460	+	0.672101i	$0.234608\pi$
$542$	−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	0.0551928	−	0.998476i	$-0.482423\pi$
$547$	−14.3090	−	5.92698i	−0.611809	−	0.253420i	−0.667002	+	0.745056i	$0.732423\pi$
$548$	−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	−0.938509	−	0.345254i	$-0.887793\pi$
$557$	−0.725757	+	1.75213i	−0.0307513	+	0.0742403i	0.907758	+	0.419495i	$0.137793\pi$
$558$	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	−0.682936	−	0.730479i	$-0.739297\pi$
$563$	7.50977	−	18.1302i	0.316499	−	0.764096i	0.999435	−	0.0336179i	$-0.0107029\pi$
$564$	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	−0.218329	+	0.975875i	$0.570061\pi$
$569$	−28.4862	+	28.4862i	−1.19420	+	1.19420i	−0.975875	+	0.218329i	$0.929939\pi$
$570$	0.900658	−	24.8057i	0.0377244	−	1.03900i
$571$	13.9367	+	33.6461i	0.583232	+	1.40805i	0.889868	+	0.456219i	$0.150797\pi$
$571$	13.9367	+	33.6461i	0.583232	+	1.40805i	−0.306636	+	0.951827i	$0.599203\pi$
$572$	−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	0.502048	−	0.864840i	$-0.332580\pi$
$587$	35.5810	−	14.7381i	1.46858	−	0.608307i	0.966536	+	0.256533i	$0.0825801\pi$
$588$	−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	$0.0450715\pi$
$593$			6.87316i			0.282247i	−0.989992	+	0.141123i	$0.954929\pi$
$594$	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	0.447556	−	0.894256i	$-0.352295\pi$
$599$	−10.9328	−	10.9328i	−0.446700	−	0.446700i	−0.894256	+	0.447556i	$0.852295\pi$
$600$	−18.4171	−	2.01318i	−0.751877	−	0.0821877i
$601$	21.8811	−	21.8811i	0.892547	−	0.892547i	−0.102215	−	0.994762i	$-0.532593\pi$
$601$	21.8811	−	21.8811i	0.892547	−	0.892547i	0.994762	+	0.102215i	$0.0325931\pi$
$602$	−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	0.833840	−	0.552006i	$-0.186137\pi$
$613$	−3.61729	−	8.73292i	−0.146101	−	0.352719i	−0.979941	+	0.199287i	$0.936137\pi$
$614$	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	0.0409019	−	0.999163i	$-0.486977\pi$
$617$	−23.8027	−	23.8027i	−0.958261	−	0.958261i	−0.999163	+	0.0409019i	$0.986977\pi$
$618$	−17.6774	−	19.0094i	−0.711087	−	0.764670i
$619$	24.8180	−	10.2800i	0.997520	−	0.413186i	0.176633	−	0.984277i	$-0.443480\pi$
$619$	24.8180	−	10.2800i	0.997520	−	0.413186i	0.820887	+	0.571091i	$0.193480\pi$
$620$	−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	0.752367	−	0.658744i	$-0.228912\pi$
$631$	2.35179	+	2.35179i	0.0936234	+	0.0936234i	−0.658744	+	0.752367i	$0.728912\pi$
$632$	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	0.361384	−	0.932417i	$-0.382304\pi$
$643$	−1.07509	−	0.445315i	−0.0423972	−	0.0175615i	−0.403781	+	0.914856i	$0.632304\pi$
$644$	−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	−0.886540	−	0.462652i	$-0.846898\pi$
$647$	−10.7821	+	10.7821i	−0.423888	+	0.423888i	0.462652	+	0.886540i	$0.346898\pi$
$648$	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	−0.981749	−	0.190183i	$-0.939092\pi$
$653$	−3.91148	+	9.44315i	−0.153068	+	0.369539i	0.828681	+	0.559722i	$0.189092\pi$
$654$	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	−0.996487	−	0.0837453i	$-0.973312\pi$
$659$	−5.97229	+	14.4184i	−0.232647	+	0.561661i	0.763840	+	0.645406i	$0.223312\pi$
$660$	−37.6183	−	18.8862i	−1.46429	−	0.735143i
$661$	37.0616	−	15.3514i	1.44153	−	0.597101i	0.481360	−	0.876523i	$-0.340143\pi$
$661$	37.0616	−	15.3514i	1.44153	−	0.597101i	0.960168	+	0.279422i	$0.0901429\pi$
$662$	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	−0.985420	−	0.170138i	$-0.945579\pi$
$677$	−10.6400	−	25.6872i	−0.408928	−	0.987241i	0.576492	−	0.817103i	$-0.304421\pi$
$678$	−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	−0.931317	−	0.364209i	$-0.881339\pi$
$683$	−34.8193	+	14.4226i	−1.33232	+	0.551866i	−0.401006	+	0.916076i	$0.631339\pi$
$684$	−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	−0.474452	−	0.880281i	$-0.657354\pi$
$691$	12.7094	−	30.6833i	0.483489	−	1.16725i	0.957941	−	0.286965i	$-0.0926462\pi$
$692$	−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	0.545779	−	0.837929i	$-0.316234\pi$
$701$	8.98073	+	3.71994i	0.339197	+	0.140500i	−0.206581	+	0.978429i	$0.566234\pi$
$702$	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	0.826104	−	0.563518i	$-0.190552\pi$
$709$	−4.16733	−	10.0608i	−0.156507	−	0.377842i	−0.982611	+	0.185676i	$0.940552\pi$
$710$	−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	$0.231762\pi$
$719$			35.6873i			1.33091i	−0.746438	+	0.665455i	$0.768238\pi$
$720$	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	0.918876	−	0.394546i	$-0.129098\pi$
$727$	14.1375	+	14.1375i	0.524331	+	0.524331i	−0.394546	+	0.918876i	$0.629098\pi$
$728$	−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	0.603996	−	0.796987i	$-0.293574\pi$
$733$	12.6579	+	5.24308i	0.467531	+	0.193658i	−0.136465	+	0.990645i	$0.543574\pi$
$734$	−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	0.980701	−	0.195511i	$-0.0626366\pi$
$739$	41.7532	+	17.2947i	1.53591	+	0.636197i	0.555213	+	0.831708i	$0.312637\pi$
$740$	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	−0.00966771	−	0.999953i	$-0.503077\pi$
$743$	26.9932	−	26.9932i	0.990286	−	0.990286i	0.999953	+	0.00966771i	$0.00307738\pi$
$744$	−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	$0.280720\pi$
$751$			42.3097i			1.54390i	−0.635681	+	0.771952i	$0.719280\pi$
$752$	−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	−0.936622	−	0.350341i	$-0.886066\pi$
$757$	−37.1760	+	15.3988i	−1.35119	+	0.559679i	−0.414563	+	0.910021i	$0.636066\pi$
$758$	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	−0.508690	−	0.860950i	$-0.669870\pi$
$761$	9.71750	−	9.71750i	0.352259	−	0.352259i	0.860950	+	0.508690i	$0.169870\pi$
$762$	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

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