LMFDB - Embedded newform 368.2.j.c.93.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [368,2,Mod(93,368)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(368, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("368.93");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 368 = 2^{4} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	368.j (of order $4$, degree $2$, 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:	$2.93849479438$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.221124989353984.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 2 x^{10} + 2 x^{9} + 12 x^{8} - 8 x^{7} - 14 x^{6} - 16 x^{5} + 48 x^{4} + 16 x^{3} + \cdots + 64 $ x^12 - 2x^11 - 2x^10 + 2x^9 + 12x^8 - 8x^7 - 14x^6 - 16x^5 + 48x^4 + 16x^3 - 32x^2 - 64*x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			93.5
Root			$-1.18970 + 0.764606i$ of defining polynomial
Character	$\chi$	$=$	368.93
Dual form			368.2.j.c.277.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.10116 + 0.887386i) q^{2} +(0.631541 + 0.631541i) q^{3} +(0.425090 + 1.95430i) q^{4} +(-2.74053 + 2.74053i) q^{5} +(0.135004 + 1.25585i) q^{6} -1.52921i q^{7} +(-1.26613 + 2.52921i) q^{8} -2.20231i q^{9} +(-5.44967 + 0.585843i) q^{10} +(-2.02278 + 2.02278i) q^{11} +(-0.965760 + 1.50268i) q^{12} +(2.71814 + 2.71814i) q^{13} +(1.35700 - 1.68390i) q^{14} -3.46152 q^{15} +(-3.63860 + 1.66151i) q^{16} +3.66304 q^{17} +(1.95430 - 2.42509i) q^{18} +(1.20231 + 1.20231i) q^{19} +(-6.52080 - 4.19086i) q^{20} +(0.965760 - 0.965760i) q^{21} +(-4.02239 + 0.432410i) q^{22} -1.00000i q^{23} +(-2.39691 + 0.797687i) q^{24} -10.0210i q^{25} +(0.581057 + 5.40514i) q^{26} +(3.28547 - 3.28547i) q^{27} +(2.98854 - 0.650053i) q^{28} +(2.52960 + 2.52960i) q^{29} +(-3.81167 - 3.07170i) q^{30} +2.74954 q^{31} +(-5.48107 - 1.39926i) q^{32} -2.55494 q^{33} +(4.03358 + 3.25054i) q^{34} +(4.19086 + 4.19086i) q^{35} +(4.30398 - 0.936182i) q^{36} +(-4.37038 + 4.37038i) q^{37} +(0.257018 + 2.39085i) q^{38} +3.43323i q^{39} +(-3.46152 - 10.4013i) q^{40} +7.70478i q^{41} +(1.92045 - 0.206450i) q^{42} +(8.96110 - 8.96110i) q^{43} +(-4.81300 - 3.09326i) q^{44} +(6.03551 + 6.03551i) q^{45} +(0.887386 - 1.10116i) q^{46} +4.24239 q^{47} +(-3.34723 - 1.24861i) q^{48} +4.66151 q^{49} +(8.89253 - 11.0347i) q^{50} +(2.31336 + 2.31336i) q^{51} +(-4.15662 + 6.46753i) q^{52} +(-7.11480 + 7.11480i) q^{53} +(6.53330 - 0.702335i) q^{54} -11.0870i q^{55} +(3.86770 + 1.93618i) q^{56} +1.51862i q^{57} +(0.540753 + 5.03023i) q^{58} +(5.81873 - 5.81873i) q^{59} +(-1.47146 - 6.76485i) q^{60} +(-6.37705 - 6.37705i) q^{61} +(3.02767 + 2.43991i) q^{62} -3.36780 q^{63} +(-4.79383 - 6.40463i) q^{64} -14.8983 q^{65} +(-2.81339 - 2.26722i) q^{66} +(-0.0827674 - 0.0827674i) q^{67} +(1.55713 + 7.15870i) q^{68} +(0.631541 - 0.631541i) q^{69} +(0.895878 + 8.33370i) q^{70} +6.62784i q^{71} +(5.57012 + 2.78842i) q^{72} -7.91866i q^{73} +(-8.69070 + 0.934256i) q^{74} +(6.32869 - 6.32869i) q^{75} +(-1.83859 + 2.86077i) q^{76} +(3.09326 + 3.09326i) q^{77} +(-3.04661 + 3.78053i) q^{78} +6.42623 q^{79} +(5.41827 - 14.5251i) q^{80} -2.45712 q^{81} +(-6.83711 + 8.48416i) q^{82} +(-11.6430 - 11.6430i) q^{83} +(2.29792 + 1.47685i) q^{84} +(-10.0387 + 10.0387i) q^{85} +(17.8195 - 1.91561i) q^{86} +3.19510i q^{87} +(-2.55494 - 7.67715i) q^{88} -2.76733i q^{89} +(1.29021 + 12.0019i) q^{90} +(4.15662 - 4.15662i) q^{91} +(1.95430 - 0.425090i) q^{92} +(1.73645 + 1.73645i) q^{93} +(4.67153 + 3.76464i) q^{94} -6.58995 q^{95} +(-2.57783 - 4.34520i) q^{96} -6.61383 q^{97} +(5.13305 + 4.13656i) q^{98} +(4.45480 + 4.45480i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} + 2 q^{3} - 4 q^{5} - 4 q^{8} - 6 q^{10} - 4 q^{11} - 8 q^{12} + 18 q^{13} - 2 q^{14} + 8 q^{16} - 8 q^{17} - 4 q^{18} - 8 q^{19} - 32 q^{20} + 8 q^{21} - 34 q^{22} + 12 q^{24} - 14 q^{26}+ \cdots + 36 q^{99}+O(q^{100}) $ 12 * q + 2 * q^2 + 2 * q^3 - 4 * q^5 - 4 * q^8 - 6 * q^10 - 4 * q^11 - 8 * q^12 + 18 * q^13 - 2 * q^14 + 8 * q^16 - 8 * q^17 - 4 * q^18 - 8 * q^19 - 32 * q^20 + 8 * q^21 - 34 * q^22 + 12 * q^24 - 14 * q^26 + 14 * q^27 + 12 * q^28 + 2 * q^29 - 30 * q^30 + 20 * q^31 - 8 * q^32 - 36 * q^33 + 10 * q^34 + 4 * q^35 + 4 * q^36 - 4 * q^37 + 24 * q^38 - 14 * q^42 + 20 * q^43 + 4 * q^44 - 20 * q^45 - 2 * q^46 - 16 * q^47 - 12 * q^48 + 52 * q^49 + 6 * q^50 - 4 * q^51 - 16 * q^53 + 16 * q^54 + 28 * q^56 + 14 * q^58 + 8 * q^59 + 48 * q^60 + 12 * q^61 - 44 * q^62 - 4 * q^63 + 24 * q^64 - 52 * q^65 + 34 * q^66 - 4 * q^67 - 16 * q^68 + 2 * q^69 + 28 * q^70 + 8 * q^72 - 26 * q^74 - 46 * q^75 - 8 * q^76 - 12 * q^77 - 44 * q^78 - 4 * q^79 + 4 * q^80 + 48 * q^81 - 6 * q^82 + 28 * q^83 + 12 * q^84 - 8 * q^85 + 44 * q^86 - 36 * q^88 + 4 * q^90 - 4 * q^92 - 14 * q^93 + 48 * q^95 + 32 * q^96 + 36 * q^97 - 2 * q^98 + 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/368\mathbb{Z}\right)^\times$.

$n$	$47$	$97$	$277$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	1.10116	+	0.887386i	0.778635	+	0.627477i
$2$	1.10116	+	0.887386i	0.778635	+	0.627477i
$3$	0.631541	+	0.631541i	0.364620	+	0.364620i	0.865511	−	0.500890i	$-0.166994\pi$
$3$	0.631541	+	0.631541i	0.364620	+	0.364620i	−0.500890	+	0.865511i	$0.666994\pi$
$4$	0.425090	+	1.95430i	0.212545	+	0.977151i
$5$	−2.74053	+	2.74053i	−1.22560	+	1.22560i	−0.259993	+	0.965611i	$0.583720\pi$
$5$	−2.74053	+	2.74053i	−1.22560	+	1.22560i	−0.965611	+	0.259993i	$0.916280\pi$
$6$	0.135004	+	1.25585i	0.0551153	+	0.512697i
$7$		−	1.52921i		−	0.577988i	−0.957331	−	0.288994i	$-0.906679\pi$
$7$		−	1.52921i		−	0.577988i	0.957331	−	0.288994i	$-0.0933207\pi$
$8$	−1.26613	+	2.52921i	−0.447645	+	0.894211i
$9$		−	2.20231i		−	0.734104i
$10$	−5.44967	+	0.585843i	−1.72334	+	0.185260i
$11$	−2.02278	+	2.02278i	−0.609892	+	0.609892i	−0.942918	−	0.333026i	$-0.891930\pi$
$11$	−2.02278	+	2.02278i	−0.609892	+	0.609892i	0.333026	+	0.942918i	$0.391930\pi$
$12$	−0.965760	+	1.50268i	−0.278791	+	0.433787i
$13$	2.71814	+	2.71814i	0.753877	+	0.753877i	0.975200	−	0.221324i	$-0.0710377\pi$
$13$	2.71814	+	2.71814i	0.753877	+	0.753877i	−0.221324	+	0.975200i	$0.571038\pi$
$14$	1.35700	−	1.68390i	0.362674	−	0.450042i
$15$	−3.46152			−0.893760
$16$	−3.63860	+	1.66151i	−0.909649	+	0.415378i
$17$	3.66304			0.888419			0.444209	−	0.895923i	$-0.353485\pi$
$17$	3.66304			0.888419			0.444209	+	0.895923i	$0.353485\pi$
$18$	1.95430	−	2.42509i	0.460634	−	0.571599i
$19$	1.20231	+	1.20231i	0.275829	+	0.275829i	0.831442	−	0.555612i	$-0.187516\pi$
$19$	1.20231	+	1.20231i	0.275829	+	0.275829i	−0.555612	+	0.831442i	$0.687516\pi$
$20$	−6.52080	−	4.19086i	−1.45810	−	0.937104i
$21$	0.965760	−	0.965760i	0.210746	−	0.210746i
$22$	−4.02239	+	0.432410i	−0.857577	+	0.0921901i
$23$		−	1.00000i		−	0.208514i
$23$		−	1.00000i		−	0.208514i
$24$	−2.39691	+	0.797687i	−0.489268	+	0.162827i
$25$		−	10.0210i		−	2.00421i
$26$	0.581057	+	5.40514i	0.113955	+	1.06004i
$27$	3.28547	−	3.28547i	0.632289	−	0.632289i
$28$	2.98854	−	0.650053i	0.564782	−	0.122849i
$29$	2.52960	+	2.52960i	0.469736	+	0.469736i	0.901829	−	0.432093i	$-0.142225\pi$
$29$	2.52960	+	2.52960i	0.469736	+	0.469736i	−0.432093	+	0.901829i	$0.642225\pi$
$30$	−3.81167	−	3.07170i	−0.695913	−	0.560814i
$31$	2.74954			0.493832			0.246916	−	0.969037i	$-0.420583\pi$
$31$	2.74954			0.493832			0.246916	+	0.969037i	$0.420583\pi$
$32$	−5.48107	−	1.39926i	−0.968925	−	0.247356i
$33$	−2.55494			−0.444758
$34$	4.03358	+	3.25054i	0.691754	+	0.557462i
$35$	4.19086	+	4.19086i	0.708384	+	0.708384i
$36$	4.30398	−	0.936182i	0.717331	−	0.156030i
$37$	−4.37038	+	4.37038i	−0.718487	+	0.718487i	−0.968295	−	0.249808i	$-0.919632\pi$
$37$	−4.37038	+	4.37038i	−0.718487	+	0.718487i	0.249808	+	0.968295i	$0.419632\pi$
$38$	0.257018	+	2.39085i	0.0416939	+	0.387847i
$39$			3.43323i			0.549757i
$40$	−3.46152	−	10.4013i	−0.547314	−	1.64458i
$41$			7.70478i			1.20328i	0.798766	+	0.601642i	$0.205487\pi$
$41$			7.70478i			1.20328i	−0.798766	+	0.601642i	$0.794513\pi$
$42$	1.92045	−	0.206450i	0.296333	−	0.0318560i
$43$	8.96110	−	8.96110i	1.36655	−	1.36655i	0.501255	−	0.865299i	$-0.332872\pi$
$43$	8.96110	−	8.96110i	1.36655	−	1.36655i	0.865299	−	0.501255i	$-0.167128\pi$
$44$	−4.81300	−	3.09326i	−0.725586	−	0.466327i
$45$	6.03551	+	6.03551i	0.899721	+	0.899721i
$46$	0.887386	−	1.10116i	0.130838	−	0.162357i
$47$	4.24239			0.618816			0.309408	−	0.950929i	$-0.399869\pi$
$47$	4.24239			0.618816			0.309408	+	0.950929i	$0.399869\pi$
$48$	−3.34723	−	1.24861i	−0.483132	−	0.180221i
$49$	4.66151			0.665930
$50$	8.89253	−	11.0347i	1.25759	−	1.56055i
$51$	2.31336	+	2.31336i	0.323935	+	0.323935i
$52$	−4.15662	+	6.46753i	−0.576419	+	0.896885i
$53$	−7.11480	+	7.11480i	−0.977292	+	0.977292i	−0.999748	−	0.0224555i	$-0.992852\pi$
$53$	−7.11480	+	7.11480i	−0.977292	+	0.977292i	0.0224555	+	0.999748i	$0.492852\pi$
$54$	6.53330	−	0.702335i	0.889070	−	0.0955757i
$55$		−	11.0870i		−	1.49497i
$56$	3.86770	+	1.93618i	0.516843	+	0.258733i
$57$			1.51862i			0.201146i
$58$	0.540753	+	5.03023i	0.0710044	+	0.660501i
$59$	5.81873	−	5.81873i	0.757534	−	0.757534i	−0.218339	−	0.975873i	$-0.570064\pi$
$59$	5.81873	−	5.81873i	0.757534	−	0.757534i	0.975873	+	0.218339i	$0.0700640\pi$
$60$	−1.47146	−	6.76485i	−0.189964	−	0.873338i
$61$	−6.37705	−	6.37705i	−0.816497	−	0.816497i	0.169101	−	0.985599i	$-0.445913\pi$
$61$	−6.37705	−	6.37705i	−0.816497	−	0.816497i	−0.985599	+	0.169101i	$0.945913\pi$
$62$	3.02767	+	2.43991i	0.384515	+	0.309868i
$63$	−3.36780			−0.424303
$64$	−4.79383	−	6.40463i	−0.599228	−	0.800578i
$65$	−14.8983			−1.84791
$66$	−2.81339	−	2.26722i	−0.346304	−	0.279075i
$67$	−0.0827674	−	0.0827674i	−0.0101116	−	0.0101116i	0.702033	−	0.712145i	$-0.252276\pi$
$67$	−0.0827674	−	0.0827674i	−0.0101116	−	0.0101116i	−0.712145	+	0.702033i	$0.752276\pi$
$68$	1.55713	+	7.15870i	0.188829	+	0.868119i
$69$	0.631541	−	0.631541i	0.0760286	−	0.0760286i
$70$	0.895878	+	8.33370i	0.107078	+	0.996067i
$71$			6.62784i			0.786579i	0.919415	+	0.393290i	$0.128663\pi$
$71$			6.62784i			0.786579i	−0.919415	+	0.393290i	$0.871337\pi$
$72$	5.57012	+	2.78842i	0.656444	+	0.328618i
$73$		−	7.91866i		−	0.926809i	−0.886147	−	0.463405i	$-0.846628\pi$
$73$		−	7.91866i		−	0.926809i	0.886147	−	0.463405i	$-0.153372\pi$
$74$	−8.69070	+	0.934256i	−1.01027	+	0.108605i
$75$	6.32869	−	6.32869i	0.730775	−	0.730775i
$76$	−1.83859	+	2.86077i	−0.210901	+	0.328153i
$77$	3.09326	+	3.09326i	0.352510	+	0.352510i
$78$	−3.04661	+	3.78053i	−0.344960	+	0.428060i
$79$	6.42623			0.723007			0.361504	−	0.932371i	$-0.382264\pi$
$79$	6.42623			0.723007			0.361504	+	0.932371i	$0.382264\pi$
$80$	5.41827	−	14.5251i	0.605781	−	1.62396i
$81$	−2.45712			−0.273013
$82$	−6.83711	+	8.48416i	−0.755033	+	0.936919i
$83$	−11.6430	−	11.6430i	−1.27799	−	1.27799i	−0.941791	−	0.336200i	$-0.890858\pi$
$83$	−11.6430	−	11.6430i	−1.27799	−	1.27799i	−0.336200	−	0.941791i	$-0.609142\pi$
$84$	2.29792	+	1.47685i	0.250724	+	0.161138i
$85$	−10.0387	+	10.0387i	−1.08885	+	1.08885i
$86$	17.8195	−	1.91561i	1.92153	−	0.206566i
$87$			3.19510i			0.342550i
$88$	−2.55494	−	7.67715i	−0.272358	−	0.818387i
$89$		−	2.76733i		−	0.293336i	−0.989186	−	0.146668i	$-0.953145\pi$
$89$		−	2.76733i		−	0.293336i	0.989186	−	0.146668i	$-0.0468549\pi$
$90$	1.29021	+	12.0019i	0.136000	+	1.26511i
$91$	4.15662	−	4.15662i	0.435732	−	0.435732i
$92$	1.95430	−	0.425090i	0.203750	−	0.0443187i
$93$	1.73645	+	1.73645i	0.180061	+	0.180061i
$94$	4.67153	+	3.76464i	0.481832	+	0.388293i
$95$	−6.58995			−0.676115
$96$	−2.57783	−	4.34520i	−0.263098	−	0.443481i
$97$	−6.61383			−0.671533			−0.335766	−	0.941945i	$-0.608995\pi$
$97$	−6.61383			−0.671533			−0.335766	+	0.941945i	$0.608995\pi$
$98$	5.13305	+	4.13656i	0.518517	+	0.417856i
$99$	4.45480	+	4.45480i	0.447724	+	0.447724i
$100$	19.5841	−	4.25985i	1.95841	−	0.425985i
$101$	11.5250	−	11.5250i	1.14678	−	1.14678i	0.159596	−	0.987182i	$-0.448981\pi$
$101$	11.5250	−	11.5250i	1.14678	−	1.14678i	0.987182	−	0.159596i	$-0.0510193\pi$
$102$	0.494527	+	4.60022i	0.0489655	+	0.455489i
$103$			0.605918i			0.0597028i	0.999554	+	0.0298514i	$0.00950341\pi$
$103$			0.605918i			0.0597028i	−0.999554	+	0.0298514i	$0.990497\pi$
$104$	−10.3163	+	3.43323i	−1.01159	+	0.336656i
$105$			5.29339i			0.516582i
$106$	−14.1481	+	1.52093i	−1.37418	+	0.147726i
$107$	6.39585	−	6.39585i	0.618310	−	0.618310i	−0.326788	−	0.945098i	$-0.605966\pi$
$107$	6.39585	−	6.39585i	0.618310	−	0.618310i	0.945098	+	0.326788i	$0.105966\pi$
$108$	7.81743	+	5.02418i	0.752233	+	0.483452i
$109$	−4.79918	−	4.79918i	−0.459678	−	0.459678i	0.438872	−	0.898550i	$-0.355378\pi$
$109$	−4.79918	−	4.79918i	−0.459678	−	0.459678i	−0.898550	+	0.438872i	$0.855378\pi$
$110$	9.83846	−	12.2085i	0.938060	−	1.16404i
$111$	−5.52015			−0.523950
$112$	2.54080	+	5.56419i	0.240083	+	0.525766i
$113$	4.58640			0.431452			0.215726	−	0.976454i	$-0.430788\pi$
$113$	4.58640			0.431452			0.215726	+	0.976454i	$0.430788\pi$
$114$	−1.34760	+	1.67224i	−0.126214	+	0.156619i
$115$	2.74053	+	2.74053i	0.255556	+	0.255556i
$116$	−3.86830	+	6.01892i	−0.359163	+	0.558843i
$117$	5.98620	−	5.98620i	0.553424	−	0.553424i
$118$	11.5708	−	1.24387i	1.06518	−	0.114507i
$119$		−	5.60157i		−	0.513495i
$120$	4.38273	−	8.75491i	0.400087	−	0.799210i
$121$			2.81670i			0.256063i
$122$	−1.36322	−	12.6810i	−0.123420	−	1.14809i
$123$	−4.86588	+	4.86588i	−0.438742	+	0.438742i
$124$	1.16880	+	5.37343i	0.104962	+	0.482549i
$125$	13.7603	+	13.7603i	1.23076	+	1.23076i
$126$	−3.70848	−	2.98854i	−0.330377	−	0.266241i
$127$	8.38407			0.743966			0.371983	−	0.928240i	$-0.378678\pi$
$127$	8.38407			0.743966			0.371983	+	0.928240i	$0.378678\pi$
$128$	0.404625	−	11.3065i	0.0357642	−	0.999360i
$129$	11.3186			0.996547
$130$	−16.4054	−	13.2206i	−1.43885	−	1.15952i
$131$	−15.3109	−	15.3109i	−1.33772	−	1.33772i	−0.898263	−	0.439459i	$-0.855170\pi$
$131$	−15.3109	−	15.3109i	−1.33772	−	1.33772i	−0.439459	−	0.898263i	$-0.644830\pi$
$132$	−1.08608	−	4.99313i	−0.0945312	−	0.434596i
$133$	1.83859	−	1.83859i	0.159426	−	0.159426i
$134$	−0.0176932	−	0.164586i	−0.00152846	−	0.0142181i
$135$			18.0079i			1.54987i
$136$	−4.63789	+	9.26461i	−0.397696	+	0.794434i
$137$			20.1453i			1.72113i	0.509339	+	0.860566i	$0.329890\pi$
$137$			20.1453i			1.72113i	−0.509339	+	0.860566i	$0.670110\pi$
$138$	1.25585	−	0.135004i	0.106905	−	0.0114923i
$139$	−11.0916	+	11.0916i	−0.940775	+	0.940775i	−0.998342	−	0.0575665i	$-0.981666\pi$
$139$	−11.0916	+	11.0916i	−0.940775	+	0.940775i	0.0575665	+	0.998342i	$0.481666\pi$
$140$	−6.40871	+	9.97169i	−0.541635	+	0.842762i
$141$	2.67924	+	2.67924i	0.225633	+	0.225633i
$142$	−5.88145	+	7.29828i	−0.493560	+	0.612458i
$143$	−10.9964			−0.919567
$144$	3.65917	+	8.01333i	0.304930	+	0.667777i
$145$	−13.8649			−1.15142
$146$	7.02691	−	8.71968i	0.581551	−	0.721646i
$147$	2.94393	+	2.94393i	0.242812	+	0.242812i
$148$	−10.3989	−	6.68325i	−0.854781	−	0.549359i
$149$	−15.6772	+	15.6772i	−1.28432	+	1.28432i	−0.346140	+	0.938183i	$0.612508\pi$
$149$	−15.6772	+	15.6772i	−1.28432	+	1.28432i	−0.938183	+	0.346140i	$0.887492\pi$
$150$	12.5849	−	1.35288i	1.02755	−	0.110462i
$151$		−	15.1976i		−	1.23677i	−0.785876	−	0.618384i	$-0.787788\pi$
$151$		−	15.1976i		−	1.23677i	0.785876	−	0.618384i	$-0.212212\pi$
$152$	−4.56319	+	1.51862i	−0.370123	+	0.123176i
$153$		−	8.06717i		−	0.652192i
$154$	0.661247	+	6.15109i	0.0532848	+	0.495669i
$155$	−7.53521	+	7.53521i	−0.605242	+	0.605242i
$156$	−6.70958	+	1.45944i	−0.537196	+	0.116848i
$157$	3.41307	+	3.41307i	0.272393	+	0.272393i	0.830063	−	0.557670i	$-0.188305\pi$
$157$	3.41307	+	3.41307i	0.272393	+	0.272393i	−0.557670	+	0.830063i	$0.688305\pi$
$158$	7.07628	+	5.70255i	0.562959	+	0.453670i
$159$	−8.98657			−0.712681
$160$	18.8558	−	11.1863i	1.49068	−	0.884357i
$161$	−1.52921			−0.120519
$162$	−2.70567	−	2.18041i	−0.212578	−	0.171310i
$163$	2.00990	+	2.00990i	0.157428	+	0.157428i	0.781426	−	0.623998i	$-0.214493\pi$
$163$	2.00990	+	2.00990i	0.157428	+	0.157428i	−0.623998	+	0.781426i	$0.714493\pi$
$164$	−15.0575	+	3.27523i	−1.17579	+	0.255752i
$165$	7.00190	−	7.00190i	0.545097	−	0.545097i
$166$	−2.48893	−	23.1527i	−0.193179	−	1.79700i
$167$		−	13.4952i		−	1.04429i	−0.852857	−	0.522144i	$-0.825132\pi$
$167$		−	13.4952i		−	1.04429i	0.852857	−	0.522144i	$-0.174868\pi$
$168$	1.21983	+	3.66539i	0.0941122	+	0.282791i
$169$			1.77659i			0.136661i
$170$	−19.9624	+	2.14597i	−1.53104	+	0.164588i
$171$	2.64787	−	2.64787i	0.202488	−	0.202488i
$172$	21.3220	+	13.7034i	1.62579	+	1.04488i
$173$	−0.604284	−	0.604284i	−0.0459429	−	0.0459429i	0.683762	−	0.729705i	$-0.260343\pi$
$173$	−0.604284	−	0.604284i	−0.0459429	−	0.0459429i	−0.729705	+	0.683762i	$0.760343\pi$
$174$	−2.83529	+	3.51830i	−0.214942	+	0.266722i
$175$	−15.3243			−1.15841
$176$	3.99922	−	10.7210i	0.301452	−	0.808123i
$177$	7.34952			0.552424
$178$	2.45569	−	3.04726i	0.184062	−	0.228402i
$179$	12.6718	+	12.6718i	0.947132	+	0.947132i	0.998671	−	0.0515388i	$-0.0164126\pi$
$179$	12.6718	+	12.6718i	0.947132	+	0.947132i	−0.0515388	+	0.998671i	$0.516413\pi$
$180$	−9.22957	+	14.3608i	−0.687932	+	1.07039i
$181$	6.30067	−	6.30067i	0.468325	−	0.468325i	−0.433046	−	0.901372i	$-0.642561\pi$
$181$	6.30067	−	6.30067i	0.468325	−	0.468325i	0.901372	+	0.433046i	$0.142561\pi$
$182$	8.26561	−	0.888559i	0.612688	−	0.0658644i
$183$		−	8.05473i		−	0.595423i
$184$	2.52921	+	1.26613i	0.186456	+	0.0933404i
$185$		−	23.9544i		−	1.76116i
$186$	0.371200	+	3.45300i	0.0272177	+	0.253186i
$187$	−7.40954	+	7.40954i	−0.541839	+	0.541839i
$188$	1.80340	+	8.29091i	0.131526	+	0.604677i
$189$	−5.02418	−	5.02418i	−0.365456	−	0.365456i
$190$	−7.25657	−	5.84784i	−0.526447	−	0.424247i
$191$	−15.8762			−1.14876			−0.574382	−	0.818588i	$-0.694757\pi$
$191$	−15.8762			−1.14876			−0.574382	+	0.818588i	$0.694757\pi$
$192$	1.01728	−	7.07228i	0.0734162	−	0.510398i
$193$	−15.8800			−1.14307			−0.571535	−	0.820578i	$-0.693652\pi$
$193$	−15.8800			−1.14307			−0.571535	+	0.820578i	$0.693652\pi$
$194$	−7.28286	−	5.86903i	−0.522879	−	0.421371i
$195$	−9.40889	−	9.40889i	−0.673785	−	0.673785i
$196$	1.98156	+	9.11000i	0.141540	+	0.650714i
$197$	−4.36304	+	4.36304i	−0.310854	+	0.310854i	−0.845240	−	0.534387i	$-0.820543\pi$
$197$	−4.36304	+	4.36304i	−0.310854	+	0.310854i	0.534387	+	0.845240i	$0.320543\pi$
$198$	0.952302	+	8.85856i	0.0676772	+	0.629551i
$199$			1.83276i			0.129921i	0.997888	+	0.0649604i	$0.0206921\pi$
$199$			1.83276i			0.129921i	−0.997888	+	0.0649604i	$0.979308\pi$
$200$	25.3453	+	12.6879i	1.79219	+	0.897173i
$201$		−	0.104542i		−	0.00737382i
$202$	22.9179	−	2.46369i	1.61250	−	0.173345i
$203$	3.86830	−	3.86830i	0.271502	−	0.271502i
$204$	−3.53762	+	5.50440i	−0.247683	+	0.385385i
$205$	−21.1152	−	21.1152i	−1.47475	−	1.47475i
$206$	−0.537683	+	0.667210i	−0.0374622	+	0.0464867i
$207$	−2.20231			−0.153071
$208$	−14.4064	−	5.37400i	−0.998907	−	0.372620i
$209$	−4.86404			−0.336452
$210$	−4.69728	+	5.82885i	−0.324143	+	0.402229i
$211$	−0.176084	−	0.176084i	−0.0121221	−	0.0121221i	0.701020	−	0.713142i	$-0.252728\pi$
$211$	−0.176084	−	0.176084i	−0.0121221	−	0.0121221i	−0.713142	+	0.701020i	$0.752728\pi$
$212$	−16.9289	−	10.8800i	−1.16268	−	0.747244i
$213$	−4.18575	+	4.18575i	−0.286803	+	0.286803i
$214$	12.7184	−	1.36724i	0.869413	−	0.0934626i
$215$			49.1164i			3.34971i
$216$	4.14982	+	12.4695i	0.282359	+	0.848442i
$217$		−	4.20463i		−	0.285429i
$218$	−1.02592	−	9.54337i	−0.0694840	−	0.646358i
$219$	5.00096	−	5.00096i	0.337933	−	0.337933i
$220$	21.6674	−	4.71298i	1.46081	−	0.317749i
$221$	9.95667	+	9.95667i	0.669758	+	0.669758i
$222$	−6.07855	−	4.89851i	−0.407966	−	0.328766i
$223$	7.23146			0.484254			0.242127	−	0.970245i	$-0.422155\pi$
$223$	7.23146			0.484254			0.242127	+	0.970245i	$0.422155\pi$
$224$	−2.13976	+	8.38171i	−0.142969	+	0.560027i
$225$	−22.0695			−1.47130
$226$	5.05034	+	4.06991i	0.335943	+	0.270726i
$227$	15.8466	+	15.8466i	1.05177	+	1.05177i	0.998584	+	0.0531903i	$0.0169390\pi$
$227$	15.8466	+	15.8466i	1.05177	+	1.05177i	0.0531903	+	0.998584i	$0.483061\pi$
$228$	−2.96784	+	0.645550i	−0.196550	+	0.0427526i
$229$	7.41129	−	7.41129i	0.489752	−	0.489752i	−0.418476	−	0.908228i	$-0.637436\pi$
$229$	7.41129	−	7.41129i	0.489752	−	0.489752i	0.908228	+	0.418476i	$0.137436\pi$
$230$	0.585843	+	5.44967i	0.0386294	+	0.359340i
$231$			3.90704i			0.257065i
$232$	−9.60071	+	3.19510i	−0.630318	+	0.209768i
$233$		−	0.641549i		−	0.0420293i	−0.999779	−	0.0210146i	$-0.993310\pi$
$233$		−	0.641549i		−	0.0420293i	0.999779	−	0.0210146i	$-0.00668966\pi$
$234$	11.9038	−	1.27967i	0.778176	−	0.0836545i
$235$	−11.6264	+	11.6264i	−0.758423	+	0.758423i
$236$	13.8450	+	8.89807i	0.901235	+	0.579215i
$237$	4.05842	+	4.05842i	0.263623	+	0.263623i
$238$	4.97076	−	6.16821i	0.322206	−	0.399825i
$239$	−7.78652			−0.503668			−0.251834	−	0.967770i	$-0.581034\pi$
$239$	−7.78652			−0.503668			−0.251834	+	0.967770i	$0.581034\pi$
$240$	12.5951	−	5.75135i	0.813008	−	0.371248i
$241$	5.29100			0.340824			0.170412	−	0.985373i	$-0.445490\pi$
$241$	5.29100			0.340824			0.170412	+	0.985373i	$0.445490\pi$
$242$	−2.49950	+	3.10162i	−0.160674	+	0.199380i
$243$	−11.4082	−	11.4082i	−0.731836	−	0.731836i
$244$	9.75186	−	15.1735i	0.624299	−	0.971384i
$245$	−12.7750	+	12.7750i	−0.816166	+	0.816166i
$246$	−9.67601	+	1.04018i	−0.616920	+	0.0663193i
$247$			6.53611i			0.415883i
$248$	−3.48128	+	6.95417i	−0.221061	+	0.441590i
$249$		−	14.7061i		−	0.931962i
$250$	2.94154	+	27.3630i	0.186039	+	1.73059i
$251$	20.1654	−	20.1654i	1.27283	−	1.27283i	0.328227	−	0.944599i	$-0.393549\pi$
$251$	20.1654	−	20.1654i	1.27283	−	1.27283i	0.944599	−	0.328227i	$-0.106451\pi$
$252$	−1.43162	−	6.58171i	−0.0901836	−	0.414608i
$253$	2.02278	+	2.02278i	0.127171	+	0.127171i
$254$	9.23218	+	7.43991i	0.579278	+	0.466822i
$255$	−12.6797			−0.794033
$256$	10.4788	−	12.0911i	0.654923	−	0.755696i
$257$	−2.15836			−0.134635			−0.0673174	−	0.997732i	$-0.521444\pi$
$257$	−2.15836			−0.134635			−0.0673174	+	0.997732i	$0.521444\pi$
$258$	12.4635	+	10.0440i	0.775946	+	0.625310i
$259$	6.68325	+	6.68325i	0.415277	+	0.415277i
$260$	−6.33313	−	29.1158i	−0.392764	−	1.80569i
$261$	5.57098	−	5.57098i	0.344835	−	0.344835i
$262$	−3.27301	−	30.4464i	−0.202207	−	1.88099i
$263$		−	13.7070i		−	0.845209i	−0.906314	−	0.422604i	$-0.861116\pi$
$263$		−	13.7070i		−	0.845209i	0.906314	−	0.422604i	$-0.138884\pi$
$264$	3.23489	−	6.46198i	0.199094	−	0.397708i
$265$		−	38.9967i		−	2.39555i
$266$	3.65612	−	0.393035i	0.224171	−	0.0240985i
$267$	1.74768	−	1.74768i	0.106956	−	0.106956i
$268$	0.126569	−	0.196936i	0.00773142	−	0.0120298i
$269$	18.5467	+	18.5467i	1.13081	+	1.13081i	0.990043	+	0.140767i	$0.0449569\pi$
$269$	18.5467	+	18.5467i	1.13081	+	1.13081i	0.140767	+	0.990043i	$0.455043\pi$
$270$	−15.9800	+	19.8295i	−0.972509	+	1.20678i
$271$	−6.66642			−0.404956			−0.202478	−	0.979287i	$-0.564900\pi$
$271$	−6.66642			−0.404956			−0.202478	+	0.979287i	$0.564900\pi$
$272$	−13.3283	+	6.08619i	−0.808149	+	0.369029i
$273$	5.25014			0.317753
$274$	−17.8767	+	22.1832i	−1.07997	+	1.34013i
$275$	20.2704	+	20.2704i	1.22235	+	1.22235i
$276$	1.50268	+	0.965760i	0.0904509	+	0.0581319i
$277$	−12.6524	+	12.6524i	−0.760208	+	0.760208i	−0.976360	−	0.216152i	$-0.930649\pi$
$277$	−12.6524	+	12.6524i	−0.760208	+	0.760208i	0.216152	+	0.976360i	$0.430649\pi$
$278$	−22.0561	+	2.37104i	−1.32284	+	0.142206i
$279$		−	6.05535i		−	0.362524i
$280$	−15.9057	+	5.29339i	−0.950549	+	0.316341i
$281$			5.57139i			0.332361i	0.986095	+	0.166181i	$0.0531435\pi$
$281$			5.57139i			0.332361i	−0.986095	+	0.166181i	$0.946856\pi$
$282$	0.572741	+	5.32778i	0.0341062	+	0.317265i
$283$	−11.5638	+	11.5638i	−0.687397	+	0.687397i	−0.961656	−	0.274259i	$-0.911567\pi$
$283$	−11.5638	+	11.5638i	−0.687397	+	0.687397i	0.274259	+	0.961656i	$0.411567\pi$
$284$	−12.9528	+	2.81743i	−0.768607	+	0.167184i
$285$	−4.16182	−	4.16182i	−0.246525	−	0.246525i
$286$	−12.1088	−	9.75808i	−0.716007	−	0.577007i
$287$	11.7822			0.695483
$288$	−3.08160	+	12.0710i	−0.181585	+	0.711292i
$289$	−3.58211			−0.210712
$290$	−15.2675	−	12.3035i	−0.896536	−	0.722489i
$291$	−4.17690	−	4.17690i	−0.244854	−	0.244854i
$292$	15.4755	−	3.36615i	0.905633	−	0.196989i
$293$	−0.585664	+	0.585664i	−0.0342149	+	0.0342149i	−0.724007	−	0.689792i	$-0.757702\pi$
$293$	−0.585664	+	0.585664i	−0.0342149	+	0.0342149i	0.689792	+	0.724007i	$0.257702\pi$
$294$	0.629324	+	5.85414i	0.0367029	+	0.341420i
$295$			31.8928i			1.85687i
$296$	−5.52015	−	16.5871i	−0.320852	−	0.964106i
$297$			13.2916i			0.771257i
$298$	−31.1747	+	3.35130i	−1.80590	+	0.194136i
$299$	2.71814	−	2.71814i	0.157194	−	0.157194i
$300$	15.0584	+	9.67791i	0.869400	+	0.558755i
$301$	−13.7034	−	13.7034i	−0.789852	−	0.789852i
$302$	13.4862	−	16.7350i	0.776043	−	0.962990i
$303$	14.5570			0.836277
$304$	−6.37239	−	2.37707i	−0.365481	−	0.136335i
$305$	34.9530			2.00140
$306$	7.15870	−	8.88321i	0.409235	−	0.507819i
$307$	20.2702	+	20.2702i	1.15688	+	1.15688i	0.985143	+	0.171738i	$0.0549382\pi$
$307$	20.2702	+	20.2702i	1.15688	+	1.15688i	0.171738	+	0.985143i	$0.445062\pi$
$308$	−4.73026	+	7.36009i	−0.269531	+	0.419380i
$309$	−0.382662	+	0.382662i	−0.0217689	+	0.0217689i
$310$	−14.9841	+	1.61080i	−0.851039	+	0.0914873i
$311$		−	10.5264i		−	0.596899i	−0.954425	−	0.298449i	$-0.903531\pi$
$311$		−	10.5264i		−	0.596899i	0.954425	−	0.298449i	$-0.0964694\pi$
$312$	−8.68338	−	4.34692i	−0.491599	−	0.246096i
$313$			17.6161i			0.995722i	0.867257	+	0.497861i	$0.165881\pi$
$313$			17.6161i			0.995722i	−0.867257	+	0.497861i	$0.834119\pi$
$314$	0.729611	+	6.78703i	0.0411743	+	0.383014i
$315$	9.22957	−	9.22957i	0.520028	−	0.520028i
$316$	2.73173	+	12.5588i	0.153672	+	0.706487i
$317$	−7.47881	−	7.47881i	−0.420052	−	0.420052i	0.465170	−	0.885222i	$-0.345993\pi$
$317$	−7.47881	−	7.47881i	−0.420052	−	0.420052i	−0.885222	+	0.465170i	$0.845993\pi$
$318$	−9.89561	−	7.97456i	−0.554918	−	0.447191i
$319$	−10.2337			−0.572976
$320$	30.6897	+	4.41445i	1.71561	+	0.246775i
$321$	8.07848			0.450897
$322$	−1.68390	−	1.35700i	−0.0938402	−	0.0756228i
$323$	4.40412	+	4.40412i	0.245052	+	0.245052i
$324$	−1.04450	−	4.80195i	−0.0580277	−	0.266775i
$325$	27.2386	−	27.2386i	1.51093	−	1.51093i
$326$	0.429656	+	3.99678i	0.0237965	+	0.221361i
$327$		−	6.06175i		−	0.335216i
$328$	−19.4870	−	9.75525i	−1.07599	−	0.538644i
$329$		−	6.48751i		−	0.357668i
$330$	13.9236	−	1.49679i	0.766467	−	0.0823958i
$331$	−1.01083	+	1.01083i	−0.0555603	+	0.0555603i	−0.734341	−	0.678781i	$-0.762509\pi$
$331$	−1.01083	+	1.01083i	−0.0555603	+	0.0555603i	0.678781	+	0.734341i	$0.262509\pi$
$332$	17.8047	−	27.7034i	0.977159	−	1.52042i
$333$	9.62495	+	9.62495i	0.527444	+	0.527444i
$334$	11.9754	−	14.8603i	0.655267	−	0.813120i
$335$	0.453653			0.0247857
$336$	−1.90939	+	5.11863i	−0.104166	+	0.279244i
$337$	27.4738			1.49659			0.748296	−	0.663366i	$-0.230873\pi$
$337$	27.4738			1.49659			0.748296	+	0.663366i	$0.230873\pi$
$338$	−1.57652	+	1.95630i	−0.0857515	+	0.106409i
$339$	2.89650	+	2.89650i	0.157316	+	0.157316i
$340$	−23.8860	−	15.3513i	−1.29540	−	0.832540i
$341$	−5.56172	+	5.56172i	−0.301184	+	0.301184i
$342$	5.26540	−	0.566034i	0.284720	−	0.0306076i
$343$		−	17.8329i		−	0.962887i
$344$	11.3186	+	34.0104i	0.610258	+	1.83372i
$345$			3.46152i			0.186362i
$346$	−0.129178	−	1.20164i	−0.00694464	−	0.0646008i
$347$	−5.81298	+	5.81298i	−0.312057	+	0.312057i	−0.845706	−	0.533649i	$-0.820820\pi$
$347$	−5.81298	+	5.81298i	−0.312057	+	0.312057i	0.533649	+	0.845706i	$0.320820\pi$
$348$	−6.24418	+	1.35820i	−0.334723	+	0.0728074i
$349$	−16.7479	−	16.7479i	−0.896495	−	0.896495i	0.0986290	−	0.995124i	$-0.468554\pi$
$349$	−16.7479	−	16.7479i	−0.896495	−	0.896495i	−0.995124	+	0.0986290i	$0.968554\pi$
$350$	−16.8744	−	13.5986i	−0.901977	−	0.726874i
$351$	17.8608			0.953337
$352$	13.9174	−	8.25661i	0.741800	−	0.440079i
$353$	33.2587			1.77018			0.885091	−	0.465418i	$-0.154096\pi$
$353$	33.2587			1.77018			0.885091	+	0.465418i	$0.154096\pi$
$354$	8.09298	+	6.52187i	0.430137	+	0.346633i
$355$	−18.1638	−	18.1638i	−0.964034	−	0.964034i
$356$	5.40819	−	1.17636i	0.286634	−	0.0623472i
$357$	3.53762	−	3.53762i	0.187231	−	0.187231i
$358$	2.70884	+	25.1983i	0.143167	+	1.33177i
$359$		−	18.6590i		−	0.984786i	−0.870373	−	0.492393i	$-0.836122\pi$
$359$		−	18.6590i		−	0.984786i	0.870373	−	0.492393i	$-0.163878\pi$
$360$	−22.9068	+	7.62334i	−1.20730	+	0.401785i
$361$		−	16.1089i		−	0.847836i
$362$	12.5292	−	1.34689i	0.658518	−	0.0707912i
$363$	−1.77886	+	1.77886i	−0.0933659	+	0.0933659i
$364$	9.89022	+	6.35635i	0.518388	+	0.333163i
$365$	21.7014	+	21.7014i	1.13590	+	1.13590i
$366$	7.14766	−	8.86952i	0.373614	−	0.463617i
$367$	−8.93581			−0.466446			−0.233223	−	0.972423i	$-0.574927\pi$
$367$	−8.93581			−0.466446			−0.233223	+	0.972423i	$0.574927\pi$
$368$	1.66151	+	3.63860i	0.0866122	+	0.189675i
$369$	16.9683			0.883336
$370$	21.2568	−	26.3775i	1.10509	−	1.37130i
$371$	10.8800	+	10.8800i	0.564863	+	0.564863i
$372$	−2.65540	+	4.13169i	−0.137676	+	0.214218i
$373$	9.78549	−	9.78549i	0.506673	−	0.506673i	−0.406830	−	0.913504i	$-0.633366\pi$
$373$	9.78549	−	9.78549i	0.506673	−	0.506673i	0.913504	+	0.406830i	$0.133366\pi$
$374$	−14.7342	+	1.58394i	−0.761887	+	0.0819034i
$375$			17.3804i			0.897520i
$376$	−5.37142	+	10.7299i	−0.277010	+	0.553352i
$377$			13.7516i			0.708246i
$378$	−1.07402	−	9.99080i	−0.0552416	−	0.513872i
$379$	23.5423	−	23.5423i	1.20928	−	1.20928i	0.238026	−	0.971259i	$-0.423500\pi$
$379$	23.5423	−	23.5423i	1.20928	−	1.20928i	0.971259	−	0.238026i	$-0.0765004\pi$
$380$	−2.80133	−	12.8788i	−0.143705	−	0.660667i
$381$	5.29488	+	5.29488i	0.271265	+	0.271265i
$382$	−17.4822	−	14.0883i	−0.894468	−	0.720823i
$383$	−33.3581			−1.70452			−0.852260	−	0.523119i	$-0.824768\pi$
$383$	−33.3581			−1.70452			−0.852260	+	0.523119i	$0.824768\pi$
$384$	7.39603	−	6.88496i	0.377427	−	0.351347i
$385$	−16.9544			−0.864075
$386$	−17.4864	−	14.0917i	−0.890035	−	0.717250i
$387$	−19.7351	−	19.7351i	−1.00319	−	1.00319i
$388$	−2.81148	−	12.9254i	−0.142731	−	0.656189i
$389$	22.4106	−	22.4106i	1.13626	−	1.13626i	0.147146	−	0.989115i	$-0.452991\pi$
$389$	22.4106	−	22.4106i	1.13626	−	1.13626i	0.989115	−	0.147146i	$-0.0470087\pi$
$390$	−2.01134	−	18.7100i	−0.101848	−	0.947417i
$391$		−	3.66304i		−	0.185248i
$392$	−5.90208	+	11.7899i	−0.298100	+	0.595482i
$393$		−	19.3389i		−	0.975521i
$394$	−8.67609	+	0.932686i	−0.437095	+	0.0469880i
$395$	−17.6113	+	17.6113i	−0.886120	+	0.886120i
$396$	−6.81233	+	10.5997i	−0.342333	+	0.532656i
$397$	1.72193	+	1.72193i	0.0864212	+	0.0864212i	0.748996	−	0.662575i	$-0.230536\pi$
$397$	1.72193	+	1.72193i	0.0864212	+	0.0864212i	−0.662575	+	0.748996i	$0.730536\pi$
$398$	−1.62636	+	2.01815i	−0.0815223	+	0.101161i
$399$	2.32229			0.116260
$400$	16.6501	+	36.4625i	0.832503	+	1.82313i
$401$	−4.68163			−0.233790			−0.116895	−	0.993144i	$-0.537294\pi$
$401$	−4.68163			−0.233790			−0.116895	+	0.993144i	$0.537294\pi$
$402$	0.0927691	−	0.115117i	0.00462690	−	0.00574151i
$403$	7.47364	+	7.47364i	0.372289	+	0.372289i
$404$	27.4225	+	17.6241i	1.36432	+	0.876834i
$405$	6.73381	−	6.73381i	0.334606	−	0.334606i
$406$	7.69228	−	0.826926i	0.381762	−	0.0410397i
$407$		−	17.6807i		−	0.876399i
$408$	−8.78000	+	2.92196i	−0.434675	+	0.144659i
$409$		−	4.60355i		−	0.227631i	−0.993502	−	0.113815i	$-0.963693\pi$
$409$		−	4.60355i		−	0.227631i	0.993502	−	0.113815i	$-0.0363073\pi$
$410$	−4.51379	−	41.9885i	−0.222920	−	2.07366i
$411$	−12.7226	+	12.7226i	−0.627559	+	0.627559i
$412$	−1.18415	+	0.257570i	−0.0583387	+	0.0126896i
$413$	−8.89807	−	8.89807i	−0.437845	−	0.437845i
$414$	−2.42509	−	1.95430i	−0.119187	−	0.0960487i
$415$	63.8163			3.13262
$416$	−11.0949	−	18.7017i	−0.543974	−	0.916926i
$417$	−14.0096			−0.686051
$418$	−5.35606	−	4.31628i	−0.261974	−	0.211116i
$419$	13.2797	+	13.2797i	0.648758	+	0.648758i	0.952693	−	0.303935i	$-0.0983006\pi$
$419$	13.2797	+	13.2797i	0.648758	+	0.648758i	−0.303935	+	0.952693i	$0.598301\pi$
$420$	−10.3449	+	2.25017i	−0.504779	+	0.109797i
$421$	−8.04601	+	8.04601i	−0.392138	+	0.392138i	−0.875449	−	0.483311i	$-0.839434\pi$
$421$	−8.04601	+	8.04601i	−0.392138	+	0.392138i	0.483311	+	0.875449i	$0.339434\pi$
$422$	−0.0376413	−	0.350150i	−0.00183235	−	0.0170450i
$423$		−	9.34306i		−	0.454275i
$424$	−8.98657	−	27.0031i	−0.436426	−	1.31139i
$425$		−	36.7075i		−	1.78058i
$426$	−8.32354	+	0.894787i	−0.403277	+	0.0433526i
$427$	−9.75186	+	9.75186i	−0.471926	+	0.471926i
$428$	15.2182	+	9.78061i	0.735601	+	0.472764i
$429$	−6.94469	−	6.94469i	−0.335293	−	0.335293i
$430$	−43.5852	+	54.0848i	−2.10186	+	2.60820i
$431$	23.9168			1.15203			0.576016	−	0.817439i	$-0.304607\pi$
$431$	23.9168			1.15203			0.576016	+	0.817439i	$0.304607\pi$
$432$	−6.49566	+	17.4134i	−0.312523	+	0.837800i
$433$	13.5472			0.651039			0.325519	−	0.945535i	$-0.394461\pi$
$433$	13.5472			0.651039			0.325519	+	0.945535i	$0.394461\pi$
$434$	3.73113	−	4.62996i	0.179100	−	0.222245i
$435$	−8.75627	−	8.75627i	−0.419831	−	0.419831i
$436$	7.33896	−	11.4191i	0.351472	−	0.546877i
$437$	1.20231	−	1.20231i	0.0575144	−	0.0575144i
$438$	9.94462	−	1.06905i	0.475172	−	0.0510814i
$439$		−	11.2376i		−	0.536343i	−0.963371	−	0.268172i	$-0.913581\pi$
$439$		−	11.2376i		−	0.536343i	0.963371	−	0.268172i	$-0.0864194\pi$
$440$	28.0414	+	14.0376i	1.33682	+	0.669216i
$441$		−	10.2661i		−	0.488862i
$442$	2.12844	+	19.7993i	0.101239	+	0.941755i
$443$	−25.7097	+	25.7097i	−1.22150	+	1.22150i	−0.254406	+	0.967098i	$0.581880\pi$
$443$	−25.7097	+	25.7097i	−1.22150	+	1.22150i	−0.967098	+	0.254406i	$0.918120\pi$
$444$	−2.34656	−	10.7880i	−0.111363	−	0.511978i
$445$	7.58395	+	7.58395i	0.359514	+	0.359514i
$446$	7.96297	+	6.41710i	0.377057	+	0.303858i
$447$	−19.8015			−0.936580
$448$	−9.79403	+	7.33078i	−0.462724	+	0.346347i
$449$	−5.13588			−0.242377			−0.121188	−	0.992630i	$-0.538671\pi$
$449$	−5.13588			−0.242377			−0.121188	+	0.992630i	$0.538671\pi$
$450$	−24.3019	−	19.5841i	−1.14560	−	0.923205i
$451$	−15.5851	−	15.5851i	−0.733873	−	0.733873i
$452$	1.94963	+	8.96320i	0.0917030	+	0.421594i
$453$	9.59793	−	9.59793i	0.450950	−	0.450950i
$454$	3.38752	+	31.5116i	0.158984	+	1.47891i
$455$			22.7827i			1.06807i
$456$	−3.84091	−	1.92277i	−0.179867	−	0.0900419i
$457$			27.2294i			1.27374i	0.770972	+	0.636870i	$0.219771\pi$
$457$			27.2294i			1.27374i	−0.770972	+	0.636870i	$0.780229\pi$
$458$	14.7377	−	1.58431i	0.688646	−	0.0740300i
$459$	12.0348	−	12.0348i	0.561738	−	0.561738i
$460$	−4.19086	+	6.52080i	−0.195400	+	0.304034i
$461$	−21.9976	−	21.9976i	−1.02453	−	1.02453i	−0.999691	−	0.0248390i	$-0.992093\pi$
$461$	−21.9976	−	21.9976i	−1.02453	−	1.02453i	−0.0248390	−	0.999691i	$-0.507907\pi$
$462$	−3.46706	+	4.30227i	−0.161302	+	0.200160i
$463$	−21.8570			−1.01578			−0.507890	−	0.861422i	$-0.669575\pi$
$463$	−21.8570			−1.01578			−0.507890	+	0.861422i	$0.669575\pi$
$464$	−13.4072	−	5.00124i	−0.622412	−	0.232177i
$465$	−9.51758			−0.441367
$466$	0.569302	−	0.706446i	0.0263724	−	0.0327255i
$467$	−8.55730	−	8.55730i	−0.395985	−	0.395985i	0.480829	−	0.876814i	$-0.340336\pi$
$467$	−8.55730	−	8.55730i	−0.395985	−	0.395985i	−0.876814	+	0.480829i	$0.840336\pi$
$468$	14.2435	+	9.15417i	0.658407	+	0.423151i
$469$	−0.126569	+	0.126569i	−0.00584441	+	0.00584441i
$470$	−23.1196	+	2.48537i	−1.06643	+	0.114642i
$471$			4.31098i			0.198640i
$472$	7.34952	+	22.0841i	0.338289	+	1.01650i
$473$			36.2527i			1.66690i
$474$	0.867569	+	8.07035i	0.0398487	+	0.370683i
$475$	12.0484	−	12.0484i	0.552819	−	0.552819i
$476$	10.9472	−	2.38117i	0.501762	−	0.109141i
$477$	15.6690	+	15.6690i	0.717434	+	0.717434i
$478$	−8.57418	−	6.90965i	−0.392174	−	0.316040i
$479$	40.7842			1.86348			0.931739	−	0.363129i	$-0.118292\pi$
$479$	40.7842			1.86348			0.931739	+	0.363129i	$0.118292\pi$
$480$	18.9728	+	4.84355i	0.865986	+	0.221077i
$481$	−23.7587			−1.08330
$482$	5.82622	+	4.69517i	0.265377	+	0.213859i
$483$	−0.965760	−	0.965760i	−0.0439436	−	0.0439436i
$484$	−5.50468	+	1.19735i	−0.250213	+	0.0544250i
$485$	18.1254	−	18.1254i	0.823033	−	0.823033i
$486$	−2.43873	−	22.6857i	−0.110623	−	1.02904i
$487$			31.6590i			1.43460i	0.696762	+	0.717302i	$0.254623\pi$
$487$			31.6590i			1.43460i	−0.696762	+	0.717302i	$0.745377\pi$
$488$	24.2031	−	8.05473i	1.09562	−	0.364621i
$489$			2.53867i			0.114803i
$490$	−25.4037	+	2.73091i	−1.14762	+	0.123370i
$491$	−16.7060	+	16.7060i	−0.753931	+	0.753931i	−0.975210	−	0.221279i	$-0.928977\pi$
$491$	−16.7060	+	16.7060i	−0.753931	+	0.753931i	0.221279	+	0.975210i	$0.428977\pi$
$492$	−11.5778	−	7.44096i	−0.521969	−	0.335464i
$493$	9.26605	+	9.26605i	0.417322	+	0.417322i
$494$	−5.80006	+	7.19728i	−0.260957	+	0.323821i
$495$	−24.4171			−1.09746
$496$	−10.0045	+	4.56839i	−0.449214	+	0.205127i
$497$	10.1354			0.454633
$498$	13.0500	−	16.1937i	0.584785	−	0.725659i
$499$	−21.7208	−	21.7208i	−0.972357	−	0.972357i	0.0272707	−	0.999628i	$-0.491318\pi$
$499$	−21.7208	−	21.7208i	−0.972357	−	0.972357i	−0.999628	+	0.0272707i	$0.991318\pi$
$500$	−21.0424	+	32.7412i	−0.941047	+	1.46423i
$501$	8.52276	−	8.52276i	0.380769	−	0.380769i
$502$	40.0997	−	4.31075i	1.78974	−	0.192398i
$503$		−	12.3248i		−	0.549534i	−0.961511	−	0.274767i	$-0.911399\pi$
$503$		−	12.3248i		−	0.549534i	0.961511	−	0.274767i	$-0.0886008\pi$
$504$	4.26408	−	8.51789i	0.189937	−	0.379417i
$505$			63.1692i			2.81099i
$506$	0.432410	+	4.02239i	0.0192230	+	0.178817i
$507$	−1.12199	+	1.12199i	−0.0498293	+	0.0498293i
$508$	3.56399	+	16.3850i	0.158126	+	0.726967i
$509$	−19.2068	−	19.2068i	−0.851326	−	0.851326i	0.138971	−	0.990296i	$-0.455621\pi$
$509$	−19.2068	−	19.2068i	−0.851326	−	0.851326i	−0.990296	+	0.138971i	$0.955621\pi$
$510$	−13.9623	−	11.2518i	−0.618262	−	0.498237i
$511$	−12.1093			−0.535684
$512$	22.2683	−	4.01551i	0.984128	−	0.177462i
$513$	7.90033			0.348808
$514$	−2.37669	−	1.91530i	−0.104831	−	0.0844802i
$515$	−1.66054	−	1.66054i	−0.0731720	−	0.0731720i
$516$	4.81143	+	22.1200i	0.211811	+	0.973777i
$517$	−8.58143	+	8.58143i	−0.377411	+	0.377411i
$518$	1.42868	+	13.2899i	0.0627724	+	0.583926i
$519$		−	0.763260i		−	0.0335034i
$520$	18.8632	−	37.6810i	0.827206	−	1.65242i
$521$			0.515650i			0.0225910i	0.999936	+	0.0112955i	$0.00359555\pi$
$521$			0.515650i			0.0225910i	−0.999936	+	0.0112955i	$0.996404\pi$
$522$	11.0781	−	1.19091i	0.484877	−	0.0521246i
$523$	−6.17927	+	6.17927i	−0.270201	+	0.270201i	−0.829181	−	0.558980i	$-0.811193\pi$
$523$	−6.17927	+	6.17927i	−0.270201	+	0.270201i	0.558980	+	0.829181i	$0.311193\pi$
$524$	23.4137	−	36.4307i	1.02283	−	1.59148i
$525$	−9.67791	−	9.67791i	−0.422379	−	0.422379i
$526$	12.1634	−	15.0935i	0.530349	−	0.658109i
$527$	10.0717			0.438730
$528$	9.29639	−	4.24506i	0.404574	−	0.184743i
$529$	−1.00000			−0.0434783
$530$	34.6051	−	42.9414i	1.50315	−	1.86526i
$531$	−12.8147	−	12.8147i	−0.556109	−	0.556109i
$532$	4.37473	+	2.81160i	0.189669	+	0.121898i
$533$	−20.9427	+	20.9427i	−0.907128	+	0.907128i
$534$	3.47534	−	0.373601i	0.150392	−	0.0161673i
$535$			35.0561i			1.51561i
$536$	0.314130	−	0.104542i	0.0135684	−	0.00451552i
$537$			16.0055i			0.690687i
$538$	3.96472	+	36.8808i	0.170931	+	1.59005i
$539$	−9.42923	+	9.42923i	−0.406145	+	0.406145i
$540$	−35.1929	+	7.65498i	−1.51446	+	0.329418i
$541$	−5.80628	−	5.80628i	−0.249632	−	0.249632i	0.571188	−	0.820819i	$-0.306483\pi$
$541$	−5.80628	−	5.80628i	−0.249632	−	0.249632i	−0.820819	+	0.571188i	$0.806483\pi$
$542$	−7.34077	−	5.91569i	−0.315313	−	0.254101i
$543$	7.95826			0.341522
$544$	−20.0774	−	5.12554i	−0.860811	−	0.219756i
$545$	26.3046			1.12677
$546$	5.78123	+	4.65891i	0.247414	+	0.199383i
$547$	16.8634	+	16.8634i	0.721029	+	0.721029i	0.968815	−	0.247786i	$-0.0797030\pi$
$547$	16.8634	+	16.8634i	0.721029	+	0.721029i	−0.247786	+	0.968815i	$0.579703\pi$
$548$	−39.3701	+	8.56359i	−1.68181	+	0.365818i
$549$	−14.0443	+	14.0443i	−0.599394	+	0.599394i
$550$	4.33320	+	40.3085i	0.184768	+	1.71876i
$551$			6.08275i			0.259134i
$552$	0.797687	+	2.39691i	0.0339518	+	0.102019i
$553$		−	9.82706i		−	0.417889i
$554$	−25.1598	+	2.70470i	−1.06894	+	0.114912i
$555$	15.1282	−	15.1282i	0.642155	−	0.642155i
$556$	−26.3912	−	16.9614i	−1.11924	−	0.719322i
$557$	12.6709	+	12.6709i	0.536885	+	0.536885i	0.922613	−	0.385728i	$-0.126050\pi$
$557$	12.6709	+	12.6709i	0.536885	+	0.536885i	−0.385728	+	0.922613i	$0.626050\pi$
$558$	5.37343	−	6.66788i	0.227476	−	0.282274i
$559$	48.7151			2.06043
$560$	−22.2120	−	8.28568i	−0.938628	−	0.350134i
$561$	−9.35886			−0.395131
$562$	−4.94398	+	6.13497i	−0.208549	+	0.258788i
$563$	−30.8676	−	30.8676i	−1.30091	−	1.30091i	−0.927777	−	0.373136i	$-0.878282\pi$
$563$	−30.8676	−	30.8676i	−1.30091	−	1.30091i	−0.373136	−	0.927777i	$-0.621718\pi$
$564$	−4.09713	+	6.37497i	−0.172520	+	0.268434i
$565$	−12.5692	+	12.5692i	−0.528789	+	0.528789i
$566$	−22.9951	+	2.47199i	−0.966557	+	0.103906i
$567$			3.75746i			0.157798i
$568$	−16.7632	−	8.39170i	−0.703368	−	0.352108i
$569$		−	26.9844i		−	1.13125i	−0.824664	−	0.565623i	$-0.808636\pi$
$569$		−	26.9844i		−	1.13125i	0.824664	−	0.565623i	$-0.191364\pi$
$570$	−0.889672	−	8.27597i	−0.0372643	−	0.346642i
$571$	−1.83019	+	1.83019i	−0.0765912	+	0.0765912i	−0.744365	−	0.667773i	$-0.767248\pi$
$571$	−1.83019	+	1.83019i	−0.0765912	+	0.0765912i	0.667773	+	0.744365i	$0.267248\pi$
$572$	−4.67447	−	21.4903i	−0.195450	−	0.898556i
$573$	−10.0265	−	10.0265i	−0.418862	−	0.418862i
$574$	12.9741	+	10.4554i	0.541528	+	0.436400i
$575$	−10.0210			−0.417906
$576$	−14.1050	+	10.5575i	−0.587708	+	0.439896i
$577$	−18.1595			−0.755991			−0.377995	−	0.925807i	$-0.623386\pi$
$577$	−18.1595			−0.755991			−0.377995	+	0.925807i	$0.623386\pi$
$578$	−3.94446	−	3.17872i	−0.164068	−	0.132217i
$579$	−10.0289	−	10.0289i	−0.416787	−	0.416787i
$580$	−5.89385	−	27.0963i	−0.244729	−	1.12511i
$581$	−17.8047	+	17.8047i	−0.738663	+	0.738663i
$582$	−0.892896	−	8.30595i	−0.0370117	−	0.344293i
$583$		−	28.7834i		−	1.19209i
$584$	20.0280	+	10.0261i	0.828763	+	0.414881i
$585$			32.8107i			1.35656i
$586$	−1.16462	+	0.125197i	−0.0481099	+	0.00517185i
$587$	−14.8262	+	14.8262i	−0.611941	+	0.611941i	−0.943452	−	0.331510i	$-0.892442\pi$
$587$	−14.8262	+	14.8262i	−0.611941	+	0.611941i	0.331510	+	0.943452i	$0.392442\pi$
$588$	−4.50190	+	7.00478i	−0.185655	+	0.288872i
$589$	3.30581	+	3.30581i	0.136213	+	0.136213i
$590$	−28.3013	+	35.1190i	−1.16514	+	1.44583i
$591$	−5.51087			−0.226687
$592$	8.64063	−	23.1635i	0.355128	−	0.952014i
$593$	31.8803			1.30917			0.654583	−	0.755990i	$-0.272844\pi$
$593$	31.8803			1.30917			0.654583	+	0.755990i	$0.272844\pi$
$594$	−11.7948	+	14.6361i	−0.483946	+	0.600527i
$595$	15.3513	+	15.3513i	0.629341	+	0.629341i
$596$	−37.3021	−	23.9737i	−1.52795	−	0.982001i
$597$	−1.15746	+	1.15746i	−0.0473717	+	0.0473717i
$598$	5.40514	−	0.581057i	0.221033	−	0.0237612i
$599$			39.1635i			1.60018i	0.599882	+	0.800088i	$0.295214\pi$
$599$			39.1635i			1.60018i	−0.599882	+	0.800088i	$0.704786\pi$
$600$	7.99366	+	24.0196i	0.326340	+	0.980594i
$601$			44.0527i			1.79695i	0.439026	+	0.898474i	$0.355324\pi$
$601$			44.0527i			1.79695i	−0.439026	+	0.898474i	$0.644676\pi$
$602$	−2.92938	−	27.2498i	−0.119393	−	1.11062i
$603$	−0.182280	+	0.182280i	−0.00742300	+	0.00742300i
$604$	29.7008	−	6.46038i	1.20851	−	0.262869i
$605$	−7.71925	−	7.71925i	−0.313832	−	0.313832i
$606$	16.0295	+	12.9177i	0.651155	+	0.524745i
$607$	21.5920			0.876393			0.438196	−	0.898879i	$-0.355617\pi$
$607$	21.5920			0.876393			0.438196	+	0.898879i	$0.355617\pi$
$608$	−4.90761	−	8.27230i	−0.199030	−	0.335486i
$609$	4.88598			0.197990
$610$	38.4887	+	31.0168i	1.55836	+	1.25583i
$611$	11.5314	+	11.5314i	0.466511	+	0.466511i
$612$	15.7657	−	3.42928i	0.637290	−	0.138620i
$613$	20.9053	−	20.9053i	0.844357	−	0.844357i	−0.145065	−	0.989422i	$-0.546339\pi$
$613$	20.9053	−	20.9053i	0.844357	−	0.844357i	0.989422	+	0.145065i	$0.0463392\pi$
$614$	4.33315	+	40.3081i	0.174872	+	1.62670i
$615$		−	26.6702i		−	1.07545i
$616$	−11.7400	+	3.90704i	−0.473018	+	0.157419i
$617$		−	4.01122i		−	0.161486i	−0.996735	−	0.0807429i	$-0.974271\pi$
$617$		−	4.01122i		−	0.161486i	0.996735	−	0.0807429i	$-0.0257293\pi$
$618$	−0.760939	+	0.0818015i	−0.0306095	+	0.00329054i
$619$	−8.52811	+	8.52811i	−0.342774	+	0.342774i	−0.857409	−	0.514635i	$-0.827927\pi$
$619$	−8.52811	+	8.52811i	−0.342774	+	0.342774i	0.514635	+	0.857409i	$0.327927\pi$
$620$	−17.9292	−	11.5229i	−0.720055	−	0.462772i
$621$	−3.28547	−	3.28547i	−0.131841	−	0.131841i
$622$	9.34101	−	11.5912i	0.374540	−	0.464766i
$623$	−4.23183			−0.169545
$624$	−5.70436	−	12.4922i	−0.228357	−	0.500086i
$625$	−25.3160			−1.01264
$626$	−15.6323	+	19.3981i	−0.624792	+	0.775304i
$627$	−3.07184	−	3.07184i	−0.122677	−	0.122677i
$628$	−5.21931	+	8.12103i	−0.208273	+	0.324064i
$629$	−16.0089	+	16.0089i	−0.638317	+	0.638317i
$630$	18.3534	−	1.97300i	0.731217	−	0.0786064i
$631$		−	14.7297i		−	0.586379i	−0.956054	−	0.293189i	$-0.905283\pi$
$631$		−	14.7297i		−	0.586379i	0.956054	−	0.293189i	$-0.0947166\pi$
$632$	−8.13644	+	16.2533i	−0.323650	+	0.646521i
$633$		−	0.222408i		−	0.00883992i
$634$	−1.59874	−	14.8719i	−0.0634942	−	0.590640i
$635$	−22.9768	+	22.9768i	−0.911808	+	0.911808i
$636$	−3.82010	−	17.5625i	−0.151477	−	0.696397i
$637$	12.6706	+	12.6706i	0.502029	+	0.502029i
$638$	−11.2689	−	9.08123i	−0.446139	−	0.359529i
$639$	14.5966			0.577431
$640$	29.8769	+	32.0946i	1.18099	+	1.26865i
$641$	−25.1609			−0.993796			−0.496898	−	0.867809i	$-0.665528\pi$
$641$	−25.1609			−0.993796			−0.496898	+	0.867809i	$0.665528\pi$
$642$	8.89567	+	7.16873i	0.351084	+	0.282927i
$643$	16.7541	+	16.7541i	0.660718	+	0.660718i	0.955549	−	0.294831i	$-0.0952634\pi$
$643$	16.7541	+	16.7541i	0.660718	+	0.660718i	−0.294831	+	0.955549i	$0.595263\pi$
$644$	−0.650053	−	2.98854i	−0.0256157	−	0.117765i
$645$	−31.0190	+	31.0190i	−1.22137	+	1.22137i
$646$	0.941469	+	8.75779i	0.0370416	+	0.344571i
$647$		−	17.2641i		−	0.678721i	−0.940656	−	0.339360i	$-0.889789\pi$
$647$		−	17.2641i		−	0.678721i	0.940656	−	0.339360i	$-0.110211\pi$
$648$	3.11103	−	6.21457i	0.122213	−	0.244132i
$649$			23.5400i			0.924027i
$650$	54.1651	−	5.82279i	2.12453	−	0.228389i
$651$	2.65540	−	2.65540i	0.104073	−	0.104073i
$652$	−3.07357	+	4.78235i	−0.120370	+	0.187291i
$653$	−29.8896	−	29.8896i	−1.16967	−	1.16967i	−0.982287	−	0.187384i	$-0.939999\pi$
$653$	−29.8896	−	29.8896i	−1.16967	−	1.16967i	−0.187384	−	0.982287i	$-0.560001\pi$
$654$	5.37912	−	6.67493i	0.210340	−	0.261011i
$655$	83.9202			3.27903
$656$	−12.8016	−	28.0346i	−0.499817	−	1.09457i
$657$	−17.4394			−0.680375
$658$	5.75693	−	7.14376i	0.224428	−	0.278493i
$659$	−18.7646	−	18.7646i	−0.730967	−	0.730967i	0.239845	−	0.970811i	$-0.422903\pi$
$659$	−18.7646	−	18.7646i	−0.730967	−	0.730967i	−0.970811	+	0.239845i	$0.922903\pi$
$660$	16.6603	+	10.7074i	0.648500	+	0.416784i
$661$	30.7092	−	30.7092i	1.19445	−	1.19445i	0.218644	−	0.975805i	$-0.429837\pi$
$661$	30.7092	−	30.7092i	1.19445	−	1.19445i	0.975805	−	0.218644i	$-0.0701635\pi$
$662$	−2.01008	+	0.216085i	−0.0781240	+	0.00839839i
$663$			12.5761i			0.488415i
$664$	44.1894	−	14.7061i	1.71488	−	0.570708i
$665$			10.0774i			0.390786i
$666$	2.05752	+	19.1396i	0.0797275	+	0.741646i
$667$	2.52960	−	2.52960i	0.0979467	−	0.0979467i
$668$	26.3737	−	5.73667i	1.02043	−	0.221959i
$669$	4.56696	+	4.56696i	0.176569	+	0.176569i
$670$	0.499543	+	0.402566i	0.0192990	+	0.0155525i
$671$	25.7988			0.995950
$672$	−6.64474	+	3.94204i	−0.256326	+	0.152068i
$673$	−18.7694			−0.723506			−0.361753	−	0.932274i	$-0.617822\pi$
$673$	−18.7694			−0.723506			−0.361753	+	0.932274i	$0.617822\pi$
$674$	30.2529	+	24.3798i	1.16530	+	0.939076i
$675$	−32.9238	−	32.9238i	−1.26724	−	1.26724i
$676$	−3.47199	+	0.755211i	−0.133538	+	0.0290466i
$677$	−7.27989	+	7.27989i	−0.279789	+	0.279789i	−0.833025	−	0.553236i	$-0.813393\pi$
$677$	−7.27989	+	7.27989i	−0.279789	+	0.279789i	0.553236	+	0.833025i	$0.313393\pi$
$678$	0.619183	+	5.75980i	0.0237796	+	0.221204i
$679$			10.1140i			0.388138i
$680$	−12.6797	−	38.1003i	−0.486244	−	1.46108i
$681$			20.0155i			0.766997i
$682$	−11.0597	+	1.18893i	−0.423499	+	0.0455264i
$683$	−12.4210	+	12.4210i	−0.475277	+	0.475277i	−0.903618	−	0.428340i	$-0.859099\pi$
$683$	−12.4210	+	12.4210i	−0.475277	+	0.475277i	0.428340	+	0.903618i	$0.359099\pi$
$684$	6.30032	+	4.04915i	0.240899	+	0.154823i
$685$	−55.2089	−	55.2089i	−2.10943	−	2.10943i
$686$	15.8247	−	19.6368i	0.604190	−	0.749738i
$687$	9.36106			0.357147
$688$	−17.7169	+	47.4948i	−0.675449	+	1.81072i
$689$	−38.6780			−1.47352
$690$	−3.07170	+	3.81167i	−0.116938	+	0.145108i
$691$	−33.8504	−	33.8504i	−1.28773	−	1.28773i	−0.936163	−	0.351565i	$-0.885650\pi$
$691$	−33.8504	−	33.8504i	−1.28773	−	1.28773i	−0.351565	−	0.936163i	$-0.614350\pi$
$692$	0.924078	−	1.43783i	0.0351282	−	0.0546581i
$693$	6.81233	−	6.81233i	0.258779	−	0.258779i
$694$	−11.5594	+	1.24264i	−0.438787	+	0.0471699i
$695$		−	60.7937i		−	2.30603i
$696$	−8.08108	−	4.04541i	−0.306312	−	0.153341i
$697$			28.2229i			1.06902i
$698$	−3.58020	−	33.3039i	−0.135513	−	1.26057i
$699$	0.405164	−	0.405164i	0.0153247	−	0.0153247i
$700$	−6.51421	−	29.9483i	−0.246214	−	1.13194i
$701$	−11.9805	−	11.9805i	−0.452498	−	0.452498i	0.443685	−	0.896183i	$-0.353671\pi$
$701$	−11.9805	−	11.9805i	−0.452498	−	0.452498i	−0.896183	+	0.443685i	$0.853671\pi$
$702$	19.6675	+	15.8494i	0.742301	+	0.598197i
$703$	−10.5091			−0.396360
$704$	22.6520	+	3.25830i	0.853731	+	0.122802i
$705$	−14.6851			−0.553073
$706$	36.6230	+	29.5133i	1.37833	+	1.11075i
$707$	−17.6241	−	17.6241i	−0.662824	−	0.662824i
$708$	3.12421	+	14.3632i	0.117415	+	0.539802i
$709$	−8.81693	+	8.81693i	−0.331127	+	0.331127i	−0.853014	−	0.521887i	$-0.825228\pi$
$709$	−8.81693	+	8.81693i	−0.331127	+	0.331127i	0.521887	+	0.853014i	$0.325228\pi$
$710$	−3.88287	−	36.1195i	−0.145722	−	1.35554i
$711$		−	14.1526i		−	0.530762i
$712$	6.99916	+	3.50380i	0.262304	+	0.131310i
$713$		−	2.74954i		−	0.102971i
$714$	7.03471	−	0.756236i	0.263267	−	0.0283014i
$715$	30.1361	−	30.1361i	1.12702	−	1.12702i
$716$	−19.3778	+	30.1511i	−0.724183	+	1.12680i
$717$	−4.91751	−	4.91751i	−0.183648	−	0.183648i
$718$	16.5578	−	20.5465i	0.617930	−	0.766789i
$719$	−41.8588			−1.56107			−0.780534	−	0.625113i	$-0.785053\pi$
$719$	−41.8588			−1.56107			−0.780534	+	0.625113i	$0.785053\pi$
$720$	−31.9888	−	11.9327i	−1.19215	−	0.444706i
$721$	0.926576			0.0345075
$722$	14.2948	−	17.7384i	0.531998	−	0.660155i
$723$	3.34148	+	3.34148i	0.124271	+	0.124271i
$724$	14.9918	+	9.63506i	0.557165	+	0.358084i
$725$	25.3493	−	25.3493i	0.941448	−	0.941448i
$726$	−3.53734	+	0.380266i	−0.131283	+	0.0141130i
$727$		−	2.66804i		−	0.0989520i	−0.998775	−	0.0494760i	$-0.984245\pi$
$727$		−	2.66804i		−	0.0989520i	0.998775	−	0.0494760i	$-0.0157551\pi$
$728$	5.25014	+	15.7758i	0.194583	+	0.584689i
$729$		−	7.03811i		−	0.260671i
$730$	4.63909	+	43.1541i	0.171701	+	1.59720i
$731$	32.8249	−	32.8249i	1.21407	−	1.21407i
$732$	15.7414	−	3.42399i	0.581818	−	0.126554i
$733$	16.3265	+	16.3265i	0.603033	+	0.603033i	0.941116	−	0.338083i	$-0.109778\pi$
$733$	16.3265	+	16.3265i	0.603033	+	0.603033i	−0.338083	+	0.941116i	$0.609778\pi$
$734$	−9.83972	−	7.92952i	−0.363191	−	0.292684i
$735$	−16.1359			−0.595181
$736$	−1.39926	+	5.48107i	−0.0515773	+	0.202035i
$737$	0.334841			0.0123340
$738$	18.6848	+	15.0575i	0.687796	+	0.554273i
$739$	−13.4540	−	13.4540i	−0.494913	−	0.494913i	0.414937	−	0.909850i	$-0.363804\pi$
$739$	−13.4540	−	13.4540i	−0.494913	−	0.494913i	−0.909850	+	0.414937i	$0.863804\pi$
$740$	46.8141	−	10.1828i	1.72092	−	0.374326i
$741$	−4.12782	+	4.12782i	−0.151639	+	0.151639i
$742$	2.32582	+	21.6354i	0.0853836	+	0.794261i
$743$		−	6.92795i		−	0.254162i	−0.991892	−	0.127081i	$-0.959439\pi$
$743$		−	6.92795i		−	0.254162i	0.991892	−	0.127081i	$-0.0405608\pi$
$744$	−6.59041	+	2.19327i	−0.241616	+	0.0804093i
$745$		−	85.9275i		−	3.14814i
$746$	19.4589	−	2.09184i	0.712440	−	0.0765878i
$747$	−25.6416	+	25.6416i	−0.938178	+	0.938178i
$748$	−17.6302	−	11.3308i	−0.644625	−	0.414294i
$749$	−9.78061	−	9.78061i	−0.357376	−	0.357376i
$750$	−15.4231	+	19.1385i	−0.563173	+	0.698841i
$751$	−18.5653			−0.677457			−0.338729	−	0.940884i	$-0.609997\pi$
$751$	−18.5653			−0.677457			−0.338729	+	0.940884i	$0.609997\pi$
$752$	−15.4363	+	7.04877i	−0.562905	+	0.257042i
$753$	25.4705			0.928196
$754$	−12.2030	+	15.1427i	−0.444408	+	0.551465i
$755$	41.6497	+	41.6497i	1.51579	+	1.51579i
$756$	7.68304	−	11.9545i	0.279430	−	0.434781i
$757$	18.6823	−	18.6823i	0.679020	−	0.679020i	−0.280759	−	0.959778i	$-0.590586\pi$
$757$	18.6823	−	18.6823i	0.679020	−	0.679020i	0.959778	+	0.280759i	$0.0905860\pi$
$758$	46.8148	−	5.03263i	1.70039	−	0.182793i
$759$			2.55494i			0.0927384i
$760$	8.34374	−	16.6674i	0.302659	−	0.604590i
$761$			43.1942i			1.56579i	0.622154	+	0.782895i	$0.286258\pi$
$761$			43.1942i			1.56579i	−0.622154	+	0.782895i	$0.713742\pi$
$762$	1.13189	+	10.5291i	0.0410039	+	0.381429i
$763$	−7.33896	+	7.33896i	−0.265688	+	0.265688i
$764$	−6.74883	−	31.0269i	−0.244164	−	1.12252i
$765$	22.1083	+	22.1083i	0.799329	+	0.799329i
$766$	−36.7325	−	29.6015i	−1.32720	−	1.06955i
$767$	31.6322			1.14217
$768$	14.2538	−	1.01828i	0.514340	−	0.0367439i
$769$	0.777724			0.0280454			0.0140227	−	0.999902i	$-0.495536\pi$
$769$	0.777724			0.0280454			0.0140227	+	0.999902i	$0.495536\pi$
$770$	−18.6694	−	15.0451i	−0.672799	−

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:	\( N \)	\(=\)	\( 368 = 2^{4} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	368.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.10116 + 0.887386i) q^{2} +(0.631541 + 0.631541i) q^{3} +(0.425090 + 1.95430i) q^{4} +(-2.74053 + 2.74053i) q^{5} +(0.135004 + 1.25585i) q^{6} -1.52921i q^{7} +(-1.26613 + 2.52921i) q^{8} -2.20231i q^{9} +(-5.44967 + 0.585843i) q^{10} +(-2.02278 + 2.02278i) q^{11} +(-0.965760 + 1.50268i) q^{12} +(2.71814 + 2.71814i) q^{13} +(1.35700 - 1.68390i) q^{14} -3.46152 q^{15} +(-3.63860 + 1.66151i) q^{16} +3.66304 q^{17} +(1.95430 - 2.42509i) q^{18} +(1.20231 + 1.20231i) q^{19} +(-6.52080 - 4.19086i) q^{20} +(0.965760 - 0.965760i) q^{21} +(-4.02239 + 0.432410i) q^{22} -1.00000i q^{23} +(-2.39691 + 0.797687i) q^{24} -10.0210i q^{25} +(0.581057 + 5.40514i) q^{26} +(3.28547 - 3.28547i) q^{27} +(2.98854 - 0.650053i) q^{28} +(2.52960 + 2.52960i) q^{29} +(-3.81167 - 3.07170i) q^{30} +2.74954 q^{31} +(-5.48107 - 1.39926i) q^{32} -2.55494 q^{33} +(4.03358 + 3.25054i) q^{34} +(4.19086 + 4.19086i) q^{35} +(4.30398 - 0.936182i) q^{36} +(-4.37038 + 4.37038i) q^{37} +(0.257018 + 2.39085i) q^{38} +3.43323i q^{39} +(-3.46152 - 10.4013i) q^{40} +7.70478i q^{41} +(1.92045 - 0.206450i) q^{42} +(8.96110 - 8.96110i) q^{43} +(-4.81300 - 3.09326i) q^{44} +(6.03551 + 6.03551i) q^{45} +(0.887386 - 1.10116i) q^{46} +4.24239 q^{47} +(-3.34723 - 1.24861i) q^{48} +4.66151 q^{49} +(8.89253 - 11.0347i) q^{50} +(2.31336 + 2.31336i) q^{51} +(-4.15662 + 6.46753i) q^{52} +(-7.11480 + 7.11480i) q^{53} +(6.53330 - 0.702335i) q^{54} -11.0870i q^{55} +(3.86770 + 1.93618i) q^{56} +1.51862i q^{57} +(0.540753 + 5.03023i) q^{58} +(5.81873 - 5.81873i) q^{59} +(-1.47146 - 6.76485i) q^{60} +(-6.37705 - 6.37705i) q^{61} +(3.02767 + 2.43991i) q^{62} -3.36780 q^{63} +(-4.79383 - 6.40463i) q^{64} -14.8983 q^{65} +(-2.81339 - 2.26722i) q^{66} +(-0.0827674 - 0.0827674i) q^{67} +(1.55713 + 7.15870i) q^{68} +(0.631541 - 0.631541i) q^{69} +(0.895878 + 8.33370i) q^{70} +6.62784i q^{71} +(5.57012 + 2.78842i) q^{72} -7.91866i q^{73} +(-8.69070 + 0.934256i) q^{74} +(6.32869 - 6.32869i) q^{75} +(-1.83859 + 2.86077i) q^{76} +(3.09326 + 3.09326i) q^{77} +(-3.04661 + 3.78053i) q^{78} +6.42623 q^{79} +(5.41827 - 14.5251i) q^{80} -2.45712 q^{81} +(-6.83711 + 8.48416i) q^{82} +(-11.6430 - 11.6430i) q^{83} +(2.29792 + 1.47685i) q^{84} +(-10.0387 + 10.0387i) q^{85} +(17.8195 - 1.91561i) q^{86} +3.19510i q^{87} +(-2.55494 - 7.67715i) q^{88} -2.76733i q^{89} +(1.29021 + 12.0019i) q^{90} +(4.15662 - 4.15662i) q^{91} +(1.95430 - 0.425090i) q^{92} +(1.73645 + 1.73645i) q^{93} +(4.67153 + 3.76464i) q^{94} -6.58995 q^{95} +(-2.57783 - 4.34520i) q^{96} -6.61383 q^{97} +(5.13305 + 4.13656i) q^{98} +(4.45480 + 4.45480i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} + 2 q^{3} - 4 q^{5} - 4 q^{8} - 6 q^{10} - 4 q^{11} - 8 q^{12} + 18 q^{13} - 2 q^{14} + 8 q^{16} - 8 q^{17} - 4 q^{18} - 8 q^{19} - 32 q^{20} + 8 q^{21} - 34 q^{22} + 12 q^{24} - 14 q^{26}+ \cdots + 36 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 + 2 * q^3 - 4 * q^5 - 4 * q^8 - 6 * q^10 - 4 * q^11 - 8 * q^12 + 18 * q^13 - 2 * q^14 + 8 * q^16 - 8 * q^17 - 4 * q^18 - 8 * q^19 - 32 * q^20 + 8 * q^21 - 34 * q^22 + 12 * q^24 - 14 * q^26 + 14 * q^27 + 12 * q^28 + 2 * q^29 - 30 * q^30 + 20 * q^31 - 8 * q^32 - 36 * q^33 + 10 * q^34 + 4 * q^35 + 4 * q^36 - 4 * q^37 + 24 * q^38 - 14 * q^42 + 20 * q^43 + 4 * q^44 - 20 * q^45 - 2 * q^46 - 16 * q^47 - 12 * q^48 + 52 * q^49 + 6 * q^50 - 4 * q^51 - 16 * q^53 + 16 * q^54 + 28 * q^56 + 14 * q^58 + 8 * q^59 + 48 * q^60 + 12 * q^61 - 44 * q^62 - 4 * q^63 + 24 * q^64 - 52 * q^65 + 34 * q^66 - 4 * q^67 - 16 * q^68 + 2 * q^69 + 28 * q^70 + 8 * q^72 - 26 * q^74 - 46 * q^75 - 8 * q^76 - 12 * q^77 - 44 * q^78 - 4 * q^79 + 4 * q^80 + 48 * q^81 - 6 * q^82 + 28 * q^83 + 12 * q^84 - 8 * q^85 + 44 * q^86 - 36 * q^88 + 4 * q^90 - 4 * q^92 - 14 * q^93 + 48 * q^95 + 32 * q^96 + 36 * q^97 - 2 * q^98 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more